Equilibrium ice sheet scaling in climate modeling

A set of simple scaling formulas related to ice sheet evolution is derived from the dynamic and thermodynamic equations for ice and is used to consider two common situations: (a) when we wish to estimate potential ice sheet characteristics given the prescribed net snow accumulation over an area; and (b) when we wish to reconstruct net snow accumulation and vertical temperature difference within the ice sheet given empirical data only concerning ice sheet area and volume. The scaling formulas are applied to the present day Antarctic and Greenland ice sheets, as well as to some ancient ice sheets, and are used to estimate the potential global sea level change due to greenhouse warming.