## 3 Results
### Variations in Climatic Elements
Figure 4 depicts the relationships between the EF and the SM and indices representing the conditions of vegetation (GPP, LAI, and NDVI) in the transitional climate zone of China. It shows that there was no significant correlation between the EF and the LAI or the NDVI, with linear correlation coefficients (R\(-\)squared) of 0.11 and 0.02, respectively (Figure 4a,b). Figure 4b,c does not pass the significance test at the 95% confidence level. Although a higher correlation was observed between the EF and the GPP, with an R\(-\)squared value of 0.37 and a confidence level of 95%, it was not very strong (Figure 4c). A further examination of the relationship of distribution between the EF and the SM reveals that the former exhibited relatively consistent patterns of distribution with the latter in both the 0-40 and 40-80 cm layers of soil, suggesting some level of coupling between them (Figure 4d,e). It is evident that the correlations between the EF and the LAI, NDVI, and GPP were weak in the transitional zone of the Chinese summer monsoon, indicating a significantly lower degree of coupling compared with that in the southern Great Plains of the United States [9]. Examining the relationship between the distributions of the EF and SM in different layers in the transitional climate zone of China revealed distinct and regular patterns. The EF had a cubic fitting relationship with the SM in all layers (0-80 cm), similar to the relation of the EF\(-\)SM distribution observed in the Qinghai-Tibet Plateau [21]. By comparison, the EF had a higher correlation with the SM in layers in the range of depth of 0-40 cm, with the fitting coefficients of the cubic distribution ranging from 100 to 200. The coefficients of the fitting of the cubic distribution of the EF and SM ranged from 200 to 300 in layers at depths of 40-60 and 60-80 cm, respectively, indicating a more consistent distribution of the correlation in these layers. Therefore, it is useful to study the SM in the transitional climate zone in two distinct layers, 0-40 and 40-80 cm, to better analyze the coupling relationship between the EF and SM. In addition to directly exploring the fitting relationship between the EF and SM, as shown in Figure 5, [PERSON] et al. [16] discovered that the EF exhibits certain regularities in its  
Figure 4: Responses of the evaporative fraction (EF) to variations in the (**a**) gross primary productivity (GPP), (**b**) leaf area index (LAI), (**c**) Normalized Difference Vegetation Index (NDVI), (**d**) SM at 0–40 cm (SM\({}_{40}\)), and (**e**) SM at 40–80 cm (SM\({}_{80}\)) in the growing season in the transitional climate zone in China. All of the data are the daily values from 2007 to 2012.  
pattern of distribution with a sequence of soil moisture percentiles (SMPs). They segmented the relationship between the EF and SM into two stages based on the SMP. For example, the coupling relationship between the EF and SMP was found to undergo significant changes when the latter approached a critical value of around 30% in the southern Great Plains of the United States [16]. The above analysis shows that the critical value of the SMP in the transitional climate zone of China was close to 35% in both the 0-40 cm layer and the 40-80 cm layer (Figure 6). Figure 6 shows that while the EF increased with the SMP in the 0-40 cm layer, there were significant differences between their trends of growth. The EF exhibited a trend of decrease in the 40-80 cm layer, with an initial increase in the SMP followed by a reduction. A comparison with the original data shows that a sufficient amount of precipitation during the growing season led to a replenishment of the SM. The EF then gradually increased due to evaporation, leading to a gradual loss of the SM and a decrease in the SMP. This decrease in the latter intersected with values of the EF at or near the 35% percentile, indicating a change in their relationship.