MODULE ldfslp !!====================================================================== !! *** MODULE ldfslp *** !! Ocean physics: slopes of neutral surfaces !!====================================================================== !! History : OPA ! 1994-12 (G. Madec, M. Imbard) Original code !! 8.0 ! 1997-06 (G. Madec) optimization, lbc !! 8.1 ! 1999-10 (A. Jouzeau) NEW profile in the mixed layer !! NEMO 1.0 ! 2002-10 (G. Madec) Free form, F90 !! - ! 2005-10 (A. Beckmann) correction for s-coordinates !! 3.3 ! 2010-10 (G. Nurser, C. Harris, G. Madec) add Griffies operator !! - ! 2010-11 (F. Dupond, G. Madec) bug correction in slopes just below the ML !!---------------------------------------------------------------------- #if defined key_ldfslp || defined key_esopa !!---------------------------------------------------------------------- !! 'key_ldfslp' Rotation of lateral mixing tensor !!---------------------------------------------------------------------- !! ldf_slp_grif : calculates the triads of isoneutral slopes (Griffies operator) !! ldf_slp : calculates the slopes of neutral surface (Madec operator) !! ldf_slp_mxl : calculates the slopes at the base of the mixed layer (Madec operator) !! ldf_slp_init : initialization of the slopes computation !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE ldftra_oce ! lateral diffusion: traceur USE ldfdyn_oce ! lateral diffusion: dynamics USE phycst ! physical constants USE zdfmxl ! mixed layer depth USE eosbn2 ! equation of states ! USE in_out_manager ! I/O manager USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE prtctl ! Print control USE wrk_nemo ! work arrays USE timing ! Timing USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) IMPLICIT NONE PRIVATE PUBLIC ldf_slp ! routine called by step.F90 PUBLIC ldf_slp_grif ! routine called by step.F90 PUBLIC ldf_slp_init ! routine called by opa.F90 LOGICAL , PUBLIC, PARAMETER :: lk_ldfslp = .TRUE. !: slopes flag ! !! Madec operator ! Arrays allocated in ldf_slp_init() routine once we know whether we're using the Griffies or Madec operator REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: uslp, wslpi !: i_slope at U- and W-points REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: vslp, wslpj !: j-slope at V- and W-points ! !! Griffies operator REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: wslp2 !: wslp**2 from Griffies quarter cells REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:,:) :: triadi_g, triadj_g !: skew flux slopes relative to geopotentials REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:,:) :: triadi , triadj !: isoneutral slopes relative to model-coordinate ! !! Madec operator ! Arrays allocated in ldf_slp_init() routine once we know whether we're using the Griffies or Madec operator REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: omlmask ! mask of the surface mixed layer at T-pt REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: uslpml, wslpiml ! i_slope at U- and W-points just below the mixed layer REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: vslpml, wslpjml ! j_slope at V- and W-points just below the mixed layer REAL(wp) :: repsln = 1.e-25_wp ! tiny value used as minium of di(rho), dj(rho) and dk(rho) !! * Substitutions # include "domzgr_substitute.h90" # include "ldftra_substitute.h90" # include "ldfeiv_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 4.0 , NEMO Consortium (2011) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE ldf_slp( kt, prd, pn2 ) !!---------------------------------------------------------------------- !! *** ROUTINE ldf_slp *** !! !! ** Purpose : Compute the slopes of neutral surface (slope of isopycnal !! surfaces referenced locally) (ln_traldf_iso=T). !! !! ** Method : The slope in the i-direction is computed at U- and !! W-points (uslp, wslpi) and the slope in the j-direction is !! computed at V- and W-points (vslp, wslpj). !! They are bounded by 1/100 over the whole ocean, and within the !! surface layer they are bounded by the distance to the surface !! ( slope<= depth/l where l is the length scale of horizontal !! diffusion (here, aht=2000m2/s ==> l=20km with a typical velocity !! of 10cm/s) !! A horizontal shapiro filter is applied to the slopes !! ln_sco=T, s-coordinate, add to the previously computed slopes !! the slope of the model level surface. !! macro-tasked on horizontal slab (jk-loop) (2, jpk-1) !! [slopes already set to zero at level 1, and to zero or the ocean !! bottom slope (ln_sco=T) at level jpk in inildf] !! !! ** Action : - uslp, wslpi, and vslp, wslpj, the i- and j-slopes !! of now neutral surfaces at u-, w- and v- w-points, resp. !!---------------------------------------------------------------------- INTEGER , INTENT(in) :: kt ! ocean time-step index REAL(wp), INTENT(in), DIMENSION(:,:,:) :: prd ! in situ density REAL(wp), INTENT(in), DIMENSION(:,:,:) :: pn2 ! Brunt-Vaisala frequency (locally ref.) !! INTEGER :: ji , jj , jk ! dummy loop indices INTEGER :: ii0, ii1, iku ! temporary integer INTEGER :: ij0, ij1, ikv ! temporary integer REAL(wp) :: zeps, zm1_g, zm1_2g, z1_16, zcofw ! local scalars REAL(wp) :: zci, zfi, zau, zbu, zai, zbi ! - - REAL(wp) :: zcj, zfj, zav, zbv, zaj, zbj ! - - REAL(wp) :: zck, zfk, zbw ! - - REAL(wp) :: zdepv, zdepu ! - - REAL(wp), POINTER, DIMENSION(:,:,:) :: zwz, zww REAL(wp), POINTER, DIMENSION(:,:,:) :: zdzr REAL(wp), POINTER, DIMENSION(:,:,:) :: zgru, zgrv REAL(wp), POINTER, DIMENSION(:,: ) :: zhmlpu, zhmlpv !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('ldf_slp') ! CALL wrk_alloc( jpi,jpj,jpk, zwz, zww, zdzr, zgru, zgrv ) CALL wrk_alloc( jpi,jpj, zhmlpu, zhmlpv ) IF ( ln_traldf_iso .OR. ln_dynldf_iso ) THEN zeps = 1.e-20_wp !== Local constant initialization ==! z1_16 = 1.0_wp / 16._wp zm1_g = -1.0_wp / grav zm1_2g = -0.5_wp / grav ! zww(:,:,:) = 0._wp zwz(:,:,:) = 0._wp ! DO jk = 1, jpk !== i- & j-gradient of density ==! DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zgru(ji,jj,jk) = umask(ji,jj,jk) * ( prd(ji+1,jj ,jk) - prd(ji,jj,jk) ) zgrv(ji,jj,jk) = vmask(ji,jj,jk) * ( prd(ji ,jj+1,jk) - prd(ji,jj,jk) ) END DO END DO END DO IF( ln_zps ) THEN ! partial steps correction at the bottom ocean level DO jj = 1, jpjm1 DO ji = 1, jpim1 zgru(ji,jj,mbku(ji,jj)) = gru(ji,jj) zgrv(ji,jj,mbkv(ji,jj)) = grv(ji,jj) END DO END DO ENDIF IF( ln_zps .AND. ln_isfcav ) THEN ! partial steps correction at the bottom ocean level DO jj = 1, jpjm1 DO ji = 1, jpim1 IF ( miku(ji,jj) > 1 ) zgru(ji,jj,miku(ji,jj)) = grui(ji,jj) IF ( mikv(ji,jj) > 1 ) zgrv(ji,jj,mikv(ji,jj)) = grvi(ji,jj) END DO END DO ENDIF ! !== Local vertical density gradient at T-point == ! (evaluated from N^2) ! interior value DO jk = 2, jpkm1 ! ! zdzr = d/dz(prd)= - ( prd ) / grav * mk(pn2) -- at t point ! ! trick: tmask(ik ) = 0 => all pn2 = 0 => zdzr = 0 ! ! else tmask(ik+1) = 0 => pn2(ik+1) = 0 => zdzr divides by 1 ! ! umask(ik+1) /= 0 => all pn2 /= 0 => zdzr divides by 2 ! ! NB: 1/(tmask+1) = (1-.5*tmask) substitute a / by a * ==> faster zdzr(:,:,jk) = zm1_g * ( prd(:,:,jk) + 1._wp ) & & * ( pn2(:,:,jk) + pn2(:,:,jk+1) ) * ( 1._wp - 0.5_wp * tmask(:,:,jk+1) ) END DO ! surface initialisation zdzr(:,:,1) = 0._wp IF ( ln_isfcav ) THEN ! if isf need to overwrite the interior value at at the first ocean point DO jj = 1, jpjm1 DO ji = 1, jpim1 zdzr(ji,jj,1:mikt(ji,jj)) = 0._wp END DO END DO END IF ! ! !== Slopes just below the mixed layer ==! CALL ldf_slp_mxl( prd, pn2, zgru, zgrv, zdzr ) ! output: uslpml, vslpml, wslpiml, wslpjml ! I. slopes at u and v point | uslp = d/di( prd ) / d/dz( prd ) ! =========================== | vslp = d/dj( prd ) / d/dz( prd ) ! IF ( ln_isfcav ) THEN DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. IF (miku(ji,jj) .GT. miku(ji+1,jj)) zhmlpu(ji,jj) = MAX(hmlpt(ji ,jj ), 5._wp) IF (miku(ji,jj) .LT. miku(ji+1,jj)) zhmlpu(ji,jj) = MAX(hmlpt(ji+1,jj ), 5._wp) IF (miku(ji,jj) .EQ. miku(ji+1,jj)) zhmlpu(ji,jj) = MAX(hmlpt(ji ,jj ), hmlpt(ji+1,jj ), 5._wp) IF (mikv(ji,jj) .GT. miku(ji,jj+1)) zhmlpv(ji,jj) = MAX(hmlpt(ji ,jj ), 5._wp) IF (mikv(ji,jj) .LT. miku(ji,jj+1)) zhmlpv(ji,jj) = MAX(hmlpt(ji ,jj+1), 5._wp) IF (mikv(ji,jj) .EQ. miku(ji,jj+1)) zhmlpv(ji,jj) = MAX(hmlpt(ji ,jj ), hmlpt(ji ,jj+1), 5._wp) ENDDO ENDDO ELSE DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zhmlpu(ji,jj) = MAX(hmlpt(ji,jj), hmlpt(ji+1,jj ), 5._wp) zhmlpv(ji,jj) = MAX(hmlpt(ji,jj), hmlpt(ji ,jj+1), 5._wp) ENDDO ENDDO END IF DO jk = 2, jpkm1 !* Slopes at u and v points DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! ! horizontal and vertical density gradient at u- and v-points zau = zgru(ji,jj,jk) / e1u(ji,jj) zav = zgrv(ji,jj,jk) / e2v(ji,jj) zbu = 0.5_wp * ( zdzr(ji,jj,jk) + zdzr(ji+1,jj ,jk) ) zbv = 0.5_wp * ( zdzr(ji,jj,jk) + zdzr(ji ,jj+1,jk) ) ! ! bound the slopes: abs(zw.)<= 1/100 and zb..<0 ! ! + kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) zbu = MIN( zbu, -100._wp* ABS( zau ) , -7.e+3_wp/fse3u(ji,jj,jk)* ABS( zau ) ) zbv = MIN( zbv, -100._wp* ABS( zav ) , -7.e+3_wp/fse3v(ji,jj,jk)* ABS( zav ) ) ! ! uslp and vslp output in zwz and zww, resp. zfi = MAX( omlmask(ji,jj,jk), omlmask(ji+1,jj ,jk) ) zfj = MAX( omlmask(ji,jj,jk), omlmask(ji ,jj+1,jk) ) ! thickness of water column between surface and level k at u/v point zdepu = 0.5_wp * ( ( fsdept(ji,jj,jk) + fsdept(ji+1,jj ,jk) ) & - 2 * MAX( risfdep(ji,jj), risfdep(ji+1,jj ) ) - fse3u(ji,jj,miku(ji,jj)) ) zdepv = 0.5_wp * ( ( fsdept(ji,jj,jk) + fsdept(ji ,jj+1,jk) ) & - 2 * MAX( risfdep(ji,jj), risfdep(ji ,jj+1) ) - fse3v(ji,jj,mikv(ji,jj)) ) ! zwz(ji,jj,jk) = ( 1. - zfi) * zau / ( zbu - zeps ) & & + zfi * uslpml(ji,jj) * zdepu / zhmlpu(ji,jj) zwz(ji,jj,jk) = zwz(ji,jj,jk) * wumask(ji,jj,jk) zww(ji,jj,jk) = ( 1. - zfj) * zav / ( zbv - zeps ) & & + zfj * vslpml(ji,jj) * zdepv / zhmlpv(ji,jj) zww(ji,jj,jk) = zww(ji,jj,jk) * wvmask(ji,jj,jk) !!gm modif to suppress omlmask.... (as in Griffies case) ! ! ! jk must be >= ML level for zf=1. otherwise zf=0. ! zfi = REAL( 1 - 1/(1 + jk / MAX( nmln(ji+1,jj), nmln(ji,jj) ) ), wp ) ! zfj = REAL( 1 - 1/(1 + jk / MAX( nmln(ji,jj+1), nmln(ji,jj) ) ), wp ) ! zci = 0.5 * ( fsdept(ji+1,jj,jk)+fsdept(ji,jj,jk) ) / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 10. ) ) ! zcj = 0.5 * ( fsdept(ji,jj+1,jk)+fsdept(ji,jj,jk) ) / MAX( hmlpt(ji,jj), hmlpt(ji,jj+1), 10. ) ) ! zwz(ji,jj,jk) = ( zfi * zai / ( zbi - zeps ) + ( 1._wp - zfi ) * wslpiml(ji,jj) * zci ) * tmask(ji,jj,jk) ! zww(ji,jj,jk) = ( zfj * zaj / ( zbj - zeps ) + ( 1._wp - zfj ) * wslpjml(ji,jj) * zcj ) * tmask(ji,jj,jk) !!gm end modif END DO END DO END DO CALL lbc_lnk( zwz, 'U', -1. ) ; CALL lbc_lnk( zww, 'V', -1. ) ! lateral boundary conditions ! ! !* horizontal Shapiro filter DO jk = 2, jpkm1 DO jj = 2, jpjm1, MAX(1, jpj-3) ! rows jj=2 and =jpjm1 only DO ji = 2, jpim1 uslp(ji,jj,jk) = z1_16 * ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & & + 4.* zwz(ji ,jj ,jk) ) vslp(ji,jj,jk) = z1_16 * ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & & + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) & & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & & + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) & & + 4.* zww(ji,jj ,jk) ) END DO END DO DO jj = 3, jpj-2 ! other rows DO ji = fs_2, fs_jpim1 ! vector opt. uslp(ji,jj,jk) = z1_16 * ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & & + 4.* zwz(ji ,jj ,jk) ) vslp(ji,jj,jk) = z1_16 * ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & & + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) & & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & & + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) & & + 4.* zww(ji,jj ,jk) ) END DO END DO ! !* decrease along coastal boundaries DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. uslp(ji,jj,jk) = uslp(ji,jj,jk) * ( umask(ji,jj+1,jk) + umask(ji,jj-1,jk ) ) * 0.5_wp & & * ( umask(ji,jj ,jk) + umask(ji,jj ,jk+1) ) * 0.5_wp & & * umask(ji,jj,jk-1) vslp(ji,jj,jk) = vslp(ji,jj,jk) * ( vmask(ji+1,jj,jk) + vmask(ji-1,jj,jk ) ) * 0.5_wp & & * ( vmask(ji ,jj,jk) + vmask(ji ,jj,jk+1) ) * 0.5_wp & & * vmask(ji,jj,jk-1) END DO END DO END DO ! II. slopes at w point | wslpi = mij( d/di( prd ) / d/dz( prd ) ! =========================== | wslpj = mij( d/dj( prd ) / d/dz( prd ) ! DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! !* Local vertical density gradient evaluated from N^2 zbw = zm1_2g * pn2 (ji,jj,jk) * ( prd (ji,jj,jk) + prd (ji,jj,jk-1) + 2. ) * wmask(ji,jj,jk) ! !* Slopes at w point ! ! i- & j-gradient of density at w-points zci = MAX( umask(ji-1,jj,jk ) + umask(ji,jj,jk ) & & + umask(ji-1,jj,jk-1) + umask(ji,jj,jk-1) , zeps ) * e1t(ji,jj) zcj = MAX( vmask(ji,jj-1,jk ) + vmask(ji,jj,jk-1) & & + vmask(ji,jj-1,jk-1) + vmask(ji,jj,jk ) , zeps ) * e2t(ji,jj) zai = ( zgru (ji-1,jj,jk ) + zgru (ji,jj,jk-1) & & + zgru (ji-1,jj,jk-1) + zgru (ji,jj,jk ) ) / zci zaj = ( zgrv (ji,jj-1,jk ) + zgrv (ji,jj,jk-1) & & + zgrv (ji,jj-1,jk-1) + zgrv (ji,jj,jk ) ) / zcj ! ! bound the slopes: abs(zw.)<= 1/100 and zb..<0. ! ! + kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) zbi = MIN( zbw ,- 100._wp* ABS( zai ) , -7.e+3_wp/fse3w(ji,jj,jk)* ABS( zai ) ) zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/fse3w(ji,jj,jk)* ABS( zaj ) ) ! ! wslpi and wslpj with ML flattening (output in zwz and zww, resp.) zfk = MAX( omlmask(ji,jj,jk), omlmask(ji,jj,jk-1) ) ! zfk=1 in the ML otherwise zfk=0 zck = ( fsdepw(ji,jj,jk) - fsdepw(ji,jj,mikt(ji,jj) ) ) / MAX( hmlp(ji,jj), 10._wp ) zwz(ji,jj,jk) = ( zai / ( zbi - zeps ) * ( 1._wp - zfk ) & & + zck * wslpiml(ji,jj) * zfk ) * wmask(ji,jj,jk) zww(ji,jj,jk) = ( zaj / ( zbj - zeps ) * ( 1._wp - zfk ) & & + zck * wslpjml(ji,jj) * zfk ) * wmask(ji,jj,jk) !!gm modif to suppress omlmask.... (as in Griffies operator) ! ! ! jk must be >= ML level for zfk=1. otherwise zfk=0. ! zfk = REAL( 1 - 1/(1 + jk / nmln(ji+1,jj)), wp ) ! zck = fsdepw(ji,jj,jk) / MAX( hmlp(ji,jj), 10. ) ! zwz(ji,jj,jk) = ( zfk * zai / ( zbi - zeps ) + ( 1._wp - zfk ) * wslpiml(ji,jj) * zck ) * tmask(ji,jj,jk) ! zww(ji,jj,jk) = ( zfk * zaj / ( zbj - zeps ) + ( 1._wp - zfk ) * wslpjml(ji,jj) * zck ) * tmask(ji,jj,jk) !!gm end modif END DO END DO END DO CALL lbc_lnk( zwz, 'T', -1. ) ; CALL lbc_lnk( zww, 'T', -1. ) ! lateral boundary conditions ! ! !* horizontal Shapiro filter DO jk = 2, jpkm1 DO jj = 2, jpjm1, MAX(1, jpj-3) ! rows jj=2 and =jpjm1 only DO ji = 2, jpim1 zcofw = tmask(ji,jj,jk) * z1_16 wslpi(ji,jj,jk) = ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & & + 4.* zwz(ji ,jj ,jk) ) * zcofw wslpj(ji,jj,jk) = ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & & + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) & & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & & + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) & & + 4.* zww(ji ,jj ,jk) ) * zcofw END DO END DO DO jj = 3, jpj-2 ! other rows DO ji = fs_2, fs_jpim1 ! vector opt. zcofw = tmask(ji,jj,jk) * z1_16 wslpi(ji,jj,jk) = ( zwz(ji-1,jj-1,jk) + zwz(ji+1,jj-1,jk) & & + zwz(ji-1,jj+1,jk) + zwz(ji+1,jj+1,jk) & & + 2.*( zwz(ji ,jj-1,jk) + zwz(ji-1,jj ,jk) & & + zwz(ji+1,jj ,jk) + zwz(ji ,jj+1,jk) ) & & + 4.* zwz(ji ,jj ,jk) ) * zcofw wslpj(ji,jj,jk) = ( zww(ji-1,jj-1,jk) + zww(ji+1,jj-1,jk) & & + zww(ji-1,jj+1,jk) + zww(ji+1,jj+1,jk) & & + 2.*( zww(ji ,jj-1,jk) + zww(ji-1,jj ,jk) & & + zww(ji+1,jj ,jk) + zww(ji ,jj+1,jk) ) & & + 4.* zww(ji ,jj ,jk) ) * zcofw END DO END DO ! !* decrease along coastal boundaries DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zck = ( umask(ji,jj,jk) + umask(ji-1,jj,jk) ) & & * ( vmask(ji,jj,jk) + vmask(ji,jj-1,jk) ) * 0.25 wslpi(ji,jj,jk) = wslpi(ji,jj,jk) * zck * wmask(ji,jj,jk) wslpj(ji,jj,jk) = wslpj(ji,jj,jk) * zck * wmask(ji,jj,jk) END DO END DO END DO ! III. Specific grid points ! =========================== ! IF( cp_cfg == "orca" .AND. jp_cfg == 4 ) THEN ! ORCA_R4 configuration: horizontal diffusion in specific area ! ! Gibraltar Strait ij0 = 50 ; ij1 = 53 ii0 = 69 ; ii1 = 71 ; uslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp ij0 = 51 ; ij1 = 53 ii0 = 68 ; ii1 = 71 ; vslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp ii0 = 69 ; ii1 = 71 ; wslpi( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp ii0 = 69 ; ii1 = 71 ; wslpj( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp ! ! ! Mediterrannean Sea ij0 = 49 ; ij1 = 56 ii0 = 71 ; ii1 = 90 ; uslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp ij0 = 50 ; ij1 = 56 ii0 = 70 ; ii1 = 90 ; vslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp ii0 = 71 ; ii1 = 90 ; wslpi( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp ii0 = 71 ; ii1 = 90 ; wslpj( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0._wp ENDIF ! IV. Lateral boundary conditions ! =============================== CALL lbc_lnk( uslp , 'U', -1. ) ; CALL lbc_lnk( vslp , 'V', -1. ) CALL lbc_lnk( wslpi, 'W', -1. ) ; CALL lbc_lnk( wslpj, 'W', -1. ) IF(ln_ctl) THEN CALL prt_ctl(tab3d_1=uslp , clinfo1=' slp - u : ', tab3d_2=vslp, clinfo2=' v : ', kdim=jpk) CALL prt_ctl(tab3d_1=wslpi, clinfo1=' slp - wi: ', tab3d_2=wslpj, clinfo2=' wj: ', kdim=jpk) ENDIF ! ELSEIF ( lk_vvl ) THEN IF(lwp) THEN WRITE(numout,*) ' Horizontal mixing in s-coordinate: slope = slope of s-surfaces' ENDIF ! geopotential diffusion in s-coordinates on tracers and/or momentum ! The slopes of s-surfaces are computed at each time step due to vvl ! The slopes for momentum diffusion are i- or j- averaged of those on tracers ! set the slope of diffusion to the slope of s-surfaces ! ( c a u t i o n : minus sign as fsdep has positive value ) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. uslp(ji,jj,1) = -1./e1u(ji,jj) * ( fsdept_b(ji+1,jj,1) - fsdept_b(ji ,jj ,1) ) * umask(ji,jj,1) vslp(ji,jj,1) = -1./e2v(ji,jj) * ( fsdept_b(ji,jj+1,1) - fsdept_b(ji ,jj ,1) ) * vmask(ji,jj,1) wslpi(ji,jj,1) = -1./e1t(ji,jj) * ( fsdepw_b(ji+1,jj,1) - fsdepw_b(ji-1,jj,1) ) * tmask(ji,jj,1) * 0.5 wslpj(ji,jj,1) = -1./e2t(ji,jj) * ( fsdepw_b(ji,jj+1,1) - fsdepw_b(ji,jj-1,1) ) * tmask(ji,jj,1) * 0.5 END DO END DO DO jk = 2, jpk DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. uslp(ji,jj,jk) = -1./e1u(ji,jj) * ( fsdept_b(ji+1,jj,jk) - fsdept_b(ji ,jj ,jk) ) * umask(ji,jj,jk) vslp(ji,jj,jk) = -1./e2v(ji,jj) * ( fsdept_b(ji,jj+1,jk) - fsdept_b(ji ,jj ,jk) ) * vmask(ji,jj,jk) wslpi(ji,jj,jk) = -1./e1t(ji,jj) * ( fsdepw_b(ji+1,jj,jk) - fsdepw_b(ji-1,jj,jk) ) & & * wmask(ji,jj,jk) * 0.5 wslpj(ji,jj,jk) = -1./e2t(ji,jj) * ( fsdepw_b(ji,jj+1,jk) - fsdepw_b(ji,jj-1,jk) ) & & * wmask(ji,jj,jk) * 0.5 END DO END DO END DO ! Lateral boundary conditions on the slopes CALL lbc_lnk( uslp , 'U', -1. ) ; CALL lbc_lnk( vslp , 'V', -1. ) CALL lbc_lnk( wslpi, 'W', -1. ) ; CALL lbc_lnk( wslpj, 'W', -1. ) if( kt == nit000 ) then IF(lwp) WRITE(numout,*) ' max slop: u',SQRT( MAXVAL(uslp*uslp)), ' v ', SQRT(MAXVAL(vslp)), & & ' wi', sqrt(MAXVAL(wslpi)), ' wj', sqrt(MAXVAL(wslpj)) endif IF(ln_ctl) THEN CALL prt_ctl(tab3d_1=uslp , clinfo1=' slp - u : ', tab3d_2=vslp, clinfo2=' v : ', kdim=jpk) CALL prt_ctl(tab3d_1=wslpi, clinfo1=' slp - wi: ', tab3d_2=wslpj, clinfo2=' wj: ', kdim=jpk) ENDIF ENDIF CALL wrk_dealloc( jpi,jpj,jpk, zwz, zww, zdzr, zgru, zgrv ) CALL wrk_dealloc( jpi,jpj, zhmlpu, zhmlpv) ! IF( nn_timing == 1 ) CALL timing_stop('ldf_slp') ! END SUBROUTINE ldf_slp SUBROUTINE ldf_slp_grif ( kt ) !!---------------------------------------------------------------------- !! *** ROUTINE ldf_slp_grif *** !! !! ** Purpose : Compute the squared slopes of neutral surfaces (slope !! of iso-pycnal surfaces referenced locally) (ln_traldf_grif=T) !! at W-points using the Griffies quarter-cells. !! !! ** Method : calculates alpha and beta at T-points !! !! ** Action : - triadi_g, triadj_g T-pts i- and j-slope triads relative to geopot. (used for eiv) !! - triadi , triadj T-pts i- and j-slope triads relative to model-coordinate !! - wslp2 squared slope of neutral surfaces at w-points. !!---------------------------------------------------------------------- INTEGER, INTENT( in ) :: kt ! ocean time-step index !! INTEGER :: ji, jj, jk, jl, ip, jp, kp ! dummy loop indices INTEGER :: iku, ikv ! local integer REAL(wp) :: zfacti, zfactj ! local scalars REAL(wp) :: znot_thru_surface ! local scalars REAL(wp) :: zdit, zdis, zdjt, zdjs, zdkt, zdks, zbu, zbv, zbti, zbtj REAL(wp) :: zdxrho_raw, zti_coord, zti_raw, zti_lim, zti_g_raw, zti_g_lim REAL(wp) :: zdyrho_raw, ztj_coord, ztj_raw, ztj_lim, ztj_g_raw, ztj_g_lim REAL(wp) :: zdzrho_raw REAL(wp), POINTER, DIMENSION(:,:) :: z1_mlbw REAL(wp), POINTER, DIMENSION(:,:,:,:) :: zdxrho , zdyrho, zdzrho ! Horizontal and vertical density gradients REAL(wp), POINTER, DIMENSION(:,:,:,:) :: zti_mlb, ztj_mlb ! for Griffies operator only !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('ldf_slp_grif') ! CALL wrk_alloc( jpi,jpj, z1_mlbw ) CALL wrk_alloc( jpi,jpj,jpk,2, zdxrho , zdyrho, zdzrho, klstart = 0 ) CALL wrk_alloc( jpi,jpj, 2,2, zti_mlb, ztj_mlb, kkstart = 0, klstart = 0 ) ! !--------------------------------! ! Some preliminary calculation ! !--------------------------------! ! DO jl = 0, 1 !== unmasked before density i- j-, k-gradients ==! ! ip = jl ; jp = jl ! guaranteed nonzero gradients ( absolute value larger than repsln) DO jk = 1, jpkm1 ! done each pair of triad DO jj = 1, jpjm1 ! NB: not masked ==> a minimum value is set DO ji = 1, fs_jpim1 ! vector opt. zdit = ( tsb(ji+1,jj,jk,jp_tem) - tsb(ji,jj,jk,jp_tem) ) ! i-gradient of T & S at u-point zdis = ( tsb(ji+1,jj,jk,jp_sal) - tsb(ji,jj,jk,jp_sal) ) zdjt = ( tsb(ji,jj+1,jk,jp_tem) - tsb(ji,jj,jk,jp_tem) ) ! j-gradient of T & S at v-point zdjs = ( tsb(ji,jj+1,jk,jp_sal) - tsb(ji,jj,jk,jp_sal) ) zdxrho_raw = ( - rab_b(ji+ip,jj ,jk,jp_tem) * zdit + rab_b(ji+ip,jj ,jk,jp_sal) * zdis ) / e1u(ji,jj) zdyrho_raw = ( - rab_b(ji ,jj+jp,jk,jp_tem) * zdjt + rab_b(ji ,jj+jp,jk,jp_sal) * zdjs ) / e2v(ji,jj) zdxrho(ji+ip,jj ,jk,1-ip) = SIGN( MAX( repsln, ABS( zdxrho_raw ) ), zdxrho_raw ) ! keep the sign zdyrho(ji ,jj+jp,jk,1-jp) = SIGN( MAX( repsln, ABS( zdyrho_raw ) ), zdyrho_raw ) END DO END DO END DO ! IF( ln_zps .AND. l_grad_zps ) THEN ! partial steps: correction of i- & j-grad on bottom DO jj = 1, jpjm1 DO ji = 1, jpim1 iku = mbku(ji,jj) ; ikv = mbkv(ji,jj) ! last ocean level (u- & v-points) zdit = gtsu(ji,jj,jp_tem) ; zdjt = gtsv(ji,jj,jp_tem) ! i- & j-gradient of Temperature zdis = gtsu(ji,jj,jp_sal) ; zdjs = gtsv(ji,jj,jp_sal) ! i- & j-gradient of Salinity zdxrho_raw = ( - rab_b(ji+ip,jj ,iku,jp_tem) * zdit + rab_b(ji+ip,jj ,iku,jp_sal) * zdis ) / e1u(ji,jj) zdyrho_raw = ( - rab_b(ji ,jj+jp,ikv,jp_tem) * zdjt + rab_b(ji ,jj+jp,ikv,jp_sal) * zdjs ) / e2v(ji,jj) zdxrho(ji+ip,jj ,iku,1-ip) = SIGN( MAX( repsln, ABS( zdxrho_raw ) ), zdxrho_raw ) ! keep the sign zdyrho(ji ,jj+jp,ikv,1-jp) = SIGN( MAX( repsln, ABS( zdyrho_raw ) ), zdyrho_raw ) END DO END DO ENDIF ! END DO DO kp = 0, 1 !== unmasked before density i- j-, k-gradients ==! DO jk = 1, jpkm1 ! done each pair of triad DO jj = 1, jpj ! NB: not masked ==> a minimum value is set DO ji = 1, jpi ! vector opt. IF( jk+kp > 1 ) THEN ! k-gradient of T & S a jk+kp zdkt = ( tsb(ji,jj,jk+kp-1,jp_tem) - tsb(ji,jj,jk+kp,jp_tem) ) zdks = ( tsb(ji,jj,jk+kp-1,jp_sal) - tsb(ji,jj,jk+kp,jp_sal) ) ELSE zdkt = 0._wp ! 1st level gradient set to zero zdks = 0._wp ENDIF zdzrho_raw = ( - rab_b(ji,jj,jk,jp_tem) * zdkt + rab_b(ji,jj,jk,jp_sal) * zdks ) / fse3w(ji,jj,jk+kp) zdzrho(ji,jj,jk,kp) = - MIN( - repsln, zdzrho_raw ) ! force zdzrho >= repsln END DO END DO END DO END DO ! DO jj = 1, jpj !== Reciprocal depth of the w-point below ML base ==! DO ji = 1, jpi jk = MIN( nmln(ji,jj), mbkt(ji,jj) ) + 1 ! MIN in case ML depth is the ocean depth z1_mlbw(ji,jj) = 1._wp / fsdepw(ji,jj,jk) END DO END DO ! ! !== intialisations to zero ==! ! wslp2 (:,:,:) = 0._wp ! wslp2 will be cumulated 3D field set to zero triadi_g(:,:,1,:,:) = 0._wp ; triadi_g(:,:,jpk,:,:) = 0._wp ! set surface and bottom slope to zero triadj_g(:,:,1,:,:) = 0._wp ; triadj_g(:,:,jpk,:,:) = 0._wp !!gm _iso set to zero missing triadi (:,:,1,:,:) = 0._wp ; triadj (:,:,jpk,:,:) = 0._wp ! set surface and bottom slope to zero triadj (:,:,1,:,:) = 0._wp ; triadj (:,:,jpk,:,:) = 0._wp !-------------------------------------! ! Triads just below the Mixed Layer ! !-------------------------------------! ! DO jl = 0, 1 ! calculate slope of the 4 triads immediately ONE level below mixed-layer base DO kp = 0, 1 ! with only the slope-max limit and MASKED DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ip = jl ; jp = jl ! jk = nmln(ji+ip,jj) + 1 IF( jk .GT. mbkt(ji+ip,jj) ) THEN !ML reaches bottom zti_mlb(ji+ip,jj ,1-ip,kp) = 0.0_wp ELSE ! Add s-coordinate slope at t-points (do this by *subtracting* gradient of depth) zti_g_raw = ( zdxrho(ji+ip,jj,jk-kp,1-ip) / zdzrho(ji+ip,jj,jk-kp,kp) & & - ( fsdept(ji+1,jj,jk-kp) - fsdept(ji,jj,jk-kp) ) / e1u(ji,jj) ) * umask(ji,jj,jk) zti_mlb(ji+ip,jj ,1-ip,kp) = SIGN( MIN( rn_slpmax, ABS( zti_g_raw ) ), zti_g_raw ) ENDIF ! jk = nmln(ji,jj+jp) + 1 IF( jk .GT. mbkt(ji,jj+jp) ) THEN !ML reaches bottom ztj_mlb(ji ,jj+jp,1-jp,kp) = 0.0_wp ELSE ztj_g_raw = ( zdyrho(ji,jj+jp,jk-kp,1-jp) / zdzrho(ji,jj+jp,jk-kp,kp) & & - ( fsdept(ji,jj+1,jk-kp) - fsdept(ji,jj,jk-kp) ) / e2v(ji,jj) ) * vmask(ji,jj,jk) ztj_mlb(ji ,jj+jp,1-jp,kp) = SIGN( MIN( rn_slpmax, ABS( ztj_g_raw ) ), ztj_g_raw ) ENDIF END DO END DO END DO END DO !-------------------------------------! ! Triads with surface limits ! !-------------------------------------! ! DO kp = 0, 1 ! k-index of triads DO jl = 0, 1 ip = jl ; jp = jl ! i- and j-indices of triads (i-k and j-k planes) DO jk = 1, jpkm1 ! Must mask contribution to slope from dz/dx at constant s for triads jk=1,kp=0 that poke up though ocean surface znot_thru_surface = REAL( 1-1/(jk+kp), wp ) !jk+kp=1,=0.; otherwise=1.0 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ! ! Calculate slope relative to geopotentials used for GM skew fluxes ! Add s-coordinate slope at t-points (do this by *subtracting* gradient of depth) ! Limit by slope *relative to geopotentials* by rn_slpmax, and mask by psi-point ! masked by umask taken at the level of dz(rho) ! ! raw slopes: unmasked unbounded slopes (relative to geopotential (zti_g) and model surface (zti) ! zti_raw = zdxrho(ji+ip,jj ,jk,1-ip) / zdzrho(ji+ip,jj ,jk,kp) ! unmasked ztj_raw = zdyrho(ji ,jj+jp,jk,1-jp) / zdzrho(ji ,jj+jp,jk,kp) ! Must mask contribution to slope for triad jk=1,kp=0 that poke up though ocean surface zti_coord = znot_thru_surface * ( fsdept(ji+1,jj ,jk) - fsdept(ji,jj,jk) ) / e1u(ji,jj) ztj_coord = znot_thru_surface * ( fsdept(ji ,jj+1,jk) - fsdept(ji,jj,jk) ) / e2v(ji,jj) ! unmasked zti_g_raw = zti_raw - zti_coord ! ref to geopot surfaces ztj_g_raw = ztj_raw - ztj_coord zti_g_lim = SIGN( MIN( rn_slpmax, ABS( zti_g_raw ) ), zti_g_raw ) ztj_g_lim = SIGN( MIN( rn_slpmax, ABS( ztj_g_raw ) ), ztj_g_raw ) ! ! Below ML use limited zti_g as is & mask ! Inside ML replace by linearly reducing sx_mlb towards surface & mask ! zfacti = REAL( 1 - 1/(1 + (jk+kp-1)/nmln(ji+ip,jj)), wp ) ! k index of uppermost point(s) of triad is jk+kp-1 zfactj = REAL( 1 - 1/(1 + (jk+kp-1)/nmln(ji,jj+jp)), wp ) ! must be .ge. nmln(ji,jj) for zfact=1 ! ! otherwise zfact=0 zti_g_lim = ( zfacti * zti_g_lim & & + ( 1._wp - zfacti ) * zti_mlb(ji+ip,jj,1-ip,kp) & & * fsdepw(ji+ip,jj,jk+kp) * z1_mlbw(ji+ip,jj) ) * umask(ji,jj,jk+kp) ztj_g_lim = ( zfactj * ztj_g_lim & & + ( 1._wp - zfactj ) * ztj_mlb(ji,jj+jp,1-jp,kp) & & * fsdepw(ji,jj+jp,jk+kp) * z1_mlbw(ji,jj+jp) ) * vmask(ji,jj,jk+kp) ! triadi_g(ji+ip,jj ,jk,1-ip,kp) = zti_g_lim triadj_g(ji ,jj+jp,jk,1-jp,kp) = ztj_g_lim ! ! Get coefficients of isoneutral diffusion tensor ! 1. Utilise gradients *relative* to s-coordinate, so add t-point slopes (*subtract* depth gradients) ! 2. We require that isoneutral diffusion gives no vertical buoyancy flux ! i.e. 33 term = (real slope* 31, 13 terms) ! To do this, retain limited sx**2 in vertical flux, but divide by real slope for 13/31 terms ! Equivalent to tapering A_iso = sx_limited**2/(real slope)**2 ! zti_lim = ( zti_g_lim + zti_coord ) * umask(ji,jj,jk+kp) ! remove coordinate slope => relative to coordinate surfaces ztj_lim = ( ztj_g_lim + ztj_coord ) * vmask(ji,jj,jk+kp) ! IF( ln_triad_iso ) THEN zti_raw = zti_lim**2 / zti_raw ztj_raw = ztj_lim**2 / ztj_raw zti_raw = SIGN( MIN( ABS(zti_lim), ABS( zti_raw ) ), zti_raw ) ztj_raw = SIGN( MIN( ABS(ztj_lim), ABS( ztj_raw ) ), ztj_raw ) zti_lim = zfacti * zti_lim & & + ( 1._wp - zfacti ) * zti_raw ztj_lim = zfactj * ztj_lim & & + ( 1._wp - zfactj ) * ztj_raw ENDIF triadi(ji+ip,jj ,jk,1-ip,kp) = zti_lim triadj(ji ,jj+jp,jk,1-jp,kp) = ztj_lim ! zbu = e1u(ji ,jj) * e2u(ji ,jj) * fse3u(ji ,jj,jk ) zbv = e1v(ji ,jj) * e2v(ji ,jj) * fse3v(ji ,jj,jk ) zbti = e1t(ji+ip,jj) * e2t(ji+ip,jj) * fse3w(ji+ip,jj,jk+kp) zbtj = e1t(ji,jj+jp) * e2t(ji,jj+jp) * fse3w(ji,jj+jp,jk+kp) ! !!gm this may inhibit vectorization on Vect Computers, and even on scalar computers.... ==> to be checked wslp2 (ji+ip,jj,jk+kp) = wslp2(ji+ip,jj,jk+kp) + 0.25_wp * zbu / zbti * zti_g_lim**2 ! masked wslp2 (ji,jj+jp,jk+kp) = wslp2(ji,jj+jp,jk+kp) + 0.25_wp * zbv / zbtj * ztj_g_lim**2 END DO END DO END DO END DO END DO ! wslp2(:,:,1) = 0._wp ! force the surface wslp to zero CALL lbc_lnk( wslp2, 'W', 1. ) ! lateral boundary confition on wslp2 only ==>>> gm : necessary ? to be checked ! CALL wrk_dealloc( jpi,jpj, z1_mlbw ) CALL wrk_dealloc( jpi,jpj,jpk,2, zdxrho , zdyrho, zdzrho, klstart = 0 ) CALL wrk_dealloc( jpi,jpj, 2,2, zti_mlb, ztj_mlb, kkstart = 0, klstart = 0 ) ! IF( nn_timing == 1 ) CALL timing_stop('ldf_slp_grif') ! END SUBROUTINE ldf_slp_grif SUBROUTINE ldf_slp_mxl( prd, pn2, p_gru, p_grv, p_dzr ) !!---------------------------------------------------------------------- !! *** ROUTINE ldf_slp_mxl *** !! !! ** Purpose : Compute the slopes of iso-neutral surface just below !! the mixed layer. !! !! ** Method : The slope in the i-direction is computed at u- & w-points !! (uslpml, wslpiml) and the slope in the j-direction is computed !! at v- and w-points (vslpml, wslpjml) with the same bounds as !! in ldf_slp. !! !! ** Action : uslpml, wslpiml : i- & j-slopes of neutral surfaces !! vslpml, wslpjml just below the mixed layer !! omlmask : mixed layer mask !!---------------------------------------------------------------------- REAL(wp), DIMENSION(:,:,:), INTENT(in) :: prd ! in situ density REAL(wp), DIMENSION(:,:,:), INTENT(in) :: pn2 ! Brunt-Vaisala frequency (locally ref.) REAL(wp), DIMENSION(:,:,:), INTENT(in) :: p_gru, p_grv ! i- & j-gradient of density (u- & v-pts) REAL(wp), DIMENSION(:,:,:), INTENT(in) :: p_dzr ! z-gradient of density (T-point) !! INTEGER :: ji , jj , jk ! dummy loop indices INTEGER :: iku, ikv, ik, ikm1 ! local integers REAL(wp) :: zeps, zm1_g, zm1_2g ! local scalars REAL(wp) :: zci, zfi, zau, zbu, zai, zbi ! - - REAL(wp) :: zcj, zfj, zav, zbv, zaj, zbj ! - - REAL(wp) :: zck, zfk, zbw ! - - !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('ldf_slp_mxl') ! zeps = 1.e-20_wp !== Local constant initialization ==! zm1_g = -1.0_wp / grav zm1_2g = -0.5_wp / grav ! uslpml (1,:) = 0._wp ; uslpml (jpi,:) = 0._wp vslpml (1,:) = 0._wp ; vslpml (jpi,:) = 0._wp wslpiml(1,:) = 0._wp ; wslpiml(jpi,:) = 0._wp wslpjml(1,:) = 0._wp ; wslpjml(jpi,:) = 0._wp ! ! !== surface mixed layer mask ! DO jk = 1, jpk ! =1 inside the mixed layer, =0 otherwise DO jj = 1, jpj DO ji = 1, jpi ik = nmln(ji,jj) - 1 IF( jk <= ik .AND. jk >= mikt(ji,jj) ) THEN omlmask(ji,jj,jk) = 1._wp ELSE omlmask(ji,jj,jk) = 0._wp ENDIF END DO END DO END DO ! Slopes of isopycnal surfaces just before bottom of mixed layer ! -------------------------------------------------------------- ! The slope are computed as in the 3D case. ! A key point here is the definition of the mixed layer at u- and v-points. ! It is assumed to be the maximum of the two neighbouring T-point mixed layer depth. ! Otherwise, a n2 value inside the mixed layer can be involved in the computation ! of the slope, resulting in a too steep diagnosed slope and thus a spurious eddy ! induce velocity field near the base of the mixed layer. !----------------------------------------------------------------------- ! DO jj = 2, jpjm1 DO ji = 2, jpim1 ! !== Slope at u- & v-points just below the Mixed Layer ==! ! ! !- vertical density gradient for u- and v-slopes (from dzr at T-point) iku = MIN( MAX( miku(ji,jj)+1, nmln(ji,jj) , nmln(ji+1,jj) ) , jpkm1 ) ! ML (MAX of T-pts, bound by jpkm1) ikv = MIN( MAX( mikv(ji,jj)+1, nmln(ji,jj) , nmln(ji,jj+1) ) , jpkm1 ) ! zbu = 0.5_wp * ( p_dzr(ji,jj,iku) + p_dzr(ji+1,jj ,iku) ) zbv = 0.5_wp * ( p_dzr(ji,jj,ikv) + p_dzr(ji ,jj+1,ikv) ) ! !- horizontal density gradient at u- & v-points zau = p_gru(ji,jj,iku) / e1u(ji,jj) zav = p_grv(ji,jj,ikv) / e2v(ji,jj) ! !- bound the slopes: abs(zw.)<= 1/100 and zb..<0 ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) zbu = MIN( zbu , -100._wp* ABS( zau ) , -7.e+3_wp/fse3u(ji,jj,iku)* ABS( zau ) ) zbv = MIN( zbv , -100._wp* ABS( zav ) , -7.e+3_wp/fse3v(ji,jj,ikv)* ABS( zav ) ) ! !- Slope at u- & v-points (uslpml, vslpml) uslpml(ji,jj) = zau / ( zbu - zeps ) * umask(ji,jj,iku) vslpml(ji,jj) = zav / ( zbv - zeps ) * vmask(ji,jj,ikv) ! ! !== i- & j-slopes at w-points just below the Mixed Layer ==! ! ik = MIN( nmln(ji,jj) + 1, jpk ) ikm1 = MAX( 1, ik-1 ) ! !- vertical density gradient for w-slope (from N^2) zbw = zm1_2g * pn2 (ji,jj,ik) * ( prd (ji,jj,ik) + prd (ji,jj,ikm1) + 2. ) ! !- horizontal density i- & j-gradient at w-points zci = MAX( umask(ji-1,jj,ik ) + umask(ji,jj,ik ) & & + umask(ji-1,jj,ikm1) + umask(ji,jj,ikm1) , zeps ) * e1t(ji,jj) zcj = MAX( vmask(ji,jj-1,ik ) + vmask(ji,jj,ik ) & & + vmask(ji,jj-1,ikm1) + vmask(ji,jj,ikm1) , zeps ) * e2t(ji,jj) zai = ( p_gru(ji-1,jj,ik ) + p_gru(ji,jj,ik) & & + p_gru(ji-1,jj,ikm1) + p_gru(ji,jj,ikm1 ) ) / zci * tmask(ji,jj,ik) zaj = ( p_grv(ji,jj-1,ik ) + p_grv(ji,jj,ik ) & & + p_grv(ji,jj-1,ikm1) + p_grv(ji,jj,ikm1) ) / zcj * tmask(ji,jj,ik) ! !- bound the slopes: abs(zw.)<= 1/100 and zb..<0. ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) zbi = MIN( zbw , -100._wp* ABS( zai ) , -7.e+3_wp/fse3w(ji,jj,ik)* ABS( zai ) ) zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/fse3w(ji,jj,ik)* ABS( zaj ) ) ! !- i- & j-slope at w-points (wslpiml, wslpjml) wslpiml(ji,jj) = zai / ( zbi - zeps ) * wmask (ji,jj,ik) wslpjml(ji,jj) = zaj / ( zbj - zeps ) * wmask (ji,jj,ik) END DO END DO !!gm this lbc_lnk should be useless.... CALL lbc_lnk( uslpml , 'U', -1. ) ; CALL lbc_lnk( vslpml , 'V', -1. ) ! lateral boundary cond. (sign change) CALL lbc_lnk( wslpiml, 'W', -1. ) ; CALL lbc_lnk( wslpjml, 'W', -1. ) ! lateral boundary conditions ! IF( nn_timing == 1 ) CALL timing_stop('ldf_slp_mxl') ! END SUBROUTINE ldf_slp_mxl SUBROUTINE ldf_slp_init !!---------------------------------------------------------------------- !! *** ROUTINE ldf_slp_init *** !! !! ** Purpose : Initialization for the isopycnal slopes computation !! !! ** Method : read the nammbf namelist and check the parameter !! values called by tra_dmp at the first timestep (nit000) !!---------------------------------------------------------------------- INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ierr ! local integer !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('ldf_slp_init') ! IF(lwp) THEN WRITE(numout,*) WRITE(numout,*) 'ldf_slp_init : direction of lateral mixing' WRITE(numout,*) '~~~~~~~~~~~~' ENDIF IF( ln_traldf_grif ) THEN ! Griffies operator : triad of slopes ALLOCATE( triadi_g(jpi,jpj,jpk,0:1,0:1) , triadj_g(jpi,jpj,jpk,0:1,0:1) , wslp2(jpi,jpj,jpk) , STAT=ierr ) ALLOCATE( triadi (jpi,jpj,jpk,0:1,0:1) , triadj (jpi,jpj,jpk,0:1,0:1) , STAT=ierr ) IF( ierr > 0 ) CALL ctl_stop( 'STOP', 'ldf_slp_init : unable to allocate Griffies operator slope' ) ! IF( ln_dynldf_iso ) CALL ctl_stop( 'ldf_slp_init: Griffies operator on momentum not supported' ) ! ELSE ! Madec operator : slopes at u-, v-, and w-points ALLOCATE( uslp(jpi,jpj,jpk) , vslp(jpi,jpj,jpk) , wslpi(jpi,jpj,jpk) , wslpj(jpi,jpj,jpk) , & & omlmask(jpi,jpj,jpk) , uslpml(jpi,jpj) , vslpml(jpi,jpj) , wslpiml(jpi,jpj) , wslpjml(jpi,jpj) , STAT=ierr ) IF( ierr > 0 ) CALL ctl_stop( 'STOP', 'ldf_slp_init : unable to allocate Madec operator slope ' ) ! Direction of lateral diffusion (tracers and/or momentum) ! ------------------------------ uslp (:,:,:) = 0._wp ; uslpml (:,:) = 0._wp ! set the slope to zero (even in s-coordinates) vslp (:,:,:) = 0._wp ; vslpml (:,:) = 0._wp wslpi(:,:,:) = 0._wp ; wslpiml(:,:) = 0._wp wslpj(:,:,:) = 0._wp ; wslpjml(:,:) = 0._wp IF(ln_sco .AND. (ln_traldf_hor .OR. ln_dynldf_hor )) THEN IF(lwp) WRITE(numout,*) ' Horizontal mixing in s-coordinate: slope = slope of s-surfaces' ! geopotential diffusion in s-coordinates on tracers and/or momentum ! The slopes of s-surfaces are computed once (no call to ldfslp in step) ! The slopes for momentum diffusion are i- or j- averaged of those on tracers ! set the slope of diffusion to the slope of s-surfaces ! ( c a u t i o n : minus sign as fsdep has positive value ) DO jk = 1, jpk DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. uslp (ji,jj,jk) = -1./e1u(ji,jj) * ( fsdept_b(ji+1,jj,jk) - fsdept_b(ji ,jj ,jk) ) * umask(ji,jj,jk) vslp (ji,jj,jk) = -1./e2v(ji,jj) * ( fsdept_b(ji,jj+1,jk) - fsdept_b(ji ,jj ,jk) ) * vmask(ji,jj,jk) wslpi(ji,jj,jk) = -1./e1t(ji,jj) * ( fsdepw_b(ji+1,jj,jk) - fsdepw_b(ji-1,jj,jk) ) * tmask(ji,jj,jk) * 0.5 wslpj(ji,jj,jk) = -1./e2t(ji,jj) * ( fsdepw_b(ji,jj+1,jk) - fsdepw_b(ji,jj-1,jk) ) * tmask(ji,jj,jk) * 0.5 END DO END DO END DO CALL lbc_lnk( uslp , 'U', -1. ) ; CALL lbc_lnk( vslp , 'V', -1. ) ! Lateral boundary conditions CALL lbc_lnk( wslpi, 'W', -1. ) ; CALL lbc_lnk( wslpj, 'W', -1. ) ENDIF ENDIF ! IF( nn_timing == 1 ) CALL timing_stop('ldf_slp_init') ! END SUBROUTINE ldf_slp_init #else !!------------------------------------------------------------------------ !! Dummy module : NO Rotation of lateral mixing tensor !!------------------------------------------------------------------------ LOGICAL, PUBLIC, PARAMETER :: lk_ldfslp = .FALSE. !: slopes flag CONTAINS SUBROUTINE ldf_slp( kt, prd, pn2 ) ! Dummy routine INTEGER, INTENT(in) :: kt REAL, DIMENSION(:,:,:), INTENT(in) :: prd, pn2 WRITE(*,*) 'ldf_slp: You should not have seen this print! error?', kt, prd(1,1,1), pn2(1,1,1) END SUBROUTINE ldf_slp SUBROUTINE ldf_slp_grif( kt ) ! Dummy routine INTEGER, INTENT(in) :: kt WRITE(*,*) 'ldf_slp_grif: You should not have seen this print! error?', kt END SUBROUTINE ldf_slp_grif SUBROUTINE ldf_slp_init ! Dummy routine END SUBROUTINE ldf_slp_init #endif !!====================================================================== END MODULE ldfslp