Quantification of sensitivity of mountain glaciers to climate change with the use of a block model

Despite comprising a small fraction of the Earth's total ice volume, melting of mountain glaciers due to climate change constitutes a significant contribution to recent sea level rise. Mathematical models of volume evolution of mountain glaciers are thus important in projecting sea level into the future. While state-of-the-art ice-flow models for glaciers exist, these rely on detailed data on the bed and surface of a glacier, data that is available for only a small sample of glaciers worldwide. Starting with a simple block model of glacier volume response, we improve it by adding the volume-area-length scaling and a more realistic representation of glacier mass balance profile. We analyze the resulting model and derive expressions for glaciers' volume sensitivity to temperature change and their volume response times. To obtain regionally differentiated estimates of glacier sensitivities, we apply the model on a global scale with data from the Randolph Glacier Inventory and a statistical model for glacier mass balance profile. Finally, we run the model forward in time with an ensemble of global climate models and compare the results to previous projections of regional glacier contributions to sea level rise.