diff --git a/src/equation_of_state/_Equation_of_State.dox b/src/equation_of_state/_Equation_of_State.dox index 791c7001b1..0e80c9652a 100644 --- a/src/equation_of_state/_Equation_of_State.dox +++ b/src/equation_of_state/_Equation_of_State.dox @@ -2,9 +2,10 @@ 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. +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 @@ -12,51 +13,96 @@ Compute the required quantities with uniform values for \f$\alpha = \frac{\parti \rho}{\partial T}\f$ 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 Equation of State +\section Wright_EOS Wright reduced range Equation of State -Compute the required quantities using the equation of state from \cite wright1997. -This equation of state is in the form: +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. +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 NEMO_EOS NEMO Equation of State +\section UNESCO_EOS UNESCO Equation of State -Compute the required quantities using the equation of state from \cite roquet2015. +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 in situ temperature). -\section UNESCO_EOS UNESCO Equation of State +\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. -Compute the required quantities using the equation of state from \cite jackett1995. +\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/). +[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 three choices for computing the freezing point 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 contants which can be set in MOM_input (TFREEZE_S0_P0, +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, but modified so that it is a function -of potential temperature rather than in situ temperature: +\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 in situ 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 contants. +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-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. +\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]. */