## 2 Materials and Methods
### Model Description and Development  
[PERSON] et al. (1996) developed the biosphere-oriented, regional-scale Integrated Biosphere Simulator (IBIS) model [20]. In order to simulate the dynamic changes in the vegetation cover in Europe and Africa, the second iteration of the IBIS model was coupled with GENESIS (version 2.0), an atmospheric circulation model. The most recent version of IBIS is version 2.6 [35]. The IBIS model consists of five modules: land surface processes, vegetation dynamics, vegetation phenology, subterranean carbon and nitrogen cycling, and soil geochemistry (Figure 2). Our study focuses on improving and refining the land surface processes and vegetation dynamics modules. (1) Land surface processes module  
The land surface processes module is used to calculate the exchange of water, heat, and carbon dioxide. The thicknesses of the six soil layers, from top to bottom, are 0.10 m, 0.15 m, 0.30 m, 0.50 m, 1.00 m, and 2.00 m. In the soil module, the rate of change in the liquid soil water content is calculated using the Richard equation, and the vertical flux of water is determined using [PERSON]'s law. At the impermeable bottom boundary of the soil module, there is no diffusion of liquids or heat. \begin{table}
\begin{tabular}{c c c c c} \hline \hline Site & SPT & CW & AS & ERDS \\ \hline Observation period & 2001–2008 & 2004–2008 & 2004–2006 & 2005 \\ Vegetation type & cropland & cropland & cropland & desert \\ Latitude & N\({}^{\circ}\) & 37\({}^{\circ}\)27\({}^{\prime}\) & 35\({}^{\circ}\)12\({}^{\prime}\) & 36\({}^{\circ}\)51\({}^{\prime}\) & 39\({}^{\circ}\)29\({}^{\prime}\) \\ Longitude & E\({}^{\circ}\) & 104\({}^{\circ}\)57\({}^{\prime}\) & 107\({}^{\circ}\)40\({}^{\prime}\) & 109\({}^{\circ}\)19\({}^{\prime}\) & 110\({}^{\circ}\)11\({}^{\prime}\) \\ Elevation & m & 1250 & 1200 & 1068 & 1290 \\ Mean precipitation & mm & 186 & 580 & 500 & 310 \\ Mean temperature & \({}^{\circ}\)C & 9.6 & 9.1 & 8.8 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Site information for (SPT, CW, AS, and ERDS) in the LP. Figure 2: Modeling framework and improvement modules (refer to [35]). To simulate the soil hydrothermal regime, we calculated the soil temperature, the water content, and the ice content of a given soil layer with the Richard equation as follows [20]:  
\[\frac{\partial\theta}{\partial t}=\frac{\partial}{\partial z}[D(\theta)\frac{ \partial\theta}{\partial z}]+\frac{\partial K(\theta)}{\partial z}-ST(z,t) \tag{1}\]  
where \(\theta\) (m\({}^{3}\)m\({}^{-3}\)) is the actual soil water content of a soil layer at a certain time and \(\theta i\) (m\({}^{3}\)m\({}^{-3}\)) is the ice rate of the soil layer. \(D(\theta)\) (mms\({}^{-1}\)) represents the soil diffusivity of the soil volumetric water content. \(K(\theta)\) (mms\({}^{-1}\)) is the hydraulic conductivity; when the soil volumetric moisture content is \(K(\theta)\), it needs to be calculated by the saturated hydraulic conductivity \(K_{s}\). \(b\) is the index of the Campbell formula. \(ST(z,t)\) (s\({}^{-1}\)) is a sink term reseting water uptake by plant roots as a function of ET. The Campbell formula is as follows:  
\[K(\theta)=K_{\text{g}}\bigg{(}\frac{\theta}{\theta_{\text{g}}}\bigg{)}^{2b+3} \tag{2}\]  
Using the heat diffusion equation [20], we can quantify the heat transfer in the soil:  
\[C\frac{\partial T(z,t)}{\partial t}=\frac{\partial}{\partial z}\bigg{[}\frac {\lambda\partial T(z,t)}{\partial z}\bigg{]}+H_{fm} \tag{3}\]  
\[H_{\text{fm}}=\rho_{ice}L_{f}\frac{\partial\theta_{ice}}{\partial t} \tag{4}\]  
where \(C\) (Jkg\({}^{-1}\)k\({}^{-1}\)) and \(\lambda\) (Wm\({}^{-1}\)k\({}^{-1}\)) are the volumetric heat capacity and the thermal conductivity, respectively, \(t\) (s) is the time, and \(z\) (mm) is the vertical depth. \(T\) (k) is the temperature. \(H_{fm}\) (Jkg\({}^{-1}\)) is the latent heat released or consumed during the phase change of soil water.