1. Introduction
Land surface albedo, defined as the ratio of upwelling to downwelling solar radiation at the land surface over the whole solar spectrum, is an important parameter determining the partition of solar energy between Earth’s surface and atmosphere [
1,
2]. Surface albedo quantifies the solar energy intercepted by components within various ecosystems to trigger more energy cycles, such as the phase transition of water via latent heat and heat transfer through conduction, convection, or radiation within components of biogeophysical and biogeochemical processes [
2,
3,
4,
5]. Land surface albedo is a major parameter of land surface models and directly affects the heat and water-vapor exchange between ground and atmosphere [
6]. The budget of energy between ground and atmosphere is influenced by surface albedo, thus it affects the atmospheric movement and medium/long-term weather forecast [
7]. Albedo changes due to land use/cover change (LUCC) such as deforestation have a profound impact on surface net radiation flux, which should not be ignored in the study of land surface temperature and monsoon [
8,
9,
10]. Therefore, land surface albedo is valuable for studies of land surface models, circulation models, LUCC and the global climate.
The accuracy requirements of albedo keep increasing with the need from various user communities or with increasing understanding of processes of earth systems. An albedo accuracy of 0.02–0.05 is required by the community of global climate change [
11,
12] but increases to 0.02 for regional investigations [
13]. Further, a revised land surface model based on albedo with higher accuracy could modify the predicted net radiation and sensible heat exchange by 5–30% [
14]. A 10% error in albedo for agricultural landscape may induce a relative uncertainty in net radiation of 5% [
15]. In evapotranspiration investigation, an uncertainty of 10% in albedo can introduce a potential error of 20 W/m
2 in net radiation [
16]. Therefore, accurate surface albedo is important to achieve relevant energy estimation for numerous molders or applications in ecosystems, the carbon cycle, and climate communities [
14,
17].
Satellite remote sensing is the only way to routinely produce regional or global albedo. In the early stage, observations with a single angle were the dominant scheme provided by satellite-based sensors. Later, multi-angle sensors represented by POLDER and MISR were launched with the ability to simultaneously provide multi-angle observations [
18,
19,
20]. In addition, multi-angle observations can be achieved in wide-swath satellite images with a trade-off between angles and time [
21,
22,
23]. Compared with previous signal-angle estimation, modern albedo algorithms rely on multiple-angle observations to first build a BRDF (bi-directional reflectance distribution function), then integrate over incident and view hemispheres to calculate albedo. Studies have pointed out that the relative errors can reach up to 45% in inferring hemispherical reflectance from nadir reflectance without consideration of angle effects [
24,
25]. Thus, multi-angle observations are essential to inverse the BRDF model and guarantee the estimation of albedo accuracy.
BRDF was defined by Nicodemus in 1977 [
26] and has been accepted widely as an intrinsic feature of land cover. Numerous studies have demonstrated that ground, airborne, or spaceborne observations exhibit obvious angle-effect phenomena [
27,
28,
29]. BRDF theoretically describes the variation of directional reflectance in terms of incident-view geometry within both hemispheres [
22,
30,
31,
32]. Multi-angle observations have been collected from ground measurements and several satellite sensors, such as POLDER [
33], MISR, and MSG, and MODIS and AVHRR have achieved angle sampling from overlapped swaths within a given period. The standard BRDF products retrieved from multi-angle satellite observations include the MODIS nominal daily anisotropy dataset at spatial scales from 500 m to 5.6 km [
34], POLDER at 6 km by 7 km spatial scale, and some other sporadic anisotropic products.
Anisotropy information at fine resolution is needed in the retrieval of surface albedo in the tens of meters spatial resolution. Compared with observations at kilometers, satellites providing observations at fine resolution are required to collect surface details in global or regional areas, such as the Sentinel series of Europe, the Landsat series of the United States, and the HuanJing and GF series of China. However, these observation systems can’t provide instantaneous multi-angle observations, nor trade-off angle with time through swath overlapping. Thus, researchers have begun to introduce BRDF priori knowledge into surface albedo retrieval, especially at high spatial resolution due to the lack of multi-angle observations. Shuai et al., 2011 and 2014, proposed the MODIS-Concurrent algorithm, which combined MODIS 500 m BRDF with corresponding Landsat surface reflectance to estimate surface albedo at 30 m resolution [
35], followed by an extension to the pre-MODIS era, back to the 1980s, through an anisotropic LUT (look-up table) established from high-quality 500 m MCD43A-BRDF data [
36]. Franch used smoothed 5.6 km MODIS BRDF with a further adjustment by NDVI in their VJB method, then decomposed it to estimate 30 m Landsat surface albedo [
37,
38]; Jiao established a BRDF archetype database by using a clustering algorithm and parameter smoothing of BRDF based on anisotropic flat index (AFX) [
39,
40]. Zhang Hu estimated surface albedo based on the archetype database classified by AFX [
41]. However, there is a lack of understanding of the difference within estimated albedo induced by the anisotropy information smoothed at spatiotemporal scales. This work will focus on this issue to investigate the effects of smoothed BRDF on albedo magnitude through case studies using MODIS operational BRDF products.
5. Discussion
It is a feasible approach to introduce BRDF priori knowledge into the estimation of surface albedo at fine resolutions, but there is a potential for apparent uncertainty existing in the derived albedo values, especially when BRDF priori knowledge at coarse scales is used in fine resolution albedo calculations. This work focused on several typical case studies to investigate its variation. Our results show that BRDFs of different land cover types can produce captured differences into the retrieval of albedo after spatiotemporal smoothing. Moreover, the differences have the seasonal characteristic that differences in spring and summer are higher in temporal smoothing and heterogeneity so that the overall correlation coefficient between sill values and absolute differences is also high. In spatial smoothing, the direct causes are changes in land surface condition in the spatial and temporal scale, such as the spatial continuity of surface biophysical characteristics, various rhythmic cycles of land surface biomes with the change of seasons, and as well as residual uncertainties left in the nominal corrected input observations [
40,
64,
65,
66]. Though observations within a 16-day period are enhanced on the most recent day of the retrieval date, it should be noted that the time–angle trade-off scheme preserves land surface signatures from other days in the nominal daily BRDF retrieval.
Regarding analysis of albedo differences due to BRDF temporal smoothing, the temporal smoothing of BRDF shows obvious scale effect and seasonality. With the increase in smoothing scale, the albedo differences gradually increase (
Figure 11a–c). This conclusion is applicable to the three broad bands (NIR, SW, and VIS) for each study site. Generally, the absolute differences caused by temporal smoothing of BRDF in the NIR band are the largest, while the relative differences in the VIS band are the largest (
Figure 11d). This may be related to the biophysical characteristic of vegetation that it needs to absorb light in the VIS band, meanwhile the light in NIR band could be strongly scattered by leaf structure. In addition, the impact of BRDF temporal smoothing shows certain seasonal characteristics, with elevated variation in spring and summer due to the vigorous growth of vegetation (
Figure 12d), and limited variation in autumn and winter due to lesser temporal changes over land surface.
The impact of spatial BRDF smoothing on albedo implies certain spectral features accompanied by connections with spatial heterogeneity. The absolute differences caused by spatial BRDF smoothing show the highest values in the NIR band and the highest relative differences in the VIS band (
Figure 14). This is consistent with the biophysical characteristics of the vegetation analyzed above, that photosynthesis needs to absorb visible light and produce higher reflectance in the NIR band. Compared with flat grassland, forest effectively increased the differences. In addition, we reconstructed the land surface albedo at 30 m based on Landsat8-OLI images to analyze the spatial heterogeneity of land covers. The results show that the spatial heterogeneity of land cover is related to the albedo differences due to spatial smoothing of BRDF (
Figure 15).
6. Conclusions
Several studies have introduced BRDF priori knowledge into albedo retrievals smoothed at different scales. This paper investigated the effects of smoothed BRDF on albedo differences through case studies over six North American regions using operational MODIS-BRDF/Albedo products. Our results show that: (1) as the BRDFs smoothed temporally from daily to monthly, and spatially from 500 m to 5600 m, variations in the magnitude and shapes during BRDF smoothing can be captured, with potential relationships with spectral band, land cover types, and characteristic of vegetation. (2) Temporally smoothed BRDF in NIR, SW, and VIS could lead to apparent relative differences of estimated albedo to smoothed values of 11.3%, 12.5%, and 27.2% and detectable absolute differences of 0.025, 0.012, and 0.013. Further, albedo differences show an obvious seasonal characteristic that differences in spring and summer are significantly higher than those in autumn and winter in the three broadbands. (3) Spatially smoothed BRDF from 500 m to 5.6 km in NIR, SW, and VIS bands could lead to albedo achieving apparent relative differences to smoothed values of 36.5%, 37.1%, and 94.7% and detectable absolute differences of 0.037, 0.024, and 0.018, while albedo differences due to BRDF spatial smoothing are related to heterogeneity of land cover and the overall correlation coefficient between sill values and absolute differences in the three broad bands was 0.8876. The introduction of BRDF priori knowledge of land cover is an important way to produce albedo at high resolution. This work demonstrated that smoothed BRDF after temporal and spatial smoothing can introduce variations in the magnitude and shape of BRDF, and the uncertainty propagating into albedo retrieval is obvious. 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.