# Elliptical Structures of Gravity Waves Produced by Typhoon Soudelor in 2015 near Taiwan
## 4 Results
Regions A, B, C and D are drawn on the Figure 8.  
Figure 10: (**a**) Vertical profiles of zonal (solid red) and meridional wind (solid green), and temperature (solid blue) at location (22\({}^{\circ}\) N, 124.3\({}^{\circ}\) E) in region C. Mean vertical profiles (dash-dotted) are retrieved using a fourth-order Butterworth low-pass filter with a 7 km wavelength cutoff. (**b**) Temperature and horizontal wind perturbations. The CWT was applied on a 6 min time series of normalized dynamical parameters (zonal, meridional and vertical wind) above two sites located at the same latitude (124\({}^{\circ}\) E, 24.3\({}^{\circ}\) N) and (131.2\({}^{\circ}\) E, 24.3\({}^{\circ}\) N), respectively, ahead and at the rear of the TC in the LS (20 km height) during the passage of TC Soudelor in the domain D3 during the 24 h period from 6 August 18:00 UTC to 7 August 18:00 UTC. The vertical wind perturbations were extracted by removing the constant trend from the time series. Then, the spectral lines, with values \(>\)20% of the maximum value, were derived from the CWT maxima to highlight the time evolution of dominant periods. In particular, they showed evidence of a dominant wavelike structure with periods of 9-14 h in the perturbations above the two sites (Figure 14). The analyses also depicted wavelike structures with periods of 3-7 h. In particular, transient high-frequency modes with period \(<\) 1 h are clearly observed ahead of the TC in vertical wind perturbations on 7 August from 04:00 UTC during the intensification phase (Figure 14b). Reference [73]  
Figure 12: (a), (b) and (c) similar as Figure 11 but in the TC eye (23\({}^{\circ}\) N, 123.2\({}^{\circ}\) E). Figure 13: (a) Normalized-spectral energy distribution of vertical wavelengths at heights of 3–10 km (solid), 8–15 km (plus) and 18–25 km (dash-dot) in zonal (black) and meridional (red) wind perturbations at latitude 23\({}^{\circ}\) N. (b) Longitude–altitude distribution of normalized intrinsic frequencies _a_f_ with contours of tangential wind (blue solid) and tropopause height (dashed) at latitude 23\({}^{\circ}\) N. (c) Normalized intrinsic frequencies _a_f_ (solid) and standard deviation (dashed) as a function of altitude at latitude 23\({}^{\circ}\) N. (d) Normalized distributions of occurrence of periods at heights of 3–10 km, 8–15 km, 18–25 km and 3–25 km at latitude 23\({}^{\circ}\) N.  
suggested that momentum flux for GWs with frequencies of 0.3-2 h produced by TC Saomai (2006) might have significantly affected the TC development. Figure 14a,b,d also visualizes a discontinuity at about 10:00 UTC-12:00 UTC in the time evolution of mode of 6 h period when TC Soudelor started to interact with the island and the TC intensity decreased. The CCM was applied to the simulated vertical profiles of wind and temperature perturbations in different regions of the domain D1 to characterize the elliptical structures of dominant GWs (Table 1). A regular spatial sampling at every 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) provided 196 vertical profiles in the domain 0 (20\({}^{\circ}\)-26\({}^{\circ}\) N; 120\({}^{\circ}\)-172\({}^{\circ}\) E) centered on the location of the TC eye (23\({}^{\circ}\) N, 123.2\({}^{\circ}\) E) at 12:00 UTC on 7 August. The fraction of upward energy _Fup_, the degree of polarization \(d\) and the direction of the horizontal wave propagation _Phi_ indicated mixed upward and downward GWs with short vertical and horizontal wavelengths of 1.6 km and 31 km, respectively, and a period of about 2 h propagated westward in the UT. In opposition, GWs were more polarized in the LS with dominant upward wave energy. They had longer vertical and horizontal wavelengths of 3.5 km and 250 km, respectively, and a period of about 6 h with eastward propagation. Then, characteristics of GWs were examined in the four equal sub-regions of the domain 0 from the TC eye (23\({}^{\circ}\) N, 123.2\({}^{\circ}\) E): 1(upper left), 2 (upper right), 3 (lower right) and 4 (lower left).