## 2 Materials and Methods  
### Radiative Transfer Process for Tower-Based SIF Observations  
The upwelling radiance at the top of the canopy consists of the contributions from both the reflected radiance and the emitted SIF, as expressed in Equation (1):  
\[L_{canopy}=\frac{E_{canopy}\cdot\rho}{\pi}+F_{canopy}, \tag{1}\]  
where \(L_{canopy}\) is the upwelling radiance at top of the canopy, \(E_{canopy}\) is the downwelling irradiance arriving at the top of canopy, \(\rho\) is the canopy reflectance, and \(F_{canopy}\) is the emitted SIF at the top of the canopy. Therefore, for the retrieval of the SIF, both the upwelling radiance and downwelling irradiance at the top of the canopy are needed. However, for tower-based spectral observations, only the upwelling radiance and downwelling irradiance arriving at the sensor height are available; due to the influence of atmospheric absorption and scattering, these are different from the TOC radiance and irradiance. The upwelling radiance at height \(H\) can be calculated as:  
\[L_{H}=\frac{L_{canopy}\cdot T_{\uparrow}}{1-\rho S}+L_{0}, \tag{2}\]  
where \(L_{H}\) is the upwelling radiance arriving at the observation platform at a height \(H\) above the surface; \(T_{\uparrow}\) is the upward transmittance of the atmospheric radiative transfer from TOC to the height of the tower-based sensor (\(H\)); \(\rho\) is the surface reflectance; \(S\) is the atmospheric spherical albedo; and \(L_{0}\) is the atmospheric path radiance. For tower-based observations, the atmospheric scattering effect between the sensor and surface is relatively weak due to the low height. Therefore, the observed upwelling radiance and downwelling irradiance at the sensor height (L\({}_{sensor}\) and E\({}_{sensor}\)) can be approximately expressed as:  
\[\langle L_{sensor}\rangle=\langle L_{canopy}\cdot T_{\uparrow}\rangle, \tag{3}\]  
and  
\[\langle E_{sensor}\rangle=\langle E_{canopy}/T_{\downarrow}\rangle, \tag{4}\]  
respectively, where \(T_{\uparrow}\) and \(T_{\downarrow}\) are the upward and downward atmospheric total transmittance (including the effects of absorption and scattering) from the TOC to height of the tower-based sensor, respectively, and \(<\)\(>\) represents convolution with the instrument spectral response function (ISRF). As the radiance or irradiance spectra by observed by spectrometers are already convolved with the ISRF, for the atmospheric absorption bands where the transmittance is spectrally unsmooth, it is not possible to calculate the top-of-canopy radiance or irradiance precisely using a fully physical approach due to the mathematical inequality between \(<\)_a\(\cdot\)b\(>\)_ and \(<\)a\(>\)\(<\)b\(>\)[32], especially for data with high spectral resolution (as shown in Figure 1). In this study, to calculate the upward and downward atmospheric transmittances from the TOC to the height of the tower-based sensor, the MODTRAN 5 model was used to simulate the downwelling irradiance and upwelling radiance arriving at the sensor height and at the TOC. Using the MODTRAN simulations, the upward and downward atmosphere transmittances can be calculated as:  
\[T^{\prime}_{\uparrow}=\frac{\langle\text{L}_{sensor}\rangle}{\langle\text{L}_ {canopy}\rangle}, \tag{5}\]  
and  
\[T^{\prime}_{\downarrow}=\frac{\langle\text{E}_{canopy}\rangle}{\langle\text{E }_{sensor}\rangle}, \tag{6}\]  
respectively, where \(T^{\prime}_{\uparrow}\) and \(T^{\prime}_{\downarrow}\) are the upward and downward atmosphere transmittances from the TOC to the sensor height, respectively. It needs to be noted that due to the convolution with the ISRF before the division shown in the equations, \(T^{\prime}\) is not strictly the \"transmittance\". However, for convenience, \"transmittance\" is used to refer to \(T^{\prime}\) in this paper. The upward and downward atmosphere transmittances are related to the atmospheric absorption and scattering effects, which are mainly influenced by the atmospheric pressure, RTPL, and AOD [29].