## 2 Materials and Methods  
### MODIS BRDF/Albedo Product  
The MODIS instruments are onboard the sun-synchronous Terra (launched in 1999) and Aqua (launched in 2002) satellites. Terra passes the equator in the morning, while Aqua passes it in the afternoon. The view swath of MODIS is 2330 km wide and covers the Earth every 1-2 days. The ground track repeat cycle is every 16 days. Thus, MODIS instruments can accumulate multiangle observations of the Earth. The obtained raw data are then radiometrically calibrated and atmospherically corrected to yield surface reflectance. High-quality multidate, multiangle surface reflectance data over a 16-day retrieval period are used to obtain the MCD43 product by fitting a kernel-driven sememipriical BRDF model to establish the surface anisotropic reflectance. The number of high-quality observations available, the root mean square error (RMSE) of the fit, and the weight of determination (WOD), which indicates whether the observations over the viewing and illumination geometry are well distributed to capture the surface anisotropy, are used to generate a high-quality full inversion retrieval. A magnitude inversion, using available observations with an _a priori_ BRDF database, is applied if a high-quality full inversion BRDF cannot be retrieved due to poor quality input or insufficient sampling of the viewing hemisphere. While this magnitude of inversion often provides reliable results, it is always flagged as a poor quality retrieval. The RossThick-LiSparseReciprocal (RTLSR) kernel-driven semiempirical BRDF model is used in the MCD43 operational processing system [21]. This type of model basically consists of three components, i.e., isotropic scattering, volumetric scattering, and GO scattering, and each component presents the product of a weight \(f_{i}\) (i.e., \(f_{iso}\), \(f_{vol}\) and \(f_{geo}\)) and a kernel \(K_{i}\) (i.e., \(K_{iso}\), \(K_{vol}\) and \(K_{geo}\)) [32; 33; 63]. The kernels are functions of the viewing and illumination geometry, which indicates physically distinct BRDF shapes. The weights are the spectrally dependent parameters inversed by multi-angular observations. \[R(\theta_{v},\theta_{s},\Delta 204\varphi,\lambda)=f_{iso}(\lambda)+f_{vol}( \lambda)K_{vol}(\theta_{v},\theta_{s},\Delta\varphi)+f_{geo}(\lambda)K_{geo} (\theta_{v},\theta_{s},\Delta\varphi) \tag{1}\]  
where \(R(\theta_{v},\theta_{s},\Delta\varphi,\lambda)\) refers to the bidirectional reflectance at the viewing and illumination geometry of view zenith \(\theta_{v}\), illumination zenith \(\theta_{s}\), and relative azimuth \(\Delta\varphi\) in the waveband \(\lambda\). The RossThick kernel derived from a single scattering approximation to radiative transfer theory for the assumption of dense leaf canopies describes the volume scattering contribution [33; 64]. The LiSparseReciprocal kernel derived from a geometric-optical mutual shadowing model for the assumption of a sparse distribution of surface objects describes the GO scattering component [34; 65]. The MODIS C5 and C6 500 m BRDF model parameter product (MCD43A1) and its corresponding quality product (MCD43A2) were used to estimate the MODIS CI in this study. The C5 product is produced every eight days using high-quality surface reflectance observations acquired by both the Terra and Aqua satellites over a 16-day period (up to four observations per day from each sensor), while the C6 product is retrieved daily by weighting all clear-sky surface reflectance observations acquired over a 16-day period [21; 31; 66]. The day of interest for the C6 product is the middle day of the period, i.e., the 9 th day, while the day of interest for the C5 product is the first day of the period. The three model parameters (isotropic, volumetric, and geometric optical) of the red band (620-670 nm) in MCD43A1 and the band-dependent BRDF quality of the red band in MCD43A2 are used to estimate the MODIS CI.