For arbitrary bed and edge geometries, solutions are obtained by means of the method of characteristics, which reduces the problem to solving simultaneously three ordinary first-order differential equations. The integration, which is performed by numerical methods, is generally begun at the edge, where the necessary boundary conditions are known.

The method has been applied to model the elevation contours and the flow pattern of the Greenlandice sheet, using the bottom topography revealed by radio echo-soundings and the present edge geometry. The result is in surprisingly good agreement with our knowledge of the ice-sheet topography and flow pattern, all significant ice divides and ice streams being reproduced. This result suggests, that the method can be applied to model the shape and flow pattern of ice sheets under glacial conditions, using information about former ice-edge positions. This has been attempted for north-west Greenland and Queen Elizabeth Islands, with various ice-margin positions. The topography and flow pattern of the reconstructed ice-age ice sheets is discussed in the light of uplift data, and long δ¹⁸O-records obtained from Greenland and north Canadian ice cores.