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& ghamv, 'W', 1.0_wp )
DO jk = 2, jpkm1
DO jj = Njs0, Nje0
DO ji = Nis0, Nie0
ghamu(ji,jj,jk) = ( ghamu(ji,jj,jk) + ghamu(ji+1,jj,jk) ) / &
& MAX( 1.0_wp, tmask(ji,jj,jk) + tmask (ji+1,jj,jk) ) * umask(ji,jj,jk)
ghamv(ji,jj,jk) = ( ghamv(ji,jj,jk) + ghamv(ji,jj+1,jk) ) / &
& MAX( 1.0_wp, tmask(ji,jj,jk) + tmask (ji,jj+1,jk) ) * vmask(ji,jj,jk)
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) * tmask(ji,jj,jk)
ghams(ji,jj,jk) = ghams(ji,jj,jk) * tmask(ji,jj,jk)
END DO
END DO
END DO
! Lateral boundary conditions on final outputs for hbl, on T-grid (sign unchanged)
CALL lbc_lnk( 'zdfosm', hbl, 'T', 1.0_wp, &
& hmle, 'T', 1.0_wp )
!
CALL zdf_osm_iomput( "ghamt", tmask * ghamt ) ! <Tw_NL>
CALL zdf_osm_iomput( "ghams", tmask * ghams ) ! <Sw_NL>
CALL zdf_osm_iomput( "ghamu", umask * ghamu ) ! <uw_NL>
CALL zdf_osm_iomput( "ghamv", vmask * ghamv ) ! <vw_NL>
CALL zdf_osm_iomput( "hbl", tmask(:,:,1) * hbl ) ! Boundary-layer depth
CALL zdf_osm_iomput( "hmle", tmask(:,:,1) * hmle ) ! FK layer depth
END IF
!
END SUBROUTINE zdf_osm
SUBROUTINE zdf_osm_vertical_average( Kbb, Kmm, knlev, pt, ps, &
& pb, pu, pv, kp_ext, pdt, &
& pds, pdb, pdu, pdv )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_vertical_average ***
!!
!! ** Purpose : Determines vertical averages from surface to knlev,
!! and optionally the differences between these vertical
!! averages and values at an external level
!!
!! ** Method : Averages are calculated from the surface to knlev.
!! The external level used to calculate differences is
!! knlev+kp_ext
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kbb, Kmm ! Ocean time-level indices
INTEGER, DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: knlev ! Number of levels to average over.
REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt, ps ! Average temperature and salinity
REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pb ! Average buoyancy
REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pu, pv ! Average current components
INTEGER, DIMENSION(T2D(nn_hls-1)), INTENT(in ), OPTIONAL :: kp_ext ! External-level offsets
REAL(wp), DIMENSION(jpi,jpj), INTENT( out), OPTIONAL :: pdt ! Difference between average temperature,
REAL(wp), DIMENSION(jpi,jpj), INTENT( out), OPTIONAL :: pds ! salinity,
REAL(wp), DIMENSION(jpi,jpj), INTENT( out), OPTIONAL :: pdb ! buoyancy, and
REAL(wp), DIMENSION(jpi,jpj), INTENT( out), OPTIONAL :: pdu, pdv ! velocity components and the OSBL
!!
INTEGER :: jk, jkflt, jkmax, ji, jj ! Loop indices
INTEGER :: ibld_ext ! External-layer index
REAL(wp), DIMENSION(T2D(nn_hls-1)) :: zthick ! Layer thickness
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REAL(wp) :: zthermal ! Thermal expansion coefficient
REAL(wp) :: zbeta ! Haline contraction coefficient
!!----------------------------------------------------------------------
!
! Averages over depth of boundary layer
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
pt(ji,jj) = 0.0_wp
ps(ji,jj) = 0.0_wp
pu(ji,jj) = 0.0_wp
pv(ji,jj) = 0.0_wp
END_2D
zthick(:,:) = epsln
jkflt = jpk
jkmax = 0
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( knlev(ji,jj) < jkflt ) jkflt = knlev(ji,jj)
IF ( knlev(ji,jj) > jkmax ) jkmax = knlev(ji,jj)
END_2D
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jkflt ) ! Upper, flat part of layer
zthick(ji,jj) = zthick(ji,jj) + e3t(ji,jj,jk,Kmm)
pt(ji,jj) = pt(ji,jj) + e3t(ji,jj,jk,Kmm) * ts(ji,jj,jk,jp_tem,Kmm)
ps(ji,jj) = ps(ji,jj) + e3t(ji,jj,jk,Kmm) * ts(ji,jj,jk,jp_sal,Kmm)
pu(ji,jj) = pu(ji,jj) + e3t(ji,jj,jk,Kmm) * &
& ( uu(ji,jj,jk,Kbb) + uu(ji - 1,jj,jk,Kbb) ) / &
& MAX( 1.0_wp , umask(ji,jj,jk) + umask(ji - 1,jj,jk) )
pv(ji,jj) = pv(ji,jj) + e3t(ji,jj,jk,Kmm) * &
& ( vv(ji,jj,jk,Kbb) + vv(ji,jj - 1,jk,Kbb) ) / &
& MAX( 1.0_wp , vmask(ji,jj,jk) + vmask(ji,jj - 1,jk) )
END_3D
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, jkflt+1, jkmax ) ! Lower, non-flat part of layer
IF ( knlev(ji,jj) >= jk ) THEN
zthick(ji,jj) = zthick(ji,jj) + e3t(ji,jj,jk,Kmm)
pt(ji,jj) = pt(ji,jj) + e3t(ji,jj,jk,Kmm) * ts(ji,jj,jk,jp_tem,Kmm)
ps(ji,jj) = ps(ji,jj) + e3t(ji,jj,jk,Kmm) * ts(ji,jj,jk,jp_sal,Kmm)
pu(ji,jj) = pu(ji,jj) + e3t(ji,jj,jk,Kmm) * &
& ( uu(ji,jj,jk,Kbb) + uu(ji - 1,jj,jk,Kbb) ) / &
& MAX( 1.0_wp , umask(ji,jj,jk) + umask(ji - 1,jj,jk) )
pv(ji,jj) = pv(ji,jj) + e3t(ji,jj,jk,Kmm) * &
& ( vv(ji,jj,jk,Kbb) + vv(ji,jj - 1,jk,Kbb) ) / &
& MAX( 1.0_wp , vmask(ji,jj,jk) + vmask(ji,jj - 1,jk) )
END IF
END_3D
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
pt(ji,jj) = pt(ji,jj) / zthick(ji,jj)
ps(ji,jj) = ps(ji,jj) / zthick(ji,jj)
pu(ji,jj) = pu(ji,jj) / zthick(ji,jj)
pv(ji,jj) = pv(ji,jj) / zthick(ji,jj)
zthermal = rab_n(ji,jj,1,jp_tem) ! ideally use nbld not 1??
zbeta = rab_n(ji,jj,1,jp_sal)
pb(ji,jj) = grav * zthermal * pt(ji,jj) - grav * zbeta * ps(ji,jj)
END_2D
!
! Differences between vertical averages and values at an external layer
IF ( PRESENT( kp_ext ) ) THEN
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
ibld_ext = knlev(ji,jj) + kp_ext(ji,jj)
IF ( ibld_ext <= mbkt(ji,jj)-1 ) THEN ! ag 09/03
! Two external levels are available
pdt(ji,jj) = pt(ji,jj) - ts(ji,jj,ibld_ext,jp_tem,Kmm)
pds(ji,jj) = ps(ji,jj) - ts(ji,jj,ibld_ext,jp_sal,Kmm)
pdu(ji,jj) = pu(ji,jj) - ( uu(ji,jj,ibld_ext,Kbb) + uu(ji-1,jj,ibld_ext,Kbb ) ) / &
& MAX(1.0_wp , umask(ji,jj,ibld_ext ) + umask(ji-1,jj,ibld_ext ) )
pdv(ji,jj) = pv(ji,jj) - ( vv(ji,jj,ibld_ext,Kbb) + vv(ji,jj-1,ibld_ext,Kbb ) ) / &
& MAX(1.0_wp , vmask(ji,jj,ibld_ext ) + vmask(ji,jj-1,ibld_ext ) )
zthermal = rab_n(ji,jj,1,jp_tem) ! ideally use nbld not 1??
zbeta = rab_n(ji,jj,1,jp_sal)
pdb(ji,jj) = grav * zthermal * pdt(ji,jj) - grav * zbeta * pds(ji,jj)
ELSE
pdt(ji,jj) = 0.0_wp
pds(ji,jj) = 0.0_wp
pdu(ji,jj) = 0.0_wp
pdv(ji,jj) = 0.0_wp
pdb(ji,jj) = 0.0_wp
ENDIF
END_2D
END IF
!
END SUBROUTINE zdf_osm_vertical_average
SUBROUTINE zdf_osm_velocity_rotation_2d( pu, pv, fwd )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_velocity_rotation_2d ***
!!
!! ** Purpose : Rotates frame of reference of velocity components pu and
!! pv (2d)
!!
!! ** Method : The velocity components are rotated into (fwd=.TRUE.) or
!! from (fwd=.FALSE.) the frame specified by scos_wind and
!! ssin_wind
!!
!!----------------------------------------------------------------------
REAL(wp), INTENT(inout), DIMENSION(jpi,jpj) :: pu, pv ! Components of current
LOGICAL, OPTIONAL, INTENT(in ) :: fwd ! Forward (default) or reverse rotation
!!
INTEGER :: ji, jj ! Loop indices
REAL(wp) :: ztmp, zfwd ! Auxiliary variables
!!----------------------------------------------------------------------
!
zfwd = 1.0_wp
IF( PRESENT(fwd) .AND. ( .NOT. fwd ) ) zfwd = -1.0_wp
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
ztmp = pu(ji,jj)
pu(ji,jj) = pu(ji,jj) * scos_wind(ji,jj) + zfwd * pv(ji,jj) * ssin_wind(ji,jj)
pv(ji,jj) = pv(ji,jj) * scos_wind(ji,jj) - zfwd * ztmp * ssin_wind(ji,jj)
END_2D
!
END SUBROUTINE zdf_osm_velocity_rotation_2d
SUBROUTINE zdf_osm_velocity_rotation_3d( pu, pv, fwd, ktop, knlev )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_velocity_rotation_3d ***
!!
!! ** Purpose : Rotates frame of reference of velocity components pu and
!! pv (3d)
!!
!! ** Method : The velocity components are rotated into (fwd=.TRUE.) or
!! from (fwd=.FALSE.) the frame specified by scos_wind and
!! ssin_wind; optionally, the rotation can be restricted at
!! each water column to span from the a minimum index ktop to
!! the depth index specified in array knlev
!!
!!----------------------------------------------------------------------
REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pu, pv ! Components of current
LOGICAL, OPTIONAL, INTENT(in ) :: fwd ! Forward (default) or reverse rotation
INTEGER, OPTIONAL, INTENT(in ) :: ktop ! Minimum depth index
INTEGER, OPTIONAL, INTENT(in ), DIMENSION(T2D(nn_hls-1)) :: knlev ! Array of maximum depth indices
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!!
INTEGER :: ji, jj, jk, jktop, jkmax ! Loop indices
REAL(wp) :: ztmp, zfwd ! Auxiliary variables
LOGICAL :: llkbot ! Auxiliary variable
!!----------------------------------------------------------------------
!
zfwd = 1.0_wp
IF( PRESENT(fwd) .AND. ( .NOT. fwd ) ) zfwd = -1.0_wp
jktop = 1
IF( PRESENT(ktop) ) jktop = ktop
IF( PRESENT(knlev) ) THEN
jkmax = 0
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( knlev(ji,jj) > jkmax ) jkmax = knlev(ji,jj)
END_2D
llkbot = .FALSE.
ELSE
jkmax = jpk
llkbot = .TRUE.
END IF
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, jktop, jkmax )
IF ( llkbot .OR. knlev(ji,jj) >= jk ) THEN
ztmp = pu(ji,jj,jk)
pu(ji,jj,jk) = pu(ji,jj,jk) * scos_wind(ji,jj) + zfwd * pv(ji,jj,jk) * ssin_wind(ji,jj)
pv(ji,jj,jk) = pv(ji,jj,jk) * scos_wind(ji,jj) - zfwd * ztmp * ssin_wind(ji,jj)
END IF
END_3D
!
END SUBROUTINE zdf_osm_velocity_rotation_3d
SUBROUTINE zdf_osm_osbl_state( Kmm, pwb_ent, pwb_min, pshear, phbl, &
& phml, pdh )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_osm_osbl_state ***
!!
!! ** Purpose : Determines the state of the OSBL, stable/unstable,
!! shear/ noshear. Also determines shear production,
!! entrainment buoyancy flux and interfacial Richardson
!! number
!!
!! ** Method :
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kmm ! Ocean time-level index
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT( out) :: pwb_ent ! Buoyancy fluxes at base
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT( out) :: pwb_min ! of well-mixed layer
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT( out) :: pshear ! Production of TKE due to shear across the pycnocline
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: phml ! ML depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pdh ! Pycnocline depth
REAL(wp), DIMENSION(T2D(nn_hls-1)) :: zekman
REAL(wp), DIMENSION(T2D(nn_hls-1)) :: zri_p, zri_b ! Richardson numbers
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REAL(wp) :: zshear_u, zshear_v, zwb_shr
REAL(wp) :: zwcor, zrf_conv, zrf_shear, zrf_langmuir, zr_stokes
!!
REAL(wp), PARAMETER :: pp_a_shr = 0.4_wp, pp_b_shr = 6.5_wp, pp_a_wb_s = 0.8_wp
REAL(wp), PARAMETER :: pp_alpha_c = 0.2_wp, pp_alpha_lc = 0.03_wp
REAL(wp), PARAMETER :: pp_alpha_ls = 0.06_wp, pp_alpha_s = 0.15_wp
REAL(wp), PARAMETER :: pp_ri_p_thresh = 27.0_wp
REAL(wp), PARAMETER :: pp_ri_c = 0.25_wp
REAL(wp), PARAMETER :: pp_ek = 4.0_wp
REAL(wp), PARAMETER :: pp_large = -1e10_wp
!!----------------------------------------------------------------------
!
! Initialise arrays
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
l_conv(ji,jj) = .FALSE.
l_shear(ji,jj) = .FALSE.
n_ddh(ji,jj) = 1
END_2D
! Initialise INTENT( out) arrays
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
pwb_ent(ji,jj) = pp_large
pwb_min(ji,jj) = pp_large
END_2D
!
! Determins stability and set flag l_conv
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( shol(ji,jj) < 0.0_wp ) THEN
l_conv(ji,jj) = .TRUE.
ELSE
l_conv(ji,jj) = .FALSE.
ENDIF
END_2D
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
pshear(ji,jj) = 0.0_wp
END_2D
zekman(:,:) = EXP( -1.0_wp * pp_ek * ABS( ff_t(T2D(nn_hls-1)) ) * phbl(T2D(nn_hls-1)) / &
& MAX( sustar(T2D(nn_hls-1)), 1.e-8 ) )
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!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( l_conv(ji,jj) ) THEN
IF ( av_db_bl(ji,jj) > 0.0_wp ) THEN
zri_p(ji,jj) = MAX ( SQRT( av_db_bl(ji,jj) * pdh(ji,jj) / MAX( av_du_bl(ji,jj)**2 + av_dv_bl(ji,jj)**2, &
& 1e-8_wp ) ) * ( phbl(ji,jj) / pdh(ji,jj) ) * &
& ( svstr(ji,jj) / MAX( sustar(ji,jj), 1e-6_wp ) )**2 / &
& MAX( zekman(ji,jj), 1.0e-6_wp ), 5.0_wp )
IF ( ff_t(ji,jj) >= 0.0_wp ) THEN ! Northern hemisphere
zri_b(ji,jj) = av_db_ml(ji,jj) * pdh(ji,jj) / ( MAX( av_du_ml(ji,jj), 1e-5_wp )**2 + &
& MAX( -1.0_wp * av_dv_ml(ji,jj), 1e-5_wp)**2 )
ELSE ! Southern hemisphere
zri_b(ji,jj) = av_db_ml(ji,jj) * pdh(ji,jj) / ( MAX( av_du_ml(ji,jj), 1e-5_wp )**2 + &
& MAX( av_dv_ml(ji,jj), 1e-5_wp)**2 )
END IF
pshear(ji,jj) = pp_a_shr * zekman(ji,jj) * &
& ( MAX( sustar(ji,jj)**2 * av_du_ml(ji,jj) / phbl(ji,jj), 0.0_wp ) + &
& pp_b_shr * MAX( -1.0_wp * ff_t(ji,jj) * sustke(ji,jj) * dstokes(ji,jj) * &
& av_dv_ml(ji,jj) / phbl(ji,jj), 0.0_wp ) )
! Stability dependence
pshear(ji,jj) = pshear(ji,jj) * EXP( -0.75_wp * MAX( 0.0_wp, ( zri_b(ji,jj) - pp_ri_c ) / pp_ri_c ) )
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Test ensures n_ddh=0 is not selected. Change to zri_p<27 when !
! full code available !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
IF ( pshear(ji,jj) > 1e-10 ) THEN
IF ( zri_p(ji,jj) < pp_ri_p_thresh .AND. &
& MIN( hu(ji,jj,Kmm), hu(ji-1,jj,Kmm), hv(ji,jj,Kmm), hv(ji,jj-1,Kmm) ) > 100.0_wp ) THEN
! Growing shear layer
n_ddh(ji,jj) = 0
l_shear(ji,jj) = .TRUE.
ELSE
n_ddh(ji,jj) = 1
! IF ( zri_b <= 1.5 .and. pshear(ji,jj) > 0._wp ) THEN
! Shear production large enough to determine layer charcteristics, but can't maintain a shear layer
l_shear(ji,jj) = .TRUE.
! ELSE
END IF
ELSE
n_ddh(ji,jj) = 2
l_shear(ji,jj) = .FALSE.
END IF
! Shear production may not be zero, but is small and doesn't determine characteristics of pycnocline
! pshear(ji,jj) = 0.5 * pshear(ji,jj)
! l_shear(ji,jj) = .FALSE.
! ENDIF
ELSE ! av_db_bl test, note pshear set to zero
n_ddh(ji,jj) = 2
l_shear(ji,jj) = .FALSE.
ENDIF
ENDIF
END_2D
!
! Calculate entrainment buoyancy flux due to surface fluxes.
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( l_conv(ji,jj) ) THEN
zwcor = ABS( ff_t(ji,jj) ) * phbl(ji,jj) + epsln
zrf_conv = TANH( ( swstrc(ji,jj) / zwcor )**0.69_wp )
zrf_shear = TANH( ( sustar(ji,jj) / zwcor )**0.69_wp )
zrf_langmuir = TANH( ( swstrl(ji,jj) / zwcor )**0.69_wp )
IF ( nn_osm_SD_reduce > 0 ) THEN
! Effective Stokes drift already reduced from surface value
zr_stokes = 1.0_wp
ELSE
! Effective Stokes drift only reduced by factor rn_zdfodm_adjust_sd,
! requires further reduction where BL is deep
zr_stokes = 1.0 - EXP( -25.0_wp * dstokes(ji,jj) / hbl(ji,jj) * ( 1.0_wp + 4.0_wp * dstokes(ji,jj) / hbl(ji,jj) ) )
END IF
pwb_ent(ji,jj) = -2.0_wp * pp_alpha_c * zrf_conv * swbav(ji,jj) - &
& pp_alpha_s * zrf_shear * sustar(ji,jj)**3 / phml(ji,jj) + &
& zr_stokes * ( pp_alpha_s * EXP( -1.5_wp * sla(ji,jj) ) * zrf_shear * sustar(ji,jj)**3 - &
& zrf_langmuir * pp_alpha_lc * swstrl(ji,jj)**3 ) / phml(ji,jj)
ENDIF
END_2D
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( l_shear(ji,jj) ) THEN
IF ( l_conv(ji,jj) ) THEN
! Unstable OSBL
zwb_shr = -1.0_wp * pp_a_wb_s * zri_b(ji,jj) * pshear(ji,jj)
IF ( n_ddh(ji,jj) == 0 ) THEN
! Developing shear layer, additional shear production possible.
! pshear_u = MAX( zustar(ji,jj)**2 * MAX( av_du_ml(ji,jj), 0._wp ) / phbl(ji,jj), 0._wp )
! pshear(ji,jj) = pshear(ji,jj) + pshear_u * ( 1.0 - MIN( zri_p(ji,jj) / pp_ri_p_thresh, 1.d0 )**2 )
! pshear(ji,jj) = MIN( pshear(ji,jj), pshear_u )
! zwb_shr = zwb_shr - 0.25 * MAX ( pshear_u, 0._wp) * ( 1.0 - MIN( zri_p(ji,jj) / pp_ri_p_thresh, 1._wp )**2 )
! zwb_shr = MAX( zwb_shr, -0.25 * pshear_u )
ENDIF
pwb_ent(ji,jj) = pwb_ent(ji,jj) + zwb_shr
! pwb_min(ji,jj) = pwb_ent(ji,jj) + pdh(ji,jj) / phbl(ji,jj) * zwb0(ji,jj)
ELSE ! IF ( l_conv ) THEN - ENDIF
! Stable OSBL - shear production not coded for first attempt.
ENDIF ! l_conv
END IF ! l_shear
IF ( l_conv(ji,jj) ) THEN
! Unstable OSBL
pwb_min(ji,jj) = pwb_ent(ji,jj) + pdh(ji,jj) / phbl(ji,jj) * 2.0_wp * swbav(ji,jj)
END IF ! l_conv
END_2D
!
END SUBROUTINE zdf_osm_osbl_state
SUBROUTINE zdf_osm_external_gradients( Kmm, kbase, pdtdz, pdsdz, pdbdz )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_osm_external_gradients ***
!!
!! ** Purpose : Calculates the gradients below the OSBL
!!
!! ** Method : Uses nbld and ibld_ext to determine levels to calculate the gradient.
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kmm ! Ocean time-level index
INTEGER, DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: kbase ! OSBL base layer index
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT( out) :: pdtdz, pdsdz ! External gradients of temperature, salinity
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT( out) :: pdbdz ! and buoyancy
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!!
INTEGER :: ji, jj, jkb, jkb1
REAL(wp) :: zthermal, zbeta
!!
REAL(wp), PARAMETER :: pp_large = -1e10_wp
!!----------------------------------------------------------------------
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
pdtdz(ji,jj) = pp_large
pdsdz(ji,jj) = pp_large
pdbdz(ji,jj) = pp_large
END_2D
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( kbase(ji,jj)+1 < mbkt(ji,jj) ) THEN
zthermal = rab_n(ji,jj,1,jp_tem) ! Ideally use nbld not 1??
zbeta = rab_n(ji,jj,1,jp_sal)
jkb = kbase(ji,jj)
jkb1 = MIN( jkb + 1, mbkt(ji,jj) )
pdtdz(ji,jj) = -1.0_wp * ( ts(ji,jj,jkb1,jp_tem,Kmm) - ts(ji,jj,jkb,jp_tem,Kmm ) ) / e3w(ji,jj,jkb1,Kmm)
pdsdz(ji,jj) = -1.0_wp * ( ts(ji,jj,jkb1,jp_sal,Kmm) - ts(ji,jj,jkb,jp_sal,Kmm ) ) / e3w(ji,jj,jkb1,Kmm)
pdbdz(ji,jj) = grav * zthermal * pdtdz(ji,jj) - grav * zbeta * pdsdz(ji,jj)
ELSE
pdtdz(ji,jj) = 0.0_wp
pdsdz(ji,jj) = 0.0_wp
pdbdz(ji,jj) = 0.0_wp
END IF
END_2D
!
END SUBROUTINE zdf_osm_external_gradients
SUBROUTINE zdf_osm_calculate_dhdt( pdhdt, phbl, pdh, pwb_ent, pwb_min, &
& pdbdz_bl_ext, pwb_fk_b, pwb_fk, pvel_mle )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_osm_calculate_dhdt ***
!!
!! ** Purpose : Calculates the rate at which hbl changes.
!!
!! ** Method :
!!
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT( out) :: pdhdt ! Rate of change of hbl
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pdh ! Pycnocline depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pwb_ent ! Buoyancy entrainment flux
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pwb_min
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pdbdz_bl_ext ! External buoyancy gradients
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT( out) :: pwb_fk_b ! MLE buoyancy flux averaged over OSBL
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pwb_fk ! Max MLE buoyancy flux
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pvel_mle ! Vvelocity scale for dhdt with stable ML and FK
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!!
INTEGER :: jj, ji
REAL(wp) :: zgamma_b_nd, zgamma_dh_nd, zpert, zpsi, zari
REAL(wp) :: zvel_max, zddhdt
!!
REAL(wp), PARAMETER :: pp_alpha_b = 0.3_wp
REAL(wp), PARAMETER :: pp_ddh = 2.5_wp, pp_ddh_2 = 3.5_wp ! Also in pycnocline_depth
REAL(wp), PARAMETER :: pp_large = -1e10_wp
!!----------------------------------------------------------------------
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
pdhdt(ji,jj) = pp_large
pwb_fk_b(ji,jj) = pp_large
END_2D
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
!
IF ( l_shear(ji,jj) ) THEN
!
IF ( l_conv(ji,jj) ) THEN ! Convective
!
IF ( ln_osm_mle ) THEN
IF ( hmle(ji,jj) > hbl(ji,jj) ) THEN ! Fox-Kemper buoyancy flux average over OSBL
pwb_fk_b(ji,jj) = pwb_fk(ji,jj) * ( 1.0_wp + hmle(ji,jj) / ( 6.0_wp * hbl(ji,jj) ) * &
& ( -1.0_wp + ( 1.0_wp - 2.0_wp * hbl(ji,jj) / hmle(ji,jj) )**3 ) )
ELSE
pwb_fk_b(ji,jj) = 0.5_wp * pwb_fk(ji,jj) * hmle(ji,jj) / hbl(ji,jj)
ENDIF
zvel_max = ( svstr(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**p2third / hbl(ji,jj)
IF ( ( pwb_ent(ji,jj) + 2.0_wp * pwb_fk_b(ji,jj) ) < 0.0_wp ) THEN ! OSBL is deepening,
! ! entrainment > restratification
IF ( av_db_bl(ji,jj) > 1e-15_wp ) THEN
zgamma_b_nd = MAX( pdbdz_bl_ext(ji,jj), 0.0_wp ) * pdh(ji,jj) / &
& ( zvel_max + MAX( av_db_bl(ji,jj), 1e-15_wp ) )
zpsi = ( 1.0_wp - 0.5_wp * pdh(ji,jj) / phbl(ji,jj) ) * &
& ( swb0(ji,jj) - MIN( ( pwb_min(ji,jj) + 2.0_wp * pwb_fk_b(ji,jj) ), 0.0_wp ) ) * pdh(ji,jj) / &
& phbl(ji,jj)
zpsi = zpsi + 1.75_wp * ( 1.0_wp - 0.5_wp * pdh(ji,jj) / phbl(ji,jj) ) * &
& ( pdh(ji,jj) / phbl(ji,jj) + zgamma_b_nd ) * &
& MIN( ( pwb_min(ji,jj) + 2.0_wp * pwb_fk_b(ji,jj) ), 0.0_wp )
zpsi = pp_alpha_b * MAX( zpsi, 0.0_wp )
pdhdt(ji,jj) = -1.0_wp * ( pwb_ent(ji,jj) + 2.0_wp * pwb_fk_b(ji,jj) ) / &
& ( zvel_max + MAX( av_db_bl(ji,jj), 1e-15_wp ) ) + &
& zpsi / ( zvel_max + MAX( av_db_bl(ji,jj), 1e-15_wp ) )
IF ( n_ddh(ji,jj) == 1 ) THEN
IF ( ( swstrc(ji,jj) / svstr(ji,jj) )**3 <= 0.5_wp ) THEN
zari = MIN( 1.5_wp * av_db_bl(ji,jj) / &
& ( phbl(ji,jj) * ( MAX( pdbdz_bl_ext(ji,jj), 0.0_wp ) + &
& av_db_bl(ji,jj)**2 / MAX( 4.5_wp * svstr(ji,jj)**2, &
& 1e-12_wp ) ) ), 0.2_wp )
ELSE
zari = MIN( 1.5_wp * av_db_bl(ji,jj) / &
& ( phbl(ji,jj) * ( MAX( pdbdz_bl_ext(ji,jj), 0.0_wp ) + &
& av_db_bl(ji,jj)**2 / MAX( 4.5_wp * swstrc(ji,jj)**2, &
& 1e-12_wp ) ) ), 0.2_wp )
ENDIF
! Relaxation to dh_ref = zari * hbl
zddhdt = -1.0_wp * pp_ddh_2 * ( 1.0_wp - pdh(ji,jj) / ( zari * phbl(ji,jj) ) ) * pwb_ent(ji,jj) / &
& ( zvel_max + MAX( av_db_bl(ji,jj), 1e-15_wp ) )
ELSE IF ( n_ddh(ji,jj) == 0 ) THEN ! Growing shear layer
zddhdt = -1.0_wp * pp_ddh * ( 1.0_wp - 1.6_wp * pdh(ji,jj) / phbl(ji,jj) ) * pwb_ent(ji,jj) / &
& ( zvel_max + MAX( av_db_bl(ji,jj), 1e-15_wp ) )
zddhdt = EXP( -4.0_wp * ABS( ff_t(ji,jj) ) * phbl(ji,jj) / MAX( sustar(ji,jj), 1e-8_wp ) ) * zddhdt
ELSE
zddhdt = 0.0_wp
ENDIF ! n_ddh
pdhdt(ji,jj) = pdhdt(ji,jj) + pp_alpha_b * ( 1.0_wp - 0.5_wp * pdh(ji,jj) / phbl(ji,jj) ) * &
& av_db_ml(ji,jj) * MAX( zddhdt, 0.0_wp ) / &
& ( zvel_max + MAX( av_db_bl(ji,jj), 1e-15_wp ) )
ELSE ! av_db_bl >0
pdhdt(ji,jj) = -1.0_wp * ( pwb_ent(ji,jj) + 2.0_wp * pwb_fk_b(ji,jj) ) / MAX( zvel_max, 1e-15_wp )
ENDIF
ELSE ! pwb_min + 2*pwb_fk_b < 0
! OSBL shoaling due to restratification flux. This is the velocity defined in Fox-Kemper et al (2008)
pdhdt(ji,jj) = -1.0_wp * MIN( pvel_mle(ji,jj), hbl(ji,jj) / 10800.0_wp )
ENDIF
ELSE ! Fox-Kemper not used.
zvel_max = -1.0_wp * ( 1.0_wp + 1.0_wp * ( svstr(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**pthird * &
& rn_Dt / hbl(ji,jj) ) * pwb_ent(ji,jj) / &
& MAX( ( svstr(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**pthird, epsln )
pdhdt(ji,jj) = -1.0_wp * pwb_ent(ji,jj) / ( zvel_max + MAX( av_db_bl(ji,jj), 1e-15_wp ) )
! added ajgn 23 July as temporay fix
ENDIF ! ln_osm_mle
!
ELSE ! l_conv - Stable
!
pdhdt(ji,jj) = ( 0.06_wp + 0.52_wp * shol(ji,jj) / 2.0_wp ) * svstr(ji,jj)**3 / hbl(ji,jj) + swbav(ji,jj)
IF ( pdhdt(ji,jj) < 0.0_wp ) THEN ! For long timsteps factor in brackets slows the rapid collapse of the OSBL
zpert = 2.0_wp * ( 1.0_wp + 0.0_wp * 2.0_wp * svstr(ji,jj) * rn_Dt / hbl(ji,jj) ) * svstr(ji,jj)**2 / hbl(ji,jj)
ELSE
zpert = MAX( svstr(ji,jj)**2 / hbl(ji,jj), av_db_bl(ji,jj) )
ENDIF
pdhdt(ji,jj) = 2.0_wp * pdhdt(ji,jj) / MAX( zpert, epsln )
pdhdt(ji,jj) = MAX( pdhdt(ji,jj), -1.0_wp * hbl(ji,jj) / 5400.0_wp )
!
ENDIF ! l_conv
!
ELSE ! l_shear
!
IF ( l_conv(ji,jj) ) THEN ! Convective
!
IF ( ln_osm_mle ) THEN
IF ( hmle(ji,jj) > hbl(ji,jj) ) THEN ! Fox-Kemper buoyancy flux average over OSBL
pwb_fk_b(ji,jj) = pwb_fk(ji,jj) * &
( 1.0_wp + hmle(ji,jj) / ( 6.0_wp * hbl(ji,jj) ) * &
& ( -1.0_wp + ( 1.0_wp - 2.0_wp * hbl(ji,jj) / hmle(ji,jj))**3) )
ELSE
pwb_fk_b(ji,jj) = 0.5_wp * pwb_fk(ji,jj) * hmle(ji,jj) / hbl(ji,jj)
ENDIF
zvel_max = ( swstrl(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**p2third / hbl(ji,jj)
IF ( ( pwb_ent(ji,jj) + 2.0_wp * pwb_fk_b(ji,jj) ) < 0.0_wp ) THEN ! OSBL is deepening,
! ! entrainment > restratification
IF ( av_db_bl(ji,jj) > 0.0_wp .AND. pdbdz_bl_ext(ji,jj) > 0.0_wp ) THEN
pdhdt(ji,jj) = -1.0_wp * ( pwb_ent(ji,jj) + 2.0_wp * pwb_fk_b(ji,jj) ) / &
& ( zvel_max + MAX( av_db_bl(ji,jj), 1e-15_wp ) )
ELSE
pdhdt(ji,jj) = -1.0_wp * ( pwb_ent(ji,jj) + 2.0_wp * pwb_fk_b(ji,jj) ) / MAX( zvel_max, 1e-15_wp )
ENDIF
ELSE ! OSBL shoaling due to restratification flux. This is the velocity defined in Fox-Kemper et al (2008)
pdhdt(ji,jj) = -1.0_wp * MIN( pvel_mle(ji,jj), hbl(ji,jj) / 10800.0_wp )
ENDIF
ELSE ! Fox-Kemper not used
zvel_max = -1.0_wp * pwb_ent(ji,jj) / MAX( ( svstr(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**pthird, epsln )
pdhdt(ji,jj) = -1.0_wp * pwb_ent(ji,jj) / ( zvel_max + MAX( av_db_bl(ji,jj), 1e-15_wp ) )
! added ajgn 23 July as temporay fix
ENDIF ! ln_osm_mle
!
ELSE ! Stable
!
pdhdt(ji,jj) = ( 0.06_wp + 0.52_wp * shol(ji,jj) / 2.0_wp ) * svstr(ji,jj)**3 / hbl(ji,jj) + swbav(ji,jj)
IF ( pdhdt(ji,jj) < 0.0_wp ) THEN
! For long timsteps factor in brackets slows the rapid collapse of the OSBL
zpert = 2.0_wp * svstr(ji,jj)**2 / hbl(ji,jj)
ELSE
zpert = MAX( svstr(ji,jj)**2 / hbl(ji,jj), av_db_bl(ji,jj) )
ENDIF
pdhdt(ji,jj) = 2.0_wp * pdhdt(ji,jj) / MAX(zpert, epsln)
pdhdt(ji,jj) = MAX( pdhdt(ji,jj), -1.0_wp * hbl(ji,jj) / 5400.0_wp )
!
ENDIF ! l_conv
!
ENDIF ! l_shear
!
END_2D
!
END SUBROUTINE zdf_osm_calculate_dhdt
SUBROUTINE zdf_osm_timestep_hbl( Kmm, pdhdt, phbl, phbl_t, pwb_ent, &
& pwb_fk_b )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_osm_timestep_hbl ***
!!
!! ** Purpose : Increments hbl.
!!
!! ** Method : If the change in hbl exceeds one model level the change is
!! is calculated by moving down the grid, changing the
!! buoyancy jump. This is to ensure that the change in hbl
!! does not overshoot a stable layer.
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kmm ! Ocean time-level index
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(inout) :: pdhdt ! Rates of change of hbl
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(inout) :: phbl ! BL depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: phbl_t ! BL depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pwb_ent ! Buoyancy entrainment flux
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pwb_fk_b ! MLE buoyancy flux averaged over OSBL
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!!
INTEGER :: jk, jj, ji, jm
REAL(wp) :: zhbl_s, zvel_max, zdb
REAL(wp) :: zthermal, zbeta
!!----------------------------------------------------------------------
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( nbld(ji,jj) - nmld(ji,jj) > 1 ) THEN
!
! If boundary layer changes by more than one level, need to check for stable layers between initial and final depths.
!
zhbl_s = hbl(ji,jj)
jm = nmld(ji,jj)
zthermal = rab_n(ji,jj,1,jp_tem)
zbeta = rab_n(ji,jj,1,jp_sal)
!
IF ( l_conv(ji,jj) ) THEN ! Unstable
!
IF( ln_osm_mle ) THEN
zvel_max = ( swstrl(ji,jj)**3 + swstrc(ji,jj)**3 )**p2third / hbl(ji,jj)
ELSE
zvel_max = -1.0_wp * ( 1.0_wp + 1.0_wp * ( svstr(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**pthird * rn_Dt / &
& hbl(ji,jj) ) * pwb_ent(ji,jj) / &
& ( svstr(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**pthird
ENDIF
DO jk = nmld(ji,jj), nbld(ji,jj)
zdb = MAX( grav * ( zthermal * ( av_t_bl(ji,jj) - ts(ji,jj,jm,jp_tem,Kmm) ) - &
& zbeta * ( av_s_bl(ji,jj) - ts(ji,jj,jm,jp_sal,Kmm) ) ), 0.0_wp ) + zvel_max
!
IF ( ln_osm_mle ) THEN
zhbl_s = zhbl_s + MIN( rn_Dt * ( ( -1.0_wp * pwb_ent(ji,jj) - 2.0_wp * pwb_fk_b(ji,jj) ) / zdb ) / &
& REAL( nbld(ji,jj) - nmld(ji,jj), KIND=wp ), e3w(ji,jj,jm,Kmm) )
ELSE
zhbl_s = zhbl_s + MIN( rn_Dt * ( -1.0_wp * pwb_ent(ji,jj) / zdb ) / &
& REAL( nbld(ji,jj) - nmld(ji,jj), KIND=wp ), e3w(ji,jj,jm,Kmm) )
ENDIF
! zhbl_s = MIN(zhbl_s, gdepw(ji,jj, mbkt(ji,jj) + 1,Kmm) - depth_tol)
IF ( zhbl_s >= gdepw(ji,jj,mbkt(ji,jj) + 1,Kmm) ) THEN
zhbl_s = MIN( zhbl_s, gdepw(ji,jj, mbkt(ji,jj) + 1, Kmm ) - depth_tol )
l_pyc(ji,jj) = .FALSE.
ENDIF
IF ( zhbl_s >= gdepw(ji,jj,jm+1,Kmm) ) jm = jm + 1
END DO
hbl(ji,jj) = zhbl_s
nbld(ji,jj) = jm
ELSE ! Stable
DO jk = nmld(ji,jj), nbld(ji,jj)
zdb = MAX( grav * ( zthermal * ( av_t_bl(ji,jj) - ts(ji,jj,jm,jp_tem,Kmm) ) - &
& zbeta * ( av_s_bl(ji,jj) - ts(ji,jj,jm,jp_sal,Kmm) ) ), 0.0_wp ) + &
& 2.0_wp * svstr(ji,jj)**2 / zhbl_s
!
! Alan is thuis right? I have simply changed hbli to hbl
shol(ji,jj) = -1.0_wp * zhbl_s / ( ( svstr(ji,jj)**3 + epsln ) / swbav(ji,jj) )
pdhdt(ji,jj) = -1.0_wp * ( swbav(ji,jj) - 0.04_wp / 2.0_wp * swstrl(ji,jj)**3 / zhbl_s - &
& 0.15_wp / 2.0_wp * ( 1.0_wp - EXP( -1.5_wp * sla(ji,jj) ) ) * &
& sustar(ji,jj)**3 / zhbl_s ) * &
& ( 0.725_wp + 0.225_wp * EXP( -7.5_wp * shol(ji,jj) ) )
pdhdt(ji,jj) = pdhdt(ji,jj) + swbav(ji,jj)
zhbl_s = zhbl_s + MIN( pdhdt(ji,jj) / zdb * rn_Dt / REAL( nbld(ji,jj) - nmld(ji,jj), KIND=wp ), &
& e3w(ji,jj,jm,Kmm) )
! zhbl_s = MIN(zhbl_s, gdepw(ji,jj, mbkt(ji,jj) + 1,Kmm) - depth_tol)
Simon Mueller
committed
IF ( zhbl_s >= gdepw(ji,jj,mbkt(ji,jj) + 1,Kmm) ) THEN
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zhbl_s = MIN( zhbl_s, gdepw(ji,jj,mbkt(ji,jj)+1,Kmm) - depth_tol )
l_pyc(ji,jj) = .FALSE.
ENDIF
IF ( zhbl_s >= gdepw(ji,jj,jm,Kmm) ) jm = jm + 1
END DO
ENDIF ! IF ( l_conv )
hbl(ji,jj) = MAX( zhbl_s, gdepw(ji,jj,4,Kmm) )
nbld(ji,jj) = MAX( jm, 4 )
ELSE
! change zero or one model level.
hbl(ji,jj) = MAX( phbl_t(ji,jj), gdepw(ji,jj,4,Kmm) )
ENDIF
phbl(ji,jj) = gdepw(ji,jj,nbld(ji,jj),Kmm)
END_2D
!
END SUBROUTINE zdf_osm_timestep_hbl
SUBROUTINE zdf_osm_pycnocline_thickness( Kmm, pdh, phml, pdhdt, phbl, &
& pwb_ent, pdbdz_bl_ext, pwb_fk_b )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_osm_pycnocline_thickness ***
!!
!! ** Purpose : Calculates thickness of the pycnocline
!!
!! ** Method : The thickness is calculated from a prognostic equation
!! that relaxes the pycnocine thickness to a diagnostic
!! value. The time change is calculated assuming the
!! thickness relaxes exponentially. This is done to deal
!! with large timesteps.
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kmm ! Ocean time-level index
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(inout) :: pdh ! Pycnocline thickness
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(inout) :: phml ! ML depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pdhdt ! BL depth tendency
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pwb_ent ! Buoyancy entrainment flux
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pdbdz_bl_ext ! External buoyancy gradients
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pwb_fk_b ! MLE buoyancy flux averaged over OSBL
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!!
INTEGER :: jj, ji
INTEGER :: inhml
REAL(wp) :: zari, ztau, zdh_ref, zddhdt, zvel_max
REAL(wp) :: ztmp ! Auxiliary variable
!!
REAL, PARAMETER :: pp_ddh = 2.5_wp, pp_ddh_2 = 3.5_wp ! Also in pycnocline_depth
!!----------------------------------------------------------------------
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
!
IF ( l_shear(ji,jj) ) THEN
!
IF ( l_conv(ji,jj) ) THEN
!
IF ( av_db_bl(ji,jj) > 1e-15_wp ) THEN
IF ( n_ddh(ji,jj) == 0 ) THEN
zvel_max = ( svstr(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**p2third / hbl(ji,jj)
! ddhdt for pycnocline determined in osm_calculate_dhdt
zddhdt = -1.0_wp * pp_ddh * ( 1.0_wp - 1.6_wp * pdh(ji,jj) / phbl(ji,jj) ) * pwb_ent(ji,jj) / &
& ( zvel_max + MAX( av_db_bl(ji,jj), 1e-15 ) )
zddhdt = EXP( -4.0_wp * ABS( ff_t(ji,jj) ) * phbl(ji,jj) / MAX( sustar(ji,jj), 1e-8 ) ) * zddhdt
! Maximum limit for how thick the shear layer can grow relative to the thickness of the boundary layer
dh(ji,jj) = MIN( dh(ji,jj) + zddhdt * rn_Dt, 0.625_wp * hbl(ji,jj) )
ELSE ! Need to recalculate because hbl has been updated
IF ( ( swstrc(ji,jj) / svstr(ji,jj) )**3 <= 0.5_wp ) THEN
ztmp = svstr(ji,jj)
ELSE
ztmp = swstrc(ji,jj)
END IF
zari = MIN( 1.5_wp * av_db_bl(ji,jj) / ( phbl(ji,jj) * ( MAX( pdbdz_bl_ext(ji,jj), 0.0_wp ) + &
& av_db_bl(ji,jj)**2 / MAX( 4.5_wp * ztmp**2, &
& 1e-12_wp ) ) ), 0.2_wp )
ztau = MAX( av_db_bl(ji,jj) * ( zari * hbl(ji,jj) ) / &
& ( pp_ddh_2 * MAX( -1.0_wp * pwb_ent(ji,jj), 1e-12_wp ) ), 2.0_wp * rn_Dt )
dh(ji,jj) = dh(ji,jj) * EXP( -1.0_wp * rn_Dt / ztau ) + &
& zari * phbl(ji,jj) * ( 1.0_wp - EXP( -1.0_wp * rn_Dt / ztau ) )
IF ( dh(ji,jj) >= hbl(ji,jj) ) dh(ji,jj) = zari * phbl(ji,jj)
END IF
ELSE
ztau = MAX( MAX( hbl(ji,jj) / ( svstr(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**pthird, epsln), 2.0_wp * rn_Dt )
dh(ji,jj) = dh(ji,jj) * EXP( -1.0_wp * rn_Dt / ztau ) + &
& 0.2_wp * phbl(ji,jj) * ( 1.0_wp - EXP( -1.0_wp * rn_Dt / ztau ) )
IF ( dh(ji,jj) > hbl(ji,jj) ) dh(ji,jj) = 0.2_wp * hbl(ji,jj)
END IF
!
ELSE ! l_conv
! Initially shear only for entraining OSBL. Stable code will be needed if extended to stable OSBL
ztau = hbl(ji,jj) / MAX(svstr(ji,jj), epsln)
IF ( pdhdt(ji,jj) >= 0.0_wp ) THEN ! Probably shouldn't include wm here
! Boundary layer deepening
IF ( av_db_bl(ji,jj) > 0.0_wp ) THEN
! Pycnocline thickness set by stratification - use same relationship as for neutral conditions
zari = MIN( 4.5_wp * ( svstr(ji,jj)**2 ) / MAX( av_db_bl(ji,jj) * phbl(ji,jj), epsln ) + 0.01_wp, 0.2_wp )
zdh_ref = MIN( zari, 0.2_wp ) * hbl(ji,jj)
ELSE
zdh_ref = 0.2_wp * hbl(ji,jj)
ENDIF
ELSE ! IF(dhdt < 0)
zdh_ref = 0.2_wp * hbl(ji,jj)
ENDIF ! IF (dhdt >= 0)
dh(ji,jj) = dh(ji,jj) * EXP( -1.0_wp * rn_Dt / ztau ) + zdh_ref * ( 1.0_wp - EXP( -1.0_wp * rn_Dt / ztau ) )
IF ( pdhdt(ji,jj) < 0.0_wp .AND. dh(ji,jj) >= hbl(ji,jj) ) dh(ji,jj) = zdh_ref ! Can be a problem with dh>hbl for
! ! rapid collapse
ENDIF
!
ELSE ! l_shear = .FALSE., calculate ddhdt here
!
IF ( l_conv(ji,jj) ) THEN
!
IF( ln_osm_mle ) THEN
IF ( ( pwb_ent(ji,jj) + 2.0_wp * pwb_fk_b(ji,jj) ) < 0.0_wp ) THEN ! OSBL is deepening. Note wb_fk_b is zero if
! ! ln_osm_mle=F
IF ( av_db_bl(ji,jj) > 0.0_wp .AND. pdbdz_bl_ext(ji,jj) > 0.0_wp ) THEN
IF ( ( swstrc(ji,jj) / MAX( svstr(ji,jj), epsln) )**3 <= 0.5_wp ) THEN ! Near neutral stability
ztmp = svstr(ji,jj)
ELSE ! Unstable
ztmp = swstrc(ji,jj)
END IF
zari = MIN( 1.5_wp * av_db_bl(ji,jj) / &
& ( phbl(ji,jj) * ( MAX( pdbdz_bl_ext(ji,jj), 0.0_wp ) + &
& av_db_bl(ji,jj)**2 / MAX( 4.5_wp * ztmp**2 , 1e-12_wp ) ) ), 0.2_wp )
ELSE
zari = 0.2_wp
END IF
ELSE
zari = 0.2_wp
END IF
ztau = 0.2_wp * hbl(ji,jj) / MAX( epsln, ( svstr(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**pthird )
zdh_ref = zari * hbl(ji,jj)
ELSE ! ln_osm_mle
IF ( av_db_bl(ji,jj) > 0.0_wp .AND. pdbdz_bl_ext(ji,jj) > 0.0_wp ) THEN
IF ( ( swstrc(ji,jj) / MAX( svstr(ji,jj), epsln ) )**3 <= 0.5_wp ) THEN ! Near neutral stability
ztmp = svstr(ji,jj)
ELSE ! Unstable
ztmp = swstrc(ji,jj)
END IF
zari = MIN( 1.5_wp * av_db_bl(ji,jj) / &
& ( phbl(ji,jj) * ( MAX( pdbdz_bl_ext(ji,jj), 0.0_wp ) + &
& av_db_bl(ji,jj)**2 / MAX( 4.5_wp * ztmp**2 , 1e-12_wp ) ) ), 0.2_wp )
ELSE
zari = 0.2_wp
END IF
ztau = hbl(ji,jj) / MAX( epsln, ( svstr(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**pthird )
zdh_ref = zari * hbl(ji,jj)
END IF ! ln_osm_mle
dh(ji,jj) = dh(ji,jj) * EXP( -1.0_wp * rn_Dt / ztau ) + zdh_ref * ( 1.0_wp - EXP( -1.0_wp * rn_Dt / ztau ) )
! IF ( pdhdt(ji,jj) < 0._wp .and. dh(ji,jj) >= hbl(ji,jj) ) dh(ji,jj) = zdh_ref
IF ( dh(ji,jj) >= hbl(ji,jj) ) dh(ji,jj) = zdh_ref
! Alan: this hml is never defined or used
ELSE ! IF (l_conv)
!
ztau = hbl(ji,jj) / MAX( svstr(ji,jj), epsln )
IF ( pdhdt(ji,jj) >= 0.0_wp ) THEN ! Probably shouldn't include wm here
! Boundary layer deepening
IF ( av_db_bl(ji,jj) > 0.0_wp ) THEN
! Pycnocline thickness set by stratification - use same relationship as for neutral conditions.
zari = MIN( 4.5_wp * ( svstr(ji,jj)**2 ) / MAX( av_db_bl(ji,jj) * phbl(ji,jj), epsln ) + 0.01_wp , 0.2_wp )
zdh_ref = MIN( zari, 0.2_wp ) * hbl(ji,jj)
ELSE
zdh_ref = 0.2_wp * hbl(ji,jj)
END IF
ELSE ! IF(dhdt < 0)
zdh_ref = 0.2_wp * hbl(ji,jj)
END IF ! IF (dhdt >= 0)
dh(ji,jj) = dh(ji,jj) * EXP( -1.0_wp * rn_Dt / ztau ) + zdh_ref * ( 1.0_wp - EXP( -1.0_wp * rn_Dt / ztau ) )
IF ( pdhdt(ji,jj) < 0.0_wp .AND. dh(ji,jj) >= hbl(ji,jj) ) dh(ji,jj) = zdh_ref ! Can be a problem with dh>hbl for
! ! rapid collapse
END IF ! IF (l_conv)
!
END IF ! l_shear
!
hml(ji,jj) = hbl(ji,jj) - dh(ji,jj)
inhml = MAX( INT( dh(ji,jj) / MAX( e3t(ji,jj,nbld(ji,jj)-1,Kmm), 1e-3_wp ) ), 1 )
nmld(ji,jj) = MAX( nbld(ji,jj) - inhml, 3 )
phml(ji,jj) = gdepw(ji,jj,nmld(ji,jj),Kmm)
pdh(ji,jj) = phbl(ji,jj) - phml(ji,jj)
!
END_2D
!
END SUBROUTINE zdf_osm_pycnocline_thickness
SUBROUTINE zdf_osm_pycnocline_buoyancy_profiles( Kmm, kp_ext, pdbdz, palpha, pdh, &
& phbl, pdbdz_bl_ext, phml, pdhdt )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_osm_pycnocline_buoyancy_profiles ***
!!
!! ** Purpose : calculate pycnocline buoyancy profiles
!!
!! ** Method :
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kmm ! Ocean time-level index
INTEGER, DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: kp_ext ! External-level offsets
REAL(wp), DIMENSION(T2D(nn_hls-1),jpk), INTENT( out) :: pdbdz ! Gradients in the pycnocline
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT( out) :: palpha
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pdh ! Pycnocline thickness
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pdbdz_bl_ext ! External buoyancy gradients
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: phml ! ML depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pdhdt ! Rates of change of hbl
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!!
INTEGER :: jk, jj, ji
REAL(wp) :: zbgrad
REAL(wp) :: zgamma_b_nd, znd
REAL(wp) :: zzeta_m
REAL(wp) :: ztmp ! Auxiliary variable
!!
REAL(wp), PARAMETER :: pp_gamma_b = 2.25_wp
REAL(wp), PARAMETER :: pp_large = -1e10_wp
!!----------------------------------------------------------------------
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
pdbdz(ji,jj,:) = pp_large
palpha(ji,jj) = pp_large
END_2D
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
!
IF ( nbld(ji,jj) + kp_ext(ji,jj) < mbkt(ji,jj) ) THEN
!
IF ( l_conv(ji,jj) ) THEN ! Convective conditions
!
IF ( l_pyc(ji,jj) ) THEN
!
zzeta_m = 0.1_wp + 0.3_wp / ( 1.0_wp + EXP( -3.5_wp * LOG10( -1.0_wp * shol(ji,jj) ) ) )
palpha(ji,jj) = 2.0_wp * ( 1.0_wp - ( 0.80_wp * zzeta_m + 0.5_wp * SQRT( 3.14159_wp / pp_gamma_b ) ) * &
& pdbdz_bl_ext(ji,jj) * pdh(ji,jj) / av_db_ml(ji,jj) ) / &
& ( 0.723_wp + SQRT( 3.14159_wp / pp_gamma_b ) )
palpha(ji,jj) = MAX( palpha(ji,jj), 0.0_wp )
ztmp = 1.0_wp / MAX( pdh(ji,jj), epsln )
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Commented lines in this section are not needed in new code, once tested !
! can be removed !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! ztgrad = zalpha * av_dt_ml(ji,jj) * ztmp + zdtdz_bl_ext(ji,jj)
! zsgrad = zalpha * av_ds_ml(ji,jj) * ztmp + zdsdz_bl_ext(ji,jj)
zbgrad = palpha(ji,jj) * av_db_ml(ji,jj) * ztmp + pdbdz_bl_ext(ji,jj)
zgamma_b_nd = pdbdz_bl_ext(ji,jj) * pdh(ji,jj) / MAX( av_db_ml(ji,jj), epsln )
DO jk = 2, nbld(ji,jj)
znd = -1.0_wp * ( gdepw(ji,jj,jk,Kmm) - phbl(ji,jj) ) * ztmp
IF ( znd <= zzeta_m ) THEN
! zdtdz(ji,jj,jk) = zdtdz_bl_ext(ji,jj) + zalpha * av_dt_ml(ji,jj) * ztmp * &
! & EXP( -6.0 * ( znd -zzeta_m )**2 )
! zdsdz(ji,jj,jk) = zdsdz_bl_ext(ji,jj) + zalpha * av_ds_ml(ji,jj) * ztmp * &
! & EXP( -6.0 * ( znd -zzeta_m )**2 )
pdbdz(ji,jj,jk) = pdbdz_bl_ext(ji,jj) + palpha(ji,jj) * av_db_ml(ji,jj) * ztmp * &
& EXP( -6.0_wp * ( znd -zzeta_m )**2 )
ELSE
! zdtdz(ji,jj,jk) = ztgrad * EXP( -pp_gamma_b * ( znd - zzeta_m )**2 )
! zdsdz(ji,jj,jk) = zsgrad * EXP( -pp_gamma_b * ( znd - zzeta_m )**2 )
pdbdz(ji,jj,jk) = zbgrad * EXP( -1.0_wp * pp_gamma_b * ( znd - zzeta_m )**2 )
END IF
END DO
END IF ! If no pycnocline pycnocline gradients set to zero
!
ELSE ! Stable conditions
! If pycnocline profile only defined when depth steady of increasing.
IF ( pdhdt(ji,jj) > 0.0_wp ) THEN ! Depth increasing, or steady.
IF ( av_db_bl(ji,jj) > 0.0_wp ) THEN
IF ( shol(ji,jj) >= 0.5_wp ) THEN ! Very stable - 'thick' pycnocline
ztmp = 1.0_wp / MAX( phbl(ji,jj), epsln )
zbgrad = av_db_bl(ji,jj) * ztmp
DO jk = 2, nbld(ji,jj)
znd = gdepw(ji,jj,jk,Kmm) * ztmp
pdbdz(ji,jj,jk) = zbgrad * EXP( -15.0_wp * ( znd - 0.9_wp )**2 )
END DO
ELSE ! Slightly stable - 'thin' pycnoline - needed when stable layer begins to form.
ztmp = 1.0_wp / MAX( pdh(ji,jj), epsln )
zbgrad = av_db_bl(ji,jj) * ztmp
DO jk = 2, nbld(ji,jj)
znd = -1.0_wp * ( gdepw(ji,jj,jk,Kmm) - phml(ji,jj) ) * ztmp
pdbdz(ji,jj,jk) = zbgrad * EXP( -1.75_wp * ( znd + 0.75_wp )**2 )
END DO
END IF ! IF (shol >=0.5)
END IF ! IF (av_db_bl> 0.)
END IF ! IF (pdhdt >= 0) pdhdt < 0 not considered since pycnocline profile is zero and profile arrays are
! ! intialized to zero
!
END IF ! IF (l_conv)
!
END IF ! IF ( nbld(ji,jj) < mbkt(ji,jj) )
!
END_2D
!
IF ( ln_dia_pyc_scl ) THEN ! Output of pycnocline gradient profiles
CALL zdf_osm_iomput( "zdbdz_pyc", wmask(T2D(0),:) * pdbdz(T2D(0),:) )
END IF
!
END SUBROUTINE zdf_osm_pycnocline_buoyancy_profiles
SUBROUTINE zdf_osm_diffusivity_viscosity( Kbb, Kmm, pdiffut, pviscos, phbl, &
& phml, pdh, pdhdt, pshear, &
& pwb_ent, pwb_min )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_osm_diffusivity_viscosity ***
!!
!! ** Purpose : Determines the eddy diffusivity and eddy viscosity
!! profiles in the mixed layer and the pycnocline.
!!
!! ** Method :
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kbb, Kmm ! Ocean time-level indices
REAL(wp), DIMENSION(T2D(nn_hls-1),jpk), INTENT(inout) :: pdiffut ! t-diffusivity
REAL(wp), DIMENSION(T2D(nn_hls-1),jpk), INTENT(inout) :: pviscos ! Viscosity
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: phml ! ML depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pdh ! Pycnocline depth
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pdhdt ! BL depth tendency
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pshear ! Shear production
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pwb_ent ! Buoyancy entrainment flux
REAL(wp), DIMENSION(T2D(nn_hls-1)), INTENT(in ) :: pwb_min
!!
INTEGER :: ji, jj, jk ! Loop indices
!! Scales used to calculate eddy diffusivity and viscosity profiles
REAL(wp), DIMENSION(T2D(nn_hls-1)) :: zdifml_sc, zvisml_sc
REAL(wp), DIMENSION(T2D(nn_hls-1)) :: zdifpyc_n_sc, zdifpyc_s_sc
REAL(wp), DIMENSION(T2D(nn_hls-1)) :: zvispyc_n_sc, zvispyc_s_sc
REAL(wp), DIMENSION(T2D(nn_hls-1)) :: zbeta_d_sc, zbeta_v_sc
REAL(wp), DIMENSION(T2D(nn_hls-1)) :: zb_coup, zc_coup_vis, zc_coup_dif
!!
REAL(wp) :: zvel_sc_pyc, zvel_sc_ml, zstab_fac, zz_b
REAL(wp) :: za_cubic, zb_d_cubic, zc_d_cubic, zd_d_cubic, & ! Coefficients in cubic polynomial specifying diffusivity
& zb_v_cubic, zc_v_cubic, zd_v_cubic ! and viscosity in pycnocline
REAL(wp) :: zznd_ml, zznd_pyc, ztmp
REAL(wp) :: zmsku, zmskv
!!
REAL(wp), PARAMETER :: pp_dif_ml = 0.8_wp, pp_vis_ml = 0.375_wp
REAL(wp), PARAMETER :: pp_dif_pyc = 0.15_wp, pp_vis_pyc = 0.142_wp
REAL(wp), PARAMETER :: pp_vispyc_shr = 0.15_wp