## 2 Materials and Methods
### SIF Simulation by SCOPE Model
#### 2.3.2 Parameter Inversion and SIF Simulation  
The values of some vegetation parameters (see details in Table 2) were retrieved from the reflectance apectra (400 to 850 nm) using the optical radiative transfer routine of SCOPE (i.e., RTMo). We used the numerical optimization (NO) method for the retrieval of required leaf and canopy parameters (Cca, Cdm, Cw, Cs, N, LIDFa and LIDFb). NO method aims to minimize the cost function that quantifies the difference between measured and simulated data by successively changing the input parameters. One set of parameter values were retrieved separately for each of the measurement days, using the canopy reflectance measured at midday [40]. Before the method started, the measured canopy reflectance spectra were linearly interpolated to a resolution of 1 nm to match the simulated one. We used the 'lsqnonlin' function listed in the optimization toolbox of MatlabR2017 and chose the 'Trust Region algorithm' for updating the values of required parameters within the ranges in [41]. With the retrieved vegetation parameters and half-hourly meteorological variables as input, we simulated diurnal cycles of SIF (SIF\({}_{\text{SCOPE}}\), i.e., SIF\({}_{\text{687}}\) and SIF\({}_{\text{760}}\)), GPP (GPP\({}_{\text{SCOPE}}\)) and canopy reflectance (Ref\({}_{\text{SCOPE}}\)) using the full SCOPE model. The SCOPE model outputs the net canopy photosynthesis, representing the total gross photosynthesis minus the CO\({}_{2}\) flux caused by leaf respiration [21]. Therefore, we added the total photosynthesis rate of leaf as one of the outputs for the codes of the biochemical module in the SCOPE model, then the total gross photosynthesis rate of the canopy, known as GPP\({}_{\text{SCOPE}}\), was calculated as the same way of net photosynthesis. The measured GPP\({}_{\text{EC}}\) and Ref were compared with the simulated ones to validate the accuracy of SCOPE model simulation (Figure 2).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variables** & **Definition** & **Unit** & **Range** & **Value/Source** \\ \hline Cab & chlorophyll a and b content & \(\upmu\)g cm\({}^{-2}\) & 0–100 & measurement \\ Cca & carotenoid content & \(\upmu\)g cm\({}^{-2}\) & 0–25 & inversion \\ Cdm & dry matter content & g cm\({}^{-2}\) & 0–0.02 & inversion \\ Cw & equivalent water thickness & cm & 0–0.2 & inversion \\ Cs & brown pigments & a.u. & 0–1 & inversion \\ N & leaf structure parameter & – & 1–3.5 & inversion \\ \hline \multicolumn{4}{c}{_Leaf biochemical_} \\ Vcmax & maximum rate of Rubisco carboxylation & \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\) & 0–200 & literature \\ \multicolumn{4}{c}{(at optimum temperature)} \\ m & Ball-Berry stomatal conductance & – & 5–20 & 9 \\ \hline \multicolumn{4}{c}{_Canopy structure_} \\ LAI & leaf area index & m\({}^{2}\) m\({}^{-2}\) & 0–7 & measurement \\ hc & vegetation height & m & / & measurement \\ LIDFa & leaf inclination & – & \(-\)1–1 & inversion \\ LIDFb & variation in leaf inclination & – & \(-\)1–1 & inversion \\ leafwidth & leaf width & m & / & 0.001 \\ \hline \multicolumn{4}{c}{_Meteorology_} \\ R\({}_{\text{in}}\) & broadband incoming shortwave radiation & W m\({}^{-2}\) & 0–1400 & measurement \\ R\({}_{\text{ii}}\) & broadband incoming longwave radiation & W m\({}^{-2}\) & 200–500 & measurement \\ Ta & air temperature & \({}^{\circ}\)C & \(-\)10–50 & measurement \\ p & air pressure & hPa & 900–1100 & measurement \\ ea & atmospheric vapor pressure & hPa & 0–60 & measurement \\ u & wind speed at canopy height & m s\({}^{-1}\) & 0–50 & measurement \\ SMC & volumetric soil moisture content & \% & 5–55 & measurement \\ \hline \multicolumn{4}{c}{_Geometry_} \\ LAT & latitude & decimal deg & / & measurement \\ LON & longitude & decimal deg & / & measurement \\ tto & observation zenith angle & decimal deg & 0–60 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Major input data of SCOPE model used in our study.