Assessing the Potential for Photochemical Reflectance Index to Improve the Relationship between Solar-Induced Chlorophyll Fluorescence and Gross Primary Productivity in Crop and Soybean  
[PERSON]  
1 State Key Laboratory of NBC Protection for Civilan, Beijing 102205, China; [EMAIL_ADDRESS] (J.C.)1 State Key Laboratory of NBC Protection for Civilan, Beijing 102205, China; [EMAIL_ADDRESS] (J.C.)1 State Key Laboratory of NBC Protection for Civilan, Beijing 102205, China; [EMAIL_ADDRESS] (J.C.)1 State Key Laboratory of NBC Protection for Civilan, Beijing 102205, China; [EMAIL_ADDRESS] (J.C.)1 State Key Laboratory of NBC Protection for Civilan, Beijing 102205, China; [EMAIL_ADDRESS] (J.C.)1 State Key Laboratory of NBC Protection for Civilan, Beijing 102205, China; [EMAIL_ADDRESS] (J.C.)1 State Key Laboratory of NBC Protection for Civilan, Beijing 102205, China; [EMAIL_ADDRESS] (J.C.)1 State Key Laboratory of NBC Protection for Civilan, Beijing 102205, China; [EMAIL_ADDRESS] (J.C.)1 State Key Laboratory of NBC Protection for Civilan, Beijing 102205, China; [EMAIL_ADDRESS] (J.C.)1 State Key Laboratory of NBC Protection for Civilan, Beijing 102205, China; [EMAIL_ADDRESS] (J.C.)1 State Key Laboratory of Civilan, Beijing 102205, China; chenjidai@aircas. energy [5]. The three energy-dissipating pathways compete with one another and display various patterns in response to the constantly changing external environment. SIF and GPP have an inherent theoretical foundation for coupling since APAR drives both SIF and GPP. In reality, the mechanism for using SIF to predict GPP is the link between the linear electron transfer rate (ETR) coupled with carboxylation processes and SIF [6]. According to the light-use-efficiency framework, GPP is computed as the product of APAR and light use efficiency (\(LUE_{p}\)), which is expressed as follows:  
\[GPP=APAR\times LUE_{p} \tag{1}\]  
Likewise, canopy observed SIF at a certain direction (\(SIF_{c}\)) can be represented as the product of APAR and the apparent yield for fluorescence, which consists of the escaping probability (\(f_{esc}\)) at the same direction and the photosystem fluorescence yield (\(\Phi_{f}\)):  
\[SIF_{c}=APAR\times\Phi_{f}\times f_{esc} \tag{2}\]  
Due to the complex horizontal and vertical structures of the canopy, the emitted SIF by leaves would experience the scattering of the reabsorption effects before sensors capture [7; 8]. Additionally, because of the limited field of view (FOV) of the sensors, the hemispherical SIF emission can only be captured in the observation direction. Based on a multi-angle observational experiment, [PERSON] et al. [9] revealed that SIF and reflectance have an angle effect that is similar. Numerous studies have shown that using the spectral invariant theory, the escaping probability of SIF at one angle can be approximately estimated by the canopy measured reflectance at the same angle divided by the product of its interception and leaf albedo [10; 11; 12; 13]. To obtain the total SIF (\(SIF_{t}\)) with more physiological information, the impacts of observed angle and canopy structure should be eliminated:  
\[SIF_{t}=\frac{SIF_{c}}{f_{esc}} \tag{3}\]  
As a result, the relationship between \(LUE_{p}\) and \(\Phi_{f}\) is the primary factor for linking GPP to SIF. However, the aforementioned LUE framework for linking SIF to GPP has clear disadvantages in describing various photosynthetic processes because it simplifies the photosynthetic process, including the light and dark reactions, which may differ in response to environmental stress [6]. Environmental variables such as air temperature, soil moisture, and light intensity have an influence on the SIF-GPP relationship. Despite the fact that APAR drives both SIF and GPP, some studies found there was a stronger relationship of APAR to SIF than that of APAR to GPP, and the ratio of GPP to SIF decreased with light intensity. These findings may be related to the differences between light and dark reactions or the irregularly varied proportion of energy allocated to SIF and photosynthesis [14].