Characteristic mass-balance scaling with valley glacier size

previous work on the relation between glacier volume and area and on accumulation area ratios suggests that balance rates measured at the glacier terminus are not constant or random from glacier to glacier but instead scale with glacier length. Using mass-balance data from a collection of 68 valley and cirque glaciers, we show that the terminus mass-balance rate scales roughly linearly with surface area and scales with length raised to an exponent constrained to fall roughly between 0.5 and 2 with 1.7 preferred if a glacier's length is dependent on the mass-balance conditions (rat her than balance being dependent on length). When these exponents are used to predict valley-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 exponent 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.