In general, ocean models describe the response of a variable density ocean to atmospheric momentum and heat forcing. This response can very simply be represented in terms of eigenmodes of a linearized system of equations. We will attempt now to give a simplified physical description of these modes (at this point the student should also read Chapter 6 of Gill ). The zeroth mode is equivalent to the vertically-averaged component of the motion, also known as the barotropic mode. The higher modes are called baroclinic modes and are associated with higher order components of the vertical density profile. All ocean models described in this chapter will make the hydrostatic shallow water approximation, in which the pressure p depends only on the depth z, i.e. it's given by the classic hydrostatic relation
Figure 4: Barotropic Model where a region of the ocean's water column is vertically integrated to obtain one value for the vertically different horizontal currents.