## Methods
### Model Development
#### 2.1.2 Dynamic Rooting Scheme and Its Implementation  
At present, although the root C pool does vary temporally, due to the static rooting scheme, there is no net change in the root fraction within each soil layer. To represent actual dynamic root growth, the dynamic rooting scheme developed by [PERSON] et al. [28] was incorporated into CESM1.2.0 by integrating it into the land component (i.e., the CLM4.5 land-surface model). This scheme enables the total new root C gain at each time step to be dynamically allocated to each soil layer according to the surrounding environment, achieving a compromise between soil water and soil mineral N, as expressed by Equation (2):  
\[\Delta\mathrm{C_{fr,}}=\Delta\mathrm{C_{fr}}[(1-\beta_{\mathrm{t}})\frac{w_{i} \Delta z_{i}}{\sum\limits_{j=1}^{10}w_{j}\Delta z_{j}}+\beta_{\mathrm{t}}\frac {n_{i}\Delta z_{i}}{\sum\limits_{j=1}^{10}n_{j}\Delta z_{j}}] \tag{2}\]  
where \(\Delta\mathrm{C_{fr}}\) (units: g C m\({}^{-2}\) s\({}^{-1}\)) is the newly assimilated C allocated to roots, \(\Delta z_{i}\) (units: m) is the soil layer thickness, \(n_{i}\) (units: g N m\({}^{-3}\)) is soil mineral \(N\) content, and \(w_{i}\) is the plant wilting factor of layer \(i\). \(\beta_{\mathrm{t}}\) is the soil water stress due to water deficiency, which depends on \(w_{i}\) and the root fraction (\(r_{i}\)) and can be expressed as:  
\[\beta_{\mathrm{t}}=\sum\limits_{i=1}^{10}w_{i}r_{i} \tag{3}\]  
\[w_{i}=\frac{\psi_{\mathrm{c}}-\psi_{i}}{\psi_{\mathrm{c}}-\psi_{\mathrm{o}}} \frac{\theta_{\mathrm{sat,}i}-\theta_{\mathrm{ice,}i}}{\theta_{\mathrm{sat,}i}} \tag{4}\]  
where \(\Psi_{i}\) is the soil water matric potential (units: mm), and \(\Psi_{\mathrm{c}}\) and \(\Psi_{\mathrm{o}}\) are the soil water potential (units: mm) when stomata are fully closed or fully open, respectively. \(\theta_{\mathrm{sat,}i}\) and \(\theta_{\mathrm{ice,}i}\) are the saturated volumetric water and ice contents, respectively (units: m\({}^{3}\) m\({}^{-3}\)). The function \(\beta_{\mathrm{t}}\) ranges from 0 to 1, with larger values indicating higher water availability. The root distribution after the new dynamic allocation is then updated based on the amount of roots C (\(\mathrm{C_{fr,}}\); units: g C m\({}^{-2}\)) in layer \(i\) and the total amount of roots C (\(\sum\limits_{i=1}^{10}\mathrm{C_{fr,}}\); units: g C m\({}^{-2}\)):  
\[r_{i}=\frac{\mathrm{C_{fr,}}_{i}}{\sum\limits_{i=1}^{10}\mathrm{C_{fr,}}_{i}} \tag{5}\]  
As the vertically resolved soil mineral N is not predicted in CLM4.5, the total N (TN) data from the Global Soil Dataset for Earth System Modeling [35] that had vertical layers consistent with CLM4.5 were used to represent soil mineral N content [28]. Although this data was time invariant, more effort should be made to resolve the original CLM4.5 TN in order to produce vertically layered data in the future. The dynamic rooting scheme influences climate modeling in CESM1.2.0 in multiple ways.  
The varying root distribution has a direct impact on \(\beta_{\text{t}}\), which affects photosynthesis and stomatal conductance. Moreover, the varying root fraction influences the effective root fraction, which affects the amount of water extracted from each layer. The aforementioned factors will ultimately influence land-atmosphere exchange processes, such as transpiration, and through these will affect latent heat, gross primary production, and the global climate. Figure 1 shows in detail the impacts of the dynamic rooting scheme on land-atmosphere interactions.  
It should be noted that in CLM4.5, the carbon allocation for new growth is only based on the allometric parameters, depending on PTFs. However, when vegetation was restricted by light, more carbon would be allocated to the stems; when restricted by water or nutrients, more carbon would be distributed to the roots. In this study, we only considered the change of root carbon allocation between different soil layers with environmental factors, and did not consider the dynamic changes of carbon allocation between leaves, stems, and roots.