COMPARISON OF FINITE DIFFERENCE METHOD AND COMPUTATIONAL CALCULUS APPROACHES IN SIMULATING LAVA FLOW PATHS ON MARS

Interest in simulating the path followed by lava flows has grown considerably in recent years, stimulated by advances in the understanding of lava flow processes, new computational algorithms, and a growing desire for rapid assessment of potential volcanic hazards. Real lava flows mostly head down slope, but deviations from this simple statement are difficult to reproduce in computational codes. Cellular automaton approaches grew from the computationally straight-forward method of searching a Digital Elevation Model (DEM) for the lowest elevation adjacent to each grid point. This previous explicit approach has been changed to an implicit Finite Difference Method (FDM) code with a shallow-water approximation applied in a semi-three-dimensional manner. This approach is contrasted with a new formulation derived from the calculus of surfaces, where the down slope direction at each point is determined by the horizontal projection of the local surface orthogonal vector, and the path is determined by an integration of the projected components for whatever scale is specified for the DEM in use. We have compared the results from both of these approaches to the path of a 480-km-long lava flow in the Tharsis region of Mars, where a flow with traceable margins extends northwest from the topographic saddle between Ascraeus and Pavonis Montes. A Mars Orbiter Laser Altimeter (MOLA) gridded data set (at 1/16th degree per element) was used as the DEM for these flow simulations. Both approaches reproduced a significant portion of the basic flow orientation, but both approaches also showed distinct local deviations from the actual flow path. The deviations may be due to 1) unmodeled flow properties that diverted the flow from the local gradient, 2) local topography below the scale of the MOLA grid, 3) post-emplacement tectonic modification of the topography, 4) or heretofore unrecognized systematic errors in the topographic data or its coregistration with the Viking images. This presentation represents a progress report in which our preliminary results are assessed in terms of the apparent strengths and weaknesses of each of these approaches for developing new inferences about the emplacement of such long flows.