## 2 Materials and Methods
### Establishment and Verification of the Model  
In this study, the field sampling data was wet weight and needed to be converted to air-dried weight. We converted the wet weights to air-dried weights using conversion coefficients for different grassland types employing \"Chinese Grassland Resources\" [30] as a reference, and we further converted the air-dried weights to dry weights with a 15% water content [31], as the indicator of the grassland aboveground biomass.  
Based on the database, regression models between the aboveground biomass and the corresponding accumulated PSNnet value were established. These models primarily consisted of unitary linear, logarithm function, power function and exponential function models (Table 1). Using the reserved ground sampling data (approximately 20% of the total samples), we calculated the root-mean-square error (RMSE) and mean relative estimation error (REE) between the estimated values and the ground-measured values to evaluate the accuracy of the models [32]. The equations employed for error calculation were as follows:  
\[\text{RMSE}=\sqrt{\frac{\sum(\text{Y}_{\text{i}}-\text{Y}_{\text{i}}^{{}^{ \prime}})^{2}}{\text{N}}} \tag{10}\]  
\[\text{REE}=\sqrt{\frac{\sum[(\text{Y}_{\text{i}}-\text{Y}_{\text{i}}^{{}^{ \prime}})/\text{Y}_{\text{i}}^{{}^{\prime}}]^{2}}{\text{N}}} \tag{11}\]  
where, \(\text{Y}_{\text{i}}\) is the actual aboveground biomass (fresh weight), \(\text{Y}_{\text{i}}^{{}^{\prime}}\) is the aboveground biomass estimated by the model and N is the sample size.  
The results indicate that the precision of the exponential function model was relatively low, whereas the precision of the unitary linear regression model was highest, at 69%. The correlation between the grassland aboveground biomass estimated by the unitary linear model and the actual aboveground biomass was significant (Figure 3). Therefore, we selected the unitary linear regression model for estimating the aboveground biomass of the Xilingol grassland, and then analyzed the temporal and spatial characteristics of the aboveground biomass of the Xilingol grassland.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{\(\mathbf{R^{2}}\) & \multirow{2}{*}{**F Value**}} & \multicolumn{2}{c}{**RMSE**} & \multirow{2}{*}{**REE**} & \multirow{2}{*}{**Precision**} \\ \cline{3-4} \cline{6-7}  & & & & & **(g-m\({}^{-2}\))** & & \\ \hline Unitary linear function & y = 1.097x \(-\) 4.776 & 0.55 & 1168.75 & 26.67 & 0.31 & 69 \\ Logarithm function & y = 71.308 \(\times\)lnx \(-\) 224.634 & 0.55 & 1154.46 & 26.77 & 0.40 & 60 \\ Power function & y = 0.361x\({}^{1.226}\) & 0.65 & 1739.58 & 27.43 & 0.39 & 61 \\ Exponential function & y = 17.038 \(\times\)e\({}^{0.0178\text{x}}\) & 0.58 & 1315.50 & 34.52 & 0.43 & 57 \\ \hline \hline \end{tabular} Note: The numbers of regression and test samples were 975 and 230, respectively; \(p<0.0001\); precision = (1 – REE) \(\times\)100%; x is the accumulated PSNnet data (C\(\_\)g\(\cdot\)m\({}^{-2}\), C presents carbon), y is the estimated aboveground biomass (g\(\cdot\)m\({}^{-2}\)).  
\end{table}
Table 1: Statistical models relating aboveground biomass to accumulated PSNnet.