## 3 Results
### Model Performances under Different Weather Conditions  
Based on \(K_{\rm t}\), weather was divided into sunny (\(K_{\rm t}\geq 0.7\)), moderate (\(0.3<K_{\rm t}<0.7\)), and cloudy days (\(K_{\rm t}\leq 0.3\)). The simulated performances of the optimal big-leaf and two-leaf LUE-GPP models under different weather conditions were analyzed (Figure 5). The performances of the optimal big-leaf LUE-GPP model varied under different weather conditions, and the slopes of 1.142, 0.861, and 0.667 between \(GPP_{\rm OBL}\) and \(GPP_{\rm EC}\) and RMSE values of 1.49, 2.80, and 4.47 g C m\({}^{-2}\) d\({}^{-1}\) for cloudy, moderate, and sunny weather, respectively, were obtained (Figure 5a, Table 7). Thus, the optimal big-leaf LUE-GPP model overestimated \(GPP\) on sunny days but underestimated \(GPP\) on cloudy days. Similar trends were observed in the other big-leaf LUE-GPP models (Figure 6). The optimal big-leaf LUE-GPP model only considered the optimal combination of various environmental constraints,  
Figure 4: The determination coefficients (\(R^{2}\)) between gross primary productivity (\(GPP\)) derived from the EC system and the simulated GPP with the integrated stress (\(T_{\rm s}\) and \(W_{\rm s}\)) using the (**a**) minimum method (Min (\(T_{\rm s}\), \(W_{\rm s}\)) or (**b**) multiplication method (\(T_{\rm s}\times W_{\rm s}\)) in different big-leaf light use efficiency-based GPP models. Figure 5: Relationship between the gross primary productivity (\(GPP\)) derived from EC measurement (\(GPP_{\rm EC}\)) and estimated by the (**a**) optimal big-leaf light use efficiency-based \(GPP\) model (\(GPP_{\rm OBL}\)) and (**b**) two-leaf LUE-GPP model (\(GPP_{\rm TL}\)) under sunny days (\(K_{\rm t}\geq 0.7\)), moderate days (\(0.3<K_{\rm t}<0.7\)), and cloudy days (\(K_{\rm t}\leq 0.3\)). although the overall simulation accuracy was improved, the model could not consider the estimation error under different weather conditions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Weather Conditions** & **BLO** & **OBL-P** & **OBL-E** & **TL** & **TL-P** & **TL-E** \\ \hline K\({}_{\text{t}}\leq 0.3\) & 1.49 & 1.63 & 1.44 & 1.42 & 1.49 & 1.62 \\
0.3 \(<\) K\({}_{\text{t}}\) \textless{} 0.7 & 2.80 & 2.54 & 2.46 & 1.95 & 2.02 & 1.94 \\ K\({}_{\text{t}}\geq 0.7\) & 4.47 & 3.72 & 2.73 & 2.10 & 2.16 & 2.02 \\ ALL & 2.58 & 2.36 & 2.14 & 1.78 & 1.84 & 1.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The difference of root mean squared errors (RMSE, g C m\({}^{-2}\) d\({}^{-1}\)) without and with incorporating clearness index (K\({}_{\text{t}}\)) into the optimal big-leaf (OBL) and two-leaf LUE-GPP (TL) models in the form of exponential (E) or power functions (P). Figure 6: The relationship between the gross primary productivity derived from EC measurement (\(GPP_{\text{EC}}\)) and estimated GPP by the six big-leaf light use efficiency-based GPP model (EF-LUE in (**a**), MODIS in (**b**), VPM in (**c**), MVPM in (**d**), TEC in (**e**), and CASA in (**f**)) under sunny days (K\({}_{\text{t}}\geq 0.7\)), moderate days (0.3 \(<\) K\({}_{\text{t}}\) \textless{} 0.7), and cloudy days (K\({}_{\text{t}}\leq 0.3\)). The slopes between \(G\)\(P\)\(P\)\({}_{\rm EC}\) and \(G\)\(P\)\(P\) simulated by the two-leaf LUE-GPP model (\(G\)\(P\)\(P\)\({}_{\rm TL}\)) for sunny, moderate, and cloudy conditions were 0.923, 1.033, and 0.952, with RMSE values of 1.42, 1.95, and 2.10 g C m\({}^{-2}\) d\({}^{-1}\), respectively (Figure 5b, Table 7). The two-leaf LUE-GPP model improved the consistency of the model performances under different weather conditions, as it considered both the diffusion effect and differences in the _LUE_ of shaded and sunlit leaves. The slopes between \(G\)\(P\)\({}_{\rm EC}\) and \(G\)\(P\)\(P\) for shaded leaves simulated by the two-leaf GPP model were 12.228, 10.339, and 8.322, whereas those for sunlit leaves were 1.164, 1.355, and 1.424, for sunny, moderate, and cloudy conditions, respectively (Figure 7).