## 2 Materials and Methods
### Measurements of SIF and VIs  
The automatic spectral monitoring system was used to collect long-time spectral data in contact (Figure 5). The system consists of QEpro (Ocean Optics, Inc., Largo, FL, USA) spectrometer, electronic switch, optical fiber, cosine corrector and so on. The spectrometer is a QEpro with spectral range of 640-800 nm and spectral resolution of 0.35 nm. One fiber is equipped with a cosine corrector at the end and is used to collect downward solar radiation within a field of view of 180\({}^{\circ}\); the other fiber collects upward radiation reflected from the canopy with a field of view of 25\({}^{\circ}\). These two fibers are fixed to a robotic arm that can be rotated by stepper motors to achieve simultaneous acquisition of spectra between different plots. They are placed in a 23 \({}^{\circ}\)C thermostat, which reduces the effect of temperature on the spectrometer. The motor-driven robot arm rotation can continuously collect solar incident spectra and vegetation reflection spectra from four plots.  
The data processing mainly includes dark current correction, Savitzky-Golay (SG) filter, radiation correction, quality control, extraction of SIF and calculation of VIs. The raw data are dark current corrected to eliminate the effect of dark current on the spectral data. After that, the spectral data are filtered using the SG filter method with a quadratic polynomial of 30 \(\times\) 30 window to eliminate the influence of other noise. The spectral data output from this step are radiation corrected to convert solar radiation and vegetation canopy radiation into irradiance (E, mW/m\({}^{2}\)/nm) and radiance (L, mW/m\({}^{2}\)/nm/sr) with energy units, respectively. The SIF is extracted, and the VIs are calculated after quality control.  
In this paper, the Spectral fitting method (SFM) is chosen as the extraction algorithm for SIF. The SFM assumes that both fluorescence values and reflectance changes near the Fraunhofer lines can be fitted by mathematical functions. Since SIF has a certain filling effect on the Fraunhofer lines, the SIF at the Fraunhofer lines can be extracted by algorithmic analysis of the measured vegetation canopy upward radiance in the band within the  
Figure 5: The automatic spectral monitoring system. The system consists of QEpro spectrometer, electronic switch, optical fiber, cosine corrector and so on. T1, T2, T3 and T4 represent well-watered, mild water stress, moderate water stress and severe water stress, respectively.  
absorption line and the simulated downward radiance spectrum. The measured canopy upward radiance L(\(\lambda\)) can be expressed as:  
\[\mathrm{L(\lambda)=r_{MOD}(\lambda)E(\lambda)/\pi+F_{MOD}(\lambda)+\varepsilon( \lambda)=L_{MOD}(\lambda)+\varepsilon(\lambda),} \tag{2}\]  
where rMOD(\(\lambda\)) is the mathematical function of reflectance used for fitting, FMOD(\(\lambda\)) is the mathematical function of fluorescence value used for fitting, LMOD(\(\lambda\)) is the radiance simulated by the algorithm and \(\varepsilon(\lambda)\) is the difference between the observed and fitted values in each band, representing the error of the model in each band. The parameters of rMOD(\(\lambda\)) and FMOD(\(\lambda\)) are obtained by solving the system of linear equations using the least squares method to calculate F and r.  
The NDVI, NDRE and OSAVI are calculated as follows:  
\[\mathrm{NDVI}=(R_{750}-R_{685})/(R_{750}+R_{685}), \tag{3}\]  
\[\mathrm{NDRE}=(R_{790}-R_{720})/(R_{790}+R_{720}), \tag{4}\]  
\[\mathrm{OSAVI}=1.16\times(R_{800}-R_{670})/(R_{800}+R_{670}+0.16) \tag{5}\]