MODULE dynhpg !!====================================================================== !! *** MODULE dynhpg *** !! Ocean dynamics: hydrostatic pressure gradient trend !!====================================================================== !! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code !! 5.0 ! 1991-11 (G. Madec) !! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates !! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg !! 8.5 ! 2002-07 (G. Madec) F90: Free form and module !! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code !! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options !! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot !! - ! 2005-11 (G. Madec) style & small optimisation !! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! dyn_hpg : update the momentum trend with the now horizontal !! gradient of the hydrostatic pressure !! dyn_hpg_init : 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) !! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial) !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE phycst ! physical constants USE trdmod ! ocean dynamics trends USE trdmod_oce ! ocean variables trends USE in_out_manager ! I/O manager USE prtctl ! Print control USE lbclnk ! lateral boundary condition USE lib_mpp ! MPP library IMPLICIT NONE PRIVATE PUBLIC dyn_hpg ! routine called by step module PUBLIC dyn_hpg_init ! routine called by opa module ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient LOGICAL , PUBLIC :: ln_hpg_zco = .TRUE. !: z-coordinate - full steps LOGICAL , PUBLIC :: ln_hpg_zps = .FALSE. !: z-coordinate - partial steps (interpolation) LOGICAL , PUBLIC :: ln_hpg_sco = .FALSE. !: s-coordinate (standard jacobian formulation) LOGICAL , PUBLIC :: ln_hpg_hel = .FALSE. !: s-coordinate (helsinki modification) LOGICAL , PUBLIC :: ln_hpg_wdj = .FALSE. !: s-coordinate (weighted density jacobian) LOGICAL , PUBLIC :: ln_hpg_djc = .FALSE. !: s-coordinate (Density Jacobian with Cubic polynomial) LOGICAL , PUBLIC :: ln_hpg_rot = .FALSE. !: s-coordinate (ROTated axes scheme) LOGICAL , PUBLIC :: ln_hpg_prj = .FALSE. !: s-coordinate (Pressure Jacobian scheme) REAL(wp), PUBLIC :: rn_gamma = 0._wp !: weighting coefficient LOGICAL , PUBLIC :: ln_dynhpg_imp = .FALSE. !: semi-implicite hpg flag INTEGER :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.3 , NEMO Consortium (2010) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/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) !!---------------------------------------------------------------------- USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released USE wrk_nemo, ONLY: ztrdu => wrk_3d_1 , ztrdv => wrk_3d_2 ! 3D workspace !! INTEGER, INTENT(in) :: kt ! ocean time-step index !!---------------------------------------------------------------------- ! IF( wrk_in_use(3, 1,2) ) THEN CALL ctl_stop('dyn_hpg: requested workspace arrays are unavailable') ; RETURN ENDIF ! 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) CASE ( 7 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian 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' ) ! IF( wrk_not_released(3, 1,2) ) CALL ctl_stop('dyn_hpg: failed to release workspace arrays') ! END SUBROUTINE dyn_hpg SUBROUTINE dyn_hpg_init !!---------------------------------------------------------------------- !! *** ROUTINE dyn_hpg_init *** !! !! ** Purpose : initializations for the hydrostatic pressure gradient !! computation and consistency control !! !! ** Action : Read the namelist namdyn_hpg and check the consistency !! with the type of vertical coordinate used (zco, zps, sco) !!---------------------------------------------------------------------- INTEGER :: ioptio = 0 ! temporary integer !! NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, ln_hpg_hel, & & ln_hpg_wdj, ln_hpg_djc, ln_hpg_rot, ln_hpg_prj, rn_gamma , ln_dynhpg_imp !!---------------------------------------------------------------------- ! REWIND( numnam ) ! Read Namelist namdyn_hpg READ ( numnam, namdyn_hpg ) ! IF(lwp) THEN ! Control print WRITE(numout,*) WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' WRITE(numout,*) '~~~~~~~~~~~~' WRITE(numout,*) ' Namelist namdyn_hpg : 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,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj WRITE(numout,*) ' weighting coeff. (wdj scheme) rn_gamma = ', rn_gamma WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp ENDIF ! IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj) ) & & CALL ctl_stop('dyn_hpg_init : variable volume key_vvl require:& & the standard jacobian formulation hpg_sco or & & the pressure jacobian formulation hpg_prj') ! ! ! 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 IF( ln_hpg_prj ) nhpg = 7 ! ! ! 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( ln_hpg_prj ) ioptio = ioptio + 1 IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) ! END SUBROUTINE dyn_hpg_init 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 , zhpj => sa ! (ta,sa) used 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 zcoef0 = - grav * 0.5_wp ! Local constant initialization ! 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 , zhpj => sa ! (ta,sa) used 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_wp ! Surface value (also valid in partial step case) 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= 1 ) THEN ! on i-direction (level 2 or more) ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj) ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend ENDIF IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj) va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend 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 , zhpj => sa ! (ta,sa) used 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_wp ! To use density and not density anomaly IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume ELSE ; znad = 0._wp ! 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._wp * 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._wp * 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 , zhpj => sa ! (ta,sa) used 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_wp ! 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 , zhpj => sa ! (ta,sa) used 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_wp zalph = 0.5_wp - rn_gamma ! weighting coefficients (alpha=0.5-rn_gamma zbeta = 0.5_wp + rn_gamma ! (beta =1-alpha=0.5+rn_gamma ! 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 , zhpj => sa ! (ta,sa) used as 3D workspace USE wrk_nemo, ONLY: drhox => wrk_3d_1 , dzx => wrk_3d_2 USE wrk_nemo, ONLY: drhou => wrk_3d_3 , dzu => wrk_3d_4 , rho_i => wrk_3d_5 USE wrk_nemo, ONLY: drhoy => wrk_3d_6 , dzy => wrk_3d_7 USE wrk_nemo, ONLY: drhov => wrk_3d_8 , dzv => wrk_3d_9 , rho_j => wrk_3d_10 USE wrk_nemo, ONLY: drhoz => wrk_3d_11 , dzz => wrk_3d_12 USE wrk_nemo, ONLY: drhow => wrk_3d_13 , dzw => wrk_3d_14 USE wrk_nemo, ONLY: rho_k => wrk_3d_15 !! 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 ! " " !!---------------------------------------------------------------------- IF( wrk_in_use(3, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) ) THEN CALL ctl_stop('dyn:hpg_djc: requested workspace arrays unavailable') ; RETURN ENDIF 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_wp z1_10 = 1._wp / 10._wp z1_12 = 1._wp / 12._wp !---------------------------------------------------------------------------------------- ! 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._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) IF( cffw > zep) THEN drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) ELSE drhow(ji,jj,jk) = 0._wp ENDIF dzw(ji,jj,jk) = 2._wp * 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._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) ELSE drhou(ji,jj,jk ) = 0._wp ENDIF IF( cffx > zep ) THEN dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) ELSE dzu(ji,jj,jk) = 0._wp ENDIF IF( cffv > zep ) THEN drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) ELSE drhov(ji,jj,jk) = 0._wp ENDIF IF( cffy > zep ) THEN dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) ELSE dzv(ji,jj,jk) = 0._wp ENDIF END DO END DO END DO !---------------------------------------------------------------------------------- ! apply boundary conditions at top and bottom using 5.36-5.37 !---------------------------------------------------------------------------------- drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * 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_wp * ( 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 , zhpj => sa ! (ta,sa) used as 3D workspace USE wrk_nemo, ONLY: zdistr => wrk_2d_1 , zsina => wrk_2d_2 , zcosa => wrk_2d_3 USE wrk_nemo, ONLY: zhpiorg => wrk_3d_1 , zhpirot => wrk_3d_2 USE wrk_nemo, ONLY: zhpitra => wrk_3d_3 , zhpine => wrk_3d_4 USE wrk_nemo, ONLY: zhpjorg => wrk_3d_5 , zhpjrot => wrk_3d_6 USE wrk_nemo, ONLY: zhpjtra => wrk_3d_7 , zhpjne => wrk_3d_8 !! 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 ! " " !!---------------------------------------------------------------------- IF( wrk_in_use(2, 1,2,3) .OR. & wrk_in_use(3, 1,2,3,4,5,6,7,8) ) THEN CALL ctl_stop('dyn:hpg_rot: requested workspace arrays unavailable') ; RETURN ENDIF 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_wp zforg = 0.95_wp zfrot = 1._wp - 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= ta ! (ta,sa) used as 3D workspace USE oce , ONLY: rhd_tmp => sa USE wrk_nemo, ONLY: zhpi => wrk_3d_3 USE wrk_nemo, ONLY: zu => wrk_3d_4 USE wrk_nemo, ONLY: zv => wrk_3d_5 USE wrk_nemo, ONLY: fsp => wrk_3d_6 USE wrk_nemo, ONLY: xsp => wrk_3d_7 USE wrk_nemo, ONLY: asp => wrk_3d_8 USE wrk_nemo, ONLY: bsp => wrk_3d_9 USE wrk_nemo, ONLY: csp => wrk_3d_10 USE wrk_nemo, ONLY: dsp => wrk_3d_11 !! !!---------------------------------------------------------------------- !! INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear INTEGER, INTENT(in) :: kt ! ocean time-step index !! INTEGER :: ji, jj, jk, jkk ! dummy loop indices REAL(wp) :: zcoef0, znad ! temporary scalars !! !! The local varialbes for the correction term INTEGER :: jk1, jis, jid, jjs, jjd REAL(wp) :: zuijk, zvijk, pwes, pwed, pnss, pnsd, deps REAL(wp) :: rhdt1 REAL(wp) :: dpdx1, dpdx2, dpdy1, dpdy2 INTEGER :: bhitwe, bhitns !!---------------------------------------------------------------------- IF( wrk_in_use(3, 3,4,5,6,7,8,9,10,11) ) THEN CALL ctl_stop('dyn:hpg_prj: requested workspace arrays unavailable') ; RETURN ENDIF IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' ENDIF !!---------------------------------------------------------------------- ! Local constant initialization zcoef0 = - grav znad = 0.0_wp IF(lk_vvl) znad = 1._wp ! Save fsde3w and rhd fsde3w_tmp(:,:,:) = fsde3w(:,:,:) rhd_tmp(:,:,:) = rhd(:,:,:) ! Clean 3-D work arraies zhpi(:,:,:) = 0. !how to add vector opt.? N.B., jpi&jpi rather than jpim1&jpjm1 are needed here ! Preparing vertical density profile for hybrid-sco coordinate DO jj = 1, jpj DO ji = 1, jpi jk = mbathy(ji,jj) IF(jk <= 0) THEN; rhd(ji,jj,:) = 0._wp ELSE IF(jk == 1) THEN; rhd(ji,jj, jk+1:jpk) = rhd(ji,jj,jk) ELSE IF(jk < jpkm1) THEN DO jkk = jk+1, jpk rhd(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1),& fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2)) END DO END IF END DO END DO DO jj = 1, jpj DO ji = 1, jpi fsde3w(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) fsde3w(ji,jj,1) = fsde3w(ji,jj,1) - sshn(ji,jj) * znad DO jk = 2, jpk fsde3w(ji,jj,jk) = fsde3w(ji,jj,jk-1) + fse3w(ji,jj,jk) END DO END DO END DO DO jk = 1, jpkm1 DO jj = 1, jpj DO ji = 1, jpi fsp(ji,jj,jk) = rhd(ji,jj,jk) xsp(ji,jj,jk) = fsde3w(ji,jj,jk) END DO END DO END DO ! ! Construct the vertical density profile with the ! !Constrained cubic spline interpolation CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type) ! Calculate the hydrostatic pressure at T(ji,jj,1) DO jj = 2, jpj DO ji = 2, jpi rhdt1 = rhd(ji,jj,1) - interp3(fsde3w(ji,jj,1),asp(ji,jj,1), & bsp(ji,jj,1),csp(ji,jj,1),dsp(ji,jj,1)) & * 0.5_wp * fsde3w(ji,jj,1) rhdt1 = max(rhdt1, 1000._wp - rau0) ! no lighter than fresh water ! ! assuming linear profile across the top half surface layer zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * rhdt1 END DO END DO ! Calculate the pressure at T(ji,jj,2:jpkm1) DO jk = 2, jpkm1 DO jj = 2, jpj DO ji = 2, jpi zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & integ2(fsde3w(ji,jj,jk-1),fsde3w(ji,jj,jk),& asp(ji,jj,jk-1),bsp(ji,jj,jk-1),& csp(ji,jj,jk-1),dsp(ji,jj,jk-1)) END DO END DO END DO ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) DO jj = 2, jpjm1 DO ji = 2, jpim1 zu(ji,jj,1) = - ( fse3u(ji,jj,1) - sshu_n(ji,jj) * znad) zv(ji,jj,1) = - ( fse3v(ji,jj,1) - sshv_n(ji,jj) * znad) END DO END DO DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = 2, jpim1 zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk) zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk) END DO END DO END DO DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = 2, jpim1 zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk) zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk) END DO END DO END DO DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = 2, jpim1 pwes = 0._wp; pwed = 0._wp pnss = 0._wp; pnsd = 0._wp zuijk = zu(ji,jj,jk) zvijk = zv(ji,jj,jk) !!!!! for u equation IF(jk <= mbku(ji,jj)) THEN IF(-fsde3w(ji+1,jj,mbku(ji,jj)) >= -fsde3w(ji,jj,mbku(ji,jj))) THEN jis = ji + 1; jid = ji ELSE jis = ji; jid = ji +1 ENDIF ! !integrate the pressure on the shallow side jk1 = jk bhitwe = 0 DO WHILE ( -fsde3w(jis,jj,jk1) > zuijk ) IF(jk1 == mbku(ji,jj)) THEN bhitwe = 1 EXIT ENDIF deps = min(fsde3w(jis,jj,jk1+1), -zuijk) pwes = pwes + & integ2(fsde3w(jis,jj,jk1),deps,& asp(jis,jj,jk1),bsp(jis,jj,jk1),& csp(jis,jj,jk1),dsp(jis,jj,jk1)) jk1 = jk1 + 1 END DO IF(bhitwe == 1) THEN zuijk = -fsde3w(jis,jj,jk1) ENDIF ! !integrate the pressure on the deep side jk1 = jk bhitwe = 0 DO WHILE ( -fsde3w(jid,jj,jk1) < zuijk ) IF(jk1 == 1) THEN bhitwe = 1 EXIT END IF deps = max(fsde3w(jid,jj,jk1-1), -zuijk) pwed = pwed + & integ2(deps,fsde3w(jid,jj,jk1),& asp(jid,jj,jk1-1),bsp(jid,jj,jk1-1),& csp(jid,jj,jk1-1),dsp(jid,jj,jk1-1)) jk1 = jk1 - 1 END DO IF(bhitwe == 1) THEN deps = fsde3w(jid,jj,1) + min(zuijk, sshn(jid,jj)*znad) rhdt1 = rhd(jid,jj,1) - interp3(fsde3w(jid,jj,1),asp(jid,jj,1), & bsp(jid,jj,1),csp(jid,jj,1),dsp(jid,jj,1)) * deps rhdt1 = max(rhdt1, 1000._wp - rau0) ! no lighter than fresh water pwed = pwed + 0.5_wp * (rhd(jid,jj,1) + rhdt1) * deps ENDIF dpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk)) IF(lk_vvl) THEN dpdx2 = zcoef0 / e1u(ji,jj) * & (REAL(jis-jid, wp) * (pwes + pwed) + (sshn(ji+1,jj)-sshn(ji,jj))) ELSE dpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (pwes + pwed) ENDIF ua(ji,jj,jk) = ua(ji,jj,jk) + (dpdx1 + dpdx2)*& & umask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji+1,jj,jk) ENDIF !!!!! for v equation IF(jk <= mbkv(ji,jj)) THEN IF(-fsde3w(ji,jj+1,mbkv(ji,jj)) >= -fsde3w(ji,jj,mbkv(ji,jj))) THEN jjs = jj + 1; jjd = jj ELSE jjs = jj ; jjd = jj + 1 ENDIF ! !integrate the pressure on the shallow side jk1 = jk bhitns = 0 DO WHILE ( -fsde3w(ji,jjs,jk1) > zvijk ) IF(jk1 == mbkv(ji,jj)) THEN bhitns = 1 EXIT ENDIF deps = min(fsde3w(ji,jjs,jk1+1), -zvijk) pnss = pnss + & integ2(fsde3w(ji,jjs,jk1),deps,& asp(ji,jjs,jk1),bsp(ji,jjs,jk1),& csp(ji,jjs,jk1),dsp(ji,jjs,jk1)) jk1 = jk1 + 1 END DO IF(bhitns == 1) THEN zvijk = -fsde3w(ji,jjs,jk1) ENDIF ! !integrate the pressure on the deep side jk1 = jk bhitns = 0 DO WHILE ( -fsde3w(ji,jjd,jk1) < zvijk ) IF(jk1 == 1) THEN bhitns = 1 EXIT END IF deps = max(fsde3w(ji,jjd,jk1-1), -zvijk) pnsd = pnsd + & integ2(deps,fsde3w(ji,jjd,jk1),& asp(ji,jjd,jk1-1),bsp(ji,jjd,jk1-1),& csp(ji,jjd,jk1-1),dsp(ji,jjd,jk1-1)) jk1 = jk1 - 1 END DO IF(bhitns == 1) THEN deps = fsde3w(ji,jjd,1) + min(zvijk, sshn(ji,jjd)*znad) rhdt1 = rhd(ji,jjd,1) - interp3(fsde3w(ji,jjd,1),asp(ji,jjd,1), & bsp(ji,jjd,1),csp(ji,jjd,1),dsp(ji,jjd,1)) * deps rhdt1 = max(rhdt1, 1000._wp - rau0) ! no lighter than fresh water pnsd = pnsd + 0.5_wp * (rhd(ji,jjd,1) + rhdt1) * deps ENDIF dpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk)) if(lk_vvl) then dpdy2 = zcoef0 / e2v(ji,jj) * & (REAL(jjs-jjd, wp) * (pnss + pnsd) + (sshn(ji,jj+1)-sshn(ji,jj))) else dpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (pnss + pnsd ) end if va(ji,jj,jk) = va(ji,jj,jk) + (dpdy1 + dpdy2)*& & vmask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji,jj+1,jk) ENDIF END DO END DO END DO ! Restore fsde3w and rhd fsde3w(:,:,:) = fsde3w_tmp(:,:,:) rhd(:,:,:) = rhd_tmp(:,:,:) ! IF( wrk_not_released(3, 3,4,5,6,7,8,9,10,11) ) & CALL ctl_stop('dyn:hpg_prj: failed to release workspace arrays') ! END SUBROUTINE hpg_prj SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type) !!---------------------------------------------------------------------- !! *** ROUTINE cspline *** !! !! ** Purpose : constrained cubic spline interpolation !! !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 !! Reference: K.W. Brodlie, A review of mehtods for curve and function !! drawing, 1980 !! !!---------------------------------------------------------------------- IMPLICIT NONE REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of ! the interpoated function INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline ! 2: Linear ! Local Variables INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: jpi, jpj, jpkm1 REAL(wp) :: df1, df2, ddf1, ddf2, tmp1, tmp2, dxtmp REAL(wp) :: dxtmp1, dxtmp2, alpha REAL(wp) :: df(size(fsp,3)) !!---------------------------------------------------------------------- jpi = size(fsp,1) jpj = size(fsp,2) jpkm1 = size(fsp,3) - 1 ! Clean output arrays asp = 0.0_wp bsp = 0.0_wp csp = 0.0_wp dsp = 0.0_wp Do ji = 1, jpi Do jj = 1, jpj If (polynomial_type == 1) Then !Constrained Cubic Spline Do jk = 2, jpkm1-1 dxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) dxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) df1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / dxtmp1 df2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / dxtmp2 alpha = ( dxtmp1 + 2._wp * dxtmp2 ) / ( dxtmp1 + dxtmp2 ) / 3._wp If(df1 * df2 <= 0._wp) Then df(jk) = 0._wp Else df(jk) = df1 * df2 / ( ( 1._wp - alpha ) * df1 + alpha * df2 ) End If End Do df(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - & & 0.5_wp * df(2) df(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - & & 0.5_wp * df(jpkm1 - 1) Do jk = 1, jpkm1 - 1 dxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) tmp1 = (df(jk+1) + 2._wp * df(jk)) / dxtmp tmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / dxtmp / dxtmp ddf1 = -2._wp * tmp1 + tmp2 tmp1 = (2._wp * df(jk+1) + df(jk)) / dxtmp ddf2 = 2._wp * tmp1 - tmp2 dsp(ji,jj,jk) = (ddf2 - ddf1) / 6._wp / dxtmp csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * ddf1 - xsp(ji,jj,jk)*ddf2 ) / 2._wp / dxtmp bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / dxtmp - & & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & & dsp(ji,jj,jk) * ( xsp(ji,jj,jk+1)**2 + & & xsp(ji,jj,jk+1) * xsp(ji,jj,jk) + & & xsp(ji,jj,jk)**2 ) asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) - & & csp(ji,jj,jk) * xsp(ji,jj,jk)**2 - & & dsp(ji,jj,jk) * xsp(ji,jj,jk)**3 End Do Else If (polynomial_type == 2) Then !Linear Do jk = 1, jpkm1-1 dxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) tmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) dsp(ji,jj,jk) = 0._wp csp(ji,jj,jk) = 0._wp bsp(ji,jj,jk) = tmp1 / dxtmp asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) End Do Else CALL ctl_stop( 'invalid polynomial type in cspline' ) End If End Do End Do End Subroutine cspline FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) !!---------------------------------------------------------------------- !! *** ROUTINE interp1 *** !! !! ** Purpose : 1-d linear interpolation !! !! ** Method : !! interpolation is straigt forward !! extrapolation is also permitted (no value limit) !! !! H.Liu, Jan 2009, POL !!---------------------------------------------------------------------- IMPLICIT NONE REAL(wp), INTENT(in) :: x, xl, xr, fl, fr REAL(wp) :: f ! result of the interpolation (extrapolation) REAL(wp) :: deltx !!---------------------------------------------------------------------- deltx = xr - xl IF(abs(deltx) <= 10._wp * EPSILON(x)) THEN f = 0.5_wp * (fl + fr) ELSE f = ( (x - xl ) * fr - ( x - xr ) * fl ) / deltx END IF END FUNCTION interp1 FUNCTION interp2(x, a, b, c, d) RESULT(f) !!---------------------------------------------------------------------- !! *** ROUTINE interp1 *** !! !! ** Purpose : 1-d constrained cubic spline interpolation !! !! ** Method : cubic spline interpolation !! !!---------------------------------------------------------------------- IMPLICIT NONE REAL(wp), INTENT(in) :: x, a, b, c, d REAL(wp) :: f ! value from the interpolation !!---------------------------------------------------------------------- f = a + x* ( b + x * ( c + d * x ) ) END FUNCTION interp2 FUNCTION interp3(x, a, b, c, d) RESULT(f) !!---------------------------------------------------------------------- !! *** ROUTINE interp1 *** !! !! ** Purpose : deriavtive of a cubic spline function !! !! ** Method : !! !!---------------------------------------------------------------------- IMPLICIT NONE REAL(wp), INTENT(in) :: x, a, b, c, d REAL(wp) :: f ! value from the interpolation !!---------------------------------------------------------------------- f = b + x * ( 2._wp * c + 3._wp * d * x) END FUNCTION interp3 FUNCTION integ2(xl, xr, a, b, c, d) RESULT(f) !!---------------------------------------------------------------------- !! *** ROUTINE interp1 *** !! !! ** Purpose : 1-d constrained cubic spline integration !! !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr !! !!---------------------------------------------------------------------- IMPLICIT NONE REAL(wp), INTENT(in) :: xl, xr, a, b, c, d REAL(wp) :: a1, a2,a3 REAL(wp) :: f ! integration result !!---------------------------------------------------------------------- a1 = 0.5_wp * b a2 = c / 3.0_wp a3 = 0.25_wp * d f = xr * ( a + xr * ( a1 + xr * ( a2 + a3 * xr ) ) ) - & & xl * ( a + xl * ( a1 + xl * ( a2 + a3 * xl ) ) ) END FUNCTION integ2 !!====================================================================== END MODULE dynhpg