## 2 Materials and Methods
### Method
#### 2.3.2 RTLSR Model  
BRDF describes the direction of the surface reflection characteristics. In the bi-directional reflectivity models, a practical method called the kernel-driven model, which has a certain physical meaning of the linear combination of the core, is used to match the surface bidirectional reflection. RTLSR is the main algorithm for MODIS diversion and albedo products are currently providing albedo and bi-directional reflectivity of global scale to users. The RTLSR algorithm is the weighted sum of two kernels, which are called \"RossThick\" and \"LiSparse-Reciprocal\". The RTLSR algorithm has the following constructs [27]:  
\[ \begin{split} R(\theta_{i},\theta_{r},\varphi,\lambda)=f_{iso}( \lambda)\\ +f_{vol}(\lambda)K_{vol}(\theta_{i},\theta_{r},\varphi)+f_{geo}( \lambda)K_{geo}(\theta_{i},\theta_{r},\varphi)\end{split}  \tag{3}\]  
where \(K_{geo}\) and \(K_{vol}\) are geometrical optics kernel and bulk scattering kernel, which are functions of observing zenith angle \(\theta_{i}\), solar zenith angle \(\theta_{r}\) and relative azimuth angle \(\varphi\), respectively. \(f_{iso}\), \(f_{geo}\), and \(f_{vol}\) are constant coefficients, which represent the proportion of isotropic scattering, geometric optical scattering, and bulk scattering. \(R(\theta_{i},\theta_{r},\varphi,\lambda)\) is the BRDF of the band. The RTLSR algorithm uses the linear regression to invert the best coefficients of the matching observation data, \(f_{iso}\), \(f_{geo}\), and \(f_{vol}\), then obtains the bi-directional reflectivity of random incident angle and observation angle by the extrapolation or interpolation of the kernel [28]. The bulk scattering kernel \"RossThick\" is suitable for describing dense homogeneous vegetation and leaf dip spherical distribution, proposed by [PERSON] [29]:\[K_{vol}(\theta_{i},\theta_{r},\varphi)=\frac{\left(0.5\pi-g\right)\cos g+\sin g}{ \cos\theta_{i}+\sin\theta_{r}}-\frac{\pi}{4} \tag{4}\]  
where \(g\) is the phase angle defined by the following formula:  
\[\cos g=\cos\theta_{i}\cos\theta_{r}+\sin\theta_{i}\sin\theta_{r}\cos\varphi \tag{5}\]  
The geometric optical kernel \"LiSparseR\" is suitable for describing a sparsely distributed canopy or other opaque geometry. It is a method based on the reciprocity principle, and it can partially improve the problems when extrapolating to the larger zenith angle without affecting the data matching ability. The expression is:  
\[K_{geo}(\theta_{i},\theta_{r},\varphi)=A(\theta_{i},\theta_{r},\varphi)\sec \theta_{i}-B(\theta_{i},\theta_{r},\varphi) \tag{6}\]  
where,  
\[ \begin{array}{l}B(\theta_{i},\theta_{r},\varphi)=sec\theta_{i}t+\sec\theta_ {r}t-O(\theta_{i},\theta_{r},\varphi)\\ A(\theta_{i},\theta_{r},\varphi)=\frac{1}{2}(1+cosa)sec\theta_{r}\\ O=\frac{1}{\pi}(t-\sin t\cos t)(sec\theta_{i}t+\sec\theta_{r}t)\\ \cos t=\frac{b}{\pi}\frac{\sqrt{D^{2}+(tan\theta_{i}ttan\theta_{r})^{2}}}{sec \theta_{r}t+\sec\theta_{r}t^{2}}\\ D=\sqrt{\tan^{2}\theta_{i}t+\tan^{2}\theta_{r}t-2\tan\theta_{i}t\cos\varphi} \\ \cos a=\cos\theta_{i}t\cos\theta_{r}t+\sin\theta_{i}t\sin\theta_{r}t\cos\varphi \\ \theta_{i}t=\arctan(\frac{b}{t}tan\theta_{i}),\ \theta_{r}=\arctan(\frac{b}{t}tan \theta_{r})\end{array}  \tag{7}\]  
where \(b\) is the vertical radius of the sphere; \(h\) is the horizontal radius of the sphere, and \(r\) is the height of the sphere. In the MODIS algorithm, \(\frac{h}{b}=2\), \(\frac{b}{r}=1\)[29]. We used this algorithm, setting the HJ-1 fusion data to 16 days as a group and 8 days as a cycle, to match a set of kernel coefficients: \(f_{iso}\), \(f_{geo}\), and \(f_{vol}\). The least squares method was applied in matching. We set the solar zenith angle in the model to \(45^{\circ}\), which was consistent with the solar zenith angle of MOD43 NBAR product data, and the observation zenith angle to the zenith direction.