Origins of Martian valley networks based on a comparative statistical analysis of Martian and terrestrial basin shape functions

Abstract

Despite more than 35 years of study since the discovery of the Martian valley networks, questions still exist as to the fluvial process responsible for their origin. As part of the investigation on the relative importance of surface runoff versus groundwater sapping in the formation of the Martian valley networks, morphometric methods provide an objective and quantitative approach. In this study, four shape indices (circularity, elongation, lemniscate index and lemniscate ratio), traditionally used to quantify the planimetric shape of terrestrial drainage basins, are adapted into shape functions to determine the evolution of basin shape with elevation. The shape functions of 39 terrestrial basins of known origins (surface runoff, groundwater sapping, or meltwater) are analyzed to determine their ability to distinguish between different formation processes. Through hierarchical clustering analysis, it is determined that regional slope exerts a stronger control on a basin's internal shape than formation process. Once basins are divided into separate groups based on their regional slope (steep vs. flat), hierarchical clustering analysis is successful at clustering basins with respect to their formation process based on their shape functions. The shape functions are then used to characterize 23 Martian valley networks. Using self-organizing maps and k-nearest neighbour, the shape functions of the Martian basins are classified as most similar to the groundwater sapping basins of Chile's Atacama Desert. However, reasons for this similarity are not limited to groundwater sapping and could also be attributed to, among other possibilities, a combination of intermittent and scarce precipitation, the effects of impact cratering, or differences in the erosional mechanics that formed the Martian valley networks.