# Equation of State¶

Within MOM6, there is a wrapper for the equation of state, so that all calls look the same from the rest of the model. The equation of state code has to calculate not just in situ density, but also the compressibility and various derivatives of the density. There is also code for computing specific volume and the freezing temperature.

## Linear Equation of State¶

Compute the required quantities with uniform values for $$\alpha = \frac{\partial \rho}{\partial T}$$ and $$\beta = \frac{\partial \rho}{\partial S}$$, (DRHO_DT, DRHO_DS in MOM_input, also uses RHO_T0_S0).

## Wright Equation of State¶

Compute the required quantities using the equation of state from [69]. This equation of state is in the form:

$\alpha(s, \theta, p) = A(s, \theta) + \frac{\lambda(s, \theta)}{P(s, \theta) + p}$

where $$A, \lambda$$ and $$P$$ are functions only of $$s$$ and $$\theta$$ and $$\alpha = 1/ \rho$$ is the specific volume. This form is useful for the pressure gradient computation as discussed in Pressure Gradient Term.

## NEMO Equation of State¶

Compute the required quantities using the equation of state from [54].

## UNESCO Equation of State¶

Compute the required quantities using the equation of state from [34].

## TEOS-10 Equation of State¶

Compute the required quantities using the equation of state from TEOS-10 .

## Freezing Temperature of Sea Water¶

There are three choices for computing the freezing point of sea water:

• Linear The freezing temperature is a linear function of the salinity and pressure:

$T_{Fr} = (T_{Fr0} + a\,S) + b\,P$

where $$T_{Fr0},a,b$$ are contants which can be set in MOM_input (TFREEZE_S0_P0, DTFREEZE_DS, DTFREEZE_DP).

• Millero The [44] equation is used, but modified so that it is a function of potential temperature rather than in situ temperature:

$T_{Fr} = S(a + (b \sqrt{\max(S,0.0)} + c\, S)) + d\,P$

where $$a,b, c, d$$ are fixed contants.

• TEOS-10 The TEOS-10 package is used to compute the freezing conservative temperature [degC] from absolute salinity [g/kg], and pressure [Pa]. This one must be used if you are using the NEMO or TEOS-10 equation of state.