# Elliptical Structures of Gravity Waves Produced by Typhoon Soudelor in 2015 near Taiwan
## 4 Results
Globally, signatures of quasi-monochromatic wavelike patterns were evident on temperature profiles in the LS. A fourth-order low-pass Butterworth filter with a cutoff of 7 km was applied to the temperature profiles to retrieve the perturbations in the troposphere (2-15 km) and stratosphere (18-30 km). Large amplitudes of temperature perturbations \(>\)1\({}^{\circ}\) K were mainly observed at heights of 6-11 km and 18-26 km with dominant vertical wavelengths of 1-3 km and 2.5-4 km, respectively (Figure 15b). The FFT was applied to temperature perturbations to highlight vertical wavelengths of dominant GW modes. In the troposphere, GWs with short vertical wavelengths of 1.5-2.5 km were observed near TC inner core, more significant in front of the TC at 08:14 UTC with a vertical wavelength of about 1.5-2 km (Figure 15c). A dominant mode, with a vertical wavelength of about 3.5 km, was observed on profiles at latitudes between 22\({}^{\circ}\) N and 25\({}^{\circ}\) N. In contrast, the FFT of the perturbation profile at 07:51 UTC revealed two peaks at 2.5 km and about 5 km far north-east of the TC. As the vertical resolution of COSMIC RO temperature profiles varied between 1 km at the tropopause and 1.4 km at 40 km height, only GWs with vertical wavelengths \(>\)2.5 km could be properly analyzed at heights of 18-30 km. Figure 15d reveals dominant modes with vertical wavelengths of 3-5 km in the LS with a peak at the vertical wavelength of 3.5 km. _Atmospme_**2019**, _10_, 260 \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Region** & **Heights (km)** & **Number** & \(\lambda_{\Psi}\) **(km)** & \(\lambda_{\hbar}\) **(km)** & **T (h)** & **Phi (\({}^{\circ}\))** & **Fup (\%)** & **d (\%)** \\ \hline
0 & 8–15 & 196 & 1.6 & 31 & 1.7 & 272 & 49 & 10 \\  & 18–25 & & 3.5 & 250 & 5.8 & 86 & 57 & 40 \\ \hline
1 & & 56 & 1.4 & 110 & 6.7 & 261 & 39 & 49 \\
2 & 8–15 & 42 & 1.8 & 110 & 5.8 & 285 & 42 & 46 \\
3 & 8–15 & 49 & 1.8 & 79 & 3.9 & 64 & 54 & 30 \\
4 & & 49 & 1.5 & 95 & 5.3 & 264 & 54 & 32 \\ \hline
1 & & 56 & 3.5 (1.4) & 340 (140) & 7.4 & 62 & 60 & 38 \\
2 & 18–25 & 42 & 3.5 & 220 & 4.8 & 68 & 62 & 72 \\
3 & & 49 & 3.5 & 230 & 6.5 & 105 & 62 & 70 \\
4 & & 49 & 3.5 & 290 & 5.3 & 109 & 53 & 16 \\ \hline  & 3–10 & & 1.8 & 130 & 6.7 & 177 & 59 & 41 \\ A & 8–15 & 30 & 1.6 & 24 & 1.2 & 142 & 51 & 25 \\  & 18–25 & & 3.5 & 140 & 3.1 & 92 & 58 & 78 \\  & 18–25 & 143 & 3.5 & 120 & 2.6 & 92 & 57 & 81 \\ \hline  & 3–10 & & 2.4 & 310 & 11 & 220 & 62 & 36 \\ C & 8–15 & 54 & 1.8 & 53 & 2.5 & 154 & 45 & 62 \\  & 18–25 & & 3.5 & 150 & 3.5 & 106 & 60 & 89 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of dominant GWs using combined conventional methods (CCM) on simulated vertical profiles of horizontal wind and temperature on 7 August 12:00 UTC. Values are derived from peaks of wave parameter distributions. Region: location of vertical profiles; heights: altitude range; number: number of extracted profiles; \(\lambda_{\Psi}\) and \(\lambda_{\hbar}\): vertical and horizontal wavelengths; \(T\): intrinsic period; _Phi:_ direction of horizontal wave propagation (clockwise from north), _Fup_: fraction of upward energy; _d:_ degree of polarization. Region 0 (20\({}^{\circ}\)–26\({}^{\circ}\) N; 120\({}^{\circ}\)–172\({}^{\circ}\) E) is divided into four sub-regions from the TC eye (23\({}^{\circ}\) N, 123.2\({}^{\circ}\) E): 1 (upper left), 2 (upper right), 3 (lower right) and 4 (lower left). Figure 15: **(a)** FormoSat-3/COSMIC RO profiles of temperature at heights of 3–30 km from 07:51 UTC to 09:57 UTC nearby the TC on 7 August 2015. **(b)** Perturbations in the troposphere (left) at 2–15 km and LS at 18–30 km (right). Part **(c)** and **(d)** correspond to spectral density as a function of vertical wavelength respectively. For all figures, refer to colors in the legend of Figure 5a for the date and location of the RO profiles and also Figure 7a for the spatial distribution.