A simplified model of the Martian atmosphere -- Part 2: a POD-Galerkin analysis

In Part I of this study Whitehouse et al. (2005) performed a diagnostic analysis of a simplied model of the Martian atmosphere, in which topography was absent and in which heating was modelled as Newtonian relaxation towards a zonally symmetric equilibrium temperature field. There we derived a reduced-order approximation to the vertical and the horizonal structure of the baroclinically unstable Martian atmosphere, retaining only the barotropic mode and the leading order baroclinic modes. Our objectives in Part II of the study are to incorporate these approximations into a Proper Orthogonal Decomposition-Galerkin expansion of the spherical quasi-geostrophic model in order to derive hierarchies of nonlinear ordinary differential equations for the time-varying coefficients of the spatial structures. Two different vertical truncations are considered, as well as three different norms and 3 different Galerkin truncations. We investigate each in turn, using tools from bifurcation theory, to determine which of the systems most closely resembles the data for which the original diagnostics were performed.Citation: Whitehouse, S. G. et al. (2005). 'A simplified model of the Martian atmosphere - Part 2: a POD-Galerkin analysis', Nonlinear Processes in Geophysics, 12(5), 625-642. [Available at http://www.nonlin-processes-geophys.net/12/625/2005/]. © 2005 the authors. This article is distributed under the terms of the Creative Commons Attribution, NonCommercial and ShareAlike License (http://creativecommons.org/licenses/by-nc-sa/2.0/deed.en). This permits the copying and distribution of the work, and the making of derivative works, provided the original authors are credited. However, you may not use this work for commercial purposes, and if you alter, transform, or build upon this work, you must distribute the resulting work under a license identical to this one. For any reuse or distribution, you must make clear to others the license terms of this work. These conditions may be waived if you get permission from the copyright holder and, in the case of commercial use during the first five years, you also get permission from Copernicus Publications and the European Geosciences Union. N.B. 'A simplified model of the Martian atmosphere - Part 1: a diagnostic analysis' is also available in ORA