The Medusae Fossae Formation (MFF) is an enigmatic group of terrain features which dominate a quarter of equatorial Mars (extending - 5,500 km east-west). The MFF is characterised by a discontinuous, highly eroded appearance and is inferred to comprise fine grained and friable materials. This long-standing interpretation is based on observations of the prevalent aeolian erosional features (yardangs), This thesis aims to improve constraint of both the materials ori gins and the processes at work during and since their emplacement. The project uses a multi-scale, geomorphological approach, and uses the latest very high resolution (25 cm/pixel), and new medium resolution (6- 12 m/pixel), high spatial coverage data and attempts to use surface characteristics to constrain the origin of the formation. This thesis describes surveys of outlying MFF materials (to infer the palaeo-extent of the MFF), and a survey of textural characteristics of the outcrop materials and the quantitative analysis of yardangs. Following on from this, an evaluation of existing facies mapping (to improve understanding of the formation and evolution of the MFF) is discussed. A survey, and detailed study in one location, of sinuous ridge features (to evalu ate the role of volatiles and fluvial transport in the MFF) is also included. The key results include a larger pre-erosional spatial extent for the formation than previously thought, wherein outliers of the MFF are found on the Tharsis volcanic region and a hitherto unmapped uppermost "draping" unit is present. The existing definition of the geological members is found to require refinement. Furthermore, volatile content within the MFF is judged to be heterogeneous, and not limited to the oldest stratigraphic units. The evidence collated in this work is consistent with the hypothesis that the Medusae Fossae Formation is an ignimbrite deposit, comprised largely of dry (at least today), low density materials. but some MFF regions had much higher volatile content than others in the past.

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.