## 2 Materials and Methods
### Data Processing and Analysis  
Apparent SIF yield and SIF yield were always used in most previous relevant literatures to indicate the dynamics of photosynthesis. Their relationships with growth and environmental parameters were also considered in our study. Apparent SIF yield is generally calculated as SIF/PAR, where PAR is the incident photosynthetically active radiation. However, in our study, PAR values were only collected during wheat growth season by using a radiance sensor (S-LIA-M003, Onset Computer Corporation), and unfortunately the records of PAR during maize growth season were missing due to damage to the sensor. Therefore, the ratio of F760/SWR (referred to as AF760 hereafter) was used to represent apparent SIF yield due to the fact that PAR was about 47% of the total incoming solar radiation [26]. For the SIF yield, it could not be calculated according to the commonly used method of SIF/APAR (APAR is the PAR absorbed by canopy), since APAR was not directly collected in our study as well. An alternative method that is expressed as the ratio of F760 to canopy radiance flux at 685 nm (F760/L685, Fy760) was used to represent SIF yield. This method is developed based on the assumption that L685 (radiance near the O\({}_{2}\)-B absorption band) is mainly linked to the variation of APAR [39].  
Pearson correlation analysis and principal component analysis (PCA) were employed to explore the relationships of F760, AF760, and Fy760 with growth and environmental parameters. Pearson correlation is often used and easily understood, while the PCA method in our study is not easy to understand because the utilized PCA method is mainly used in numerical ecology to indicate the relationship among variables [40; 41]. In its application, PCA generally reduces a multidimensional sample space into fewer dimensions (i.e., principal components) by assuming a linear relationship between each dimension with all variables [42]. Results of PCA, including the samples and variables, can be plotted on a two-dimensional PCA projection: a biplot [41]. The biplot not only groups the samples, but also determines relationships between samples and variables. Relationships among variables were indicated by vector angles: if the vector angle between two variables is acute, they are positively correlated; else if the angel is obtuse, these two variables were negatively correlated (the right angle represents uncorrelated) [41]. From the biplot, we can sort out a pattern of variables among the samples and provide relational information about the variables [43]. In our study, we only analyzed relationships between variables. Furthermore, all averaged hourly and daily measurements were used in the analysis of the Pearson correlation and PCA for separately indicating the relationship of SIF with growth and environmental parameters at diurnal and seasonal scales. PCA was performed using the package \"vegan\" (version 2.5-5, [[https://mirrors.tuna.tsinghua.edu.cn/CRAN/](https://mirrors.tuna.tsinghua.edu.cn/CRAN/)]([https://mirrors.tuna.tsinghua.edu.cn/CRAN/](https://mirrors.tuna.tsinghua.edu.cn/CRAN/))) of R software (version 3.4.0, [[https://www.r-project.org/](https://www.r-project.org/)]([https://www.r-project.org/](https://www.r-project.org/))) [44], and the Pearson correlation coefficients (r) were calculated using the R software built-in package \"stats\".