## 2 Methodology  
### Model Description  
As the diagnostic parameter for the model, FPAR's accuracy reflects justifications of the land surface solar radiation scheme, but is not limited to this. Solar radiation (_i.e._, direct _vs._ diffuse radiation) and plant phenology (_i.e._, leaf area index (LAI)) are two factors also entering into the model's calculation of FPAR. In this study, solar radiation (including direct and diffuse radiation), as prescribed in forcing data CRUNCEP [34], as estimated based on meteorological station observations (CRU dataset) and reanalysis product (NCEP dataset).  
CLM4 represents the land surface as a hierarchy of subgrid types including glacier, lake, wetland, urban, and vegetated landunits. The vegetated part is further divided into patches of 16 PFTs and bare soil. Each subgrid land cover type is a separate column for energy and water calculation [18].  
In each PFT patch, the vegetation fractional coverage is 100%. The two-stream module is employed to calculate the solar radiant fluxes that are reflected, transmitted, absorbed by the canopy, and that are absorbed by the underlying soil. Several assumptions are made, including that fluxes are isotropic in only two directions (upward and downward), the canopy is horizontally homogenous and elements inside the canopy (including leaves, stems, and trunks) are randomly distributed. The daily output of CLM4 sums up the fluxes from each PFT that includes bare soil and accounts for the fraction of vegetated area in the grid. In this study, CLM4 FPAR is defined as:  
\[FPAR=\frac{\sum_{i=1}^{16}w_{i}I_{b,i}+\sum_{i=1}^{16}w_{i}I_{d,i}}{\sum_{l=0}^ {16}w_{i}S_{b,i}^{1}+\sum_{i=0}^{16}w_{i}S_{d,i}^{1}} \tag{1}\]  
where \(I_{b,i}(I_{d,i})\) is the direct (diffuse) solar radiation absorbed by the canopy in the visible band for plant type \(i\). \(S_{b,i}^{1}(S_{d,i}^{1})\) is the direct (diffuse) incident solar radiation at the land part of the grid in the visual band for plant type \(i\)[35], and \(w_{i}\) is the areal weighting of the plant functional type in the grid, \(\sum_{i=0}^{16}w_{i}=1\), including bare soil (\(i=0\)).  
As for plant phenology, the plant phenology cycle in the CLM4 is fully-prognostic, resulting from coupling Carbon-Nitrogen (CN) model: the seasonal timing of new vegetation growth and litterfall responds to soil and air temperature, soil water availability, and day-length, in varying degrees depending on a specified phenology type for each PFT. LAI calculation is based mainly on the specific leaf area \(SLA\) (m\({}^{2}\) one-sided leaf area per gC) and the total canopy leaf carbon (\(C_{L}\), gC \(\cdot\) m\({}^{-2}\) ground area) [36]. A linear relationship between \(SLA\) and canopy depth is assumed as:  
\[SLA(X)=SLA_{0}+mx \tag{2}\]  
where \(SLA_{0}\) is \(SLA\) at the top of the canopy, m is a linear coefficient, and x is a parameter describing the canopy depth as an overlying leaf area index. \(SLA_{0}\) and \(m\) are both fixed for each PFT. Total canopy leaf carbon \(C_{L}\) can be found by integrating over the canopy:  
\[C_{L}=\int_{0}^{L}\frac{1}{SLA(x)}\,dx=\frac{ln\left[(mL+SLA_{0})\right]-ln \left(SLA_{0}\right)}{m} \tag{3}\]  
Given \(C_{L}\) calculated from the CLM4, \(L\) can be solved as:  
\[L=\frac{SLA_{0}[exp(mC_{L})-1]}{m} \tag{4}\]  
\(C_{L}\) is a dynamic carbon pool affected by gains from photosynthesis, and losses to litterfall and mortality, including from fire [37,38]. In addition to the dynamics of leaf carbon pool, feedbacks between carbon cycle and nitrogen cycle are also considered, which would also limit the rate of carbon accumulation in canopy leaf carbon [18].