Small fluctuations in the density and thickness of a dry firn column

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Abstract
It is of practical importance to have a description on time-scales of 1–100 years of the relationship between the mass imbalance of an ice sheet and its rate of change of thickness. In this paper, a linearized treatment of the relationship is described. Closed-form expressions are derived that relate the time-variant density in an isothermal firn layer to the fluctuations in accumulation rate and density that occur at the surface. These expressions are used to provide a spectral description of the contribution of surface accumulation and surface density fluctuations to the rate of change of thickness of an ice sheet. Using these, the contribution of firn densification to the variability of ice-sheet thickness is examined as a function of the time interval over which the ice sheet is observed. This contribution is illustrated for sites in Antarctica and Greenland. It is concluded that it is important to give greater attention than hitherto to the spatial scale of accumulation fluctuations if satellite observations of ice-sheet elevation change are to be used to estimate ice-sheet imbalance over short time intervals.