## 3 Results
### Effects of LAI and Climatic Factors on WUE  
The study area was divided into high-correlation (G\({}_{01}>0.7\)) and low-correlation (G\({}_{01}<0.7\)) areas according to threshold (0.7) of the grey relational degree between the WUE and the influencing factors [37]. Generally speaking, there was significant regional differences in the grey relational degrees between the WUE and the influencing factors (Figure 6). The grey relational degree between the WUE and LAI was between 0.475-0.998, averaging 0.816 (Figure 6a). The high-correlation areas accounted for 85.87% of the study area, and meadow, shrub and cultivated vegetation were major vegetation types with a mean LAI of about 0.6. The grey relational degree between the WUE and LAI in Erdos and middle Xilingol League was higher than 0.9. The low-correlation areas accounted for 14.13%, mainly including cultivated vegetation in south Bayannur, meadow in southeast Chifeng and forest and swamp in central Hulunbuir with a mean LAI of over 1.5. Areas with a large LAI had a low grey relational degree between the WUE and LAI. These areas often had high precipitation or were mainly irrigated agricultural areas, indicating a weak influence of LAI on the WUE under sufficient water content. The values of the grey relational degree between WUE and the following climate factors were as follows in decreasing order: precipitation (0.730), relative humidity (0.689), wind speed (0.649), temperature (0.640), water vapor  
Figure 5: Spatial distribution of (**a**) WUE variation trends and (**b**) variation types for the period of 2001–2018 over Inner Mongolia. SD = significant decrease; ISD = insignificant decrease; ISI = insignificant increase; SI = significant increase. pressure (0.634), and sunshine duration (0.606). The areal proportions of high correlation between the WUE and the climate factors in descending order were: precipitation (70.72%), relative humidity (41.25%), wind speed (18.76%), temperature (9.51%), water vapor pressure (8.61%), and sunshine duration (3.05%). The areas of high correlation between the WUE and precipitation were concentrated in east Bayannur, north Baotou, north Ulanqab, Xilingol League and west Hulunbuir (Figure 6b), while those of low correlation were in southeast Chifeng, northeast Hulunbuir, south Erdos and south Bayannur. The grey relational degree between the WUE and precipitation in meadow in the southeast Chifeng was relatively low. The areas of high correlation between the WUE and relative humidity were mainly concentrated in north Baotou, north Ulanqab, central Xilingol League, north Chifeng, Hinggan League and southwest Hulunbuir (Figure 6c), while those of low correlation were in southwest Erdos, Hohhot, south Ulanqab, south Tongliao as well as west and north Hulunbuir. The areas of high correlation between the WUE and wind speed were mainly distributed in Erdos, Hohhot and central Hulunbuir, with some areas scattered in northwest Xilingol League and south Chifeng (Figure 6d). The areas of high correlation between the WUE and temperature were in north Hulunbuir, south Chifeng and east Erdos (Figure 6e). The areas of high correlation between the WUE and water vapor pressure were in east Chifeng and central Tongliao (Figure 6f). The areas of high correlation between the WUE and sunshine duration were only scattered in west Hohhot, southeast Chifeng and north Hulunbuir (Figure 6g). After the comprehensive comparison of the grey relational degree between the WUE and all the factors (Figure 6h), LAI was the most strongly correlated with WUE in about 78.54% of the study area. The proportions of areas where precipitation, relative humidity, water vapor pressure, wind speed, temperature and sunshine duration were most strongly correlated with WUE were 10.23%, 2.99%, 2.74%, 2.56%, 2.13% and 0.92%, respectively. Precipitation was the most strongly correlated factor with WUE in the central and north Hulunbuir, as temperature was in the northeast Hulunbuir.