| Summary: | In glacial landscape evolution models, subglacial erosion rates are often related to basal sliding or ice discharge by a power-law. This relation can be justified when considering bed abrasion, where rock debris transported in the basal ice drives erosion. However, the relation is not well supported when considering models for quarrying of rock blocks from the bed. Field observations indicate that the principal mechanism of glacial erosion is quarrying, which emphasize the importance of a better way of implementing erosion by quarrying in glacial landscape evolution models. Iverson (2012) introduced a new model for subglacial erosion by quarrying that operates from the theory of adhesive wear. The model is based on the fact that cavities, with a high level of bedrock differential stress, form in the lee of bed obstacles when the sliding velocity is too high to allow for the ice to creep around the obstacles. The erosion rate is quantified by considering the likelihood of rock fracturing on topographic bumps. The model includes a statistical treatment of the bedrock weakness, which is neglected in previous quarrying models. Sliding rate, effective pressure, and average bedslope are the primary factors influencing the erosion rate of this new quarrying model [Iverson, 2012]. We have implemented the quarrying model in a depth-integrated higher-order ice-sheet model [Egholm et al. 2011], coupled to a model for glacial hydrology. In order to also include the effects of cavitation on the subglacial sliding rate, we use a sliding law proposed by Schoof (2005), which includes an upper limit for the stress that can be supported at the bed. Computational experiments show that the combined influence of pressure, sliding rate and bed slope leads to realistically looking landforms such as U-shaped valleys, cirques, hanging valleys and overdeepenings. The influence of the effective pressure leads naturally to overdeepenings. However, in contrast to previously used erosion models, this quarrying rule is without unstable run-away effects because hydrology provides stabilization. For the water to escape the overdeepening, the average water pressure must rise, which keeps the effective pressure low and prevents the overdeepening from growing infinitely. In addition, the strong influence of effective pressure indicates that erosion rate depends strongly on ice thickness. This could associate to sudden jumps in erosion rate and fjord formation along margins that experienced periodic ice sheet configurations in the Quaternary. Egholm, D. L. et al. Modeling the flow of glaciers in steep terrains: The integrated second-order shallow ice approximation (iSOSIA). Journal of Geophysical Research, 116, F02012 (2011). Iverson, N. R. A theory of glacial quarrying for landscape evolution models. Geology, v. 40, no. 8, 679-682 (2012). Schoof, C. The effect of cavitation on glacier sliding. Proc. R. Soc. A , 461, 609-627 (2005).
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