4.2.2 Hydrostatic pressure and the equation of state

The pressure p is diagnosed through the hydrostatic equation (4.4). In this equation, the in situ density $\rho$is employed, where $\rho = \rho(\theta,s,p)$ is a diagnostic expression for the equation of state. Note that traditionally, $\rho = \rho(\theta,s,z)$ is used to evaluate the equation of state, rather than $\rho = \rho(\theta,s,p)$. Due to the strong hydrostatic nature of the ocean, the horizontal pressure variations are neglected for the purpose of evaluating the equation of state. Dewar et al. (1997) discuss the potential inaccuracies associated with this approach. Recent MOM implementations include the ability to diagnose density using the actual pressure from the previous model time step.