Controls of 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 to quantitatively determine the controls on glacial valley spacing assuming an initially-undissected landscape, an initially-fluvially-dissected landscape, and an initially-cratered landscape. The characteristic spacing of glacial valleys produced by the model is controlled by a competition between the thickening of ice in incipient glacial valleys, which acts to enhance flow and valley deepening, and viscous/sidewall drag, which acts to limit flow and deepening. The glacial valley spacing that represents the best compromise between these two competing effects is found to be a function of valley slope, the threshold basal shear stress for ice motion, the effective ice viscosity, a bed-friction parameter, and gravity. This model framework provides the preliminary basis for understanding the relative spacing of glacial valleys on Earth and Mars. On Mars, montane glacial valleys have widths and spacings that are approximately 10-20 times larger than those on Earth. Model results suggest that this difference is predominantly a consequence of lower bed slopes and larger temperature-controlled ice viscosities of glacial ice on Mars compared to Earth.