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 some-what 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.