Modelling large‐scale landform‐evolution with a stream‐power law for glacial erosion: Benchmarking experiments against a more process based description of ice flow.

The topographic imprint of glacial erosion is visible by characteristic landforms in mountain ranges worldwide. These forms represent some of the most consistent observations related to the interaction between glaciers and their beds. However, modeling large-scale glacial landscape evolution built on a process-based understanding of ice dynamics is challenging and the few existing models require a high numerical effort.
Recently, Hergarten (2021) developed a glacial landscape evolution model based on a stream-power law for glacial erosion and coupled it with a fluvial erosion model considering both incision and sediment transport. This approach directly computes the glacial erosion rates from topographic properties and simple climate assumptions. In this manner, it requires an initial parameterization of the glacier width and length as a function of ice flux. In contrast, models based on the shallow-ice approximation (SIA) do not need these empirical relations, as they compute the ice flow based on the initial valley geometry, its slope and ice flux parameters. Hence, this simplification restricts the glacial stream power law to valley glaciers but allows for large-scale simulations over the million years' time scale, while ice flow models (e.g., SIA) are restricted to smaller domains and/or shorter timescales.
In this study, we benchmark Hergarten’s (2021) approach against a state-of-the-art surface process model for glacial erosion (iSOSIA) (Egholm et al., 2011). We highlight the limitations and advantages of each model and show that the simple model is also suited to reproduce large-scale landscape patterns observed in natural glacially shaped landscapes.

Egholm, D. L., Knudsen, M. F., Clark, C. D., and Lesemann, J. E. (2011), Modeling the flow of glaciers in steep terrains: The integrated second-order shallow ice approximation (iSOSIA), J. Geophys. Res., 116, F02012, doi:10.1029/2010JF001900.
Hergarten, S.: A stream-power law for glacial erosion and its implementation in large-scale landform-evolution models, Earth Surf. Dynam. Discuss. [preprint], https://doi.org/10.5194/esurf-2021-1, in review, 2021.