## 1 Introduction
Amongst these drought indices, SPEI is the most sophisticated and widely used tool because it is designed to consider both precipitation and potential evapotranspiration (PET) while determining drought, and it can capture multi-temporal characteristics of drought [3; 12]. When considering a given drought event, scientists usually focus on several quantified characteristics of the drought, such as duration, severity, and intensity [30]. However, as the SPEI index cannot directly and quantitatively describe the characteristics of drought events, there is a need to use other techniques along with SPEI. By defining multiple thresholds, the run-theory [21] method can be used as a powerful tool to distinguish drought and non-drought statuses and extract drought characteristics from drought indices [31]. For example, [PERSON] et al. [32] proposed a method for urban drought disaster risk analysis and assessment by integrating the run theory, the copula function, the crop growth model, and natural disaster risk assessment technology. [PERSON] et al. [33] classified droughs using the run theory and reported that the probability of occurrence of moderate drought events is relatively higher than that of severe and extreme drought events in Uttarakhand (India). [PERSON] et al. [31] used the run theory to identify the frequency, duration, severity, and intensity of all droughs in China on the basis of the monthly percentage of the precipitation anomaly rate index and found that China has five obvious meteorological drought-prone areas. These studies have shown that the run theory method can effectively identify and detect the temporal characteristics of drought [34; 35]. Hence, determining whether the run theory can effectively and efficiently detect temporal drought features from SPEI sequences is an interesting topic. With regard to the spatial distribution of drought characteristics, drought cluster analysis methods are widely used to identify homogeneous regions with similar drought characteristics. These methods include fuzzy c-means [5], quantile regression [2], and K-means. Drought indices, such as PCI, TCI, SPI, and SPEI, are normally set as input data for these cluster analysis methods to detect the spatial distribution of drought characteristics [2; 5; 25; 36; 37; 38]. [PERSON] et al. [2] utilized the hierarchical agglomerative clustering algorithm to analyze the different quantile slopes of SPI-3 at 12 stations in Taiwan, and the results showed that stations along the east coast were likely to be severely affected. [PERSON] et al. [37] used k-means clustering to divide Xinjiang's drought spatial distribution patterns into three clusters on the basis of SPI. By using the standardized precipitation temperature index as a feature, [PERSON] et al. [38] partitioned the 52 meteorological stations in Pakistan into nine clusters. However, despite reflecting the statuses of drought and wetness, these drought index values were used directly in cluster analysis methods, which might be inappropriate for effectively distinguishing the two statuses. Introducing quantitative characteristics that indicate the degree and severity of drought may be a better option for describing drought in spatial and temporal aspects. In this study, we developed a method to identify the spatiotemporal distribution of drought characteristics on the basis of meteorological station records in Hunan Province, China, which is a major grain-producing area and is often affected by floods and droughs [39]. This method consists of two steps. Firstly, it is designed to derive drought characteristics, including drought duration, severity, and intensity, from the SPEI index, by integrating the run-theory method. Secondly, drought spatial distribution patterns are derived by clustering drought characteristics via the K-means cluster method. Hunan Province is located in a subtropical region with relatively abundant rainfall, but it is still susceptible to seasonal drought events.