## 4 Discussion and Conclusions  
Conventional drought indices that work based on stationary assumptions are no longer suitable for characterizing drought under the influence of factors, such as climate change or anthropogenic influences. Thus, in this study, we applied a six-month scale NSPEI with t covariates using GAMLSS to identify hotspot areas in China that were sensitive to nonstationary models. By comparing the drought characteristics (duration and severity) of the stationary model and nonstationary models, this study investigated the over-estimation or under-estimation of droughts using the current stationary SPEI index under four classifications of changes in distribution parameters. Long-term trends in precipitation and temperature in China during the period 1979-2020 indicated that precipitation had increased in China over the past 42 years, with the increase in temperature being more pronounced. This was consistent with the findings of [PERSON] et al. [55] for a warming environment. [PERSON] et al. [56] identified an increase in precipitation in Western and Southeastern China between 1960 and 2020; the evapotranspiration, which was assessed using the Thorthwaite formula, has increased significantly over the past 42 years. These results revealed that both evapotranspiration and nonstationarity needed to be considered in drought assessment because if only precipitation was focused on, the severity of the drought would be misjudged as less severe, and if nonstationary was not considered, the changes  
Figure 9: Probability density of severity estimated by SPEI and NSPEI in the nine river basins of China under different classifications of (\(\mu\), \(\sigma\)) changes in the fall–winter season. produced would not be accurately captured. The change in the D series suggested that Northwest China would become drier. Using the AIC, we obtained good fits for both the nonstationary and stationary models. From Southeast to Northwest China, the AIC values decreased, indicating a better model performance. Based on the model coefficients extracted from the return objects of the GAMLSS, four types of location (\(\mu\)) and scale (\(\sigma\)) parameter changes under a 95% confidence level were obtained: (0, 0), (1, 0), (0, 1), and (1, 1). This study selected the results of the second and eighth months from the GAMLSS, which represented the spring-summer and fall-winter seasons, respectively. The analysis results showed that Northwest China (CRB) was the main region wherein the distribution parameters varied; it was the main nonstationary hotspot response area. This was consistent with the significant D-series trend that was mainly observed in the CRB. The nonstationary and stationary models did not have significant spatial distribution characteristics in terms of drought duration. Due to the decrease in the D series in the spring-summer season and reduced or no evapotranspiration during the fall-winter season, the under-estimation of drought severity under the stationary SPEI was obvious in the CRB during the spring-summer season, while the over-estimated area expanded and the under-estimated area decreased in the fall-winter season. The comparative results of drought assessments based on changes in the distribution parameters (\(\mu\), \(\sigma\)) indicated that drought conditions would be underestimated by the stationary SPEI in cases with changes in both the location and scale parameters (1, 1). Drought assessment was influenced by both precipitation and evapotranspiration only when the location parameters varied (1, 0). Meanwhile, this study revealed that the stationary SPEI under-estimated the occurrence of drought events with longer durations and greater severity in China. Similar findings have been previously published [6; 28] on nonstationary being able to capture more extreme events. Among the study regions, Northwest and Southwest China were of interest; one of them was under-estimated in the spring-summer seasons and the other was under-estimated in the fall-winter season.