When ice melts from a large ice sheet and the melt water runs into the ocean, global-mean sea level rises but, surprisingly, local sea level near the ice sheet may well drop. This is largely because the loss of mass reduces the gravitational pull of the ice sheet. We present a simple, analytically tractable model to illustrate this effect. We look first at a flat earth with a circular continent containing an ice sheet that is modeled as a point mass at its center and then extend the calculation to a rigid spherical non-rotating earth. With a bit more mathematical sophistication, we then carry out calculations for somewhat more realistic ice distributions and include the additional gravitation of the mass of displaced sea water. We give numerical results for the “fingerprint” of sea level change resulting from a 1000-Gt (1015-kg) loss of ice on a rigid, non-rotating earth, with parameter values appropriate to the Greenland and Antarctic ice sheets.
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