## 3 Results  
### Dynamic Characteristics of Seasonal Drought  
The averages of SPEI\({}_{3}\) from March to May, June to August, September to November, and December to February of the following year were used to characterize the seasonal variation of drought in spring, summer, fall, and winter, respectively, on the Loess Plateau. From a seasonal perspective (Figure 2), the interannual SPEI values of the Loess Plateau increased in the spring and summer from 2001 to 2019, showing a trend of increasing humidity (R\({}^{2}\) = 0.0041 and R\({}^{2}\) = 0.1112, respectively), whereas the SPEI value for the fall decreased overall, showing a trend of increasing aridity (R\({}^{2}\) = 0.0481). In the spring, SPEI increased slowly at a rate of 0.02/10a, with the lowest value of SPEI appearing in 2013. The cumulative anomaly curve shows that the SPEI value fluctuates considerably in the spring, and a decreasing trend was found in 2003-2009 and 2012-2013. In the summer, there was a pervasive drought from 2001 to 2019, and SPEI increased at a rate of 0.16/10a over the entire study period, with SPEI showing a trend of \"rising-falling-rising\" during the periods of 2001-2004, 2004-2011, and 2011-2019, with average SPEI values of \(-0.91\), \(-1.08\), and \(-0.82\), respectively. The lowest SPEI values were in 2001, when the drought was at its most serious, reaching a moderate grade of drought. In the fall season of the 2001-2019 period, the SPEI value decreased at a rate of 0.2/10a, showing a decreased trend as a whole. The SPEI value was lowest in 2019, and the magnitude of the drought was moderate. The trend of SPEI values in winter is not clear, but they were more than zero from 2001 to 2019, indicating that there was no drought in winter during the study period. It can be seen from the cumulative anomaly curve that the winter SPEI showed a \"rising-falling-rising\" trend during the periods of 2001-2005, 2005-2014, and 2014-2019, with average SPEI values of 0.66, 0.61, and 0.68, respectively. A clear seasonal divergence was identified in the spatial patterns of drought index and magnitude of drought (Figure 3). The seasonal ordering of magnitude of drought was: summer > spring > fall > winter. In spring, SPEI increased from southeast to northwest with the decrease in precipitation gradient, indicating that the spring drought in the southeast with more precipitation is more severe (Figure 3(a1)). The drought intensities were mainly mild (40.9%) and no drought (59.1%) in spring (Table 2). The mild droughts in the spring were mainly located in the southeast of the Loess Plateau and Qinghai, with the drought being most severe in central Shaanxi, most of Shanxi, eastern Gansu, and Qinghai, where the vegetation types were mainly forest and grassland (Figure 3(b1), Table 11). In the summer, the drought grade is no drought (2.5%), mainly distributed in Qinghai and southern Shaanxi, and most regions experienced mild drought (39.8%) or moderate drought (57.2%) (Table 2). The drought index (SPEI) increased gradually with the increase in precipitation from the northwest (moderate drought) to the southeast (mild drought), that is, the summer drought in the northwest of the Loess Plateau, with less precipitation, is more serious (Figure 3(a2, b2)). Severe drought (0.5%) was found in some areas of Inner Mongolia, Ningxia, and Gansu, where the main vegetation types are shrubs and grasslands  
Figure 2: Long-term dynamic characteristics of seasonal standardized precipitation evapotranspiration index (SPEI) in the Loess Plateau. (Table 2, Table A1). The magnitude of the drought in the forest was mild (Table A1), and the drought magnitude in the summer was the most severe of all four seasons (Figure 3(b2)).