## 2 Data and Methods
### Method for Extracting Long-Term Changes of GW Activities  
After obtaining all the qualified GW Ep profiles through the steps introduced in the previous two subsections, these GW Ep profiles are averaged within a single month and binned into \(360^{\circ}\times 5^{\circ}\) longitude[---]latitude grids, with an overlap of \(2.5^{\circ}\) in latitude to calculate the monthly and zonal-mean Ep for each height level at the altitude range of 20-35 km. For each latitude band and each height level, the linear trend in monthly zonal-mean Ep time series and the responses of the monthly zonal-mean Ep to solar activity, QBO wind, and ENSO are derived by the method of multivariate linear regression (MLR) [9; 45]. The equation for the MLR method is expressed as:  
\[\begin{split} E_{p}\big{(}t_{i,j}\big{)}&=\mu+\alpha t _{i,j}+\delta solar\big{(}t_{i,j}\big{)}+\gamma QBO\big{(}t_{i,j}\big{)}+\kappa ENSO \big{(}t_{i,j}\big{)}+Residual\\ &\text{With }I\ =2007,\ 2008,\ \ldots,\ 2020;\ j\ =\ 1,\ 2,\ \ldots,\ 12\end{split} \tag{4}\]  
In Equation (4), \(E_{p}\big{(}t_{i,j}\big{)}\) represents the monthly zonal-mean value of GW Ep at month (\(j\)) and year number (\(i\)) and the quantity \(\mu\) represents a constant Ep value. The parameter \(\alpha\), which reflects the change in GW Ep with time, represents the linear trend of monthly zonal-mean Ep during 2007-2020. The parameters \(\beta\), \(\gamma\), and \(\kappa\), which demonstrate the correlation between the time series of GW Ep and the time series of the three indices, represent the responses of the monthly zonal-mean Ep to solar activity, to QBO, and to ENSO. The variance-covariance matrix and student \(t\)-test can be used to evaluate whether the estimated regression coefficients are significant at a given confidence level. Giving a significance level \(s\), which means that the corresponding confidence level is set as \((1-s)\times 100\%\), then the corresponding critical value of the \(t\) distribution can be obtained in the look-up table. If the absolute value of the ratio between the regression coefficient and its corresponding standard deviation is larger than the critical value of the \(t\) distribution at the given significance level \(s\), then it is claimed that the regression coefficient is significant at the confidence level \((1-s)\times 100\%\)[46]. In the present study, the confidence level for the \(t\)-test is set as 90%.  
Figure 3 presents the reference time series of solar activity, QBO, and ENSO during 2007 to 2020. The monthly mean values of radio emissions from the sun at a wavelength of 10.7 centimetres (the 10.7 cm solar flux, F10.7) are used to represent the solar activity [47], and F10.7 is given in solar flux units (\(\delta fu\), \(1\,\delta fu=10^{-22}\) W m\({}^{-2}\) Hz\({}^{-1}\)) in Figure 3a. It should be noted that during the studied time period, the solar activity was the most intensive during 2014 to 2015, and declined after the year 2015. In Figure 3b, the temporal variation of 30 hPa zonal-mean zonal wind over the equator is used as the reference time series for QBO [48]. In Figure 3c, the temporal variations of the ENSO phases are shown by the  
Figure 2: (**a**) Global distribution and (**b**) yearly number of qualified GW Ep profiles derived from the RO observations during 2007–2020.  
values of the bi-monthly Multivariate El Nino/Southern Oscillation (ENSO) index (MEI), which is the time series of the leading combined Empirical Orthogonal Function (EOF) of five different variables (sea level pressure (SLP), sea surface temperature (SST), zonal and meridional components of the surface wind, and outgoing longwave radiation (OLR)) over the tropical Pacific basin (30\({}^{\circ}\) S-30\({}^{\circ}\) N and 100\({}^{\circ}\) E-70\({}^{\circ}\) W) [49; 50; 51].