## 4 Discussion
Therefore, canopy temperature is highly sensitive to changes in plant water status [21]. This study found that on sunny days, after using PWSI to modify the water stress scalar in the LUE models, the accuracy of simulating GPP in all models was significantly improved, as were the explanatory powers for the GPP variations. In most models, the fitting curves of the simulated and measured values are very close to the 1:1 line (Figures 7 and 8). This verifies that the quantification method of the water stress scalar is the main error source of the seven LUE models, and the traditional water stress indicators cannot accurately indicate the limitation of water stress on photosynthesis. PWSI, which contains both soil and atmospheric drought information, had the best performance in indicating the limitation of water stress on photosynthesis. This result is consistent with the findings of [PERSON] et al. [24] and [PERSON] et al. [23]. However, on cloudy days, the radiant energy reaching the ground will change drastically because of cloud cover, which will affect the energy balance of the canopy, cause the canopy temperature to change rapidly, and reduce the performance of PWSI in indicating the water status of plants. Therefore, on cloudy days, the LUE models modified based on the PWSI exhibited poor performance (Figure 7). [PERSON] et al. [73] pointed out that it is not suitable to observe the canopy temperature for plant water status detection when the solar radiation changes rapidly. According to the PWSI and EF behaviors, the performance of water stress indicators varied significantly under different weather conditions, especially the optical indicators based on remote sensing. These indicators are always considered superior to atmospheric and soil moisture indicators; however, frequent cloud contamination limits their application in LUE models [7; 30; 31]. Therefore, weather factors must be considered when improving the performance of LUE models. Most LUE models include two or three environmental stress factors, such as MOD17, which considers water and temperature stress factors based on VPD and T\({}_{\text{a}}\), and the GLO-PEM model based on SWC, SHD, and T\({}_{\text{a}}\). In terms of integrating environmental stress factors, most LUE models use the multiplication method to integrate environmental stress factors (such as MOD17, GLO-PEM, and VPM models). However, some studies have shown that the minimum method based on [PERSON]'s law introduced into the model is also useful (e.g., EC-LUE and 3-PG models) [7]. Our study found that the performance of the ECM-LUE model was better than that of the EC-LUE model on cloudy days, and the performance of the ECM-LUE model modified by PWSI was better than that of the EC-LUE model modified by PWSI on sunny days (Figures 6-8). However, [PERSON] et al. [12] found that the minimum method was better than the multiplication method for integrating multiple environmental stress factors in the VPM and EC-LUE models. They pointed out that, in the growing season, the LUE mainly depends on water conditions rather than temperature conditions, resulting in the minimum method working well. However, the occurrence of drought stress is often accompanied by high-temperature stress, and the co-effects of water and temperature stress can significantly reduce the photosynthetic efficiency of plants compared to single-factor stress [74; 75; 76]. The minimum approach based on Liebig's law only considers one of the environmental stresses, which underestimates the impact of environmental stress on LUE, resulting in an overestimation of GPP by the LUE model. This is the main reason that the simulated values of the modified MOD17 and EC-LUE models were higher than the measured values in our study (Figure 7a,e and Figure 8a,c). Another point that should be noted is that the water stress scalar (EF) in the EC-LUE model does not vary from 0 to 1, which may be the that why the EC-LUE model with the minimum method to integrate multiple environmental stress factors also performs well in some studies [6; 12].