Obliquity variation in a Mars climate evolution model

The existence of layered terrain in both polar regions of Mars is strong evidence supporting a cyclic variation in climate. It has been suggested that periods of net deposition have alternated with periods of net erosion in creating the layered structure that is seen today. The cause for this cyclic climatic behavior is variation in the annually averaged latitudinal distribution of solar insolation in response to obliquity cycles. For Mars, obliquity variation leads to major climatological excursion due to the condensation and sublimation of the major atmospheric constituent, CO2. The atmosphere will collapse into the polar caps, or existing caps will rapidly sublimate into the atmosphere, dependent upon the polar surface heat balance and the direction of the change in obliquity. It has been argued that variations in the obliquity of Mars cause substantial departures from the current climatological values of the surface pressure and the amount of CO2 stored in both the planetary regolith and polar caps. In this new work we have modified the Haberle et al. model to incorporate variable obliquity by allowing the polar and equatorial insolation to become functions of obliquity, which we assume to vary sinusoidally in time. As obliquity varies in the model, there can be discontinuities in the time evolution of the model equilibrium values for surface pressure, regolith, and polar cap storage. The time constant, tau r, for the regolith to find equilibrium with the climate is estimated--depending on the depth, thermal conductivity, and porosity of the regolith--between 10(exp 4) and 10(exp 6) yr. Thus, using 2000-yr timesteps to move smoothly through the 0.1250 m.y. obliquity cycles, we have an atmosphere/regolith system that cannot be assumed in equilibrium. We have dealt with this problem by limiting the rate at which CO2, can move between the atmosphere and regolith, mimicking the diffusive nature and effects of the temperature and pressure waves, by setting the time rate of change of regolith storage proportional to the difference between equilibrium storage and current storage