Glacier volume‐area relation for high‐order mechanics and transient glacier states

Glacier volume is known for less than 0.1% of the world's glaciers, but this information is needed to quantify the impacts of glacier changes on global sea level and regional water resources. Observations indicate a power‐law relation between glacier area and volume, with an exponent γ ≈ 1.36. Through numerical simulations of 3D, high‐order glacier mechanics, we demonstrate how different topographic and climatic settings, glacier flow dynamics, and the degree of disequilibrium with climate systematically affect the volume‐area relation. We recommend more accurate scaling relations through characterization of individual glacier shape, slope and size. An ensemble of 280 randomly‐generated valley glaciers spanning a spectrum of plausible glaciological conditions yields a steady‐state exponent γ = 1.46. This declines to 1.38 for glaciers that are 100 years into a sustained retreat, which corresponds exceptionally well with the observed value for present‐day glaciers.

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