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 0.5 ! 2002-10 (G. Madec) Free form, F90 !! 1.0 ! 2005-10 (A. Beckmann) correction for s-coordinates !!---------------------------------------------------------------------- #if defined key_ldfslp || defined key_esopa !!---------------------------------------------------------------------- !! 'key_ldfslp' Rotation of lateral mixing tensor !!---------------------------------------------------------------------- !! ldf_slp : compute the slopes of neutral surface !! ldf_slp_mxl : compute the slopes of iso-neutral surface !! 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 USE ldfdyn_oce USE phycst ! physical constants USE zdfmxl ! mixed layer depth USE eosbn2 USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE in_out_manager ! I/O manager USE prtctl ! Print control IMPLICIT NONE PRIVATE PUBLIC ldf_slp ! routine called by step.F90 PUBLIC ldf_slp_init ! routine called by opa.F90 PUBLIC ldf_slp_grif ! " LOGICAL , PUBLIC, PARAMETER :: lk_ldfslp = .TRUE. !: slopes flag REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: uslp, wslpi !: i_slope at U- and W-points REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: vslp, wslpj !: j-slope at V- and W-points REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: wslp2 !: wslp**2 from Griffies quarter cells REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: alpha, beta !: alpha,beta at T points REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: tfw,sfw,ftu,fsu,ftv,fsv,ftud,fsud,ftvd,fsvd REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: psix_eiv REAL(wp), PUBLIC, DIMENSION(jpi,jpj,jpk) :: psiy_eiv REAL(wp), DIMENSION(jpi,jpj,jpk) :: omlmask ! mask of the surface mixed layer at T-pt REAL(wp), DIMENSION(jpi,jpj) :: uslpml, wslpiml ! i_slope at U- and W-points just below the mixed layer REAL(wp), DIMENSION(jpi,jpj) :: vslpml, wslpjml ! j_slope at V- and W-points just below the mixed layer !! * Substitutions # include "domzgr_substitute.h90" # include "ldftra_substitute.h90" # include "ldfeiv_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.2 , LOCEAN-IPSL (2009) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/License_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) ('key_traldfiso'). !! !! ** 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. !!---------------------------------------------------------------------- USE oce , zgru => ua ! use ua as workspace USE oce , zgrv => va ! use va as workspace USE oce , zwy => ta ! use ta as workspace USE oce , zwz => sa ! use sa as workspace !! INTEGER , INTENT(in) :: kt ! ocean time-step index REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: prd ! in situ density REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: 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, zmg, zm05g, zalpha ! temporary scalars REAL(wp) :: zcoef1, zcoef2, zcoef3 ! - - REAL(wp) :: zcofu , zcofv , zcofw ! - - REAL(wp) :: zau, zbu, zai, zbi, z1u, z1wu ! - - REAL(wp) :: zav, zbv, zaj, zbj, z1v, z1wv ! REAL(wp), DIMENSION(jpi,jpj,jpk) :: zww ! 3D workspace !!---------------------------------------------------------------------- zeps = 1.e-20 ! Local constant initialization zmg = -1.0 / grav zm05g = -0.5 / grav ! zww(:,:,:) = 0.e0 zwz(:,:,:) = 0.e0 ! ! horizontal density gradient computation DO jk = 1, jpk 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 # if defined key_vectopt_loop DO jj = 1, 1 DO ji = 1, jpij-jpi ! vector opt. (forced unrolling) # else DO jj = 1, jpjm1 DO ji = 1, jpim1 # endif iku = MIN ( mbathy(ji,jj), mbathy(ji+1,jj) ) - 1 ! last ocean level ikv = MIN ( mbathy(ji,jj), mbathy(ji,jj+1) ) - 1 zgru(ji,jj,iku) = gru(ji,jj) zgrv(ji,jj,ikv) = grv(ji,jj) END DO END DO ENDIF CALL ldf_slp_mxl( prd, pn2 ) ! Slopes of isopycnal surfaces just below the mixed layer ! I. slopes at u and v point | uslp = d/di( prd ) / d/dz( prd ) ! =========================== | vslp = d/dj( prd ) / d/dz( prd ) ! ! !* Local vertical density gradient evaluated from N^2 DO jk = 2, jpkm1 ! zwy = d/dz(prd)= - ( prd ) / grav * mk(pn2) -- at t point DO jj = 1, jpj DO ji = 1, jpi zwy(ji,jj,jk) = zmg * ( prd(ji,jj,jk) + 1. ) * ( pn2 (ji,jj,jk) + pn2 (ji,jj,jk+1) ) & & / MAX( tmask(ji,jj,jk) + tmask(ji,jj,jk+1), 1. ) END DO END DO END DO 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 = 1. / e1u(ji,jj) * zgru(ji,jj,jk) zav = 1. / e2v(ji,jj) * zgrv(ji,jj,jk) zbu = 0.5 * ( zwy(ji,jj,jk) + zwy(ji+1,jj ,jk) ) zbv = 0.5 * ( zwy(ji,jj,jk) + zwy(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.*ABS( zau ), -7.e+3/fse3u(ji,jj,jk)*ABS( zau ) ) zbv = MIN( zbv, -100.*ABS( zav ), -7.e+3/fse3v(ji,jj,jk)*ABS( zav ) ) ! uslp and vslp output in zwz and zww, resp. zalpha = MAX( omlmask(ji,jj,jk), omlmask(ji+1,jj,jk) ) zwz (ji,jj,jk) = ( ( 1. - zalpha) * zau / ( zbu - zeps ) & & + zalpha * uslpml(ji,jj) & & * 0.5 * ( fsdept(ji+1,jj,jk)+fsdept(ji,jj,jk)-fse3u(ji,jj,1) ) & & / MAX( hmlpt(ji,jj), hmlpt(ji+1,jj), 5. ) ) * umask(ji,jj,jk) zalpha = MAX( omlmask(ji,jj,jk), omlmask(ji,jj+1,jk) ) zww (ji,jj,jk) = ( ( 1. - zalpha) * zav / ( zbv - zeps ) & & + zalpha * vslpml(ji,jj) & & * 0.5 * ( fsdept(ji,jj+1,jk)+fsdept(ji,jj,jk)-fse3v(ji,jj,1) ) & & / MAX( hmlpt(ji,jj), hmlpt(ji,jj+1), 5. ) ) * vmask(ji,jj,jk) END DO END DO END DO CALL lbc_lnk( zwz, 'U', -1. ) ; CALL lbc_lnk( zww, 'V', -1. ) ! lateral boundary conditions ! zcofu = 1. / 16. !* horizontal Shapiro filter zcofv = 1. / 16. DO jk = 2, jpkm1 DO jj = 2, jpjm1, jpj-3 ! rows jj=2 and =jpjm1 only DO ji = 2, jpim1 uslp(ji,jj,jk) = zcofu * ( 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) = zcofv * ( 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) = zcofu * ( 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) = zcofv * ( 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. z1u = ( umask(ji,jj+1,jk) + umask(ji,jj-1,jk) )*.5 z1v = ( vmask(ji+1,jj,jk) + vmask(ji-1,jj,jk) )*.5 z1wu = ( umask(ji,jj,jk) + umask(ji,jj,jk+1) )*.5 z1wv = ( vmask(ji,jj,jk) + vmask(ji,jj,jk+1) )*.5 uslp(ji,jj,jk) = uslp(ji,jj,jk) * z1u * z1wu vslp(ji,jj,jk) = vslp(ji,jj,jk) * z1v * z1wv 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 ) ! ! !* Local vertical density gradient evaluated from N^2 DO jk = 2, jpkm1 ! zwy = d/dz(prd)= - mk ( prd ) / grav * pn2 -- at w point DO jj = 1, jpj DO ji = 1, jpi zwy(ji,jj,jk) = zm05g * pn2 (ji,jj,jk) * ( prd (ji,jj,jk) + prd (ji,jj,jk-1) + 2. ) END DO END DO END DO DO jk = 2, jpkm1 !* Slopes at w point DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! ! horizontal density i-gradient at w-points zcoef1 = MAX( zeps, umask(ji-1,jj,jk )+umask(ji,jj,jk ) & & +umask(ji-1,jj,jk-1)+umask(ji,jj,jk-1) ) zcoef1 = 1. / ( zcoef1 * e1t (ji,jj) ) zai = zcoef1 * ( zgru(ji ,jj,jk ) + zgru(ji ,jj,jk-1) & & + zgru(ji-1,jj,jk-1) + zgru(ji-1,jj,jk ) ) * tmask (ji,jj,jk) ! ! horizontal density j-gradient at w-points zcoef2 = MAX( zeps, vmask(ji,jj-1,jk )+vmask(ji,jj,jk-1) & & +vmask(ji,jj-1,jk-1)+vmask(ji,jj,jk ) ) zcoef2 = 1.0 / ( zcoef2 * e2t (ji,jj) ) zaj = zcoef2 * ( zgrv(ji,jj ,jk ) + zgrv(ji,jj ,jk-1) & & + zgrv(ji,jj-1,jk-1) + zgrv(ji,jj-1,jk ) ) * tmask (ji,jj,jk) ! ! bound the slopes: abs(zw.)<= 1/100 and zb..<0. ! ! static instability: kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) zbi = MIN( zwy (ji,jj,jk),- 100.*ABS(zai), -7.e+3/fse3w(ji,jj,jk)*ABS(zai) ) zbj = MIN( zwy (ji,jj,jk), -100.*ABS(zaj), -7.e+3/fse3w(ji,jj,jk)*ABS(zaj) ) ! ! wslpi and wslpj output in zwz and zww, resp. zalpha = MAX( omlmask(ji,jj,jk), omlmask(ji,jj,jk-1) ) zcoef3 = fsdepw(ji,jj,jk) / MAX( hmlp(ji,jj), 10. ) zwz(ji,jj,jk) = ( zai / ( zbi - zeps) * ( 1. - zalpha ) & & + zcoef3 * wslpiml(ji,jj) * zalpha ) * tmask (ji,jj,jk) zww(ji,jj,jk) = ( zaj / ( zbj - zeps) * ( 1. - zalpha ) & & + zcoef3 * wslpjml(ji,jj) * zalpha ) * tmask (ji,jj,jk) END DO END DO END DO CALL lbc_lnk( zwz, 'T', -1. ) ; CALL lbc_lnk( zww, 'T', -1. ) ! lateral boundary conditions on zwz and zww ! ! !* horizontal Shapiro filter DO jk = 2, jpkm1 DO jj = 2, jpjm1, jpj-3 ! rows jj=2 and =jpjm1 DO ji = 2, jpim1 zcofw = tmask(ji,jj,jk) / 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) / 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. z1u = ( umask(ji,jj,jk) + umask(ji-1,jj,jk) ) *.5 z1v = ( vmask(ji,jj,jk) + vmask(ji,jj-1,jk) ) *.5 wslpi(ji,jj,jk) = wslpi(ji,jj,jk) * z1u * z1v wslpj(ji,jj,jk) = wslpj(ji,jj,jk) * z1u * z1v 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.e0 ij0 = 51 ; ij1 = 53 ii0 = 68 ; ii1 = 71 ; vslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0.e0 ii0 = 69 ; ii1 = 71 ; wslpi( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0.e0 ii0 = 69 ; ii1 = 71 ; wslpj( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0.e0 ! ! ! Mediterrannean Sea ij0 = 49 ; ij1 = 56 ii0 = 71 ; ii1 = 90 ; uslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0.e0 ij0 = 50 ; ij1 = 56 ii0 = 70 ; ii1 = 90 ; vslp ( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0.e0 ii0 = 71 ; ii1 = 90 ; wslpi( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0.e0 ii0 = 71 ; ii1 = 90 ; wslpj( mi0(ii0):mi1(ii1) , mj0(ij0):mj1(ij1) , : ) = 0.e0 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 ! 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) ('key_traldfiso') !! at W-points using the Griffies quarter-cells. Also calculates !! alpha and beta at T-points for use in the Griffies isopycnal !! scheme. !! !! ** 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). !! !! ** Action : - alpha, beta !! wslp2 squared slope of neutral surfaces at w-points. !! !! History : !! 9.0 ! 06-10 (C. Harris) New subroutine !!---------------------------------------------------------------------- !! * Modules used USE oce , zdit => ua, & ! use ua as workspace zdis => va, & ! use va as workspace zdjt => ta, & ! use ta as workspace zdjs => sa ! use sa as workspace !! * Arguments INTEGER, INTENT( in ) :: kt ! ocean time-step index !! * Local declarations INTEGER :: ji, jj, jk, ip, jp, kp ! dummy loop indices INTEGER :: iku, ikv ! temporary integer REAL(wp) :: & zt, zs, zh, zt2, zsp5, zp1t1, & ! temporary scalars zdenr, zrhotmp, zdndt, zdddt, & ! " " zdnds, zddds, znum, zden, & ! " " zslope, za_sxe, zslopec, zdsloper,& ! " " zfact, zepsln, zatempw,zatempu,zatempv, & ! " " ze1ur,ze2vr,ze3wr,zdxt,zdxs,zdyt,zdys,zdzt,zdzs,zvolf,& zr_slpmax,zdxrho,zdyrho,zabs_dzrho REAL(wp), DIMENSION(jpi,jpj,jpk,0:1,0:1) :: & zsx,zsy REAL(wp), DIMENSION(jpi,jpj,0:1,0:1) :: & zsx_ml_base,zsy_ml_base REAL(wp), DIMENSION(jpi,jpj,jpk) :: & zdkt,zdks REAL(wp), DIMENSION(jpi,jpj) :: & zr_ml_basew !!---------------------------------------------------------------------- ! 0. Local constant initialization ! -------------------------------- zr_slpmax = 1.0_wp/slpmax ! zslopec=0.004 ! zdsloper=1000.0 zepsln=1e-25 SELECT CASE ( nn_eos ) CASE ( 0 ) ! Jackett and McDougall (1994) formulation ! ! =============== DO jk = 1, jpk ! Horizontal slab ! ! =============== DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 zt = tb(ji,jj,jk) ! potential temperature zs = sb(ji,jj,jk) - 35.0 ! salinity anomaly (s-35) zh = fsdept(ji,jj,jk) ! depth in meters beta(ji,jj,jk) = ( ( -0.415613e-09 * zt + 0.555579e-07 ) * zt & & - 0.301985e-05 ) * zt & & + 0.785567e-03 & & + ( 0.515032e-08 * zs & & + 0.788212e-08 * zt - 0.356603e-06 ) * zs & & +( ( 0.121551e-17 * zh & & - 0.602281e-15 * zs & & - 0.175379e-14 * zt + 0.176621e-12 ) * zh & & + 0.408195e-10 * zs & & + ( - 0.213127e-11 * zt + 0.192867e-09 ) * zt & & - 0.121555e-07 ) * zh alpha(ji,jj,jk) = - beta(ji,jj,jk) * & & (((( - 0.255019e-07 * zt + 0.298357e-05 ) * zt & & - 0.203814e-03 ) * zt & & + 0.170907e-01 ) * zt & & + 0.665157e-01 & & + ( - 0.678662e-05 * zs & & - 0.846960e-04 * zt + 0.378110e-02 ) * zs & & + ( ( - 0.302285e-13 * zh & & - 0.251520e-11 * zs & & + 0.512857e-12 * zt * zt ) * zh & & - 0.164759e-06 * zs & & +( 0.791325e-08 * zt - 0.933746e-06 ) * zt & & + 0.380374e-04 ) * zh) ENDDO ENDDO ENDDO CASE ( 1 ) alpha(:,:,:)=-rn_alpha beta(:,:,:)=0.0 CASE ( 2 ) alpha(:,:,:)=-rn_alpha beta (:,:,:)=rn_beta CASE ( 3 ) DO jk =1, jpk DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 zt = tb(ji,jj,jk) zs = sb(ji,jj,jk) zh = fsdept(ji,jj,jk) zt2 = zt**2 zsp5 = sqrt(ABS(zs)) zp1t1=zh*zt znum=9.99843699e+02+zt*(7.35212840e+00+zt*(-5.45928211e-02+3.98476704e-04*zt)) & +zs*(2.96938239e+00-7.23268813e-03*zt+2.12382341e-03*zs) & +zh*(1.04004591e-02+1.03970529e-07*zt2+5.18761880e-06*zs+ & zh*(-3.24041825e-08-1.23869360e-11*zt2)) zden=1.00000000e+00+zt*(7.28606739e-03+zt*(-4.60835542e-05+zt*(3.68390573e-07+zt*1.80809186e-10))) & +zs*(2.14691708e-03+zt*(-9.27062484e-06-1.78343643e-10*zt2)+zsp5*(4.76534122e-06+1.63410736e-09*zt2)) & + zh*(5.30848875e-06+zh*zt*(-3.03175128e-16*zt2-1.27934137e-17*zh)) zdenr=1.0/zden zrhotmp=znum*zdenr zdndt=7.35212840e+00+zt*(-1.091856422e-01+1.195430112e-03*zt)-7.23268813e-03*zs & +zp1t1*(2.07941058e-07-2.4773872e-11*zh) zdddt=7.28606739e-03+zt*(-9.21671084e-05+zt*(1.105171719e-06+7.23236744e-10*zt)) & +zs*(-9.27062484e-06+zt*(-5.35030929e-10*zt+3.26821472e-09*zsp5)) & +zh*zh*(-9.09525384e-16*zt2-1.27934137e-17*zh) zdnds=2.96938239e+00-7.23268813e-03*zt+2*2.12382341e-03*zs+5.18761880e-06*zh zddds=2.14691708e-03+zt*(-9.27062484e-06-1.78343643e-10*zt2)+zsp5*(7.14801183e-06+2.45116104e-09*zt2) alpha(ji,jj,jk)=(zdndt-zrhotmp*zdddt)*zdenr beta(ji,jj,jk)=zdenr*(zdnds-zrhotmp*zddds) END DO END DO END DO CASE DEFAULT IF(lwp) WRITE(numout,cform_err) IF(lwp) WRITE(numout,*) ' bad flag value for nn_eos = ', nn_eos nstop = nstop + 1 END SELECT CALL lbc_lnk( alpha, 'T', 1. ) CALL lbc_lnk( beta, 'T', 1. ) ! --------------------------------------- ! 1. Horizontal tracer gradients at T-level jk ! --------------------------------------- DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ! i-gradient of T and S at jj zdit (ji,jj,jk) = ( tb(ji+1,jj,jk)-tb(ji,jj,jk) ) * umask(ji,jj,jk) zdis (ji,jj,jk) = ( sb(ji+1,jj,jk)-sb(ji,jj,jk) ) * umask(ji,jj,jk) ! j-gradient of T and S at jj zdjt (ji,jj,jk) = ( tb(ji,jj+1,jk)-tb(ji,jj,jk) ) * vmask(ji,jj,jk) zdjs (ji,jj,jk) = ( sb(ji,jj+1,jk)-sb(ji,jj,jk) ) * vmask(ji,jj,jk) END DO END DO END DO IF( ln_zps ) THEN ! partial steps correction at the last level # if defined key_vectopt_loop && ! defined key_mpp_omp jj = 1 DO ji = 1, jpij-jpi ! vector opt. (forced unrolling) # else DO jj = 1, jpjm1 DO ji = 1, jpim1 # endif ! last ocean level iku = MIN( mbathy(ji,jj), mbathy(ji+1,jj ) ) - 1 ikv = MIN( mbathy(ji,jj), mbathy(ji ,jj+1) ) - 1 ! i-gradient of T and S zdit (ji,jj,iku) = gtsu(ji,jj,jp_tem) zdis (ji,jj,iku) = gtsu(ji,jj,jp_sal) ! j-gradient of T and S zdjt (ji,jj,ikv) = gtsv(ji,jj,jp_tem) zdjs (ji,jj,ikv) = gtsv(ji,jj,jp_sal) # if ! defined key_vectopt_loop || defined key_mpp_omp END DO # endif END DO ENDIF ! --------------------------------------- ! 1. Vertical tracer gradient at w-level jk ! --------------------------------------- DO jk = 2, jpk zdkt(:,:,jk) = ( tb(:,:,jk-1) - tb(:,:,jk) ) * tmask(:,:,jk) zdks(:,:,jk) = ( sb(:,:,jk-1) - sb(:,:,jk) ) * tmask(:,:,jk) END DO zdkt(:,:,1) = 0.0 zdks(:,:,1) = 0.0 ! --------------------------------------- ! Depth of the w-point below ML base ! --------------------------------------- DO jj = 1, jpj DO ji = 1, jpi jk = nmln(ji,jj) zr_ml_basew(ji,jj)=1.0/fsdepw(ji,jj,jk+1) END DO END DO wslp2(:,:,:)=0.0 tfw(:,:,:) = 0.0 sfw(:,:,:) = 0.0 ftu(:,:,:) = 0.0 fsu(:,:,:) = 0.0 ftv(:,:,:) = 0.0 fsv(:,:,:) = 0.0 ftud(:,:,:) = 0.0 fsud(:,:,:) = 0.0 ftvd(:,:,:) = 0.0 fsvd(:,:,:) = 0.0 psix_eiv(:,:,:) = 0.0 psiy_eiv(:,:,:) = 0.0 ! ---------------------------------------------------------------------- ! x-z plane ! ---------------------------------------------------------------------- ! calculate limited triad x-slopes zsx in interior (1= l=20km with a typical velocity !! of 10cm/s) !! !! ** Action : Compute uslp, wslpi, and vslp, wslpj, the i- and j-slopes !! of now neutral surfaces at u-, w- and v- w-points, resp. !!---------------------------------------------------------------------- USE oce , zgru => ua ! ua, va used as workspace and set to hor. USE oce , zgrv => va ! density gradient in ldf_slp !! REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: prd ! in situ density REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in) :: pn2 ! Brunt-Vaisala frequency (locally ref.) !! INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ik, ikm1 ! temporary integers REAL(wp) :: zeps, zmg, zm05g ! temporary scalars REAL(wp) :: zcoef1, zcoef2 ! - - REAL(wp) :: zau, zbu, zai, zbi ! - - REAL(wp) :: zav, zbv, zaj, zbj ! - - REAL(wp), DIMENSION(jpi,jpj) :: zwy ! 2D workspace !!---------------------------------------------------------------------- zeps = 1.e-20 ! Local constant initialization zmg = -1.0 / grav zm05g = -0.5 / grav ! uslpml (1,:) = 0.e0 ; uslpml (jpi,:) = 0.e0 vslpml (1,:) = 0.e0 ; vslpml (jpi,:) = 0.e0 wslpiml(1,:) = 0.e0 ; wslpiml(jpi,:) = 0.e0 wslpjml(1,:) = 0.e0 ; wslpjml(jpi,:) = 0.e0 ! ! surface mixed layer mask DO jk = 1, jpk ! =1 inside the mixed layer, =0 otherwise # if defined key_vectopt_loop DO jj = 1, 1 DO ji = 1, jpij ! vector opt. (forced unrolling) # else DO jj = 1, jpj DO ji = 1, jpi # endif ik = nmln(ji,jj) - 1 IF( jk <= ik ) THEN ; omlmask(ji,jj,jk) = 1.e0 ELSE ; omlmask(ji,jj,jk) = 0.e0 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. !----------------------------------------------------------------------- ! zwy(:,jpj) = 0.e0 !* vertical density gradient for u-slope (from N^2) zwy(jpi,:) = 0.e0 # if defined key_vectopt_loop DO jj = 1, 1 DO ji = 1, jpij-jpi ! vector opt. (forced unrolling) # else DO jj = 1, jpjm1 DO ji = 1, jpim1 # endif ik = MAX( 1, nmln(ji,jj) , nmln(ji+1,jj) ) ! avoid spurious recirculation ik = MIN( ik, jpkm1 ) ! if ik = jpk take jpkm1 values zwy(ji,jj) = zmg * ( prd(ji,jj,ik) + 1. ) * ( pn2 (ji,jj,ik) + pn2 (ji,jj,ik+1) ) & & / MAX( tmask(ji,jj,ik) + tmask(ji,jj,ik+1), 1. ) END DO END DO CALL lbc_lnk( zwy, 'U', 1. ) ! lateral boundary conditions NO sign change ! !* Slope at u points # if defined key_vectopt_loop DO jj = 1, 1 DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) # else DO jj = 2, jpjm1 DO ji = 2, jpim1 # endif ! horizontal and vertical density gradient at u-points ik = MAX( 1, nmln(ji,jj) , nmln(ji+1,jj) ) ik = MIN( ik, jpkm1 ) zau = 1./ e1u(ji,jj) * zgru(ji,jj,ik) zbu = 0.5*( zwy(ji,jj) + zwy(ji+1,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.*ABS(zau), -7.e+3/fse3u(ji,jj,ik)*ABS(zau) ) ! uslpml uslpml (ji,jj) = zau / ( zbu - zeps ) * umask (ji,jj,ik) END DO END DO CALL lbc_lnk( uslpml, 'U', -1. ) ! lateral boundary conditions (i-gradient => sign change) ! !* vertical density gradient for v-slope (from N^2) # if defined key_vectopt_loop DO jj = 1, 1 DO ji = 1, jpij-jpi ! vector opt. (forced unrolling) # else DO jj = 1, jpjm1 DO ji = 1, jpim1 # endif ik = MAX( 1, nmln(ji,jj) , nmln(ji,jj+1) ) ik = MIN( ik, jpkm1 ) zwy(ji,jj) = zmg * ( prd(ji,jj,ik) + 1. ) * ( pn2 (ji,jj,ik) + pn2 (ji,jj,ik+1) ) & & / MAX( tmask(ji,jj,ik) + tmask(ji,jj,ik+1), 1. ) END DO END DO CALL lbc_lnk( zwy, 'V', 1. ) ! lateral boundary conditions NO sign change ! !* Slope at v points # if defined key_vectopt_loop DO jj = 1, 1 DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) # else DO jj = 2, jpjm1 DO ji = 2, jpim1 # endif ! horizontal and vertical density gradient at v-points ik = MAX( 1, nmln(ji,jj) , nmln(ji,jj+1) ) ik = MIN( ik,jpkm1 ) zav = 1./ e2v(ji,jj) * zgrv(ji,jj,ik) zbv = 0.5*( zwy(ji,jj) + zwy(ji,jj+1) ) ! bound the slopes: abs(zw.)<= 1/100 and zb..<0 ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) zbv = MIN( zbv, -100.*ABS(zav), -7.e+3/fse3v(ji,jj,ik)*ABS( zav ) ) ! vslpml vslpml (ji,jj) = zav / ( zbv - zeps ) * vmask (ji,jj,ik) END DO END DO CALL lbc_lnk( vslpml, 'V', -1. ) ! lateral boundary conditions (j-gradient => sign change) ! !* vertical density gradient for w-slope (from N^2) # if defined key_vectopt_loop DO jj = 1, 1 DO ji = 1, jpij ! vector opt. (forced unrolling) # else DO jj = 1, jpj DO ji = 1, jpi # endif ik = nmln(ji,jj) + 1 ik = MIN( ik, jpk ) ikm1 = MAX ( 1, ik-1) zwy (ji,jj) = zm05g * pn2 (ji,jj,ik) * & & ( prd (ji,jj,ik) + prd (ji,jj,ikm1) + 2. ) END DO END DO ! !* Slopes at w points # if defined key_vectopt_loop DO jj = 1, 1 DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling) # else DO jj = 2, jpjm1 DO ji = 2, jpim1 # endif ik = nmln(ji,jj) + 1 ik = MIN( ik, jpk ) ikm1 = MAX ( 1, ik-1 ) ! horizontal density i-gradient at w-points zcoef1 = MAX( zeps, umask(ji-1,jj,ik )+umask(ji,jj,ik ) & & +umask(ji-1,jj,ikm1)+umask(ji,jj,ikm1) ) zcoef1 = 1. / ( zcoef1 * e1t (ji,jj) ) zai = zcoef1 * ( zgru(ji ,jj,ik ) + zgru(ji ,jj,ikm1) & & + zgru(ji-1,jj,ikm1) + zgru(ji-1,jj,ik ) ) * tmask (ji,jj,ik) ! horizontal density j-gradient at w-points zcoef2 = MAX( zeps, vmask(ji,jj-1,ik )+vmask(ji,jj,ikm1) & & +vmask(ji,jj-1,ikm1)+vmask(ji,jj,ik ) ) zcoef2 = 1.0 / ( zcoef2 * e2t (ji,jj) ) zaj = zcoef2 * ( zgrv(ji,jj ,ik ) + zgrv(ji,jj ,ikm1) & & + zgrv(ji,jj-1,ikm1) + zgrv(ji,jj-1,ik ) ) * tmask (ji,jj,ik) ! bound the slopes: abs(zw.)<= 1/100 and zb..<0. ! static instability: ! kxz max= ah slope max =< e1 e3 /(pi**2 2 dt) zbi = MIN ( zwy (ji,jj),- 100.*ABS(zai), -7.e+3/fse3w(ji,jj,ik)*ABS(zai) ) zbj = MIN ( zwy (ji,jj), -100.*ABS(zaj), -7.e+3/fse3w(ji,jj,ik)*ABS(zaj) ) ! wslpiml and 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 CALL lbc_lnk( wslpiml, 'W', -1. ) ; CALL lbc_lnk( wslpjml, 'W', -1. ) ! lateral boundary conditions ! 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 !!---------------------------------------------------------------------- IF(lwp) THEN WRITE(numout,*) WRITE(numout,*) 'ldf_slp : direction of lateral mixing' WRITE(numout,*) '~~~~~~~' ENDIF ! Direction of lateral diffusion (tracers and/or momentum) ! ------------------------------ ! set the slope to zero (even in s-coordinates) uslp (:,:,:) = 0.e0 vslp (:,:,:) = 0.e0 wslpi(:,:,:) = 0.e0 wslpj(:,:,:) = 0.e0 uslpml (:,:) = 0.e0 vslpml (:,:) = 0.e0 wslpiml(:,:) = 0.e0 wslpjml(:,:) = 0.e0 IF( (ln_traldf_hor .OR. ln_dynldf_hor) .AND. .NOT. (lk_vvl .AND. ln_rstart) ) 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 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(ji+1,jj,jk) - fsdept(ji ,jj ,jk) ) * umask(ji,jj,jk) vslp (ji,jj,jk) = -1./e2v(ji,jj) * ( fsdept(ji,jj+1,jk) - fsdept(ji ,jj ,jk) ) * vmask(ji,jj,jk) wslpi(ji,jj,jk) = -1./e1t(ji,jj) * ( fsdepw(ji+1,jj,jk) - fsdepw(ji-1,jj,jk) ) * tmask(ji,jj,jk) * 0.5 wslpj(ji,jj,jk) = -1./e2t(ji,jj) * ( fsdepw(ji,jj+1,jk) - fsdepw(ji,jj-1,jk) ) * tmask(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. ) ENDIF ! 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_init ! Dummy routine END SUBROUTINE ldf_slp_init #endif !!====================================================================== END MODULE ldfslp