_Equation_of_State.dox

/*! \page Equation_of_State 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 or potential density, but also the compressibility and various

derivatives of the density. There is also code for computing specific volume and the

freezing temperature, and for converting between potential and conservative

temperatures and between practical and reference (or absolute) salinity.

\section Linear_EOS Linear Equation of State

Compute the required quantities with uniform values for \f$\alpha = \frac{\partial

\rho}{\partial T}\f$ and \f$\beta = \frac{\partial \rho}{\partial S}\f$, (DRHO_DT,

DRHO_DS in MOM_input, also uses RHO_T0_S0).

\section Wright_EOS Wright reduced range Equation of State

Compute the required quantities using the equation of state from \cite wright1997

as a function of potential temperature and practical salinity, with

coefficients based on the reduced-range (salinity from 28 to 38 PSU, temperature

from -2 to 30 degC and pressure up to 5000 dbar) fit to the UNESCO 1981 data. This

equation of state is in the form:

\f[

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

\f]

where \f$A, \lambda\f$ and \f$P\f$ are functions only of \f$s\f$ and \f$\theta\f$

and \f$\alpha = 1/ \rho\f$ is the specific volume. This form is useful for the

pressure gradient computation as discussed in \ref section_PG.  This EoS is selected

by setting EQN_OF_STATE = WRIGHT or WRIGHT_RED, which are mathematically equivalent,

but the latter is refactored for consistent answers between compiler settings.

\section Wright_full_EOS Wright full range Equation of State

Compute the required quantities using the equation of state from \cite wright1997

as a function of potential temperature and practical salinity, with

coefficients based on a fit to the UNESCO 1981 data over the full range of

validity of that data (salinity from 0 to 40 PSU, temperatures from -2 to 40

degC, and pressures up to 10000 dbar).  The functional form of the WRIGHT_FULL

equation of state is the same as for WRIGHT or WRIGHT_RED, but with different

coefficients.

\section Jackett06_EOS Jackett et al. (2006) Equation of State

Compute the required quantities using the equation of state from Jackett et al.

(2006) as a function of potential temperature and practical salinity, with

coefficients based on a fit to the updated data that were later used to define

the TEOS-10 equation of state over the full range of validity of that data

(salinity from 0 to 42 PSU, temperatures from the freezing point to 40 degC, and

pressures up to 8500 dbar), but focused on the "oceanographic funnel" of

thermodynamic properties observed in the ocean.  This equation of state is

commonly used in realistic Hycom simulations.

\section UNESCO_EOS UNESCO Equation of State

Compute the required quantities using the equation of state from \cite jackett1995,

which uses potential temperature and practical salinity as state variables and is

a fit to the 1981 UNESCO equation of state with the same functional form but a

replacement of the temperature variable (the original uses <em>in situ</em> temperature).

\section ROQUET_RHO_EOS ROQUET_RHO Equation of State

Compute the required quantities using the equation of state from \cite roquet2015,

which uses a 75-member polynomial for density as a function of conservative temperature

and absolute salinity, in a fit to the output from the full TEOS-10 equation of state.

\section ROQUET_SPV_EOS ROQUET_SPV Equation of State

Compute the required quantities using the specific volume oriented equation of state from

\cite roquet2015, which uses a 75-member polynomial for specific volume as a function of

conservative temperature and absolute salinity, in a fit to the output from the full

TEOS-10 equation of state.

\section TEOS-10_EOS TEOS-10 Equation of State

Compute the required quantities using the equation of state from

[TEOS-10](http://www.teos-10.org/), with calls directly to the subroutines

in that code package.

\section section_TFREEZE Freezing Temperature of Sea Water

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

\li Linear The freezing temperature is a linear function of the salinity and

pressure:

\f[

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

\f]

where \f$T_{Fr0},a,b\f$ are constants which can be set in MOM_input (TFREEZE_S0_P0,

DTFREEZE_DS, DTFREEZE_DP).

\li Millero The \cite millero1978 equation is used to calculate the freezing

point from practical salinity and pressure, but modified so that returns a

potential temperature rather than an <em>in situ</em> temperature:

\f[

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

\f]

where \f$a,b, c, d\f$ are fixed constants.

\li 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 or

TEOS_poly must be used if you are using the ROQUET_RHO, ROQUET_SPV or TEOS-10

equation of state.

\li TEOS_poly A 23-term polynomial fit refactored from the TEOS-10 package is

used to compute the freezing conservative temperature [degC] from absolute

salinity [g/kg], and pressure [Pa].

*/