# Elliptical Structures of Gravity Waves Produced by Typhoon Soudelor in 2015 near Taiwan
## 4 Results  
The analyses of ECMWF (European Centre for Medium-Range Weather Forecasts) revealed a strong TC on 7 August 2015 prior to landfall over Taiwan. Indeed, Figure 7a in Reference [71] shows a compact TC structure with an elliptical shaped eye at a 4 km height on 7 August 12:00 UTC. The WN1 asymmetry was reproduced on the right side of the TC but with intense wind, smaller size and closer to the TC center in comparison with Figure 4b. In contrast, the size of the structure, circular shaped eye and WN1 wind asymmetry were reasonably captured by NCEP GFS (National Centers for Environmental Prediction Global Forecast System) analyses but with less intense wind speeds (not shown). Unlike NCEP GFS analyses, the isosurfaces of vertical velocity derived from the ECMWF analyses showed evidence of quasi-circularly stratospheric GWs with horizontal wavelengths between 100 km and 200 km in the UT and LS propagating upward in the stratosphere (Figure 7 in Reference [71]). Considering the observations mentioned above, NCEP GFS analyses were used to initialize a WRF-ARW model for the simulation of TC Soudelor and the generation of stratospheric TC-induced GWs as observed in the ECMWF operational analyses. Indeed, the simulation revealed the presence of TC-induced wavelike patterns on horizontal cross sections of simulated vertical velocity in the troposphere and LS on 7 August 12:00 UTC (Figure 8). It showed evidence of a mesoscale wavelike structure with a dominant horizontal wavelength of about 140 km in Region A at the rear of TC Soudelor at 20 km height in the LS (Figure 8a) and fine-scale structures with horizontal wavelength of about 20 km in Regions B and C at a 12 km height in the UT (Figure 8b). The latter ones were located above intense convection in the spiral rainbands. In addition, the filtered field of vertical velocity in the Region D of the domain D1 (Figure 8c) also depicted a mesoscale semi-circular GW structure in the LS with a horizontal wavelength of about 200 km. Indeed, the application of the FFT on the simulated vertical velocity perturbations at the latitude 23\({}^{\circ}\) N supported the presence of dominant wavelike structures with horizontal wavelengths of 150-250 km at 20 km height in the LS. Structures with long horizontal wavelengths of 400-600 km are also found as observed in references [20; 72]. Figure 7: (a) Distribution of FormoSat-3/COSMIC (Formosa Satellite Mission-3/Constellation Observing System for Meteorology, Ionosphere, and Climate) RO (radio occultation) data on 6 and 7 August 2015 (triangle and plus sign, respectively) superimposed on horizontal cross section of WRF simulated wind speed (m/s) at a 4 km height on 7 August 0830 UTC. Labels (black) indicate the time in UTC of soundings. Black dots visualize TC Soudelor’s best track at 06:00 and 12:00 UTC. (b) Mean profiles of potential temperature and standard deviation (multiplied by 10) at geographical location of COSMIC RO soundings derived from COSMIC RO and WRF data (left), corresponding absolute differences and standard deviation in mean potential temperature (middle), and relative bias (right). Figure 9a,c,e display the horizontal distributions of mean wave energy density at 12:00 UTC on 7 August, for vertical layers of 3-10 km, 8-15 km and 18-25 km, respectively. The value of E\({}_{\mathrm{w}}\) was small in comparison with those computed with horizontal wind perturbations and, consequently, it was neglected in the calculation of the total kinetic energy density. At heights of 3-10 km, GW energy density was observed to be mainly imbedded within the eyewall and spiral rain bands (Figure 9a). The longitudinal cross-section at latitude 23\({}^{\circ}\) N revealed the dominance of \(E_{k}\) in \(E_{t}\) and an asymmetry at longitudes between 124\({}^{\circ}\) E and 128\({}^{\circ}\) E at the rear of the TC with peaks of intensity in the eyewall (Figure 9b). The asymmetry was strengthened by the orography at 12:00 UTC. The asymmetry in \(E_{k}\) and \(E_{p}\) was clearly visualized in the UT (Figure 9c,d) and LS (Figure 9e,f).