## 2 Materials and Methods
### Research Methods
#### 2.3.2 Integrated Drought Index Model  
Drought can be of several different types, depending on whether they are mainly caused by meteorology, hydrology, landforms, human activities or other factors which can all impact the ecosystem. Currently, many types of drought indices are used to assess different types of drought, such as single, multidimensional, and composite drought indices. A single drought index considers only one variable such as precipitation, temperature, river flow, or soil moisture. The multidimensional drought index can contain the effects of more variables on drought, and in this study, drought research in the HHHP was carried out based on the mISDI. In this study, the mISDI model selected the self-calibration palmer drought severity index (scPDSI) as a dependent variable, and the independent variable \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Abbreviation** & **Resolution** \\ \hline land surface temperature & LST & 1 km \\ normalized difference vegetation index & NDVI & 1 km \\ gross primary production & GPP & 500 m \\ evapotranspiration & ET & 500 m \\ land cover & LC & 500 m \\ digital elevation model & DEM & 1 km \\ available water capacity & AWC & 1 km \\ Asian irrigated area map & IAA & 250 m \\ longitude and latitude & LON and LAT & 1 km \\ standardized precipitation index & SPI & stations \\ standardized precipitation evapotranspiration index & SPEI & stations \\ self-calibration palmer drought severity index & scPDSI & stations \\ palmer drought severity index & PDSI & stations \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Information about the data in this study. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Equation** & **Calculation** & **Time Resolution** \\ \hline \multirow{4}{*}{SOSA} & \multirow{4}{*}{SOSA\({\rm i}={\rm SOST}_{\rm i}-{\rm SOST}_{\rm med}\)} & SOST\({}_{\rm i}\) represents the start of the growing season in year n, & \multirow{4}{*}{year} \\  & & and SOST\({}_{\rm med}\) represents the median of the start of the & \\ \cline{1-1} \cline{3-4}  & & growing season for the entire time series. SOST is calculated & \\ \cline{1-1} \cline{3-4}  & & by TIMESAT based on the Savitzky–Golay filtered NDVI in the bear toolbox. & \\ \hline VSWI & \multirow{2}{*}{VSWI \(=\)\(\frac{\rm NDVI}{\rm LST}\)} & Pixel ratio of the NDVI to the LST per month & month \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculation methods for the start of season anomaly (SOSA) and the vegetation supply water index (VSWI). input combinations were divided into six different combinations (Table 4). The resulting mISDI values were classified into one of 8 levels of drought severity (Table 5). The drought grades intervals of the mISDI were set according to [30]. The calculation flow of the mISDI is divided into the following three steps (Figure 3). First, the standardized precipitation index (SPI), the standardized precipitation evapotranspiration index (SPEI), and the scPDSI [31; 32; 33; 34] of each station according to the meteorological station data were calculated using the R software. Then, the point data were converted to raster data by using the inverse distance weight (IDW) of ArcGIS 10.2, with a 1 km spatial resolution. Next, for the preprocessed raster data, the cubist algorithm was used to establish the mISDI model according to the combinations of Table 4.