Abstract
Abstract. Glacier volume response time is a measure of the time taken for a glacier to adjust its geometry to a climate change. It has been previously proposed that the volume response time is given approximately by the ratio of glacier thickness to ablation at the glacier terminus. We propose a new conceptual model of glacier hypsometry (area-altitude relation) and derive the volume response time where climatic and topographic parameters are separated. The former is expressed by mass balance gradients which we derive from glacier-climate modelling and the latter are quantified with data from the World Glacier Inventory. Aside from the well-known scaling relation between glacier volume and area, we establish a new scaling relation between glacier altitude range and area, and evaluate it for seven regions. The presence of this scaling parameter in our response time formula accounts for the mass balance elevation feedback and leads to longer response times than given by the simple ratio of glacier thickness to ablation at the terminus. Volume response times range from decades to thousands of years for glaciers in maritime (wet-warm) and continental (dry-cold) climates respectively. The combined effect of volume-area and altitude-area scaling relations is such that volume response time can increase with glacier area (Axel Heiberg Island and Svalbard), hardly change (Northern Scandinavia, Southern Norway and the Alps) or even get smaller (The Caucasus and New Zealand).
Highlights
Global warming is causing increased melt of grounded ice and contributing to sea level rise (Meier, 1984; IPCC, 2007)
More detailed dynamic flow modelling of glaciers will undoubtedly contribute to our better understanding of individual glaciers but for an overall view of sea level rise from glaciers several authors have proposed the alternative use of more conceptual models with volume-area scaling
We propose a new derivation of the volume response time where the climate and geometric parameters are separated
Summary
Global warming is causing increased melt of grounded ice and contributing to sea level rise (Meier, 1984; IPCC, 2007). The classic approach to changes in glacier volume as a result of climate forcing is to solve partial differential equations for glacier dynamics and thermodynamics This can be done analytically for simplified glacier geometry (Nye, 1963) but will generally require numerical methods. A number of authors have sought to express volume response time analytically as a relatively simple function of climate and glacier geometry (Johannesson et al, 1989a; Raper et al, 1996; Bahr et al, 1998; Pfeffer et al, 1998; Harrison et al, 2001; Oerlemans, 2001). We hope that our work follows the philosophy that it is “better to think exactly with simplified ideas than to reason inexactly with complex ones” (Nye, 1948)
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