We have embarked upon this exposition of ocean models with three goals: (a) to outline the hydrodynamic and numerical foundations upon which the current ocean models rest; (b) to provide the initial tools for beginners (and even for more advanced modelers) to simulate and forecast the oceanic environment; and (c) to provide a general overview for technical people in all fields on the current approaches in modeling the circulation and thermodynamic state of the ocean. In general, most of the methods that we will consider have been proven to be successful in depicting at least some part of the ocean, and to be consistent with available hydrographic and remotely sensed observations. We will reference some of the papers containing model-data verification at the proper stages in the presentation, so that the reader can follow up and be able to form a more complete understanding of the overall success of these models with an insight into the current prospects for simulating and forecasting the oceanic environment.
Clearly, changes in the world ocean are going to be important factors in any global change processes. Even on shorter time scales, such as the 4--7 year El Nino cycle, the ocean has been shown to have a profound effect on our weather and climate. The global ice--ocean system is also a vast storehouse of ``stored'' water, heat and carbon dioxide, and thus becomes one of the main controllers of global warming. Some semi-enclosed seas, for example the Mediterranean and the Arctic with limited flushing capabilities, have been the site of dumping of non-radioactive and radioactive wastes with serious environmental consequences.