## 1 Introduction
To our knowledge, only the photochemical reflectance index (PRI), which is based on the sensitivity of the reflectance at 531 nm to xanthophyll pigments, has been shown to be sensitive to tracking actual photosynthesis through its correlation with the non-photochemical quenching (NPQ) [30]. The PRI was designed to track NPQ that is related to the de-epoxidation cycle of xanthophyll at leaf level [30]. The potential of PRI as a remote sensing proxy of photosynthetic capacity has been demonstrated [31]. However, the PRI has also been proven to be very sensitive to soil background, canopy structure and viewing angle [32]. Additionally, PRI has been shown to be controlled by the changes in leaf pigments rather than NPQ over seasonal scales [33]. Unlike the PRI, the SIF signal is emitted by the photosynthetic machinery of vegetation and is thus linked to the actual photosynthesis. Although canopy SIF can also be affected by canopy structure [34], viewing angle [35] and leaf pigment contents [36], SIF observations can provide an additional way to track the functional status of plant photosynthesis. Recent field studies have demonstrated that SIF shows strong links to the GPP at the canopy level [25; 37; 38; 39]. As SIF be successfully retrieved using orbiting platforms such as the Japanese Greenhouse gases Observing SATellite (GOSAT) [23; 40], the Scanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) [41], the Global Ozone Monitoring Experiment-2 (GOME-2) [42], and the Orbiting Carbon Observatory-2 (OCO-2) [43], high correlations between SIF and GPP at ecosystem, landscape and regional scales have been shown by [PERSON] et al. [23], [PERSON] et al. [24; 44], [PERSON] et al. [7], and [PERSON] et al. [45], and simple regression models between remotely sensed SIF and GPP have been established. On the other hand, SIF has also been considered to be more sensitive in tracking the GPP than the traditionally used normalized difference vegetation index (NDVI) and the enhanced vegetation index (EVI) [34; 46]. In addition, some studies have also shown the potential use of SIF data to calibrate parameters (maximum carboxylation capacity, \(V_{\text{cmax}}\)) in the photosynthesis model and provide an accurate estimation of agricultural productivity [47; 48]. Despite the experimental evidence of the direct and highly linear correlation between SIF and GPP, the applications of SIF-based GPP models are relatively rare when compared to other GPP models due to data availability and quality. Moreover, little research has been conducted to compare the performances of SIF-based models and other GPP models. To the best of our knowledge, there is only one study that has compared SIF-based, LUE-based, and process-based GPP models [49], in which they used satellite-derived data combined with field observations to derive the daily GPP of crops. However, some uncertainties arise due to spatial mismatches between satellite remote sensing data and EC footprints and temporal mismatches between instant SIF and daily GPP measurements. These mismatches should be reduced before assessing the performance of GPP models. In this context, the objective of this study is to compare the performance of three GPP modeling approaches, SIF-based, LUE-based MuSyQ-GPP and process-based BEPS models, in estimating the diurnal courses of GPP for cropland. We focus on field observations with relatively small spatial and temporal scales in this study, and data-driven models are beyond the scope of our research. This study lays the foundation for accurately estimating the GPP of croplands at larger spatial and temporal resolutions.