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 !! 3.7 ! 2013-12 (F. Lemarie, G. Madec) add limiter on triad slopes !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! 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) !!---------------------------------------------------------------------- USE len_oce ! ocean sizes USE phycst ! physical constants USE in_out_manager ! I/O manager ! mjb 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_mxl REAL(wp), PUBLIC :: rn_slpmax = 0.01_wp !: slope limit (nam_traldf namelist) !! * Substitutions # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL licence (./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE ldf_slp( ln_zps, ln_isfcav, prd, pn2, tmask, umask, vmask, wmask, gru, grv, & & e1t, e2t, r1_e1u, r1_e2v, e3u_n, e3v_n, e3w_n, gdept_n, gdepw_n, mbku, mbkv, & & mikt, miku, mikv, nmln, hmlp, hmlpt, risfdep, & & omlmask, uslpml, vslpml, wslpiml, wslpjml, uslp, vslp, wslpi, wslpj ) !!---------------------------------------------------------------------- !! *** 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. !!---------------------------------------------------------------------- LOGICAL , INTENT(in) :: ln_zps, ln_isfcav REAL(wp), INTENT(in), DIMENSION(:,:,:) :: prd ! in situ density REAL(wp), INTENT(in), DIMENSION(:,:,:) :: pn2 ! Brunt-Vaisala frequency (locally ref.) REAL(wp), INTENT(in), DIMENSION(:,:,:) :: tmask, umask, vmask, wmask REAL(wp), INTENT(in), DIMENSION(:,:) :: gru, grv, e1t, e2t, r1_e1u, r1_e2v REAL(wp), INTENT(in), DIMENSION(:,:,:) :: e3u_n, e3v_n, e3w_n, gdept_n, gdepw_n INTEGER , INTENT(in), DIMENSION(:,:) :: mbku, mbkv, mikt, miku, mikv, nmln REAL(wp), INTENT(in), DIMENSION(:,:) :: hmlp, hmlpt, risfdep REAL(wp), INTENT(out),DIMENSION(:,:,:) :: omlmask REAL(wp), INTENT(out),DIMENSION(:,:) :: uslpml, vslpml, wslpiml, wslpjml REAL(wp), INTENT(out),DIMENSION(:,:,:) :: uslp, vslp, wslpi, wslpj !! INTEGER :: ji , jj , jk ! dummy loop indices INTEGER :: ii0, ii1 ! temporary integer INTEGER :: ij0, ij1 ! temporary integer REAL(wp) :: zeps, zm1_g, zm1_2g, z1_16, zcofw, z1_slpmax ! 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) :: zdepu, zdepv ! - - REAL(wp),ALLOCATABLE, DIMENSION(:,:) :: zslpml_hmlpu, zslpml_hmlpv ! Make global scratch at some point REAL(wp),ALLOCATABLE, DIMENSION(:,:,:) :: zgru, zwz, zdzr REAL(wp),ALLOCATABLE, DIMENSION(:,:,:) :: zgrv, zww !!---------------------------------------------------------------------- ! ALLOCATE(zslpml_hmlpu(jpi,jpj)) ALLOCATE(zslpml_hmlpv(jpi,jpj)) ALLOCATE(zgru(jpi,jpj,jpk)) ALLOCATE(zwz(jpi,jpj,jpk)) ALLOCATE(zdzr(jpi,jpj,jpk)) ALLOCATE(zgrv(jpi,jpj,jpk)) ALLOCATE(zww(jpi,jpj,jpk)) ! mjb IF( ln_timing ) CALL timing_start('ldf_slp') ! 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 z1_slpmax = 1._wp / rn_slpmax ! 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 ! MJB next lines commented out for simplicity ! 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 ! zdzr(:,:,1) = 0._wp !== Local vertical density gradient at T-point == ! (evaluated from N^2) 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 ! ! !== Slopes just below the mixed layer ==! CALL ldf_slp_mxl( prd, pn2, zgru, zgrv, zdzr, nmln, e1t, e2t, r1_e1u, r1_e2v, e3u_n, e3v_n, e3w_n, & & tmask, umask, vmask, omlmask, 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. zslpml_hmlpu(ji,jj) = uslpml(ji,jj) / ( MAX(hmlpt (ji,jj), hmlpt (ji+1,jj ), 5._wp) & & - MAX(risfdep(ji,jj), risfdep(ji+1,jj ) ) ) zslpml_hmlpv(ji,jj) = vslpml(ji,jj) / ( MAX(hmlpt (ji,jj), hmlpt (ji ,jj+1), 5._wp) & & - MAX(risfdep(ji,jj), risfdep(ji ,jj+1) ) ) END DO END DO ELSE DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zslpml_hmlpu(ji,jj) = uslpml(ji,jj) / MAX(hmlpt(ji,jj), hmlpt(ji+1,jj ), 5._wp) zslpml_hmlpv(ji,jj) = vslpml(ji,jj) / MAX(hmlpt(ji,jj), hmlpt(ji ,jj+1), 5._wp) END DO END DO 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) * r1_e1u(ji,jj) zav = zgrv(ji,jj,jk) * r1_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, - z1_slpmax * ABS( zau ) , -7.e+3_wp/e3u_n(ji,jj,jk)* ABS( zau ) ) zbv = MIN( zbv, - z1_slpmax * ABS( zav ) , -7.e+3_wp/e3v_n(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 * ( ( gdept_n (ji,jj,jk) + gdept_n (ji+1,jj,jk) ) & - 2 * MAX( risfdep(ji,jj), risfdep(ji+1,jj) ) - e3u_n(ji,jj,miku(ji,jj)) ) zdepv = 0.5_wp * ( ( gdept_n (ji,jj,jk) + gdept_n (ji,jj+1,jk) ) & - 2 * MAX( risfdep(ji,jj), risfdep(ji,jj+1) ) - e3v_n(ji,jj,mikv(ji,jj)) ) ! zwz(ji,jj,jk) = ( ( 1._wp - zfi) * zau / ( zbu - zeps ) & & + zfi * zdepu * zslpml_hmlpu(ji,jj) ) * umask(ji,jj,jk) zww(ji,jj,jk) = ( ( 1._wp - zfj) * zav / ( zbv - zeps ) & & + zfj * zdepv * zslpml_hmlpv(ji,jj) ) * vmask(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 * ( gdept_n(ji+1,jj,jk)+gdept_n(ji,jj,jk) ) / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 10. ) ) ! zcj = 0.5 * ( gdept_n(ji,jj+1,jk)+gdept_n(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 !MJB CALL lbc_lnk_multi( zwz, 'U', -1., 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 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 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. ) ! !* 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 * wmask (ji,jj,jk) zaj = ( zgrv (ji,jj-1,jk ) + zgrv (ji,jj,jk-1) & & + zgrv (ji,jj-1,jk-1) + zgrv (ji,jj,jk ) ) / zcj * wmask (ji,jj,jk) ! ! 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/e3w_n(ji,jj,jk)* ABS( zai ) ) zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/e3w_n(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 = ( gdepw_n(ji,jj,jk) - gdepw_n(ji,jj,mikt(ji,jj) ) ) / MAX( hmlp(ji,jj) - gdepw_n(ji,jj,mikt(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 = gdepw(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 ! MJB CALL lbc_lnk_multi( zwz, 'T', -1., 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 = wmask(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 = wmask(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 in vicinity of topography 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 wslpj(ji,jj,jk) = wslpj(ji,jj,jk) * zck END DO END DO END DO ! IV. Lateral boundary conditions ! =============================== ! mjb CALL lbc_lnk_multi( uslp , 'U', -1. , vslp , 'V', -1. , wslpi, 'W', -1., wslpj, 'W', -1. ) ! mjb IF( ln_timing ) CALL timing_stop('ldf_slp') ! END SUBROUTINE ldf_slp SUBROUTINE ldf_slp_mxl( prd, pn2, p_gru, p_grv, p_dzr, nmln, e1t, e2t, r1_e1u, r1_e2v, e3u_n, e3v_n, e3w_n, & & tmask, umask, vmask, omlmask, uslpml, vslpml, wslpiml, wslpjml ) !!---------------------------------------------------------------------- !! *** 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, DIMENSION(:,:) , INTENT(in) :: nmln REAL(wp), DIMENSION(:,:), INTENT(in) :: e1t, e2t, r1_e1u, r1_e2v REAL(wp), DIMENSION(:,:,:), INTENT(in) :: e3u_n, e3v_n, e3w_n, tmask, umask, vmask REAL(wp), DIMENSION(:,:,:), INTENT(out):: omlmask REAL(wp), DIMENSION(:,:), INTENT(out):: uslpml, vslpml, wslpiml, wslpjml !! INTEGER :: ji , jj , jk ! dummy loop indices INTEGER :: iku, ikv, ik, ikm1 ! local integers REAL(wp) :: zeps, zm1_g, zm1_2g, z1_slpmax ! local scalars REAL(wp) :: zci, zfi, zau, zbu, zai, zbi ! - - REAL(wp) :: zcj, zfj, zav, zbv, zaj, zbj ! - - REAL(wp) :: zck, zfk, zbw ! - - !!---------------------------------------------------------------------- ! zeps = 1.e-20_wp !== Local constant initialization ==! zm1_g = -1.0_wp / grav zm1_2g = -0.5_wp / grav z1_slpmax = 1._wp / rn_slpmax ! 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 ) 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( 1, nmln(ji,jj) , nmln(ji+1,jj) ) , jpkm1 ) ! ML (MAX of T-pts, bound by jpkm1) ikv = MIN( MAX( 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) * r1_e1u(ji,jj) zav = p_grv(ji,jj,ikv) * r1_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 , - z1_slpmax * ABS( zau ) , -7.e+3_wp/e3u_n(ji,jj,iku)* ABS( zau ) ) zbv = MIN( zbv , - z1_slpmax * ABS( zav ) , -7.e+3_wp/e3v_n(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/e3w_n(ji,jj,ik)* ABS( zai ) ) zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/e3w_n(ji,jj,ik)* ABS( zaj ) ) ! !- i- & j-slope at w-points (wslpiml, wslpjml) wslpiml(ji,jj) = zai / ( zbi - zeps ) * tmask (ji,jj,ik) wslpjml(ji,jj) = zaj / ( zbj - zeps ) * tmask (ji,jj,ik) END DO END DO !!gm this lbc_lnk should be useless.... ! MJB CALL lbc_lnk_multi( uslpml , 'U', -1. , vslpml , 'V', -1. , wslpiml, 'W', -1. , wslpjml, 'W', -1. ) ! END SUBROUTINE ldf_slp_mxl !!====================================================================== END MODULE ldfslp