## 2 Data and Methods
### Construction of the 3D Grids for Monthly LS GW Ep and Influencing Factors  
Using the qualified GW Ep profiles derived from the COSMIC-2 temperature data, the spatiotemporal 3D grid dataset of the monthly averaged GW Ep for the height range of 20-30 km over the Indian region is obtained. First, the studied region (0\({}^{\circ}\)-30\({}^{\circ}\)N, 60\({}^{\circ}\)E-100\({}^{\circ}\)E) is gridded into 2.5\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\) (longitude \(\times\) latitude) bins. Then, the monthly averaged GW Ep profile corresponding to each grid point is derived by averaging all the qualified GW Ep profiles within the 5\({}^{\circ}\)\(\times\) 5\({}^{\circ}\) region centered on it. For example, the averaged GW Ep profile for the grid point of (10\({}^{\circ}\)N, 80\({}^{\circ}\)E) is calculated by averaging the qualified GW Ep profiles in the four bins of (7.5\({}^{\circ}\)-10\({}^{\circ}\)N, 77.5-80\({}^{\circ}\)E), (7.5\({}^{\circ}\)-10\({}^{\circ}\)N, 80\({}^{\circ}\)-82.5\({}^{\circ}\)E), (10\({}^{\circ}\)-12.5\({}^{\circ}\)N, 77.5\({}^{\circ}\)-80\({}^{\circ}\)E), and (10\({}^{\circ}\)-12.5\({}^{\circ}\)N, 80\({}^{\circ}\)-82.5\({}^{\circ}\)E). There will be an overlap between the 5\({}^{\circ}\)\(\times\) 5\({}^{\circ}\) area corresponding to a certain grid point and its neighboring grid points. This is based on the method proposed in [13]. For each month, the monthly averaged LS GW Ep value for a specific grid point is obtained by averaging the GW Ep values at all the height levels between 20 and 30 km. Finally, the spatiotemporal 3D grid data of the monthly averaged LS GW Ep, which has a resolution of 2.5\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\)\(\times\) 1 month, is obtained for the studied area during December 2019 and November 2021. To study the contribution of each considered factor to the LS GW activities in the Indian region, the 3D grid data with a resolution of 2.5\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\)\(\times\) 1 month is also prepared for the proxy of each influencing factor. Nine factors are considered, including the OLR, which represents the convection; the mean zonal (meridional) wind and wind shear in the height range of 20-30 km, which represent the background wind field; and the mean zonal (meridional) wind and wind shear in the height range of 15-17 km, which represent the TEJ. The OLR data from the NOAA CDC, which is used as the proxy for convection, is provided directly with a resolution of 2.5\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\)\(\times\) 1 month. The monthly zonal (meridional) wind speed field from the ERA 5, which has a horizontal resolution of 2.5\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\), is interpolated with the height interval of 0.1 km at first. At each grid point and for each height level, the monthly zonal (meridional) wind shear, which refers to the magnitude of the change in wind speed in the vertical direction [30], is calculated as the derivative of the monthly zonal (meridional) wind speed to height by using Equations (2) and (3) [45]. \[us_{i}=\frac{du}{dz}=\frac{u_{i+1}-u_{i}}{z_{i+1}-z_{i}} \tag{2}\]  
\[vs_{i}=\frac{dv}{dz}=\frac{v_{i+1}-v_{i}}{z_{i+1}-z_{i}} \tag{3}\]  
where \(i\) is the height level number in the wind speed profile, \(dz\) is the vertical resolution of the interpolated wind speed profile, which is equal to 0.1 km here to be consistent with the vertical resolution in calculating GW Ep, \(u\) and \(v\) are the zonal and meridional wind profiles, respectively, and \(us_{i}\) and \(vs_{i}\) are the zonal and meridional wind shears at the \(i\)th height level. Note that the eastward (northward) wind phase is defined as the positive direction of the zonal (meridional) wind speed and wind shear. At each 2.5\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\) grid point, the monthly averaged zonal (meridional) wind speeds and zonal (meridional) wind shears for each of the two height ranges, 15-17 km and 20-30 km, are obtained by averaging the monthly wind speeds and wind shears at all the height levels of the corresponding height range.