## 2 Materials and Methods
### Methodology
#### 2.3.3 Estimation of Drought Event Characteristics  
In this study, meteorological and ecological drought events are estimated on the basis of the run theory. Run theory, also known as the cycle theory, is a time series analysis method used to analyze similar events that occur continuously [52]. In drought analysis, the run course theory can be used to identify the beginning and end of drought events, as well as their characteristics, such as the duration, intensity, and frequency. In this study, the threshold of meteorological drought was set at \(-0.5\), and the threshold of ecological drought was set at \(-10\%\). The setting of the former is determined by reference to Section 2.3.2 above and the SPI classification table (Table 2) [54; 55], and the setting of the latter is determined by the definition of ecological drought anomalies in Section 2.3.1 above [49].  
This study will identify drought events by following the following steps:  
Step 1: The initial phase involves organizing each raster image chronologically, identifying those with an SPI value below \(-0.5\) or exhibiting an abnormal GPP (abGPP), and annotating them accordingly.  
Step 2: The preceding procedure is executed for all raster images across all months, identifying raster pixels with corresponding values for three or more consecutive months, signifying a drought occurrence.  
Step 3: According to the basic definition of drought event characteristics, the characteristics of drought events are identified and the results are output.  
Combined with previous research results, this study gives the basic definition of drought characteristics as follows [49]:  
(1) Drought frequency  
\[DF=\frac{N_{d}}{T_{s}} \tag{7}\]  
where \(N_{d}\) is the total number of drought events occurring on the same grid pixel during the study period and \(T_{s}\) is the study years (total time). Unit: times/year.  
(2) Drought duration  
\[DD=\frac{\sum D_{i}}{N_{d}} \tag{8}\]  
where \(D_{i}\) is the duration of the \(i\) drought event of the same grid element. Unit: month/time.  
(3) Drought intensity  
\[DI=\frac{\sum I_{i}}{\sum D_{i}} \tag{9}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Grade** & **Type** & **SPI Value** \\ \hline
1 & Normal drought and moist conditions & \(-0.5<\) SPI \\
2 & Mild drought & \(-1.0<\) SPI \(\leq-0.5\) \\
3 & Moderate drought & \(-1.5<\) SPI \(\leq-1.0\) \\
4 & Severe drought & \(-2.0<\) SPI \(\leq-1\) \\
5 & Extreme drought & SPI \(\leq-2.0\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: SPI classification criteria.  
where \(I_{i}\) is the cumulative value of drought degrees in each month on the same grid pixel where the drought index in the \(i\) drought event is lower than the threshold value (positive). Drought intensity is a dimensionless index.  
As shown in Figure 4, taking meteorological drought as an example, it is assumed that only three places have one meteorological drought event each in 2020.  
The example study period Ts is 1 year, and the drought frequency Nd of the three places is 1 time each, so the drought frequency DF of the three places is 1 time/year.  
The duration of drought in place A is 4 months/times, the duration of drought in place B is 3 months/times, and the duration of drought in place C is 4 months/times.  
The arity degree values of the four months in which drought occurred in place A were \(-0.6\), \(-0.75\), \(-0.6\), and \(-0.9\), respectively, so the DI in place A was 0.71. Similarly, the DI at D was 0.87 and the DI at C was 0.85.