Numerical modeling of glacial erosion and headwall processes in alpine valleys

How rock relief is developed by glacial erosion in alpine landscapes is a key question in understanding the controls on mountain range topography. Any generation of relief by glaciers at the highest elevations in mountain ranges can affect the distribution of precipitation in alpine landscapes, creating feedbacks between glacier mass balance and glacial erosion. Relief production at high-elevation mountain crests is addressed using a numerical model that incorporates glacier dynamics and subglacial erosion, as well as relevant hillslope processes. Blowing snow from a valley-bounding plateau, and avalanching onto the accumulation zone of the glacier is included in the model. Furthermore, temperature-dependent frost cracking is used as a proxy for headwall backwearing. The parameterization of subglacial erosion produces about 500 m of erosion over the 400 ka of each numerical simulation. In steady and varying climate scenarios, valley floors flatten as headwalls increase in height and retreat headward over time. Headwall slopes increase in simulations in which quarrying is explicitly incorporated; rates of quarrying are high near the base of the headwall, increasing headwall length and slope as a result of valley floor lowering. High rates of subglacial erosion and production of headwall relief also result when elastic flexural uplift occurs in response to mass unloading. Small overdeepenings form at the base of the headwall in steady-climate simulations, when the glacier is small at the end of the model run. While the final profiles are relatively insensitive to the erosion rule used, quarrying is most effective near the head of the glacier, whereas rates of abrasion reflect the instantaneous pattern of integrated ice discharge, or ice flux. In simulations in which cirques are formed, the equilibrium line altitude is hundreds of meters above the cirque floor; however, the time-averaged horizontal position of the equilibrium line corresponds well with the downvalley position of the cirques.