## Materials and Methods
### Retrieval Algorithm
#### 2.3.2 The Lookup Table (LUT) Inversion  
The lookup table (LUT) method is by nature the direct comparison of radiative transfer model simulated spectra against the observed spectra. It is a simple and widely-used inversion method in the field of vegetation parameter retrieval from remote sensing data [18]. LUT consists two main steps: LUT generation and LUT searching.  
LUT generation: 100,000 parameter combinations were firstly randomly generated following uniform distributions. The ranges (minimum and maximum) for each of the 8 main model parameters are summarized in Table 2. The fraction of diffuse incoming solar radiation was set as 0, i.e., diffuse incoming solar radiation was ignored, given the fact that MCD43A4 is a bi-directional reflectance product. As for the sun-view geometry, the incidence zenith angle was set from 10\({}^{\circ}\) to 55\({}^{\circ}\) with a step of 5\({}^{\circ}\). The dynamic range of the sun zenith angle was determined according to the its temporal variation for the MCD43A4 imageries over our study area simulated by the astronomical model [32]. (Figure 2). The view zenith angle and the relative azimuth angle were both set as 0\({}^{\circ}\), to simulate the nadir-viewing condition. The incidence zenith angle range was determined by the annual variation of the local solar noon zenith angle in our study area (see Figure 2). Each parameter combination was then used to drive the PROSAIL model, and obtain simulated spectra covering wavelength from 400 nm to 2500 nm. As recommended by similar studies [18; 39], a 5% Gaussian white noise was added to the simulated spectra to account for the remote sensing observation uncertainty. Finally, the continuous spectrums were converted into MODIS 1-7 channels reflectance values by means of the sensor relative spectral response (RSR).  
LUT searching: To find the solution to the inverse problem for a given MCD43A4 pixel, the relative root mean squared error (R-RMSE) between measured and LUT-stored spectra is calculated as  
\[RRMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(\frac{R_{i}^{\text{{MCD}}}-R_{i}^{ LUT}}{R_{i}^{\text{{MCD}}}}\right)^{2}}, \tag{1}\]  
where \(n\) (=7) is the number of spectral bands used, \(R_{i}^{\text{{MCD}}}\) is the MCD43A4 reflectance at band \(i\), and \(R_{i}^{\text{{LUT}}}\) is the PROSAIL simulated reflectance stored in LUT. The relative RMSE rather than the absolute RMSE is used to account for the range discrepancy existed in the 7 MCD43A4 bands, e.g., the values for near infrared band is much larger than those for red band, and the red band will exert negligible influence if absolute RMSE is used. The solution corresponding the minimum RRMSE is not always the optimal solution because of the ill-posed nature of the inversion problem [38]. To alleviate this issue, we adopted the multi-solution method, i.e., the mean of the corresponding multiple target parameter values was provided as output estimate [18; 34]  
\[AGB=\frac{1}{t}\sum_{j=1}^{t}LAI_{j}\cdot Cm_{j}, \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Parameter** & **Unit** & **Min** & **Max** \\ \hline Canopy & Leaf area index & m\({}^{2}\)-m\({}^{2}\) & 0.1 & 8.0 \\  & Averaged leaf inclination angle & \({}^{\circ}\) & 60 & 70 \\  & Hot spot size & Unitless & 0.05 & 0.1 \\ Leaf & Leaf chlorophyll content & mg\(\cdot\)cm\({}^{-2}\) & 15 & 55 \\  & leaf structure parameter & Unitless & 1.5 & 1.9 \\  & Leaf equivalent water thinness & g\(\cdot\)cm\({}^{-2}\) & 0.01 & 0.02 \\  & Leaf dry matter content & g\(\cdot\)cm\({}^{-2}\) & 0.005 & 0.01 \\ Soil & Brightness coefficient & Unitless & 0.5 & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Distribution of the canopy, leaf, and soil parameters used in the PROSAIL parameterization. Parameters values are drawn randomly within these specific ranges.  
where \(t\) is the number of best matching spectra, \(LAI_{j}\) and \(Cm_{j}\) is the LAI and Cm corresponding the \(j\)-th best matching spectra. \(t\) was set as 50 based on literature [18; 23; 34; 37] and our own tests and trials.