## 3 Methodology
### Extraction of Drought Characteristics
#### 3.1.2 Drought Characteristics  
The run theory is a useful tool to extract drought characteristics, such as drought duration, drought severity and drought intensity, from a drought index; it was proposed by [PERSON] [21]. By setting appropriate thresholds to segment drought index time series, the run theory can identify the start and end times of a single drought event. Many characteristics can be used to describe a given drought event [7; 35] by setting certain thresholds [7; 44] on the basis of the drought index time series. For representativeness and simplicity, several classic drought characteristics were selected from previous studies. Their detailed definitions and formulations are shown in Table 2. The rules for determining these  
\begin{table}
\begin{tabular}{c c} \hline \hline
**SPEI Value** & **Wet/Dry Status** \\ \hline \(>\)2 & Extremely wet \\ \(1.5\) to \(2\) & Severely wet \\ \(1\) to \(1.5\) & Moderately wet \\ \(0.5\) to \(1\) & Slightly wet \\ \(-0.5\) to \(0.5\) & Normal \\ \(-1\) to \(-0.5\) & Mildly dry \\ \(-1.5\) to \(-1\) & Moderately dry \\ \(-2\) to \(-1.5\) & Severely dry \\ \(<\)\(-2\) & Extremely dry \\ \hline \hline \end{tabular}
\end{table}
Table 1: Wet and dry status partitions based on SPEI.  
drought characteristics from the SPEI-1 time series by using the run theory (Figure 3) are listed as follows [35]:  
1. If the values of SPEI-1 are less than \(R_{1}\), they will be regarded as drought preliminary events (preliminary judgments), as shown in Figure 3, where \(a\), \(b\), \(d\), and \(e\) denote four drought preliminary events.
2. If the length of a preliminary judgment is only one month and the corresponding SPEI-1 value is larger than \(R_{2}\), it will be removed from the preliminary judgments. For example, in Figure 3, drought event \(a\) should be removed from preliminary judgments because it has a length of only one month.
3. If two consecutive drought events are separated only by a month interval and their corresponding SPEI-1 values are less than \(R_{0}\), they can be merged as one drought event. In Figure 3, because drought events \(b\) and \(d\) are separated by \(c\) by only one month, \(b\) and \(d\) can be merged into one drought event.  
The aforementioned rules were executed on each SPEI-1 index to derive the drought characteristics for corresponding meteorological stations.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Drought Characteristics** & **Content** & **Formula (Value)** \\ \hline Drought Duration (DD) & Duration from the beginning to the end & \(DD=DD_{b}+DD_{d}+1\) \\  & of the drought event & \((DD=DD_{e})\) \\  & Cumulative sum of the difference & \(DS=DS_{b}+DS_{d}\) \\ Drought Severity (DS) & between the drought index value and its & \((DS=DS_{e})\) \\  & threshold during drought events & \(DI=DD/DS\) \\ Drought Intensity (DI) & Drought duration & \(0\) \\ \(R_{0}\) & Combined adjacent drought threshold & \(0\) \\ \(R_{1}\) & Drought occurrence threshold & \(-0.5\) \\ \(R_{2}\) & Identified individual drought practices & \(-1\) \\  & with high severity & \(-1\) \\ \hline \hline \end{tabular}
\begin{tabular}{l l} \hline \hline \(DD_{b},DD_{d},DD_{e}\) and \(DS_{b},DS_{d},DS_{e}\) represent the duration and the severity of drought events b, d, and e (Figure 3), respectively. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Definitions and formulas of drought characteristics and several parameter settings in the applications of the run theory.  
Figure 3: Identification of drought characteristics by the run theory. **R0**, **R1**, and **R2** are thresholds for combining adjacent drought, determining drought occurrence and identifying individual drought practices. a (brown color), c (sea-blue color) and b, d, and e (red color) represent normal, wet, and dry states, respectively.