A method for detecting rapid mass flux of small glaciers using local sea level variations

There is increasing evidence that the global reservoir of small (or mountain) glaciers is presently experiencing an accelerated phase of net melting, perhaps linked to climatic warming. We argue that relative sea level and sea surface fingerprints local to such events provide a potentially powerful, integrated diagnostic for the mass imbalance. For example, we demonstrate, using an inference of glacier mass balance near Alaska over the last 50 years, that the present-day relative sea level fall at nearby sites can reach amplitudes that are ~2 orders of magnitude greater than the ongoing eustatic sea level rise associated with the melting. The peak sea surface subsidence is a factor of ~15 greater than the eustatic amplitude. We find that the predicted present-day sea surface change arising from the 50-year loading history is sensitive only to the ongoing rate of accelerated melting. In contrast, the present-day relative sea level fingerprint becomes increasingly sensitive to the \textquotelefthistory\textquoteright of the recent loading when the viscosity of the asthenosphere adopted in the prediction is progressively reduced below 10^20 Pa s. Specifically, the relative sea level fingerprint becomes more localized, and reaches higher amplitudes, close to the glacier system as viscous effects become active. Our results have application in efforts to constrain small glacier mass balance using tide gauge records of relative sea level change or satellite-derived constraints on sea surface (geoid) rates.