MODULE eosbn2 !!============================================================================== !! *** MODULE eosbn2 *** !! Ocean diagnostic variable : equation of state - in situ and potential density !! - Brunt-Vaisala frequency !!============================================================================== !! History : ! 89-03 (O. Marti) Original code !! 6.0 ! 94-07 (G. Madec, M. Imbard) add bn2 !! 6.0 ! 94-08 (G. Madec) Add Jackett & McDougall eos !! 7.0 ! 96-01 (G. Madec) statement function for e3 !! 8.1 ! 97-07 (G. Madec) introduction of neos, OPA8.1 !! 8.1 ! 97-07 (G. Madec) density instead of volumic mass !! ! 99-02 (G. Madec, N. Grima) semi-implicit pressure gradient !! ! 01-09 (M. Ben Jelloul) bugfix onlinear eos !! 8.5 ! 02-10 (G. Madec) add eos_init !! 8.5 ! 02-11 (G. Madec, A. Bozec) partial step, eos_insitu_2d !! 9.0 ! 03-08 (G. Madec) F90, free form !! 9.0 ! 06-08 (G. Madec) add tfreez function !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! eos : generic interface of the equation of state !! eos_insitu : Compute the in situ density !! eos_insitu_pot : Compute the insitu and surface referenced potential !! volumic mass !! eos_insitu_2d : Compute the in situ density for 2d fields !! eos_bn2 : Compute the Brunt-Vaisala frequency !! tfreez : Compute the surface freezing temperature !! eos_init : set eos parameters (namelist) !!---------------------------------------------------------------------- USE dom_oce ! ocean space and time domain USE phycst ! physical constants USE in_out_manager ! I/O manager USE zdfddm ! vertical physics: double diffusion USE prtctl ! Print control IMPLICIT NONE PRIVATE !! * Interface INTERFACE eos MODULE PROCEDURE eos_insitu, eos_insitu_pot, eos_insitu_2d END INTERFACE INTERFACE bn2 MODULE PROCEDURE eos_bn2 END INTERFACE PUBLIC eos ! called by step, istate, tranpc and zpsgrd modules PUBLIC bn2 ! called by step module PUBLIC tfreez ! called by sbcice_... modules !!* Namelist (nameos) INTEGER , PUBLIC :: neos = 0 !: = 0/1/2 type of eq. of state and Brunt-Vaisala frequ. REAL(wp), PUBLIC :: ralpha = 2.0e-4 !: thermal expension coeff. (linear equation of state) REAL(wp), PUBLIC :: rbeta = 7.7e-4 !: saline expension coeff. (linear equation of state) NAMELIST/nameos/ neos, ralpha, rbeta INTEGER :: neos_init = 0 !: control flag for initialization !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! OPA 9.0 , LOCEAN-IPSL (2006) !! $Id$ !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE eos_insitu( ptem, psal, prd ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_insitu *** !! !! ** Purpose : Compute the in situ density (ratio rho/rau0) from !! potential temperature and salinity using an equation of state !! defined through the namelist parameter neos. !! !! ** Method : 3 cases: !! neos = 0 : Jackett and McDougall (1994) equation of state. !! the in situ density is computed directly as a function of !! potential temperature relative to the surface (the opa t !! variable), salt and pressure (assuming no pressure variation !! along geopotential surfaces, i.e. the pressure p in decibars !! is approximated by the depth in meters. !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 !! with pressure p decibars !! potential temperature t deg celsius !! salinity s psu !! reference volumic mass rau0 kg/m**3 !! in situ volumic mass rho kg/m**3 !! in situ density anomalie prd no units !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, !! t = 40 deg celcius, s=40 psu !! neos = 1 : linear equation of state function of temperature only !! prd(t) = 0.0285 - ralpha * t !! neos = 2 : linear equation of state function of temperature and !! salinity !! prd(t,s) = rbeta * s - ralpha * tn - 1. !! Note that no boundary condition problem occurs in this routine !! as (ptem,psal) are defined over the whole domain. !! !! ** Action : compute prd , the in situ density (no units) !! !! References : Jackett and McDougall, J. Atmos. Ocean. Tech., 1994 !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: ptem ! potential temperature [Celcius] REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: psal ! salinity [psu] REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( out) :: prd ! in situ density !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: & zt , zs , zh , zsr, & ! temporary scalars zr1, zr2, zr3, zr4, & ! " " zrhop, ze, zbw, zb, & ! " " zd , zc , zaw, za , & ! " " zb1, za1, zkw, zk0 ! " " REAL(wp), DIMENSION(jpi,jpj,jpk) :: zws ! temporary workspace !!---------------------------------------------------------------------- IF( neos_init == 0 ) CALL eos_init ! initialization (in not already done) SELECT CASE ( neos ) ! CASE ( 0 ) ! Jackett and McDougall (1994) formulation ! !CDIR NOVERRCHK zws(:,:,:) = SQRT( ABS( psal(:,:,:) ) ) ! ! =============== DO jk = 1, jpkm1 ! Horizontal slab ! ! =============== DO jj = 1, jpj DO ji = 1, jpi zt = ptem(ji,jj,jk) zs = psal(ji,jj,jk) ! depth zh = fsdept(ji,jj,jk) ! square root salinity zsr= zws(ji,jj,jk) ! compute volumic mass pure water at atm pressure zr1= ( ( ( ( 6.536332e-9*zt-1.120083e-6 )*zt+1.001685e-4)*zt & -9.095290e-3 )*zt+6.793952e-2 )*zt+999.842594 ! seawater volumic mass atm pressure zr2= ( ( ( 5.3875e-9*zt-8.2467e-7 ) *zt+7.6438e-5 ) *zt & -4.0899e-3 ) *zt+0.824493 zr3= ( -1.6546e-6*zt+1.0227e-4 ) *zt-5.72466e-3 zr4= 4.8314e-4 ! potential volumic mass (reference to the surface) zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 ! add the compression terms ze = ( -3.508914e-8*zt-1.248266e-8 ) *zt-2.595994e-6 zbw= ( 1.296821e-6*zt-5.782165e-9 ) *zt+1.045941e-4 zb = zbw + ze * zs zd = -2.042967e-2 zc = (-7.267926e-5*zt+2.598241e-3 ) *zt+0.1571896 zaw= ( ( 5.939910e-6*zt+2.512549e-3 ) *zt-0.1028859 ) *zt - 4.721788 za = ( zd*zsr + zc ) *zs + zaw zb1= (-0.1909078*zt+7.390729 ) *zt-55.87545 za1= ( ( 2.326469e-3*zt+1.553190)*zt-65.00517 ) *zt+1044.077 zkw= ( ( (-1.361629e-4*zt-1.852732e-2 ) *zt-30.41638 ) *zt + 2098.925 ) *zt+190925.6 zk0= ( zb1*zsr + za1 )*zs + zkw ! masked in situ density anomaly prd(ji,jj,jk) = ( zrhop / ( 1.0 - zh / ( zk0 - zh * ( za - zh * zb ) ) ) & - rau0 ) / rau0 * tmask(ji,jj,jk) END DO END DO ! ! =============== END DO ! End of slab ! ! =============== ! CASE ( 1 ) ! Linear formulation function of temperature only ! ! ! =============== DO jk = 1, jpkm1 ! Horizontal slab ! ! =============== DO jj = 1, jpj DO ji = 1, jpi zt = ptem(ji,jj,jk) zs = psal(ji,jj,jk) ! ... density and potential volumic mass prd(ji,jj,jk) = ( 0.0285 - ralpha * zt ) * tmask(ji,jj,jk) END DO END DO ! ! =============== END DO ! End of slab ! ! =============== ! CASE ( 2 ) ! Linear formulation function of temperature and salinity ! ! ! =============== DO jk = 1, jpkm1 ! Horizontal slab ! ! =============== DO jj = 1, jpj DO ji = 1, jpi zt = ptem(ji,jj,jk) zs = psal(ji,jj,jk) ! ... density and potential volumic mass prd(ji,jj,jk) = ( rbeta * zs - ralpha * zt ) * tmask(ji,jj,jk) END DO END DO ! ! =============== END DO ! End of slab ! ! =============== ! CASE DEFAULT ! WRITE(ctmp1,*) ' bad flag value for neos = ', neos CALL ctl_stop( ctmp1 ) ! END SELECT ! IF(ln_ctl) CALL prt_ctl(tab3d_1=prd, clinfo1=' eos : ', ovlap=1, kdim=jpk) ! END SUBROUTINE eos_insitu SUBROUTINE eos_insitu_pot( ptem, psal, prd, prhop ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_insitu_pot *** !! !! ** Purpose : Compute the in situ density (ratio rho/rau0) and the !! potential volumic mass (Kg/m3) from potential temperature and !! salinity fields using an equation of state defined through the !! namelist parameter neos. !! !! ** Method : !! neos = 0 : Jackett and McDougall (1994) equation of state. !! the in situ density is computed directly as a function of !! potential temperature relative to the surface (the opa t !! variable), salt and pressure (assuming no pressure variation !! along geopotential surfaces, i.e. the pressure p in decibars !! is approximated by the depth in meters. !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 !! rhop(t,s) = rho(t,s,0) !! with pressure p decibars !! potential temperature t deg celsius !! salinity s psu !! reference volumic mass rau0 kg/m**3 !! in situ volumic mass rho kg/m**3 !! in situ density anomalie prd no units !! !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, !! t = 40 deg celcius, s=40 psu !! !! neos = 1 : linear equation of state function of temperature only !! prd(t) = ( rho(t) - rau0 ) / rau0 = 0.028 - ralpha * t !! rhop(t,s) = rho(t,s) !! !! neos = 2 : linear equation of state function of temperature and !! salinity !! prd(t,s) = ( rho(t,s) - rau0 ) / rau0 !! = rbeta * s - ralpha * tn - 1. !! rhop(t,s) = rho(t,s) !! Note that no boundary condition problem occurs in this routine !! as (tn,sn) or (ta,sa) are defined over the whole domain. !! !! ** Action : - prd , the in situ density (no units) !! - prhop, the potential volumic mass (Kg/m3) !! !! References : Jackett and McDougall, J. Atmos. Ocean. Tech., 1994 !! Brown and Campana, Mon. Weather Rev., 1978 !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: ptem ! potential temperature [Celcius] REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: psal ! salinity [psu] REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( out) :: prd ! in situ density REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( out) :: prhop ! potential density (surface referenced) INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: & ! temporary scalars zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & zb, zd, zc, zaw, za, zb1, za1, zkw, zk0 REAL(wp), DIMENSION(jpi,jpj,jpk) :: zws !!---------------------------------------------------------------------- IF( neos_init == 0 ) CALL eos_init ! initialization (in not already done) SELECT CASE ( neos ) ! CASE ( 0 ) ! Jackett and McDougall (1994) formulation ! !CDIR NOVERRCHK zws(:,:,:) = SQRT( ABS( psal(:,:,:) ) ) ! ! =============== DO jk = 1, jpkm1 ! Horizontal slab ! ! =============== DO jj = 1, jpj DO ji = 1, jpi zt = ptem(ji,jj,jk) zs = psal(ji,jj,jk) ! depth zh = fsdept(ji,jj,jk) ! square root salinity zsr= zws(ji,jj,jk) ! compute volumic mass pure water at atm pressure zr1= ( ( ( ( 6.536332e-9*zt-1.120083e-6 )*zt+1.001685e-4)*zt & -9.095290e-3 )*zt+6.793952e-2 )*zt+999.842594 ! seawater volumic mass atm pressure zr2= ( ( ( 5.3875e-9*zt-8.2467e-7 ) *zt+7.6438e-5 ) *zt & -4.0899e-3 ) *zt+0.824493 zr3= ( -1.6546e-6*zt+1.0227e-4 ) *zt-5.72466e-3 zr4= 4.8314e-4 ! potential volumic mass (reference to the surface) zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 ! save potential volumic mass prhop(ji,jj,jk) = zrhop * tmask(ji,jj,jk) ! add the compression terms ze = ( -3.508914e-8*zt-1.248266e-8 ) *zt-2.595994e-6 zbw= ( 1.296821e-6*zt-5.782165e-9 ) *zt+1.045941e-4 zb = zbw + ze * zs zd = -2.042967e-2 zc = (-7.267926e-5*zt+2.598241e-3 ) *zt+0.1571896 zaw= ( ( 5.939910e-6*zt+2.512549e-3 ) *zt-0.1028859 ) *zt - 4.721788 za = ( zd*zsr + zc ) *zs + zaw zb1= (-0.1909078*zt+7.390729 ) *zt-55.87545 za1= ( ( 2.326469e-3*zt+1.553190)*zt-65.00517 ) *zt+1044.077 zkw= ( ( (-1.361629e-4*zt-1.852732e-2 ) *zt-30.41638 ) *zt + 2098.925 ) *zt+190925.6 zk0= ( zb1*zsr + za1 )*zs + zkw ! masked in situ density anomaly prd(ji,jj,jk) = ( zrhop / ( 1.0 - zh / ( zk0 - zh * ( za - zh * zb ) ) ) & - rau0 ) / rau0 * tmask(ji,jj,jk) END DO END DO ! ! =============== END DO ! End of slab ! ! =============== ! CASE ( 1 ) ! Linear formulation function of temperature only ! ! ! =============== DO jk = 1, jpkm1 ! Horizontal slab ! ! =============== DO jj = 1, jpj DO ji = 1, jpi zt = ptem(ji,jj,jk) zs = psal(ji,jj,jk) ! ... density and potential volumic mass prd (ji,jj,jk) = ( 0.0285 - ralpha * zt ) * tmask(ji,jj,jk) prhop(ji,jj,jk) = ( rau0 * prd(ji,jj,jk) + rau0 ) * tmask(ji,jj,jk) END DO END DO ! ! =============== END DO ! End of slab ! ! =============== ! CASE ( 2 ) ! Linear formulation function of temperature and salinity ! ! ! =============== DO jk = 1, jpkm1 ! Horizontal slab ! ! =============== DO jj = 1, jpj DO ji = 1, jpi zt = ptem(ji,jj,jk) zs = psal(ji,jj,jk) ! ... density and potential volumic mass prd (ji,jj,jk) = ( rbeta * zs - ralpha * zt ) * tmask(ji,jj,jk) prhop(ji,jj,jk) = ( rau0 * prd(ji,jj,jk) + rau0 ) * tmask(ji,jj,jk) END DO END DO ! ! =============== END DO ! End of slab ! ! =============== ! CASE DEFAULT ! WRITE(ctmp1,*) ' bad flag value for neos = ', neos CALL ctl_stop( ctmp1 ) ! END SELECT ! IF(ln_ctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-p: ', tab3d_2=prhop, clinfo2=' pot : ', ovlap=1, kdim=jpk ) ! END SUBROUTINE eos_insitu_pot SUBROUTINE eos_insitu_2d( ptem, psal, pdep, prd ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_insitu_2d *** !! !! ** Purpose : Compute the in situ density (ratio rho/rau0) from !! potential temperature and salinity using an equation of state !! defined through the namelist parameter neos. * 2D field case !! !! ** Method : !! neos = 0 : Jackett and McDougall (1994) equation of state. !! the in situ density is computed directly as a function of !! potential temperature relative to the surface (the opa t !! variable), salt and pressure (assuming no pressure variation !! along geopotential surfaces, i.e. the pressure p in decibars !! is approximated by the depth in meters. !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 !! with pressure p decibars !! potential temperature t deg celsius !! salinity s psu !! reference volumic mass rau0 kg/m**3 !! in situ volumic mass rho kg/m**3 !! in situ density anomalie prd no units !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, !! t = 40 deg celcius, s=40 psu !! neos = 1 : linear equation of state function of temperature only !! prd(t) = 0.0285 - ralpha * t !! neos = 2 : linear equation of state function of temperature and !! salinity !! prd(t,s) = rbeta * s - ralpha * tn - 1. !! Note that no boundary condition problem occurs in this routine !! as (ptem,psal) are defined over the whole domain. !! !! ** Action : - prd , the in situ density (no units) !! !! References : Jackett and McDougall, J. Atmos. Ocean. Tech., 1994 !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ptem ! potential temperature [Celcius] REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu] REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pdep ! depth [m] REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: prd ! in situ density !! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: & ! temporary scalars zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & zmask REAL(wp), DIMENSION(jpi,jpj) :: zws !!---------------------------------------------------------------------- IF( neos_init == 0 ) CALL eos_init ! initialization (in not already done) prd(:,:) = 0.e0 SELECT CASE ( neos ) ! CASE ( 0 ) ! Jackett and McDougall (1994) formulation ! !CDIR NOVERRCHK DO jj = 1, jpjm1 !CDIR NOVERRCHK #if defined key_mpp_omp DO ji = 1, jpim1 #else DO ji = 1, fs_jpim1 ! vector opt. #endif zws(ji,jj) = SQRT( ABS( psal(ji,jj) ) ) END DO END DO ! ! =============== DO jj = 1, jpjm1 ! Horizontal slab ! ! =============== #if defined key_mpp_omp DO ji = 1, jpim1 #else DO ji = 1, fs_jpim1 ! vector opt. #endif zmask = tmask(ji,jj,1) ! land/sea bottom mask = surf. mask zt = ptem (ji,jj) ! interpolated T zs = psal (ji,jj) ! interpolated S zsr= zws(ji,jj) ! square root of interpolated S zh = pdep(ji,jj) ! depth at the partial step level ! compute volumic mass pure water at atm pressure zr1 = ( ( ( ( 6.536332e-9*zt-1.120083e-6 )*zt+1.001685e-4)*zt & -9.095290e-3 )*zt+6.793952e-2 )*zt+999.842594 ! seawater volumic mass atm pressure zr2= ( ( ( 5.3875e-9*zt-8.2467e-7 )*zt+7.6438e-5 ) *zt & -4.0899e-3 ) *zt+0.824493 zr3= ( -1.6546e-6*zt+1.0227e-4 ) *zt-5.72466e-3 zr4= 4.8314e-4 ! potential volumic mass (reference to the surface) zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 ! add the compression terms ze = ( -3.508914e-8*zt-1.248266e-8 ) *zt-2.595994e-6 zbw= ( 1.296821e-6*zt-5.782165e-9 ) *zt+1.045941e-4 zb = zbw + ze * zs zd = -2.042967e-2 zc = (-7.267926e-5*zt+2.598241e-3 ) *zt+0.1571896 zaw= ( ( 5.939910e-6*zt+2.512549e-3 ) *zt-0.1028859 ) *zt -4.721788 za = ( zd*zsr + zc ) *zs + zaw zb1= (-0.1909078*zt+7.390729 ) *zt-55.87545 za1= ( ( 2.326469e-3*zt+1.553190)*zt-65.00517 ) *zt+1044.077 zkw= ( ( (-1.361629e-4*zt-1.852732e-2 ) *zt-30.41638 ) *zt & +2098.925 ) *zt+190925.6 zk0= ( zb1*zsr + za1 )*zs + zkw ! masked in situ density anomaly prd(ji,jj) = ( zrhop / ( 1.0 - zh / ( zk0 - zh * ( za - zh * zb ) ) ) - rau0 ) & & / rau0 * zmask END DO ! ! =============== END DO ! End of slab ! ! =============== ! CASE ( 1 ) ! Linear formulation function of temperature only ! ! ! =============== DO jj = 1, jpjm1 ! Horizontal slab ! ! =============== #if defined key_mpp_omp DO ji = 1, jpim1 #else DO ji = 1, fs_jpim1 ! vector opt. #endif prd(ji,jj) = ( 0.0285 - ralpha * ptem(ji,jj) ) * tmask(ji,jj,1) END DO ! ! =============== END DO ! End of slab ! ! =============== ! CASE ( 2 ) ! Linear formulation function of temperature and salinity ! ! ! =============== DO jj = 1, jpjm1 ! Horizontal slab ! ! =============== #if defined key_mpp_omp DO ji = 1, jpim1 #else DO ji = 1, fs_jpim1 ! vector opt. #endif prd(ji,jj) = ( rbeta * psal(ji,jj) - ralpha * ptem(ji,jj) ) * tmask(ji,jj,1) END DO ! ! =============== END DO ! End of slab ! ! =============== ! CASE DEFAULT ! WRITE(ctmp1,*) ' bad flag value for neos = ', neos CALL ctl_stop( ctmp1 ) ! END SELECT IF(ln_ctl) CALL prt_ctl( tab2d_1=prd, clinfo1=' eos2d: ' ) ! END SUBROUTINE eos_insitu_2d SUBROUTINE eos_bn2( ptem, psal, pn2 ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_bn2 *** !! !! ** Purpose : Compute the local Brunt-Vaisala frequency at the time- !! step of the input arguments !! !! ** Method : !! * neos = 0 : UNESCO sea water properties !! The brunt-vaisala frequency is computed using the polynomial !! polynomial expression of McDougall (1987): !! N^2 = grav * beta * ( alpha/beta*dk[ t ] - dk[ s ] )/e3w !! If lk_zdfddm=T, the heat/salt buoyancy flux ratio Rrau is !! computed and used in zdfddm module : !! Rrau = alpha/beta * ( dk[ t ] / dk[ s ] ) !! * neos = 1 : linear equation of state (temperature only) !! N^2 = grav * ralpha * dk[ t ]/e3w !! * neos = 2 : linear equation of state (temperature & salinity) !! N^2 = grav * (ralpha * dk[ t ] - rbeta * dk[ s ] ) / e3w !! The use of potential density to compute N^2 introduces e r r o r !! in the sign of N^2 at great depths. We recommand the use of !! neos = 0, except for academical studies. !! Macro-tasked on horizontal slab (jk-loop) !! N.B. N^2 is set to zero at the first level (JK=1) in inidtr !! and is never used at this level. !! !! ** Action : - pn2 : the brunt-vaisala frequency !! !! References : McDougall, J. Phys. Oceanogr., 17, 1950-1964, 1987. !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: ptem ! potential temperature [Celcius] REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: psal ! salinity [psu] REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( out) :: pn2 ! Brunt-Vaisala frequency [s-1] INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zgde3w, zt, zs, zh, & ! temporary scalars & zalbet, zbeta ! " " #if defined key_zdfddm REAL(wp) :: zds ! temporary scalars #endif !!---------------------------------------------------------------------- ! pn2 : first and last levels ! --------------------------- ! bn^2=0. at jk=1 and jpk set in inidtr.F : no computation ! pn2 : interior points only (2=< jk =< jpkm1 ) ! -------------------------- SELECT CASE ( neos ) ! CASE ( 0 ) ! Jackett and McDougall (1994) formulation ! ! ! =============== DO jk = 2, jpkm1 ! Horizontal slab ! ! =============== DO jj = 1, jpj DO ji = 1, jpi zgde3w = grav / fse3w(ji,jj,jk) zt = 0.5 * ( ptem(ji,jj,jk) + ptem(ji,jj,jk-1) ) ! potential temperature at w-point zs = 0.5 * ( psal(ji,jj,jk) + psal(ji,jj,jk-1) ) - 35.0 ! salinity anomaly (s-35) at w-point zh = fsdepw(ji,jj,jk) ! depth in meters at w-point zalbet = ( ( ( - 0.255019e-07 * zt + 0.298357e-05 ) * zt & ! ratio alpha/beta & - 0.203814e-03 ) * zt & & + 0.170907e-01 ) * zt & & + 0.665157e-01 & & + ( - 0.678662e-05 * zs & & - 0.846960e-04 * zt + 0.378110e-02 ) * zs & & + ( ( - 0.302285e-13 * zh & & - 0.251520e-11 * zs & & + 0.512857e-12 * zt * zt ) * zh & & - 0.164759e-06 * zs & & +( 0.791325e-08 * zt - 0.933746e-06 ) * zt & & + 0.380374e-04 ) * zh zbeta = ( ( -0.415613e-09 * zt + 0.555579e-07 ) * zt & ! beta & - 0.301985e-05 ) * zt & & + 0.785567e-03 & & + ( 0.515032e-08 * zs & & + 0.788212e-08 * zt - 0.356603e-06 ) * zs & & +( ( 0.121551e-17 * zh & & - 0.602281e-15 * zs & & - 0.175379e-14 * zt + 0.176621e-12 ) * zh & & + 0.408195e-10 * zs & & + ( - 0.213127e-11 * zt + 0.192867e-09 ) * zt & & - 0.121555e-07 ) * zh pn2(ji,jj,jk) = zgde3w * zbeta * tmask(ji,jj,jk) & ! N^2 & * ( zalbet * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) & & - ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) ) #if defined key_zdfddm ! !!bug **** caution a traiter zds=dk[S]= 0 !!!! zds = ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) ! Rrau = (alpha / beta) (dk[t] / dk[s]) IF ( ABS( zds) <= 1.e-20 ) zds = 1.e-20 rrau(ji,jj,jk) = zalbet * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) / zds #endif END DO END DO ! ! =============== END DO ! End of slab ! ! =============== ! CASE ( 1 ) ! Linear formulation function of temperature only ! ! ! =============== DO jk = 2, jpkm1 ! Horizontal slab ! ! =============== DO jj = 1, jpj DO ji = 1, jpi zgde3w = grav / fse3w(ji,jj,jk) * tmask(ji,jj,jk) pn2(ji,jj,jk) = zgde3w * ralpha * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) END DO END DO ! ! =============== END DO ! End of slab ! ! =============== ! CASE ( 2 ) ! Linear formulation function of temperature and salinity ! ! ! =============== DO jk = 2, jpkm1 ! Horizontal slab ! ! =============== DO jj = 1, jpj DO ji = 1, jpi zgde3w = grav / fse3w(ji,jj,jk) * tmask(ji,jj,jk) pn2(ji,jj,jk) = zgde3w * ( ralpha * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) & & - rbeta * ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) ) END DO END DO #if defined key_zdfddm ! ! Rrau = (alpha / beta) (dk[t] / dk[s]) zalbet = ralpha / rbeta DO jj = 1, jpj DO ji = 1, jpi zds = ( psal(ji,jj,jk-1) - psal(ji,jj,jk) ) IF ( ABS( zds ) <= 1.e-20 ) zds = 1.e-20 rrau(ji,jj,jk) = zalbet * ( ptem(ji,jj,jk-1) - ptem(ji,jj,jk) ) / zds END DO END DO #endif ! ! =============== END DO ! End of slab ! ! =============== ! CASE DEFAULT ! WRITE(ctmp1,*) ' bad flag value for neos = ', neos CALL ctl_stop( ctmp1 ) ! END SELECT IF(ln_ctl) CALL prt_ctl(tab3d_1=pn2, clinfo1=' bn2 : ', ovlap=1, kdim=jpk) #if defined key_zdfddm IF(ln_ctl) CALL prt_ctl(tab3d_1=rrau, clinfo1=' rrau : ', ovlap=1, kdim=jpk) #endif ! END SUBROUTINE eos_bn2 FUNCTION tfreez( psal ) RESULT( ptf ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_init *** !! !! ** Purpose : Compute the sea surface freezing temperature [Celcius] !! !! ** Method : UNESCO freezing point at the surface (pressure = 0???) !! freezing point [Celcius]=(-.0575+1.710523e-3*sqrt(abs(s))-2.154996e-4*s)*s-7.53e-4*p !! checkvalue: tf= -2.588567 Celsius for s=40.0psu, p=500. decibars !! !! Reference : UNESCO tech. papers in the marine science no. 28. 1978 !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu] REAL(wp), DIMENSION(jpi,jpj) :: ptf ! freezing temperature [Celcius] !!---------------------------------------------------------------------- ptf(:,:) = ( - 0.0575 + 1.710523e-3 * SQRT( psal(:,:) ) & & - 2.154996e-4 * psal(:,:) ) * psal(:,:) END FUNCTION tfreez SUBROUTINE eos_init !!---------------------------------------------------------------------- !! *** ROUTINE eos_init *** !! !! ** Purpose : initializations for the equation of state !! !! ** Method : Read the namelist nameos and control the parameters !!---------------------------------------------------------------------- neos_init = 1 ! indicate that the initialization has been done REWIND( numnam ) ! Read Namelist nameos : equation of state READ ( numnam, nameos ) ! Control print IF(lwp) THEN WRITE(numout,*) WRITE(numout,*) 'eos_init : equation of state' WRITE(numout,*) '~~~~~~~~' WRITE(numout,*) ' Namelist nameos : set eos parameters' WRITE(numout,*) ' flag for eq. of state and N^2 neos = ', neos WRITE(numout,*) ' thermal exp. coef. (linear) ralpha = ', ralpha WRITE(numout,*) ' saline exp. coef. (linear) rbeta = ', rbeta ENDIF SELECT CASE ( neos ) CASE ( 0 ) ! Jackett and McDougall (1994) formulation IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' use of Jackett & McDougall (1994) equation of state and' IF(lwp) WRITE(numout,*) ' McDougall (1987) Brunt-Vaisala frequency' ! CASE ( 1 ) ! Linear formulation function of temperature only IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' use of linear eos rho(T) = rau0 * ( 1.0285 - ralpha * T )' IF( lk_zdfddm ) CALL ctl_stop( ' double diffusive mixing parameterization requires', & & ' that T and S are used as state variables' ) ! CASE ( 2 ) ! Linear formulation function of temperature and salinity IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' use of linear eos rho(T,S) = rau0 * ( rbeta * S - ralpha * T )' ! CASE DEFAULT ! E R R O R in neos WRITE(ctmp1,*) ' bad flag value for neos = ', neos CALL ctl_stop( ctmp1 ) END SELECT END SUBROUTINE eos_init !!====================================================================== END MODULE eosbn2