Algorithmic Classification of Drainage Networks on Mars and Its Relation to Martian Geological Units

We present an algorithmic classification of drainage networks on Mars. Altogether, 368 drainage networks were computationally extracted using MOLA topographical data from various martian locations covering 16 major geological units. The classification is quantitative and objective, as it is based on a numerical description of drainage networks. Applying a clustering algorithm to our dataset, we have found that the networks can be best divided into 9 clusters. These clusters are separated from each other, so they can be used for classification purposes. Our partition does not correlate with an existing division into geological units. A morphological interpretation for this emergent classification is still been developed. One particular cluster was studied in detail, and we have determined that it groups networks overlaying landscapes dominated by topographical basins. Introduction. The morphology of martian landscapes is of great interest because it helps to identify physical processes responsible for the presently observable topography. Traditionally, the descriptive morphology has been used to study and categorize different types of martian landscapes. This resulted in dividing the martian surface into a number of geological units, terrains with common morphological features (1). Our long-term goal is to devise an algorithm capable of classifying martian landscapes objectively and quantitatively, solely on the basis of topographical data provided by the Mars Orbiter Laser Altimeter (MOLA). Such an algorithmic classification may cut across existing divisions. In this paper we present the first step toward our goal, an algorithmic classification of martian drainage networks. Using MOLA topographical data, a drainage network can be computationally extracted (2) from any terrain, including terrains that never experienced any real flow. We prefer to work with drainage networks because they are much simpler than their underlaying landscapes. We assume that there is enough correspondence between a landscape and its drainage network that the classification of networks is tantamount to the classification of landscapes. A morphology of a drainage network can be encapsulated (3) in a so-called "network descriptor", a list of four numbers A = (τ, γ, β, ρ). Briefly, τ , γ, and β are parameters that characterize distributions of contributing areas, lengths of main streams, and dissipated energy, respectively. The parameter ρ measures the spatial uniformity of drainage. The network descriptor offers an abstract but very compact characterization of a drainage network. Our methodology is to classify drainage networks based on the values of their network descriptors (two networks are similar if the values of their descriptors are similar). Our dataset consist of values of A derived from martian drainage networks. We applied a clustering algorithm over our dataset that produces as output a set of clusters {c1, c2, · · · , ck}, where each cluster ci covA B C D E F G H I A B C D E F G H I Figure 1: The matrix of normalized distances between clusters A to I. The matrix is symmetric. Black color corresponds to d = 0, red colors correspond to d < 1, green colors correspond to d > 1. Lighter green, turning into blue corresponds to larger value of d (bigger separation). ers certain number of network descriptors (networks) that are similar to each other and distinct from the rest. The set of clusters is mutually exclusive and exhaustive, it constitutes a good basis for classification if the resulting clusters are well separated from each other. Data and Methods We have extracted 386 drainage networks from martian locations with a wide range of latitudes and elevations that 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). There are 152 (39%) networks extracted from Noachian surfaces, 145 (38%) from Hesperian, and 89 (23%) from Amazonian. The probabilistic clustering algorithm used in our experiments (4) groups records into clusters by modelling each cluster through a probability density function. Each record in dataset then has a probability of class membership and is assigned to the cluster with highest posterior probability. Unless known a priori, the optimal number of clusters is normally not known and one must employ some form of cross-validation to estimate this value. The implementation we used (5) varies the number of clusters automatically until it reaches an optimum value. Results. Applying the clustering algorithm directly over Algorithmic Classification of Drainage Networks on Mars: T. F. Stepinski et al.