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MODULE zdfgls
!!======================================================================
!! *** MODULE zdfgls ***
!! Ocean physics: vertical mixing coefficient computed from the gls
!! turbulent closure parameterization
!!======================================================================
!! History : 3.0 ! 2009-09 (G. Reffray) Original code
!! 3.3 ! 2010-10 (C. Bricaud) Add in the reference
!! 4.0 ! 2017-04 (G. Madec) remove CPP keys & avm at t-point only
!! - ! 2017-05 (G. Madec) add top friction as boundary condition
!!----------------------------------------------------------------------
!!----------------------------------------------------------------------
!! zdf_gls : update momentum and tracer Kz from a gls scheme
!! zdf_gls_init : initialization, namelist read, and parameters control
!! gls_rst : read/write gls restart in ocean restart file
!!----------------------------------------------------------------------
USE oce ! ocean dynamics and active tracers
USE dom_oce ! ocean space and time domain
USE zdfdrg , ONLY : ln_drg_OFF ! top/bottom free-slip flag
USE zdfdrg , ONLY : r_z0_top , r_z0_bot ! top/bottom roughness
USE zdfdrg , ONLY : rCdU_top , rCdU_bot ! top/bottom friction
USE sbc_oce ! surface boundary condition: ocean
USE phycst ! physical constants
USE zdfmxl ! mixed layer
USE sbcwave , ONLY : hsw ! significant wave height
#if defined key_si3
USE ice, ONLY: hm_i, h_i
#endif
#if defined key_cice
USE sbc_ice, ONLY: h_i
#endif
!
USE lbclnk ! ocean lateral boundary conditions (or mpp link)
USE lib_mpp ! MPP manager
USE prtctl ! Print control
USE in_out_manager ! I/O manager
USE iom ! I/O manager library
USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
IMPLICIT NONE
PRIVATE
PUBLIC zdf_gls ! called in zdfphy
PUBLIC zdf_gls_init ! called in zdfphy
PUBLIC gls_rst ! called in zdfphy
!
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: hmxl_n !: now mixing length
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: zwall !: wall function
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: ustar2_surf !: Squared surface velocity scale at T-points
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: ustar2_top !: Squared top velocity scale at T-points
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: ustar2_bot !: Squared bottom velocity scale at T-points
! !! ** Namelist namzdf_gls **
LOGICAL :: ln_length_lim ! use limit on the dissipation rate under stable stratification (Galperin et al. 1988)
LOGICAL :: ln_sigpsi ! Activate Burchard (2003) modification for k-eps closure & wave breaking mixing
INTEGER :: nn_mxlice ! type of scaling under sea-ice (=0/1/2/3)
INTEGER :: nn_bc_surf ! surface boundary condition (=0/1)
INTEGER :: nn_bc_bot ! bottom boundary condition (=0/1)
INTEGER :: nn_z0_met ! Method for surface roughness computation
INTEGER :: nn_z0_ice ! Roughness accounting for sea ice
INTEGER :: nn_stab_func ! stability functions G88, KC or Canuto (=0/1/2)
INTEGER :: nn_clos ! closure 0/1/2/3 MY82/k-eps/k-w/gen
REAL(wp) :: rn_clim_galp ! Holt 2008 value for k-eps: 0.267
REAL(wp) :: rn_epsmin ! minimum value of dissipation (m2/s3)
REAL(wp) :: rn_emin ! minimum value of TKE (m2/s2)
REAL(wp) :: rn_charn ! Charnock constant for surface breaking waves mixing : 1400. (standard) or 2.e5 (Stacey value)
REAL(wp) :: rn_crban ! Craig and Banner constant for surface breaking waves mixing
REAL(wp) :: rn_hsro ! Minimum surface roughness
REAL(wp) :: rn_hsri ! Ice ocean roughness
REAL(wp) :: rn_frac_hs ! Fraction of wave height as surface roughness (if nn_z0_met > 1)
REAL(wp) :: rcm_sf = 0.73_wp ! Shear free turbulence parameters
REAL(wp) :: ra_sf = -2.0_wp ! Must be negative -2 < ra_sf < -1
REAL(wp) :: rl_sf = 0.2_wp ! 0 <rl_sf<vkarmn
REAL(wp) :: rghmin = -0.28_wp
REAL(wp) :: rgh0 = 0.0329_wp
REAL(wp) :: rghcri = 0.03_wp
REAL(wp) :: ra1 = 0.92_wp
REAL(wp) :: ra2 = 0.74_wp
REAL(wp) :: rb1 = 16.60_wp
REAL(wp) :: rb2 = 10.10_wp
REAL(wp) :: re2 = 1.33_wp
REAL(wp) :: rl1 = 0.107_wp
REAL(wp) :: rl2 = 0.0032_wp
REAL(wp) :: rl3 = 0.0864_wp
REAL(wp) :: rl4 = 0.12_wp
REAL(wp) :: rl5 = 11.9_wp
REAL(wp) :: rl6 = 0.4_wp
REAL(wp) :: rl7 = 0.0_wp
REAL(wp) :: rl8 = 0.48_wp
REAL(wp) :: rm1 = 0.127_wp
REAL(wp) :: rm2 = 0.00336_wp
REAL(wp) :: rm3 = 0.0906_wp
REAL(wp) :: rm4 = 0.101_wp
REAL(wp) :: rm5 = 11.2_wp
REAL(wp) :: rm6 = 0.4_wp
REAL(wp) :: rm7 = 0.0_wp
REAL(wp) :: rm8 = 0.318_wp
REAL(wp) :: rtrans = 0.1_wp
REAL(wp) :: rc02, rc02r, rc03, rc04 ! coefficients deduced from above parameters
REAL(wp) :: rsbc_tke1, rsbc_tke2, rfact_tke ! - - - -
REAL(wp) :: rsbc_psi1, rsbc_psi2, rfact_psi ! - - - -
REAL(wp) :: rsbc_zs1, rsbc_zs2 ! - - - -
REAL(wp) :: rc0, rc2, rc3, rf6, rcff, rc_diff ! - - - -
REAL(wp) :: rs0, rs1, rs2, rs4, rs5, rs6 ! - - - -
REAL(wp) :: rd0, rd1, rd2, rd3, rd4, rd5 ! - - - -
REAL(wp) :: rsc_tke, rsc_psi, rpsi1, rpsi2, rpsi3, rsc_psi0 ! - - - -
REAL(wp) :: rpsi3m, rpsi3p, rpp, rmm, rnn ! - - - -
!
REAL(wp) :: r2_3 = 2._wp/3._wp ! constant=2/3
!! * Substitutions
# include "do_loop_substitute.h90"
# include "domzgr_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/OCE 4.0 , NEMO Consortium (2018)
!! $Id: zdfgls.F90 15145 2021-07-26 16:16:45Z smasson $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
INTEGER FUNCTION zdf_gls_alloc()
!!----------------------------------------------------------------------
!! *** FUNCTION zdf_gls_alloc ***
!!----------------------------------------------------------------------
ALLOCATE( hmxl_n(A2D(0),jpk) , ustar2_surf(A2D(0)) , &
& zwall (A2D(0),jpk) , ustar2_top (A2D(0)) , ustar2_bot(A2D(0)) , STAT= zdf_gls_alloc )
!
CALL mpp_sum ( 'zdfgls', zdf_gls_alloc )
IF( zdf_gls_alloc /= 0 ) CALL ctl_stop( 'STOP', 'zdf_gls_alloc: failed to allocate arrays' )
END FUNCTION zdf_gls_alloc
SUBROUTINE zdf_gls( kt, Kbb, Kmm, p_sh2, p_avm, p_avt )
!!----------------------------------------------------------------------
!! *** ROUTINE zdf_gls ***
!!
!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
!! coefficients using the GLS turbulent closure scheme.
!!----------------------------------------------------------------------
USE zdf_oce , ONLY : en, avtb, avmb ! ocean vertical physics
!!
INTEGER , INTENT(in ) :: kt ! ocean time step
INTEGER , INTENT(in ) :: Kbb, Kmm ! ocean time level indices
REAL(wp), DIMENSION(A2D(0) ,jpk), INTENT(in ) :: p_sh2 ! shear production term
REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: p_avm ! vertical eddy viscosity (w-points)
REAL(wp), DIMENSION(A2D(0) ,jpk), INTENT(inout) :: p_avt ! vertical eddy diffusivity (w-points)
!
INTEGER :: ji, jj, jk ! dummy loop arguments
INTEGER :: ibot, ibotm1 ! local integers
INTEGER :: itop, itopp1 ! - -
REAL(wp) :: zesh2, zsigpsi, zcoef, zex1 , zex2 ! local scalars
REAL(wp) :: ztx2, zty2, zup, zdown, zcof, zdir ! - -
REAL(wp) :: zratio, zrn2, zflxb, sh , z_en ! - -
REAL(wp) :: prod, buoy, diss, zdiss, sm ! - -
REAL(wp) :: gh, gm, shr, dif, zsqen, zavt, zavm ! - -
REAL(wp) :: zmsku, zmskv ! - -
REAL(wp), DIMENSION(T2D(0)) :: zdep
REAL(wp), DIMENSION(T2D(0)) :: zkar
REAL(wp), DIMENSION(T2D(0)) :: zflxs ! Turbulence fluxed induced by internal waves
REAL(wp), DIMENSION(T2D(0)) :: zhsro ! Surface roughness (surface waves)
REAL(wp), DIMENSION(T2D(0)) :: zice_fra ! Tapering of wave breaking under sea ice
REAL(wp), DIMENSION(T2D(0),jpk) :: eb ! tke at time before
REAL(wp), DIMENSION(T2D(0),jpk) :: hmxl_b ! mixing length at time before
REAL(wp), DIMENSION(T2D(0),jpk) :: eps ! dissipation rate
REAL(wp), DIMENSION(T2D(0),jpk) :: zwall_psi ! Wall function use in the wb case (ln_sigpsi)
REAL(wp), DIMENSION(T2D(0),jpk) :: psi ! psi at time now
REAL(wp), DIMENSION(T2D(0),jpk) :: zd_lw, zd_up, zdiag ! lower, upper and diagonal of the matrix
REAL(wp), DIMENSION(T2D(0),jpk) :: zstt, zstm ! stability function on tracer and momentum
!!--------------------------------------------------------------------
!
! Preliminary computing
ustar2_surf(ji,jj) = 0._wp ; ustar2_top(ji,jj) = 0._wp ; ustar2_bot(ji,jj) = 0._wp
END_2D
psi(ji,jj,jk) = 0._wp ; zwall_psi(ji,jj,jk) = 0._wp
END_3D
SELECT CASE ( nn_z0_ice )
CASE( 0 ) ; zice_fra(:,:) = 0._wp
CASE( 1 ) ; zice_fra(:,:) = TANH( fr_i(T2D(0)) * 10._wp )
CASE( 2 ) ; zice_fra(:,:) = fr_i(T2D(0))
CASE( 3 ) ; zice_fra(:,:) = MIN( 4._wp * fr_i(T2D(0)) , 1._wp )
END SELECT
! Compute surface, top and bottom friction at T-points
DO_2D( 0, 0, 0, 0 ) !== surface ocean friction
ustar2_surf(ji,jj) = r1_rho0 * taum(ji,jj) * tmask(ji,jj,1) ! surface friction
END_2D
!
!!gm Rq we may add here r_ke0(_top/_bot) ? ==>> think about that...
!
IF( .NOT.ln_drg_OFF ) THEN !== top/bottom friction (explicit before friction)
DO_2D( 0, 0, 0, 0 ) ! bottom friction (explicit before friction)
zmsku = 0.5_wp * ( 2._wp - umask(ji-1,jj,mbkt(ji,jj)) * umask(ji,jj,mbkt(ji,jj)) )
zmskv = 0.5_wp * ( 2._wp - vmask(ji,jj-1,mbkt(ji,jj)) * vmask(ji,jj,mbkt(ji,jj)) ) ! (CAUTION: CdU<0)
ustar2_bot(ji,jj) = - rCdU_bot(ji,jj) * SQRT( ( zmsku*( uu(ji,jj,mbkt(ji,jj),Kbb)+uu(ji-1,jj,mbkt(ji,jj),Kbb) ) )**2 &
& + ( zmskv*( vv(ji,jj,mbkt(ji,jj),Kbb)+vv(ji,jj-1,mbkt(ji,jj),Kbb) ) )**2 )
END_2D
IF( ln_isfcav ) THEN
zmsku = 0.5_wp * ( 2. - umask(ji-1,jj,mikt(ji,jj)) * umask(ji,jj,mikt(ji,jj)) )
zmskv = 0.5_wp * ( 2. - vmask(ji,jj-1,mikt(ji,jj)) * vmask(ji,jj,mikt(ji,jj)) ) ! (CAUTION: CdU<0)
ustar2_top(ji,jj) = - rCdU_top(ji,jj) * SQRT( ( zmsku*( uu(ji,jj,mikt(ji,jj),Kbb)+uu(ji-1,jj,mikt(ji,jj),Kbb) ) )**2 &
& + ( zmskv*( vv(ji,jj,mikt(ji,jj),Kbb)+vv(ji,jj-1,mikt(ji,jj),Kbb) ) )**2 )
END_2D
ENDIF
ENDIF
SELECT CASE ( nn_z0_met ) !== Set surface roughness length ==!
CASE ( 0 ) ! Constant roughness
zhsro(:,:) = rn_hsro
CASE ( 1 ) ! Standard Charnock formula
zhsro(ji,jj) = MAX( rsbc_zs1 * ustar2_surf(ji,jj) , rn_hsro )
END_2D
CASE ( 2 ) ! Roughness formulae according to Rascle et al., Ocean Modelling (2008)
!!gm faster coding : the 2 comment lines should be used
!!gm zcof = 2._wp * 0.6_wp / 28._wp
!!gm zdep(:,:) = 30._wp * TANH( zcof/ SQRT( MAX(ustar2_surf(:,:),rsmall) ) ) ! Wave age (eq. 10)
zcof = 30.*TANH( 2.*0.3/(28.*SQRT(MAX(ustar2_surf(ji,jj),rsmall))) ) ! Wave age (eq. 10)
zhsro(ji,jj) = MAX(rsbc_zs2 * ustar2_surf(ji,jj) * zcof**1.5, rn_hsro) ! zhsro = rn_frac_hs * Hsw (eq. 11)
END_2D
CASE ( 3 ) ! Roughness given by the wave model (coupled or read in file)
DO_2D( 0, 0, 0, 0 )
zhsro(ji,jj) = MAX(rn_frac_hs * hsw(ji,jj), rn_hsro) ! (rn_frac_hs=1.6 see Eq. (5) of Rascle et al. 2008 )
END_2D
END SELECT
!
! adapt roughness where there is sea ice
SELECT CASE( nn_mxlice ) ! Type of scaling under sea-ice
!
CASE( 1 ) ! scaling with constant sea-ice roughness
zhsro(ji,jj) = ( (1._wp-zice_fra(ji,jj)) * zhsro(ji,jj) + zice_fra(ji,jj) * rn_hsri )*tmask(ji,jj,1) + (1._wp - tmask(ji,jj,1))*rn_hsro
END_2D
!
CASE( 2 ) ! scaling with mean sea-ice thickness
#if defined key_si3
zhsro(ji,jj) = ( (1._wp-zice_fra(ji,jj)) * zhsro(ji,jj) + zice_fra(ji,jj) * hm_i(ji,jj) )*tmask(ji,jj,1) + (1._wp - tmask(ji,jj,1))*rn_hsro
END_2D
#endif
!
CASE( 3 ) ! scaling with max sea-ice thickness
#if defined key_si3 || defined key_cice
zhsro(ji,jj) = ( (1._wp-zice_fra(ji,jj)) * zhsro(ji,jj) + zice_fra(ji,jj) * MAXVAL(h_i(ji,jj,:)) )*tmask(ji,jj,1) + (1._wp - tmask(ji,jj,1))*rn_hsro
END_2D
#endif
!
END SELECT
!
DO_3D( 0, 0, 0, 0, 2, jpkm1 ) !== Compute dissipation rate ==!
eps(ji,jj,jk) = rc03 * en(ji,jj,jk) * SQRT( en(ji,jj,jk) ) / hmxl_n(ji,jj,jk)
END_3D
! Save tke at before time step
eb (ji,jj,jk) = en (ji,jj,jk)
hmxl_b(ji,jj,jk) = hmxl_n(ji,jj,jk)
END_3D
IF( nn_clos == 0 ) THEN ! Mellor-Yamada
zup = hmxl_n(ji,jj,jk) * gdepw(ji,jj,mbkt(ji,jj)+1,Kmm)
zdown = vkarmn * gdepw(ji,jj,jk,Kmm) * ( -gdepw(ji,jj,jk,Kmm) + gdepw(ji,jj,mbkt(ji,jj)+1,Kmm) )
zcoef = ( zup / MAX( zdown, rsmall ) )
zwall (ji,jj,jk) = ( 1._wp + re2 * zcoef*zcoef ) * tmask(ji,jj,jk)
END_3D
ENDIF
!!---------------------------------!!
!! Equation to prognostic k !!
!!---------------------------------!!
!
! Now Turbulent kinetic energy (output in en)
! -------------------------------
! Resolution of a tridiagonal linear system by a "methode de chasse"
! computation from level 2 to jpkm1 (e(1) computed after and e(jpk)=0 ).
! The surface boundary condition are set after
! The bottom boundary condition are also set after. In standard e(bottom)=0.
! zdiag : diagonal zd_up : upper diagonal zd_lw : lower diagonal
! Warning : after this step, en : right hand side of the matrix
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!
buoy = - p_avt(ji,jj,jk) * rn2(ji,jj,jk) ! stratif. destruction
!
diss = eps(ji,jj,jk) ! dissipation
!
zdir = 0.5_wp + SIGN( 0.5_wp, p_sh2(ji,jj,jk) + buoy ) ! zdir =1(=0) if shear(ji,jj,jk)+buoy >0(<0)
!
zesh2 = zdir*(p_sh2(ji,jj,jk)+buoy)+(1._wp-zdir)*p_sh2(ji,jj,jk) ! production term
zdiss = zdir*(diss/en(ji,jj,jk)) +(1._wp-zdir)*(diss-buoy)/en(ji,jj,jk) ! dissipation term
!!gm better coding, identical results
! zesh2 = p_sh2(ji,jj,jk) + zdir*buoy ! production term
! zdiss = ( diss - (1._wp-zdir)*buoy ) / en(ji,jj,jk) ! dissipation term
!!gm
!
! Compute a wall function from 1. to rsc_psi*zwall/rsc_psi0
! Note that as long that Dirichlet boundary conditions are NOT set at the first and last levels (GOTM style)
! there is no need to set a boundary condition for zwall_psi at the top and bottom boundaries.
! Otherwise, this should be rsc_psi/rsc_psi0
IF( ln_sigpsi ) THEN
zsigpsi = MIN( 1._wp, zesh2 / eps(ji,jj,jk) ) ! 0. <= zsigpsi <= 1.
zwall_psi(ji,jj,jk) = rsc_psi / &
& ( zsigpsi * rsc_psi + (1._wp-zsigpsi) * rsc_psi0 / MAX( zwall(ji,jj,jk), 1._wp ) )
ELSE
zwall_psi(ji,jj,jk) = 1._wp
ENDIF
!
! building the matrix
zcof = rfact_tke * tmask(ji,jj,jk)
! ! lower diagonal, in fact not used for jk = 2 (see surface conditions)
zd_lw(ji,jj,jk) = zcof * ( p_avm(ji,jj,jk ) + p_avm(ji,jj,jk-1) ) &
& / ( e3t(ji,jj,jk-1,Kmm) * e3w(ji,jj,jk,Kmm) )
! ! upper diagonal, in fact not used for jk = ibotm1 (see bottom conditions)
zd_up(ji,jj,jk) = zcof * ( p_avm(ji,jj,jk+1) + p_avm(ji,jj,jk ) ) &
& / ( e3t(ji,jj,jk ,Kmm) * e3w(ji,jj,jk,Kmm) )
! ! diagonal
zdiag(ji,jj,jk) = 1._wp - zd_lw(ji,jj,jk) - zd_up(ji,jj,jk) + rn_Dt * zdiss * wmask(ji,jj,jk)
! ! right hand side in en
en(ji,jj,jk) = en(ji,jj,jk) + rn_Dt * zesh2 * wmask(ji,jj,jk)
END_3D
!
zdiag(ji,jj,jpk) = 1._wp
!
! Set surface condition on zwall_psi (1 at the bottom)
zwall_psi(ji,jj, 1 ) = zwall_psi(ji,jj,2)
zwall_psi(ji,jj,jpk) = 1._wp
END_2D
!
! Surface boundary condition on tke
! ---------------------------------
!
SELECT CASE ( nn_bc_surf )
!
CASE ( 0 ) ! Dirichlet boundary condition (set e at k=1 & 2)
! First level
en (ji,jj,1) = MAX( rn_emin , rc02r * ustar2_surf(ji,jj) * (1._wp + (1._wp-zice_fra(ji,jj))*rsbc_tke1)**r2_3 )
zd_lw(ji,jj,1) = en(ji,jj,1)
zd_up(ji,jj,1) = 0._wp
zdiag(ji,jj,1) = 1._wp
!
! One level below
en (ji,jj,2) = MAX( rn_emin , rc02r * ustar2_surf(ji,jj) * (1._wp + (1._wp-zice_fra(ji,jj))*rsbc_tke1 &
& * ((zhsro(ji,jj)+gdepw(ji,jj,2,Kmm)) / zhsro(ji,jj) )**(1.5_wp*ra_sf) )**r2_3 )
zd_lw(ji,jj,2) = 0._wp
zd_up(ji,jj,2) = 0._wp
zdiag(ji,jj,2) = 1._wp
END_2D
!
IF( ln_isfcav) THEN ! top boundary (ocean cavity)
IF( mikt(ji,jj) > 1 )THEN
itop = mikt(ji,jj) ! k top w-point
itopp1 = mikt(ji,jj) + 1 ! k+1 1st w-point below the top one
! ! mask at the
! ocean surface
! points
z_en = MAX( rc02r * ustar2_top(ji,jj), rn_emin ) * ( 1._wp - tmask(ji,jj,1) )
!
! Dirichlet condition applied at:
! top level (itop) & Just below it (itopp1)
zd_lw(ji,jj,itop) = 0._wp ; zd_lw(ji,jj,itopp1) = 0._wp
zd_up(ji,jj,itop) = 0._wp ; zd_up(ji,jj,itopp1) = 0._wp
zdiag(ji,jj,itop) = 1._wp ; zdiag(ji,jj,itopp1) = 1._wp
en (ji,jj,itop) = z_en ; en (ji,jj,itopp1) = z_en
ENDIF
END_2D
ENDIF
!
CASE ( 1 ) ! Neumann boundary condition (set d(e)/dz)
!
! Dirichlet conditions at k=1
en (ji,jj,1) = MAX( rn_emin , rc02r * ustar2_surf(ji,jj) * (1._wp + (1._wp-zice_fra(ji,jj))*rsbc_tke1)**r2_3 )
zd_lw(ji,jj,1) = en(ji,jj,1)
zd_up(ji,jj,1) = 0._wp
zdiag(ji,jj,1) = 1._wp
!
! at k=2, set de/dz=Fw
!cbr
! zdiag zd_lw not defined/used on the halo
zdiag(ji,jj,2) = zdiag(ji,jj,2) + zd_lw(ji,jj,2) ! Remove zd_lw from zdiag
zd_lw(ji,jj,2) = 0._wp
!
zkar (ji,jj) = (rl_sf + (vkarmn-rl_sf)*(1.-EXP(-rtrans*gdept(ji,jj,1,Kmm)/zhsro(ji,jj)) ))
zflxs(ji,jj) = rsbc_tke2 * (1._wp-zice_fra(ji,jj)) * ustar2_surf(ji,jj)**1.5_wp * zkar(ji,jj) &
& * ( ( zhsro(ji,jj)+gdept(ji,jj,1,Kmm) ) / zhsro(ji,jj) )**(1.5_wp*ra_sf)
!!gm why not : * ( 1._wp + gdept(:,:,1,Kmm) / zhsro(:,:) )**(1.5_wp*ra_sf)
en(ji,jj,2) = en(ji,jj,2) + zflxs(ji,jj) / e3w(ji,jj,2,Kmm)
END_2D
!
IF( ln_isfcav) THEN ! top boundary (ocean cavity)
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IF( mikt(ji,jj) > 1 )THEN
itop = mikt(ji,jj) ! k top w-point
itopp1 = mikt(ji,jj) + 1 ! k+1 1st w-point below the top one
! ! mask at the
! ocean surface
! points
z_en = MAX( rc02r * ustar2_top(ji,jj), rn_emin ) * ( 1._wp - tmask(ji,jj,1) )
!
! Bottom level Dirichlet condition:
! Bottom level (ibot) & Just above it (ibotm1)
! Dirichlet ! Neumann
zd_lw(ji,jj,itop) = 0._wp ! ! Remove zd_up from zdiag
zdiag(ji,jj,itop) = 1._wp ; zdiag(ji,jj,itopp1) = zdiag(ji,jj,itopp1) + zd_up(ji,jj,itopp1)
zd_up(ji,jj,itop) = 0._wp ; zd_up(ji,jj,itopp1) = 0._wp
en (ji,jj,itop) = z_en
ENDIF
END_2D
ENDIF
!
END SELECT
! Bottom boundary condition on tke
! --------------------------------
!
SELECT CASE ( nn_bc_bot )
!
CASE ( 0 ) ! Dirichlet
! ! en(ibot) = u*^2 / Co2 and hmxl_n(ibot) = rn_lmin
! ! Balance between the production and the dissipation terms
!!gm This means that bottom and ocean w-level above have a specified "en" value. Sure ????
!! With thick deep ocean level thickness, this may be quite large, no ???
!! in particular in ocean cavities where top stratification can be large...
ibot = mbkt(ji,jj) + 1 ! k bottom level of w-point
ibotm1 = mbkt(ji,jj) ! k-1 bottom level of w-point but >=1
!
z_en = MAX( rc02r * ustar2_bot(ji,jj), rn_emin )
!
! Dirichlet condition applied at:
! Bottom level (ibot) & Just above it (ibotm1)
zd_lw(ji,jj,ibot) = 0._wp ; zd_lw(ji,jj,ibotm1) = 0._wp
zd_up(ji,jj,ibot) = 0._wp ; zd_up(ji,jj,ibotm1) = 0._wp
zdiag(ji,jj,ibot) = 1._wp ; zdiag(ji,jj,ibotm1) = 1._wp
en (ji,jj,ibot) = z_en ; en (ji,jj,ibotm1) = z_en
END_2D
!
CASE ( 1 ) ! Neumman boundary condition
!
ibot = mbkt(ji,jj) + 1 ! k bottom level of w-point
ibotm1 = mbkt(ji,jj) ! k-1 bottom level of w-point but >=1
!
z_en = MAX( rc02r * ustar2_bot(ji,jj), rn_emin )
!
! Bottom level Dirichlet condition:
! Bottom level (ibot) & Just above it (ibotm1)
! Dirichlet ! Neumann
zd_lw(ji,jj,ibot) = 0._wp ! ! Remove zd_up from zdiag
zdiag(ji,jj,ibot) = 1._wp ; zdiag(ji,jj,ibotm1) = zdiag(ji,jj,ibotm1) + zd_up(ji,jj,ibotm1)
zd_up(ji,jj,ibot) = 0._wp ; zd_up(ji,jj,ibotm1) = 0._wp
en (ji,jj,ibot) = z_en
END_2D
!
END SELECT
! Matrix inversion (en prescribed at surface and the bottom)
! ----------------------------------------------------------
!
DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1
zdiag(ji,jj,jk) = zdiag(ji,jj,jk) - zd_lw(ji,jj,jk) * zd_up(ji,jj,jk-1) / zdiag(ji,jj,jk-1)
END_3D
DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! Second recurrence : Lk = RHSk - Lk / Dk-1 * Lk-1
zd_lw(ji,jj,jk) = en(ji,jj,jk) - zd_lw(ji,jj,jk) / zdiag(ji,jj,jk-1) * zd_lw(ji,jj,jk-1)
END_3D
DO_3DS( 0, 0, 0, 0, jpkm1, 2, -1 ) ! Third recurrence : Ek = ( Lk - Uk * Ek+1 ) / Dk
en(ji,jj,jk) = ( zd_lw(ji,jj,jk) - zd_up(ji,jj,jk) * en(ji,jj,jk+1) ) / zdiag(ji,jj,jk)
END_3D
! ! set the minimum value of tke
en(ji,jj,jk) = MAX( en(ji,jj,jk), rn_emin )
END_3D
!!----------------------------------------!!
!! Solve prognostic equation for psi !!
!!----------------------------------------!!
! Set psi to previous time step value
!
SELECT CASE ( nn_clos )
!
CASE( 0 ) ! k-kl (Mellor-Yamada)
psi(ji,jj,jk) = eb(ji,jj,jk) * hmxl_b(ji,jj,jk)
END_3D
!
CASE( 1 ) ! k-eps
psi(ji,jj,jk) = eps(ji,jj,jk)
END_3D
!
CASE( 2 ) ! k-w
psi(ji,jj,jk) = SQRT( eb(ji,jj,jk) ) / ( rc0 * hmxl_b(ji,jj,jk) )
END_3D
!
CASE( 3 ) ! generic
psi(ji,jj,jk) = rc02 * eb(ji,jj,jk) * hmxl_b(ji,jj,jk)**rnn
END_3D
!
END SELECT
!
! Now gls (output in psi)
! -------------------------------
! Resolution of a tridiagonal linear system by a "methode de chasse"
! computation from level 2 to jpkm1 (e(1) already computed and e(jpk)=0 ).
! zdiag : diagonal zd_up : upper diagonal zd_lw : lower diagonal
! Warning : after this step, en : right hand side of the matrix
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!
! psi / k
zratio = psi(ji,jj,jk) / eb(ji,jj,jk)
!
! psi3+ : stable : B=-KhN²<0 => N²>0 if rn2>0 zdir = 1 (stable) otherwise zdir = 0 (unstable)
zdir = 0.5_wp + SIGN( 0.5_wp, rn2(ji,jj,jk) )
!
rpsi3 = zdir * rpsi3m + ( 1._wp - zdir ) * rpsi3p
!
! shear prod. - stratif. destruction
prod = rpsi1 * zratio * p_sh2(ji,jj,jk)
!
! stratif. destruction
buoy = rpsi3 * zratio * (- p_avt(ji,jj,jk) * rn2(ji,jj,jk) )
!
! shear prod. - stratif. destruction
diss = rpsi2 * zratio * zwall(ji,jj,jk) * eps(ji,jj,jk)
!
zdir = 0.5_wp + SIGN( 0.5_wp, prod + buoy ) ! zdir =1(=0) if shear(ji,jj,jk)+buoy >0(<0)
!
zesh2 = zdir * ( prod + buoy ) + (1._wp - zdir ) * prod ! production term
zdiss = zdir * ( diss / psi(ji,jj,jk) ) + (1._wp - zdir ) * (diss-buoy) / psi(ji,jj,jk) ! dissipation term
!
! building the matrix
zcof = rfact_psi * zwall_psi(ji,jj,jk) * tmask(ji,jj,jk)
! ! lower diagonal
zd_lw(ji,jj,jk) = zcof * ( p_avm(ji,jj,jk ) + p_avm(ji,jj,jk-1) ) &
& / ( e3t(ji,jj,jk-1,Kmm) * e3w(ji,jj,jk,Kmm) )
! ! upper diagonal
zd_up(ji,jj,jk) = zcof * ( p_avm(ji,jj,jk+1) + p_avm(ji,jj,jk ) ) &
& / ( e3t(ji,jj,jk ,Kmm) * e3w(ji,jj,jk,Kmm) )
! ! diagonal
zdiag(ji,jj,jk) = 1._wp - zd_lw(ji,jj,jk) - zd_up(ji,jj,jk) + rn_Dt * zdiss * wmask(ji,jj,jk)
! ! right hand side in psi
psi(ji,jj,jk) = psi(ji,jj,jk) + rn_Dt * zesh2 * wmask(ji,jj,jk)
END_3D
!
zdiag(ji,jj,jpk) = 1._wp
END_2D
! Surface boundary condition on psi
! ---------------------------------
!
SELECT CASE ( nn_bc_surf )
!
CASE ( 0 ) ! Dirichlet boundary conditions
!
! Surface value
zdep (ji,jj) = zhsro(ji,jj) * rl_sf ! Cosmetic
psi (ji,jj,1) = rc0**rpp * en(ji,jj,1)**rmm * zdep(ji,jj)**rnn * tmask(ji,jj,1)
zd_lw(ji,jj,1) = psi(ji,jj,1)
zd_up(ji,jj,1) = 0._wp
zdiag(ji,jj,1) = 1._wp
!
! One level below
zkar (ji,jj) = (rl_sf + (vkarmn-rl_sf)*(1._wp-EXP(-rtrans*gdepw(ji,jj,2,Kmm)/zhsro(ji,jj) )))
zdep (ji,jj) = (zhsro(ji,jj) + gdepw(ji,jj,2,Kmm)) * zkar(ji,jj)
psi (ji,jj,2) = rc0**rpp * en(ji,jj,2)**rmm * zdep(ji,jj)**rnn * tmask(ji,jj,1)
zd_lw(ji,jj,2) = 0._wp
zd_up(ji,jj,2) = 0._wp
zdiag(ji,jj,2) = 1._wp
END_2D
!
CASE ( 1 ) ! Neumann boundary condition on d(psi)/dz
!
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! Surface value: Dirichlet
zdep (ji,jj) = zhsro(ji,jj) * rl_sf
psi (ji,jj,1) = rc0**rpp * en(ji,jj,1)**rmm * zdep(ji,jj)**rnn * tmask(ji,jj,1)
zd_lw(ji,jj,1) = psi(ji,jj,1)
zd_up(ji,jj,1) = 0._wp
zdiag(ji,jj,1) = 1._wp
!
! Neumann condition at k=2, zdiag zd_lw not defined/used on the halo
zdiag(ji,jj,2) = zdiag(ji,jj,2) + zd_lw(ji,jj,2) ! Remove zd_lw from zdiag
zd_lw(ji,jj,2) = 0._wp
!
! Set psi vertical flux at the surface:
zkar (ji,jj) = rl_sf + (vkarmn-rl_sf)*(1._wp-EXP(-rtrans*gdept(ji,jj,1,Kmm)/zhsro(ji,jj) )) ! Lengh scale slope
zdep (ji,jj) = ((zhsro(ji,jj) + gdept(ji,jj,1,Kmm)) / zhsro(ji,jj))**(rmm*ra_sf)
zflxs(ji,jj) = (rnn + (1._wp-zice_fra(ji,jj))*rsbc_tke1 * (rnn + rmm*ra_sf) * zdep(ji,jj)) &
& *(1._wp + (1._wp-zice_fra(ji,jj))*rsbc_tke1*zdep(ji,jj))**(2._wp*rmm/3._wp-1_wp)
zdep (ji,jj) = rsbc_psi1 * (zwall_psi(ji,jj,1)*p_avm(ji,jj,1)+zwall_psi(ji,jj,2)*p_avm(ji,jj,2)) * &
& ustar2_surf(ji,jj)**rmm * zkar(ji,jj)**rnn * (zhsro(ji,jj) + gdept(ji,jj,1,Kmm))**(rnn-1.)
zflxs(ji,jj) = zdep(ji,jj) * zflxs(ji,jj)
psi (ji,jj,2) = psi(ji,jj,2) + zflxs(ji,jj) / e3w(ji,jj,2,Kmm)
END_2D
!
END SELECT
! Bottom boundary condition on psi
! --------------------------------
!
!!gm should be done for ISF (top boundary cond.)
!!gm so, totally new staff needed ===>>> think about that !
!
SELECT CASE ( nn_bc_bot ) ! bottom boundary
!
CASE ( 0 ) ! Dirichlet
! ! en(ibot) = u*^2 / Co2 and hmxl_n(ibot) = vkarmn * r_z0_bot
! ! Balance between the production and the dissipation terms
ibot = mbkt(ji,jj) + 1 ! k bottom level of w-point
ibotm1 = mbkt(ji,jj) ! k-1 bottom level of w-point but >=1
zdep(ji,jj) = vkarmn * r_z0_bot
psi (ji,jj,ibot) = rc0**rpp * en(ji,jj,ibot)**rmm * zdep(ji,jj)**rnn
zd_lw(ji,jj,ibot) = 0._wp
zd_up(ji,jj,ibot) = 0._wp
zdiag(ji,jj,ibot) = 1._wp
!
! Just above last level, Dirichlet condition again (GOTM like)
zdep(ji,jj) = vkarmn * ( r_z0_bot + e3t(ji,jj,ibotm1,Kmm) )
psi (ji,jj,ibotm1) = rc0**rpp * en(ji,jj,ibot )**rmm * zdep(ji,jj)**rnn
zd_lw(ji,jj,ibotm1) = 0._wp
zd_up(ji,jj,ibotm1) = 0._wp
zdiag(ji,jj,ibotm1) = 1._wp
END_2D
!
IF( ln_isfcav) THEN ! top boundary (ocean cavity)
IF ( mikt(ji,jj) > 1 ) THEN
itop = mikt(ji,jj) ! k top w-point
itopp1 = mikt(ji,jj) + 1 ! k+1 1st w-point below the top one
!
zdep(ji,jj) = vkarmn * r_z0_top
psi (ji,jj,itop) = rc0**rpp * en(ji,jj,itop)**rmm *zdep(ji,jj)**rnn
zd_lw(ji,jj,itop) = 0._wp
zd_up(ji,jj,itop) = 0._wp
zdiag(ji,jj,itop) = 1._wp
!
! Just above last level, Dirichlet condition again (GOTM like)
zdep(ji,jj) = vkarmn * ( r_z0_top + e3t(ji,jj,itopp1,Kmm) )
psi (ji,jj,itopp1) = rc0**rpp * en(ji,jj,itop )**rmm *zdep(ji,jj)**rnn
zd_lw(ji,jj,itopp1) = 0._wp
zd_up(ji,jj,itopp1) = 0._wp
zdiag(ji,jj,itopp1) = 1._wp
END IF
END_2D
END IF
!
CASE ( 1 ) ! Neumman boundary condition
!
ibot = mbkt(ji,jj) + 1 ! k bottom level of w-point
ibotm1 = mbkt(ji,jj) ! k-1 bottom level of w-point but >=1
!
! Bottom level Dirichlet condition:
zdep(ji,jj) = vkarmn * r_z0_bot
psi (ji,jj,ibot) = rc0**rpp * en(ji,jj,ibot)**rmm * zdep(ji,jj)**rnn
!
zd_lw(ji,jj,ibot) = 0._wp
zd_up(ji,jj,ibot) = 0._wp
zdiag(ji,jj,ibot) = 1._wp
!
! Just above last level: Neumann condition with flux injection
zdiag(ji,jj,ibotm1) = zdiag(ji,jj,ibotm1) + zd_up(ji,jj,ibotm1) ! Remove zd_up from zdiag
zd_up(ji,jj,ibotm1) = 0.
!
! Set psi vertical flux at the bottom:
zdep(ji,jj) = r_z0_bot + 0.5_wp*e3t(ji,jj,ibotm1,Kmm)
zflxb = rsbc_psi2 * ( p_avm(ji,jj,ibot) + p_avm(ji,jj,ibotm1) ) &
& * (0.5_wp*(en(ji,jj,ibot)+en(ji,jj,ibotm1)))**rmm * zdep(ji,jj)**(rnn-1._wp)
psi(ji,jj,ibotm1) = psi(ji,jj,ibotm1) + zflxb / e3w(ji,jj,ibotm1,Kmm)
END_2D
!
IF( ln_isfcav) THEN ! top boundary (ocean cavity)
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IF ( mikt(ji,jj) > 1 ) THEN
itop = mikt(ji,jj) ! k top w-point
itopp1 = mikt(ji,jj) + 1 ! k+1 1st w-point below the top one
!
! Bottom level Dirichlet condition:
zdep(ji,jj) = vkarmn * r_z0_top
psi (ji,jj,itop) = rc0**rpp * en(ji,jj,itop)**rmm *zdep(ji,jj)**rnn
!
zd_lw(ji,jj,itop) = 0._wp
zd_up(ji,jj,itop) = 0._wp
zdiag(ji,jj,itop) = 1._wp
!
! Just below cavity level: Neumann condition with flux
! injection
zdiag(ji,jj,itopp1) = zdiag(ji,jj,itopp1) + zd_up(ji,jj,itopp1) ! Remove zd_up from zdiag
zd_up(ji,jj,itopp1) = 0._wp
!
! Set psi vertical flux below cavity:
zdep(ji,jj) = r_z0_top + 0.5_wp*e3t(ji,jj,itopp1,Kmm)
zflxb = rsbc_psi2 * ( p_avm(ji,jj,itop) + p_avm(ji,jj,itopp1)) &
& * (0.5_wp*(en(ji,jj,itop)+en(ji,jj,itopp1)))**rmm * zdep(ji,jj)**(rnn-1._wp)
psi(ji,jj,itopp1) = psi(ji,jj,itopp1) + zflxb / e3w(ji,jj,itopp1,Kmm)
END IF
END_2D
END IF
!
END SELECT
! Matrix inversion
! ----------------
!
DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1
zdiag(ji,jj,jk) = zdiag(ji,jj,jk) - zd_lw(ji,jj,jk) * zd_up(ji,jj,jk-1) / zdiag(ji,jj,jk-1)
END_3D
DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! Second recurrence : Lk = RHSk - Lk / Dk-1 * Lk-1
zd_lw(ji,jj,jk) = psi(ji,jj,jk) - zd_lw(ji,jj,jk) / zdiag(ji,jj,jk-1) * zd_lw(ji,jj,jk-1)
END_3D
DO_3DS( 0, 0, 0, 0, jpkm1, 2, -1 ) ! Third recurrence : Ek = ( Lk - Uk * Ek+1 ) / Dk
psi(ji,jj,jk) = ( zd_lw(ji,jj,jk) - zd_up(ji,jj,jk) * psi(ji,jj,jk+1) ) / zdiag(ji,jj,jk)
END_3D
! Set dissipation
!----------------
SELECT CASE ( nn_clos )
!
CASE( 0 ) ! k-kl (Mellor-Yamada)
eps(ji,jj,jk) = rc03 * en(ji,jj,jk) * en(ji,jj,jk) * SQRT( en(ji,jj,jk) ) / MAX( psi(ji,jj,jk), rn_epsmin)
END_3D
!
CASE( 1 ) ! k-eps
eps(ji,jj,jk) = psi(ji,jj,jk)
END_3D
!
CASE( 2 ) ! k-w
eps(ji,jj,jk) = rc04 * en(ji,jj,jk) * psi(ji,jj,jk)
END_3D
!
CASE( 3 ) ! generic
zcoef = rc0**( 3._wp + rpp/rnn )
zex1 = ( 1.5_wp + rmm/rnn )
zex2 = -1._wp / rnn
eps(ji,jj,jk) = zcoef * en(ji,jj,jk)**zex1 * psi(ji,jj,jk)**zex2
END_3D
!
END SELECT
! Limit dissipation rate under stable stratification
! --------------------------------------------------
DO_3D( 0, 0, 0, 0, 1, jpkm1 ) ! Note that this set boundary conditions on hmxl_n at the same time
! limitation
eps (ji,jj,jk) = MAX( eps(ji,jj,jk), rn_epsmin )
hmxl_n(ji,jj,jk) = rc03 * en(ji,jj,jk) * SQRT( en(ji,jj,jk) ) / eps(ji,jj,jk)
END_3D
IF( ln_length_lim ) THEN ! Galperin criterium (NOTE : Not required if the proper value of C3 in stable cases is calculated)
zrn2 = MAX( rn2(ji,jj,jk), rsmall )
hmxl_n(ji,jj,jk) = MIN( rn_clim_galp * SQRT( 2._wp * en(ji,jj,jk) / zrn2 ), hmxl_n(ji,jj,jk) )
END_3D
ENDIF
!
! Stability function and vertical viscosity and diffusivity
! ---------------------------------------------------------
!
SELECT CASE ( nn_stab_func )
!
CASE ( 0 , 1 ) ! Galperin or Kantha-Clayson stability functions
! zcof = l²/q²
zcof = hmxl_b(ji,jj,jk) * hmxl_b(ji,jj,jk) / ( 2._wp*eb(ji,jj,jk) )
! Gh = -N²l²/q²
gh = - rn2(ji,jj,jk) * zcof
gh = MIN( gh, rgh0 )
gh = MAX( gh, rghmin )
! Stability functions from Kantha and Clayson (if C2=C3=0 => Galperin)
sh = ra2*( 1._wp-6._wp*ra1/rb1 ) / ( 1.-3.*ra2*gh*(6.*ra1+rb2*( 1._wp-rc3 ) ) )
sm = ( rb1**(-1._wp/3._wp) + ( 18._wp*ra1*ra1 + 9._wp*ra1*ra2*(1._wp-rc2) )*sh*gh ) / (1._wp-9._wp*ra1*ra2*gh)
!
! Store stability function in zstt and zstm
zstt(ji,jj,jk) = rc_diff * sh * tmask(ji,jj,jk)
zstm(ji,jj,jk) = rc_diff * sm * tmask(ji,jj,jk)
END_3D
!
CASE ( 2, 3 ) ! Canuto stability functions
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! zcof = l²/q²
zcof = hmxl_b(ji,jj,jk)*hmxl_b(ji,jj,jk) / ( 2._wp * eb(ji,jj,jk) )
! Gh = -N²l²/q²
gh = - rn2(ji,jj,jk) * zcof
gh = MIN( gh, rgh0 )
gh = MAX( gh, rghmin )
gh = gh * rf6
! Gm = M²l²/q² Shear number
shr = p_sh2(ji,jj,jk) / MAX( p_avm(ji,jj,jk), rsmall )
gm = MAX( shr * zcof , 1.e-10 )
gm = gm * rf6
gm = MIN ( (rd0 - rd1*gh + rd3*gh*gh) / (rd2-rd4*gh) , gm )
! Stability functions from Canuto
rcff = rd0 - rd1*gh +rd2*gm + rd3*gh*gh - rd4*gh*gm + rd5*gm*gm
sm = (rs0 - rs1*gh + rs2*gm) / rcff
sh = (rs4 - rs5*gh + rs6*gm) / rcff
!
! Store stability function in zstt and zstm
zstt(ji,jj,jk) = rc_diff * sh * tmask(ji,jj,jk)
zstm(ji,jj,jk) = rc_diff * sm * tmask(ji,jj,jk)
END_3D
!
END SELECT
! Boundary conditions on stability functions for momentum (Neumann):
! Lines below are useless if GOTM style Dirichlet conditions are used
zstm(ji,jj,1) = zstm(ji,jj,2)
zstm(ji,jj,jpk) = 0. ! default value, in case jpk > mbkt(ji,jj)+1
! ! Not needed but avoid a bug when looking for undefined values (-fpe0)
END_2D
DO_2D( 0, 0, 0, 0 ) ! update bottom with good values
zstm(ji,jj,mbkt(ji,jj)+1) = zstm(ji,jj,mbkt(ji,jj))
END_2D
zstt(:,:, 1) = wmask(A2D(0), 1) ! default value not needed but avoid a bug when looking for undefined values (-fpe0)
zstt(:,:,jpk) = wmask(A2D(0),jpk) ! default value not needed but avoid a bug when looking for undefined values (-fpe0)
!!gm should be done for ISF (top boundary cond.)
!!gm so, totally new staff needed!!gm
! Compute diffusivities/viscosities
! The computation below could be restrained to jk=2 to jpkm1 if GOTM style Dirichlet conditions are used
! -> yes BUT p_avm(:,:1) and p_avm(:,:jpk) are used when we compute zd_lw(:,:2) and zd_up(:,:jpkm1). These values are
! later overwritten by surface/bottom boundaries conditions, so we don't really care of p_avm(:,:1) and p_avm(:,:jpk)
! for zd_lw and zd_up but they have to be defined to avoid a bug when looking for undefined values (-fpe0)
zsqen = SQRT( 2._wp * en(ji,jj,jk) ) * hmxl_n(ji,jj,jk)
zavt = zsqen * zstt(ji,jj,jk)
zavm = zsqen * zstm(ji,jj,jk)
p_avt(ji,jj,jk) = MAX( zavt, avtb(jk) ) * wmask(ji,jj,jk) ! apply mask for zdfmxl routine
p_avm(ji,jj,jk) = MAX( zavm, avmb(jk) ) ! Note that avm is not masked at the surface and the bottom
END_3D
CALL prt_ctl( tab3d_1=en , clinfo1=' gls - e: ', tab3d_2=p_avt, clinfo2=' t: ' )
CALL prt_ctl( tab3d_1=p_avm, clinfo1=' gls - m: ' )
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ENDIF
!
END SUBROUTINE zdf_gls
SUBROUTINE zdf_gls_init
!!----------------------------------------------------------------------
!! *** ROUTINE zdf_gls_init ***
!!
!! ** Purpose : Initialization of the vertical eddy diffivity and
!! viscosity computed using a GLS turbulent closure scheme
!!
!! ** Method : Read the namzdf_gls namelist and check the parameters
!!
!! ** input : Namlist namzdf_gls
!!
!! ** Action : Increase by 1 the nstop flag is setting problem encounter
!!
!!----------------------------------------------------------------------
INTEGER :: jk ! dummy loop indices
INTEGER :: ios ! Local integer output status for namelist read
REAL(wp):: zcr ! local scalar
!!
NAMELIST/namzdf_gls/rn_emin, rn_epsmin, ln_length_lim, &
& rn_clim_galp, ln_sigpsi, rn_hsro, rn_hsri, &
& nn_mxlice, rn_crban, rn_charn, rn_frac_hs, &
& nn_bc_surf, nn_bc_bot, nn_z0_met, nn_z0_ice, &
& nn_stab_func, nn_clos
!!----------------------------------------------------------
!
READ ( numnam_ref, namzdf_gls, IOSTAT = ios, ERR = 901)
901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_gls in reference namelist' )
READ ( numnam_cfg, namzdf_gls, IOSTAT = ios, ERR = 902 )
902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namzdf_gls in configuration namelist' )
IF(lwm) WRITE ( numond, namzdf_gls )
IF(lwp) THEN !* Control print
WRITE(numout,*)
WRITE(numout,*) 'zdf_gls_init : GLS turbulent closure scheme'
WRITE(numout,*) '~~~~~~~~~~~~'
WRITE(numout,*) ' Namelist namzdf_gls : set gls mixing parameters'
WRITE(numout,*) ' minimum value of en rn_emin = ', rn_emin
WRITE(numout,*) ' minimum value of eps rn_epsmin = ', rn_epsmin
WRITE(numout,*) ' Limit dissipation rate under stable stratif. ln_length_lim = ', ln_length_lim
WRITE(numout,*) ' Galperin limit (Standard: 0.53, Holt: 0.26) rn_clim_galp = ', rn_clim_galp
WRITE(numout,*) ' TKE Surface boundary condition nn_bc_surf = ', nn_bc_surf
WRITE(numout,*) ' TKE Bottom boundary condition nn_bc_bot = ', nn_bc_bot
WRITE(numout,*) ' Modify psi Schmidt number (wb case) ln_sigpsi = ', ln_sigpsi
WRITE(numout,*) ' Craig and Banner coefficient rn_crban = ', rn_crban
WRITE(numout,*) ' Charnock coefficient rn_charn = ', rn_charn
WRITE(numout,*) ' Surface roughness formula nn_z0_met = ', nn_z0_met
WRITE(numout,*) ' surface wave breaking under ice nn_z0_ice = ', nn_z0_ice
SELECT CASE( nn_z0_ice )
CASE( 0 ) ; WRITE(numout,*) ' ==>>> no impact of ice cover on surface wave breaking'
CASE( 1 ) ; WRITE(numout,*) ' ==>>> roughness uses rn_hsri and is weigthed by 1-TANH( fr_i(:,:) * 10 )'
CASE( 2 ) ; WRITE(numout,*) ' ==>>> roughness uses rn_hsri and is weighted by 1-fr_i(:,:)'
CASE( 3 ) ; WRITE(numout,*) ' ==>>> roughness uses rn_hsri and is weighted by 1-MIN( 1, 4 * fr_i(:,:) )'
CASE DEFAULT
CALL ctl_stop( 'zdf_gls_init: wrong value for nn_z0_ice, should be 0,1,2, or 3')
END SELECT
WRITE(numout,*) ' Wave height frac. (used if nn_z0_met=2) rn_frac_hs = ', rn_frac_hs
WRITE(numout,*) ' Stability functions nn_stab_func = ', nn_stab_func
WRITE(numout,*) ' Type of closure nn_clos = ', nn_clos
WRITE(numout,*) ' Surface roughness (m) rn_hsro = ', rn_hsro
WRITE(numout,*) ' type of scaling under sea-ice nn_mxlice = ', nn_mxlice
IF( nn_mxlice == 1 ) &
WRITE(numout,*) ' Ice-ocean roughness (used if nn_z0_ice/=0) rn_hsri = ', rn_hsri
SELECT CASE( nn_mxlice ) ! Type of scaling under sea-ice
CASE( 0 ) ; WRITE(numout,*) ' ==>>> No scaling under sea-ice'
CASE( 1 ) ; WRITE(numout,*) ' ==>>> scaling with constant sea-ice thickness'
CASE( 2 ) ; WRITE(numout,*) ' ==>>> scaling with mean sea-ice thickness'
CASE( 3 ) ; WRITE(numout,*) ' ==>>> scaling with max sea-ice thickness'
CASE DEFAULT
CALL ctl_stop( 'zdf_gls_init: wrong value for nn_mxlice, should be 0,1,2,3 ')
IF ( (nn_mxlice>0).AND.(nn_ice==0) ) THEN
CALL ctl_warn( 'zdf_gls_init: with no ice at all, nn_mxlice is set to 0 ')
nn_mxlice = 0
ELSEIF ( (nn_mxlice>1).AND.(nn_ice==1) ) THEN
CALL ctl_stop( 'zdf_gls_init: with no ice model, nn_mxlice must be 0 or 1')
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WRITE(numout,*)
ENDIF
! !* allocate GLS arrays
IF( zdf_gls_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'zdf_gls_init : unable to allocate arrays' )
! !* Check of some namelist values
IF( nn_bc_surf < 0 .OR. nn_bc_surf > 1 ) CALL ctl_stop( 'zdf_gls_init: bad flag: nn_bc_surf is 0 or 1' )
IF( nn_bc_surf < 0 .OR. nn_bc_surf > 1 ) CALL ctl_stop( 'zdf_gls_init: bad flag: nn_bc_surf is 0 or 1' )
IF( nn_z0_met < 0 .OR. nn_z0_met > 3 ) CALL ctl_stop( 'zdf_gls_init: bad flag: nn_z0_met is 0, 1, 2 or 3' )
IF( nn_z0_met == 3 .AND. .NOT. (ln_wave .AND. ln_sdw ) ) CALL ctl_stop( 'zdf_gls_init: nn_z0_met=3 requires ln_wave=T and ln_sdw=T' )
IF( nn_stab_func < 0 .OR. nn_stab_func > 3 ) CALL ctl_stop( 'zdf_gls_init: bad flag: nn_stab_func is 0, 1, 2 and 3' )
IF( nn_clos < 0 .OR. nn_clos > 3 ) CALL ctl_stop( 'zdf_gls_init: bad flag: nn_clos is 0, 1, 2 or 3' )
SELECT CASE ( nn_clos ) !* set the parameters for the chosen closure
!
CASE( 0 ) ! k-kl (Mellor-Yamada)
!
IF(lwp) WRITE(numout,*) ' ==>> k-kl closure chosen (i.e. closed to the classical Mellor-Yamada)'
IF(lwp) WRITE(numout,*)
rpp = 0._wp
rmm = 1._wp
rnn = 1._wp
rsc_tke = 1.96_wp
rsc_psi = 1.96_wp
rpsi1 = 0.9_wp
rpsi3p = 1._wp
rpsi2 = 0.5_wp
!
SELECT CASE ( nn_stab_func )
CASE( 0, 1 ) ; rpsi3m = 2.53_wp ! G88 or KC stability functions
CASE( 2 ) ; rpsi3m = 2.62_wp ! Canuto A stability functions
CASE( 3 ) ; rpsi3m = 2.38 ! Canuto B stability functions (caution : constant not identified)
END SELECT
!
CASE( 1 ) ! k-eps
!
IF(lwp) WRITE(numout,*) ' ==>> k-eps closure chosen'
IF(lwp) WRITE(numout,*)
rpp = 3._wp
rmm = 1.5_wp
rnn = -1._wp
rsc_tke = 1._wp
rsc_psi = 1.2_wp ! Schmidt number for psi
rpsi1 = 1.44_wp
rpsi3p = 1._wp
rpsi2 = 1.92_wp
!
SELECT CASE ( nn_stab_func )
CASE( 0, 1 ) ; rpsi3m = -0.52_wp ! G88 or KC stability functions
CASE( 2 ) ; rpsi3m = -0.629_wp ! Canuto A stability functions
CASE( 3 ) ; rpsi3m = -0.566 ! Canuto B stability functions
END SELECT
!
CASE( 2 ) ! k-omega
!
IF(lwp) WRITE(numout,*) ' ==>> k-omega closure chosen'