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Possible biases in scaling-based estimates of mountain-glacier contribution to the sea level

Abstract. Predicting mountain-glacier contribution to sea-level rise involves computing global-scale glacier loss under a given climate-change scenario. Such calculations are usually done with low-complexity and computationally-efficient approximate models of glacier dynamics. A statistical power-law relation between glacier volume and area (and/or length) is the basis of several such models. We simulate transient response of an ensemble of 551 glaciers from Ganga basin, the Himalaya, using a scaling-based method and a two-dimensional ice-dynamical model based on shallow-ice approximation (SIA). A comparison of the model outputs suggests that the scaling-based method systematically underestimates long-term ice loss due to a violation of the assumed time-invariant scaling. We derive expressions for the response time and climate sensitivity of glaciers simulated using a time-invariant scaling assumption, and validate them with results from the scaling-based simulation of the ensemble of glacier. These expressions are modified empirically to obtain similar parameterisations of the response properties of glaciers simulated with SIA. These new parameterisation yields a linear-response model which significantly reduces the above biases, while retaining the advantage of numerical efficiency.