CONTROLS ON GLACIAL VALLEY SPACING ON EARTH AND MARS

Low-order alpine glacial valleys on Earth commonly have a characteristic spacing of 1-3 km. Here we develop analytic and numerical solutions of a coupled numerical model for alpine glacial flow and subglacial bedrock erosion in two dimensions (2D) and three dimensions (3D) to quantitatively determine the controls on glacial valley spacing assuming an initially-undissected landscape and an initially-fluvially-dissected landscape. The characteristic spacing of glacial valleys produced by the model is controlled by a competition between the topographic steering of ice flow into incipient glacial valleys, which acts to enhance flow and valley deepening, and viscous drag, which acts to limit them. The glacial valley spacing that represents the best compromise between these two opposing effects is found to be a function of the ice viscosity, the threshold basal shear stress for ice motion, a bed friction parameter, and the valley slope. This model framework provides a basis for understanding the relative glacial valley spacing on Earth and Mars. On Mars, glacial valleys have widths and spacings that are 20-50 times larger than those on Earth. This difference is most likely a consequence of the larger ice viscosities that result from lower temperatures on Mars compared to Earth.