ABSTRACT 
Title of Dissertati on: SCAUNG OF SURFAC E ENERGY FLUXES USING 
REMOTELY SENS ED DATA 
Andrew Nichols French, Doctor of Philosophy, 200 I 
Di ssertati on directed by : Professor Kaye L. Brubaker 
Department of Civil and Environmental Engineering 
Accurate estimates of evapotranspiration (ET) across multiple terrains would greatly 
ease challenges faced by hydrologists, climate modelers, and agronomists as they at-
tempt to apply theoretical models to real-world situations. One ET estimation approach 
uses an energy balance model to interpret a combination of meteorological observa-
tions taken at the surface and data captured by remote sensors. However, results of 
this approach have not been accurate because of poor understanding of the relationship 
between surface energy flux and land cover heterogeneity, combined with limits in avail-
able resolution of remote sensors. The purpose of this study was to determine how land 
cover and image resolution affect ET estimates. Using remotely sensed data collected 
over El Reno, Oklahoma, during four days in June and July 1997, scale effects on the es-
timation of spatially distributed ET were investigated. Instantaneous estimates of latent 
and sensible heat flux were ca lculated using a two-source surface energy balance model 
driven by therma l infrared, vis ible-near infrared, and meteorological data. The heat flux 
estimates were ve rified by comparison to independent eddy-cova ri ance observations. 
Outcomes o f observati ons taken at coarser reso luti ons were s imulated by aggregating 
remote senso r data and estimated surface energy balance components from the finest 
sensor reso lution ( 12 meter) to hypotheti ca l reso lutions as coarse as one kil ometer. Es-
timated surface energy flux components were found to be s ignificantly dependent on 
observa ti on sca le. For example, average evaporative fraction varied from 0.79, using 
12-m reso lution data, to 0.93 , using 1-km reso lution data. Reso lution effects upon flux 
estimates were related to a measure of landscape heterogeneity k.nown as operationa l 
sca le, re fl ecting the s ize of dominant landscape features. Energy flux estimates based 
on data at reso lutions less than I 00 m and much greater than 400 m showed a scale-
dependent bias. But estimates derived from data taken at about 400-m reso lution (the 
operati onal sca le at E l Reno) were susceptible to large error due to mixing of surface 
types. The El Reno experiments show that accurate instantaneous estimates of ET re-
quire prec ise image a lignment and image reso lutions finer than landscape operational 
sca le. T hese findings are valuable for the design of sensors and experiments to quantify 
spatially-varying hydrologic processes. 
S ALING OF SURFA E ENERGY FLUXES USING 
REMOTELY SENSED DATA 
by 
Andrew Nichols French 
Dissertation ubmitted to the Faculty of the Graduate School of the 
University of Maryland, College Park in partial fulfillment 
of the requirements for the degree of 
Doctor of Philosophy 
200 1 
Advisory Committee: 
Professor Kaye L. Brubaker, Chair/ Advisor 
Professor Richard H. McCuen 
Professor Glenn E. Mo glen 
Professor Rachel T. Pinker 
Dr. Thomas J. Schmugge 
? Copyright by 
Andrew Nichols French 
2001 
ACKNOWLEDGEMENTS 
This research wou ld not have been poss ible without he lp from my com-
mittee, many co ll eagues, family member and fr iends. Financial support 
was provided by the ASTER project of NASA's EOS-Terra program. Dr. 
Kaye Brubaker, my adviser, made the whole project possible. Without her 
advocacy, sponsorship and willingness the spend many hours reading, and 
re-reading my proposa ls and reports, I wou ld not have undertaken this re-
search nor sought the Ph.D. Dr. Tom Schmugge provided the essential fi-
nancial support, taught me about thermal infrared, and allowed me to devote 
substantial time on this research. Dr. Bill Kustas got me started at the Hy-
drology Lab, let me use hi s surface energy flux model s, and showed me 
how to use them. Much of the data for this research was collected during 
the Southern Great Plains 1997 experiment, a project funded by NASA's 
Land Surface Hydrology program and coordinated by Dr. Tom Jackson. 
Rob Parry and Chri s Pooley provided essential help maintaining my com-
puter hardware and software. Much of my research has been helped by dis-
cuss ions with Mark Chopping, Craig Daughtry, Paul Doraiswamy, Simon 
Hook, Ann Hsu, Frederic Jacob, Anna Oldak, John Prueger, Jerry Ritchie, 
Al Rango, Pat Starks, and Charlie Walthall. 
II 
I wo uld never have been able to prepare my proposa ls, research, and de-
fense w ithout the help of my wife, Cynthi a Elek, my son, Emerson French 
and from Eli zabeth French, M.D., Gordon French, M.D ., Debbie Peverill , 
Ri chard French, Ell en Schoe llkopf, Karl Schoellkopf, Ruth and Dave Cli-
nard , Helen and Joe Elek, and Pam Hines. 
Ill 
TABLE OF CONTENTS 
List of Tables X 
List of Figures xiii 
List of Symbols xviii 
Introduction l 
1.1 Hydro logic Importance of Evapotranspiration 
1.2 Remote Sensing of ET: Opportunity and Cha llenges . 2 
1.3 Research Goals and Objectives 4 
1.4 Report Overview . . . . . 7 
2 Theory and Literature Review 8 
2.1 Chapter Overview . 8 
2.2 Scaling Studies . . 9 
2.2.1 Resolution and Scale 9 
2.2.2 Analysis of Heterogeneity 11 
2.3 Estimating Evapotranspiration . 15 
2.3.1 Penman-Type Methods . 17 
2.3.2 Temperature Based Methods 20 
2.3.3 Surface Energy Balance Modeling 22 
2.4 Two-Source Model . . . . . . . . . . . . 24 
2.4. 1 General Expression for Net Radiation 24 
2.4.2 Albedo of Vegetation Canopy . . .. 25 
2.4.3 Soil Albedo and Incident Radiation to the Soil 30 
IV 
2.4.4 Long Wave Radiation ... .. . . 3 1 
2.4.5 Net Radiati on to Canopy and Soi l 33 
2.4 .6 The Resistance Model for Turbulent Fluxes 35 
2.4.7 Resistance Network in the Two-Source Model . 38 
2.4.8 Solution Method ... 41 
2.5 Turbulent Flux Measurements 48 
2.6 Sur face Temperature Estimation 53 
2 .6. I Phys ical Basis of Radiometri c Temperature Measurement 53 
2 .6.2 Atmospheric Effects 54 
2 .6.3 Surface Emissivity . 6 1 
2.6.4 Instrumental Designs and Limitati ons 66 
2.6.5 Radiance-Temperature Inversion . 70 
2.7 Vegetati ve Cover Estimation . . . . . . . 71 
3 Methods: ET Estimation and 
Scaling using Remote Sensing 77 
3. l Methods Overview . . . 77 
3 .2 El Reno Data Collection 78 
3.2. l Aircraft Remote Sensing Observations . 80 
3.2.2 Ground Flux Measurements ..... . 83 
3.2.3 Aircraft Flux Measurements 84 
3.2.4 Radiosonde Data . . . . . . . . . . . . . 86 
3.2.5 Sensitivity of Surface Temperature to Uncertainty in Radiosonde 
Data . . .. .. . 88 
3.2.6 Soil Emissivities 96 
3.3 Jornada Data Collection . . . . . . 101 
V 
L 
3.4 Gcorcgistration . . . . . . 105 
3.5 TIM S alibration Assessment 109 
3.6 Atmospheri c Correction of Thermal Infrared Data 11 7 
3.6.1 Computation of T, L >.. ,up111rll i119 and L >.. ,dmvn w l'lling 1 18 
3.6.2 Empirical Relationships . . . . . 11 9 
3 .6.3 Band-Averaged Atmospheri c Corrections 128 
3.7 Atmospheri c Correction of Visible-Near Infrared Data 129 
3.8 Vegetati on Cover Estimation . . . .. . 134 
3.8 .1 NOVI , Fractional Cover and LAI 136 
3.8.2 Vegetation Height and Land Use 141 
3.9 Two-Source Model Flux Computations . 14 1 
3.10 Operati onal Sca le Analys is 146 
3. I I Aggregation of Spatial Data 147 
3. 11 .1 Range of Scales . . 150 
3. 11 .2 Aggregation Issues 150 
3.11.3 Aggregation of Continuous Data 151 
3.11.4 NOVI Ambiguity . . . ... . 154 
3. 11 .5 Aggregation of Discrete Data 158 
3.12 Methods Summary . .... 160 
3.12.1 Surface Temperature 161 
3 .12.2  Vegetation Cover . 162 
3.12.3 Flux Computation 162 
3.12.4 Operational Scale Analysis . 162 
3.12.5 Aggregation Procedures .. 163 
VI 
4 Results: ET Estimates and Sca lin g Properties 164 
4 .1 Chapter Overview .. .. . . . .. .. . . . 164 
4 .2 El Reno, Oklahoma: Accuracy of Remotely 
Estimated Sur face Temperature . . . . . . . 164 
4 .3 El Reno, Oklahoma: Validation and Calibration of Vegetation Measures 172 
4.4 El Reno, Oklahoma: Estimation and Eva luation of Surface Energy Fluxes 175 
4.4 .1 Ground-Based Flux Measurement for Va lidation . . . . . . . 175 
4.4 .2 Validation of Two-Source Model Estimates: Morning Surveys 179 
4.4.3 Validation for Two-Source Model Estimates: Afternoon 
Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . 186 
4.4.4 Comparison of Two-Source Model Estimates with Aircraft Flux 
Measurements . . . . . . . . . . . . . . 188 
4 .5 El Reno, Oklahoma: Operational Scale Analysis . 195 
4.5. 1 Surface Temperature Scale Analysis 197 
4.5.2 Vegetative Cover Scale Analysis 207 
4.5.3 Land Use Scale Analysi s . . .. 218 
4.6 El Reno, Oklahoma: Aggregation Experiments 220 
4 .6. l Latent Heat Flux (Evapotranspiration) 221 
4.6.2 Sensible Heat Flux 226 
4.6.3 Net Radiation . . . 232 
4.6.4 Ground Heat Flux 233 
4.6.5 Flux Moments and Scale 237 
4 .7 Studies at Jornada Experimental Range, 
New Mexico ...... . . . 243 
4.7.1 Surface Temperature 244 
V II 
4 . 7.2 Vegetati ve Cover .. . .. . 245 
4.7 .3 Operati onal Sca le Analys is . 248 
5 Conclusions and Discussion 259 
5. 1 Research Contributi ons . 259 
5.2 Accuracy of Remotely Sensed Model Inputs 260 
5.3 Accuracy o f Modeled Surface Fluxes . 262 
5.4 Operati onal Sca le . .. .. . . . .. . 264 
5.5 Reso lution, Sca le, and Surface Flux Estimates 265 
5.5.1 Impli cati ons of the Res ults . .. . .. . 266 
6 Recommendations for Applications and Future Work 271 
6.1 Potentia l Appli cations o f the Two-Source Energy 
Balance Model . . . . .. 272 
6.2 Improved Data Acquisition 273 
6.3 Improved Model Algorithms 273 
6.4 Comparison with Other Models . 275 
Appendix 277 
A El Reno TMS and TIMS 
Data Calibration 277 
A. I TMS . 277 
A.2 TIMS 281 
A.2 .1 Fort Cobb Reservoir Remote Sensing Flights 281 
A .2.2 Sensitivity of TIMS Temperature Estimates to Columnar Water 
Vapor . .. . . .. .. . . . . .. . ........ . .. . ... 282 
VIII 
A.2 .3 Emiss ivit y ...... . . . . . . . .. . . . . 283 
A.2.4 Va lidati on o f TJM S Cent ra l Wave length Va lues 285 
B Two-Source Model Sensitivity 290 
C El Reno Study Site Data 291 
D MODTRAN 294 
E Useful Formulae 299 
E. l Radi ometri c Conversions 299 
E.1.1 Temperature to Spectra l Radiance 299 
E.1.2 Spectral Radi ance Units Conversion 307 
E.2 Water Vapor Conversions . . . . . . . . . . 308 
E.2. 1 Air-Vapor Densiti es from Vapor Press ure 3 12 
E.2.2 Spec ific Humidity . .. 3 12 
E.2.3 Dew Point Temperature 313 
E.2.4 Specific Heat of Moist Air at Constant Pressure 314 
E.2 .5 Latent Heat of Vaporization of Water 314 
E.2.6 Psychrometric Constant 314 
F Example Flux Computation 314 
F. l Remote Sensing Observations 315 
F.2 Meteorological Observations 315 
F.3 Initialize Parameters . 315 
F.4 Compute Net Radiation 317 
F.5 Compute Flux Components . 323 
IX 
Bibliography 328 
X 
LIST O F TA BL ES 
2. 1 Geographic vari ance scheme . . . . . . . . 15 
2 .2 Leaf angle probability di stribution fun cti ons 27 
2.3 Nominal so il and leaf absorptiviti es. . . . . 30 
2.4 Spectral we ight fac tors, lV , fo r di rec t(beam or be) and di ffu se radi ation. 30 
2.5 TSEB unknowns and assoc iated fo rmulae. 47 
3. I Remote sensing radi ometer spec ificati ons 81 
3.2 El Reno TIM S/TMS fli ght conditions. 82 
3 .3 MASTER spec ifications. . . . . . . I 05 
3.4 Jornada MASTER fli ght conditions. 105 
3 .5 Fort Cobb Reservoir fli ghts . . . . . 114 
3 .6 Coeffici ents for estimating atmospheric properti es . 126 
3.7 Simulation of temperature error estimate from empirical relations. 128 
3.8 Thermal infrared correction simulation . . . . . . . . . . . . . . . 130 
3.9 El Reno leaf area indices. Field averaged measurements 25 June to 2 
July 1997. Wheat fie lds are harvested stubble . 137 
3 .10 Nominal land use values 142 
3.11 NOVI Aggregation .. . 157 
4 .1 El Reno temperatures compared. 168 
4 .2 El Reno treatment pond temperatures. 172 
4.3 Leaf Area Index estimates . .. .. . 173 
4.4 Vegetation vs . evaporative flux measured by eddy-covariance observa-
tions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 
XI 
4.5 El Reno mean flu xes at eddy-covariance sites . ?: Mid-morning, x: 
Mid-afternoon . . . ..... . 178 
4 .6 El Reno surface meteorology stati stics 179 
4 .7 Validation of El Reno A.M. flux components: Basic data 183 
4.8 Vali dation of El Reno A.M. flux components : corre lation and regress ion 
95% confidence intervals. . . . . . . .. 183 
4 .9 El Reno Flux means and differences, in W m - 2 . 185 
4 .1O  Validation of El Reno P.M. flux components: Basic data . 188 
4. 11 Validation of El Reno P.M . flux components: correlation and slope 95% 
confidence intervals. 190 
4.12 Flux profile comparisons 194 
4.1 3 Inter-quartile range of surface temperature vs. resolution . 202 
4 .14 Land use sca ling . . . . . . . . . . . . . . . . . . 219 
4 .15 Latent heat flux (canopy) aggregation regression statistics. 223 
4.16 Soil heat flux aggregation regress ion statistics. . . . . . 228 
4.17 Sensible heat flux aggregation regression statistics (bare soil only). 230 
4.18 Net radiation aggregation regression statistics. . . 233 
4.19 Ground heat flux aggregation regression statistics. 237 
4 .20 Mesquite area surface temperature vs . resolution . 257 
A. l TMS calibration data . . . . . . . . . . . . 278 
A.2 Fort Cobb Reservoir TIMS/TMS flight data 281 
A.3 TIMS band emissivities. . . 287 
A.4 TIMS band emissivities cont. 288 
A.5 TIMS central wavelengths 290 
C. l Approximate El Reno flux station locations . 293 
Xll 
.2  El Reno meteoro logy. . . . . . . . . . . . 294 
C .3 El Reno Meteorological Data Field ERO l . 295 
.4 El Reno Meteorological Data Field EROS. 296 
C. 5 El Reno Meteorological Data Field ER09. 297 
.6 El Reno Meteorological Data Field ER 13 298 
LI ST OF FIGU RES 
2. 1 Loca l standard dev iation scheme 14 
2 .2 Geographic variance scheme .. 16 
2.3 Leaf angle probability distribution functions 28 
2.4 Net radiation components at the surface 34 
2.5 Two-Source model configura tio ns .. . 40 
2.6 Two-Source algorithm, unstable condi tions 42 
2.7 Flux foo tprint scheme . . 5 1 
2.8 Radiation at the sur face . 55 
2.9 Thermal infrared response functions fo r low-reso lution satellites 58 
2. 10 Generic MMD relation . . . . . . . . . . . . 64 
2.11 Example of temperature-emiss ivity separation 67 
2. 12 Thermal infrared properties . ... .... . . 69 
2 .1 3 Visible-near infrared spectra of alfal fa and bare so il 73 
2 .14 Solar irradiance spectra above the atmosphere and at the surface 75 
3.1 SGP97 study area . . 79 
3 .2 El Reno Fields, SGP97 83 
3.3 SGP97 mid-day fluxes 85 
3.4 Twin Otter flight path . 86 
3.5 ARM-Cart Sonde Sites 87 
3 .6 Example sonde data . . 89 
3.7 Simulated radiosonde profiles. 93 
3.8 Radiosonde error effects 94 
3.9 Total water vapor vs . time 95 
XI V 
3. 10 Surface temperature sensiti vity analys is 97 
3. I I Contoured water vapor over SG P97 98 
3.12 Soil emiss ivity example . . .. 100 
3. 13 Minimum emissivity function . 102 
3. 14 Jornada site map . .... 104 
3 . 15 TIMS scan characteristics . 108 
3. 16 Fort Cobb Reservo ir. 11 0 
3.17 Water em iss ivity . . 112 
3.18 Sensitivity ana lysis scheme for T IMS response funct ions 113 
3 .19 Sca led response functions . 11 5 
3.20 Shifted response functions 11 6 
3.2 1 Atmospheric effects on scanning rad iometers 120 
3 .22 Transmissivity vs. co lumnar water vapor . 122 
3.23 Upwelling radiance vs. transmissivi ty .. 123 
3 .24 Oownwelling radiance vs. upwelling radiance 124 
3.25 Atmospheric downwelling radiance vs . view zenith ang le 127 
3.26 NOVI : Solar irradiance correction . .. . . . .. . 132 
3 .2 7 NOVI: correction for attenuated reflected irradiance 133 
3 .28 NOVI corrected and uncorrected . . . . . . . . . 135 
3.29 Sensitivity of vegetation coefficients /3 and (1/~) 138 
3.30 NOVI vs. LAI . . .. 140 
3.31 Aggregation scheme 149 
3.32 Image aggregation methods . 152 
3.33 Thermal infrared aggregation 155 
3 .34 Vegetation cover and NOVI . . 156 
xv 
3.35 Scaling and NOVI .... .. .. . .. . 159 
4 .1 Fort Cobb Reservoir, TIMS-derived temperatures 166 
4.2 Surface temperature va lidation at E l Reno 169 
4 .3 Leaf Area Index observations vs . estimates 174 
4.4 TSEB flux estimates . . . .. . 180 
4 .5 El Reno A.M. flux comparisons 182 
4.6 El Reno P.M. flux comparisons 189 
4.7 Aircra~ flux profiles .. . . 191 
4.8 NOVI image and profile of bare soil patch .. 193 
4.9 Twin Otter/ Two-Source flux correlations 196 
4.10 El Reno surface temperatures from TIMS 197 
4.11 Reso lution scaling of surface temperature at El Reno 199 
4 .12 Surface temperature hi stograms vs. resolution at El Reno, OK on 2 July 
1997 . . . . . .. ... ... ... . . .... . 201 
4.13 Inter-quartile range of surface temperature vs. resolution 202 
4.14 Surface temperature from TIMS over mixed land cover types 203 
4.15 Mixed land use surface temperature semivariogram 205 
4.16 Surface temperature local standard deviation . 206 
4.17 Surface temperature geographic variance . 208 
4.18 El Reno NDYI . . . . . . . . . . . . .. 210 
4.19 NOVI vs. surface temperature histogram . 211 
4.20 Resolution scaling ofNDVI at El Reno. 212 
4 .2 1 NDYI histograms vs. resolution 213 
4 .22 NIR vs. Red reflectance histogram 215 
4.23 Mixed land use NDVI semivariogram 216 
XVI 
4.24 NOVI local standard deviation 217 
4 .25 Geographic variance of NOVI 218 
4.26 Latent heat aggregation . ... 222 
4 .27 Georegistration error simulation 224 
4 .28 Sensible heat aggregat ion . . . 229 
4.29 Evaporative fraction and resolution . 230 
4.3 0 Sens ible heat aggregat ion over bare soi l 23 1 
4 .31 Net radiation aggregation 234 
4.32 Ground heat flux .. 236 
4 .33 Histograms of sensible heat from so il 238 
4.34 Scaling moments: sensible heat from soil, aggregated inputs 240 
4.35 Scaling moments: sensible heat from soi l . . . . . . . 242 
4 .36 Scaling moments: latent heat from canopy, aggregated inputs 243 
4 .37 Mesquite grid surface brightness temperatures 246 
4.38 Mesquite site brightness temperatures . .. . 247 
4.39 NOVI vs . surface temperature at the Mesquite site . 249 
4.40 Mesquite site NDVI . . . ..... 250 
4.41 Histogram of Mesquite site NDVI 251 
4.42 Mesquite site from Ikonos . . . 252 
4.43 Resolution effects, Mesquite site 253 
4.44 Semivariance at Mesquite site 254 
4.45 Local standard deviation at Mesquite site . 255 
4.46 Geographic variance at Mesquite site . . . 256 
4.47 Surface temperature sca ling over Mesquite site 258 
A. I TMS filter functions . . . . . . . . . . . .... 279 
XVII 
A.2 TMS radiometri c distributions 280 
A.3 Sensi ti vi ty of temperature estimates 284 
A.4 SGP97 so il emissivities . . 286 
A.5 TIMS central wavelengths 289 
8 .1 H so il flux sensitivity .. 291 
8.2 LE canopy flux sensitivity 292 
0.1 Atmospheric transmiss ivity in VNIR ( I) 300 
0 .2 Atmospheric transmiss ivity in VN IR (2) 301 
0 .3 Atmospheric transmiss ivity in VNI R (3) 302 
D.4 Atmospheric transmissivity in TIR ( I) 303 
0 .5 Atmospheric transmissivity in TIR (2) 304 
D.6 Atmospheric transmissivity in TIR (3) 305 
0 .7 Atmospheric transmiss ivity in TIR ( 4) 306 
E. I Saturation vapor pressure vs. temperature 309 
E.2 Vapor density vs. relative humidity . .. 311 
E.3 Specific humidity vs. relative humidity . 313 
XV IJI 
LIST OF SYMBOLS 
Symbols defined, along with common units ([] indicates non-dimensional) 
rl, 13, C Empirica l coefficients for minimum emissivity determination in Temperature-
Emissivity Separation algorithm ([]) 
.?10, A 1, A2 Split-window coefficients (Ao in m 2 s- 2 J< - 1, A I and A2 dimensionless 
n Albedo ([]) 
n.r Canopy albedo ([]) 
n.,.8 Empirical coeffic ient to compute rs (m s- 1) 
a8(. Wind attenuation coefficient in the subcanopy ([]) 
a-y Semi-variogram function coefficient (m) 
h,. 8 Empirical coefficient to compute rs ([]) 
cc Empirical coefficient to compute G from Rn,s ([]) 
Cr Specific heat of moist air at constant pressure (m 2 s - 2 1<- 1) 
Cpd Specific heat of dry air at constant pressure (m2 s- 2 J(- 1) 
c,.8 Empirical coefficient to compute rs (m s- 1 J(~/) 
c 1 Planck's first radiation constant, 3.7417749 x 10- 16W m 2 
c2 Planck's second radiation constant, 0.01438769m K 
d Earth-sun distance (a.u.) 
XIX 
d0 Displacement height (m) 
ea Ambient water vapor pressure (mbar) 
D Probability density of leaf angle distribution ([]) 
r .w t. Saturation water vapor pressure (mbar) 
E Water vapor mass flux , kg m - 2 s 
Em Water vapor, liquid depth equivalent (mm) 
E 1sun Solar irradiance (W m- 2 1,.m- ) 
EF Evaporative fraction ([]) 
F Correction factor for solar zenith angle and ea1th-sun distance ([]) 
Jo Fractional vegetative cover, if 0 present, spec ifies view angle ([]) 
G Ground heat flux , i.e conducted flux into or out of the soil (W m - 2 ) 
g Acceleration of gravity (m s-2) 
H Sensible heat flux, additiona l subsripts S for soi l, C for canopy, t for total (W m - 2 ) 
h Semi-variogram lag distance (m) 
ho Height of vegetation canopy (m) 
I Surface infiltration of water (mm) 
I<be Extinction coefficient of canopy of black leaves with an ellipsoidal leaf angle dis-
tribution for beam radiation ([]) (Campbell and Norman, 1998) 
I< d Extinction coefficient of canopy of black leaves for diffuse radiation ([]) 
xx 
k Visible and near infrared light extinction coeffic ient [m - 1] 
kr rn Thermal infrared light extinction coefficient [m - 1 ] 
k vk von Karman 's constant, usually 0.4 ([]) 
l>. Spectral rad iance (W m- 2 ster- 1 ;1,m- 1) 
LMo Monin-Obukhov roughness length (m) 
L .rni? fn r1, ,r, Apparent surface spectra l rad iance (W m- 2 ster- 1 ;1,m- 1) 
LAI Lea f area index ([]) 
LE Latent heat flu x, additional subsripts S for so il , C for canopy, t for total (Wm - 2 ) 
MMD Minimum-Maximum emissivity Difference ([]) 
rn Number of samples in semi-variogram analysis ([]) 
NOVI Normalized Difference Vegetation Index ([]) 
N DV I m ax NDVI over I 00% vegetation cover (Choudhury et al. , 1994) ([]) 
N DV Imin NDVI over bare soi l (Choudhury et al., 1994) ([]) 
NIR Near infrared radiation (wavelengths 0.7-1.l JJm) 
P Precipitation depth (mm) 
p Shape factor for canopy leaf angle distribution ([]) (Goudriaan, 1988) 
q Specific humidity (g kg - 1) 
q' Specific humidity transient (g kg - 1) 
XXI 
7?0 Resistance to water vapor or heat transport above the canopy (s m - 1) 
re Resistance of canopy (Penman-Monteith) (s m - 1) 
fl Radi ant fl ux (W m- 2 ) 
R 1, Downwell ing longwave rad iation (W 
1 
111 - 2 ster- 11,m- 1) 
R ,, or Rn Net rad iation, additi onal subscripts: a fo r atmosphere, c fo r canopy, s fo r soil 
(W 111 - 2 ) 
rs Resistance to water vapor or heat transport from so il to air (s m - 1) 
R.rnt Solar radiation (W 2111 - ) 
rx Resistance to water or heat transport between canopy and canopy airspace (s m - 1) 
R >. Sensor spectra l response function we ight ([ ]) 
RO Surface runoff depth (mm) 
T Temperature (0 I( or ?C ) 
Ta Air temperature (0 J( or ?C ) 
Taero Aerodynamic temperature (0 J( or ?C ) 
T0 1, T02 Sensor apparent temperature, split-window application (
0 I( or ?C) 
Tc Canopy temperature (0 I< or ?C) 
Tn Radiometric temperature (0 I( or ?C) 
Ts Soil temperature (0 I( or ?C ) 
T.m,'far.e Earth surface temperature (0 J( or ?C ) 
XX II 
U Wind speed (m .,, - i) 
Us Wind speed above so il (m s - 1) 
n* Friction ve loc ity (m s- 1) 
:i: Distance (m) 
:r u , Shape parameter for canopy leaf angle distribution ([]) (Campbe ll and Norman, 
1998) 
V Visible radiation (wavelengths 0.4-0.7 11 m) 
l JI Spectra l we ighting factors for direct and diffuse radiation ([]) 
w' Vert ica l component of wind transient (ms - 1) 
z Height (m) 
Zijk .. . Sum of pixe l hiera rchica l components f l, a, /3, 1 ... (various units) 
z(.1:i) Pixe l va lue, at position 'i (various units) 
z0 Effective momentum roughness lenght (m) 
Z M Momentum roughness length (m) 
Zr Height of air temperature measurement (m) 
zu Height of wind speed measurement (m) 
ai Geographic variance between grand mean and first hierarchical level (various units) 
rY,x Absorptivity ([]) 
O'. p r Priestl ey-Taylor ratio, (actual ET/equilibrium ET), over saturated surfaces ([]) 
XXIII 
/J Coe fficient to convert between fractional cover and LAI (Choudhury et al., 1994) ([]) 
(-3;1 Geographical variance between first hierarchica l leve l and second hierarchical level 
(various units) 
1 (/1) Functional fi t semi-variance (various units) 
1,Ah) Expe rimenta l sem i-variance al lag h, using resolution v (various units) 
r iJk Geographica l variance between second hierarchica l level and third hierarchi cal 
level (vari ous units) 
ry* Modified psycrometri c constant (mbar K - 1) 
~ Slope of saturation vapor pressure vs. temperature (mba r K - 1) 
r Emi ss ivity ([]) 
( Surface layer sca ling parameter ([]) 
02 Solar zenith angle (degrees) 
J\ Leaf angle (degrees) 
A Wavelength (JJ,m) 
Av Latent heat of vaporization (J kg- 1) 
/J, Mean sample value 
v Resolution of sample in semi-variogram analysis (m) 
~ Exponent factor to convert NDVI to fractiona l cover (Choudhury et al. , 1994) ([]) 
p Reflectivity ([]) 
XXIV 
/Jr Reflectivity of vegeta tion canopy ([]) 
/JN 1H Reflecti vity in the TM near infrared wave length band (0. 75-0.88 pm) 
/J,wt Re flectivity in the TM red wavelength band (0.63-0.69 / lm) 
()8 Re flectivity of so il ([ ]) 
fJ""P Mo ist air dens it y (kg rn - :i) 
<J Stefa n-Boltzmann co nstant (5.67051 x 10- 8 W rn - 2 J< - 4) 
T Transmiss ivity of radiation ([]) 
?111 Uni versa l stab ility function for momentum ([]) 
\Ji 11 Diabatic correcti on facto r for sensibl e heat flux ([]) 
'11 /If Diabatic correc ti on factor for momentum flu x ([]) 
'Ip Solar zenith angle (degrees) 
XXV 
1 Introduction 
1.1 Hydrologic Importance of Evapotranspiration 
Thi s is a study to improve the use of remote sensing tool s to quantify spati a l varia tions of 
evapotranspiration (ET). ET is just as important to the hydrological cycle as are ground 
water fl ow an d surface runoff, but study of ET requires a different point of view. While 
ground wa ter and surface water hydro logists meas ure movement of liquid water using 
mass balance eq uations, surface layer hydrologis ts need to use energy balance equat ions 
to measure wa ter vapor movement. 
Et, at times the most s ignificant component of the hydrologic cycle, is one of the 
most di fll cult components to measure or es timate. Water transported from so il and plants 
into the atmosp here during one day can easily exceed 60- 100 mm, while the remaining 
water flow com ponents ground water, surface water, and prec ipitation) can be neg lig ible. 
Accounting for ET under such conditions is important for bas ic hydrologi ca l resea rch. 
There are unresolved problems mode ling the transfer o f water from soils and vege-
tation into the atmosphere, in time and space, over resolution scales ranging from cen-
timeters to thousands of kilometers. Plant scale modeling considers transpiration from 
indi vidual leaves. At the globa l climatological scale, evaporative processes are modeled 
in aggregates hundreds of kilometers in scale. How to bridge the methodological gap 
remains to be solved. 
Accounting for ET is also an important problem in agriculture and engineering. By 
assess ing how much water evaporates from the soils and plants, water management can 
be more inte lligently implemented, and crop failures more accurately predicted. Some 
decisions are needed on a daily basis, depending, for example, upon the water stress 
of acti ve ly growing crop. Other dec isions arc seasonal, poss ibly multi -seasonal, where 
climati c changes and chronic water shortages require reasonabl y accurate predi ctions or 
fo recasts of water ga ins and losses. ET estimates are also needed to va lidate di stributed 
hydrolog ica l models of watersheds, including water transport and water quality. 
1.2 Remote Sensing of ET: Opportunity and Challenges 
Traditional approaches to estimating ET have been point measurements, such as from 
ca libra ted evaporati ve pans, where water mass is directly measured . But pan measure-
ments represent a potential, rather than actual, ET rate, and do not account for soil and 
vegetation control when water is limited. Seasonal estimates of evapotranspiration have 
been made from the res idual left from measurements of rainfall, runoff, storage and in-
filtrati on. These approaches are inadequate. Residual calculations are difficult on short 
time scales and in forecasting. ET is hi ghly variable in space and time, and neither the 
po int nor the residual approach can adequately account for these variabilities . 
The development of remote sensing tools , on the other hand, offers ways to detect 
and quantify the spatial and temporal variation of ET. For example, the amount of evap-
otranspiration is intimately related to the surface type (such as a lake, a bare field, or a 
thickly vegetated grassland) and the distribution of these surface types is readily mea-
sured by remote sensing in visible and near infrared wavelengths. The remote sensing 
can be done from aircraft for a specific site or from satellites for regional studies . Fur-
ther, remote sensing can make observations repeatedly, permitting time series analyses. 
Currently there are a variety of remote sensing detectors available for commercial 
and research purposes . Their reso lution capabilities span from 1 m to over 4 km, and 
they measure light in the visible, near infrared and thermal infrared wavelengths. From 
2 
the hydro logica l point of view, two potenti a ll y use ful remote sensing detectors are the 
Advanced Spaceborne Thermal Emiss ion and Refl ection Radiometer (ASTER) and the 
Moderate Reso lution Imag ing Spectroradi ometer (MODI S), on-board NASA's recently 
launc hed Terra satellite. Together, ASTER and MODIS continuously view the earth at 
resolut ions from 15 m to 1 km over most of the optica l wave lengths. Their observations 
and esti mates of earth sur face cove r, temperature, so lar radi ati on and atmospheric water 
va por arc free ly ava ilable. 
Of cour e, the remote sensing approach to ET estimation is not w ithout its own dif-
fic ult ies and ambiguities ' . As fo r any geophysica l method, remote sensing relies upon 
auxili ary information and a veri fied, preferably phys ically-based, model. Auxiliary in-
fo rmation typica ll y consists of surface meteorologica l observati ons and descriptions of 
surface vegetati on characteristi cs, imposs ible to retrieve remotely. The model used, in 
turn, must be able to combine the auxiliary information with the remote sensing informa-
tion and yield estimates that reasonably match ground-based point measurements. But 
it has onl y been recently that both well-calibrated remote sensing tools and physically-
sound hydrological models have been developed to work together. Multi-disciplinary 
fi e ld ex periments are ongoi ng to deve lop and improve hydrological models, in conjunc-
tion wi th technological improvements, to better constrain and verify ET estimates. 
This research focuses on the improvement of one particular remote sensing ap-
proach: estimation of ET by measuring surface temperatures. The essential idea is 
the recognition that transport of water vapor mass is equivalent to transport of energy. 
Due to the very large amount of heat represented by the evaporation process, it is not 
difficu lt to accurately estimate water mass transport once the energy transport quantity 
is known. Since energy transport of water vapor is directly connected to them1al and 
1Clouds are at the top of the list! 
3 
water vapor gradients, one can estimate ET from knowledge of four readily obtained 
quantities: surface temperature and vegetation density, from rem ote sensing, and near 
surface ai r temperature, along with nea r surface humidity, from ground observations. 
But though it is simple in concept, the estimation of ET from surface temperature, 
in practi ce, is nevertheless a complex task and involves many s implifications. One of 
the most important simplifications is the assumption that, at some observab le scale, 
ET is homoge neous. Rea l surfaces, though, are highly heterogeneous. Actua l water 
vapor transpo11 is controlled by a mix of diffusive, advective, vegetative and turbulent 
processes. For remote sensing, many o f these complexities are unmanageable. In the 
first place, most remote sensing instruments that include thennal infrared detectors-
ASTER excepted- have moderate to low reso lutions, typically I km or coarser. At this 
reso lution, the different kinds of evaporati ve processes that are known to be intimately 
related to surface condi ti ons, such as thi ck vegetation and ponds, are inevitably mixed 
into one sample point. In the second place, obtai ning high resolution remote sensing 
data is difficult, expensive and episod ic. 
But despite these obstacles, there remains little choice. Estimation of the spatial 
patterns of ET is infeasible except with some kind of remote sensing approach. The 
actual process of ET is complex and remote sensing cannot resolve all of the complexity. 
But when some of the complexities are simplified, and appropriate models selected, it is 
possible to make remote sensing observations that result in meaningful ET estimates. 
1.3 Research Goals and Objectives 
This research addresses the difficulties caused by reducing the complexity of ET. Actual 
ET is a result of nonlinear, interacting processes occurring within soil, plants and the 
4 
overly ing air. In modeling ET with remote sensing data, the deta ils of these interacting 
processes are igno red, such as occurs on the surfaces o f indi vidual leaves. T he difficul-
ties encountered when modeling ET are directly analogous to those seen by surface and 
ground water hydro logists. In seeking practi ca l ways to es timate watershed response, 
surface wa ter hydro log ists reduce watershed complex ity by aggregating surface prop-
erti es ove r some minimal area. Simil arly, ground water hydrologists frequently invoke 
effecti ve bulk para meters in Darcy's law to avoid deta il ed treatment of subsurface het-
erogeneity. 
Here, the resea rch addresses the difficulties caused by resolution limitati ons in re-
mote sensing observa ti ons. In particular, satellite-based remote sensing observations 
have fi xed reso lutions, and may produce inadequate data for ET modeling . What is 
needed is an assessment o f the ca pabiliti es of exi sting remote sensing systems . What 
is the re lationship between the resolution of remote sensing observations, resulting ET 
estimates, and different leve ls of heterogeneity in the landscape? It is fairly obvious that 
a coarsely resol ved view of a g iven surface shows less variability than a finely resolved 
view of the same surface. But it is unknown how rapidly the variability changes with 
resolution . How do the estimates of ET- a nonlinear function of observed quantities-
change with resolution? 
To he lp answer these questions, an existing energy-based ET model is used in con-
junct:on with remote sensing observations of two different landscapes: central Okla-
homa and southern New Mexico. The Oklahoma landscape study, from an area known 
as El Reno, consists of sub-humid grazing lands along with a mix of harvested and 
p lowed wheat fields . The New Mexico landscape study is from a semi-arid, degraded 
grass land with encroaching mesquite bush. The remote sensing data sets consist ofrela-
tively high resolution data, ranging from 3 to 12 meters. Along with the remote sensing 
5 
data are the required surface observa ti ons, as we ll as independentl y-measured energy 
nux es timates. The basic objectives arc fourfo ld : 
? Establish the leve l o f accuracy in the original, best reso lution, observations of 
surface temperature and vegetati on cover. 
? Determ ine how well th e resulting modeled surface energy nuxes match the independently-
obtain ed meas urements. 
? Quantify the leve l of heterogeneity in the landscape, so that flux estimates and 
reso lution can be mea ningfully related. 
? Using data aggrega ti on techniques, determine the relationship between estimated 
surface energy nuxcs over a range of reso lutions (3 to 1000+ meters). 
To facilitate thi s approac h, four working hypotheses have been formulated . 
? Remote cnsing observations of surface temperature and vegetation density are 
sufficiently accurate for surface energy flux modeling. 
? Modeled surface energy fluxes match within 15% relative error, 2 independently 
measured (using eddy covariance instruments) fluxes . 
? Landscape heterogeneity over the El Reno site occurs at scales significantly greater 
than the best reso lution data available, 12 meters. Heterogeneity over the Jornada 
site occurs at scales significantly greater than the 3 meter resolution data available 
there. 
2The choice of' I 5%' is on ly a point of reference. Assuming random errors from less experimental 
model s range between 5 and I 0%, and recognizi ng the large di meulties encountered with ET models, the 
I 5% error was chosen to represent idea l agreement. 
6 
? As long a the original observations are made at resolutions finer than the pri-
mary landscape heterogeneity sca le, surface energy flu x estimates wi ll be sca le 
independent , with relative agreement maintained within 15%. 
1.4 Report Overview 
Chapter 2 reviews relevant theory and current approaches to the issues of scaling, ET 
modeling and measurement, land surface temperature measurement, and estimation of 
vegetati ve cover. Chapter 3 presents the specific data and methods used in thi s study. 
Results are presented in Chapter 4 with conclusions and discussion in Chapter 5. Finally, 
recommendations for appli cations and future research are provided in Chapter 6. 
7 
2 Theory and Literature Review 
2.1 Chapter Overview 
Previous work has shown that retrieval of surface fluxes from a combination of remote 
sensing observations and surface meteorological observati ons is achievable. Work has 
also shown that surface fluxes are strongly influenced by landscape heterogeneity. In 
this study, these ach ievements are brought together in order to answer thi s question : 
? How do sur face energy flu x est imates change with sensor resolution and landscape 
heterogeneity? 
To do this, a number of existing techniques and results need to be assembled, includ-
111g: 
? How to quantify and interpret the relati onship between the heterogeneity sca le of 
the landscape and sensor resolution. 
? How to estimate and measure surface energy fluxes 
? How to retrieve the driving inputs to energy flux modeling: 
I . Surface temperature 
2. Vegetative cover 
This chapter reviews these techniques. 
8 
2.2 Scaling Studies 
Because estimating landscape-sca le evapotranspi ra ti on is a young fie ld, there has been 
little experience with the e fTects of surface reso lution upon the accuracy of these esti -
mates (Pclgrum, 2000b; Wood and Lakshmi , 1993 ; Se ll ers et a l. , 1995) . Remote sensing 
resolution is an important design considerati on when building satellite sensors, because 
once launched the resolution can not be changed. Reso lution is also a des ign issue, 
because the potentia l volumes of spati ally-di stributed data sets can easil y overwhelm 
human abilities to store, analyze and interpret any resulting measurements. 
2.2.1 Resolution and Scale 
There are differing opinions on resolution e fTects upon estimates o f evapotranspiration. 
Some suggest that algorithms based upon fractal concepts might be created that are 
resolution independent (Lovejoy et al. , 200 I; Dubayah et a l. , 1997) . Rastetter et al. 
( 1992), on the other hand, suggest that different resolutions can be empirically linked 
with estimates of probability distributions of model input variables . Nevertheless, prac-
tical experience (Moran et al. , 1997) shows that linkage between scales is complex. The 
difficulties might be because surface processes occurring at one scale might not be ob-
servable at other scales. Grace et al. (I 997) and Woodcock et al. (I 997), for example, 
show that surface properties occur on a hierarchical range of scales. This implies that 
a hydrological model developed and validated at one scale can not be re-applied at a 
different scale by mere adjustment of the input parameters (Avissar, 1995). Both higher 
and lower resolutions might be needed in a landscape model, and transformation be-
tween scales may be more complex than developing fractal algorithms or probability 
distribution estimates . 
9 
There has been some practical experience gained investigating resolution and scale 
of surface processes (Cao and Lam, 1997). Blyth and Harding ( 1995) describe an 
African field study (HAPEX-Sahe l, also see Goutorbe et al. , 1994), where aggregation 
experiments measured the sensi tivity of different energy balance approaches (i.e.they 
compared one model which treated so il and vegetation components independently with 
another model , where the components interacted). Moran et al. ( 1997), in an Arizona 
study, demonstrate that large di screpancies (> 50%) in es timated surface flu xes occur 
over heterogeneous terra in . Their ex peri menta l approach, sometimes referred to as 'flux 
match ing' (Raupach, 1995 ; Raupach and Finnigan, 1995; Wood, 1998), followed two 
pathways. In one, remote sensing-derived observations were modeled for surface fluxes, 
and then aggregated to simulate coarser resolution data . In the other, the same remote 
sensing-derived products were aggregated first, and then modeled for surface fluxes. If 
the resulting flux estimates are in close agreement, then the non- linearity effects from 
aggregating input variables are unimportant. However, Moran et a l. ( I 997) found that 
non-linear effects were important. In particular, they aggregated surface roughness and 
aerodynamic resistances and found that estimated surface fluxes had large variabilities. 
There are two approaches to reconcile scale-related discrepancies: either adjust the 
sca le-dependent input parameters, or to reconfigure the model structure. Adjusting the 
input parameters is known as creating 'effective' parameters (Lhomme et al., 1994; 
Lhomme, 1992; Raupach and Finnigan, 1995; Blyth et al., 1993). The adjustment may 
be algorithmically derived, as in the fonnulation of effective flux resistances (Raupach 
and Finnigan, 1995), or they could be empirically derived . In either event, the goal is 
the same: force the hydrological model output from a coarser resolution, to agree with 
model output from a finer resolution . The underlying assumption is that the finer resolu-
tion result is closer to 'truth ' than is the courser reso lution output. 'Effective ' parameters 
10 
may be a use ful approach when measurements are acquired over different sca les. But, 
as pointed out by others (e.g. Seven ( 1995)), 'e ffecti ve' parameters obscure the fac t that 
the processes, and not merely the parameters, are sca le dependent. When the model 's 
representation of underlying physical processes is 11xed, adjustment of parameters may 
become large and irrational. For example, in surface energy flux modeling, the concept 
o f surface roughness is scale dependent. At the sca le of an individual plant, roughness 
might be parameterized at the leaf sca le, while at the sca le of continents, the parameter-
ization of roughness needs to consider the aggrega te of vegetation and terrain geometry. 
2.2.2 Analysis of Heterogeneity 
There exist we ll -estab li shed techniques to diagnose relative sca les oflandscape elements 
statistically. Three tools are discussed: the semivariogra m, the local standard deviation, 
and the geographic variance . They provide three different ways to identify the dominant 
spatial scale or sca les of vari ation in a landscape or image. 
One method is the semiva riogram analysis (Atkinson, 1997a; Webster and Oliver, 
1990; Isaaks and Srivastava, 1989; Goovaerts, 1997; Cressie, 1993). Semivariograms 
measure spatial variability by comparing data points with their neighbors . They are 
seemingly just a complementary form of autocorrelation. Semivariograms, however, 
provide a superior measure because they are insensitive to non-stationary data sets 
(Cressie, 1993). An experimental semivariogram for gridded data can be generated by 
applying the following formula: 
(2 .1) 
where the semivariance i v(h) , at a reso lution 1.1 and lag distance h is determined by 
11 
averaging the squared difTerences between the spatial va lues z(:i;, y), z(:r. + h, y), and 
z(x , y + h). Each sample point is denoted by the indices :ri, Yi, which correspond to 
its row and column locati ons in the image. When semivariance is plotted against lag 
di stance, there is genera lly low semivariance at short lag di stances because data points 
close in space tend to have dependency. With increas ing lags, the semivariance increases 
because the compared data are further apart and less likely to be corre lated. Commonly, 
a threshold semivariance is reached where data points are relati ve ly uncorrelated. The 
lag distance at which thi s occurs is known as the range, and the corresponding semivari-
ance threshold is known as the sill. Spatial data sets spanning several orders of di stances 
relative to the data resolution may also exhibit multiple sills, each representing a differ-
ent hierarchica l level of landscape organization. The term ' nugget' is used to describe 
vari ance observed at a lag of zero di stance. This variance is taken to be irreducib le, and 
is poss ibly due to samp li ng or measurement error (Jsaaks and Srivastava, 1989). 
In a sca ling/aggregation study, knowledge of the data range and si ll can be very 
useful , but not in a way some might expect. ln other studies using semivariograms, 
the objective may be to develop the best poss ible spatial interpolator, where data points 
may be irregularly distributed. But the objective in this study is to use semivariogram 
measures, namely the range and si ll values, to determine the minimum reso lution neces-
sary to resolve dominant landscape feature. In this way, the range and sill represent the 
beginning of the transition between non-predictabi lity and predictability and is essen-
tially an indicator of spatial heterogeneity. The degree of heterogeneity determines the 
minimum resolution required if discrete land surface types are to be resolved (Atkinson, 
1997b). This 'minimum' resolution is alternatively known as operational scale, which 
means that this is the maximum dimension of the surface element being measured (e .g., 
a farm's quarter section would have an operational sca le of 1/4 of a mi le). Resolutions 
12 
coarser than operati onal sca le will inev itabl y mi x land surface types, and o ne will never 
have image samples of relatively homogeneous land surfaces. Reso lutions fin er than 
operati onal sca le, on the other hand, will contain some homogeneous land surface sam-
ples. The objective in determining operational sca le is to determine the reso lution at 
whi ch these homogeneous sampl es begin to be di stinguished. 
For remote sensing imagery, the operati onal scale can a lso be detem1ined by tech-
niques other than semivariogram analysis. These a lte rnatives may be des irable when the 
semivari ogram appears to be insensitive to va ri ations in a subset o f the overall region 
be ing considered . 
One such alternative is to develop a ' loca l ' standard dev iation measure (Woodcock 
and Strahl er, 1987) . Several steps are required. As shown in the le ft part of Fig. 2. 1, a 
J x3 window is moved over a scene and the mean of all the 9-element standard devi ations 
is determined. Then, the image is degraded by areal averaging, and mean local standard 
deviations are again determined . The process is repeated until the image limits are 
reached. When the mean local standard deviations are plotted against resolution (Fig. 
2. 1, right) , the relationship between image data variability and resolution can be seen. 
Image data with higher resolutions correspond to values to the left of the peak of the 
curve. In this domain, image pixel values tend to be similar to their neighbors, and 
local standard deviation values are low. Image data with lower resolutions correspond 
to values to the right of the peak. Here the effects of heterogeneity are reduced by 
areal averaging, and the local standard deviation is also relatively low. Operational scale 
occurs at the peak of the curve, corresponding to the resolution with the largest mean 
local standard deviation . 
Another alternative technique to analyze spatial variability of the landscape is a hi-
erarchically based method (Webster and Oliver, 1990; Moellering and Tobler, 1972). 
13 
Loca l SD 
0 
(/) 
C 
0 
Q) 
2 
Reso lu ti on 
Figure 2. 1: Local standard deviation scheme. A 3x3 window is moved over the image 
data (le ft), generating a standard dev iation for 9 pixe l values for each posi tion . A plot of 
the mean loca l standard dev iations for a range of resolutions (right) shows operational 
sca le at the max imum mean local standard deviation. 
Following an analysis of variance approach (Scheffe, 1959), but without an error term, 
a surface data point is modeled as a concatenation of estimates made at different resolu-
tions. For example, a surface measurement pixel contained within a square image could 
be considered as follows: 
Zijk ... = /L + a i + /3i j + "/i jk ? ? ? (2.2) 
where the measurement z is the sum of overall image mean, and a series of sub-level 
means . The number of sub-levels (indicated by subscripts) is pre-detennined by the 
image size and resolution. In the Moel lering and Tobler ( 1972) approach, each level 
consists of four components derived from the adjacent coarser resolution component 
(Fig. 2.2). The a level variations consist of the differences between the grand mean, 
?, and each of the four patches indicated in the upper right plot. The (3 level variations 
consist of the differences between an a level patch and each of the correspond ing four 
(3 level patches. Moellering and Tobler ( 1972) compute the sums of squared differences 
for each hierarchical level, plus the grand total sum of squared differences (Table 2.1 ). 
The ratio of the hierarchical sums of squares to the grand total provides a measure of the 
14 
Table 2. 1: Geographic variance scheme(Moell ering and Tobler, 1972). Hierarchy level 
is ind icated by Greek letters, sums of squared differences by SS, and degrees of freedom 
by DOF. 
Level ss %SS DOF 
'Y LL L (Zijk - Zij)2 100 X SS1 / SStolal 4 X 4 X 3 
(J LL 2 (zij - zi ) 100 X SS1 / SSu,tal 4 X 3 
a L(zi-z)2 100 X ss 'r Is S1,0/.al 4 
Total LL L 2 ( ziJk - z) 100 Pixels x Li nes- 1 
sca le variati on and can be tabul ated and plotted in a manner equivalent to that done for 
the loca l standard deviation method. 
2.3 Estimating Evapotranspiration 
Estimation of the spat ial distribution of evapotranspiration (ET) requires the incorpora-
tion of data from both remote sensing instruments and surface level observations. For the 
most part, estimation of ET is restated in terms of surface energy balance. An important 
reason for this is that fluxes of energy are more readily measured than fluxes of water 
vapor mass. Another reason is that ET time variabilities are considerably different from 
other hydrological processes, such as surface runoff and infiltration. Measuring ET in 
energy terms can represent rapid variations in time, and space, whereas mass techniques 
are point measures integrated over many hours. 
A traditional approach to estimating evapotranspiration for vegetated surfaces is to 
apply the water mass balance relation and determine evapotranspiration as a residual 
tenn: 
Em = P - RO - I - 6. S (2.3) 
15 
Grand Mean: ? ex Leve l 
(3 Level y Leve l 
Figure 2.2: Geographical variance scheme. Four hierarchical levels are depicted in this 
example, with original image resolution depicted at the I level. Following the fomiat of 
Eq. 2.2, an image pixel is represented by the concatenation of means over levels /J,, o: 
and (3 , plus a residual term 1 . 
16 
where the mass tra ns fer of water vapor, Em, is equal to prec ipitatio n, P, minus surface 
runoff, R O, minus ground infiltration, I , and minus change in storage, 6 S (a ll in units 
o f mass/ time). In Eq . 2.3, P and RO are measurabl e (a lthough at different sca les), whil e 
J must be estimated . Practical applica ti ons of the mass balance also need to conside r the 
potenti al evapotranspi ra ti on (computed from pan data) and phenology of the vegetation 
(Kerr et a l. , 1989) . 
2.3.1 Penman-Type Methods 
A more direct approach quantifies the phys ical process of evapotranspiration at a po int 
using a Penman-type (Penman, 1948) type equation: 
LE = f(n et radi a tion)+ f(m ass t ra nsfer) (2.4) 
where LE is energy flux (W m- 2) due lo vapori zation of water. Eq. 2.4 is simply linked 
to Eq. 2.3 by the relation: 
(2.5) 
where >-v is latent heat of vaporization (J kg - 1 ) , and E is water mass flux (kg m - 2 s). 
>-v is a large number, ~ 2.5xl06J kg- 1, and it is therefore easy to see why latent heat is 
such an important component of the surface energy balance. Eq. 2.4 uses measurements 
of energy and mass vapor fluxes, instead of liquid phase fluxes, and generally requires a 
parameterized model of bulk transfer for the second term (Stewart, 1989). 
Conceptually, the Penman approach to estimating ET is a significant advance over 
mass ba lance approaches. Because the Penman estimates are based on the physical pro-
cess of evaporation, the estimation errors are not dependent on propagated measurement 
errors in surface runoff, ground infiltration and precipitation. Originally configured to 
model ET over a homogeneous canopy, the method has been extended to include a 
17 
wider variety of land cover condi tions. The most fami li ar form , known as the Penma n-
Monteith equation (Montei th and Unsworth, 1990),consists of a resistor mode l with two 
terms: d iabatic energy flu x and adiabat ic energy fl ux. 
(2.6) 
The first term on the right hand side accounts fo r energy added to the system: R n - G. 
R n is net radi ati on, whi ch inc ludes so lar rad iation (a lso known as short wave radi ation), 
absorbed downwelling thermal band atmospheric radiation (or long wave radia tion), as 
well as re-abso rbed soil and vegetati on thermal band radiation (also long wave radia-
ti on components). G represents energy conducted into the so il. 6. is the slope of the 
temperature-satura tion vapor pressure functi on. Its use reflects the Penman assumption 
that saturated air in contact with a source of water vapor remains satu rated even when 
heat is added. Jn Eq. 2.6, ,* is the modifi ed psychrometri c constant, 1 x (re+ ra)lra, 
where I is the rati o of volumetric heat capac ity of air to the latent heat of vapori zati on, 
re is the vegetation canopy res istance, and ra is the atmospheric resistance. The second 
term on the right-hand-side of Eq. 2.6 accounts for the vapor pressure gradi ent, esat - e a . 
Priestley and Taylor ( 1972) show how the Penman approach can be extended to be 
generalized. In particular they show how latent heat flux might be computed when the 
surface is not evaporating at capacity, namely: 
? LE 6. 
L E + H = o:.n 6. + , (2 .7) 
Here, the left hand side represents evaporative fraction flux ratio (EF), latent heat to total 
heat flux. H is sensible heat flux. 6. is the slope of the saturation pressure/temperature 
curve (see Appendix for formul a), and o:. is a proportionality constant. Priestley and Tay-
lor (1 972) found empirically that actual ET over saturated surfaces exceeded equilibrium 
ET by ~ 1.26, which is the usual va lue for a . Subsequent research has shown that CY. can 
18 
ter than or less than 1.26, depending upon a vari ety of factor
s, inc ludi ng canopy 
be grea
densit y, vegetati on water stress and canopy averaged stom
ata! resista nce (Kustas and 
Norma n, 1999a; Jarvis and McNaughton, 1986; McNaughto
n and Spriggs, 1989). 
evapo-
In the Penman approach, complexi ti es in the actual turbule
nt processes of 
on and sensible heat fl ow are re-characterized as di screte en
ergy sources and 
transpi ra ti
sinks whi ch are linked together by a small number of tra nsp
ort pathways. The amount, 
ined by param-
type and di stribution of energy fl owing through these pathwa
ys is detenn
i ng the phys ica l process with 'e ffecti ve' res istances (S tewar
t, 1989) . 
eteriz
Because of its relati ve simplicity, Penman-Monte ith remains
, even today, to be a ba-
sis of ET model development. In general circulation models
 (GCM), which are chiefly 
teorol og ical and climatological problems, Penman-Monteith
 contin-
concerned with me
ues to be w idely applied for the land-atmosphere boundary, a
s for example in the Simple 
require nominal inputs, 
Biosphere Model (S iB2) (Sellers et al. , 1986). Penman mod
els 
ch as estimated net radi ation and surface meteorological cond
itions, and do not require 
su
surface temperature measurements. 
man approach has its limitations because it considers the 
land surface to 
The Pen
be spatially homogeneous, and so others have sought to eith
er refine the Penman-type 
 refine-
model or to discover better performing alternatives. Dolma
n (1993) show how
ments can be made to better represent at least three major lan
d cover types. Shuttleworth 
and Wallace ( 1985) partition surface components into soil a
nd vegetation, thereby ac-
commodating more spatial heterogeneity. 
There also exist of class of models, closely related to Pen
man-Monteith, that es-
l phases of sur-
timate ET as part of a physically-detailed, dynamical simu
lation of al
face water movement. This class is under active developme
nt and is known as a Soil-
Vegetation-Atmosphere Transfer (SVAT) scheme. For exam
ple, Liang et a l. (I 996) de-
19 
scribe a grid-based, va ri able- infiltration-capac ity model (VIC), and show how it can be 
applied over a wide range of sca les. Another example is the 'soil water energy and tran-
spiration ' model (S WEAT), which emphasizes a rigorous representation of the Richards ' 
so il water equation . Burke et al. (1997) show that ET may be estimated from model 
estimates of soil and vegetation water content, along with nominal meteorological mea-
surements. 
2.3.2 Temperature Based Methods 
As reso lution of the land surface becomes finer and finer, moving from global scale 
models to landscape models- where resolutions can be as good as a few meters- the 
Penman modeling approach presents difficulti es. Despite continued advocacy of the 
Penman approach at landscape sca les (Stewart, 1989), others argue that an important 
boundary condition- surface temperature- can no longer be assumed (Kustas and 
Norman, 1996a). 
With the practical development of thermal infrared remote sensing instrumentation 
(Price, 1980), research increasingly has focused on developing temperature-driven en-
ergy flux models . Recent studies (Norman et al., 2000; Kustas et al., 2000; Kustas and 
Norman, 1996a; Diak and Stewart, 1989; Carlson et al. , 1995; Anderson et al., 1997) 
have shown that it is possible to make ET estimates remotely using important factors 
such as surface temperature. Estimates of surface energy fluxes are feasible by combin-
ing control data, obtained either from the ground or aircraft, with spatially distributed 
remote sensing data. The control data are measurements of properties currently un-
obtainable remotely (e .g. wind speed, humidity, air temperature), which constrain the 
est imates of evaporative heat flux. The remote sensing data provide spatial components 
of surface temperature and vegetation cover. 
20 
An early temperature-driven application (Jackson et al. , 1977) is mainly based upon 
an empirical re lati onship between surface tem perature observations and estimated air 
temperatures. This 's implified ' method estimates ET from temperature measurements 
at two different times of day. Seguin and Jtier (1983) revised the approach to use one 
mid-day temperature observa tion . From thi s it is possible to estimate the integrated 
daily eva potranspiration , by e ither modeling the s inusoida l diurnal solar irradiance or by 
assuming the es timated evaporative fraction is constant for the day (Zhang and Lemeu r, 
1995). Seguin et al. ( 199 I) show a regional application of the surface-air temperature 
di fTerence approach. 
Si nce then, a variety of flux models have been developed with stronger physical 
basi , primarily by establi shing a functional relati onship between surface temperature 
and vegetative cover. 
In the ' tri angle method' , Gillies and Carlson ( 1995) show that reasonable estimates 
of surface so il moi sture, and of ET, can be derived from simultaneous observations of 
surface temperature and vegetative cover. The triangle method relies upon the conjecture 
that a full range of soil moisture conditions can be observed (i.e. field capacity to min-
imum extractable water) and associated with a full range of land cover (fully vegetated 
to bare soil). Based upon field results from a Kansas study (FIFE) (Sellers et aJ. , I 992b) 
and a southern Arizona experiment (MONSOON '90) (Kustas et al., 1991 ), Gillies et al. 
( 1997) claim an overall precision of 10-30% in soil moisture estimates. 
Bastiaansen et al. (1998) develop a 'one-layer' remote sensing model (SEBAL) that 
incorporates surface temperature and vegetation cover to produce ET estimates over 
landscapes. It is based upon physical principles. But in a manner similar to the triangle 
method, SEBAL relies upon logical, empirical observations relating surface albedo to 
surface moisture. 
21 
Foll ow-up studies show that each of these models can make reasonable ET esti-
mates. Yet under some common conditions, such as in heterogeneous landscapes, there 
is evidence that they either produce poor estimates of ET or they require physically im-
plausibl e adjustments to their parameterizations to produce good estimates. A common 
cause for some difficulties is the model characterization of the land surface into what has 
become known as the ' big leaf'. Here, the details of vegetation- leaves and branches-
are represented as one unit (K.ruijt et al. , 1997; Sellers et al., 1992a). Real vegetation, 
particularly if it is c lumped or if it forms an incomplete cover, is not well represented 
by a ' big leaf' . For example, in an Australian study over incomplete cover, Kai ma and 
Jupp ( 1990) show large discrepancies between modeled ET estimates and measured ET. 
2.3.3 Surface Energy Balance Modeling 
When using remotely sensed data, the surface energy balance at some given location can 
be represented , over any sca le (Brutsaert, 1982; McNaughton and Spriggs, 1989) by: 
H +LE = ~l - G (2.8) 
where H is energy flux due to temperature, or sensible heat, LE is latent energy flux 
from Eq. 2.3, R,1 is net radiation absorbed by the earth's surface, and G is heat flux 
into the soil. The sign convention used is for H, LE and G to be positive for flux away 
from the surface, and Rn to be positive for flux toward the surface. All components are 
usually in units W m- 2. Additional energy flux components that could also be included 
are photosynthesis (Stewart, 1989) and vegetation canopy storage (Shuttleworth and 
Wallace, 1985), but for short-term measurements, or for non-forested regions, these 
terms are neg ligible (Brutsaert, 1982; Stewart and Thom, 1973). The basic statement of 
Eq. 2.8 is that the sum of turbulent, conductive and radiative fluxes between the surface 
and the atmospheric boundary layer balances energy supplied to the surface. 
22 
Typica ll y, the sensible heat, latent and soil heat fl uxes, a long with net rad
iation, are 
est ima ted by an energy flu x model (Norman et a l. , 1995b; Kustas and No
rman, 1996a). 
del uses observati ons with physica lly-based relati onships, and mathema
tically 
The mo
represents rad iative, conductive and convecti ve energy transport mechani
sms. Radi ated 
energy is rece ived at the surface either as solar radiation- which inclu
des both visi-
 near infrared wavelengths- or as thermal radiati on from the atmosphere
 in the 
ble and
th erma l in frared wave lengths. The Rn term represents energy ava ilable from these tw
o 
sources aft er accounting for radiati on re fl ected and emitted from the surfa
ce. Conducted 
energy is tra nsported between the surface and underlying soil , G, and is essen
tia lly a 
Fouri er di ffusion law process controll ed by thermal gradients and soil cond
uctivity (Gar-
ratt, 1992). Convecti ve energy, represented by the H and LE terms, includes tur
bulent 
fluxes o f sensible and latent heat. Without questi on, turbulent convective
 processes are 
th e most intractable of all. Both stati sti cal and empirical relationships ar
e required, in 
e rough-
addition to bas ic observations of temperature, humidity, wind speeds and s
urfac
ness, to determine values of these energy flux components. Consequen
tly, accuracy 
in surface energy balance estimates is commonly limited by difficulties p
arameterizing 
turbul ent energy components. 
In remote sensing approaches, there is an additional limitation. The laten
t heat flux 
-
cannot be directly observed remotely, but must be inferred from physically r
ealistic mea
surements of cover type and temperature. As a consequence, latent heat 
flux estimates 
also contain accumulated errors from the remaining measured flux terms (
i .e. H , G and 
 1996b ). 
~). Fortunately, these errors do not overwhelm results (Kustas and Nor
man,
Estimated evapotranspiration from remote sensing based energy budgets
 have greater 
accuracy than do estimates derived from equivalent water mass measurem
ents (Eq.2.3). 
23 
2.4 Two-Source Model 
The two-source approach (Norman et al. , 1995b; Kustas and Nonnan , 1999a) is an en-
ergy balance model that addresses the landscape heterogene ity difficulties . It is based 
on a res istor network , si mil ar to the Penman-Monteith network. There are two surface 
energy sources : vegeta ti on canopy and bare so il. To see how resistor network models 
fun cti on, and the two-source mode l in particular, a few details are required. (The fol-
lowing section is based on French ct a l. (2000b ). A worked exa mple, ass imilating all of 
th e releva nt eq uati ons, is show n in Append ix F.) 
Two input variables derived from remote sensing instruments are key to all models 
based on Eq. 2 .8. The first is sur face temperature, which is used in the estimation of 
sens ibl e heat flux. The second is fracti onal vegetated cover, which controls partitioning 
of energy between surface vegetation (if there is any) and the underlying soil. This sec-
tion describes how these variables are incorporated into the two-source energy ba lance 
model by re-examining each of the ten11S in Eq . 2.8. The radiation term in Eq. 2.8 is 
discussed first, followed by the turbulent fluxes. 
2.4.1 General Expression for Net Radiation 
Net radiation, Rn, is the sum of the incoming and outgoing short and long wave radiation 
fluxes: 
R,l = (1 - a)Rsol + ERu - wT4 (2.9) 
where a is the surface albedo, R.~01 is the incoming solar radiation, E is the surface emis-
sivity, Rti is the incoming long wave radiation, CJ is the Stefan-Boltzmann constant 1 
and T is the surface temperature in Kelvin. In the two-source approach, a is estimated 
1a = 5.67051 x 10- sw m- 2 K- \ (Cohen and Taylor, 1999) 
24 
separately for vegetation and soi l using remote sensing vegetation indices, know
ledge 
from ground-leve l observations and theoreti ca l considerations, as described below
. R sot 
is taken from grou nd leve l measurement s. R,,,._ is es timated from an empirical relation, 
a lso described below. T and f are products from thermal infrared observations and are 
described in detail in the surface temperatures section. 
2.4.2 Albedo of Vegetation Canopy 
do (n) is the hemi spherica l reflectance of an object for the whole solar spectrum. J
t 
Albe
can be estimated by considering attenuation and reflectance of incoming radiation,
 from 
all direc ti ons, in the visible and near infrared bands separate ly. One way to estima
te the 
reflectance (and subsequently albedo) of vegetated surfaces is to determine reflec
tance 
from un-vegetated surfaces, and to apply an attenuation function to the incomin
g and 
2
outgoing radiation . A commonly used formulation is Beer's Law (Beer, 1853), 
which 
models attenuation according to exponential absorption without scattering. The d
iffer-
ential form is : 
clL>. = -k L;.(x ) 
cl.r, (2.10) 
where the change in radiance, L;., with depth x into the medium, is proportional (by 
factor k) to the incident radiance at that depth. Integration of Eq. 2.1 O results in Beer's 
Law: 
L >. = L - k x >. ,oe (2.11) 
where the ultimate radiance, L, after traversing a thickness of x, is related to the inci-
dent radiance, L;.,o times an exponential term. The k factor is known as an extinction
 
coefficient and measures the infinitesimal transparency of the medium. 
2The law appears under various guises in the literature, including Lambert Law (
Lambert, 1760) and 
Bouguer's Law (Bouguer, 1729). 
25 
A use ful meas ure that compares the unabsorbed radiance to the incident radiance is 
known as transmis iv ity, ,: 
= _L(.1_:ma_x)  = e - k x m.a x 
1 (2. 12) 
Lo 
Radiation re flected from the underlying surface traverses the attenuating medium twice-
first as incoming radiation , and second as outgoing radiation. So the resultant reflectance 
is , 2 X /JO., ,c/,,,,o.,,<f,., X l o, T is medi um transmissivity. /J011, ,1> 11,0s,c/,., is surface reflectivity 
(independent of th e attenuating med ium), and is a complex function of so lar illumination 
angles and viewing angles . 
A more realisti c estimate of reflectance accounts not o nly for direct light attenua-
ti on, but a lso for diffuse li ght attenuation. This is a multipl e scattering model, and is 
considerab ly more complex than the Beer exponential extinction model. If the scatter-
ing is isotropic, the Kubeika-Munk equations (Kubeika and Munk, 1931) can be used, 
where reflectivity from hori zontally oriented e lements in any part icular wavelength (>.) 
is related to medium absorpti vity a (Monteith and Unsworth, 1990): 
1 - ~ 
Ph.or,>.. = l + ~ (2.13) 
But reflectance is a lso dependent upon the orientation of the reflecting surface with 
respect to the sun and to the radiometer, and Eq. 2.13 only considers horizontal orienta-
tions. 
To model vegetated surfaces, which consist of many thousands of orientations of 
leaf and stem components, a statistical approach is needed . The usual approach is to 
select a spatia l probability distribution function that mimics real vegetation. Common 
nomenclature for these functions (De Wit, 1965) is descriptive, as shown in Table 2.2 . 
There a re severa l ex isting representations of leaf angle distributions within a canopy 
[ e .g. Ross ( J9 8 1) ]. The di stribution representations used in this study is based on 
26 
Tab le 2.2: Lea f angle probability distribution fun cti ons. 
Name Descripti on Exa mple 
Spheri ca l Projected to a sphere Trees 
Erectophile Mainl y verti ca l e lements Grass 
Planophile Mainly hori zonta l e lements Soybean 
Uni fo rm Evenly di stribut ed 
Plagiophile Dominantly inc lined e lements Wet vegetation 
Ex tremophile Either vertica l or hori zontal 
Goudriaa n ( I 988) , which allows three di stributions (Fig. 2 .3)- planophile, spherical 
and erec tophile - to be approximated by a simple fomrnla : 
D = sin /\ eP" (2 .14) 
D is the density of the leaf angle di stribution . Other representations of canopy distribu-
tions exi st (Ross, 1981). 
The term s in /\ is an isotropy factor in the spherical distribution, and eP" as the 
relative deviation from isotropy. A is the leaf angle from horizontal. p is the shape 
factor, where -3.7 is planophile, 0 is spherical, and 0.8 is erectophile. 
Goudriaan (1988) shows how the Kubeika-Munk equations can be adapted to ellip-
soidally (i .e . a generalized spherical distribution model) distributed leaves: 
(2.15) 
where Pc(' l/;) is the adjusted vegetation reflection coefficient, for direct or diffuse radi-
ation, at solar zenith angle, 'I/;. Phor,>. is derived from Eq. 2.13. Kbe,d is the vegetation 
extinction coefficient for either direct beam or diffuse radiation into a deep canopy, with 
leaf angle distribution function. 
27 
Lea f Ang l Dis lri bulion Fun c l ions 
0.030 
p = -3 . 7 
Dens ity = sin(/\) e(??> 
0.025 
0.020 
/ 
>, / 
~ 
/ 
(/) 
C 0.0 15 , (. .... ..... . Q) .. 
0 .--?/ 
/ 
/ 
0.0 10 
p = 0 .? ? 
/ 
0.005 / / 
,,. / 
,,. ,,. 
0.000 .?,,.. 
0 20 40 60 80 
Lea f Ang le, /\ (Degrees f rom hor izon ta l) 
Figure 2.3 : Leaf angle probability distribution functions, from Goudriaan (1988). A 
functional form describing in a statistical way the leaf angle distribution density of a 
canopy is useful for modeling surface reflectance and consequently net radiation at the 
surface. The distributions shown here are: planophile (solid), spherical (short dashes) 
and erectophile (long dashes), with respective shape factors (p) equal to -3.7, o, and 0.8 . 
28 
Campbell ( 1986) shows a fl ex ible way to spec ify I<1;,,: 
/:1:2+  Lan 2 'V; 
I:+ 1.77Ll (:1; + 1.182) - 0?7:!:J (2 . 16) ](bP('lj; ) = .'
Here the .7' para meter performs the shape functi on provid
ed earli er by JJ in Eq. 2. 14, 
r spheri ca l and x=0.5 for 
but va ry ing in an oppos it e sense (x=J for planophile, x= J f
o
erectophile). 
it as 
Di ff use radi ation ex tinction, J<,1 , can be determined from Eq. 2. J
6  by modeling 
oothly varying function 
the integra ti on o f beam radiation from a ll direc tions. J(d is 
a sm
of LA I. A typica l va lue is 0. 7 at an LAI of 3 (Campbell , 19
86). 
k equations are furth er developed by Monte ith and Uns
worth 
The Kubeika- Mun
to estimate surface reflectivity when th e vegetation is not t
hick. 
( 1990), who show how 
In thi s case, the contribution of soil to the overall refl ectanc
e becomes significant. Their 
bas ic formul a can be used for diffuse and for direct radi atio
n: 
(2 . 17) 
The factor ( is a scaled exponential term: 
( = ( Pc - Ps ) e - 2,/o l<be('I/J) LAI (2 .18) 
P,?Ps - 1 
Pc is canopy reflectivity in diffuse light, Ps is soil reflectivity,
 a is leaf absorptivity, and 
(be,d is the same extinction coefficient as described in Eq. 2
.15. LAI is leaf area index 
J
tio of projected leaf area in a canopy to the ground covered
), and is determined from 
(ra
a remotely sensed spectral vegetation index. 
Canopy albedo, ac, can now be determined from Eq. 2 .18 for direc
t and diffuse 
radiation in visible and near infrared wavelengths; four com
ponents in all. Typical ab-
hat could be used are listed in Table 2.3 (Campbell and N
orman, 199 ). 
sorptivities t 8
Absorptivities are dependent upon the wavelength of illumi
nating light. An approxima-
29 
Table 2.3 : Nominal so il and lea f absorptivities. 
Component n \I n N If? 
Dry so il 0.85 0.75 
Wet so il 0.25 0.20 
Green vegetation 0.85 0.15 
Table 2.4: Spectra l weight factors, lt ?, for direct(beam or be) and diffuse radiation . 
Radiation Visible Near Infrared 
Direct 0.8 0.2 
DifTuse 0.9 0. 1 
tion of this dependency is shown, where the spectra l characteristics are categorized 
by 
visible (V) and near infrared (N IR) li ght. Actual absorptivities also vary with moistu
re 
 
content. Canopy albedo is then a weighted average (Eq . 2. 19) of surface reflectiv
ity
components for direct and difTuse, V and NIR, light. Reasonable weight fac-(fJth inVJ) 
tors (Norman et al. , 1995b) are li sted in Table 2.4. Assuming that direct and diffuse lig
ht 
contribute equally to canopy albedo, the following relation holds: 
ac 0.5 x (l,Vv,be (}thin,V,be + W N I R,be Pt.hin,N I R,be + 
W V,d Pthi n , \f,d + Hf N l R,d Pthin,N l R,d) (2.19) 
where spectral weights for direct and diffuse radiation, lV, separately sum to 1.0 fo
r 
visible V and near-infrared, N l R. 
' ' 
2.4.3 Soil Albedo and Incident Radiation to the Soil 
Jn the two-source approach, surface energy fluxes are partitioned between vegetati
on 
canopy and the underlying soil. But even though the properties of vegetation and soil a
re 
30 
very different, both the incoming radiation and energy fluxes from the two components 
interact. For example, if the vegetation is not thick , s ignificant amounts of radiation 
are transmitted to the underlying soil , some of which is in turn reflected back into the 
canopy. Based upon the Kubeika-M unk equations, radiati on incident at the soi l can be 
estimated from (Monte ith and Unsworth, 1990; Goudriaan, 1977) : 
((rli-(1/;))2 - ] ) e - fo /(1,, ,,1(if, ) !, 
(2.20) 
where ( 7/;) can represent transmissivity of direct or diffuse radiat ion in the visible or 
7
near infrared wave lengths. Values for T are derived from Eq. 2 .20 by so lving it fo r 
the four combinations of direct and diffuse rad iation in the vis ible and near infrared 
wave lengths. 
So il a lbedo in the two-source model is treated very simply and ass umes no multiple 
scattering. It is determined as the average of so il reflectivities (() s = 1 - a) in the visible 
and near infrared wavelengths: 
a s = 0.5 X (fJs,\I + ()s ,N IR) (2 .2 1) 
Incident solar radi ation at the soil can be determined by using the same spectral 
weights for direct and diffusion radiation as for canopy albedo. Norman et al. ( 1995b) 
use a weighted average: 
Tv = 0.5 X (Wv ,be Tv,be + WNTR,be TNfn,he + 
(2.22) 
2.4.4 Long Wave Radiation 
In addition to the direct contribution from short wave solar radiation, there is energy 
contributed to, and lost from , the surface via long wave radiation. Long wave radiation 
is a lso known as terrestrial radiation. 
31 
Incident long wave (therma l radiation) is computed assuming multiple 
scattering is 
unimportant. Reverting to the Beer's exponentia l ex tinction law, (Eq . 2.
11 ) transmiss iv-
ity of long wave radiation, T7'f fl is: 
(2.23) 
where the nominal value of leaf absorpti vity for long wave infrared, kr, fl , is typ
ically 
set to 0.95 . LAI, is lea f area index (LA I), as previously indicated in Eq. 2.20
. 
The amount of long wave radiation created is eva luated from the Stefan
-Boltzmann 
relation ( e.g. Brutsaert ( .1 982)): 
R = w-T4 (2.24) 
where R is the radiant flux density, f is the surface emiss ivity, a is the Stefan-Bolt
zmann 
constant (prev iously described in Eq. 2.9), and T is temperature. 
 lost from the surface is determined by the so il and vegetation surface
 
The energy
temperatures and emiss iviti es, and is discussed in detail in the surface te
mperature sec-
rage 
tion of thi s rev iew. Surface temperatures typically range between 25-55 ?C
 . Ave
surface emiss iviti es would typically be ~ 0.97
3
. A nominal emi ssivity value for soil 
alone is 0.96, while vegetation canopy is on the order of 0.99. Applying Eq. 
2.24 shows 
that outgoing radiation commonly ranges ~350-650 W m -
2 . 
Energy is gained by the surface from downward propagating atmospheri
c radiation. 
Although the air has no actual 'surface' , it may be considered to have one
 which radiates 
ar-surface air temperatures. The emissivity of this 'surface ', in clear s
ky 
energy at ne
conditions4 (Brutsaert, 1982), can be estimated from a ratio of water vapor p
ressure, ea 
en all thermal wavelengths 
JTypical soil emissivities can range 0.75-0.99 over narrow bands, but wh
are considered, the surface emissivity is close to a blackbody. 
4Cloudy skies are not considered in this study. 
32 
in mbar, to air tempera ture, Tr, in Kelvin : 
fatm = .]  .2..J (Te,a )i  (2.25) 
(/, 
e, fo r air at 25?C, and relati ve humidity of 0.5, water vapor pres
sure is 
For exa mpl
~ 15 mbar. Thi s res ults in an atm ospheri c emissivity of 0. 8 1. Us ing Eq. 2.24, c lear-sky 
2
downwe lling radi ati on, l?u,, is ~3 60 W m- . 
2.4.5 Net Radiation to Canopy and Soil 
Now that the separate components ofradiation at the surface have 
been formul ated, they 
can all be brought together to determine the net radi ati on. A sche
matic showing visible 
nea r-infrared and thermal infrared radiation components is shown
 in Fig. 2.4. 
Net radi ati on to the vegetation canopy, neglecting multiple reflecti
ons, has four com-
ponents: 
J. Incoming sky long wave radiation (Sky to Node 2) 
2. Soil emitted long wave radiation (Node 4 to 2) 
n) 
3. Outgoing canopy long wave radiation (From Node 2 up and do
w
4. Incoming solar radiation (Sun to Node 1) 
Accounting for flux densities from the sun, sky and soil surface, a
long with soil and 
canopy reflectivities and transmissivities, the net radiation at the c
anopy is fonnulated : 
Rn, c = (1 - TTfn)(Rr!R,a + Rr!R,s - 2Rrm,c) + 
(1 - TvNTn)(l - ac)Rsol (2 .26) 
Net radiation at the soil surface, also neglecting multiple reflectio
ns, has these four 
radiation components : 
33 
_ Sun 
Canopy 
.3 4 
Soil 
figure 2.4: Net radiation at the surface. The surface is schematically shown with two 
components: vegetation canopy, as a rectangle, and soil, as the baseline. Radiation 
components are summed at the numbered nodes: I. Canopy VNIR, 2. Canopy TJR, 3_ 
Soil VNIR and 4. Soil TJR. 
34 
I. Incom ing sky long wave radi ati on (Sky lo Node 4) 
2. Incoming canopy long wave radiation (Node 2 to Node 4)
 
3. Outgo ing so il long wave radiati on (From node 4 up) 
4. Incoming so lar radi ation (Sun to Node 3) 
same manner as for Eq. 2.26, the net radiation at the so il is: In the 
TvN rn(J - as) Rsol (2.2 7) 
Total net radi ation at the surface is the sum of Eqs . 2.26 and 
2.27 : 
(2 .28) 
2.4.6 The Resistance Model for Turbulent Fluxes 
If the land surface is considered as aggregated soil and vegeta
tion, the sensible heat term 
H from Eq. ( 2.8) is given by: 
(2.29) 
e p is the air density, Cp is the specific heat at constant press
ure, Taero is the aero-
wher
dynamic temperature, T a is the near-surface air temperature 
(usually at a standard mea-
 
surement height), and r a is the aerodynamic resistance. Neithe
r Taero nor ra are simple
to determine. 
dynamic temperature is the temperature of the combined so
urces for con-
The aero
vective heat transfer (i .e. both soil and vegetation contribu
te) and can be determined 
from profiles of temperatures and wind speed within the at
mospheric boundary layer 
(Brutsaert, 1982). 
35 
Ti,PTo is frequentl y approx imated by T,-11d , the radiometric temperature seen by a ther-
mal infrared radiometer. T,-ad is al so known as a ' brightness temperature', whic h means 
that it is the temperature of an equivalent blackbody (Norman and Becker, 1995). But 
even though the surface brightness temperature is approximately the same as aerody-
namic temperature over non-vegetated surfaces, it is not the same over most natura lly 
vegetated surfaces . This has been demonstrated by Hall et al. ( I 992) working with data 
from the First ISLSCP Fie ld Experiment (FIFE). Furthermore, when a model using Eq. 
(2.29) is applied to sparse ly vegetated surfaces, there are significant e rrors in predicted 
heat fluxes (Verhoef et a l. , 1997). 
The aerodynamic resistance is a parameteriza tion representing the resistance to trans-
port of heat through the canopy airspace. Res istance is a complex functi on encapsulating 
the combined e ffects of surface roughness and the vertical profiles of wind speed, tem-
perature and humidity. The turbulence process at the surface is so complex (Garratt, 
1992; Stull, J 988), that it can only be assessed with stati stical measures. Schemes are 
continually being developed to help evaluate how aerodynamic resistance can be for-
mulated in a practical way. A major assumption of surface energy flux models is that 
there exists a surface boundary layer in which surface energy fluxes are constant with 
height and that a logarithmic wind speed profile exists. When this assumption holds, 
Monin-Obukhov similarity theory applies. The utility of Monin-Obukhov is that vertical 
profiles of sensible heat, latent heat, and momentum flux can be estimated under a wide 
range of unstable (i .e. turbulent) and stable conditions . The profiles of the flux quan-
tities can be represented in terms of 'universal' functions (Wilson, 1989; Stull, 1988; 
Brutsaert, 1982; Paulson, 1970; Garratt and Hicks, 1973), which in turn can be used as 
correction factors to determine aerodynamic resistance, r a (Norman et al. , 1995b) : 
ln ( 7( zr - do) _ \}i ) 
Z M II 
Ta = ku* (2.30) 
36 
where zr is the height of air tempera ture measurements, 11, * is the
 wind friction veloc-
 the windspeed 
ity, dis a displacement height (to adjust for canopy height e
ffects upon
in-Obukhov theory (Brut-
profile), w1 1 is a 'diabatic ' correction factor derived from Mon
uted (Paulson, 
saert, 1982) and k is von Karman 's constant. The tli II factor 
is comp
1970): 
(2 .3 1) 
rsal function for heat defined by (Bru tsaert, 1982; Paulson
, 1970; 
where </J is a unive
Dyer, 1974): 
(2.32) 
The ( term is a dimensionless variable relati ng observation h
eight, z , to Monin-Obukov 
stabi lity, L: 
z - do 
( =--
L (2 .33) 
L 5 1110 is approximately the height at which aerodynamic she
ar, or mechanical, energy, 
r density gradient). It is 
is equal to buoyancy energy (i.e. convection caused by an 
ai
determined from : 
LMo = -Pvap k (_jj_ O (2.34) 
vk.9 c T. + .
 6 1 [', E) 
p a A v 
where H is observed sensible heat flux, and LE is observed laten
t heat flux. The factor 
1 ratt 
'7' is derived from an interpretation by Norman et al. ( 1995b) of t
he kB - factor (Gar
and Hicks, 1973): 
(2.35) 
e kB- 1 is an experimental parameter relating roughness height for
 momentum 
where th ' 
ughness height for sensible heat, z 11 . In Eq. 2.30, ln kB-
1 ,..__, In 7 ,..__, 2_ z M, and ro
5Note the dependence of L MO upon H and LE flux, the terms 
being sought. Because of this, the 
va lue of L M O is detennined iteratively. 
37 
Ab ent deta il ed study, Z /lf and rlo can be approx imated from vegetation canopy height , 
h0 (Brutsaert, 1982): 
Z /lf = ho/8 (2.36) 
2 
d0 = 3ho (2.3 7) 
Friction ve loc ity, 11 *, is a measure o f shea r stress at the surface, and can be fo und from 
the logarithmic w ind pro fil e relationship (Dyer, 1974): 
* kn 
11, = (2. 38) In [ zu - rlo - \fl ] 
2 Af /If 
where 11 is the w ind speed and WA t is the diabatic correc tion for momentum . 
2.4.7 Resistance Network in the Two-Source Model 
An important limitation to the preceding formu lation of heat flux is that it implicitly 
aggregates the landscape into a single source with a sing le temperature. To illustra te the 
difficulty created with this assumption, consider the representation of temperature. In 
Eq. (2 .29) aerodynamic temperature is unmeasurable. It represents an effective temper-
ature required for a pa1iicular amount of heat transfer. The brightness temperature, on 
the other hand, is a radiometric observation and is affected by the spatial variability of 
temperature, surface orientations and viewing angle (Norman et al., 1995a). 
The two-source model addresses this limitation (Norman et al., 1995b) . It predicts 
heat flux by first partitioning net radiation, Rn, between soil and canopy elements, using 
an algorithm that computes net short wave and long wave balance for the canopy and 
soil. Using two sources of energy flux, rather than one, accommodates differing absorp-
tions of net radiation by vegetation and soil. Available energy for the sensible heat flux , 
H, and latent heat flux , LE , is determined by subtracting the heat lost into the ground: 
R..,.-G. 
38 
gorithm uses a macroscopic, resistance networ
k model in which 
The two-so urce al
s are conceptually inter-connected by energy
 flux res istors. 
energy sources and sink
These resistors represent the resistance of ener
gy flux between the soil surface, vege-
ere. As illus-
tation canopies (including stomata! effects) and
 the surrounding atmosph
ies of resistor networks for the two-source mod
el: 
trated in Fig. 2.5, there are two variet
 
a parallel configuration (left) and a series conf
iguration (right). The parallel network
the vegetation com-
determines energy fluxes for the soi l compone
nt separately from 
rmines energy fluxes for these components as ponent, whereas the series network dete
an interactive system. However, even in the pa
rallel configuration, there is interaction 
between so il and vegetation components. As dis
cussed in Kustas and Nomian (1999b), 
 radiation and the wind profile above the vegeta
tion 
this interaction is due to the way net
 
are computed. Consequently, it is unclear wheth
er one network model is to be preferred
. 
over the other. The parallel version of the two-s
ource model is used in this study
The algorithm for the parallel two-source mode
l depends upon modeling of atmo-
 earlier, the surface layer consists of 
spheric stabi lity within the surface layer. As no
ted
the lower-most atmosphere, within which it is 
assumed that the energy fluxes do not 
vary w(th height. Typically the surface layer is o
n the order of~ 1O  m thick . 
lt of the interaction between 
Surface layer stability or instability is primarily
 a resu
o vertical density differences caused by temper
ature and humidity 
air buoyancy- due t
differences- and mechanically created turbule
nce- due to wind blowing over an ir-
forces over mechanical forces can 
regular surface. The relative importance of buoy
ancy 
ngth parameter, LMo- LMo can range from lar
ge neg-
be assessed with the Obukhov le
ative values to large positive values, with negati
ve values indicating unstable conditions 
hen soil and plant 
(Stull, I 988). If the surface layer is unstable, a n
ormal condition w
e model estimates 
temperatures exceed the surrounding air tempe
rature, the two-sourc
39 
Two-So urce Netw ork Models 
Porol l I Se r i s 
ro ro 
ho 
do 
rs rs 
Zo 
Figure 2.5: Two-Source model configurations. The parallel network model is at left, and 
the series network is at right. In the parallel network there are two unique resistances: 
resistance from the soil, rs, and resistance from the canopy airspace to the overlying 
atmospheric surface layer, r a ? In the series version, an additional resistance element, 
r x , allows for direct interaction between the canopy fluxes and the soil fluxes. Canopy 
height is ho, roughness length is z0 , and displacement height is d0 . These components 
are used in Eq. 2.30. 
40 
the energy flu xes iterative ly (Fig. 2.6). If the surface layer 
is stable, the two-source 
layer is sta-
model es timates the flu xes direc tly. Determining whether or
 not the surface 
stic 
ble or unstable is critical fo r surface flux modeling because
 the stabili ty charac teri
de te,mines how effective ly surface hea t can be transported a
way from the surface. 
Surface layer stability can be indirectly assessed by measu
rements of surface and 
nea r-surface air temperature, humidity, wind speed and am
ount of vegetati on present. 
 promoting buoyancy 
During the day, soil and plants are hotter than the adjacent ai
r, thus
hanica l turbulence is 
and instability. If wind is present, and the surface is vegetate
d, mec
generated. The two-source model considers both of these cha
racteri stics when assessing 
for bare 
stability. In the less usual c ircumstance where the surface is 
not vegetated- as 
so il fi e lds- a separate routine is used. The two-source m
odel effectively becomes a 
e-source model, with surface roughness and stability charact
eristics determined from 
on
a simplified wind profil e. 
2.4.8 Solution Method 
e 
Considering the usual daytime case, where the surface ha
s some vegetation and th
atmosphere within the surface layer is unstable, the sensible 
and latent heat flux compo-
nents for the vegetation are computed: 
Rnc - H c - LEc = 0 (2.39) 
Rns - Hs - LEs - G = 0 (2.40) 
 the flux components are now distinguished by subscripts: t
he canopy, C and the 
where
s. q. 2.8, storage of heat within the canopy and energy for photosynthesis soil, As for E
are considered negligible for the instantaneous measurement
s. The total computed heat 
41 
Two Sources So il Resistance 
r - I 
Unstab le Conditions s - b+a x n., 
t 
Light Environment Soil Sensible Heat 
Albedo & Transmissivity H . = pc Ts-Tq 
-~
(  soi l & /J c r,a . +n 1o ?.,p  y) 
t t 
Wind Parameters Soil Latent Heat 
rn 11,* Do LEs = R,,,1,s 7 -l ,rn Gi l  a -win Hd s LMO   
t t 
Component Radiation Check for Condensation 
R,,, if R L,, E,i,r s  G <  0 then LE = Rn,.,R -G,,,-1  1 ,s ' - s 1-,'j 
t 1f He > R,,,i,c tth en He = R,ri ,c.  
Canopy Latent Heat 
LEc = _{c Sa u Rn.,c m Flux Components 6 ~ 7
t Ht = Hs + He 
Canopy Sensible Heat LEt = f s + Le 
He = R,i ,c - LEc Revise Stability Length 
t L - u?3 MO r ev = --,,--
Soil Temperature ' kg ...!
-!.-.L'"+- '"-------0.61 /, Et 
? c pTa .>i, 11 
T _ 1~-nr fTc 
s - 1- f t 
t Compare Stability Lengths 
Canopy Temperature 
= + if LT M, O ,rev ~ Ltv10T  t, hen Done !fe rn 
can pep a else Iterate 
Figure 2.6: Two-Source algorithm, unstable conditions. The resistances to surface en-
ergy fluxes are strongly affected by atmospheric stability. Resistance is adjusted based 
upon Monin-Obukhov stability length, L MO, but this length is in turn dependent upon 
surface fluxes . By iteration, L and resistances r a and rs are determined. From these ' 
sensible heat H and latent heat, LE, are determined . 
' ' 
42 
flux components arc then: 
(2.4 I) 
LEr = LEc + LEs (2.42) 
where the subscript T indicates total heat flux . 
tent 
The canopy heat fluxes , Eq.(2.39), are solved by f
irst estimating the canopy la
hea t flux from the Priestley and Taylor ( 1972) relat
ion: 
LEc = O:!Yf?./cR,1c [ 'Y : .6 ] (2.43) 
aylor 
where LEc is the latent heat flux from the vegetation
 canopy, a is the Priestley-T
m Eq. 2.7 (typically 1.26 from empirica l results),
 f c is the fraction of 
coefficient fro
Eq. 2.75), Rnc is the net radiation absorbed by green vegetati on (di scussed shortly, 
the canopy (Eq . 2.26), 'Y is the thermodynamic ps
ychrometric constant 6 and .6 is the 
at Eq. (2.43) provides 
slope of the tempera ture-saturation vapor pressure c
urve. Note th
an initi al ca lculation of the canopy fluxes, and can 
be overridden if vegetation is under 
stress (Norman et al. , 1995b). 
x-
One indicator of stressed vegetation occurs when 
the computed value for H c e
ceeds ~i,C? Allowing this condition would force t
he energy balance equation to com-
for LEc, indicative of condensation on the canopy. Si
nce this is an 
pute negative values 
he normal evaluation procedure is overridden by setting
 LEc to 
unrealistic condition, t
0 and the remaining flux components are balanced. 
LEs becomes negative, indicative of condensation Another indicator occurs when 
is lso an unrealistic condition, LEs  is recomputed by 
assuming 
on the soil. Since this a
that the Bowen ratio (Hsi LEs ) is correct. 
= ?, is spec ific heat, P is pressure and Av is latent heat of vaporization. 'Y is nearly 6'Y where Cp 
" 
But since latent heat of vaporization, Av, has some temp
erature dependence, 
constant,~ 67Pa _ J( - 1. 
0 1 ell and Noonan, 1998) 
it is not strictly constant. The dependence is about 0
.01 %- c- (Campb
43 
From the energy balance requirement, canop
y sensible heat flux, H c, is determined 
as the res idual: 
He = R n,C - L Ec (2.44) 
es, Eq.(2.40), on the other hand, are solved 
by computing the sen-
The so il heat flux
sible hea t flux first: 
(2.45) 
ransfer be-
where the new terms are: Ts for soil temperature, T
all for resistance to heat t
een the vegetation and the overlying air, and
 rs , for the additional resistance to heat 
tw
 
transfer from the soil surface boundary layer
 as described by Norman et al. ( J9 95b) . In
to solve Eq .2.45, additional computations ar
e needed to determine soil tempera-
order 
Ts , and the resistance terms, Taff and rs, but as w
ill become apparent, they must 
ture, 
be solved iteratively. 
ed ra-
Soil temperature is determined from two eq
uations: one to relate the observ
iometric temperature to the soil and vegeta
tion canopy temperature, and another to 
d
d to 
determine the vegetation canopy temperatur
e. The composite temperature is relate
soil and canopy temperatures by: 
I 
4 
Tn ~ [foT<5 + (I - foTJ] (2.46) 
nd Jo is the fractional vegetative cover as seen where TR is the radiometric temperature a
erature is estimated from canopy sensible h
eat, 
by the radiometer
7
. The canopy temp
He, and an inverted form of the resistance equatio
n: 
(2.47) 
q . 2.24). It is an approximation be-
7The exponent of 4 reflects the Stefan-Bolt
zmann relation (E
 blackbody spectral 
cause superposition of two temperatures resu
lts in two superimposed, rather than one,
distributions. 
44 
ce components are determined fro m Eq. 2.30, for r", and the fo llow
ing 
The resis tan
equation (Sa uer ct al. , 1995) for rs-: 
1 
rs=----+ (2 .48) <Lrs brJJ.c; 
Us is wind speed above the soil where soil surface roughness is minim
al (Norman 
where 
a,. .~ d hrs are empiri cally determined constants. Us is more diffic
ult 
ct a l. , 1995 b) , and an
to know than wind speeds just above the vegetation canopy 
because the wind no longer 
ys loga rithmica lly. Using empirica l relations from Campbel
l and Norman (1998): 
deca
Us = U1,, ex p [a sc ( Ti - 1)] (2.49) 
where U1, is the wind speed at the top of the vegetation canopy,
 asc is an attenuation 
h is 
coeffic ient , z is the height above the soil of the desired wind 
speed estimate and 
 
height of the vegetation canopy. U1i is not the same as the measure
d wind speed, but can
 
be computed from the logarithmic wind profile re lationship
 and friction velocity from
Eq. 2.38: 
(2.50) 
Results from Goudriaan ( 1977), show one way to compute a8c: 
(2.51) 
995b) approximate asc 
where lm is the mean distance between leaves. Norman et a
l. (1
by: 2 I 
LAJ:i /i":i 
a sc = 0.28 2 (2.52) 
s?i 
where s is leaf width . 
Returning to Eq. 2.48, wind speed studies of Kondo and Ishid
a (1997) can be used in 
re gradient 
the two-source flux model, where the ars term is a function of
 the temperatu
45 
between the vegetation canopy and the soi l: 
(2 .53) 
Another empirical term, rrs, is introduced
. Crs ranges between 0.0011 to 
1 1 3 ica lly smooth and rough surfaces, respectively 
(Kus-
0.0038 in s- K - 1 , for aerodynam
tas and Norman, 1999a). The b,.8 term is set to 0.0
012 (Sauer et al., 1995). 
ponents, the downgoing soi l heat 
To complete the so lution of the soi l heat flux c
om
il surface (Choudhury 
flux G can be computed as a fraction of net radiati
on at the so
ct al. , 1987): 
G = ccRn,s (2.54) 
he net radiation 
where re is a fractional facto r, here estimated to b
e 0.3, and Rn,s is t
flux components (Eq. 2.40) 
at the soil surface. Applying energy balance f
or the soil 
resolves the soil latent heat flux : 
LEs = R,n,S - Hs - G (2.55) 
iewing the computational detai ls for solving the
 surface energy balance, one can 
Rev
see that there are ten primary unknowns and ten
 associated equations (Table 2.5) 
reached directly because of the 
However, the solution for surface fluxes canno
t be 
ctions, near surface wind speeds, 
interdependence between atmospheric stability
 corre
and surface resistances (Eq. 2.30). In this equatio
n, the stability correction factors 
y flux components H and 
\JIM and \JI H (Brutsaert, 1982) depend upon the s
urface energ
LE, via the Monin-ObukJ1ov roughness length L (E
q. 2.34). These are the same terms 
ately being sought, so an iterative solution is ne
eded. 
ultim
un by setting L to a large, negative value, indi-The chosen iterative process is beg
 of stability 
cating highly unstable atmospheric cond itions
. This permits an initial set
46 
Table 2.5: TSEB unknowns and associated formulae. 
Unknown Formula 
H.s () 1Jap C T,, - Ta ' P ra r., 
He R~, ,c - LEc 
LEs R~,,s  - G- Hs 
LEc O'.pT f 6~-y 
G ccRn.,s 
Rn,s F(Rsol, Ta, f) 
Rn,c F (R .rnl, Tc,, ./) 
I 
T.s (JTc4 + (1 - j)Ts4) 4 
Tc _!!_i;_ + Ta PvapCp 
f F(NDVI) 
47 
correc tion fac tors, \Ji M and ir,,, , to be computed. The reasonabl
e, and tentative, assump-
near surface air 
tion is then made that the canopy temperature, Tr, , is the same a
s the 
the sensible heat 
temperature, Ta. Using the composite temperature formula , Eq.
 2.46, 
components for both vegetation and soil can be solved direc
tly. Forcing energy balance 
 can 
then reso lves the latent hea t flux components. The roughn
ess length estimate, L,
then be revised and the process repeated until L converges. 
2.5 Turbulent Flux Measurements 
The surface energy flux can be directly measured on the g
round with widely-accepted 
technique known as eddy-covariance. Eddy-covariance is 
a technique that makes fre-
ments of vertical wind speed, water vapor, and air temperat
ure. 
quent (,.__, IO Hz) measure
If the mean of these values are removed (a typical smooth
ing interval is 30 minutes), 
ain. It can be shown (Brutsaert, 1982; Campbell and Nor-only transient variations rem
man, 1998; Monteith and Unsworth, 1990; Stull, 1988) that th
e average co-variances 
can be directly related to sensible and latent heat fluxes. 
Latent heat flux is : 
(2 .56) 
 
where latent heat flux , LE, is a function of air density, Pvap, laten
t heat of vaporizations,
>-vap (~ 2.48k.1/g), and w'q', the average covariance of vertical 
wind transients and 
specific humidity transients. 
Using a similar averaging process, sensible heat is: 
H = PvapCpd ( w'T~ + 0.84Ta w'q') (2.57) 
1- o.oo T , 
B> -vnp has a small dependence on temperature . lt is more clos
ely approximated by: 2.50 237
wi th temperature Tin ?C. 
48 
where sensible heat, H , is primarily determined from the averag
e covariance of vertical 
9 is 
wind transients, w', and ai r temperature transients, T' . p is air den
sity and Cpd, 10 
the specific heat of dry air. The additiona l parenthetical term i
ncludes specific humid-
 transients, q' , and is an approx imately 10% correction for using a
 dry specific heat 
ity
constant (Stull , 1988). 
ossible to use the eddy covariance technique on aircraft. These 
flux mea-
It is al so p
surements arc very different in character from the fixed-station m
easurements taken at 2 
m above the surface. The different character has severa l causes: 
? Aircraft measurements are both spatiall y and temporally varia
ble. 
? Aircraft sampling time is dictated by aircraft speed, sample
 rate and length of 
profile. 
? Turbulence charac teristics at 30 m are significantly different f
rom 2 111 heights. 
But if these differences can be reconciled, the aircraft data pote
ntially provides valida-
e sensing surface flux estimates, independent of ground measure
ments. 
tion of remot
To help validate the two-source model results at El Reno, techn
iques are needed to 
e possi-
relate aircraft time-space profile flux data to imagery-based flux
 estimates. On
ble technique, di scussed by Mahrt et al. (2001 ), uses a physica
l-statistical approach to 
ce the series of aircraft profiles to spatially meaningful fluxes . 
What these spatial 
redu
estimates actually represent, however, is uncertain. In light win
ds, where advection is 
ing derived fluxes. 
minimal, the estimates may be directly comparable to remote 
sens
Alternatively, with significant near-surface winds, advection is n
o longer negligible and 
additional techniques are probably needed before comparisons c
an be made. 
9Dry air density is 1.292 ?f{r . 
10Spcc ifi c heat of dry air at constant pressure is I 005 A:g~J<. 
49 
chniques are known as 'footprint ' methods, because th
ey consider flux mea-
Such te
rface 
surements to represent an i11tegration of advec ted, upw
ind flux es from a defined su
There appear to be two main classes of foo tprint ana
lyses: advection-diffusion 
area . 
models and Langrangian-stochastic models. The La
grangian-stochastic models trace 
rce area (Lec lerc and Thurtell, 
idealized particles in space and time to identify the so
u
1990; Sawford, 1985) . They are not pursued here. 
The advection-diffusion models 
r numerica ll y (e .g. Schuepp et al. (1990); Kormann an
d 
can be developed analytica lly o
Meixner (200 I); Schmid ( I 994)). Beca use of its relat
ive simplicity, the Schuepp et al. 
is to compute a vertica l wind profile, 
( 1990) method is pursued here. The bas ic approac h 
based upon the surface roughness, and then to apply a 
concentration formula derived by 
esult is a one-dimensional weighting function that ca
n be applied 
Gash ( 1986). The r
ages, as shown in Fig. 2. 7. The underlying theory is to the spatially di stributed flux im
compl ex, but fortunately the implementation is not too
 difficult. 
First , loca l meteorological conditions are required: air
 temperature, 7~,, wind speed, 
u, and moist air density, p. Also required are estimat
es of surface roughness height, 
ights related to the local topography, ac-
z0 , and di splacement height, do. These are he
can be 
counting for soil roughness, height, density and distri
bution of vegetation, and 
approximated from Eqs. 2.36 and 2.37. 
), then com-
The Schuepp et al. ( 1990) approach, with modification
 by Kustas (200 I
he average wind speed, U, between the displacement h
eight, d , and the observa-
putes t 0
tion height, z : 
(2 .58) 
tion velocity, 11,*, is a measure of air shear stress at th
e surface (Dyer, J 974; Brut-
Fric
ertical 
saert, 1982). It can be determined from measurement o
f the covariance between v
50 
0.0.3 
_, 
C 
CJl 
- QJ 0.02 
,,.-.. 2 :s: 
E 
.....x...,. ,, - - ---I 
CJl 
C 
. I- / -~ - '- QJ _c,  0:: 
'-
0 u 
z 0 0. 00 IL-- - '----__J 
0 2 0 2 
Fa st in g (km) Upw ind (km) 
Figure 2.7 : Flux footprint scheme. Eddy-covariance flux measurements represent an 
integration of upwind contributions. The Schuepp et al. ( 1990) approach is applied to 
the El Reno imagery by summing weighted values of upwind pixels. On the left, the flux 
measurement position is at the arrow head. Flux values directly under the path indicated 
are selected. The relative weights change with distance upwind from the measurement. 
Truncation of the weighting function is necessary because of limited image area. 
51 
and horizontal wind speeds ( - w' 111 ) . Alternative ly, it can be determined from Eq. 2.58 
itself, by using an actual measured wind speed (i.e., V would become u*, the measured 
wind speed wo uld replace n* on the ri ght-hand side, and z would be set to the height of 
wi nd speed measurement). k is a dimensionless va lue 11 known as von Karman's con-
stant (usually = 0.4) . z is the flu x observation height. \Ji m is an empirica l aerodynamic 
momentum stability correction functio n, and is based on similarit y theory (Brutsaert , 
1982). The determination of \V 111 will now be described. 
From the dimensionless vari able, ( (Eq . 2.33), the ' universa l function ' for momen-
tum, rf>m (Brutsaert, 1982; Paul son, 1970; Dyer, 1974), can be found. <Pm is universal in 
the sense that it establ ishes a flu x-profile relationship under all stabi lity conditions. 
I 
?111 = (1 - 16() 4 (2.59) 
Then, the stability correcti on fac tor, \V m, can be determined from the following re-
lationship (Paulson, 1970): 
Wm= 2 1n 1 + <Pm ) + In ( 1 + ?~ 1 ) ( - 2arctan(?m) + 
1r 
2 (2 .60) 2 2 
Knowing Wm, the average wind speed can at last be determined from Eq. 2.58 . Then 
the relative, one-dimensional flux 'footprint' can be determined from: 
(2.61) 
where :F( z, x ) represents the relative contribution of a surface flux at a distance x from 
the observation at height z . The distance to the maximum weighted contribution is : 
V z- do 
X - -* --k -. max - (2.62) 
U 2 vk 
11 Brutsaert ( 1982) notes that k vA? is included fo r traditional reasons, thus suggesting that it is unneces-
sary. 
52 
2.6 Surface Temperature Estimation 
The es timation of oi l and vegeta tion temperatur
es, when combined with observations 
of surface layer thermal gradients. 
of near surface ai r temperatures, allow computati
on 
. The magnitude of surface 
These gradients arc the driving force of sensible h
eat fluxes
temperature also ha ? a profound effect upon longw
ave energy radiation into space. Both 
turbulent and radiative processes are intimately re
lated to the total available energy and 
o ET fluxes. Accurate surface temperatures, prefe
ra bly within I ?C, are essential to the 
t
ing accurate temperatures requires an attempt to surface energy balance method. Obtain
understand the underlying physical radiation proc
esses. Temperature measurements of 
a trivi al task. For example, there 
real-world objects, over a range of resolutions, is
 not 
lumina-
are large variabi lities due to land cover type and sh
ape, solar heating, shading, il
tion and viewing angles (Norman and Becker, 19
95). Nevertheless, current technology 
 surface temperature estimates accurate within I
 0 c 
is adequate to potentially produce
by compensation for three factors: the confoundi
ng effects of the atmosphere, surface 
d limitations. After discussing each 
emissivity properties and instrumental designs an
en be 
of these in tum, techniques to convert observed r
adiances to temperatures will th
reviewed. 
2.6.1 Physical Basis of Radiometric Temperature M
easurement 
lationship to its kinetic temper-
All matter emits electromagnetic radiation in a di
rect re
 1974; Gillespie et al., 1996; Jentoft-
ature. The Planck formula (Eisberg and Resnick,
Nilsen and Alley, J9 96) shows the relationship b
etween temperature T, wavelength ,\, 
and emitted radiance L>. : 
(2.63) 
53 
The va lues ( ' i and (?2 ( ohen and Taylor, 1999) are Planck radia ti on constants 
12 and 
f i the body's emi ss ivi ty, a measure of rad iati ve ' effic iency'. The formula indicates, 
roughly speaking, that emi tted radiance is directly related to body temperature: radiance 
increases as the body temperature increases, but in a non-linear way. For temperatures 
commonly encoun tered in hydrology, 30-60?C , peak spectral radiances range between 
10- 15 wm - 2 ster- 1 ,,m- 1and fall within the wavelength range 6- 13 11.m, as shown by 
the posi tions of the vertica l line segments in Fig. 2.8A . Note that so lar radiation (Fig. 
2.88 ), desp ite its much greater irradiance than seen from thermal radiation, is negligible 
in the 6-13 11m band. 
Surface temperatures are determined radiomctrically from observations wi thin the 
infrared band , which for a ll practi ca l purposes extend from ~ 3-1411111. The most useful 
portion within these wavelengths lies between 8- 12.5 Jt.m. The reasons lie primarily with 
two factors: first, that the peak radiation for common surface temperatures occurs here, 
and second, that the atmosphere is relatively transpare nt within this interval (Fig .2.8C). 
This is known as the thermal infrared atmospheric window. 
2.6.2 Atmospheric Effects 
The radiance received at a remote sensing detector is different from that emitted at the 
earth's surface. Most of this difference is due to simultaneous atmospheric effects: 
? Absorption and scattering of terrestrial thermal infrared radiation 
? Propagation of atmospheric therma l radiation 
The primary atmospheric constituent responsib le is water vapor, a greenhouse gas. 
123.74 I 7749x 10- 16 \.-V m 2 and 0.0 1438769 m I<, respectively 
54 
Blackbody Radiat io n 
20 
Q) 
u 
C 
0 15 
"Cl 
0 
O:'. 10 - ! I 
~ ! I 
u 
Q) 5 I I : mW m 
7 sler-? ?m 
Q_ 
V) 
0 -
2 4 6 8 10 12 14 16 
Wavelength (?m) 
So lar lrradia nce 
0. 12 (B) 
0 . 10 
Q) 
u 
C 0.08 
0 
"Cl 0.06 
2 
'- 0 .04 
0.02 
0.00 
2 4 6 8 10 12 14 16 
Waveleng th (? m) 
At mosph er ic Transmiss iv ity 
1.0 
'"' 
'"' (C) 
.--? 0.8 
.?: 
V) 
V) 0 .6 
E 
V) 0. 4 
C 
2 
f- 0.2 
0 .0 
6 
2 4 8 10 
12 14 16 
Wavele ngth (?m ) 
Figure 2.8: Radiation at the surface. Thermal infrared rad iation (A), solar radiation (B), 
and atmospheric transmissivity (C). 
55 
ting for these effects is partl y a question of knowin
g the d istribution and 
Compensa
water vapor 
temperature of atmospheri c water vapor. Because
 nea rly a ll atmospheric 
~ 5 km (S tull , 1988), observati ons at 5km or highe
r are above virtually 
is fo und below 
nsation also considers the spectra l charac teristics a ll atmospheri c water vapor. Compe
of water vapor attenuation. As can be seen in the
 third plot o f F ig. 2.8, water vapor 
 between ~ 8-
effecti ve ly blocks all outgo ing thermal radi ation in
 the 6-711,m band . But
ar sky transmissivity typically ranges from 0.6 to 0.
8. Ozone, another strong 
12.5/tm, cle
thermal infrared absorber, affects the 9.5-lOJLm ban
d. 
 thermal 
There are four techniques in general use to remove a
tmospheric effects in the
infrared bands: 
I. Direct correction of sing le-band measurements. 
2. Split-window correction for two- and three-band
 measurements. 
3. Multi-angle correction for sing le or multi-band m
easurements. 
4. Temperature-emissivity separation correction fo
r multi-band measurements. 
rvational equipment. The bulk 
The choice of technique is in part determined by th
e obse
d capabilities and 
of satellite and aircraft remote sensors have limit
ed thermal infrare
uncertain calibration. 
2.9. 
The thermal infrared spectra of some better-known
 satellites are shown in Fig. 
 to bottom are shown the sensors AVHRR-14, GOE
S-9, METEOSAT-7, GMS-
From top
, and INSAT 1 B. A VHRR14 is one of several p
olar-orbiting satellites operated by 
5
ly used satellite in hydrolog-
NOAA, has I km resolution, and is one of the most frequ
ent
 resolu-
ical and meteorological research. GOES satellites
 are geostationary, with 4km
AT are European operated geostationary satellites,
 with 5km resolution. 
tion . METEOS
atellites 
GMS is a Japanese geostationary satellite with 5k
m resolution. The INSAT s
56 
nary and have 8km resolution . It is readily apparent 
that few contain more 
are geostatio
in the 8- 1o ,.m 
than two detectors in the thermal bands and none 
of them measure with 1
e chosen is also determined by how much is known
 of the prevailing 
band. The techniqu
atmospheric conditions. In most instances, the atm
osphere is known only at mesoscale 
 correction can on ly be roughly 
(I O's to I 000's km), and in these cases the atmosph
eric
approximated. 
diance 
Because of the non-linear relati onship between te
mperature and spectral ra
2.63), the atmospheric correction is frequently app
li ed in the radiance domain, as 
(Eq.
fo ll ows: 
(2.64) 
ture is represented by L>.,.rnr Jnce , surface emitted ra
diance. 
The desired surface tempera
The measured tempera ture is represented by L>. ,s
ensor , radiance at the detector. At-
ted radiance L, . 
mospheric em iss ion has two components: directl
y propaga
, A 11tp1oe 11zn_q, 
and surface-reflected, downward propagated radia
nce, L>.,rtownwelling? Eq. 2.64 shows 
the downwelling radiance, are attenuated by at-that both L sur f ace and L>. ,d awnwelling, 
rface 
mospheric transmissivity, r, between the surface and 
the detector. The role of su
emissivity, E>., is discussed below. 
Direct correction of single band infrared measurem
ents is done by estimating band-
h radiative transfer 
averaged atmospheric radiances and transmissiviti
es, either throug
els such as MODTRAN (Berk et al., 1998), throu
gh mesoscale models (NOAA, 
mod
200 I), standard atmosphere models, or possibly throug
h local soundings (radiosondes, 
ghly susceptible to uncertainty 
aircraft profiling, 1idar). Single band measurements
 are hi
or cal-
in the atmospheric correction, surface emissivity, an
d to the reliability of the sens
urtado et al., I 996). Landsat TM5 (United States G
eological Survey, 200 I) 
ibration (H
.5/tm with 
thermal infrared data, for example, is from a sing
le band spanning 10.0- 12
57 
AVHRR- 14 
J: :1.____ _ _j y~-1~ j 
8 10 12 14 6 
Wavel ength (?m) 
GOES-9 
J: :L--[1-J..-L f_  _[__1,__f_ J~ j 
8 10 12 14 6 
Wavelength (?m) 
METEOSAT - 7 
-- - - ---------;:::::;
;;r---.;;;;;;:~-------~ 
., 1.0 r
1/) 
C 
g_ 0.5 
.1,/)  _ J 
----.,__
__ _ _ _
_~ ~ --
a:: 0 .0 
_
L__ __.. _ 
____
8 10 12 14 6 
Wavelength (?m) 
GMS- 5 
J /.1..-f, ______ __f__X__ ___:,._S__,._ j ::'---....L
10 12 14 
6 8 
Wavelength (?m) 
INSAT 18 
j 
10 12  14 6 8
Wave length (?m) 
resolution satellites. 
Figure 2.9: Thermal infrared response funct
ions for low-
58 
(Markham and Barker, 1986) and from 198
9 (Wukelic et al 
rations from 1986 ., calib
imes within 1-2 ?c 
1989) sti ll being used . Resulting tempera tu
re estimates are somet
' 
?C (Wukeli c et al., 1989; Goetz et al., 1995
; Kalluri 
but on other occasions err by 3- l 2
and Dubayah, 1995). 
1967; Anding and Kauth, 1970? McMillin 19
75? 
Split-window correcti on (Sa unders, ' ' ' 
h-
Vida l, 199 1) is a popular empi ri ca l technique
 that can remove atmospheric effects wit
 therefore wi th out 
out any direct knowledge of the atmospheric wa
ter vapor profi le, and
seful for radiometers with two bands, the sp
lit-window algo-
app li cation of Eq. 2.64. U
cMillin, 1975) 
rithm is a linear combination of the two measur
ements. One version (M
is the simple form : 
(2 .65) 
face temperature, T.mr face is a linear function o
f apparent temperatures 
where the sur
ficients, Ai are empirica lly de-
in two thermal infrared bands, TRI and TR2. T
he coef
 formula-
rived (Czajkowski et a l. , 1998). Aside from th
e limitation of an empirical
tly representative of a physical process- th
e 
namely that the coefficients are not direc
split-window approach does not work well o
ver land surfaces. This is caused by emis-
mputations in Eqs. 2.63 and 2.64. Over 
sivity variations, which affect temperature co
oceans and large water bodies, emissivity un
certainty is not an issue. Here, the surface 
ace temperatures are probably reliable with
in a few 
emissivity is nearly 1.0, and surf
, the emissivity varies widely, and surface degrees (McClain et al., 1985). Over land
temperature errors are potentially much gre
ater. Nevertheless, Becker and Li ( 1990), 
ircum-
Price (1984) and Cooper and Asrar (1989) s
how that it is possible under some c
temperatures to within 3 ?C . But the limitat
ions of the 
stances to retrieve land surface 
 will al-
two-band split-window approach are unavo
idable and emissivity uncertainties
ways be troublesome. 
59 
ethod is another differencing approach to atmosphe
ric correction 
The multi -angle m , 
ctrally-based. Whereas the split-window method pr
ovides correction based 
but is not spe
upon differences between measurements at multip
l e wavelengths, the multi -angle cor-
 to provide the 
rection method relies upon effective atmospheric p
ath length differences
l. , 1999; Singh, J 984; Malkevich and Gorodetsky, 
J 988; 
required adjustment (Jacob et a
Becker, 1982). Atmospheric attenuation varies ro
ugh ly in proportion to the secant of 
ltipl e perspectives provides 
the view ang le. Viewing a g iven surface location 
from mu
oratory calibrated, way of correcting measuremen
ts. 
a phys ica lly-based, rather than lab
However, unless th e multi-angle method is used wi
th multi -band sensors, the emissivity 
 than other 
unce11ainty remains a difficulty. The acq uisition p
rocedure is more difficult
SR sensor on-boa rd the European ERS- 1 is a platfo
rm designed for 
approaches. The A T
multi-angle corrections (A TSR Project, 200 l ). 
e of atmospheric correcti on is a multi -band approach
, known as temperature-
A final typ
emissivity separation . Although it may appear to 
be simply an extension of the split-
trally located to sample a ma-
window method, it is much more. Multi-bands are
 spec
y of the thermal infrared window, including those 
wavelengths (8-1 0 ?m) that are 
jorit
avo ided by the split-window sensors due strong em
issivity variations in surface materi-
he preceding methods because 
als. The multi-band approach is also different from all 
t
eric effects is accomplished simultaneously with th
e accounting 
the removal of atmosph
.64: 
of emissivity effects. The logic of this approach is 
seen by re-arranging Eq. 2
L.>. ,sensor - L.>.,npwellin.9 (l )L 
= T_>. - - f._>. .>.,downwelling (2.66) L.>. ,.rnrface 
e that effect of downwelling radiance cannot be re
moved unless 
In this form one can se
the surface emissivity is known. Frequently, as ov
er thickly vegetated areas and water 
an be ig-
bodies, the surface emissivity is nearly 1.0 and the
 downwelling component c
etation (as in 
nored. However, in regions that have sparse or irre
gularly di stributed veg
60 
face emissivities can be less than 0.9, and the 
downwelling component 
this study), sur
ch requires estimates 
cannot be ignored. The temperature-emissivity
 separation approa
rrection method. 
of atmospheric properties, obtained in the sam
e way as the direct co
Unlike that method, however, the estimates are
 constrained by multi-spectral observa-
ethod. 1f images of a surface with known emis
sivities 
ti ons akin to the split-window m
ospheric radiation and transmissivity properties
 
can be made (e.g. water bodies), the atm
can be adjusted to minimize correction errors (S
chmugge and Schmidt, 1998). Through 
ce emissivities for an entire 
a subsequent iterative process (described below
), the surfa
age is es timated and revised surface rad iances a
nd temperatures determined. 
im
2.6.3 Surface Emissivity 
t reflector), 
Emissivity is a measure of rad iation 'efficiency '
 and ranges from 0.0 (perfec
to 1.0 (perfect emitter, or blackbody): 
L>. 
f=-- (2.67) 
. L>. ,nn 
, and L>. ,nD is the spectral ra-
where L>. is the observed spectral radiance from
 a surface
erature as L>.. If transmission through 
diance from a blackbody surface at the same tem
p
k, 
the medium (transparency) can be neglected, 
Kirchoff's law (Eisberg and Resnic
1
1974) gives a very simple relationship between 
emissivity and reflectivity (p) 3: 
f. = 1 - p (2.68) 
rty, 
Emissivity is wavelength dependent (Eq 2.63). S
ince it is an intrinsic physical prope
missivity is independent of surface temperature
. Emissivity has a direct effect upon 
e
adiated energy. Even small changes in emissivi
ty can have large effects 
the amount of r
 
13 ectivityThis assumes hemispherical emissivity and hem
ispherical refl
61 
ce. Changes, or uncertainty, of 0.0 l can ca
use temperature esti-
upon resulting radian
d those due to uncertainty in atmospheric c
orrections (Wan and 
mate errors that excee
Dozier, 1989). Slater ( 1980) numerically sho
ws how an apparently small change in sur-
itted radiation than a 
face emissivi ty, 0.90 to 0.92, can be much m
ore significant to em
I ?C change in surface temperature. Using 
a power law approximation to the Planck 
rvation that uncertainty of 0.0 J in emis-
formu la, Price ( 1989) makes the similar obs
e
ating temperature from 
siv ity at 27?C produces a temperature error o
f0.7?C when est im
issivity is known, significant improvements i
n 
measured radiance. If the true surface em
temperature estimation (and long wave energ
y radiation amounts) should result. 
fo,tunately, what constitutes a true emissivit
y is not clear. Emissivity spectra of 
Un
common surface material s, such as soil , gras
ses and water, are well-known from labo-
vidge, 1988; Jet Propulsion Laboratory, 
ratory studies (Salisbury and D ' Aria, 1992; E
l
lb; Wan, 200 J; Taylor, l 979). But how these sp
ectra appear at coarser resolutions, 
200 
 not well estab lished. For example, when veg
etation is viewed as a canopy, rather than 
is
 effects are presumed to increase effective 
as an assemblage of leaves, multiple scatterin
g
mith, 
emissivities to nearly 1.0 (Norman et al., 1995
a; Palluconi et al. , 1990; Zhang and S
 
1990). Emissivity has directional properties
, where an isothermal body viewed from
 different temperatures (Labed and Stoll, 
different perspectives might appear to have
t al., 200 I b; Kimes, 1980), and it can vary
 depending upon surface par-
1991; Gu e
icle size (Salisbury and Eastes, 1985), surfac
e moisture, and vegetative cover (French 
t
se complications, current remote sensing 
et al. , 2000a). Although they cannot resolve t
he
ination procedures are worthwhile. Emissiv
ity approximations from 
emissivity determ
es-
temperature-emissivity separation algorithms
 result in better temperature estimates, 
ise be possible. 
pecially over sparsely vegetated region, than
 would otherw
missivity estima-
With one exception (the 'day-night algorithm
' of Watson, 1992), e
62 
e an under-determined problem. The emiss ivity ef
fect is detected 
tion algorithms a ll fac
 thermal infrared bands based upon their relatively d
ifferent estimates of sur-
by multiple
face temperature. Since the surface has only one te
mperature, the differences (provided 
trally varying emis-
the atmospheric corrections are not highly uncertain
) are due to spec
s represent relative, but not absolute, emissivities.
 Absolute 
sivities . These difference
emiss ivity values cannot be retri eved without addi
tional information. In other words, 
e unknown than nwnber of bands: 
for any surface observation there is always one mo
r
ture, plus an unknown emissivity for each thermal 
band. 
one unknown surface tempera
The additional information is obtained by developin
g an empirical relationship (Wat-
son, 1992), or by making an assumption about 
the surface properties. The excep-
ves the under-determination problem (in fact it is 
over-
tional ' day-night' method remo
determined) by making two observations: one at
 day, another at night. In practice, 
gistering the two observa-
however, the technique performs poorly, due to diff
iculty in re
tions. 
y separation algorithm chosen for this study (TES)
 is the 
The temperature-emissivit
one used for the ASTER project (Jet Propulsion 
Laboratory, 200 I a). It is one of at 
 
least ten existing algorithms and has been chosen b
ecause it appears to provide the best
et al., 1996). Further experience will show if it can temperature estimates (Gillespie 
consistently provide temperature estimates accurate
 to 1 ?C . The TES approach relies on 
 is functionally related 
the empirical observation that the minimum observ
ed emissivity
vities (Gillespie et al., 1998). The observation is
 a 
to the maximum range of emissi
consequence of the fact that typical surfaces show a
t least one thermal band with nearly 
, the range of 
blackbody behavior, or E ~0.98-1.0. Since the u
pper limit is bounded
irectly determined by the minimum emissivity. The
 general relationship 
emissivities is d
ig. 2.1 0): 
is curvi linear, and can be approximated by a power
 function of the form (F
63 
MMD Re lat ion 
1.00 
>- 0.95 
~ 
> A + B (/) 0.90 * 
MM DC 
(/) 
E 
w 0.85 
E 
:::J 
E 0.80 
2 
0. 75 -
~......_._ 
0. 70 ._~_._._~~..J..........~_.._J
,_
L.,._~....._.1_~~.,_
0.00 0.05 0.10 0. 15 0.20 0 .25 
0.30 
Mox- Min Em issiv ity Difference (MMD
) 
-
Figure 2.10: Generic MMD relation . The min
imum observed emissivity is inversely re
curvilinear form is typical oflaboratory-
lated to the range of observed emissivities. Th
e 
derived emissivities. 
(2.69) 
ivity estimate, Emin, is a function of the ma
ximum-minimum 
The minimum emiss
ity difference, MMD. The terms A, Band C
are power function coefficients. 
emissiv
A is typically set within ~0.2 of blackbody emis
sivity ( 1.0). 
lgorithm, graphically summarized in Fig.2.1
1, operates simultaneously 
The TES a
ions for atmospheric transmissivity, upwelling
 radiance and reflected down-
with correct
elling radiance. The TES algorithm steps may
 be followed in Fig. 2.1 I row-wise from 
w
to 
top to bottom. At Fig. 2. 11 (a), observed ra
diances, L sensor,i ( +) are transformed 
nents: the 
apparent surface radiance values, Lsur Jace,i,a 
( *) , using the following compo
d (e.g. radiosonde data 
atmospheric correction equation (Eq. 2.66), in
dependently derive
sivity (typically 
and MODTRAN) atmospheric properties, and
 an assumed surface emis
64 
-0.98). At Fig. 2. 1 l (b), the radiances are converted to
 brightness temperatures, 
~ 0.97
t ra l 
using any one of the techniques described in the section
 2.6.5 ( e.g. Eq. 2. 72 and cen
s). Temperature corrections in this example are about 
5?C . The max imum 
wave length
observed temperatu re ( ci rcled) is taken as the current be
st surface temperature estimate 
' 
arent emissivities, /Ji for 
and converted to black body band radiances (Eq. 2.63
). App
each band i [shown in Fig. 2. 1 l (c)] are then determined
 by fo rming ra tios of the atmo-
spherica lly corrected radi ances to these blackbody band
 radiances: 
/3 - Ld Li, IJ/] ,'T;,,,, ,. 
1 (2 .70) 
- L/ Lon,T,,,,, ,. 
nces from the top curve (*)of Fig. 2.11 (a). Li,tW,'l ;,"' x ar
e the 
where L; are surface radia
black body radi ances, fo r bands i, at the max imum obse
rved temperature, Tmn x, in Fig. 
on,Tn,,,x is the 
2. 1 I (b). L is 
. L
the mean observed radiance (i .e. the mean of a ll L; values)
ean blackbody radi ance at temperature T, ,wx? Eq. 2. 70 is act
ually not as complicated 
m
as may first appear. The numerator is an estimated b
and emissivity, and foll ows the 
issivity for all the bands 
same form as Eq. 2.67. The denominator is an estima
ted em
sampled, and its sole purpose is to normalize the appare
nt emissivities around the va lue 
of 1.0. Hence, Eq. 2. 70 is an equation of relative emissi
vities. 
 the range of true 
The range of these relative emissivities is taken to be t
he same as
emissivities, or MMD. The estimated actual minimum
 emissivity, cmin, is then deter-
the functional relationship previously illustrated in Fig.
 2.1o . 
mined Fig. 2.11 ( d) using 
The number of unknowns now equals knowns, and the
 emissivities for the remaining 
bands, ci, can be found from the following relation: 
?min 
?i = (3 i X -- (2. 71) 
f3min 
he band emissivities, ci in Fig. 2.11 ( e) , are detennined fro
m the relative emissiv-
where t
 The 
ities in panel Fig. 2.11 (c), and from the minimum emissiv
ity found in Fig. 2. l l (d).
65 
 Fig. 2.11 (f), fo r each band, by us
ing these Fi 
r face temperature can now be es
timated
su
formation from L .wmsor,i to L ,rnr f
arP,i,a 
va lues (rather than a sumed (' va
lues), in the trans
nd temperature es timates are mu
ch closer to each other than 
in Fig. 2. 1 I (a). These ba
re can only be one radiometric 
surface 
ver, the
prev iously es timated in 2.1 l (b).
 Howe
1( b)-(() . The tem-
perature. This is remedied by re
peating steps shown in Fig. 2.1
tem
urther 
es qu ick ly converge (typica lly 3-
5 iterations) to within 0. I ?C . F
perature estimat
 may be fo und in Gillespie et al.
 (1998); Schmugge et al. 
de tai Is of the TES algori thm
( I 998). 
mitations 
2.6.4 Instrumental Designs and
 Li
 surface temperature es timation 
is determined by the perfor-
The third fac tor affect ing
red radiometers measure emitted
 
nfra
mance of the radiometer itse lf. B
ecause thermal i
ble to detect in-
e thermal energy, ra ther than refle
cted solar energy, they must be a
surfac
d detec-
y that is a factor of J 000 less than 
required by visible-near infrare
coming energ
ade with transducers of various d
esigns, 
he actual measurement of radiati
on is m
tors. T
singer, 1995). 
such as semi-conductors, thermo
couples and gas-cells (Schles
ral 
s ign used for most of this study, 
the Thermal Infrared M ultispect
The detector de
id-state 
), is an aircraft mounted, gyro-s
tabilized, nitrogen-cooled, sol
Scanner (TIMS
MS uses six bands over 8-12p,m  Meeks, I 985). TI
Hg-Cd-Te device (Palluconi and
ds, surface radiated 
d is sensitive to 0.1? C . The rel
ationship between these six ban
an
s 
eric absorption is shown in Fig. 2.
12. The TIMS response function
energy and atmosph ' 
12.4 ?m. This wavelength range  from 8.2-
shown in Fig. 2. I 2a, detect therm
al radiation
. 2.12b ). Fortuitously, 
includes commonly encountered 
earth surface temperatures (Fig
ly atmospheric transmissivities (
Fig. 2.12c) , 
se temperatures correspond to re
lative
the
mospheric water vapor is relative
ly 
which means that s ignal attenuati
on caused by the at
66 
Bond SR ua rd faia cn ec  e T emperature 
50 
14 (o (b) Tm o, = 44.5 
l;) 
., Brighlness Temperature 
u ~ ::J 
C 
-~ 40 12 ~ 
"CJ ., 
0 Q. 
Cl'. .E,  
I- ~ 
Ts ensor 
10~-~__,_  __,_  __,,_.....i.._  _.,_.. 3_ 0~   
0 2 3 4 5 6 
7 0 2 3 4 5 6 7 
Bond 
Bond 
M
R ine il mat uiv me   E Emm iis ss si iv vi it ty y  
I . I ,_...........,,--~-~-~-~-'--'~--, 1.00 ( d) 
( C {3mo, -~ E"'" 0 =.9  5 0 .995-0.864?MM0??"
0 
> 
'iii 
.E<Jl  0.90 
0 w 
~ 1.0 E 
::J 0.85 
E 
?2 
'i 0.80 
0.75 
0.05 
6 7 0.00 0. 10 5 0. 15 0 2 3 4 Mox - Min Beto Difference 
Bond 
Rev ised
E  s St uim rfa at ce ed   TE em mi ps esi rv ai tti ue rs e  50 
1.00 (f) (e p-
0.95 ~ ~
:::-  ~ 
?;; 0.90 ::J \ 
'iii 40 
-~ ~.,  T
Q. s urface E 0.85 
w Em;n = 0.880 .E,  
I-
0.80 
30 
0.75 2 3 4 
6 7 0 5 6 7 
0 2 3 4 5 Bond 
Bond 
Figure 2. 11 : Example of temperature-emissivity separation. The TES algorithm con-
verts multi-band thermal infrared radiance measurements into temperature and emissiv-
ity estimates . 
67 
nge. Similarly, the interference caused by
 thermal radiation of 
low in thi s wave length ra
The other detector used 
atmospheric water vapor is also relativel
y low (Fig. 2.12d). ' 
ore 
ASTER, is also aircraft mo unted and is 
similar in design principles, but has m
M
more thermal bands ( l O) (Hook et al. , 200
 I). 
ra lly-scanning mirror and 
Imagery is produced fro m combined mov
ements of a late
ost aircra ft . The incoming radiation is fo
cused by a parabolic mirror and germa-
the h
es-
m lenses, and band-separated by a diffrac
tion grating and an optica l filter. Image r
niu
can contains 638 samples with 8-bi t depth
. 
14 h s
olution is 2.094 mrad ( ~ 0.1 2?) and eac
that the TIMS instrument has a ~ 76? fiel
d-
The implica ti ons of these spec ifications a
re 
 with 
of-view and a digitized temperature resolu
tion of ~ 0.3 ?C. TIMS produces imagery
i stortions. Lateral resolution varies with a
ircra ft altitude and scan 
di stinct and irregular d
n-rate 
angle, while longitudinal coverage is det
ermined by aircraft altitude, mirror sca
ertain image di stortions, the overall radio
metric 
and aircraft speed. ln addition to unc
tain . The calibration of TIMS based on sp
ec-
acc uracy of TIMS is, unfortunately, uncer
al 
ications, is good (Hook and Okada, 1996
). The instrument is designed for minim
if
every scan line against reference blackbod
ies. Laboratory study by 
drift by calibrating 
ver, 
ea lmuto et al. (1995a), indicate l .0?C ac
curacy for all the thermal bands. Howe
R
992), and by Realmuto et al. (1995b ), in
di-
1
actual field experiments by Hook et al. (
?C . Because this level of 
cate that temperature measurement errors
 may even exceed 5
sequent surface flux estimates (in this stud
y errors < 2?C are 
error would invalidate sub
desired) the calibration of TIMS is invest
igated further. 
14
1 mrad == 10- 3 radian 
68 
TIM S Ba nd s 
QJ 
Cf) 
C 
0 
Q_ 
Cf) ii Co) fY-W:Y:1~ QJ J 
Cl:'. 
8 9 10 11 
12 1 .3 
Wa veleng th (?m) 
Bla c kb ody Radiation 
7 .0 ? C 
QJ 13 .3
u (b) 
C 
0 11 
u 2 
0 /(m s ter ?m) 
0:: 
W
9 
9 10 11 12 1 .3 8 
Wavelength (?m) 
Tran smiss ivi ty 
9 10 11 12 1 .3 8 
Wavel eng th (?m) 
Upwell ing Radiance 
1:~ 
10 11 12 
1.3 
8 9 
Wavelength (?m) 
a-
al infrared properties. (a) TIMS b
ands, (b) surface blackbody radi
Figure 2.12: Therm
thin 
ivity, and (d) typical atmospheric 
radiance wi
tion, (c) typical atmospheric trans
miss
ths. 
the 8-1211,m thermal infrared wav
eleng
69 
2.6.5 Radiance-Temperatur
e Inversion 
k relation (Eq. 
era ture can apparently be retr
ieved by inverting the Planc
Surface temp
2.63): 
(2.72) 
.mr f acP = ). In ( rr? + l ) T 5 
,,\ 7f / ,). ,,<;ur fru?e 
eas urements 
easurement at a spec ified wav
elength, >.. Actual radiance m
but onl y fo r m ' 
erage of radiances spanning a 
range of wave-
n the other hand, represent a w
eighted av
o
, 1996). For blackbody radiation
: 
lengths (Jentoft -Nil sen and A
ll ey
.f}/ R>.L>. d). 
.rnr f are = [, >. 2 R d). (
2.73) 
L
. >.1 ). 
length and L>. is the correspond
ing 
ar wave
where R>. is the sensor response
 for a particul
be inverted 
 va lue. The combination of Eq
. 2. 73 and Eq. 2.63 can not 
spectral radiance
et emperature, alternatives are ne
eded. There 
g t
to return a temperature value. 
In order to 
are four poss ible ways : 
l. Iterative solution 
2. Look-up table construction
 
3. Empirical curve-fit 
entral wavelength approximat
ion 
4. C
ted temperature and emissivity
 and 
ima
The iterative solution approac
h starts with an est
ution ofEqs. 2.63 and 2.73. Th
e resulting estimated surface 
then computes a forward sol
w temperature estimates repea
t-
radiance is compared with the mea
sured value, with ne
nce. Although 
 to Eq. 2.63 until the solution 
converges to a specified tolera
edly supplied
mputationally time consuming. 
an accurate method, iteration 
is co
he full range of anticipated tem
peratures and 
Look-up tables can be constru
cted for t
ated temperature-radiance rela
tionship 
at close sample intervals. In t
his way, the integr
70 
me and stored in a database. 
When conver-
 2.73) can be computed one ti(Eqs. 2.63 and
s approach is 
etrieved from a data file . Th
i
sion to temperature is neede
d, it is simply r
STER project (Jct Propulsion
 Laboratory, 2001 a). 
used, fo r example, by the A
 fit to the computed tempera
ture-
cti on) can be
An arbit ra ry curve (e .g. a p
ower fun
eratures within a specified 
nce relationship . Provided th
e absolute errors at all temp
radi a
a set threshold, this method is
 comparable in accuracy 
temperature interva l are less 
than 
ut the data storage overhead. to th e look-up tables, witho
at adequately 
is a method that finds an opt
imum central wavelength th
Las tly, there 
-
ance relationship for a given r
ange of temperatures (Sospe
represents the temperature-ra
di
 and J. Volchok, 1985; Goetz 989; Singh, 1988; Schott
dra ct al. , l 998; Wukelic et 
al. , 1
s) and for temper-
 For radiometers with narrow
 bandwidths ( ~ lp,m or les
et a l. , 1995).
.1 ?c 
wavelength method can have
 accuracies <0
atures spanning 30-60?C , the
 central 
wavelength (Jentoft-Nilsen a
nd Alley, 1996). This is 
r an error of ~ 0.025 11m of
 
fo
he instrumental accuracies (0.
J ?C) and errors due to 
n t
substantially more accurate 
tha
ic uncertainties (l.0?C or mor
e). 
atmospher
r approaches to invert band-a
veraged radiances 
To summarize, there are at leas
t fou
hey vary in computational tim
e and 
to temperature. All can be suffi
ciently accurate, but t
-
ementation, the central wave
torage requirements. Due to 
its simplicity and easy impl
s
 of TIMS and MASTER data
. Further 
length approach is used in th
is study's application
pendix. 
avelengths are discussed in th
e ap
details on identifying the opt
imal central w
2. 7 Vegetative Cover Estima
tion 
emperature, is a critical inpu
t to surface 
as for surface t
Estimation of vegetative cov
er, 
lth 
ation model chosen. The abu
ndance, hea
energy flux models, regardle
ss of the applic
71 
egetation all have important implications for
 a model because these 
and di stribution of v
ing rad iation is intercepted and how the n
et radiation is re-
fa ctors affect how incom
rtitioned. Vegetation not only scatters and r
edistributes incoming radia tion, it also is 
pa
vegetation is a living organism, it 
an important source of latent heat flux. And
 because 
has a dynamic, ra ther than passive, ro le with
in the surroundings. 
, in current practice, is the re-
The bas is of remote sensing detection of ve
getation
m, respec-
lationship bet ween near infrared and red ref1
cctancc (~ 0.8,,m and ~ 0.G811
ly) . Healthy green plant s arc strongly refl e
ctive in near infrared light and poorly 
tive
ong contrast between a surface of green 
reflective in the red light (Jensen, 1996). The
 str
 
vegetation and an unvegctatcd, bare so il surf
ace, can be seen in Fig. 2. 13. Green alfalfa
 
efl ects 65% of TMS Band 7 near infrared 
light , but only about 5% of TMS Band 5
r
Bare so il , on the other hand, reflects 
red light. This is a large ( l 3X) spectral con
trast. 
ut 15% of light in both the near infrared and
 red bands, resulting in negligible spec-
abo
 
tra l contrast. Note, however, that these con
trasts are based on reflectances measured
ld be seen in typical remote sensing data. 
at the ground level, and are greater than wo
u
 
Ground level observations are able to view in
dividual leaves and bare soil patches, while
theless, despite reduced contrast, the spectra
l 
remote sensing observations cannot. Never
relationships just shown between green vege
tation and bare soil remain for remote sens-
ns. There exist many formulations, known a
s spectral vegetation indices 
ing observatio
SVI), that quantify relative abundance of g
reen vegetation(Sellers, 1989). SVI's are 
(
ology 15
 
n and health and are routinely used 
extremely use ful in assess ing vegetation phe
e and meteorological satellites such as TMS
 and AVHRR [e.g. Gao 
on reconnaissanc
(2000); Gutman ( 1991 ); Baret et al. (1995)].
 
15 rin g biological events and their rclation~h
ip with climate (U .S. International Bio-
Thc study of rec ur
 in the Ii fe cycle of green plants . 
logical Program Phenology Committee, 2
00 I). Herc the interest is
72 
80 
TM S5 :. _LTM S7 ~. t fo(_ :;Jk 
60 ~
:  :: ~  ~ ? 
? ? 
Q) 
u 
C 
_0_ , 
u 40 ? 
Q) 
Q) o: 
O::'. 
20 
0 
0 .50 0.60 0 .70 0 .80 0 .90 1.00 1. 10 1.20 
Wave length (?m) 
Figure 2.13: Visible-near infrared spectra of alfalfa and bare soil. Data from Laboratory 
for Applications of Remote Sensing (2001 ), 1988 field experiment in Williston, ND. 
73 
s study is ca lled the Norma lized
 Difference Vegetation Index, 
The SV/ used for thi
or NOV I (Rouse ct al. , 1973; Sc
hott , 1997)): 
ND \ r I = p N I n - p,'P([ (2. 74) 
P N tn + PrPd 
tance in nea r infrared light and 
p,.,,d is surface reflectance 
where p,,,,. is surface refl ec
r NDVJdoes not use re flectanc
es, but uses 
nal idea fo
in red li gh t. tric tly, the origi
 ignores the influence of 
digital co unt s recorded at the se
nsor. However, thi s approac h
man, 200 I). These e ffects, thou
gh not large, can 
th e atmospheri c fi ltering e ffects
 (Rah
nd 
lready known from the thermal 
ba
be reduced because atmospheri
c properties are a
inves tiga ti ons . 
elationship between red and nea
r infrared light 
r exa mple, Fig. 2. 14 shows the rFo
g on 2 July 1997 and 
ceived at the ea rth 's surface for 
a tmospheric properties occ urrin
re
he top curve is exo-a tmospheric
 irradiance and the lower 
modeled by MODTRAN . T
s 
ce. The dashed lines indicate the
 bound
curve is irradiance received at th
e ea rth 's surfa
 sensors. The adjacent numbers
 
e TM and TMS
for the red and near infrared ban
ds in th
and-averaged irradiances. Spectr
al vegetation indices use these 
represent the respecti ve b
 red light is more strong ly affec
ted by 
how that
bands, and the MODTRAN ana
lyses s
red light. By comparing relative va
lues, one 
ar infra
atmospheric transmittance than 
is ne
tion of near 
 attenuation of red light is 1064
11507, or 71 %, while attenua
can see that
r iation in red wavelengths is abo
ut 
nce, sola rad
infrared light is 8 14/ I076, or 76%
. He
7% greater than attenuation in nea
r infrared wavelengths. 
e it is simple to compute and its 
relationship 
 becaus
NOVI was chose n for thi s study
en well stud ied. NOVI does ha
ve some limitations, 
to abundance of vegetation has 
be
94), its de-
turation e ffect above LAI va lues
 of ~ 3 (Choudl1Ury et al. , 19
namely its sa
, 1998) and its susceptibility to pbell and Norman
pendence upon viewing angle (
Cam
son, 1988). 
bias by soil background reflec tan
ce (Huete and Jack
74 
So lar Atlen uo li on 
2000 1507 
/ Above Atmosphere 
?li 076 
Q) 
u l  
C 
~ 1000 
0 
\... 
\... 
Al Surfa ce 
1064 
1076 
W/( m ' s ter ?m) 
0 
0.8 1.0 
0.4 0.6 
Wave length (?m ) 
Figure 2.14: Solar irradiance spectra above the atmosphere and at the surface. Ra-
diosonde data from 2 July J9 97 near El Reno, Oklahoma and the MODTRAN program 
produced these spectral curves. 
75 
ver 
onships between NOVI a
nd percent vegetation co
ti
A part icularly important 
rela
94; Choudhury, 1987) is: (Cho udhury et a l. , 19
N DV/ 11111.r - N DVJ ) 'I f
. 
(2 .75) 
J ( N D \1111111.r - N DV f ,11 i
n 
= ] -
 
J,  determi ned from a renonnaJize
d NDV l based on
over, is
where fra ctional vegetate
d c
e tation cover, N DV Imax-
re soi l surfaces , N D I ' l mi11, 
and complete veg
observations of ba
ibutions within a canopy.
 The 
  orientation di str
The exponent f, 
16 is a function of leaf
I, but for a re lated (and 
ry et al. (1 994) for NOV
range of f, is not stated by
 Choudhu
fo r planophile 
wn as SAVI (Huete, 1988
), it ranges between 0.8 
more linear) index kno t in-
e right hand term, in pare
ntheses no
canopies and > 1.4 fo r erectop
hile canopies. Th
is a linear transformation
 from 
denoted N DV / *. lt 
cluding the exponent, is f
requently 
er at O and bare soi l at I . ov
NOVI and ranges betwee
n O and I, with full c
AI), which is the ra tio of 
the leaf area 
ted to frac tional cover is le
a f area index (L
Rela
t al. , 1994) : 
o the g round area the leav
es overlie (Choudhury e
(s ing le-s ide) t
LAI = _ln,_(1_-_J_) (2. 76) 
-(] 
0.91 and 
leaf orientation ang les, ra
nging between 0.42 to 
where fJ is also a function 
 to uncertain calibration o
f this fonnula, 
er, J must be less than 1.0. Duefractional cov t 
aves) is chosen. Where 
leaves are no
a nominal value of 0.67 (
randomly oriented le
lationship between LAI, f a
nd Rn is no 
cur in clumps, the re
randomly oriented, but oc
ht penetrates to the soil f
or a given 
tation, more lig
longer the same. Jn clw
nped vege
ping can be compensated
 
m
n would normally be esti
mated. The effects of clu
LAI , tha
an, 1998; Gijzen 
eveloped clumping factor
s , D (Campbell and Norm
using empirically d
aan J 989? Chen and Cihl
ar, 1995). 
and Goudri ' ' 
tween an extinction coeffi c
ient 
16 m the ,X parameter used in 
Eq. 2.14 . ( is the ra tio be
( is different fro
 fun ction from Ross ( 198 1) 
. 
k' and a lea f angle proba bil
i ty distribution
76 
3 Methods: ET Estimation an
d 
Scaling using Remote Sensing 
3.1 Methods Overview 
s necessary lo analyze the 
e previous chapter reviewed th
e backgro und and technique
Th
using a remote sensing based
 
imation of ET 
spatial scaling properties of E
T. The est
s shown how 
wo-Source Energy Balance (T
SEB), was discussed. It wa
model , the T
ons and surface energy flu x e
stimates could be 
maps of the remote sensing o
bservati
as shown that observations 
ana lyzed objectively for mea
su res of heterogeneity. It w
r can be combined with comm
only 
d surface cove
of land surface tempera ture a
nd lan
ons to make estimates of surfa
ce energy 
ical observati
ava ilable near surface meteoro
log
sfered from ET are closely 
alance. Since the surface energ
y balance and latent heat tran
b
entially contain instantaneous 
ET estimates. 
linked, the TSEB estimates es
s
 the scaling experi-
n hi s chapter, the assembly of a
ll the components needed for
1 t
tudy sites. The main emphasis
 
me from two s
ments is discussed. The data c
ollections co
zinglands Research Laborator
y at El 
 the USDA Gra
is upon a site in central Oklah
oma:
outhern New Mexico: 
USDA, 200 l ). A preliminary a
nalysis over a second site in s
Reno(
Mexico State 
ada Experimental Range, New
 Mexico (USDA and New 
the USDA Jom
University, 2001) is also ment
ioned. 
, including remote sensing ob
-
d
The composition of these data
 sets will be reviewe
 
ions and atmospheric radioson
de measurements. Since this
servations, ground observat
mulated data, practical issues 
such as data georegistra-
study uses actual, rather than 
si
ssed. Im-
or atmospheric effects are dis
cu
tion , calibration, sensitivity an
d correction f
77 
rature es timation and vegeta
ti on cover is 
mentation of techniques for 
surface tempe
plc
 flux estimation from the tw
o-
shown in further deta il. Aft
er reviewing surface energy
y will be described. These g heterogeneit
source model, three techniq
ues fo r analyzin
riments because 
measures are use ful as referen
ce points in the sca ling expe
heterogeneity 
s to modeled surface energy
 fluxes. 
al landscape pat1ern
they help re late known spat
i
e discussed. 
a tion procedures needed for
 the sca ling experiments ar
Lastly, the aggreg
rface energy fluxes, the relati
onship 
ng observa tions and su
By aggrega ting remote sensi
eity and modeled surface ene
rgy fluxes 
ape heterogen
between sensor resolution, la
ndsc
can be determined. 
3.2 El Reno Data CoJJectio
n 
 a subset of Southern Grea t 
Plains 
rises
The I Reno, Oklahoma dat
a collection comp
gy and Remote Sensing Lab
oratory, ARS-
7 (SGP97) fi eld experiment
s (Hydrolo
199
area much larger than just 
DA, 2001 ; Goddard DAAC, 
2001 ). SGP97 covered an 
US
ath through central Oklahom
a and 
 north-south sw
El Reno (Fig. 3.1) , spanning
 a large
f hydrological studies, includ
ing soil mois-
o
part of Kansas . It included a
 wide array 
asurements, thermal infrared
 
ure studies on the ground, ai
rcraft passive microwave me
t
round and in aircraft. Two im
portant meteoro-
xes on the g
flights , and surface energy flu
on Measurement Program [A
RM, At-
logical data sources are the A
tmospheric Radiati
oma Mesonet (Uni-
 Radiation Measurement Pro
gram (2001)] and the Oklah
mospheric
ata sets also include 
 Oklahoma & Oklahoma State
 Univeristy, 2001). The d
versity of
ugh data from El Reno were 
col-
e field notes. Altho
local meteorological and des
criptiv
en 
 used here only ranges betwe
lected over most of June and 
July 1997, the El Reno data
29 June to 2 July 1997. 
78 
a is about 200 km north-s
outh and 50 
igure 3.1: SGP97 study a
rea. The full study are
F
th. Fort Cobb Reservoir estern margin of the swa
km east-west. El Reno li
es near the w
nd outside of the swath. 
The dashed 
hwest of El Reno, a
is about 40 km to the so
ut
m the Central 
ARM-CART study area, 
which is coordinated fro
rectangle encloses the 
s are Mesonet sites. Ope
n 
 extended facilities, gray
 dot
Facility. Black dots are 
ARM
easurements. 
circles are Mesonet sites 
with soil moisture m
79 
3.2.l Aircraft Remote Sensing Observations 
Remote sen ing surveys over El Reno were conducted from 29 June- 2 July 1997 using 
two instruments mounted on-board a U.S. Department o f Energy Cessna C itation air-
craft. One ins trument, the Thermal Infrared Multi spectra l Scannner (TIM S), Pa lluconi 
and Meeks ( J 985); Goddard DAAC (200 I)), is exc lusive ly a thermal infrared dev ice 
wi th six bands. The other instrument, Thematic Mapper Si mulator (TMS) Daedalus 
1268 Scan ner, is a 12-band instrument. It spans vis ibl e, near infrared, mid infrared and 
thermal infrared bands' . Both the TIMS and TMS radiometers are scanning dev ices, 
wh ich means that imagery is created by a combination o f lateral scanning, from a rota t-
ing mirror, wi th forward scanning along the long itudinal a ircra ft fli ght path. Resultant 
images are quite unlike aerial photographs because they have irregular and systemati c 
di stortions, some due to irregu lar aircraft movements, and some are due to inherent 
geometri c characteristi cs of the scanners. 
As shown in Table 3. 1, the geometric sca nning properties o f the two instrument s are 
s imilar. However, they differ in one important respect: TIMS is stab ilized and TMS 
is not. The consequence of this- discussed further below in the Georegistration sec-
tion and in the Results chapter- is that co-registration of imagery is sometimes difficult. 
Co-registration of image data is important because an incorrect association between re-
flected and emitted radiation will produce highly erroneous surface flux estimates. 
Information recorded by remote sensors is stored in units known as digital counts. 
' 
The information must be converted to physically-meaningful values, spectral radiance 
( e.g. mW m - 2
 ster- 1 /Lm- 1 ). The conversion process is linear, with coefficients deter-
mined in a controlled laboratory setting. TIMS data were processed by the Jet Propul-
1 
The thennal band was not ca libra ted for thi s campaign and was not used. It is recorded at two gai n 
level s, occupyi ng channel s I I and 12 
80 
Table 3.1: Remote sensing radi ometer spec ifications. TIMS is a thermal infrared scan-
ner and TMS is a visibl e-near infrared- middle infrared scanner (TMS also has a thermal
 
band, but it was un-ca librated for SGP97). IFOV is instantaneous fi eld-of-view in milli -
radians, PixSep is the pixe l-to-pixe l separation. 
Sensor TIMS TMS 
Wave lengths (Jtm) 8-12 0.42-3.22 (8-11.5) 
Bands 6 12 
!FOY (mrad) 2.5 2.5 
PixSep (mrad) 2.1 2. J 
Pixels/scan 638 716 
Scan Angle 86? 76.56? 
Scan Rates (Hz) 7.3/8. 7I  12/25 12.5/25/50/ 100 
Remarks Gyro-stabilized No stabilization 
81 
: El Reno TlM S/TMS fligh
t cond it ions. 
Table 3.2
End Duration A ltitude Total Scan
li nes 
Juli an Run Start 
MS MS 
Day (UT hms) (UT
 hms) (s) (m) TI T
:36: 14.3 273.3 4877 69 1
8 3419 
180 13:3 1:41.0 13
1 
80 2 13:44 : 18.0 13:48
:40.6 262.6 4877 6702 327
1
13:58:25.0 14:02 :51.2 
266.2 4877 68 16 3156 
180 3 
 
 4 16:47:20.0 16:5 1:5
3 .0 273 .0 4877 7134 34 15
180
 366 3 101 
18 1 20:40: 11 .0 20:4
4:20.0 249.0 4877 6
 I 2 20:54:52 .0 20:59:0
8.0 256.0 4877 6384 3365 
18
:40.5 16:59:21.0 28
0.5 4877 7332 3503 
182 16:54
 20: 17:37.5 20:21:55
.9 258.4 4877 7098 3248 
182 2
6.9 278 .0 4877 7176 3396 
183 12:22 :18.9 12:2
6:5
: 3 1.0 16:06:39.1 308.
1 1524 7703 7733 
183 2 16:01
1.0 290.4 4877 7260 4083 
183 3 J6 : l 7:00.6 l 6:
21:5
 (mW m - 2 ster- 1 /tm- 1) . T
he 
nits of spectral radiances
sion Laboratory and delive
red in u
or Fa-
 digital counts (Airborne S
ens
TMS data, on the other han
d, were delivered as raw
ng with the necessary calib
ration 
oratory, 200 I), alo
cility, 200 l; Sensor Calibra
tion Lab
 Appendix A, and in table 
A.1. 
cedure is detailed in
coefficients. The conversio
n pro
Reno SGP97 
ll the TIMS/TMS remote s
ensing flights over the El 
Table 3.2 shows a
e mid-
s, including four mid-morn
ing surveys, thre
study area. There were ele
ven flight
ne were flown at 
, and three early-morning 
surveys. All flights but o
afternoon surveys
solution of ~ 12 m. The exc
eptional 
~ sulting image re5 km above the ground, with re  m 
as flown at~ 1.5 km abov
e the ground yielding~ 3
ght occurred on 2 July, and
 w
fli  - 1. 
ed ~28 km, at ground spee
d of ~ JOO m 8
image resolution. Each flig
ht survey cover
82 
[ 1 f-'r>no r? ielri Loco lions ,-, 
.3113 i 
E-
""~ [P05 ? [ROG 
7.,- 393 --1 -
,-2_  ~r (PO~ [P08 F~;l1  
::, 
.3933 
393 
_.---1 -~ ~- ' 
58 588 :,Q() 58 1 
UlM 14E ( km ) 
Figure 3.2 : El Reno Fields, SGP97. Locations of study fields are outlined. Th
e four 
flux station locations are indicated with boxes in fields ERO I, EROS , ER09 and ER
13 . 
The area shown is approximately 8 km east-west and 6 km north-south . Fields ER
O 1-04 
contain thick grass and are the core of the USDA-A RS Grazing lands Research L
abora-
tory. Fields EROS-13 are a mix of grazing land, harvested winter wheat and bare s
oi ls 
and are mainly delineated by quarter-sections. Fields ER 15 and 16 are bare soi l 
and 
pasture lands, respectively, and are adjacent to the North Canadian River. Project
ion in 
UTM zone 14 coordinates. 
Total scanlines collected are listed, but usable scanlines may be slightly less. The 
TIMS 
scan rate was 25 Hz, TMS was 12.5 Hz. 
3.2.2 Ground Flux Measurements 
Ground level observations of su rface energy fluxes (Kustas et al., 1999) were mad
e with 
eddy-covariance instruments at four sites (Fig. 3.2), the theory of which was b
riefly 
discussed in section 2.5 . 
83 
Sensible Heal r lux 
800 -
600 w 7 
r 400 -- - ? 
...,. "!: 
200,.. _,, ~\  
"' 
J ___ 
0 -
1 '.:- 180 1e5 l 'JO 195 
Doy o f Yeo, 
Latent I lea l Flux 
800 
w rri2 
600 
- -
A 
'j ,100 
200 I 
0 
175 180 185 190 195 
Doy ol Year 
Rainfall 
80 
[R0 1 I 
mos y 
60 [R09 0 
E ER 13 t. ..s  
.c 40 a. 
0" ' 
20 
0 
175 180 185 190 195 
Doy o f Yeo , 
Figure 3.3: SGP97 mid-day fluxes . Eddy-covariance measurements and associated rain-
fall data for days 172-195 (21 June- 14 July 1997). Both sensible and latent heat fluxes 
over vegetated fields ERO I , EROS and ERO9 are relatively insensitive to the rainfall 
events. Bare soil field ER 13 , however, shows large flux variabilities directly responding 
to rainfall. 
85 
Between 2 1 June and 14 Jul y 1997 at El Reno, average covari ances during daytime 
1 
for sensibl e heat typicall y range between 0 and 0.4 m s- K and fo r latent heat between 
o and 1.2 x 10- 4 m s- 1. T hese result in flux values respectively rang ing l 00-300 W m -
2 
for H and 100-600 W m- 2 for LE (Fig. 3 .3) . Covariance values were continuo usly 
) 
measured 2 meters above the ground at 10 Hz, and block averaged in 30 minute intervals 
(Ku tas, 200 l ). At the bottom o f Fig. 3 .3 are prec ipitatio n data fro m site E ROS . Plotted 
are cumulative dail y ra infall amo unts collected at 6-hour interval s. Note that the 60 mm 
ra in fa ll event on J 179 (28 June 1997) is expressed directly and strongly by LE eddy 
covariance measurements over the bare soil site, ER 13 . 
3.2.3 Aircraft Flux Measurements 
El Reno surface 11ux measurements from aircraft were also collected during the SGP97 
experiment. These measurements were obtained from a Twin Otter aircraft flown at 30 
meters above the ground (MacPherson, 1998) and used eddy-covariance instruments . 
The El Reno flight track (Fig. 3.4), an east-west profile about 12 km long, was repeat-
edly flown 12 times, over a period of 2 ? hours. Flux measurements were made at 30 
Hz. At aircraft speeds of ~ 58 m s- 1 , this resulted in over-the-ground samples at ~ 2 m 
intervals. The individual flux sample values, however, show very large variations from 
2
sample to sample (sometimes more than 1000 W m - ) and do not represent meaningful 
surface fluxes unless they are averaged over suitable distances. In the El Reno case, the 
minimum averaging distance is believed to be ~250 m (Mahrt, 2001). But even after 
averaging, the aircraft flux data are difficult to compare directly with two-source flux es-
timates . Aircraft data represent surface fluxes contributed over a broad upwind surface 
area, while two-source flux estimates represent surface fluxes from a small surface area . 
A flux-footprint technique, previously described in section 2 .5, was used to transform 
84 
3 
7' 3 3-\ ~~-?? 
''- 
0 
z 
30.0 35 0 40 .0 45 .0 50 .0 5 .0 
Su ,t oc l em p ro lur (C ls iu s) 
Figure 3.4: Twin Otter flight path. 
two-source flux estimates into an equivalent aircraft-based reference frame. 
3.2.4 Radiosonde Data 
Radiosondes are weather balloons sampling pressure, temperature and dew point at fixed 
time intervals as they ascend. After processing, a one-dimensional profile of these at-
mosphere properties vs. altitude can be created. Because atmospheric water vapor has 
a strong influence on remote sensing data, these radiosonde profiles are important for 
atmospheric correction routines2 . 
For the El Reno study, date were available from radiosondes launched at three-hour 
intervals by the CART-Arm facility (Atmospheric Radiation Measurement Program, 
2001). The six radiosonde launch sites are shown in Fig. 3.5. The site closest to El 
2 A good overview of how radiosondes data are collected, processed and displayed is found at: 
http://www.crh.noaa .gov/fsd/upper.htm 
86 
AR M So nd e Sit es 
4300 
4200 
~ 4 100 
E 
-"' 
z 0 
- Lamon t , OK (CF) "::a  
>-
:::, 4000 
v;$?oK (b4) 
? 
Morri s, OK (b5) 
X 
El Reno *O K c ay 
3900 -
0 
Purcell, OK (b6) 
400 500 600 700 800 
UTM 14E (km) 
Figure 3.5: ARM-Cart Sonde Sites. Locations of radiosonde launch sites managed by 
the ARM-Cart facility (CF). The El Reno Grazinglands site is indicated by the 'X' and 
downtown Oklahoma City is by the asterisk. Radiosondes were launched every three 
hours from the sites b 1, b4, b5 , b6 and CF. 
87 
ndes ascend at ~ 4 rr u, - 1, and so o
no is ' b4 ', 86 km to the
 north west. The radios
Re ondes dri ft 
at ~ 25km. During ascent
, rad ios
take abou t J ! hours to reach burs t altitude  in the 
mple, the early July laun
ches drifted over 20 km
considerab le distances . 
For exa
. Radiosondes bracketi n
g in time the 
g
preva iling upper level w
esterlies before burstin
ng. A 
ere profi le generation an
d modeli
aircraft survey times we
re se lected for atmosph
terpolating in time betwe
en two bracket-
e was creating by in
synthetic rad iosonde pro
fi l
3.6. For example, the int
erpolated 
es. The scheme is indica
ted at the top of Fig . 
ing sond
10 km is derived from a  at 
e va lues o f pressure, tem
perature and humidity
radiosond
t on the sonde launched 
 the sonde law1ched at J4
:30 UT, and 39% weigh 
6 1%  weight on  to 83% 
 va lues at 20 km, the prop
ortions have changed
lated
at l 7:34 UT. For interpo
 are shown at the bottom
 
alues from both sondes
and 17%, respectively. 
The profil e v
essure 
ative humidity. The cha
nge in pr
of Fig . 3.6: pressure, a
ir temperature and rel
e change in air temperatu
re is small , typically 
 sonde launches in neglig
ib le. Th
between
seen at 4 km. A lso plotte
d is the 
umidity, however, is easi
ly 
~ 5?C . Change in relativ
e h
ative humidity, it is indep
endent o f pressure and 
ed absolute humidity. Un
like rel
comput
 effects are most 
efore is a better indicato
r of where atmospheric
temperature and ther
ter vapor above 5 km, an
d that, 
 that there is virtually no
 wa
significant. The plot sho
ws
elative humidity plot, the
 water vapor density 
n created by the r
contrary to the impressio
1 irtually constant from 2.5
-4 km. 
s v
ncertainty in Radiosonde
 
3.2.5 Sensitivity of Surfa
ce Temperature to U
Data 
e 
cts is critical to the deriv
ation of reliable surfac
Because removal of atm
ospheric effe
onde 
flux estimates), sensitivi
ty studies on the radios
ntly 
temperatures (and conse
que
nde measure-
ated the consequences of
 radioso
data were performed. On
e study investig
88 
Ascent Tim e 
25 
20 0. 17 0. 83 
E 
.._..,..,. ., 15 
(l) 
u 
:, 
?- 10 0.39 0 .6 1 
<( 
5 
0 17 18 19 
20 
15 16 Time (UT) 
Re la ti ve Hum idity Abso lute Humidity 
Tempe rature 25 z5r--~_:___~ 
Press ure 
25 25 
20 20 
20 20 
? 15 ? 15 
I 15 ? 15 ;:!., -"' ;:!., u"  u"  
u"  u"  ~ :~ 3 ~ 10 ~ 10 
~ 
10 ~ 10 <( 
5 
5 5 
0L--..c...::.---' 
0 L--'--.:;_J 0 50 100 0 10 20 0 
- 100 -20 60 R. H. (percent) Va por Dens ity (g/m') 0 500 1000 Toir (Ce lsi us ) 
P (mbor) 
Figure 3.6: Example sonde data. Two sequential ARM radiosondes launched from site 
'B6' , 2 July 1997 at 14:30 and 17:34 UT. Remote sensing aircraft survey time, indicated 
by the dashed line at top, was at 16: 19 UT. Air pressure, temperature, relative humidity 
are recorded by the sonde, as shown at the bottom. Computed water vapor density is 
also shown to indicate virtually no water vapor exists above 5 km. 
89 
mcnt error. Another investi gated the uncertainty due to variabili ty in atmospheric water 
apor. 
The sensitivity of surface temperature estimates due to radiosonde instrumental error 
was evaluated by Monte-Carlo simulation . This was done by modifying a radiosonde 
profile derived from a balloon launched from site ' b6' on 2 July 1997. Manufacturer 
specified \ -a errors for the Vaisala RS80 radiosonde (Vaisala Group, 2001) were used: 
0.4? , 0.5 mbar and 2% relative humidity. 400 simulated profiles were generated (F ig. 
3.7) by assuming normally distributed errors. Then, two more profiles were generated 
from the envelope of these simulat ions . Using all 402 profiles, the effect upon estimated 
surface temperatures was then evaluated using the radiative transfer program MOD-
TRAN and extracting apparent atmospheric transmissivity and spectral radiance values 
for T IMS' six thermal infrared bands (Palluconi and Meeks, 1985). Using assumed 
surface temperatures ranging between 30 and 60?C, and thermal emissivities between 
0.75 and 1.00, surface radiances were propagated through the original, unperturbed, at-
mospheric profile to an altitude of 5 km. These propagated radiance values were then 
'corrected' using Eq. 2.66 and the data derived from the simulated 402 profiles. The 
resultant surface radiance values, upon conversion to surface temperatures, were com-
pared with the originally defined temperatures. Fig. 3.8 shows deviations for the worst 
case simulation. With all inputs perturbed by one standard deviation, estimated surface 
temperatures differed from actual surface temperatures by~ 0.6? or less in TIMS bands 
I , 2, and 3. TIMS bands 4 , 5 and 6 showed possible errors up to 0.8-1.2? with commonly 
expected emissivities (0 .80-0.99). 
The radiosonde simulations also show that surface temperature estimate errors are 
not only a function of uncertainty in atmospheric properties, but are also controlled by 
surface temperature and emissivity. Nevertheless, the estimate errors are nearly linear. 
90 
The curves shown in Fig. 3.8 actually consist of two sets of nearly linear branches: one 
set to the left of the minima, where the modeled atmosphere contains less water vapor 
than it should , and another set to the ri ght o f the minima, where the modeled atmosphere 
contains more water vapor than it should . The precise relationship o f the branches can 
be found by using the atmospheric correction fo rmulae Eq. 2.64 and Eq. 2.66, where 
Eq. 2.64 models the true atmospheric properties and Eq. 2 .66 models the estimated 
atmospheric properties. The difference between estimated and actual surface radi ance, 
resulting from using an estimated atmospheric profile, can then be represented by a 
linear equation: 
6. L.rnrface = a X L .mr far P,lr11e + b (3. 1) 
Here the error in the sur face emitted radi ance, 6. L.mrfn.ce , is a linear function of the 
true surface emitted radiance, Lsur f <Lce, trne, for any fi xed set of atmospheric properties. 
And since the relati onship between surface temperature and surface emitted radiance is 
nearly linear over small temperature intervals ( < 15 - 20?C ), the observed temperature 
error relationships in Fig. 3 .8, are also nearly linear. The coefficient a is determined 
by the relationship between true atmospheric transmissivity, Tt.rne, and estimated atmo-
spheric transmissivity, Test: 
Tt.r 11e 
a=--- 1 (3 .2) 
Test. 
Eq. 3.2 shows that the sensitivity of the surface temperature estimate error is indepen-
dent of surface temperature and emissivity. On the other hand, the intercept value b 
(Eq. 3 .3) is dependent surface emissivity, as well as the true and estimated atmospheric 
properties: 
1 
b - [ L u pwelling ,lr11e - L11pwellin9 ,est1 
Te,q l 
+ (l _ ) lLdowmv ell in9, t,r11e _ L . 1 E clawnwell inq ,es t. (3 .3) 
T es t. ? 
9 1 
For fi xed true and estimated atmospheric properties, sur face emissivity alone determines 
the intercept value /J, and consequently explains why there are different error curves fo r 
each surface emissivity in Fig. 3.8 . 
Sensitivity of sur face temperature estimates due to uncertainty in total atmospheric 
water vapor abundance was also analyzed. Fig. 3.9 (top), shows the observed columnar 
water vapor from all five radiosonde sites over the period 29 June-2 July 1997. All four 
days were clear, and no major weather systems passed through the area. Stations closest 
to the El Reno site, ' b4 ' and ' b6' (respectively, asterisks and squares), sometimes show 
over I cm differences. The plot at the bottom considers all sondes, and shows that over 
scales of ~ 300 km, water vapor abundances differed by at least 0.5 cm, and sometimes 
over 2.0 cm. Clearly, there are significant spatial and temporal variations of atmospheric 
water vapor for the study period over El Reno. 
This spatial variability can cause large errors estimating surface temperature. Re-
sults of a simulation study demonstrating this are shown in Fig. 3.10. The study was 
performed in a similar fashion to the sensitivity analysis of radiosonde error. A ' true ' 
surface temperature was set (in this case, 37?C) , and estimated surface temperatures 
were made assuming a range of incorrect atmospheric water vapor abundances. The re-
sulting errors are nonlinear, and show that underestimating water vapor is less ham1ful 
than overestimating water vapor because the temperature sensitivity is less when atmo-
spheric water vapor is underestimated. Fig. 3.10 simulates realistic cases, where gross 
estimate errors (> l cm water vapor) are unlikely. In this instance,temperature estimate 
errors are nearly linearly related to columnar water vapor errors. Fig. 3.10 shows these 
linear approximations. Each curve shows the sensitivity over a range of columnar water 
vapor abundances for each of the six TIMS bands. For example, if the actual atmosphere 
1
contains 4 cm of water vapor, then the sensitivity for band six would be ~ 6.5?C cm - . 
92 
Re la tive Hum id i ty 
25 
20 
20 
20 
15 
15 
15 
? ? 
E ~
-"' ~ ., 
 
., ., u u 
u ?.3;:; 3  :, 
~ ~ 
~ 
10 
10 
10 
5 
5 
0 L-1-J-.I._._'-'---'-"----'-' 
0 L.J.J.JLLLJ..LU-.LLLJLLLJ...Ll.J..J 0 5 50 0 0 10 10 0 00 
Pre
- s1 s0 100 u0 re  (mbar0 )  Rela tive Humidity (%) 
Temperature (?C) 
Figure 3.7: Simulated radiosonde profiles. An atmospheric profile derived from launch 
site ' b6' on 2 July I 997 was modified. 400 simulations, based upon normally distributed 
errors taken from radiosonde specifications (Vaisala Group, 2001), generated the profile 
values indicated. Error bars plotted at each altitude are ?lcr. Note that uncertainty in 
humidity is greater than temperature and pressure uncertainties. 
93 
Radioso nde Error Effe c ts 
Rad iosonde Error Eff ec ts 1.4 ..-~-.-,-~--.---...--.-:..--.-::,.:..:.:;_ 
Emiss ivity 
1.4 Em iss ivity 
Bond 1 E *+  0.80 
Bond 2 
~ *~  0.80 0.90 0.90 1.00 C 
9 1.00 
.0> .,  
0 
E 
::, 
s 
~ 
0 
::, 
35 40 45 50 55 
30 35 45 
50 55 Sur[ace Tempera ture (?C) 
Sur [ace Temperature (?C) 
Radiosonde Error Effects 
Radioso nd e Error Eff ee l s 1.4 ..-~-.-,-~--.---.,--.--~......:...:..:..:--
E mi ss ivi ty 
1.4 Emi ssiv ity + 0.80 Bond 4 
~ I 0.80 Bond .3 * 0.90 
1.00 
C * 0.90 
9 1.00 
.>0 .,  0.7 
0 
E 
::, 
E 
?;; 
0 
::, 
0.0 35 40 45 50 55 
35 40 45 50 55 Surface Te mperature ('C) 30 
Sur[ace Te mperature (?C) 
Radiosond e Error Eff ee l s 
Radiosonde Error Eff ee l s 1.4 ,....~--,-.~--r~~r--;:..._~:.:;__-
I .4 ,-.--...-~~--,-,--..--,....-.-,-~~ Emissivi ty 
Emissivity + 0.80 
+ 0.80 Bond 5 E * 0.90 * C 0.90 .2 1.00 C 
.9 . 1.00 .0> .,  
.0> .,  0 
0 E 
::, 
E E 
::, ?;; 
E 0 
?;; ::;; 
0 
::;; 0.0 L--_.c.i..:._ _. ,____......L ___ .__  _J 
0.0 L....-....:a<:.........-...,_ __., ___ _ _,__  ___, 30 35 40 45 50 55 55 
35 40 45 50 Surface Temperature (?C) 30 
Surface Temperature (?C) 
Figure 3.8: Radiosonde error effects. Surface temperature errors caused by radiosonde 
measurement error are shown for each of the six TIMS bands. 
94 
.. \ o lu l Wul e r Vo po , . ) . u? 11? 
h lol 
I I 0 
O ,:;,,_ m U-. -.:J/ 
,~fl) '\, u 
~ ' ;el? r- , '+ +-
u 
Cl I t 
() 
I I b 1 1 
Qi 2 I I b? I :; 
I I b '.) I I 
0 
I bb [7 II I I 
. I . cf 9 - II . J . I . 
\ 8 1 182 183 
Doy of Yea r (GM1) 
ng e o f Wal r Vap o r 
?r, 
I I I + . 
I I 
l ?.O I I
u 
~ 
0 
0 I l
 
I lI I r 
0 I I 
-~<; 
I I 
Q,Q,___ __  
180 18 \ 182 183 18 4 
Doy of Year (GMT) 
figure 3.9: Total water vapor vs. time. Total atmospheric water vapor as measured 
by ARM-Cart radiosondes from five sites for the El Reno study days (a). Maximum 
variation in water vapor estimates between the sondes is also shown (b ) . 
95 
This means that the estimated surface temperature wo uld differ from the correct su rface 
temperature by 6.5?C if e ither I cm too much, or I cm too littl e wa ter vapor, is used 
in th e correcti on mode l. Fig. 3. 10 also shows the spectra l dependency of co lumnar 
water vapor uncertain ti es. While uncertain atmospheric water vapor causes temperature 
es tim ate errors fo r a ll thermal infrared wave length s, the e ffect is most pronounced for 
TIM S band 6( x ), wh ich li es at the upper edge of the thermal infrared window ( 1211,m, 
sec Fig. 2.12). If the TIMS instrument had a band at the lower edge of the thermal in-
frared w indow (811m), th at band would also show hi gh sensi tivity to atmospheric water 
va por uncertai nty. 
To reduce the poss ibilit y of introducing thi s leve l of uncertainty for the E l Reno 
surface temperature es tima tes, water vapor contour plots were made from the observed 
time sequence in Fig. 3.9 and checked fo r large spatial gradients. Based on the contours, 
radioso nde data that were c losest to El Reno conditi ons were used. For example, the plot 
for the time corresponding to ai rcraft surveys on 2 July 1997 (Fig. 3. 11 ) suggests that 
radiosonde ' b4 ' is likely to be most representative of El Reno conditions at l 0:48 am 
(CST) . The contours, however, are only suggestive. A more thorough and physically 
mea ningful analys is- not undertaken here- wou ld use mesosca le atmospheric models 
(NOAA, 200 I) to perform an interpolated profile . 
Further processing of radiosonde data, to determine atmospheric transmissivity and 
radiance, is described be low in 'Atmospheric Correction' 
3.2.6 Soil Emissivities 
In addition to the basic remote sensing and meteorological data sets, a data set containing 
laboratory measurements of emissivities from some El Reno samples was avai lable. As 
mentioned in secti on 2.6.3, an empirical relationship (Eq. 2.69) is needed to solve for 
96 
Temperature Se nsiti vity 
1 2 
J7 oc 
10 TIM S Bond s 
,,.....___ 1 + 
E 2 
u 
0"u  ' J 
* 
? 
8 4 L;, '--" 
......, 5 ? 
> 6 X 
(J) 
C 
(lJ 
U) 
4 
2 J 4 5 
Co lu mn a r Wa te r Vap or (cm) 
Figure 3.10: Surface temperature sensitivity analysis. Uncertainty in columnar water 
vapor causes uncertainty in surface temperature estimates. Bands I, 2 and 3 are least 
sensitive, while band 6 is most sensitive, to changes in atmospheric water vapor. Simu-
lation made for 37?C surface temperature. 
97 
=1-83. 700 G'v1l Da
ys 
4300-
Figure 3. l l : Contoured water vapor over SG P97 . Columnar water vapor derived from 
radiosondes contoured for day 183 at I 0:45 am local time. Radiosonde launch sites are 
indicated by diamonds (see Fig. 3.5). The line traces from these sites are positions (for 
altitudes between launch and 20 km) of the sondes launched at 11 :30 am. Gradients 
indicated by the plot suggest that the radiosonde to the west of El Reno, 'b4', is most 
representative of conditions at El Reno (X). 
98 
re and surface emissivities using the TES metho
d. Although a tandard 
surface temperatu
irable to have 
power functi on curve is available (Gi llespie et
 al., 1998), it is more des
erified emissivi ties. The analyse? avai lable con
tains 43 soi l samples. 
locally v
The laboratory measurements of emissivi ty s
pectra were obtained using a Fast-
m shown in Fig. 3. 12 is typi-
Fourier spectrometer (Grove, 1999). The exam
ple spectru
Within the thermal infrared window, these soi ls
 show emissivities 
cal for siliceous so il s. 
f a spectrum also depends upon soi l texture and ranging ~ 0.85-0.98. The precise shape o
moisture content (Salisbury and Eastes, 1985). 
The effects detected by multiband ther-
band 
mal infrared detectors, due to their finite bandw
idths, are not as detailed. The multi 
st computing band average emissivities, f.;, for 
each of the 
responses are obtained by fir
six TIM S thermal infrared bands: 
_ J <= >. R>.rl>. (3.4) 
f.; = J R>. d>. 
plification of dif-
Response function values, R>. , are weights representi
ng the relative am
articular sensor. For thi s study, TIMS response
 were needed. 
ferent wavelengths for a p
cesses 
They are shown in the top graph of Fig. 2.12. 
The results of these averaging pro
are indicated by horizontal lines in Fig. 3.12. 
y filtering the laboratory spectra with the app
ropriate sensor response functions 
B
rmined. Neglecting scale effects, 
( e.g. Fig. 2.12), band averaged emissivities ar
e dete
erived emis-
these averaged emissivities represent the best e
stimate of remote sensing d
le, the range and minimum emissivity are selec
ted 
sivities for soils. For each soil samp
and plotted as shown in Fig. 3. 13. The resultin
g points show a nearly linear trend with 
e customary power function formu-
local scatter on the order of 2%. Keeping wit
h th
 (Section 2.6.3, Eq. 2.69), the best fit using 
least squares approximation is as 
lation
follows: 
<'m.in  = 41\[ M D
0 870 
O 0.86 ? (3.5) - r~,g r.;:)  -
99 
So il ER 13 Emiss ivity 
1.00 
1 
0.95 0 .967 
0 .969 
>--
> 
(/) 
(/) 0.90 
E 
w Th ermal Wind ow: 
0.85 
7 8 9 10 11 1 2 1 3 14 
Wa ve length (?m) 
Figure 3.12: Soil emissivity example. This spectrum is one of 42 obtained from soils in 
the El Reno area (Grove, 1999) . Thick lines indicate TIMS band-average emissivities. 
where the minimum, band-averaged emissiv ity, <'rni11, is determined from the maximum-
minimum emiss ivity difference (J\J Al D). The coefficients A, Band C in Eq. 2.69 are 
0 .995, -0 .864 and 0.870, respectively. This equation establi shes the function to be used 
in the TES method , as illustrated in the mid ri ght-hand panel in Fig. 2. 11 . 
3.3 Jornada Data Collection 
Al though the focus of thi s study is upon the El Reno data sets, an additional data set was 
used to begin the surface energy flux scale assessment o f a different landscape: semi-
arid range land . Can the observations and conclusions made at El Reno be extended to a 
very different grassland environment? 
The data were co ll ected in the USDA Jornada Experimental Range in south-centra l 
New Mexico, ~ 35 km to the northeast of Las Cruces, and are part of series of semi-
annua l surveys co nducted since 1995 . The Jornada site, lying at the northern end of the 
Chihuahuan desert , is a National Science Foundation Long-Term Eco logica l Research 
(LTER) site, as well as United Nations Man and Biosphere (MAB) s ite. Average prec ipi-
tation at Jornada is 241 mm yr- 1, occurring mainly from localized thunderstorms during 
July-September(Havstad et al., 2000). The surveys are timed to occur before onset and 
after conclusion of this relatively high precipitation period. In this way, observations 
can be made when the differences in surface vegetation due to the wet and dry periods 
are greatest. 
The flight profile locations are shown Fig. 3.14, which are placed to sample a vari-
ety of land cover types . Beneath each flight profile are one or two surface temperature 
validation grid sites (indicated by D symbols). Each site is 30 x 30 m, with re ference 
flags placed at 5 m grid intersections. During flight days, hand-held infrared thermome-
101 
MMD Function 
.00 
0.95 
_>,- 0.90 
> 
(/) 
(/) 
E 
QJ 0.85 -
E S, /S, = 0.0262 
:::i 
E MAD= 0.0042 
C 
2 0.80 
0.75 
. = 0 995-0.864MM D o.s?o 
Em,n ? 
0 . 7 0 LJ___J_._JL.--L-_L.-1--'-..J--L-'--.L--L---'-L.--L---'--'--'-..J--L-'--'----'--'-L-.L---'-'-"'--
0.20 0.25 0.30 
o. oo  0 .05 0. 10 0. 15 MMD 
Figure 3 .13 : Minimum emissivity function . The TES algorithm assumes a functional re-
lationship between an surface observation's minimum emissivity and the range of emis-
sivities. Here the range is labeled 'MMD', for 'maximum-minimum difference' in band 
averaged emissivities. MAD is mean absolute difference. This function is applicable 
for TIMS band averaged emissivities of soil samples from El Reno and ARM-CART, 
Oklahoma. 
102 
ourly intervals. The tempe
ratures obtained ( 49 
 were wa lked through eac
h grid at h
ters
res inferred from 
rvey) can then be compare
d with surface temperatu
fo r eac h ho urly su
ts. 
aircraft and sate llite remo
te sensing instrumen
apart from 
erence between the Jornad
a and the E l Reno sites, 
Another striking diff
t E l Reno 
all , is the loca l topograph
y of the grazi ng lands. A
the obvious an nua l rainf  a 
d homogeneous, whi le at 
Jornada the lands contain
n
the lands are re lati vely sm
ooth a
oppice dunes (Buffington 
and 
shrubs and large c
mix of grasses, numerou 
encroaching 
Herbel, 1965; Rango et al.
, 2000). 
ta are a sign ificant improv
e-
f view, the Jornada da
From the remote sensing 
point o
DJS/ASTER Sim-
 Reno data . At Jornada, 
a single instrument, MO
ment over the El
aboratory, 2001c), made r
a-
ASTER) (Jet Propuls ion L
ulator3, Hook et al. (200 1))
 (M
ed 
, near-infrared wavelength
s up to the thermal infrar
visible
diometric observations for
 
ASTER Airborne Simulato
r col-
I
velengths (tabl e 3.3). Beca
use MASTER (MODIS
wa
t were collected from two 
instruments at El Reno, 
rom a single instrument da
ta tha
lects f
ration of MASTER is tigh
tly con-
greatly reduced. The calib
data registration errors are
 
ands are less than 0.5%) a
nd consequently esti-
lled (differences between 
thermal b
tro s 
d to be consistent ( differe
nces between band
mated surface temperatur
es are expecte
< 1.0?C). 
tudy occurred on 27 Sept
ember 1999 
chosen for this s
The remote sensing fligh
t 
EI 
erformed included the ini
tial steps used in for the 
(table 3.4). The data ana
lyses p
f thermal and visible-near 
infrared data (Section 
eno studies: atmospheric corr
ection o
R  
ection 3.4). The operation
al scale of
3 es (S-6), data registration in ge
odetic coordinat
ea averaged aggregations 
of the surface 
tion 3 .10) from ar
the surface was assessed (
Sec
ting sa tellite on a five-
3 sensors on board the Terra
 satellite, a currently orbi
MODJS and ASTER are 
Year mission . 
103 
Jo rnada Sludy Area 
3620 
2 
36 15 Me qui te 6 
36 10 rronsil ion D HQ 
,,--.... 
E 0 Gro ss 
.Y 
'-1" 3 60 5 
z 
2 
f--
:::) 
3600 
CJ Creoso te 
3595 
32 0 325 330 335 340 
UTM E14 (km) 
Figure 3.14: Jomada site map. Surface temperature grid 
sites,'Mesquite' ,'Transition' ,'Grass' and 'Creosote' are located as shown. USDA 
Ranch Headquarters lies to the east, at 'HQ' . MASTER low altitude flight tracks ( 1254 
meters above the ground) are also indicated. 
104 
Table 3.3 : MASTER specifications. 
Sensor MASTER 
Wavelengths (/tm) 0.44-13.0 
Bands 50 
IFOV (mrad) 2.5 
PixSep (rnrad) 2. 1 
Pixels/Scan 716 
Scan Angle 85.92 
Scan Rates (Hz) 6.25112.5/25 
Remarks 16-bit dynamic range 
Table 3.4: Jornada MASTER flight condi
tions. 
Julian Run Start End Duration
 Altitude Lines 
Day (UT hms) (UT hms) (s) 
(rn) 
7 1254 2685 
271 17:05 :28 17:07:15 10
temperature, serni-variograrns and geogra
phical variance analyses. 
3.4 Georegistration 
e energy balance model needs co-registe
red spatial data of the 
The two-source surfac
se coding. The co-registration 
following kinds: surface temperature, NO
VI and land u
portant because the association between 
surface temperature and land cover con-
is im
 energy flux . In order to compare energy bala
nce models 
ditions determines the surface
the spatial data must 
from survey to survey, an additional regi
stration constraint is that 
I 05 
be placed in one common coordinate system. 
The most general way to accomplish both of these objectives is to elastically deform, 
or 'rubbersheet', un-registered data to a common geographic projection and datum. 
'Rubbersheeting' is a general term describing a process of differentially re-configuring 
a two-dimensional data set into a desired coordinate system. The reconfiguration can 
be based upon a functional form , such as a polynomial, or it can be based upon spl ine 
approximations. At El Reno , image data were registered to the Zone 14, Universal 
Transverse Mercator (UTM) projection system on the 1927 North American Datum 
(NAD27)4 . The UTM system is a cylindrical projection with its axis in the equatorial 
plane, aligned perpendicular to the surface being considered. Because of this orienta-
tion , good scale representation occurs only along north-south longitudinal bands, known 
as Zones. UTM Zones have longitudinal widths of 6? and absolute scale errors of less 
than 0.1 % (Snyder, 1982). 
The geometries of remote sensing image data in this study are of two kinds: Landsat 
TM5, satellite push-broom data (United States Geological Survey, 2001), and aircraft-
mounted (TIMS and TMS) whisk-broom scanners (Palluconi and Meeks, 1985). Push-
broom data are data acquired by a two-dimensional array of detectors (one dimension 
for the spectral bands, another for lateral observations), obviating transverse scanning. 
Whisk-broom scanners have only a one-dimensional array of detectors (corresponding 
to spectral bands being measured), and need a lateral scanning mirror to create a scene. 
The satellite data have excellent line to line and row to row coordination and can be re-
projected to UTM 14 coordinates with little image stretch or distortion. The aircraft data, 
4 NAD27 is based upon the Clarke 1866 ellipsoid and with a datum origin at Meades Ranch, Kansas. 
It has been superseded by NAD83 , which is based upon the (nearly) geocentric ellipsoid, GRS80, with 
datum origin at the center of the earth. Most USGS topographic sheets, however, were surveyed long 
before the establishment ofNAD83 . 
106 
nificant anisotropic distortions (F
ig. 3. 15) and sati sfactory 
on the other hand, have sig
 effort. Under idea l conditions, w
ith no changes 
f
re-projection requires a great dea
l o
 a slightly S-
111 fl attitude or altitude, the footpri
nt of an aircraft scanner follows
aircra
ocations are dependent upon 
shaped pattern (Fig. 3. 15, top).
 The cross-track data l
th scan angle, while the along-track
 data locations are dependent 
e aircraft height and 
changes 
 variable, elliptically shaped, and 
upon aircraft ground speed. Pixel
 resolution is
 platform altitude (Fig. 3. 15, th
ird plot, 
with scan angle (Fig. 3. 15, seco
nd plot) and
nad ir view). Data coverage is als
o variable (Fig. 3.15, bottom), 
showi ng resolution at 
, and scan angle. Actual imagery 
from the 
can rate
and depends upon platform altitud
e, s
 and low-
paign showed both these expected
 distortions, plus high-frequency
El Reno cam
movement. 1t is for this latter con
dition 
lar aircraft 
frequency di stortions due to irreg
u
. 
that algorithmic geometric correctio
n was considered unsuitable
rrections are linear scal-
For very simple georegistration ta
sks, where the required co
k 
g or rotating, it is possible to cre
ate affi11e matrices to do the tas
ll1g, shifting, skewin
 add an additional column vector 
to permit trans-
 that
(Strang, 1993). These are matrice
s
d with soft-
 more complex cases, the georeg
istration process is accomplishe
lations. In
. In this study, this software was
 
ess
ware designed to perform the rub
bersheeting proc
ictable orienta-
d because the aircraft and remote
 sensing instruments had unpred
neede
ENVI (Re-
ere are several choices of softwa
re product available, including 
tions. Th
I 
c. , 2001), ERDAS (ERDAS, 2001),
 ARCView (ESRI, 2001) and PC
search Systems In
5
 study is called GCPWorks , a pr
od-
duct used for this
(PCI, 200 I). The commercial pro
. 
ates in a manner similar to the oth
er geographic imaging software
uct of PCI, and oper
are selected that are recognizable ints (GCP) 
Known ground locations, ground 
control po
P's on 
sensing imagery. GCPWorks was
 used interactively to choose GC
on the remote 
5 ndorsement 
Use of trademark name does not imp
ly e
107 
TIM S Sca n Foo tprint 
-----. 
E 
.::L 
u 
0 
~ 0.2 
I 
CJ' 
C 
0  
<i' -0. 1 '-------------'-
--------_J
0 4000 
-4000 -2000 0
 200
Cro ss - Track (m) 
Pixe l Reso lution vs. Sca n 
Ang le 
-----. 16 
E 
C 
0 
 14 ~
:J 
0 
(/) 
QJ 
0:: 12 
- 20 0 2
0 
Scan Ang le (deg rees) 
Re so lution vs . Alt i tude 
--------~--
----- - --
-----. 60 ,--
E 
C 40 -
0 
:J  o 20 
(/) 
QJ 
0:: 
15 20 
5 10 
Alt itude (km) 
vs Alti tude and Sca n Rote
 
-----. 
~ ----.- .- .- .- ---.... .. ?s~-~~. R~?t?;. (H~) -.. -. -.____. 0 
a.. 
0 
-.:: + 7.3 o 1
2.0 
QJ - 100 
> * 8 .7 t::. 25.0 
0 
-200 15 20 
5 10 
Alt itude (km) 
meter scanner resolution and foo
tprint po-
io
Figure 3 .15 : TIMS scan characte
ristics. Rad
 
y scanner altitude, scan rate, inst
antaneous field of view (IFOV),
sitioning is controlled b
his series of plots shows the cha
racteris-
latform. T
scan angle and ground speed of
 the p
. Negative overlap 
or the TIMS scanner moving at 
50 mis with no attitudinal errors
tics f
IS equi? valent to coverage gap. 
108 
reference image. For each p
ai r of points selected a 
 the source image and on a th ' bo
ining the coordinates of the a
ssoc iated points. 
database is bui lt conta
nned 7.5min 
no study, the GCP 's were ob
tained from spliced and sca
For the El Re
were selected 
h ic maps (themselves georeg
istered!). Over l 00 GCP 's 
USGS topograp
: ther-
registration. Two sets of data
 needed to be georegistered
for El Reno imagery geo
ata . Although both rad iomete
rs 
ar infrared TMS d
mal infrared TIMS data and v
isible-ne
haracteri stics were not the sa
me (table 
ir geometric c
were fl own on the same aircra
ft, the
rences between radiometers c
ause registra ti on difficul-
 l) . 1n prac tica l terms, the di ff
e
J. at 
ble-near infrared data. The m
ain cause is th
ties between thermal infrared
 data and visi
istra tion errors, the georegist
ra-
To reduce reg
TIMS is gyro-sta bilized and 
TMS is not. 
ed 
in two steps. In the fi rst step, 
the TMS data were register
tion process was perfo rmed 
ly regis-
wo radiometer data sets were
 joint
to the TIMS data. In the sec
ond step, the t
tes. This two-step process is b
etter than registering each 
ered to UTM zone J4  coordin
a
t
he raw radiometer coordinate
s 
inates because t
radi ometer data separately to
 UTM coord
TM system. In addition, the 
align-
are more similar to each othe
r than they are to the U
 important in the energy flux m
odeling routines 
ment between radiometers is 
much more
odetic coordinates. 
than is the alignment with res
pect to ge
3.5 TIMS Calibration Assess
ment 
and the two-source energy b
alance model, Eq. 
k between surface temperatu
re 
The lin
ra-
ces and the surface-air temp
erature g
2.45, is created by estimating
 surface resistan
 from similarity 
 study, resistances are assume
d to be accurately estimated
dient. 1n this 
 to be spatially invariant ove
r any particular 
th hile air temperature is assum
ed
eory, w
 the sole, verifiable input to s
urface en-
scene. Surface temperature t
herefore remains as
109 
Figure 3.16: Fort Cobb Reservoir, 35? I O'N , 98?30'W. NDVI image from TMS on 30 
June \ 997 at 4877 m altitude. Black is water, dark gray tones are bare soi l or senescent 
vegetation. Light tones are surfaces with green vegetation. North is to the upper left 
comer. The reservoir is ~ 10 km long. Display is shown in original scan line coordinates. 
ergy flux estimates. Since the better estimates of .H, for example , are accurate to ~ 50 
w - 2 111 (e.g., Twine et al. , 2000), the required temperature accuracy can be determined 
from the derivative of Eq. 2.45 : 
8Hs Pvap Cp (3.6) 
BTs Ta fl + rs 
1f  the total resistance is assumed to be ~ 50 s m- 1, moist air density, Pvap, is ~ 1.225 
kg m- 3 and specific heat of moist air, cp, is ~ l 005 J kg- 1 K - 1 , then surface temperature 
accuracy needs to be ::;2?C to result in a flux estimate target accuracy of 50 W rn- 2 . 
To determine whether or not observations with this level of accuracy are possible, 
some preliminary assessment is needed to check the performance of the six-band TIMS 
instrument. Previous experience (Hook et al., 1992; Jaggi, 1992; Hoover, 1992; Real-
muto et al., 1995b) , had shown that the TIMS instrument was not always precise, and so 
reassurance was needed for the El Reno study. 
At the beginning of the El Reno flights , five TIMS surveys (Table 3.5) were flown 
over a nearby lake, Fort Cobb Reservoir (Fig. 3.16). Imagery of water bodies provides 
110 
ental and data processing tech
niques for thermal infrared 
a use ful way to assess instrum
sivity uncertainties are neglig
ible. Emis-
ts because errors induced by 
emis
measuremen
ared band 
 nearly equal to 1.0 and its varia
bility within the thermal infr
sivi ty of water is
iation over water, the import
ant 
is less than I% (Fig. 3. J 7). B
y measuring thermal rad
 
d temperature error are confi
ned to the radiometer itself
remaining sources of estima
te
e were 
ties. Since the TIMS flights o
n 29 Jun
(TIM S), and uncertain atmos
pheric proper
could 
nty due to atmospheric prop
erties 
made at three different altitu
des, the uncertai
ater near the southeastern -
done by selecting a patch of
 w
be greatly reduced. This was
 
 temperature did not change 
d of Fort Cobb Reservoir an
d assuming that the surface
en
 ARM 
vey period. Time-interpolate
d radiosonde data from the
over the 20 minute sur
) was then 
6 ' (Atmospheric Radiation M
easurement Program, 200 I
ex tended facility ' b
ic transmissivities and radian
ces 
to detem1ine atmospher
used as input for MODTRAN
 
surement were then prelimin
arily 
ual TIMS mea
for each of the six TIMS ba
nds. Act
sing the known water emissiv
ities), followed by the 
orrected by applying Eq. 2.6
4 (u
c
ant surface temperatures wer
e then 
Eq. 2.63. The result
central wavelength solutions
 to 
Schmidt (1998), the initial atm
osphere 
red. Following methods of Sc
hmugge and 
compa
ds. Having 
caled to minimize temperatur
e discrepancies between ban
model was then res
the 
he temperature ?variability ov
er 
now established an optimum
 atmospheric model, t
e 11 ti?r e reservoir was then measure
d. 
996) suggested that some rad
iometric errors 
(1
Hook et al. (1992); Hook and
 Okada 
 incorrect spectral response f
unctions. Although there 
could be induced from apply
ing
-
ccurred, it is possible to asses
s the po
is no way, post-experiment, t
o determine if this o
3.18, the specified spectral re
sponse 
tential magnitudes of such er
ror. As shown in Fig. 
be perturbed by scaling or shi
 fling. 
function for each thermal ban
d can 
1997 (Fig. 2. J 2), and temper
a-
By using the measured atmo
sphere from 30 June 
I J J 
Wa ter Em iss ivity 
.
....
.  
0.995 ..  
2 4 
5 6 
0 .990 
>, .. ... .
... ..  
 
> ...  .... 
 
..  .
.. 
,, .  
0 .98 
VJ ....  ....  ". VJ ...  
" . , 
E :o.986:: .".  ,, 
w 0 .985 ., .,  .. 
:o .984: , , 
.,., ..  ",
.,.,  ....
 , 
  
, , .,., ....  .'   ' , , ..' ..  
'. 
0 .980 , . ",  , " , , .' . ,, ....
. 
,,  
 
10 1 1 1 2 
8 9 
Wa velength (?m) 
Figure 3.17: Water emissivity. Thermal infrared band emissivity spectrum for water (Jet 
Propulsion Laboratory, 200 I b), with TIMS band-averaged responses overlain. 
I 12 
 Bond 3 Response S --~ TIM
--- - -,-------'---
:,,.......s------.----
.or-------.---1
0.8 
11 
C 
g 
t O 6 
0: 
~ 
i a ? 
g 
z 
0 7 
9.5 
9 .0 
8 5 Wovclcnglh (?m) 
?m 
TIMS Bond 3 Respo
nse? Shil led - 0. I 
---,...-._.,,,.......s---'---r-
--- -~ 
----',----
1o r------.-- --
-=--- / 
I 
I 
\ 
~ 0.B I 
\ 
gC
  I 
:: 0 6 
I 
0: 
~ I 
i O 4 
E I 
z0 
 
02 \ 
I ----'=:...ca=-=:a==
..---_J 
_____ =L---o.oL__ _ ___ 95 9.0 
8 5 Wavelength (?m) 
 o f bond widlh , 
 Bond 3 Response:
 Scaled by + 1007. --,-----------TIMS ...,
-=..=..::......::....-=---
.--:..--,----~...--,;;;,,....
1.o r---- I 
I 
~ 0 .8 I 
C 
g 
:! 0 .6 
0: 
~ 
1 0.4 
E \ 
0 
z I 
0.2 I 
9 .5 
9.0 
8 .5 Wavelength (?m) 
unctions . Atmospheric
 
cheme for TIMS respo
nse f
Figure 3.18: Sensitivit
y analysis s
nty is assessed in two w
ays. The 
n errors caused by resp
onse function uncertai
correctio
iddle), and rescaled (bo
ttom) to estimate 
ified response function 
(top), is shifted (m
spec d. 
heric correction is perfo
rme
th ors after atmospe consequent temperatu
re err
l 13 
lar zenith 
voir flights. Altitude is ab
ove water level, SZ is so
Ta ble 3.5: Fort Cobb Re
ser
angle. 
sz 
JD Date Time Run
 Alt 
UT (m) Degree
s 
97 12:49 1524 
72.0 
180 6-29-
180 6-29-97 12: 56 
2 1524 73.0 
29-97 13:08 3 3
048 74.5 
180 6-
 
180 6-29-97 13: 16 
4 4877 75.5
 
181 6-30-97 21 :07 
4877 34.5
 can be demonstrated by
 
 from 35-45?C, the effec
ts of these perturbations
tures ranging se 
mperature of 37 ?C, the T
IMS respon
simulation. Fig. 3.19 sho
ws that at a nominal te
dwidth and show 
pressed or expanded on th
e order of I 00% of ban
fun ctions can be com
nds I , 2, 3 and 4, to l ?C 
or less for bands 5 
rors ranging from less th
an 0.5?C, for ba
er
and 6. 
nt errors in estimated 
esponse function (Fig. 3.2
0) shows slightly differe
Shifting the r
5 ?C, bands 2, 3, 4 and 5 
show less than 
temperatures. For examp
le, in a simulation at 4
75, 
andwidths (TIMS effecti
ve bandwidths are 0.37
0 5 er shifts up to IO% of b- ?C ov
 1-6). 
0 566 p,m
, respectively for bands
-3792, 0.3199, 0.6989, 0.
8326, and 0.6
ared bands 
 and between thermal infr
Investigation of temperat
ure consistency within
uns over Fort Cobb Reser
voir, the modeled atmo-
as performed. For each o
f the TIMS r
W
at-sensor measurements a
ccording to Eq. 2.66. 
oved from the 
spheric effects can be rem adi-
erms are atmospheric tran
smissivity and spectral r
on t
The most significant corr
ecti
nimportant. Consequently
, 
u
the reflected downwelling
 atmospheric radiance is 
ance, but 
 other than uncertainty in
 
 factors
rs in estimated surface te
mperature will be due to
erro
114 
Bond 2 T vs. Resp Fu nc Sca le 
Jg r-~B_o_n_d,-l_ T_ v.;..s:.. ..._R_e: ;..:s:.,;P:....? _F.:;..un....;c;.:... ~S.;..co::l.;..e ~~ J9 
8 
-;;;- J8 
-~ 
s?  .,____, 
~ 7 ,/ V\,,J J7 ~-r,;-r-rl-:,..t...J,1....~l-.l -,.,f..-l,-+-+-+--++"d!..1.-ri 
~ 
a. 
~ 
' J6 
J5 0 .5 1.0 
1.0 - 1 0 
-0.5 0 .0 
Wav
0 el0 0.5 
eng th Scale Foc lor 
-0 5 
Wavelength Scale Factor Bond 4 T vs. Resp Fune . Sca le 
J9 ,...-----,-~--.-:.--:.......;.:...;:_~::_...-
Jg ....-~B_o_n_d_3c_.T... _v.;..s. _Re:;..s.;..P:....? _Fu :;..n....;c.:.. ._S.;..co:..l..e--~ 
-;;;- J8 
-~ 
s?  
~ .:s1 r _ ___. ..;:..;,....::...b,,~.-d"""-.-.,--;::c,.-J 
~ 
f 
~ J6 -
J5 L...... ___ ,__ __ _,L...... ___ .._ ___ j 
1.0 
J5 L..... 0. .5-  --'-~--L...---'-~---' 0 .0 1.0 - 1 0 -0.5 0 .5 Wavelength Sca le Fac tor 
- 1 0 -0.5 0 .0 
Waveleng th Sca le Foc1or 
,-..-_B_on_d'-r-6-T_vs;..... _R,e.c:sP:;..?_F_u:;:..n.:;..c. ~Sc:;.::Ol::e; :....__ 
,........~B_o_n_d_Sc_....T_ v.;..s? :_R._e:;..s.;..P?:. ..._Fu :;..n..c..;.:... _s_co_i_e --~ 39 
39 
. J8 
. 2 
'J: 
s.,   37 
t 
a. 
! J6 
J5 1.0 
- 1.0 -0.5 
0 .0 0 .5 
0 .5 1.0 Wavelength Scale Foc lor 
-0.5 0 .0 
Wovctcng lh Scale Fac tor 
Figure 3 .19: Scaled response functions. Simulated temperature estimates for each TIMS 
band when the response function is expanded or compressed relative to bandwidth. Sen-
sitivities in these simulations are small. For all bands, temperature uncertainty is less 
than l ?C for bandwidth changes up to 0.1 ?m. The greater apparent deviations for bands 
5 and 6 are due to their larger inherent bandwidths. 
l 15 
? B o. no dr  -. 1,  . T-  - v~ s-  . R., e.. s.- p. ..  ,. r. u.: n:. e. ..  .~ Sh.. ;. f; t.  ....:;.,.,......-,...~ _ ,.......,.......;;.B.;;.o..,.,nd:;..,.;:2_T...,..4 ..v6 ;:..s~ R..;;e,S.;.P:...?_F_u~ne_ _. . .:S..,.,;hr_ 0 t_   _,...., 
~ 45.0 f------- -+- - -"-- .c,__-~ 
0 
~ 
t 
>-- ? 4 5 
44 0L,...,-_.,,___....__. ..... _ ....... _~_. ....... ..,J 
-0 OJ0-0 020-0 0 10 0 000 O 010 0 020 0 OJO -0 OJ0-0 020-0.0 10 0 000 0 .0 10 0 020 O.OJ
w Oa  ve le ng th S hift (?m) Wovelength $ hilt (,,m) 
46 B.0 on~ d.  , 3.  .. T.  . v. s-  ~ R- e. s.. p.. . ,. F.. u-~ ne.:. . .. S.. h-. ;. f. t;  
Bond 4 T vs
..  ._ Res_ p. _ Fu, n... e.. ..  Sh;ft 46.0 
., o.__,__.,__  _.__....J..._~-....J.-~c...J 44 .0L..-,-_.,__....__. ....._  ......._ ~_. ....... ..,J 
-0.0J0 - 0 020-0 0 10 0 000 0 .0 10 0 .020 O.OJO - 0 .0JO - 0 .020 - 0 .0 10 0 .000 0 .0 10 0 .020 O.OJO 
Woveleng lh $ hi ll (?m) Wavelength $ hil t (1tm) 
_ ,.......,........;;B.;;.o...,.n.;;.d, .;5_T,..v.;;.s_R_e:,.s;:;,p.;_ . ;.F;;;un..e;
6 :;... 0 .:S ;h;,.;.;f.:t. ,-~
Bond
4  ?6.0  , 6.  .. T..  . v,. s..  . R... e,. s. p.. ..  .. F,. u.. n.. e.- . .. S., h.. ;. J. t-  ......:-.....,...-~--....., 
~ 45.5 
"? 
~ 
44 .0 L-.....__....__  _.__ ......._ ~-....J.-~c...J ., .o...._.....__.,__.....,_..,__.......,_~_......,....J 
-O .OJ0-0 .020-0.0 10 0 .000 0.0 10 0 .020 O.OJO -O.OJ0 - 0 .020 - 0 .0 10 0 .000 0 .0 10 0 .020 O.OJ
W Oa  ve leng th S hift (?m) wave leng th Sh il t (?m) 
Figure 3.20: Shifted response functions. Simulated temperature estimates for each 
TIMS band when the response function is shifted in wavelength. The plots show two 
sources of variation: an overall slope change due to the response functions' position with 
respect to the blackbody spectrum for 45?C, and erratic slope changes due to positioning 
with respect to water vapor absorption bands. 
116 
emiss ivity. 
rrection of Thermal Infra
red Data 
3.6 Atmospheric Co
 in the literature 
ed to correct thermal infr
ared data was discussed
The formu lation need
eated here : 
review chapter (Eq . 2.66
) and is rep
)L 
L >.,sen sor - L>. ,upw
elling (l 
- f _; >. ,dm11nwellin.9
 (3 . 7) 
T;>.. -
L>. ,.rnrfnrr = 
tmospheric components: 
lication requires reasonab
le estimates of the three a
Practical app
 radiative transfer progra
m, MOD-
ic
and L>. ,downwf' ll in .9? The a
tmospher
L >.,up,uelling , T;>.. , 
iosonde (Vaisala Group, 
n 4.0 Berk et al. ( 1998), 
in conjunction with rad
TRAN versio
 200 l) data, is used to cre
ate these 
easurement Program,200 I; Atmospheric Radiat
ion M
hich can model atmosphe
ric properties 
 a Fortran77 program w
est imates. MODTRAN is
hen operated in theI111al lengths. W
m visi ble wavelengths to
 thermal infrared wave
fro
spheric transmissivity an
d thermal radiance are 
s of atmo
radiance mode, spectral 
value
computed. 
ional layered atmospheric
 model. 
e-dimens
The required input to MO
DTRAN is a on
e derived models, are ava
i lable as part of the 
defined models, rather th
an radiosond
Pre-
s study. For example, th
e program in-
ackage, but were not use
d in thi
MODTRAN p
mmer' atmosphere, but t
hese 
the 'U.S. Standard' atmo
sphere and a 'Spring/Su
cludes time of 
dence to the actual atmos
pheric properties at the 
probably have little corre
spon
ected thermal in-
rvations. For this study, 
all atmospherically-corr
remote sensing obse
 radiosonde data . For t
he El 
upon atmospheres define
d from
frared data were based 
a (B4) and Purcell, Oklaho
ma 
 at Vici, Oklahom
Reno study site, radioson
des from sites
Program (2001). These s
ites are 
6 Were used Atmospheric R
adiation Measurement 
(B ) ds. At the 
pectively, from El Reno 
Grazinglan
approximately 85 km and 
J2 0 km, res
117 
l Paso, Texas NOAA
 (2001) were 
sondes lau nched fi-o
m E
Jornada Experimen
tal Range, 
used. 
 atmosphere. Fi rst,
 radiosonde 
proced ure was used
 to define a model
The standard and pressure were 
plotted 
re , pressure, re la tiv
e humidity 
observations of air
 temperatu
the number of obse
rva-
 va lues. For the Ok
lahoma da ta sets, 
and checked for sp
urious
h little conseq uence
. 
e can be removed w
it
d spurio us va lu
tions per sound ing 
is large, an
) relating minimum e
miss ivities to the 
ired is an empi ri ca l 
fo rmula (Eq. 3.5
Also requ
sed in Section 3.2.6. ously discus
ge of em issivities. T
h is has been previ
ran
 L). ,dmvnwPlli11_q 
3 nd
?6-1 Computation
 of T, L>. ,u71111elli11 _q a
lex 
bservations, howev
er, is more comp
radiometric o
The atmospheric c
orrecti on of 
 radiation. As show
n 
ce
r atmospheric attenu
ati on of the surfa
th g fo
an j ust compensatin diome-
re itself contributes 
radiation into the ra
g. 3.2 1, the atmosph
e
schematically in Fi e and the radiomete
r, 
rfac
etween the earth 's s
u
 either direc tly from
 the atmosphere b
ter,
of the entire overlyi
ng atmosphere. 
ndirectly by reflecti
on 
or i
ia tion components 
in Eq. 3. 7, 
atmospheric rad
For the transmissiv
ity and upwelling 
ly time con-
ng angle. But this i
s unnecessari
DTRAN could be r
un for every viewi
MO th view angle and we
ll ap-
ling are smoothly va
rying wi
suming because T>. 
and L>. ,upwel
 secant function of
 the form: 
proximated by a
+ (3.8
) 
Y = asec O b 
res fitting, 0 is the vie
w angle, 
etermined by least-
squa
Where coefficients a 
and b are d
gle. Note that the n
adir view 
ecified an
311d ts either T>. or L>. ,up
welling at a sp
Y represen
quantity is the sum 
of a and b. 
t com-
eric radiation compo
nent, the sign ifican
nwelling atmosph
For the reflected do
w
of moist air. MOD
-
erlying hemisphere
 
n of the ov
putation required is
 the integratio
118 
TRAN simulations are run for a range of propagation ang les (0-85?). However, ra-
di ometer view ang le modeling is not needed because it is assumed that reflection is 
Lambertian (i.e. isotropic reflection). The desired quantity is spectra l radiance, dL z, 
which is the vertica lly downward propagated spectral radiance. In spherica l coordinates, 
an infinites imal area propagates : 
d[, z = dLtolal X COS O X sin Od O d</> (3.9) 
where dL10 101 is determined from MODTRAN output, 0 is the zenith angle, and 1> is the 
azimuth . For the hemisphere, integrate Eq. 3.9: 
= ?rr / 2 l 2rr E 
.l n dLtolal COS OS ill Od 0 d</> (3. 10) 0 . 0 
or 
E = -I 1 rr/21 2rr dL,0101 sin 20 dO dcp (3.1 l) 
2 0 0 
where E is spectral irradiance, typically W m - 2 1,,m - 1? Dividing by the projected area, 
returns the average downwelling spectral radiance, L>. ,dow 1n  welling W m - 2,  ster- pm - 1: 
E 
L ). ,down w elling =r-rr /""'2_r_2_rr-,- o_?_e__d0_d_,./, (3.12) 
JO .JO COS Slll '// 
3.6.2 Empirical Relationships 
Although the previously discussed formulations were used throughout the El Reno study, 
alternative empirical procedures were developed to check that the analyses were done 
correctly and also to help estimate atmospheric properties when nearby radiosonde data 
are unavailable. 192 ARM-Cart radiosonde data sets, spanning the period 29 June- 2 
July 1997, were used to develop the formulations. Range of validity of these are specific 
to the El Reno surveys at 5 km altitude. Water vapor abundances spanned ~ 1.2-6 cm. 
119 
Sensor 
? Sensor 
Atm osph er ic o
tl enuo t ion 
well ing Rad iati
on 
Up
ters. The atmosp
heric attenua-
iome
tmospheric effects
 on scanning rad
Figure 3 .21: A cted thermal radiat
ion 
onal to the path le
ngth (top). Dete
roporti
tion is approxima
tely p ctor, and from 
re between the sur
face and the dete
ace, the atmosphe
comes from the su
rf
spheric radiation (
bottom). 
pagated atmo
reflected downwa
rd pro
120 
losely related 
st6 of the thermal 
infrared band is c
 for mo
Atmo pheric tran
smissivity
y integrating each 
radiosonde's 
w1dance. This is v
erified b
to atmospheric wa
ter vapor ab
's transmissivity ODTRAN
nts and plotting th
e result against M
Water vapor meas
ureme
nship between ban
d 
e a nearly linear r
elati o
st  for each thermal 
band. One can se
e imate ter
 
 3.22). For a gi
ven columnar wa
d co lumnar water
 vapor (Fig.
transmissivities an 0.02 and 0.04. 
issivity estimates r
ange between 
quantity, standard
 errors of transm
n can then be es tim
ated from 
radiatio
i ssivities are es tim
ated, upwelling 
Once transm non-linear as 
and T , however, is
 increasing ly 
etween L upw<%n.9 th
em. The relations
hip b
. 3.23, a quadratic
 relationship 
s shown in Fig
th aches sa tu rat ion. 
A
e atmosphere app
ro  of spectral 
 data es timates wi
th standard errors
MODTRAN
can be fit to the rad
iosonde/
- 2 ster- 1 Jlm -
1. 
ing between ~ I 0
0 and 150 mW m
radiance est imates
 rang in 
onent, downwellin
g radiation, can 
c tion comp
The remaining at
mospheric corre
l relationship betw
een Lr1ownwelling 
A rationa
om the upweJJing 
radiation. 
turn be es timated f
r  
 Fig. 3.24. The int
ercept is at the
n, and is shown innd wer fun ctio
a L,,p,u,,llin.9 is a
 po
ar function used 
by 
e line
ying and is in close
 agreement to th
var
origin, is smoothly
 
,upwelling)-
( 1 )(Lr1ownwellin
g ~ 1.6Lnadir
Schmugge et a l. 
199 fwic-
n be further simpl
ified by fitting a 
g radiation compu
tation ca
The downwellin  t-isual inspection of s
ome actual ou
N modeling result
s . V
DTRA
tional form to the 
MO
g radiance. The rad
iance 
 angular dependen
ce of downwellin
e
put (Fig. 3.25) show
s th es as the 
from zenith, and the
n rapidly increas
 flat up to 40? aw
ay 
Pattern is relatively provide a good estim
ate 
es not 
 Hence the secant 
curve do
horizontal view is ap
proached.
 it had done for upw
elling radi-
own welling radiance
, as
th
of e angular dep
endence of d
tted in Fig. 3.25 
as dashed lines, 
ationship, plo
. However, a stri
ctly empirical rel
ance
n band, ~ 9.4-9.811.
m 
61h e ozone absorpt
io
e exception occurs
 at th
121 
Bond 2 
Bond 1 0,90 T.......,.......~?~? ...? ""f""""~. ....... T 
0 .90 
0 .80 
0.80 
0.70 
0.70 ,-. 
,-. :~ 0 .60 
:j + 0 .60 I 
E + j 0.50 j 0.50 _ R?2 : 0 .90 4 
0 40 
o.?O Se : 0.020 R?2 : 0 904 0 .J l0 
Se . 0.021 S
e/Sy 
O.JO Tou02 = - 0.0782 ? Water + 0 8959 
Se/Sy 0 J l 1 
O.JO Tou8 1 ? -0.08 16? Wo\er + 0.82 16 
0 .20'--"~-'-_,,_....,._....,.,_..l 
5 
020t--~-"~-'-_,,_  _..._..., J 0 
2 J 5 Columnar Water (cm) 0 
Columnar Water (cm ) Bo nd 4 ,...........,.r ......... ~ 
Bond 3 
__ ___  0 .
90 
0 .90 __
0.80 
0 .80 
0 .70 
0 .70 ,._ 
:~ 0 .60 
-~ 
j 0.50 
+ 
_ R?2 : 0 .804 
o. + 0
40 
Se : 0 .034 
40 R?2 : 0 .874 Se/Sy : 0 . 44 ? 
Se : 0 .022 a.JO TouB4 ? - 0.0863 ? Wotcf,- + 0.7 
Se/Sy : 0 .J57 
O.JO TouBJ .. -0.0734? Water+ 0.8399 0.20 .... _ _,___.._..,.......,.,.._+_............., 
2 J 5 
0 .20 t....-'---'"_  _._....,,_...,._..., 0 
Cotu rmior Wa ter (cm) 
0 2 J 
Columnar Wa ter (cm) 
0.90 ______Bo_nd_ 6_ __ ,......... 
0.80 
0 .80 
0.70 
0 .70 
,-. :f 0 .60 
:] 0 .60 + ?l 
?i j 0.50 
g 0 .50 
,!: 0 .40 
0 .40 ll--2 : 0 .8 75 
Se : 0 .0 J7 
Se/Sy : 0 .J55 
0 .J0 
O.JO Tou85 ? - 0.12 12? Water+ 1.0 11 0 .20 ...._.....,_....c_....,._.....,_...,_-',...J 
0 .20L..-.....J~__._....,,_...,._.....,_..., 0 2 Columnar Waler (cm) 
2 J 5 
0 
Columnar Wa l er (cm} 
Figure 3.22: Transmissivity vs. columnar water vapor. TIMS band-averaged transmis-
sivities are nearly linearly related to atmospheric column water vapor. Estimates of T 
from MODTRAN. Radiosonde measurements taken from ARM-Cart data from 29 June 
to 2 July 1997. 
122 
Bond 2 .,...........,. 
Bond 1 6000 
6000 
. f.  5000 
5000 g 
~ .E 4000 
?~ 4000 i~ ~  3000 
' 3000 
~ :::: ?3: 2 000 ' Se 11 7, .3 2000 s:   
-g /;_ 1000 c:i LuP ? JJ00.0 + 5 700 0 ? lou02 a:: 1000 Se/Sy O 795 ::> - 9700 0 ? rou82?7 
0. lvp - J!:,00.0 , 6100 .0 ? lou01 Ot..-_ _,__...,__..,___..,.._.....,_.....J 
:> - 110000 ? lou8 1?2 
Oi....-.,_._...,.._..,___..,.._  __,_ _ _, O.JO 0 .40 0 .50 0 .60 0 .70 0 .80 0 .90 
,o Tronsm issivity 0 .30 0 O 50 0 60 0 70 0 80 0 .90 
rr onsrnissivi ty 
----...,........B ond 3 ..... ~-~~ 
6000 
. 15000 
f 5000 
0 ?E ,aoo ? 
-~ 4000 
~ i 
;; i 3000 
' 3000 
~ ? 2000 
:::: ~ Se : 107. 
3: 2000 
~ Se : 106. a"0 :  1000 Lup ? 5100.0 ? 1100.0 ? lou0 4 
a"0:   1000 ci. - 6700.0 ? Tou84?2 
Lup - J500.0 ? 5!>00 0 ? TouBJ ::, 
ci. - 9~.0 ? TouB.)-2 a 
::, o .40 o .5o 0 .60 a 10 0 .80 o .90 
a 0 .30 a smissivi ly o .40 o .5o 0 .60 10 o.80 o.90 Tr on
0 .30 
Trori smissivi ty Bond 6 
Bond 5 
6000=----..;..,-------
. i 5000 
? 5000 g 
?e 4000 
?i 4000 
i z
~  .3000 
1 3000 e 
~ ? 2000 
'l  ? Se : 136. 2000 ~ 1000 Se/Sy : 0.149 
-g Lup ? 6600.0 t - JOOO,O ? Tou86 
ci. - 41 00.0 ? Tou86-2 a: 1000 
Lup .. 6400.0 -t - 2000.0 ? fou05 ::, Ot.-_.,..._.,.__..,.._...,._  __,__...., 
ci. - ? 600 .0 ? Jou85'"2 
::, 0 .30 Q.40 0 .50 Q.60 0 .70 0 .80 0 .90 
Tronsmissivily 
0.30 Q.40 0 .50 0 .60 0 .70 0 .80 0 .90 
Tronsmissivi ty 
pi?g ure 3.23: Upwelling radiance vs. transmissivity. L upwelling is non-linearly related to 
nted by a second-order polynomial. 
7 ' in a form that can be well-represe
123 
Bond 1 Bond 2 
8000 8000 
f. f. 
i"  6000 " 6000~   
1'  1'  
::::: ? 000 ' 4000 
~ ~ 
_?__ _?__ 
1 "0 
c 2000 "
 
' 2000 
J S e ; I \J . 
c Se : 95 
0 i Se/Sy ?
0 Se/Sy? 0 175  0 141 0 
Ld own ? 5 985 ? I up? ,_ Ldown ? 5. 986 ? Lup?-
0 0 
0 1000 2000 3000 4000 5000 6000 0 1000 7000 J000 4000 5000 6000 
Up . Rod (mw/( rrr2 - s tcr- ?m )) Up. Rod . (mW/ (m"2 - s ter - ?m )) 
Bond 3 B
8000 8000 ~ ---~?..,._.,..
o.n._d, ,4.. ........., 
1 f. + 
i 6000 I- i"  6000 ? 
1'  1'  
::::: 4000 :::;:: 4000 
~ ~ 
_?__ _?__ 
1 -g 
c 2000 "c' 2000 ? 
i Se : 105. 
 Se . 184 . 
0 Se/Sy : 0 . I 6 1 i Se/Sy : 0 .23 1 0 
Ldo wn ? 6 .007 ? Lup??-'0 Ldo wn ? 5.99 4 ? Lup. ., ., 
0 0 
0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 500 0 6000 
Up Rad. (mW/(rrr2-s ter - ?m)) Up . Rod (mW/(m-2 - s lcr - ?m)) 
Bond Bond 6 
8000 ,....._.,..._..,.._...,;....c5~ --,...... ..... 8000 
14  1 6000 ' 6000 
' I 1 1 
~ 4000 ' 4000 
~ 
_?__ _?__ 
-g 
a:: 2000 ? 1 
c c 2000 ? Se : 80. Se : 100. 
~ Se/Sy : 0 .078 i Se/Sy :0   0 .096 0 
Ld own ? 5 . 99 1 ? lup?--- Ldown ? 5. 984 ? Lupo ur m..  ._....__..,.._...,._  _.._....,_...., 
0 I 000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 
Up. Rod . (mw/ (m-2 -ster-?m)) Up . Rod . (mW/ (m"2 - s ter- ?m)) 
Figure 3.24: Downwelling radiance vs . upwelling radiance. Note that the coefficients 
are nearly the same for all TIMS bands (Ldownwell in_g ~ 6.0L~:~~llin_g)-
124 
ide a good model: does prov
(3.13) 
. l I and 3. 12, and t
hen 
is that it can be com
bined wi th Eqs. 3
 3. 13 
The advantage of E
q.
hip: 
the simple relations
analytica lly integra
ted to yie ld 
(3. 14) 
= a/3 + L zenith L>. 
 all the TIMS 
ameter a was virtual
ly constant for
or the modeled atm
osphere, the par
F  the 
a lue of L>.,downwelli
ng lies within
th bands (a = 3-, 00). Becaus
e the v
ermal infrared qua l to each other 
relations can be set
 e
, the two 
nge of va lues repre
sented by Eq. 3.13
ra
nd r the zenith angle: a solved fo
./scc0 i 0 = 55. 77? (3
.1 5) 
'v
= a( vsec0 - l) + L unith 'v
i 4/3 = 
n,/3 + L zPm:11, 
vides a simple way
 to ap-
 conditions, althou
gh empirical, pro
ky
This result for clea
r s
ed atmosphere can
 
ce witlwut integrat
ion. The specifi
lling radian
proximate downwe ~55. 77 ?. 
iew angle need be s
imulated: 
input to MODTRA
N and only one v
describing 
 functions were fit
 to relationships 
derived
To summarize, em
pirically-
pheric radiance 
ic transmissivity (1">
.), upwelling atmos
columnar water vap
or, atmospher
a points for the rela
tion-
,111,>.)- The dat
 down welling atmo
spheric radiance (L
(Lup,>.), and e radiative transfer , th
2, 3-hourly sequent
ial radiosoundings
rom I 9
ships were derived
 f
The starting point i
s to ob-
 response functions
. 
rogram MODTRAN
, and TIMS band
P
 estimate of atmosp
heric columnar 
 band, from an
tain an estimate of
 7 for each T
IMS
' 
mote sensing detec
tor: 
the re
Water vapor beneat
h 
(3.16) 
= a+b(Water_Vapor) T>. 
T>., find 
le atmospheric wat
er vapor. From 
of precipitab
Where Water_ Vapo
r, is cm 
L . : 
1'P,>. via a quadratic f
orm
125 
g atmospheric propert
ies. 
imatin
Table 3.6: Coefficient
s for est
e f g 
Band 
d 
a b C 
.0 -11000.0 5.985 0.
8254 
-0.08 l 6 0.82 16 3500.0 
6!00
0.0 5.986 0.8246 
2 -0.0782 0.8959 3300.0 
5700.0 -970
500.0 -9500.0 6.0
07 0.8293 
3 -0.0734 0.8399 3500.0 
5
.8342 
 0.
0 -6700.0 5.994 0
4 -0.0863 0.7878 5100.0 
110
 -4600.0 5.991 0.8
245 
5 2 .0118 6400.0 -200
0.0
-0.12 1 1
0.0 -4100.0 5.984
 0.8221 
6 -0.1406 0.9820 6600.0 
-300
(3 .17) 
Lup,>. = C+  d 1), + eTJ 
t L ,,p,>.: Las ly, determine L dn,>. 
from 
(3 . l 8) 
Lr1n,>. = f L ;,p,>. 
IMS band are listed in
 table 3.6. 
The coefficients for ea
ch T
y was then performed
 
rror simulation stud
Using Eqns. 3.16, 3.1
7, and 3.18, an e
 
edure can work. The 
simulation specified a
mine how well this al
ternative proc
to deter
diation (asswning an e
mis-
ltant ra
mperature (37?C ), the
n propagated the resu
surface te reated a set of 192, 
 through all 192 meas
ured profiles. This c
sivity of 0.98) outwar
ds
otal atmo-
adiance spectra. Then
, assuming that the t
urface r
atmospherically-filtere
d s
ph  en?  
di"a t1? 0n was corrected c ra
Spher? 1 nar water vapor was kn
own, the exo-atmos
1c co um  listed in table 3.6. 
7, and 3. J 8, and the app
ropriate coefficients
by using Eqns. 3.16, 3
.1
shown in 
 J9 2 simulations for ea
ch TIMS band, are 
for the
The standard deviatio
ns 
retrieved, using the 
ow that actual surface
 temperatures can be 
table 3. 7. The results 
sh
to within J .5-2.0?C ? 
empirical method outl
ined 
' 
126 
Bond 2 
Bond I 10000 
10000. 834 .0 
gra tio n 4 7 1.3 .0
 ri c Integration
 3
Num 
Numeric Inte
ant Integration
 38 12 .5 
Secon In t gro
tion Sec
u" "u'  C  0 
C 
0 6000 u 0 
0"
0: 
0 
:  
 s ter ?m -=---- 2000 W/  m
' s te r J-Lm 
W/m'
1..._:.J..~-----.!
.~ ----=
2000 50 -50 0 50 
-50 O ; th Ang le (degre s) 
Zen;th Angle (deg
rees) Zen
Bond 4 
Bond 3 
10000 
ration 384 7 .0 Nume
r ic Integra t ion 39 4 3 0 
Numeric Integ
n 384 4 .3 Secan t In teg ra
tio n 3950 .0 
Secant Integra
tio
 ., ., u 
u C 
C 0 
0 ''6 
u 0 
0 0: 
0: 
"????? 
/ m 's t e r ?m ~-----=-:---- 2000 W/
m' s t e r ? m 
W
L--..!..-..Jc..
_.__
2000 o 50 0 
50 
-5o -50 s) 
Zen, th Angle (deg
rees) Zen; th Angle (deg
ree
nd 5 Bo nd 6
 
Bo
10000 
06.0 ra tio n 439 1 .0 
Numer ic Integ
ra tion 38 Nu meri c Integ
 
nt In teg ra t ion 
38 18.5 Seca nt Integra
tio n 
Seca
., ., u 
u C 
C 0 
0  
''6 u0 
0 0: 
0: 
______  _ ?_m_ ____
_ _ 
 _ _t e_r
2000 '---w~ /~m-'_s_t
e_ r_?_ 2000 _ w_ / _m_'_s
0 50 - 50 0 50 -50 
Zen;th Ang le (deg
rees) en;th Angle (deg
rees) 
Z
nith angle. Derive
d from 
ownwel!ing radian
ce vs. view ze
eric d
Figure 3 .25: Atm
osph
nch s ite. The six
 plots 
997 from the Vici
, Oklahoma lau
nde data on 2 Jul
y 1
ODTRAN results rndioso epresenting M
nds, with the solid
 lines r
correspond to the 
six TIMS ba
odel: L, ~ a(~ - 1) +  the m
 Ii nes representing
 the best fit using
and the dashed
127 
Table 3.7: Simul ation of temperature error es timate from empirical re lations. 
Band Surface Temperature Error 
Std.Dev.?C 
1. 5 
2 1.4 
3 1.6 
4 1.9 
5 1.6 
6 1.8 
3.6.3 Band-Averaged Atmospheric Corrections 
These radiation components are combined a long with Eq. 2.68 as follows to produce 
radi ance at th e remote sensing detector: 
(3.19) 
Eq. 3.19 shows that both the surface emitted radiance, L.rnr f ace and the reflected down-
welling radiance, Lclownw Lling, are attenuated by atmospheric transmissivity, T, between 
the surface and the detector. 
Eq. 3.19 also indicates that the atmospheric propagation model is wavelength (A) 
dependent. Realizable detectors, however, do not have infinitesimal bandwidths and 
band averaged values for the wavelength dependent components are required: 
(3 .20) 
The first tenn on the right hand side of Eq. 3.20 is nonlinear and computing atmospheric 
effects might cause difficulties (Jacob et al., 1999). 
128 
Fortunate ly, the non-linear terms are very sma ll and certainly less than instrumen-
tal capabi lities. A simu lati on study shows why thi s is so. Cons ider, for example, a 
s implified form of Eq. 3.20, where the reflected down welling component is neglected: 
(3.2 1) 
Separating the mean and difference components resu lt s in three terms: 
(3 .22) 
Eq. 3.22 respectively consists of a product of means term, a covariance term and an 
ordinary mean tenn . Using standard thermal infrared spectral response functions and 
the atmospheric rad iative transfer model program MODTRAN (Berk et al., 1998), the 
va lues of T_x, L>.. ,.mrface and L.x,upwelling were computed. Table 3.8 shows that the covari-
ance term is insignificant- < 0.02%- and can be neglected. By extension, the magnitude 
of the covariance term induced in the reflected down we lling radiance (Eq. 3.20) is even 
small er, and can also be neglected. This means that, even for large bandwidth thermal 
infrared detectors , a reliable correction formula is as follows: 
L .x,sen.rnr = T L.x,mr face + L.x ,upwell + (1 - ?.)L.x,dawnw ell (3.23) 
3.7 Atmospheric Correction of Visible-Near Infrared Data 
Atmospheric correction of visible-near infrared data collected by the TMS Daedalus 
scanner was done to reduce solar irradiance differences and atmospheric path length ef-
fects . Removal of these effects reduces a significant amount of bias in the computation 
of vegetation indices and land use c lassification. These corrections, however, can only 
129 
Atmospheric corre
ctions are simu-
ection simulation.
 
ed corr
able 3.8: Thennal
 infrar
, and an actual at-T missivity of 1.0
ace temperature o
f 3 7?C, surface e
lated with a surf . Radiance value
s are in 
2 July J9 97 over 
central Oklahoma
mospheric profile
 from 
S bands, TM5 ban
d 6, 
r functions used in
clude the six TIM
2 
mW/ (m - ster - p
m) . Filte g 
nd Gu et al. (2001 a
). Band averagin
frared ba
ICS 760 thermal i
n
and the INFRAME
TR
ospheric transmis-
 surface radiance t
o atm
king
. 3.21 induces a co
variance term, lin
of Eq e is much less than
 T>. L>. ,.rnrfnce? 
rianc
ever, simulation sh
ows that the cova
sivity. How  
face 
'
T 'L >. ,surface 
Band T>,L>. ,.m
r
1.98 
TIMSl 9
629.5 
S2 1034
9.5 0.61 
TIM
305.0 -0.03
 
MS3 10TI
4 10499
.1 -2.21 
TIMS
10427.9 -0.6
2 
TIMS5 
 
MS6 9
577.0 2.04
TI
9790.3 8.5
6 
TM5 
-6.99 
INFRAMETRICS
 8851.7 
130 
be considered approximate. Properl y done, atmospheric correction to the reflected mea-
surements considers atmospheric aerosols ( e.g. , Rahman, 200 I)) and bidirectional re-
flection distribution function (BRDF) effects, as well as solar spectrum and transmissive 
losses. Neither the aeroso l properties, nor the BRDF effects, however, are adequately 
sampled by th e TMS radiometer. 
The correction proced ure first considered the attenuation effects of the entire atmo-
sphere upon incoming so lar radiation (Fig. 3.26. As shown earlier in Fig. 2. 14, there is 
~ 6% grea ter atmospheric attenuation of red solar radiation than for near infrared solar 
radiation . Using the same radiosonde profile data used for the thennal infrared data cor-
rection, the MODTRAN program was run in a mode to determine direc tl y transmitted 
so lar irradiance, E sun>., at the earth 's surface (i.e diffuse radiation was not considered). 
The atmospheric properties in the red and near infrared wavelengths are the greatest 
concern because these wavelengths form the bas is of the spectral vegetation indices. ln 
Fig. 3.26, the most important atmospheric absorbers are water vapor (band-type) and 
aerosol absorption. 
The second part of the correction considered attenuation of reflected radiation be-
tween the surface and the sensor. Attenuation was modeled as a function of path length 
between the surface sample point and the sensor, as shown earlier in Fig. 3.21. The 
MODTRAN program was run once again, but in a mode to estimate the path length 
effect. The result (Fig. 3.27), is then filtered by the TMS sensor response functions . 
Note that TMS bands 5 and 7 have nearly the same transmissivities (0.764 and 0.780, 
respectively), which means that correction to the reflected portion of the solar irradiance 
is not important. 
The estimated surface reflectance, P>. was then determined by an equation similar 
to that used by Markham and Barker (I 986) and by National Aeronautics and Space 
13 1 
So lar lrrod ionce 
2000 
,--.... 
E 
:::l.. 
I 
'-
Q) 
(f) 
I 
N 
< 
E 
'--.. 1000 
s: 
Q) 
u 
C 
0 
u 
0 
'-
'-
0 .60 0. 70 0 .80 0 .90 1.00 1.10 
Wave leng th (?m) 
Figure 3 .26: NDVI solar irradiance correction. Solar irradiance above the atmosphere 
(top curve), and solar irradiance on the ground (middle curve) . Response functions 
for the TMS bands 5 and 7, used to create NDVI images, are shown at the bottom. 
Atmospherically attenuated irradiances are 1036.63 and 764.71 W m- 2 ster- 1 ?m - 1 for 
bands 5 and 7 respectively. 
132 
997 
El Reno 2 
1
E 
VJ 
C 
0 
I... 
I-
'-(-l-)- 
VJ 
C 
0 
Q 
VJ 
(l) 
0::: 
0 .60 0 . 70 0.80 0.90 1.00 1.10 
Waveleng th (?m) 
Figure 3.27: NDVI: correction for attenuated reflected irradiance. The band averaged 
transmissivities for IMS bands 5 and 7 are nearly the same: r= 0.764 and 0.780, re-
spectively. 
133 
Administration (2
00 1) : 
1rL>.F (3-24) 
P>. = Esun>. T>. 
ospheric transmis
sivity be-
brated band obser
vation, T>. is atm
Where L >. is the T
MS ca li
 and distance fact
or: 
 zenith angle
and the radiomete
r, and Fis solar
tween the surface
 
(3.25) 
0), and Oz is the so
lar 
ose to 1.
un distance in astro
nomical units (cl
Here, dis the Earth
-S uted from 
 ed and near infra
red bands comp
The reflectivities f
rom the r
zenith angle. ce between NDV
I 
e differen
VI formula 2.74. 
Th
3.24 are then app
lied to the ND
Eq. ances alone can 
be seen 
d from sensor radi
ay, and NDVI esti
mate
computed in this
 w
iances is shown a
s the thin line 
sor rad
NDVJ computed 
directly from sen
in Fig. 3.28. 
. vy 
e reflectance 1s s
hown as the hea
 surfac
h1"s t d f
rom
ogram, while the N
DVI compute f two modes. 
s are arrows indica
ting locations o
e histogram
e histogram. Ab
ove th
dense vegetation.
 
lin mode represents gher 
e represents bare
 soil, and the hi al 
The low mod ctr
fted version of the
 uncorrected spe
ce-based NDVI is m
ainly a shi
as 
Note that reflectan d NDVI h
all reduction in ran
ge. The reflecte
s a sm
he other change i d 
radiance NDVI. T odes are separat
e
, while the uncorrec
ted NDVI m
des separated by 0
.43 NDVI units
l11o
by 0.46 NDVJ unit
s. 
3  Vegetation Cov
er Estimation 
-8
? ? d ? th e ur
ci.a s ce energy b
alance 
 reqmre rn  r 1s
The s ?a 1  di?s
 tribution of vegeta
tion cove
pati urface tem-
s. 2.20 and 2.23), 
partitioning of s
adiation (Rn, Eq
tnodel to determi
ne net r otranspira-
ponents (Eq. 2.46
), potential evap
n com
 soil and vegetatio
peratures betwee
n
transport (Eq. 2.3
0). 
ent heat 
c res istance to tur
bul
tion (Eq. 2.43), an
d aerodynami
134 
NOVI 
0 .050 
0 .4.3 
0.040 ~ 10.46 J; i l 
>-, 
u 0.0.30 
C 
Q) 
::) 
0-
Q) 
L 
L,_ 0 .020 ~ 
0.0 10 . 
0 . 0 0 0 .......:"'-'--.......,.""-'-......__,'-'-__,_,_.__J_.L.._...L--'--"-.....J..--........... __..__. 
- 0.2 0 .0 0 .2 0.4 0.6 0 .8 
NOVI 
Figure 3.28: NOVI corrected (thick line) and uncorrected (thin line) for solar irradiance 
and atmospheric transmissivity. Example data from El Reno, OK on 2 July l 997 . 
135 
3.8.1 NOVI, Fractional Cover and LAI 
NOVI (Eq. 2 .74), as prev iously discussed, is a spectral vegetation index . Theoretically 
it ranges between - 1 and 1, but in practice mostly ranges ~ -0.1-0.8. Values near zero 
represe nt surfaces with no green vegetation, such as water bodies, bare soi l and senes-
cent vegetation. Values towards 0.8 represent surfaces with thick, green vegetation. To 
faci litate the estimation of actua l vegetation, an index alone is insufficient . The repre-
sentati on o f vegetation by NOVI needs to reformulated . Approaches used by Choudhury 
ct al. ( 1987), and shown in Eqs. 2.75 and 2.76, are therefore adopted . These equations 
require local ca libration with respect to bare soil and thick vegetation . This does present 
a difficulty for the El Reno area because the number of field samples is limited to 15 
field -averaged values of leaf-area-indices (LAl , table 3.9) . However, some of the cali-
bration difficulty is not too severe when the sensitivities of the coefficients are reviewed. 
Differentiation of Eqs . 2.76 and 2.75 shows that sensitivities of leaf area index (LAI) 
and fracti onal cover are relative to the /3 and 1 /~coeffic ients is small. 
The sens itivity of LAT to changes in /3 is : 
8(LAI) ln(N DV I *) 
8/3 132 
(3.26) 
where N DV I * is a re-normalized NDVJ. Values near zero represent full cover and val-
ues near one represent bare soil. Remembering that the original NDVI is indirectly 
related to N DV I *, the sensitivity plot of LAI vs. f3 in Fig. 3.29 (top), makes sense. 
For a given value of NDVI, the sensitivity of LAI estimates is inversely related to f3 . 
More significantly, for f3 ranging between 0.5 and 0.65, the sensitivity is typically less 
than 0.2 LAI, except for thickly vegetated areas. For LAI values over 3.0, the canopy 
transpiration rate is essentially at capacity in the two source model configuration, and 
the resultant uncertainty of f3 becomes unimportant. 
136 
Ta ble 3.9 : El Reno lea f area indices . Fie ld averaged measurements 25 June to 2 July 
1997 . Wheat fi e lds are harves ted stubbl e. 
Field Cover LAI Sensescent NOVI 
Total Green Fraction (2 July) 
ERO! Pas ture 4 .66 3.85 . 174 .603 
ER02 Pas ture 3.78 3.31 .124 .601 
ER03 Pasture 4.45 3.57 . l 98 .562 
ER04 Pasture 4.40 4.36 .009 .574 
EROS Pas ture 2 .37 2.24 .055 .5 l I 
ER06 Pasture 3. 19 3.05 .044 .467 
ER07 Pasture 4.42 4.12 .068 .505 
EROS Pasture 3.60 2.76 .023 .436 
ER09 Pasture 2 .73 2.14 .216 .401 
ERIO Wheat 0.65 0.00 1.000 -0.079 
ERi 1 Wheat 0 .58 0.02 .916 .098 
ER12 Wheat I.I l 0.00 1.000 -0.033 
ERI3 Bare 0.00 0.00 0.00 0.020 
ERIS Wheat 1.92 0.06 .969 .034 
ER16 Wheat 3.96 2.90 .268 .570 
137 
Lea f Area Ind ex Sensili vily 
0.50 + 
0.55 * 
0.60 ? 
0.65 6 
<( 
_j 
0 1,r...,,,~ m.........,_._....J.,.,..,.,........,..L.,~,_,_J~ ............~ ~~. ...........~ .....J 
0 .00 0 10 0.20 0 .30 0 .40 0 .50 0 .60 0. 70 
NOVI 
Sensiti vi ty 
Fra c l iona l Cover 
1.0 1/( 
0.5 + 
0.8 
I... 0 .6 
ClJ 
> 0.7 *0  
0 
u 0.6 
0 
C 
..0... , 0. 4 
u 
0 
I... 
u... 
0. 2 
0 .0 ~ ~~.._._._....J.,.,.. ........~ . ........., ....,..~..,.._J.. ............ ,_._._,_~. ........... 
0.00 0 .10 0 .20 0 .30 0 .40 0.50 0 .60 0 .70 
NOVI 
F.i gure 3.29: Sensitivity of vegetation coefficients /3 and (1/~). See Eqs. 2.75 and 2.76 
for LAJ and fractional cover, respectively Sensitivity of LAI is greater than fractional 
cover b ecause the fonner is unbounded, whi.l e the latter ranges between O and I. 
138 
Sens itivi ty o f fractio nal cover- which is c lose ly re lated to LAI- is similarly shown 
in F ig. 3.29 (bottom). Takin g a partial de rivative of frac tional cover w ith respect to the 
(1/c;) coe ffi c ient: 
of = - (N DV !*11{) In (N DV I*) (3.27) 
D(l /0 
w here f is fracti ona l vegetative cover. Fractional cover, as a energy flux variable, has an 
advantage over LAI because it is bounded . As show n in the example plots of Fig . 3.29, 
th e mode led upper lim it of NDVI is 0 .7. 1f an input NOVI value from imagery were 
greater than 0 .7, an infinit e LA I would result. 
T hi s co mput ati ona l hazard is further illustrated in Fig. 3.30. For fi xed coeffic ient 
va lues, f3 = 0.625 and (1 / c;) = O.G, a family o f curves is plotted with a fi xed minimum 
NOVI ofO and an NOV I maximum rang ing between 0.4 and 0 .8 . Such a range is rea li stic 
fo r E l Reno, Okl ahoma. Plotted as asteri sks are green LAI va lues fo r the E l Reno fi e lds: 
OJ, 02 , 03 , 04, 05 , 06 , 07, 08, 09, JO, 11 , 12 13, 15 and 16. Because there are only 
fifteen da ta po ints, it is d ifficult to establi sh with certainty the best empirical re lationship 
to choose. For the flux computations, the curve corresponding to an NOVI maxi mum 
of 0.7 was used. Thi s choice is a compromise between trying to fit green LAI values 
in Fie ld ERO 1 and EROS and avoiding the computation of infinite LAI values. Also 
note that Fie lds ER06-ER09 lie a long a curve best represented by an NOVI maximum 
threshold o f ~ 0.5 . This is not a realistic NOVI threshold for the El Reno site as a whole, 
Because of this, and because LAI in three of four flux monitored sites (the exception 
being ER09) is reasonably predicted when the NOVI maximum is set to 0. 7, no special 
accommodation was made for the anomalous fields. 
139 
t iDVI vs . Lea f Ar ea Ind ex 
8 
o, im um L I 
.c 
v> 
a, 
.c 
t-
0 l__i___i..,,_d~~~uL..L.-L-'-L-'---'---1-'-_j_...J_L-'--'L.J__ 
- 0 .2 o.o 0.2 o.~ o. 6 o s 1.0 
NOVI 
Figure 3.30: NDVl vs. LAI. Observed green LAI (asterisks) are plotted against their 
corresponding image NDVI values. The curves are derived from the Choudhury et al. 
(I 87) relationship. In Eq. 2.75, the empirical value, 1/~ represents soil darkness, rang-
9
mg from 0.5 for dark soils to 0.7 for light soils . A mid-value, 0.6, was used. In Eq. 2.76, 
f3 is a relatively insensitive parameter, and is set to 0.625. This value provides a reason-
able curvature fit between the most heavily vegetated fields ER01-ER05, at the cost of 
underestimating fields ER06-ER09. Conversion to LAI from NDVI is very sensitive to 
e maximum NDVI threshold. Thresholds are needed because of the asymptotic rela-
th 
tionship. The effects of selecting different maximum thresholds is shown by the family 
of curves, where the particular threshold is apparent from its asymptote. 
140 
getation Height and Lan
d Use 
3.8.2 Ve
s of vegetative cover, t
hey 
can retri eve es timate
Although spectra l veget
ati on indices 
terrain, canopy height is
 
 vegetated 
 not measure vegetation
 canopy height. But in
can and 
tant control on surface r
oughness . The degree 
 an impor
important because it has
bul ent energy 
 roughness determines th
e characteristics of tur
spatial patterns of surfa c
e
ld be difficult to obtain,
 
y di stributed canopy hei
ghts wou
exchange. However, sp
ati all
pproach used is to create
 a land 
ist. Therefore the a
and fo r the El Reno stud
y, do not ex
py heights upon the emp
irical Egs. 2.36 and 
use class ifica tion map a
nd to base cano
approach on 30 
2 ken fro
m an unsupervised 
-3 7. Initially, a land use 
class ification was ta
, but also the whole of th
e 
ed not only El Reno
meter reso lution TM5 im
agery that includ
998). The 14 land use ty
pes used for SGP97, 
Gp97 study area (Dorai
swamy et al. , 1
S ere 
able 3.10. However, at E
l Reno, th
along with their nomina
l heights, are listed in T
e, 
pes (indicated by * symb
ols in Table 3.10): Bar
and use ty
Were only fi ve dominan
t l
f these land use types, F
orage and 
Winter Wheat. Two o
Forage, Pas ture, Water 
and 
e same canopy height (0
.5 m). 
igned th
as
t and were ass
P ure, have similar cha
racteristics 
one using finer resolutio
n, 
d
ng the same categories, 
the classification was re
Followi
classification showed gr
eater 
e the TM5 land cover 
TMs data. This was don
e becaus
 
t El Reno. To this end,
 a maximum-likelihood
y than believed to exist
 a
heterogeneit
ed. 
ution imagery was perfo
rm
supervised classification
 of J2  meter resol
3 rce Model Flux Computa
tions 
-9 Two-Sou
e surface energy flux mo
del of Norman et al. 
 and processing scheme
 for th
The theory
 However, implementat
ion of the 
199Sb) has been discussed i
n the previous chapter.
( 
ther explanation. 
lllodeJ in this spatial app
lication requires fur
141 
Table 3.10: Nomina l land use va lues . Land use, canopy height and roughness parame-
ters. Symbols ( *) indica te dominant land use types at EI Reno. 
Cover Code Height (m) Roughness (m) Displacement (m) 
Alfa lfa 0.25 0.03 1 0.167 
* Bare 2 0.1 0 0.01 3 0.067 
Corn 3 0.50 0.063 0.333 
* Forage 4 0.50 0.063 0.333 
Legume 5 0.25 0.03 1 0. 167 
* Pasture 6 0.50 0.063 0.333 
Trees 7 7.50 0. 938 5. 000 
Urban 8 0.10 0.013 0.067 
* Water 9 0.10 0.013 0.067 
* Wheat 10 0.10 0.013 0.067 
Summer corn 11 0.50 0.063 0.333 
Summer legume 12 0.25 0.031 0.167 
Shrubs 13 0.50 0.063 0.333 
Unknown 14 0.10 0.013 0.067 
142 
The two-source model so ftware code was written in the IDL (Research Systems Inc., 
200 I), a vector-based language wi th a large library of mathematical and graphical func-
ti ons. The code was written accord ing to the para llel resistance confi guration (Fig. 2.5), 
and then tested and va lidated aga inst a reference, scalar-based (Quick Basic) program 
(Kustas, 200 l ). The I DL code consists of a main control procedure, two data definition 
procedures, and 6 1 subroutines and functions. Remote sensing data are input in the form 
o f a georegiste red, data array containing three layers7 : surface temperature, NDVI and 
land use. The surface temperature layer is created from multi spectral thermal infrared 
data- TIMS at El Reno and MASTER at Jornada- and processed using techniques de-
scribed in Sections 2.6 and 3.6 The NDVI layer is created from red and near infrared 
bands- TMS at El Reno and MASTER at Jornada- and aga in processed according to 
techniques described in Secti ons 2 .7 and 3.8 . 
The land use layer is created from a supervi sed classification built using ground 
information and all the visible-near infrared bands in TMS. Classification codes used 
are li sted in table 3.10. These codes were created for the entire SGP97 study area, a 
much larger area than the El Reno site, and therefore include land use types not seen at 
El Reno. There are only five significant land use types over the El Reno site: bare soil, 
forage, pasture, water bodies and harvested winter wheat fields . These are indicated by 
* symbols in table 3.10. 
To run the two-source code, a number of control variables need to be set: 
? Meteorological conditions: surface temperature, pressure, humidity and wind 
speed and their respective measurement heights 
? Solar radiation and zenith angle 
7 A fourth layer, emissivity contrast , can also be used to help discriminate senescent vegetation 
143 
? Vegetation and soil rcflectivit ies 
? NOVI thresho lds and empirical coefficients for vegetation (LAI and fractional 
cover) 
? Land use/vegetat ion canopy height table 
? Remote sensor geometry: altitude, view angle and azimuth, instantaneous field-
of-view (!FOY) 
? Data array dimensions and file name 
The two-source model code reads one data entry at a time, combining the surface tem-
perature, NDV1 and land use data values for each surface sample area (pixel) inde-
pendently of every other sample point. The evaluation scheme follows the processing 
path shown in Fig. 2.6 for unstable surface atmospheric conditions. The evaluation 
scheme for stable atmospheric conditions is simi lar, except that no computation of sta-
bility length is made and therefore no iteration is performed. 
The processing passes through three stages: surface cover assessment, energy bal-
ance solving, and iterative revision . 
In the first evaluation stage, the amount of vegetation present is estimated, from 
which estimates of short and long wave radiation penetrating the plant and soil are made. 
By then combining the following components: surface temperature, vegetation density, 
canopy height and meteorological data; the thermal and humidity gradients, along with 
transport resistances, can be estimated. 
In the second stage, these gradients are combined with the previously computed net 
radiation components in the soil and vegetation, to provide an estimate of surface energy 
balance. 
144 
T hen, in the third stage, boundary conditions are checked for constra ints (e.g . no 
condensa ti o n o n so il or vegetati on is allowed during the day) . Co ntingent upon these 
conditi ons, s ur face fluxes from vegetati on and soil are swnmed, the Monin-Obukhov 
stability length is revised (if unstable conditions ex ist), and the proced ure is repeated 
until the estimated Monin-Obukhov length changes neglig ibly ( < 0.00 I). 
The two-so urce model routine, upon compl etion, outputs an eleven-layer map with 
the sa me spatial ex tent as input. The layers a re: 
? So il sens ible hea t flux (W m - 2) 
? Soil latent heat flux (W m - 2) 
? Vegetation sens ible heat flux (W m - 2) 
? Vegetation latent heat flux (W m - 2) 
? Ground heat flux (W m - 2) 
? Net radiation flux (W m - 2) 
? Surface temperature as read from input fi le (?C) 
? NOVI as read from input fi le 
? Land use code as read from input fi le 
? LAI computed from NDVI and control coefficients 
? Aerodynamic resistance in the canopy airspace (s m - 1) 
145 
3.10 Operational Scale Analysis 
Before proceeding to perform the aggregati on experiments upon the TSEB su rface flux 
estim ates, a n assessment of landscape heterogeneity is done to identify the relationship 
between resolution of the remote sensing observat ions and the scales of vegetation on 
the land surface. The dimension of surface fea tures contro lling the surface energy fluxes 
is known as the operational sca le. While there ex ists a full range of operational sca les 
over any surface- from infinitesimal sca les at the molecular level to I OOO 's o f km on 
the g lobal sca le- at the landscape range of resolutions in this study the practical range 
of operat iona l scale is quite narrow. Specifically considering imagery that spans reso-
lutions from ~ 3 meters up to ~ IO km, the operational scale is controlled by vegetation 
size and by human-created land use patterns. 
The identification of the dominant operational scale is expected to show how remote 
sensing image resolution affects surface energy flux estimates. Spatial patterns of veg-
etati on, fo r exampl e, exert a strong influence upon the amount and spatia l patterning of 
ET. For example, a landscape patterned on quarter-section plots should also show 1/4-
mile patterns in ET estimates. But the directness of this relationship is not a certainty, 
given the non-linearity of modeling surface energy fluxes . It may turn out, for example, 
that the mean surface energy flux estimates are similar across a wide range of resolu-
tions, despite confusion of land use cover. By establishing scale measures, based upon 
source data, the sensitivity of flux estimates to resolution can then be referenced to the 
scale of land cover. 
In an effort to maintain objectivity, three slightly different operational scale mea-
suring techniques are used: semi-variograms, local standard devi ation and geographical 
variance. All of these techniques are similar in their use of statistical variance, but, as 
di scussed previously in Section 2.2.2 , they differ in how the spatial variations are com-
146 
putcd . By analyzing spatial patterns in different ways, indications of operational scale 
c an be either confirmed or shown to be ambiguous. 
To summarize: 
? Semi-variograms consider every data point simultaneously and inter-compare them 
by relative distance (or lag). The result is a plot that shows the rate at which data 
points become less correlated with their neighbors. 
? The local standard deviation technique measures heterogeneity by computing the 
average standard deviation of 3x.3 data point clusters. The source data are succes-
sively degraded, with the average standard dev iation computed at each degrada-
tion step . The result is a plot of relative variance vs . scale and is roughly similar 
to the first derivative of the semi-variogram. 
? Geographical variance is a variant of the local standard dev iation technique: it 
computes heterogeneity from a hierarchy of scales in groups of four data points. 
The heterogeneity is computed from the sum of squared differences between each 
group of four values with the groups arithmetic mean. 
These three techniques are applied to the best estimates of surface temperature and 
NDVl for different land cover types . At El Reno, these include: Pasture/rangeland, bare 
soil fields , irrigated fields , and mixed land cover containing harvested winter wheat, bare 
soil and pasture . At the Jomada range, two land cover types are analyzed: mesquite and 
a degraded grassland. 
3.11 Aggregation of Spatial Data 
The purpose of data aggregation in this study is to simulate data observations, and their 
resultant surface flux estimates, at different resolutions . ln particular, the underlying ob-
147 
jcctive is to determine how resolution affects estimates of surface energy fluxes . Us ing 
the highest ava il ab le resolution data sets as a reference, how docs the relative accuracy 
of flux estimates change as progressively lower resolutions are used? 
The basic aggregation scheme is outlined in Fig. 3.3 I . Originall y high resolu-
ti on data sets a re successively degraded towards lower resolutions a long two pathways. 
Along one pathway, derived fluxes, or model outputs, are aggregated . Fo ll owing th is 
pathway, one expects to retrieve the best estimate of aggregate fluxes because the ag-
gregati ons are derived by arithmetic averaging of the best resolution data . Along the 
other pathway, the radiometric observations, or model inputs, are aggregated. The re-
sultant values represent the best estimate of a rad iometric observation at the coarser 
sca le . These aggregated observa tions are input to the two-source flux model, and then 
compared w ith !luxes obta ined from the first pathway. The essential comparison, there-
fore, is between two different flux estimates at a g iven resolution . Because the surface 
ene rgy flu x model is nonlinear, the following inequa lity is true: 
(3 .28) 
In other words, the mean aggregate flux value at any given resolution, does not equal the 
modeled flux value of an aggregate input value. 
The benefit of this approach is that it permits data analyses over a range of scales 
using the same radiometric observations. While it is feasible to construct experiments 
with simultaneous observations using different observation platforms (such experiments 
are in fact being conducted semi-annually over the Jornada study site), the aggregation 
of a single remote sensing data set minimizes instrumental calibration concerns. Instru-
mental errors in one resolution occur equally in all other simulated resolutions . 
148 
AGGREGATION -
L.rn.r J, >. 
L .m.rf ,>. 
P>. 
()>. 
Land11,sem.ode 
Landuse 
TES/SVI 7 1 
r;:;;; 
Tsu.rf 
NDVI 
NDVJ 
Landusem.ode 
Landuse j 
Two-Source~ 
Flux1 
Sur faceFluxes 
Flm;2 
eme. TES is the temperature-emis
sivity separation algo-
Figure 3.3 I: Aggregation sch
 Index ( e.g. NDVI). 
rithm. SVI means Spectral Vegeta
tion
149 
3.11.1 Range of Scales 
The range o f sca les s imulated, for both the El Reno data sets and the Jornada data sets, 
span ~ 3- 1500 m . This range is determined by data limitations, but it is a lso fortuitous , 
because it provides a link between most of the highest ava ilable remote sens ing data and 
the much more common moderate reso lution data (e.g AVHRR's 1.1 km). 
The scale limits are set on the lower end by the best available reso lution. At El 
Reno, a ll the data surveys but one were acquired at 12 m resolution . The exceptional 
survey was at 3 m resolution, but was of limited use. Only the 12 m data had coverage 
over all four flu x sites and on a ll four survey days (29 June-2 July 1997). The other end 
of the sca le range is constrained by the maximum lateral scanning dimension and the 
need to avo id extreme wide view angles8 . For the 12 m surveys, the TIMS/TMS aircraft 
fl ew at ~ 5 km above the ground and had an un-vignetted view of the ground ? 26?. 
This resulted in ~ ?2.5 km coverage to e ither side of the flight path . Considering 
edge effects, alignment of the original data , and the need to retain enough sample points 
(> I 00) for stable moment estimation, the consequent upper scale limit is ~ 1.5 km. 
At Jomada the limitations are similar, with MASTER-derived survey data practi-
cally constrained to scales ranging between 3 m and 1.5 km. However, recently acquired 
imagery from Ikonos (Space Imaging, 2001) has l m resolution. Since much of the het-
erogeneity of the Jornada is known to occur at 5 meter scales or less (Pelgrum, 2000a), 
this is a very useful addition. 
3.11.2 Aggregation Issues 
The aggregation procedures for observations need to address two basic issues: 
8This study assumes Lamberti an reflection for a II wavelengths, but this assumption becomes untenable 
as view angles approach 40 ? from nadir 
150 
? Sampling sca le 
? Data continuity 
Sampling sca les can either be chosen to be integral multiples of the source imagery, or 
they can be chosen to best repre ent resolutions viewed by a variety of remote sensi ng 
ai rcraft and satellites . For the most part , the approach used here was to sample on inte-
gra l multipl es of two because it grea tl y simplified the sca ling process. When resampling 
is done at non-integra l multiples, a partial-pixel resampling procedure needs to be used. 
For the analyses on broad-based sca ling relationships, sa mpling sca les have been 
chosen to be multipl es of 2 times the original hi gh-resolution data. The first interval at 
El Reno and Jornada (respecti ve ly corresponding to 24 and 6 m) was skipped to limit 
the amount of data regeneration. For El Reno the simulated reso lutions were: 12, 48, 
96, 192, 384, 768 and 1536 m . For Jornada the simulated resolutions were : 3, 12, 24, 
48, 96 m. 
The aggregation procedures for observations are of two kinds: one for continuous 
quantities, such as radiometric observations, and another for discrete data such as land 
use classification (Fig. 3.32). 
3.11.3 Aggregation of Continuous Data 
Continuous data includes any spatial data that were observed, or derived from, radio-
metric observations . These observations of spectra l radiance (Wm- 2 ster- 1 ?m - 1) are, 
for all practica l purposes conservative quantities 9, and are aggregated by arithmetic areal 
9 Ifmultip le scattering is significant at the observation scale, then radiances are not conservative. But 
here it is assumed that mu lt ip le scattering effects upon aggregation are negligible. The scales in this study 
are never finer than 3 meters, which means that multiple scattering at the leaf and branch scale cou ld never 
be reso lved. 
15 1 
Moda l Resamp ling 
Figure 3.32: Image aggregation methods. Resampling example, where the original res-
olution is reduced by 1/3. Equally weighted, arithmetic areal average resampling (left) 
was used for continuous quantities (e.g. fluxes) . Modal resampling (right) was used for 
the categorical land use data. 
152 
averagi ng. The prec ise approach depends upon the specific quantity. 
In cases where the derived quantities are physically related to the ori g inal observa-
tions, it is convenient to aggregate the derived quantities to avo id difficulties correcting 
fo r scan angle geometry in geodetic coordinates. This applies to surface fluxes, surface 
refl ectance and emitted surface radiation observations. In other cases, the quantity is a 
derived measure, such as NOVI, LAI and fracti onal cover, a ll of which are considered 
va lid onl y with respect to original spectral observations. In thi s case, it is preferable to 
aggregate the observations. 
The thermal infrared data, from which surface temperature images are created, are 
processed as shown in Fig. 3.33 . Because temperature is not a conservative quantity, the 
aggregated quantiti es must be in terms for the conservative quantity, spectra l radiance 
(W m - 2 ster- 1 /lm- 1 ). Remote sensing observations, Lsen sor at the upper left, are first 
corrected for atmospheric transmissivity (T) and upwelling radiance (L ,,p,>. ) (Section 
3.6). The observations are not corrected for surface emissivity effects. The result is an 
intermediate product known as surface radiance (L .mr f ), which is then processed in two 
ways: 
? L.mrI  is modeled with the TES algorithm at its original , high-resolution scale 
? L.mr f is aggregated, by arithmetic areal averaging, to a coarser-resolution, and 
then modeled with TES. 
The reason an intermediate product, L .mr 1, is created is entirely a practical one. 
TIMS observations are obtained in aircraft-based coordinates (Fig. 3.21 , but the des ired 
aggregations are performed in a geodetic coordinates. The thermal infrared data needs 
to be corrected for atmospheric effects, some of which (T and Lup,>. ) are scan angle 
dependent. These corrections can be made, us ing Eq. 3.7, at the original resolution . 
153 
 coordinates, and the res
ultant values 
ns are done with data in 
aircraft-based
The correctio an then be 
: spectral radiance'
0. Maps of L surf c
are maintained in a con
servative form
stments 
tes and modeled with TE
S without making adju
ina
registered to geodetic co
ord
perature, T.rnrf or T.~ur J
, along with 
e output from TES, surf
ace tem
for scan angle. Th
ith both visible-near inf
rared reflectivity and 
emissivities, f>. and 1:;,, 
is then merged w
land use maps (Fig. 3.31
. 
ectances are estimated, 
is processed 
le-near infrared data, fro
m which refl
The visib ent factor, pro-
ere is only scan angle d
epend
and aggregated similarly
. In this case, th
 ~ ? 20?). 
ately Lamberti an over th
e needed view angles (
m
vided the surface is app
roxi
 is atmospheric transmis
sivity, T>-. (Eq. 3.24). 
The factor dex 
fractional vegetative cov
er, leaf-area-in
The derived quantities, 
surface fluxes, 
n surface,>-.) are also c
on-
(L
ace reflectance (p) and e
mitted surface radiatio
(LAI), surf
re obtained in a non-lin
ear way, they too are 
hough they a
servative quantities. Ev
en t
aggregated by areal aver
aging. 
3-11.4 NOVI Ambiguity
 
cial consideration. Unlike
 the re-
pe
 continuous, derived qu
antity NDVI requires s
The
sure of vegetation 
r and LAI quantities, ND
VI is a non-linear mea
lated fractional cove
. As previously stated, 
aggre-
 is therefore non-conser
vative
abundance (Fig. 3.34). 
It
ct estimates of the quan
tities at 
ould result in corre
gation of conservative q
uantities sh
d quantities are subsequ
ently converted into 
 aggregate
any coarser scale. But wh
en the
NDVJ b. . , am 1gu1.
 ty anses. 
ig. 3.35, 
plest possible aggregation:
 two pixel values. In F
To illustrate, take the sim
ouni et al. (200 I) discus
s 
hb
  the surface emitted radia
tion is Lamberti an. Che
10L,.,,,1 is conserva6ve if
n-Lambertian behavior. 
some implications of no
154 
r Correct for To ,, & Lo,, ,""'"' '""' 
Aggregate 
L.m,.J 
L .mrf 
TES Modeling 
T.mrf 
l ,x 
12 Meter Data 12 x n Meter Data 
Figure 3.33: Thermal infrared aggregation. Surface radiance, rather than sensor radi-
ance, is aggregated because it has presumed to have negligible scan angle dependence. 
155 
LAI 
Frn c tiona l Cove r 
1 .0 
0.8 
0.6 
0 .4 2 
0.2 1 
0 i..,e::_._,_~--'-"~_,_._......_._J 
0.0 ~----'-~-'-~_,_.........-, 0.0 0.2 0.4 0.6 0.8 
0.0 0.2 0.4 0.6 0.8 NOVI 
NOVI 
Figure 3.34: Vegetation cover and NDVI. The relationship between the radiometrically 
derived NDVI and the two quantities fractional vegetation cover and LAI is in general 
non-linear. Non-linearity effects, however, are less severe for sparse vegetation or for 
very thick vegetation. The three labeled curves correspond to the leaf angle distribution 
parameter~' in Eq. 2.75. The f3 parameter, required in Eq. 2.76 for the LAI computa-
tion, is 0.67. 
156 
able 3.11 : NDVI Aggre
gation. 
T
NDVI Fractional L
AI 
Cover 
2 
0.24 0.34 
0.6
0.40 0.57 
1.26 
2 0.89 3.2
9 
0.6
h NDVI of 0.7. 
I of0.l , the other wi
t
th o va lues were consid
ered: one with NDV
e tw
 vegeta ted surface, res
pectively. In 
are soil, and a thickly
These co uld represent
 a nearly-b
traight contour lines. 
servations, these NDV
I values project as s
terms of radiometric 
ob
ear infrared domain, 
while NDVI of o. 7 
 l has a shallow slope
 in the red-n
NOVI of 0. servative, arithmeti c 
VJ values, by the con
as a steep slope. Agg
regation of these ND
h  result in a value falli
ng 
ances, can potentially
averagi ng of red and 
near infrared reflect
. The NDVI ambiguit
y 
d shaped area, depicte
d with crosses
anywhere within the r
homboi
 origin, but the aggre-
ontour lines radiate ap
proximately from the
now appears: NDVI c
id shaped area spans 
a wide 
 shown in Fig. 3.35, 
the rhombo
gate NDVI does not. 
As
ese values, along 
he precise NDVI rang
e is 0.24 to 0.62. Th
range of NDVI value
s. T
es directly) mean NDV
I can be translated 
th the apparent (i .e., a
ggregated NDVI valu
Wi using Eq. 2. 75 and Eq
. 
ely 
ctional vegetative cov
er and LAI (respectiv
Into equivalent fra
2 1. ? 76) as shown in Table
 3.1 -
on are significant for s
urface heat flux mod
plications of this NDV
I simulati
The im he simulation shows oduced by NDVI. T
g because there is a s
cale dependency intr
elin n of 
e soil, with NDVI of 0
.1, and an observatio
th ervation of ba
r
at, for example, an ob
s
between 
 d have an apparent aggr
egate NDVI ranging 
I of o. 7, coul
vegetation, with NDV ing between 
h estimated fractional
 cover rang
0.24 and 0.62 . This 
is a large range, wit
157 
parse vegetation (0 .34) and thick vegetation (0.89). ln heat flux models, a range of thi s 
magnitude is equiva lent to changing the latent heat flux from vegeta tion by 2.5 times 
(Eq. 2.43). The sim ulation also shows that estimating the aggregate NDVl from an 
arithmetic average of higher resolution NDVI observa tions resu lts in a relatively small, 
but noticeable bias of ~ 0.03 (0.5 x (0.24 + 0.62) = o. ,13). 
Fortunate ly, the practical difficulty is likely less than the simulation study suggests, 
as wil l be veri fied in the results chapter. The reasons for this appear to be twofold: first 
because adjacent pixel va lues tend to be similarly vegetated, and second because the 
probability density function of reflectances is mounded rather than uniform (Fig. A.2). 
Consequently, aggregated reflectances tend to be s imilar to the contributing higher reso-
lution reflectances. Further, when the reflectances are aggregated, their values converge 
towards an overa ll image mean value. 
3.11.S Aggregation of Discrete Data 
The non-continuous data consist of land use classifications. Because these are cate-
gorica l, rather than conservative scalars, they cannot be areally averaged. One way to 
preserve some meaning as resolution is reduced is to resample by mode (Fig. 3.32). 
Modal resampling is simple to apply, and is most representative when there is clear 
dominance of one land use type. Where no mode exists, a randomly chosen value can 
be selected. However, this condition was not an issue in this study because the image 
sample population was large with few categories, none of which had simi lar abundances. 
The choice of aggregation procedure does expose a limitation in the current two-
source model implementation. Specifically, the two-source model uses land use to rep-
resent vegetat ion height and roughness. Land use, however, is hierarchical in nature and 
its meaning must change with resolution . Categories that ex ist at a higher resolution 
158 
+ 
- ++ + -I 
.30 t I++ + ++ t ++ + +++++ 
NOVI 0. 7 i +  ++ + ++ +-I-+ 
t NOVI 0 .4 LAI 2.4 * + -1- + LAI 0 .9 +
+ ++   ++   -1-+ ++   
25 f l- + + + + + + + -1-
t + + + 
+ + + + 
+ + + 
++ + + 
+ + + 
+ 
+ + 
Q) 
u + ++ + -1-+ + 
C 
.s 20 - + 
+ 
+ + 
+ + 
u + + 
-Q) + + + Q) + 
O::'. + 
+ + + 
-1- + 
+ 
O::'. 
z + 
+ + 
+ +  
+ + 
+ + + 
15 + + 
+ 
+ + + 
+ + + 
+ + 
+ 
+ 
+ NOVI 0 . 1 
10 + LAI 0 .1 
5 LL--'---....J.L..--'---'-----'--L._...L___[__L__L__l_L._..1.-_L__..L__J_____L___J 
5 10 15 20 
Red Re fl ectan c e 
Figure 3.35: Aggregation of NDVI. Example of NDVI contours in spectral radiance 
space. 
159 
may not ex ist at a lower resolution . For exa mple, the largest extent o f bare soil fi elds at 
El Reno are on the order of I km. So resolut ions coarser than I km would always mix 
the bare so il land use category with some other land use. In the two-source model used 
here, bare soi I exerts no influence upon surface roughness, even if it consisted of 49% of 
the land use image patch. There is some research indicating appropriate ways out o f thi s 
di fn culty ( e.g. Raupach and Finnigan ( 1995) discuss aggregation rul es for resistances), 
but these ways introduce additional complexity and uncertainty that can not be resolved 
with the data available. Vegetation canopy heights are known only approximately on a 
fie ld -by-field bas is, and only for certain field sites. Therefore, no matter what aggrega-
ti on approach is to used for land use, it can only be considered a crude approximation of 
th e actual conditions. Under these circumstances, the modal resampling procedure for 
land use was used. 
3.12 Methods Summary 
This chapter has discussed the techniques that will be used to evaluate the scaling prop-
erties of surface energy fluxes. The remote sensing data sets available include surveys 
over two different landscapes: one in central Oklahoma and another in southern New 
Mexico. Most of the analyses will use just the Oklahoma data. The remote sensing data 
include multispectral visible-near infrared and them1al infrared data at resolutions rang-
ing between 3 and 12 m. At the Oklahoma site, the remote sensing data are augmented 
by ground-level flux measurements as well as low-level aircraft flux measurements, both 
of which are useful for validation purposes. Considerable data processing is required to 
convert the remote sensing observations into surface temperature and vegetation cover 
estimates. 
160 
3.12.J Surface Temperature 
One of the processing steps is to minimize confounding atmospheric effects upon the 
remote sens ing measurements, particularly for the thermal infrared observations. Im-
plementation o f atmospheric correction procedures, discussed in section 2.6.2, is facil-
itated by radiosonde profile data . Later, it was shown that empirical corrections are 
also feasible, but with some loss in accuracy of atmospheric property es timates. The 
profil e data ava ilable over the central Oklahoma site was discussed, including the nec-
essary time-space interpolations. Simulation studies showed that surface tempera ture 
estimates derived from thermal infrared observations corrected by radiosonde data are 
reliable within 0.6- l.2?C. 
Another processing step, correction for surface emissivity (section 2.6.3), was final-
ized by ca librating the MMD relationship in section 3.3. The fitted function was plotted 
and shown to predict minimum soil emissivities within 0.4%. 
The transformation procedure of scanned remote sensing data into geodetic coor-
dinates was discussed, noting that irregular aircraft movements made spatial alignment 
difficult. Although a geometrical reduction procedure- utilizing known aircraft and 
scanner properties- is feasible , the most practical and accurate approach to georegis-
tration is to elastically defom1 every image individually. 
Because previous workers have found instrumental inaccuracy in the TIMS instru-
ment, a procedure to evaluate surface temperature accuracies over a large water body, 
was discussed. However, a preliminary assessment showed that instrumental calibra-
tion is unlikely to be a source of significant temperature estimate error. A series of 
simulations, performed by perturbing the system response functions, were done and the 
result showed that temperature errors due calibration uncertainty are likely to be Jess 
than ~ 0.5?C . 
161 
3.12.2 Vegetation Cover 
Procedures to convert YJS-NIR observations into vegetation cover were then reviewed. 
It was shown that, unlike the TIR observations, atmospherically induced distortions are 
not a major concern but could neverthel ess be accounted for. 1t was shown that the 
vegetation estimates can be derived by transforming spectral indices, such as NDVI, 
into phys ica lly meaningful measures such as fractional cover and LAI. These measures, 
however, are sometimes inaccurate, with LAI estimates off by over 50% under some 
co nditi o ns. Nevertheless, vegetation cover information is essential to surface flux mod-
e ling, and so these estimates must be used . 
On the other hand , es timates of surface roughness caused by vegetation, cannot be 
determined from remote sensing data. In this case, a tabulation of vegetation type and 
typical vegetation heights was presented. 
3.12.3 Flux Computation 
Once the surface temperatures and vegetation cover estimates are made, spatial surface 
energy flux estimates can be made. The implementation of the two-source model-
di scussed in detail in section 2.4- was then described, including a listing of needed 
control variables and order of computation. 
3.12.4 Operational Scale Analysis 
Three ana lysis of heterogenei ty procedures, previously reviewed in section 2.2 .2, were 
then summarized. The procedures are semi-variograms, local standard deviation, and 
geographical variance techniques, and will be app li ed to both the observational remote 
sensi ng data and the modeled surface energy flux images. 
162 
3.J 2.5 Aggregation Pro
cedures 
n. It was shown how 
apter di scussed the mecha
nics of image aggregatio
Lastly, thi s ch
nces at higher resolutions
 can be aggregated to 
ensing observa ti ons of ra
dia
remote s
ation of derived 
ns at lower resolutions. 1t w
as also shown that aggreg
simulate observatio g 
uity problems that are not p
resent when aggregatin
quant ities can crea te bias 
and ambig
deling, the main difficulty 
lies with the aggregation 
es . In surface energy flux 
mo
rad ianc
lationship between remot
e 
use of the non-linear re
of vegetation re lated mea
sures beca
nsity. 
sensing observa tions and 
vegetation de
163 
T Estimates and Sc
aling 
4 Results: E
Properties 
4.J Chapter Over
view 
he results from the El
 Reno, 
e two study sites wi ll 
now be presented. T
The resu lts from th de: vali-
) remote sensing surv
eys inclu
 Great Plains Exper
iment 1997 (SGP97
Southern terogeneity, and 
 fluxes, determinatio
n of landscape he
ace energy
dation of modeled s
urf
. Preliminary analy
sis 
estimates made ove
r a range of scales
comparison betwee
n flu x 
co, was also perform
ed 
ew Mexi
ite, the Jornada Exp
erimental Range, N
from a second s to opera-
obustness of the agg
regation approach 
y to test the r
to provide an opport
unit
elected to illustrate 
t from one flight line
 over Jornada was s
tional sca le. A surve
y segmen
ected by viewing a c
om-
f
 surface temperature
 and NDVI are af
how scaling propert
ies of
ions are discussed 
pe. These results an
d research conclus
dsca
pletely different kin
d oflan
in Chapter 5. 
curacy of Remotely ma: Ac
4.2 El Reno, Okla
ho
d Surface Temperat
ure 
Estimate
El Reno were inves
tigated 
acy of derived surfa
ce temperatures at 
Consistency and acc
ur
ements. The consist
ency 
sed measur
g TIMS measureme
nts with ground-ba
by comparin  from TIMS 
 sample of greater t
han 100,000 pixels
ecting a
estimates were mad
e by sel
own in Table A.2). light details sh
une 1997 over Fort C
obb Reservoir (f
run I on 29 J
b reservoir were no
t taken, so 
rt Cob
e temperature meas
urements of the Fo
Water surfac
164 
an accuracy test could not be done. However, because water has a known, and nearly 
constant ( ~ 98%) emissiv ity, uncertainty in atmospheric corrections to sensor measured 
rad iances is significant ly reduced. Hence, the reservoir imagery can be used to check 
for preci s ion of the TJ MS-derived temperatures with in and between bands. 
The needed correct ions were performed by atmospheric profile construction from ra-
diosondes launched at ARM extended facility site ' b4 ', modeling with the MODTRAN 
program, and direct applica tion of Eq. 2.66 . Because four sequent ial TIMS flights were 
made over the reservoir at a ltitudes ranging from I 500 to 5000 m, the derived atmo-
spheric profile cou ld be checked. 
The data include over I 00,000 samples for each band and are shown (Fig. 4 . I) as 
a series of s ix box plots, one for each TIMS band. The median temperatures plotted 
represent the water skin temperature in an area ~ J x I km near the dam. The first and 
third quartiles are indicated by the box limits and represent not on ly the samples from 
this se lected area, but also de-trended samples from the full length of the 20 km lake. 
The whiskers indicate the extent of the lower and upper fences, at 1.5 x the inter-quartile 
range. 
The temperature consistency results (Fig. 4.1) show less than 0.3 ?C variation within 
each TIMS band and ~ l .5?C variation between TIMS bands. Bands 4 and 5 show 
the least variation (? I ?C ), while band 6 has the greatest variation (? 3?C ). These 
results show that stability of individual bands is good, although not quite as good as 
the 0.1 ?C sensitivity discussed in Palluconi and Meeks (1985). The more significant 
result is the l .5 ?C variation observed between thermal bands. Since thermal emissivity 
of water is we ll known, thi s variation is due either to atmospheric correction errors or to 
instrument calibration problems. Since the sensitivity of the modeled atmosphere was 
evaluated according to the methods of Schmugge and Schmidt ( 1998) and found not to 
165 
TIM S a t Fort Cobb Rese rvoi r 
.32 
,--..... 
V) 
::i 
V) .30 
QJ 
u 
-----
QJ 
'--
::i 
0 28 
QJ 
Q_ 
E .......'??? l?? rn 
QJ 
f-
'--
QJ 26 
~ 
0 
3:: 
24 
8 9 10 11 12 
Wavelength (?m) 
Figure 4.1 : Fort Cobb Reservoir, TIMS-derived temperatures. Box plot of TIMS derived 
temperatures for all six thermal bands from 29 June 1997. Median temperatures, dashed 
mid-line , are within 1.3 ?C for all bands. Each box is bounded by the first and third 
quartiles. Whiskers extend to the upper and lower fence at 1.5 x IQ range. 
be a source of significant error, it is likely that the 1.5?C error is almost entirely due to 
TIMS inaccuracies. Although J .5?C is greater than the preferable l ?C accuracy (Section 
2.6), it is close to I ?C , and should still permit meaningful energy flux modeling. 
The TIMS surface temperature accuracy was assessed by viewing selected targets 
over the core El Reno study sites (ERO!, EROS, ERO9, and ERl3). The mean TIMS sur-
face temperatures were obtained from a 3x3 pixel cluster ( each pixel at 12 m resolution) 
centered over the study site tower. Surface temperatures were measured by continuously 
recording, tower-mounted infrared them1ometers simultaneous with the TIMS surveys. 
The temperatures obtained at each site for each survey day are listed in Table 4 .1. They 
166 
are also plotted in Fig. 4 .2. 
Some cau tion is necessary when interpreting these results. The tower-mounted ther-
mometers have a small footprint compared with TIMS footprint , 2 m vs. 12 m. This can 
cause a strong bias beca use the tower thermometers may be measuring a pa tch of the 
surface atypical of the immediate surroundings. The tower th ermometers a/so return a 
difTerent kind of tempera ture from that es timated by TIMS. lt is known as a brightness 
tempera ture (Norman an d Becker, 1995) and assumes that the surface is a blackbody. 
Brightness tempera ture and ac tua l tempera ture are nea rly the same over thick ly vege-
tated surfaces ( e.g. , ERO 1 and EROS), but surface brightness tempera ture over areas with 
s ignificant exposed so il (e.g. , ER1 3) will be lower than the actual surface temperature, 
because emissivi ty effec t in these conditions are significant. This can be readily seen 
by inverting Eq. 2.24: 
(4. 1) 
When emissivity, f, is ass umed to be 1. 0, T is a brightness tempera ture. If the ac tual 
emissivity is substantially less than 1.0, T is greater than the brightness temperature. 
TIMS temperatures have been derived from the TES algorithm (Section 2.6.3) and rep-
resent actual surface temperature, not surface brightness temperature. 
Mindful of these differences in temperature measures, the comparison between TIMS 
and ground measurements shows agreement within a range of ~ 1.5?C for morning sur-
veys, but absolute differences of 3?C or greater for afternoon surveys. The differences 
seen for the morning surveys are consistent with precision estimates made over Fort 
Cobb reservoir. Ground observations of bare soil fi eld ER 13 brightness temperatures 
are lower than TIMS estimates by 3?C or less, which is consistent with expectations. 
The differences observed for the afternoon are significantly greater than the target I ?C 
accuracy and are difficu lt to explain. There were no changes in operational procedures, 
167 
Table 4.1 : El Reno temperatures compared. 
Surface Temp. ?C Temperature 
Site Day Time (CST) 
0
Ground TIMS Difference c 
33 .10 33.70 -0.60 180 l 0.75 
l 81 14.75 33.00 
36.20 -3.20 
182 10.75 32.80 
33.80 -1.00 
33.70 39.90 -6 .20 182 14.25 
183 10.25 33.10 
32. 10 1.00 
34.80 36.00 -1.20 
5 180 10.75 
I 81 14.75 36.40 
39.00 -2.60 
5 
36. 10 36.10 0.00 
5 182 10.75 
43.40 -5.50 
5 182 14.25 
37 .90 
37.50 34.50 3.00 
5 l 83 10.25 
30.60 35 .70 -5 .10 
9 180 10.75 
31.60 39.00 -7.40 
9 181 14.75 
30.30 36.50 -6.20 
9 182 10.75 
14.25 31.90 
44.40 -12.50 
9 182 
10.25 30.40 
35.20 -4.80 
9 183 
10.75 31.10 
34.10 -3.00 
13 180 
39.40 -6.003  3.40 
13 I 81 14.75 
38.30 -2.00 
13 182 10.75 
36.30 
52.60 -10.904  
13 182 14.25 
1.70 
42.50 -1.20 41.30 
13 183 10.25 
168 
El Re no Sur face T empero tu res 
55 , --
? AM Surveys 
X P M Surveys 
50 ER09 Sil 
,--.. 
l/1 
::J 
l/1 45 
Q) 
._u__ _, 
r-
~ X 
u 40 
C 
::J 
0 
Cl X 
D< 
35 
X % 
~ 
30 ~ 
30 35 40 45 50 55 
TI MS (Celsius) 
Figure 4.2: Surface temperature validation at El Reno . Radiometric temperatures ob-
tained from TIMS observations and from tower-mounted infrared thermometers at four 
fields sites, EROl, EROS, ER09 and ER13 . They are compared by time of day, for sur-
vey days 29 June-2 July 1997. Mid-morning surveys are shown with D symbols, and 
mid-afternoon surveys are shown with x symbols . ER09 measurements are additionally 
labeled with 6. symbols. 
169 
ei ther for the ground-based meas urements or for the TIMS observations, yet the compar-
ison consistently shows no less than a 2.6?C di sc repancy between them. This suggests 
that the afternoon surveys may not permit accurate surface energy flu x estimates. 
The plotted temperatures in Fig. 4.2 a lso show the anomalous behav ior of field ER09 
(~ symbols). Fie ld ER09 appears in TIMS imagery to be 5 to l 2?C warmer than the 
ground-based measurements, and the temperatures are anomalous for both morning and 
afternoon hours. Whereas temperature comparisons for fields ERO I , EROS , and ER 13 
occasionally show di screpancies greater than 4?C, none of which occur in the morning 
surveys, the temperature comparisons for ER09 are always greater than 4?C . Because 
the TIMS observati ons are otherwise consistent wi th gro und based measurements, there 
is no reason to expect that TIMS observations of ER09 should be subject to specia l 
observational errors. The most plausible explanations for the temperature discrepancies 
therefore are that e ither the ground-based temperature measurements are inaccurate, 
or that the surface sampling area seen by the ground-based radiometer is significantly 
different from the TIMS sampling area. In the latter case, the ground-based radiometer 
might have sampled a 2 m footprint of wet, cool soil , whereas the 12 m footprint sampled 
by T IMS was mostly dry, warm soil. In either event, ER09 TIMS observations cannot be 
corroborated by ground-based measurements. This result, however, has only a limited 
implication. Since three out of four sites showed good temperature comparisons, the 
poor comparisons at ER09 mean only that further flux modeling results there should 
be viewed as tentative. Had there been less than three good site comparisons, then the 
evidence would strongly suggest that TIMS observations were inaccurate. 
When field ER09 temperatures are excluded from the comparison, a consistent pat-
tern is seen. Morning surveys by TIMS agree within ~ I ?C of ground observations. 
Mean temperature error is -0.6?C, with a relative error of -1 .6%. This assumes that a 
170 
small ( ~ 1-2? ) increase to ER I 3 ground observati on can be made to correct for emis-
s ivity effects. Exc luding the field ER09 results and performing a pair-wise /-test on the 
morning observati ons shows that the difference between mean tower temperatures and 
mean TIMS temperatures (l va lue=0.953 , n =0.368, N=9) is not significant. A similar 
test on the afternoon observations, however, shows that the mean tower temperature 
and mean TIMS temperature are significantly different (t value=4 .774 , n=0.005 , N=6) . 
Mid-a fternoon TIMS temperatures, on average, are too high by ~ 5.7?C ( 13.7% re lative 
error). As previously noted, there is no verifiable explanation for thi s increased error for 
the afte rnoon surveys. It is possible that TIMS calibration or aircraft configurations are 
causes (e.g., Hook et a l. , 1992), but it is now impossible to check these possibilities. 
Surface temperatures obtai ned from the City of El Reno sewage treatment ponds 
provide some additional , semi-quantitative corroboration (Table 4.2 , N= north cell , S= 
south cell) to the land surface temperatures. Temperatures listed for TIMS were obta ined 
by averaging ~ 200x400 m of water surface in the two treatment cells. The ground-based 
measurements were taken at an unspecified, mid-day time by co llecting jugs of water 
samples and measuring the temperature with a contact thermometer. Temperature dis-
crepancies of 1.5 to 2.5?C are small considering the uncertainties of the ground data. 
The uncertainties are caused, in part, because radiometric temperature of the water sur-
face is frequently different from water temperatures just below the surface. This occurs 
because water at the surface is subject to evaporative cooling effects not present below 
the surface. Additional uncertainty is caused because the precise time and method of 
temperature measurement of the jugs of water are unknown. Considering these prob-
lems, discrepancies of 1.5 to 2.5 ?c are small. This result gives additional support to 
consider ER09 temperatures as experimental error. 
171 
Table 4.2: El Reno treatment pond temperatures . 
Site Day Time (CST) Surface Temperature 
Temperature 0 c Di ffercnce ?C 
Water TIMS 
P(N) 181 mid-day 26. 1 28.5 -2.4 
P(N) 182 mid-day 26.7 29.0 -2.3 
P(S) 181 mid-day 26.3 28.4 -2 . 1 
P(S) 182 mid-day 27.3 28.9 -1.6 
4.3 El Reno, Oklahoma: Validation and Calibration of 
Vegetation Measures 
Va lidation and ca libration of NDVI and LAI relationships were performed according 
to methods described in Sections 2. 7 and 3.8. Fourteen field sites were avai lable with 
measured LAI values. Table 4.3 shows these, along with LAI estimates. The parameters 
selected for Eqns. 2.75 and 2.76 were as follows: NDVImin = 0.0, NDVIma:,: = 0.65, 
f, = 0.6, and /3 = 0.625. 
Applying these values results in the curve shown in Fig. 4.3. It is readily apparent 
that the model underestimates LAI values in every case. In some cases, LAI is under-
estimated by 50%. A significantly better fit could have been made if the N DVI  max 
threshold was set to a lower value of about 0.55. However, the subjective optimization 
with the imposed constraint on NDVI limits was chosen because it does not truncate 
high NDVI values in the TMS imagery. 
172 
Table 4.3: Leaf Area Index estimates 
LAI 
Site NOVI L
AI 
Field TMS Difference 
EROl 0.603 3.85 
2.53 1.32 
0.601 3.31 2.48 
0.83 
ER02 
ER03 0.562 3.57 
1.92 1.65 
2.06 2.30 
ER04 0.574 4.36 
J. 48 0.76 
EROS 0.511 2.24 
ER06 0.467 3.05 
1.22 1.83 
2.68 
ER07 0.505 4.12 
1.44 
ER08 0.436 2.76 
1.07 1.69 
ER09 0.401 2.14 
0.92 1.23 
ER IO -0.079 0.00 
-0 .12 0.12 
0.02 0.16 -0.14 ERi 1 0.098 
ER12 -0.033 0.00 
-0.05 0.05 
-0.020 0.00 -0.03 
0.03 
ERl3 
0.06 0.05 0.01 ER15 0.034 
0.89 
ER16 0.570 2
.90 2.01 
173 
LAI vs. NOVI 
6 
5 
6. 
6. 
4 
6. 
6 
6. 
<( 3 6. _j 
6. 
 
6. 
6.
2 
0 L.__L-.J'-A-,U .v.Li..a::>J_Jj'---'--'.--l__l.__!.___l___l__L_J_--1....__J___J___J__j_---'-....J 
- 0 .2 0 .0 0 .2 0. 4 0 .6 0 .8 
NOVI 
Figure 4.3: Leaf Area Index observations vs . estimates. The curve is based on the 
empirical relations from (Choudhury, 1987; Choudhury et al., 1994). The relations set 
are: bare soil at NOVI of 0.0, I 00% cover at NOVI of 0.65. Field measured values are 
shown as 6, and are also listed in table 4 .3. 
174 
4.4 El Reno, Oklahoma: Estimation and Evaluation of 
Surface Energy Fluxes 
The El Reno remote sensi ng surveys consisted o f e leven fli ghts starting on 29 June and 
ending 2 July 1997 (Table 3.2). Four remote sensing survey were flown just a ft er sunrise. 
Beca use the sensible and latent heat flu xes during this time are low, these fli ghts were 
not used in thi s study. Another fo ur were fl own during mid-morning (~ I 0:30 CST), 
of which three conta ined sufficient coverage for flux modeling'. The remaining three 
fli ghts occurred during the mid-a fternoon (~ 2:30 CST), o f which two were flown within 
15 minutes o f each other. Because the amount and partiti oning of surface energy flux 
is highly dependent upon the time of day, va lidation of modeled flu xes is considered 
separate ly for mid-morning and mid-afternoon times. 
4.4.1 Ground-Based Flux Measurement for Validation 
Independent estimates of the surface energy flu x are required to va lidate the implemen-
tation o f the two-source model technique at El Reno. The primary validation source 
is from the four eddy-covari ance stations : ERO! , EROS, ER09, and ERl3 (Fig. 3.2). 
These sites range from heavily vegetated grassland (ERO!) to bare soil (ER13). The 
eddy-covariance (E-C) measurement of fluxes (Section 2.5) is currently considered the 
most accurate way to measure surface sensible and latent heat fluxes. Although the E-
C technique does have its own limitations, such as an inability to work in very light 
winds and uncertainty about the necessary averaging period, the results from E-C mea-
surements appear to be very sensitive to mean changes in flux. At El Reno, the E-C 
measurements of evaporative flux are sensitive to LAl, as indicated in Tab le 4.4. With 
1T he fourth was a low-a ltitude run and had limited north-south coverage. 
175 
evaporative flux measured by eddy-cova
riance observations. 
Table 4.4: Vegetation vs. 
Site LAI Evapora
tive Flux 
 oefficient of 
Green Total Mean Standard C
Deviation Variation 
(wm- 2) (wm-
2) 
03 
ERO! 3.85 4.66 512 
53 0.1
53 0.112 
EROS 2.24 2.37 470 
0.082 
ER09 2.14 2.73 585 
48 
ERIJ 0.0 0.0 254 
144 0.569 
face temperature 
the exception of field ER09 (which is 
wetter than expected from sur
vegetation and evaporative 
observations), a consistent relationship 
exists between green 
ases 
. As leaf area index (LAI) decreases fro
m 3.85 to 0, the evaporative flux decre
flux 
 m- 2 indicating that about half of the to
tal ET originates from vege-
from 512 to 254 W , 
tation and ha! f from the soi I. 
sponding to the re-
The complete set of JO-minute average
d E-C observations corre
ention adopted is for H, LE, 
mote sensing surveys is shown in Table
 4.5. The sign conv
 
  be positive for fluxes away from the su
rface, and Rn to be positive for fluxes
and G to
. The 
ards the surface. The table is organized
 vertically by survey time and location
tow
source 
x components are tabulated in pairs ho
rizontally. Each pair contains the two-
flu
nce estimate. The two-source estimate
s are based 
estimate, and then the eddy covaria
lux esti-
upon the nearest nine pixel values to th
e flux site. This is a 12-meter based f
 meters. This averaging has been done f
or two reasons. 
mate, but averaged over 36 x 36
 errors induced by data registration erro
rs (discussed later 
First, averaging reduces flux
observations are not point 
in Section 4.6.1 ). Second, averaging ref
lects the fact that E-C 
176 
measurements, but are integrations of an uncertain upwind surface Oux footprint (as il -
lustrated in Fig. 2. 7) . The precise shape and weighting function needed to represent the 
Oux footpri nt is unknown , wi th an upwind fetch varying from 50x to 1O Ox the height of 
the E-C instrument (Schuepp et al. , 1990). Since the E-C instrument was mounted at 2 
m, the extent of fetch could vary between I 00 and 200 rn . Recogniz ing that most of the 
we ight in footpr int weighting schemes occurs within the first 1/3 of the fetch extent (see 
right hand illustra tion in Fig. 2.7), a minimum averaging window should extend at least 
to 33 m. Averaging over a 36 x 36 meter area, or 3 x 3 pixe ls, approx imates this fetch 
foo tprint estimate. 
Si nce only four E-C validation sites were avail able, a stati stica l comparison on a 
survey-by-survey basis is difficult to evaluate. However, if surveys can be mean ingfully 
grouped by time of day, when turbulent energy flux conditions are most similar, the 
sample sizes can be increased. A review of the near-surface meteorology for 29 June-2 
July (Table C.2) shows no significant changes in weather, suggesting that time-of-day 
grouping can be done. Air temperature, humidity and solar radiation did not have large 
variations from survey to survey. As shown in Table 4.6, the coefficient of variation 
for these quantities were 6%, 15%, and 3%, respective ly. These values mean that the 
meteorological observations are quite similar over the four days. The observations also 
show that relative humidity is the most variable component. Consequently, the greatest 
errors caused by time-of-day grouping will be seen in the LE estimates. The least errors 
will be seen in estimates of net radiation, since the solar radiation values show low 
di spersion over the 29 June-2 July time period. 
When all the flux data from Table 4.5 are plotted (Fig. 4.4), it is seen that estimated 
fluxes do tend to cluster by time of day. In the figure, morning energy flux values are 
indicated with asterisks and afternoon flux values are indicated with open squares. Note 
177 
Table 4.5: El Reno mean fluxes at eddy-covariance sites. ?: Mid-morning, x : Mid-
afternoon. 
Day Run Site H LE G Rn 
TSEB E-C TSEB E-C TSEB E-C TSEB E-C 
June 29 40 ERO ! 102 125 456 377 64 126 623 628 
June 29 40 EROS 86 160 448 404 81 67 617 632 
June 29 40 ER09 74 J 10 428 397 111 129 613 637 
June 29 40 ER l3 139 90 291 432 184 150 615 67 1 
June 30 Jx ERO ! 83 43 493 523 52 41 629 607 
June 30 Ix EROS 128 85 409 468 65 66 603 619 
June 30 Ix ER09 90 46 411 574 108 - I 6 609 604 
June 30 I x ER l3 264 153 155 397 180 51 600 60 1 
July OJ ID ERO! 90 77 507 471 44 79 642 627 
July OJ ID EROS 117 132 431 423 76 57 625 612 
July 01 JD ER09 45 69 471 461 121 103 638 634 
July 01 l ? ERJ3 258 218 167 276 182 112 608 606 
July 01 2x ER0l 48 -20 564 624 32 45 645 649 
July OJ 2x EROS 1 J3 55 443 538 61 65 618 658 
July 01 2x ER09 170 0 341 683 96 -32 607 651 
July 01 2x ER13 335 275 33 239 158 91 526 606 
July 02 30 ERO! 38 89 493 422 71 69 602 580 
July 02 3 ? EROS 66 132 447 365 72 56 586 553 
July 02 30 ER09 31 72 452 399 109 1 I 0 592 582 
July 02 3 ? ERI3 205 259 169 142 160 133 535 535 
178 
Table 4 .6: El Reno surface meteorology statistics. Near surface air temperature, relative 
humidity and solar radiation for all surveys flown from 29 June to 2 July 1997, with 
mid-morning and mid-afternoon flights considered together. 
Mean S.D. C.Y. 
0
Ta ir ( C) 31.2 1.9 0.06 
RH 0.59 0.09 0.15 
R.rnlar (W m- 2 ) 861 28 0.03 
that the morning LE flux estimates, for example, li e close to the one-to-one line, with 
a slight overestimate bias ( ~ 60 W m- 2) in the two-source estimates. Conversely, the 
afternoon LE fluxes derived by the two-source approach are relatively underestimated 
(~  175 W m- 2) with respect to eddy-covariance estimates. 
4.4.2 Validation of Two-Source Model Estimates: Morning Surveys 
When two-source modeled fluxes for the three mid-morning surveys over four sites are 
considered together, the objective is to reveal whether or not there is close agreement 
between the two sets of flux values, and in particular to determine if there exists bias 
between two-source model estimates and E-C observations. The assumption is made 
that the surface energy balance conditions at ~1 0:30 AM are similar from day to day, 
a reasonable assumption based upon the meteorological observations just discussed. 
As shown in Fig. 4 .5, the two-source (TSEB) estimated flux components, H, LE, G, 
and R-n , are in general good agreement with E-C estimates. Flux values cluster near 
the one-to-one lines in each plot. The plots also indicate some bias in the H and LE 
components, and negligible bias in the G and Rn components. The actual mean values 
for the estimates are shown in Table 4.7, which confirms the bias. But the biases are 
179 
11 rlu x u x 
600 --- ....,.-?-?-,.....-....,.._.......,_..,.....~ 
L[ il
700 "-???,--?.,.---,~?-.,...-?-?1---
500 x 
400 '---. 
:--:: 500 
~ 
.300 n Q) 
X -100 X D 0 
200 D ?E .300 VJ X D I-f) 
1,1 X 
100 l,J 
u  u 20
0
I 
w 0 I w 100 
- 100 "-~-'--- _ _,__.,___,__ , 0 ~ ........................... 1._L..~.-?~~ 
- 1 00 0 100 200 J OO 400 '.:JOO 600 0 100 200 JOO 400 '.:JOO 600 100 
TS EB Es limo le (W/ rn ') TSEB Es lirnol e (W/ rn ' ) 
G il ux 
600 ~.,....,..,...,..,. . .....,..,....~.. , -,...T"'=..-.....,?n??.....,, ... T" '-.-? 900 m?~~~~-......,_,,,,,..,._ _, T' __,  
500 ~ 800 
"E 
400 '---- 700 
~ 
Q) .300 a, 600 
0 0 
-~ 200 E 500 
VJ 
w If) 0 Lu 400 
u 1
0
u 
I 
w 0 ~ .300 
- 100~--...... _,__..__,__.,_....., 200~~--~-...... _,__.,__...., 
- 1 00 0 1 00 200 .300 400 500 600 200 .300 400 500 600 700 800 900 
TS EB Es limote (W/ m') TSEB Es ti mate (W/ m') 
Figure 4.4: TSEB flux estimates. Two-source energy balance flux components from 
surveys on 29 June-2 July 1997 compared with ground-based eddy-covariance mea-
surements. Mid-morning survey results are indicated by ? symbols, and mid-afternoon 
survey results by x. 
180 
small. TSEB estimates of H on average are less than E-C estimates by 23 .5 W m- 2 . 
TSEB estimates of LE on average are greater than E-C estimates by 15 .9 W m- 2 . TSEB 
estimates of G and Rn show insignificant bias (< IO W m- 2) relative to E-C estimates. 
Using linear regression to fu11her assess the relationship between two-source es-
timates and E-C measurements shows that standard errors of estimate are also small, 
where the Se values for all components in Table 4.8 are less than 60 W m - 2 . Since E-C 
systems at El Reno have energy closure errors on the order of 60 W m- 2 (Twine et al. , 
2000), the TSEB fluxes for the morning surveys are as good as instrumental accuracy. 
These morning flux comparisons, however, do not allow development of an accurate 
prediction model between two-source estimates and E-C measurements. In particular, 
conelation and coefficient of determination values (Tab le 4.8) are not strong for any 
flux component. For example, the best R and R 2 values are only 0.818 and 0.669, 
respectively for H flux. Analysis of the significance of R values, using the method of 
Fisher ( 192 I); Snedecor and Cochran ( I 989)2 also shows that the R values have large 
uncertainties (Table 4.8) because of the small sample size (N= 12) and is exacerbated by a 
short data range ( e.g., H. ranges between 38 and 160 W m- 2 , except for two points at 218 
and 259 W m- 2). Confidence intervals (at 5% level of significance) for R range between 
0.42 to 0 .94 for H, LE and Rn, and between 0.20 and 0 .91 for G. These wide ranges are 
too great to allow calibration of a linear prediction model. A similar conclusion can also 
be reached by viewing the confidence intervals for the linear regression slope parameter 
(Table 4 .8). All surface energy flux components have highly uncertain slope values. For 
example, the slope parameter for H flux, at 95% confidence, ranges between 0.359 and 
1.064. 
2The pdf of the correlation coefficient is highly skewed, but in this method the skew is removed by 
using the transformation z = tanh - 1 (r). 
181 
H LE 
400 
,...._ 500 
N 
E E 
'--... 300 '--... 
3 400 3 
'---" 6 '---" 
X X 
:J 200 - 0 :J 
c;:: c 3;:: 00 0 
u u 
I I 
w 100 w 200 
D 
0 100 
0 100 200 300 400 100 200 300 400 500 
TSEB Flux (W/m') TSEB Flux (W/ m') 
G Rn 
700 
400 
N N 
E E 600 
'--... 300 '--... 
3 3 
'---" '---" 500 
X X 
:J :J 
c;:: 200 c;:: 
u u 400 
I I 
w w 
300 
0 
0 100 200 300 400 300 400 500 600 700 
TSEB Fl ux (W/ m') TSEB Flu x (W/ m' ) 
Figure 4.5: El Reno A.M. flux comparisons. Symbols indicate survey date: + for 29 
June, o for 1 July, and 1:-:,. for 2 July for 12 samples . 
182 
 
tion of El Reno AM. flu x
 components: Basic data
Table 4.7: Valida
N = 12 
E-C 
Flux TSEB 
Min Max Mean SD
 Min Max 
Component Mean SD 
58.0 127.8 59.4 69.0 259.0 
104.3 68.3 31.0 2H 
 6.7 119.3 167.0 507
.0 380.8 90.5 142.0 471.0 
LE 39
.2 44.0 184.0 99.
2 32.5 56.0 150.0 
G 106.2 47
28.3 534.0 641.0 6
07.8 39.1 534.0 672.0 
Rn 607.2 
n 95% 
o AM. flux components: 
correlation and regressio
Table 4.8: Validation of E
l Ren
confidence intervals. 
R Slope 
N = 12 Se R2 
 Interval 
Confidence Interval Conf
idence
Flux 
Lower Mean Uppe
r Lower Mean Upper 
Component 
0.947 0.359 0.712 1.064 
H 35.8 0.669 0.461
 0.818 
54 0.438 0.809 
0.944 0.299 0.613 0.928 
LE 55.8 0.6
 27 
0.481 0.199 0.6
94 0.907 0.128 0.478 0.8
G 24.6 
 0.942 0.524 1.108 1.691 
R,,,i 24.6 0.641 0.4
20 0.801
183 
ur over the bare soi l and
 sparsely 
st discrepancies betwee
n flux est imates occ
The large  EROS). 
 the thickly vegetated s
ites (ERO I and
vegetated sites (ER 13 
and ER09), not over
 plot in Fig. 
etated data points can b
e identified on the LE
The bare soil and spar
sely veg
- 2 Since these areas a
re minimally 
 200 W m . 
4.5 as the two wi th TS
EB fluxes less than
 residual 
m TSEB is mostly infl
uenced by a
affected by vegetation
, the LE estimate fro
d to balance previous 
TSEB esti-
 LE is the flux neede
computation (Eq. 2.55
), where
rtainty is surface temp
erature, 
e
H , G, and Rn . One sour
ce of the large LE unc
mates of  ould also be caused by
 
 in LE c
ctly controls es timates
 of H. The uncertainty
which dire 2 greater than the 
s of G flux, which are 
sometimes 70 W m-
inaccurate TSEB estim
ate
E-C estimates. 
B model overes-
 si te flux estimates are
 considered, the TSE
When only vegetated
es. This is supported 
by a 
ct to eddy-covariance 
estimat
timates latent heat wi
th respe
es (N=9). The hypoth
esis that 
d to the remaining valu
pair-wise t-test for me
ans applie
ever, 
nt is rejected at the 0.3%
 level (t=J .82). How
 not significa
the difference in mean
s is
estimates of LE fluxes
 is not 
e between TSEB and E
-C 
the magnitude of the d
ifferenc
el is 459 W m -
2, only 51 
n of LE estimates from
 the two-source mod
large. The mea
ment (409 W m- 2) and
 
2 n LE eddy-covarianc
e measure
W m- greater than th
e the mea
 et al. (2000). 
ss than typical closure
 errors seen by Twine
le
d by listing (Table 4.9)
 
of the morning El Reno 
surveys is summarize
The validation ative 
ponents, H, LE, G, 
r
and R.n,, plus the evapo
he flux com
mean val ues of each o
f t
 individual comparison
s 
s small, considering th
at
fraction, EF. 
 i
Relative disagreement
mean values of compon
ents 
0%. Except for H, all 
can sometimes differ b
y more than 10
hin l 0% of eddy covari
ance measurements. 
o-source model agree w
it
estimated by the tw
st, 18%, i.e., less than 2
5 wm - 2. 
s mode
The disagreement for 
Hi
184 
Table 4.9: El Reno Flux means and differences, in W 111 - 2 . 
Flux Two Source Eddy Flux Relative 
Energy Balance Covariance Difference Difference(%) 
Morning Surveys 
H 104.3 127.8 -23.5 -18 
LE 396.7 380.8 15.9 4 
G 106.2 99.2 7.0 7 
R,,, 607.2 607.8 -0.6 0 
EF 0.792 0.749 0.043 6 
Afternoon Surveys 
H 153.9 79.6 74.3 93 
LE 356.1 505.8 -149.7 -30 
G 94.0 38.9 55.1 142 
R-n 604.0 624.2 -20.2 -3 
EF 0.698 0.864 -0.166 -19 
185 
4.4.3 Validation for Two-Source Model Estimates: Afternoon 
Surveys 
The objective for grouping afternoon surveys is the same as for the morning surveys, 
namely to determine how closely two-source flux esti mates and E-C flux measurements 
agree. The task for this group, however, is more difficult because the sample size is even 
small er than before (N=9 instead of 12). Because of the experience with the analysis of 
the morning surveys, the expectation is that flux biases can be determined, but that no 
meaningful linear regression prediction model can be built from the afternoon surveys. 
Results from the afternoon surveys show generally good agreement between TSEB 
and E-C flux component estimates (Fig. 4.6), but the agreement is not as good as it 
2 
was for the morning surveys. Most two-source flux estimates are within I 00 W m -
of E-C measurements, whereas agreement for the morning surveys was more typically 
within 50 W m- 2 . Comparison of mean flux components (Table 4.10) also shows that 
the bias direction for some components has changed. Afternoon two-source estimates 
of H are greater than E-C measurements, and LE estimates are less than E-C measure-
ments . TSEB estimates of H average 153.9 W m - 2, 74 W m- 2 greater than the E-C 
measurements . TSEB estimates of LE average 356.1 W m-2, or about 150 W m- 2 less 
than E-C measurements. The mean TSEB estimate of G for the afternoon, unlike the 
morning, now shows significant bias, with a relative over-estimate of 55 W m - 2. TSEB 
estimated R..i remains close to E-C observations, with only a 20 W m - 2 difference. 
The reason for the bias shift from morning to afternoon is unknown. One possible 
explanation is that the bias is an artifact of TIMS calibration errors, which might be ex-
acerbated by afternoon flight conditions. There is no obvious reason for this , although 
calibration difficulties with TIMS have been noted (e.g., Hook et al., 1992). However, 
previous comparisons of surface temperature estimates (Fig. 4.2) show that TIMS tern-
186 
perature estimates for the afternoon are consistently greater than ground-based observa-
tions by at least 3?C . Temperature bias of this magnitude wi ll strongly influence flux 
es timates from the two-source model , with a resu lting higher proportion of H flux to LE 
flux . Th is is prec isely the re lati onship observed for the afternoon surveys. 
Linear regress ion ana lysis (Table 4. 1 I ) of the afternoon survey data confirms earli er 
ex pectations: no accurate prediction model re lating TSEB est imates to E-C observations 
ca n be created. The best observed corre lation occurs between TSEB H flux and E-C H 
flu x, w ith a mea n va lue of0.893. The comparable correlati on for LE flux is 0.791. While 
th ese correlations are moderately good, the 95% confidence intervals for these values 
arc wide (0 .5 1 to 0.98 for H and 0.20 to 0.96 for LE). Neither G nor Rn have sufficient 
co rrelations to differ from 0.0. The cause for these uncertain corre lation va lues is a small 
sample size (N=8) and short data range (especially for G and Rn, which respectively 
span -32-180 W m- 2 and 526-658 W m- 2) . 
One s imilar aspect o f the a fternoon survey results to the morning survey results is the 
greater di sagreement between flux estimates over the bare soi I site, ER 13, than between 
flu x estimates over vegetated sites ERO! , EROS, and ER09. In the afternoon surveys, 
the disagreement is exaggerated because TIMS temperatures are 6-11 ?C greater than 
ground-level observations. This surface temperature discrepancy is very large, and no 
further investigation into modeling details is needed to understand why the two-source 
model fails to closely agree with E-C estimates. Regardless of modeling approach, 
afternoon TIMS surface temperature estimates over the bare soil field ERi 3 are not close 
enough to ground-based observations to permit validation of flux components over this 
particular site. 
Referring to Table 4 .9, a summary view of the afternoon El Reno survey results show 
that H and R-n TSEB flux values, on average, reasonably agree with E-C measurements. 
187 
Tab le 4 .1 0 : Va lidati on of El Reno P.M . flux components : Basic data 
N = 8 
Fl ux TSEB E-C 
Component Mean SD Mi n Max Mean SD Min Max 
H 153 .9 98.5 48 .0 335 .0 79 .6 94.8 -20.0 275.0 
LE 356. 1 177.4 33.0 564.0 505 .8 139.3 239.0 683.0 
G 94.0 52.4 32.0 180.0 38.9 42 .0 -32.0 9 1.0 
R,I 604 .0 34.8 526.0 644 .0 624.2 24 .2 60 1.0 658.0 
The remai ning TSEB fl ux components, LE and G, do not show close agreement with 
E-C measurements. When the a fternoon results are compared with morning results, it is 
seen that morn ing survey res ults are superior in every respect. 
4.4.4 Comparison of Two-Source Model Estimates with Aircraft Flux 
Measurements 
An additional opportunity to validate the two-source fl ux model results comes from 
the Twin Otter aircraft eddy-covariance measurements. The Twin Otter measurements 
consist of spatially and temporally smoothed sensible and latent heat fluxes distributed 
along a 12 km profile (Fig. 3.4). The processing required to create the estimates used 
here is described in Mahrt et al. (2001 ) and discussed briefly in Section 2.5 Analysis 
of aircra ft-acquired flux data is a new field of research, with process ing techniques un-
der continual refinement. To make a meaningful comparison with the Twin Otter data 
profile, the two-source fluxes along the profi le track need to be extracted and trans-
fo rmed into an equivalentl y smoothed form . Using aircraft meteorological data and 
188 
H LE 
700 n,n , ,np nnm,1?=?"'l'Q'" l'' ' ' "mr?nn?m-pnnm 
600 ? 
,-.... 600 0 ,-.... 
N 500 N 
E E
-........_ -........_
  500 
s: 400 2:.- 400 
X 300 X 
:J 0 ::i 300 
i..J_ 200 i ..J_ 
u u 200 
I 
w 100 
I 
w 
0 0 ..._. u .u .J .u.u~.....J ,~u.u .;..;.......,.L...u , ,.......i......,.,,u....l, u .U.>-'-? 
0 100200300400500600 0 1002003004005006007 00 
2
TSEB Flux (W/m 2 ) TSEB Flux (W/m ) 
G Rn 
rtn 'JT""'? ??,....,-p ...,.....n,..,..T,?,--.-,TTn-.p-.-.TT.......-,T"""???m?.-,=rrr- ,,, , m--rpTn"TI......-!'?'",........9 ..,... .0 ?~ 0 ,. .. , .. HTIT'IT.--.n? , ,-.-,Tn-.-,HTO 600 
,-.... ,-.... 800 ? 
N 500 N 
E E 
-........_ -........_ 700 
._s_:_ 400 ,, ._s_:_ ,, 600 
X 300 X 
:J :J 500 
i..J_ 200 ~ 
u u 400 
I 
w 100 
I 
w 300 
0 
I ,-,ili.~ 200 
0 100200300400500600 200300400500600700800900 
TSEB Flu x (W/ m2 ) TSEB Flu x (W/ m2 ) 
Figure 4.6: El Reno P.M. flux comparisons. Symbols indicate survey date: * for 30 
June, and o for I July. There are 8 samples. At the upper left of each plot are indicated 
the coefficient of determination, mean slope and confidence interval for the slope. 
189 
Tab le 4.11 : Validation of El Reno P.M . flux components: correlation and slope 95% 
confidence intervals. 
N = 8 S,, R2 R Slope 
Flux Confidence Interval Confidence Interval 
Component Lower Mean Upper Lower Mean Upper 
H 46. 1 0 .797 0.508 0.893 0.98 1 0.427 0.860 1.290 
LE 92.0 0.626 0.196 0.791 0.960 0.142 0.621 1.10 I 
G 45.2 0.008 -0.658 0.088 0.746 -0.727 0.070 0.868 
fl~, 23.5 0. 197 -0.380 0.444 0.875 -0.3 14 0.309 0.932 
the footprint-weighting approach (Schuepp et al. , 1990) described in Section 2.5 a two-
source profile was created in the same coordinates as the Twin Otter data. Sensible heat 
fluxes appear in Fig. 4.7a, whi le latent heat fluxes appear in Fig. 4 .7b. The continu-
ous lines represent the Twin Otter flux measurements and the unconnected ? sy mbols 
represent the extracted and transfonned two-source model estimates. 
Qualitatively there appears to be some agreement between the Twin Otter flux mea-
surements and the two-source flux estimates . When Twin Otter flux values increase or 
decrease, two-source estimates increase and decrease at approximately the same posi-
tion. The profile data are shown in Fig. 4.7 . H fluxes (Fig. 4.7a) are less variable, and 
mostly lower, over the eastern grazing lands ( distances greater than 8 km in the plot), 
than they are to the west, where the land use types range between bare soils, winter 
wheat fields (harvested but untilled), and some grazing lands. 
Within the eastern potion, in the vicinity of the distance marks I 0-11 km, a peak 
of H flux occurs in both data sets , at approximately the same position and magnitude. 
Even though the peak magnitudes and locations are not identical , these H flux peaks 
190 
H Flu x 
300 
(a) 
250 
? 
200 
,,---. ? 
E 
3 
'-------'-  150 <:ooo 
X 
::J 
LL. <:o< :o? 
100 (f)o 
O::fff> 
o? 
~?
50 - <J> 
 
(f)?><> oo 
00 <P 
0 
0 2 4 6 8 10 12 
Dis tance (km) 
LE Flux 
500 
(b) 
0< Po~~  
400 0 ?0 ? 
00 
? 
? 
,,---. 0 
N 
E 300 
Oo 
3 
'-------'-  
X 
::J 200 
LL. 
100 
WE ST EAST 
0 ~-'---L-'-------'-'--'--'--~~'-'--'--'--_.___._-'---'-'--'-----'---'--'-"--" 
0 2 4 6 8 10 1 2 
Dis tance (km) 
Figure 4.7: Aircraft flux profiles. Twin Otter flux profile data (lines) vs. Two-Source 
footprint weighted profile(?). Sensible heat flux , H (a), latent heat flux, LE (b). 
19 1 
represent the same surface fea ture: a I km stretch of bare soi l surrounded by grazing 
lands. This can be justified by comparing NOVI va lues derived from the Twin Otter 
observations with the NOVI values derived from TMS observations. If the two sets of 
NOVI observations are in close agreement, then it is likely that the reported H va lues 
are retrieved from the same surface location. The surface location in question is the 
bare soi l patch illustrated in Fig. 4 .8. The TMS-derived NOVI response (Fig. 4.8a), 
shows bare so il s as dark gray, and grazing lands as light gray to white. The Twin Otter 
flight path is shown as the east-west line with ? symbols located at sta tion averaging 
points. These averag ing points, created by Mahrt el a l. (200 I), are positioned at 250 
meter intervals. The independently observed NOVI values (Fig. 4.8b, Twin Otter data 
at * 's, and TMS data at O 's.) show that alignment of Twin Otter data and TMS data is, 
wi th some qualification , appa rently good. The minimum NOVI for each observation is 
0 .1, and both occur at the same station point (Easting of 586.75 km). There are NOVI 
discrepancies, ranging up lo 0.3, away from the station minimum. These cannot be 
readi ly explained by aircraft position errors , and further study of the Twin Otter data 
would be needed to resolve the differences. 
Within the western portion of the Twin Otter transect (distances less than 8 km), 
there also appears to be simi lar patterns in the H profiles, although the discrepancies 
are greater. A Twin Otter peak at 7.5 km matches a Two Source estimate in position, 
but have large magnitude differences (I 50 W m- 2 vs. 27 W 111 - 2 respectively) . An H 
flux minimum seen by the Twin Otter at 6.7 km appears to match a Two Source estimate 
minimum at 5.7 km. Both H flux estimates show low values(~ 50-80 wm - 2) at 0-1 
km distances. 
When comparing the LE flux profiles (Fig. 4 .7b), the differences in most portions 
appear to be even less than seen in the H flux comparison. In the eastern grazing lands 
192 
El Reno , 2 Ju ly 1997 
3935 6 
3935.4 
3935.2 
3935 .0 
3934.8 
3934.6 
'\ 
3934.4 ., 
585 .5 586.0 586 5 587 .0 587 .5 
0 .8 
0 .6 
o>  0 .4 
z 
0 .2 
585 .5 586. 0 586 .5 587.0 587 .5 
East ing (km) 
Figure 4.8: NDVI image and profile of bare soil patch at El Reno. TMS NOVI image 
with Twin Otter flight path at top. TMS NDVI data shown as O's and Twin Otter data 
as * at bottom. 
193 
Table 4.12: Flux profile comparisons. Two-source model results are compared with 
Twin Otter a ircraft results as processed by Mah rt (200 I) at Oregon State University 
(OS U) . 
Source 1-1 LE 
II" II ' 
:;;;'I m2 
Mean S.D. Mean S.D. 
TSEB 12 1 69 3 19 98 
OSU Tw in Otter 11 5 39 273 57 
segment, between 9 and 12 km di stances, the Twin Otter measurements are about 50-80 
W m - 2 lower than the two- so urce estimat es . In the wes tern mixed land types, between 
3 and 6 km differences in I, E flu xes are sma ll , less than 50 W 2111 - . Between 6 and 8 
' 
2
km, the LE di screpancies are large, ~ 150-200 W m- . However, a view o f the curve 
shapes suggests there may be positioning problems. Since the navigational positioning 
has just been shown to be reasonably good (Fig. 4.8) , it is possible that the positions 
of eddies measured by the Twin Otter are diffe~ent from the source of those eddi es, as 
estimated by the two so urce model. 
The partitioning of the flux characteri stics between east and west is even more pro-
nounced in the latent heat Jlux plot, although there is disagreement about the transition 
between grazing lands and the mixed lands (i.e. between the 6 and 8 km marks, Fig. 
4.7b). 
Quantitatively, agreement between the flux estimates is more difficult to confirm. 
When the flux profile is viewed as an aggregate, the Twin Otter and Two-Source flux 
values are in close agreement (Table 4 .12). Aggregation of the flux profile is the sim-
plest, and most meaningful way to compare flu x estimates because the large random 
errors detected by the Twin Otter meas ureme nts are minimized as much as possible. 
194 
Mean I I fluxes differ by 6 W m- 2, and mean LE fluxes differ by 46 W m- 2 . These dif-
ferences are small , and less than the uncertainty of even ground-based eddy covariance 
measurements. However, when the flux profiles are compared point-by-point (Fig. 4.9), 
agreement is poor, wi th R2 values less than 0.5 for both H and LE components. The 
agreement cou ld be considerably improved if the apparent mis-positioning errors just 
described could be removed. But how this might be done in a physica lly meaningful 
way is not yet known . Aircraft flux profi les are inherently noisy observations requiring 
both spat ial and temporal averaging and the resultant flux va lues are an integral efTect of 
an upwind fetch area not easily determined. For the present, one can say that compari-
son of aircraft flux data, aggregated over 12 km, with Two-Source estimates aggregated 
over the same distance, shows exce llent agreement. When spatia l meaning over shorter 
distances is attempted, the compari son shows large di sc repancies, and ai rcraft data do 
not corroborate two source model estimates. 
4.5 El Reno, Oklahoma: Operational Scale Analysis 
Operational sca le, previously di scussed in Section 2.2.1, is a measure of the minimum 
resolution required to discriminate the dominant landscape features. The operational 
scale of the El Reno landscape, as described in Section 3.10, was analyzed for each of 
the three observational inputs to TSEB: surface temperature, as determined in Section 
4.2, NDVI, as determined in Sections 2.7 and 4.3 , and land use, as determined in Section 
3.8.2. 
195 
H Flu x 
500 ""]''" ' " 'I' I I 
(a) 
400 
2
E 300 1~ 0 .33 
'--- S. / Sy 0.826 
'-
(1) 200 -
0 
I 00 -
O' 
- 100 
- 100 0 100 200 300 400 500 
rsrn (w/ m' ) 
LE Fluy 
500 
(b) 
400 
E 300 
'---
~ 
'-
(1) 200 -
0 
C 
"j 100 
I-
0 -
- 100 .......... ~.Lu......~.Lu......~..L....u~..L....u~..L....u...........J 
- 1 00 0 1 00 200 300 400 500 
TSEB (W/ m') 
Figure 4.9: Twin Otter/ Two-Source flux correlations. Sensible heat fluxes (a), latent 
fluxes (b). 
196 
Vl 
_) 
Vl 
-a~i u  
3 7.5 
~ 
I W 
Q_ 
E 
,(-l/ 
75.0 
Figure 4.10: El Reno surface temperatures from TIMS. Light tones indicate warmer 
temperatures and correspond to bare soil or and poorly vegetated fi elds. Dark tones in-
dicate cooler temperatures and correspond to water bodies and thickly vegetated fields. 
Image taken 2 July 1997 at 16: I 9UT. Study fields containing eddy-covariance measure-
ments, ERO! , EROS, ER09 & ER13 are outlined. Also outlined, ERIO, did not have 
flux measurements but is denoted because it is has been used for an emissivity variation 
study (French et al., 2000a). 
4.5.1 Surface Temperature Scale Analysis 
Surface temperatures over the El Reno site are closely related to the land surface cover 
(Fig. 4.10). Grazing lands and pasture, as in fields ERO!, EROS and ER09, are mostly 
covered with green vegetation and are relatively cool, mainly ranging 30-3S?C. Despite 
the summer heat and strong so lar radiation ( ~860 W m- 2), the vegetation is able to 
maintain a low temperature by evaporative cooling. Bare soil fields and harvested win-
ter wheat fields, as in ER13 and ERi 0, respectively lack biological regulation and are 
relatively hot, ranging 4S-S0?C. 
Using a portion of the total image area, a series of aggregations of surface tempera-
197 
ture images shows that the distinct re lationship between temperature and land cover type 
becomes less di stinct with decreasing resolution (Fig. 4.11 ). The image seq uence shows 
actual data obtained at 3 and 12 meters (from flights at 1.5 and 5 km, respectively), fol-
lowed by aggregated temperature data from 48 to 1536 meters. Each image panel covers 
the same area, rv 1.5 x 1.5 km in dimension. The image is centered over field ER 11 (see 
Fig. 3.2 for locati on map), which is planted in the section and quarter-section pattern. 
Two sca ling and resolution characteristics are apparent in Fig. 4.11 : 
? Significant information is lost with decreased resolution, as measured by the global 
standard dev iation (shown in parentheses at the top of each image) . The biggest 
changes occur at 48 m and at 192 m, where the standard deviations drop by ~25% 
in both cases . 
? Definition of field boundaries is mostly lost at 192 m, top of right hand column. 
This is readily apparent when viewing the boundary between the relatively hot 
field ER IO and the adjacent pasture land to the east. 
In addition to decreased variance and loss of boundary definition, the statistical dis-
tribution of surface temperature shows three additional characteristic resolution effects: 
mode shifting, increased symmetry and reduced range. (Fig. 4.12). In these plots, all 
of the El Reno image area is used, and hence the full range of observed temperatures, 
from hot, bare soil to cool water bodies, is included. Since the full image also includes 
some erroneous temperatures at the image edges, quartile statistics have been computed 
to minimize the biasing effects of extreme values. They are listed at the left edge of each 
resolution plot. The inter-quartile ranges (IQR) of surface temperature are shown just 
to the right of these lists. The IQR decreases by 50% when image resolution decreases 
from 12 m to 1536 m, reflecting the fact that coarser resolutions can resolve neither ho-
mogeneous bare soil patches, nor homogeneous dense vegetation patches. The modal 
198 
.3m .38 . 1(4.4) 19 2 m .357(.3 .5) 
12 m .39.8( 4.6) .384m .35 .3(2.6) 
'1 8m .35 .5(.35) 768 m .36 1( 1.0) 
96 m .35 .5(.3.4) 15.36 m .35 .6() 
Tempera tu re (?C) 
.,,.,,-----, 
30 35 40 45 
Figure 4.11: Resolution scaling of surface temperature at El Reno, 2 July 1997, near 
field ERI 1. Temperature means and standard deviations (in parentheses) are indicated 
above each figure. Three meter data are taken from run 2, and twelve meter data from 
run 3. The remaining coarser resolutions are aggregations based on the twelve meter 
data . 
199 
temperature at 12 m resolution is 34 ?C, but at reso lutions over 200 m the mode has in-
creased to 35?C, and is due to smoothing of a posit ively skewed distributi on. Thi s effect 
can be seen in Fig. 4 .12 by comparing the modal temperature at 12 m (35.2 ?C )with the 
lower and upper quartil es (respectively 32.9 ?C and 37.8 ?C ). The shift in mode could 
introduce bias in the estimated surface energy fluxes by increasing sensible heat flux at 
the ex pense o f latent heat flu x. 
When the IQR of surface temperature are plotted aga inst the logarithm of resolution, 
the resulting trend is nearly linear. An example from the survey from Run 3, 2 July is 
shown in Fig. 4. 13. One survey, Run 2, I July, is an exception to the linea r trend. It 
shows an abrupt drop in surface temperature range, on the order o f ~ 0.5?C , at the 
200 m critica l thresho ld previously observed in Fig. 4 . 1 I. But for the other surveys 
the estimated surface temperatures have negligible sensitivity to resolution sca le. As 
shown in table 4 .13, the sensitivity changes from day to day and is probably indicative 
of differing surface soil moisture conditions. On 29 June, for example, the soil was 
saturated from the previous days ' rainfall and the IQR of surface temperature changes 
by 1.7?C over resolutions from 12 m to 1.5 km. For the mid-afternoon survey on I 
July, the soil surface was dry and temperatures changed by 3.2?C for the same range of 
resolutions. This result indicates that the scaling behavior of surface temperature is a 
function of soil moisture, as well as resolution . 
When operational scale measures - semivariograms, local standard deviation, and 
geographical variance- are used over a broader El Reno area (Fig. 4.14) than viewed 
previously (Fig. 4.10), the initial qualitative impressions made from the image sequence 
in Fig. 4.11 are supported. There does exist a dominant operational scale at ~ 400 m, as 
shown in Figs.4.15, 4 .16 and 4.17. 
The experimental semivariogram of surface temperature (Fig. 4 . 15), for example, 
200 
T_  Resolution ? 12m 
30 35 40 45 50 
T_  Reso lution : 48m 
~.~~i~
o ~. ., ~o  - 33. 1 4 .4 ~ 
0.05 
0 .00 t....-_--c~:=---------------~-----------==~- - -----" 
25 30 35 40 45 50 
T_  Resolution : 96 m 
30 35 40 45 50 
T. .... Reso lu tion 19 2m 
30 35 40 45 50 
T_ Resolution ? 384m 
~o.. ~ro~ i- ~3~3..9~  31 ~ ~ 
0 .05 -
o.oo ..__ ___ --<=----------'=-- - --------" 
25 30 35 40 45 50 
T- Resolut ion ? 768m 
30 35 40 45 50 
1- Resolution : 1 536m 
g0.~20g ,3365..45 2 2 i-. 
~ :~ 34 .1 ~ 
0.0 5 
0.00"------=-=L '='----------=>....C=----3 
25 30 35 40 45 50 
Figure 4.12: Surface temperature histograms vs. resolution at El Reno, OK on 2 July 
1997. 
201 
5 
,,.....__ 
u 
0 
,,.....__ 
0 
'-
\.... 
::J 2 
V) 
I-
Tsurf ( IQ) = 4 .89 - 0.8 1 log, 0Res . 
0 c___  _.___.___.__,_-'-'--.L...L.L---'----'--'---'--'--'---'--'-L---' 
10 100 1000 
Reso lution (m) 
Figure 4.13: Inter-quartile range of surface temperature vs. resolution. From run 3 
imagery over El Reno, OK on 2 July 1997. 6 symbols, connected by solid line indicates 
measured range. Dashed line indicates regression fit . 
Table 4.13: Inter-quartile range of surface temperature vs. resolution . 
Survey Scale (m) IQR Fit 
(Run) 12 48 96 192 384 768 1536 
29 June (4) 3.90 3.61 3.38 3.05 2.86 2.54 2.23 4.89-0.81 x log(Res.) 
1 July (2) 7.70 6.93 6.43 5.94 4.89 4 .64 4.59 9 .56-1 .65 x log(Res .) 
2 July (3) 4.9 4.4 4.0 3.6 3.1 2.7 2.2 6.49-1.3 \ x log(Res.) 
202 
El Reno Tempe ratures 
=,v,m-.r-rr,--,-,-,"""'"',.,... 
3936 
3935 
3934 
E 
z 3933 
2 
:) 
3932 
393 1 
584 585 586 587 588 589 590 
UTME 14 (km) 
30 35 40 45 
Celsiu s 
Figure 4.14: Surface temperature from TIMS over mixed land cover types. Source 
image at 12 m resolution, 2 July 1997. 
203 
shows that measurements spaced at d istances on the order of 400 m, re lative to shorter 
di stances, are poorly correlated. This correlation does not significantl y change up to 
600 111 distances, and therefore represents a semivariogram sill with a 6 ?C semi vari ance 
at a range of 400 m. As previously noted (Section 2.2.2), opera ti onal scale occurs at 
the range indicated by a semivariogram sill. Note that operational scale represents the 
minimum, and not an optimum resolution, required to discriminate between dominant 
landscape patterns. The range of 400 m is indicative of the size of fi e lds at El Reno, 
which range between quarter section plots and full section plots (l /4 of a mil e and I mi le 
respec ti vely, or 400- 1600 m). Semivariance changes most rapidly from 12 m resolution 
to I 00 m, which shows that about ~ 1/4 of the total observed semi va riance is contained 
within surface features less than I 00 m in dimension. The semi variance at a lag of 12 
m suggests that the nugget is ~ I .2?C, which is indicati ve of the combination of natu ra l 
va ri ability at 12 111 scales and the uncertainty contained in TIMS temperature es timates. 
The local standard deviation (previously described in Section 2.2 .2) of surface tem-
perature (Fig. 4.16) shows a max imum at 400 m resolution, and is consistent with the 
semivariogram behavior. Note that the local standard deviation analysis in Fig. 4.16 
has been extended to a 1500 m to emphasize the existence of a local standard deviation 
maximum. The local standard deviation rapidly increases from 1.0 to ~2.0 ?C when 
resolution changes from 12 m to 250 m. This is similar to the semivariogram obser-
vations . The local standard deviation plot, however, also shows that image variability 
remains within 0.5?C of the maximum deviation, even at 1500 m resolution. This means 
that significant information remains in the surface temperature image at this coarse res-
olution, despite the considerable mixing of land use information. 
The geographic variance analysis (Section 2.2.2) over the same El Reno fi elds il -
lustrated in Fig. 4 . 14, is shown in Fig. 4.17. The geographic variance plot reconfirms 
204 
Surface Temp ro lure, C ls ius 
8 
6 
Q) 
u 
C 
0 
~ 4 
> 
E 
Q) 
(/) 
2 
0 '---'----'----'--1-'--'--'--'-------'-------'----'---'----'--"--'----'--'--,___._--' 
0 200 400 600 800 1000 
Log (m) 
Figure 4.15: Mixed land use surface temperature semivariogram. There is a local sill 
forming at a range of ~450 m. 
205 
Surf ace T mpera ture, El Reno 
3.0 
--V-J- 
:i 2.5 
V) 
(I) 
u 
'-' 
C 2.0 
0 
0 
> 
~ 1.5 
u 
\... 
0 
u 
6 1.0 
....., 
V) 
0 
g 0.5 
_J 
0.0 L-..,_....1.__.l.--'------'------'--'---'---'-_c__-'----'----'-------'--.l_....J 
0 500 1000 1500 
Reso lution (m) 
Figure 4.16: Surface temperature local standard deviation. 
206 
the operational sca le characteristics seen previously. The geographic variance shows 
surface temperature variance versus image resolution, and is plotted logarithm ica lly to 
show the hierarchica l sca le levels at even increments. Recall that the geographic vari-
ance approach compares image values based upon a hierarchy of scales at multiple of 2 
times the original scale, and that the va ri ance measured is between four sample va lues 
at a given scale. 
A majority of image vari ability, 58%, is contained within scales ranging between 
12 m and 48 m. An inflection in the geographic vari ance plot at 400 m, where there 
is a loca l maximum of 11 %, represents the geometric patterning of land use at the l/4 
section scale. The geographic va ri ance increases aga in at 3 km, but the estimate at thi s 
scale is uncertain because the limits of the image have been reached, and may represent 
sampling variation. 
Jn short, the geographic vari ance analys is depicts two different aspects about the El 
Reno landscape. First, it shows that there is significant heterogeneity at very fine scales, 
less than 12 m, that is unresolved by the ex isting remote sensing data. This heterogeneity 
consists of clumps of vegetati on and interspersed patches of bare soil , each of which 
vary on scales less than 12 m. Second, the geographic variance analysis shows that 
there exists a larger scale of landscape organization at ~ 400 m. This dimension is not a 
natural one, but is a result of land ownership patterns. 
4.5.2 Vegetative Cover Scale Analysis 
Like surface temperature, NOVI is closely related to surface land cover properties. In 
Fig. 4.18, bright areas correspond to NDVI values ~ 0.6-0.7 and indicate thick green 
vegetation because of its high near infrared (NIR) reflectivity. Dark areas correspond 
to NOVI values ~ 0.0-0.1 and indicate several possible conditions, including bare soil, 
207 
Mi xed Land 
35 
Q) 
u 
C 
0 25 
'-
0 
> 
.s 20 
0 
I-
0 15 
+-' 
C 
Q) 
u 
'- 10 
Q) 
0... 
5 
0 
10 100 100
R 0e  so lution (meters) 
Figure 4.17: Surface temperature geographic variance. 
208 
 The thickest vegetation lies with
in fields ERO l-
water bodies, or senescent vegeta
tion.
age in Fig. 4.18. In most instance
s 
ER04, which li e in the northeaste
rn corner of the im ' 
ver green vegetation, due to the pl
ant's ability to regulate 
surface temperatures are cool o
ures tend to be hot over bare soil 
surfaces 
ce temperat
itself through transpiration . Surfa
to-one relationship 
cause they are less reflective and
 are not self-regulating. A one-
be
re. fig. 4. l 9 illustrates that surfac
e 
e temperatu
does not exist between NOVI and
 surfac
vegetated, or possibly covered wi
th senescent 
eratures over areas that are sparse
ly 
temp
n over green vegetation 
vegetation (low NDVl), have a w
ider range- ~40-50?C - tha
rse green vegetation could be stre
ssed, 
 with spa
(high NDVI) - 35-39?C . Some
 areas
might be moist from 
ue to water shortage, and therefor
e be hotter than usual. Bare soils 
d
recent rainfall, or dew, and theref
ore be cooler than usual. 
 
age patch areas as for surface tem
perature, the effect of resolution
Using the same im
Because of the high NDVJ con-
upon NDV1 can be seen in the se
quence in Fig. 4.20. 
n 
re soil fields and the vegetated fie
lds, field boundary discriminatio
trast between the ba
hereas the field boundaries becam
e in-
tions. W
is preserved at somewhat coarser
 resolu
erature, the boundaries viewed by
 
distinguishable between 200-400
 m for surface temp
VI are preserved up to ~400 m (F
ig. 4.20). 
ND
istogram series (Fig. 4 .21 ). 
The quantitative effects of resolu
tion are shown in the h
 to single mode NDVI distribution
s 
om bimodal
The histogram sequence shows a 
shift fr
le. Whereas the bare soil and thi
ckly 
al sca
at ~200 m, a strong indicator of
 operation
t coarser resolution. 
egetated fields are distinct at fine
r resolution, they are confused a
v
n 
odal change is therefore expecte
d to have noticeable effects upo
This bimodal-unim
d cover 
surface energy flux estimates, sin
ce the fluxes are sensitive to lan
subsequent 
 H flux and increase in LE flux 
values 
in
types. The expected effects are 
a decrease 
 soil fields . 
because the coarse resolution data
 cannot resolve bare
209 
El Reno NOVI 
z 
:::,; 
1-
::i 
584 585 586 587 588 589 590 
UTME 14 ( km ) 
0 .00 0 .10 0.20 0.30 0.40 0. 50 0.60 0 .70 
NOVI 
Figure 4 .18: El Reno NDVI. Source image from 12 m resolution TMS survey on 2 July 
1997. Study sites are delineated and labeled. 
210 
NOVI vs . Tsurf 
0.8 
0.6 
> 
0 0.4 
z 
0.2 
0.0 L.a~___,____.____L_L-J--'--..1--1---'--'-~~.-J-..-L--_,__.J...-J._..J__.l.--L~ ----'---' 55 
35 40 45 50 
30 Tem perature (Ce lsius) 
800 
200 400 600 
0 Co un ts 
Figure 4.19: NOVI vs. surface temperature histogram. Source data from 12 m El Reno 
imagery on 2 July 1997. 
211 
3m Q_LI 3( 0 75) 
~: -]' 
'.;. " 
384m 043( 0 . 18) 
768m O 39( 0 08) 
48m 040( 0 22) 
.. 
96m 0.41 ( 0 22) 
NOVI 
0.00 0 .1 0 0.20 0 . .30 0.40 0.50 0.60 0. 70 
Figure 4.20: Resolution scaling of NDVI at El Reno, 2 July 1997. NDVI means and 
, 
standard deviations for each scale are indicated. Three meter data are taken from run 2 
and twelve meter data from run 3. The remaining coarser resolutions are aggregations 
based on the twelve meter data . Each image is 1.5 x 1.5 km. 
212 
: NOVI Reso lution : 12m ~~i 00..547053  0. 4 23 i 
0 ,o - ~ ~ 
o .o5 ? L ,c__ ~ 
oooL_j_o_o ____o _2_ ____0 _,-------?~.6---=~o.8 
:~~i  0. NOVI Resolution : 48m ~-
578 
0 10 0.4 44 0.342 
0 .23 . 
0.05 
o .ooL._ _. .J... __________________- =~-:" 
QO 02 Q4 Q6 IQ8 g; ;_ 0. NOVI Resolu tion : 96m  
568 
g6g _ 0. 44 2 0.3 14 _ 
0061 ~ ~: 0 .04 ~   8831s_. _o_  _o -L_ ___o _.2 ____0 _, _____0 _ 6_ ---=---~o.8 
NOVI Re so lut ion : 192 m 
;;;E.J_ __~ __co_ _ 2_7 _7_ ~___=___~___=___!_. ._ _.J,  
QO 02 0 4 Q6 Q8 
NOVI Resolution : 384m 
:0_211 0 5l 00..543353  0.236 1 
0 299 
0 .05 -
0 .00E__ _ --=='-----------------==--- ....:i 
0.0 0 .2 0.4 0.6 0 .8 
NOVI Resolut ion : 768m 
0.0 0 .2 0 .4 0 .6 0 .8 
NOVI Resolut ion : 1536m 
rnt.f_ __~ :_!_!_!_ .=o=_:1...5_9._ __c____~_____ .__ ___ _1,,  
0.0 0 .2 0 .4 0 .6 0 .8 
Figure 4.2 1: NDVI histograms vs . reso lution. The sequence shows the sca le depen-
dency ofNDVI. Relati ve frequency plotted along the ordinate, NOVI along the absc issa . 
The quartiles are li sted to the left of each plot, and the IQR is to the ri ght of this list. 
2 13 
One consequence of decreas ing resolution of NOVI imagery is its potentially large 
uncertainty when adj acen t, contrasti ng land cover types, cannot be separately resolved. 
This condition, prev iously di scussed in Secti on 3. 11 .4, meant that NOVI at finer reso lu-
tions might not close ly resemble NOVI at coarser resolutions. Specifically, ambigu ities 
of NOVI in the example shown in Section 3. 11.4 cou ld range between 0.3 to 0.6. This 
range is wide, approxima tely equivalent to a variat ion in fractional vegetative cover of 
40 to 90%, and has direct effec t upon LE flux estimates (Eq. 2.7). 
Fortunate ly, NOVI am biguit y does not appear to be as serious a problem as it could 
be. A two-dimensiona l hi stogra m (F ig. l 22) of NIR-Red reflectance in a 2 Jul y TMS 
image shows an ac tual di stribution of red and near infrared reflectances. Note that the 
highest occurrences li e along the NOVI =O. l contour and in a relatively narrow swath 
extending from NOVI =0.4 up to NOVI=0.7. When the same aggregation experiment 
is performed as was shown in Fig . 3.35, the resultant aggregate has an NDVI range 
from 0.38 to 0.51 (shown by the short white line segments) . As before, the aggregate 
of radiances result in a di stinctly higher (in thi s case, about 0.05) NDVI than would 
be determined from simple arithmetic averaging of NOVI values themselves. The ag-
gregation range corresponds to fractional vegetative cover of ~ 54-73%. Although the 
effects upon LE flux estimates in Eq. 2.7 ue sti ll significant, they are much less than the 
postulated 40-90% range. When one considers that the likelihood of aggregating highly 
contrasting land cover types at El Reno is low, when the resolutions are greater than op-
eration scale (400 m), the net result is that NDVl aggregation ambigu ity will normally 
not be important. This resu lt , however, will not hold under much more heterogenous 
land cover conditions. 
Semivariogram analys is of NOVI (F ig. 4.23) is consistent with the image sequence 
prev iously shown (Fig. 4.20) . A local sill forms at a range of ~ 400 m, which agrees 
2 14 
(lJ 
u 
r 
0 
u 
(lJ 
(lJ 
Cl:'. 
Cl:'. 
z 
5 10 15 20 
Red Refl ec tan ce (%) 
0 100 200 300 400 
Counts 
Figure 4.22: NIR vs. Red reflectance histogram. NOVI contours in white. Simulated 
aggregates of NOVI 0.1 and 0.7 shown as * symbols. 
215 
NOVI 
0 .0 40 
~f-
0.0.30 
QJ 
u 
C 
0 
'-
0 0 0 20 
> 
E 
QJ 
V) 
0.0 10 
0 . 0 0 0 l__c__L_~L___>__L_-'--L___,_-'---'--l--L-'---'--J__J.~--'-_.j 
0 200 400 600 800 1000 
Log (m) 
Figure 4.23 : Mixed land use NOVI semivariogram. Data from the same area as for Fig. 
4.15. Two sills may be present: one at 400 m and another at 700 m. 
with the semivariogram analysis of surface temperature. A secondary sill forms at a 
range of ~ 700 m, a range not distinct in surface temperature analyses. This suggests 
that green vegetation variability at 700 mis important and confirms the need to use both 
temperature and NOVI inputs to the two-source model. 
Local standard deviation analysis of NOVI shows very similar results to that seen 
with surface temperature. Operational scale is depicted by the maximum local standard 
deviation of 0.1 l NOVI at 400 m resolution. Loss of information at finer resolutions 
is the same as for temperature: most image variance is contained within dimensions of 
~ 50 m. The data point at 1.5 km resolution suggests there is yet another, coarser, op-
erational scale dimension. This suggestion is only tentative because there are relatively 
216 
NOVI, El Reno 
0. 14 
0 .12 
C 
0 
0 
> 0. 10 
Q) 
0 
"D 
I... 0 .08 
0 
"D 
C 
0 0.06 
l/) 
0 
u 
0 0.04 
_J 
0.02 
0.00 
0 500 1000 1500 
Reso lu ti on (m) 
Figure 4 .24: NDVI local standard deviation. 
few samples ( I 6) available at the 1.5 km resolution, and the increase in local standard 
deviation could be due to sampling variation. 
Geographic variance analysis of NDVI Fig. 4.25 confirms the previous observation 
of an operational scale of 400 m, with 20% of the total variance accounted for. To 
search for a potentially larger operational scale, as suggested by the local standard de-
viation analysis, variance data were taken over the full extent of the extracted image, 
or approximately 2 km greater in both north-south and east-west directions . The result 
indicates no operational scale at 1.5 km, and that the local standard deviation result is 
likely due to sampling variation. This geographic variance analysis, however, is not im-
mune to sampling variation difficulties . In Fig. 4 .25, there is a suggested variance peak 
at 3 km, but because there are only 4 samples at this scale, there is no confidence in its 
217 
Mixed Land NOVI 
35 
30 
(I) 
u 
C 
0 25 -
I... 
0 
> 
0 20 
~ 
0 
I-
0 15 
C 
(I) 
u 
I... 10 
(I) 
0.. 
5 
0 
10 100 1000 
Reso luti on (meters) 
Figure 4.25: Geographic variance of NOVI. Extract from TMS imagery, 2 July 1997. 
significance. 
4.5.3 Land Use Scale Analysis 
The resolution effects upon land use categorization are summarized in Table 4.14. Only 
three land use categories are distinguished: forage/pasture, bare soil fields, and wa-
ter bodies. The remaining land use categories listed in Table 3.10 are grouped under 
miscellaneous and comprise less than 10% of the El Reno study area . As the image 
resolution decreases, established categories begin to lose their meaning. At 12 meter 
resolution , the dominant categories, forage/pasture, bare soil fields, and water, are eas-
ily distinguished. At 96 meter resolution, these three categories are still distinct, but 
a significant bias in the distribution has developed: forage/pasture has increased from 
2 18 
Table 4.14: Land use sca ling. Percent distribution of main land use types by resolution 
scale. 
Scale (m) Forage/Pasture Bare Water Misc. 
12 59.7 23.9 7.5 8.9 
48 80.7 15.8 2.2 1.3 
96 89.1 10.0 0.7 0.2 
192 95 .6 4.2 0.2 0.0 
384 99.2 0.8 0.0 0.0 
768 100.0 0.0 0.0 0.0 
1536 100.0 0.0 0.0 0.0 
59.7% to 89.1% of total land use, and bare soil fields decreased from 7.5% to 0.7% of 
land use. Water bodies, originally estimated as 8.9% of land use, decreased to 0.2%. 
The dominance of the the forage/pasture category increases further, until ~ 400 meter 
resolution, where it accounts for I 00% of land use . These results indicate that land use 
categorization, as a tool for characterizing land surface roughness (Section 3.8.2) has 
limited utility when resolutions are coarser than 192 m. 
Operational scale analyses of both NDVI and surface temperature are consistent 
with this land use aggregation pattern. Land cover, represented either by its vegetative 
greenness (NOVI), or by its thermal response (surface temperature), has characteristic 
dimensions similar to those derived from a combination of remote sensing data and 
actual field observations. 
219 
4.6 El Reno, Oklahoma: Aggregation Experiments 
Thus far, the presented results have shown that estimated surface energy fluxes have 
some reasonable agreement with independentl y obtained flux est imates. Then the input 
observations to the surface energy flux model were analyzed over sca les between 12 and 
1500 m, and it was detem1ined that there is at least one dominant landscape sca le, ~ 400 
111. 
The task now is to present the results o f sca ling experiments on the flux estimates 
themselves . The first step is to compare flux estimates made in two different ways, using 
the aggregation scheme described in Section 3. 11 : 
? Simulated fluxes derived from aggrega ting the highest resolution fluxes . 
? Simulated fluxes derived from aggregating the hi ghest resolution input observa-
tions. 
These comparisons are shown in the next section. Following the comparisons of the 
surface energy flux components, the statistical properties of scaled fluxes wi ll be shown, 
including a qualitative and quantitative view of the individual energy flux components 
(i.e., sensible and latent heat fluxes from vegetation and the soil). 
The surface energy fluxes estimated by the two-source model consist of six compo-
nents: two sensible heat flux estimates from the soil and vegetation (Hs and He), two 
latent heat flux estimates from the soil and vegetation (LEs and LEc ), conducted ground 
heat flux ( G) and net radiation (Rn). The most significant of these components in this 
study are LEc, Hs , G, and Rn . As deve loped in Chapter 2, the basic conservation rules 
apply: 
H+L E = n ,,,-G (4.2) 
220 
where the tota l sensible heat flux is H H., + He, and the total latent heat flux is 
L E = LE.,+ LEr. 
4.6.l Latent Heat Flux (Evapotranspiration) 
The si mulation results for transpiration component, LEc , over scales ranging from 12 
m to 1.3 km, are shown in Fig. 4.26. Each point represents a pair-wise match of latent 
heat flu x from the vegetation over vegeta ted sites. The matching is performed on fluxes 
estimated at sca les of 48, 96, 192, 384, 768, and 1536 m. As mentioned in the methods 
chapter, by using scales that are even multiple of the source image (here it is 12 m), the 
sampling methodology is greatly simplified. The first interva l, 24 m, is skipped beca use 
it did not show large changes from the 12 m results. The abscissa represents fluxes at 
the indicated scale derived from aggregated 12 m fluxes. The ordinate represents flu xes 
modeled at the indicated scale derived from aggregated 12 m observations. Two diago-
nal lines appear in each plot: a one-to-one line, which is the line of perfect agreement, 
and a linear regression line. 
The regression results (Table 4.15) show that where LEc values are hi gh, typically 
greater than 250 W m- 2, there is essentially no scale dependency between 12 m and 
1536 m, and that agreement between aggregated inputs and aggregated outputs (as mea-
sured by S e) is less than 50 W m- 2 . There is some bias induced in the regressions, which 
is caused by disagreement in flux estimates where LEc values are low ( < 200 W 111 - 2). 
The reason for the relative over-estimate of LEc values from aggregated input data is 
due to the tendency of coarser NOVI observations to overestimate vegetation density. 
This tendency has been previously in Section 4.5.2, and will be discussed further when 
reviewing results from aggregating sensible heat fluxes. 
At the higher resolutions, 48 and 96 m, there is excellent agreement between flux 
221 
LEconopy 48 m LEconopy 384 m 
500 500 
400 400 
, 
0. 
E 300 
l 
~ 200 
f 
100 ?? 
0 lf....=--'---...c..--i....---'----' 
200 300 400 500 0 100 200 300 400 500 
Aggrega ted Output Aggrega ted Output 
LEconopy 96 m LEconopy 768 m 
500 500 
400 ., 400 
, , 
0. 
C 300 0. .S JOO 
~ " 
O' i 
~ 200 
f ... ~ 200 O' < 
0 100 200 300 400 500 100 200 300 400 500 
Aggregated Output Aggrega ted Ou tput 
LEconopy 1536 m 
500,.......=...,.,==~.:.,...,-,.......=....,-=........., 
400 400 
, , 
0. 
.!; 300 r Joo 
'l 
0 'l 
O' 0 O' 
~ 200 ~ 200 
f f 
0 100 200 300 400 500 100 200 300 400 500 
Aggrega ted Output Aggregated Output 
Figure 4.26: Latent heat aggregation. Data aggregation experiments from El Reno run 
3, July 2, 1997 for latent heat flux from vegetation only. 
222 
Table 4.15 : Latent heat flux (canopy) aggregation regress ion statistics. 
Scale (m) N Intercept Slope J?,2 Se Sp/Sy 
48 65 14 68. 1 0.746 0.722 48.9 0.527 
96 185 1 64.0 0.778 0.824 39.3 0.419 
192 548 59.8 0.810 0.905 29.4 0.309 
384 165 61.5 0.866 0.919 27.3 0.285 
768 52 62 .7 0.821 0.958 16.3 0.208 
1536 14 57.3 0.845 0.968 12.3 0.186 
estimates at flux va lues ranging between 200 and 400 W m- 2. However, there is also 
cons iderable scatter of points away from the one-to-one line, with greater scatter at 
LEc values ranging between 0 and 200 W m- 2. The preponderance of scatter at lower 
flux values suggest that the two-source model does not accurately estimate vegetation 
transpiration when the fractional vegetation cover is small. As simulated pixel size 
increases, the scatter greatly decreases. 
The large scatter, with some points over 200 W 111 - 2 away from the one-to-one line, 
suggests that data processing, rather than model induced errors, are occurring. Prev i-
ously, it has been shown that the two-source model, in general, returns fluxes that differ 
from eddy covariance flux estimates by less than 100 W m- 2? So the two-source model 
itself is unlikely to be the cause of the scatter. 
A plausible explanation for the scatter is georegistration error between the input ob-
servations. As discussed in Section 3.4, georegistration is the alignment of imagery into 
a single geodetic coordinate system. The alignment is frequently achieved by resam-
pling the original image elastically and constrained by ground control points. But when 
the original image has irregular distortions , as occurs from aircraft-acquired data, good 
223 
NOVI V S . Tsurf Flu xes 
0.70 600 'l" " ""'I "'"' I"'" "'J ?f'TTT 
1 8} ~s-reg;s lered oggrego le 0 .60 + ? 4 500 
0.50 400 ~eclly reg;s ler ed oggrego le ,,..-.._ 
N 
0. 40 Mea n TC and NOVI > Ok:' E .......___ 300 0 
z 5 0.30 .._,, 
w 200 +2 
_j 
0.20 
100 
0. 10 ? 3 + 2 
0 
0 .00 
25 30 35 40 45 50 55 0 100200 300 400500600 
S urfa ce Te mp e ra ture (C e ls iu s ) H (W/ m 2 ) 
Figure 4.27: Georegistration error simulation. Errors in estimated fluxes due to mis-
registered imagery are exacerbated by aggregating the outputs (fluxes), but are amelio-
rated by aggregating the inputs ( observed temperatures and NOVI). Two different input 
scenarios are shown on the left: mixing points 1 and 2, and mixing points 3 and 4. The 
resulting fluxes are shown in the right hand plot. 
alignment for the entire image is very difficult to achieve. Where alignment of differ-
ent input data sets is poor, the resulting model results will also be poor. Figure 4.27 
demonstrates the nature of the results, in a simulation where surface temperature and 
NOVI values are incorrectly associated. To illustrate the effect, two pairs of points are 
chosen that have the same mean surface temperature and NOVI. These pairs are input to 
the two-source model separately, and as aggregate values. Realistic values for land use 
cover are also assigned, with pasture assigned to the values with high NOVI and bare 
soil assigned to the values with low NOVI. 
Looking at the plot on the left half of Fig. 4.27, one can see the two pairs of sim-
ulated input values : I & 2, and 3 & 4. Typical conditions, as demonstrated in the 
224 
hi stogram plot in Fig. 4. 19, include points I and 2. Point 3 represent a poss ible, but 
not observed condition, of co ld (probably wet), bare so il. Point 4 is improbable, since it 
indicates hot, green vegetati on. 
The simulation results are shown on the right half of Fig. 4.27, where sensible heat 
flux lies along the abscissa and latent heat flux along the ordinate. The simulated correct 
surface conditions, points I & 2, are indicated by + signs. Mis-registered va lues, points 
3 & 4, are indicated by small o signs. Simulation shows that aggregating observed 
fluxes fo r points 1 & 2 is essentially identical to aggregating the corresponding mean 
input temperature and NOVI. Since the mean input va lues are the same fo r both pairs 
of points, a good estimate of surface flux would result from aggregated inputs, despite 
the large mis-registrati on. However, if the flu xes corresponding to points 3 & 4 are 
aggregated, the estimated flux components err by I 00 W 111 - 2 for H , and by 120 W m- 2 
for LE. 
This exercise supports the claim that much of the scatter in Fig. 4.26, particularly at 
48 m resolutions, may be due to registration errors between the different remote sens-
ing data sets. This is an important finding, because it shows that higher reso lution data 
will not result in higher accuracies unless there is low georegistration error. Neverthe-
less, registration errors in the current study do not invalidate modeling results because 
well georegistered data dominate poorly georegistered data. When TSEB flux estimates 
were compared with E-C station measurements, extra care was taken to ensure good 
alignment of data inputs in the immediate area of the ground flux sites. While perfect 
alignment of all points is not possible, good alignment for most data points outside of 
the flux site areas was also achieved by using a large number (> 100) of widely dis-
tributed ground control points. This condition is verified by the high density of points 
lying close to the one-to-one line in Fig. 4.26. 
225 
4.6.2 Sensible Heat Flux 
Two-source model scaling results for sensible heat are now discussed. Since the mod-
eled sens ible heat from the vegetati on (He) is, zero, or nearly so, the comparison plots 
only need show sensible heat from the soil component, Hs , in Fig. 4 .28. Regression 
statisti cs fo r Hs are shown in Table 4.16. 
The sca ling regression stati stics apparently show poor correlations (0 .343-0.670) for 
resolutions up to 384 m, with significantly improved correlati on ( ~ 0.8) at resolutions 
of 768 m and 1536 m. However, these results obscure a more significant observati on: 
aggregation of Hs values at El Reno produce two very different patterns. One pattern 
is excellent correlation between aggregated inputs and output and is predominant up to 
192 m sca les. The correlation fo r these points is very close to 1.0. The points in thj s 
pattern are almost entirely pure bare soil samples. The other pattern is a lso linear, but 
with a shallow slope and more scatter away from the trend. Points falling in thi s pat-
tern represent aggregated pixels that contain both bare soil and vegetated samples. As 
aggregation of the input values proceeds to coarser values, this linear pattern becomes 
increasingly dominant over the pure bare soil pattern. This scaling trend can be com-
pared with the NDVI scaling trend observed in the histogram sequence in Fig. 4.21, 
where the mode at ~ 0.1 , representing bare soil, disappears at resolutions coarser than 
96 m. The disappearance of distinct bare soil patches, as measured by NDVI, is directly 
related to the dominance of lower slope pattern in Fig. 4.28. As image resolution de-
creases, NDYI recognizes fewer and fewer patches of distinctly bare soil areas. Instead, 
the bare soil patches are mixed with vegetated patches. 
The consequence of this land cover mixing phenomenon is a shift in the relative 
importance of LEc flux to Hs flux , and is illustrated in Fig. 4.29. The figure combines 
the aggregated input results from LE and H by plotting image mean evaporative frac-
226 
tion (EF) aga inst image resolutions ra nging between 12 and 1536 m. EF is the ratio 
LE/(LE + ff), and indicates the fraction of turbulent surface energy fl ux represented 
by latent heat flux (EF was first int roduced in the Priestley-Taylor fo rmulati on fo r un-
stressed transpi ra tion from vegetati on, Eq. 2.7). Since evaporative fraction over a region 
should be independent of image reso lution, the observed resu lt shows that resolution has 
two undes irable e ffects upon the two-source model est imates. First, EF increases with 
decreas ing reso lution. Second, Er es timates are inaccurate at reso lutions comparab le to 
operational sca le. 
The first effect is readily seen by comparing EF at the finest and coarsest resolutions. 
At the best reso lution, 12 m, EF is 0.79, while at poorest reso lut ion, 1536 m, EF is 0.9 1. 
Thi s is a relative change of 15%, a large cifTerence. Fig. 4.29 shows that EF estimates, 
in almost every aggregation s imulation, in: rease as resolution is decreased. Thi s results 
fro m the sensitivity o fN DY I to reso lution, which is biased in favor of vegetati on when 
resolution decreases. 
The second undesirable reso luti on e ffect is the inaccuracy created when viewing a 
landscape at a reso lution similar to operational sca le. The inaccuracy can be seen in 
Fig . 4.29, where the increasing EF trend is broken at 384 m. It can also be seen in 
the upper right hand plot o f Fig. 4.28, w1ere the two linear aggregation patterns are 
diffused. Both figures represent the same phenomenon: modeling at resolutions too 
coarse to resolve homogeneous land use types and too fine to adequately average the 
now-mixed land use types. 
These observations of resolution effects are important because they show how much 
the modeling of the surface energy ba lance can be significantly affected by image res-
olution. In this study, the energy balance s resolution biased, with up to 15% greater 
LE fluxes estimated for a landscape viewed at 1536 m, relative to the same landscape 
227 
Table 4.16: So il heat flux aggregation regress ion statistics. 
Scale (m) N Intercept Slope R2 Se Se/Sy 
48 92 12 4.5 0.739 0.655 28 .8 0.587 
96 2350 l 0.9 0.536 0.452 30.0 0.740 
192 6 11 17.9 0.355 0.343 23 .5 0.811 
384 168 46.9 0.123 0.670 18.4 0.967 
768 52 2 1.4 0.300 0.796 5.4 0.456 
1536 14 23 .0 0.266 0.806 3.8 0.458 
viewed at 12 m reso lution. Furthermore, the use of image data with resolutions similar 
to the operati onal sca le will result in inaccurate flux estimates. ln this particular case, 
the inaccuracy is ~ 6%. Inaccuracy of this magnitude is not large, but still significant. 
For example, the 2 July 1997 ET estimates over El Reno would have an excess LE flux 
of 23 W 111 - 2 (using E-C morning results from Table 4.9 : 380 x 0.06 = 22.8 W 111 - 2) . 
Confirmat ion of the source of the two observed linear patterns in Fig. 4.28 can be 
made by stratifying the output data by land cover class. When the land cover class is 
specified as pure bare soil, the matched Hs flu x values (Fig. 4 .30) do not show the 
low slope pattern points. Linear regression (Table 4.17), shows slope values of 1.0 I , 
correlations over 0.99, and very low prediction error values (Se :::; 2.8W m- 2) . Fig. 
4.30 indicates that sensible heat from the soil has virtually no scale dependency as long 
as the pixel samples remain uncontaminated by vegetation samples. Because of the 
~ 400 rn operational scale at El Reno, no pure bare soil samples exist beyond the 192 
rn resolution. As previously explained in Section 4.5 .3, at resolutions of 384 rn and 
coarser, all the pixels are identified as vegetated. 
228 
Hsoil 384 m 
400 400 
, 
f 300 
l l 
~ 200 ~ 200 -
l' l' 
0 100 200 400 500 100 200 300 400 500 
Aggrego \cd Oulpu l Aggrcgolcd Ou tput 
Hso;I 96 m Hsoil 768 m 
500 
400 400 
, 
?. 
~ 
 300 E.  300 u u g, 0 
~ 200 "' 
f ~ 200 l' 
100 100 
0r.<...-....J..o--=-......J-=....i..----' 
0 100 200 400 500 0 100 200 300 400 
Aggrego ted Output Aggrega ted Output 
Hsoil 1536 m 
500 
400 
, , 
E 300 0. ? 300 
~ 
"~'  200 
~ 
100 
0 100 200 300 400 500 
Aggregated Output Aggrcgo led Output 
Figure 4.28: Sensible heat aggregation. Data aggregation experiments from El Reno run 
3, July 2, 1997 for sensible heat flux from soil over all cover types . 
229 
Eva poro t ive Fr oct ion 
1.00 
0 .95 
0.90 
LL 
w 
0 85 
0.80 
0. 7 5 ~----'-'----'---'---'-'-'-LI-..-.,__...,__,__,__~~-~ 
10 100 1000 
Reso lu ti on ( m) 
Figure 4.29: Evaporative fraction and resolution. As resolution decreases (increase in 
pixel size), the mean evaporative fraction increases. 
Table 4.17: Sensible heat flux aggregation regression statistics (bare soil only). 
Scale (m) N Intercept Slope R2 Se Se/Sy 
48 1887 -3.9 1.01 0.998 1.8 0.041 
96 272 -4.0 1.01 0.995 2.8 0.070 
192 23 -2.3 1.00 0.998 2.2 0.050 
230 
Hsoil 48 m 
500 
400 
0 
a. 
.E 300 
~ 
0 
"~'  200 
:r 
100 
0 
0 100 200 300 400 500 
Aggrcgo led Output 
Hsoil 96 m 
500 
400 
0 
a. 
..!: u  300 
0 
"~'  200 
:r 
100 
0 
0 100 200 300 400 500 
Aggregated Output 
Hsoil 192 m 
500 
400 
0 
a. 
.E 300 
~ 
0 
"~'  200 
:r 
100 
0 
0 100 200 JOO 400 500 
Aggregated Output 
Figure 4.30: Sensible heat aggregation over bare soil. These are taken from the same 
data set shown in Fig. 4.28, but in this case the vegetated sites were excluded. 
23 1 
4.6.3 Net Radiation 
vely small range of 
va lues, ~ 530-670 
 over El Reno ex hib
ited a relati
Net radia tion el shows little differ-
 range of sca les, the tw
o-source mod
2
W m- . When model
ed over a
2 st points 
er flux va lues (500-58
0 W m- ) , where mo
or low
ence in aggregation a
pproach f
n (Ta ble 4.18) confi rm
s this 
r regress io
ong the one- to-one li
ne (Fig. 4.3 1). Li nea
fa ll al
les between 12 m and
 1536 
 for all sca
 with correlation coe f
fi cients exceeding 0.9
pattern, s develops. For 
x values (600-700 W m
- 2 bia) , a significant 
m. Nevertheless, at hi
gher flu
ti ve to aggre-
ut va lues underestima
te net radiation, rela
ted inp
these va lues the aggr
ega
olution slightly less th
an 
2
 W m - . By 192 m re
solution, a res
50
ga ted output values, b
y ~
isappears. The bias is
 caused by inad-
nal sca le of 400 m, th
e net radiation bias d
opera ti o
enomenon similar to 
that 
nse vegetation, and is 
a result of a ph
e
equate modeling of th
e d
on data (~ 384 
t section, where coars
e resoluti
previously di scussed 
in the Sensible hea
r. In the current situa
tion, coarse 
rely bare soil land co
ve
m) is unable to di stin
guish pu
ds. Note in Fig. 4.2 1 
that 
ly distinguishes thickl
y vegetated lan
resolution data inadeq
uate
 the NDVJ histogram
 shift 
sens, the upper bound
 and upper mode of
as resolution coar  at J 2 m 
pper mode occurs at a
n NDVI of 0.55
towards lower values
. For example, the u J 
esolution image. The 
upper bound of NDV
 0.50 at the 384 m r
resolution, but shifts 
to
at 1536 m resolution,
 
olution, the maximum
 NDVI is 0. 78, but 
res
also shifts. At 12 m  a 
 the NDVJ upper mod
e and maximum are
um NDVI is 0.62 . Th
e shifts of
the maxim
uent bias in net radiati
on estimation 
veraging, and the cons
eq
ic a
natural result of arithm
et
e two-source model b
y 
ly controlled in th
e outcome. Net radia
tion values are strong
is th ry bare 
.4.5). Since thick veg
etation, relative to d
(Section 2
apparent vegetation d
ensity 
 radiation, net radia-
ore solar radiation, an
d emits less thermal
soil, usually absorbs 
m
ion density 
 vegetation. When the
 maximum vegetat
tion at El Reno is gre
atest for thick
he m ax imum net radi
ation 
ions, t
duced by 48 to J9 2 m
 resolution observa t
estimate is re
232 
Table 4.18: Net radiation aggregation regression statistics . 
Scale (m) N Intercept Slope R2 Se Se/Sy 
48 9212 80.2 0.861 0.920 5.7 0.283 
96 2350 83.I 0.856 0.930 4.9 0.265 
192 611 79.4 0.863 0.943 4.1 0.239 
384 168 69.6 0.868 0.903 4.7 0.313 
768 52 85 .6 0.852 0.933 3.4 0.262 
1536 14 77.9 0.866 0.960 2.1 0.209 
values are also reduced. Because of nonlinearity in converting NDVI to fractional veg-
etative cover, the rate of the vegetation density decrease with resolution is greater than 
should actually occur. The result is a local modeling bias for Rn values > 600 W m- 2 
displayed in Fig. 4 .3 1. When the observation resolution coarsens beyond 192 m, the 
local bias disappears. This happens because vegetation density cover estimates at and 
beyond operational scales are the same for aggregated inputs or outputs. 
4.6.4 Ground Heat Flux 
Ground heat flux , G, aggregation results are shown in Fig. 4 .32, with linear regres-
sion statistics in Table 4.19. In general, G values conform to previous results, where 
agreement is contingent upon land cover type at finer resolutions, but at coarser res-
olutions agreement between aggregation approaches is good regardless of land cover 
type . There is significant scatter at 48-96 m resolutions with moderate correlation val-
ues (R2 ~0.75), but diminished scatter and better correlation values (R2 > 0.80) at 
resolutions coarser than 96 m. 
Because G flux is computed as a fraction of net radiation received at the soil (Eq. 
233 
750 
~ 700 
E 
~ 700 i"  650 
u 
r50 O> Y.' 600 ? 
!f 600 
550 
550 
500tL...._  _.__.~. .....- ~c.....-..L-~.......L~ ......J 
500 550 600 650 700 750 BOO 
500J?...-....L--~-........- -'~_  _.__. _ _, Aggrego led Ou tput 
500 550 600 650 700 750 BOO 
Aggrcgo ted Ou lpu l 
750 
f 700 i",  650 
"~ 650 O> 
[ Y.? 600 -
9' 600 -
500 
0 650 700 750 
BOO 
OO 50
0 550 60
B Aggrega ted Ou tput 500 650 700 
750 
500 550 600 Aggrcgo led Outpu l 
Rn 1536 m 
Rn 192 m BOO 
BOO 
750 
750 
, 700 
a. 
, E 700 
f "i  650 
"~ 650 [ 
Ir 1 600 
O> 
fl' 600 
550 
500 650 700 750 BOO 
500 550 600 
750 BOO Aggrega ted Outp1.1t 500 700 
500 550 600 
650 
Aggrcgoled Ou tput 
Figure 4.31: Net radiation aggregated from El Reno 12 m data, 2 July 1997. 
234 
estimated vegetatio
n density. 
o the accuracy of 
.54), its acc uracy i
s directly related t
2 by fluxes between 
> 1.0) are represented
 
eas (LAI 
The moderate to th
ickly vegetated ar
resented by flux 
ly vegetated areas (
LAI < 1.0) are rep
60 and J0 0 W m-
2, while sparse
 thickly and thinly ve
getated areas 
I 00 W m-
2 . The difference bet
ween
values exceeding  
solar radiation. Ve
getated areas have
ading from 
is due to the relativ
e amounts of sh
g wave radiation a
nd not to 
pected G flux is large
ly due to lon
x
shaded soi ls and th
e e
short wave radiatio
n . 
ows two kinds of s
ca tter. One 
s sh
arance of the aggre
gation experiment
The appe 2 from the one-to-on
e line, 
rge deviations (> I 0
0 W m - ) away 
kind is random, w
ith la
of scatter is non-ran
dom and is 
r kind 
ed by georegistratio
n errors. The othe
and are caus ight 
from 48 to J 92 m, th
ere is a relatively t
ging 
t. For resolutions ra
n
resolution dependen values less than I 00
 W m - 2 
g of aggregated ' 
 symmetric clusterin
( < 10 W m- 2 variation
) 
on induced variatio
n in 
kly vegetated areas h
ave little resoluti
which indicates tha
t thic
for those G values  192 m 
xists for resolutions
 between 48 and
G flux. However, a b
ias e
sparsely vegetated 
areas. The 
o the 
00 W m-
2 . These values corr
espond t
greater than J tation of the same 
scale 
es
 W m-
2, but significant. It
 is a manif
bias is not large, ~ 2
0  H LE 
gation experiments
 performed on the ' ' 
uracy of NOVI obs
erved for aggre
inacc erestimate vegetatio
n 
 vegetation is sparse
, NOVI tends to ov
here
and Rn components. 
W
nderestimate the a
mount of 
ly, aggregated inpu
t values tend to u
density. Conseque
nt
 ~20 W m - 2. 
ce, and hence under
estimate G flux by
soil surfa
solar radiation reac
hing the 
is to confirm the sca
le 
 of the G aggregation
 experiments 
ations
The overall implic es. But the scale er
rors 
vegetation density e
stimate inaccuraci
dependencies induc
ed by 
e they are relativel
y 
tant as H and LE sc
ale errors becaus
s impor
for G flux are not a onent (typically < 15%
 of Rn) 
nt comp
also because G flux 
is a less significa
small and 
 balance. 
in the surface energ
y
235 
150 -
, 
<> 
.f 
0 
~ 100 
[ 
~ 
50 100 150 200 
0 "'--~-'--~-J---~--'-"--,__J
,oo ,so 20
 0 
50 Aggrega ted Ou lput 
0 Aggregoled Oulpu l 
G 768 rn 
G 96 rn 200 
200 
,so 
,so , 
<> 
C 
l1 00 
~ 
50 
50 
0 
50 100 150 200 
OIL----'--~-'--~-.,_.---2'0 0 0 Aggregated Out pu t 
50 100 1SO 
0 Aggregoled Output 
G 192 rn 
200 
, ,so 
<> 
.f 
~ 100 
~ 
} 
50 100 150 200 
OIL..-~-'-~--'--_,,_,-~__, 
0 50 100 ,so 
Aggregated Ou tput 
200 
Aggregated Output 
Figure 4.32: Ground heat flux aggregated from El Reno 12 m data, 2 July 1997. 
236 
Table 4 .19: Gro und heat fl ux aggregation regression statistics. 
Sca le (m) N Intercept Slope R2 Se Se/Sy 
48 92 12 2 1. 8 0.778 0.752 13.6 0.498 
96 2350 23 .6 0.749 0.762 12.0 0.488 
192 6 11 24.2 0.73 1 0.807 9.7 0.440 
384 168 12.4 0.799 0.842 8.6 0.399 
768 52 26.2 0.705 0.830 7.0 0.4 16 
1536 14 2 1.2 0.758 0.923 4.1 0 .289 
4.6.5 Flux Moments and Scale 
Review ing the aggregati on results, the general pattern that has emerged is that there is 
generally good agreement between flux estimates made from 12 m observations directly 
and flu x estimates made from aggregated input va lues. There are some exceptions, no-
tably with H.~a nd R11 , where di sagreements are caused by the way vegetati on abundance 
is determined. In the aggregated input approach, NOVI va lues are recomputed to simu-
late lower reso lution data. In the aggregation process, low and hi gh NOVI va lues con-
verge towards a mean value. For low NOVI, H 8 dominates over LEc. Upon aggregating 
the input values, the estimated vegetated cover in these regions is increased, causing an 
underestimate of Hs. For hi gh NOVI, LEc dominates over H8 . When samples with 
these values are aggregated, the estimated vegetated cover is decreased, leading to an 
underestimate of LEc . 
These results suggest that actua l remote sensing data acquired over moderately to 
heavily vegetated regions, at resolutions up to 1.5 km, would also show good agree-
ment with simultaneously acquired high resolution ( ~1 2 m) data. Areas with sparse 
vegetation, however, have sca le-dependent flu x estimates and rather than showing good 
237 
Hsoil 17_:0c__ ____. .., Hsoit 120 0 
80 
woo 
,o 
]::, )?1 
0 LJ ?--?...J--="'-?J,,o- ~~,oo~ ----~ >O 250 
??,o,1 "'" 
Hsoil :!?I 0 
,o 
>O ,oo 200 250 ,00 200 ,so JOO 
l?hoi l 90 0 Hsoit 400 0 
lO 
so ,C)() 200 2>0 JOO 
Hsoi l 160.0 Hsoi l 600 0 
,oo 
"
6  0 
,o 
8 
,o 
,o ,oo 200 2>0 JOO ,oo ,,. 200 
H,oil 
Hso il 200 0 H:5oi l1 000.0 
,oo '50 200 250 JOO ,oo 200 lOO 
H,oo! 
Figure 4.33: Histograms of sensible heat from soil. The bimodal characteristic distribu-
tion seen at 12 m reso lution is mostly lost when operational scales are reached ( ~ 200 
m) . 
238 
agreement, would show biased estimates. As the resolution is decreased towards 1.5 km 
resolutions, the sparsely vegetated areas become confused with moderately vegetated 
areas, with a resultant increase in apparent evaporative fraction. The El Reno study 
indicates that thi s change could be on the order of 15%. 
The resolution dependence of evaporati ve fraction estimates, shown prev iously in 
Fig. 4.29, is also represented by decreased sensible heat from the soil component (Fig. 
4.33), which shows a series of H8 hi stograms at reso lutions ranging from 12 m to I km. 
A slightly different resampling ro utine was used in order to highlight aggregation results 
in the vicinity of 192 m, which is the resolution, depicted in Fig. 4.28, where modeled 
Hs fluxes no longer represent any purely bare so il patches. The routine sub-samples 
12 m data to IO m data to all ow finer reso lution aggregation intervals to be generated, 
and is otherwise identica l to the prev ious aggregation experiments. Note that the bi-
modal di stribution, seen at 12-24 m resolutions, is lost at 96 m resolutions. Most of 
the change in hi stogram appearance occurs with the fairly abrupt loss of high ( I 00-300 
W 111 - 2) H,5 va lues, between 90-200 m reso lutions. At 200 m resolution, virtually no 
high Hs values remain in the hi stogram, which indicates that the surface energy balance 
model no longer detects pure bare soil areas. The revised aggregation procedure thus 
illustrates another important finding, namely that resolution dependence of surface en-
ergy flux estimates is not a smoothly changing function, but can change abruptly over 
a few tens of meters. In the El Reno study, the change occurs at ~ 200 m, a resolution 
somewhat less than operational scale. 
The distributional changes can be summarized in a series of moment diagrams (Fig. 
4.34). These moment diagrams illustrate the statistical distribution of fluxes for aggrega-
tion experiments performed over scales ranging between 12 m and l km. They are use-
ful because they can show whether or not there ex ists a functional relationship between 
239 
Second Hso il 
Fi rs l Hsoi l 
100 C (l) 10000 
C E 
(l)  0 
E ~ 2 
0 
2 
1000 
10 --- 10 100 1000 1000 
10 100 
Fourth Hso il 
Third Hso il 109 
107 
....., 108 
C 
6 (l) 
C 10 E 
(l) 0 
E 2 107 
0 
2 105 
106 
104 10 100 1000 
100 1000 10 
Figure 4.34: Scaling moments: sensible heat from soil, aggregated inputs. 
240 
flux estimates made at different sca les. If there are functional re lationships, then one 
cou ld predict stati stica l distributions of fluxes at an arbitrary sca le, given flu x estimates 
at some other scale. This ability would be very useful because flux estimates made, 
for example, at I km resolution, could be used to predict the range of fluxes expected 
at a 12 m resolution. The moment diagrams in Fig. 4.34 show the first fo ur statistica l 
moments (i. e., mean, variance, skewness, and kurtosis) for Hs flux va lues derived from 
aggregated input va lues. A ll four pl ots show simil ar features, with smoothl y decreas ing 
moments from 12 m to 200 m resolutions, anomalous increased moments at 400 m, and 
greatly diminished moments at ~ 800 m reso lution. These moment plots indi cate that 
there does exist a functional relationship between 12 m and 200 m resolutions, but not 
at 400 m resolution . This resu lt is important and shows that as long as image resolution 
is finer than operational sca le, modeled flux estimates can be related to flux estimates at 
any other sca le finer than operational sca le. Once reso lutions approach operational sca le 
(which in the El Reno example, begin at 200 m), modeled flux estimates become inac-
curate and are difficult to relate to any other sca le. With only one sample point beyond 
operational scale, results in Fig. 4 .34 are insufficient to conc lude what kind of statistica l 
functional relationship exists for reso lutions greater than operational sca le. 
The behavior of the aggregated input, H .~ flux , just seen can be contrasted with the 
conservative ly aggregated 12 m fluxes in Fig. 4.35. In this case, the moment plot show 
the resolution effects if surface flux modeling were a linear process. The first moment, 
or mean, is virtually flat (it should be exactly flat, but some numerical rounding has 
occurred). The second, third, and fourth moments show smoothly changing slopes with 
resolution, and no abrupt transition at operational scale. Furthermore, the slopes for the 
second, third, and fourth moments are all substantially less ( e.g., the variance for aggre-
ga ted output decreases from 15000 to 6000 W 2 m- 4 over the 12 m to I km range, while 
24 1 
Seco nd Hso il 
Firs t Hso il 
_. 
100 
? 0 0 O ? ----0 ~ 10000 ~ 
C 
(lJ 0 
E 2 
0 
2 
1000 ~-~-~---...._J: 
10 100 1000 10 1000 
10 100 
Fourt h Hso il 
Third Hso il 9 10 
10 7 ~----- - - -.......-, 
8 
C 10~ 
(lJ 
C 1 0 6 E 
(lJ 0 7 
E 2 10
~ 10 5 -
4 '--___ .......... ____ _,__, 
10 1000 
10 100 
Figure 4.35: Scaling moments: sensible beat from soil , aggregated outputs. 
2 1
the variance from aggregated input decreases to 1500 W m- , for the same range). Th is 
means that surface energy balance modeling is very sensitive to small changes in remote 
sensing observations. 
A more dramatic difference between moments obtained from aggregated inputs and 
aggregated outputs can be seen in the plots for LE, flux (Fig. 4 .36). The previously 
observed partitioning shift from H soil flux to LE canopy flux (Fig. 4.29 is seen in the 
very moment expected to show the least variability, namely the mean (upper left plot in 
2 
Fig. 4.36). Here the LEc would be expected to remain close to 150 W m- for all mod-
2 
eled resolutions. Instead, LEc flux increases by 50 W m- between 12 m and l km. the 
moment diagrams also show slope discontinuities at 200-400 m resolutions, similar to, 
242 
Firs t LE co nopy Second LEconopy 
105 
_,__, 
C C 
Q) Q) 
E E 
0 0 
2 2 
100.__ __~ ---~...,__, 410 '----~-~--~ 
10 100 1000 10 100 1000 
Third LEco nopy Fou rth LEco nopy 
10 8 .-----~----~ 10 10~---~----.....---, 
___, 
C C 
Q) Q) 
E E 
0 
~ 2 10 7 ~ 
9 
1o '----~----~ 
10 100 1000 10 100 1000 
Figure 4 .36: Scaling moments: latent heat from canopy, aggregated inputs. 
but of lower magnitude than the slope discontinuities seen in the Hs moment diagrams. 
This means that LEc flux est imates are also inaccurate when made at operational sca le 
resolutions. 
4. 7 Studies at Jornada Experimental Range, 
New Mexico 
As di scussed in Section 3.3, remote sensing surveys have been conducted semi-annually 
over the Jornada Experimental Range in New Mexico. The Jornada landscape is quite 
different from the E l Reno landscape; it is a semi-arid rangeland and has no cultivated 
243 
 it is a degraded gras
sland con-
tle,
erns. Although it is 
used for grazing cat
fie ld patt n-grazing vegetation. her no
 bush, and a va riety o
f ot
ta ining mesquite, aca
cia, creosote
or the El Reno study, 
one can 
chniques over Jomada
 as used f
e
By applying the same
 t
hange signi ficantly. 
ues perform when the
 surface conditions c
see how well the tech
niq
ironment than seen at
 El 
 estimate ET from a m
uch drier env
Ultimate ly, the goa l i
s to
Reno. 
 the same extent as per
formed 
ysis of Jornada data to
However, time did not
 allow anal
 of data over Jornada
 are underway and 
n
er El Reno. Process
ing and interpretatio
ov perature and 
de surface property es
timates (tem
the res ults currently a
va ilable only inclu
ogeneity over the Mes
quite site. 
of surface heter
NDVI) and measurem
ents 
4.7.1 Surface Tempe
rature 
3.14) were measured 
over a 
id (Fig. 
 temperatures at the M
esquite reference gr
Surface
MASTER remote sen
sing survey 
s before and after the
 
six-hour period, span
ning time
face brightness tempe
ratures from 
measurements of the s
ur
The 
on 27 September I 99
9. 
. Each patch contain
s 
in Fig. 4.37
ld thermal infrared rad
iometers are shown 
hand-he tica l dashed line 
 7x7 grid (30 meters x
 30 meters). The ver
49 measurements from
 the
 each patch 
. Along the top edge o
f the plot, and above
e
indicates the MASTE
R flight tim
ard devia-
ans and, in parenthese
s, temperature stand
e
of points, are the tem
perature m
ne time is large, over 20
?C . Hotter 
temperatures at any o
tions. The range of br
ightness 
 At 
ooler temperature occ
ur over the mesquite.
r bare soil while c
temperatures occur ov
e
erature for the grid is 
~34.5?C. 
rightness temp
MASTER flight time,
 the average b
s (i. e., the emission i
s as-
re
id measurements are 
brightness temperatu
Since the gr
al temperatures, MAS
TER measure-
ody), rather than phys
ic
ckb
sumed to be from a b
la
s values. However, th
e spectra l response 
brightnes
ments should also be
 converted to 
244 
o f the handhe ld radi ometers is uncertain, and direct compari son is difficult. As shown 
in Fig. 4.38, MASTER brightness temperatures vary strongly with wave length due to 
so il emissivity e ffects . Note how the shapes of the temperature curves mimic typical 
quartz-bearing soil emiss ivities at 8-1 2 f- l l11 wavelengths, as seen in Fig. 3. 12. 
A rough compari son between the ground radiometers and the MASTER radi omet-
ric measurements can be made by considering onl y wave lengths greater than ~ J 011.m, 
si nce surfaces viewed at these wave lengths tend to have hi gh emiss ivities, regardless 
of surface cover. For MASTER, bands 46-50 fall in this category. Observing the at-
mospheri ca ll y corrected values (denoted by D symbols), one can see that MASTER 
brightness temperatures for the Mesquite site range ~38-39?C . Thi s is 5?C greater than 
observed from ground measurements. Based upon this bias, and upon the large scat-
ter in the ground-based temperature measurements, it appears that the MASTE R nadir 
observations are relatively insensitive to the mesquite vegetation. 
4.7.2 Vegetative Cover 
The relative insensitivity to vegetation appears to be confirmed in NOVI imagery (Fig. 
4.40. Although ground based temperature measurements have a 4+?C range, indicative 
of significant sampling from both vegetation and bare soil , the NOVI image is dominated 
by low NOVI values (0.0-0. 1). Since mesquite is the main contributor of the cooler 
temperatures, a large portion of the vegetation must be non-green (i. e., branches and 
stems). The relationship between surface temperature and NOVI, shown in Fig. 4.39, is 
much more constrained than seen earlier at El Reno, meaning that most of the land cover 
at Jornada is either bare soil or sparsely vegetated. The roughly triangular distribution 
commonly seen over regions with both bare soil and thick vegetation (Fig. 4 .19), and 
discussed in detail by Gillies et al. (1997), is absent here. Note, however, that scatter of 
245 
Mesqu il e Si te 27 Sep l. 1999 
60 
18.9 26.9 33. 1 35.9 39. 4 41.3 40.6 
(3. 7) (3.5) (4.6) (4.7) (54) (5.5) (5 2) 
,,...__ 
[/) 
::i 
[/) 50 
QJ 
._u__ , 
QJ 
L 
::i 40 
0 
L 
QJ 
Q_ 
E 
QJ 
I- .30 
[/) 
[/) 
QJ 
C 
..c 
CJ) 20 
L 
m 
10 
8 9 10 11 12 1 .3 14 15 
Time (hrs, MDT) 
Figure 4.37: Mesquite grid surface brightness temperatures. Measured temperatures, 
taken from 7 time periods, of a 30 meter square patch on September 27, 1999. Mean and 
standard deviation of each temperature group is indicated along the top. The MASTER 
overflight time is indicated by the dashed vertical line. 
246 
Mes qu ile Site Brig ht. Temp. 
40 Surface Rad ian ce 
,.-.. 
(/) 
:J 
(/) 
(lJ 
2, 35 -
(lJ 
I... 
_:...J.,  Obse rved Rad iance 
0 
I... 
(lJ 
0.. 
~ 30 -
I-
2 5L..-,.__...l...__,__,_...1---.L-''--"__,____,__,_...1---.,____L-'--'---'-~ 
46 48 50 
42 44 
MASTER Bond 
Figure 4.38: Mesquite site brightness temperatures, 27 Sep. 1999. Temperatures de-
rived without atmospheric correction are shown for each MASTER band as + signs. 
Brightness temperatures obtained by removing atmospheric effects between the surface 
and the sensor are indicated by the D symbols. 
247 
points away from the main diagonal is lower than seen for the El Reno TMS/TIMS data . 
This is due to the much improved registration between VNIR data and TIR data. 
When a hi stogram of the NOVI values is viewed (Fig. 4.41), the sparsity of green 
vegetation is readily apparent. There is no mode in the histogram representing vegeta-
tion. Instead the density of vegetation varies continuously at 3 meter reso lutions. Con-
sequently, at the Mesquite site it is difficult to apply the NOVI normalization technique 
o f Choudhury et al. ( 1994) because I 00% vegetative cover does not exist. 
4.7.3 Operational Scale Analysis 
Because of the clumped patterns of dunes and mesquite bush at Jomada, the operational 
sca le of the landscape is short, on the order of 3 m. Fortunately, imagery of very high 
resolution recently became avai lable to examine how this vegetation heterogeneity is re-
lated to more regional patterns. The imagery is derived from the lkonos satellite (Space 
Imaging, 200 I), which in the panchromatic3 band has one-meter resolution (Fig. 4.42). 
Individual clumps of mesquite bush atop the coppice dunes are seen in dark tones. The 
mesquite site temperature grid is outlined in the lower left of the image. Even though 
the panchromatic image represents neither surface temperature nor NOVI , it is closely 
correlated to these surface properties. Indication of operational scale, therefore, can be 
seen in the series of histograms in Fig. 4.43. Resolutions are simulated in powers of 
two, starting with the source image at upper left with I m resolution, and progressing 
downwards to 64 m resolution. The final plot (logarithmic on the x-axis) in the lower 
right shows the decrease in standard deviation of the panchromatic measurements. Both 
the histograms, and this last plot, show that a majority of image variability is contained 
3The lkonos panchromatic band spans the wavelengths 0.53-0 .93 ?m, which includes both the red and 
near infrared wavelengths used for NOVI. 
248 
Jornada 2 7 Sept. 1999 
0.3 
0.2 -
> 
0 
z 
0.1 
0.0 -
- 0 .1 '--' --'~~~~~~~~-~~~~~~~~~~~ 
30 35 40 45 50 
Surface Tempe ra tu re (Ce ls iu s) 
C 
500 1JOO 1500 2000 
Ccunts 
Figure 4.39: NOVI vs. surface temperature at the Mesquite site, 27 Sept. 1999. Source 
resolution is 3 m. At the Mesquite site, vegetation is sparse, clumped and dominated by 
woody matter. 
249 
Mes quite Sit e, 27 Sep t. 1999 
0.00 0 .10 0. 20 0. 30 0 .40 0 .50 
NOVI 
Figure 4.40: Mesquite site NDVI at 3 m resolution. The mesquite temperature grid 
is approximately in the center of the image. Bare soils appear as dark tones, while 
mesquite bush appear as light tones. 
250 
Mesquite Site 27 Se pl. 1999 
0. 14 
0. 12 
0. 10 
>, 
u 
C 
Q) 0.08 -
::J 
er 
Q) 
\.._ 
LI... 0.06 -
0.04 
0 02 
0 . 00 .L.LI...U-LU.-'-LI..L..uw.,..,...._._,._L_uu_,_._L.L..L=. .
.........~  
LI...U-LU...w.
0 .00 0. 10 0.20 0.30 0 .40 
0.50 
NOVI 
3 m MASTER imagery on 27 
Figure 4.41 : Histogram of Mesquite site NOVI
, from 
Sept. 1999. 
25 1 
Mes qu it e Site , 23 Moy 200 1 
z 
2 
f-
=:) 
.32 4. 50 .32 4. 60 .32 4 . 70 .32 4 .80 .32 4 .90 
UTM E 1.3 (km) 
Figure 4.42: Mesquite site from Ikonos. Dark objects are mainly mesquite bush, and 
light tones represent sandy soil. Approximate location of 30 m x 30 m temperature grid 
is shown by the box. Bowen ratio site is ~ IO m to the southeast of the grid. 
252 
16 
O0 .2JO~ I 
0 .20 
0 . 15 
0 . 10 
0 05 r0 .n051 ?  J1'i I 
0 .00 ---c:C'. ooo~-----L~ I~,~~ 
500 600 700 800 900 500 600 700 800 900 
2 32 
o0 .~25 0 .20 I 
0 . 15 
0.10 
0 05 
0 00 Ill! ----~-- -~-l ooo~- -
500 600 700 800 900 500 600 700 800 900 
4 64 
0 25 
0~J.2O0 I I 
0 .15 
0. 10 
gg g.____~~~\ 
500 600 700 800 900 500 600 700 800 900 
8 
0 .2~ I 100 0 ~J 120 f 0.2O0 I 
0 . 15 n ~~ 0 0. 10 ?O . ? 
g_gi;'--------"--_/':::\~ 2g O ? 
500 600 700 800 900 10 100 
Resolution (m) 
Figure 4.43 : Resolution effects, Mesquite site. lkonos imagery, 23 May 200 I shows bare 
soil as large numbers, and mesquite bush as small numbers. Distribution of reflectances 
become much more symmetrical at 8 meter resolution with significant loss of range. 
within 1-4 m scales. The importance of the fine scale heterogeneity is reinforced when 
the three measures of heterogeneity are applied: semivariograms (Fig. 4.44), local stan-
dard deviation (Fig. 4.45), and geographic variance (Fig. 4.46). In these cases, opera-
tional scale lies between 2 and 4 m. 
Hence the low-altitude (1500 m) MASTER flights, with 3 m resolution, are just 
barely adequate to distinguish between vegetation clumps and bare soil patches. When 
MASTER-derived surface temperatures are aggregated, the range in the temperature 
distribution is reduced by 1/2 in the first step. Table 4.20 shows that standard deviation 
in temperature is reduced from ~ 3?C at 3 m resolution, to l.5 ?C at 12 m resolution . 
253 
Mesq ui le Sile Sem i- va ri an ce
2.0x 10 4
 
 
1.5x 1 o4 
QJ 
u 
C 
0 
'--
0 
> 1.0x 1 o4 
I 
E 
QJ 
(/) 
5.0x 1 o3 
0 '--'--'--'--'--''--'---'-_L.....-'--'--'--'--'--'--'--'----'-'--'-_J 
0 20 40 60 80 100 
Lag (m) 
Figure 4.44: Semivariance at Mesquite site. Ikonos extract, 23 May 2001. 
254 
Mesq uite Sit e, lkonos Imag e 
80 
C 
0 60 
0 
> 
Cl> 
0 
u 
'-
0 40 
u 
C 
0 
~ 
(/) 
0 
u 
0 
_J 20 
0 '---~__,____,___.__.,_,_,__,___._ __ ,___,___.___,_,_~_,_, 
10 100 
Reso lut ion (m) 
Figure 4.45: Local standard deviation at Mesquite site. Ikonos extract, 23 May 200 I , I 
m resolution . 
255 
Mes quit e Si te 
.30 
25 
(l) 
u 
C 
0 
'- 20 
0 
> 
0 
~ 
0 
I- 15 
~-
0 
C 
(l) 10 
u 
'-
(l) 
CL 
5 
0 
10 100 
Reso lut ion (me ters) 
Figure 4.46: Geographic variance at Mesquite site. Ikonos extract, 23 May 200 I, I m 
resolution. 
256 
Table 4.20: Mesqu ite area surface temperature vs. resolution. 
Resolution Temperature (0 C) 
(m) Mean Std . Dev. 
3 42.5 3.13 
12 42.5 1.69 
24 42.5 1.34 
48 42.5 1.21 
96 42.5 1.11 
Thereafter, the standard deviation decreases minimally when imagery are aggregated 
to 96 m resolution. The effect is also seen in Fig. 4.47. The fi ne speckly pattern at 
3 m resolution represents individual clumps of mesquite, and is mostly lost at 12 m 
resolution. From 12 m to 96 m resolution, only larger scale variations, on the order of 
500 m, can be distinguished. 
257 
3 m 12 m 24 m 48 m 96 m 
i.:? ,:?~~ 
?' ' 
35 40 45 50 
T- ,~? Ce lsius 
Figure 4.47: Surface temperature scaling over Mesquite site. The black dot lies over the 
approximate location of the Mesquite site temperature grid . Source MASTER imagery 
at 3 meter resolution aggregated to 12, 24 , 48 and 96 meter resolutions. 
258 
5 Conclusions and Discussion 
5.1 Research Contributions 
This study has developed three significant findings. First, it has shown that thermal 
infrared and visib le-near infrared data can be used wi th a surface energy flux model 
to make reasonable surface energy flux estimates . The estimates in several instances 
have been validated aga inst ground-based eddy-covariance measurements, whi ch are 
the best available in-situ flux observations. Second, it has shown that quantitative mea-
sures of landscape heterogeneity agree with qualitative views of landscapes at EI Reno, 
Oklahoma, and Jornada, New Mexico. The landscape scale heterogeneity was shown 
to have well-defined operational sca les, and the ex istence of these sca les is reflected 
in both the remote sensing observations and in the modeled energy fluxes . Third, it has 
quantified the interdependence exists between landscape sca le heterogeneity, sensor res-
olution, and estimated surface energy fluxes. Where the heterogeneity is relatively low, 
as occurs over extensive thick vegetation and bare soils, the estimated surface energy 
fluxes showed little scale variation ( < 50 W m- 2). Where the heterogeneity is relatively 
high, as occurs over sparse and unevenly distributed vegetation, the estimated surface 
energy fluxes showed significant scale variation (sometimes > I 00 W m - 2) and signif-
icant model bias (> 50 W m- 2) . Furthermore, it has been shown over El Reno that as 
sensor resolution decreases, the estimated evaporative fraction increases by as much as 
15%. 
In Chapter 1, questions were posed about the difficulties encountered when esti-
mating ET in the face of heterogeneity. Could a one-dimensional, point-based surface 
energy flux model be used to make accurate estimates over scales ranging from 12 m 
259 
to 1.5 km? Previous experience with the model used in this study- the two-source 
approach (section 2.4)- has shown that it performs well under a range of surface con-
ditions, from semi-arid to humid environments. This study shows that the two-source 
model can, under some conditions, be employed to produce moderately accurate surface 
energy flux estimates over scales ranging between 12 m and 1.5 km. 
By using an aggregation-flux matching approach with 12 m remote sensing observa-
tions, two causes of resolution-induced uncertainty in the surface energy balance mod-
eling could be identified: georegistration errors and bias in the vegetation estimator, 
NDVI. Georegistration errors are exacerbated by the use of higher-resolution data , with 
potentially large flux modeling errors (> 100 wm - 2 , or more than 30% relative error). 
These errors, however, can be greatly reduced through technological and data processing 
improvements. Bias in NDVI , on the other hand, is a more intractable problem. The El 
Reno experiments show that NDVI has negligible bias as resolution is varied over thick 
vegetation (LAI > 1) , but that it has significant bias ( ~ 50 W m - 2) over sparse vegetation 
(LAI < I) . When the entire El Reno study area ( ~6 km x 4 km) is considered, NDVI 
bias causes the aggregate evaporative fraction to increase by ~1 5%. Future energy flux 
modeling experiments over terrain similar to that at El Reno will need to consider this 
potentially significant source of uncertainty in evaporative flux. 
Chapter I presented four hypotheses that motivated and guided the work. The results 
are now discussed in tem1s of those hypotheses. 
5.2 Accuracy of Remotely Sensed Model Inputs 
? Hypothesis 1- Remote sensing observations of surface temperature and vegeta-
tion density are sufficiently accurate for surface energy flux modeling. 
260 
Remote sensing observations of surface temperature and vegetation dens ity at El 
Reno, Oklahoma are suffic ientl y accurate fo r surface flux mode ling. Observations at 
Jo rnada , New Mexico, as currently processed, are not. A general implication of these 
resul ts is that current technologies to extract surface temperature and vegetation density 
are adeq uate for well-watered, unstressed vegetation, but not for sparse, water-stressed 
vegetati on. Spec ifica lly for this study, remotely sensed surface tempera tures over Jor-
nada were fo und inadequate, and consequently cannot be used fo r fl ux modeling. Fur-
ther algorithmic development is req uired to improve surface temperature estimates over 
the sparsely vegetated Jornada area. 
For the El Reno study, preci sion and accuracy of surface temperatu re estimates were 
assessed by analyz ing observations over an extended water body, Fort Cobb Reservo ir, 
and by comparing remotely sensing temperature estimates with ground-based tempera-
ture observations. Surface temperatures obtained from the Fort Cobb Reservoir TIMS 
surveys (section 4.2) showed that thermal infrared estimates for all bands were prec ise 
within J .3 ?C of the mean water surface temperature. Error within any thermal band 
was < 0.5?C . Remote sensing surface temperature accurac ies were fo und to vary by 
time-of-day. Mid-morning surface temperature estimates were accurate within J .5?C of 
ground-based observations for mid-morning surveys over three out o f four study sites. 
The mean temperature difference for mid-morning surveys was 0.6?C , w ith a relative 
error of -1 .6%. These errors are less than the 2?C maximum error estimated in Section 
3.5, where it was shown for typical conditions at El Reno that a 2?C error corresponds 
to typical eddy-covariance accuracy, ~ 50 W m- 2 . Mid-afternoon surface temperature 
estimates showed poorer accuracy, with a mean remote sensing over-estimate of 5.7?C 
( 13.7% relative error). The fourth study site, field ER09, was anomalous. Disagree-
ment between remote sensing derived temperatures and ground-based observations can 
26 1 
be explained, but cannot be compensated. It is probable that differences in surface tem-
peratures at ER09 are due to differences in sampling locations and are not caused by 
instrumental error. 
Observations of vegetation density (section 4.3) over El Reno fields were adequately 
modeled with re-normalization of TMS NOVI observations and gro und level measure-
ments of LAI. Despite a significant bias on the order of LAI= l , NOVI re-normali zation 
allowed the representation of fractional cover to be consistent with the full-range of 
remote sensing observations. 
Observations of surface temperatures at one site at Jomada (mesquite dunes area, 
section 4 .7.1), showed poor agreement (> 5?C) between ground obtained brightness 
temperatures and MASTER-based surface temperatures. This current result means that 
further work is needed to reduce the discrepancy before flux modeling can be pursued. 
Calibration of the MASTER instrument, however, is believed to be excellent, and there-
fore prospects for improved temperature results are good. Comparison of remote sensing 
derived vegetation indices and ground-level observations has not yet been done. 
5.3 Accuracy of Modeled Surface Fluxes 
? Hypothesis 2- Modeled surface energy fluxes closely match, possibly within 
J 5%, relative error independently measured fluxes. 
Efforts to validate modeled surface energy fluxes were made in two ways. First, the 
modeled surface fluxes were compared with ground-based eddy covariance measure-
ments. Second, the modeled fluxes were compared with aircraft-based eddy covariance 
measurements. 
On the whole, modeled fluxes from mid-morning surveys over El Reno (section 
262 
4.4) showed exce llent agreement, typi ca lly less than 10% relative error, with respect 
to ground-based eddy covariance measureirents. Eddy covariance measurements arc 
considered the best in-situ ET measurement technique. Eddy covariance instruments 
measure sensible heat (H) and latent heat (LE) independently. Modeled fluxes from mid-
2
afte rnoon surveys, however, showed errors ranging between 75 and 150 W m - , which 
resulted in errors for H and LE rang ing between 30 and 93%. The contrast between 
morning and afternoon survey flux values is consistent with the surface temperature re-
sults just discussed in Sect ion 5.2, where morning remote sensing temperatures were 
significantly more accurate than temperatures acquired in the afternoon. This relation-
ship between surface te mperatures and surface flu x estimates confirms the importance 
of accurate surface temperatures in the flux model. 
Validation of two-source flux estimates using aircraft flux measurements was more 
ambiguous. Relative errors between two-source estimates and aircraft-based eddy co-
variance measurements, when averaged over the flight path, showed good agreement 
for the mid-morning survey data . Mean H values differed by 6 W m - 2, or 5% relative 
error. Mean LE values differed by 36 W m- 2, or 17% relative error. On the other hand, 
when the aircraft flux profile va lues were compared point-by-point along the flight path, 
they were inconsistent with the two source flux estimates. In some instances the H and 
LE components from the aircra ft were nearly identical to the two-source estimates, and 
in other instances the components differed by > 100 wm - 2, with a relative error also 
> I 00%. When plots of the two different sets of flux values are viewed, particularly for 
the LE component, there appears to be some qualitative agreement because of similar 
curve shapes. But this observation on ly indicates that the two methods, in general terms, 
are responding to surface co nditions in the same way. Bare soils have high H and low 
LE. Thick vegetation has low H and high L~. The va lidation difficulties encountered 
263 
o ways. First, aircraft fl ux m
easurements at 
a fl data can be explained in t
w
wi th the ai rcr
econd, the av-
as flu x va lues at two meters. S
30 meters above the ground a
re not the same 
ed for the aircra ft flux data p
rocessing are uncertain. 
eraging periods and distance
s need
ed eddy covariance measurem
ents, as 
at aircrafl-bas
The implica tion of these resu
lts is th
ntly processed, cannot be use
d for flux model va lidation. 
curre
5.4 Operational Scale 
e occurs at scales 
hesis 3- Landscape heterogen
eity over the El Reno sit
? Hypot
a ilable, l 2 meters. Hetero-on da ta av
significantly greater than the
 best resoluti
greater than the 3 meter 
eneity over the Jornada site o
ccurs at sca les signifi cantly 
g
resolution data ava ilable ther
e. 
 by ident ifying the dominant
 size of fea-
scape heterogeneity can be q
uantified
Land
. This dominant size is know
n 
tures on a land surface that c
haracterize a particular area
ree techniques (semi-variog
rams, loca l 
udy employed th
as operational scale. This s
t
es over the 
 and geographical variance) 
to identify opera tional sca l
standard deviation,
ver the semi-arid Jornada site
. 
sub-humid El Reno site and o
on 4.5) had operational sca le
s 
o site (secti
Landscape heterogeneity ove
r the El Ren
m TIMSITMS 
 200 and 400 m, which is sign
ificantly greater than the 12 
ranging between
at El Reno is that 12 meter re
solution is 
. The implication 
remote sensing resolution da
ta
d 
patterns, which are determine
more than sufficient to repres
ent the dominant land cover 
means that large sca le distrib
uted 
intervals. This 
by land use boundaries at qu
arter-mile 
ma could make use of coarse
r 
nd around central Oklaho
hydrologic studies in regions
 in a
g data are cheaper 
 ~1 00 m) remote sensing data sets. Coarser remote se
nsin
resolution (
lution data. 
and easier to acquire than hig
h reso
264 
.3), however, showed 
a much 
er the Jomada site (sec
tion 4. 7
Study of heterogeneity
 ov
typical 3 m 
This is not significantl
y different from the 
shorter operati onal sca
le, ~ 2-4 m. 
TER sensor. The very
 fi ne scale 
rom the MAS
remote sensing resolu
tion data available f
 sensing imagery has 
 Jornada mesquite dun
es shows that remote
of heterogeneity in th
e
mps of vegetation tha
t control 
 to adequately disting
uish the clu
insuffic ient resolution
gh resolution remote 
sensing 
eans that even wi th hi
the landscape heterog
eneity. This m
on lumped or effectiv
e 
 hydrological model w
ould have to rely up
data, any distributed
treatments of model p
arameters . 
d Surface Flux Estima
tes 
.5 Resolution, Scale,
 an
5
e at reso lutions better 
riginal observations ar
e mad
? Hypothesis 4- As 
long as the o
tes will 
erogeneity scale, surfa
ce energy flu x estima
pe het
than the primary lands
ca
intained within 15%. 
le independent, with r
elative agreement ma
be sca
, spanning 12 meters 
eriments (section 4.6)
Results from the El R
eno aggregation exp
dency that va ries from
 
 have a scale depen
 l .5 km, show that su
rface flux estimates
to
biases on the order of
 15%. 
negligible levels up to
 
ed 
 source data to 48 m a
ggregate data, show
xperiments, stepping 
from 12 m
Initial e  
2
- between aggregate
d flux values and flux
 W m ) 
significant scale depen
dence (J 00-200
uently shown (Fig. 4
.26) 
 inputs. It was subseq
values derived from a
ggregated model
d by data mis-registra
tion, 
 could be cause
at some of this appar
ent scale dependency
th ence (to ~ 50 W m - 2) 
at 
pend
dly diminishing scale 
de
a condition supported
 by the rapi
larger scales (96-192m)
. 
e considered, the scale d
e-
 scales wer
en aggregations from 
96 m scales to 1.5 km
Wh  sca le induced 
ound flux (G) was mini
mal. Typical
pendence of net radia
tion (Rn) and gr
265 
differences were less than 10 wm- 2 fo r R,1 and less than 15 w m- 2 for G. The sca le 
dependence of latent heat fl ux over dense vegetation (LEc) and over bare so il surfaces 
(L Es ) is also min imal, with differences on the order of 45 W m- 2 and 3 W m- 2, respec-
tively. The two-source estimated so il sensible heat fluxes (H.~) and canopy latent heat 
fluxes ( LEc ) do show some scale dependency, but the magnitude of this dependency is 
usually on the order of 50-100 W m- 2. The consequence for the overall surface energy 
balance is scale-induced bias in the evaporative fraction [LE /(L E + H) ]. It has been 
shown (Fig. 4.29) that the bias is significant and on the order of 15% when comparing 
evaporative fraction estimates at 12 m to estimates at 1.5 km. 
The practica l significance of these aggregation experimental resul ts at El Reno is 
two-fold. First, there is little va lue in collecting high reso lution remote sensing data 
if the spectral bands are not close ly aligned. Mis-alignment can be compensated by 
spatial averaging, but then the very usefulness of high resolution data is subsequently 
lost. Second, scale dependencies in surface flux modeling between 12 m and 1.5 km 
is small, often less than 50 W m- 2. This is less than uncertainties inherent even with 
the eddy-covariance technique ( ~ 50 W m- 2) , which is considered the best poss ible ET 
measurement. This means that the constra int on resolution, ~ I 00 m, established in 
Section 5.4, can be relaxed even further. Contingent upon the accuracy and precision of 
the remote sensing data, and its subsequent processing, these aggregation experiments 
imply that even 1.5 km resolution data can produce accurate surface flux estimates. 
5.5.1 Implications of the Results 
This investigation of the scaling properties of surface energy fluxes has shown (Section 
4.6) that consistent, instantaneous estimates of ET can be made over resolutions from 
12 m to 1.5 km. Agreement between estimates spanning thi s range is best for thickly 
266 
vegetated terrain, where bias is negli gibl e. Agreement between est imates made over 
sparsely vegetated terrain are a lso good, despi te some bias. Coarser resolution based 
2
inputs, up to I .5 km, tend to overes timate latent heat flux ( ~ 50- l OOW m - ) by ~ J 5%. 
A study of the sca ling properties of surface energy fluxes has also shown that, while 
mean estimates at resolutions up to l .5 km appear to be scale invariant, w ithin ~ I 00 
w m-2, distinct relationships between flux components contributed by the soil surface 
and by the vegetation ca nopy are lost at di sta nces as short as 200 m. At EI Reno, the op-
erational scale ranged between 200 and 400 m and was largely determined by c ultivated 
land use practices. Homogeneous land use sa mples of bare soi l or continuous pasture 
do not occur at resolutions poorer than 200 m. One consequence is that estimates of 
surface resistances- a critica l component in the two-source energy balance approach-
are no longer representative of the aggregate fbx resistance. Another consequence of 
diminishing resolution is that over 60% of image information, as represented by local 
variance of surface temperature and NDVI , is lost at 200 m resolution . 
Although the flux modeling and aggrega ti o11 experiments generall y appear to pro-
vide moderately satisfactory resu lts, there remain several significant problems. 
First, the results from the surface energy flux model were inaccurate for afternoon 
surveys. Sometimes flux estimates exceeded ground-based flux measurements by more 
than 100 W m- 2 . The large inaccuracies are iu part caused by overestimated surface 
temperatures, derived from the afternoon TIMS surveys. In addition, inaccuracies could 
be caused by large discrepancies between the estimated radiometric temperatures and 
the aerodynamic temperature, as discussed in Section 2.4.6. Some of the overestimates 
could be excluded, namely those sourced from field ER09, because the ground-based 
temperatures there were anoma lous for both morning and afternoon surveys. In these 
cases, differences between grou nd observati ons ,md TIMS estimates ranged between 4 .8 
267 
and I 2.5?C and are not reconcilable with the other sets of temperature estimates. It is not 
possible, long after the SGP97 experiment, to reconstruct the source of the temperature 
problem at ER09. The ER09 problem, however, is moot because discrepancies between 
remote sensing and ground-based temperature estimates remain even when the ER09 
temperatures are excluded. Typical afternoon temperature differences, after excluding 
ER09 results, were ~ 5?C . This is substantially greater than temperature differences ob-
served during the morning surveys ( I .5?C ), and also greater than the maximum desired 
temperature error of I .5-2?C (Section 3.5). The effect of the relatively high afternoon 
surface temperatures from TIMS are reflected in the relatively high (+50 W m- 2) H 
flux values (Fig. 4.6), which re-confirms the importance of accurate radiometric sur-
face temperature in the two-source energy balance model. The inaccurate afternoon 
surface temperature, when considered against the reasonably accurate morning surface 
temperature estimates, implies that the TIMS instrument has an unstable ca libration. 
Since atmospheric correction and temperature-emissivi ty correction procedures did not 
change, errors from them would not be expected to systematically change from morning 
to afternoon. Future thermal infrared surveys, particularly with MASTER- the succes-
sor to TIMS- therefore should include multiple ground-based validation points, so that 
instrument instability can be identified. 
A second problem is that surface energy flux estimates over sparse vegetation have 
a scale induced bias. Evaporative flux (EF) is relatively overestimated at coarser resolu-
tions by ~ 12% because vegetation density estimates are also too high. In the two-source 
model, scale effects upon vegetation density are seen in three ways. First, the amount of 
surface of flux assigned to soi l and vegetation components are directly proportional (Eq. 
2.43) to the estimated fractional vegetative cover. Second, the estimated net radiation 
at the surface is affected by changes in vegetation density (Section 2.4.5) because the 
268 
albedo of so il s and vegeta tion a re different. Third, the computed component tempera-
tures of soil and vegetation are a lso a ffected by changes in vegetation density. Jn the 
two-source model, remote-sensing derived composite radiometric temperatures a re par-
titioned into apparent so il and vege tati on temperatu res according to Eq. 2.46. Because 
Eq . 2.46 is 4-th order, it is sensiti ve to sma ll changes in vegetation dens ity, parti cu larly 
when the density is c lose to 0 or to 100%. Since sensible heat from the so il (Eq. 2.45) is 
direc tly proportional to the soil co mponent temperature, changes in vegetation density 
also affect energy flu x es timates at the so il surface. 
A third problem is that remote sensing estimates o f vegetation lea f density, using 
NOVI at 12 m resoluti on, were inacc ura te. Estimates of leaf area indi ces (LA I) were 
sometimes over 30% less than gro und-based measurements of LA I. Despite the use of 
phys ica ll y-based LAJ estimator (Choudhury, 1987), LAI values derived from remote 
sensing observations could not be eas il y reconciled with the ground-based measure-
ments. Whil e an empirica l re lationship could have been establi shed between NDVJ 
and LAI observati ons, thi s was not done because it would have only local va lidity and 
no phys ica l bas is. Instead, a subj ective optimization, reta ining the C houdhury ( 1987) 
approach, was chosen. In this case the effects of systematic bias (LAI~ 1.0) could be 
ameliorated by NDVJ re-normalization (Carlson et al. , 1994), an empirica l technique 
requiring the selection ofNDVI threshold5 corresponding to homogeneous bare soil and 
homogeneous thick vegetation. But in othe r cases, NOVI re-normalization may not be 
feasible, either because these land cover end members do not exist, or because image 
resolution is insufficient to di scriminate them. Consequently, remote sensing estimation 
of vegetation density cannot rely upon NDVI observations alone. 
Fourth , poor a lignment of remote sensing bands seriously hampers accuracy o f flux 
estimates at the higher reso lut ions. At El Reno the different scanning geometries for 
269 
rs caused persistent diffic ulties (Fig.
 4.27) that could not 
the TMS and TIMS senso
gistration procedures. Alignment pro
blems can be grea tly 
be eas ily resolved with geore
ntly reduces 
duced by area l averaging ofremote se
nsing observa tions, but this signifi ca
re
esults from operational sca le stud ies
 using 
the effec ti ve remote sensing resolut
ion. R
align ment 
STER data in New Mexico (section
 4. 7.3), however, suggest that the 
MA
resolved. This implies that future sc
ale-dependency studi es of 
can be technolog ica lly 
spiration can focus on high reso lution
 (3-l 2 m) surface energy flux 
landscape evapotran
-induced inaccurac ies. 
model development without concern 
for alignment
270 
6 Recommendations for Applica
tions 
and Future Work 
ing experiments were summarized  sensing scal
In Chapter 5, the results from the re
mote
are that 
implications discussed. The most 
important results from this study 
and some 
El Reno, can be made over a rang
e 
ne study site, 
surface energy flux estimates over
 o
2
ate accuracy, < I 00 W m- ), provided the
 resolution used is either 
of scales with moder
perational landscape sca le of 400 
s ignificantly finer, or significantly 
coarser than the o
s, when 
e flux estimates are more accurate,
 and show Jess latent heat flux bia
m. Surfac
olutions ( < 96 m). Nevertheless, if i
nstantaneous estimates 
the input data have higher res
a lue, these model accuracies need 
to be significantly improved, 
are to have practical v
2
preferably to within 50 W m- . 
e used to seek this improvement ar
e 
Fortunately, remote sensing data se
ts that can b
observa-
lly becoming avai lable, including 
the ground, aircraft, and satellite 
continua
Jornada, New Mexico studies. Dat
a sets such 
tions from the semi-annual USDA
/ARS 
mponents to modeling evapotransp
iration: aligned and 
as these conta in the essential co
mperature, vegetation and energy 
calibrated remote sensors along w
ith ground level te
flux va lidation sites. 
ce and results gained from using the t
wo-source energy 
Based upon the experien
 ways the newer data sets can 
balance model at El Reno, Oklaho
ma, there are several
tial applications of the two-source e poten
be useful in future work. Discusse
d below ar
s ition, pro-
 balance model, as well as suggest
ed research to improve data acqui
energy
cessing, and modeling. 
27 1 
6.1 Potential Applications of the Two-Source Energy 
Balance Model 
Estimati on of ET is now becoming fea sible from d ifferent approaches. Surface water 
budget models produce ET as a residual. Seil moisture estima tion approaches also pro-
duce ET es timates. As d iscussed here, surface temperature ET estimation is a th ird 
approach. By integra ting several, independent ET estimat ion techniques, it may be 
possib le to convert what is a substanti all y under-constrained problem into one that is 
over-constra ined. This would bene fit ET model development by forcing compatibility 
between the different tec hniques. 
T he potential application of thi s integration is the development of landscape and 
regional sca le hydro logica l monito ring of agricu ltura l regions. Accura te knowledge of 
ET over these regions would be use fu l fo r assess ing crop hea lth and productivity. Ac-
curate knowledge of ET wou ld also be uscrul in climate, climate change, and carbon 
sequestration studies, since ET is an import ant boundary condition. 
An outcome of the aggregation ex peri m. nts performed in this study is that hetero-
geneity effects upon water flux models are not as severe as one might expect. This 
suggests that sensors with reso lutions on th ::! order of I 00- 1000 m can be used to ac-
curately estimate area l averaged ET. If true, this suggestion has practical value because 
the need for high resolution data (1-10 m) can be reduced. Working with moderate res-
olution data ( ~90-250 m as in the ASTER and MO DIS sensors) is ana logous to land 
surface aggregation in watershed modeling, known as the representat ive e lementary area 
(REA e.g., Wood, 1998). The benefit of both approaches is reduced model complexity, 
with possibly negligible loss in modeled water flux accuracy. 
272 
6.2 Improved Data Acquisition 
equire technological improvement 
over sensors previ-
Improved accuracy of ET will r
ously used at El Reno (TIMS and T
MS). 
perature and emissivity are sensitiv
e to 
urrent procedures to estimate surfa
ce tem
C
d assumptions about emissivity prop
-
ic correction an
instrumental calibration, atmospher
ensors, such 
 of the surface. Reflectance and em
issive measurements using new s
erties
rnada) to re-assess 
as MASTER and ASTER, should b
e used in field studies (such as Jo
uracy and precision of temperature 
and emissivity estimates. 
the acc
, need to be acquired in the same 
Multispectral data , including therma
l infrared bands
n processing higher resolution dat
a 
reference frame. Significant diffic
ulties arise whe
. 
ands are mis-registered, as occurre
d with the TJMS/TMS data sets
where spectra l b
 but the smoothing cancels 
The registration errors can be redu
ced by areal smoothing,
surveys 
its originally sought from higher re
solutions. Future high resolution 
any benef
l-synchronized and aligned sensors
, such as MASTER 
shou ld be performed using wel
and ASTER. 
6.3 Improved Model Algorithms 
 that surface energy flux estimates 
Previous experience with two-sourc
e model has shown
tation conditions, from sparsely dis
tributed 
e
can be accurate under a wide range
 of veg
ent of the 
ted to thick vegetation (e.g., Kusta
s and Norman, 1999a). Improvem
vegeta
re used, will be possible when repr
esen-
lutions a
model, especially when differing re
so
egetation density, surface temperatu
res, 
proved: v
tations of the following factors are 
im
surface aerodynamic resistances an
d soil moisture. 
tion estimators need to be reduced.
 The vegeta-
First, scale dependencies of vegeta
273 
VI, which cont ro ls energy partiti
oning between 
tion estimator used in this study w
as ND
iati on computati ons and surface  net rad
the soil and the vegetati on. NOV
J is also used in
mates. But it has been shown tha
t NOVI viewed at coarse 
fl ux transport resistance esti
w at fi ne resolution. Vegetation d
ensity 
a lues vie
reso lution is not an average of N
DVI v
t ca libra tion and at-
imate inaccurac ies are exacerbat
ed by uncertainties in instrumen
est
n. 
s, problems only partially reduced
 through NOVI re-normaliza tio
mospheri c condition
equire 
d to reduce sca le dependency o
f NDVI . Achieving this may r
A way is neede
 of current research using multip
le 
e, incorpora tion
additional information. For exa
mpl
nction (BROF), 
ng les and es timation of the bidire
c tional refl ec tance distribution fu
view a
ege tation ca nopy that could be u
sed 
ut the v
could prov ide geometrical inform
ation abo
corporate multiband 
n lieu o f high resolution imager
y. It may also be possible to in
i
inate living and dead vegetation.
 
to help discrim
thermal infrared data into the mo
del 
era tures 
T estimates will become accura te w
hen radiometric surface temp
Second, E
a tions. To achieve this level of 
ac-
d-level observ
are consistently within I ?C of g
roun
temperature retrieva l 
uracy, furth er research is needed
 to seek ways to refine current 
c
ation (TES) and split-window ap
-
 separ
algorithms, such as the temperat
ure-emissivity
s should be poss ible 
oaches. Improved accuracy of s
urface temperature observation
pr
iband thermal infrared instr umen
ts (e.g. ASTER, 
by using the recently available m
ult
ded to improve the partitioning o
f radio-
 nee
MOD TS and MASTER). Resear
ch is also
 Current implemen-
tric temperatures into apparent so
il and vegetation temperatures.
m e
in the two-source model is unsta
ble when frac-
 with
tation of temperature partitionin
g
ique needs 
r is either very low or nearly co
mplete. The partitioning techn
tional cove
ile also maintaining surface 
to have reduced sensitivity to in
accurate temperatures, wh
energy balance. 
x tending the two-source model 
Third, improved es timates of ET 
can be achieved by e
274 
from one-dimension into two-dimensions. The current implementati on consists o f a 
spatia ll y-ana lyzed, o ne-dimensiona l model with a si mplified representation of surface 
roughness . By extending the model to two-dimensions, variations in fluxes due to spatial 
va riations in sur face roughness and advccti on could be used to more realistica ll y specify 
sur face tra nsport res istances. Research on spati al va riations of surface res istance ex ists 
(e.g., Maso n, 1988; Ra upach and Finni gan, 1995), and the ideas could be incorporated 
into the two-source mode l. 
Fowih , ET estima tes co uld be imp:oved by incorporating soil mo isture informa-
tion deri ved from pass ive mi crowave ob,ervati ons. Current implementa ti on o f the two-
source model relies upon estimated so il sur face tempera tures to incorporate the energy 
flux effec ts o f chang ing so il moisture. Because the spec ific heat o f liquid water is large 
(4200 J kg- 1 1< - 1) , so il mois ture has a luge influence upon its tempera ture. But in the 
use o f thermal infra red observations, the es timated so il temperature is representative of 
on ly the very surface o r the so il, and rn ay be poorly correlated with soil moisture at 
depths as shall ow as 5 cm. Recent resecrch, however, shows that soil mo isture can be 
retrieved from observa ti ons o f emitted microwaves (e.g., Jackson et a l. , 1999, 1995). 
Therefore it may be possibl e to incorporate microwave-based observations of soil mo is-
ture into the two-source mode l and thereby improve the accuracy of surface energy flux 
estimates . 
6.4 Comparison with Other Models 
The two-source model ex ists alongs ide olher surface water balance models (e.g., Si82, 
SEBAL, VIC and SW EAT), and its perfcrmance needs to be compared with them. Im-
portant comparison criteria include: fl u:< estimation accuracy and prec ision, re lative 
275 
-
in the presence of noisy data,
 mode l constra int s, and avail
simplicity, model stability 
ability of input data. 
276 
A El Reno TMS and TIMS 
Data Calibration 
A.1 TMS 
The base ca libration va lues for the El Reno surveys are shown in table A. I. The conver-
sion formu la is: 
L; = (DN - Gain x IJB 1 ) x Rad/Ct, (A.I) 
where the band spectral radiance, L;, is a linear function of the sensor digital count, 
D N. The offset term, Gain x BB1, can on ly be determined at survey time. It is revised 
for each scan line by reading the digital count for TMS' cold-reference blackbody, BB 1 
(typica lly ~ 10). The slope term, Rad/Ct, is in units of cm 2 - ms t.ewr - Jtm /DN. TMS ca li-
bration values for J 183, Runs 2 & 3 (2 July 1997), were used for the other three survey 
days (29-30 June, 1 July 1997). Run I coefficients were for an early morning flight. 
The resulting radiances are band-averaged, which means that they represent the 
summation of incoming radiation weighted by sensor dependent response functions. 
The response functions for a detector can change over time. The response functions 
used for the TMS El Reno data in 1997 are shown in Fig. A. I. 
Actual radiance distributions (12 meter resolution) for each of the TMS bands are 
shown in Fig. A.2. Most of the distributions are positively skewed, but all have well 
defined modes. The significance of this is that as observation resolution decreases, 
observed radiances will tend to converge smoothly towards the mean value. 
277 
Table A. I : TMS calibration data . Cocfiic icn ts lo convert digital counts to spectral radi-
ances . 
Channe l Band J 183/Run 1 J 183/Run 2-3 
(11,111) Go in Rad/Ct Gain R ad/C t 
0.423-0.448 8 D.O 1937 4 0.03874 
2 O.455-O.5 19 4 D.O4385 2 0.08770 
3 0.520-0 .600 4 D.O3361 0.13445 
4 0.592-0.634 8 0.02633 2 0.10533 
5 0.634-0.688 4 0.03062 0.12248 
6 0.683-0.759 4 0.03309 0. 13237 
7 0.744-0.879 4 0.03 125 0. 12500 
8 0.838-1.027 8 0.01632 2 0.06527 
9 1.58-1.797 4 0.01341 2 0.02681 
10 2.073-3 .2 19 4 0.00480 0.01919 
278 
1.0 1.0 
0.8 08 6 
0 .6 0.6 
0.4 0. 4 
0.2 - 0.2 
0.0b._- - ----L--~----== = - --l 0.0 L - - -=:.:::..__ ______ ;:==--l 
0 .J6 0 .J8 0.40 0.42 0.44 0.46 0.48 0.50 0.55 0 60 0 65 0 .70 0 75 0 .80 0.85 
Waveleng th (?m) Waveleng th (J.1.m) 
1.0 1.0 
0.8 2 0.8 7 
0 .6 0 .6 
0. 4 0.4 
0.2 0.2 -
0.0 L.-.....L----~-.:::::==---...l 0.0L---=----------"'------' 
0 .40 0.45 0.50 0.55 0.60 0 60 0 70 0.80 0.90 1.00 1. 10 
Wove leng lh (?m) Woveleng lh (?.m) 
1.0 1.0 -
0.8 ,3 0.8 8 
0 .6 - 06 
0 .4 0 .4 
0.2 0.2 -
0.0L.--.L.-------.::C::==--____i 0.0L---~=::::::--~---_::,,._ _ ____1 
0.45 0 50 0 .55 0.60 0 .65 0.70 0.60 0.10 0 .80 0.90 1 00 1.10 
Wave leng th {Jim) Waveleng th (;,m) 
1.0 
0.8 4 0.8 9 
0 .6 0.6 -
0.4 o. , 
0 .2 0 .2 
0.0'--==-~-------===-- - 0.01.---::.....-------~;,..._ __ __, 
0.55 0.60 0 .65 0 .70 1.40 1.50 1.60 1.70 1 80 1.90 2.00 
Wavelength (?m) Wave length (?m) 
1.0 
0.8 5 0.8 10 
0 .6 0.6 
0 .4 0.4 
0 .2 0.2 
0.0L.--a==::.__ _~  ____ _:==-..J 0.01.----- ?-------~--~__, 
0.55 0.60 0.65 0.70 0.75 1.8 2.0 2.2 2.4 2.6 
Wavelength (?m) Wavelength (?m) 
Figure A. I: IMS fi lter function s. Visible-near infrared bands 1-10. 
279 
0.40 0 20 
0.J0 1020. 0. 15 1287. 
0 .20 ( 89.) 0 . 10 ( 240.) 
0 . 10 0.05 
0 .00 0 .00 
600 800 1000 1200 1'100 500 1000 1500 2000 2500 
0 .-40 0 . 10 
0 .J0 2 9.35. 0.08 7 
( 182.) 0.06 /1~72( 445 7 0 .20 .) 
0 0 4 
0 . 10 
0 .02 - LL 
0 .00 0 .00 
0 500 l000 1500 2000 500 1000 1500 2000 2500 J000 
0 .4 0 0 .20 
0 .J0 .3 888. 0 . 15 8 1 4.39. 
0 .20 ( 189 .) 010 ( .349 .) 
0 . 10 0.05 
0 .00 0 .00 
0 500 1000 1500 2000 500 1000 1500 2000 2500 J000 
0. 40 0 .J0 
0 .25 
0.J0 4 770 9 9 4 4. 
0.20 -
0 .20 ( 242 .) 0 . 15 ( 298.) 
0 . 10 
0 . 10 
0.05 
0 .00 0 .00 
0 500 1000 1500 2000 0 500 \000 1500 2000 
0 .30 0. 10 
0 .25 
5 70.3. 1789. 
0 .20 
o. 15 ( 26 1.) (1 0.3 1.) 
0 .0 4 
0 . 10 
0 .05 0 .02 
0 .00 
0 500 l000 1500 2000 1000 2000 J0OO 4000 
Figure A.2: TMS radiometric di stributions. Observations fo r TMS bands 1-10. Band 
number indicated in upper left. Mean and standard dev iation for entire 2 July 1997 scene 
in upper right. 
280 
. 
bb Reservoir TIMS/TMS flight d
ata Surveys flown 29-30 June 
Table A.2: Fort Co ' 
1997. 
de can Spd can lines 
Julian Run Start End 
Duration Altitu S S
hms) (UT hms) (s) (m) (Hz) Day (UT 
0 1524 25 5252 
180 12:47:08.0 12:50:3
8.0 2 10.
12:58:42.8 224.8 1524 25 6498
 
180 2 12:54:58.0 
80 3 13:07:00.0 13 :09:
43 .3 163.3 3048 25 5166 
1
.2 4877 25 4512 
180 4 13: 15:26.0 13 :1
7:51.2 145
2 1: 06: 18.0 21:08:30.0 2
73 .0 4877 25 3762 
18 1 
MS) 21: 06: 18.0 21:08:30.0
 273.0 4877 12.5 1626 
181 l (T
A.2 TIMS 
ues not 
s section discusses some TIMS-rela
ted ca libra tion and validation iss
Thi
mentioned elsewhere. 
ights 
A.2.1 Fort Cobb Reservoir Rem
ote Sensing Fl
20 km long, were made over Fort C
obb Reservoir on 29 and 30 
Remote sensing runs, ~
f the radiometers. Five runs were 
made 
ty o
June 1997 to check calibration and s
tabili ' 
0, day J 181) included both TfMS an
d TMS sensors. All the others 
one of which (June 3
ust after sunrise, and over altitude
s 
ts were made j
were TIMS-only flights . Four flig
h
n. flight 
m~ 1500 to 5000 m. The remaining
 flight was during mid-afternoo
ranging fro
.2 . 
characteristics are shown in table A
28 1 
A.2.2 Sensitivity of TJMS Temperature Estimates to Columnar 
Water Vapor 
One of the essential process ing steps in ex tracting surface temperatures from remote 
sensi ng observations in the thermal infrared is to minimize atmospheric efTects. Most 
of these effects are due to atmospheric water vapor, which scatters, absorbs and 
re-radia tes thermal infrared light. In many 111stances the atmospheric water vapor 
abundance and di stribution at the time of the remote sensing observation is interpolated 
spatia lly and temporally. Even for the intensive SGP97 campaign, atmospheric water 
vapor was inferred from radiosondes launched over I 00 km away from the image 
targets and separated in time by over an ho ur. 
To investigate the consequences o f estimati1g surface temperature with an erroneous 
atmospheric model, a sensitivity ana lys is was performed. The analysis was done by 
starting with a known water surface temperature (water was used because of its 
well-defined emissivity) and known atmospheric water vapor distribution . By 
propagating the surface and atmospheric therma l radiation upwards, simulated sensor 
radiances were created. Then, the known atmospheric model was rescaled to both 
lower and higher water vapor abundances, and the simulated sensor radiance was 
downwards propagated to the surface. T hi s backward propagated radiance was then 
converted to a surface temperature and compared with the original starting surface 
temperature (Fig. A .3). Two plots are show11 : one to show the mean differences in 
water temperature estimates for T IMS' six thermal bands, and another to show the 
mean estimated water surface temperature (bottom). The x-axis in each plot represents 
the atmospheric water vapor sca ling factor, where a factor of 1.0 represents downward 
propagation through the same atmosp heri c ,nodel used for upward propagation . 
The plots he lp make two significant observations. First, that for thi s simulation, surface 
282 
5-2?C differences
. Second, that 
MS inherently hav
e 1.
TI
ture estimates fr
om  is much worse tempera eater vapor abund
anc
of over-estimatin
g atmospheric w
 m all 
the consequence an temperature f
ro
lot of Fig. A.3, t
he me
er-es timating it. 
In the bottom p
than und for a water sc
ale 
ter surface temper
ature by ~1 ? C 
om the true wa  
six bands depart
s fr
1.5. Note also tha
t the
~5?C for a water 
scale factor of 
factor of 0.5, but 
departs by 
 to 8?C when the 
 increases from 2
?C
)
 between bands 
(top of Fig. A.3
discrepancy ts original state. 
mn is increased by
 50% over i
r colu
atmospheric wa
te
2.3 Emissivity A. e TES method 
face emissivities
 derived from th
2.6, the sur
As discussed in 
section 3.
n that the range 
in 
vatio
 the empirical ob
ser
IMS observation
s is based upon
and T  minimum emiss
ivity 
ands is a function
 of the
ween thermal b
apparent emissiv
ities bet
r model (Eq. 3.5
), 
 powe
orm chosen is a 
three-parameter
l f
present. The fun
ctiona
ve (I 999); Jet Pro
pulsion 
e of 42 laboratory
 specimens Gro
mpl
calibrated from a 
sa
is repeated here:
 
s A.3 and A.4. T
he equation 
boratory (200 J b) ,
 listed in Table
La
0 870 (A.2) 
.995 - 0.864MM 
 D ?
?min= 0
viation ratio (Se/ 
Sy) 
 de
acy. The standar
d error-standard
ur
The fitted form h
as high acc the 
rence between th
e function and 
n absolute diffe
is small, 0.0262. 
The mea
 less than the over
all expected 
nd much
surements is also 
small, 0.0042, a
mea
TES-technique. 3%) in the oi l 
uncertainty (?2
 -
etermined by int
egration of the s
olumn were d
 emissivities (B J
-B6) for each c
and ables A
.3 
B
unction values, R>
. (Fig. 2. 12a). T
ith TIMS respon
se f
 soi l 
emissivity spect
ra w
ange (MMD), fo
r each
ivi ty r
aximum and emi
ss
 A.3 also show th
e minimum, m
and
sample. 
283 
i:1 T vs . Woler Sc a le Fa c to r 
10 -
~ 
VJ 
:J 8 -
VJ 
(I) 
.u._ ,, 6 
I-
<J 
C 4 
0 
(I) 
2 2 -
0 
0 .6 0 .8 1.0 1.2 1.4 
Wa l r Scale Faclo r 
Me n T vs . Wo ter Se a l Facto r 
-35 
~ 
VJ 
:J 
(/) 
(I) 30 
u 
I-
C 
0 
(I) 25 
2 
20 
0 . 0.8 1.0 1.2 1.4 
Wol e, Sco le Faclo r 
Figure A.3 : Sensitivity of temperature estimates. Atmospheric correction sensitivities 
of TIMS-based water surface temperatures are shown. At the top, the mean and standard 
deviation of temperature differences between TIMS bands 1-6 are shown fo r different 
water vapor abundances. The actual estimated columnar water vapor, based on radioson-
des, is at a scale factor of 1.0. The top plot shows that underestimating columnar water is 
less serious than overestimating. The bottom plot shows that a I 0% increase or decrease 
from the 'actual' columnar water abundance causes about I ?C temperature di screpancy. 
284 
he soil samples used includes a va ri ety o f so il , fro m c
ent ra l Oklahoma and Jornada, 
T
ica l 
New Mex ico. Nevertheless, the group shows ccnsiste
nt behav ior, with a typ
emiss ivity range o f 0 .06 in the 8-9 ;1,m bands and 0.02 in
 the I 0-1 2 ;1.m bands. 
A.2.4 Validation of TIMS Central Wavelength Valu
es 
nces into 
As noted in the section 2.6. 5, one way to co nvert band
-averaged radia
temperature is to use an optimum central wave length 
fo r each band. When the TIM S 
data were delivered, they a lso inc luded a li sting o f cen
t ra l wavelengths. Because 
re criti ca l to the surface energy balance modeling done
 
acc ura te surface temperatures a
in this study, the accuracy o f the provided central wav
elengths was checked. 
ula for spec ified 
The check was performed by so lving the Pl anck bl ack
body fo rm
emperatures and wave lengths. Eqs. 2.63 and 2.73 wer
e solved fo r temperatures 
t
ranging between 20 and 65?C, us ing JPL supplied spe
ctra l respo nse functions fo r each 
o f temperatures, Eq. 2.63 was 
o f the six TIMS bands (Fi g. 2. 12a). For the same range 
um centra l wave length 
again solved, but this time using a single wa velength . The 
optim
was determined by findin g the least mean abso lute dif
ference (MA D) in radiance 
values, considering the entire range of spec ified tempe
ratures. 
The optimum wavelength for each TIM S band i; well define
d (Fig. A.5) . As shown in 
gths from those 
table A.5, the MAD criteria resulted in diffe rent central w
avelen
provided by JPL. However, the differences are of negl
igible consequence. Temperature 
estimates from the two sets differ by less than 0.2 ?C. T
he JPL-provided centra l 
wavelengths are consistent with the provided spectral 
response functions. 
285 
0 .9 0 
.?;-
> 
en 
en 
en 
E 
w 
0 85 
0.75 I , I I I I I I I L.,L..LLJ _.L J J I I ' I I I I ' I I I I I I I I 
8 9 10 1 1 1 2 
Wavelen gth (? m) 
Figure A.4: SGP97 soil emissivities. Box plot of TIMS band-averaged emissivities fo r 
42 soil samples. Mean emissivities are indicated by diamonds, standard deviation by the 
box, range by whi skers. Median va les, long clas1es, are nearly identical to mean values. 
Quartiles are shown as short dashes. 
286 
Table A.3: TIMS band emissivities. 
B4 BS B6 Mi n Max MMD 
Soil B l B2 B3 
ERO! 0.877 0.873 0.866 
0.923 0.949 0.958 0.866 0.958 0.092 
0.966 0.973 0.887 0.973 0.086 
ER05a 0.894 0.894 0.887 
0.942 
0.936 0.933 0.963 0.974 0.979 0.933 0.979 0.046 ER05b 0.936 
0.895 0.893 0.888 0.936 
0.958 0.965 0.888 0.965 0.078 
ER09 
0.908 0.9 12 0.9 10 0.953 0.967 0 .969 0.908 
0.969 0.06 1 
ER1 3 
0.8 0.854 0.844 0.906 0.943 0.955 0.844 0.955 05 .7 1 11 ERI S 
l aa 0.894 0.902 0.90 1 0.95 1 
0.968 0.972 0.894 0.972 0.078 
l ab 0.902 0.9 11 0.9 10 0.956 0.970 
0.974 0.902 0.974 0.07 1 
Iba 0.883 0.893 0.893 0.95 2 0.96 1 
0.96 1 0.883 0.96 1 0.078 
lbb 0.892 0.90 1 0.90 1 0.955 0.964 0.965 0.892 0.965 0.073 
2aa 0.834 0.832 0.826 0.934 0.957 0.963 0.826 0.963 0. 137 
2ab 0.836 0.834 0.828 0.935 0.958 0.964 0.828 0.964 0.1 36 
2ba 0.864 0.863 0. 857 0.947 0.965 0.969 0.857 0.969 0.11 2 
2bb 0.861 0.860 0.854 0.945 0.964 0.969 0.854 0.969 0.11 4 
3aa 0.888 0.897 0.895 0.955 0.975 0.983 0.888 0.983 0.095 
3ab 0.881 0.882 0.875 0.949 0.970 0.978 0.875 0.978 0.103 
3ba 0.881 0.887 0.885 0.953 0.973 0.982 0.88 1 0.982 0. 101 
3bb 0.879 0.88 1 0.875 0.950 0.971 0.978 0.875 0.978 0.103 
287 
Table A.4: TIMS band emissivities cont. 
84 85 86 Min Max MMD Soil Bl 82 B3 
0.952 0.969 0.975 0.876 0.975 0.099 4aa 0.878 0.881 0.876   
0.869 0.950 0.967 0.972 
0.869 0.972 0.103 
4ab 0.874 0.875 
0.933 0.957 0.964 0.822 0.964 
0.142 
4ba 0.831 0.828 0.822 
0.799 0.924 0.953 
0.962 0.799 0.962 0.163 
4bb 0.810 0.806  
0.934 0.954 0.960 0.843 0.960 
0.118 
Saa 0.843 0.845 0.843 
0.845 0.935 0.955 0.961 
0.845 0.961 0.116 
5ab 0.845 0.848 
0.935 0.949 0.779 0.949 0.170 
Sac 0.784 0.779 0.782 
0.898 
0.956 0.974 0.982 0.897 0.982 
0.084 
5ba 0.897 0.904 0.900 
0.891 0.888 0.951 
0.971 0.977 0.888 0.977 0.089 
5bb 0.888 
0.838 0.836 0.933 
0.957 0.963 0.836 0.963 0.126 
6aa 0.837 
0.958 0.964 0.839 0.964 0.125 
6ab 0.839 0.841 0.839 
0.935 
0.906 0.903 0.958 
0.976 0.981 0.902 0.981 0.079 
6ba 0.902 
0.889 0.887 0.9
0
52 0.972 0.977 0.886 0.977 
.091 
6bb 0.886 
0.957 0.974 0.979 0.922 
0.979 0.058 
7aa 0.924 0.925 0.922 
0.973 0.977 0.919 0.977 0.058 
7ab 0.920 0.922 0.919 
0.956 
0.943 0.964 0.970 0.884 
0.970 0.086 
7ac 0.884 0.886 0.899 
0.948 0.971 0.977 0.910 
0.977 0.067 
 
7ba 0.918 0.915 0.910 
0.950 0.971 0.976 0.911 
0.976 0.065 
7bb 0.917 0.916 0.9 l l 
0.931 0.957 0.964 0.863 
0.964 0.101 
7bc 0.863 0.864 0.868 
0.976 0.916 0.976 0.060 
8aa 0.916 0.920 0.918 
0.952 0.971 
0.954 0.971 0.975 
0.916 0.975 0.060 
8ab 0.916 0.920 0.918 
0.914 0.950 0.969 
0.973 0.897 0.973 0.076 
8ba 0.897 0.914 
0.970 0.973 0.900 0.973 0.073 
8bb 0.900 0.917 0.917 
0.952 
0.965 0.101 
0.882 0.887 0.94
0.962 0.965 0.863 4  
8bc 0.864  
288 
1 Cl rl. Wove. Opl. , Bond : 2 Ctrl. Wove. Opt., !~ 
20 14 
8 .4 67 : E 12 
8 .8 7 1 
~"  10 
I 
E 8 
3' 
!. 6 
u 
0 
"' 
~ 
Oc....-...L----'-- -......._-...J.J 
0 8 450 8 .460 8 .86 8.87 8.68 8 89 8 470 8 480 Centra l W
. Ce on vt era iel nW go tnv  e (le mn ig c\ rh o m( m e ti ec rr so )m  e1 ers) 
Ctrl. Wov
C e.t  rl O. Wove. Opt., Bon_.'1~ 3or-r~ ..--,
p
- l., -,: B.c o;.: n.:; d.-=  :~  4-  -',-~ 
20 
'[ 25 9 . 99.3 
E 9.288 
.~  15 ' ~ 20 
.E' 
.E' 
 
 
',. ~ 15 - 10 !. 
!. 
u ~  10 ,r 
0 
"' 
~ 
:, 
0 l..,..--~ -.....,._"_,.,_.........., 
9 .270 9.280 9 .99 8  29 90 . 96 9 JOO 
Cen1ro t Wo'llele Cn cg nth lr o( lm  Wic ar vo em lee n1 ge tr hs  ) (micrometers) 
Ctrl. Wove . Opl., Bond : 5 Ctrl. Wove. Opt ., Bond : 6 60~--~~-,-:...--,.:.,,::..__.;._~::.._ 
60 
- 50 1 0 .8.38 '[ 50 11.76.3 
[ I 
I 
~ ~ 40 40 I 
I ?E 
l,.  30 3' 30 
!. !. 
i ~ 20 20 0: 
QC 
~ ~ 10 10 
0 l....J._ _,_ ____ _ _.___....,___  __,___.., 
10 .80 10 .82 10 .84 10 .86 10.8 18 1 .72 11 .74 11 .76 11.78 11.80 
Central Waveleng th (micrometers) Centra l Waveleng th (micrometers) 
Figure A.5 : TIMS centra l wavelengths. Graphs of mean absolute di ffe rences (MAD) in 
estimated radiances, over 25-65?C, between using spectral response functions and using 
a central wavelength . Minimum MAD fo r each band determines the optimum central 
wavelength . 
289 
TIMS centra l wave lengths. Two sets are compared: one provided by Table A.5 : 
Wavelengths in ,,,m. Spectra l radiances in 
JPL another created in thi s study. 
' 
mW m- 2 ster - I 11,m - 1 . 
Band >-(111! Radiance @37?C 6 6 >-.1 ! ' /, 
L.1 p1, L"nf L T (OC) 
8.467 8.4673 11 473 11 473 0 0.00 1 
2 8.940 8.87 13 11698 11 677 2 1 -0.108 
3 9.344 9.2879 11754 11 753 -0.006 
4 9.962 9.9932 11 64 1 11 630 11 -0.063 
5 10.800 I 0.8383 11 203 111 77 26 -0. 165 
6 11.740 11.7627 10470 10450 20 -0.145 
B Two-Source Model Sensitivity 
The following fi gures (Figs. 8 .1 and 8 .2) il lustrate typica l so il H flux and canopy LE 
flux for conditions at El Reno during 29 June-2 July 1997. Each plot shows the 
computed two-source flux response for surface temperatures ranging from 2O-6O?C and 
for NDVI ranging from -0.1 to 0.75 . The air temperature was set to 3O.2?C , relative 
humidity to 59.5%, wind speed to 1.4 m s- 1, and solar radiation to 824 W m- 2. Land 
cover was set to pasture (type 4). In Fig. B. I one can see that when the radiometric 
temperature equals the air temperature, the soil sensible heat flux is OW m- 2. At El 
Reno, the pasture is well watered, and even for surface-a ir temperature gradients of 
~2O?C, the soil H flu x is only about 200 wm- 2. The contours on the canopy LE flux 
(Fig. B.2) are close to perpendicular to so il H flux, which shows that evaporative flux is 
290 
2
H Soil Flu x (W/m
0.8 )  r-r..,-,---,-r-r,.--,,-rrr-,--,--,rrr-r,r.-n--,--i--rrrm---rr-,...,.....~ 
0.6 
0.4 
> 
0 
z 
t--J 
0 
0 
0 
o.o L() 
40 50 60 
20 30 
Surface Temperature ( Celsius) 
Figure B.1 : H soil sensitivity. Contour plot of modeled sensible heat flux from the soil 
component for mi d-moming conditions on 2 Ju Iy  I 997. A land use type of pasture was 
assumed. 
much more sensitive to vegetative cover density than it is to surface-air temperature 
gradient. In this example, full vegetative cover (ND VI ~ O. 7) corresponds to LE flux 
2
values of at least 400 W m- . 
C El Reno Study Site Data 
The El Reno study area consisted of 15 fields, each with vegetation and soil moisture 
studies. Four f these fields, ERO I , ER05, ER 09 and ER I 3, were instrumented with 
O
291 
LE Canopy Flux (W /111 2 ) 
0 .8 
0.6 -
0.4 
> 
0 
z 
5 
0.2 
100 
5 
a.a 
30 40 50 
60 
20 Surface Temperature (Celsius) 
Figure B.2: LE canopy flux sensitivity. Contour plot of modeled latent heat flux from 
the canopy component for mid-morning conditions on 2 July I 997. A land use type of 
pasture was assumed. 
292 
pproximate El Reno flux s
tation locations. 
Table C. 1: A
4N 
Station Latitude Lon
gitude UTM 14E UTM1
(ON) 0( W) (m) (m) 
98.0 16105 589183 3934056 ER0J 35.54793 7 
 35.548397 98.03622
1 587359 3934089 
EROS
5170 98.062856 58492
7 3935926 
ER09 35.56
.541016 98.06 1747 58
5053 3933248 
ERl3 35
. EROS 
The locations of these syste
ms are listed in table C. J
eddy-covariance systems.
 
tate 
esonet site (Univers ity of Ok
lahoma & Oklahoma S
is also an ongoing M
Un iveris ty, 200 1) 
ce model input was fixed f
or 
our
e surface meteoro logy at E
l Reno used for the Two-S
Th
mation to create 
g survey. This was done th
ere was insufficient infor
each remote sensin
. Given that the study area
 
d set of meteorological map
s
an accurate spatially distr
ibute
conditions throughout 
~ 6x JO lan), and also given
 mostly clear and steady 
is not large ( 
 used for 
reasonable approach. Valu
es
the period (29 June to 2 Ju
ly 1997), this is a 
ind speeds were 
nd mid-a fternoon surveys 
are shown in table C.2. W
mid-morning a
umidity and air temperatu
re were 
 ground, while h
measured at JO meters abo
ve the
hown in the table are meas
ured 
ground. Also s
measured at 9 meters abo
ve the 
 
solar radiation and the com
puted solar zenith angle.
incoming 
-minute averages of wind 
speed, air 
The flux station sites cont
inuously recorded 15
erature. These are listed bel
ow, by time for all 
temperature and surface b
rightness temp
 tables C.3, C.4, C.5, and C.
6. 
n
four flux-instrumented sit
es i
293 
 .2: El Reno meteorology
. 
Table C
ind Air Rs sz 
JD Date Time Run R
el. Abs. W
Hum. Hum. (mis) 
(OC) (W/m,2) Deg. 
UT 
(g/m3) 
hrs:min 
2 1.2 6.4 29. 1 850 26.07 
180 6-29-97 16:50 4 
72.4 
55.9 19.6 9.9 32.3 856
 30.00 
18 1 6-30-97 20:42 
18.4 6.6 30.6 882 24. 74 .5 
182 7-0 1-97 16:57 
57
 2 48. 1 18
.4 8.9 33.8 894 25.77 
182 7-01 -97 20:20
 
16: 04 2 59.5 
18.6 2.5 30.9 800 35.14
183 7-02-97 
2.4 30.2 824 32.12 
183 7-02-97 16: 19 3 
59.5 18.6 
D MODTRAN 
the thermal infrared and th
e visible-near in fra red 
Atmospheric corrections
 to both 
 program 
s from the radiative transfe
r
observa tions were based
 upon model result
 is run by creating a contro
l fi le consisting 
998). MODTRAN
MODTRAN (Berk et al. , 1
TRAN written in 
e nomenclature is a relic o
f older versions of MOD
of 'cards' . Th
Input data, commonly ca
lled 
on. 
FORTRAN IV, but is still 
used in the documentati
n example TAPES fil e is 
not free-form, so correct
 formatting is essential. A
' TAPES ', is 
f the input deck). 
w (The parenthetical card
 numbers are not part o
shown belo
0. 00 (CARD 1 ) 0 10. 000 
(CARD 1A ) 
't 7 
. 0 l. 0 0 ) 0 . 318 (CARD 2
 ) 
 OF O 3 55.0
0
p 0 . 000 0. 0
00 0 . 000 
O. 000 (CARD 2C ) 
0 0 
El Reno, OK 21 No
v 00 
(CARD 2Cl) 
1 0 O 
0.000e +00 0 . O00e
+OOABH 
 9.867e? 0 2 1. 4 J0e
+0l 4 . J00e +0l (CARD 2Cl ) 
0 . 318
0 0.00Oe -t OOABH 
l. 297e+0 l J . 924e
+0l 0.000e?0 (CARD 2Cl ) 
0.358 9.82 l e +02  
9Je+0J 0.000e-+00
 0.0OOe ? OOABH D 2CI ) 
0 . 101 9.77Je .. 02 
J. 24Je +0 l 4 . 0 (CAR
oe +OOABH 
0 l 0.000e?00 o.oo l) 
. 445 9.719e+02 l.
1 98e +0 J 4.l 2 Se + (CARD 2C
0 e+OOABH 
58e?0 J 4 .207e +0 J
 o . oooe+00 o . ooo (CARD 2Cl) 
o . 1ae 9 . 6 70e +02 
l.1
.oooe+00 0.0OOe? OOAB
H 
o
 9.6 1 9e+02 1.ll2e
+0J 4 . J95 e +0 l (CARO 2CI) 
0 . 532
. 000e?00 0 . 00Oe+O
OABH 
0
 9 . 569e+0i J . 0S?
e+0l 4 _4 Jle?0l 
0,575
294 
Table C.3: El Reno Meteorological Data Field ERO!. 
Site Julian Time Wind Air Surface 
Day (UT hrs) (mis) (?C) (?C) 
180 16.25 4.7 29.7 31.8 
180 16.75 4.1 30.5 33 . l 
180 17.25 4.4 31.1 33 .3 
181 20.25 5. 7 32.9 33 .6 
181 20.75 6.1 32.9 33 .0 
181 21.25 6.4 32.8 32.5 
182 16.25 5.4 30.5 31.7 
182 16.75 4.9 31.3 32.8 
182 17.25 5.3 31.8 33 .2 
182 19.75 5.7 33 .7 34.2 
182 20.25 6.1 34.0 33.7 
182 20.75 6.2 34.2 33.5 
183 15.75 2.3 30.6 32.l 
183 16.25 1.9 31.5 33.1 
183 16.75 1.6 32.5 33.9 
295 
Table C.4: El Reno Meteorological Data Field ER05 . 
Site Julian Time Wind Air Surface 
Day (UT hrs) (mis) (QC) (QC) 
5 180 16.25 5.0 29.4 33.4 
5 180 16.75 4.6 30.1 34.8 
5 180 17.25 4.6 30.5 36.1 
5 181 20.25 6.3 33 .0 37.2 
5 I 81 20.75 6.8 33 .0 36.4 
5 181 21.25 7.0 33 .0 35 .8 
5 182 16.25 5.6 30.6 34.6 
5 182 )6.75 5.2 31.3 36.1 
5 182 17.25 5.2 32. I 37.3 
5 182 )9.75 6.0 34.0 38.1 
5 182 20.25 6.3 34.3 37.9 
5 182 14.75 6.7 34.5 37.3 
5 I 83 I 5.75 2.7 30.5 36.0 
5 183 16.25 2.3 31.2 37.5 
5 I- 83 -I 6.75 2.0 32.0 39.0 
296 
Table C. 5: El Reno Meteorological Data Field ER09. 
Site Julian Time Wind Air Surface 
Day (UT hrs) (mis) (?C) (?C) 
9 180 16.25 5.2 29.3 29.7 
9 180 16.75 5.0 30.0 30.6 
9 180 17.25 4.7 30.5 31.4 
9 181 20.25 6.9 32.9 31.7 
9 181 20.75 6.6 33 .2 31.6 
9 181 21 .25 6.7 33.3 31.0 
9 182 16.25 5.4 30.7 29.7 
9 182 16.75 5.5 31.3 30.3 
9 182 17.25 5.9 31.9 30.6 
9 182 I 9.75 6.4 33.9 32.1 
9 182 20.25 6.8 34.4 31.9 
9 182 20.75 7.6 34.6 31.3 
9 183 15.75 2.9 30.3 29.0 
9 183 16.25 2.2 31.2 30.4 
9 183 16.75 2.2 31.8 31.2 
297 
Table C.6: El Reno Meteorological Data Field ER 13 
Si te Julian Time 
Wind Air Surface 
(QC) 
Day (UT hrs) (mis) 
(QC) 
16.25 6. 1 28.8 
30.2 
13 180 
180 16.75 5.8 
29.5 31. I 
13 
5.4 30.0 32.2 
13 180 17.25 
8.4 35.5 33.4 
13 181 20.25 
181 20.75 8.5 
35.9 33.4 
13 
33 .6 
13 181 21.25 
8.1 36.5 
16.25 6.3 31.I 
34.4 
13 182 
6.3 32.0 36.3 
13 182 16.75 
6 32.6 37.7 
13 1
.
8 17.25 72   
19.75 7.8 35.4 
41.8 
13 182 
41.7 
13 182 
20.25 8.1 35 .7 
20.75 8.8 36. 1 
41.2 
13 182 
3.5 30.6 38.2 
13 183 
15 .7
 5 
16.25 2.5 31.6 
41.3 
13 183 
44.2 
!6
1 !83 .73 5 
2.2 32.4 
 
298 
{CARD 2 CJ ) 
 0 . 000e ? 00 0.000
e?00ABH 
e ? 0l 4. J95e ? 0l
0 . 619 9 . !>l8e ? 02
 l.002  {CARD 2Cl) 00ABH
00 4 .5 He+0l 0.0
00e?00 0.000e ?
62 9 . 4 70e +02 9
.600e -t
0.6  (CARD 2CJ/ 
3e ? 0l 0.000e ? 00 
0.000c ? 00ADH
.'/06 9.4J9e ? 02 
9. l00e-t00 4. 70
0 (CARD J 
) 
25. 8 1 0 0.318 JB0.000
 
(CARD 4 I 
800 1 250 (CARD 5 I 
 
ittance mode, it outputs
 transmittance spectral
ODTRAN is run in its 
transm
When M ittances for 
 atmosphere. The follow
ing plots show transm
s ignatures for the speci
fied
ew of the plots shows th
e 
 revi
l Reno modeled atmosp
here on 2 July 1997. A
the E
water vapor contin uum 
absorption in the 
 of water vapor band-ty
pe and 
importance
VNCR and TIR bands. 
E Useful Formulae 
.l Radiometric Conve
rsions 
E
ce 
E.1.1 Temperature to
 Spectral Radian
nce: 
To convert temperature to
 spectral radia
(E.1) 
. is surface emissivity fo
r the wavelength 
. mW . f>
L>. is spectral radi?ance
 1?11 
' m 2-ste
r - 11m 
are Planck radiation const
ants. c, = 
d c
considered. The values c1 
an 2 
104;tm - K. Note that th
e constant 
:1 6912 x_ c = l.4387
3.7417749 x 1Q-22mw-
m 2 
?m 
n in Eq. 2.63 to accommo
date 
sed here are in different u
nits from those show
va lues u . ? mW 
ra diance 111 m2-stPr - ?m ?
 
wavelength measured in ;
1,m and spectral 
299 
,.or-------- - - -----To-tal- Tr~ans-m-"it-l-o-n'-c-e ----~ --------
O B 
0 .6 
o., 
02 
OoD.,~ ----- - - - ~---- - - - ~------'-"--~--------~ 0 .6 O.B 1.0 1.2 
Woveleng th (?m) 
OB 
06 
0 .4 
02 
ODo.~, --- - ----~--------'--- - - --'--'--~- -------' 0 .6 O.B 1.0 1.2 
Wove leng th(? m ) 
Un iform ly Mi >ce d Coses Tro nsmi ttonce 
1,0 r r 
0 .8 1-
0 .6 -
o, -
0 .2 -
o.o~--------~------ - -'-- --- - ---~--------' 
o., 0 .6 O.B 1.0 1,2 
Wovelength(?m) 
Ozone Tronsmittance 
o., 0 ,6 0.B 1,0 1.2 
Wovelength(?m) 
Figure 0 . 1: Atmospheric transmissivity in VNJR (1). 
300 
Trace Gases Tronsrni1tance 
0.9970
o. '? : """"-------oo.6 'i ;---------;;o :.e ; ----------:'-: '' Wovelength (1lm) 1.0 --------J 
OM
o.:?;- -------~;o.6: ---------:;--------~------Wo -
1.2 
vel ~eon.geth  (J"'") 1.o 
Molecu lar Scattering Transmittance 
o.?oc,-------
o -.? ;;';~-
1.2
-  --
o -.6 - :;:-----o -.e - ::'------~ Wovelenglh(J,'m) 1.0 
Aerosol ond Hydrorneteor Transmittance 
o?~~.?-  -------o--_'6- --------:o'.=e-
Wo -"l"' -glh -(~m -) ---,.. _.o --------~ 
1.2 
Figure D.2: Atmospheric transmissivity in VNJR (2). 
301 
, .ooor---------~-A~?:...'.::.o:...so:...1_0:...n.:.:d:....,.H!...yd:_r.::.o.c,m.:.:cct:.e:_o:..r..:.:A.:.::b.:s:.:o:r,!p:.:l.::.ocn:.c:e;:___~-------~ 
0 995 
0 990 
0.975~-----~-~~-------~--------~------------' 
o., 0 6 OB 1.0 
WoYtlerigth(?m) 
0 9968 
0.4 0 .6 0.6 1.0 
,., 
Wo,.t ltn9th(?m) 
02 Transmittance 
I 00 
0 .951- -
0 .90 ...,_ 
0 .6~ ~ 
0 .60 
o., 0 .6 0.6 1.0 1.2 
W0Ytlen9 lh(?m) 
N02 Transmitt ance 
O . ? 0.6 1.0 
,., 
W0Ytleri9lh(?m) 
Figure D.3 : Atmospheric transmissivity in VNIR (3). 
302 
fo tol Transmittance 
1a 
1 16 
1 47   
10 WoYr>lt'fl91h(?rn) 
oo~--..J1JJ~-------:=--------'-
1 :2 ----"_ ,_---~:
1.6_ J~-- 1a-  :1 
WOYt:lt'flg tti (p.m ) 
o.o;:-- --~- --- __,_----~--- 16 1> 8 14 
10 ----
Woye:len1
_L;i.'._._--- j 
g2t h(?m) 
ozone Tronsmiltonce 
18 
14 
12 
10 Woye:lt-ngtti(?.m) 
Figure D.4: Atmospheric transmissivity in TIR (I). 
303 
Trace Coses Tronsrnitt once 
0.995 
0 .990 
0 .98~ 
09 80~-----~---10 -------------,.- ------- - ---~ 6 17 16 18 
Wove leng th(?.m ) 
10~-----~----~Wa-te-r -Va'p-or- C-on-t in.u-um- T~ron-sr-nit-t o-nc-e ------~-----, 
08 
0 6 
o , -
02 
OD'----~--'----1-0 -~-----~-----,~. -----~-------' 6 12 16 18 
Woveleng th(?.m) 
Aerosol and Hydrometeor Transmittance 
8 10 12 ,. 16 18 
Wovelen9 lh(?.m) 
Ni lric Acid Transmittance 
1.000 
0.995 -
0.990 
0 .98~ 
0 .980 
10 12 ,. 16 18 
Wovelenglh(?.m} 
Figure D.5: Atmospheric transmissivity in TIR (2). 
304 
1.000.------r------Are-ro-so-l -on.d: .H.yd-ro-m-e-te-or- A-bs.o'r-pt~on-ce --------- -~ 
0.960 
097'~-----~-----~-----'-----~-------'-- ----.J 
6 10 " 16 IB Woveleng t h (?m) " 
CO2 Transmi ttance 
OB 
0 .6 
o., 
02 
oo~-----~-----~-----'-----~---- ---"---"-----~ 
6 10 " " 16 1a Woveleng lh(?m) 
,or--,,--,----,-,=-----.----'.--C-H:4 .T.r.a.n,s;m.i.tt.a.n.c_e '--'.-----,--~-.--,.-----, 
0 B '-
0 .6- -
0.4 -
0 .2 l-
0.0~-----~-----'~-----'------'-,. -------'------ -' 10 12 16 18 
Woveleng th{?m) 
N20 Transmittance 
0 .95 -
0 .90 
O. B~ 
10 12 ,. 16 18 
Woveleng lh{?m) 
Figure D.6: Atmospheric transmiss ivi ty in TJR (3). 
305 
02 Tronsmittonce 
I 00 
0 .95 -
0.90 
0 .85 
080 
? 8 10 12 14 10 18 Wove lenglh{?.m ) 
Figure D .7: Atmospheric transmissivity in TIR (4). 
306 
E.1.2 Spectral Radiance Units Conversion 
To convert spectra l radiances, over a narrow bandwidth , from wavenumber domain to 
wavelength domain : 
(E.2) 
w here L >. is spectra l radiance in units rn 2 - s ~,\,/, ?-11m , the centra l wavelength, ~, is in 111n, 
2 
and Lk is in units m2 -st:;~_e1 _ 1 . The rati onale fo r the ~ facto r comes fro m the 11
re lati onship between wavelength, ,.\, and wavenumber, k : 
>.k = l (E.3) 
Taking the deriva tive : 
>. dk + k d>. = 0 (E.4) 
Solving fo r the differentia l wavenumber: 
dk = - k d,.\ (E .5) 
>. 
Then from Eq. E.3 , replace k : 
dk = -_d~,.\ (E.6) 
,.\ 
The Stefan-Boltzmann equation relates temperature to emi ttance: 
M = aT4 (E.7) 
Where a is 5.67051 x 10- sw - m- 2 - K 4 (Cohen and Taylor, 1999), T is the surface 
temperature in Kelvin, and M is emittance, or flux per unit area, in W - m - 2. 
Emittance is the same, whether measured per wavelength : 
(E.8) 
307 
e relationship betwee
n 
egration reflects the i
nvers
f int
or per waven umbe
r (note order o
,\ and k : 
(E.9) 
te Eq. E.5 for the dk 
term, reverse 
tu
nto wavelength term
s, substi
To convert Eq. E.9 i velength integration:
 
verses the sign) to ag
ree with wa
 re
the order of integr
ation (which
(E. J 0) 
 wavelength in cm to
 /tm. 
oing from4  conversion factor g
Fina lly, the fac tor 
10 is a
s 
E.2 Water Vapor 
Conversion
rt 
s, are taken from Cha
p ter 3, Brutsae
 with slight modifica t
ion
ions,
The fol/owing equat
List ( 1966), and to G
off and Gratch 
rence to Table 93, 
( 1982), 
e
with additiona l ref
(1946). 
Saturation Vapor P
ressure 
oist air temperature
 is the 
n of vapor pressure f
rom m
The most precise fo
mwlatio
Fig. E. l : 
h equation 1
 (Goff and Gratch, 1
946), 
Goff-Gratc
(E. 1 I) 
373.16 
(E.12) 
t 'Ts/'I'air 
t + a3(10b1(1- f>) + 
 a, 
(t - 1) + a2 log10 
X (E. 13) 
ws 
a (10b2(t-1) - 1) + log10 e4 
(E .14) 
(E. 15) 
. 
t as it is in units of st
andard atmospheres
/ eren
1T l bl ?  c d 
. ht
versi.o
 n 1.s  s1 1g Y 
di?f f
Jc pu 1s1 J
308 
Sa turat io n Vapo r Pressure 
100 
~ 
\..-
0 
.0 60 __
E _- 1---__. -1-- --'--1...-~- ~ 
'--' 1 
Q) 
\..-
:J 
en 
en 
Q) 
\..-
0.. 
\..-
0 
0.. 
0 
> 
20 
0 LJ__LJ.JJ.-J_JJ..J..LL-LJJ..JlJJ.-JlJJ.-JL.J.-'-'__;J..J.__;J..J.JJ---l.JJ---l._u.J4-_0u. J-J_LJ 10 20 30 
0 Tem pera tu re (?C) 
igure E. l: Saturation vapor pressure vs. temperature. The Goff-Grat
F ch  equation was used for this plot, although the Richards vapor pressure formulation would be indistin-
guishable from Goff-Gratch. 
309 
where T.~ is steam point temperature, Tair is air temperature, both in Kelvin . ew1? is 
saturatio n vapor pressure in mbar. The constants are as foll ows: cws = 1013. 25, 
0. 1 = - 7.90298, 0.2 = 5. 02808, O.:i = - 1.3816 7X 10- , o,/4 = 8. 1328 X 10- \ 
b1 = 11 .344 , b2 = - 3.49149. ews is the saturation pressure o f liquid water at steam 
poi nt temperature, or in other words, I standard atmosphere ( IO 13 .25 mbar). 
The Ri chards vapor pressure equation (Richards, 1971 ) is a more convenient fom, to 
determine satu ration vapor pressure, and produces virtually the same result as 
Goff-Gratch 2. Tt is an exponenti al with a polynomial exponent: 
esat. = 1013.25 exp(tn( l 3.3185 + ln( - 1.9760 + ln( - 0.644 5 - 0. 1299ln)))) (E. 16) 
where tn = l - (373.15/T), with T in Kelvin. 
The slope of the saturation vapor pressure curve, .6. , is the derivative o f Eq. E.16: 
ddeTsa l -_ 373T.l 5e.rnt ( . ( ( 5 - (O .or: l9Gt,n )) ) ) (E .17) 2 13.3185 - ln 3.952 - tn 1.933
Relative Humidity to Vapor Pressure 
Relative humidity is approximately the same as the ratio of vapor pressure, e, to 
saturation vapor pressure, e.sat? Strictly, relative humidity is the ratio of water vapor 
mixing ratio to saturation water vapor mixing ratio, rh = _,_.  . Given fractional (i.e. not 
Tsnt 
percentage) relative humidity, vapor pressure can be determined in a few steps. Also 
see Fig. E.2 . First, find the saturation mixing ratio, r sat, from the saturation vapor 
pressure, e .sat (found from Eq. E.16): 
0.62197 
rsat = ...E.... - 1 (E.1 8) 
e.,rn t 
2The Richards estimate differs from Goff-Gratch by less than 0.0035 mbar. 
3 10 
vc)? . 111 
- , p I ,---. 
50 
Air I ressu r 1000 11 bo r 
,---_ 
~ '1 0 
E 
'-... 
er> 
>-- .30 
l/) 
(1) 
0 / 
L 
0 20 
Q_ 
0 
> 
10 
........ 
-
0 _, 
00 0.2 0.4 0. 6 08 1.0 
R lo l ive Hurn di ty 
Figure E.2: Vapor density vs. rch1tive humidity. 
3 11 
Pis atmospheric pressure. The term 0.62197 is dimensionless and is the ratio of water 
molecular weight to dry air molecular weight ( 18.016/28.966). Second, the water vapor 
mixing ratio is found : 
r = rh X Tsai, (E.19) 
Third, the vapor pressure is found: 
r 
e=---+- P (E.20) 0.62197 7? 
E.2.1 Air-Vapor Densities from Vapor Pressure 
Vapor density is: 
0.62197e 
(E.21) 
where the dry air constant is Rei is 2.8704 x 10- 3mbar m:i K- 1 g- 1, e is vapor pressure 
in mbar, temperature, Tis in Kelvin, and Pv is in kg m - :i_ 
Dry air density is: 
P -e 
Pd = RdT (E.22) 
The total moist air density is: 
_ _!_ ( _ 0.37803e) 
(J - RdT l p (E.23) 
E.2.2 Specific Humidity 
Specific humidity, the ratio of water vapor mass to the total moist air mass, Pv/ p, can 
be converted to total moist air density: 
p 
p = T Rd(l + (E.24) 0.60787q) 
Specific humidity has a simple relationship to the mixing ratio: 
r q 
q = --orr = - - (E.25) 
r+l 1 - q 
312 
q vs . rh 
50 
Air ress ur : 1000 m bor 
..--.. 40 
0' 
.:x. 
"-.. 
0' 
'--' 
30 
-0 
E 
I 
u 20 
u 
QJ 
0.. 
(./) 
10 
0 -
0.0 0.2 0.4 0.6 0.8 1.0 
Rela t ive Hum id ity 
Figure E.3: Specific humidity vs. relative humidity. 
To convert specific humidity to relative humidity (also see Fig. E.3): 
q P - e.rnl 
r h =-- x ---- (E.26) 
1 - Q 0.60787e.rnl 
E.2.3 Dew Point Temperature 
The dew point temperature, Td , detennines vapor pressure, e, which can be determined 
by substituting Td for T in Eq. E.16. Using dry bulb temperature in Eq. E.16 returns 
saturation vapor pressure, esat? Relative humidity is then closely determined from 
e/ esat? Alternatively, Eq. E.18 can be solved twice, once using e .rnt as indicated, and 
second, by substituting e for esal to determiner. Relative humidity is then r/rsat? 
313 
E.2.4 Specific Heat of Moist Air at Constant Pressure 
Spec ific heat, Cp is the weighted average o f the atmospheric components: dry air and 
water vapor (Brutsaert, 1982): 
(E.27) 
where cpd, specific heat of dry ai r, is I 005 J kg- 1 K- 1, and q is the specific humidity. 
E.2.5 Latent Heat of Vaporization of Water 
Latent heat is a slowly varying function of temperature (Brutsaert, 1982) and can be 
computed over the range -20-40?C from: 
Avap = 2.501] G - 0.00237839 X T (E.28) 
where Avap is 106 J kg- 1 and T is temperature in Celsius. 
E.2.6 Psychrometric Constant 
CpP 
,y=--- (E.29) 
0.622>-vnp 
where cp is specific heat at constant pressure, P is pressure, and Avap is latent heat of 
vaporization. 'Y is typically in w1its, mbar K- 1 . 
F Example Flux Computation 
To illustrate what kinds of values to expect from surface energy balance modeling, an 
example solution is shown. 
3 14 
F.1 Remote Sensing Observations 
I . Radiometric surface temperature: 37?C 
2. NOVI: 0 .5 
3. Landuse: 4 (Pasture) 
F.2 Meteorological Observations 
I . Air temperature at 9 m: 35.0?C 
2. Relative humidity at 9 m: 0.3 
3. Air pressure: 960 mbar 
4. Wind speed at 10 m : 2.0 m s- 1 
5. Solar zenith angle 32.0? 
6. Incoming solar radiation 824.0 W m- 2 
F.3 Initialize Parameters 
I. Dry soil absorbtivity in visible/near-infrared: 0.85/0. 75 
2. Green vegetation absorbtivity in visible/near-infrared: 0.85/0.15 
3. Leaf absorbtivity in thennal infrared: 0.95 
4. Dry soil thermal band emissivity: 0.96 
5. Vegetation canopy thermal band emissivity: 0.99 
315 
d: 0.8/0.2 
 radiation in visib
le/near-infrare
6 r direct b
eam
? Spec tra/ weig
hting fo
/0.1 
diation in visible/n
ear-infrared: 0.9
or diffuse beam ra7 Spectral weightin
g f
-
tion: 0. 7 
ction coefficient
 for diffuse radia
8- Canopy ex tin
1,): 1.0, spherical 
distribution 
ion function param
eter (.
9 distribut- Canopy leaf an
gle 
1 : 1
.0 m 
O . Canopy heigh
t (Pasture)
11 I minimum/maxim
um: 0.0/0. 7 
- NOV
 
12 n of vegetation th
at is green: 1.0
- Fractio
0.625 
3 al cover paramete
rs ( and ,8: 0.6, 
1 - Fraction
?C (Air temperatu
re) 
0
14 opy temperature
: 35.
- Can
15- Leaf width: 0.0
2 m 
: 0.0O 12
 
et al., 1995) b
16 Soil resistance pa
rameter (Sauer 
-
 and Ishida, 1997)
 c: 
namic roughness 
parameter (Kondo
17. Soil aerody
1 
1  "7i
0.00245 m s- K
iation coefficien
t cc: 0.3 
l 8. Soil rad
ind speed: 0.0
5 m 
9. Reference heig
ht for soil w
.1
9 
ess length L: -1.0X
 io -
20- Monin-Obukho
v roughn
2 e height, z: JO.O
m 
1. Referenc
.4 
22. Von Karman 's
 constant, k: 0
316 
F.4 Compute Net Radiation 
I . Fracti ona l cover and LAI (Eqs. 2.75 and 2.76): 
1 - (0.7 - 0.5 ) 1/ 0.6 
f 
0.7 - 0.0 
0.876 
In (1 - 0.876) 
L AI 
- 0.625 
3.340 
2. Canopy reflectivity from horizontally-oriented leaves (Eq. 2.13): 
1 - y"Q.85 
Ptwr,\/ TS 
1 + y"Q.85 
0.04 
1 - ,/o.15 
Ptwr,N /[I. 
1 + v'015 
0.44 
3. Canopy extinction coefficient for beam radiation (Eq. 2.16): 
J12 + tan2 32? 
1 + 1.774 X (1 + 1.182) - 0.733 
0.5892 
4 . Canopy reflectivity for non-horizontally distributed leaf angles (Eq. 2. 15): 
2 X 0.5892 X 0.0
P c,be,V TS + 4 0.5892 1 
0.030 
317 
2 X 0.5892 0 
---- X .4 4 
fJc,be, NI R 0.5892 + 1 
0.326 
2 X 0.7 X 0.04 
(Jc,d, \I I S 0.7 + 1 
0.033 
2 X 0.7 X 0.44 
fJr, d,N I 17 0.7 + 1 
0.3G2 
5. Thin canopy reflectivity in visib le and nea r-infrared bands for direc
t and diffuse 
radiation (Eqs. 2. J 7 and 2. J 8): 
0.030 - 0.15 ) e-2v'o.Bsx 0. 5892x3. :l40 
f.h,,y 1s ( 0.030 X 0.15 - 1 
0.00320 
0.030 + 0.00320 
fJ/./1.i n ,be, \I I S 1 + 0.00320 
0.033 
0.326 - 0.25 ) e-2v'Olsxo.s892 x 3.340 
( 0.326 X 0.25 - 1 
- 0.01802 
0.326 - 0.01802 
Pthin,be,N l R 1 - 0.01802 
0.314 
0.033 - 0. 15 ) e-2v'o.Bsx0.7x3.340 
( 0.033 X 0.15 - 1 
0.00158 
0.033 + 0.001 58 
Pthin,d, V I S 1 + 0.00158 
0.0345 
0-362 - o.25 ) e-2v'OTix 0.7 x 3.340 
~d,N f R ( 0.362 X 0.25 - ] 
318 
- 0.02013 
0.362 - 0.02013 
P11i;n,d,N I fl 1 - 0.02013 
0.349 
6. Canopy albedo in vis ible and near-infrared bands (Eq. 2. 19): 
flr 0. 5 X (0.8 X 0.033 + 0.2 X 0.31 4 + 
0.9 X 0.0345 + 0.1 X 0.349) 
0.078 
7. Transmissivity of short wave radiation at the soi l surface (Eqs. 2.20 and 2.22): 
exp te rm be - /o.85 X 0.5892 X 3.340 
- 1.81434 
(0.0302 - 1) e-1.s1434 
(0.030 X 0.15 - 1) + 0.030 X (0.030 - 0.15)e2 x- l.8l434 
0.164 
(0 .3262 - 1) e- 1.81434 
(0.326 X 0.25 - 1) + 0.326 X (0.326 - 0.25)e2X- l.81431 
0.457 
exptermd -/o.85 X 0. 7 X 3.340 
-2.15553 
(0.0332 _ l) e- 2. 15553 
T"?l,V !S(32?) (0 .033 X 0.15 - 1) + 0.033 X (0.033 - 0.15)e2x-2. l555.1 
0.116 
(0 _3622 _ l) e- 2. 15553 
'T"d,N IR (32?) 
(0.362 X 0.25 - l) + 0.362 X (0.362 - 0.25) e2 x-2.l 555:l 
319 
0.GG2 
TVN/17. = 0. 5 X (0.8 X 0.]64 + 0.2 X 0.457 + 
0.9 X 0.116 + 0.1 X 0.662) 
= 0.197 
8. Soil albedo (Eq. 2.21): 
a., = 0.5 X [(l - 0.85) + (1 - 0.75)] 
= 0.20 
9. Transmissivity of long wave radiation to the so il surface (Eq. 2.23): 
= 0.042 
I 0 . Water vapor pressure (Eqs. E.16, E.18, E.19, E.20, E.21 ): 
tn 1 - (373. 15/(35.0 + 273.15)) 
- 0.210936 
e.,at 1013.25 x exp(- 0.210936 x (13.3185 - 0.210936 x 
(- 1.9760 - 0.210936 x (- 0.6445 - 0.1299 X - 0.21093G)))) 
56.23mbar 
 0.6
2197 
Tsat = 1)60.0 _ ] 
56 .2:l 
320 
0.038697 
r 0.3 X 0.038697 
0.011609 
0.011609 X _960 0 
e 
0.62197 + 0.011609 
17.59rnbar 
0.62197 X 17.59 
= 2.8704 X 10- :i X (35.0 + 273.15) Pv 
= 3 12.37g m-
11 . Atmospheric long wave emiss
ivity (Eq. 2.25): 
= 1. X ( 17.59 ) i 
fn.t.m 24 35.0 + 273.15 
0.824 
12. Soil component temperature (
Eq. 2.46): 
I 
+ 73.15)4 0.876 X (35.0 + 273.15)
4) 4 
(37.0 2 -
Ts ( (1 - 0.876) 
323.3?I < 
50.l?C 
Long wave radiation from the sky
, soil and canopy (Eq: 2.24): 
13. 
4 
0.824 X 5.67051 X 10- B X (35.0 + 273.15)RTIR,a 
= 421.3Wm - 2 
4 
Rr1n,s 0.96 X 5.67051 X
 10-B X (323.3)
321 
594.7Wm -
2 
4 
.99 5.6705] X 10- R X (35
.0 + 273. 15)
Rr1R,c 0 X 
2 
421.3 w m -
opy (Eq: 2.26): 
14. Net radiati on at the can
 
 + 594. 7 - 2 X 421.3) +
R,,,. ,c = (1 - 0.042) X ( 42 1.3
(1 - 0.1 97) X (1 - 0. 078) 
X 824.0 
2Wm - 2
 
776.
rface (Eq. 2.27): 
15. Net radi ation at the soil
 su
- 594. 7 + 
Rn,s = 0.042 X 42 1.3 + (1 - 0.042
) X 421.3 
0.197 X (1 - 0.2) X 824 .0 
2 
- 43.5W m -
6. Net radiation at the surf
ace (Eq. 2.28): 
1
R,,. 776.2 - 43.5 
2 
732.6Wm -
322 
F.5 Compute Flux Components 
I. Slope of sa turation water vapor vs. temperture curve (Eq. E.17): 
de.mt 373 .1 5 x 5G.23 
= - 0.2109362 (13.3185 + 0.210936(3.952 + dT 
0.210936(1.9335 - (0.519G x - 0.210936)))) 
= 3.1092 mbar I< - 1 
2. LE flux from canopy (Eqs. E.25, E.27, E.28 , E.29, 2.43): 
0.011609 
q = 0.011609 + l 
= 0.0114758 
Cp = 1005 X (1 + 0.84 X 0.0114758) 
1014.7.Jkg- 1 IC ' 
>.,,mp = 2.50116 - 0.00237839 X 35.0 
2.418 x ,or. .J kg- 1 
1014.7 X 960.0 
'Y 0.622 X 2.418 X 106 
= 0.6477mbar IC 1 
[ 3.1092 ] 
LEc 1.26 X 1.0 X 776.2 X _ + _0 6477 3 1092 
809.4 W m- 2 
3. H flux from canopy (Eqs. 2.44): 
He = 776.2 - 809.4 
= - 33.3 W m- 2 
323 
parameters (Eq. 2.36, 2.37, 2.33, 2.
59, 2.60, 2.31: 
4. Stabi lity 
Zo 1.0/8.0 
= 0.125 rn 
2 
do = - X l .0 3 
= 0.667 rn 
10.0 - 0.GG7 
(ref = - 1.0  X 109
= 0.0 
9.0 - 0.667 
(r -1 X 109 
= 0.0 
10.0 - 0.667 
(u = - 1 X 109 
0.0 
I 
<Pm,1?ef = (J - J6 x 0.0)
4 
1.0 
I 
0.0) 4 
<Pm,T = (1 - 16 X 
1.0 
I 
4 
<Pm,U (1 - 16 X 0.0
1.0 
I 
(1 - 16 X 0.0) 4 <Ph,T 
<Pm,T 
1.0 
 02+ 1. ) -
Wm,ref 2 In C+ 1.0) + ln (l2 2
7r 
2 arctan( l .0) + 2 
324 
0.0 
0 02
\Jim;/' 2 In (1 +/ - ) + In (1 + )? ) -
2 arct.nn(l.0) + 
7r 
2 
0.0 
\V111 ,/J 2 111 c?o ;J .O) + In C+2 1.02) -
7r 
2 arctn11(l.0) + 2 
0.0 
1.0 + l.02 
2 In  
2 
0.0 
5. Canopy airspace resistance (Eq. 2.38, 2.30): 
0.4 X 10.0 
In [ 10.0- 0~667 _ o.o] 
0. 12,, 
0.185ms- 1 
l 7(9.o- o.667) _ o) n ( 0.1 25 0 ? 
0.4 X 0.185 
83.0sm- 1 
6. Transport resistance from soil (Eqs. 2.50, 2.51 , 2.49, 2.53, 2.48 
In ((1.0- 0.667) )] 
2 0 0.125 ? [ o.4 2.0 0.185 
0.453 m s- 1 
2 I 
3.340:i x l.0 ?i 
asc 0. 28  2 
0.02:i 
2.305 
325 
Us = 0.453 exp [2 .305 (01..
005  - 1)  ] 
1 
= 0.051 ms-
I 
a,.s = 0.00245 X (37.0 - 35.0) :i 
= 0. 0030868 
1 
r s = 0.0030868 + 0.0()] 2 X 0.051 
1 
= 317.7srn -
7. H flux from soil (Eq. 2.45): ~~:~;J 
Hs = 12.37 x 1014.7 u~?~(~-3
= 2 62.8Wm
8. G flux (Eq. 2. 54): 
G = 0.3 x - 43.5 
= 2 - 13.1 Wm
9. LE flux from soil (Eq. 2.55): 
LEs = - 43.5 - 62.8 + 13.1 
2 
-93.2W m
10. Sum flux components (Eq. 
2.41 , 2.42): 
Hr = - 33.3 + 62.8 
326 
= 29.5 w rn 2 
LET 809.4 - 93.2 
716.2W m2 
11 . Revise Monin-Obukkhov stability parameter (Eq. 2.34): 
0.1 35:3 
LAio - 12.37----,----- ~ 
0 4 X 9 8] ( W .r, +
- () ---6] 71f'i .2 ) 
. . I0l ~.7x :l5 .0 . 2.48 1 x J(JG 
- 19.826 m 
J2 . Iteration: (Repeat from step 4, until L MO revision changes by less than 0 .00 I . 
327 
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