## 2 Data and Methods
### Correlation Analysis and Dominance Analysis  
At each 2.5\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\) grid point, the correlation analysis is carried out between the time series of each factor in **X**, which varies from December 2019 to November 2021 with a step of 1 month (24 months in total), and the time series of LS GW Ep, based on which the spatial distribution of the Pearson correlation coefficients (CCs) between each factor and LS GW Ep over the Indian region is obtained.  
In addition to the correlation analysis, the DA method is further applied to evaluate the influences of the nine different factors on the LS GWs over the Indian region by using the time series of each factor in **X** and the time series of \(Y\). The DA method, which is developed based on the multiple linear regression (MLR) model, can be used to evaluate the relative importance of a single factor in the MLR model by examining the change in \(R^{2}\) (coefficient of determination) resulting from adding a predictor to all possible subset regression models [46; 47; 48]. As a supplement to the regression analysis, when there is multicollinearity between independent variables, the dominance analysis can de-emphasize redundant predictors, thus reducing the impact of collinearity between independent variables and better representing the statistical contribution of independent variables [49; 50]. Similar to correlation analysis, for each grid point in the Indian region, the time series of each factor in **X** and those of LS GW Ep (denoted as _Y_) are used to build an MLR model:  
\[Y=a_{0}+a_{1}X_{1}+a_{2}X_{2}+\dots+a_{p}X_{p}+e \tag{4}\]  
where \(p=9\) is the influencing factors number, \(a_{0}\), \(a_{1}\), \(\dots\), \(a_{p}\) are the regression coefficients, and \(e\) is the residual. There are \(2^{p}\) possible subset models containing various possible combinations of these factors. Let \(\textbf{X}_{-i}\) represent a subset of **X** that does not contain the factor \(X_{i}\), and the coefficient of determination (\(R^{2}\)) of the model subset \(\textbf{X}_{-i}\) is represented by \(R^{2}_{\textbf{Y}|\textbf{X}_{-i}}\). For all possible subsets \(\textbf{X}_{-i}\), the difference between the coefficient of determination (\(R^{2}\)) of the model subsets with and without the factor \(X_{i}\), denoted as \(Diff\_R^{2}_{X_{i}}(\textbf{X}_{-i})=R^{2}_{\textbf{Y}|\textbf{X}_{i}\textbf{ X}_{-i}}-R^{2}_{\textbf{Y}|\textbf{X}_{-i}}\), are calculated, and the contribution of the factor \(X_{i}\), which denotes as \(C_{X_{i}}\), is the average of \(Diff\_R^{2}_{X_{i}}(\textbf{X}_{-i})\) for all possible subsets \(\textbf{X}_{-i}\). The value of \(C_{X_{i}}\) is non-negative, and the larger the value of \(C_{X_{i}}\), the higher the explanatory power of \(X_{i}\) in predicting \(Y\). Therefore, \(C_{X_{i}}\) can be regarded as the relative importance coefficient (RIC) of the factor \(X_{i}\). The sum of the RICs of all factors should equal the \(R^{2}\) of the MLR model [47; 48; 51]. By applying the dominance analysis over all the 2.5\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\) grid points, the spatial distributions of the RICs of all the nine influencing factors that affect the LS GWs over the Indian region are obtained.