Mass balance of polar ice from long wavelength features of the earth's gravitational field

We have used satellite solutions to the low degree zonal harmonics of the Earth's gravitational potential, and rates of surface accumulation to partially constrain, by means of repeated forward solution, the time rates of thickness change over the Antarctic and Greenland Ice Sheets (dTA and dTG respectively). In addition to the observed zonal coefficients j2 through j5 we impose only one other constraint: That dTA and dTG are proportional to surface accumulation. The lagged response of the Earth to secular changes in ice thickness spanning recent time periods (up to 2000 years before present) and the late Pleistocene is accounted for by means of two viscoelastic rebound models. The sea level contributions from the ice sheets, calculated from dTA and dTG, lower mantle viscosity, and the start time of present-day thickness change are all variables subject to the constraints. For a given set of post glacial rebound inputs, a family of solutions that have similar characteristics and that agree well with observation are obtained from the large number of forward solutions. The off axis position of the Greenland ice sheet makes its contribution to the low degree zonal coefficients less sensitive to the spatial details of the mass balance than to the overall sea level contribution. dTG is therefore modeled as surface mass balance offset by a uniform and constant mass loss. Though dTA varies widely with choices of input parameters, the combined sea level contribution from both ice sheets is reasonably well constrained by the gravity coefficients, and is predicted to range from -0.9 to +1.6 mm yr-1. The sign of the slope of the low degree zonal coefficients versus sea level contribution for Greenland is positive, but for Antarctica, the sign of the slope is positive for even degree and negative for odd degree harmonics. By using this property of the zonal coefficients, it is possible to determine the individual sea level contributions for Greenland and Antarctica. They vary from -0.6 to +0.3 mm yr-1 for the Greenland Ice Sheet, and from -0.3 to +1.3 mm yr-1 for the Antarctic Ice Sheet.[PUBLICATION ABSTRACT]