## 1 Introduction  
As the largest component of the terrestrial carbon cycle [1; 2; 3], the accurate estimation of terrestrial gross primary productivity (GPP) is vital for understanding global carbon cycle processes, climate changes, and ecosystem services [1; 4; 5; 6]. To date, GPP estimation is difficult, as no direct measures are available at regional and global scales. The eddy covariance flux tower provides a direct measure of carbon dioxide (CO\({}_{2}\)) between the land surface and the atmosphere that can be used for indirect GPP estimation [7]. Flux-based GPP has been widely used as reference data for calibrating and validating GPP models [8; 9; 10; 11; 12]. With the development of GPP estimation theories and methods in recent decades, researchers have developed many remote sensing models for GPP estimation [3; 13; 14]. Light use efficiency (LUE) models have been widely used to estimate terrestrial GPP at regional and global scales due to their theoretical basis, few parameters, and high practicality [15]. Since [PERSON] [16] proposed the concept of LUE, following the theoretical basis of LUE [17], researchers have optimized the input parameters for calculating LUEand developed dozens of LUE models [2]. As a key parameter of the LUE model, the maximum LUE (LUE\({}_{\text{max}}\), same as \(\mathcal{E}_{\text{max}}\)) is crucial for the accurate estimation of GPP and for the interpretability of the LUE model. The \(\mathcal{E}_{\text{max}}\) in existing LUE models can be roughly divided into three main categories: (1) global constant \(\mathcal{E}_{\text{max}}\), such as the constant \(\mathcal{E}_{\text{max}}\) used in C-Fix [18] and EC-LUE [12]; (2) constant \(\mathcal{E}_{\text{max}}\) for each type, such as the constant \(\mathcal{E}_{\text{max}}\) varying from vegetation types in MOD17 [17] and VPRM [19], the constant \(\mathcal{E}_{\text{max}}\) for C3 and C4 in VPM [10; 20; 21] and TEC [22], the constant \(\mathcal{E}_{\text{max}}\) for sunlit and shaded leaves in TL-LUE [23] and DTEC [24], and the constant \(\mathcal{E}_{\text{max}}\) for different phenological stages in TS-LUE [25]; and (3) dynamic \(\mathcal{E}_{\text{max}}\), such as the cloudiness index-regulated dynamic \(\mathcal{E}_{\text{max}}\) in CFlux [26], CI-LUE [27], and CI-EF [28], and the spatial dynamic \(\mathcal{E}_{\text{max}}\) based on the enhanced vegetation index (EVI) and visible albedo [29]. With the development of LUE models, an increasing number of researchers have considered \(\mathcal{E}_{\text{max}}\) as a dynamic value rather than a constant. Dynamic \(\mathcal{E}_{\text{max}}\) is more consistent with vegetation physiology, and studies have proven that in their own study area, dynamic \(\mathcal{E}_{\text{max}}\) performed better than static \(\mathcal{E}_{\text{max}}\) in GPP estimation [30; 31]. Although researchers have proposed methods to estimate dynamic \(\mathcal{E}_{\text{max}}\), the nonlinear response of vegetation photosynthesis to solar radiation variation was rarely considered in these studies. As the energy source of vegetation photosynthesis, solar radiation variation directly regulated the vegetation \(\mathcal{E}_{\text{max}}\). Most LUE models implied a linear relationship between GPP and PAR, which apparently ignored the saturation of vegetation photosynthesis to solar radiation under high solar radiation. In fact, vegetation photosynthesis varies with the dynamics of solar radiation [32]. For the low radiation situation, especially when vegetation photosynthesis is limited only by radiation, photosynthesis would increase linearly with increasing radiation. For the high radiation situation (plentiful radiation), photosynthesis would become radiation-saturated and no longer respond to the changes in radiation supply [32; 33; 34; 35; 36].