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_triad : calculates the triads of isoneutral slopes (Griffies 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 isf_oce ! ice shelf USE dom_oce ! ocean space and time domain ! USE ldfdyn ! lateral diffusion: eddy viscosity coef. USE phycst ! physical constants USE zdfmxl ! mixed layer depth USE eosbn2 ! equation of states ! USE in_out_manager ! I/O manager USE prtctl ! Print control USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE lib_mpp ! distribued memory computing library USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) USE timing ! Timing IMPLICIT NONE PRIVATE PUBLIC ldf_slp ! routine called by step.F90 PUBLIC ldf_slp_triad ! routine called by step.F90 PUBLIC ldf_slp_init ! routine called by nemogcm.F90 LOGICAL , PUBLIC :: l_ldfslp = .FALSE. !: slopes flag LOGICAL , PUBLIC :: ln_traldf_iso = .TRUE. !: iso-neutral direction (nam_traldf namelist) LOGICAL , PUBLIC :: ln_traldf_triad = .FALSE. !: griffies triad scheme (nam_traldf namelist) LOGICAL , PUBLIC :: ln_dynldf_iso !: iso-neutral direction (nam_dynldf namelist) LOGICAL , PUBLIC :: ln_triad_iso = .FALSE. !: pure horizontal mixing in ML (nam_traldf namelist) LOGICAL , PUBLIC :: ln_botmix_triad = .FALSE. !: mixing on bottom (nam_traldf namelist) REAL(wp), PUBLIC :: rn_sw_triad = 1._wp !: =1 switching triads ; =0 all four triads used (nam_traldf namelist) REAL(wp), PUBLIC :: rn_slpmax = 0.01_wp !: slope limit (nam_traldf namelist) LOGICAL , PUBLIC :: l_grad_zps = .FALSE. !: special treatment for Horz Tgradients w partial steps (triad operator) ! !! Classic operator (Madec) 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 ! !! triad operator (Griffies) 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 ! !! both operators REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ah_wslp2 !: ah * slope^2 at w-point REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: akz !: stabilizing vertical diffusivity ! !! 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 "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE ldf_slp( kt, prd, pn2, Kbb, Kmm ) !!---------------------------------------------------------------------- !! *** 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 INTEGER , INTENT(in) :: Kbb, Kmm ! ocean time level indices 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 ! 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), DIMENSION(jpi,jpj) :: zslpml_hmlpu, zslpml_hmlpv REAL(wp), DIMENSION(jpi,jpj,jpk) :: zgru, zwz, zdzr REAL(wp), DIMENSION(jpi,jpj,jpk) :: zgrv, zww !!---------------------------------------------------------------------- ! 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 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, Kmm ) ! 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. 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(ji,jj,jk,Kmm)* ABS( zau ) ) zbv = MIN( zbv, - z1_slpmax * ABS( zav ) , -7.e+3_wp/e3v(ji,jj,jk,Kmm)* ABS( zav ) ) ! ! Fred Dupont: add a correction for bottom partial steps: ! ! max slope = 1/2 * e3 / e1 IF (ln_zps .AND. jk==mbku(ji,jj)) & zbu = MIN( zbu, - z1_slpmax * ABS( zau ) , - 2._wp * e1u(ji,jj) / e3u(ji,jj,jk,Kmm)* ABS( zau ) ) IF (ln_zps .AND. jk==mbkv(ji,jj)) & zbv = MIN( zbv, - z1_slpmax * ABS( zav ) , - 2._wp * e2v(ji,jj) / e3v(ji,jj,jk,Kmm)* 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 (ji,jj,jk,Kmm) + gdept (ji+1,jj,jk,Kmm) ) & - 2 * MAX( risfdep(ji,jj), risfdep(ji+1,jj) ) - e3u(ji,jj,miku(ji,jj),Kmm) ) zdepv = 0.5_wp * ( ( gdept (ji,jj,jk,Kmm) + gdept (ji,jj+1,jk,Kmm) ) & - 2 * MAX( risfdep(ji,jj), risfdep(ji,jj+1) ) - e3v(ji,jj,mikv(ji,jj),Kmm) ) ! 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(ji+1,jj,jk,Kmm)+gdept(ji,jj,jk,Kmm) ) / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 10. ) ) ! zcj = 0.5 * ( gdept(ji,jj+1,jk,Kmm)+gdept(ji,jj,jk,Kmm) ) / 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_multi( 'ldfslp', 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(ji,jj,jk,Kmm)* ABS( zai ) ) zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/e3w(ji,jj,jk,Kmm)* 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(ji,jj,jk,Kmm) - gdepw(ji,jj,mikt(ji,jj),Kmm) ) / MAX( hmlp(ji,jj) - gdepw(ji,jj,mikt(ji,jj),Kmm), 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 CALL lbc_lnk_multi( 'ldfslp', 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 ! =============================== CALL lbc_lnk_multi( 'ldfslp', uslp , 'U', -1. , vslp , 'V', -1. , wslpi, 'W', -1., wslpj, 'W', -1. ) IF(sn_cfctl%l_prtctl) 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 ! IF( ln_timing ) CALL timing_stop('ldf_slp') ! END SUBROUTINE ldf_slp SUBROUTINE ldf_slp_triad ( kt, Kbb, Kmm ) !!---------------------------------------------------------------------- !! *** ROUTINE ldf_slp_triad *** !! !! ** Purpose : Compute the squared slopes of neutral surfaces (slope !! of iso-pycnal surfaces referenced locally) (ln_traldf_triad=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 , INTENT(in) :: Kbb, Kmm ! ocean time level indices !! 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, zdkt, zbu, zbti, zisw REAL(wp) :: zdjt, zdjs, zdks, zbv, zbtj, zjsw 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) :: zbeta0, ze3_e1, ze3_e2 REAL(wp), DIMENSION(jpi,jpj) :: z1_mlbw REAL(wp), DIMENSION(jpi,jpj,jpk,0:1) :: zdxrho , zdyrho, zdzrho ! Horizontal and vertical density gradients REAL(wp), DIMENSION(jpi,jpj,0:1,0:1) :: zti_mlb, ztj_mlb ! for Griffies operator only !!---------------------------------------------------------------------- ! IF( ln_timing ) CALL timing_start('ldf_slp_triad') ! !--------------------------------! ! 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 = ( ts(ji+1,jj,jk,jp_tem,Kbb) - ts(ji,jj,jk,jp_tem,Kbb) ) ! i-gradient of T & S at u-point zdis = ( ts(ji+1,jj,jk,jp_sal,Kbb) - ts(ji,jj,jk,jp_sal,Kbb) ) zdjt = ( ts(ji,jj+1,jk,jp_tem,Kbb) - ts(ji,jj,jk,jp_tem,Kbb) ) ! j-gradient of T & S at v-point zdjs = ( ts(ji,jj+1,jk,jp_sal,Kbb) - ts(ji,jj,jk,jp_sal,Kbb) ) zdxrho_raw = ( - rab_b(ji+ip,jj ,jk,jp_tem) * zdit + rab_b(ji+ip,jj ,jk,jp_sal) * zdis ) * r1_e1u(ji,jj) zdyrho_raw = ( - rab_b(ji ,jj+jp,jk,jp_tem) * zdjt + rab_b(ji ,jj+jp,jk,jp_sal) * zdjs ) * r1_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 ) * r1_e1u(ji,jj) zdyrho_raw = ( - rab_b(ji ,jj+jp,ikv,jp_tem) * zdjt + rab_b(ji ,jj+jp,ikv,jp_sal) * zdjs ) * r1_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 = ( ts(ji,jj,jk+kp-1,jp_tem,Kbb) - ts(ji,jj,jk+kp,jp_tem,Kbb) ) zdks = ( ts(ji,jj,jk+kp-1,jp_sal,Kbb) - ts(ji,jj,jk+kp,jp_sal,Kbb) ) 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 & & ) / e3w(ji,jj,jk+kp,Kmm) 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 / gdepw(ji,jj,jk,Kmm) 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 > 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) & & - ( gdept(ji+1,jj,jk-kp,Kmm) - gdept(ji,jj,jk-kp,Kmm) ) * r1_e1u(ji,jj) ) * umask(ji,jj,jk) ze3_e1 = e3w(ji+ip,jj,jk-kp,Kmm) * r1_e1u(ji,jj) zti_mlb(ji+ip,jj ,1-ip,kp) = SIGN( MIN( rn_slpmax, 5.0_wp * ze3_e1 , ABS( zti_g_raw ) ), zti_g_raw ) ENDIF ! jk = nmln(ji,jj+jp) + 1 IF( jk > 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) & & - ( gdept(ji,jj+1,jk-kp,Kmm) - gdept(ji,jj,jk-kp,Kmm) ) / e2v(ji,jj) ) * vmask(ji,jj,jk) ze3_e2 = e3w(ji,jj+jp,jk-kp,Kmm) / e2v(ji,jj) ztj_mlb(ji ,jj+jp,1-jp,kp) = SIGN( MIN( rn_slpmax, 5.0_wp * ze3_e2 , 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 * ( gdept(ji+1,jj ,jk,Kmm) - gdept(ji,jj,jk,Kmm) ) * r1_e1u(ji,jj) ztj_coord = znot_thru_surface * ( gdept(ji ,jj+1,jk,Kmm) - gdept(ji,jj,jk,Kmm) ) * r1_e2v(ji,jj) ! unmasked zti_g_raw = zti_raw - zti_coord ! ref to geopot surfaces ztj_g_raw = ztj_raw - ztj_coord ! additional limit required in bilaplacian case ze3_e1 = e3w(ji+ip,jj ,jk+kp,Kmm) * r1_e1u(ji,jj) ze3_e2 = e3w(ji ,jj+jp,jk+kp,Kmm) * r1_e2v(ji,jj) ! NB: hard coded factor 5 (can be a namelist parameter...) zti_g_lim = SIGN( MIN( rn_slpmax, 5.0_wp * ze3_e1, ABS( zti_g_raw ) ), zti_g_raw ) ztj_g_lim = SIGN( MIN( rn_slpmax, 5.0_wp * ze3_e2, 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) & & * gdepw(ji+ip,jj,jk+kp,Kmm) * 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) & & * gdepw(ji,jj+jp,jk+kp,Kmm) * 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*zti_lim / zti_raw ztj_raw = ztj_lim*ztj_lim / 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 ! ! switching triad scheme zisw = (1._wp - rn_sw_triad ) + rn_sw_triad & & * 2._wp * ABS( 0.5_wp - kp - ( 0.5_wp - ip ) * SIGN( 1._wp , zdxrho(ji+ip,jj,jk,1-ip) ) ) zjsw = (1._wp - rn_sw_triad ) + rn_sw_triad & & * 2._wp * ABS( 0.5_wp - kp - ( 0.5_wp - jp ) * SIGN( 1._wp , zdyrho(ji,jj+jp,jk,1-jp) ) ) ! triadi(ji+ip,jj ,jk,1-ip,kp) = zti_lim * zisw triadj(ji ,jj+jp,jk,1-jp,kp) = ztj_lim * zjsw ! zbu = e1e2u(ji ,jj ) * e3u(ji ,jj ,jk ,Kmm) zbv = e1e2v(ji ,jj ) * e3v(ji ,jj ,jk ,Kmm) zbti = e1e2t(ji+ip,jj ) * e3w(ji+ip,jj ,jk+kp,Kmm) zbtj = e1e2t(ji ,jj+jp) * e3w(ji ,jj+jp,jk+kp,Kmm) ! wslp2(ji+ip,jj,jk+kp) = wslp2(ji+ip,jj,jk+kp) + 0.25_wp * zbu / zbti * zti_g_lim*zti_g_lim ! masked wslp2(ji,jj+jp,jk+kp) = wslp2(ji,jj+jp,jk+kp) + 0.25_wp * zbv / zbtj * ztj_g_lim*ztj_g_lim END DO END DO END DO END DO END DO ! wslp2(:,:,1) = 0._wp ! force the surface wslp to zero CALL lbc_lnk( 'ldfslp', wslp2, 'W', 1. ) ! lateral boundary confition on wslp2 only ==>>> gm : necessary ? to be checked ! IF( ln_timing ) CALL timing_stop('ldf_slp_triad') ! END SUBROUTINE ldf_slp_triad SUBROUTINE ldf_slp_mxl( prd, pn2, p_gru, p_grv, p_dzr, Kmm ) !!---------------------------------------------------------------------- !! *** 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 , INTENT(in) :: Kmm ! ocean time level indices !! 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(ji,jj,iku,Kmm)* ABS( zau ) ) zbv = MIN( zbv , - z1_slpmax * ABS( zav ) , -7.e+3_wp/e3v(ji,jj,ikv,Kmm)* 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(ji,jj,ik,Kmm)* ABS( zai ) ) zbj = MIN( zbw , -100._wp* ABS( zaj ) , -7.e+3_wp/e3w(ji,jj,ik,Kmm)* 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.... CALL lbc_lnk_multi( 'ldfslp', uslpml , 'U', -1. , vslpml , 'V', -1. , wslpiml, 'W', -1. , wslpjml, 'W', -1. ) ! END SUBROUTINE ldf_slp_mxl SUBROUTINE ldf_slp_init !!---------------------------------------------------------------------- !! *** ROUTINE ldf_slp_init *** !! !! ** Purpose : Initialization for the isopycnal slopes computation !! !! ** Method : !!---------------------------------------------------------------------- INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ierr ! local integer !!---------------------------------------------------------------------- ! IF(lwp) THEN WRITE(numout,*) WRITE(numout,*) 'ldf_slp_init : direction of lateral mixing' WRITE(numout,*) '~~~~~~~~~~~~' ENDIF ! ALLOCATE( ah_wslp2(jpi,jpj,jpk) , akz(jpi,jpj,jpk) , STAT=ierr ) IF( ierr > 0 ) CALL ctl_stop( 'STOP', 'ldf_slp_init : unable to allocate ah_slp2 or akz' ) ! IF( ln_traldf_triad ) THEN ! Griffies operator : triad of slopes IF(lwp) WRITE(numout,*) ' ==>>> triad) operator (Griffies)' ALLOCATE( triadi_g(jpi,jpj,jpk,0:1,0:1) , triadj_g(jpi,jpj,jpk,0:1,0:1) , & & triadi (jpi,jpj,jpk,0:1,0:1) , triadj (jpi,jpj,jpk,0:1,0:1) , & & wslp2 (jpi,jpj,jpk) , 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 IF(lwp) WRITE(numout,*) ' ==>>> iso operator (Madec)' ALLOCATE( omlmask(jpi,jpj,jpk) , & & uslp(jpi,jpj,jpk) , uslpml(jpi,jpj) , wslpi(jpi,jpj,jpk) , wslpiml(jpi,jpj) , & & vslp(jpi,jpj,jpk) , vslpml(jpi,jpj) , wslpj(jpi,jpj,jpk) , 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 !!gm I no longer understand this..... !!gm IF( (ln_traldf_hor .OR. ln_dynldf_hor) .AND. .NOT. (.NOT.ln_linssh .AND. ln_rstart) ) 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 dep has positive value ) ! DO jk = 1, jpk ! DO jj = 2, jpjm1 ! DO ji = fs_2, fs_jpim1 ! vector opt. ! uslp (ji,jj,jk) = - ( gdept(ji+1,jj,jk,Kmm) - gdept(ji ,jj ,jk,Kmm) ) * r1_e1u(ji,jj) * umask(ji,jj,jk) ! vslp (ji,jj,jk) = - ( gdept(ji,jj+1,jk,Kmm) - gdept(ji ,jj ,jk,Kmm) ) * r1_e2v(ji,jj) * vmask(ji,jj,jk) ! wslpi(ji,jj,jk) = - ( gdepw(ji+1,jj,jk,Kmm) - gdepw(ji-1,jj,jk,Kmm) ) * r1_e1t(ji,jj) * wmask(ji,jj,jk) * 0.5 ! wslpj(ji,jj,jk) = - ( gdepw(ji,jj+1,jk,Kmm) - gdepw(ji,jj-1,jk,Kmm) ) * r1_e2t(ji,jj) * wmask(ji,jj,jk) * 0.5 ! END DO ! END DO ! END DO ! CALL lbc_lnk_multi( 'ldfslp', uslp , 'U', -1. ; CALL lbc_lnk( 'ldfslp', vslp , 'V', -1., wslpi, 'W', -1., wslpj, 'W', -1. ) !!gm ENDIF ENDIF ! END SUBROUTINE ldf_slp_init !!====================================================================== END MODULE ldfslp