MODULE eosbn2 !!============================================================================== !! *** MODULE eosbn2 *** !! Ocean diagnostic variable : equation of state - in situ and potential density !! - Brunt-Vaisala frequency !!============================================================================== !! History : OPA ! 1989-03 (O. Marti) Original code !! 6.0 ! 1994-07 (G. Madec, M. Imbard) add bn2 !! 6.0 ! 1994-08 (G. Madec) Add Jackett & McDougall eos !! 7.0 ! 1996-01 (G. Madec) statement function for e3 !! 8.1 ! 1997-07 (G. Madec) density instead of volumic mass !! - ! 1999-02 (G. Madec, N. Grima) semi-implicit pressure gradient !! 8.2 ! 2001-09 (M. Ben Jelloul) bugfix on linear eos !! NEMO 1.0 ! 2002-10 (G. Madec) add eos_init !! - ! 2002-11 (G. Madec, A. Bozec) partial step, eos_insitu_2d !! - ! 2003-08 (G. Madec) F90, free form !! 3.0 ! 2006-08 (G. Madec) add tfreez function (now eos_fzp function) !! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA !! - ! 2010-10 (G. Nurser, G. Madec) add alpha/beta used in ldfslp !! 3.7 ! 2012-03 (F. Roquet, G. Madec) add primitive of alpha and beta used in PE computation !! - ! 2012-05 (F. Roquet) add Vallis and original JM95 equation of state !! - ! 2013-04 (F. Roquet, G. Madec) add eos_rab, change bn2 computation and reorganize the module !! - ! 2014-09 (F. Roquet) add TEOS-10, S-EOS, and modify EOS-80 !! - ! 2015-06 (P.A. Bouttier) eos_fzp functions changed to subroutines for AGRIF !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! 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 !! bn2 : Compute the Brunt-Vaisala frequency !! eos_rab : generic interface of in situ thermal/haline expansion ratio !! eos_rab_3d : compute in situ thermal/haline expansion ratio !! eos_rab_2d : compute in situ thermal/haline expansion ratio for 2d fields !! eos_fzp_2d : freezing temperature for 2d fields !! eos_fzp_0d : freezing temperature for scalar !! 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 lib_mpp ! MPP library USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) USE prtctl ! Print control USE wrk_nemo ! Memory Allocation USE lbclnk ! ocean lateral boundary conditions USE timing ! Timing USE stopar ! Stochastic T/S fluctuations USE stopts ! Stochastic T/S fluctuations IMPLICIT NONE PRIVATE ! !! * Interface INTERFACE eos MODULE PROCEDURE eos_insitu, eos_insitu_pot, eos_insitu_2d END INTERFACE ! INTERFACE eos_rab MODULE PROCEDURE rab_3d, rab_2d, rab_0d END INTERFACE ! INTERFACE eos_fzp MODULE PROCEDURE eos_fzp_2d, eos_fzp_0d END INTERFACE ! PUBLIC eos ! called by step, istate, tranpc and zpsgrd modules PUBLIC bn2 ! called by step module PUBLIC eos_rab ! called by ldfslp, zdfddm, trabbl PUBLIC eos_pt_from_ct ! called by sbcssm PUBLIC eos_fzp ! called by traadv_cen2 and sbcice_... modules PUBLIC eos_pen ! used for pe diagnostics in trdpen module PUBLIC eos_init ! called by istate module ! !!* Namelist (nameos) * INTEGER , PUBLIC :: nn_eos ! = 0/1/2 type of eq. of state and Brunt-Vaisala frequ. LOGICAL , PUBLIC :: ln_useCT ! determine if eos_pt_from_ct is used to compute sst_m ! !!! simplified eos coefficients ! default value: Vallis 2006 REAL(wp) :: rn_a0 = 1.6550e-1_wp ! thermal expansion coeff. REAL(wp) :: rn_b0 = 7.6554e-1_wp ! saline expansion coeff. REAL(wp) :: rn_lambda1 = 5.9520e-2_wp ! cabbeling coeff. in T^2 REAL(wp) :: rn_lambda2 = 5.4914e-4_wp ! cabbeling coeff. in S^2 REAL(wp) :: rn_mu1 = 1.4970e-4_wp ! thermobaric coeff. in T REAL(wp) :: rn_mu2 = 1.1090e-5_wp ! thermobaric coeff. in S REAL(wp) :: rn_nu = 2.4341e-3_wp ! cabbeling coeff. in theta*salt ! TEOS10/EOS80 parameters REAL(wp) :: r1_S0, r1_T0, r1_Z0, rdeltaS ! EOS parameters REAL(wp) :: EOS000 , EOS100 , EOS200 , EOS300 , EOS400 , EOS500 , EOS600 REAL(wp) :: EOS010 , EOS110 , EOS210 , EOS310 , EOS410 , EOS510 REAL(wp) :: EOS020 , EOS120 , EOS220 , EOS320 , EOS420 REAL(wp) :: EOS030 , EOS130 , EOS230 , EOS330 REAL(wp) :: EOS040 , EOS140 , EOS240 REAL(wp) :: EOS050 , EOS150 REAL(wp) :: EOS060 REAL(wp) :: EOS001 , EOS101 , EOS201 , EOS301 , EOS401 REAL(wp) :: EOS011 , EOS111 , EOS211 , EOS311 REAL(wp) :: EOS021 , EOS121 , EOS221 REAL(wp) :: EOS031 , EOS131 REAL(wp) :: EOS041 REAL(wp) :: EOS002 , EOS102 , EOS202 REAL(wp) :: EOS012 , EOS112 REAL(wp) :: EOS022 REAL(wp) :: EOS003 , EOS103 REAL(wp) :: EOS013 ! ALPHA parameters REAL(wp) :: ALP000 , ALP100 , ALP200 , ALP300 , ALP400 , ALP500 REAL(wp) :: ALP010 , ALP110 , ALP210 , ALP310 , ALP410 REAL(wp) :: ALP020 , ALP120 , ALP220 , ALP320 REAL(wp) :: ALP030 , ALP130 , ALP230 REAL(wp) :: ALP040 , ALP140 REAL(wp) :: ALP050 REAL(wp) :: ALP001 , ALP101 , ALP201 , ALP301 REAL(wp) :: ALP011 , ALP111 , ALP211 REAL(wp) :: ALP021 , ALP121 REAL(wp) :: ALP031 REAL(wp) :: ALP002 , ALP102 REAL(wp) :: ALP012 REAL(wp) :: ALP003 ! BETA parameters REAL(wp) :: BET000 , BET100 , BET200 , BET300 , BET400 , BET500 REAL(wp) :: BET010 , BET110 , BET210 , BET310 , BET410 REAL(wp) :: BET020 , BET120 , BET220 , BET320 REAL(wp) :: BET030 , BET130 , BET230 REAL(wp) :: BET040 , BET140 REAL(wp) :: BET050 REAL(wp) :: BET001 , BET101 , BET201 , BET301 REAL(wp) :: BET011 , BET111 , BET211 REAL(wp) :: BET021 , BET121 REAL(wp) :: BET031 REAL(wp) :: BET002 , BET102 REAL(wp) :: BET012 REAL(wp) :: BET003 ! PEN parameters REAL(wp) :: PEN000 , PEN100 , PEN200 , PEN300 , PEN400 REAL(wp) :: PEN010 , PEN110 , PEN210 , PEN310 REAL(wp) :: PEN020 , PEN120 , PEN220 REAL(wp) :: PEN030 , PEN130 REAL(wp) :: PEN040 REAL(wp) :: PEN001 , PEN101 , PEN201 REAL(wp) :: PEN011 , PEN111 REAL(wp) :: PEN021 REAL(wp) :: PEN002 , PEN102 REAL(wp) :: PEN012 ! ALPHA_PEN parameters REAL(wp) :: APE000 , APE100 , APE200 , APE300 REAL(wp) :: APE010 , APE110 , APE210 REAL(wp) :: APE020 , APE120 REAL(wp) :: APE030 REAL(wp) :: APE001 , APE101 REAL(wp) :: APE011 REAL(wp) :: APE002 ! BETA_PEN parameters REAL(wp) :: BPE000 , BPE100 , BPE200 , BPE300 REAL(wp) :: BPE010 , BPE110 , BPE210 REAL(wp) :: BPE020 , BPE120 REAL(wp) :: BPE030 REAL(wp) :: BPE001 , BPE101 REAL(wp) :: BPE011 REAL(wp) :: BPE002 !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.7 , NEMO Consortium (2014) !! $Id: eosbn2.F90 5540 2015-07-02 15:11:23Z jchanut $ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE eos_insitu( pts, prd, pdep ) !!---------------------------------------------------------------------- !! *** 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 nn_eos. !! !! ** Method : prd(t,s,z) = ( rho(t,s,z) - rau0 ) / rau0 !! with prd in situ density anomaly no units !! t TEOS10: CT or EOS80: PT Celsius !! s TEOS10: SA or EOS80: SP TEOS10: g/kg or EOS80: psu !! z depth meters !! rho in situ density kg/m^3 !! rau0 reference density kg/m^3 !! !! nn_eos = -1 : polynomial TEOS-10 equation of state is used for rho(t,s,z). !! Check value: rho = 1028.21993233072 kg/m^3 for z=3000 dbar, ct=3 Celcius, sa=35.5 g/kg !! !! nn_eos = 0 : polynomial EOS-80 equation of state is used for rho(t,s,z). !! Check value: rho = 1028.35011066567 kg/m^3 for z=3000 dbar, pt=3 Celcius, sp=35.5 psu !! !! nn_eos = 1 : simplified equation of state !! prd(t,s,z) = ( -a0*(1+lambda/2*(T-T0)+mu*z+nu*(S-S0))*(T-T0) + b0*(S-S0) ) / rau0 !! linear case function of T only: rn_alpha<>0, other coefficients = 0 !! linear eos function of T and S: rn_alpha and rn_beta<>0, other coefficients=0 !! Vallis like equation: use default values of coefficients !! !! ** Action : compute prd , the in situ density (no units) !! !! References : Roquet et al, Ocean Modelling, in preparation (2014) !! Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006 !! TEOS-10 Manual, 2010 !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] ! ! 2 : salinity [psu] REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT( out) :: prd ! in situ density [-] REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pdep ! depth [m] ! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zt , zh , zs , ztm ! local scalars REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - - !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('eos-insitu') ! SELECT CASE( nn_eos ) ! CASE( -1, 0 ) !== polynomial TEOS-10 / EOS-80 ==! ! DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi ! zh = pdep(ji,jj,jk) * r1_Z0 ! depth zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity ztm = tmask(ji,jj,jk) ! tmask ! zn3 = EOS013*zt & & + EOS103*zs+EOS003 ! zn2 = (EOS022*zt & & + EOS112*zs+EOS012)*zt & & + (EOS202*zs+EOS102)*zs+EOS002 ! zn1 = (((EOS041*zt & & + EOS131*zs+EOS031)*zt & & + (EOS221*zs+EOS121)*zs+EOS021)*zt & & + ((EOS311*zs+EOS211)*zs+EOS111)*zs+EOS011)*zt & & + (((EOS401*zs+EOS301)*zs+EOS201)*zs+EOS101)*zs+EOS001 ! zn0 = (((((EOS060*zt & & + EOS150*zs+EOS050)*zt & & + (EOS240*zs+EOS140)*zs+EOS040)*zt & & + ((EOS330*zs+EOS230)*zs+EOS130)*zs+EOS030)*zt & & + (((EOS420*zs+EOS320)*zs+EOS220)*zs+EOS120)*zs+EOS020)*zt & & + ((((EOS510*zs+EOS410)*zs+EOS310)*zs+EOS210)*zs+EOS110)*zs+EOS010)*zt & & + (((((EOS600*zs+EOS500)*zs+EOS400)*zs+EOS300)*zs+EOS200)*zs+EOS100)*zs+EOS000 ! zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0 ! prd(ji,jj,jk) = ( zn * r1_rau0 - 1._wp ) * ztm ! density anomaly (masked) ! END DO END DO END DO ! CASE( 1 ) !== simplified EOS ==! ! DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zt = pts (ji,jj,jk,jp_tem) - 10._wp zs = pts (ji,jj,jk,jp_sal) - 35._wp zh = pdep (ji,jj,jk) ztm = tmask(ji,jj,jk) ! zn = - rn_a0 * ( 1._wp + 0.5_wp*rn_lambda1*zt + rn_mu1*zh ) * zt & & + rn_b0 * ( 1._wp - 0.5_wp*rn_lambda2*zs - rn_mu2*zh ) * zs & & - rn_nu * zt * zs ! prd(ji,jj,jk) = zn * r1_rau0 * ztm ! density anomaly (masked) END DO END DO END DO ! END SELECT ! IF(ln_ctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-insitu : ', ovlap=1, kdim=jpk ) ! IF( nn_timing == 1 ) CALL timing_stop('eos-insitu') ! END SUBROUTINE eos_insitu SUBROUTINE eos_insitu_pot( pts, prd, prhop, pdep ) !!---------------------------------------------------------------------- !! *** 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 nn_eos. !! !! ** Action : - prd , the in situ density (no units) !! - prhop, the potential volumic mass (Kg/m3) !! !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] ! ! 2 : 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) REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pdep ! depth [m] ! INTEGER :: ji, jj, jk, jsmp ! dummy loop indices INTEGER :: jdof REAL(wp) :: zt , zh , zstemp, zs , ztm ! local scalars REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - - REAL(wp), DIMENSION(:), ALLOCATABLE :: zn0_sto, zn_sto, zsign ! local vectors !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('eos-pot') ! SELECT CASE ( nn_eos ) ! CASE( -1, 0 ) !== polynomial TEOS-10 / EOS-80 ==! ! ! Stochastic equation of state IF ( ln_sto_eos ) THEN ALLOCATE(zn0_sto(1:2*nn_sto_eos)) ALLOCATE(zn_sto(1:2*nn_sto_eos)) ALLOCATE(zsign(1:2*nn_sto_eos)) DO jsmp = 1, 2*nn_sto_eos, 2 zsign(jsmp) = 1._wp zsign(jsmp+1) = -1._wp END DO ! DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi ! ! compute density (2*nn_sto_eos) times: ! (1) for t+dt, s+ds (with the random TS fluctutation computed in sto_pts) ! (2) for t-dt, s-ds (with the opposite fluctuation) DO jsmp = 1, nn_sto_eos*2 jdof = (jsmp + 1) / 2 zh = pdep(ji,jj,jk) * r1_Z0 ! depth zt = (pts (ji,jj,jk,jp_tem) + pts_ran(ji,jj,jk,jp_tem,jdof) * zsign(jsmp)) * r1_T0 ! temperature zstemp = pts (ji,jj,jk,jp_sal) + pts_ran(ji,jj,jk,jp_sal,jdof) * zsign(jsmp) zs = SQRT( ABS( zstemp + rdeltaS ) * r1_S0 ) ! square root salinity ztm = tmask(ji,jj,jk) ! tmask ! zn3 = EOS013*zt & & + EOS103*zs+EOS003 ! zn2 = (EOS022*zt & & + EOS112*zs+EOS012)*zt & & + (EOS202*zs+EOS102)*zs+EOS002 ! zn1 = (((EOS041*zt & & + EOS131*zs+EOS031)*zt & & + (EOS221*zs+EOS121)*zs+EOS021)*zt & & + ((EOS311*zs+EOS211)*zs+EOS111)*zs+EOS011)*zt & & + (((EOS401*zs+EOS301)*zs+EOS201)*zs+EOS101)*zs+EOS001 ! zn0_sto(jsmp) = (((((EOS060*zt & & + EOS150*zs+EOS050)*zt & & + (EOS240*zs+EOS140)*zs+EOS040)*zt & & + ((EOS330*zs+EOS230)*zs+EOS130)*zs+EOS030)*zt & & + (((EOS420*zs+EOS320)*zs+EOS220)*zs+EOS120)*zs+EOS020)*zt & & + ((((EOS510*zs+EOS410)*zs+EOS310)*zs+EOS210)*zs+EOS110)*zs+EOS010)*zt & & + (((((EOS600*zs+EOS500)*zs+EOS400)*zs+EOS300)*zs+EOS200)*zs+EOS100)*zs+EOS000 ! zn_sto(jsmp) = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0_sto(jsmp) END DO ! ! compute stochastic density as the mean of the (2*nn_sto_eos) densities prhop(ji,jj,jk) = 0._wp ; prd(ji,jj,jk) = 0._wp DO jsmp = 1, nn_sto_eos*2 prhop(ji,jj,jk) = prhop(ji,jj,jk) + zn0_sto(jsmp) ! potential density referenced at the surface ! prd(ji,jj,jk) = prd(ji,jj,jk) + ( zn_sto(jsmp) * r1_rau0 - 1._wp ) ! density anomaly (masked) END DO prhop(ji,jj,jk) = 0.5_wp * prhop(ji,jj,jk) * ztm / nn_sto_eos prd (ji,jj,jk) = 0.5_wp * prd (ji,jj,jk) * ztm / nn_sto_eos END DO END DO END DO DEALLOCATE(zn0_sto,zn_sto,zsign) ! Non-stochastic equation of state ELSE DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi ! zh = pdep(ji,jj,jk) * r1_Z0 ! depth zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity ztm = tmask(ji,jj,jk) ! tmask ! zn3 = EOS013*zt & & + EOS103*zs+EOS003 ! zn2 = (EOS022*zt & & + EOS112*zs+EOS012)*zt & & + (EOS202*zs+EOS102)*zs+EOS002 ! zn1 = (((EOS041*zt & & + EOS131*zs+EOS031)*zt & & + (EOS221*zs+EOS121)*zs+EOS021)*zt & & + ((EOS311*zs+EOS211)*zs+EOS111)*zs+EOS011)*zt & & + (((EOS401*zs+EOS301)*zs+EOS201)*zs+EOS101)*zs+EOS001 ! zn0 = (((((EOS060*zt & & + EOS150*zs+EOS050)*zt & & + (EOS240*zs+EOS140)*zs+EOS040)*zt & & + ((EOS330*zs+EOS230)*zs+EOS130)*zs+EOS030)*zt & & + (((EOS420*zs+EOS320)*zs+EOS220)*zs+EOS120)*zs+EOS020)*zt & & + ((((EOS510*zs+EOS410)*zs+EOS310)*zs+EOS210)*zs+EOS110)*zs+EOS010)*zt & & + (((((EOS600*zs+EOS500)*zs+EOS400)*zs+EOS300)*zs+EOS200)*zs+EOS100)*zs+EOS000 ! zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0 ! prhop(ji,jj,jk) = zn0 * ztm ! potential density referenced at the surface ! prd(ji,jj,jk) = ( zn * r1_rau0 - 1._wp ) * ztm ! density anomaly (masked) END DO END DO END DO ENDIF CASE( 1 ) !== simplified EOS ==! ! DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zt = pts (ji,jj,jk,jp_tem) - 10._wp zs = pts (ji,jj,jk,jp_sal) - 35._wp zh = pdep (ji,jj,jk) ztm = tmask(ji,jj,jk) ! ! potential density referenced at the surface zn = - rn_a0 * ( 1._wp + 0.5_wp*rn_lambda1*zt ) * zt & & + rn_b0 * ( 1._wp - 0.5_wp*rn_lambda2*zs ) * zs & & - rn_nu * zt * zs prhop(ji,jj,jk) = ( rau0 + zn ) * ztm ! ! density anomaly (masked) zn = zn - ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zh prd(ji,jj,jk) = zn * r1_rau0 * ztm ! END DO END DO END DO ! END SELECT ! IF(ln_ctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-pot: ', tab3d_2=prhop, clinfo2=' pot : ', ovlap=1, kdim=jpk ) ! IF( nn_timing == 1 ) CALL timing_stop('eos-pot') ! END SUBROUTINE eos_insitu_pot SUBROUTINE eos_insitu_2d( pts, 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 nn_eos. * 2D field case !! !! ** Action : - prd , the in situ density (no units) (unmasked) !! !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] ! ! 2 : 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, jk ! dummy loop indices REAL(wp) :: zt , zh , zs ! local scalars REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - - !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('eos2d') ! prd(:,:) = 0._wp ! SELECT CASE( nn_eos ) ! CASE( -1, 0 ) !== polynomial TEOS-10 / EOS-80 ==! ! DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ! zh = pdep(ji,jj) * r1_Z0 ! depth zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity ! zn3 = EOS013*zt & & + EOS103*zs+EOS003 ! zn2 = (EOS022*zt & & + EOS112*zs+EOS012)*zt & & + (EOS202*zs+EOS102)*zs+EOS002 ! zn1 = (((EOS041*zt & & + EOS131*zs+EOS031)*zt & & + (EOS221*zs+EOS121)*zs+EOS021)*zt & & + ((EOS311*zs+EOS211)*zs+EOS111)*zs+EOS011)*zt & & + (((EOS401*zs+EOS301)*zs+EOS201)*zs+EOS101)*zs+EOS001 ! zn0 = (((((EOS060*zt & & + EOS150*zs+EOS050)*zt & & + (EOS240*zs+EOS140)*zs+EOS040)*zt & & + ((EOS330*zs+EOS230)*zs+EOS130)*zs+EOS030)*zt & & + (((EOS420*zs+EOS320)*zs+EOS220)*zs+EOS120)*zs+EOS020)*zt & & + ((((EOS510*zs+EOS410)*zs+EOS310)*zs+EOS210)*zs+EOS110)*zs+EOS010)*zt & & + (((((EOS600*zs+EOS500)*zs+EOS400)*zs+EOS300)*zs+EOS200)*zs+EOS100)*zs+EOS000 ! zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0 ! prd(ji,jj) = zn * r1_rau0 - 1._wp ! unmasked in situ density anomaly ! END DO END DO ! CALL lbc_lnk( prd, 'T', 1. ) ! Lateral boundary conditions ! CASE( 1 ) !== simplified EOS ==! ! DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ! zt = pts (ji,jj,jp_tem) - 10._wp zs = pts (ji,jj,jp_sal) - 35._wp zh = pdep (ji,jj) ! depth at the partial step level ! zn = - rn_a0 * ( 1._wp + 0.5_wp*rn_lambda1*zt + rn_mu1*zh ) * zt & & + rn_b0 * ( 1._wp - 0.5_wp*rn_lambda2*zs - rn_mu2*zh ) * zs & & - rn_nu * zt * zs ! prd(ji,jj) = zn * r1_rau0 ! unmasked in situ density anomaly ! END DO END DO ! CALL lbc_lnk( prd, 'T', 1. ) ! Lateral boundary conditions ! END SELECT ! IF(ln_ctl) CALL prt_ctl( tab2d_1=prd, clinfo1=' eos2d: ' ) ! IF( nn_timing == 1 ) CALL timing_stop('eos2d') ! END SUBROUTINE eos_insitu_2d SUBROUTINE rab_3d( pts, pab ) !!---------------------------------------------------------------------- !! *** ROUTINE rab_3d *** !! !! ** Purpose : Calculates thermal/haline expansion ratio at T-points !! !! ** Method : calculates alpha / beta at T-points !! !! ** Action : - pab : thermal/haline expansion ratio at T-points !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature & salinity REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT( out) :: pab ! thermal/haline expansion ratio ! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zt , zh , zs , ztm ! local scalars REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - - !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('rab_3d') ! SELECT CASE ( nn_eos ) ! CASE( -1, 0 ) !== polynomial TEOS-10 / EOS-80 ==! ! DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi ! zh = fsdept(ji,jj,jk) * r1_Z0 ! depth zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity ztm = tmask(ji,jj,jk) ! tmask ! ! alpha zn3 = ALP003 ! zn2 = ALP012*zt + ALP102*zs+ALP002 ! zn1 = ((ALP031*zt & & + ALP121*zs+ALP021)*zt & & + (ALP211*zs+ALP111)*zs+ALP011)*zt & & + ((ALP301*zs+ALP201)*zs+ALP101)*zs+ALP001 ! zn0 = ((((ALP050*zt & & + ALP140*zs+ALP040)*zt & & + (ALP230*zs+ALP130)*zs+ALP030)*zt & & + ((ALP320*zs+ALP220)*zs+ALP120)*zs+ALP020)*zt & & + (((ALP410*zs+ALP310)*zs+ALP210)*zs+ALP110)*zs+ALP010)*zt & & + ((((ALP500*zs+ALP400)*zs+ALP300)*zs+ALP200)*zs+ALP100)*zs+ALP000 ! zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0 ! pab(ji,jj,jk,jp_tem) = zn * r1_rau0 * ztm ! ! beta zn3 = BET003 ! zn2 = BET012*zt + BET102*zs+BET002 ! zn1 = ((BET031*zt & & + BET121*zs+BET021)*zt & & + (BET211*zs+BET111)*zs+BET011)*zt & & + ((BET301*zs+BET201)*zs+BET101)*zs+BET001 ! zn0 = ((((BET050*zt & & + BET140*zs+BET040)*zt & & + (BET230*zs+BET130)*zs+BET030)*zt & & + ((BET320*zs+BET220)*zs+BET120)*zs+BET020)*zt & & + (((BET410*zs+BET310)*zs+BET210)*zs+BET110)*zs+BET010)*zt & & + ((((BET500*zs+BET400)*zs+BET300)*zs+BET200)*zs+BET100)*zs+BET000 ! zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0 ! pab(ji,jj,jk,jp_sal) = zn / zs * r1_rau0 * ztm ! END DO END DO END DO ! CASE( 1 ) !== simplified EOS ==! ! DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zt = pts (ji,jj,jk,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0) zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0) zh = fsdept(ji,jj,jk) ! depth in meters at t-point ztm = tmask(ji,jj,jk) ! land/sea bottom mask = surf. mask ! zn = rn_a0 * ( 1._wp + rn_lambda1*zt + rn_mu1*zh ) + rn_nu*zs pab(ji,jj,jk,jp_tem) = zn * r1_rau0 * ztm ! alpha ! zn = rn_b0 * ( 1._wp - rn_lambda2*zs - rn_mu2*zh ) - rn_nu*zt pab(ji,jj,jk,jp_sal) = zn * r1_rau0 * ztm ! beta ! END DO END DO END DO ! CASE DEFAULT IF(lwp) WRITE(numout,cform_err) IF(lwp) WRITE(numout,*) ' bad flag value for nn_eos = ', nn_eos nstop = nstop + 1 ! END SELECT ! IF(ln_ctl) CALL prt_ctl( tab3d_1=pab(:,:,:,jp_tem), clinfo1=' rab_3d_t: ', & & tab3d_2=pab(:,:,:,jp_sal), clinfo2=' rab_3d_s : ', ovlap=1, kdim=jpk ) ! IF( nn_timing == 1 ) CALL timing_stop('rab_3d') ! END SUBROUTINE rab_3d SUBROUTINE rab_2d( pts, pdep, pab ) !!---------------------------------------------------------------------- !! *** ROUTINE rab_2d *** !! !! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked) !! !! ** Action : - pab : thermal/haline expansion ratio at T-points !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj,jpts) , INTENT(in ) :: pts ! pot. temperature & salinity REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ) :: pdep ! depth [m] REAL(wp), DIMENSION(jpi,jpj,jpts) , INTENT( out) :: pab ! thermal/haline expansion ratio ! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zt , zh , zs ! local scalars REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - - !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('rab_2d') ! pab(:,:,:) = 0._wp ! SELECT CASE ( nn_eos ) ! CASE( -1, 0 ) !== polynomial TEOS-10 / EOS-80 ==! ! DO jj = 1, jpj DO ji = 1, jpi ! zh = pdep(ji,jj) * r1_Z0 ! depth zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity ! ! alpha zn3 = ALP003 ! zn2 = ALP012*zt + ALP102*zs+ALP002 ! zn1 = ((ALP031*zt & & + ALP121*zs+ALP021)*zt & & + (ALP211*zs+ALP111)*zs+ALP011)*zt & & + ((ALP301*zs+ALP201)*zs+ALP101)*zs+ALP001 ! zn0 = ((((ALP050*zt & & + ALP140*zs+ALP040)*zt & & + (ALP230*zs+ALP130)*zs+ALP030)*zt & & + ((ALP320*zs+ALP220)*zs+ALP120)*zs+ALP020)*zt & & + (((ALP410*zs+ALP310)*zs+ALP210)*zs+ALP110)*zs+ALP010)*zt & & + ((((ALP500*zs+ALP400)*zs+ALP300)*zs+ALP200)*zs+ALP100)*zs+ALP000 ! zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0 ! pab(ji,jj,jp_tem) = zn * r1_rau0 ! ! beta zn3 = BET003 ! zn2 = BET012*zt + BET102*zs+BET002 ! zn1 = ((BET031*zt & & + BET121*zs+BET021)*zt & & + (BET211*zs+BET111)*zs+BET011)*zt & & + ((BET301*zs+BET201)*zs+BET101)*zs+BET001 ! zn0 = ((((BET050*zt & & + BET140*zs+BET040)*zt & & + (BET230*zs+BET130)*zs+BET030)*zt & & + ((BET320*zs+BET220)*zs+BET120)*zs+BET020)*zt & & + (((BET410*zs+BET310)*zs+BET210)*zs+BET110)*zs+BET010)*zt & & + ((((BET500*zs+BET400)*zs+BET300)*zs+BET200)*zs+BET100)*zs+BET000 ! zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0 ! pab(ji,jj,jp_sal) = zn / zs * r1_rau0 ! ! END DO END DO ! CASE( 1 ) !== simplified EOS ==! ! DO jj = 1, jpj DO ji = 1, jpi ! zt = pts (ji,jj,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0) zs = pts (ji,jj,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0) zh = pdep (ji,jj) ! depth at the partial step level ! zn = rn_a0 * ( 1._wp + rn_lambda1*zt + rn_mu1*zh ) + rn_nu*zs pab(ji,jj,jp_tem) = zn * r1_rau0 ! alpha ! zn = rn_b0 * ( 1._wp - rn_lambda2*zs - rn_mu2*zh ) - rn_nu*zt pab(ji,jj,jp_sal) = zn * r1_rau0 ! beta ! END DO END DO ! CASE DEFAULT IF(lwp) WRITE(numout,cform_err) IF(lwp) WRITE(numout,*) ' bad flag value for nn_eos = ', nn_eos nstop = nstop + 1 ! END SELECT ! IF(ln_ctl) CALL prt_ctl( tab2d_1=pab(:,:,jp_tem), clinfo1=' rab_2d_t: ', & & tab2d_2=pab(:,:,jp_sal), clinfo2=' rab_2d_s : ' ) ! IF( nn_timing == 1 ) CALL timing_stop('rab_2d') ! END SUBROUTINE rab_2d SUBROUTINE rab_0d( pts, pdep, pab ) !!---------------------------------------------------------------------- !! *** ROUTINE rab_0d *** !! !! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked) !! !! ** Action : - pab : thermal/haline expansion ratio at T-points !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpts) , INTENT(in ) :: pts ! pot. temperature & salinity REAL(wp), INTENT(in ) :: pdep ! depth [m] REAL(wp), DIMENSION(jpts) , INTENT( out) :: pab ! thermal/haline expansion ratio ! REAL(wp) :: zt , zh , zs ! local scalars REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - - !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('rab_2d') ! pab(:) = 0._wp ! SELECT CASE ( nn_eos ) ! CASE( -1, 0 ) !== polynomial TEOS-10 / EOS-80 ==! ! ! zh = pdep * r1_Z0 ! depth zt = pts (jp_tem) * r1_T0 ! temperature zs = SQRT( ABS( pts(jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity ! ! alpha zn3 = ALP003 ! zn2 = ALP012*zt + ALP102*zs+ALP002 ! zn1 = ((ALP031*zt & & + ALP121*zs+ALP021)*zt & & + (ALP211*zs+ALP111)*zs+ALP011)*zt & & + ((ALP301*zs+ALP201)*zs+ALP101)*zs+ALP001 ! zn0 = ((((ALP050*zt & & + ALP140*zs+ALP040)*zt & & + (ALP230*zs+ALP130)*zs+ALP030)*zt & & + ((ALP320*zs+ALP220)*zs+ALP120)*zs+ALP020)*zt & & + (((ALP410*zs+ALP310)*zs+ALP210)*zs+ALP110)*zs+ALP010)*zt & & + ((((ALP500*zs+ALP400)*zs+ALP300)*zs+ALP200)*zs+ALP100)*zs+ALP000 ! zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0 ! pab(jp_tem) = zn * r1_rau0 ! ! beta zn3 = BET003 ! zn2 = BET012*zt + BET102*zs+BET002 ! zn1 = ((BET031*zt & & + BET121*zs+BET021)*zt & & + (BET211*zs+BET111)*zs+BET011)*zt & & + ((BET301*zs+BET201)*zs+BET101)*zs+BET001 ! zn0 = ((((BET050*zt & & + BET140*zs+BET040)*zt & & + (BET230*zs+BET130)*zs+BET030)*zt & & + ((BET320*zs+BET220)*zs+BET120)*zs+BET020)*zt & & + (((BET410*zs+BET310)*zs+BET210)*zs+BET110)*zs+BET010)*zt & & + ((((BET500*zs+BET400)*zs+BET300)*zs+BET200)*zs+BET100)*zs+BET000 ! zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0 ! pab(jp_sal) = zn / zs * r1_rau0 ! ! ! CASE( 1 ) !== simplified EOS ==! ! zt = pts(jp_tem) - 10._wp ! pot. temperature anomaly (t-T0) zs = pts(jp_sal) - 35._wp ! abs. salinity anomaly (s-S0) zh = pdep ! depth at the partial step level ! zn = rn_a0 * ( 1._wp + rn_lambda1*zt + rn_mu1*zh ) + rn_nu*zs pab(jp_tem) = zn * r1_rau0 ! alpha ! zn = rn_b0 * ( 1._wp - rn_lambda2*zs - rn_mu2*zh ) - rn_nu*zt pab(jp_sal) = zn * r1_rau0 ! beta ! CASE DEFAULT IF(lwp) WRITE(numout,cform_err) IF(lwp) WRITE(numout,*) ' bad flag value for nn_eos = ', nn_eos nstop = nstop + 1 ! END SELECT ! IF( nn_timing == 1 ) CALL timing_stop('rab_2d') ! END SUBROUTINE rab_0d SUBROUTINE bn2( pts, pab, pn2 ) !!---------------------------------------------------------------------- !! *** ROUTINE bn2 *** !! !! ** Purpose : Compute the local Brunt-Vaisala frequency at the !! time-step of the input arguments !! !! ** Method : pn2 = grav * (alpha dk[T] + beta dk[S] ) / e3w !! where alpha and beta are given in pab, and computed on T-points. !! N.B. N^2 is set one for all to zero at jk=1 in istate module. !! !! ** Action : pn2 : square of the brunt-vaisala frequency at w-point !! !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature and salinity [Celcius,psu] REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pab ! thermal/haline expansion coef. [Celcius-1,psu-1] REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT( out) :: pn2 ! Brunt-Vaisala frequency squared [1/s^2] ! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zaw, zbw, zrw ! local scalars !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('bn2') ! DO jk = 2, jpkm1 ! interior points only (2=< jk =< jpkm1 ) DO jj = 1, jpj ! surface and bottom value set to zero one for all in istate.F90 DO ji = 1, jpi zrw = ( fsdepw(ji,jj,jk ) - fsdept(ji,jj,jk) ) & & / ( fsdept(ji,jj,jk-1) - fsdept(ji,jj,jk) ) ! zaw = pab(ji,jj,jk,jp_tem) * (1. - zrw) + pab(ji,jj,jk-1,jp_tem) * zrw zbw = pab(ji,jj,jk,jp_sal) * (1. - zrw) + pab(ji,jj,jk-1,jp_sal) * zrw ! pn2(ji,jj,jk) = grav * ( zaw * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) & & - zbw * ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) ) & & / fse3w(ji,jj,jk) * tmask(ji,jj,jk) END DO END DO END DO ! IF(ln_ctl) CALL prt_ctl( tab3d_1=pn2, clinfo1=' bn2 : ', ovlap=1, kdim=jpk ) ! IF( nn_timing == 1 ) CALL timing_stop('bn2') ! END SUBROUTINE bn2 FUNCTION eos_pt_from_ct( ctmp, psal ) RESULT( ptmp ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_pt_from_ct *** !! !! ** Purpose : Compute pot.temp. from cons. temp. [Celcius] !! !! ** Method : rational approximation (5/3th order) of TEOS-10 algorithm !! checkvalue: pt=20.02391895 Celsius for sa=35.7g/kg, ct=20degC !! !! Reference : TEOS-10, UNESCO !! Rational approximation to TEOS10 algorithm (rms error on WOA13 values: 4.0e-5 degC) !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ctmp ! Cons. Temp [Celcius] REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu] ! Leave result array automatic rather than making explicitly allocated REAL(wp), DIMENSION(jpi,jpj) :: ptmp ! potential temperature [Celcius] ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zt , zs , ztm ! local scalars REAL(wp) :: zn , zd ! local scalars REAL(wp) :: zdeltaS , z1_S0 , z1_T0 !!---------------------------------------------------------------------- ! IF ( nn_timing == 1 ) CALL timing_start('eos_pt_from_ct') ! zdeltaS = 5._wp z1_S0 = 0.875_wp/35.16504_wp z1_T0 = 1._wp/40._wp ! DO jj = 1, jpj DO ji = 1, jpi ! zt = ctmp (ji,jj) * z1_T0 zs = SQRT( ABS( psal(ji,jj) + zdeltaS ) * r1_S0 ) ztm = tmask(ji,jj,1) ! zn = ((((-2.1385727895e-01_wp*zt & & - 2.7674419971e-01_wp*zs+1.0728094330_wp)*zt & & + (2.6366564313_wp*zs+3.3546960647_wp)*zs-7.8012209473_wp)*zt & & + ((1.8835586562_wp*zs+7.3949191679_wp)*zs-3.3937395875_wp)*zs-5.6414948432_wp)*zt & & + (((3.5737370589_wp*zs-1.5512427389e+01_wp)*zs+2.4625741105e+01_wp)*zs & & +1.9912291000e+01_wp)*zs-3.2191146312e+01_wp)*zt & & + ((((5.7153204649e-01_wp*zs-3.0943149543_wp)*zs+9.3052495181_wp)*zs & & -9.4528934807_wp)*zs+3.1066408996_wp)*zs-4.3504021262e-01_wp ! zd = (2.0035003456_wp*zt & & -3.4570358592e-01_wp*zs+5.6471810638_wp)*zt & & + (1.5393993508_wp*zs-6.9394762624_wp)*zs+1.2750522650e+01_wp ! ptmp(ji,jj) = ( zt / z1_T0 + zn / zd ) * ztm ! END DO END DO ! IF( nn_timing == 1 ) CALL timing_stop('eos_pt_from_ct') ! END FUNCTION eos_pt_from_ct SUBROUTINE eos_fzp_2d( psal, ptf, pdep ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_fzp *** !! !! ** Purpose : Compute the freezing point temperature [Celcius] !! !! ** Method : UNESCO freezing point (ptf) in Celcius is given by !! ptf(t,z) = (-.0575+1.710523e-3*sqrt(abs(s))-2.154996e-4*s)*s - 7.53e-4*z !! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m !! !! 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), INTENT(in ), OPTIONAL :: pdep ! depth [m] REAL(wp), DIMENSION(jpi,jpj), INTENT(out ) :: ptf ! freezing temperature [Celcius] ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zt, zs ! local scalars !!---------------------------------------------------------------------- ! SELECT CASE ( nn_eos ) ! CASE ( -1, 1 ) !== CT,SA (TEOS-10 formulation) ==! ! DO jj = 1, jpj DO ji = 1, jpi zs= SQRT( ABS( psal(ji,jj) ) / 35.16504_wp ) ! square root salinity ptf(ji,jj) = ((((1.46873e-03_wp*zs-9.64972e-03_wp)*zs+2.28348e-02_wp)*zs & & - 3.12775e-02_wp)*zs+2.07679e-02_wp)*zs-5.87701e-02_wp END DO END DO ptf(:,:) = ptf(:,:) * psal(:,:) ! IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:) ! CASE ( 0 ) !== PT,SP (UNESCO formulation) ==! ! ptf(:,:) = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal(:,:) ) & & - 2.154996e-4_wp * psal(:,:) ) * psal(:,:) ! IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:) ! CASE DEFAULT IF(lwp) WRITE(numout,cform_err) IF(lwp) WRITE(numout,*) ' bad flag value for nn_eos = ', nn_eos nstop = nstop + 1 ! END SELECT ! END SUBROUTINE eos_fzp_2d SUBROUTINE eos_fzp_0d( psal, ptf, pdep ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_fzp *** !! !! ** Purpose : Compute the freezing point temperature [Celcius] !! !! ** Method : UNESCO freezing point (ptf) in Celcius is given by !! ptf(t,z) = (-.0575+1.710523e-3*sqrt(abs(s))-2.154996e-4*s)*s - 7.53e-4*z !! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m !! !! Reference : UNESCO tech. papers in the marine science no. 28. 1978 !!---------------------------------------------------------------------- REAL(wp), INTENT(in ) :: psal ! salinity [psu] REAL(wp), INTENT(in ), OPTIONAL :: pdep ! depth [m] REAL(wp), INTENT(out) :: ptf ! freezing temperature [Celcius] ! REAL(wp) :: zs ! local scalars !!---------------------------------------------------------------------- ! SELECT CASE ( nn_eos ) ! CASE ( -1, 1 ) !== CT,SA (TEOS-10 formulation) ==! ! zs = SQRT( ABS( psal ) / 35.16504_wp ) ! square root salinity ptf = ((((1.46873e-03_wp*zs-9.64972e-03_wp)*zs+2.28348e-02_wp)*zs & & - 3.12775e-02_wp)*zs+2.07679e-02_wp)*zs-5.87701e-02_wp ptf = ptf * psal ! IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep ! CASE ( 0 ) !== PT,SP (UNESCO formulation) ==! ! ptf = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal ) & & - 2.154996e-4_wp * psal ) * psal ! IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep ! CASE DEFAULT IF(lwp) WRITE(numout,cform_err) IF(lwp) WRITE(numout,*) ' bad flag value for nn_eos = ', nn_eos nstop = nstop + 1 ! END SELECT ! END SUBROUTINE eos_fzp_0d SUBROUTINE eos_pen( pts, pab_pe, ppen ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_pen *** !! !! ** Purpose : Calculates nonlinear anomalies of alpha_PE, beta_PE and PE at T-points !! !! ** Method : PE is defined analytically as the vertical !! primitive of EOS times -g integrated between 0 and z>0. !! pen is the nonlinear bsq-PE anomaly: pen = ( PE - rau0 gz ) / rau0 gz - rd !! = 1/z * /int_0^z rd dz - rd !! where rd is the density anomaly (see eos_rhd function) !! ab_pe are partial derivatives of PE anomaly with respect to T and S: !! ab_pe(1) = - 1/(rau0 gz) * dPE/dT + drd/dT = - d(pen)/dT !! ab_pe(2) = 1/(rau0 gz) * dPE/dS + drd/dS = d(pen)/dS !! !! ** Action : - pen : PE anomaly given at T-points !! : - pab_pe : given at T-points !! pab_pe(:,:,:,jp_tem) is alpha_pe !! pab_pe(:,:,:,jp_sal) is beta_pe !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature & salinity REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT( out) :: pab_pe ! alpha_pe and beta_pe REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT( out) :: ppen ! potential energy anomaly ! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zt , zh , zs , ztm ! local scalars REAL(wp) :: zn , zn0, zn1, zn2 ! - - !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('eos_pen') ! SELECT CASE ( nn_eos ) ! CASE( -1, 0 ) !== polynomial TEOS-10 / EOS-80 ==! ! DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi ! zh = fsdept(ji,jj,jk) * r1_Z0 ! depth zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity ztm = tmask(ji,jj,jk) ! tmask ! ! potential energy non-linear anomaly zn2 = (PEN012)*zt & & + PEN102*zs+PEN002 ! zn1 = ((PEN021)*zt & & + PEN111*zs+PEN011)*zt & & + (PEN201*zs+PEN101)*zs+PEN001 ! zn0 = ((((PEN040)*zt & & + PEN130*zs+PEN030)*zt & & + (PEN220*zs+PEN120)*zs+PEN020)*zt & & + ((PEN310*zs+PEN210)*zs+PEN110)*zs+PEN010)*zt & & + (((PEN400*zs+PEN300)*zs+PEN200)*zs+PEN100)*zs+PEN000 ! zn = ( zn2 * zh + zn1 ) * zh + zn0 ! ppen(ji,jj,jk) = zn * zh * r1_rau0 * ztm ! ! alphaPE non-linear anomaly zn2 = APE002 ! zn1 = (APE011)*zt & & + APE101*zs+APE001 ! zn0 = (((APE030)*zt & & + APE120*zs+APE020)*zt & & + (APE210*zs+APE110)*zs+APE010)*zt & & + ((APE300*zs+APE200)*zs+APE100)*zs+APE000 ! zn = ( zn2 * zh + zn1 ) * zh + zn0 ! pab_pe(ji,jj,jk,jp_tem) = zn * zh * r1_rau0 * ztm ! ! betaPE non-linear anomaly zn2 = BPE002 ! zn1 = (BPE011)*zt & & + BPE101*zs+BPE001 ! zn0 = (((BPE030)*zt & & + BPE120*zs+BPE020)*zt & & + (BPE210*zs+BPE110)*zs+BPE010)*zt & & + ((BPE300*zs+BPE200)*zs+BPE100)*zs+BPE000 ! zn = ( zn2 * zh + zn1 ) * zh + zn0 ! pab_pe(ji,jj,jk,jp_sal) = zn / zs * zh * r1_rau0 * ztm ! END DO END DO END DO ! CASE( 1 ) !== Vallis (2006) simplified EOS ==! ! DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zt = pts(ji,jj,jk,jp_tem) - 10._wp ! temperature anomaly (t-T0) zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0) zh = fsdept(ji,jj,jk) ! depth in meters at t-point ztm = tmask(ji,jj,jk) ! tmask zn = 0.5_wp * zh * r1_rau0 * ztm ! ! Potential Energy ppen(ji,jj,jk) = ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zn ! ! alphaPE pab_pe(ji,jj,jk,jp_tem) = - rn_a0 * rn_mu1 * zn pab_pe(ji,jj,jk,jp_sal) = rn_b0 * rn_mu2 * zn ! END DO END DO END DO ! CASE DEFAULT IF(lwp) WRITE(numout,cform_err) IF(lwp) WRITE(numout,*) ' bad flag value for nn_eos = ', nn_eos nstop = nstop + 1 ! END SELECT ! IF( nn_timing == 1 ) CALL timing_stop('eos_pen') ! END SUBROUTINE eos_pen SUBROUTINE eos_init !!---------------------------------------------------------------------- !! *** ROUTINE eos_init *** !! !! ** Purpose : initializations for the equation of state !! !! ** Method : Read the namelist nameos and control the parameters !!---------------------------------------------------------------------- INTEGER :: ios ! local integer !! NAMELIST/nameos/ nn_eos, ln_useCT, rn_a0, rn_b0, rn_lambda1, rn_mu1, & & rn_lambda2, rn_mu2, rn_nu !!---------------------------------------------------------------------- ! REWIND( numnam_ref ) ! Namelist nameos in reference namelist : equation of state READ ( numnam_ref, nameos, IOSTAT = ios, ERR = 901 ) 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nameos in reference namelist', lwp ) ! REWIND( numnam_cfg ) ! Namelist nameos in configuration namelist : equation of state READ ( numnam_cfg, nameos, IOSTAT = ios, ERR = 902 ) 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nameos in configuration namelist', lwp ) IF(lwm) WRITE( numond, nameos ) ! rau0 = 1026._wp !: volumic mass of reference [kg/m3] rcp = 3991.86795711963_wp !: heat capacity [J/K] ! IF(lwp) THEN ! Control print 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 nn_eos = ', nn_eos IF( ln_useCT ) THEN WRITE(numout,*) ' model uses Conservative Temperature' WRITE(numout,*) ' Important: model must be initialized with CT and SA fields' ELSE WRITE(numout,*) ' model does not use Conservative Temperature' ENDIF ENDIF ! ! Consistency check on ln_useCT and nn_eos IF ((nn_eos .EQ. -1) .AND. (.NOT. ln_useCT)) THEN CALL ctl_stop("ln_useCT should be set to True if using TEOS-10 (nn_eos=-1)") ELSE IF ((nn_eos .NE. -1) .AND. (ln_useCT)) THEN CALL ctl_stop("ln_useCT should be set to False if using TEOS-80 or simplified equation of state (nn_eos=0 or nn_eos=1)") ENDIF ! SELECT CASE( nn_eos ) ! check option ! CASE( -1 ) !== polynomial TEOS-10 ==! IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' use of TEOS-10 equation of state (cons. temp. and abs. salinity)' ! rdeltaS = 32._wp r1_S0 = 0.875_wp/35.16504_wp r1_T0 = 1._wp/40._wp r1_Z0 = 1.e-4_wp ! EOS000 = 8.0189615746e+02_wp EOS100 = 8.6672408165e+02_wp EOS200 = -1.7864682637e+03_wp EOS300 = 2.0375295546e+03_wp EOS400 = -1.2849161071e+03_wp EOS500 = 4.3227585684e+02_wp EOS600 = -6.0579916612e+01_wp EOS010 = 2.6010145068e+01_wp EOS110 = -6.5281885265e+01_wp EOS210 = 8.1770425108e+01_wp EOS310 = -5.6888046321e+01_wp EOS410 = 1.7681814114e+01_wp EOS510 = -1.9193502195_wp EOS020 = -3.7074170417e+01_wp EOS120 = 6.1548258127e+01_wp EOS220 = -6.0362551501e+01_wp EOS320 = 2.9130021253e+01_wp EOS420 = -5.4723692739_wp EOS030 = 2.1661789529e+01_wp EOS130 = -3.3449108469e+01_wp EOS230 = 1.9717078466e+01_wp EOS330 = -3.1742946532_wp EOS040 = -8.3627885467_wp EOS140 = 1.1311538584e+01_wp EOS240 = -5.3563304045_wp EOS050 = 5.4048723791e-01_wp EOS150 = 4.8169980163e-01_wp EOS060 = -1.9083568888e-01_wp EOS001 = 1.9681925209e+01_wp EOS101 = -4.2549998214e+01_wp EOS201 = 5.0774768218e+01_wp EOS301 = -3.0938076334e+01_wp EOS401 = 6.6051753097_wp EOS011 = -1.3336301113e+01_wp EOS111 = -4.4870114575_wp EOS211 = 5.0042598061_wp EOS311 = -6.5399043664e-01_wp EOS021 = 6.7080479603_wp EOS121 = 3.5063081279_wp EOS221 = -1.8795372996_wp EOS031 = -2.4649669534_wp EOS131 = -5.5077101279e-01_wp EOS041 = 5.5927935970e-01_wp EOS002 = 2.0660924175_wp EOS102 = -4.9527603989_wp EOS202 = 2.5019633244_wp EOS012 = 2.0564311499_wp EOS112 = -2.1311365518e-01_wp EOS022 = -1.2419983026_wp EOS003 = -2.3342758797e-02_wp EOS103 = -1.8507636718e-02_wp EOS013 = 3.7969820455e-01_wp ! ALP000 = -6.5025362670e-01_wp ALP100 = 1.6320471316_wp ALP200 = -2.0442606277_wp ALP300 = 1.4222011580_wp ALP400 = -4.4204535284e-01_wp ALP500 = 4.7983755487e-02_wp ALP010 = 1.8537085209_wp ALP110 = -3.0774129064_wp ALP210 = 3.0181275751_wp ALP310 = -1.4565010626_wp ALP410 = 2.7361846370e-01_wp ALP020 = -1.6246342147_wp ALP120 = 2.5086831352_wp ALP220 = -1.4787808849_wp ALP320 = 2.3807209899e-01_wp ALP030 = 8.3627885467e-01_wp ALP130 = -1.1311538584_wp ALP230 = 5.3563304045e-01_wp ALP040 = -6.7560904739e-02_wp ALP140 = -6.0212475204e-02_wp ALP050 = 2.8625353333e-02_wp ALP001 = 3.3340752782e-01_wp ALP101 = 1.1217528644e-01_wp ALP201 = -1.2510649515e-01_wp ALP301 = 1.6349760916e-02_wp ALP011 = -3.3540239802e-01_wp ALP111 = -1.7531540640e-01_wp ALP211 = 9.3976864981e-02_wp ALP021 = 1.8487252150e-01_wp ALP121 = 4.1307825959e-02_wp ALP031 = -5.5927935970e-02_wp ALP002 = -5.1410778748e-02_wp ALP102 = 5.3278413794e-03_wp ALP012 = 6.2099915132e-02_wp ALP003 = -9.4924551138e-03_wp ! BET000 = 1.0783203594e+01_wp BET100 = -4.4452095908e+01_wp BET200 = 7.6048755820e+01_wp BET300 = -6.3944280668e+01_wp BET400 = 2.6890441098e+01_wp BET500 = -4.5221697773_wp BET010 = -8.1219372432e-01_wp BET110 = 2.0346663041_wp BET210 = -2.1232895170_wp BET310 = 8.7994140485e-01_wp BET410 = -1.1939638360e-01_wp BET020 = 7.6574242289e-01_wp BET120 = -1.5019813020_wp BET220 = 1.0872489522_wp BET320 = -2.7233429080e-01_wp BET030 = -4.1615152308e-01_wp BET130 = 4.9061350869e-01_wp BET230 = -1.1847737788e-01_wp BET040 = 1.4073062708e-01_wp BET140 = -1.3327978879e-01_wp BET050 = 5.9929880134e-03_wp BET001 = -5.2937873009e-01_wp BET101 = 1.2634116779_wp BET201 = -1.1547328025_wp BET301 = 3.2870876279e-01_wp BET011 = -5.5824407214e-02_wp BET111 = 1.2451933313e-01_wp BET211 = -2.4409539932e-02_wp BET021 = 4.3623149752e-02_wp BET121 = -4.6767901790e-02_wp BET031 = -6.8523260060e-03_wp BET002 = -6.1618945251e-02_wp BET102 = 6.2255521644e-02_wp BET012 = -2.6514181169e-03_wp BET003 = -2.3025968587e-04_wp ! PEN000 = -9.8409626043_wp PEN100 = 2.1274999107e+01_wp PEN200 = -2.5387384109e+01_wp PEN300 = 1.5469038167e+01_wp PEN400 = -3.3025876549_wp PEN010 = 6.6681505563_wp PEN110 = 2.2435057288_wp PEN210 = -2.5021299030_wp PEN310 = 3.2699521832e-01_wp PEN020 = -3.3540239802_wp PEN120 = -1.7531540640_wp PEN220 = 9.3976864981e-01_wp PEN030 = 1.2324834767_wp PEN130 = 2.7538550639e-01_wp PEN040 = -2.7963967985e-01_wp PEN001 = -1.3773949450_wp PEN101 = 3.3018402659_wp PEN201 = -1.6679755496_wp PEN011 = -1.3709540999_wp PEN111 = 1.4207577012e-01_wp PEN021 = 8.2799886843e-01_wp PEN002 = 1.7507069098e-02_wp PEN102 = 1.3880727538e-02_wp PEN012 = -2.8477365341e-01_wp ! APE000 = -1.6670376391e-01_wp APE100 = -5.6087643219e-02_wp APE200 = 6.2553247576e-02_wp APE300 = -8.1748804580e-03_wp APE010 = 1.6770119901e-01_wp APE110 = 8.7657703198e-02_wp APE210 = -4.6988432490e-02_wp APE020 = -9.2436260751e-02_wp APE120 = -2.0653912979e-02_wp APE030 = 2.7963967985e-02_wp APE001 = 3.4273852498e-02_wp APE101 = -3.5518942529e-03_wp APE011 = -4.1399943421e-02_wp APE002 = 7.1193413354e-03_wp ! BPE000 = 2.6468936504e-01_wp BPE100 = -6.3170583896e-01_wp BPE200 = 5.7736640125e-01_wp BPE300 = -1.6435438140e-01_wp BPE010 = 2.7912203607e-02_wp BPE110 = -6.2259666565e-02_wp BPE210 = 1.2204769966e-02_wp BPE020 = -2.1811574876e-02_wp BPE120 = 2.3383950895e-02_wp BPE030 = 3.4261630030e-03_wp BPE001 = 4.1079296834e-02_wp BPE101 = -4.1503681096e-02_wp BPE011 = 1.7676120780e-03_wp BPE002 = 1.7269476440e-04_wp ! CASE( 0 ) !== polynomial EOS-80 formulation ==! ! IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' use of EOS-80 equation of state (pot. temp. and pract. salinity)' ! rdeltaS = 20._wp r1_S0 = 1._wp/40._wp r1_T0 = 1._wp/40._wp r1_Z0 = 1.e-4_wp ! EOS000 = 9.5356891948e+02_wp EOS100 = 1.7136499189e+02_wp EOS200 = -3.7501039454e+02_wp EOS300 = 5.1856810420e+02_wp EOS400 = -3.7264470465e+02_wp EOS500 = 1.4302533998e+02_wp EOS600 = -2.2856621162e+01_wp EOS010 = 1.0087518651e+01_wp EOS110 = -1.3647741861e+01_wp EOS210 = 8.8478359933_wp EOS310 = -7.2329388377_wp EOS410 = 1.4774410611_wp EOS510 = 2.0036720553e-01_wp EOS020 = -2.5579830599e+01_wp EOS120 = 2.4043512327e+01_wp EOS220 = -1.6807503990e+01_wp EOS320 = 8.3811577084_wp EOS420 = -1.9771060192_wp EOS030 = 1.6846451198e+01_wp EOS130 = -2.1482926901e+01_wp EOS230 = 1.0108954054e+01_wp EOS330 = -6.2675951440e-01_wp EOS040 = -8.0812310102_wp EOS140 = 1.0102374985e+01_wp EOS240 = -4.8340368631_wp EOS050 = 1.2079167803_wp EOS150 = 1.1515380987e-01_wp EOS060 = -2.4520288837e-01_wp EOS001 = 1.0748601068e+01_wp EOS101 = -1.7817043500e+01_wp EOS201 = 2.2181366768e+01_wp EOS301 = -1.6750916338e+01_wp EOS401 = 4.1202230403_wp EOS011 = -1.5852644587e+01_wp EOS111 = -7.6639383522e-01_wp EOS211 = 4.1144627302_wp EOS311 = -6.6955877448e-01_wp EOS021 = 9.9994861860_wp EOS121 = -1.9467067787e-01_wp EOS221 = -1.2177554330_wp EOS031 = -3.4866102017_wp EOS131 = 2.2229155620e-01_wp EOS041 = 5.9503008642e-01_wp EOS002 = 1.0375676547_wp EOS102 = -3.4249470629_wp EOS202 = 2.0542026429_wp EOS012 = 2.1836324814_wp EOS112 = -3.4453674320e-01_wp EOS022 = -1.2548163097_wp EOS003 = 1.8729078427e-02_wp EOS103 = -5.7238495240e-02_wp EOS013 = 3.8306136687e-01_wp ! ALP000 = -2.5218796628e-01_wp ALP100 = 3.4119354654e-01_wp ALP200 = -2.2119589983e-01_wp ALP300 = 1.8082347094e-01_wp ALP400 = -3.6936026529e-02_wp ALP500 = -5.0091801383e-03_wp ALP010 = 1.2789915300_wp ALP110 = -1.2021756164_wp ALP210 = 8.4037519952e-01_wp ALP310 = -4.1905788542e-01_wp ALP410 = 9.8855300959e-02_wp ALP020 = -1.2634838399_wp ALP120 = 1.6112195176_wp ALP220 = -7.5817155402e-01_wp ALP320 = 4.7006963580e-02_wp ALP030 = 8.0812310102e-01_wp ALP130 = -1.0102374985_wp ALP230 = 4.8340368631e-01_wp ALP040 = -1.5098959754e-01_wp ALP140 = -1.4394226233e-02_wp ALP050 = 3.6780433255e-02_wp ALP001 = 3.9631611467e-01_wp ALP101 = 1.9159845880e-02_wp ALP201 = -1.0286156825e-01_wp ALP301 = 1.6738969362e-02_wp ALP011 = -4.9997430930e-01_wp ALP111 = 9.7335338937e-03_wp ALP211 = 6.0887771651e-02_wp ALP021 = 2.6149576513e-01_wp ALP121 = -1.6671866715e-02_wp ALP031 = -5.9503008642e-02_wp ALP002 = -5.4590812035e-02_wp ALP102 = 8.6134185799e-03_wp ALP012 = 6.2740815484e-02_wp ALP003 = -9.5765341718e-03_wp ! BET000 = 2.1420623987_wp BET100 = -9.3752598635_wp BET200 = 1.9446303907e+01_wp BET300 = -1.8632235232e+01_wp BET400 = 8.9390837485_wp BET500 = -1.7142465871_wp BET010 = -1.7059677327e-01_wp BET110 = 2.2119589983e-01_wp BET210 = -2.7123520642e-01_wp BET310 = 7.3872053057e-02_wp BET410 = 1.2522950346e-02_wp BET020 = 3.0054390409e-01_wp BET120 = -4.2018759976e-01_wp BET220 = 3.1429341406e-01_wp BET320 = -9.8855300959e-02_wp BET030 = -2.6853658626e-01_wp BET130 = 2.5272385134e-01_wp BET230 = -2.3503481790e-02_wp BET040 = 1.2627968731e-01_wp BET140 = -1.2085092158e-01_wp BET050 = 1.4394226233e-03_wp BET001 = -2.2271304375e-01_wp BET101 = 5.5453416919e-01_wp BET201 = -6.2815936268e-01_wp BET301 = 2.0601115202e-01_wp BET011 = -9.5799229402e-03_wp BET111 = 1.0286156825e-01_wp BET211 = -2.5108454043e-02_wp BET021 = -2.4333834734e-03_wp BET121 = -3.0443885826e-02_wp BET031 = 2.7786444526e-03_wp BET002 = -4.2811838287e-02_wp BET102 = 5.1355066072e-02_wp BET012 = -4.3067092900e-03_wp BET003 = -7.1548119050e-04_wp ! PEN000 = -5.3743005340_wp PEN100 = 8.9085217499_wp PEN200 = -1.1090683384e+01_wp PEN300 = 8.3754581690_wp PEN400 = -2.0601115202_wp PEN010 = 7.9263222935_wp PEN110 = 3.8319691761e-01_wp PEN210 = -2.0572313651_wp PEN310 = 3.3477938724e-01_wp PEN020 = -4.9997430930_wp PEN120 = 9.7335338937e-02_wp PEN220 = 6.0887771651e-01_wp PEN030 = 1.7433051009_wp PEN130 = -1.1114577810e-01_wp PEN040 = -2.9751504321e-01_wp PEN001 = -6.9171176978e-01_wp PEN101 = 2.2832980419_wp PEN201 = -1.3694684286_wp PEN011 = -1.4557549876_wp PEN111 = 2.2969116213e-01_wp PEN021 = 8.3654420645e-01_wp PEN002 = -1.4046808820e-02_wp PEN102 = 4.2928871430e-02_wp PEN012 = -2.8729602515e-01_wp ! APE000 = -1.9815805734e-01_wp APE100 = -9.5799229402e-03_wp APE200 = 5.1430784127e-02_wp APE300 = -8.3694846809e-03_wp APE010 = 2.4998715465e-01_wp APE110 = -4.8667669469e-03_wp APE210 = -3.0443885826e-02_wp APE020 = -1.3074788257e-01_wp APE120 = 8.3359333577e-03_wp APE030 = 2.9751504321e-02_wp APE001 = 3.6393874690e-02_wp APE101 = -5.7422790533e-03_wp APE011 = -4.1827210323e-02_wp APE002 = 7.1824006288e-03_wp ! BPE000 = 1.1135652187e-01_wp BPE100 = -2.7726708459e-01_wp BPE200 = 3.1407968134e-01_wp BPE300 = -1.0300557601e-01_wp BPE010 = 4.7899614701e-03_wp BPE110 = -5.1430784127e-02_wp BPE210 = 1.2554227021e-02_wp BPE020 = 1.2166917367e-03_wp BPE120 = 1.5221942913e-02_wp BPE030 = -1.3893222263e-03_wp BPE001 = 2.8541225524e-02_wp BPE101 = -3.4236710714e-02_wp BPE011 = 2.8711395266e-03_wp BPE002 = 5.3661089288e-04_wp ! CASE( 1 ) !== Simplified EOS ==! IF(lwp) THEN WRITE(numout,*) WRITE(numout,*) ' use of simplified eos: rhd(dT=T-10,dS=S-35,Z) = ' WRITE(numout,*) ' [-a0*(1+lambda1/2*dT+mu1*Z)*dT + b0*(1+lambda2/2*dT+mu2*Z)*dS - nu*dT*dS]/rau0' WRITE(numout,*) WRITE(numout,*) ' thermal exp. coef. rn_a0 = ', rn_a0 WRITE(numout,*) ' saline cont. coef. rn_b0 = ', rn_b0 WRITE(numout,*) ' cabbeling coef. rn_lambda1 = ', rn_lambda1 WRITE(numout,*) ' cabbeling coef. rn_lambda2 = ', rn_lambda2 WRITE(numout,*) ' thermobar. coef. rn_mu1 = ', rn_mu1 WRITE(numout,*) ' thermobar. coef. rn_mu2 = ', rn_mu2 WRITE(numout,*) ' 2nd cabbel. coef. rn_nu = ', rn_nu WRITE(numout,*) ' Caution: rn_beta0=0 incompatible with ddm parameterization ' ENDIF ! CASE DEFAULT !== ERROR in nn_eos ==! WRITE(ctmp1,*) ' bad flag value for nn_eos = ', nn_eos CALL ctl_stop( ctmp1 ) ! END SELECT ! rau0_rcp = rau0 * rcp r1_rau0 = 1._wp / rau0 r1_rcp = 1._wp / rcp r1_rau0_rcp = 1._wp / rau0_rcp ! IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' volumic mass of reference rau0 = ', rau0 , ' kg/m^3' IF(lwp) WRITE(numout,*) ' 1. / rau0 r1_rau0 = ', r1_rau0, ' m^3/kg' IF(lwp) WRITE(numout,*) ' ocean specific heat rcp = ', rcp , ' J/Kelvin' IF(lwp) WRITE(numout,*) ' rau0 * rcp rau0_rcp = ', rau0_rcp IF(lwp) WRITE(numout,*) ' 1. / ( rau0 * rcp ) r1_rau0_rcp = ', r1_rau0_rcp ! END SUBROUTINE eos_init !!====================================================================== END MODULE eosbn2