## 3 Results
### Optimization of the LUE-GPP Model by Introducing \(K_{t}\)  
Various models that consider the dynamic _LUE_ well simulated the seasonal variations in \(G\)\(P\)\(P\)\({}_{\rm EC}\) during the growing seasons (Figure 8). The \(R^{2}\) between \(G\)\(P\)\(P\)\({}_{\rm OBL\)-P}\) and \(G\)\(P\)\({}_{\rm EC}\) was 0.748 (\(p<\) 0.01), and the slopes between \(G\)\(P\)\(P\)\({}_{\rm OBL\)-P}\) and \(G\)\(P\)\({}_{\rm EC}\) for sunny, moderate, and cloudy conditions were 0.728, 0.939, and 1.246, with RMSE values of 1.63, 2.54, and 3.72 g C m\({}^{-2}\) d\({}^{-1}\), respectively (Figure 9a, Table 7). The \(R^{2}\) between \(G\)\(P\)\({}_{\rm OBL\)-E}\) and \(G\)\(P\)\({}_{\rm EC}\) was 0.762 (\(p<\) 0.01), and their respective slopes were 0.878, 0.908, and 0.900, for sunny, moderate, and cloudy conditions, with RMSE values of 1.44, 2.46, and 2.73 g C m\({}^{-2}\) d\({}^{-1}\), respectively (Figure 9b). Thus, the \(K_{t}\)-based dynamic LUE-GPP model with exponential form greatly improved the inconsistent performance of the traditional big-leaf LUE-GPP model under different weather conditions, achieving an overall high simulation accuracy. Figure 7: Relationship between the gross primary productivity (\(G\)\(P\)\(P\)) derived from the EC measurement (\(G\)\(P\)\({}_{\rm EC}\)) and estimated (**a**) shade leaves \(G\)\(P\)\((G\)\(P\)\({}_{\rm TL\)-sh}\) and (**b**) sunlit leaves \(G\)\(P\)\((G\)\(P\)\({}_{\rm TL\)-su}\) by the two-leaf light use efficiency-based \(G\)\(P\)\(P\)\(P\) model under sunny days (\(K_{t}\geq 0.7\)), moderate days (\(0.3<K_{t}<0.7\)), and cloudy days (\(K_{t}\leq 0.3\)). Figure 8: Seasonal variations of the measured and estimated gross primary productivity (\(GPP\)) during 2018–2020 in a humid region orchard ecosystem. \(GPP\) was estimated by constructing clearness index-based dynamic LUE with power function and exponential function formulations in big-leaf (\(GPP_{\text{OBL-P}}\) in (**a**), \(GPP_{\text{OBL-E}}\) in (**b**)), and two-leaf light use efficiency-based \(GPP\) model (\(GPP_{\text{TL-P}}\) in (**c**), \(GPP_{\text{TL-E}}\) in (**d**)), respectively. Figure 9: Relationship between the gross primary productivity derived from the EC measurement (\(GPP_{\text{EC}}\)) and the estimated by introducing clearness index (\(K_{\text{t}}\))-based dynamic LUE in optimal big-leaf LUE-GPP model with power function (\(GPP_{\text{OBL-P}}\), (**a**)) and exponential function (\(GPP_{\text{OBL-E}}\), (**b**)) under sunny days (\(K_{\text{t}}\geq 0.7\)), moderate days (\(0.3<K_{\text{t}}<0.7\)), and cloudy days (\(K_{\text{t}}\leq 0.3\)). For the two-leaf LUE-GPP model, the \(R^{2}\) between \(GPP_{\text{TL-P}}\) and \(GPP_{\text{EC}}\) was 0.758 (\(p<0.01\)), with slopes of 0.965, 1.013, and 1.000 and RMSE values of 1.49, 2.02, and 2.16 g C m\({}^{-2}\) d\({}^{-1}\) for sunny, moderate, and cloudy conditions, respectively (Figure 10a, Table 7). The \(R^{2}\) between \(GPP_{\text{TL-Z}}\) and \(GPP_{\text{EC}}\) was 0.759 (\(p<0.01\)), with slopes of 0.930, 0.950, and 0.90 and RMSE values of 1.62, 1.94, and 2.02 g C m\({}^{-2}\) d\({}^{-1}\), for sunny, moderate, and cloudy conditions, respectively (Figure 10b). The accuracy and the consistent performance under different weather conditions of the \(K_{\text{t}}\)-based two-leaf LUE-GPP model and the traditional two-leaf model are comparable. Figure 10: Relationship between the gross primary productivity derived from the EC measurement (\(GPP_{\text{EC}}\)) and the estimated total (\(GPP_{\text{TL-P}}\) in (**a**), \(GPP_{\text{TL-E}}\) in (**b**)), shade leaves \(GPP\) (\(GPP_{\text{TL-P-sh}}\) (**c**), \(GPP_{\text{TL-E-sh}}\) (**d**)), and sunlit leaves \(GPP\) (\(GPP_{\text{TL-P-sh}}\) in (**e**), \(GPP_{\text{TL-E-sh}}\) in (**f**)) by introducing clearness index (\(K_{\text{t}}\))-based dynamic LUE into the two-leaf LUE-GPP model with power function and exponential function under sunny days (\(K_{\text{t}}\geq 0.7\)), moderate days (\(0.3<K_{\text{t}}<0.7\)), and cloudy days (\(K_{\text{t}}\leq 0.3\)).