## 2 Materials and Methods
### Sensitivity Analysis  
Sensitivity analysis is a crucial step in the calibration process of the model parameters [35], which serves to evaluate the influence of each parameter in the model on the output results. The EFAST method is often used by researchers for sensitivity analysis in Biome-BGC models [11; 12; 13]. In this study, the EFAST method was adopted for the sensitivity analysis of the Biome-BGC model to quantify the contribution of input parameters to GPP and NEP, filtering out the parameters that have a high influence on the model output results for subsequent parameter optimization. EFAST is a global sensitivity analysis method proposed by [PERSON] based on the Fourier amplitude sensitivity test (FAST) method combined with [PERSON]'s method [36; 37; 38]. This method is based on variance theory, which considers that the output results of the model are not only influenced by the parameters themselves but also correlated with the interactions between parameters. Through the decomposition of the variance, the contribution to the total variance is generated by the independent and mutual coupling of parameters, respectively, namely, the sensitivity index.  
EFAST defines the total variance of the model outputs as the sum of the model parameters themselves and the interactions between their different parameters, as shown in Equation (1) [39]:  
\[V_{Y}=\sum_{i}V_{i}+\sum_{i}\sum_{j>i}V_{ij}+\sum_{i}\sum_{j>i}\sum_{k>j}V_{ijk}+ \cdots+V_{12\cdots n} \tag{1}\]  
where \(V_{Y}\) is the total variance of the model output; \(V_{i}\) is the variance of individual factors; and \(V_{ij}\)-\(V_{(12\..n)}\) is the variance of interactions between parameters.  
The total order index (\(S_{iT}\)) of parameter \(X_{i}\) is the sum of the first-order sensitivity index (\(S_{i}\)) of the parameter and each order sensitivity index of the parameter in interaction with other parameters, which can be represented as [39]:  
\[S_{iT}=S_{i}+S_{ij}+\cdots+S_{12\cdots i\cdots n} \tag{2}\]  
where \(S_{i}=V_{i}/V_{Y}\) is the direct contribution of parameter \(X_{i}\) to the total variance of the model output results, namely, the first-order sensitivity index; \(S_{ij}=V_{ij}/V_{Y}\) is the influence degree of the interaction between parameters \(X_{i}\) and \(X_{j}\) on the output results of the model, namely, the second-order sensitivity index, and so on.  
Here, we conducted a sensitivity analysis for the ecophysiological parameters of the model, which was implemented with the EFAST module of the sensitivity and uncertainty analysis software SimLab 2.2. In accordance with the fluctuation range of the input parameters, the Monte Carlo method was used to randomly sample each parameter [40], and we set the number of samples for each parameter to 130. (EFAST prescribes that the number of samples for each parameter should be more than 65.) The Biome-BGC model was executed in batches according to the generated input parameters. After that, we simulated the GPP and NEP over 30 years (1989-2018) and calculated the average value of multiple years, which were input to SimLab to obtain the sensitivity index of each parameter. Based on the total order index ranking, we divided the parameters into two groups. Among them, the top five parameters in the ranking of the total order index were the sensitive parameters; otherwise, they were insensitive parameters. Additionally, the key sensitivity parameters were those ranked in the top five for both the total order index and the first-order sensitivity index.