Response of a zonal climate-ice sheet model to the orbital perturbations during the Quaternary ice ages¹

The astronomical theory of the ice ages is investigated using a simple climate model which includes the ice sheets explicitly. A one-level, zonally averaged, seasonal energy-balance equation is solved numerically for sea-level temperature T as a function of latitude and month (similar to North, 1975). Seasonally varying snow cover (which affects planetary albedo) is included diagnostically by parameterizing monthly snowfall and snowmelt in simple ways. The net annual accumulation and ablation on the ice sheet surface at each latitude are computed using the same parameterizations as for snow cover above (with T corrected for ice sheet height using a lapse rate of -6.5 °C km^-1). Treatment of the ice sheets follows Weertman (1976) with ice flow approximated as perfect plasticity, which constrains the ice sheet profiles to be parabolic. The northern hemisphere’s ice sheet is constrained to extend equatorward from 75°N (corresponding to the Arctic Ocean shoreline).

Model ice age curves are generated for the last several 100 Kyears by computing the seasonal climate as above once every 2 Kyears, with insolation calculated from actual Earth orbit perturbations. The change in ice sheet size for each 2 Kyear time step depends only on the net annual snow budget integrated over the whole ice sheet surface. In these model runs, the equatorward tip of the northern hemisphere’s ice sheet oscillates through ~ 7° in latitude, correctly simulating the phases and approximate amplitude of the higher frequency components (~43 Kyear and 22 Kyear) of the deep-sea core data (Hays et al., 1976). However, the model fails to simulate the dominant glacial-interglacial cycles (~100 to 120 Kyear) of this data. The sensitivity of the model ice age curves to various parameter changes is described, but none of these changes significantly improve the fit of the model ice age curves to the data. In the concluding section we generalize about the types of mechanisms that might yield realistic glacial-interglacial cycles.