THE PHYSICAL BASIS OF GLACIER VOLUME-AREA SCALING

Ice volumes are known for only a few of the roughly 160,000 glaciers w orldwide but are important components of many climate and sea level st udies which require water flux estimates. A scaling analysis of the ma ss and momentum conservation equations shows that glacier volumes can be related by a power law to more easily observed glacier surface area s. The relationship requires four closure choices for the scaling beha vior of glacier widths, slopes, side drag and mass balance. Reasonable closures predict a volume-area scaling exponent which is consistent w ith observations, giving a physical and practical basis for estimating ice volumes. Glacier volume is insensitive to perturbations in the ma ss balance scaling, but changes in average accumulation area ratios re flect significant changes in the scaling of both mass balance and ice volume.