## 2 Materials and Methods
### Methods  
#### 2.3.1 Comprehensive Drought Index (CDI)  
The soil-plant-atmosphere continuum (SPAC) is a unified, dynamic, and continuous system with mutual feedback [31], and there are response relationships among different types of drought indicators, such as meteorology, soil, and vegetation data. Therefore, we first selected the SPEI, considering the effects of precipitation and temperature to represent the meteorological index; SMCI, considering root-zone soil moisture to represent the soil index; and VHI, considering the vegetation condition (VCI) and temperature condition (TCI) to represent the vegetation index to construct the CDI. Second, the SIF data of the short time series (2000-2020), which is more sensitive to high temperatures and drought, were used as dependent variables, and the SPEI, VHI, and SMCI after standardization were used as independent variables. The relative weights analysis (rwa, [[https://github.com/martinct/rwa](https://github.com/martinct/rwa)]([https://github.com/martinct/rwa](https://github.com/martinct/rwa)) (accessed on 17 March 2022)) [38] was used to determine the weights of the independent variables to construct the CDI for the long time series (1982-2020). Figure 2 shows the framework for CDI based on the SPAC. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Data Type** & **Data Contents** & **Resolution** & **Time Span** & **Data Sources** \\ \hline Soil data & Daily root-zone soil moisture & 0.25\({}^{\circ}\times\) 0.25\({}^{\circ}\) & 1980–2020 & The Global Land Evaporation Amsterdam Model (GEALV 3.63) datasets ([[https://www.gealm.eu/](https://www.gealm.eu/)]([https://www.gealm.eu/](https://www.gealm.eu/)), accessed on 17 March 2022) \\ \hline Historical disaster data & Drought-affected agricultural areas & Provines in NEC & 1986–2015 & The Crop and Disaster Databases of the Ministry of Agriculture of the People’s Republic of China ([[http://www.zzys.moao.gov.cn/](http://www.zzys.moao.gov.cn/)]([http://www.zzys.moao.gov.cn/](http://www.zzys.moao.gov.cn/)), accessed on 17 March 2022) \\ \hline Yield data & Maize yield and area & Provines in NEC & 1980–2020 & National Bureau of Statistics of China ([[https://data.stats.gov.cn/](https://data.stats.gov.cn/)]([https://data.stats.gov.cn/](https://data.stats.gov.cn/)), accessed on 17 March 2022) \\ \hline Other data & scPDSI & 4 \(\times\) 4 km & 1960–2020 & Terra climate data sets ([[http://www.climatologylab.org](http://www.climatologylab.org)]([http://www.climatologylab.org](http://www.climatologylab.org)), accessed on 17 March 2022) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 2: Framework for comprehensive drought index based on the soil-plant-atmosphere continuum (SPAC). 1 SPEI  
The SPEI was developed from the SPI, which describes the intensity and duration of droughts at different time scales. It considers not only the impact of precipitation but also the potential evapotranspiration factor influenced by temperature, and is widely used for the identification of monthly drought events [20]. The specific calculation process for the SPEI was as follows: (i) the Penman-Monteith method [41] was used to calculate the monthly cumulative potential evapotranspiration (PET); (ii) the difference between the monthly cumulative precipitation (Pc) and PET was used to calculate the water deficit (D); and (iii) the three-parameter log-logistic theory distribution function was selected to fit the D time series data and normalized. The SPEI calculation equation is as follows:  
\[SPEI=W-\frac{C_{0}+C_{1}W+C_{2}W^{2}}{1+d_{1}W+d_{2}W^{2}+d_{3}W^{3}} \tag{1}\]  
\[W=\sqrt{-2 In(P)} \tag{2}\]  
where \(P\) is the cumulative probability of exceeding the undetermined D value, when \(P\leq 0.5\), \(P=1-F(x)\); when \(P>0.5\), \(P=1-P\). \(C_{0}=2.515517\), \(C_{1}=0.802853\), \(C_{2}=0.010328\), \(d_{1}=1.432788\), \(d_{2}=0.189269\), \(d_{3}=0.001308\). In general, SPEI values ranged from \(-2.5\)-\(2.5\).