## 3 Results
### Relationship Between the SIF Yield and Photosynthetic Efficiency  
Similar to the diurnal patterns of AF760, Fy760 showed different responses to the APAR variation in the morning and afternoon for the soybean measurements but tracked positively with the diurnal dynamics of APAR for the sweet potato measurements (Figure 4a,b), which further revealed that different crops show a different regulation of the SIF efficiency when the PAR changes. Simultaneously with the regulation of the SIF efficiency, the PSII operating efficiency also changed continually but irregularly with the APAR variation. The regulation of the PSII operating efficiency was also discrepant between soybean and sweet potato. For the soybean, the value of \(F^{\prime}_{q}/F^{\prime}_{m}\) progressively increased no matter how the APAR changed, while the \(F^{\prime}_{q}/F^{\prime}_{m}\) in sweet potato tracked well with the variation of APAR, except for the measurements in the early morning (Figure 4). These complicated responses of the SIF efficiency and PSII operating efficiency to the APAR variations made their relationship indistinct; therefore, a linear relationship was not found between them in our study (Figure 5a). Figure 3: Diurnal patterns of F760, AF760 and simultaneously measured PAR in (a) soybean and (b) sweet potato. This nonlinear relationship between the SIF efficiency (Fy760) and PSII operating efficiency (\(F_{q}^{\prime}/F_{m}^{\prime}\)) can be explained by the concurrent variation in non-photochemical quenching (\(F_{m}/F_{m}^{\prime}-1\), \(NPQ\)), which is another way of excess energy dissipation. In our study, we found that \(NPQ\) was also gradually changing in the diurnal pattern but without any correlation with the APAR variation (Figure 4), which also resulted in the unfixed relationship between the \(F_{q}^{\prime}/F_{m}^{\prime}\) and \(NPQ\) for different crops (Figure 5b). It can be seen that the \(NPQ\) in soybean tended to decrease first and then increase with an increased \(F_{q}^{\prime}/F_{m}^{\prime}\) (Figure 5b). In contrast, the \(NPQ\) in sweet potato exponentially declined when the \(F_{q}^{\prime}/F_{m}^{\prime}\) was increasing (Figure 5b). Since APAR is used for photochemistry (with efficiency \(\Phi_{P}\)), nonradiatively as heat and SIF (with efficiency \(\Phi_{N}\) and \(\Phi_{F}\), respectively), the sum of the above efficiency can be approximatively expressed as: \(\Phi_{P}+\Phi_{N}+\Phi_{F}=1\)[39]. Thus, the relationship between the SIF yield and PSII operating efficiency was mainly determined by way of \(NPQ\) in relating to the PSII operating efficiency. This finding of an unfixed and nonlinear relationship between the \(F_{q}^{\prime}/F_{m}^{\prime}\) and \(NPQ\) resulted in the nonlinear relationship between the SIF yield and the \(F_{q}^{\prime}/F_{m}^{\prime}\). Figure 4: Diurnal patterns of (**a**) and (**b**) Fy760 accompanied by the absorbed photosynthetically active radiation (APAR), (**c**) and (**d**) PSII operating efficiency (\(F_{q}^{\prime}/F_{m}^{\prime}\)) accompanied by \(NPQ\) in soybean (upper panel) and sweet potato (lower panel). The values of APAR in left column was calculated based on Equation (2). Figure 5: Relationship of the PSII operating efficiency (\(F_{q}^{\prime}/F_{m}^{\prime}\)) with (**a**) the solar-induced chlorophyll fluorescence (SIF) yield (Fy760) and (**b**) non-photochemical quenching (\(F_{m}/F_{m}^{\prime}-1\), \(NPQ\)) based on the diurnal measurements of soybean (black) and sweet potato (red). The measurements of gas exchange could provide further insights into the photosynthetic processes responsible for the nonlinear relationship between the SIF efficiency and the \(F_{q}^{\prime}/F_{m}^{\prime}\). Similar to Fy760, the net photosynthetic rates (A) of soybean and sweet potato were not linearly related to the variation in PAR (Figure 6a,b). This response might be attributed to the complicated variations in intercellular carbon dioxide concentration (Ci) and stomatal conductance (gsw).