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The Sliding Ice Incision Model: A New Approach to Understanding Glacial Landscape Evolution

Analytical long‐profile models of fluvial incision are fundamental in geomorphology for building intuition about long‐term landscape evolution and interpreting the climatic and tectonic histories of landscapes. However, analogous models are missing for glaciers, despite the fact that glaciers are important and widespread agents of physical erosion. We introduce a new model of glacial erosion in terms of catchment area, ice accumulation rate, and ice surface slope in a form that is similar to the classic stream power incision model for fluvial erosion. We derive an analytical solution for coupled glacial‐fluvial networks under steady‐state climate and uplift, predict an ice surface slope–catchment area power‐law relationship, and predict the scaling of orogen relief with uplift rate. Finally, we note that this theory should enable glacial landscape evolution models that rival modern fluvial models in efficiency.