## 3 Results and Discussion
### Comparison of Relative Effects of Critical Factors on ELUE by Path Analysis  
The path analysis showed that the controlling variables considered in this study can account for 73.7%, 85.3%, 75.3% and 65.5% of the total ELUE variation (Figure 10), while relative effects of unconsidered variables on ELUE (i.e., nutrition content in soil/leaf, CO\({}_{2}\) concentration, etc.) still accounted for 26.3%, 14.7%, 24.7% and 34.5% in the rice, soybean, maize and winter wheat fields, respectively. The quantified standardized total effects of the controlling variables on ELUE in four agroecosystems are shown in Figure 11. NDVI is the most critical controlling variables for ELUE in all the fields. Previous researchers also demonstrated that ELUE variation patterns  
Figure 10: The explanation rate of the variables on crop ecosystem light use efficiency based on path analysis. Figure 9: The variation of soil water content (SWC), ecosystem light use efficiency (ELUE) and gross primary production (GPP) after precipitation at a representative (**a**) soybean site (US-CRT) and (**b**) winter wheat site (CH-Oe2). were mainly determined by vegetation index (LAI, NDVI, EVI etc.) [4; 7]. [PERSON] et al. (2013) reported that the seasonal variations of GPP were mainly exerted by LAI on carbon assimilation [80]. Analysis done by a process-based model also showed that vegetation indices had significant positive effects on GPP [81], as canopy development can influence the biophysical properties of vegetation, carbon and the absorption of energy as discussed in Section 3.2.1 [59; 82; 83]. In addition to NDVI, there was one variable (T\({}_{\text{a}}\)) in the rice fields, three variables (EF, g\({}_{\text{c}}\), and VPD) in the soybean fields, four variables (EF, g\({}_{\text{c}}\), T\({}_{\text{a}}\) and R\({}_{\text{n}}\)) in the maize fields and two variables (EF and g\({}_{\text{c}}\)) in the wheat fields that significantly affected ELUE (\(p<0.01\), Figure 11). Crop growth sometimes suffered adverse environmental conditions, such as high T\({}_{\text{a}}\), low water availability, etc. T\({}_{\text{a}}\) was generally considered as an essential driver of GPP when analyzing biomes and increasing importance in the coldest and energy-limited areas [7; 84]. Therefore, the warming climate may increase GPP and ELUE in an energy-limited area. However, we found that the total effects of EF on ELUE were higher than that of T\({}_{\text{a}}\) among the typical crops, except for paddy rice, which indicated that water availability was more important than T\({}_{\text{a}}\) in controlling agroecosystem ELUE. A similar conclusion was also found in the Mediterranean environment, where water stress significantly affected ELUE inter-annual variations, while T\({}_{\text{a}}\) marginally affected ELUE [85]. Our analysis supports the idea that ELUE is constrained by water availability more than temperature at the typical crop sites, except for paddy rice. Water availability affects nearly all aspects of plant growth and most physiological processes. Meanwhile, the stress response depends on intensity, rate, duration and the stage of plant growth [7; 7; 73]. Plants close their stomates, and thereby lower g\({}_{\text{c}}\), to prevent further water loss by transpiration in the early drought stages [86]. Consequently, the supply of CO\({}_{2}\) for the carboxylation through stomatal is reduced and thereof GPP. Studies also demonstrated the decrease in APAR was likely caused by photoprotective mechanisms such as changes in leaf inclination/leaf rolling as the cumulative deficit on soil water [10; 87]. However, the long-term effect of soil water deficit on canopy assimilation is a limitation in canopy structure development (i.e., LAI,  
Figure 11: The standardized total effects of the controlling variables on ELUE. R\({}_{n}\), PAR, T\({}_{\text{a}}\), VPD, NDVI, g\({}_{\text{c}}\) and EF are net radiation, photosynthetically active radiation, air temperature, normalization difference vegetation index, canopy conductance and evaporation fraction, respectively.