## 2 Materials and Methods
### Estimation of \(q_{\text{L}}\)  
According to [PERSON] et al. [22], \(q_{\text{L}}\) can be modeled as follows:  
\[q_{\text{L}\text{\_MOD}}=\frac{m}{\text{ChFl}_{\text{PSII}}^{1/m}+m} \tag{2}\]  
where \(q_{\text{L}\text{\_MOD}}\) represents the \(q_{\text{L}}\) simulated from ChFl\({}_{\text{PSII}}\); ChFl\({}_{\text{PSII}}\) (\(\mu\)mol m\({}^{-2}\) s\({}^{-1}\)) indicates the broadband chlorophyll fluorescence from PSII; \(m\) is a dimensionless parameter representing the impact of temperature on \(q_{\text{L}}\) simulation. [PERSON] et al. [22] demonstrated that \(m\) can be modeled by a peaked function:  
\[m=m_{\text{opt}}\times\frac{H_{\text{d}}\times\exp\left(\frac{H_{\text{d}} \times\left(T_{\text{leaf},\text{K}}-T_{\text{opt}}\right)}{T_{\text{leaf}, \text{K}}\times\text{K}\times T_{\text{opt}}}\right)}{H_{\text{d}}-H_{\text{a }}\times\left[1-\exp\left(\frac{H_{\text{d}}\times\left(T_{\text{leaf},\text {K}}-T_{\text{opt}}\right)}{T_{\text{leaf},\text{K}}\times\text{K}\times T_{ \text{opt}}}\right)\right]} \tag{3}\]where \(m_{\rm opt}\) represents the \(m\) at the optimal leaf temperature; \(T_{\rm leaf\_K}\) is the leaf temperature in Kelvin (K); \(T_{\rm opt}\) is the optimal leaf temperature (K); \(H_{\rm d}\) and \(H_{\rm a}\) are the rates of decline and increase in the peaked function above and below the optimal leaf temperature (J mol\({}^{-1}\)), respectively; \(R\) is the universal gas constant (8.314 J mol\({}^{-1}\) K\({}^{-1}\)). Here, we utilized the observed data to determine the parameters required for estimating \(q_{\rm L}\), namely \(m_{\rm opt}\), \(H_{\rm d}\), \(H_{\rm a}\), and \(T_{\rm opt}\). Using Equation (2), parameter \(m\) was fitted using \(q_{\rm L}\) and ChlFPSII, both derived from measurements across varying temperatures with the developed system. Subsequently, the fitted values of \(m\) and their corresponding temperatures were used to estimate the parameters in Equation (3), i.e., \(m_{\rm opt}\), \(H_{\rm d}\), \(H_{\rm a}\), and \(T_{\rm opt}\). Below, we describe the methods for obtaining \(q_{\rm L}\) and ChlFPSII from the collected measurements. Based on the lake model, \(q_{\rm L}\) can be derived from PAM parameters (\(q_{\rm L\_PAM}\)) [32]. Specifically,  
\[q_{\rm L\_PAM}=\frac{\rm F_{m}\prime-F_{s}}{\rm F_{m}\prime-F_{o}\prime}\times \frac{\rm F_{o}\prime}{F_{s}} \tag{4}\]  
In this study, ChlFPSII was derived from passive chlorophyll fluorescence (ChFlPSII_fPSII) following the method of [PERSON] et al. [19]:  
\[\rm ChFl_{\rm FPSII\_fPSII}=ChlF_{PS\_\_\lambda}\times f_{\rm FSI\_\_\lambda} \times f_{\rm C\_\lambda} \tag{5}\]  
where ChlFPS\(\_\lambda\) (mW m\({}^{-2}\) nm\({}^{-1}\)) is the total chlorophyll fluorescence at the photosystem level at \(\lambda\) nm;\(f_{\rm FSI\_\_\lambda}\) represents the contribution of PSII to the total chlorophyll fluorescence at \(\lambda\) nm;\(f_{\rm C\_\lambda}\), derived from the elementary fluorescence emission spectrum of PSII (Figure S1), represents the conversion factor translating the photosystem-level PSII chlorophyll fluorescence at \(\lambda\) nm (in units of mW m\({}^{-2}\) nm\({}^{-1}\)) into ChlFPSII_FULL; \(\lambda\) ranges from 640 to 850 nm. ChlFPS\(\_\lambda\) can be derived by correcting leaf-emitted chlorophyll fluorescence spectra (i.e., ChlFUP and ChlFDOWN) [27]:  
\[\rm ChlF_{\_\_\lambda}=\frac{ChlF_{\_\_\lambda}+ChlF_{\_\_\lambda}}{\rho_{ \_\lambda}+\tau_{\_\lambda}}\times\pi \tag{6}\]  
SIF retrieval on ground-based platforms often selects absorption bands with wide and deep absorption features, such as the O\({}_{2}\)-A band (-760 nm) [13]. Therefore, \(f_{\rm FSI}\) at 760 nm (\(f_{\rm PSII\_760}\)) was calculated following the method proposed by [PERSON] et al. [33] to estimate ChlFPSII_fPSII (see Supplementary Materials (Text S1) for details). It should be noted that this study also estimated \(f_{\rm PSII}\) at 740 nm (\(f_{\rm PSII\_740}\)), as satellite measurements typically target solar Fraunhofer lines that are less affected by atmospheric absorption, such as the band near 740 nm [34].