The principal balance in the equations of motion comes from a balance of momentum acceleration, vertical momentum diffusion and the Coriolis force due to the Earth's rotation:
where U and V are the E--W and N--S components of the velocity, f is the Coriolis parameter and is the coefficient of turbulent momentum diffusion. The transport equation for heat balances vertical diffusion of heat and incident solar radiation in 1-D models, and also advection of heat in 3-D models (1-D meaning that the spatial gradients in only one direction, in this case z, are retained. In other words, fluid flow is regarded as horizontally homogeneous). Thus,
where T is the temperature. There is similarly a transport equation for salt,
where and are turbulent diffusion coefficients for heat and salt, respectively, and S is salinity.