# Elliptical Structures of Gravity Waves Produced by Typhoon Soudelor in 2015 near Taiwan
## 1 Introduction  
Atmospheric chemistry and climate are very sensitive to the variability of the tropical lower stratosphere (LS) [1]. In particular, tropical wave forcing significantly affects this key region [2]. Small-scale gravity waves (GWs) are ubiquitous multi-scale atmospheric waves in the tropical troposphere, which remain hard to fully observe and represent in models. Indeed, climate modeling has revealed that GWs could account for 59% of the 2% per decade increase of annual mean tropical upwelling in the LS and reduce cold-pole bias in the Southern Hemisphere [3, 4]. Both parameterized and resolved GW simulations with Global Climate Models (GCM) supported the vertical coupling in the atmosphere-ionosphere system [5], with increasing dominance of GWs at higher altitudes and significant impacts on the large-scale flow [6]. Recently, Reference [7] reported that orographic and nonorographic GWs contributed evenly to GW forcing in the stratosphere. Thus, many operational numerical weather prediction (NWP) models now extend into the stratosphere and forecast seasonal time scales, requiring the implementation of accurate computationally optimalGW drag parameterizations [8]. Reference [9] proposed some key modifications and a stochastic approach to producing a quasi-biennial oscillation (QBO) with realistic amplitude and a period in a high-altitude NWP model. However, the ability to quantify GWs is subject to open debate in the tropical atmosphere [6; 10]. Among GW sources, tropical cyclones (TCs) are well-organized mesoscale convective systems that produce a wide variety of intermittent nonorographic GWs in the tropics. However, both observations and modeling partially captured GW characteristics depending respectively on the observational instruments [11; 12; 13; 14; 15] and the model setup [16; 17; 18; 19]. Reference [20] derived dominant low-frequency GWs with short vertical wavelengths of 1-3 km, horizontal wavelengths of 80-400 km and periods of 4.6-13 h in the upper troposphere (UT) and LS from radiosonde and FormoSat-3/COSMIC (Formosa Satellite Mission-3/Constellation Observing System for Meteorology, Ionosphere, and Climate) radio occultation (RO) datasets, while mesoscale modelling with a vertical resolution of about 500 m highlighted a wide spectrum of resolved GWs with horizontal wavelengths of 20-2000 km, short vertical wavelengths of 1.5-4 km and periods of 20 min-2 days and up to 25 km height in the LS. The accuracy of the first measurements of the vertical atmospheric profiles, of the refractivity, temperature, and pressure from FormoSat-3/COSMIC, was demonstrated by Reference [21]. Using FormoSat-3/COSMIC temperature profiles, both deep convections and GW activity were shown to affect the variations of the tropopause parameters in the tropics [22]. Significant progress has been made in the forecasting of TCs in the last decades, including track, intensity, and structure [23]. Nevertheless, forecasting intensity changes in the TCs remains a challenging issue strongly dependent on our understanding of multiscale dynamical processes, such as wave processes. Improving TC intensity forecasting is one of the highest priorities, especially prior to and during landfall because of fast coastal population growth. In particular, some observation and numerical studies supported that TC-induced GWs in the UT and LS could be indicative of TC intensity. Reference [24] correlated the maximum surface wind speeds of TCs Dina (2002) and Faxai (2001) with GW energy density. A 10-season climatology confirmed the link between increasing GW energy density and TC activity [25]. Recently, atmospheric infrared sounder (AIRS) observation indicated a correlation between the activity of stratospheric GWs with horizontal and vertical wavelengths of about 90-100 km and 10-15 km, respectively, and TC intensity change [26]. At lower altitudes, Reference [27] reported a correlation between TC intensity and the wave amplitudes of high-frequency GWs (periods \(<\) 1 h) with radial wavelengths of 2-10 km.