## 2 Materials and Methods
### Modeling Strategy  
All the monthly-measured data in each year was used for \(R_{\mathrm{s}}\) model construction (n = 58) to explore the relationship between \(R_{\mathrm{s}}\) and environmental factors. Also, all measured or downloaded data were verified for assumptions of normality and variance homogeneity before conducting statistical analyses using the Kolmogorov-Smirnov test and [PERSON]'s test. In this study, a three-step reliable model was developed to quantify the temporal variations of \(R_{\mathrm{s}}\) within environmental factors. First, a one-factor equation was constructed to study the relationship between \(R_{\mathrm{s}}\) and temperature or vegetation index:  
\[R_{s}=aT+b \tag{2}\]  
\[R_{s}=ae^{bT},\ \mathrm{Q_{10}}=e^{10b}\ \mathrm{and}\ \mathrm{R_{10}}=ae^{10b} \tag{3}\]  
\[R_{s}=a\mathrm{NDVI}+b \tag{4}\]  
\[R_{s}=ae^{b\mathrm{NDVI}}. \tag{5}\]  
Second, a bivariate equation was constructed by adding another independent variable:  
\[R_{\mathrm{s}}=a LST+b\mathrm{NDVI}+c \tag{6}\]  
\[R_{\mathrm{s}}=a\exp\left(b\mathrm{LST}+c\mathrm{NDVI}\right) \tag{7}\]  
\[R_{\mathrm{s}}=aM_{\mathrm{s}}+bM_{\mathrm{s}}{}^{2}+cT_{s}+d. \tag{8}\]  
\[R_{\mathrm{s}}=a\exp\left(bM_{\mathrm{s}}+cM_{\mathrm{s}}{}^{2}+dT_{\mathrm{ s}}\right). \tag{9}\]  
Finally, a fitting model of the \(R_{\mathrm{s}}\) temporal variation is formulated by compounding all three kinds of variables:  
\[R_{\mathrm{s}}=aM_{\mathrm{s}}+bM_{\mathrm{s}}{}^{2}+cT+d\mathrm{NDVI}+e \tag{10}\]  
\[R_{\mathrm{s}}=a\exp\left(bM_{\mathrm{s}}+cM_{\mathrm{s}}{}^{2}+dT+e\mathrm{ NDVI}\right) \tag{11}\]where \(R_{\rm s}\) is the soil respiration rate (\(\mu\)mol CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)), T is the soil temperature (\({}^{\circ}\)C) or land surface temperature (\({}^{\circ}\)C), \(M_{\rm s}\) is the soil moisture (%), NDVI is the vegetation index, and a, b, c, d, and e are fitting parameters. Q\({}_{10}\) is the temperature sensitivity index of \(R_{\rm s}\), indicating the proportional change in \(R_{\rm s}\) for 10 \({}^{\circ}\)C increase in temperature, while R\({}_{10}\) is the soil respiration rate at a soil temperature of 10 \({}^{\circ}\)C, i.e., soil basal respiration. This value is widely applied for comparison of \(R_{\rm s}\) among ecosystems.  
The fitness and accuracy of the model were evaluated by three standards: the coefficient of determination (R\({}^{2}\)), root-mean-square error (RMSE), and [PERSON]'s information criterion (AIC) [23], where R\({}^{2}\) can be directly obtained by SPSS 17.0. The two remaining indexes were calculated as follows:  
\[\rm RMSE=\sqrt{RSS/n} \tag{12}\]  
\[\rm AIC=nlnRSS+2(p\,+\,1)-nlnn, \tag{13}\]  
where RSS is the residual sum of squares, n is the sample size, and p is the number of independent variables. The main environmental factor driving \(R_{\rm s}\) temporal variation and the optimal fitting model was selected based on the higher R\({}^{2}\) and the lower RMSE and AIC.  
All statistical analyses were performed using the Statistical Package for the Social Sciences (SPSS 17.0) (SPSS Inc., Chicago, IL, USA) and graphs were generated with SigmaPlot 12.5 (Systat Software, Inc., San Jose, CA, USA).