## 3 Methodology
### Model Parameterization
#### 3.3.1 Sensitivity Analysis  
Global sensitivity analysis typically requires a large amount of computational resources and is quite time-consuming. To overcome this limitation, we used a combination of qualitative sensitivity analysis and quantitative sensitivity analysis to identify those parameters that have a significant impact on the GPP simulation. Specifically, we first collected the probability distribution function (PDF) of the ecophysiological parameters of C3 grass from relevant literature, as shown in Table 1. Subsequently,we used the [PERSON] qualitative analysis method [57] to screen out those ecophysiological parameters that have negligible effects on the GPP simulation and set them to the default values. Finally, we used the [PERSON]' quantitative analysis method [58] to evaluate the influence of each of the remaining parameters on the GPP simulation and further determine which parameters to be calibrated. A detailed description of these steps is as follows. * Distribution of ecophysiological parameters  
In addition to the two phenological parameters for prescribing the phenological states within the model, the Biome-BGC includes a total of 28 tunable ecophysiological parameters for C3 grass. In addition, there is no evidence of periodic fires in alpine grasslands of the TP in the past few decades, so we set the fire mortality parameter to zero and did not calibrate it. Finally, a total of 27 parameters are left for the next sensitivity analysis, and their PDFs were collected from relevant literature, as shown in Table 1.
* Qualitative sensitivity analysis based on the Morris method  
The Morris method is a typical One-at-a-Time sensitivity analysis method [57]. Due to its low computational cost, it is often used as the first step in global sensitivity analysis to remove parameters that have negligible effects on the simulated results. Two sensitivity indices, mean (\(\mu\)) and standard deviation (\(\sigma\)), are calculated by the Morris method to qualitatively evaluate the relative importance of each parameter. To perform the analysis, the Morris method needs to be executed \(r\times(n+1)\) times, where \(r\) represents the number of trajectories and \(n\) represents the number of input parameters. In this study, \(r\) was set to 10 [56] and the value of \(n\) was 27. In addition, we used the average of the annual GPP between 1982 and 2015 as the output variable of the Morris method and set a low threshold value of \(\mu=0.05\) to distinguish between influential and non-influential parameters. That is, parameters with \(\mu\leq 0.05\) were considered to have negligible effects on the GPP simulation and were excluded from the next quantitative analysis. Further information on the [PERSON] method can be found in the Supplementary Materials. * Quantitative sensitivity analysis based on the Sobol' method  
The Sobol' method is a widely used quantitative global sensitivity analysis method, which can decompose the variance of the model output into the contribution of each input parameter and their interactions [58]. Given that \(V_{Y}\) represents the total variance of the model output, it can be decomposed into the following components:  
\[V_{Y}=\sum_{i}V_{i}+\sum_{i}\sum_{j>i}V_{ij}+\sum_{i}\sum_{j>i}\sum_{k>j}V_{ ijk}+\cdots+V_{1,2,\ldots,n} \tag{2}\]  
where \(V_{i}\) represents the variance explained by the \(i\)th input parameter, \(V_{ij}\) represents the variance explained by the interactions between the \(i\)th and \(j\)th input parameters, and \(n\) represents the number of input parameters. Based on Equation (2), the first order sensitivity index can be defined as \(S_{i}=V_{i}/V_{Y}\), and the higher order sensitivity indices can be defined as \(S_{ij}=V_{ij}/V_{Y}\), \(S_{ijk}=V_{ijk}/V_{Y}\), \(\ldots\), \(S_{1,2,\ldots,i,\ldots,n}=V_{1,2,\ldots,i,\ldots,n}/V_{Y}\). Accordingly, the total order sensitivity index of the \(i\)th parameter can be defined as the sum of its first order sensitivity index and all higher order sensitivity index involving it.