Consistency of MODIS surface bidirectional reflectance
distribution function and albedo retrievals:
1. Algorithm performance
Yufang Jin, Crystal B. Schaaf, Feng Gao,
1
Xiaowen Li,
1
and Alan H. Strahler
Department of Geography and Center for Remote Sensing, Boston University, Boston, Massachusetts, USA
Wolfgang Lucht
Potsdam-Institut fu?r Klimafolgenforschung, Potsdam, Germany
Shunlin Liang
Department of Geography, University of Maryland, College Park, Maryland, USA
Received 26 July 2002; revised 5 November 2002; accepted 8 November 2002; published 8 March 2003.
[1] The first consistent year (November 2000 to November 2001) of global albedo product
was produced at 1-km resolution every 16 days from the observations of the Moderate-
Resolution Imaging Spectroradiometer (MODIS) instrument aboard NASA?s Terra
spacecraft. We evaluated the quality of the operational albedo retrievals in two ways: (1) by
examining the algorithm performance using the product quality assurance (QA) fields (this
paper) and (2) by comparing retrieved albedos with those observed at ground stations and
by other satellite instruments (in a companion paper). The internal diagnostics of the
retrieval algorithm adequately reflect the goodness of the model fit and the random noise
amplification in the retrieved albedo. Global QA statistics show that the RossThick-
LiSparse-Reciprocal model fits the atmospherically corrected surface reflectances very
well, and the random noise amplification factors for white sky albedo and reflectance are
generally less than 1.0. Cloud obscuration is the main reason for the activation of the
backup magnitude retrieval algorithm. Over the 60C176Sto60C176N latitude band, 50% of the
land pixels acquire more than six clear looks during 14?29 September 2001, and only 5%
of these pixels are inverted with the backup algorithm. The latitude dependence and
temporal distribution of the QA fields further demonstrate that the retrieval status mainly
follows the pattern of angular sampling determined by cloud climatology and the
instrument/orbit characteristics. A case study over the west coast of the United States shows
that white sky shortwave albedos retrieved from magnitude inversions agree on average
with those from full inversions to within 0.033 in reflectance units and have a slightly lower
bias ranging from 0.014 to 0.023. We also explored the effect of residual cloud and aerosol
contamination in the atmospherically corrected surface reflectance inputs in another case
study over southern Africa. The quality assurance procedure of the operational MODIS
bidirectional reflectance distribution function and albedo algorithm compensates for some
of these residual effects and improves the albedo retrieval results by an order of 0.005
(10%) in the visible for more than 12% of pixels. INDEX TERMS: 3322 Meteorology and
Atmospheric Dynamics: Land/atmosphere interactions; 3359 Meteorology and Atmospheric Dynamics:
Radiative processes; 3360 Meteorology and Atmospheric Dynamics: Remote sensing; KEYWORDS: MODIS,
bidirectional reflectance distribution function, surface albedo, algorithm evaluation
Citation: Jin, Y., C. B. Schaaf, F. Gao, X. Li, A. H. Strahler, W. Lucht, and S. Liang, Consistency of MODIS surface bidirectional
reflectance distribution function and albedo retrievals: 1. Algorithm performance, J. Geophys. Res., 108(D5), 4158,
doi:10.1029/2002JD002803, 2003.
1. Introduction
[2] Surface albedo is defined as the fraction of incident
solar radiation reflected by Earth?s surface. It characterizes
the radiative property of the surface and is a primary
controlling factor for the surface energy budget [Dickinson,
1983]. A recent report of the Intergovernmental Panel on
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. D5, 4158, doi:10.1029/2002JD002803, 2003
1
Also at Research Center for Remote Sensing, Beijing Normal
University, Beijing, China.
Copyright 2003 by the American Geophysical Union.
0148-0227/03/2002JD002803$09.00
ACL 2 - 1
Climate Change (IPCC) [2001] identifies surface albedo
effect due to land use change as an important radiative
forcing agent. Such change in land use, mainly by defor-
estation, appears to have produced a negative radiative
forcing of C00.2 ? 0.2 Wm
C02
[Hansen et al., 1998]. Several
simulation studies have also shown regional and global
climate changes due to perturbations of a few percent in
land albedo in tropical regions [Nobre et al., 1991; Lean
and Rowntree, 1997], in semiarid regions [Charney et al.,
1977; Sud and Fennessy, 1982; Knorr et al., 2001], and in
global land surface [Lofgren, 1995]. A consistent and
accurate global albedo data set is hence essential to the
investigation of the sensitivity of climate to various types of
forcing and to the identification of the effects of human
activities [King, 1999]. The increasing fineness of spatial
resolutions from 100 km to 50 km (and even 10 km) in
modern climate models also calls for a high-resolution
albedo inventory or a spatially explicit albedo specification
[Hahmann and Dickinson, 2001]. It was suggested that an
absolute accuracy of 0.02?0.05 is desirable for the albedo
characterization at spatial and temporal scales compatible
with climate studies [Henderson-Sellers and Wilson, 1983;
Sellers, 1993].
[3] Traditionally, climate models rely on a global land
cover map and a set of compiled field measurements to
prescribe the surface albedo. However, significant albedo
differences were shown to occur in various models due to
complex observation conditions and inconsistent land cover
classifications [Henderson-Sellers and Wilson, 1983]. Land
surface models such as NCAR LSM [Bonan, 1996], BATS
[Dickinson et al., 1993], and SiB2 [Sellers et al., 1996],
adopt a two-stream approximation to calculate the surface
albedo, which still depend on an accurate parameterization
of the soil and vegetation system. Satellite remote sensing
provides an efficient tool for a consistent global albedo
characterization with high spatial and temporal resolutions.
Atmospheric correction, directional-to-hemispherical con-
version, and spectral interpolation, however, are the main
sources of uncertainties in the retrieval of surface albedo
from space.
[4] The Moderate-Resolution Imaging Spectroradiometer
(MODIS), a key instrument aboard NASA?s Terra (EOS
AM-1) satellite, acquires global data in 36 spectral bands
every one to two days. The rich spectral information
improves our understanding of the Earth?s atmosphere and
reduces the uncertainty of atmospheric correction [Justice et
al., 1998]. The utilization of a surface bidirectional reflec-
tance distribution function (BRDF) model [Lucht et al.,
2000] further improves the quality of surface albedo retriev-
als, compared to retrievals under a Lambertian assumption
[Hu et al., 1999]. Moreover, comprehensive quality assur-
ance (QA) fields are embedded in the various levels of
MODIS products and are taken into account in the higher-
level processing streams [Justice et al., 1998]. These
advances make the MODIS BRDF and albedo products of
particular value for global albedo characterization.
[5] Any satellite-derived products are not directly meas-
ured and hence an after-launch evaluation is critical for the
assurance of product quality [Justice and Townshend,
1994]. The retrieval quality is essential to the user com-
munities, without which the subsequent science would be
open to question. In particular, the global performance of
the albedo retrieval algorithm and the uncertainties of the
albedo product must be addressed before the climate com-
munity is able to accept and correctly apply the global
albedo data set in their modeling efforts. The evaluation also
helps algorithm developers accordingly to refine the product
in the future [Schaaf et al., 2002].
[6] In this study we use the first consistent year (Novem-
ber 2000 to November 2001) of reprocessed MODIS BRDF
and albedo products to investigate the performance of the
MODIS BRDF and albedo retrieval algorithm. A detailed
analysis of the quality assurance (QA) fields associated with
the MODIS products serves as the internal diagnostics of
the retrieval algorithm. We particularly address the effects of
sparse angular sampling and atmospheric correction uncer-
tainties on the MODIS surface BRDF and albedo products.
Global statistics of the algorithm performance are also
generated and analyzed. This study is the first part of our
ongoing evaluation of operational MODIS BRDF and
albedo products. In an accompanying paper [Jin et al.,
2003], we use the field measurements to assess the accuracy
of the MODIS BRDF and albedo product and also examine
its consistency with two commonly used global albedo
products derived from other sensors.
2. MODIS BRDF and Albedo Retrieval
Algorithm
2.1. Atmospherically Corrected
Directional Reflectances
[7] A directional sampling of surface reflectances from
MODIS can only be obtained by the accumulation of
sequential observations over a specified time period. Cloud
obscuration routinely reduces the number of clear looks. We
chose a 16-day period as a trade-off between the sufficiency
of angular samples and the stability of surface reflectivity
[Wanner et al., 1997; Gao et al., 2001]. The well specified
MODIS spectral bands improve the quality of cloud, aero-
sol, and water vapor retrievals. The high spatial resolution
of the MODIS instrument also reduces the sub-pixel cloud
contamination problem commonly found in the surface
reflectances derived from coarse resolution sensors. By
incorporating the atmospheric products in the atmospheric
correction procedure, the uncertainty of MODIS surface
reflectances is significantly reduced [Vermote et al., 1997,
2002]. The theoretical typical relative error of surface
reflectance ranges from 10% to 33% in the red and 3% to
6% in the near infrared, and is generally higher in cases of
high aerosol loading and over sparsely vegetated areas
[Vermote et al., 1997]. The MODIS surface reflectance
product contains extensive QA fields on cloud information,
aerosol status, and spatial aggregation characteristics.
2.2. RossThick-LiSparse-Reciprocal BRDF Model
[8] The reflectance of naturally occurring land surface
types is anisotropic and a BRDF model is employed to
derive surface albedo from a limited number of angular
samples [Roujean et al., 1992; Walthall et al., 1985; Rah-
man et al., 1993; Wanner et al., 1997]. The MODIS BRDF
and albedo algorithm adopts the three-parameter, kernel-
driven, RossThick-LiSparse-Reciprocal (RTLSR) BRDF
model to characterize the directional distribution of surface
reflectance. A volumetric kernel and a geometric kernel
ACL 2 - 2 JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM
represent two scattering patterns typified by homogeneous
dense vegetation and by discrete shadow-casting objects,
respectively. The readers are referred to Wanner et al.
[1995] and Lucht et al. [2000] for detailed kernel deriva-
tions and expressions. The capacity of the RTLSR model to
represent BRDF shapes was validated with field measure-
ments over a variety of land cover types [Hu et al., 1997].
Privette et al. [1997] and Bicheron and Leroy [2000] also
demonstrated the high accuracy and efficiency of the
RTLSR model inversion with sparse directional samplings
from both field and satellite measurements. The small
number of required parameters and the linear property of
the RTLSR model is advantageous for operational BRDF
and albedo retrievals from space on a global basis and at
high spatial-temporal resolutions.
2.3. Inversion Strategy
2.3.1. Linear Regression
[9] The inversion strategy of the MODIS BRDF retrieval
is to minimize the squared errors between model predicted
and observed reflectances. The merit function of the inverse
problem can be written as the following matrix:
Minimize M
nC21
C0 K
nC23
X
3C21
??
T
C
E
M
nC21
C0K
nC23
X
3C21
??
no
; ?1?
where M is the measurement vector in n different viewing
and illuminating geometry, K is the kernel matrix, and X is a
vector of kernel coefficients to be derived, and C
E
is the
measurement covariance matrix [Lucht et al., 2000]. Note
that the noise in atmospherically corrected surface reflec-
tances is not quantitatively estimated. However, to take into
account the uncertainty in input data, the MODIS BRDF
and albedo processing stream first checks the QA fields of
surface reflectance product, rejects any cloudy and high
aerosol-loaded pixels, and assigns penalties to those
observations with a lower quality [Schaaf et al., 2002].
Furthermore, a possible outlier can be detected and
discarded before the inversion begins.
[10] The BRDF is an intrinsic property of surface reflec-
tance, depending only on canopy structure and elemental
optical properties, whereas the actual surface albedo is
affected by atmospheric illumination conditions. MODIS
derives two intrinsic albedo products, black sky albedo
(BSA) and white sky albedo (WSA), directly from the
inverted RTLSR model. BSA (directional-hemispherical
reflectance) refers to the special case of illumination from
a collimated beam [Martonchik et al., 2000]. It is derived
through the angular integration of the BRDF over the full
viewing hemisphere. WSA (bihemispherical reflectance) is
similar in definition to BSA except that the illuminating
radiation field is isotropic and covers the full illuminating
hemisphere. The actual albedo occurring in nature can be
approximated as a linear combination of BSA and WSA
weighted by the fractions of direct and diffuse irradiance
[Lewis and Barnsley, 1994]. Albedo is also wavelength-
dependent. MODIS albedos are first derived for the 7 finite
spectral bands (centered at 648, 858, 470, 555, 1240, 1640,
and 2130 nm, respectively) and then spectral-to-broadband
coefficients are used to derive three broadband albedos in
the visible, near infrared, and total shortwave bands [Liang
et al., 1999].
2.3.2. Quality Assurance of MODIS BRDF
and Albedo Product
[11] The covariance C
X
of the parameters is given by C
X
=
(K
T
C
E
C01
K)
C01
. In the ideal case of independent errors with
equal variances s
2
, the covariance matrix is simplified as
C
X
? K
T
K
C0C1
C01
s
2
; ?2?
where (K
T
K)
C01
describes the propagation of measurement
noise to the BRDF parameters [Gao et al., 2001]. Similarly,
noise in measurements is propagated to any quantities
derived from the BRDF parameters. Due to the linear
property of the RTLSR BRDF model, the variance of
reflectances and albedo can also be estimated analytically.
Lucht and Lewis [2000] derived a so-called weight of
determination (WoD) to represent the magnitude of noise
amplification from measurements to reflectances and
albedo. A WoD smaller than one means that the variance
in retrieved quantities will be less than that in the original
measured reflectances. The WoD is determined by the
angular sampling and the kernel values at those angular
geometries,
WoD ? U
T
K
T
K
C0C1
C01
U; ?3?
where U is a vector composed of the weighting of the
kernels, such as kernel values at given angles for the noise
amplification in reflectances and angular integrals of kernels
for the albedo noise amplification Lucht and Lewis [2000].
[12] The root mean square error (RMSE) is an indicator
of the deviation of the RTLSR model fit from the atmos-
pherically corrected surface reflectances. Two possible
reasons for this residual error are noise inherent in the
observations and the partial inability of the model to fit
the observed reflectances. As part of the MODIS BRDF and
albedo products, the RMSE and noise amplification factors
for both nadir-view reflectance and white sky albedo are
stored as several QA fields in each band. Table 1 summa-
rizes the MODIS BRDF and albedo QA fields.
2.3.3. Backup Algorithm
[13] A backup algorithm (magnitude inversion) is imple-
mented if there are insufficient angular samples or the
internal quality check indicates a low confidence in the
retrieval with the main algorithm. The basic concept behind
the magnitude inversion is that the BRDF shapes for a
certain land cover type are similar and thus can be pre-
scribed. A global land cover classification, defined in terms
of typical BRDFs, was derived from the Olson classification
[Olson, 1994] and a seasonal model. The archetypal BRDFs
for each land cover were compiled from various field
measurements [Strugnell and Lucht, 2001; Strugnell et al.,
2001]. For each pixel, the corresponding archetypal BRDF is
assumed as an a priori guess and a multiplicative factor is
then derived from the available actual observations to adjust
the aprioriguess. Currently the archetypal BRDF database is
being updated on a pixel-by-pixel basis and high quality
BRDFs retrieved from MODIS full inversions are being used
to replace the at-launch archetypes [Schaaf et al., 2002].
3. Sampling Effects on MODIS BRDF and
Albedo Retrievals
[14] Both the number and the variability of directional
observations affect the quality of the BRDF retrievals
JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM ACL 2 - 3
[Privette et al., 1997]. In the MODIS BRDF and albedo QA
fields, the number of clear looks is implicitly contained in
the category of magnitude inversions or full inversions, and
the distribution of angular sampling is partly represented by
the weights of determination.
3.1. Spatial Distribution of the QA Fields
[15] Figure 1 shows the spatial distribution of the MODIS
BRDF and albedo QA fields in the red band over the western
United States (Tile h08v05: 30C176Nto40C176N, 104C176Wto
130C176W) and over the Sahel region (Tile h18v07: 10C176Nto
20C176N, 0C176Eto10C176E). The observation periods start in late
May and middle September, respectively. In tile h08v05
(Figure 1a), the BRDF and albedo are retrieved with the
highest quality (QA = 0) for the majority of pixels, and only
small regions are retrieved with magnitude inversions using
4?6 clear observations (QA = 9). The pixels with a good
RTLSR fit but moderate noise amplification (QA= 1) mainly
occur adjacent to the regions with the magnitude inversion.
Several small patches (QA= 8) occur in the east, where more
than 6 clear looks are available but the magnitude inversion
is performed.
[16] In tile h18v07 (Figure 1b), no retrievals, or retrievals
with magnitude inversions using less than three clear looks,
appear in the southern part. Moving towards the north, the
number of clear looks increases and the retrieval status
moves from the backup algorithm to the main algorithm.
The rainy season in the Sahel region (8C176Nto18C176N, 17C176Wto
20C176E) occurs during the months of June through September
when the Intertropical Convergence Zone (ITCZ) reaches its
farthest northward extension (15C176N). Also shown in tile
h18v07 are apparent orbital boundaries indicating the effect
of angular sampling geometry. Along the transitional area
between the backup algorithm and the main algorithm, there
are actually more than 7 clear looks but the main algorithm
fails.
3.2. Case Studies of Sampling Effects
[17] To check the angular sampling patterns associated
with the various QA designations, we selected individual
pixels with various QAs and plotted their angular sampling
as well as the individual surface directional reflectances in
the red and near infrared. The observations of four such
pixels in tile h08v05 (western United States) during May 25
to June 11, 2001 are shown in Figures 2 and 3. The QA flag
Table 1. Band-Specific Quality Assurance Fields in MODIS
BRDF and Albedo Products (MOD43B)
Bit
Fields Value RMSE
WoD
(ref)
WoD
(WSA)
0000 0 good good good
0001 1 good good moderate
0010 2 good moderate good
0011 3 good moderate moderate
0100 4 moderate good good
0101 5 moderate good moderate
0110 6 moderate moderate good
0111 7 moderate moderate moderate
1000 8 magnitude inversion (num. obs. > = 7)
1001 9 magnitude inversion (num. obs. >3 and <7)
1010 10 magnitude inversion (num. obs.< = 3)
1011 11 currently not used
1111 15 fill value
WoD(ref) and WoD(WSA) refer to noise amplification factor for nadir
reflectance at 45C176 solar zenith angle and white sky albedo, respectively.
Thresholds used for RMSE and WoD indicators are as follows: RMSE
(good 0?0.10, moderate 0.10?0.20, poor > 0.40), WoD (good 0?0.75,
moderate 0.75?1.25, poor > 2.00).
Figure 1. Images of MODIS BRDF and albedo QA in the
red. MODIS tile h08v05 (Figure 1a) is in the west coast of
the United States; the observations for BRDF and albedo
retrieval are acquired within May 25 to June 11, 2001.
MODIS tile h18v07 (Figure 1b) is in Sahara region and the
observations are acquired within September 14 to Septem-
ber 29, 2001.
ACL 2 - 4 JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM
of Pixel 1 shows that it represents the best quality of
inversion. The noise amplification factor is 0.75. Figure
2a shows how good its angular sampling is. Fifteen clear
looks are available and its viewing zenith angles are evenly
distributed from 0C176 to 60C176 in both forward and backward
directions. The solar zenith angles range from 10C176 to 25C176
and the observations are mainly in the principal plane. The
right panel of Figure 2a shows that the retrieved BRDF
parameters predict well the surface reflectances observed by
MODIS with the RMSE equal to 0.005. The hot spot
phenomenon, a large peak in the backscattered radiation
near the Sun?s illumination direction arising from the
absence of shadows in the direction of sensor [Roujean,
2000], is evident in the red and near infrared near 20
viewing zenith angle in the backward scattering direction.
[18] Compared to Pixel 1, Pixel 2 lacks the sampling
between 0C176 to 40C176 in the backward direction and between 0C176
to 20C176 in the forward direction (Figure 2b). The QA flag
indicates the noise amplification factor for white sky albedo
is larger than that of Pixel 1. Pixel 3 has smaller ranges of
viewing zenith angles and thus the noise amplification for
both white sky albedo and nadir reflectance are relatively
large (Figure 3a). For Pixel 4, viewing angles cover only the
forward direction and the retrieval uncertainty is very
sensitive to the noise of input data. The QA flag clearly
indicates that the full inversion would be of such low
quality that a magnitude inversion is made although there
are more than seven clear looks available.
[19] We also examined a transitional area in tile h18v07
in Sahel, where there are a sufficient number of clear looks
but the main algorithm still fails. For some pixels, the
angular sampling is mainly distributed in the forward
direction as in Pixel 4. The others cover a sufficient range
of viewing angles as does Pixel 1, but MODIS acquires
observations closer to the cross principal plane over North
Africa in September. In this case, the WoD and hence the
noise amplification are slightly higher than those of Pixel 1
and the algorithm turns to a magnitude inversion since a
fixed threshold is set for the quality check.
[20] The above analysis shows that the QA fields of
MODIS BRDF and albedo products characterize the angular
sampling pattern and indicate the confidence and the
processing stream of the inversion. To utilize the highest
quality MODIS BRDF and albedo products, the users
should check this QA information.
3.3. Full Inversion Versus Magnitude Inversion
[21] To examine the stability of the retrieval and the effect
of the angular sampling on the albedo values, we plotted
temporalsequencesofalbedoduring2001intheredandnear
infrarednarrowbandsforsixpixelsinh08v05(Figure4).The
time series of albedo are generally smooth for evergreen
needleleaf forests in both the red and near infrared. The
seasonal change of albedo is apparent for mixed forests,
shrublands, savannas, grasslands, and croplands, especially
in the near infrared band where leaf chlorophyll has very low
Figure 2. (a and b) MODIS angular samplings (left panels) and MODIS surface directional surface
reflectance (right panels). The radius represents the zenith angle with an interval of 10C176 and the polar angle
represents the azimuth. Solid circles refer to the viewing direction and open circles refer to the location of
the sun. The weight of determination (WoD) for white sky albedo and root mean square error (RMSE) are
also shown at the top of left panels as well as the QA field associated with the MODIS BRDF and albedo
products. In the right panels, MODIS atmospherically-corrected surface reflectances are shown as solid
symbols while those predicted by the MODIS BRDF model are shown as open symbols.
JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM ACL 2 - 5
absorption. Specifically, for these land cover types, albedo
values in the near infrared start to increase in late April,
become stable in summer, and then began to decrease in
September. Obviously the time series of albedo capture the
phenology of vegetation.
[22] A small number of apparently spurious retrievals are
also shown on the temporal plots. We checked the corre-
sponding QAs and identified the QAs with values greater
than 3 in Figure 4. We found that lower quality magnitude
inversions are the primary reason for these anomalous
values. For the open shrubland pixel (Pixel 3, Figure 4b),
for example, high quality full retrievals are obtained over
Julian days 193?208 and 225?240, whereas the magnitude
inversion is undertaken with only 4?6 clear looks available
between these two periods. In this case, the albedo values
are similar for the first and third time periods but are lower
by up to 0.05 in the red and near infrared during the second
time period. For pixel 3, we also noted a less abrupt
decrease of the near infrared albedo by 0.025 over Julian
days 129?145 compared to that over Julian days 113?128,
although QAs indicate retrievals of good quality during
growing season. It is probably due to the systematic
atmospheric correction error in surface reflectances acquired
over Julian days 129?145.
[23] To further investigate the difference between the
retrievals from the main algorithm and the backup algo-
rithm, we extracted all the pixels in tile h08v05 that have
high quality full inversions for both the 193?208 and 225?
240 time periods but are retrieved with magnitude inver-
sions within Julian days 209?224 for each IGBP land cover
type. The top panels of Figures 5?6 show the scatterplots of
the albedo retrieval from the magnitude inversion versus
that from the main algorithm for open shrublands and
barren, respectively. Generally the magnitude inversion
agrees well with the full inversion. The correlation coef-
ficient is above 0.94 and the RMSE is less than 0.033. The
top panels show that the broadband white sky albedo from
the magnitude inversion has a slightly lower bias of 0.014 in
the visible and 0.023 in the near infrared for open shrub-
lands. For barren areas, this lower bias is 0.017 and 0.019,
respectively. To examine if this bias is caused by surface
change from one period to the next, we plotted the full
inversion albedos from the 193?208 period against those
from the 225?240 time period in the bottom panels of
Figures 5?6. The albedos from two time periods of full
inversion are clearly in better agreement than the albedos
from full and magnitude inversion. The above analysis
indicates that the magnitude inversion results in a lower
albedo bias over shrublands and barren. This bias may result
from differences between the BRDF archetype and the
actual BRDF. Currently the BRDF database is being
updated with actual MODIS based parameters of the highest
quality, which will reduce the uncertainty of BRDF arche-
types [Schaaf et al., 2002]. Also note that the magnitude
inversion is more sensitive to noise in atmospherically
corrected surface reflectances, especially when the number
of observations is very small.
4. Effect of Atmospheric Correction Uncertainties
on BRDF and Albedo Retrievals
4.1. Residual Atmospheric Effects in
Surface Reflectances
[24] In addition to insufficient independent samples, pos-
sible noise in the atmospherically corrected surface reflec-
tances may contribute to the uncertainty of the BRDF and
Figure 3. (a and b) Same as Figure 2, but for other pixels with different quality assurances.
ACL 2 - 6 JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM
albedo retrievals. It is clear that an exact assessment of the
uncertainty of atmospheric correction and its effect on the
BRDF and albedo retrievals can only be undertaken in
conjunction with the validation of the atmospheric products.
Moreover, the accuracy of both the atmospheric products
and the atmospheric correction vary from region to region
and time to time. Quality assessment thus becomes a
challenging task. Various efforts are being undertaken to
assess the accuracy of the atmospherically corrected surface
reflectance product [Vermote et al., 2002; Liang et al.,
2002]. Liang et al. [2002] used ground measured aerosol
optical depth and water vapor content to perform atmos-
pheric correction over the Beltsville Agricultural Research
Center (BARC) agricultural test site, one of the EOS core
validation site, and found that the MODIS surface reflec-
tances agree well with their results. The typical relative error
is within 5%.
[25] The relative accuracy of the atmospherically cor-
rected surface reflectances is generally lower in cases of
high aerosol loading and over sparsely vegetated areas
[Vermote et al., 1997]. As a case study, we examine if there
is some residual effect from cloud or aerosol contamination
in the surface reflectance product over semiarid regions. We
chose an southern Africa tile (h20v10) as an example.
Figure 7 shows the directional reflectances in the red and
near infrared for a cropland pixel. There are 11 clear
observations (no cloud, no cloud shadow, no high aerosol
loading) as indicated by the QA fields associated with the
MODIS surface reflectance product. The angular samplings
are between the principal and cross principal plane. The
NDVI values of the majority of the observations are in the
range of 0.5?0.65, except for three observations marked as
1,2,3 in the figure. The surface reflectance of the marked
observation 1 is extremely high in all visible bands and the
NDVI is as low as 0.13. It is obviously contaminated by
clouds. The NDVI values of observations 2 and 3 are 0.34,
also much lower than those of the adjacent observations.
Most probably, under-corrected aerosol increases their
reflectance values and reduces their NDVI values.
4.2. Effects on BRDF and Albedo Retrievals
[26] To assure a best fit with those surface reflectances of
higher quality, the current MODIS BRDF and albedo
processing stream begins with a detailed check of each
atmospherically corrected surface reflectance and assigns
various penalty weights to the individual observations
Figure 4. (a?c) Time series of surface white sky albedos during 2001 in the red (solid line) and near
infrared (dashed line) narrowbands for selected pixels. The QA values greater than 3 (thus of lower
quality) are marked along the near infrared white sky albedo. Note that the missing data in June is due to
the Power Supply 2 shutdown anomaly of the MODIS instrument from 15 June 2001 to 2 July 2001.
JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM ACL 2 - 7
according to the QA flag contained in surface reflectance
product [Schaaf et al., 2002]. For example, observations
with high aerosol quantities are rejected and observations
corrected with only aerosol climatology are assigned a
penalty. Furthermore, one possible outlier is discarded and
additional quality checks are then performed to assure that
the BRDF parameters remain positive.
[27] For the pixel shown in Figure 7, the most apparent
outlier, observation 2, is discarded. The BRDF parameters
retrieved with the remaining observations are then all
positive. Figure 7 shows how well the observed reflectances
fit the reflectances predicted by the MODIS BRDF param-
eters and how the effects of the three contaminated obser-
vations are adjusted. The predicted bidirectional NDVI
curve is also smoother than that derived from the original
surface reflectances. However, if the most serious outlier is
included in the retrieval, the inversion RMSE is very high
and the shape of the BRDF appears incorrect. This indicates
that the MODIS quality assurance process, the outlier
detection in particular, improves the quality of MODIS
BRDF retrievals.
[28] To further investigate to what degree the MODIS
albedo product is improved by undertaking the quality
assurance process, we calculated the relative and absolute
differences between the operational MODIS white sky
albedos and those retrieved without any checks or con-
straints for the entire tile h20v10. The histogram of relative
difference (Figure 8) shows that the QA procedure has the
largest impact in the blue band. The MODIS white sky
albedo agrees with the albedo retrieved without quality
checks or constraints to within 10% for 88% of pixels in
the green, 82% in the red, and 99% in the near infrared. We
infer that the retrievals of around 20% of pixels are
improved by taking into account the uncertainties in the
surface reflectance product and by constraining the BRDF
models in the visible bands.
4.3. Uncertainties of BRDF and Albedo Retrievals
[29] The MODIS BRDF and albedo processing mainly
relies on the QA fields of the surface reflectance product
and its internal quality checks to take the quality of the input
data into account. A new retrieval method has recently been
developed to assign weights to each observation based on
the bidirectional NDVI values through an iterative proce-
dure [Gao et al., 2002]. It does not need ancillary informa-
tion and higher weights are given to observations acquired
under relatively clearer conditions. For the pixel shown in
Figure 7, this method produces surface reflectances and
albedos similar to those of the MODIS product. We con-
sider that the retrievals by this algorithm provide a way to
independently test the quality assurance. The difference
between the retrievals using the biNDVI-based iterative
algorithm and the operational MODIS albedo products
can thus be taken as the uncertainties of the MODIS albedo
products in a relative sense. The analysis of the retrievals for
the tile h20v10 in late May shows that both agree within
Figure 5. White sky albedos from magnitude inversion (backup algorithm) versus full inversion (main
algorithm) in the visible (Figures 5a and 5c) and near infrared (Figures 5b and 5d) broadbands. Three
consecutive 16-day periods are chosen to represent full inversion (193?208), magnitude inversion (209?
224), and full inversion (225?240), respectively. Pixels shown are open shrublands.
ACL 2 - 8 JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM
10% for 86% of pixels in the red, 93% of pixels in the
green, and 61% of pixels in the blue. This implies that the
uncertainties from atmospheric correction are generally
within 10 percent in the green and red bands. The largest
impact is found in the blue, whereas the smallest impact is
in the near infrared with the relative difference less than 5%.
5. Global Performance of MODIS BRDF
and Albedo Retrieval Algorithm
5.1. Global Statistics and Latitude Distribution
[30] To examine the performance of the MODIS BRDF
and albedo retrieval algorithm over the globe, we analyzed
the global reprocessed 1-km data acquired between Sep-
tember 14 to September 29, 2001. A land mask was applied
to calculate the QA statistics for only the land pixels. Over
the latitude bands between 60C176N and 60C176S, 50% of the land
pixels receive more than 6 clear looks during this 16 day
period and among these there are only 5% of pixels where
the backup algorithm is performed instead of the main
algorithm. Poor sampling and the contamination of atmos-
phere are the main reasons for the failure of the main
algorithm in such cases. In total, 47% of the land pixels
are retrieved with the full inversion, 45% with the magni-
tude inversion, and 8% cannot be retrieved. It is obvious
that the loss of observations due to cloud cover is the main
reason for the use of the backup magnitude inversion.
Among those pixels with full inversion retrievals, the
RTLSR model fits the atmospherically corrected surface
reflectance very well for 99.9% of pixels, the noise ampli-
fication factor of white sky albedo is very small (less than
0.10) for 87% of pixels, and the noise amplification factor
of nadir-view reflectances is very small (less than 0.75) for
74% of pixels. This indicates that the majority of pixels
have very reliable albedo retrievals.
[31] Figure 9 shows that the latitude distribution of the
magnitude retrievals and non-retrievals follows the pattern
of cloud climatology in September 2001. Around 70% of
pixels obtain less than 4 clear looks in the ITCZ zone
between 10C176Sto10C176N, and around 35% of pixels between
10C176Sto20C176S and between 10C176Nto20C176N. Over the region
40C176Nto30C176S, the majority of the full-inversion pixels are
retrieved with very high confidences (QA = 0) for both
white sky albedo and nadir-view reflectance. We found that
the MODIS angular sampling is closer to the principal plane
over these latitude bands than it is in the more northern or
southern tiles.
5.2. Temporal Distribution
[32] In addition to the latitude dependence, the angular
sampling varies with season due to orbital change and cloud
dynamics. Due to the large data volume of the global data at
1-km resolution, we chose several tiles to investigate the
dynamics of the performance of the MODIS BRDF and
albedo retrieval algorithm. Figure 10 shows the temporal
distribution of the retrieval status in 2001 for a tile over the
west coast of the United States (h08v05), which is usually
less cloudy than other regions. It is obvious that the number
of the pixels retrieved with the magnitude inversion is larger
in winter because of higher frequency of cloud cover in this
Figure 6. Same as Figure 5, but for barren pixels.
JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM ACL 2 - 9
region during this time than in other seasons. In addition,
the most significant change in angular geometries happens
in the azimuthal dimension during various seasons. In tile
h08v05, for example, the angular sampling is closer to the
principal plane in spring and summer and then moves
towards the cross principal plane in fall. Figure 10 shows
that the majority of the pixels with more than 6 clear looks
have the highest confidence of retrieval in spring and
summer, whereas the pixels with moderate noise amplifica-
tion factors increase in fall and winter, and the percentage of
main algorithm failure to fit the observations also increases.
It is well known that the anisotropy of canopy reflectance is
more apparent in the principal plane and thus the RTLSR
model is more sensitive to the observations in the principal
plane and the accuracy of the BRDF inversion tends to be
higher.
6. Discussions and Summary
[33] The operational MODIS BRDF and albedo products
became provisional with the data from 31 October 2001
[Schaaf et al., 2002]. A detailed evaluation is critical for the
correct interpretation and usage of the product by the
science community. This study used the first consistent year
of MODIS reprocessed products to provide the evaluation
of the performance of the MODIS BRDF and albedo
retrieval algorithm. We found that the Quality Assurance
(QA) fields embedded in the product adequately reflect the
processing stream, goodness of model fitting, angular sam-
pling patterns, and random noise amplification of the
retrieved BRDF and albedo products as well. Users of the
product are therefore strongly advised to check these QA
fields and to consider the specific quality requirement of an
individual application. A case study, for example, showed
that white sky albedos from the backup magnitude inversion
algorithm agree with those from the main full inversion
algorithm to within 0.033 in reflectance units, but have a
slight bias toward lower values ranging from 0.014 in the
visible to 0.023 in the near infrared broadband.
[34] We also examined the effect of the uncertainty of the
MODIS atmospheric correction on the MODIS BRDF and
albedo retrievals. Some residual cloud and aerosol effects
were identified in atmospherically corrected surface reflec-
tances from a case study in Southern Africa. However, in
addition to using the QA information associated with the
input surface reflectance product, the MODIS BRDF and
albedo algorithm also performs a series of internal checks to
avoid residual input problems and ensure high quality
retrievals. Compared to the albedo retrieved without
accounting for the quality of the input data and without
constraints to avoid negative non-physical BRDF parame-
ters, the operational MODIS white sky albedo is improved
for around 15?20% of the pixels in the visible bands and
for 10% of the pixels in the near infrared.
[35] The global statistics of the QA fields show that the
MODIS BRDF and albedo retrieval algorithm generally
performs quite well. During the period 14?29 September
2001 and over 60C176Sto60C176N, 50% of the land pixels acquire
more than 6 clear looks and only 5% of these are ultimately
inverted with the backup algorithm due to atmospheric
contamination or an inability of the model to fit the
observations. The RMSEs of the RTLSR model in fitting
the atmospherically corrected surface reflectances are gen-
Figure 8. Histogram of relative differences between the
operational MODIS white sky albedo and that derived
without any quality check or BRDF parameter constraints in
the blue, green, red and near infrared. Results are derived
from MODIS observations in tile h20v10 during May 25 to
June 11, 2001.
Figure 7. MODIS atmospherically corrected surface re-
flectances in the red (open triangles) and near infrared (open
circles) and NDVIs (pluses). Values are for a cropland pixel
located in MODIS tile h20v10 (16.0041C176S, 26.7056C176E),
sampled during May 25 to June 11, 2001. Three cloud/
aerosol contaminated observations are marked besides their
extremely low NDVI values. The reflectances and NDVIs
predicted by the MODIS retrieved BRDF parameters are
represented by solid symbols and crosses. Shown here is the
good prediction ability of the operational MODIS BRDF
product with the quality-assurance procedure.
ACL 2 - 10 JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM
erally small. Among those pixels retrieved with full inver-
sions, the random noise amplification factor of white sky
albedo is very small (less than 0.75) for 87% of pixels and
that of nadir-view reflectance is also very small for 74% of
pixels. Our analysis shows that cloud cover poses the most
serious problem to surface retrieval. In September, 8% of
the pixels can not be retrieved due to an absence of clear
observations and 45% rely on the backup magnitude
retrieval. The percentage of pixels inverted with full inver-
sions is expected to be lower in other seasons when the
large land area in Northern Hemisphere is typically more
cloudy.
[36] The latitude dependence and temporal distribution
of the QA fields also show that the retrievals tend to be
more reliable when the observations are closer to the
principal plane. In view of this often insufficient angular
sampling, a synergistic usage of multi-sensor observations
is important to improve both the coverage and the quality
of global albedo retrieval. The Multi-angle Imaging Spec-
troradiometer (MISR) [Diner et al., 1998], aboard the same
Figure 9. Latitude distributions of the frequency of BRDF and albedo retrieval status for September
2001. The solid line refers to the best quality of retrieval, the dashed line refers to all the magnitude
inversions, and the long dashed line refers to no retrievals. Also shown are magnitude inversion with
more than 6 looks (dotted), 3?7 looks (dashed-dotted) and less than three looks (dashed-dotted-dotted).
Figure 10. Temporal distributions of the frequency of BRDF and albedo retrieval status for tile h08v05
in 2001. Three series of QA information are plotted: QA = 0; QA = 1?3; QA = 9 (bottom), 10 (middle),
8(top). The retrievals with moderate RMSEs (QA = 4?7) generally occupy less than 1% of the total land
pixels and therefore are not included here.
JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM ACL 2 - 11
EOS-Terra platform as MODIS, acquires observations
almost perpendicular to those of MODIS in the azimuth
plane and is thus of particular value for future improvement
of MODIS BRDF and albedo product [Jin et al., 2002]. A
second MODIS instrument was launched on the EOS-Aqua
platform and cloud free observations from this afternoon
sensor will bring additional solar zenith angle variations to
this synergism, which implies that the quality of the
MODIS BRDF and albedo product will improve in the
near future.
[37] The evaluation of algorithm performance here relied
on the product QAs, analysis of the input data, and
intercomparisons with results from different retrieval algo-
rithms. In the second part of our evaluation study [Jin et al.,
2003], the MODIS albedo is validated with coincident field
measurements from NOAA?s Surface Radiation Network
(SURFRAD) stations and from the Southern Great Plains
(SGP) sites of the DOE?s Atmospheric Radiation Measure-
ment (ARM) Program. The global MODIS albedo is also
compared to commonly used global albedo data sets derived
from other sensors.
[38] Acknowledgments. This work was supported by NASA?s
MODIS project under contract NAS5-31369. W.L. was supported by the
German Ministry of Education and Research in the DEKLIM Programme.
References
Bicheron, P., and M. Leroy, Bidirectional reflectance distribution function
signatures of major biomes observed from space, J. Geophys. Res., 105,
26,669?26,681, 2000.
Bonan, G. B., A land surface model (LSM version 1.0) for ecological,
hydrological, and atmospheric studies: Technical description and user?s
guide, NCAR Tech. Note NCAR/TN-147+STR, Natl. Cent. for Atmos.
Res., Boulder, Colo., 1996.
Charney, J., W. J. Quirk, S. Chow, and J. Kornfield, A comparative study of
the effects of albedo change on drought in semi-arid regions, J. Atmos.
Sci., 34, 1366?1385, 1977.
Dickinson, R. E., Land surface processes and climate: Surface albedos and
energy balance, Adv. Geophys., 25, 305?353, 1983.
Dickinson, R. E., A. Henderson-Sellers, and P. J. Kennedy, Biosphere-
Atmosphere Transfer Scheme (BATS) Version 1e as coupled to the
NCAR community model, NCAR Tech. Note NCAR/TN-387+STR, Natl.
Cent. for Atmos. Res., Boulder, Colo., 1993.
Diner, D. J., et al., Multi-angle Imaging Spectroradiometer (MISR) instru-
ment description and experiment overview, IEEE Trans. Geosci. Remote
Sens., 36, 1072?1085, 1998.
Gao, F., C. B. Schaaf, A. H. Strahler, and W. Lucht, Using a multi-
kernel least-variance approach to retrieve and evaluate albedo from
limited bidirectional measurements, Remote Sens. Environ., 76,57?
66, 2001.
Gao, F., Y. Jin, X. Li, C. Schaaf, and A. Strahler, Bidirectional NDVI and
atmospherically resistant BRDF inversion for vegetation canopy, IEEE
Trans. Geosci. Remote Sens., 40, 1269?1278, 2002.
Hahmann, A. N., and R. E. Dickinson, A fine-mesh land approach for
general circulation models and its impact on regional climate, J. Clim.,
14, 1634?1646, 2001.
Hansen, J., M. Sato, A. Lacis, R. Ruedy, I. Tegen, and E. Matthews,
Climate forcings in the industrial era, Proc. Natl. Acad. Sci. U.S.A., 95,
12,753?12,758, 1998.
Henderson-Sellers, A., and M. F. Wilson, Surface albedo data for climatic
modeling, Rev. Geophys., 21, 1743?1778, 1983.
Hu, B., W. Lucht, X. Li, and A. H. Strahler, Validation of kernel-driven
models for global modeling of bidirectional reflectance, Remote Sens.
Environ., 62, 201?214, 1997.
Hu, B., W. Lucht, and A. H. Strahler, The interrelationship of atmospheric
correction of reflectances and surface BRDF retrieval: A sensitivity study,
IEEE Trans. Geosci. Remote Sens., 37, 724?738, 1999.
Intergovernmental Panel on Climate Change (IPCC), Climate Change
2001: The Scientific Basis, Cambridge Univ. Press, New York, 2001.
Jin, Y., F. Gao, C. B. Schaaf, X. Li, A. H. Strahler, C. J. Bruegge, and J. V.
Martonchik, Improving MODIS surface BRDF/Albedo retrieval with
MISR observations, IEEE Trans. Geosci. Remote Sens., 40,1593?
1604, 2002.
Jin, Y., C. B. Schaaf, C. E. Woodcock, F. Gao, X. Li, A. H. Strahler,
W. Lucht, and S. Liang, Consistency of MODIS surface bidirectional
reflectance distribution function and albedo retrievals: 2. Validation,
J. Geophys. Res., 108, doi:10.1029/2002JD002804, in press, 2003.
Justice, C. O., and J. R. G. Townshend, Data sets for global remote sensing:
Lessons learnt, Int. J. Remote Sens., 15, 3621?3639, 1994.
Justice, C. O., et al., The Moderate Resolution Imaging Spectroradiometer
(MODIS): Land remote sensing for global change research, IEEE Trans.
Geosci. Remote Sens., 36, 1228?1249, 1998.
King, M. D., EOS Science Plan: The State of Science in the EOS Program,
Natl. Aeronaut. and Space Admin., Washington, D.C., 1999.
Knorr, W., K.-G. Schnitzler, and Y. Govaerts, The role of bright desert
regions in shaping North African climate, Geophys. Res. Lett., 28,
3489?3492, 2001.
Lean, J., and P. R. Rowntree, Understanding the sensitivity of a GCM
simulation of Amazonian deforestation to the specification of vegetation
and soil characteristics, J. Clim., 10, 1217?1235, 1997.
Lewis, P., and M. J. Barnsley, Influence of the sky radiance distribution on
various formulations of the Earth surface albedo, paper presented at
International Symposium on Physical Measurements and Signatures in
Remote Sensing, Int. Sco. for Photogramm. and Remote Sens., Val
d?Isere, France, 1994.
Liang, S., A. H. Strahler, and C. W. Walthall, Retrieval of land surface
albedo from satellite observations: A simulation study, J. Appl. Meteorol.,
38, 712?725, 1999.
Liang, S., H. Fang, M. Chen, C. J. Shuey, C. Walthall, C. Daughtry,
J. Morisette, C. Schaaf, and A. Strahler, Validating MODIS land surface
reflectance and albedo products: Methods and preliminary results, Remote
Sens. Environ., 83, 149?162, 2002.
Lofgren, B. M., Sensitivity of land-ocean circulations, precipitation, and
soil moisture to perturbed land surface albedo, J. Clim., 8, 2521?2542,
1995.
Lucht, W., and P. Lewis, Theoretical noise sensitivity of BRDF and albedo
retrieval from the EOS-MODIS and MISR sensors with respect to angular
sampling, Int. J. Remote Sens., 21, 81?98, 2000.
Lucht, W., C. B. Schaaf, and A. H. Strahler, An algorithm for the retrieval
of albedo from space using semiempirical BRDF models, IEEE Trans.
Geosci. Remote Sens., 38, 977?998, 2000.
Martonchik, J. V., C. J. Bruegge, and A. H. Strahler, A review of reflectance
nomenclature used in remote sensing, Remote Sens. Rev., 19, 9?20,
2000.
Nobre, C. A., P. J. Sellers, and J. Shukla, Amazonian deforestation and
regional climate change, J. Clim., 4, 957?988, 1991.
Olson, J. S., Global ecosystem framework: Definitions, internal report, 37
pp., USGS EROS Data Cent., Sioux Falls, S.D., 1994.
Privette, J. L., T. F. Eck, and D. W. Deering, Estimating spectral albedo and
nadir reflectance through inversion of simple BRDF models with
AVHRR/MODIS-like data, J. Geophys. Res., 102, 29,529?29,542, 1997.
Rahman, H., B. Pinty, and M. M. Verstraete, Coupled surface-atmosphere
reflectance (CSAR) model, 1, Model description and inversion on syn-
thetic data, J. Geophy. Res., 98, 20,779?20,789, 1993.
Roujean, J.-L., A parametric hot spot model for optical remote sensing
applications, Remote Sens. Environ., 71, 197?206, 2000.
Roujean, J. L., M. Leroy, and P. Y. Deschamps, A bidirectional reflec-
tancemodeloftheEarth?ssurfaceforthecorrectionofremotesensingdata,
J. Geophys. Res., 97, 20,455?20,468, 1992.
Schaaf, C. B., et al., First operational BRDF, albedo and nadir reflectance
products from MODIS, Remote Sens. Environ., 83, 135?148, 2002.
Sellers, P. J., Remote sensing of the land surface for studies of global
change, NASA/GSFC International Satellite Land Surface Climatology
Project report, NASA Goddard Space Flight Cent., Greenbelt, Md.,
1993.
Sellers, P. J., D. A. Randall, G. J. Collatz, J. A. Berry, C. B. Field, D. A.
Dazlich, C. Zhang, G. D. Collelo, and L. Bounoua, A revised land sur-
face parameterization (SiB2) for atmospheric GCMs, part I, Model for-
mulation, J. Clim., 9, 676?705, 1996.
Strugnell, N. C., and W. Lucht, An algorithm to infer continental-scale
albedo from AVHRR data, land cover class, and field observations of
typical BRDFs, J. Clim., 14, 1360?1376, 2001.
Strugnell, N. C., W. Lucht, and C. Schaaf, A global albedo data set derived
from AVHRR data for use in climate simulations, Geophys. Res. Lett., 28,
191?194, 2001.
Sud, Y. C., and M. Fennessy, A study of the influence of surface albedo on
july circulation in semi-arid regions using the glas gcm, J. Clim., 2, 105?
125, 1982.
Vermote, E. F., N. Z. Saleous, C. O. Justice, Y. J. Kaufman, J. Privette,
L. Remer, J. C. Roger, and D. Tarne, Atmospheric correction of visible
to middle infrared EOS-MODIS data over land surface, background, op-
ACL 2 - 12 JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM
erationalalgorithm and validation,J. Geophys.Res., 102, 17,131?17,141,
1997.
Vermote, E. F., N. Z. E. Saleous, and C. O. Justice, Atmospheric correction
of MODIS data in the visible to middle infrared: First results, Remote
Sens. Environ., 83, 97?111, 2002.
Walthall, C. L., J. M. Norman, J. M. Welles, G. Campbell, and L. B.
Blad, Simple equation to approximate the bidirectional reflectance from
vegetative canopies and bare soil surfaces, Appl. Opt., 24, 383?387,
1985.
Wanner, W., X. Li, and A. H. Strahler, On the derivation of kernels for
kernel-driven models of bidirectional reflectance, J. Geophys. Res., 100,
21,077?21,089, 1995.
Wanner, W., A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. B.
Schaaf, and M. J. Barnsley, Global retrieval of bidirectional reflectance
and albedo over land from EOS MODIS and MISR data: Theory and
algorithm, J. Geophys. Res., 102, 17,143?17,162, 1997.
C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0
F. Gao, Y. Jin, X. Li, C. B. Schaaf, and A. H. Strahler, Department of
Geography and Center for Remote Sensing, Boston University, Boston, MA
02215, USA. (yfj@bu.edu; fgao@crsa.bu.edu; lix@crsa.bu.edu;schaaf@
crsa.bu.edu; alan@bu.edu)
S. Liang, Department of Geography, 2181 LeFrak Hall, College Park,
MD 20742, USA. (sliang@geog.umd.edu)
W. Lucht, Potsdam-Institut fu?r Klimafolgenforschung (PIK), Telegrafen-
berg C4, Postfach 60 12 03, D14412 Potsdam, Germany. (wolfgang.lucht@
pik-potsdam.de)
JIN ET AL.: PERFORMANCE OF MODIS ALBEDO RETRIEVAL ALGORITHM ACL 2 - 13