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

Abstract

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 -6.5OC km-I). 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 75ON (corresponding to the Arctic Ocean shoreline).Model ice age curves are generated for the last several I00 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 O 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.

Sensitivity of an energy balance climate model with predicted snowfall rates

“…Pollard et al (1980) used the observed precipitation rate and an empirical snowmelt formula based on observations. Suarez and Held (1979) adapted some methods from general circulation models by computing a surface energy balance from simplified radiation calculations and predicting melt rates.…”

Conditions for Growth and Retreat of the Laurentide Ice Sheet

“…SUAREZ (1974,1978); HELD (1976,1979); SCHNEIDER and THOMPSON (1979); POLLARD (1982a); Le TREUT and GHIL (1983) ;ROBOCK (1983) ;OERLEMANS (1980a);NORTH and COAKLEY (1979); POLLARD et al (1980);NORTH et al (1981);SELLERS (1984);FLANNERY (1984); BOWMAN (1982BOWMAN ( , 1985. The energy balance models can be tuned to the present day climate, but, for the climates of other periods with ice sheets or different radiation regimes, they need to be checked against paleo-data and with global climate General Circulation Models (GCMs).…”

Snow and ice balance in britain at the present time, and during the last glacial maximum and late glacial periods

“…For a study of snowmelt during past periods it is particularly important to include solar radiation because it has varied during the ice ages due to changes in the Earth's orbit (the Milankovitch mechanism). A suitable parameterization has been obtained by Pollard (1980) and tested on a variety of present-day data. According to Pollard (1980) where a, b and c are constants based on crude surface energy balance estimates and actual glacial measurements; Q is the monthly mean solar radiation incident at the top of the atmosphere (W mP2); and T is the monthly mean air temperature ("C).…”

“…A suitable parameterization has been obtained by Pollard (1980) and tested on a variety of present-day data. According to Pollard (1980) where a, b and c are constants based on crude surface energy balance estimates and actual glacial measurements; Q is the monthly mean solar radiation incident at the top of the atmosphere (W mP2); and T is the monthly mean air temperature ("C). Pollard (1978) arrived at the following values for a, b and c ; a = 0.32 (g cm-2 month-'), b = 10.0 (g cm-2 month-')("C)-' and c = 47.0 (g cmP2 month-').…”