!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !! !! !! GNU General Public License !! !! !! !! This file is part of the Flexible Modeling System (FMS). !! !! !! !! FMS is free software; you can redistribute it and/or modify !! !! it and are expected to follow the terms of the GNU General Public !! !! License as published by the Free Software Foundation. !! !! !! !! FMS is distributed in the hope that it will be useful, !! !! but WITHOUT ANY WARRANTY; without even the implied warranty of !! !! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the !! !! GNU General Public License for more details. !! !! !! !! You should have received a copy of the GNU General Public License !! !! along with FMS; if not, write to: !! !! Free Software Foundation, Inc. !! !! 59 Temple Place, Suite 330 !! !! Boston, MA 02111-1307 USA !! !! or see: !! !! http://www.gnu.org/licenses/gpl.txt !! !! !! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !$Id: eqstate.F90,v 1.1.2.1 2007/09/11 13:01:46 smg Exp $ #include"cppdefs.h" !----------------------------------------------------------------------- !BOP ! ! !MODULE: eqstate --- the equation of state \label{sec:eqstate} ! ! !INTERFACE: MODULE eqstate ! ! !DESCRIPTION: ! Computes in-situ density, $\rho_{is}$, and buoyancy from the ! salinity, $s$, the potential temperature, $\theta$, ! and thermodynamic pressure, $p$, according to a specified ! \emph{equation of state}, ! \begin{equation} ! \label{DefEOS} ! \rho_{is} = \hat{\rho} (s,\theta,p) ! \point ! \end{equation} ! At present, two different modes and four different methods ! are implemented. ! Modes: ! \begin{enumerate} ! \item The UNESCO equation of state according to \cite{FofonoffMillard83} ! \item The \cite{JACKETTea05} equation of state ! \end{enumerate} ! Methods: ! \begin{enumerate} ! \item the full equation of state --- including pressure effects ! \item the full equation of state --- without pressure effects ! \item the linearised equation of state ! \item a general linear form of the equation of state ! \end{enumerate} ! ! !USES: IMPLICIT NONE ! default: all is private. private ! ! !PUBLIC MEMBER FUNCTIONS: public init_eqstate,eqstate1,eos_alpha,eos_beta,unesco,rho_feistel ! ! !REVISION HISTORY: ! Original author(s): Hans Burchard & Karsten Bolding ! ! $Log: eqstate.F90,v $ ! Revision 1.1.2.1 2007/09/11 13:01:46 smg ! Add these files to the mom4p1 branch. ! AUTHOR:Griffies ! REVIEWERS: ! TEST STATUS: ! CHANGES PUBLIC INTERFACES? ! CHANGES ANSWERS? ! ! Revision 1.7 2007-01-06 11:49:13 kbk ! namelist file extension changed .inp --> .nml ! ! Revision 1.6 2005/06/27 13:44:07 kbk ! modified + removed traling blanks ! ! Revision 1.5 2003/03/28 09:20:36 kbk ! added new copyright to files ! ! Revision 1.4 2003/03/28 08:06:33 kbk ! removed tabs ! ! Revision 1.3 2003/03/10 08:54:16 gotm ! Improved documentation and cleaned up code ! ! Revision 1.2 2001/11/27 19:44:32 gotm ! Fixed an initialisation bug ! ! Revision 1.1.1.1 2001/02/12 15:55:58 gotm ! initial import into CVS ! !EOP ! ! private data memebers integer :: eq_state_method, eq_state_mode REALTYPE :: T0,S0,p0,dtr0,dsr0 ! !----------------------------------------------------------------------- contains !----------------------------------------------------------------------- !BOP ! ! !IROUTINE: Read the namelist {\tt eqstate} ! ! !INTERFACE: subroutine init_eqstate(namlst) ! ! !DESCRIPTION: ! Here, the namelist {\tt eqstate} in the namelist file {\tt gotmrun.nml} ! is read. ! ! !USES: IMPLICIT NONE ! ! !INPUT PARAMETERS: integer, optional, intent(in) :: namlst ! ! !REVISION HISTORY: ! Original author(s): Hans Burchard & Karsten Bolding ! !EOP ! ! !LOCAL VARIABLES: namelist /eqstate/ eq_state_mode,eq_state_method,T0,S0,p0,dtr0,dsr0 ! !----------------------------------------------------------------------- !BOC LEVEL1 'init_eqstate' if(present(namlst)) then read(namlst,nml=eqstate,err=80) end if return 80 FATAL 'I could not read "eqstate" namelist' stop 'init_eqstate' end subroutine init_eqstate !EOC !----------------------------------------------------------------------- !BOP ! ! !IROUTINE: Select an equation of state ! ! !INTERFACE: REALTYPE function eqstate1(S,T,p,g,rho_0) ! ! !DESCRIPTION: ! Calculates the in-situ buoyancy according to the selected method. ! {\tt S} is salinity $S$ in psu, {\tt T} is ! potential temperature $\theta$ in $^{\circ}$C (ITS-90), {\tt p} is ! gauge pressure (absolute pressure - 10.1325 bar), {\tt g} is the ! gravitational acceleration in m\,s$^{-2}$ and {\tt rho\_0} the reference ! density in kg\,m$^{-3}$. {\tt eqstate1} is the in-situ-density ! in kg\,m$^{-3}$. ! For {\tt eq\_state\_method}=1, the UNESCO equation of state is used, ! for {\tt eq\_state\_method}=2, the \cite{JACKETTea05} equation ! of state is used. Here, some care is needed, since the UNESCO equation ! used bar for pressure and the \cite{JACKETTea05} uses dbar for pressure. ! For values of ! {\tt eq\_state\_method} ranging from 1 to 4, one of the following methods ! will be used. ! ! \begin{enumerate} ! \item the full equation of state for sea water ! including pressure dependence. ! \item the equation of state for sea water ! with the pressure evaluated at the sea surface as ! reference level. This is the choice ! for computations based on potential temperature and density. ! \item a linearised equation of state. ! The parameters {\tt T0}, ! {\tt S0} and {\tt p0} have to be specified in the namelist. ! \item a linear equation of state with prescribed {\tt rho0}, {\tt T0}, ! {\tt S0}, {\tt dtr0}, {\tt dsr0} according to ! \begin{equation} ! \label{eosLinear} ! \rho = \rho_0 + \text{\tt dtr0} (T - T_0) ! + \text{\tt dsr0} (S - S_0) ! \point ! \end{equation} ! \end{enumerate} ! ! !USES: IMPLICIT NONE ! ! !INPUT PARAMETERS: REALTYPE,intent(in) :: S,T,p REALTYPE,optional,intent(in) :: g,rho_0 ! ! !REVISION HISTORY: ! Original author(s): Hans Burchard & Karsten Bolding ! !EOP ! ! !LOCAL VARIABLES: REALTYPE :: x REALTYPE, save :: rh0,dtr,dsr REALTYPE :: dTT,dSS logical :: press logical, save :: first=.true. ! !----------------------------------------------------------------------- !BOC select case (eq_state_mode) case(1) select case (eq_state_method) case (1) press=.true. x=unesco(S,T,p,press) case (2) press=.false. x=unesco(S,T,p,press) case (3) if (first) then press=.true. ! This allows for choosing potentials other than p=0 dTT=0.001 dSS=0.001 rh0= unesco(S0,T0,p0,press) dtr=(unesco(S0,T0+0.5*dTT,p0,press) & -unesco(S0,T0-0.5*dTT,p0,press))/dTT dsr=(unesco(S0+0.5*dSS,T0,p0,press) & -unesco(S0-0.5*dSS,T0,p0,press))/dSS first=.false. end if x=rh0+dtr*(T-T0)+dsr*(S-S0) case (4) x=rho_0+dtr0*(T-T0)+dsr0*(S-S0) case default end select case(2) select case (eq_state_method) case (1) press=.true. x=rho_feistel(S,T,p*10.,press) case (2) press=.false. x=rho_feistel(S,T,p*10.,press) case (3) if (first) then press=.true. ! This allows for choosing potentials other than p=0 dTT=0.001 dSS=0.001 rh0= rho_feistel(S0,T0,p0*10.,press) dtr=(rho_feistel(S0,T0+0.5*dTT,p0*10.,press) & -rho_feistel(S0,T0-0.5*dTT,p0*10.,press))/dTT dsr=(rho_feistel(S0+0.5*dSS,T0,p0*10.,press) & -rho_feistel(S0-0.5*dSS,T0,p0*10.,press))/dSS first=.false. end if x=rh0+dtr*(T-T0)+dsr*(S-S0) case (4) x=rho_0+dtr0*(T-T0)+dsr0*(S-S0) case default end select case default end select eqstate1=-g*(x-rho_0)/rho_0 return end function eqstate1 !EOC !----------------------------------------------------------------------- !BOP ! ! !IROUTINE: Compute thermal expansion coefficient ! ! !INTERFACE: REALTYPE function eos_alpha(S,T,p,g,rho_0) ! ! !DESCRIPTION: ! Computes the thermal expansion coefficient defined by ! \begin{equation} ! \label{eosAlpha} ! \alpha = ! - \dfrac{1}{\rho_0} ! \left( \partder{\rho_{is}}{T} \right)_S ! = ! \dfrac{1}{g} ! \left( \partder{B_{is}}{T} \right)_S ! \comma ! \end{equation} ! where $B_{is}$ denotes the in-situ buoyancy. The computation is carried ! out by a finite difference approximation of \eq{eosAlpha}, ! requiring two evaluations of the equation of state. ! Note, that comparing \eq{eosAlpha} with \eq{eosLinear} it follows that ! $\alpha = - \text{\tt dtr0}/\rho_0$. ! ! !USES: IMPLICIT NONE ! ! !INPUT PARAMETERS: REALTYPE,intent(in) :: S,T,p REALTYPE,optional,intent(in) :: g,rho_0 ! ! !REVISION HISTORY: ! Original author(s): Lars Umlauf ! !EOP ! ! !LOCAL VARIABLES: ! REALTYPE,parameter :: delta = 0.01 REALTYPE :: buoy_a,buoy_b !----------------------------------------------------------------------- !BOC buoy_a = eqstate1(S,T+0.5*delta,p,g,rho_0) buoy_b = eqstate1(S,T-0.5*delta,p,g,rho_0) eos_alpha = (buoy_a - buoy_b) / (g*delta) end function eos_alpha !EOC !----------------------------------------------------------------------- !BOP ! ! !IROUTINE: Compute saline contraction coefficient ! ! !INTERFACE: REALTYPE function eos_beta(S,T,p,g,rho_0) ! ! !DESCRIPTION: ! Computes the saline contractioncoefficient defined by ! \begin{equation} ! \label{eosBeta} ! \beta = ! \dfrac{1}{\rho_0} ! \left( \partder{\rho_{is}}{S} \right)_T ! = ! - \dfrac{1}{g} ! \left( \partder{B_{is}}{S} \right)_T ! \comma ! \end{equation} ! where $B_{is}$ denotes the in-situ buoyancy. The computation is carried ! out by a finite difference approximation of \eq{eosBeta}, ! requiring two evaluations of the equation of state. ! Note, that comparing \eq{eosBeta} with \eq{eosLinear} it follows that ! $\beta = \text{\tt dsr0}/\rho_0$. ! ! ! !USES: IMPLICIT NONE ! ! !INPUT PARAMETERS: REALTYPE,intent(in) :: S,T,p REALTYPE,optional,intent(in) :: g,rho_0 ! ! !REVISION HISTORY: ! Original author(s): Lars Umlauf ! !EOP ! ! !LOCAL VARIABLES: ! REALTYPE,parameter :: delta = 0.01 REALTYPE :: buoy_a,buoy_b !----------------------------------------------------------------------- !BOC buoy_a = eqstate1(S+0.5*delta,T,p,g,rho_0) buoy_b = eqstate1(S-0.5*delta,T,p,g,rho_0) eos_beta = -(buoy_a - buoy_b) / (g*delta) end function eos_beta !EOC !----------------------------------------------------------------------- !BOP ! ! !IROUTINE: The UNESCO equation of state ! ! !INTERFACE: REALTYPE function unesco(S,T,p,UNPress) ! ! !DESCRIPTION: ! Computes the in-situ density in \eq{DefEOS} according to the ! UNESCO equation of state for sea water (see \cite{FofonoffMillard83}). ! The pressure ! dependence can be switched on ({\tt UNPress=.true.}) or off ! ({\tt UNPress=.false.}). {\tt S} is salinity $S$ in psu, {\tt T} is ! potential temperature $\theta$ in $^{\circ}$C (ITS-90), {\tt p} is ! gauge pressure (absolute pressure - 10.1325 bar) and ! {\tt unesco} is the in-situ density in kg\,m$^{-3}$. ! The check value is {\tt unesco(35,25,1000) = 1062.53817} . ! ! !USES: IMPLICIT NONE ! ! !INPUT PARAMETERS: REALTYPE, intent(in) :: S,T,p LOGICAL, intent(in) :: UNPress ! ! !REVISION HISTORY: ! Original author(s): Hans Burchard & Karsten Bolding ! !EOP ! ! !LOCAL VARIABLES: REALTYPE :: x,K REALTYPE :: T2,T3,T4,T5,S15,S2,S3,p2 ! !----------------------------------------------------------------------- !BOC T2 = T*T T3 = T*T2 T4 = T2*T2 T5 = T*T4 S15= S**1.5 S2 = S*S S3 = S*S2 x=999.842594+6.793952e-02*T-9.09529e-03*T2+1.001685e-04*T3 x=x-1.120083e-06*T4+6.536332e-09*T5 x=x+S*(0.824493-4.0899e-03*T+7.6438e-05*T2-8.2467e-07*T3) x=x+S*5.3875e-09*T4 x=x+sqrt(S3)*(-5.72466e-03+1.0227e-04*T-1.6546e-06*T2) x=x+4.8314e-04*S2 if ((UNPress).and.(p.gt.0)) then p2=p*p K= 19652.21 & +148.4206 *T -2.327105 *T2 & + 1.360477E-2*T3 -5.155288E-5 *T4 & + 3.239908 *p +1.43713E-3 *T *p & + 1.16092E-4 *T2*p -5.77905E-7 *T3*p & + 8.50935E-5 *p2 -6.12293E-6 *T *p2 & + 5.2787E-8 *T2*p2 & + 54.6746 *S -0.603459 *T *S & + 1.09987E-2 *T2 *S -6.1670E-5 *T3 *S & + 7.944E-2 *S15+1.6483E-2 *T *S15 & - 5.3009E-4 *T2 *S15+2.2838E-3 *p *S & - 1.0981E-5 *T *p *S -1.6078E-6 *T2*p *S & + 1.91075E-4 *p *S15-9.9348E-7 *p2*S & + 2.0816E-8 *T *p2*S +9.1697E-10 *T2*p2*S x=x/(1.-p/K) end if unesco=x return end function unesco !EOC !----------------------------------------------------------------------- !BOP ! ! !IROUTINE: The \cite{JACKETTea05} equation of state ! ! !INTERFACE: REALTYPE function rho_feistel(s,th,p,UNPress) ! ! !DESCRIPTION: ! Computes the in-situ density in \eq{DefEOS} according to the ! \cite{JACKETTea05} equation of state for sea water, which is based ! on the Gibbs potential developed by \cite{FEISTEL03}. The pressure ! dependence can be switched on ({\tt UNPress=.true.}) or off ! ({\tt UNPress=.false.}). {\tt s} is salinity $S$ in psu, {\tt th} is ! potential temperature $\theta$ in $^{\circ}$C (ITS-90), {\tt p} is ! gauge pressure (absolute pressure - 10.1325 dbar) and ! {\tt rho\_feistel} is the in-situ density in kg\,m$^{-3}$. ! The check value is {\tt rho\_feistel(20,20,1000) = 1017.728868019642} . ! ! !USES: IMPLICIT NONE ! ! !INPUT PARAMETERS: REALTYPE, intent(in) :: s,th,p LOGICAL, intent(in) :: UNPress ! ! !REVISION HISTORY: ! Original author(s): Hans Burchard & Karsten Bolding ! !EOP ! ! !LOCAL VARIABLES: REALTYPE :: th2,sqrts,pth,anum,aden ! !----------------------------------------------------------------------- !BOC th2 = th*th sqrts = sqrt(s) anum = 9.9984085444849347d+02 + & th*( 7.3471625860981584d+00 + & th*(-5.3211231792841769d-02 + & th* 3.6492439109814549d-04)) + & s*( 2.5880571023991390d+00 - & th* 6.7168282786692355d-03 + & s* 1.9203202055760151d-03) aden = 1.0000000000000000d+00 + & th*( 7.2815210113327091d-03 + & th*(-4.4787265461983921d-05 + & th*( 3.3851002965802430d-07 + & th* 1.3651202389758572d-10))) + & s*( 1.7632126669040377d-03 - & th*( 8.8066583251206474d-06 + & th2* 1.8832689434804897d-10) + & sqrts*( 5.7463776745432097d-06 + & th2* 1.4716275472242334d-09)) if((UNPress).and.(p.gt.0.d0)) then pth = p*th anum = anum + p*( 1.1798263740430364d-02 + & th2* 9.8920219266399117d-08 + & s* 4.6996642771754730d-06 - & p*( 2.5862187075154352d-08 + & th2* 3.2921414007960662d-12)) aden = aden + p*( 6.7103246285651894d-06 - & pth*(th2* 2.4461698007024582d-17 + & p* 9.1534417604289062d-18)) end if rho_feistel = anum/aden ! Note: this function should always be run in double precision ! (since rho is returned rather than sigma = rho-1.0d3) return end function rho_feistel !EOC end module eqstate !----------------------------------------------------------------------- ! Copyright by the GOTM-team under the GNU Public License - www.gnu.org !-----------------------------------------------------------------------