A two-dimensional energy balance model (EBM) with a seasonal cycle and a realistic land–ocean distribution is used to study climate sensitivity and the properties of equilibrium climate states. The land–ocean distribution is represented by the heat capacity of the surface. The horizontal heat flux is parameterized by diffusion. Nonlinearity is introduced into the model by the albedo–temperature feedback. A multi-grid finite difference method is used to solve the model equation. This method shows great advantages compared to other numerical methods.

The sensitivity of snow cover to changes in the solar constant is examined. It is found that the climate is more sensitive in summer due to a more effective albedo–temperature feedback. The local annual mean temperature and the amplitude of the seasonal cycle depend on the land–ocean distribution. Because Eurasia has the largest annual cycle of temperature and is the coldest in winter, winter snow appears first in Eurasia as the solar constant is reduced. Wintertime snow appears next in Greenland because of its low annual mean temperature and last in North America. Perennial snow cover appears first in Greenland because of the low annual mean temperature and the small annual cycle, and next appears in North America. Perennial snow in Eurasia appears only when the solar constant is reduced to a very low value, since the Eurasian land mass is too hot in summer for perennial snow cover. The sensitivity of the model climate to changes in the orbital parameters is also investigated and discussed.

Small polar ice caps in one-dimensional mean-annual EBMs are unstable to small perturbations. The ice caps either vanish or grow to a stable finite size. This phenomenon, referred to as the small ice-cap instability (SICI), is a consequence of the multiple stable equilibrium states in one-dimensional models. The SICI may be related to glacial–interglacial transitions. However, numerical results with the two-dimensional EBM demonstrate that the existence of the SICI depends on the land–ocean distribution. The SICI exists in the southern hemisphere, but not in the northern hemisphere. This casts doubt on the role of the SICI in northern hemisphere glaciations. Experiments with a one-dimensional seasonal EBM with simplified geography have been made to analyze the two-dimensional results. Mechanisms for the existence of the SICI in seasonal EBMs are discussed.