Possible biases in scaling-based estimates of glacier change: a case study in the Himalaya

Abstract. Approximate glacier models are routinely used to compute the future evolution of mountain glaciers under any given climate-change scenario. A majority of these models are based on statistical scaling relations between glacier volume, area, and/or length. In this paper, long-term predictions from scaling-based models are compared with those from a two-dimensional shallow-ice approximation (SIA) model. We derive expressions for climate sensitivity and response time of glaciers assuming a time-independent volume–area scaling. These expressions are validated using a scaling-model simulation of the response of 703 synthetic glaciers from the central Himalaya to a step change in climate. The same experiment repeated with the SIA model yields about 2 times larger climate sensitivity and response time than those predicted by the scaling model. In addition, the SIA model obtains area response time that is about 1.5 times larger than the corresponding volume response time, whereas scaling models implicitly assume the two response times to be equal to each other. These results indicate the possibility of a low bias in the scaling model estimates of the long-term loss of glacier area and volume. The SIA model outputs are used to obtain parameterisations, climate sensitivity, and response time of glaciers as functions of ablation rate near the terminus, mass-balance gradient, and mean thickness. Using a linear-response model based on these parameterisations, we find that the linear-response model outperforms the scaling model in reproducing the glacier response simulated by the SIA model. This linear-response model may be useful for predicting the evolution of mountain glaciers on a global scale.