###### Abstract  
It has been demonstrated that solar-induced chlorophyll fluorescence (SIF) is linearly related to the primary production of photosynthesis (GPP) in various ecosystems. However, it is unknown whether such linear relationships have been established in senescent crops. SIF and GPP can be expressed as the products of absorbed photosynthetically active radiation (APAR) with the SIF yield and photosystem II (PSII) operating efficiency, respectively. Thus, the relationship between SIF and GPP can be represented by the relationship between the SIF yield and PSII operating efficiency when the APAR has the same value. Therefore, we analyzed the relationship between the SIF yield and the PSII operating efficiency to address the abovementioned question. Here, diurnal measurements of the canopy SIF (760 nm, F760) of soybean and sweet potato were manually measured and used to calculate the SIF yield. The PSII operating efficiency was calculated from measurements of the chlorophyll fluorescence at the leaf level using the FluorImager chlorophyll fluorescence imaging system. Meanwhile, field measurements of the gas exchange and other physiological parameters were also performed using commercial-grade devices. The results showed that the SIF yield was not linearly related to the PSII operating efficiency at the diurnal scale, reflecting the nonlinear relationship between SIF and GPP. This nonlinear relationship mainly resulted from the heterogeneity and diurnal dynamics of the PSII operating efficiency and from the intrinsic diurnal changes in the maximum efficiency of the PSII photochemistry and the proportion of opened PSII centers. Intensifying respiration was another factor that complicated the response of photosynthesis to the variation in environmental conditions and negatively impacted the relationship between the SIF yield and the PSII operating efficiency. The nonlinear relationship between the SIF yield and PSII efficiency might yield errors in the estimation of GPP using the SIF measurements of senescent crops. SIF; GPP; SIF yield; PSII operating efficiency; non-linear relationship; senescent crops 2020 heat dissipation) for the same excitation energy [1]. Pioneer applications of SIF have sought to diagnose the impacts of environmental stress (e.g., water stress, heat stress, and chemical stress) on photosynthesis and plant growth [2; 3; 4; 5; 6; 7]. In recent years, relevant studies have tried to explore the detailed relationship between SIF and the gross primary production of photosynthesis (GPP) over various ecosystems at different spatial-temporal scales [8; 9; 10; 11; 12; 13; 14]. A linear relationship between SIF and GPP was successfully found based on the measurements of spaceborne, airborne, and continuous ground-based conditions [15; 16; 11]. Therefore, such empirical linear relationships of SIF have been successfully used to directly estimate the GPP. The underlying mechanism for the linear relationship between SIF and GPP is interpreted from the rationale of the GPP and SIF. The GPP and SIF can be expressed as \(\text{GPP}=\text{PAR}\times\text{fPAR}\times L\text{{LUE}}_{P}\) and \(\text{SIF}\left(\lambda\right)=\text{PAR}\times\text{fPAR}\times L\text{{ LUE}}_{F}(\lambda)\times f_{\text{esc}}(\lambda)\), where PAR is received photosynthetically active radiation, \(\lambda\) is the spectral wavelength, fPAR is the fraction of absorbed PAR, \(L\text{{LUE}}_{P}\) and \(L\text{{LUE}}_{F}(\lambda)\) are the efficiencies with which the absorbed PAR is used for photosynthesis and re-emitted as SIF at wavelength \(\lambda\), and \(f_{\text{esc}}(\lambda)\) denotes the fraction of SIF escaping from the canopy [1; 15]. Combining these two equations, GPP can be rewritten as \(\text{GPP}=\text{SIF}(\lambda)\times\frac{L\text{{LUE}}_{P}}{L\text{{LUE}}_{F }(\lambda)}\times f_{\text{esc}}(\lambda)\); therefore, the relationship between SIF and GPP is related to the product of \(\frac{L\text{{LUE}}_{P}}{L\text{{LUE}}_{F}(\lambda)}\) and \(f_{\text{esc}}(\lambda)\).