The Moderate Resolution Imaging Spectroradiometer (MODIS) bidirectional reflectance distribution function (BRDF)/albedo algorithm uses multiday, multiband MODIS surface reflectance products from Terra and Aqua to produce a global albedo product at a 500 m resolution (Collection 5). This paper evaluates the ability of the MODIS albedo product to represent albedos at all diurnal solar zenith angles through a comparison with field measurements from the Surface Radiation Budget Network (SURFRAD) and the Atmospheric Radiation Measurement Southern Great Plains (ARM/SGP) stations. The results show that, for most of the sites, the overall accuracy of the MODIS albedo is within 0.05 and shows an increasing negative bias and increased RMSE as zenith angle increases beyond 70°–75° as compared to the ground observations. The full inversion of the MODIS BRDF/albedo algorithm has a higher inversion quality than the backup algorithm. Site heterogeneity and spatial-scale mismatch between the MODIS and ground observations are the major factors contributing to the discrepancy between the MODIS albedo and the field measurements.
 Land surface albedo is defined as the fraction of incident solar irradiance reflected by Earth's surface over the whole solar spectrum [Dickinson, 1983]. It has long been recognized as a key land surface radiative property in that it directly determines the amount of solar radiation absorbed by land surface, thus, a primary controlling factor for the surface energy budget. An absolute accuracy of 0.02–0.05 is required for the albedo characterization at spatial and temporal scales compatible with climate studies [Sellers, 1993]. Therefore, for climate model research, a consistent and accurate global albedo data set is essential to the investigation of the sensitivity of climate to various types of forcing and to the identification of the effects of human activities [Lawrence and Chase, 2007]. The traditional way to produce such a global albedo data set has been to assign albedo values from field measurements to different land cover types on the basis of a global land cover map. Therefore, its accuracy and temporal coverage have been very limited. Satellite remote sensing provides the only practical way of producing high-quality global albedo data sets with high spatial and temporal resolutions.
 The Moderate Resolution Imaging Spectroradiometer (MODIS) instruments aboard both NASA's Terra and Aqua satellites now acquire daily images of the globe and routinely provide global land surface albedos [Schaaf et al., 2002; Gao et al., 2005]. The MODIS albedo product provides black-sky albedo and white-sky albedo values that are calculated by first establishing a surface reflectance anisotropy model and then integrating over the viewing hemisphere for a certain solar zenith angle and both viewing hemisphere and illumination hemisphere, respectively. Therefore, retrieval of the bidirectional reflectance distribution function (BRDF) that characterizes the surface reflectance anisotropy of the land surface from the MODIS observations is essential. The surface anisotropy model, the white sky albedo and the black sky albedo at local solar noon are all provided as routine MODIS products. Validation of such satellite-derived products is critical for users as its accuracy may limit its potential applications. However, scale is a major factor that limits the validation of albedo products as it is not possible to measure albedo directly on the ground at the resolution of the satellite sensors. Field measurements represent point measurements on the ground and are not easily comparable to the satellite data unless the assumption of homogeneity of the land surface is made. Therefore, sites with homogeneous land covers are preferable for validating all satellite products, particularly albedo products.
Jin et al.  evaluated the accuracy of the MODIS albedo product at local solar noon using only observations from the MODIS instrument aboard NASA's Terra (EOS AM-1) platform and found that the MODIS surface albedo generally met an absolute accuracy requirement of 0.02 in spring and summer time for the sites at the Surface Radiation Budget Network (SURFRAD) and at the ARM Cloud and Radiation Testbed–Southern Great Plains (ARM/CART/SGP). Salomon et al.  further evaluated this product using combined observations from both NASA's Terra and Aqua (EOS PM-1) platforms and found that the combined product resulted in an increase in the quantity of high-quality retrievals obtained over the original Terra-only albedo product. Liang et al.  compared the MODIS albedo with albedo derived from the Enhanced Thematic Mapper Plus (ETM+) imagery around a field site with diverse soils, crops, and natural vegetation covers in Maryland, United States, and once scaled to MODIS spatial resolutions, found good agreement. Wang et al.  evaluated 3 years of MODIS albedo product using the ground observations at Gaize Automatic Weather Station on the western Tibetan Plateau with semidesert or desert soil, and found that the MODIS global land surface albedo met an absolute accuracy requirement of 0.02 with no distinctive bias between the MODIS-derived albedo and the ground-measured albedo. Roesch et al.  compared MODIS surface albedo at 0.05-degree resolution with in situ field measurements collected at Baseline Surface Radiation Network (BSRN) sites during snow-free periods. Their results showed very good agreements between the MODIS surface albedo and the field measurements. To assess the accuracy of the MODIS albedo product on snow, Stroeve et al.  used ground-based albedo observations over spatially homogeneous snow and semihomogeneous ice-covered surfaces on the Greenland ice sheet, and found, for high-quality full retrievals the MODIS albedo algorithm retrieves snow albedo with an average root mean square error (RMSE) of 0.04 as compared to the station measurements, which have 0.035 RMSE uncertainty.
 All of these previous validation exercises were for albedo values at local solar noon or at the satellite overpass time (when the satellite observations used for the BRDF model retrievals were made). However, both field measurements and remote sensing data from the satellite and aircraft platforms have shown that land surface albedo is strongly solar zenith angle dependent, and thus, may vary throughout a day. As early as 1961, Monteith and Szeice  showed that measured bare soil albedo increases from 0.16 at 30 degrees of solar zenith angle to 0.19 at 70 degrees of solar zenith angle with a daily mean of 0.17. As some applications are interested in using albedo values for solar zenith angles other than local solar noon or satellite overpass time, such as for the derivation of daily and monthly mean surface albedo, the validation of MODIS albedo product throughout the whole solar zenith angle range is required.
2. Data Used
2.1. Surface Albedo Ground Measurements
 The Surface Radiation Budget Network (SURFRAD), part of the worldwide Baseline Surface Radiation Network (BSRN), was established in 1993 by NOAA's Surface Radiation Research Branch [Augustine et al., 2000] to support satellite retrieval validation, modeling, and climate, hydrology, and weather research. Currently, there are seven SURFRAD stations operating in climatologically diverse regions, four of which, being associated with relatively homogeneous land cover types over an extended region, are used in this study (Table 1). The three primary components of a SURFRAD station are a main platform 1.5–2 m above the ground level, a 10-m tower within 100 m of the main platform and to the north, and a solar tracker stand. The land cover types associated with these stations are typically grasslands or agricultural lands rather than forests or dense shrublands. The Fort Peck station (FPK), located on the Fort Peck Tribes Reservation in Montana, is in a flat prairie with native grasses and very few trees. The landform at The Goodwin Creek station (GWN), located to the west of Oxford, Mississippi, is rolling hills covered with pasture grass and sparsely distributed deciduous trees. The Table Mountain station (TBL) in Colorado is sandy with a mix of exposed rocks, sparse grasses, desert shrubs and small cactus. The Bondville site in Illinois is associated with a patchwork of extensive agricultural fields. This site, thus, is assigned a uniform crop land cover. However, the mixture of crops, as well as ditches and a variety of harvesting and fallowing practices, means that this is still quite a heterogeneous scene at satellite resolutions.
Table 1. Ground Stations Used in the SURFRAD and SGP Radiation Testbed of ARM Programa
Land Cover Type
MODIS Tile Identification
Surface Radiation Budget Network, SURFRAD; Southern Great Plains, SGP; and Atmospheric Radiation Measurements, ARM.
Grasslands and shrublands
Station 1 at the Central Facility
Station 15 of the Extended Facility
 Among the primary measurements for the SURFRAD site are both the downwelling and the upwelling components of broadband solar irradiance (0.28–3.0 μm). Downwelling and upward global irradiance are measured by an upward facing pyranometer on the main platform and a downward facing pyranometer at an end of a 2.4-m cross arm near the top of the tower, respectively [Augustine et al., 2000]. In addition, the direct and diffuse components of downwelling solar irradiance are measured independently by an Eppley normal incidence pyrheliometer (NIP) and a ventilated and shaded Spectrosun pyranometer, respectively. The sum of these components is considered to be the best measure of downwelling global solar irradiance, thus, is used in this study, because at large solar zenith angles, when the sun is not obstructed by clouds, the global solar measurements may be degraded by cosine errors [Albrecht and Cox, 1977]. The reported uncertainties in these irradiance measurements generally range from ±2% to ±5% for pyranometers and ±2% to ±3% for pyrheliometers [Augustine et al., 2000]. Estimates of cloud fraction as viewed from the skyward looking pyranometer were measured for certain dates [Long and Ackerman, 2000].
 In addition to the four SURFRAD stations, two stations in Southern Great Plains (SGP) radiation test bed, established by the Department of Energy's (DOE) Atmospheric Radiation Measurement (ARM) Program, are also used in this study. They are station 1 at the Central Facility in Lamont, Oklahoma, and station 15 of the Extended Facility in Ringwood, Oklahoma [Ackerman et al., 2004]. Both of these two stations are located in agricultural fields. The locations of the instruments were chosen so that the measurements reflect conditions over the typical distribution of land uses with the site. The configuration of these ARM sites and the radiation measurement equipment are almost exactly the same as in the SURFRAD sites.
 The SURFRAD and ARM stations acquire data continuously with average radiation measurements recorded once every three minutes. These data sets were averaged to 15-min intervals by the Clouds and the Earth's Radiant Energy System (CERES) ARM Validation Experiment (CAVE) [Rutan et al., 2001]. In this study, the CAVE database is used to compare directly to the MODIS albedo product.
2.2. MODIS Albedo
 The operational Version 005 MODIS BRDF/albedo algorithm uses registered, multidate, atmospherically corrected surface reflectance data to establish the best fit BRDF (Bidirectional Reflectance Distribution Function) models in seven spectral bands at 500 m resolution every 16 days on an 8-day cycle. The algorithm, a linear kernel-based semiempirical model, uses a constant term for isotropic scattering, the RossThick kernel for volumetric scattering and the LiSparse-Reciprocal kernel for geometric scattering (RTLSR) [Lucht et al., 2000]. The resulting BRDF shape is defined by three parameters corresponding to the weights for isotropic kernel, volumetric kernel and geometric kernel. These three parameters are estimated using sixteen days of sequential MODIS surface reflectance product (MOD09), which is an estimate of the surface spectral reflectance for each band as it would have been measured at ground level if there were no atmospheric scattering or absorption. The algorithm is run every 8 days with the following 16 days of MODIS surface reflectance as the input for a better temporal resolution. In such a way, one retrieval period would have 8-day overlap with both the previous period and the next period. Multiple observations can be acquired every day for each MODIS instrument owing to the wide swath width of MODIS and its frequent overpasses at higher latitudes. The algorithm evaluates each observation on the basis of the Quality Assessment (QA) flag in MOD09. It rejects those observations flagged with “cloud,” “aerosol high” or “cirrus high” and takes the rest as “good observations” (hereafter called observations) after removing outliers. If the majority of observations for a 16-day period are recorded as snow covered, then the algorithm uses only snow covered observations for the parameter retrieval. Conversely, the algorithm uses only snow-free observations for parameter retrieval if the majority of the surface reflectance observations during the period are snow-free. A full retrieval of the parameters for the RTLSR BRDF model is attempted if there are seven or more high-quality observations well distributed over the viewing hemisphere. When the number of observations is less than seven and greater than 2, or if observations are not well sampled or do not fit the BRDF model well, a backup magnitude inversion algorithm is used. The backup algorithm uses a priori estimates of the BRDF shape for each pixel around the globe, and fits these predetermined shapes to the available surface reflectance observations in order to estimate the model parameters. A fill value is stored if the number of good observations is less than three.
 Given that the three BRDF parameters are retrieved from MODIS observations, then spectral black-sky (directional hemispherical) albedo at any solar zenith angle and white-sky (bihemispherical) albedo can then be derived through angular integrations using the BRDF shape defined by these three parameters for each spectral band. In addition to seven spectral albedos, MODIS BRDF/albedo products also provide three broadband albedos for the visible (0.3–0.7 μm), near infrared (0.7–5.0 μm), and shortwave (0.3–5.0 μm), using the spectral to broadband conversion approach developed by Liang et al. . In this study, the shortwave broadband albedo is used as it is the closest spectral match to the broadband pyranometers used by the field measurements. Since the atmospherically corrected MODIS surface reflectance product (MOD09) is used for the retrieval, the derived broadband albedo is comparable with the ground measurements.
 Note that both MODIS black-sky albedo (for direct beam at a certain solar zenith angle) and white-sky albedo (for isotropic diffuse radiation) are intrinsic surface albedo quantities, while the field albedos correspond to an actual solar illumination with both direct beam and diffuse radiation. To make the MODIS albedos directly comparable with the ground albedo calculated from the total downwelling irradiance and upwelling irradiance, actual albedos (also called blue-sky albedo, αblue-sky) need to be obtained from the intrinsic black-sky albedo (αblack-sky) and white-sky albedo (αwhite-sky). In this study, the following equation is used to calculate the MODIS actual albedo (αactual) at a certain solar zenith angle (θi) [Lewis and Barnsley, 1994]:
where SKYL(θi) is the proportion of diffuse irradiance at a certain time, therefore, a certain solar zenith angle (θi), when the field observation is made. Lewis and Barnsley  as well as Lucht et al.  recognized that this relationship with an assumption of a constant white-sky albedo breaks down at very high solar zenith angles. Therefore, the MODIS product has only been recommended for applications under solar zenith angles of 70°–75° and less and not for dusk and dawn calculations.
 It is apparent from equation (1) that the blue-sky albedo changes with the solar position as both the proportion of diffuse irradiance and black-sky albedo changes as the solar position changes. Figure 1 shows an example of MODIS albedo as a function of solar zenith angle. White-sky albedo stays a constant throughout a day while black-sky albedo shows a “U” shape and reaches the minimum at local solar noon time. The diffuse proportion may vary dramatically as the cloud condition changes. In the clear-sky case shown in Figure 1, the diffuse proportion increases with the solar zenith angle, and, combined with the change in black-sky albedo, results in the characteristic “U” shape of blue-sky albedo.
2.3. Comparison Between Ground-Measured and MODIS-Derived Albedos
 In this study, the MODIS albedo and field measurements acquired from the SURFRAD and ARM/SGP stations for the years from 2003 to 2005 are used. During this period, MODIS albedo data are derived from both the Terra and Aqua platforms. Any MODIS data with filled value are omitted from analysis. Theoretically, MODIS blue-sky albedo can be calculated in any time step throughout a day using equation (1) from a retrieved BRDF shape. To be consistent with the field measurements, MODIS blue-sky albedo is calculated at each 15-min interval. The field albedos are derived from the sum of downwelling beam and diffuse and the upwelling irradiance whenever both the downwelling beam and diffuse measurement are available. Both 15-min MODIS blue-sky albedo and the field measurements are then averaged over all snow-free days or snow days for each 16-day period in each solar zenith angle range used for quantitative comparison purpose. The snow flag embedded in the MODIS albedo Quality Assessment (QA) product is used to determine snow/snow-free days for MODIS blue-sky albedo. A threshold of 0.5 for the ground albedo measurements is used to identify snow conditions owing to the lack of snow information in the CAVE data set.
 Note that the 15-min time interval would be enough for capturing the change in albedo as a function of solar zenith angle, using 15-min average of field data would be sufficient for investigating the effect of solar zenith angle on the albedo. For MODIS blue-sky albedo, we assume that the BRDF shape for a particular MODIS 500-m pixel stays unchanged throughout a 16-day period while the change in actual albedo for a particular solar zenith angle in different days is solely caused by the partitioning of total irradiance into diffuse radiation and direct beam. This assumption might not be valid when sudden events, such as rainfall and snowfall, happen during the 16-day MODIS BRDF retrieval period.
Figure 2 shows an example of albedo values both from field measurements and derived from MODIS retrievals at FPK site. Comparison will be undertaken for each data point that has valid data after quality checking both from the MODIS product and the field measurements.
3. Results and Discussion
3.1. Diurnal Variation of Surface Albedo
Figure 3 shows four consecutive days of diurnal variation of both ground-measured albedo and the MODIS albedo reconstructed for that day, plotted along with cloud fraction and diffuse irradiance fraction at the ARM Central Facility (C01). Both ground albedo and MODIS albedo generally show similar “U” shapes for all sky conditions while the variations throughout a day are different depending on the sky conditions. For clear-sky conditions, such as day 226, albedo values show deep “U” shapes while, for cloudy conditions, such as day 229, albedo values are higher at dawn and dusk but keep almost constant throughout a day. For vegetated areas, this “U” shape of surface albedo is well explained by a mechanism discussed by Kimes et al. , in which, photons will penetrate deeper into the vegetation at smaller solar zenith angles such that they are more likely to be absorbed by the vegetation canopy and the chance of escaping from the canopy is lower, resulting in lower albedos. This also explains the relatively flat shape of albedo in cloudy conditions when the amount of direct beam is significantly reduced.
 In terms of comparison between ground albedo and MODIS albedo, ground albedo shows a more pronounced daily “U” shape than the MODIS albedo does, although these two albedo values are very close at the local solar noon time. As discussed in the previous section, the solar zenith angle dependence of MODIS albedo is governed by both black-sky albedo and the diffuse proportion of downwelling radiation. The diffuse proportion is usually a small value in clear conditions, resulting in a deep “U” shape in these conditions, and it is positively related to the cloud fraction, resulting in relatively flat MODIS albedo shapes in cloudy conditions.
 Another interesting feature in Figure 3 is the morning-afternoon asymmetry in ground albedo that varies in strength with cloud conditions. Albedo is generally higher in the morning than in the afternoon, which, according to Minnis et al. , can in some places be explained by the brightening of vegetation by morning dew as well as an often reduced diffuse fraction and cloudiness in the early morning. Note that the asymmetry showing in MODIS albedo is solely resulted from the change in diffuse proportion as both the satellite-derived black-sky albedo and white-sky albedo are theoretically symmetric with respect to noontime.
 The spatial-scale mismatch between the ground measurements and the MODIS albedo might have great impact on the degree of agreement between these two for field sites with heterogeneous land surface. Although the pyranometer has a hemispherical field-of-view, cosine reduction limits the effective field-of-view to about 75 degrees from zenith, which translates to a circled area on the ground with around 37 m radius. MODIS observations, however, have much larger footprint size (1 km × 1 km at nadir), resulting in a mismatch of spatial scale of these two. Since the uncertainty caused by the heterogeneity of the land surface is hard to quantify, sites with relatively homogenous land surface are preferable for this validation work.
3.2. Time Series of Surface Albedo
 The 15-min albedo values from both the field measurements and the MODIS product are further averaged over16-day periods corresponding to MODIS retrieval periods for three different solar zenith angle ranges: local solar noon, 55–65 degrees, and 75–85 degrees. Ground albedo averages use only snow-covered or snow-free observations, depending on the snow flag in the MODIS albedo product embedded QA. Figures 4 and 5show the annual trend of ground albedo and the MODIS albedo at these three solar zenith angle ranges for ARM-C01 site and SURFRAD-FPK site, respectively. Figures 4 and 5 (top) are the comparison of albedos at local solar noon with corresponding solar zenith angle value depicted as the dashed line. Figures 4 and 5 (middle) are the comparisons of albedos with solar zenith angles ranging from 55 to 65 degrees, and Figures 4 and 5 (bottom) are for solar zenith angles ranging from 75 to 85 degrees. Solid circles and open circles represent full retrievals and backup retrievals from MODIS BRDF/albedo, respectively.
 One dominant feature from this analysis is that the MODIS albedo is following the change in ground albedo well. The MODIS albedo can capture the seasonal pattern in ground albedo throughout these years at different solar zenith angles. For ARM-C01 site, MODIS albedo can capture the decrease in surface albedo in green-up time, and the slight rise at senescence time. It can also capture the sudden decrease in surface albedo caused by rainfall in the later summer of 2003, for example. Snow albedo is also nicely retrieved in winter time at SURFRAD-FPK site. The MODIS albedo is relatively stable even when the algorithm is switching between backup algorithm and full retrieval.
 Another feature we can observe from these time series of surface albedo comparisons is that the systematic bias in MODIS albedo seems to increase as the solar zenith angle increases. The MODIS albedo closely matches the ground observations and does the best within the overpass times, encompassing the local solar noon time. As the solar zenith angle increases however, the MODIS albedo underestimates the ground observations. The absolute error differs at different sites probably because of different land surface types and site homogeneity. Even so, for the two sites in Figures 4 and 5, the mean bias of MODIS albedo is still under 0.05 for the local solar range of 75 to 85 degrees as compared with the ground observations.
3.3. Overall Accuracy
 To further explore the solar zenith angle effect on differences in albedo values from the ground measurements and the MODIS product, all the valid 15-min data points are grouped in four solar zenith angle ranges. Scatterplots of ground albedo and the MODIS albedo are then made for all six sites with different color indicating data from different solar zenith angle range (Figure 6). The agreement between these two albedos is the best when the solar zenith angle is small (<30 degrees, red points) and the difference increases as the solar zenith angle increases. As mentioned previously, the kernels used for BRDF retrieval are reciprocal, meaning that the same results will be retrieved if the view zenith angle and solar zenith angle for each observation are switched. This further means that the view zenith angle range of the available observations during a 16-day period can be treated as the solar zenith angle range used. Knowing that the MODIS view zenith angle ranges from 0 to 55 degrees, the derived MODIS albedo values are more reliable in this solar zenith angle range than in other ranges with larger solar zenith angle values. For those 16-day MODIS retrieval time periods with solar zenith angle values less than 55 degrees at the MODIS overpass time, extrapolation would definitely occur when deriving the MODIS albedo values from the retrieved parameters for solar zenith angle greater than 55 degrees. Therefore, poorer MODIS albedo quality is expected for large solar zenith angles than the small solar zenith angles. This may explain why the differences between the ground measurements and the MODIS albedo increases as the solar zenith angle increases.
 Again, Figure 6 shows that the MODIS albedo values generally are lower than the ground albedo values except for the SURFRAD-TBL site where these two albedo values show excellent agreement at all solar zenith angle ranges, and there is no systematic bias between these two. These might be caused by the local heterogeneity at different sites. SURFRAD-TBL site is mainly barren rocks with sparse grasses, thus, the ground observations are representative for the larger MODIS footprint size, resulting in better agreement between the albedo values from the ground measurements and the MODIS retrievals. Other sites, however, have taller vegetation cover around the measurement sites, such as trees, or are agricultural fields and the areas around the measurement sites are usually disturbed with less vegetation coverage. Therefore, there is a higher chance that the larger MODIS footprint size may include more vegetated areas than the smaller ground measurement footprint does, resulting in systematically lower albedo values from MODIS retrievals than those from ground measurements.
Table 2 summarizes the general comparison results between snow-free ground albedo and MODIS albedo in three solar zenith angle ranges for all six sites during this 3-year period. Two cloud conditions, clear sky and all sky, are considered to evaluate the effect of cloud conditions on the comparison. MODIS data from the full inversion are also separated from the “all data” case to investigate the inversion quality difference when different inversion methods are applied.
Table 2. Comparison Results Between the Albedos From Ground Measurements and the MODIS Algorithm for Three Solar Zenith Angle (SZN) Rangesa
Solar zenith angle, SZN; root-mean-square error, RMSE; and mean value from the ground measurements, Ground Mean. Numbers before and after slash are for full retrieval only and all retrievals from the MODIS algorithm, respectively.
Local Solar Noon
55° < SZN < 65°
75° < SZN < 85°
 First of all, for almost all cases, the correlation coefficients between the ground albedo and the MODIS albedo are very high (not shown in Table 2), meaning high correlations between these two and resulting in consistent trends throughout these 3 years, which we can also observe from Figures 4 and 5. In some rare cases, in which the observations used for the MODIS retrieval are mainly from either early or late in a 16-day period while something that can dramatically change the albedo value has happened in the middle of the period (e.g., vegetation destruction, snowmelt, or excessive rainfall), discrepancies between the changing trends of the ground albedo and the MODIS albedo can occur.
 Second, in most of the cases, the mean biases are negative while the magnitudes of the bias generally increases as the solar zenith angle increases, meaning the MODIS algorithm underestimates albedo as compared with the ground measurements, particularly for high solar zenith angles, which we can also observe from Figures 4 and 5. There is no obvious trend of mean bias as a function of mean albedo value from the ground measurements.
 Third, as a measure of overall difference, RMSE increases as the solar zenith angle increase and the magnitudes of the change differ with different sites. For the two ARM sites and the TBL site of SURFRAD, the RMSE are all below 0.05 for all three solar zenith angle ranges. The worst case happens at SURFRAD-BON site, at which the RMSE values are all above 0.05. The spatial analysis at a 30-m resolution derived from Landsat Enhanced Thematic Mapper Plus (ETM+) observations by Jin et al.  and Salomon et al.  reveals that the subpixel heterogeneity of MODIS observations (due to varying crop types and water channels) is responsible for the discrepancies at this site, particularly in the fall and winter time.
 Fourth, the results from different sky conditions are not apparently different. Clear-sky conditions usually have slightly better results than all sky conditions in terms of RMSE values but there is no significant difference between these two. This means that the MODIS BRDF shapes can be used to derive albedo values for all sky conditions without too much concern over quality.
 Finally, the results from the MODIS full inversion method demonstrate that it performs better than the magnitude inversion method, although the differences between these two methods are minor. Note that this conclusion is in terms of the derived albedo values, which is mainly determined by the overall height of the BRDF shape at nadir. The actual BRDF shapes from the full inversion and the magnitude inversion could be different, particularly for those angle ranges where there is no observation available for magnitude inversion. In this sense, full inversion is preferred when there are enough number of observations.
 The diurnal performance of the MODIS BRDF/albedo algorithm is evaluated using the field measurements over six sites through three consecutive years. For most of the sites, the overall accuracy of MODIS albedo is within 0.05 and shows an increasing negative bias and increased RMSE as zenith angle increases compared with the ground observations. The MODIS BRDF shape derived from clear-sky observations can be well used to derive albedo values in all sky conditions. The full inversion of the MODIS BRDF/albedo algorithm gives higher quality of retrieved albedo than the magnitude inversion (backup algorithm) does but the difference is minor. Site heterogeneity and spatial scale are major factors contributing to the discrepancy between the MODIS albedo and the ground albedo for those sites that the MODIS BRDF/albedo algorithm does not perform as well. The results of this study confirm that the MODIS product can be used with some confidence in concert with timely measures of atmospheric condition to characterize the actual albedo at a location throughout the better part of the diurnal cycle.