Recent studies of long-term climate variations which have employed zonally-averaged ice-sheet models and an equilibrium-line net-budget parameterization (Reference Oerlemans and BienfaitOerlemans and Bienfait 1981, Reference PollardPollard 1982) have been able to reproduce many of the complete deglaciations and reinitiations of the northern-hemisphere ice sheets found in the geologic record. However, when the equilibrium-line net-budget parameterization is replaced with an energy-balance equation designed to compute the temperature and ablation at the ice surface, the reinitiation of a zonally-averaged ice sheet is much more difficult than previously indicated.

In order to investigate what magnitude changes in air temperature and surface albedo are necessary to initiate ice-sheet growth, an energy-balance net-budget parameterization, in which these terms are varied, is applied to a zonally-averaged ice sheet that is initiated with either ice-free conditions (low summer surface albedo of 0.16) or with a 10 m-thick ice field (high-surface albedo ranging from 0.7 to 0.8).

The energy-balance net-budget parameterization is made up of two parts: the accumulation rate and the ablation rate. The accumulation rate is parameterized as follows:

S_n = P_r * r_a * F_y * e_s/e_si

where P_r is the present precipitation rate, r_a is the ratio of the density of water to ice, F_y is the fraction of precipitation that falls as snow, and e_s/e_si is the ratio of the saturation vapor pressure at the surface air temperature to that at the present surface air temperature. The ablation rate is derived from a surface-energy balance equation of the form:

F_p + F_s + (1-a) F_sw + F_lw + F_ir = 0

where F_p is the latent heat flux , F_s is the sensible heat flux, a is the surface albedo, F_sw is the short-wave radiation available at the surface, F_lw is the long-wave radiation from the atmosphere, and F_ir is the long-wave radiation from the surface. The accumulation and ablation rates are computed at approximately two-week time steps through the seasonal cycle and then summed over the year to obtain the annual net budget.

Using this net-budget parameterization and a solar insolation regime at 120 ka BP, preliminary experiments were performed.

First the ice-sheet model was initiated with ice-free conditions. In this case it was found that a drop in mean air temperature in all seasons of between 20 and 25 K was required to initiate an ice sheet. This is a very large mean temperature change; however, it must be viewed with caution for two reasons. First, the reduction of the mean annual temperature is probably not climatically realistic. In the model there is a decrease the in winter snowfall due to its dependence on saturation vapor pressure, despite the cooling. Second, there are computational constraints in defining the surface albedo that are presently part of the model which may enhance the difficulty in initiating an ice sheet.

The reason for the difficulty in initiating the growth of an ice sheet from ice-free conditions is that low summer albedos associated with these conditions increase the amount of absorbed solar radiation to such an extent that any modest decrease in air temperature is overwhelmed resulting in complete snow/ice ablation.

In order to examine how important the surface albedo is to the inititiation of an ice sheet a few experiments were performed which were initiated with a ten meter ice field with a surface albedo ranging from 0.7 to 0.8. In the case when the snow/ice surface albedo was set to 0.8 a reduction in mean air temperature of only 3 K produced ice-sheet growth with about 350 m of ice accumulating at 72.5°N after 5 ka. This was the only case in these preliminary experiments which produced ice-sheet growth. In the cases where the snow/ice surface albedo was set to 0.8 and 0.75 and the mean air temperature was decreased 2.5 and 3 K respectively the 10 m-ice field melted away slowly with a residual ice field, present after 1 ka, completely disappearing after 5 ka. In other experiments in which the snow/ice surface albedo was set to 0.8 and mean air temperature was decreased 2 K, and in which the snow/ice surface albedo was set to 0.7 and mean air temperature was decreased 2.25, 3 and 4 K, the 10 m-ice field melted away within the first thousand years.

Despite the fact that these results are preliminary and must be viewed with caution, the magnitude of the difference between the reduction in mean air temperature required to initiate ice-sheet growth when an initial ice field is assumed compared to when ice-free conditions are assumed is quite large. This suggests the critical importance of the summer surface albedo in determining ice-sheet initiation.

In conclusion, these results suggest that there is great difficulty in making the transition from interglacial to glacial conditions using zonally-averaged conditions, and that making that transition requires the crossing of a climatic threshold in which ice and snow accumulation in the winter season, and thus high surface albedo, can be maintained through the summer season.