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C $Header: /u/gcmpack/MITgcm/model/src/find_alpha.F,v 1.8 2002/08/19 14:21:30 mlosch Exp $ |
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C $Name: $ |
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|
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#include "CPP_OPTIONS.h" |
5 |
#define USE_FACTORIZED_POLY |
6 |
|
7 |
CBOP |
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C !ROUTINE: FIND_ALPHA |
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C !INTERFACE: |
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SUBROUTINE FIND_ALPHA ( |
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I bi, bj, iMin, iMax, jMin, jMax, k, kRef, eqn, |
12 |
O alphaloc ) |
13 |
|
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C !DESCRIPTION: \bv |
15 |
C *==========================================================* |
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C | o SUBROUTINE FIND_ALPHA |
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C | Calculates [drho(S,T,z) / dT] of a horizontal slice |
18 |
C *==========================================================* |
19 |
C | |
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C | k - is the Theta/Salt level |
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C | kRef - determines pressure reference level |
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C | (not used in 'LINEAR' mode) |
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C | eqn - determines the eqn. of state: 'LINEAR' or 'POLY3' |
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C | |
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C | alphaloc - drho / dT (kg/m^3/C) |
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C | |
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C *==========================================================* |
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C \ev |
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|
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C !USES: |
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IMPLICIT NONE |
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c Common |
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#include "SIZE.h" |
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#include "DYNVARS.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "EOS.h" |
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#include "GRID.h" |
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|
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C !INPUT/OUTPUT PARAMETERS: |
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c Arguments |
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integer bi,bj,iMin,iMax,jMin,jMax |
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integer k ! Level of Theta/Salt slice |
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integer kRef ! Pressure reference level |
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character*(*) eqn |
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_RL alphaloc(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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|
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C !LOCAL VARIABLES: |
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c Local |
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integer i,j |
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_RL refTemp,refSalt,tP,sP |
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_RL t1, t2, t3, s1, s3o2, p1, p2, sp5, p1t1 |
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_RL drhoP0dtheta, drhoP0dthetaFresh, drhoP0dthetaSalt |
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_RL dKdtheta, dKdthetaFresh, dKdthetaSalt, dKdthetaPres |
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_RL rhoP0(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL bulkMod(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL dnum_dtheta, dden_dtheta |
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_RL rhoDen(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL rhoLoc(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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integer myThid |
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CEOP |
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|
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Cml stop 'myThid is not properly defined in this subroutine' |
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|
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if (equationOfState.eq.'LINEAR') then |
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|
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do j=jMin,jMax |
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do i=iMin,iMax |
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alphaloc(i,j) = -rhonil * tAlpha |
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enddo |
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enddo |
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|
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elseif (equationOfState.eq.'POLY3') then |
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|
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refTemp=eosRefT(kRef) |
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refSalt=eosRefS(kRef) |
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|
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do j=jMin,jMax |
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do i=iMin,iMax |
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tP=theta(i,j,k,bi,bj)-refTemp |
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sP=salt(i,j,k,bi,bj)-refSalt |
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#ifdef USE_FACTORIZED_POLY |
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alphaloc(i,j) = |
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& ( eosC(6,kRef) |
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& *tP*3. |
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& +(eosC(7,kRef)*sP + eosC(3,kRef))*2. |
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& )*tP |
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& +(eosC(8,kRef)*sP + eosC(4,kRef) )*sP + eosC(1,kRef) |
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& |
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#else |
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alphaloc(i,j) = |
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& eosC(1,kRef) + |
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& eosC(3,kRef)*tP*2. + |
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& eosC(4,kRef) *sP + |
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& eosC(6,kRef)*tP*tP*3. + |
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& eosC(7,kRef)*tP*2. *sP + |
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& eosC(8,kRef) *sP*sP |
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#endif |
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enddo |
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enddo |
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|
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elseif ( equationOfState(1:5).eq.'JMD95' |
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& .or. equationOfState.eq.'UNESCO' ) then |
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C nonlinear equation of state in pressure coordinates |
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|
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CALL FIND_RHOP0( |
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I bi, bj, iMin, iMax, jMin, jMax, k, |
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I theta, salt, |
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O rhoP0, |
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I myThid ) |
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|
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CALL FIND_BULKMOD( |
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I bi, bj, iMin, iMax, jMin, jMax, k, kRef, |
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I theta, salt, |
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O bulkMod, |
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I myThid ) |
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|
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do j=jMin,jMax |
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do i=iMin,iMax |
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|
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C abbreviations |
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t1 = theta(i,j,k,bi,bj) |
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t2 = t1*t1 |
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t3 = t2*t1 |
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|
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s1 = salt(i,j,k,bi,bj) |
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if ( s1 .lt. 0. _d 0 ) then |
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C issue a warning |
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write(*,'(a,i3,a,i3,a,i3,a,e13.5)') |
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& ' FIND_ALPHA: WARNING, salinity(', |
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& i,',',j,',',k,',',bi,',',bj,') = ', s1 |
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s1 = 0. _d 0 |
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end if |
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s3o2 = sqrt(s1*s1*s1) |
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|
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p1 = pressure(i,j,kRef,bi,bj)*SItoBar |
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p2 = p1*p1 |
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|
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C d(rho)/d(theta) |
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C of fresh water at p = 0 |
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drhoP0dthetaFresh = |
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& eosJMDCFw(2) |
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& + 2.*eosJMDCFw(3)*t1 |
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& + 3.*eosJMDCFw(4)*t2 |
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& + 4.*eosJMDCFw(5)*t3 |
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& + 5.*eosJMDCFw(6)*t3*t1 |
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C of salt water at p = 0 |
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drhoP0dthetaSalt = |
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& s1*( |
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& eosJMDCSw(2) |
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& + 2.*eosJMDCSw(3)*t1 |
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& + 3.*eosJMDCSw(4)*t2 |
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& + 4.*eosJMDCSw(5)*t3 |
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& ) |
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& + s3o2*( |
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& + eosJMDCSw(7) |
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& + 2.*eosJMDCSw(8)*t1 |
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& ) |
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C d(bulk modulus)/d(theta) |
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C of fresh water at p = 0 |
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dKdthetaFresh = |
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& eosJMDCKFw(2) |
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& + 2.*eosJMDCKFw(3)*t1 |
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& + 3.*eosJMDCKFw(4)*t2 |
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& + 4.*eosJMDCKFw(5)*t3 |
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C of sea water at p = 0 |
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dKdthetaSalt = |
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& s1*( eosJMDCKSw(2) |
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& + 2.*eosJMDCKSw(3)*t1 |
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& + 3.*eosJMDCKSw(4)*t2 |
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& ) |
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& + s3o2*( eosJMDCKSw(6) |
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& + 2.*eosJMDCKSw(7)*t1 |
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& ) |
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C of sea water at p |
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dKdthetaPres = |
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& p1*( eosJMDCKP(2) |
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& + 2.*eosJMDCKP(3)*t1 |
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& + 3.*eosJMDCKP(4)*t2 |
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& ) |
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& + p1*s1*( eosJMDCKP(6) |
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& + 2.*eosJMDCKP(7)*t1 |
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& ) |
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& + p2*( eosJMDCKP(10) |
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& + 2.*eosJMDCKP(11)*t1 |
186 |
& ) |
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& + p2*s1*( eosJMDCKP(13) |
188 |
& + 2.*eosJMDCKP(14)*t1 |
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& ) |
190 |
|
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drhoP0dtheta = drhoP0dthetaFresh |
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& + drhoP0dthetaSalt |
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dKdtheta = dKdthetaFresh |
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& + dKdthetaSalt |
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& + dKdthetaPres |
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alphaloc(i,j) = |
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& ( bulkmod(i,j)**2*drhoP0dtheta |
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& - bulkmod(i,j)*p1*drhoP0dtheta |
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& - rhoP0(i,j)*p1*dKdtheta ) |
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& /( bulkmod(i,j) - p1 )**2 |
201 |
|
202 |
|
203 |
end do |
204 |
end do |
205 |
elseif ( equationOfState.eq.'MDJWF' ) then |
206 |
|
207 |
CALL FIND_RHO( bi, bj, iMin, iMax, jMin, jMax, k, kRef, |
208 |
& eqn, theta, salt, rhoLoc, myThid ) |
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CALL FIND_RHODEN( bi, bj, iMin, iMax, jMin, jMax, k, kRef, |
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& theta, salt, rhoDen, myThid ) |
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|
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do j=jMin,jMax |
213 |
do i=iMin,iMax |
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t1 = theta(i,j,k,bi,bj) |
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t2 = t1*t1 |
216 |
s1 = salt(i,j,k,bi,bj) |
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if ( s1 .lt. 0. _d 0 ) then |
218 |
C issue a warning |
219 |
write(*,'(a,i3,a,i3,a,i3,a,e13.5)') |
220 |
& ' FIND_ALPHA: WARNING, salinity(', |
221 |
& i,',',j,',',k,',',bi,',',bj,') = ', s1 |
222 |
s1 = 0. _d 0 |
223 |
end if |
224 |
sp5 = sqrt(s1) |
225 |
|
226 |
p1 = pressure(i,j,kRef,bi,bj)*SItodBar |
227 |
p1t1 = p1*t1 |
228 |
|
229 |
dnum_dtheta = eosMDJWFnum(1) |
230 |
& + t1*(2.*eosMDJWFnum(2) + 3.*eosMDJWFnum(3)*t1) |
231 |
& + eosMDJWFnum(5)*s1 |
232 |
& + p1t1*(2.*eosMDJWFnum(8) + 2.*eosMDJWFnum(11)*p1) |
233 |
|
234 |
dden_dtheta = eosMDJWFden(1) |
235 |
& + t1*(2.*eosMDJWFden(2) |
236 |
& + t1*(3.*eosMDJWFden(3) |
237 |
& + 4.*eosMDJWFden(4)*t1 ) ) |
238 |
& + s1*(eosMDJWFden(6) |
239 |
& + t1*(3.*eosMDJWFden(7)*t1 |
240 |
& + 2.*eosMDJWFden(9)*sp5 ) ) |
241 |
& + p1*p1*(3.*eosMDJWFden(11)*t2 + eosMDJWFden(12)*p1) |
242 |
|
243 |
alphaLoc(i,j) = rhoDen(i,j)*(dnum_dtheta |
244 |
& - rhoLoc(i,j)*dden_dtheta) |
245 |
|
246 |
end do |
247 |
end do |
248 |
|
249 |
else |
250 |
write(*,*) 'FIND_ALPHA: equationOfState = ',equationOfState |
251 |
stop 'FIND_ALPHA: "equationOfState" has illegal value' |
252 |
endif |
253 |
|
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return |
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end |
256 |
|
257 |
subroutine FIND_BETA ( |
258 |
I bi, bj, iMin, iMax, jMin, jMax, k, kRef, eqn, |
259 |
O betaloc ) |
260 |
C /==========================================================\ |
261 |
C | o SUBROUTINE FIND_BETA | |
262 |
C | Calculates [drho(S,T,z) / dS] of a horizontal slice | |
263 |
C |==========================================================| |
264 |
C | | |
265 |
C | k - is the Theta/Salt level | |
266 |
C | kRef - determines pressure reference level | |
267 |
C | (not used in 'LINEAR' mode) | |
268 |
C | eqn - determines the eqn. of state: 'LINEAR' or 'POLY3' | |
269 |
C | | |
270 |
C | betaloc - drho / dS (kg/m^3/PSU) | |
271 |
C | | |
272 |
C \==========================================================/ |
273 |
implicit none |
274 |
|
275 |
c Common |
276 |
#include "SIZE.h" |
277 |
#include "DYNVARS.h" |
278 |
#include "EEPARAMS.h" |
279 |
#include "PARAMS.h" |
280 |
#include "EOS.h" |
281 |
#include "GRID.h" |
282 |
|
283 |
c Arguments |
284 |
integer bi,bj,iMin,iMax,jMin,jMax |
285 |
integer k ! Level of Theta/Salt slice |
286 |
integer kRef ! Pressure reference level |
287 |
character*(*) eqn |
288 |
_RL betaloc(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
289 |
|
290 |
c Local |
291 |
integer i,j |
292 |
_RL refTemp,refSalt,tP,sP |
293 |
_RL t1, t2, t3, s1, s3o2, p1, sp5, p1t1 |
294 |
_RL drhoP0dS |
295 |
_RL dKdS, dKdSSalt, dKdSPres |
296 |
_RL rhoP0(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
297 |
_RL bulkMod(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
298 |
_RL dnum_dsalt, dden_dsalt |
299 |
_RL rhoDen(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
300 |
_RL rhoLoc(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
301 |
integer myThid |
302 |
CEOP |
303 |
|
304 |
Cml stop 'myThid is not properly defined in this subroutine' |
305 |
|
306 |
if (equationOfState.eq.'LINEAR') then |
307 |
|
308 |
do j=jMin,jMax |
309 |
do i=iMin,iMax |
310 |
betaloc(i,j) = rhonil * sBeta |
311 |
enddo |
312 |
enddo |
313 |
|
314 |
elseif (equationOfState.eq.'POLY3') then |
315 |
|
316 |
refTemp=eosRefT(kRef) |
317 |
refSalt=eosRefS(kRef) |
318 |
|
319 |
do j=jMin,jMax |
320 |
do i=iMin,iMax |
321 |
tP=theta(i,j,k,bi,bj)-refTemp |
322 |
sP=salt(i,j,k,bi,bj)-refSalt |
323 |
#ifdef USE_FACTORIZED_POLY |
324 |
betaloc(i,j) = |
325 |
& ( eosC(9,kRef)*sP*3. + eosC(5,kRef)*2. )*sP + eosC(2,kRef) |
326 |
& + ( eosC(7,kRef)*tP |
327 |
& +eosC(8,kRef)*sP*2. + eosC(4,kRef) |
328 |
& )*tP |
329 |
#else |
330 |
betaloc(i,j) = |
331 |
& eosC(2,kRef) + |
332 |
& eosC(4,kRef)*tP + |
333 |
& eosC(5,kRef) *sP*2. + |
334 |
& eosC(7,kRef)*tP*tP + |
335 |
& eosC(8,kRef)*tP *sP*2. + |
336 |
& eosC(9,kRef) *sP*sP*3. |
337 |
#endif |
338 |
enddo |
339 |
enddo |
340 |
|
341 |
elseif ( equationOfState(1:5).eq.'JMD95' |
342 |
& .or. equationOfState.eq.'UNESCO' ) then |
343 |
C nonlinear equation of state in pressure coordinates |
344 |
|
345 |
CALL FIND_RHOP0( |
346 |
I bi, bj, iMin, iMax, jMin, jMax, k, |
347 |
I theta, salt, |
348 |
O rhoP0, |
349 |
I myThid ) |
350 |
|
351 |
CALL FIND_BULKMOD( |
352 |
I bi, bj, iMin, iMax, jMin, jMax, k, kRef, |
353 |
I theta, salt, |
354 |
O bulkMod, |
355 |
I myThid ) |
356 |
|
357 |
do j=jMin,jMax |
358 |
do i=iMin,iMax |
359 |
|
360 |
C abbreviations |
361 |
t1 = theta(i,j,k,bi,bj) |
362 |
t2 = t1*t1 |
363 |
t3 = t2*t1 |
364 |
|
365 |
s1 = salt(i,j,k,bi,bj) |
366 |
if ( s1 .lt. 0. _d 0 ) then |
367 |
C issue a warning |
368 |
write(*,'(a,i3,a,i3,a,i3,a,e13.5)') |
369 |
& ' FIND_BETA: WARNING, salinity(', |
370 |
& i,',',j,',',k,',',bi,',',bj,') = ', s1 |
371 |
s1 = 0. _d 0 |
372 |
end if |
373 |
s3o2 = 1.5*sqrt(s1) |
374 |
|
375 |
p1 = pressure(i,j,kRef,bi,bj)*SItoBar |
376 |
|
377 |
C d(rho)/d(S) |
378 |
C of fresh water at p = 0 |
379 |
drhoP0dS = 0. _d 0 |
380 |
C of salt water at p = 0 |
381 |
drhoP0dS = drhoP0dS |
382 |
& + eosJMDCSw(1) |
383 |
& + eosJMDCSw(2)*t1 |
384 |
& + eosJMDCSw(3)*t2 |
385 |
& + eosJMDCSw(4)*t3 |
386 |
& + eosJMDCSw(5)*t3*t1 |
387 |
& + s3o2*( |
388 |
& eosJMDCSw(6) |
389 |
& + eosJMDCSw(7)*t1 |
390 |
& + eosJMDCSw(8)*t2 |
391 |
& ) |
392 |
& + 2*eosJMDCSw(9)*s1 |
393 |
C d(bulk modulus)/d(S) |
394 |
C of fresh water at p = 0 |
395 |
dKdS = 0. _d 0 |
396 |
C of sea water at p = 0 |
397 |
dKdSSalt = |
398 |
& eosJMDCKSw(1) |
399 |
& + eosJMDCKSw(2)*t1 |
400 |
& + eosJMDCKSw(3)*t2 |
401 |
& + eosJMDCKSw(4)*t3 |
402 |
& + s3o2*( eosJMDCKSw(5) |
403 |
& + eosJMDCKSw(6)*t1 |
404 |
& + eosJMDCKSw(7)*t2 |
405 |
& ) |
406 |
|
407 |
C of sea water at p |
408 |
dKdSPres = |
409 |
& p1*( eosJMDCKP(5) |
410 |
& + eosJMDCKP(6)*t1 |
411 |
& + eosJMDCKP(7)*t2 |
412 |
& ) |
413 |
& + s3o2*p1*eosJMDCKP(8) |
414 |
& + p1*p1*( eosJMDCKP(12) |
415 |
& + eosJMDCKP(13)*t1 |
416 |
& + eosJMDCKP(14)*t2 |
417 |
& ) |
418 |
|
419 |
dKdS = dKdSSalt + dKdSPres |
420 |
|
421 |
betaloc(i,j) = |
422 |
& ( bulkmod(i,j)**2*drhoP0dS |
423 |
& - bulkmod(i,j)*p1*drhoP0dS |
424 |
& - rhoP0(i,j)*p1*dKdS ) |
425 |
& /( bulkmod(i,j) - p1 )**2 |
426 |
|
427 |
|
428 |
end do |
429 |
end do |
430 |
elseif ( equationOfState.eq.'MDJWF' ) then |
431 |
|
432 |
CALL FIND_RHO( bi, bj, iMin, iMax, jMin, jMax, k, kRef, |
433 |
& eqn, theta, salt, rhoLoc, myThid ) |
434 |
CALL FIND_RHODEN( bi, bj, iMin, iMax, jMin, jMax, k, kRef, |
435 |
& theta, salt, rhoDen, myThid ) |
436 |
|
437 |
do j=jMin,jMax |
438 |
do i=iMin,iMax |
439 |
t1 = theta(i,j,k,bi,bj) |
440 |
t2 = t1*t1 |
441 |
s1 = salt(i,j,k,bi,bj) |
442 |
if ( s1 .lt. 0. _d 0 ) then |
443 |
C issue a warning |
444 |
write(*,'(a,i3,a,i3,a,i3,a,e13.5)') |
445 |
& ' FIND_BETA: WARNING, salinity(', |
446 |
& i,',',j,',',k,',',bi,',',bj,') = ', s1 |
447 |
s1 = 0. _d 0 |
448 |
end if |
449 |
sp5 = sqrt(s1) |
450 |
|
451 |
p1 = pressure(i,j,k,bi,bj)*SItodBar |
452 |
p1t1 = p1*t1 |
453 |
|
454 |
dnum_dsalt = eosMDJWFnum(4) |
455 |
& + eosMDJWFnum(5)*t1 |
456 |
& + 2.*eosMDJWFnum(6)*s1 + eosMDJWFnum(9)*p1 |
457 |
dden_dsalt = eosMDJWFden(5) |
458 |
& + t1*( eosMDJWFden(6) + eosMDJWFden(7)*t2 ) |
459 |
& + 1.5*sp5*(eosMDJWFden(8) + eosMDJWFden(9)*t2) |
460 |
|
461 |
betaLoc(i,j) = rhoDen(i,j)*( dnum_dsalt |
462 |
& - rhoLoc(i,j)*dden_dsalt ) |
463 |
|
464 |
end do |
465 |
end do |
466 |
|
467 |
else |
468 |
write(*,*) 'FIND_BETA: equationOfState = ',equationOfState |
469 |
stop 'FIND_BETA: "equationOfState" has illegal value' |
470 |
endif |
471 |
|
472 |
return |
473 |
end |