MODULE tramle !!====================================================================== !! *** MODULE tramle *** !! Ocean tracers: Mixed Layer Eddy induced transport !!====================================================================== !! History : 3.3 ! 2010-08 (G. Madec) Original code !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! tra_mle_trp : update the effective transport with the Mixed Layer Eddy induced transport !! tra_mle_init : initialisation of the Mixed Layer Eddy induced transport computation !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers variables USE dom_oce ! ocean space and time domain variables USE phycst ! physical constant USE zdfmxl ! mixed layer depth ! USE in_out_manager ! I/O manager USE iom ! IOM library USE lib_mpp ! MPP library USE lbclnk ! lateral boundary condition / mpp link IMPLICIT NONE PRIVATE PUBLIC tra_mle_trp ! routine called in traadv.F90 PUBLIC tra_mle_init ! routine called in traadv.F90 ! !!* namelist namtra_mle * LOGICAL, PUBLIC :: ln_mle !: flag to activate the Mixed Layer Eddy (MLE) parameterisation INTEGER :: nn_mle ! MLE type: =0 standard Fox-Kemper ; =1 new formulation INTEGER :: nn_mld_uv ! space interpolation of MLD at u- & v-pts (0=min,1=averaged,2=max) INTEGER :: nn_conv ! =1 no MLE in case of convection ; =0 always MLE REAL(wp) :: rn_ce ! MLE coefficient ! ! parameters used in nn_mle = 0 case REAL(wp) :: rn_lf ! typical scale of mixed layer front REAL(wp) :: rn_time ! time scale for mixing momentum across the mixed layer ! ! parameters used in nn_mle = 1 case REAL(wp) :: rn_lat ! reference latitude for a 5 km scale of ML front REAL(wp) :: rn_rho_c_mle ! Density criterion for definition of MLD used by FK REAL(wp) :: r5_21 = 5.e0 / 21.e0 ! factor used in mle streamfunction computation REAL(wp) :: rb_c ! ML buoyancy criteria = g rho_c /rho0 where rho_c is defined in zdfmld REAL(wp) :: rc_f ! MLE coefficient (= rn_ce / (5 km * fo) ) in nn_mle=1 case REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: rfu, rfv ! modified Coriolis parameter (f+tau) at u- & v-pts REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: r1_ft ! inverse of the modified Coriolis parameter at t-pts !! * Substitutions # include "do_loop_substitute.h90" # include "domzgr_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_mle_trp( kt, kit000, pu, pv, pw, cdtype, Kmm ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_mle_trp *** !! !! ** Purpose : Add to the transport the Mixed Layer Eddy induced transport !! !! ** Method : The 3 components of the Mixed Layer Eddy (MLE) induced !! transport are computed as follows : !! zu_mle = dk[ zpsi_uw ] !! zv_mle = dk[ zpsi_vw ] !! zw_mle = - di[ zpsi_uw ] - dj[ zpsi_vw ] !! where zpsi is the MLE streamfunction at uw and vw points (see the doc) !! and added to the input velocity : !! p.n = p.n + z._mle !! !! ** Action : - (pu,pv,pw) increased by the mle transport !! CAUTION, the transport is not updated at the last line/raw !! this may be a problem for some advection schemes !! !! References: Fox-Kemper et al., JPO, 38, 1145-1165, 2008 !! Fox-Kemper and Ferrari, JPO, 38, 1166-1179, 2008 !!---------------------------------------------------------------------- INTEGER , INTENT(in ) :: kt ! ocean time-step index INTEGER , INTENT(in ) :: kit000 ! first time step index INTEGER , INTENT(in ) :: Kmm ! ocean time level index CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) REAL(wp), DIMENSION(ST_2D(nn_hls),jpk), INTENT(inout) :: pu ! in : 3 ocean transport components REAL(wp), DIMENSION(ST_2D(nn_hls),jpk), INTENT(inout) :: pv ! out: same 3 transport components REAL(wp), DIMENSION(ST_2D(nn_hls),jpk), INTENT(inout) :: pw ! increased by the MLE induced transport ! INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ii, ij, ik, ikmax ! local integers REAL(wp) :: zcuw, zmuw, zc ! local scalar REAL(wp) :: zcvw, zmvw ! - - INTEGER , DIMENSION(ST_2D(nn_hls)) :: inml_mle REAL(wp), DIMENSION(ST_2D(nn_hls)) :: zpsim_u, zpsim_v, zmld, zbm, zhu, zhv, zn2, zLf_MH REAL(wp), DIMENSION(ST_2D(nn_hls),jpk) :: zpsi_uw, zpsi_vw ! TEMP: These changes not necessary if using XIOS (subdomain support) REAL(wp), DIMENSION(:,:), ALLOCATABLE, SAVE :: zLf_NH REAL(wp), DIMENSION(:,:,:), ALLOCATABLE, SAVE :: zpsiu_mle, zpsiv_mle !!---------------------------------------------------------------------- ! ! !== MLD used for MLE ==! ! ! compute from the 10m density to deal with the diurnal cycle DO_2D( 1, 1, 1, 1 ) inml_mle(ji,jj) = mbkt(ji,jj) + 1 ! init. to number of ocean w-level (T-level + 1) END_2D IF ( nla10 > 0 ) THEN ! avoid case where first level is thicker than 10m DO_3DS( 1, 1, 1, 1, jpkm1, nlb10, -1 ) IF( rhop(ji,jj,jk) > rhop(ji,jj,nla10) + rn_rho_c_mle ) inml_mle(ji,jj) = jk ! Mixed layer END_3D ENDIF ikmax = MIN( MAXVAL( inml_mle(:,:) ), jpkm1 ) ! max level of the computation ! ! zmld(:,:) = 0._wp !== Horizontal shape of the MLE ==! zbm (:,:) = 0._wp zn2 (:,:) = 0._wp DO_3D( 1, 1, 1, 1, 1, ikmax ) zc = e3t(ji,jj,jk,Kmm) * REAL( MIN( MAX( 0, inml_mle(ji,jj)-jk ) , 1 ) ) ! zc being 0 outside the ML t-points zmld(ji,jj) = zmld(ji,jj) + zc zbm (ji,jj) = zbm (ji,jj) + zc * (rho0 - rhop(ji,jj,jk) ) * r1_rho0 zn2 (ji,jj) = zn2 (ji,jj) + zc * (rn2(ji,jj,jk)+rn2(ji,jj,jk+1))*0.5_wp END_3D SELECT CASE( nn_mld_uv ) ! MLD at u- & v-pts CASE ( 0 ) != min of the 2 neighbour MLDs DO_2D( 1, 0, 1, 0 ) zhu(ji,jj) = MIN( zmld(ji+1,jj), zmld(ji,jj) ) zhv(ji,jj) = MIN( zmld(ji,jj+1), zmld(ji,jj) ) END_2D CASE ( 1 ) != average of the 2 neighbour MLDs DO_2D( 1, 0, 1, 0 ) zhu(ji,jj) = ( zmld(ji+1,jj) + zmld(ji,jj) ) * 0.5_wp zhv(ji,jj) = ( zmld(ji,jj+1) + zmld(ji,jj) ) * 0.5_wp END_2D CASE ( 2 ) != max of the 2 neighbour MLDs DO_2D( 1, 0, 1, 0 ) zhu(ji,jj) = MAX( zmld(ji+1,jj), zmld(ji,jj) ) zhv(ji,jj) = MAX( zmld(ji,jj+1), zmld(ji,jj) ) END_2D END SELECT ! ! convert density into buoyancy DO_2D( 1, 1, 1, 1 ) zbm(ji,jj) = + grav * zbm(ji,jj) / MAX( e3t(ji,jj,1,Kmm), zmld(ji,jj) ) END_2D ! ! ! !== Magnitude of the MLE stream function ==! ! ! di[bm] Ds ! Psi = Ce H^2 ---------------- e2u mu(z) where fu Lf = MAX( fu*rn_fl , (Db H)^1/2 ) ! e1u Lf fu and the e2u for the "transport" ! (not *e3u as divided by e3u at the end) ! IF( nn_mle == 0 ) THEN ! Fox-Kemper et al. 2010 formulation DO_2D( 1, 0, 1, 0 ) zpsim_u(ji,jj) = rn_ce * zhu(ji,jj) * zhu(ji,jj) * e2_e1u(ji,jj) & & * ( zbm(ji+1,jj) - zbm(ji,jj) ) * MIN( 111.e3_wp , e1u(ji,jj) ) & & / ( MAX( rn_lf * rfu(ji,jj) , SQRT( rb_c * zhu(ji,jj) ) ) ) ! zpsim_v(ji,jj) = rn_ce * zhv(ji,jj) * zhv(ji,jj) * e1_e2v(ji,jj) & & * ( zbm(ji,jj+1) - zbm(ji,jj) ) * MIN( 111.e3_wp , e2v(ji,jj) ) & & / ( MAX( rn_lf * rfv(ji,jj) , SQRT( rb_c * zhv(ji,jj) ) ) ) END_2D ! ELSEIF( nn_mle == 1 ) THEN ! New formulation (Lf = 5km fo/ff with fo=Coriolis parameter at latitude rn_lat) DO_2D( 1, 0, 1, 0 ) zpsim_u(ji,jj) = rc_f * zhu(ji,jj) * zhu(ji,jj) * e2_e1u(ji,jj) & & * ( zbm(ji+1,jj) - zbm(ji,jj) ) * MIN( 111.e3_wp , e1u(ji,jj) ) ! zpsim_v(ji,jj) = rc_f * zhv(ji,jj) * zhv(ji,jj) * e1_e2v(ji,jj) & & * ( zbm(ji,jj+1) - zbm(ji,jj) ) * MIN( 111.e3_wp , e2v(ji,jj) ) END_2D ENDIF ! IF( nn_conv == 1 ) THEN ! No MLE in case of convection DO_2D( 1, 0, 1, 0 ) IF( MIN( zn2(ji,jj) , zn2(ji+1,jj) ) < 0._wp ) zpsim_u(ji,jj) = 0._wp IF( MIN( zn2(ji,jj) , zn2(ji,jj+1) ) < 0._wp ) zpsim_v(ji,jj) = 0._wp END_2D ENDIF ! ! !== structure function value at uw- and vw-points ==! DO_2D( 1, 0, 1, 0 ) zhu(ji,jj) = 1._wp / zhu(ji,jj) ! hu --> 1/hu zhv(ji,jj) = 1._wp / zhv(ji,jj) END_2D ! zpsi_uw(:,:,:) = 0._wp zpsi_vw(:,:,:) = 0._wp ! DO_3D( 1, 0, 1, 0, 2, ikmax ) zcuw = 1._wp - ( gdepw(ji+1,jj,jk,Kmm) + gdepw(ji,jj,jk,Kmm) ) * zhu(ji,jj) zcvw = 1._wp - ( gdepw(ji,jj+1,jk,Kmm) + gdepw(ji,jj,jk,Kmm) ) * zhv(ji,jj) zcuw = zcuw * zcuw zcvw = zcvw * zcvw zmuw = MAX( 0._wp , ( 1._wp - zcuw ) * ( 1._wp + r5_21 * zcuw ) ) zmvw = MAX( 0._wp , ( 1._wp - zcvw ) * ( 1._wp + r5_21 * zcvw ) ) ! zpsi_uw(ji,jj,jk) = zpsim_u(ji,jj) * zmuw * umask(ji,jj,jk) zpsi_vw(ji,jj,jk) = zpsim_v(ji,jj) * zmvw * vmask(ji,jj,jk) END_3D ! ! !== transport increased by the MLE induced transport ==! DO jk = 1, ikmax DO_2D( 1, 0, 1, 0 ) pu(ji,jj,jk) = pu(ji,jj,jk) + ( zpsi_uw(ji,jj,jk) - zpsi_uw(ji,jj,jk+1) ) pv(ji,jj,jk) = pv(ji,jj,jk) + ( zpsi_vw(ji,jj,jk) - zpsi_vw(ji,jj,jk+1) ) END_2D DO_2D( 0, 0, 0, 0 ) pw(ji,jj,jk) = pw(ji,jj,jk) - ( zpsi_uw(ji,jj,jk) - zpsi_uw(ji-1,jj,jk) & & + zpsi_vw(ji,jj,jk) - zpsi_vw(ji,jj-1,jk) ) END_2D END DO ! TEMP: These changes not necessary if using XIOS (subdomain support) IF( cdtype == 'TRA') THEN !== outputs ==! IF( kt == nit000 .AND. (ntile == 0 .OR. ntile == 1) ) THEN ! Do only on the first tile and timestep ALLOCATE( zLf_NH(jpi,jpj), zpsiu_mle(jpi,jpj,jpk), zpsiv_mle(jpi,jpj,jpk) ) ENDIF ! DO_2D( 1, 1, 1, 1 ) zLf_NH(ji,jj) = SQRT( rb_c * zmld(ji,jj) ) * r1_ft(ji,jj) ! Lf = N H / f END_2D ! ! divide by cross distance to give streamfunction with dimensions m^2/s DO_3D( 1, 1, 1, 1, 1, ikmax+1 ) zpsiu_mle(ji,jj,jk) = zpsi_uw(ji,jj,jk) * r1_e2u(ji,jj) zpsiv_mle(ji,jj,jk) = zpsi_vw(ji,jj,jk) * r1_e1v(ji,jj) END_3D IF( ntile == 0 .OR. ntile == nijtile ) THEN ! Do only on the last tile CALL iom_put( "Lf_NHpf" , zLf_NH ) ! Lf = N H / f CALL iom_put( "psiu_mle", zpsiu_mle ) ! i-mle streamfunction CALL iom_put( "psiv_mle", zpsiv_mle ) ! j-mle streamfunction ENDIF ENDIF ! END SUBROUTINE tra_mle_trp SUBROUTINE tra_mle_init !!--------------------------------------------------------------------- !! *** ROUTINE tra_mle_init *** !! !! ** Purpose : Control the consistency between namelist options for !! tracer advection schemes and set nadv !!---------------------------------------------------------------------- INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ierr INTEGER :: ios ! Local integer output status for namelist read REAL(wp) :: z1_t2, zfu, zfv ! - - ! NAMELIST/namtra_mle/ ln_mle , nn_mle, rn_ce, rn_lf, rn_time, rn_lat, nn_mld_uv, nn_conv, rn_rho_c_mle !!---------------------------------------------------------------------- READ ( numnam_ref, namtra_mle, IOSTAT = ios, ERR = 901) 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namtra_mle in reference namelist' ) READ ( numnam_cfg, namtra_mle, IOSTAT = ios, ERR = 902 ) 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namtra_mle in configuration namelist' ) IF(lwm) WRITE ( numond, namtra_mle ) IF(lwp) THEN ! Namelist print WRITE(numout,*) WRITE(numout,*) 'tra_mle_init : mixed layer eddy (MLE) advection acting on tracers' WRITE(numout,*) '~~~~~~~~~~~~~' WRITE(numout,*) ' Namelist namtra_mle : mixed layer eddy advection applied on tracers' WRITE(numout,*) ' use mixed layer eddy (MLE, i.e. Fox-Kemper param) (T/F) ln_mle = ', ln_mle WRITE(numout,*) ' MLE type: =0 standard Fox-Kemper ; =1 new formulation nn_mle = ', nn_mle WRITE(numout,*) ' magnitude of the MLE (typical value: 0.06 to 0.08) rn_ce = ', rn_ce WRITE(numout,*) ' scale of ML front (ML radius of deformation) (rn_mle=0) rn_lf = ', rn_lf, 'm' WRITE(numout,*) ' maximum time scale of MLE (rn_mle=0) rn_time = ', rn_time, 's' WRITE(numout,*) ' reference latitude (degrees) of MLE coef. (rn_mle=1) rn_lat = ', rn_lat, 'deg' WRITE(numout,*) ' space interp. of MLD at u-(v-)pts (0=min,1=averaged,2=max) nn_mld_uv = ', nn_mld_uv WRITE(numout,*) ' =1 no MLE in case of convection ; =0 always MLE nn_conv = ', nn_conv WRITE(numout,*) ' Density difference used to define ML for FK rn_rho_c_mle = ', rn_rho_c_mle ENDIF ! IF(lwp) THEN WRITE(numout,*) IF( ln_mle ) THEN WRITE(numout,*) ' ==>>> Mixed Layer Eddy induced transport added to tracer advection' IF( nn_mle == 0 ) WRITE(numout,*) ' Fox-Kemper et al 2010 formulation' IF( nn_mle == 1 ) WRITE(numout,*) ' New formulation' ELSE WRITE(numout,*) ' ==>>> Mixed Layer Eddy parametrisation NOT used' ENDIF ENDIF ! IF( ln_mle ) THEN ! MLE initialisation ! rb_c = grav * rn_rho_c_mle /rho0 ! Mixed Layer buoyancy criteria IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) ' ML buoyancy criteria = ', rb_c, ' m/s2 ' IF(lwp) WRITE(numout,*) ' associated ML density criteria defined in zdfmxl = ', rho_c, 'kg/m3' ! IF( nn_mle == 0 ) THEN ! MLE array allocation & initialisation ALLOCATE( rfu(jpi,jpj) , rfv(jpi,jpj) , STAT= ierr ) IF( ierr /= 0 ) CALL ctl_stop( 'tra_adv_mle_init: failed to allocate arrays' ) z1_t2 = 1._wp / ( rn_time * rn_time ) DO_2D( 0, 1, 0, 1 ) zfu = ( ff_f(ji,jj) + ff_f(ji,jj-1) ) * 0.5_wp zfv = ( ff_f(ji,jj) + ff_f(ji-1,jj) ) * 0.5_wp rfu(ji,jj) = SQRT( zfu * zfu + z1_t2 ) rfv(ji,jj) = SQRT( zfv * zfv + z1_t2 ) END_2D CALL lbc_lnk_multi( 'tramle', rfu, 'U', 1.0_wp , rfv, 'V', 1.0_wp ) ! ELSEIF( nn_mle == 1 ) THEN ! MLE array allocation & initialisation rc_f = rn_ce / ( 5.e3_wp * 2._wp * omega * SIN( rad * rn_lat ) ) ! ENDIF ! ! ! 1/(f^2+tau^2)^1/2 at t-point (needed in both nn_mle case) ALLOCATE( r1_ft(jpi,jpj) , STAT= ierr ) IF( ierr /= 0 ) CALL ctl_stop( 'tra_adv_mle_init: failed to allocate r1_ft array' ) ! z1_t2 = 1._wp / ( rn_time * rn_time ) r1_ft(:,:) = 1._wp / SQRT( ff_t(:,:) * ff_t(:,:) + z1_t2 ) ! ENDIF ! END SUBROUTINE tra_mle_init !!============================================================================== END MODULE tramle