Surface albedo, as a key parameter determining the partition of solar radiation at the Earth’s surface, has been developed into a satellite-based product from various Earth observation systems to serve numerous global or regional applications. Studies point out that apparent uncertainty can be introduced into albedo retrieval without consideration of surface anisotropy, which is a challenge to albedo estimation especially from observations with fewer angular samplings. Researchers have begun to introduce smoothed anisotropy prior knowledge into albedo estimation to improve the inversion efficiency, or for the scenario of observations with signal or poor angular sampling. Thus, it is necessary to further understand the potential influence of smoothed anisotropy features adopted in albedo estimation. We investigated the albedo variation induced by BRDF smoothing at both temporal and spatial scales over six typical landscapes in North America using MODIS standard anisotropy products with high quality BRDF inversed from multi-angle observations in 500 m and 5.6 km spatial resolutions. Components of selected typical landscapes were assessed with the confidence of the MCD12 land cover product and 30 m CDL (cropland data layer) classification maps followed by an evaluation of spatial heterogeneity in 30 m scale through the semi-variogram model. High quality BRDF of MODIS standard anisotropy products were smoothed in multi-temporal scales of 8 days, 16 days, and 32 days, and in multi-spatial scales from 500 m to 5.6 km. The induced relative and absolute albedo differences were estimated using the RossThick-LiSparseR model and BRDFs smoothed before and after spatiotemporal smoothing. Our results show that albedo estimated using BRDFs smoothed temporally from daily to monthly over each scenario exhibits relative differences of 11.3%, 12.5%, and 27.2% and detectable absolute differences of 0.025, 0.012, and 0.013, respectively, in MODIS near-infrared (0.7–5.0 µm), short-wave (0.3–5.0 µm), and visible (0.3–0.7 µm) broad bands. When BRDFs of investigated landscapes are smoothed from 500 m to 5.6 km, variations of estimated albedo can achieve up to 36.5%, 37.1%, and 94.7% on relative difference and absolute difference of 0.037, 0.024, and 0.018, respectively, in near-infrared (0.7–5.0 µm), short wave (0.3–5.0 µm), and visible (0.3–0.7 µm) broad bands. In addition, albedo differences caused by temporal smoothing show apparent seasonal characteristic that the differences are significantly higher in spring and summer than those in autumn and winter, while albedo differences induced by spatial smoothing exhibit a noticeable relationship with sill values of a fitted semi-variogram marked by a correlation coefficient of 0.8876. Both relative and absolute albedo differences induced by BRDF smoothing are demonstrated to be captured, thus, it is necessary to avoid the smoothing process in quantitative remote sensing communities, especially when immediate anisotropy retrievals are available at the required spatiotemporal scale.

As the inherent attribute of land cover, anisotropy leads to the heterogeneity of directional reflection; meanwhile, it creates the opportunity for retrieving characteristics of land surface based on multi-angle observations. BRDF (Bidirectional Reflectance Distribution Function) is the theoretical expression of anisotropy and describes the reflectance in terms of incident-view geometry. Prior BRDF knowledge is used to achieve the multi-angle retrieval for earth observation systems with a narrow FOV (Field of View). Shape indicators are a feasible way to capture the characteristics of BRDF or to build an a priori database of BRDF. However, existing shape indicators based on the ratio of reflectance or the weight of scattering effects are too rough to describe the BRDF’s shape. Thus, it is necessary to propose new shape vectors to satisfy the demand. We selected six typical land covers from MODIS-MCD12 on the homogeneous underlayers as the study sites in North America. The daily BRDF is retrieved by MODIS-BRDF parameters and the RossThick-LiSparseR model. When the SZA (Solar Zenith Angle) is set at 45°, seven directions (−70°, −45°, −20°, 0°, 20°, 45°, and 70°) including edge spot, zenith spot, hot spot and approximate dark spot of the BRDF principal plane were selected to construct two vectors by the change rate of reflectance and angle formulation: Partial Anisotropic Vector (PAV) and Angular Effect Vector (AEV). Then, we assessed the effectiveness of PAV and AEV compared with ANIX (Anisotropic Index), ANIF (Anisotropic Factor) and AFX (Anisotropic Flat Index) by two typical BRDF shapes. The representativeness of PAV and AEV for the original BRDF was also assessed by cosine similarity and error transfer function. Lastly, the application of hot spot components in AEV for land cover classification, the monitoring of land cover in mining areas and the adjustment effect by NDVI (Normalized Difference Vegetation Index) were investigated. The results show that (1) the shape vectors have good representativeness compared with original BRDF. The representativeness of PAV assessed by cosine similarity is 0.980, 0.979 and 0.969, and the representativeness of AEV assessed by error transfer function is 0.987, 0.991 and 0.994 in the three MODIS broadbands of Near Infrared (NIR, 0.7–5.0 µm), Short Wave (SW, 0.3–5.0 µm) and Visible (VIS, 0.3–0.7 µm). (2) Some components of shape vectors have high correlation with AFX. The correlation coefficient between hot spot components in AEV and AFX is 0.936, 0.945 and 0.863, respectively, in NIR, SW and VIS bands. (3) The shape vectors show potentiality for land cover classification and the monitoring of land cover in mining areas. The correlation coefficients of hot spot components in AEV for MODIS-pixels with the same types (0.557, 0.561, 0.527) are significantly higher than MODIS-pixels with various types (0.069, 0.055, 0.051) in NIR, SW and VIS bands. The coefficients of variation for hot spot components are significantly higher after land reclamation (0.0071, 0.0099) than before land reclamation (0.0020, 0.0028). (4) The correlation between NDVI and the BRDF shapes is poor in three MODIS broad bands. The correlation coefficients between NDVI and the BRDF shapes in three temporal scales of annual, seasonal and monthly phases are only 0.134, 0.063 and 0.038 (NIR), 0.199, 0.185 and 0.165 (SW), and 0.323, 0.320 and 0.337 (VIS), on average.

BRDF as the intrinsic feature of surface targets, is an important parameter required by albedo inversion from multi-angle observations, especially for satellite data suit with less directional measurements. Several studies have shown up to introduce BRDF priori knowledge into albedo retrievals at different scale by spatial or temporal smoothing. Thus, it is necessary to further understand what’s the influence induced by BRDF smoothing on albedo retrieval. This work investigated effects of smoothed BRDF on albedo magnitude through case studies over North America region using operational MCD43A&C BRDF products respectively smoothed in spatial and temporal scales. Our results show that BRDF of seasonal DBF samples smoothed from daily to monthly can lead to apparent relative difference to smoothed values of 10.97%, 9.42%, 8.24% and detectable absolute differences of 0.0172, 0.0095 and 0.0035 on related albedo respectively at Near Infrared, Short Wave and Visible broadband. The spatial smoothing of BRDF from 500m to 5600m results in relative differences to smoothed values of 17.38%, 14.38%, 27.23% and absolute differences of 0.0250, 0.0139, 0.0052 for the inversed albedo at above three broadbands.