## 2 Materials and Methods
### Measurements of Solar-Induced Fluorescence  
An automatic long-term SIF observation system was fixed to an 18-m high platform on the flux tower at the DM site (Figure 1). The SIF observation system mainly consisted of a customized Ocean Optics QE65 PRO spectrometer (Ocean Optics, Dunedin, FL, USA), an automatic refrigeration system, and a control PC for data collection and storage. The Ocean Optics QE65 PRO spectrometer covers 645-805 wavelength ranges with a high spectral resolution of around 0.34 nm, a sampling interval of about 0.17 nm, and a signal to noise ratio (SNR) higher than 1000 [27]. The spectrometer splits the optical signal into two channels to measure both downwelling incident radiance and upwelling radiance simultaneously using a cosine corrector (CC3-3-UV-S, Ocean Optics, Inc., Dunedin, FL, USA) and a conical fore-optic (bare fiber), respectively. In the upward direction, the cosine corrector can capture the downwelling incident radiance with a large field view (FOV) of 180\({}^{\circ}\), and the conical fore-optic can capture the upward radiance with a small FOV of about 20\({}^{\circ}\) when pointing at the maize canopy. The measuring mode was set to a'sandwich' type: that is, by alternately opening the up and down channels, the downwelling solar irradiance was first collected, the upwelling irradiance of the canopy was then measured, and the downwelling solar irradiance was finally collected again (Figure 2). To reduce the effects of weather changes caused by the time delay, we calculated the average of the two downwelling solar irradiance measurements. Generally, it takes about 15 s at midday for the observation system to complete a spectral measurement cycle, and about 2 min at sunrise or sunset. Before each of the measurements, the integrated time was optimized depending on the light intensity, and it was generally 0.7-6 s.  
SIF retrieval algorithms are generally based on the Fraunhofer Line Discrimination (FLD) principle. In this study, we applied the 3 FLD approach to acquire the SIF signals, assuming that the fluorescence and reflectance varied linearly: this approach has been proven to be more robust and accurate than the improved FLD method [57; 58]. The 3 FLD method needs spectral data from three bands, including one absorption band and the two shoulders of the absorption band. Although some studies have reported that the red band SIF may contain more information about photosystem II (PS II), the canopy structure and varying solar-view geometries have more complex effects on the red SIF than on the far-red SIF [9; 59]. Therefore, in order to better rule out the influence of retrievals and the strong re-absorption, we only considered the relationship between canopy GPP and far-red SIF. For the O\({}_{2}\)-A band, we employed 761 nm as the inside channel, and 755 nm and 771 nm were taken as the shorter- and longer-wavelength channels, respectively. The weights for the two shoulders of the absorption band can be expressed as  
\[w_{755}=\frac{\rho_{771}-\rho_{761}}{\rho_{771}-\rho_{755}}\wedge w_{771}=\frac{ \rho_{761}-\rho_{755}}{\rho_{771}-\rho_{755}}, \tag{6}\]  
where \(w\) is the weight coefficient, \(\rho\) represents the reflectance, and the subscripts indicate the wavelengths adjacent to the absorption valley. Then, the \(\mathit{SIF}\) can be calculated using  
\[\mathit{SIF}=\frac{(E_{755}w_{755}+E_{771}w_{771})L_{761}-E_{761}(L_{755}w_{75 5}+L_{771}w_{771})}{(E_{755}w_{755}+E_{771}w_{771})-E_{761}}, \tag{7}\]  
where \(E\) represents the solar irradiance, and \(L\) represents the canopy reflectance. In addition, as the strong absorption effect at the O\({}_{2}\)-A absorption bands has an obvious influence on SIF retrieval, atmospheric correction is required even for tower-based SIF observations made with a sensor located tens of meters above the canopy [60].