## 3 Results
### Modeling \(R_{\rm s}\) Seasonal Variations  
The relationship between \(R_{\rm s}\) and environmental factors can be expressed by linear, exponential, double exponential, power, hyperbolic curve, quadratic, and Lloyd and Taylor models, as well as their composites. The linear and exponential models expressed the relationships between \(R_{\rm s}\) and temperature or vegetation cover well. The model with the best fit was selected by comparing three model performance indicators (R\({}^{2}\), RMSE, AIC). For the response of \(R_{\rm s}\) to \(M_{\rm s}\), the quadratic equation had a better empirical fit. Correlation analyses showed that there was an extremely significantly positive correlation between \(R_{\rm s}\) and \(T_{\rm s}\) (r = 0.896**), LST (r = 0.834**) and NDVI (r = 0.753**) (Table 1), but no significant correlation between \(R_{\rm s}\) and \(M_{\rm s}\). Overall, for the same environmental factors, the exponential model fitted better than the linear form, with higher R\({}^{2}\) and lower RMSE and AIC values (Table 2). The exponential model based entirely on in situ measured \(T_{\rm s}\) (R\({}^{2}\) = 0.842, \(p\) \(<\) 0.001) showed a relatively higher explanation capacity than the exponential model based on LST (R\({}^{2}\) = 0.762, \(p\) \(<\) 0.001). The further addition of \(M_{\rm s}\) explained an additional 1.3% of the \(R_{\rm s}\) seasonal variation based on the \(T_{\rm s}\) linear model and 0.8% of the \(R_{\rm s}\) seasonal variation based on the \(T_{\rm s}\) exponential model. The model based entirely on the plant photosynthesis-related NDVI exhibited the poorest fit for \(R_{\rm s}\) (R\({}^{2}\) = 0.568 for the linear model, and R\({}^{2}\) = 0.605 for the exponential model). However, the addition of LST improved the explanation by 15% for the linear model and 17.7% for the exponential model. Taking \(M_{\rm s}\), temperature and NDVI into account together, the explanation of the model showed a slight improvement relative to the exponential models with two variables. Overall, the model based on the in situ observed data had a slightly higher explanation than the model based on the spatial products, with higher \(R^{2}\) values and lower RMSE and AIC values. Considering that the three model performing indicators of three exponential models with good fitting effects (based on \(T_{\rm s}\), both \(T_{\rm s}\) and \(M_{\rm s}\), and together with \(M_{\rm s}\), \(T_{\rm s}\), and NDVI) showed minor differences and the models all reached significant levels, we selected the simplest exponential model based on \(T_{\rm s}\) as the optimum fitting model to describe seasonal variations in \(R_{\rm s}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(R_{\rm s}\) & \(R_{\rm s}\) & \(T_{\rm s}\) & \(M_{\rm s}\) & LST & NDVI \\ \hline r & 1.000 & 0.896 ** & \(-\)0.183 & 0.834 ** & 0.753 ** \\ \(p\) value & 0.000 & 0.169 & 0.000 & 0.000 \\ \hline \hline \end{tabular} **Correlation is significant at 0.01 level (two-tailed); n = 58. \(R_{\rm s}\) is measured soil respiration (\(\upmu\)mol CO\({}_{2}\) m\({}^{-2}\)s\({}^{-1}\)), \(T_{\rm s}\) is soil temperature (\({}^{\circ}\)C), LST is the nighttime land surface temperature observed by the Moderate Resolution Imaging Spectro radiometer (MODIS) onboard terra satellite (\({}^{\circ}\)C), and NDVI is the normalized difference vegetation index.**  
\end{table} 
Table 1: Correlation coefficients (r) and \(p\) values between soil respiration (\(R_{\rm s}\)) and its related factors.