Characteristic mass-balance scaling with valley glacier size

previous work on the relation between glacier volume and area and on accumu lation area ratios suggests that balance rates measured at the glacier term inus are not constant or random from glacier to glacier but instead scale w ith glacier length. Using mass-balance data from a collection of 68 valley and cirque glaciers, we show that the terminus mass-balance rate scales rou ghly linearly with surface area and scales with length raised to an exponen t constrained to fall roughly between 0.5 and 2 with 1.7 preferred if a gla cier's length is dependent on the mass-balance conditions (rat her than bal ance being dependent on length). When these exponents are used to predict v alley-glacier volume-area scaling, the results are very close to empirical volume-area observations. Although the data are noisy and the proposed fits could be modified by improved observations, the scaling trend for terminus balance vs length remains clear. Although the exact value of the scaling e xponent is not well determined, establishing the existence of this scaling relation will be important far studies of climate change and the impact of glacier recession on sea level.