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 gamma approximate to 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 gamma = 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. Citation: Adhikari, S., and S. J. Marshall (2012), Glacier volume-area relation for high-order mechanics and transient glacier states, Geophys. Res. Lett., 39, L16505, doi:10.1029/2012GL052712.