## 2 Materials and Methods
### Model Description and Improvement
#### 2.1.2 Dynamic Root Option  
The UA version of Noah-MP incorporates a layered root biomass model to simulate dynamic root water uptake at macroscopic scales [26]. The fine root biomass in the \(i\)th soil layer (\(m_{R,i}\), g m\({}^{-2}\)) is given by:  
\[\frac{\Delta m_{R,i}}{\Delta t}=GPP_{\text{\it{root}},i}-EX_{\text{\it{root}},i}-rs_{\text{\it{root}},i}-gs_{\text{\it{root}},i}-Ovt_{\text{\it{root}},i} \tag{8}\]  
where \(GPP_{\text{\it{root}},i}\) (g m\({}^{-2}\cdot\)s\({}^{-1}\)) represents carbon allocation to fine roots in the \(i\)th soil layer, \(rs_{\text{\it{root}},i}\) and \(gs_{\text{\it{root}},i}\) are the maintenance and growth respiration of fine roots in the \(i\)th soil layer (g m\({}^{-2}\cdot\)s\({}^{-1}\)), \(EX_{\text{\it{root}},i}\) (g m\({}^{-2}\cdot\)s\({}^{-1}\)) is the root exudates in the \(i\)th soil layer, and \(Ovt_{\text{\it{root}},i}\) (g m\({}^{-2}\cdot\)s\({}^{-1}\)) is the turnover rate of fines roots in the \(i\)th soil layer. The equation for \(GPP_{\text{\it{root}},i}\) is:  
\[GPP_{\text{\it{root}},i}=f_{\text{\it{root}}}\times PSN\times 10^{-6} \frac{\Delta z_{i}\times w_{i}}{\sum\limits_{i}^{\text{\it{proof}}}\left( \Delta z_{i}\times w_{i}\right)} \tag{9}\]  
\[w_{i}=e^{-\Delta z_{i}}\times\sqrt{\frac{\theta_{i}-\theta_{\text{\it{wilt}} }}{\theta_{\text{\it{ref}}}-\theta_{\text{\it{wilt}}}}} \tag{10}\]  
where \(PSN\) (umol m\({}^{-2}\cdot\)s\({}^{-1}\)) is the total photosynthetic rates from sunlit and shaded leaves, \(w_{i}\) is the weighting factor in the \(i\)th soil layer, \(z_{i}\) is the node depth in the \(i\)th soil layer (m), \(\theta_{i}\), \(\theta_{\text{\it{ref}}}\), and \(\theta_{\text{\it{wilt}}}\) (cm\({}^{3}\) cm\({}^{-3}\)) are the actual soil moisture, field capacity, and wilting point in the \(i\)th soil layer, \(\Delta z_{i}\) (m) is the layer thickness in the \(i\)th soil layer, and \(a\) is an empirical parameter.  
Water uptake by fine roots in each soil layer is related to the predicted root surface areas (\(A_{R}\), m\({}^{2}\cdot\)m\({}^{-2}\)), which are converted from root biomass. The change in plant water storage (\(M_{\text{\it{eff}}}\) mm) is related to the total water uptake (\(Q_{R}\), mm\(\cdot\)s\({}^{-1}\)) and plant transpiration (\(Q_{T}\), mm\(\cdot\)s\({}^{-1}\)):  
\[\frac{\Delta M_{\text{\it{q}}}}{\Delta t}=\sum\limits_{1}^{\text{\it{root}}}Q _{R,i}-Q_{T} \tag{11}\]  
\[Q_{R,i}=A_{R,i}\bigg{(}\frac{h_{\text{\it{s}},i}-h_{R}}{\Omega_{R}+\Omega_{ \text{\it{s}},i}}\bigg{)} \tag{12}\]where _uroot_ is the total number of soil layers containing fine roots for a specific plant functional type, \(h_{R}\) and \(h_{s,i}\) (mm) are the water potential of fine roots and soil water near the root in the \(i\)th soil layer, and \(\Omega_{\text{R}}\) (s) and \(\Omega_{\text{S,i}}\) (s) are the resistance to water flows through fine roots and soil matrix near the root surface in the \(i\)th soil layer.  
Another improvement is that \(\beta\) is specified as a function of plant water storage:  
\[\beta=\frac{M_{q}-M_{q,wilt}}{M_{q,\text{max}}-M_{q,wilt}} \tag{13}\]  
where \(M_{q,wilt}\) (mm) is plant water storage at the wilting point and \(M_{q,max}\) (mm) is the maximum plant water storage. The value of \(\beta\) ranges from 0 to 1, suggesting a maximum fraction of 30% for carbon allocation to fine roots under severe water stress. As \(\beta\) approaches 0, \(M_{q}\) approaches \(M_{q,wilt}\), resulting in stomatal closure to prevent severe desiccation.