1. Results We first best-fit the zonal wind and temperature simulated in the 3D PlanetWRF using the semi- analytic 2D model with,,, and. See Fig 2. The similarity between these two models strongly suggest that the dynamics of Titan’s stratosphere can be adequately described in terms of three parameters. The fact that implies that mechanical damping dominates Titan’s stratosphere. With this choice of parameters, we further compare the seasonal differences of meriodional and vertical winds in Fig 3. The semi-analytic model qualitatively reproduces the magnitudes of these two variables. However, there are large differences in the altitudes of maximum seasonal responses, which may be results of non-linear dynamics or upper boundary effects in the 3D model that are absence in the semi-analytic model. A cyclostrophic transformed Eulerian zonal mean model for the middle atmosphere of slowly rotating planets Kaixuan Yao 1, King-Fai Li 2,$, Cameron Taketa 2, Xi Zhang 3, Mao-Chang Liang 4, Xun Jiang 5, Claire Newman 6, Ka-Kit Tung 2, Yuk L. Yung 7 1 Chinese University of Hong Kong 2 University of Washington, Seattle, WA 3 University of California, Santa Cruz, CA 4 Academia Sinica, Taiwan 5 University of Houston, Houston, TX 6 Ashima Research, Pasadena, CA 7 California Institute of Technology, Pasadena, CA Summary  Here we develop a semi-analytic zonally averaged, cyclostrophic residual Eulerian model for Titan’s stratosphere with simple thermal (e.g. solar heating) and mechanical (the Eliassen-Palm flux divergence) forcings.  This model is a generalization of that for fast rotating planets such as the Earth, where geostrophy dominates [Andrews et al., 1987]. The governing equation is a generalized Laplace’s tidal equation with the cyclostrophic effects.  The seasonal variations of temperature and zonal wind of Titan’s stratosphere can be well reproduced by adjusting only three parameters in the semi-analytic model: the Brunt–Väisälä buoyancy frequency, the Newtonian radiative cooling rate, and the Rayleigh friction damping rate.  There are quantitative differences in the meridional and vertical winds that require further diagnostics of the semi-analytic and the 3D models. Motivation  The Huygens-Cassini missions has been providing observations of Titan’s atmosphere since 2004 (till 2018).  Seasonal cycle is radiatively balanced and is a good starting point of model validation. To date, only 1/3 of the seasonal cycle has been observed (1 Titan year = 26 Earth years).  Currently, the Huygen-Cassini data has been used for simulating the whole seasonal cycle in PlanetWRF [Richardson et al. 2007]. However, such 3D GCMs are usually very complicated and the simulations are sometimes difficult to understand.  To better diagnose the dynamics of Titan’s stratosphere, we develop a 2D circulation model [Plumb 1982; Garcia 1987] for the seasonal cycle and examine the Eulerian residual circulation that is important for latitudinal transport of chemical species. Semi-Analytic Model The zonally averaged, cyclostrophic residual Eulerian model to be used is described by the following equations: The terms in red are cyclostrophic effects that are usually ignored in Earth’s stratosphere. This set of equations are applicable to Titan’s stratospheric region at 150–500 km (above the haze layer). The above system of equations is nonlinear. To obtain a semi- analytic solution, the zonal wind is linearized into mean + seasonal difference (summer minus winter): where ω=26 years is the annual frequency. Then the above equations can be recast into the following modified tidal equation where The ordinary tidal equation is obtained if. As a test, we assume radiative equilibrium where and that the seasonal cycle is a slow process relative to radiative heating/cooling:. The difference in seasonal hemispheric solar heating is assumed to take the following analytic form: References. Andrews et al. (1987) Middle atmosphere dynamics; Richardson et al. (2007) JGR, 112, E09001; Plumb (1982) JAS, 39, 983; Garcia (1987) JAS, 44, 3599. $ Correspondence author: kfli@uw.edu Momentum equation Thermal wind relation Hydrostatic equation Heat equation Continuity equation Figure 1. Schematics of Huygens-Cassini missions Figure 2. Comparisons of u and T from the semi-analytic 2D model (left column) with those from the 3D Planet WRF (right column). Figure 3. Same as Fig 2 except for v and w.