Response time of glaciers as a function of size and mass balance: 1. Theory

A simple interpretation of the traditional definitions of glacier and ice sheet response time (e.g., thickness divided by mass balance rate, h/b) suggests that larger glaciers respond more slowly than small glaciers to a perturbation in climate. However, with reasonable choices for mass balance behavior, a scaling analysis shows that the response time of valley glaciers decreases as a function of increasing size when other variables are held constant. In essence, this is because larger valley glaciers push further into the ablation zone, and ablation increases more rapidly than the thickness (so that h/b gets smaller). Ice sheets have different mass balance regimes than valley glaciers, and as they grow larger, the ablation does not increase faster than the thickness. Therefore, as ice sheets grow in surface kea, the response time increases. For both ice sheets and valley glaciers, the response time also depends on a mass balance index, which is defined as the slope of the balance curve as a function of horizontal distance dong the glacier surface (rather than elevation). The response time decreases as the balance index increases, so for valley glaciers, an increase in the balance index and an increase in glacier size have opposite;effects on the response time. The balance index is typically larger for smaller valley glaciers. Therefore a small glacier will typically respond faster than a large glacier, but this quicker response is because of mass balance considerations and not because of the dynamic characteristics of the glacier arising from its small size, as often assumed.