## 2 Materials and Methods
### Multi-Angle Observations of Canopy PRI and SIF  
A multi-angle spectra system was mounted at 4 m above the ground on an adjacent tower in a paired maize field (details in [PERSON] et al. [50]). The system consisted of two spectrometers (HR2000+ and QEPro, Ocean Optics, Dunedin, FL, USA) for measuring high-resolution spectra, which can be used for retrieving PRI and SIF, respectively. The single optical path of each spectrometer was separated into two paths and switched via a \(2\times 2\) shutter and a Y-shaped splitter fiber (Ocean Optics, Dunedin, FL, USA), pointing towards the sky (up-looking) and the canopy (down-looking) directions to measureirradiance and radiance signals, respectively. In the up-looking direction, cosine-corrected optics (CC3-UV-S, Ocean Optics, Dunedin, FL, USA) were used to collect the hemispherical irradiance signals with a large field of view (FOV) of 180\({}^{\circ}\); while the canopy radiance in the down-looking direction was measured using a bare fiber with a small FOV of 25\({}^{\circ}\). The down-looking fiber optics were installed on a rotating device PTU-D46 (FLIR Motion Systems Inc., Burlingame, CA, USA) to collect canopy radiance from different view angles. In each half-hour observation cycle, the two spectrometers synchronously measured the canopy radiance at varying view azimuth angle (VAA) moving from 60\({}^{\circ}\) to 300\({}^{\circ}\) at a 10\({}^{\circ}\) step. The view zenith angle (VZA) was dynamically set as the solar zenith angle (SZA) and was set as 40\({}^{\circ}\) when SZA \(>\) 40\({}^{\circ}\) to avoid the measurements at large VZA [51]. Radiometric calibration was conducted before the growing season using an integrated sphere (Labsphere, North Sutton, NH, USA) and a tungsten halogen light source (HL-CAL-2000, Ocean Optics, Dunedin, FL, USA) [52].  
While utilizing the irradiance and radiance signals, the observed PRI (PRI\({}_{\text{obs}}\)) was estimated by the reflectance of 531 nm (R\({}_{531}\)) and 570 nm (R\({}_{570}\)) as follows:  
\[\text{PRI}_{\text{obs}}=\frac{\text{R}_{531}-\text{R}_{570}}{\text{R}_{531}+ \text{R}_{570}} \tag{4}\]  
R\({}_{531}\) was calculated using the average reflectance of three wavebands centered on 530.87 nm, 531.33 nm, and 531.79 nm; R\({}_{570}\) was calculated using the average reflectance of three wavebands centered on 570.07 nm, 570.53 nm, and 570.98 nm.  
In comparison with the estimation of GPP, SIF was estimated from incident irradiance (I) and canopy radiance (L) around the O\({}_{2}\)-A absorption using Spectral fitting methods (SFM). The methods assume that suitable mathematical function (e.g., polynomial) fitted by wavelength (\(\lambda\)) can be used to describe the spectral characteristics of reflectance (R) and fluorescence (F) [53; 54; 55]. Here, we assumed the linear function of \(\lambda\) could represent R and F [50]. The measured canopy radiance (L(\(\lambda\))) was expressed as follows, the observed SIF (SIF\({}_{\text{obs}}\)) was calculated using the function F(\(\lambda\)):  
\[\left\{\begin{array}{l}\text{L}(\lambda)=\frac{\text{R}(\lambda)\text{I}( \lambda)}{\pi}+\text{F}(\lambda)+\varepsilon(\lambda),\lambda\in[\lambda_{1},\lambda_{2}]\\ \text{SIF}_{\text{obs}}=\text{F}(\lambda_{\text{m}})\end{array}\right. \tag{5}\]  
where \(\varepsilon(\lambda)\) was the bias of observed and modeled radiance. \(\lambda_{1}\) and \(\lambda_{2}\) were specified as 757 and 768 nm, respectively. \(\lambda_{\text{m}}\) represented the wavelength with the minimum irradiance in the O\({}_{2}\)-A absorption band around 760 nm.  
The highly frequent (around 1 min) multi-angle observed PRI and SIF at each view angle were used to calculate the canopy PRI and SIF. The half-hourly canopy PRI (PRI\({}_{\text{can}}\)) was calculated as a simple arithmetic average using all available multi-angle PRI\({}_{\text{obs}}\) within 30 min intervals to match half-hourly EC flux data. SIF\({}_{\text{obs}}\) were also averaged every half an hour to obtain the canopy SIF (SIF\({}_{\text{can}}\)) for half-hourly comparison with GPP.