A POD-Galerkin approach to the atmospheric dynamics of Mars - Martínez-Alvarado, O; Oscar Martinez-Alvarado (2007)
The observation of less chaoticity and enhanced interannual periodicity of transient waves in the Martian atmosphere in comparison with that of the Earth suggests the hypothesis of a low-dimensional underlying atmospheric attractor. Grounded on this hypothesis, two questions can be asked: is there a small set of atmospheric modes, measured and classified by a suitable norm, capable of describing the atmosphere of Mars? If this set exists, are those atmospheric modes able to reproduce the dynamical behaviour of the atmosphere of Mars? The answer to these questions, constituting the central focus of this thesis, has led to the first application of POD-Galerkin methods to a state-of-the-art Mars general circulation model. The proper orthogonal decomposition (POD) as a method for extracting coherent structures, called empirical orthogonal functions (EOFs), provided a means to answer the first question in the positive. An important amount of atmospheric total energy (TE) was found to be concentrated in a few EOFs (e.g., 90% TE in 20 EOFs). The most energetic EOFs were identified with atmospheric motions such as thermal tides and transient waves. The Galerkin projection of the hydrostatic primitive equations onto the span of the EOFs provided a systematic method to establish physically plausible interactions between the most energetic EOFs. These interactions were complemented with closure schemes representing interactions with unresolved modes. This requirement proved to be essential in order to obtain bounded behaviour. In the diagnostic analysis, represented by the POD alone, increasing the number of EOFs directly leads to a better approximation of the atmospheric state. In contrast, the dynamic reconstruction of the atmospheric evolution does not depend only on the number of included EOFs. Other important factors to obtain realistic evolution are the inclusion of every mode involved in the description of a particular kind of motion (diurnal tide, semidiurnal tide or transients) and the retention of higher order modes that may interact strongly with the modes of interest. Once these conditions are satisfied the behaviour of the reduced models is greatly improved. Implications of these findings for future work are discussed.