## 1 Introduction  
Gross primary productivity (GPP) is the amount of carbon dioxide (CO\({}_{2}\)) uptake via photosynthesis by vegetation per unit of time [1]. GPP is a key parameter for understanding global carbon exchange and effectively mitigating climate change [2], and is even viewed as an important basis for measuring ecological services and products such as fiber, wood, and food [3; 4]. However, annual and interannual GPP estimations have greater uncertainties in different regions and ecosystem types [5] than the uncertainties at a global scale [6; 7]. GPP estimation models are generally classified as data-driven, process-based, and remote-sensing models [8; 9; 10; 11]. Furthermore, remote-sensing models are divided into light use efficiency (LUE) models [12; 13] and vegetation index models, which are both favored by numerous researchers due to their relatively simple theories, practical applications, and easily accessible model driving data at the global scale [14; 15]. LUE models based on LUE and photosynthetically active radiation absorbed by the vegetation canopy (APAR), such as the MOD17 GPP model [16], are easy to implement and have great potential for exploring the temporal and spatial dynamics of global or regional GPP [17; 18; 19; 20]. Therefore, LUE models are suitable for the study of continuous spatiotemporal changes in GPP [21]. LUE models have been used for widespread estimation of GPP [9; 22; 23; 24; 25], of which the classical fundamental theory is as follows [8; 26]:  
\[GPP=PAR\times FPAR\times\varepsilon_{\max}\times\sigma \tag{1}\]  
where \(PAR\) is the incoming photosynthetically active radiation (MJ m\({}^{-2}\)), \(FPAR\) is the fraction of \(PAR\) absorbed by the vegetation canopy, \(\varepsilon_{max}\) is theoretically the maximum LUE (g C MJ\({}^{-1}\)), and \(\sigma\) represents the scale of environmental stress factors such as soil water and air temperature on \(\varepsilon_{max}\), ranging from 0 to 1. Recently, various LUE models have shown major differences in the constraint of \(\varepsilon_{\max}\) from environmental stress factors and APAR calculations [4]. Most models assume that the canopy is a large leaf that equally utilizes direct and diffuse radiation and that GPP increases linearly with APAR [27]. Nevertheless, there is a difference between the LUE values of sunlit and shaded leaves in that they are restricted by the maximum carboxylation rate and maximum electron transport rate, respectively [28; 29; 30]. Compared to sunlit leaves, shaded leaves absorb only diffuse radiation, resulting in low APAR [31] values due to the direct radiation limitation of sunlit leaves. Consequently, neglecting the distinct difference in APAR values between sunlit and shaded leaves will lead to errors in GPP estimation [4]. An accurate estimation of canopy-level GPP must separate the canopy into sunlit and shaded leaves [27; 30]. The MOD17 GPP model underestimates the GPP in dense vegetation regions due to its insufficient consideration of shaded leaves [32; 33], indicating that the GPP estimation is affected by the canopy structure of vegetation, such as sunlit and shaded leaves, in LUE models [34; 35; 36]. The two-leaf light use efficiency (TL-LUE) model [4] separates the canopy into sunlit and shaded leaves by the method proposed in the Boreal Ecosystem Productivity Simulator (BEPS) [29], which performed well in 298 site-year validation data from the FLUNNET2015 dataset and outperformed the MOD17 GPP model in various ecosystems [36]. Hence, the TL-LUE model has received attention in the study of remote sensing of vegetation. In the TL-LUE model, the vegetation canopy is divided into sunlit and shaded leaves based on the foliage clumping index (CI), which qualifies the degree of leaf gathering relative to a random distribution within the specific canopy structure [37] and is a core variable for describing the canopy structure of vegetation [38] and retrieving the leaf area index (LAI), one of the key parameters in LUE models.