Glacier Volume-Area Scaling: Refinements and Expansion

Volume-area power law scaling has become an increasingly important and widely-used method for estimating the future response of the world`s glaciers and ice caps to global warming. The application of the theory is not entirely straightforward, however, and many of the recently published results contain analyses that are in conflict with the original theory. In collaboration with faculty at the University of Innsbruck, we will re-derive a more general and detailed theory of volume-area scaling that corrects the many misconceptions currently in the literature. In particular, the expanded theory will correct misunderstandings about the scaling theory`s application to the non- equilibrium conditions prevalent as glaciers retreat and contribute to sea level. Using the generalized volume-area theory, we will also expand scaling techniques to explore the theoretical origins of glacier equilibrium conditions used as the foundation of some sea-level rise predictions. Specifically, we will derive the theoretical basis of equilibrium "accumulation area ratios" (the percentage of a glacier that has a net accumulation of snow and ice). Current glaciers have too little accumulation which is an indication that they will retreat and contribute to future changes in sea level. The ultimate extent of their contribution to sea level will depend on how much mass each glacier must ablate to achieve (or move part of the way towards) the theoretical equilibrium. While field data has already indicated that the equilibrium accumulation area ratio is 0.577, we will provide a theoretical foundation for this value. This will pin down the correct values for sea level predictions and will correct the widely misquoted value of 2/3, often seen in the glaciological and geomorphological literature. While volume-area scaling is statistically independent of glacier size, the special transition between large glaciers and small ice cap geometries will be explored in the context of the expanded scaling theory. Ice caps and glaciers have different responses to changing climate with different volume-area scaling exponents, but the most complete and current global inventories do not label which ice masses are glaciers and which are ice caps. This can introduce significant errors when volume-area scaling is used to estimate the total global volume of ice. Using the expanded theory to help distinguish ice caps from glaciers will improve estimates of both this total and associated predictions of sea-level rise.