## 2 Materials and Methods
### Parameter Sensitivity Analysis and Inverse Estimation of Key Parameters  
The physiological parameters related to SIF and GPP simulation are summarized in Table 1. The modules rely on different empirical parameterizations, which are based on a limited set of leaf-level data under some specific conditions. To examine the capability of the SCOPE model to predict SIF at satellite overpass time and assess how well the key parameters such as the V\({}_{\text{cmax}}\) of RuBisCO can be constrained by OCO-2 SIF and flux tower \begin{table}
\begin{tabular}{c c c c c c} \hline
**Parameters** & **Acronyms** & **Definition** & **Initial Values** & **Value Ranges** & **References** \\ \hline Chlorophyll content & Cab & \(\mu\)g cm\({}^{-2}\) & 40 & 0–100 & [24] \\ Carotenoid content & Cca & \(\mu\)g cm\({}^{-2}\) & 10 & 0–30 & [24] \\ Dry matter content & Cdm & mg cm\({}^{-2}\) & 5 & 0–20 & [24] \\ Equivalent water thickness & Cw & mg cm\({}^{-2}\) & 20 & 0–100 & [62] \\ Senescent material & Cs & - & 0.1 & 0–12 & [62] \\ Anthocyanins & Cant & \(\mu\)g cm\({}^{-2}\) & 0 & 0–40 & [59] \\ Leaf structure parameters & N & - & 1.4 & 1–3 & [24] \\ Maximum carboxylation capacity & V\({}_{\text{cmax}}\) & \(\mu\)mol m\({}^{-1}\) s\({}^{-1}\) & 30 & 0–200 & [62] \\ Stomatal conductance parameter & m & - & 8 & 2–20 & [62] \\ Extinction coefficient for canopy & Kv & - & 0.64 & 0–0.8 & [62] \\ Dark respiration parameter & Rd & - & 0.015 & 0.001–0.03 & [62] \\ Fluorescence quantum efficiency & fge & - & 0.01 & 0.001–0.03 & [63] \\ Leaf area index & LAI & m\({}^{2}\) m\({}^{-2}\) & 3 & 0–7 & [24] \\ Leaf angle distribution parameter a & LIDFa & - & \(-\)0.35 & \(-\)1–1 & [24] \\ Leaf angle distribution parameter b & LIDPb & - & \(-\)0.15 & \(-\)1–1 & [24] \\ \hline \end{tabular}
\end{table} 
Table 1: Physiological and structural parameters in the PROSAIL and Soil Canopy Observation, Photochemistry and Energy Fluxes (SCOPE) model. Figure 2: Seasonality of (**a**) leaf area index (LAI) and (**b**) chlorophyll (Cab) at the Park Falls site retrieved by inverting the PROSAIL model with Moderate Resolution Imaging Spectroradiometer (MODIS) reflectance (bands 1–7). GPP, we conducted a parameter sensitivity analysis and estimated the key parameters. Three different objective functions were used to assess the sensitivity of physiological parameters: optimization using SIF as the constraint (F\({}_{SIF}\), Equation (4)), optimization using GPP as the constraint (F\({}_{GPP}\), Equation (5)), and optimization using both SIF and GPP as constraints (F\({}_{SIF\_GPP}\), Equation (6)). The performance of the model was evaluated using the coefficient of determination (R\({}^{2}\)) of the linear regression between the measured and estimated values of SIF and GPP, measuring how much variation in the observations was explained by the models. The root mean square error (RMSE) was also used to evaluate the performance of the model. We minimized the following objective functions, respectively. \[\mathrm{F}_{SIF}=\sqrt{\frac{1}{m}\sum_{i=1}^{m}(SIF_{i,sim}-SIF_{i,obs})^{2}} \tag{4}\]  
\[\mathrm{F}_{GPP}=\sqrt{\frac{1}{m}\sum_{i=1}^{m}(GPP_{i,sim}-GPP_{i,obs})^{2}} \tag{5}\]  
\[\mathrm{F}_{SIF\_GPP}=0.5\times\left(\frac{\mathrm{F}_{GPP}}{std_{GPP}}+ \frac{\mathrm{F}_{SIF}}{std_{SIF}}\right) \tag{6}\]  
where \(SIF_{i,sim}\) and \(SIF_{i,obs}\) are the simulated and observed SIF at each time step, respectively; and \(GPP_{i,sim}\) and \(GPP_{i,obs}\) are the simulated and observed GPP at each time step, respectively; m is the number of timesteps; and \(std_{GPP}\) and \(std_{SIF}\) are the standard deviations of the observed GPP and SIF, respectively. The cost function for the optimization based on both SIF and GPP as constraints (Equation (6)) used the summed normalized errors of SIF and GPP to represent the total model error in simulating both SIF and GPP. To identify the key parameters that are responsible for most of the variability in GPP and SIF simulated by SCOPE, both GSA method [31] and local SA approach were performed.