MODULE dynhpg !!====================================================================== !! *** MODULE dynhpg *** !! Ocean dynamics: hydrostatic pressure gradient trend !!====================================================================== !! History : 1.0 ! 87-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code !! 5.0 ! 91-11 (G. Madec) !! 7.0 ! 96-01 (G. Madec) hpg_sco: Original code for s-coordinates !! 8.0 ! 97-05 (G. Madec) split dynber into dynkeg and dynhpg !! 8.5 ! 02-07 (G. Madec) F90: Free form and module !! 8.5 ! 02-08 (A. Bozec) hpg_zps: Original code !! 9.0 ! 05-10 (A. Beckmann, B.W. An) various s-coordinate options !! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot !! 9.0 ! 05-11 (G. Madec) style & small optimisation !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! dyn_hpg : update the momentum trend with the now horizontal !! gradient of the hydrostatic pressure !! hpg_ctl : initialisation and control of options !! hpg_zco : z-coordinate scheme !! hpg_zps : z-coordinate plus partial steps (interpolation) !! hpg_sco : s-coordinate (standard jacobian formulation) !! hpg_hel : s-coordinate (helsinki modification) !! hpg_wdj : s-coordinate (weighted density jacobian) !! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial) !! hpg_rot : s-coordinate (ROTated axes scheme) !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE phycst ! physical constants USE in_out_manager ! I/O manager USE trdmod ! ocean dynamics trends USE trdmod_oce ! ocean variables trends USE prtctl ! Print control USE lbclnk ! lateral boundary condition IMPLICIT NONE PRIVATE PUBLIC dyn_hpg ! routine called by step module !!* Namelist nam_dynhpg : Choice of horizontal pressure gradient computation LOGICAL :: ln_hpg_zco = .TRUE. ! z-coordinate - full steps LOGICAL :: ln_hpg_zps = .FALSE. ! z-coordinate - partial steps (interpolation) LOGICAL :: ln_hpg_sco = .FALSE. ! s-coordinate (standard jacobian formulation) LOGICAL :: ln_hpg_hel = .FALSE. ! s-coordinate (helsinki modification) LOGICAL :: ln_hpg_wdj = .FALSE. ! s-coordinate (weighted density jacobian) LOGICAL :: ln_hpg_djc = .FALSE. ! s-coordinate (Density Jacobian with Cubic polynomial) LOGICAL :: ln_hpg_rot = .FALSE. ! s-coordinate (ROTated axes scheme) REAL(wp) :: gamm = 0.e0 ! weighting coefficient INTEGER :: nhpg = 0 ! = 0 to 6, type of pressure gradient scheme used ! ! (deduced from ln_hpg_... flags) !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! OPA 9.0 , LOCEAN-IPSL (2005) !! $Header$ !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE dyn_hpg( kt ) !!--------------------------------------------------------------------- !! *** ROUTINE dyn_hpg *** !! !! ** Method : Call the hydrostatic pressure gradient routine !! using the scheme defined in the namelist !! !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend !! - Save the trend (l_trddyn=T) !!---------------------------------------------------------------------- INTEGER, INTENT(in) :: kt ! ocean time-step index !! REAL(wp), DIMENSION(jpi,jpj,jpk) :: ztrdu, ztrdv ! 3D temporary workspace !!---------------------------------------------------------------------- IF( kt == nit000 ) CALL hpg_ctl ! initialisation & control of options IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) ztrdu(:,:,:) = ua(:,:,:) ztrdv(:,:,:) = va(:,:,:) ENDIF SELECT CASE ( nhpg ) ! Hydrastatic pressure gradient computation CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) CASE ( 3 ) ; CALL hpg_hel ( kt ) ! s-coordinate (helsinki modification) CASE ( 4 ) ; CALL hpg_wdj ( kt ) ! s-coordinate (weighted density jacobian) CASE ( 5 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) CASE ( 6 ) ; CALL hpg_rot ( kt ) ! s-coordinate (ROTated axes scheme) END SELECT IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) CALL trd_mod( ztrdu, ztrdv, jpdyn_trd_hpg, 'DYN', kt ) ENDIF ! IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) ! END SUBROUTINE dyn_hpg SUBROUTINE hpg_ctl !!---------------------------------------------------------------------- !! *** ROUTINE hpg_ctl *** !! !! ** Purpose : initializations for the hydrostatic pressure gradient !! computation and consistency control !! !! ** Action : Read the namelist namdynhpg and check the consistency !! with the type of vertical coordinate used (zco, zps, sco) !!---------------------------------------------------------------------- INTEGER :: ioptio = 0 ! temporary integer NAMELIST/nam_dynhpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, ln_hpg_hel, & & ln_hpg_wdj, ln_hpg_djc, ln_hpg_rot, gamm !!---------------------------------------------------------------------- REWIND ( numnam ) ! Read Namelist nam_dynhpg : pressure gradient calculation options READ ( numnam, nam_dynhpg ) IF(lwp) THEN ! Control print WRITE(numout,*) WRITE(numout,*) 'dyn:hpg_ctl : hydrostatic pressure gradient control' WRITE(numout,*) '~~~~~~~~~~~' WRITE(numout,*) ' Namelist nam_dynhpg : choice of hpg scheme' WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco WRITE(numout,*) ' s-coord. (helsinki modification) ln_hpg_hel = ', ln_hpg_hel WRITE(numout,*) ' s-coord. (weighted density jacobian) ln_hpg_wdj = ', ln_hpg_wdj WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc WRITE(numout,*) ' s-coord. (ROTated axes scheme) ln_hpg_rot = ', ln_hpg_rot WRITE(numout,*) ' weighting coeff. (wdj scheme) gamm = ', gamm ENDIF IF( lk_vvl .AND. .NOT. ln_hpg_sco ) THEN CALL ctl_stop( 'hpg_ctl : variable volume key_vvl compatible only with the standard jacobian formulation hpg_sco') ENDIF ! ! Set nhpg from ln_hpg_... flags IF( ln_hpg_zco ) nhpg = 0 IF( ln_hpg_zps ) nhpg = 1 IF( ln_hpg_sco ) nhpg = 2 IF( ln_hpg_hel ) nhpg = 3 IF( ln_hpg_wdj ) nhpg = 4 IF( ln_hpg_djc ) nhpg = 5 IF( ln_hpg_rot ) nhpg = 6 ! ! Consitency check ioptio = 0 IF( ln_hpg_zco ) ioptio = ioptio + 1 IF( ln_hpg_zps ) ioptio = ioptio + 1 IF( ln_hpg_sco ) ioptio = ioptio + 1 IF( ln_hpg_hel ) ioptio = ioptio + 1 IF( ln_hpg_wdj ) ioptio = ioptio + 1 IF( ln_hpg_djc ) ioptio = ioptio + 1 IF( ln_hpg_rot ) ioptio = ioptio + 1 IF ( ioptio /= 1 ) CALL ctl_stop( ' NO or several hydrostatic pressure gradient options used' ) ! END SUBROUTINE hpg_ctl SUBROUTINE hpg_zco( kt ) !!--------------------------------------------------------------------- !! *** ROUTINE hpg_zco *** !! !! ** Method : z-coordinate case, levels are horizontal surfaces. !! The now hydrostatic pressure gradient at a given level, jk, !! is computed by taking the vertical integral of the in-situ !! density gradient along the model level from the suface to that !! level: zhpi = grav ..... !! zhpj = grav ..... !! add it to the general momentum trend (ua,va). !! ua = ua - 1/e1u * zhpi !! va = va - 1/e2v * zhpj !! !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend !!---------------------------------------------------------------------- USE oce, ONLY : zhpi => ta ! use ta as 3D workspace USE oce, ONLY : zhpj => sa ! use sa as 3D workspace !! INTEGER, INTENT(in) :: kt ! ocean time-step index !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zcoef0, zcoef1 ! temporary scalars !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' ENDIF ! Local constant initialization zcoef0 = - grav * 0.5 ! Surface value DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zcoef1 = zcoef0 * fse3w(ji,jj,1) ! hydrostatic pressure gradient zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj) zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) ! add to the general momentum trend ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) END DO END DO ! ! interior value (2= ta ! use ta as 3D workspace USE oce, ONLY : zhpj => sa ! use sa as 3D workspace !! INTEGER, INTENT(in) :: kt ! ocean time-step index !! INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: iku, ikv ! temporary integers REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' ENDIF ! Local constant initialization zcoef0 = - grav * 0.5 ! Surface value DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zcoef1 = zcoef0 * fse3w(ji,jj,1) ! hydrostatic pressure gradient zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj) zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) ! add to the general momentum trend ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) END DO END DO ! interior value (2= 2 ) THEN ! subtract old value ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! compute the new one zhpi (ji,jj,iku) = zhpi(ji,jj,iku-1) & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj) ! add the new one to the general momentum trend ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ENDIF ! on j-direction IF ( ikv > 2 ) THEN ! subtract old value va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! compute the new one zhpj (ji,jj,ikv) = zhpj(ji,jj,ikv-1) & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj) ! add the new one to the general momentum trend va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ENDIF # if ! defined key_vectopt_loop END DO # endif END DO ! END SUBROUTINE hpg_zps SUBROUTINE hpg_sco( kt ) !!--------------------------------------------------------------------- !! *** ROUTINE hpg_sco *** !! !! ** Method : s-coordinate case. Jacobian scheme. !! The now hydrostatic pressure gradient at a given level, jk, !! is computed by taking the vertical integral of the in-situ !! density gradient along the model level from the suface to that !! level. s-coordinates (ln_sco): a corrective term is added !! to the horizontal pressure gradient : !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] !! add it to the general momentum trend (ua,va). !! ua = ua - 1/e1u * zhpi !! va = va - 1/e2v * zhpj !! !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend !!---------------------------------------------------------------------- USE oce, ONLY : zhpi => ta ! use ta as 3D workspace USE oce, ONLY : zhpj => sa ! use sa as 3D workspace !! INTEGER, INTENT(in) :: kt ! ocean time-step index !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' ENDIF ! Local constant initialization zcoef0 = - grav * 0.5 ! To use density and not density anomaly IF ( lk_vvl ) THEN ; znad = 1. ! Variable volume ELSE ; znad = 0.e0 ! Fixed volume ENDIF ! Surface value DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! hydrostatic pressure gradient along s-surfaces zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) ! s-coordinate pressure gradient correction zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2*znad ) & & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2*znad ) & & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) ! add to the general momentum trend ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap END DO END DO ! interior value (2= ta ! use ta as 3D workspace USE oce, ONLY : zhpj => sa ! use sa as 3D workspace !! INTEGER, INTENT(in) :: kt ! ocean time-step index !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zcoef0, zuap, zvap ! temporary scalars !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn:hpg_hel : hydrostatic pressure gradient trend' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, helsinki modified scheme' ENDIF ! Local constant initialization zcoef0 = - grav * 0.5 ! Surface value DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! hydrostatic pressure gradient along s-surfaces zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj ,1) * rhd(ji+1,jj ,1) & & - fse3t(ji ,jj ,1) * rhd(ji ,jj ,1) ) zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3t(ji ,jj+1,1) * rhd(ji ,jj+1,1) & & - fse3t(ji ,jj ,1) * rhd(ji ,jj ,1) ) ! s-coordinate pressure gradient correction zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) & & * ( fsdept(ji+1,jj,1) - fsdept(ji,jj,1) ) / e1u(ji,jj) zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) & & * ( fsdept(ji,jj+1,1) - fsdept(ji,jj,1) ) / e2v(ji,jj) ! add to the general momentum trend ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap END DO END DO ! ! interior value (2= ta ! use ta as 3D workspace USE oce, ONLY : zhpj => sa ! use sa as 3D workspace !! INTEGER, INTENT(in) :: kt ! ocean time-step index !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zcoef0, zuap, zvap ! temporary scalars REAL(wp) :: zalph , zbeta ! " " !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn:hpg_wdj : hydrostatic pressure gradient trend' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ Weighted Density Jacobian' ENDIF ! Local constant initialization zcoef0 = - grav * 0.5 zalph = 0.5 - gamm ! weighting coefficients (alpha=0.5-gamm) zbeta = 0.5 + gamm ! (beta =1-alpha=0.5+gamm) ! Surface value (no ponderation) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! hydrostatic pressure gradient along s-surfaces zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * rhd(ji+1,jj ,1) & & - fse3w(ji ,jj ,1) * rhd(ji ,jj ,1) ) zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * rhd(ji ,jj+1,1) & & - fse3w(ji ,jj ,1) * rhd(ji, jj ,1) ) ! s-coordinate pressure gradient correction zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) & & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) & & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) ! add to the general momentum trend ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap END DO END DO ! Interior value (2= ta ! use ta as 3D workspace USE oce, ONLY : zhpj => sa ! use sa as 3D workspace !! INTEGER, INTENT(in) :: kt ! ocean time-step index !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zcoef0, zep, cffw ! temporary scalars REAL(wp) :: z1_10, cffu, cffx ! " " REAL(wp) :: z1_12, cffv, cffy ! " " REAL(wp), DIMENSION(jpi,jpj,jpk) :: drhox, dzx, drhou, dzu, rho_i ! 3D workspace REAL(wp), DIMENSION(jpi,jpj,jpk) :: drhoy, dzy, drhov, dzv, rho_j ! " " REAL(wp), DIMENSION(jpi,jpj,jpk) :: drhoz, dzz, drhow, dzw, rho_k ! " " !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' ENDIF ! Local constant initialization zcoef0 = - grav * 0.5 z1_10 = 1.0 / 10.0 z1_12 = 1.0 / 12.0 !---------------------------------------------------------------------------------------- ! compute and store in provisional arrays elementary vertical and horizontal differences !---------------------------------------------------------------------------------------- !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1) drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk ) drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk ) END DO END DO END DO !------------------------------------------------------------------------- ! compute harmonic averages using eq. 5.18 !------------------------------------------------------------------------- zep = 1.e-15 !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. cffw = 2.0 * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) cffu = 2.0 * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) cffx = 2.0 * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) cffv = 2.0 * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) cffy = 2.0 * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) IF( cffw > zep) THEN drhow(ji,jj,jk) = 2.0 * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) ELSE drhow(ji,jj,jk) = 0.e0 ENDIF dzw(ji,jj,jk) = 2.0 * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) IF( cffu > zep ) THEN drhou(ji,jj,jk) = 2.0 * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) ELSE drhou(ji,jj,jk ) = 0.e0 ENDIF IF( cffx > zep ) THEN dzu(ji,jj,jk) = 2.0*dzx(ji+1,jj,jk)*dzx(ji,jj,jk) & & /(dzx(ji+1,jj,jk)+dzx(ji,jj,jk)) ELSE dzu(ji,jj,jk) = 0.e0 ENDIF IF( cffv > zep ) THEN drhov(ji,jj,jk) = 2.0 * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) ELSE drhov(ji,jj,jk) = 0.e0 ENDIF IF( cffy > zep ) THEN dzv(ji,jj,jk) = 2.0 * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) ELSE dzv(ji,jj,jk) = 0.e0 ENDIF END DO END DO END DO !---------------------------------------------------------------------------------- ! apply boundary conditions at top and bottom using 5.36-5.37 !---------------------------------------------------------------------------------- drhow(:,:, 1 ) = 1.5 * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5 * drhow(:,:, 2 ) drhou(:,:, 1 ) = 1.5 * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5 * drhou(:,:, 2 ) drhov(:,:, 1 ) = 1.5 * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5 * drhov(:,:, 2 ) drhow(:,:,jpk) = 1.5 * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5 * drhow(:,:,jpkm1) drhou(:,:,jpk) = 1.5 * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5 * drhou(:,:,jpkm1) drhov(:,:,jpk) = 1.5 * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5 * drhov(:,:,jpkm1) !-------------------------------------------------------------- ! Upper half of top-most grid box, compute and store !------------------------------------------------------------- !!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified ! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) & & * ( rhd(ji,jj,1) & & + 0.5 * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) & & * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) & & / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) ) END DO END DO !!bug gm : here also, simplification is possible !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) & & - grav * z1_10 * ( & & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & & ) rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) & & - grav* z1_10 * ( & & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & & ) rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) & & - grav* z1_10 * ( & & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & & ) END DO END DO END DO CALL lbc_lnk(rho_k,'W',1.) CALL lbc_lnk(rho_i,'U',1.) CALL lbc_lnk(rho_j,'V',1.) ! --------------- ! Surface value ! --------------- DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj) zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj) ! add to the general momentum trend ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) END DO END DO ! ---------------- ! interior value (2= ta ! use ta as 3D workspace USE oce, ONLY : zhpj => sa ! use sa as 3D workspace !! INTEGER, INTENT(in) :: kt ! ocean time-step index !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zforg, zcoef0, zuap, zmskd1, zmskd1m ! temporary scalar REAL(wp) :: zfrot , zvap, zmskd2, zmskd2m ! " " REAL(wp), DIMENSION(jpi,jpj) :: zdistr, zsina, zcosa ! 2D workspace REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpiorg, zhpirot, zhpitra, zhpine ! 3D workspace REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpjorg, zhpjrot, zhpjtra, zhpjne ! " " !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn:hpg_rot : hydrostatic pressure gradient trend' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, rotated axes scheme used' ENDIF ! ------------------------------- ! Local constant initialization ! ------------------------------- zcoef0 = - grav * 0.5 zforg = 0.95e0 zfrot = 1.e0 - zforg ! inverse of the distance between 2 diagonal T-points (defined at F-point) (here zcoef0/distance) zdistr(:,:) = zcoef0 / SQRT( e1f(:,:)*e1f(:,:) + e2f(:,:)*e1f(:,:) ) ! sinus and cosinus of diagonal angle at F-point zsina(:,:) = ATAN2( e2f(:,:), e1f(:,:) ) zcosa(:,:) = COS( zsina(:,:) ) zsina(:,:) = SIN( zsina(:,:) ) ! --------------- ! Surface value ! --------------- ! compute and add to the general trend the pressure gradients along the axes DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! hydrostatic pressure gradient along s-surfaces zhpiorg(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3t(ji+1,jj,1) * rhd(ji+1,jj,1) & & - fse3t(ji ,jj,1) * rhd(ji ,jj,1) ) zhpjorg(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3t(ji,jj+1,1) * rhd(ji,jj+1,1) & & - fse3t(ji,jj ,1) * rhd(ji,jj ,1) ) ! s-coordinate pressure gradient correction zuap = -zcoef0 * ( rhd (ji+1,jj ,1) + rhd (ji,jj,1) ) & & * ( fsdept(ji+1,jj ,1) - fsdept(ji,jj,1) ) / e1u(ji,jj) zvap = -zcoef0 * ( rhd (ji ,jj+1,1) + rhd (ji,jj,1) ) & & * ( fsdept(ji ,jj+1,1) - fsdept(ji,jj,1) ) / e2v(ji,jj) ! add to the general momentum trend ua(ji,jj,1) = ua(ji,jj,1) + zforg * ( zhpiorg(ji,jj,1) + zuap ) va(ji,jj,1) = va(ji,jj,1) + zforg * ( zhpjorg(ji,jj,1) + zvap ) END DO END DO ! compute the pressure gradients in the diagonal directions DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zmskd1 = tmask(ji+1,jj+1,1) * tmask(ji ,jj,1) ! mask in the 1st diagnonal zmskd2 = tmask(ji ,jj+1,1) * tmask(ji+1,jj,1) ! mask in the 2nd diagnonal ! hydrostatic pressure gradient along s-surfaces zhpitra(ji,jj,1) = zdistr(ji,jj) * zmskd1 * ( fse3t(ji+1,jj+1,1) * rhd(ji+1,jj+1,1) & & - fse3t(ji ,jj ,1) * rhd(ji ,jj ,1) ) zhpjtra(ji,jj,1) = zdistr(ji,jj) * zmskd2 * ( fse3t(ji ,jj+1,1) * rhd(ji ,jj+1,1) & & - fse3t(ji+1,jj ,1) * rhd(ji+1,jj ,1) ) ! s-coordinate pressure gradient correction zuap = -zdistr(ji,jj) * zmskd1 * ( rhd (ji+1,jj+1,1) + rhd (ji ,jj,1) ) & & * ( fsdept(ji+1,jj+1,1) - fsdept(ji ,jj,1) ) zvap = -zdistr(ji,jj) * zmskd2 * ( rhd (ji ,jj+1,1) + rhd (ji+1,jj,1) ) & & * ( fsdept(ji ,jj+1,1) - fsdept(ji+1,jj,1) ) ! back rotation zhpine(ji,jj,1) = zcosa(ji,jj) * ( zhpitra(ji,jj,1) + zuap ) & & - zsina(ji,jj) * ( zhpjtra(ji,jj,1) + zvap ) zhpjne(ji,jj,1) = zsina(ji,jj) * ( zhpitra(ji,jj,1) + zuap ) & & + zcosa(ji,jj) * ( zhpjtra(ji,jj,1) + zvap ) END DO END DO ! interpolate and add to the general trend the diagonal gradient DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! averaging zhpirot(ji,jj,1) = 0.5 * ( zhpine(ji,jj,1) + zhpine(ji ,jj-1,1) ) zhpjrot(ji,jj,1) = 0.5 * ( zhpjne(ji,jj,1) + zhpjne(ji-1,jj ,1) ) ! add to the general momentum trend ua(ji,jj,1) = ua(ji,jj,1) + zfrot * zhpirot(ji,jj,1) va(ji,jj,1) = va(ji,jj,1) + zfrot * zhpjrot(ji,jj,1) END DO END DO ! ----------------- ! 2. interior value (2=