## 3 Results
### Lag Analysis of Temperature, Precipitation, and ET in Annual Drought and Different Seasons  
Figure 13a,c reveal that summer precipitation and TVDI exhibited the highest mean partial correlation value (0.13), with higher values observed in the northeast and central sections compared to the northwest and south, particularly at higher altitudes in Otog Banner and the southern half of Shanxi. Temperature and TVDI displayed the largest mean partial correlation value in winter (0.25), with 30% of the research region exhibiting values above 0.3, primarily in the northeast. The correlation between ET and TVDI had the highest annual mean partial correlation value (0.48), with strong spatial patterns observed in the middle and northern regions, while the south showed a lower correlation. The region  
Figure 12: The significant pixel statistics of the correlation between TVDI and precipitation, temperature, and ET in diverse types of land use and seasons in MUSL. Each legend represents, from left to right, the statistics of significant pixels between TVDI and precipitation, temperature, and evapotranspiration. with the highest partial correlation value between 0.4 and 0.6 encompassed 79% of the area. As indicated in Figure 13d,f, the greatest effect of precipitation was observed in spring (0.3 months), with the minimum effect in autumn. The greatest effect of temperature occurred in autumn (1.2 months), while the minimum occurred at emergence. For ET, the greatest effect was in summer (0.3 months), with the minimum in spring, suggesting that TVDI in spring is more sensitive to precipitation but responds slowly to temperature (1.8 months) and ET (2 months). The standard deviation of TVDI lag time for temperature (0.8) and ET (1.1) was greater in autumn than in spring (0.4). The average lag times of TVDI to the three factors on an annual scale were 2.37 (with a standard deviation of 2.04 months), 2.97 (with a standard deviation of 0.37 months), and 2.58 (with a standard deviation of 0.75 months), respectively, indicating that the lagged response of TVDI to precipitation is more complex. About 42% of the regions showed no observed lag of TVDI to precipitation, while 50% of the regions exhibited a 4-month lag. Only 0.2% of regions had no lag in TVDI for temperature, with 93% showing a 3-month lag. In response to ET, 41% and 53% of regional TVDI exhibited 2-month and 3-month lags, respectively. The 6-month lag region was primarily located in the southern portion of Jingbian County, accounting for about 2% of the entire area, with sporadic distribution in its northern section. Figure 13: (**a–c**) TVDI greatest biased correlation value and (**d–f**) lag times regarding precipitation, temperature, and the ET through MUSL (2001–2020). The greatest biased correlation values (between 0.16 and 0.51) of ET with various land use categories are much bigger than those of temperature and precipitation (Figure 14a). ET has the strongest impact on desert land in the spring and the whole year, while the weakest impact is on cropland. Figure 14b indicates that several land utilization patterns exhibit shorter seasonal lag times to precipitation in summer and fall, with average lag times ranging between 0.1 and 0.9 months. Forestland has the fastest response to temperature in spring, and various land use types are more sensitive to ET in the rest of the seasons, with the average lag time ranging between 0.1 and 1.2 months; all land use types were slowest responsive to temperature in summer and winter, while spring and autumn have the weakest sensitivity to ET and precipitation, respectively.