## 2 Materials and Methods
### Methods
#### 2.3.1 Comprehensive Drought Index (CDI)
A value of less than \(-0.5\) is considered to be a drought event, and Table 2 illustrates the classification of drought levels based on SPEI [22,42]. (2) VHI  
VHI was developed to detect vegetation drought and consists of VCI and TCI, which are obtained from NDVI and BT, respectively; the lower the NDVI value and the higher the BT value, the poorer the vegetation health. The VHI considers the local biophysics (soil and slope) and climatic conditions. This method can be used for practical agro-drought monitoring in various agro-climatic zones. In particular, during crucial stages of crop growth, VHI and crop yield are strongly correlated [27]. \[VHI_{i}=\alpha\times VCI_{i}+(1-\alpha)\times TCI_{i} \tag{3}\]  
\[VCI_{i}=\frac{NDVI_{i}-NDVI_{min}}{NDVI_{max}-NDVI_{min}} \tag{4}\]  
\[TCI_{i}=\frac{BT_{max}-BT_{i}}{BT_{max}-BT_{min}} \tag{5}\]  
where \(NDVI\), \(NDVI_{max}\), and \(NDVI_{min}\) (\(BT\), \(BT_{max}\), \(BT_{min}\)) are the smoothed \(NDVI\) (\(BT\)) and the maximum and minimum values of \(NDVI\) (\(BT\)) for each month in 1982-2020, respectively; and \(\alpha\) represents the weighting coefficient of VCI. in this study, VHI correlates with SIF most closely when \(\alpha\) = 0.7. The value of VHI ranges from 0 to 1, and the smaller the value, the more severe the vegetation drought. [PERSON] et al. [43,44] proposed that agricultural drought occurs when the VHI is less than 0.4, and the classification of drought levels based on the VHI [45] is shown in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Drought** & \
\begin{tabular}{c} **Meteorological** \\ **Index** \\ \end{tabular} & **Vegetation Index** & **Soil Index** &
\begin{tabular}{c} **Comprehensive** \\ **Index** \\ \end{tabular} \\ \hline Disaster levels & SPEI & VHI & SMCI & CDI \\ \hline None & \((-0.5,+\infty)\) & \((0.4,1]\) & \((0.4,1]\) & \((-0.2,1]\) \\ Light & \((-1.0,-0.5]\) & \((0.3,0.4]\) & \((0.3,0.4]\) & \((-0.2,-0.4]\) \\ Moderate & \((-1.5,-1.0]\) & \((0.2,0.3]\) & \((0.2,0.3]\) & \((-0.4,-0.6]\) \\ Severe & \((-2.0,-1.5]\) & \((0.1,0.2]\) & \((0.1,0.2]\) & \((-0.6,-0.8]\) \\ Extreme & \((-\infty,-2.0]\) & \([0,0.1]\) & \([0,0.1]\) & \([-1,-0.8]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Classification of drought disaster levels. 3 SMCI Agricultural drought is characterized primarily by insufficient soil moisture for plant root uptake and normal transpiration, which results in lower crop and pasture yields [30]. The SMCI, which describes drought in terms of soil moisture, is based on the standardization of the monthly mean values of root-zone soil moisture (SM) over a long time series. The calculation equation is as follows:  
\[SMCI_{i}=\frac{SM_{i}-SM_{min}}{SM_{max}-SM_{min}} \tag{6}\]  
where \(SM_{i}\), \(SM_{max}\) and \(SM_{min}\) denote the root-zone soil moisture at time \(i\) and the maximum and minimum values of soil moisture during the same period from 1982 to 2020, respectively. The SMCI value is between 0 and 1. The calculation principle was the same as that of VCI, and the classification of the drought class based on SMCI [45] was identical to that of the VHI (Table 2). (4) CDI Based on the SPAC theory, the CDI developed from the response of meteorological drought, soil drought, and vegetation to drought was calculated using the following equations:  
\[CDI=w_{1}\times SPEI^{\prime}+w_{2}\times VHI^{\prime}+w_{3}\times SMCI^{\prime} \tag{7}\]  
\[SPEI^{\prime}=SPEI/2.5 \tag{8}\]  
\[SPEI=\left\{ \begin{array}{rl}2.5&SPEI\geq-2.5\\ SPEI&2.5>SPEI>-2.5\\ -2.5&SPEI\leq-2.5\end{array} \right. \tag{9}\]  
\[VHI^{\prime}=(VHI-0.5)\times 2 \tag{10}\]  
\[SMCI^{\prime}=(SMCI-0.5)\times 2 \tag{11}\]  
where \(SPEI^{\prime}\), \(VHI^{\prime}\), and \(SMCI^{\prime}\) represent the meteorological, vegetation and soil drought indicators after standardization of \(-1\)-\(1\), respectively, and their drought classification criteria are the same as those of CDI (Table 1); the specific process of standardization is shown in Equation (8) to (11).