# Elliptical Structures of Gravity Waves Produced by Typhoon Soudelor in 2015 near Taiwan
## 3 Overview of TC Soudelor and Model Validation
### Model Validation
Indeed, the GPM product reconstructed the precipitation with nearly 62% accuracy, with an overestimation that gradually decreased away from the TC center [59]. Compared with the observed 24 h rainfall (Figure 4 in Reference [55]) from 7 August 12:00 UTC to 8 August 12:00 UTC, the spatial rainfall distribution was well simulated above the CMR (Figure 5b). Figure 6 shows the vertical cross sections of tangential and radial wind speed, equivalent potential temperature and temperature anomalies with respect to a TC-unperturbed environment, on 7 August 12:00 UTC passing through the TC center at latitude 23\({}^{\circ}\) N (Figure 4b). This provided insight into a realistic structure of a mature TC as previously described in References [28; 60]. Figure 6a visualizes the primary TC circulation with increasing radius of maximum winds (RMW) with height in agreement  
Figure 5: (a) Cumulative rainfall (mm) from 6 August 00:00 UTC to 8 August 00:00 UTC from WRF outputs. The solid black (red) line displays the best (WRF) track. (b) A close up, from Image a), of Taiwan. with the eyewall slopes radially outward height. The isocontours of 60 m/s bordered the intense wind core from the ground to about a height of 5 km (3 km) on the eastern (western) side and highlighted the wind asymmetry with height, especially above 3 km. Large wind speeds, >80 m/s, were mostly located on the eastern side at about 1 km above the surface. The freezing levels of the TC-unperturbed environment and those above the TC eye agreed with climatological monthly values over Taiwan during the TC season [61] and those in the TC inner core [60], respectively. The simulation also indicated that both the freezing level and the tropopause height were affected by the topography. Tangential wind speed of 40 m/s can be visualized up to about a 14 km height below the tropopause at about longitude 124.5\({}^{\circ}\) E. The cross section of radial wind showed the asymmetric low-level inflows in the PBL and upper-level outflows below the tropopause (Figure 6b). At 12:00 UTC, the topography affected the low-level inflow and upper tropospheric outflow ahead of the TC. Near the eyewall region, equivalent potential temperature \(\theta_{e}\) (Figure 6c) depicted the divergent, slantwise, moist isentrope slope, the strong gradient in the eyewall and at the top of the marine PBL, the high values in the TC eye in the PBL, the descent of dry air into the TC eye and along the outer side of the eyewall, and the warm and dry central core at about a 5 km height [28; 60; 62]. The vertical cross section of temperature anomalies, beyond the longitude 123.2\({}^{\circ}\) east of the TC eye, revealed the presence of a double warm core with maxima of +9 K and +7 K at heights of about 4-5 km and 14 km, respectively (Figure 6d). The second warm core had a similar amplitude, but located about 1.5 km higher at 00:00 UTC. The observation of the two warm anomalies in the troposphere within a radius of 75-100 km was consistent with previous studies on relatively intense TCs [63; 64]. Reference [65] described the formation of an upper-level warm core from the subsidence of stratospheric air into the eye, which coincided with the onset of the rapid intensification of TC Wilma (2005). Reference [66] argued that the location of warm cores is dependent on the vertical profiles of static stability and mean descent. The double warm core of intense simulated TCs, is usually accompanied by a thin upper-level inflow layer in the LS above the typical upper outflow layer (Figure 6b), which can advect potentially warm air from the LS (Figure 6d) toward the inner core region [64]. Reference [67] concluded that such interactions of intense TCs with the LS are responsible for the presence of the upper-level warm anomaly and possible episodes of TC intensification. At present, the dynamics of a double warm core and its relationship with TC intensity as well as intensity change still need to be explored [65; 66].