Mathematics – Probability
Scientific paper
May 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005agusm.p32a..05l&link_type=abstract
American Geophysical Union, Spring Meeting 2005, abstract #P32A-05
Mathematics
Probability
1815 Erosion And Sedimentation, 1824 Geomorphology (1625), 6225 Mars
Scientific paper
Whether the Martian valley networks were formed predominantly by groundwater sapping or surface fluvial runoff continues to be debated and has profoundly different implications for the climatic history of Mars and the possible evolution of life there. This paper attempts to evaluate the relative role of groundwater sapping vs. surface runoff in valley networks generation through quantitative morphometic analysis at watershed basin scale using the highest resolution MOLA DEM data. Treating the hypsometric curve of each basin as a cumulative probability distribution, its integral, skewness, kurtosis, density skewness, and density kurtosis (collectively called hypsometric attributes) can serve as quantitative measures of the basin's morphology. The hypsometric attributes are sensitive to variations in overall basin characteristics and thus are diagnostic of possible processes. These attributes of typical terrestrial sapping basins, typical terrestrial fluvial basins, and typical lunar impact cratering basins were used as endmembers to establish discriminant functions to classify Martian basins. The posteriori probability of each class membership for each Martian basin then serves as the measure of the relative role of sapping, fluvial or cratering process in forming that basin. Initial results in Margaritifer Sinus area show that groundwater sapping played a more dominant role than surface runoff, generally consistent with previous findings based on lower resolution data and supporting a precipitation-recharged groundwater sapping origin for valley networks. Using a circularity function (a ratio of area and perimeter as a function of elevation) as the measure for basin morphology in the discriminant analysis produced similar results. Other traditional morphometric parameters such as drainage density, width function, cumulative area distribution, and slope-area relationship will also be derived for Margaritifer and other areas. The overall spatial pattern of the distribution will be examined to shed more light on past climatic conditions for generating the Martian valley networks.
Arvidson Ray E.
Howard Alan D.
Luo Wenchen
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