###### Abstract  
The spatial-temporal distribution of the global gravity wave (GW) potential energy (Ep) at the lower stratosphere of 20-35 km is studied using the dry temperature profiles from multi- Global Navigation Satellite System (GNSS) radio occultation (RO) missions, including CHAMP, COSMIC, GRACE, and METOP-A/B/C, during the 14 years from 2007 to 2020, based on which the linear trends of the GW Ep and the responses of GW Ep to solar activity, quasi biennial oscillation (QBO), and El Nino-Southern Oscillation (ENSO) are analyzed using the multivariate linear regression (MLR) method. It is found that the signs and the magnitudes of the trends of GW Ep during each month vary at different altitude ranges and over different latitudes. At 25-35 km of the middle and high latitudes, GW Ep values generally show significant negative trends in almost all months, and the values of the negative trends become smaller in the regions closer to the poles. The distribution of the deseasonalized trends in the monthly zonal-mean GW Ep demonstrates that the GW activities are generally declining from 2007 to 2020 over the globe. The responses of GW Ep to solar activity are found to be mostly positive at 20-35 km over the globe, and the comparison between the distribution pattern of the deseasonalized trends in the GW activities and that of the responses of GWs to solar activity indicates that the sharp decline in solar activity from 2015 to 2017 might contribute to the overall attenuation of gravity wave activity during the 14 years. Significant negative responses of GW Ep to QBO are found at 30-35 km over 30\({}^{\circ}\) S-25\({}^{\circ}\) N, and the negative responses extend to the mid and high latitudes in the southern hemisphere at 20-30 km. The responses of GW Ep to QBO change to be significantly positive at 20-30 km over 15\({}^{\circ}\) S-15\({}^{\circ}\) N, which demonstrates that the zonal wind field should be the main factor affecting the GW activities at 20-30 km over the tropics. The responses of GW Ep at 20-35 km to ENSO are found to be positive over 15\({}^{\circ}\) S-15\({}^{\circ}\) N, while at 30-35 km over 15\({}^{\circ}\) N-30\({}^{\circ}\) N and at 20-35 km near 50\({}^{\circ}\) N, significant negative responses of GW Ep to ENSO exist. gravity waves (GW); potential energy (Ep); Radio Occultation (RO); linear trend; solar activity; quasi biennial oscillation (QBO); El Nino-Southern Oscillation (ENSO) +
Footnote †: journal: _remote sensing_  
0000-0 To reproduce realistic atmospheric structure in the general circulation models (GCMs), it is necessary to include the GW effects [7, 8]. Nowadays, it is still difficult to resolve GWs and the associated eddy diffusions explicitly in a GCM due to the high computational cost [9, 10, 11, 12]. Therefore, it is of great significance to obtain the relevant parameters of gravity waves through observation methods, which will improve the accuracy and the reliability of GCMs forecasts. Being valuable complements to conventional ground-based measurements of GWs, satellite observations can provide realistic information on the spatial and temporal distributions of GWs over the globe and can contribute to some constraints on GW parameterizations in GCMs [9]. As a satellite-based observation technology developed rapidly in recent twenty years, the Global Navigation Satellite System (GNSS) radio occultation (RO) can provide atmospheric and ionospheric products with global coverage, all-weather capability, and long-term stability. RO temperature profiles are of vertical resolution better than 1 km and temperature accuracy higher than 1K in the upper troposphere and lower stratosphere [13, 14, 15], which are ideal data sources for the study of gravity wave activities in this altitude range [2, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]. Using the RO temperature data from the Challenging Minisatellite Payload (CHAMP) mission during 2001 to 2003, [PERSON] et al.