In this paper we present a numerical simulation of the observation that most alpine glaciers have reached peak velocities in the early 1980s followed by nearly exponential decay of velocity in the subsequent decade. We propose that similarity exists between precipitation and associated runoff hydrograph in a river basin on one side and annual mean specific mass balance of the accumulation area of alpine glaciers and ensuing changes in ice flow on the other side. The similarity is expressed in terms of a linear reservoir with fluctuating input where the year to year change of ice velocity is governed by two terms, a fraction of the velocity of the previous year as a recession term and the mean specific balance of the accumulation area of the current year as a driving term. The coefficients of these terms directly relate to the timescale, the mass balance/altitude profile, and the geometric scale of the glacier. The model is well supported by observations in the upper part of the glacier where surface elevation stays constant to within ¿5 m over a 30 year period. There is no temporal trend in the agreement between observed and modeled horizontal velocities and no difference between phases of acceleration and phases of deceleration, which means that the model is generally valid for a given altitude on a given glacier.