Martian Geomorphology from Statistics of Drainage Networks

Martian terrains are represented as a series of drainage basins, regardless of the historical presence or absence of actual fluid flow. A statistical analysis of each drainage network, computationally extracted from an underlying topography based on the MOLA data, yields a network descriptor, a compact, numerical characterization of a network. These descriptors are used to compare different martian surfaces. Altogether, 386 drainage networks, representing all major epochs and geological units, were extracted and analyzed. We have found that our approach can distinguish morphologically different terrains, but only in a statistical sense. In particular, the method could be used to measure the degree of surface cratering and thus the age of the surface. In addition, for surfaces that are not heavily cratered the method is capable of distinguishing between different geological units. We have found no global trends in the character of martian drainage networks, their network descriptors show no systematic dependence on location or elevation. Introduction. We propose that a drainage network, overlaying a given martian terrain, constitutes a convenient compression of the entire topographical information contained in this terrain. Although the network does not uniquely determine the terrain, it nevertheless, reflects its general character. Thus, we submit that a quantitative comparison of drainage networks is tantamount to a quantitative comparison of landscapes. It is important to stress that a “drainage network" can be computationally extracted from any terrain, including terrains that never experienced any real flow. Comparative geomorphology of landscapes based on the Drainage Network Analysis (DNA) constitutes a quantitative and objective method that supplements traditional, descriptive comparative geomorphology. The purpose of this work is to study whether the DNA method is sensitive to the age of the terrain and whether it can recognize geological units. Data and Methods The martian terrains are modeled by digital elevation models (DEMs) that were constructed using the 1/64 degree per pixel MOLA data set. We have chosen 74 locations from around the martian globe to represent all three major epochs and 16 geological units: Npl1, Npl2, Npld, Nple, Nplr, Nh1, Had, Hh3, HNu, Hpl3, Hr, Hvk, Ael1, Aoa, Apk, Aps (1). Together, these terrains cover ∼ 3% of the martian surface, and the sampled geological units are representative of ∼ 50% of the planet. We have computationally extracted 386 drainage networks from these chosen locations using an algorithm developed for studies of terrestrial river basins (2). We describe networks in terms of probability distribution functions (PDFs) of drainage quantities defined at any point S on a network. Thus, in our DNA method the statistics of drainage quantities constitute the fingerprints of a landscape. Following (3) we describe the network by statistical properties of the following drainage quantities: a a total contributing area at S, l length of the longest upstream path starting from S, e dissipated potential energy, a product of the flow and the elevation rise along a segment of the network terminating at S. Because networks are fractals, the PDFs of these quantities are power laws, P (a) ∝ a−(1+τ), P (l) ∝ l−(1+γ), P (e) ∝ e−(1+β), and a given network can be statistically characterized by the power law indices τ , γ, and β. In addition, a drainage density, D, is defined for a sub-basin terminating at S and measures the average area drained per unit length of stream. We cannot unambiguously calculate the value of D, however we can calculate ρ, the ratio of the mean to the dispersion of the random variable D. The quantity ρ measures the uniformity of D, large values of ρ indicate high uniformity of D and point to a highly eroded surface. A morphology of a given network, and thus the morphology of an underlying landscape, can be encapsulated in a list, A, of four numbers A = (τ, γ, β, ρ) which we call the network descriptor. In our study several networks are extracted from a landscape of interest and the network descriptor, A, is calculated for every network. 0.2 0.3 0.4 0.5 0.6 τ 0.5 0.75 1 1.25 1.5 1.75 2