A two-dimensional, one-basin thermohaline oceanic circulation (THC) model coupled to an atmospheric energy balance model (EBM) with land ice albedo effect and a thermodynamic sea ice model is used to study global climate on centennial, and longer, timescales. The model is interpreted to represent the effect of the global ocean, rather than the Atlantic, as is commonly done. It is forced by symmetric insolation and includes a diagnostic parameterization of the hydrologic cycle. Here the strength of the ocean's haline forcing is controlled by a parameter, which reflects the effect of river runoff. This parameter is varied in a set of experiments, which also differ by the magnitude of solar insolation. In wide ranges of the hydrologic cycle, multiple climatic equilibria exist, consisting of circulations with different degrees of asymmetry. More symmetric states have a higher global atmospheric temperature, characteristic of modern climate, whereas less symmetric states are colder and resemble glacial conditions. The maximum global atmospheric temperature difference between such states is consistent with proxy-data-derived temperature drop of about 4¿C during the glacial, in contrast to EBM-only sensitivity of about 0.4¿C. The mechanics of climate transitions in the model are due to amplification of the orbitally induced global heat budget changes by a major reorganization of the oceanic heat transport. In our model this reorganization is caused by the nonlinear dynamics of the ocean's THC, whose stability regime shifts subject to variable external forcing. Sea ice enhances model climate sensitivity by anchoring deep-ocean temperature to be near freezing <Kravtsov, 2000> and by affecting atmospheric temperature and land ice extent near the poles because of sea ice insulating properties.