Simple Energy Balance Model Resolving the Seasons and the Continents' Application to the Astronomical Theory of the Ice Ages

A one-level seasonal energy balance climate model which has explicit two-dimensional land-sea geography is introduced and its properties analyzed. The model distinguishes land from sea surface strictly by the local thermal inertia employed. The transport is governed by a smooth latitude dependent diffusion mechanism. The model's seasonal cycle is solved for, with and without ice feedback. In each case, good agreement with real data is accomplished with minimal tuning of the adjustable parameters. The model sensitivity for small solar constant changes is in agreement with that of other accepted models. However, when the solar constant is lower a few percent, the ice cap grows discontinuously from covering Greenland and vicinity to a size three times larger and mostly into Northern Canada. A similar discontinuous growth occurs when the orbital elements are changed to favor cool summers in the Northern Hemisphere. This discontinuous sensitivity is discussed in the context of the Milankovitch theory of the ice ages, and the associated branch structure is shown to be analogous to the so called 'small ice cap' instability known from simpler models. Although the discontinuity in sensitivity is somewhat conjectural, both linear and nonlinear models have their largest sensitivity to orbital parameter changes in the northern portions of the large continents; in the western hemisphere this also corresponds to the ice sheet boundary, suggesting that the land-sea configuration is crucial to large glacier growth irrespective of moisture budgets. Other experiments and implications are also discussed. The remarkable paper by Hays et al. [1976], hereafter HIS, presented compelling empirical evidence that continental ice sheet volume changes and sea surface temperature variations in the last 700,000 years are correlated with the changes in the earth's orbital elements. Theoretical arguments for such a connection date back to the last century, but the most detailed and convincing arguments are due to Milankovitch [1941], and the theory usually is associated with his name. If the hypothesis is correct, the theory and observations provide the cleanest experiment to determine the sensitivity of the earth's climate to truly external influences. Such a measure of climate sensitivity is of obvious importance considering the recent interest in estimating the change in climate due to other forcings, such as the enhanced greenhouse effect due to increased levels of CO2 in the atmosphere [e.g., Ramanathan, 1981; Hansen et al., 1981; Manabe and Stouffer, 1980]. In effect, climate models might be tested or calibrated by this natural experiment. Climate modeling has progressed dramatically in the last decade with the construction and testing of several general circulation models (GCM's). Although some interesting ice age experiments have been done with these models [Gates, 1976; Manabe and Hahn, 1977], they still include only crude parameterizations of the slower components such as the oceans. These numerical models are the ultimate tool that can be brought to bear upon the climate problem; however, they are almost as complicated as the climate itself. Hence experiments must be carefully designed, and the interpretation is often difficult due to the expense of obtaining definitively long runs. In parallel with GCM construction has been the development of x Permanently at Applied Research Corporation, Landover, Maryland 20785.