4. Ocean Modelling and Prediction 4.1 Introduction 4.1.1 What Is an Ocean Model?

The ocean plays a vital role in our environment. As such, an ability to model and predict its circulation can be of enormous value. Modelling and prediction of ocean currents in coastal regions is important for many reasons, including innuences on recreation, navigation, algal bloom formation, eeuent dispersion, search and rescue operations, and oil spills. Ocean currents near the coast also aaect beach conditions that impact upon the near-shore zone. Severe wave climates and storm surges can cause enormous destruction of the built environment. At larger scales, vast ocean currents carry heat around the globe, aaecting climate and weather patterns such as those associated with the El-Ni~ no event and the North Atlantic Oscillation. The oceans also have a vast capacity to absorb and redistribute gases such as carbon dioxide. They will therefore play a crucial role in determining our future climate. To understand and predict the way the ocean aaects our environment, a number of ocean models have been developed during the past half century. Some are computationally simple and predict a limited number of oceanic variables, such as tidal models or a wave climate model. Others, such as primitive equation ocean general circulation models (OGCMs), are compu-tationally expensive and solve several equations in order to predict three-dimensional ocean currents and temperature-salinity (T ?S). In this chapter we describe the state-of-the-art in ocean modelling. The World's oceans can be viewed as a turbulent stratiied uid on a rotating sphere with a multiply-connected domain and an uneven bottom bathymetry. More simply, the rotating earth has an ocean system divided by land masses and with varying water density and ocean depth. The external forcing of the ocean occurs through the mechanical forcing of the winds, the so-called \thermohaline" forcing via heat and freshwater uxes across the air-sea interface , and through planetary forces manifest in tides. An ocean model is