# Elliptical Structures of Gravity Waves Produced by Typhoon Soudelor in 2015 near Taiwan
## 2 Description of the Model and Methods of Analysis  
The Advanced Research Weather Research and Forecasting model (WRF-ARW) version 3.7.1 [32] was used to simulate TC Soudelor's (2015) approach to Taiwan between 5 August 00:00 UTC and 8 August 00:00 UTC. The control run (CTL) was based on a triple two-way interactive nested grid of 27 km (domain D1), 9 km (domain D2) and 3 km (domain D3), with respective time steps of 90 s, 30 s and 10 s, and grid points of 100 \(\times\) 60, 174 \(\times\) 135 and 498 \(\times\) 381 (Figure 1a). A terrain elevation with 30 s resolution was included in the simulation (Figure 1b). Prior to landfall, the time and spatial evolution of the sea's surface temperature (SST) and the ocean's heat content (OHC) data varied little (not shown), so that the SST field was fixed at 00:00 UTC on 5 August for the experiment. In particular, warmer waters of about 30 \({}^{\circ}\)C were displayed at longitudes between 124\({}^{\circ}\) E and 128\({}^{\circ}\) E on the right side of the TC track during its intensification late on 6 August. The WRF-ARW model also used a terrain-following hydrostatic pressure vertical eta coordinate. The vertical height up to 27 km was divided into 130 levels, tightly packed and increased linearly in the boundary layer and constant at higher altitudes (Figure 1c). The vertical step varied between 30 m and 230 m at heights below 3 km, and about 240 m up to 27 km heights. A 5-km Rayleigh damping layer above 27 km height was used to prevent spurious reflections of GWs at the model's top. The initial field and lateral boundary conditions were derived from the National Centers for Environmental Prediction Final's (NCEP FNL) 6-hourly analyses with a horizontal resolution of 1\({}^{\circ}\) and 26 sigma levels from the surface to 10 hPa. The physical processes resulted from the cumulus parameterization scheme of [PERSON] [33], the Yonsei-University planetary boundary layer (YSU PBL) described in Reference [34], the microphysical scheme of [PERSON] [35], the Rapid Radiative Transfer Model longwave radiation scheme [36], and the Dudhia scheme for shortwave radiation [37]. The YSU PBL scheme is commonly used in research and operational models for TC prediction [38]. The skill of the microphysical scheme of [PERSON] is evaluated via the forecasts of TC track and intensity in References [39; 40]. Explicitly resolving the convection with sufficiently high spatial and time resolutions is required to improve TC intensity and structure [41]. Thus, increased vertical resolution and reduced time-step size have been shown to significantly improve the structure of the inner core, but have little impact on the TC track [41]. The PBL and cumulus convection processes are highly sensitive to vertical resolution. Therefore, increasing vertical resolution in the lower layer could effectively strengthen the TC [42; 43]. Reference [44] reported no significant changes in maximum intensity when the horizontal grid spacing was decreased from 5 to 1 km and suggested a horizontal grid spacing of 3 km to resolve the rainbands. In the present study, wavelike structures with vertical wavelengths ranging between 500 m and 7 km were characterized with numerical and observational datasets. Vertical profiles of the dynamic parameters, such as the wind and temperature, were resampled at a resolution of 100 m, using a cubic spline interpolation, and then analyzed with different methods to derive the spectral characteristics of the GWs. First, the vertical profiles of the perturbations were retrieved using a fourth-order low-pass Butterworth filter with a 7 km cutoff.