## 3 Results
### Parameter Estimation of the SCOPE Model  
The optimized values of the three most important parameters (V\({}_{\rm{Cmax}}\), Rd, and fqe) in SIF and GPP simulations are given in Table 2. These optimized values were used for the SCOPE model simulation at Park Falls. Figure 6 shows the performance of SCOPE for estimating GPP and SIF at Park Falls, which illustrates the seasonal trajectories of GPP and SIF simulated by SCOPE with the objective function of SIF and GPP, respectively. The simulated GPP and SIF were validated with the flux tower-based GPP and OCO-2 SIF data, respectively. We found that the simulated GPP was well correlated with flux tower GPP with R\({}^{2}\) values of 0.45 and 0.88 (RMSE = 2.11 and 1.20 gC m\({}^{2}\) day\({}^{-1}\)) at the daily time scale for the objective function of SIF and GPP, respectively. The simulated SIF was strongly correlated with OCO-2 SIF with R\({}^{2}\) values of 0.77 and 0.76 for the 757 nm wavelength (the RMSE were 0.14 and 0.54 W m\({}^{-2}\) um\({}^{-1}\) sr\({}^{-1}\)), and 0.75 and 0.74 for the 771 nm wavelength (the RMSE were 0.06 and 0.27 W m\({}^{-2}\) um\({}^{-1}\) sr\({}^{-1}\)) for the objective functions of SIF and GPP, respectively. Our results showed that the model performance varied with the objective function: GPP was better simulated with GPP as the objective function, and similarly, SIF was better simulated with SIF as the objective function. \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameters** & **Initial Values** & **Optimized SIF (F\({}_{SIF}\))** & **Optimized GPP (F\({}_{GPP}\))** & **Optimized SIF and GPP (F\({}_{SIF\_GPP}\))** \\ \hline V\({}_{\rm{Cmax}}\) & 30 & 66.648 & 34.22 & 32.88 \\ Rd & 0.015 & 0.021 & 0.002 & 0.006 \\ fqe & 0.01 & 0.008 & 0.030 & 0.008 \\ \hline \end{tabular}
\end{table} 
Table 2: The key physiological parameters related to SIF and GPP estimation in the SCOPE model. The initial values and optimized values using three different objective functions were shown: (1) F\({}_{SIF}\), optimized SIF; (2) F\({}_{GPP}\), optimized GPP; (3) F\({}_{SIF\_GPP}\), optimized SIF and GPP. The units of V\({}_{\rm{Cmax}}\) are μmol m\({}^{-2}\) s\({}^{-1}\), and the units of SIF and GPP are W m\({}^{-2}\) μm\({}^{-1}\) sr\({}^{-1}\) and gC m\({}^{-2}\) day\({}^{-1}\), respectively. Figure 7 shows the performance of the optimized SCOPE model using both GPP and SIF as constraints for simulating GPP and SIF at Park Falls. Generally, the original model based on the default parameters had a good performance. The SCOPE model with the optimized parameters improved the performance of GPP and SIF simulations, with R\({}^{2}\) = 0.90 and RMSE = 0.90 gC m\({}^{-2}\) day\({}^{-1}\) for daily GPP, R\({}^{2}\) = 0.77 and RMSE = 0.15 W m\({}^{-2}\) \(\upmu\)m\({}^{-1}\) sr\({}^{-1}\) for SIF at the 757 nm wavelength, and R\({}^{2}\) = 0.74 and RMSE = 0.07 W m\({}^{-2}\) \(\upmu\)m\({}^{-1}\) sr\({}^{-1}\) for SIF at the 771 nm wavelength. Figure 6: Seasonal trajectories of GPP and SIF simulated by the SCOPE model at the Park Falls site. The black lines stand for the model results with the default parameters. The green lines and blue lines represent the simulations based on the parameters optimized with SIF and GPP, respectively (i.e., using the objective functions of F\({}_{SIF}\) and F\({}_{GPP}\), respectively). The symbols stand for flux tower GPP (**a**) and OCO-2 SIF (**b**,**c**). Figure 7: Seasonal trajectories of GPP and SIF simulated by the SCOPE model at the Park Falls site. The black lines and blue lines represent the modeled GPP based on the default parameters and GPP based on the parameters optimized from both SIF and GPP (using the objective function of F\({}_{SIF,GPP}\)), respectively. The magenta symbols stand for flux tower GPP data (**a**) and OCO-2 SIF observations (**b**,**c**). To further evaluate the performance of the optimized model, we validated the model optimized with both SIF and GPP as constraints independently at the Willow Creek site.