Solutions to the Stefan problems for the motion of the base of ice-bearing permafrost in response to changes in paleoclimate were obtained using perturbation, finite difference, and finite element methods. Paleotemperature models were used to investigate the thickness response, to compare solution methods, to determine the current state of the permafrost, and to determine constraints on the models. The perturbation and finite difference methods used the approximation of linear temperature profiles, while the finite element method did not. There was a transient thickness response of about 41 kyr, implying that paleotemperature records of greater length are needed for models and that the peramfrost loses its ''memory'' of past conditions for much longer times. Faster thawing rates, slower freezing rates, and greater variations in thickness were found for the perturbation and finite difference solutions compared to the finite element solution. These results appear to be caused by the simplifying assumptions in the former solutions. A lag (about 20 kyr) exists between changes in surface temperature and thickness response, and a small thermal offset is apparent in the finite element solution.

Small asymmetries exist in the freezing and thawing rates and the thickness response. Paleotemperature models based on ice cores predict current permafrost thicknesses that are too large. Models with the long-term mean surface temperature of permafrost within a few degrees of the current value of -11¿C and with the last glacial period temperature no more than 6¿--8¿C lower are compatible with current Prudhoe Bay conditions. These include models developed for East Siberia, from isotopic profiles in deep-sea sediments, and for Barrow, Alaska, modified for Prudhoe Bay. These models predict that the permafrost thickness at Prudhoe Bay varied by about ¿10% or less (¿60 m) over the last glacial cycle. Freezing and thawing rates were less than 6 mm yr-1. At present this permafrost should be near its long-term equilibrium thickness and thawing at <1 mm yr-1. ¿American Geophysical Union 1991