## 3 Results
### Impact of Bio-Meteorological Factors on the Spatial Variation of WUE  
Factor detection showed that all eight bio-meteorological factors (AT, PR, HUM, WS, SR, VT, SM, and LAI) had a significant impact on the spatial variation of WUE (\(p<0.01\)). As far as the whole study area is concerned, the impact of temperature on the spatial variation of WUE was the largest, and the explanatory power was up to 66.1%. The following factors, in order, were specific humidity, vegetation type, and LAI, with an explanatory power of 52.6%, 34.2%, and 29.6%, respectively. Shortwave radiation, precipitation, and wind speed explained only 17.3%, 16.6%, and 16.2%, respectively. The explanatory power of soil moisture was the lowest (5%).  
However, the explanatory power of factors for the spatial variation of WUE varied somewhat across regions (Figure 12). For example, the explanatory power of shortwave radiation varied considerably in different zones. It was 7.5% in the eastern QM, whereas as high as 30.9% in the western QM. In terms of precipitation, its explanatory power was stronger in desert regions with arid climates, such as the western QM and HC. Nevertheless, it was weaker in the relatively humid eastern and central QM (only 6.3% in the central QM). The explanatory power of LAI was close in different zones, with \(q\) values ranging from 0.169 to 0.376 and was the weakest in western QM where vegetation is sparse. The explanatory power of temperature was higher than other bio-meteorological factors. It reached over 42% in all sub-areas and even up to 59.3% in HC Oases.  
An interaction detector was used to assess the explanatory power of factor interactions on the spatial variation of WUE (Figure 13). If the \(q\) value of the two-factor interaction is greater than the maximum of the \(q\) values of factors \(X_{1}\) and \(X_{2}\) but less than the sum of both, it implies that the two factors are mutually enhanced. If the \(q\) value of the two-factor  
Figure 12: Factor detector-based explanatory power ranking of bio-meteorological variables for WUE in different regions. AT: air temperature; PR: precipitation; HUM: specific humidity; WS: wind speed; SR: shortwave radiation; VT: vegetation type; SM: soil moisture; LAI: leaf area index.  
interaction is greater than the sum of the \(q\) values of \(X_{1}\) and \(X_{2}\), the two factors are non-linearly enhanced. The results of this paper showed that the \(q\) value of any two-factor interaction on the spatial variation of WUE was greater than that of a single factor, which means that the explanatory power of a single factor could be enhanced when interacting with others. The interaction of the two factors on the spatial variation of WUE was greater than the impact of either factor acting alone. In 35% of the cases, the \(q\) values of the two-factor interaction were higher than the total \(q\) values of the two single factors, which showed that the two-factor interaction was non-linearly enhanced.  
The impact of various bio-meteorological factors on the WUE of different vegetation types was investigated using the Geodetector method (Figure 14). The magnitude of the impact of bio-meteorological factors on WUE varied with vegetation type. It was found, however, that temperature was the most critical factor for most vegetation types.  
Figure 13: The explanatory power of interaction between factors for spatial stratified heterogeneity of the study area. The underlined numbers in the figure show that the interaction of the two factors is non-linearly enhanced, and the numbers with no underline suggest that the interaction of the two factors is mutually enhanced.