## 2 Methodology
### New FQE Retrieval Method  
Normally, empirical coefficients are used for the simulation because it is difficult to measure the quantum efficiency of PS II and PS I. The peaks represent PS II and PS I (FQE II and I). This is because the signals of PS II and PS I are mixed, so it is difficult to identify each by simple measurements. Moreover, these values may vary with weather conditions such as illumination and temperature; hence, the default FQE II and I do not produce an accurate simulation. The solution to this problem is to add an FQE inversion code to the model and tune the coefficients to the measured fluorescence. In this study, (1) we used a nonlinear least squares regression method to retrieve the parameters of \(C_{ab}\), \(C_{dm}\), \(C_{w}\), \(C_{s}\), \(C_{ca}\), and \(N\) for all the live leaves, and the optical coefficients of PROSPECT-D were used. \(F\) is the calculated spectral data corresponding to a function, and _params0_ is the corresponding measurement parameter. (2) Then, the doubling equations with fluorescence \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Explanation** & **Unit** & **Range** & **Default Value** \\ \hline \(C_{ab}\) & Chlorophyll \(a+b\) content & [\(\mathrm{\SIUnitSymbolMicro g}\) cm\({}^{-2}\)] & 0–100 & 40 \\ \(C_{dm}\) & Dry matter content & [\(\mathrm{\SIUnitSymbolMicro g}\) cm\({}^{-2}\)] & 0–0.5 & 0.012 \\ \(C_{w}\) & Water equivalent thickness, & & \\  & an indicator of leaf water content & [cm] & 0–0.4 & 0.009 \\ \(C_{s}\) & Senescent material & [-] & 0–0.6 & 0 \\ \(C_{ca}\) & Carotenoid & [\(\mathrm{\SIUnitSymbolMicro g}\) cm\({}^{-2}\)] & 0–30 & 5 \\ \(N\) & Leaf mesophyll structure parameter & [-] & 0–4 & 1.5 \\ \(FQE\) II & Fluorescence quantum efficiency for & [-] & 0–0.2 & 0.01 \\  & Photosystem II. & & \\ \(FQE\) I & Fluorescence quantum efficiency for & [-] & 0–0.2 & 0.002 \\  & Photosystem I. & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Vegetation parameters retrieved by the model. Figure 3: (**A**) The sequence of steps in the process of fluorescence simulation; (**B**) reflectivity and transmittance data obtained from measurements as input to the model; (**C**) vegetation parameter data; (**D**) the comparison between simulated and measured chlorophyll fluorescence spectra in the upward and downward direction. included were derived. (3) Finally, the leaf-air interfaces were added again to obtain the final leaf-level fluorescence. (4) The final parameters were obtained using the nonlinear least squares equation. The upper (UB) and lower (LB) boundaries of the corresponding eight parameters were set accordingly. Stokes equations were used to compute the properties of the next \(N-1\) layers (in which \(N\) is real). The cost function was a long array consisting of backward and forward fluorescence for all the leaves. The spectrum of ChlF in each band was derived using the multiplication equation with fluorescence, and the fluorescence curve between 640 nm and 850 nm was obtained. Then, the \"_lsqnonlin_\" function in MATLAB 2013a was used to directly calculate the optimal solution and obtain the parameters. The ChlF between 640 nm and 850 nm was calculated for each spectrum. Overall, by adding this code, the model can effectively invert the FQE values. It is worth paying attention to the FQE values since they are relevant and significant for fluorescence on both sides of the leaf. FQE I controls the fluorescence on the second peak, while FQE II influences the fluorescence on the first peak. In this study, through the inversion of these two parameters, we can obtain the simulated values of FQE I and FQE II to make the simulated fluorescence more accurate. Additionally, the fitted values of FQE I and FQE II can also provide information about the physiology of the plants. In contrast to our research methods, [PERSON] et al. (2016) used a routine called \"RTMF\" of SCOPE to scale the fluorescence from the leaf to the canopy using the output of Fluspect.