## 2 Materials and Methods
### Parameter Sensitivity Analysis and Inverse Estimation of Key Parameters
In this study, we applied the [PERSON]'s method [31] (i.e., extended Fourier amplitude sensitivity test, EFAST), a quantitative variance-based SA method that can identify the effects of both parameters and the interactions of parameters on model simulations [31]. The EFAST combined [PERSON]'s method and the Fourier amplitude sensitivity test (FAST) together [32], which can effectively quantify the main sensitivity effects (i.e., the first-order sensitivity index, SI 1 st, representing the contribution of each input variable to the variance of model output), and total sensitivity effects of input variables (i.e., the total sensitivity index, SI total, the contribution to the total variance by the interactions between parameters) [32]. The sensitivity indices, SI 1 st and SI total, are expressed as follows:  
\[\mathrm{SI}\ \mathrm{1 st}=\ \frac{V_{i}}{V(Y)}=\frac{V[E(Y|X_{i})]}{V(Y)} \tag{7}\]  
\[\mathrm{SI}\ \mathrm{total}=\ SI\ \mathrm{1 st}+\sum_{j\
eq i}SI_{ij}+\ldots= \frac{E[V(Y|X_{\sim i})]}{V(Y)} \tag{8}\]  
where \(V_{i}\) is the partial variance of the \(i\)-\(th\) parameter on output \(Y\); \(V(Y)\) is the total unconditional output variance; \(S_{ij}\) is the contribution to the total variance by the interactions between parameters \(i\) and \(j\); and \(X_{\sim i}\) denotes variation in all input parameters. Following previous studies [32; 64], the sensitivity indices of the EFAST can be derived at the cost of nk model evaluations for robust results (n is the sample size and k is the number of input parameters). Aside from the GSA approach that is based on the SIMLAB, we also used a local SA approach, the \"one-factor-at-a-time\" (OAT) approach to analyze the sensitivity of SIF and GPP simulations to V\({}_{\mathrm{cmax}}\) and light conditions. Since GOME-2 and OCO-2 SIF products are based on different wavelengths, we conducted a sensitivity analysis with different V\({}_{\mathrm{cmax}}\) values at different wavelengths to identify the feasibility and sensitivity of satellite-derived SIF in constraining GPP simulations. With the parameter sensitivity analysis, we selected the key parameters for GPP and SIF simulations, and inverted these parameters by minimizing the differences between the observed and modeled values. The SCOPE model employs complicated radiative transfer processes [15], which has a high demand for computational resources and thus hinders the estimation of V\({}_{\text{Cmax}}\) easily. To reduce the computational burden, we also used an adaptive surrogate modeling-based optimization method [38] to optimize the key parameters of the model in simulating GPP and SIF. Although the surrogate-based method might not be able to provide exactly the same optimal solutions as the original models, it has been proven to be effective and efficient in obtaining approximate optimal parameters for land surface and radiative transfer models [36; 37; 62]. The surrogate-based method can acquire acceptable optimized results with fewer simulations. Following a previous study [62], we applied an adaptive, nonlinear regression method, Gaussian processes regression (GPR), to approximate and replace the original computation model with the surrogate model [38]. Previous studies [37; 62] showed that the GPR method outperformed other surrogate methods. According to the results of the parameter sensitivity, we selected the key physiological parameters (i.e., V\({}_{\text{Cmax}}\), Rd, and fqe) that are related to SIF and GPP estimation in the model for optimization. The SCE method [35] was used to find the optimal parameters. Similar to the parameter sensitivity analysis, the estimation of the parameters was also based on three different objective functions using SIF and GPP to optimize parameters separately and also using both SIF and GPP to constrain parameters at the same time. We used the data from 2015 to 2017 for calibration, and the remaining data for validation. We evaluated the performance of the SCOPE model for simulating SIF using both OCO-2 and GOME-2 SIF observations.