THE INFLUENCE OF CLIMATE AND TOPOGRAPHY ON GLACIER EROSION RATES

Over the past three decades the scientific community interested in glacial erosion has grown significantly, and the field has advanced considerably through field studies of sediment yields from glaciers, theoretical studies of erosion processes, and numerical models of glacial landforms (U-shaped valleys and over-deepenings) and terrain shaped by ice. These models are very instructive and quite successful for specific applications, but their complexity makes them ill-suited for understanding general issues such as how erosion rates vary with climate and topography, and why basin scale glacier erosion rates vary by over 3 orders of magnitude. We propose a simple approach, and hypothesize that erosion rates scale directly with the energy available for the work of erosion per unit area and per unit time. We derive analytically a simple metric for this energy: φ=m_bΔz², where Δz is the glacier basin relief and m_b the gradient of net annual snow accumulation (the mass balance) with elevation. The metric is a measure of the gravitational potential energy (mass·gravity·elevation) supplied annually by snow fall. We assume the mass balance increases linearly with elevation above the terminus. The dependence of φ on the square of the relief, Δz, arises from the mass balance increasing with elevation as well as the potential energy of any mass also increasing with elevation. We test φ using the results of a recent comprehensive study of erosion rates paired with corresponding glaciological data along a transect extending from Southern Patagonia down to the Antarctic Peninsula, (Koppes et al. 2015, Nature, 526(7571), 100). Along this transect φ accounts for 75% ± 12% of the variation in the measured erosion rates. These promising results suggest the approach outlined here may well prove useful in other studies of large-scale glacial erosion and likely has significant implications for the broader community interested in the interaction between climate, topography, and glaciers.