## 2 Materials and Methods
### Measurements of CO\({}_{2}\) Fluxes and Meteorological Variables  
A CO\({}_{2}\) flux observation system based on the eddy covariance (EC) technique [50; 51], was used to measure the CO\({}_{2}\) exchange between the maize canopy and the atmosphere. The EC system was fixed to a 5-m high platform on a flux tower located in the DM irrigation district. The turbulent flux data were sampled at a frequency of 10 Hz [27] and stored by a data logger (CR5000 at YK and GT, Campbell Scientific Inc., Logan, UT, USA). The raw EC data were processed to obtain the net ecosystem exchange of CO\({}_{2}\) (NEE). [PERSON] et al. [52] have reported that the in situ GPP can be estimated from the EC-measured NEE and ecosystem respiration (Re) using the equation GPP = R\(2-\)NEE. In addition, [PERSON] et al. [53] found that the EC-measured net ecosystem exchange (NEE) was equivalent to the night-time ecosystem respiration. [PERSON] et al. [54] also reported that the night-time Re was related to the air temperature relationship. Therefore, we used the night-time partitioning algorithm to partition the GPP (as the measured values of GPP) from the daytime NEE values in this study. In addition, half-hourly mean and daily mean data were processed using the averaging method proposed in [PERSON] et al. [28].  
Environmental and meteorological variables, including the photosynthetically active radiation (PAR), air temperature (AT), and humidity (RH), were continuously observed using an automatic weather station (AWS) system, which was also fixed to the EC flux tower. The AWS included a 3D sonic anemometer (CSAT3, Campbell Scientific Inc., Logan, UT, USA) and an open-path infrared gas analyzer (Li-7500, Li-Cor, Lincoln, NE, USA). PAR and all other meteorological variables were averaged to 30-min values to correspond to the flux observations.  
The vapor pressure deficit (VPD) was quantified as follows [55]:  
\[\mathrm{VPD}=0.611\times\mathrm{e}^{\frac{17.27\times\mathrm{AT}}{\mathrm{AT}} }\times\left(1-\frac{\mathrm{RH}}{100}\right), \tag{1}\]  
where AT is the air temperature and, RH indicates the relative humidity.  
For a better understanding of the effects of different incident light conditions on the SIF-GPP relationship, we considered the overall influence of the solar zenith angle (SZA) and PAR.  
The clearness index (CI) is an important weather metric that is used to describe the relative intensity of solar incident radiation. In this study, CI was quantified as the ratio of the solar radiation  
Figure 1: Location of the study site and observation tower.  
arriving at the top of canopy to the solar radiation at the top of atmosphere. Therefore, half-hourly CI (CI\({}_{30}\)) was calculated using the following formula [56]:  
\[\mathrm{PAR}_{30}=S_{0}\times(1+0.033\times\cos(2\pi\times\mathrm{DOY}/365)) \times\cos(\mathrm{SZA}_{\mathrm{T30}}), \tag{2}\]  
\[\mathrm{CI}_{30}=\mathrm{PAR}_{\mathrm{T30}}/\mathrm{PAR}_{30}, \tag{3}\]  
where \(\mathrm{PAR}_{\mathrm{T30}}\) represents the magnitude of PAR over a 30-min interval, \(\mathrm{PAR}_{30}\) represents the maximal PAR at the top of atmosphere (TOA), also over a 30-min interval, and \(S_{0}\) is the solar constant (1367 W/m\({}^{2}\)).  
The daily CI (CI\({}_{\mathrm{day}}\)) was calculated as follows:  
\[\mathrm{PAR}=\int_{T_{sourise}}^{T_{sonset}}\mathrm{PAR}(t)dt\approx\sum _{T_{sourise}}^{T_{sonset}}\mathrm{PAR}_{\mathrm{T30}}(t)\times\Delta t_{30}, \tag{4}\]  
\[\mathrm{CI}_{\mathrm{day}}=\mathrm{PAR}_{\mathrm{day}}/\mathrm{PAR}_{0}, \tag{5}\]  
where \(\Delta t_{30}\) is the 30-min temporal interval, \(\mathrm{PAR}_{\mathrm{day}}\) is the integrated value of all half-hourly PAR measurements made from sunrise to sunset in Equation (4), and \(\mathrm{PAR}_{0}\) represents the sum of daily TOA PAR [56].