MODULE zdfosm
!!======================================================================
!! *** MODULE zdfosm ***
!! Ocean physics: vertical mixing coefficient compute from the OSMOSIS
!! turbulent closure parameterization
!!=====================================================================
!! History : NEMO 4.0 ! A. Grant, G. Nurser
!! 15/03/2017 Changed calculation of pycnocline thickness in unstable conditions and stable conditions AG
!! 15/03/2017 Calculation of pycnocline gradients for stable conditions changed. Pycnocline gradients now depend on stability of the OSBL. A.G
!! 06/06/2017 (1) Checks on sign of buoyancy jump in calculation of OSBL depth. A.G.
!! (2) Removed variable zbrad0, zbradh and zbradav since they are not used.
!! (3) Approximate treatment for shear turbulence.
!! Minimum values for zustar and zustke.
!! Add velocity scale, zvstr, that tends to zustar for large Langmuir numbers.
!! Limit maximum value for Langmuir number.
!! Use zvstr in definition of stability parameter zhol.
!! (4) Modified parametrization of entrainment flux, changing original coefficient 0.0485 for Langmuir contribution to 0.135 * zla
!! (5) For stable boundary layer add factor that depends on length of timestep to 'slow' collapse and growth. Make sure buoyancy jump not negative.
!! (6) For unstable conditions when growth is over multiple levels, limit change to maximum of one level per cycle through loop.
!! (7) Change lower limits for loops that calculate OSBL averages from 1 to 2. Large gradients between levels 1 and 2 can cause problems.
!! (8) Change upper limits from ibld-1 to ibld.
!! (9) Calculation of pycnocline thickness in unstable conditions. Check added to ensure that buoyancy jump is positive before calculating Ri.
!! (10) Thickness of interface layer at base of the stable OSBL set by Richardson number. Gives continuity in transition from unstable OSBL.
!! (11) Checks that buoyancy jump is poitive when calculating pycnocline profiles.
!! (12) Replace zwstrl with zvstr in calculation of eddy viscosity.
!! 27/09/2017 (13) Calculate Stokes drift and Stokes penetration depth from wave information
!! (14) Buoyancy flux due to entrainment changed to include contribution from shear turbulence.
!! 28/09/2017 (15) Calculation of Stokes drift moved into separate do-loops to allow for different options for the determining the Stokes drift to be added.
!! (16) Calculation of Stokes drift from windspeed for PM spectrum (for testing, commented out)
!! (17) Modification to Langmuir velocity scale to include effects due to the Stokes penetration depth (for testing, commented out)
!! ??/??/2018 (18) Revision to code structure, selected using fortran macro. Inline code moved into subroutines. Changes to physics made,
!! (a) Pycnocline temperature and salinity profies changed for unstable layers
!! (b) The stable OSBL depth parametrization changed.
!! 16/05/2019 (19) Fox-Kemper parametrization of restratification through mixed layer eddies added to revised code.
!! 23/05/19 (20) Remove old code excluded by fortran macro along with the fortran macro that is not needed
!! 4.2 ! 2021-05 (S. Mueller) Efficiency improvements, source-code clarity enhancements, and adaptation to tiling
!!----------------------------------------------------------------------
!!----------------------------------------------------------------------
!! 'ln_zdfosm' OSMOSIS scheme
!!----------------------------------------------------------------------
!! zdf_osm : update momentum and tracer Kz from osm scheme
!! zdf_osm_vertical_average : compute vertical averages over boundary layers
!! zdf_osm_velocity_rotation : rotate velocity components
!! zdf_osm_velocity_rotation_2d : rotation of 2d fields
!! zdf_osm_velocity_rotation_3d : rotation of 3d fields
!! zdf_osm_osbl_state : determine the state of the OSBL
!! zdf_osm_external_gradients : calculate gradients below the OSBL
!! zdf_osm_calculate_dhdt : calculate rate of change of hbl
!! zdf_osm_timestep_hbl : hbl timestep
!! zdf_osm_pycnocline_thickness : calculate thickness of pycnocline
!! zdf_osm_diffusivity_viscosity : compute eddy diffusivity and viscosity profiles
!! zdf_osm_fgr_terms : compute flux-gradient relationship terms
!! zdf_osm_pycnocline_buoyancy_profiles : calculate pycnocline buoyancy profiles
!! zdf_osm_zmld_horizontal_gradients : calculate horizontal buoyancy gradients for use with Fox-Kemper parametrization
!! zdf_osm_osbl_state_fk : determine state of OSBL and MLE layers
!! zdf_osm_mle_parameters : timestep MLE depth and calculate MLE fluxes
!! zdf_osm_init : initialization, namelist read, and parameters control
!! zdf_osm_alloc : memory allocation
!! osm_rst : read (or initialize) and write osmosis restart fields
!! tra_osm : compute and add to the T & S trend the non-local flux
!! trc_osm : compute and add to the passive tracer trend the non-local flux (TBD)
!! dyn_osm : compute and add to u & v trensd the non-local flux
!! zdf_osm_iomput : iom_put wrapper that accepts arrays without halo
!! zdf_osm_iomput_2d : iom_put wrapper for 2D fields
!! zdf_osm_iomput_3d : iom_put wrapper for 3D fields
!!----------------------------------------------------------------------
USE oce ! Ocean dynamics and active tracers
! ! Uses ww from previous time step (which is now wb) to calculate hbl
USE dom_oce ! Ocean space and time domain
USE zdf_oce ! Ocean vertical physics
USE sbc_oce ! Surface boundary condition: ocean
USE sbcwave ! Surface wave parameters
USE phycst ! Physical constants
USE eosbn2 ! Equation of state
USE traqsr ! Details of solar radiation absorption
USE zdfdrg, ONLY : rCdU_bot ! Bottom friction velocity
USE zdfddm ! Double diffusion mixing (avs array)
USE iom ! I/O library
USE lib_mpp ! MPP library
USE trd_oce ! Ocean trends definition
USE trdtra ! Tracers trends
USE in_out_manager ! I/O manager
USE lbclnk ! Ocean lateral boundary conditions (or mpp link)
USE prtctl ! Print control
USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
IMPLICIT NONE
PRIVATE
! Public subroutines
PUBLIC zdf_osm ! Routine called by step.F90
PUBLIC zdf_osm_init ! Routine called by nemogcm.F90
PUBLIC osm_rst ! Routine called by step.F90
PUBLIC tra_osm ! Routine called by step.F90
PUBLIC trc_osm ! Routine called by trcstp.F90
PUBLIC dyn_osm ! Routine called by step.F90
! Public variables
LOGICAL, PUBLIC :: ln_osm_mle !: Flag to activate the Mixed Layer Eddy (MLE)
! ! parameterisation, needed by tra_mle_init in
! ! tramle.F90
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ghamu !: Non-local u-momentum flux
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ghamv !: Non-local v-momentum flux
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ghamt !: Non-local temperature flux (gamma/<ws>o)
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ghams !: Non-local salinity flux (gamma/<ws>o)
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hbl !: Boundary layer depth
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hml !: ML depth
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: hmle !: Depth of layer affexted by mixed layer eddies in Fox-Kemper parametrization
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: dbdx_mle !: Zonal buoyancy gradient in ML
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: dbdy_mle !: Meridional buoyancy gradient in ML
INTEGER, PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: mld_prof !: Level of base of MLE layer
INTERFACE zdf_osm_velocity_rotation
!!---------------------------------------------------------------------
!! *** INTERFACE zdf_velocity_rotation ***
!!---------------------------------------------------------------------
MODULE PROCEDURE zdf_osm_velocity_rotation_2d
MODULE PROCEDURE zdf_osm_velocity_rotation_3d
END INTERFACE
!
INTERFACE zdf_osm_iomput
!!---------------------------------------------------------------------
!! *** INTERFACE zdf_osm_iomput ***
!!---------------------------------------------------------------------
MODULE PROCEDURE zdf_osm_iomput_2d
MODULE PROCEDURE zdf_osm_iomput_3d
END INTERFACE
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: etmean ! Averaging operator for avt
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: dh ! Depth of pycnocline
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: r1_ft ! Inverse of the modified Coriolis parameter at t-pts
! Layer indices
INTEGER, ALLOCATABLE, SAVE, DIMENSION(:,:) :: nbld ! Level of boundary layer base
INTEGER, ALLOCATABLE, SAVE, DIMENSION(:,:) :: nmld ! Level of mixed-layer depth (pycnocline top)
! Layer type
INTEGER, ALLOCATABLE, SAVE, DIMENSION(:,:) :: n_ddh ! Type of shear layer
! ! n_ddh=0: active shear layer
! ! n_ddh=1: shear layer not active
! ! n_ddh=2: shear production low
! Layer flags
LOGICAL, ALLOCATABLE, SAVE, DIMENSION(:,:) :: l_conv ! Unstable/stable bl
LOGICAL, ALLOCATABLE, SAVE, DIMENSION(:,:) :: l_shear ! Shear layers
LOGICAL, ALLOCATABLE, SAVE, DIMENSION(:,:) :: l_coup ! Coupling to bottom
LOGICAL, ALLOCATABLE, SAVE, DIMENSION(:,:) :: l_pyc ! OSBL pycnocline present
LOGICAL, ALLOCATABLE, SAVE, DIMENSION(:,:) :: l_flux ! Surface flux extends below OSBL into MLE layer
LOGICAL, ALLOCATABLE, SAVE, DIMENSION(:,:) :: l_mle ! MLE layer increases in hickness.
! Scales
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: swth0 ! Surface heat flux (Kinematic)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: sws0 ! Surface freshwater flux
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: swb0 ! Surface buoyancy flux
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: suw0 ! Surface u-momentum flux
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: sustar ! Friction velocity
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: scos_wind ! Cos angle of surface stress
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ssin_wind ! Sin angle of surface stress
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: swthav ! Heat flux - bl average
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: swsav ! Freshwater flux - bl average
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: swbav ! Buoyancy flux - bl average
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: sustke ! Surface Stokes drift
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: dstokes ! Penetration depth of the Stokes drift
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: swstrl ! Langmuir velocity scale
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: swstrc ! Convective velocity scale
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: sla ! Trubulent Langmuir number
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: svstr ! Velocity scale that tends to sustar for large Langmuir number
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: shol ! Stability parameter for boundary layer
! Layer averages: BL
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_t_bl ! Temperature average
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_s_bl ! Salinity average
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_u_bl ! Velocity average (u)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_v_bl ! Velocity average (v)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_b_bl ! Buoyancy average
! Difference between layer average and parameter at the base of the layer: BL
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_dt_bl ! Temperature difference
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_ds_bl ! Salinity difference
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_du_bl ! Velocity difference (u)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_dv_bl ! Velocity difference (v)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_db_bl ! Buoyancy difference
! Layer averages: ML
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_t_ml ! Temperature average
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_s_ml ! Salinity average
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_u_ml ! Velocity average (u)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_v_ml ! Velocity average (v)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_b_ml ! Buoyancy average
! Difference between layer average and parameter at the base of the layer: ML
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_dt_ml ! Temperature difference
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_ds_ml ! Salinity difference
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_du_ml ! Velocity difference (u)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_dv_ml ! Velocity difference (v)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_db_ml ! Buoyancy difference
! Layer averages: MLE
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_t_mle ! Temperature average
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_s_mle ! Salinity average
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_u_mle ! Velocity average (u)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_v_mle ! Velocity average (v)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: av_b_mle ! Buoyancy average
! Diagnostic output
REAL(WP), ALLOCATABLE, SAVE, DIMENSION(:,:) :: osmdia2d ! Auxiliary array for diagnostic output
REAL(WP), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: osmdia3d ! Auxiliary array for diagnostic output
LOGICAL :: ln_dia_pyc_scl = .FALSE. ! Output of pycnocline scalar-gradient profiles
LOGICAL :: ln_dia_pyc_shr = .FALSE. ! Output of pycnocline velocity-shear profiles
! !!* namelist namzdf_osm *
LOGICAL :: ln_use_osm_la ! Use namelist rn_osm_la
REAL(wp) :: rn_osm_la ! Turbulent Langmuir number
REAL(wp) :: rn_osm_dstokes ! Depth scale of Stokes drift
REAL(wp) :: rn_zdfosm_adjust_sd = 1.0_wp ! Factor to reduce Stokes drift by
REAL(wp) :: rn_osm_hblfrac = 0.1_wp ! For nn_osm_wave = 3/4 specify fraction in top of hbl
LOGICAL :: ln_zdfosm_ice_shelter ! Flag to activate ice sheltering
REAL(wp) :: rn_osm_hbl0 = 10.0_wp ! Initial value of hbl for 1D runs
INTEGER :: nn_ave ! = 0/1 flag for horizontal average on avt
INTEGER :: nn_osm_wave = 0 ! = 0/1/2 flag for getting stokes drift from La# / PM wind-waves/Inputs into
! ! sbcwave
INTEGER :: nn_osm_SD_reduce ! = 0/1/2 flag for getting effective stokes drift from surface value
LOGICAL :: ln_dia_osm ! Use namelist rn_osm_la
LOGICAL :: ln_kpprimix = .TRUE. ! Shear instability mixing
REAL(wp) :: rn_riinfty = 0.7_wp ! Local Richardson Number limit for shear instability
REAL(wp) :: rn_difri = 0.005_wp ! Maximum shear mixing at Rig = 0 (m2/s)
LOGICAL :: ln_convmix = .TRUE. ! Convective instability mixing
REAL(wp) :: rn_difconv = 1.0_wp ! Diffusivity when unstable below BL (m2/s)
! OSMOSIS mixed layer eddy parametrization constants
INTEGER :: nn_osm_mle ! = 0/1 flag for horizontal average on avt
REAL(wp) :: rn_osm_mle_ce ! MLE coefficient
! Parameters used in nn_osm_mle = 0 case
REAL(wp) :: rn_osm_mle_lf ! Typical scale of mixed layer front
REAL(wp) :: rn_osm_mle_time ! Time scale for mixing momentum across the mixed layer
! Parameters used in nn_osm_mle = 1 case
REAL(wp) :: rn_osm_mle_lat ! Reference latitude for a 5 km scale of ML front
LOGICAL :: ln_osm_hmle_limit ! If true arbitrarily restrict hmle to rn_osm_hmle_limit*zmld
REAL(wp) :: rn_osm_hmle_limit ! If ln_osm_hmle_limit true arbitrarily restrict hmle to rn_osm_hmle_limit*zmld
REAL(wp) :: rn_osm_mle_rho_c ! Density criterion for definition of MLD used by FK
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_osm_mle=1 case
REAL(wp) :: rn_osm_mle_thresh ! Threshold buoyancy for deepening of MLE layer below OSBL base
REAL(wp) :: rn_osm_bl_thresh ! Threshold buoyancy for deepening of OSBL base
REAL(wp) :: rn_osm_mle_tau ! Adjustment timescale for MLE
! General constants
REAL(wp) :: epsln = 1.0e-20_wp ! A small positive number to ensure no div by zero
REAL(wp) :: depth_tol = 1.0e-6_wp ! A small-ish positive number to give a hbl slightly shallower than gdepw
REAL(wp) :: pthird = 1.0_wp/3.0_wp ! 1/3
REAL(wp) :: p2third = 2.0_wp/3.0_wp ! 2/3
!! * Substitutions
# include "do_loop_substitute.h90"
# include "domzgr_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/OCE 4.0 , NEMO Consortium (2018)
!! $Id: zdfosm.F90 14921 2021-05-28 12:19:26Z smueller $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
INTEGER FUNCTION zdf_osm_alloc()
!!----------------------------------------------------------------------
!! *** FUNCTION zdf_osm_alloc ***
!!----------------------------------------------------------------------
INTEGER :: ierr
!!----------------------------------------------------------------------
!
zdf_osm_alloc = 0
!
ALLOCATE( ghamu(jpi,jpj,jpk), ghamv(jpi,jpj,jpk), ghamt(jpi,jpj,jpk), ghams(jpi,jpj,jpk), hbl(jpi,jpj), hml(jpi,jpj), &
& hmle(jpi,jpj), dbdx_mle(jpi,jpj), dbdy_mle(jpi,jpj), mld_prof(jpi,jpj), STAT=ierr )
zdf_osm_alloc = zdf_osm_alloc + ierr
!
ALLOCATE( etmean(A2D(nn_hls-1),jpk), dh(jpi,jpj), r1_ft(A2D(nn_hls-1)), STAT=ierr )
zdf_osm_alloc = zdf_osm_alloc + ierr
!
ALLOCATE( nbld(jpi,jpj), nmld(A2D(nn_hls-1)), STAT=ierr )
zdf_osm_alloc = zdf_osm_alloc + ierr
!
ALLOCATE( n_ddh(A2D(nn_hls-1)), STAT=ierr )
zdf_osm_alloc = zdf_osm_alloc + ierr
!
ALLOCATE( l_conv(A2D(nn_hls-1)), l_shear(A2D(nn_hls-1)), l_coup(A2D(nn_hls-1)), l_pyc(A2D(nn_hls-1)), &
& l_flux(A2D(nn_hls-1)), l_mle(A2D(nn_hls-1)), STAT=ierr )
zdf_osm_alloc = zdf_osm_alloc + ierr
!
ALLOCATE( swth0(A2D(nn_hls-1)), sws0(A2D(nn_hls-1)), swb0(A2D(nn_hls-1)), suw0(A2D(nn_hls-1)), &
& sustar(A2D(nn_hls-1)), scos_wind(A2D(nn_hls-1)), ssin_wind(A2D(nn_hls-1)), swthav(A2D(nn_hls-1)), &
& swsav(A2D(nn_hls-1)), swbav(A2D(nn_hls-1)), sustke(A2D(nn_hls-1)), dstokes(A2D(nn_hls-1)), &
& swstrl(A2D(nn_hls-1)), swstrc(A2D(nn_hls-1)), sla(A2D(nn_hls-1)), svstr(A2D(nn_hls-1)), &
& shol(A2D(nn_hls-1)), STAT=ierr )
zdf_osm_alloc = zdf_osm_alloc + ierr
!
ALLOCATE( av_t_bl(jpi,jpj), av_s_bl(jpi,jpj), av_u_bl(jpi,jpj), av_v_bl(jpi,jpj), &
& av_b_bl(jpi,jpj), STAT=ierr)
zdf_osm_alloc = zdf_osm_alloc + ierr
!
ALLOCATE( av_dt_bl(jpi,jpj), av_ds_bl(jpi,jpj), av_du_bl(jpi,jpj), av_dv_bl(jpi,jpj), &
& av_db_bl(jpi,jpj), STAT=ierr)
zdf_osm_alloc = zdf_osm_alloc + ierr
!
ALLOCATE( av_t_ml(jpi,jpj), av_s_ml(jpi,jpj), av_u_ml(jpi,jpj), av_v_ml(jpi,jpj), &
& av_b_ml(jpi,jpj), STAT=ierr)
zdf_osm_alloc = zdf_osm_alloc + ierr
!
ALLOCATE( av_dt_ml(jpi,jpj), av_ds_ml(jpi,jpj), av_du_ml(jpi,jpj), av_dv_ml(jpi,jpj), &
& av_db_ml(jpi,jpj), STAT=ierr)
zdf_osm_alloc = zdf_osm_alloc + ierr
!
ALLOCATE( av_t_mle(jpi,jpj), av_s_mle(jpi,jpj), av_u_mle(jpi,jpj), av_v_mle(jpi,jpj), &
& av_b_mle(jpi,jpj), STAT=ierr)
zdf_osm_alloc = zdf_osm_alloc + ierr
!
IF ( ln_dia_osm ) THEN
ALLOCATE( osmdia2d(jpi,jpj), osmdia3d(jpi,jpj,jpk), STAT=ierr )
zdf_osm_alloc = zdf_osm_alloc + ierr
END IF
!
CALL mpp_sum ( 'zdfosm', zdf_osm_alloc )
IF( zdf_osm_alloc /= 0 ) CALL ctl_warn( 'zdf_osm_alloc: failed to allocate zdf_osm arrays' )
!
END FUNCTION zdf_osm_alloc
SUBROUTINE zdf_osm( kt, Kbb, Kmm, Krhs, p_avm, &
& p_avt )
!!----------------------------------------------------------------------
!! *** ROUTINE zdf_osm ***
!!
!! ** Purpose : Compute the vertical eddy viscosity and diffusivity
!! coefficients and non local mixing using the OSMOSIS scheme
!!
!! ** Method : The boundary layer depth hosm is diagnosed at tracer points
!! from profiles of buoyancy, and shear, and the surface forcing.
!! Above hbl (sigma=-z/hbl <1) the mixing coefficients are computed from
!!
!! Kx = hosm Wx(sigma) G(sigma)
!!
!! and the non local term ghamt = Cs / Ws(sigma) / hosm
!! Below hosm the coefficients are the sum of mixing due to internal waves
!! shear instability and double diffusion.
!!
!! -1- Compute the now interior vertical mixing coefficients at all depths.
!! -2- Diagnose the boundary layer depth.
!! -3- Compute the now boundary layer vertical mixing coefficients.
!! -4- Compute the now vertical eddy vicosity and diffusivity.
!! -5- Smoothing
!!
!! N.B. The computation is done from jk=2 to jpkm1
!! Surface value of avt are set once a time to zero
!! in routine zdf_osm_init.
!!
!! ** Action : update the non-local terms ghamts
!! update avt (before vertical eddy coef.)
!!
!! References : Large W.G., Mc Williams J.C. and Doney S.C.
!! Reviews of Geophysics, 32, 4, November 1994
!! Comments in the code refer to this paper, particularly
!! the equation number. (LMD94, here after)
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt ! Ocean time step
INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! Ocean time level indices
REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: p_avm, p_avt ! Momentum and tracer Kz (w-points)
!!
INTEGER :: ji, jj, jk, jl, jm, jkflt ! Dummy loop indices
!!
REAL(wp) :: zthermal, zbeta
REAL(wp) :: zesh2, zri, zfri ! Interior Richardson mixing
!! Scales
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zrad0 ! Surface solar temperature flux (deg m/s)
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zradh ! Radiative flux at bl base (Buoyancy units)
REAL(wp) :: zradav ! Radiative flux, bl average (Buoyancy Units)
REAL(wp) :: zvw0 ! Surface v-momentum flux
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zwb0tot ! Total surface buoyancy flux including insolation
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zwb_ent ! Buoyancy entrainment flux
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zwb_min
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zwb_fk_b ! MLE buoyancy flux averaged over OSBL
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zwb_fk ! Max MLE buoyancy flux
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zdiff_mle ! Extra MLE vertical diff
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zvel_mle ! Velocity scale for dhdt with stable ML and FK
!! Mixed-layer variables
INTEGER, DIMENSION(A2D(nn_hls-1)) :: jk_nlev ! Number of levels
INTEGER, DIMENSION(A2D(nn_hls-1)) :: jk_ext ! Offset for external level
!!
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zhbl ! BL depth - grid
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zhml ! ML depth - grid
!!
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zhmle ! MLE depth - grid
REAL(wp), DIMENSION(A2D(nn_hls)) :: zmld ! ML depth on grid
!!
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zdh ! Pycnocline depth - grid
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zdhdt ! BL depth tendency
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zdtdz_bl_ext, zdsdz_bl_ext ! External temperature/salinity gradients
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zdbdz_bl_ext ! External buoyancy gradients
REAL(wp), DIMENSION(A2D(nn_hls)) :: zdtdx, zdtdy, zdsdx, zdsdy ! Horizontal gradients for Fox-Kemper parametrization
!!
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zdbds_mle ! Magnitude of horizontal buoyancy gradient
!! Flux-gradient relationship variables
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zshear ! Shear production
!!
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zhbl_t ! Holds boundary layer depth updated by full timestep
!! For calculating Ri#-dependent mixing
REAL(wp), DIMENSION(A2D(nn_hls)) :: z2du ! u-shear^2
REAL(wp), DIMENSION(A2D(nn_hls)) :: z2dv ! v-shear^2
REAL(wp) :: zrimix ! Spatial form of ri#-induced diffusion
!! Temporary variables
REAL(wp) :: znd ! Temporary non-dimensional depth
REAL(wp) :: zz0, zz1, zfac
REAL(wp) :: zus_x, zus_y ! Temporary Stokes drift
REAL(wp), DIMENSION(A2D(nn_hls-1),jpk) :: zviscos ! Viscosity
REAL(wp), DIMENSION(A2D(nn_hls-1),jpk) :: zdiffut ! t-diffusivity
REAL(wp) :: zabsstke
REAL(wp) :: zsqrtpi, z_two_thirds, zthickness
REAL(wp) :: z2k_times_thickness, zsqrt_depth, zexp_depth, zf, zexperfc
!! For debugging
REAL(wp), PARAMETER :: pp_large = -1e10_wp
!!----------------------------------------------------------------------
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
nmld(ji,jj) = 0
sustke(ji,jj) = pp_large
l_pyc(ji,jj) = .FALSE.
l_flux(ji,jj) = .FALSE.
l_mle(ji,jj) = .FALSE.
END_2D
! Mixed layer
! No initialization of zhbl or zhml (or zdh?)
zhbl(:,:) = pp_large
zhml(:,:) = pp_large
zdh(:,:) = pp_large
!
IF ( ln_osm_mle ) THEN ! Only initialise arrays if needed
zdtdx(:,:) = pp_large ; zdtdy(:,:) = pp_large ; zdsdx(:,:) = pp_large
zdsdy(:,:) = pp_large
zwb_fk(:,:) = pp_large ; zvel_mle(:,:) = pp_large
zhmle(:,:) = pp_large ; zmld(:,:) = pp_large
DO_2D_OVR( nn_hls, nn_hls, nn_hls, nn_hls )
dbdx_mle(ji,jj) = pp_large
dbdy_mle(ji,jj) = pp_large
END_2D
ENDIF
zhbl_t(:,:) = pp_large
!
zdiffut(:,:,:) = 0.0_wp
zviscos(:,:,:) = 0.0_wp
!
DO_3D_OVR( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpk )
ghamt(ji,jj,jk) = pp_large
ghams(ji,jj,jk) = pp_large
ghamu(ji,jj,jk) = pp_large
ghamv(ji,jj,jk) = pp_large
END_3D
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpk )
ghamt(ji,jj,jk) = 0.0_wp
ghams(ji,jj,jk) = 0.0_wp
ghamu(ji,jj,jk) = 0.0_wp
ghamv(ji,jj,jk) = 0.0_wp
END_3D
!
zdiff_mle(:,:) = 0.0_wp
!
! Ensure only positive hbl values are accessed when using extended halo
! (nn_hls==2)
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
hbl(ji,jj) = MAX( hbl(ji,jj), epsln )
END_2D
!
!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
! Calculate boundary layer scales
!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!
! Turbulent surface fluxes and fluxes averaged over depth of the OSBL
zz0 = rn_abs ! Assume two-band radiation model for depth of OSBL - surface equi-partition in 2-bands
zz1 = 1.0_wp - rn_abs
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
zrad0(ji,jj) = qsr(ji,jj) * r1_rho0_rcp ! Surface downward irradiance (so always +ve)
zradh(ji,jj) = zrad0(ji,jj) * & ! Downwards irradiance at base of boundary layer
& ( zz0 * EXP( -1.0_wp * hbl(ji,jj) / rn_si0 ) + zz1 * EXP( -1.0_wp * hbl(ji,jj) / rn_si1 ) )
zradav = zrad0(ji,jj) * & ! Downwards irradiance averaged
& ( zz0 * ( 1.0_wp - EXP( -hbl(ji,jj)/rn_si0 ) ) * rn_si0 + & ! over depth of the OSBL
& zz1 * ( 1.0_wp - EXP( -hbl(ji,jj)/rn_si1 ) ) * rn_si1 ) / hbl(ji,jj)
swth0(ji,jj) = - qns(ji,jj) * r1_rho0_rcp * tmask(ji,jj,1) ! Upwards surface Temperature flux for non-local term
swthav(ji,jj) = 0.5_wp * swth0(ji,jj) - ( 0.5_wp * ( zrad0(ji,jj) + zradh(ji,jj) ) - & ! Turbulent heat flux averaged
& zradav ) ! over depth of OSBL
END_2D
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
sws0(ji,jj) = -1.0_wp * ( ( emp(ji,jj) - rnf(ji,jj) ) * ts(ji,jj,1,jp_sal,Kmm) + & ! Upwards surface salinity flux
& sfx(ji,jj) ) * r1_rho0 * tmask(ji,jj,1) ! for non-local term
zthermal = rab_n(ji,jj,1,jp_tem)
zbeta = rab_n(ji,jj,1,jp_sal)
swb0(ji,jj) = grav * zthermal * swth0(ji,jj) - grav * zbeta * sws0(ji,jj) ! Non radiative upwards surface buoyancy flux
zwb0tot(ji,jj) = swb0(ji,jj) - grav * zthermal * ( zrad0(ji,jj) - zradh(ji,jj) ) ! Total upwards surface buoyancy flux
swsav(ji,jj) = 0.5_wp * sws0(ji,jj) ! Turbulent salinity flux averaged over depth of the OBSL
swbav(ji,jj) = grav * zthermal * swthav(ji,jj) - & ! Turbulent buoyancy flux averaged over the depth of the
& grav * zbeta * swsav(ji,jj) ! OBSBL
END_2D
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
suw0(ji,jj) = -0.5_wp * (utau(ji-1,jj) + utau(ji,jj)) * r1_rho0 * tmask(ji,jj,1) ! Surface upward velocity fluxes
zvw0 = -0.5_wp * (vtau(ji,jj-1) + vtau(ji,jj)) * r1_rho0 * tmask(ji,jj,1)
sustar(ji,jj) = MAX( SQRT( SQRT( suw0(ji,jj) * suw0(ji,jj) + zvw0 * zvw0 ) ), & ! Friction velocity (sustar), at
& 1e-8_wp ) ! T-point : LMD94 eq. 2
scos_wind(ji,jj) = -1.0_wp * suw0(ji,jj) / ( sustar(ji,jj) * sustar(ji,jj) )
ssin_wind(ji,jj) = -1.0_wp * zvw0 / ( sustar(ji,jj) * sustar(ji,jj) )
END_2D
! Calculate Stokes drift in direction of wind (sustke) and Stokes penetration depth (dstokes)
SELECT CASE (nn_osm_wave)
! Assume constant La#=0.3
CASE(0)
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
zus_x = scos_wind(ji,jj) * sustar(ji,jj) / 0.3_wp**2
zus_y = ssin_wind(ji,jj) * sustar(ji,jj) / 0.3_wp**2
! Linearly
sustke(ji,jj) = MAX( SQRT( zus_x * zus_x + zus_y * zus_y ), 1e-8_wp )
dstokes(ji,jj) = rn_osm_dstokes
END_2D
! Assume Pierson-Moskovitz wind-wave spectrum
CASE(1)
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
! Use wind speed wndm included in sbc_oce module
sustke(ji,jj) = MAX ( 0.016_wp * wndm(ji,jj), 1e-8_wp )
dstokes(ji,jj) = MAX ( 0.12_wp * wndm(ji,jj)**2 / grav, 5e-1_wp )
END_2D
! Use ECMWF wave fields as output from SBCWAVE
CASE(2)
zfac = 2.0_wp * rpi / 16.0_wp
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( hsw(ji,jj) > 1e-4_wp ) THEN
! Use wave fields
zabsstke = SQRT( ut0sd(ji,jj)**2 + vt0sd(ji,jj)**2 )
sustke(ji,jj) = MAX( ( scos_wind(ji,jj) * ut0sd(ji,jj) + ssin_wind(ji,jj) * vt0sd(ji,jj) ), 1e-8_wp )
dstokes(ji,jj) = MAX( zfac * hsw(ji,jj) * hsw(ji,jj) / ( MAX( zabsstke * wmp(ji,jj), 1e-7 ) ), 5e-1_wp )
ELSE
! Assume masking issue (e.g. ice in ECMWF reanalysis but not in model run)
! .. so default to Pierson-Moskowitz
sustke(ji,jj) = MAX( 0.016_wp * wndm(ji,jj), 1e-8_wp )
dstokes(ji,jj) = MAX( 0.12_wp * wndm(ji,jj)**2 / grav, 5e-1_wp )
END IF
END_2D
END SELECT
!
IF (ln_zdfosm_ice_shelter) THEN
! Reduce both Stokes drift and its depth scale by ocean fraction to represent sheltering by ice
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
sustke(ji,jj) = sustke(ji,jj) * ( 1.0_wp - fr_i(ji,jj) )
dstokes(ji,jj) = dstokes(ji,jj) * ( 1.0_wp - fr_i(ji,jj) )
END_2D
END IF
!
SELECT CASE (nn_osm_SD_reduce)
! Reduce surface Stokes drift by a constant factor or following Breivik (2016) + van Roekel (2012) or Grant (2020).
CASE(0)
! The Langmur number from the ECMWF model (or from PM) appears to give La<0.3 for wind-driven seas.
! The coefficient rn_zdfosm_adjust_sd = 0.8 gives La=0.3 in this situation.
! It could represent the effects of the spread of wave directions around the mean wind. The effect of this adjustment needs to be tested.
IF(nn_osm_wave > 0) THEN
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
sustke(ji,jj) = rn_zdfosm_adjust_sd * sustke(ji,jj)
END_2D
END IF
CASE(1)
! Van Roekel (2012): consider average SD over top 10% of boundary layer
! Assumes approximate depth profile of SD from Breivik (2016)
zsqrtpi = SQRT(rpi)
z_two_thirds = 2.0_wp / 3.0_wp
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
zthickness = rn_osm_hblfrac*hbl(ji,jj)
z2k_times_thickness = zthickness * 2.0_wp / MAX( ABS( 5.97_wp * dstokes(ji,jj) ), 1e-7_wp )
zsqrt_depth = SQRT( z2k_times_thickness )
zexp_depth = EXP( -1.0_wp * z2k_times_thickness )
sustke(ji,jj) = sustke(ji,jj) * ( 1.0_wp - zexp_depth - &
& z_two_thirds * ( zsqrtpi * zsqrt_depth * z2k_times_thickness * ERFC(zsqrt_depth) + &
& 1.0_wp - ( 1.0_wp + z2k_times_thickness ) * zexp_depth ) ) / &
& z2k_times_thickness
END_2D
CASE(2)
! Grant (2020): Match to exponential with same SD and d/dz(Sd) at depth 10% of boundary layer
! Assumes approximate depth profile of SD from Breivik (2016)
zsqrtpi = SQRT(rpi)
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
zthickness = rn_osm_hblfrac*hbl(ji,jj)
z2k_times_thickness = zthickness * 2.0_wp / MAX( ABS( 5.97_wp * dstokes(ji,jj) ), 1e-7_wp )
IF( z2k_times_thickness < 50.0_wp ) THEN
zsqrt_depth = SQRT( z2k_times_thickness )
zexperfc = zsqrtpi * zsqrt_depth * ERFC(zsqrt_depth) * EXP( z2k_times_thickness )
ELSE
! Asymptotic expansion of sqrt(pi)*zsqrt_depth*EXP(z2k_times_thickness)*ERFC(zsqrt_depth) for large
! z2k_times_thickness
! See Abramowitz and Stegun, Eq. 7.1.23
! zexperfc = 1._wp - (1/2)/(z2k_times_thickness) + (3/4)/(z2k_times_thickness**2) - (15/8)/(z2k_times_thickness**3)
zexperfc = ( ( -1.875_wp / z2k_times_thickness + 0.75_wp ) / z2k_times_thickness - 0.5_wp ) / &
& z2k_times_thickness + 1.0_wp
END IF
zf = z2k_times_thickness * ( 1.0_wp / zexperfc - 1.0_wp )
dstokes(ji,jj) = 5.97_wp * zf * dstokes(ji,jj)
sustke(ji,jj) = sustke(ji,jj) * EXP( z2k_times_thickness * ( 1.0_wp / ( 2.0_wp * zf ) - 1.0_wp ) ) * &
& ( 1.0_wp - zexperfc )
END_2D
END SELECT
!
! Langmuir velocity scale (swstrl), La # (sla)
! Mixed scale (svstr), convective velocity scale (swstrc)
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
! Langmuir velocity scale (swstrl), at T-point
swstrl(ji,jj) = ( sustar(ji,jj) * sustar(ji,jj) * sustke(ji,jj) )**pthird
sla(ji,jj) = MAX( MIN( SQRT( sustar(ji,jj) / ( swstrl(ji,jj) + epsln ) )**3, 4.0_wp ), 0.2_wp )
IF ( sla(ji,jj) > 0.45_wp ) dstokes(ji,jj) = MIN( dstokes(ji,jj), 0.5_wp * hbl(ji,jj) )
! Velocity scale that tends to sustar for large Langmuir numbers
svstr(ji,jj) = ( swstrl(ji,jj)**3 + ( 1.0_wp - EXP( -0.5_wp * sla(ji,jj)**2 ) ) * sustar(ji,jj) * sustar(ji,jj) * &
& sustar(ji,jj) )**pthird
!
! Limit maximum value of Langmuir number as approximate treatment for shear turbulence
! Note sustke and swstrl are not amended
!
! Get convective velocity (swstrc), stabilty scale (shol) and logical conection flag l_conv
IF ( swbav(ji,jj) > 0.0_wp ) THEN
swstrc(ji,jj) = ( 2.0_wp * swbav(ji,jj) * 0.9_wp * hbl(ji,jj) )**pthird
shol(ji,jj) = -0.9_wp * hbl(ji,jj) * 2.0_wp * swbav(ji,jj) / ( svstr(ji,jj)**3 + epsln )
ELSE
swstrc(ji,jj) = 0.0_wp
shol(ji,jj) = -1.0_wp * hbl(ji,jj) * 2.0_wp * swbav(ji,jj) / ( svstr(ji,jj)**3 + epsln )
ENDIF
END_2D
!
!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
! Mixed-layer model - calculate averages over the boundary layer, and the change in the boundary layer depth
!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! BL must be always 4 levels deep.
! For calculation of lateral buoyancy gradients for FK in
! zdf_osm_zmld_horizontal_gradients need halo values for nbld
!
! agn 23/6/20: not clear all this is needed, as hbl checked after it is re-calculated anyway
! ##########################################################################
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
hbl(ji,jj) = MAX(hbl(ji,jj), gdepw(ji,jj,4,Kmm) )
END_2D
DO_2D_OVR( nn_hls, nn_hls, nn_hls, nn_hls )
nbld(ji,jj) = 4
END_2D
DO_3D_OVR( nn_hls, nn_hls, nn_hls, nn_hls, 5, jpkm1 )
IF ( MAX( hbl(ji,jj), gdepw(ji,jj,4,Kmm) ) >= gdepw(ji,jj,jk,Kmm) ) THEN
nbld(ji,jj) = MIN(mbkt(ji,jj)-2, jk)
ENDIF
END_3D
! ##########################################################################
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
zhbl(ji,jj) = gdepw(ji,jj,nbld(ji,jj),Kmm)
nmld(ji,jj) = MAX( 3, nbld(ji,jj) - MAX( INT( dh(ji,jj) / e3t(ji,jj,nbld(ji,jj)-1,Kmm) ), 1 ) )
zhml(ji,jj) = gdepw(ji,jj,nmld(ji,jj),Kmm)
zdh(ji,jj) = zhbl(ji,jj) - zhml(ji,jj)
END_2D
!
! Averages over well-mixed and boundary layer, note BL averages use jk_ext=2 everywhere
jk_nlev(:,:) = nbld(A2D(nn_hls-1))
jk_ext(:,:) = 1 ! ag 19/03
CALL zdf_osm_vertical_average( Kbb, Kmm, jk_nlev, av_t_bl, av_s_bl, &
& av_b_bl, av_u_bl, av_v_bl, jk_ext, av_dt_bl, &
& av_ds_bl, av_db_bl, av_du_bl, av_dv_bl )
jk_nlev(:,:) = nmld(A2D(nn_hls-1)) - 1
jk_ext(:,:) = nbld(A2D(nn_hls-1)) - nmld(A2D(nn_hls-1)) + jk_ext(:,:) + 1 ! ag 19/03
CALL zdf_osm_vertical_average( Kbb, Kmm, jk_nlev, av_t_ml, av_s_ml, &
& av_b_ml, av_u_ml, av_v_ml, jk_ext, av_dt_ml, &
& av_ds_ml, av_db_ml, av_du_ml, av_dv_ml )
! Velocity components in frame aligned with surface stress
CALL zdf_osm_velocity_rotation( av_u_ml, av_v_ml )
CALL zdf_osm_velocity_rotation( av_du_ml, av_dv_ml )
CALL zdf_osm_velocity_rotation( av_u_bl, av_v_bl )
CALL zdf_osm_velocity_rotation( av_du_bl, av_dv_bl )
!
! Determine the state of the OSBL, stable/unstable, shear/no shear
CALL zdf_osm_osbl_state( Kmm, zwb_ent, zwb_min, zshear, zhbl, &
& zhml, zdh )
!
IF ( ln_osm_mle ) THEN
! Fox-Kemper Scheme
DO_2D_OVR( nn_hls, nn_hls, nn_hls, nn_hls )
mld_prof(ji,jj) = 4
END_2D
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 5, jpkm1 )
IF ( hmle(ji,jj) >= gdepw(ji,jj,jk,Kmm) ) mld_prof(ji,jj) = MIN( mbkt(ji,jj), jk)
END_3D
jk_nlev(:,:) = mld_prof(A2D(nn_hls-1))
CALL zdf_osm_vertical_average( Kbb, Kmm, jk_nlev, av_t_mle, av_s_mle, &
& av_b_mle, av_u_mle, av_v_mle )
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
zhmle(ji,jj) = gdepw(ji,jj,mld_prof(ji,jj),Kmm)
END_2D
!
! Calculate fairly-well-mixed depth zmld & its index mld_prof + lateral zmld-averaged gradients
CALL zdf_osm_zmld_horizontal_gradients( Kmm, zmld, zdtdx, zdtdy, zdsdx, &
& zdsdy, zdbds_mle )
! Calculate max vertical FK flux zwb_fk & set logical descriptors
CALL zdf_osm_osbl_state_fk( Kmm, zwb_fk, zhbl, zhmle, zwb_ent, &
& zdbds_mle )
! Recalculate hmle, zmle, zvel_mle, zdiff_mle & redefine mld_proc to be index for new hmle
CALL zdf_osm_mle_parameters( Kmm, zmld, zhmle, zvel_mle, zdiff_mle, &
& zdbds_mle, zhbl, zwb0tot )
ELSE ! ln_osm_mle
! FK not selected, Boundary Layer only.
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
l_pyc(ji,jj) = .TRUE.
l_flux(ji,jj) = .FALSE.
l_mle(ji,jj) = .FALSE.
IF ( l_conv(ji,jj) .AND. av_db_bl(ji,jj) < rn_osm_bl_thresh ) l_pyc(ji,jj) = .FALSE.
END_2D
ENDIF ! ln_osm_mle
!
!! External gradient below BL needed both with and w/o FK
jk_ext(:,:) = nbld(A2D(nn_hls-1)) + 1
CALL zdf_osm_external_gradients( Kmm, jk_ext, zdtdz_bl_ext, zdsdz_bl_ext, zdbdz_bl_ext ) ! ag 19/03
!
! Test if pycnocline well resolved
! DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) Removed with ag 19/03 changes. A change in eddy diffusivity/viscosity
! IF (l_conv(ji,jj) ) THEN should account for this.
! ztmp = 0.2 * zhbl(ji,jj) / e3w(ji,jj,nbld(ji,jj),Kmm)
! IF ( ztmp > 6 ) THEN
! ! pycnocline well resolved
! jk_ext(ji,jj) = 1
! ELSE
! ! pycnocline poorly resolved
! jk_ext(ji,jj) = 0
! ENDIF
! ELSE
! ! Stable conditions
! jk_ext(ji,jj) = 0
! ENDIF
! END_2D
!
! Recalculate bl averages using jk_ext & ml averages .... note no rotation of u & v here..
jk_nlev(:,:) = nbld(A2D(nn_hls-1))
jk_ext(:,:) = 1 ! ag 19/03
CALL zdf_osm_vertical_average( Kbb, Kmm, jk_nlev, av_t_bl, av_s_bl, &
& av_b_bl, av_u_bl, av_v_bl, jk_ext, av_dt_bl, &
& av_ds_bl, av_db_bl, av_du_bl, av_dv_bl )
jk_nlev(:,:) = nmld(A2D(nn_hls-1)) - 1
jk_ext(:,:) = nbld(A2D(nn_hls-1)) - nmld(A2D(nn_hls-1)) + jk_ext(:,:) + 1 ! ag 19/03
CALL zdf_osm_vertical_average( Kbb, Kmm, jk_nlev, av_t_ml, av_s_ml, &
& av_b_ml, av_u_ml, av_v_ml, jk_ext, av_dt_ml, &
& av_ds_ml, av_db_ml, av_du_ml, av_dv_ml ) ! ag 19/03
!
! Rate of change of hbl
CALL zdf_osm_calculate_dhdt( zdhdt, zhbl, zdh, zwb_ent, zwb_min, &
& zdbdz_bl_ext, zwb_fk_b, zwb_fk, zvel_mle )
! Test if surface boundary layer coupled to bottom
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
l_coup(ji,jj) = .FALSE. ! ag 19/03
zhbl_t(ji,jj) = hbl(ji,jj) + ( zdhdt(ji,jj) - ww(ji,jj,nbld(ji,jj)) ) * rn_Dt ! Certainly need ww here, so subtract it
! Adjustment to represent limiting by ocean bottom
IF ( mbkt(ji,jj) > 2 ) THEN ! To ensure mbkt(ji,jj) - 2 > 0 so no incorrect array access
IF ( zhbl_t(ji,jj) > gdepw(ji, jj,mbkt(ji,jj)-2,Kmm) ) THEN
zhbl_t(ji,jj) = MIN( zhbl_t(ji,jj), gdepw(ji,jj,mbkt(ji,jj)-2,Kmm) ) ! ht(:,:))
l_pyc(ji,jj) = .FALSE.
l_coup(ji,jj) = .TRUE. ! ag 19/03
END IF
END IF
END_2D
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
nmld(ji,jj) = nbld(ji,jj) ! use nmld to hold previous blayer index
nbld(ji,jj) = 4
END_2D
!
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 4, jpkm1 )
IF ( zhbl_t(ji,jj) >= gdepw(ji,jj,jk,Kmm) ) THEN
nbld(ji,jj) = jk
END IF
END_3D
!
!
! Step through model levels taking account of buoyancy change to determine the effect on dhdt
!
CALL zdf_osm_timestep_hbl( Kmm, zdhdt, zhbl, zhbl_t, zwb_ent, &
& zwb_fk_b )
! Is external level in bounds?
!
! Recalculate BL averages and differences using new BL depth
jk_nlev(:,:) = nbld(A2D(nn_hls-1))
jk_ext(:,:) = 1 ! ag 19/03
CALL zdf_osm_vertical_average( Kbb, Kmm, jk_nlev, av_t_bl, av_s_bl, &
& av_b_bl, av_u_bl, av_v_bl, jk_ext, av_dt_bl, &
& av_ds_bl, av_db_bl, av_du_bl, av_dv_bl )
!
CALL zdf_osm_pycnocline_thickness( Kmm, zdh, zhml, zdhdt, zhbl, &
& zwb_ent, zdbdz_bl_ext, zwb_fk_b )
!
! Reset l_pyc before calculating terms in the flux-gradient relationship
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( av_db_bl(ji,jj) < rn_osm_bl_thresh .OR. nbld(ji,jj) >= mbkt(ji,jj) - 2 .OR. &
& nbld(ji,jj) - nmld(ji,jj) == 1 .OR. zdhdt(ji,jj) < 0.0_wp ) THEN ! ag 19/03
l_pyc(ji,jj) = .FALSE. ! ag 19/03
IF ( nbld(ji,jj) >= mbkt(ji,jj) -2 ) THEN
nmld(ji,jj) = nbld(ji,jj) - 1 ! ag 19/03
zdh(ji,jj) = gdepw(ji,jj,nbld(ji,jj),Kmm) - gdepw(ji,jj,nmld(ji,jj),Kmm) ! ag 19/03
zhml(ji,jj) = gdepw(ji,jj,nmld(ji,jj),Kmm) ! ag 19/03
dh(ji,jj) = zdh(ji,jj) ! ag 19/03
hml(ji,jj) = hbl(ji,jj) - dh(ji,jj) ! ag 19/03
ENDIF
ENDIF ! ag 19/03
END_2D
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! Limit delta for shallow boundary layers for calculating
dstokes(ji,jj) = MIN ( dstokes(ji,jj), hbl(ji,jj) / 3.0_wp ) ! flux-gradient terms
END_2D
!
!
! Average over the depth of the mixed layer in the convective boundary layer
! jk_ext = nbld - nmld + 1
! Recalculate ML averages and differences using new ML depth
jk_nlev(:,:) = nmld(A2D(nn_hls-1)) - 1
jk_ext(:,:) = nbld(A2D(nn_hls-1)) - nmld(A2D(nn_hls-1)) + jk_ext(:,:) + 1 ! ag 19/03
CALL zdf_osm_vertical_average( Kbb, Kmm, jk_nlev, av_t_ml, av_s_ml, &
& av_b_ml, av_u_ml, av_v_ml, jk_ext, av_dt_ml, &
& av_ds_ml, av_db_ml, av_du_ml, av_dv_ml )
!
jk_ext(:,:) = nbld(A2D(nn_hls-1)) + 1
CALL zdf_osm_external_gradients( Kmm, jk_ext, zdtdz_bl_ext, zdsdz_bl_ext, zdbdz_bl_ext )
! Rotate mean currents and changes onto wind aligned co-ordinates
CALL zdf_osm_velocity_rotation( av_u_ml, av_v_ml )
CALL zdf_osm_velocity_rotation( av_du_ml, av_dv_ml )
CALL zdf_osm_velocity_rotation( av_u_bl, av_v_bl )
CALL zdf_osm_velocity_rotation( av_du_bl, av_dv_bl )
!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
! Eddy viscosity/diffusivity and non-gradient terms in the flux-gradient relationship
!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
CALL zdf_osm_diffusivity_viscosity( Kbb, Kmm, zdiffut, zviscos, zhbl, &
& zhml, zdh, zdhdt, zshear, zwb_ent, &
& zwb_min )
!
! Calculate non-gradient components of the flux-gradient relationships
! --------------------------------------------------------------------
jk_ext(:,:) = 1 ! ag 19/03
CALL zdf_osm_fgr_terms( Kmm, jk_ext, zhbl, zhml, zdh, &
& zdhdt, zshear, zdtdz_bl_ext, zdsdz_bl_ext, zdbdz_bl_ext, &
& zdiffut, zviscos )
!
!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
! Need to put in code for contributions that are applied explicitly to
! the prognostic variables
! 1. Entrainment flux
!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!
! Rotate non-gradient velocity terms back to model reference frame
jk_nlev(:,:) = nbld(A2D(nn_hls-1))
CALL zdf_osm_velocity_rotation( ghamu, ghamv, .FALSE., 2, jk_nlev )
!
! KPP-style Ri# mixing
IF ( ln_kpprimix ) THEN
jkflt = jpk
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( nbld(ji,jj) < jkflt ) jkflt = nbld(ji,jj)
END_2D
DO jk = jkflt+1, jpkm1
! Shear production at uw- and vw-points (energy conserving form)
DO_2D( nn_hls, nn_hls-1, nn_hls, nn_hls-1 )
z2du(ji,jj) = 0.5_wp * ( uu(ji,jj,jk-1,Kmm) - uu(ji,jj,jk,Kmm) ) * ( uu(ji,jj,jk-1,Kbb) - uu(ji,jj,jk,Kbb) ) * &
& wumask(ji,jj,jk) / ( e3uw(ji,jj,jk,Kmm) * e3uw(ji,jj,jk,Kbb) )
z2dv(ji,jj) = 0.5_wp * ( vv(ji,jj,jk-1,Kmm) - vv(ji,jj,jk,Kmm) ) * ( vv(ji,jj,jk-1,Kbb) - vv(ji,jj,jk,Kbb) ) * &
& wvmask(ji,jj,jk) / ( e3vw(ji,jj,jk,Kmm) * e3vw(ji,jj,jk,Kbb) )
END_2D
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( jk > nbld(ji,jj) ) THEN
! Shear prod. at w-point weightened by mask
zesh2 = ( z2du(ji-1,jj) + z2du(ji,jj) ) / MAX( 1.0_wp , umask(ji-1,jj,jk) + umask(ji,jj,jk) ) + &
& ( z2dv(ji,jj-1) + z2dv(ji,jj) ) / MAX( 1.0_wp , vmask(ji,jj-1,jk) + vmask(ji,jj,jk) )
! Local Richardson number
zri = MAX( rn2b(ji,jj,jk), 0.0_wp ) / MAX( zesh2, epsln )
zfri = MIN( zri / rn_riinfty, 1.0_wp )
zfri = ( 1.0_wp - zfri * zfri )
zrimix = zfri * zfri * zfri * wmask(ji, jj, jk)
zdiffut(ji,jj,jk) = MAX( zdiffut(ji,jj,jk), zrimix*rn_difri )
zviscos(ji,jj,jk) = MAX( zviscos(ji,jj,jk), zrimix*rn_difri )
END IF
END_2D
END DO
END IF ! ln_kpprimix = .true.
!
! KPP-style set diffusivity large if unstable below BL
IF ( ln_convmix) THEN
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
DO jk = nbld(ji,jj) + 1, jpkm1
IF ( MIN( rn2(ji,jj,jk), rn2b(ji,jj,jk) ) <= -1e-12_wp ) zdiffut(ji,jj,jk) = MAX( rn_difconv, zdiffut(ji,jj,jk) )
END DO
END_2D
END IF ! ln_convmix = .true.
!
IF ( ln_osm_mle ) THEN ! Set up diffusivity and non-gradient mixing
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( l_flux(ji,jj) ) THEN ! MLE mixing extends below boundary layer
! Calculate MLE flux contribution from surface fluxes
DO jk = 1, nbld(ji,jj)
znd = gdepw(ji,jj,jk,Kmm) / MAX( zhbl(ji,jj), epsln )
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) - ( swth0(ji,jj) - zrad0(ji,jj) + zradh(ji,jj) ) * ( 1.0_wp - znd )
ghams(ji,jj,jk) = ghams(ji,jj,jk) - sws0(ji,jj) * ( 1.0_wp - znd )
END DO
DO jk = 1, mld_prof(ji,jj)
znd = gdepw(ji,jj,jk,Kmm) / MAX( zhmle(ji,jj), epsln )
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) + ( swth0(ji,jj) - zrad0(ji,jj) + zradh(ji,jj) ) * ( 1.0_wp - znd )
ghams(ji,jj,jk) = ghams(ji,jj,jk) + sws0(ji,jj) * ( 1.0_wp -znd )
END DO
! Viscosity for MLEs
DO jk = 1, mld_prof(ji,jj)
znd = -1.0_wp * gdepw(ji,jj,jk,Kmm) / MAX( zhmle(ji,jj), epsln )
zdiffut(ji,jj,jk) = zdiffut(ji,jj,jk) + zdiff_mle(ji,jj) * ( 1.0_wp - ( 2.0_wp * znd + 1.0_wp )**2 ) * &
& ( 1.0_wp + 5.0_wp / 21.0_wp * ( 2.0_wp * znd + 1.0_wp )**2 )
END DO
ELSE ! Surface transports limited to OSBL
! Viscosity for MLEs
DO jk = 1, mld_prof(ji,jj)
znd = -1.0_wp * gdepw(ji,jj,jk,Kmm) / MAX( zhmle(ji,jj), epsln )
zdiffut(ji,jj,jk) = zdiffut(ji,jj,jk) + zdiff_mle(ji,jj) * ( 1.0_wp - ( 2.0_wp * znd + 1.0_wp )**2 ) * &
& ( 1.0_wp + 5.0_wp / 21.0_wp * ( 2.0_wp * znd + 1.0_wp )**2 )
END DO
END IF
END_2D
ENDIF
!
! Lateral boundary conditions on zvicos (sign unchanged), needed to caclulate viscosities on u and v grids
! CALL lbc_lnk( 'zdfosm', zviscos(:,:,:), 'W', 1.0_wp )
! GN 25/8: need to change tmask --> wmask
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 )
p_avt(ji,jj,jk) = MAX( zdiffut(ji,jj,jk), avtb(jk) ) * tmask(ji,jj,jk)
p_avm(ji,jj,jk) = MAX( zviscos(ji,jj,jk), avmb(jk) ) * tmask(ji,jj,jk)
END_3D
!
IF ( ln_dia_osm ) THEN
SELECT CASE (nn_osm_wave)
! Stokes drift set by assumimg onstant La#=0.3 (=0) or Pierson-Moskovitz spectrum (=1)
CASE(0:1)
CALL zdf_osm_iomput( "us_x", tmask(A2D(0),1) * sustke(A2D(0)) * scos_wind(A2D(0)) ) ! x surface Stokes drift
CALL zdf_osm_iomput( "us_y", tmask(A2D(0),1) * sustke(A2D(0)) * ssin_wind(A2D(0)) ) ! y surface Stokes drift
CALL zdf_osm_iomput( "wind_wave_abs_power", 1000.0_wp * rho0 * tmask(A2D(0),1) * sustar(A2D(0))**2 * sustke(A2D(0)) )
! Stokes drift read in from sbcwave (=2).
CASE(2:3)
CALL zdf_osm_iomput( "us_x", ut0sd(A2D(0)) * umask(A2D(0),1) ) ! x surface Stokes drift
CALL zdf_osm_iomput( "us_y", vt0sd(A2D(0)) * vmask(A2D(0),1) ) ! y surface Stokes drift
CALL zdf_osm_iomput( "wmp", wmp(A2D(0)) * tmask(A2D(0),1) ) ! Wave mean period
CALL zdf_osm_iomput( "hsw", hsw(A2D(0)) * tmask(A2D(0),1) ) ! Significant wave height
CALL zdf_osm_iomput( "wmp_NP", ( 2.0_wp * rpi * 1.026_wp / ( 0.877_wp * grav ) ) * & ! Wave mean period from NP
& wndm(A2D(0)) * tmask(A2D(0),1) ) ! spectrum
CALL zdf_osm_iomput( "hsw_NP", ( 0.22_wp / grav ) * wndm(A2D(0))**2 * tmask(A2D(0),1) ) ! Significant wave height from
! ! NP spectrum
CALL zdf_osm_iomput( "wndm", wndm(A2D(0)) * tmask(A2D(0),1) ) ! U_10
CALL zdf_osm_iomput( "wind_wave_abs_power", 1000.0_wp * rho0 * tmask(A2D(0),1) * sustar(A2D(0))**2 * &
& SQRT( ut0sd(A2D(0))**2 + vt0sd(A2D(0))**2 ) )
END SELECT
CALL zdf_osm_iomput( "zwth0", tmask(A2D(0),1) * swth0(A2D(0)) ) ! <Tw_0>
CALL zdf_osm_iomput( "zws0", tmask(A2D(0),1) * sws0(A2D(0)) ) ! <Sw_0>
CALL zdf_osm_iomput( "zwb0", tmask(A2D(0),1) * swb0(A2D(0)) ) ! <bw_0>
CALL zdf_osm_iomput( "zwbav", tmask(A2D(0),1) * swbav(A2D(0)) ) ! Upward BL-avged turb buoyancy flux
CALL zdf_osm_iomput( "ibld", tmask(A2D(0),1) * nbld(A2D(0)) ) ! Boundary-layer max k
CALL zdf_osm_iomput( "zdt_bl", tmask(A2D(0),1) * av_dt_bl(A2D(0)) ) ! dt at ml base
CALL zdf_osm_iomput( "zds_bl", tmask(A2D(0),1) * av_ds_bl(A2D(0)) ) ! ds at ml base
CALL zdf_osm_iomput( "zdb_bl", tmask(A2D(0),1) * av_db_bl(A2D(0)) ) ! db at ml base
CALL zdf_osm_iomput( "zdu_bl", tmask(A2D(0),1) * av_du_bl(A2D(0)) ) ! du at ml base
CALL zdf_osm_iomput( "zdv_bl", tmask(A2D(0),1) * av_dv_bl(A2D(0)) ) ! dv at ml base
CALL zdf_osm_iomput( "dh", tmask(A2D(0),1) * dh(A2D(0)) ) ! Initial boundary-layer depth
CALL zdf_osm_iomput( "hml", tmask(A2D(0),1) * hml(A2D(0)) ) ! Initial boundary-layer depth
CALL zdf_osm_iomput( "zdt_ml", tmask(A2D(0),1) * av_dt_ml(A2D(0)) ) ! dt at ml base
CALL zdf_osm_iomput( "zds_ml", tmask(A2D(0),1) * av_ds_ml(A2D(0)) ) ! ds at ml base
CALL zdf_osm_iomput( "zdb_ml", tmask(A2D(0),1) * av_db_ml(A2D(0)) ) ! db at ml base
CALL zdf_osm_iomput( "dstokes", tmask(A2D(0),1) * dstokes(A2D(0)) ) ! Stokes drift penetration depth
CALL zdf_osm_iomput( "zustke", tmask(A2D(0),1) * sustke(A2D(0)) ) ! Stokes drift magnitude at T-points
CALL zdf_osm_iomput( "zwstrc", tmask(A2D(0),1) * swstrc(A2D(0)) ) ! Convective velocity scale
CALL zdf_osm_iomput( "zwstrl", tmask(A2D(0),1) * swstrl(A2D(0)) ) ! Langmuir velocity scale
CALL zdf_osm_iomput( "zustar", tmask(A2D(0),1) * sustar(A2D(0)) ) ! Friction velocity scale
CALL zdf_osm_iomput( "zvstr", tmask(A2D(0),1) * svstr(A2D(0)) ) ! Mixed velocity scale
CALL zdf_osm_iomput( "zla", tmask(A2D(0),1) * sla(A2D(0)) ) ! Langmuir #
CALL zdf_osm_iomput( "wind_power", 1000.0_wp * rho0 * tmask(A2D(0),1) * & ! BL depth internal to zdf_osm routine
& sustar(A2D(0))**3 )
CALL zdf_osm_iomput( "wind_wave_power", 1000.0_wp * rho0 * tmask(A2D(0),1) * &
& sustar(A2D(0))**2 * sustke(A2D(0)) )
CALL zdf_osm_iomput( "zhbl", tmask(A2D(0),1) * zhbl(A2D(0)) ) ! BL depth internal to zdf_osm routine
CALL zdf_osm_iomput( "zhml", tmask(A2D(0),1) * zhml(A2D(0)) ) ! ML depth internal to zdf_osm routine
CALL zdf_osm_iomput( "imld", tmask(A2D(0),1) * nmld(A2D(0)) ) ! Index for ML depth internal to zdf_osm
! ! routine
CALL zdf_osm_iomput( "jp_ext", tmask(A2D(0),1) * jk_ext(A2D(0)) ) ! =1 if pycnocline resolved internal to
! ! zdf_osm routine
CALL zdf_osm_iomput( "j_ddh", tmask(A2D(0),1) * n_ddh(A2D(0)) ) ! Index forpyc thicknessh internal to
! ! zdf_osm routine
CALL zdf_osm_iomput( "zshear", tmask(A2D(0),1) * zshear(A2D(0)) ) ! Shear production of TKE internal to
! ! zdf_osm routine
CALL zdf_osm_iomput( "zdh", tmask(A2D(0),1) * zdh(A2D(0)) ) ! Pyc thicknessh internal to zdf_osm
! ! routine
CALL zdf_osm_iomput( "zhol", tmask(A2D(0),1) * shol(A2D(0)) ) ! ML depth internal to zdf_osm routine
CALL zdf_osm_iomput( "zwb_ent", tmask(A2D(0),1) * zwb_ent(A2D(0)) ) ! Upward turb buoyancy entrainment flux
CALL zdf_osm_iomput( "zt_ml", tmask(A2D(0),1) * av_t_ml(A2D(0)) ) ! Average T in ML
CALL zdf_osm_iomput( "zmld", tmask(A2D(0),1) * zmld(A2D(0)) ) ! FK target layer depth
CALL zdf_osm_iomput( "zwb_fk", tmask(A2D(0),1) * zwb_fk(A2D(0)) ) ! FK b flux
CALL zdf_osm_iomput( "zwb_fk_b", tmask(A2D(0),1) * zwb_fk_b(A2D(0)) ) ! FK b flux averaged over ML
CALL zdf_osm_iomput( "mld_prof", tmask(A2D(0),1) * mld_prof(A2D(0)) ) ! FK layer max k
CALL zdf_osm_iomput( "zdtdx", umask(A2D(0),1) * zdtdx(A2D(0)) ) ! FK dtdx at u-pt
CALL zdf_osm_iomput( "zdtdy", vmask(A2D(0),1) * zdtdy(A2D(0)) ) ! FK dtdy at v-pt
CALL zdf_osm_iomput( "zdsdx", umask(A2D(0),1) * zdsdx(A2D(0)) ) ! FK dtdx at u-pt
CALL zdf_osm_iomput( "zdsdy", vmask(A2D(0),1) * zdsdy(A2D(0)) ) ! FK dsdy at v-pt
CALL zdf_osm_iomput( "dbdx_mle", umask(A2D(0),1) * dbdx_mle(A2D(0)) ) ! FK dbdx at u-pt
CALL zdf_osm_iomput( "dbdy_mle", vmask(A2D(0),1) * dbdy_mle(A2D(0)) ) ! FK dbdy at v-pt
CALL zdf_osm_iomput( "zdiff_mle", tmask(A2D(0),1) * zdiff_mle(A2D(0)) ) ! FK diff in MLE at t-pt
CALL zdf_osm_iomput( "zvel_mle", tmask(A2D(0),1) * zvel_mle(A2D(0)) ) ! FK velocity in MLE at t-pt
END IF
!
! Lateral boundary conditions on ghamu and ghamv, currently on W-grid (sign unchanged), needed to caclulate gham[uv] on u and
! v grids
IF ( .NOT. l_istiled .OR. ntile == nijtile ) THEN ! Finalise ghamu, ghamv, hbl, and hmle only after full domain has been
! ! processed
IF ( nn_hls == 1 ) CALL lbc_lnk( 'zdfosm', ghamu, 'W', 1.0_wp, &
& 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(A2D(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(A2D(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(A2D(nn_hls-1)) :: zthick ! Layer thickness
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(A2D(nn_hls-1)) :: knlev ! Array of maximum depth indices
!!
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(A2D(nn_hls-1)), INTENT( out) :: pwb_ent ! Buoyancy fluxes at base
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT( out) :: pwb_min ! of well-mixed layer
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT( out) :: pshear ! Production of TKE due to shear across the pycnocline
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phml ! ML depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdh ! Pycnocline depth
!!
INTEGER :: jj, ji ! Loop indices
!!
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zekman
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zri_p, zri_b ! Richardson numbers
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(A2D(nn_hls-1)) ) * phbl(A2D(nn_hls-1)) / &
& MAX( sustar(A2D(nn_hls-1)), 1.e-8 ) )
!
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(A2D(nn_hls-1)), INTENT(in ) :: kbase ! OSBL base layer index
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT( out) :: pdtdz, pdsdz ! External gradients of temperature, salinity
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT( out) :: pdbdz ! and buoyancy
!!
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(A2D(nn_hls-1)), INTENT( out) :: pdhdt ! Rate of change of hbl
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdh ! Pycnocline depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pwb_ent ! Buoyancy entrainment flux
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pwb_min
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdbdz_bl_ext ! External buoyancy gradients
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT( out) :: pwb_fk_b ! MLE buoyancy flux averaged over OSBL
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pwb_fk ! Max MLE buoyancy flux
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pvel_mle ! Vvelocity scale for dhdt with stable ML and FK
!!
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(A2D(nn_hls-1)), INTENT(inout) :: pdhdt ! Rates of change of hbl
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(inout) :: phbl ! BL depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phbl_t ! BL depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pwb_ent ! Buoyancy entrainment flux
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pwb_fk_b ! MLE buoyancy flux averaged over OSBL
!!
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)
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,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(A2D(nn_hls-1)), INTENT(inout) :: pdh ! Pycnocline thickness
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(inout) :: phml ! ML depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdhdt ! BL depth tendency
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pwb_ent ! Buoyancy entrainment flux
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdbdz_bl_ext ! External buoyancy gradients
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pwb_fk_b ! MLE buoyancy flux averaged over OSBL
!!
INTEGER :: jj, ji
INTEGER :: inhml
REAL(wp) :: zari, ztau, zdh_ref, zddhdt, zvel_max
REAL(wp) :: ztmp ! Auxiliary variable
!!
REAL(wp), 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(A2D(nn_hls-1)), INTENT(in ) :: kp_ext ! External-level offsets
REAL(wp), DIMENSION(A2D(nn_hls-1),jpk), INTENT( out) :: pdbdz ! Gradients in the pycnocline
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT( out) :: palpha
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdh ! Pycnocline thickness
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdbdz_bl_ext ! External buoyancy gradients
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phml ! ML depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdhdt ! Rates of change of hbl
!!
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(A2D(0),:) * pdbdz(A2D(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(A2D(nn_hls-1),jpk), INTENT(inout) :: pdiffut ! t-diffusivity
REAL(wp), DIMENSION(A2D(nn_hls-1),jpk), INTENT(inout) :: pviscos ! Viscosity
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phml ! ML depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdh ! Pycnocline depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdhdt ! BL depth tendency
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pshear ! Shear production
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pwb_ent ! Buoyancy entrainment flux
REAL(wp), DIMENSION(A2D(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(A2D(nn_hls-1)) :: zdifml_sc, zvisml_sc
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zdifpyc_n_sc, zdifpyc_s_sc
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zvispyc_n_sc, zvispyc_s_sc
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zbeta_d_sc, zbeta_v_sc
REAL(wp), DIMENSION(A2D(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
!!----------------------------------------------------------------------
!
zb_coup(:,:) = 0.0_wp
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( l_conv(ji,jj) ) THEN
!
zvel_sc_pyc = ( 0.15_wp * svstr(ji,jj)**3 + swstrc(ji,jj)**3 + 4.25_wp * pshear(ji,jj) * phbl(ji,jj) )**pthird
zvel_sc_ml = ( svstr(ji,jj)**3 + 0.5_wp * swstrc(ji,jj)**3 )**pthird
zstab_fac = ( phml(ji,jj) / zvel_sc_ml * &
& ( 1.4_wp - 0.4_wp / ( 1.0_wp + EXP(-3.5_wp * LOG10( -1.0_wp * shol(ji,jj) ) ) )**1.25_wp ) )**2
!
zdifml_sc(ji,jj) = pp_dif_ml * phml(ji,jj) * zvel_sc_ml
zvisml_sc(ji,jj) = pp_vis_ml * zdifml_sc(ji,jj)
!
IF ( l_pyc(ji,jj) ) THEN
zdifpyc_n_sc(ji,jj) = pp_dif_pyc * zvel_sc_ml * pdh(ji,jj)
zvispyc_n_sc(ji,jj) = 0.09_wp * zvel_sc_pyc * ( 1.0_wp - phbl(ji,jj) / pdh(ji,jj) )**2 * &
& ( 0.005_wp * ( av_u_ml(ji,jj) - av_u_bl(ji,jj) )**2 + &
& 0.0075_wp * ( av_v_ml(ji,jj) - av_v_bl(ji,jj) )**2 ) / &
& pdh(ji,jj)
zvispyc_n_sc(ji,jj) = pp_vis_pyc * zvel_sc_ml * pdh(ji,jj) + zvispyc_n_sc(ji,jj) * zstab_fac
!
IF ( l_shear(ji,jj) .AND. n_ddh(ji,jj) /= 2 ) THEN
ztmp = pp_vispyc_shr * ( pshear(ji,jj) * phbl(ji,jj) )**pthird * phbl(ji,jj)
zdifpyc_n_sc(ji,jj) = zdifpyc_n_sc(ji,jj) + ztmp
zvispyc_n_sc(ji,jj) = zvispyc_n_sc(ji,jj) + ztmp
ENDIF
!
zdifpyc_s_sc(ji,jj) = pwb_ent(ji,jj) + 0.0025_wp * zvel_sc_pyc * ( phbl(ji,jj) / pdh(ji,jj) - 1.0_wp ) * &
& ( av_b_ml(ji,jj) - av_b_bl(ji,jj) )
zvispyc_s_sc(ji,jj) = 0.09_wp * ( pwb_min(ji,jj) + 0.0025_wp * zvel_sc_pyc * &
& ( phbl(ji,jj) / pdh(ji,jj) - 1.0_wp ) * &
& ( av_b_ml(ji,jj) - av_b_bl(ji,jj) ) )
zdifpyc_s_sc(ji,jj) = 0.09_wp * zdifpyc_s_sc(ji,jj) * zstab_fac
zvispyc_s_sc(ji,jj) = zvispyc_s_sc(ji,jj) * zstab_fac
!
zdifpyc_s_sc(ji,jj) = MAX( zdifpyc_s_sc(ji,jj), -0.5_wp * zdifpyc_n_sc(ji,jj) )
zvispyc_s_sc(ji,jj) = MAX( zvispyc_s_sc(ji,jj), -0.5_wp * zvispyc_n_sc(ji,jj) )
zbeta_d_sc(ji,jj) = 1.0_wp - ( ( zdifpyc_n_sc(ji,jj) + 1.4_wp * zdifpyc_s_sc(ji,jj) ) / &
& ( zdifml_sc(ji,jj) + epsln ) )**p2third
zbeta_v_sc(ji,jj) = 1.0_wp - 2.0_wp * ( zvispyc_n_sc(ji,jj) + zvispyc_s_sc(ji,jj) ) / ( zvisml_sc(ji,jj) + epsln )
ELSE
zdifpyc_n_sc(ji,jj) = pp_dif_pyc * zvel_sc_ml * pdh(ji,jj) ! ag 19/03
zdifpyc_s_sc(ji,jj) = 0.0_wp ! ag 19/03
zvispyc_n_sc(ji,jj) = pp_vis_pyc * zvel_sc_ml * pdh(ji,jj) ! ag 19/03
zvispyc_s_sc(ji,jj) = 0.0_wp ! ag 19/03
IF(l_coup(ji,jj) ) THEN ! ag 19/03
! code from SUBROUTINE tke_tke zdftke.F90; uses bottom drag velocity rCdU_bot(ji,jj) = -Cd|ub|
! already calculated at T-points in SUBROUTINE zdf_drg from zdfdrg.F90
! Gives friction velocity sqrt bottom drag/rho_0 i.e. u* = SQRT(rCdU_bot*ub)
! wet-cell averaging ..
zmsku = 0.5_wp * ( 2.0_wp - umask(ji-1,jj,mbkt(ji,jj)) * umask(ji,jj,mbkt(ji,jj)) )
zmskv = 0.5_wp * ( 2.0_wp - vmask(ji,jj-1,mbkt(ji,jj)) * vmask(ji,jj,mbkt(ji,jj)) )
zb_coup(ji,jj) = 0.4_wp * SQRT(-1.0_wp * 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 ) )
zz_b = -1.0_wp * gdepw(ji,jj,mbkt(ji,jj)+1,Kmm) ! ag 19/03
zc_coup_vis(ji,jj) = -0.5_wp * ( 0.5_wp * zvisml_sc(ji,jj) / phml(ji,jj) - zb_coup(ji,jj) ) / &
& ( phml(ji,jj) + zz_b ) ! ag 19/03
zz_b = -1.0_wp * phml(ji,jj) + gdepw(ji,jj,mbkt(ji,jj)+1,Kmm) ! ag 19/03
zbeta_v_sc(ji,jj) = 1.0_wp - 2.0_wp * ( zb_coup(ji,jj) * zz_b + zc_coup_vis(ji,jj) * zz_b**2 ) / &
& zvisml_sc(ji,jj) ! ag 19/03
zbeta_d_sc(ji,jj) = 1.0_wp - ( ( zb_coup(ji,jj) * zz_b + zc_coup_vis(ji,jj) * zz_b**2 ) / &
& zdifml_sc(ji,jj) )**p2third
zc_coup_dif(ji,jj) = 0.5_wp * ( -zdifml_sc(ji,jj) / phml(ji,jj) * ( 1.0_wp - zbeta_d_sc(ji,jj) )**1.5_wp + &
& 1.5_wp * ( zdifml_sc(ji,jj) / phml(ji,jj) ) * zbeta_d_sc(ji,jj) * &
& SQRT( 1.0_wp - zbeta_d_sc(ji,jj) ) - zb_coup(ji,jj) ) / zz_b ! ag 19/03
ELSE ! ag 19/03
zbeta_d_sc(ji,jj) = 1.0_wp - ( ( zdifpyc_n_sc(ji,jj) + 1.4_wp * zdifpyc_s_sc(ji,jj) ) / &
& ( zdifml_sc(ji,jj) + epsln ) )**p2third ! ag 19/03
zbeta_v_sc(ji,jj) = 1.0_wp - 2.0_wp * ( zvispyc_n_sc(ji,jj) + zvispyc_s_sc(ji,jj) ) / &
& ( zvisml_sc(ji,jj) + epsln ) ! ag 19/03
ENDIF ! ag 19/03
ENDIF ! ag 19/03
ELSE
zdifml_sc(ji,jj) = svstr(ji,jj) * phbl(ji,jj) * MAX( EXP ( -1.0_wp * ( shol(ji,jj) / 0.6_wp )**2 ), 0.2_wp)
zvisml_sc(ji,jj) = zdifml_sc(ji,jj)
END IF
END_2D
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( l_conv(ji,jj) ) THEN
DO jk = 2, nmld(ji,jj) ! Mixed layer diffusivity
zznd_ml = gdepw(ji,jj,jk,Kmm) / phml(ji,jj)
pdiffut(ji,jj,jk) = zdifml_sc(ji,jj) * zznd_ml * ( 1.0_wp - zbeta_d_sc(ji,jj) * zznd_ml )**1.5
pviscos(ji,jj,jk) = zvisml_sc(ji,jj) * zznd_ml * ( 1.0_wp - zbeta_v_sc(ji,jj) * zznd_ml ) * &
& ( 1.0_wp - 0.5_wp * zznd_ml**2 )
END DO
!
! Coupling to bottom
!
IF ( l_coup(ji,jj) ) THEN ! ag 19/03
DO jk = mbkt(ji,jj), nmld(ji,jj), -1 ! ag 19/03
zz_b = -1.0_wp * ( gdepw(ji,jj,jk,Kmm) - gdepw(ji,jj,mbkt(ji,jj)+1,Kmm) ) ! ag 19/03
pviscos(ji,jj,jk) = zb_coup(ji,jj) * zz_b + zc_coup_vis(ji,jj) * zz_b**2 ! ag 19/03
pdiffut(ji,jj,jk) = zb_coup(ji,jj) * zz_b + zc_coup_dif(ji,jj) * zz_b**2 ! ag 19/03
END DO ! ag 19/03
ENDIF ! ag 19/03
! Pycnocline
IF ( l_pyc(ji,jj) ) THEN
! Diffusivity and viscosity profiles in the pycnocline given by
! cubic polynomial. Note, if l_pyc TRUE can't be coupled to seabed.
za_cubic = 0.5_wp
zb_d_cubic = -1.75_wp * zdifpyc_s_sc(ji,jj) / zdifpyc_n_sc(ji,jj)
zd_d_cubic = ( pdh(ji,jj) * zdifml_sc(ji,jj) / phml(ji,jj) * SQRT( 1.0_wp - zbeta_d_sc(ji,jj) ) * &
& ( 2.5_wp * zbeta_d_sc(ji,jj) - 1.0_wp ) - 0.85_wp * zdifpyc_s_sc(ji,jj) ) / &
& MAX( zdifpyc_n_sc(ji,jj), 1.0e-8_wp )
zd_d_cubic = zd_d_cubic - zb_d_cubic - 2.0_wp * ( 1.0_wp - za_cubic - zb_d_cubic )
zc_d_cubic = 1.0_wp - za_cubic - zb_d_cubic - zd_d_cubic
zb_v_cubic = -1.75_wp * zvispyc_s_sc(ji,jj) / zvispyc_n_sc(ji,jj)
zd_v_cubic = ( 0.5_wp * zvisml_sc(ji,jj) * pdh(ji,jj) / phml(ji,jj) - 0.85_wp * zvispyc_s_sc(ji,jj) ) / &
& MAX( zvispyc_n_sc(ji,jj), 1.0e-8_wp )
zd_v_cubic = zd_v_cubic - zb_v_cubic - 2.0_wp * ( 1.0_wp - za_cubic - zb_v_cubic )
zc_v_cubic = 1.0_wp - za_cubic - zb_v_cubic - zd_v_cubic
DO jk = nmld(ji,jj) , nbld(ji,jj)
zznd_pyc = -1.0_wp * ( gdepw(ji,jj,jk,Kmm) - phbl(ji,jj) ) / MAX(pdh(ji,jj), 1.0e-6_wp )
ztmp = ( 1.75_wp * zznd_pyc - 0.15_wp * zznd_pyc**2 - 0.2_wp * zznd_pyc**3 )
!
pdiffut(ji,jj,jk) = zdifpyc_n_sc(ji,jj) * &
& ( za_cubic + zb_d_cubic * zznd_pyc + zc_d_cubic * zznd_pyc**2 + zd_d_cubic * zznd_pyc**3 )
!
pdiffut(ji,jj,jk) = pdiffut(ji,jj,jk) + zdifpyc_s_sc(ji,jj) * ztmp
pviscos(ji,jj,jk) = zvispyc_n_sc(ji,jj) * &
& ( za_cubic + zb_v_cubic * zznd_pyc + zc_v_cubic * zznd_pyc**2 + zd_v_cubic * zznd_pyc**3 )
pviscos(ji,jj,jk) = pviscos(ji,jj,jk) + zvispyc_s_sc(ji,jj) * ztmp
END DO
! IF ( pdhdt(ji,jj) > 0._wp ) THEN
! zdiffut(ji,jj,nbld(ji,jj)+1) = MAX( 0.5 * pdhdt(ji,jj) * e3w(ji,jj,nbld(ji,jj)+1,Kmm), 1.0e-6 )
! zviscos(ji,jj,nbld(ji,jj)+1) = MAX( 0.5 * pdhdt(ji,jj) * e3w(ji,jj,nbld(ji,jj)+1,Kmm), 1.0e-6 )
! ELSE
! zdiffut(ji,jj,nbld(ji,jj)) = 0._wp
! zviscos(ji,jj,nbld(ji,jj)) = 0._wp
! ENDIF
ENDIF
ELSE
! Stable conditions
DO jk = 2, nbld(ji,jj)
zznd_ml = gdepw(ji,jj,jk,Kmm) / phbl(ji,jj)
pdiffut(ji,jj,jk) = 0.75_wp * zdifml_sc(ji,jj) * zznd_ml * ( 1.0_wp - zznd_ml )**1.5_wp
pviscos(ji,jj,jk) = 0.375_wp * zvisml_sc(ji,jj) * zznd_ml * ( 1.0_wp - zznd_ml ) * ( 1.0_wp - zznd_ml**2 )
END DO
!
IF ( pdhdt(ji,jj) > 0.0_wp ) THEN
pdiffut(ji,jj,nbld(ji,jj)) = MAX( pdhdt(ji,jj), 1.0e-6_wp) * e3w(ji, jj, nbld(ji,jj), Kmm)
pviscos(ji,jj,nbld(ji,jj)) = pdiffut(ji,jj,nbld(ji,jj))
ENDIF
ENDIF ! End if ( l_conv )
!
END_2D
CALL zdf_osm_iomput( "pb_coup", tmask(A2D(0),1) * zb_coup(A2D(0)) ) ! BBL-coupling velocity scale
!
END SUBROUTINE zdf_osm_diffusivity_viscosity
SUBROUTINE zdf_osm_fgr_terms( Kmm, kp_ext, phbl, phml, pdh, &
& pdhdt, pshear, pdtdz_bl_ext, pdsdz_bl_ext, pdbdz_bl_ext, &
& pdiffut, pviscos )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_osm_fgr_terms ***
!!
!! ** Purpose : Compute non-gradient terms in flux-gradient relationship
!!
!! ** Method :
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kmm ! Time-level index
INTEGER, DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: kp_ext ! Offset for external level
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phml ! ML depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdh ! Pycnocline depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdhdt ! BL depth tendency
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pshear ! Shear production
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdtdz_bl_ext ! External temperature gradients
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdsdz_bl_ext ! External salinity gradients
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdbdz_bl_ext ! External buoyancy gradients
REAL(wp), DIMENSION(A2D(nn_hls-1),jpk), INTENT(in ) :: pdiffut ! t-diffusivity
REAL(wp), DIMENSION(A2D(nn_hls-1),jpk), INTENT(in ) :: pviscos ! Viscosity
!!
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zalpha_pyc !
REAL(wp), DIMENSION(A2D(nn_hls-1),jpk) :: zdbdz_pyc ! Parametrised gradient of buoyancy in the pycnocline
REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: z3ddz_pyc_1, z3ddz_pyc_2 ! Pycnocline gradient/shear profiles
!!
INTEGER :: ji, jj, jk, jkm_bld, jkf_mld, jkm_mld ! Loop indices
INTEGER :: istat ! Memory allocation status
REAL(wp) :: zznd_d, zznd_ml, zznd_pyc, znd ! Temporary non-dimensional depths
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zsc_wth_1,zsc_ws_1 ! Temporary scales
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zsc_uw_1, zsc_uw_2 ! Temporary scales
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zsc_vw_1, zsc_vw_2 ! Temporary scales
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: ztau_sc_u ! Dissipation timescale at base of WML
REAL(wp) :: zbuoy_pyc_sc, zdelta_pyc !
REAL(wp) :: zl_c,zl_l,zl_eps ! Used to calculate turbulence length scale
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: za_cubic, zb_cubic ! Coefficients in cubic polynomial specifying
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zc_cubic, zd_cubic ! diffusivity in pycnocline
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zwt_pyc_sc_1, zws_pyc_sc_1 !
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zzeta_pyc !
REAL(wp) :: zomega, zvw_max !
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zuw_bse,zvw_bse ! Momentum, heat, and salinity fluxes
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zwth_ent,zws_ent ! at the top of the pycnocline
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: zsc_wth_pyc, zsc_ws_pyc ! Scales for pycnocline transport term
REAL(wp) :: ztmp !
REAL(wp) :: ztgrad, zsgrad, zbgrad ! Variables used to calculate pycnocline
!! ! gradients
REAL(wp) :: zugrad, zvgrad ! Variables for calculating pycnocline shear
REAL(wp) :: zdtdz_pyc ! Parametrized gradient of temperature in
!! ! pycnocline
REAL(wp) :: zdsdz_pyc ! Parametrised gradient of salinity in
!! ! pycnocline
REAL(wp) :: zdudz_pyc ! u-shear across the pycnocline
REAL(wp) :: zdvdz_pyc ! v-shear across the pycnocline
!!----------------------------------------------------------------------
!
!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
! Pycnocline gradients for scalars and velocity
!<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
CALL zdf_osm_pycnocline_buoyancy_profiles( Kmm, kp_ext, zdbdz_pyc, zalpha_pyc, pdh, &
& phbl, pdbdz_bl_ext, phml, pdhdt )
!
! Auxiliary indices
! -----------------
jkm_bld = 0
jkf_mld = jpk
jkm_mld = 0
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( nbld(ji,jj) > jkm_bld ) jkm_bld = nbld(ji,jj)
IF ( nmld(ji,jj) < jkf_mld ) jkf_mld = nmld(ji,jj)
IF ( nmld(ji,jj) > jkm_mld ) jkm_mld = nmld(ji,jj)
END_2D
!
! Stokes term in scalar flux, flux-gradient relationship
! ------------------------------------------------------
WHERE ( l_conv(A2D(nn_hls-1)) )
zsc_wth_1(:,:) = swstrl(A2D(nn_hls-1))**3 * swth0(A2D(nn_hls-1)) / &
& ( svstr(A2D(nn_hls-1))**3 + 0.5_wp * swstrc(A2D(nn_hls-1))**3 + epsln )
zsc_ws_1(:,:) = swstrl(A2D(nn_hls-1))**3 * sws0(A2D(nn_hls-1)) / &
& ( svstr(A2D(nn_hls-1))**3 + 0.5_wp * swstrc(A2D(nn_hls-1))**3 + epsln )
ELSEWHERE
zsc_wth_1(:,:) = 2.0_wp * swthav(A2D(nn_hls-1))
zsc_ws_1(:,:) = 2.0_wp * swsav(A2D(nn_hls-1))
ENDWHERE
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, MAX( jkm_mld, jkm_bld ) )
IF ( l_conv(ji,jj) ) THEN
IF ( jk <= nmld(ji,jj) ) THEN
zznd_d = gdepw(ji,jj,jk,Kmm) / dstokes(ji,jj)
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) + 1.35_wp * EXP( -1.0_wp * zznd_d ) * &
& ( 1.0_wp - EXP( -2.0_wp * zznd_d ) ) * zsc_wth_1(ji,jj)
ghams(ji,jj,jk) = ghams(ji,jj,jk) + 1.35_wp * EXP( -1.0_wp * zznd_d ) * &
& ( 1.0_wp - EXP( -2.0_wp * zznd_d ) ) * zsc_ws_1(ji,jj)
END IF
ELSE ! Stable conditions
IF ( jk <= nbld(ji,jj) ) THEN
zznd_d = gdepw(ji,jj,jk,Kmm) / dstokes(ji,jj)
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) + 2.15_wp * EXP( -0.85_wp * zznd_d ) * &
& ( 1.0_wp - EXP( -4.0_wp * zznd_d ) ) * zsc_wth_1(ji,jj)
ghams(ji,jj,jk) = ghams(ji,jj,jk) + 2.15_wp * EXP( -0.85_wp * zznd_d ) * &
& ( 1.0_wp - EXP( -4.0_wp * zznd_d ) ) * zsc_ws_1(ji,jj)
END IF
END IF ! Check on l_conv
END_3D
!
IF ( ln_dia_osm ) THEN
CALL zdf_osm_iomput( "ghamu_00", wmask(A2D(0),:) * ghamu(A2D(0),:) )
CALL zdf_osm_iomput( "ghamv_00", wmask(A2D(0),:) * ghamv(A2D(0),:) )
END IF
!
! Stokes term in flux-gradient relationship (note in zsc_uw_n don't use
! svstr since term needs to go to zero as swstrl goes to zero)
! ---------------------------------------------------------------------
WHERE ( l_conv(A2D(nn_hls-1)) )
zsc_uw_1(:,:) = ( swstrl(A2D(nn_hls-1))**3 + &
& 0.5_wp * swstrc(A2D(nn_hls-1))**3 )**pthird * sustke(A2D(nn_hls-1)) / &
& MAX( ( 1.0_wp - 1.0_wp * 6.5_wp * sla(A2D(nn_hls-1))**( 8.0_wp / 3.0_wp ) ), 0.2_wp )
zsc_uw_2(:,:) = ( swstrl(A2D(nn_hls-1))**3 + &
& 0.5_wp * swstrc(A2D(nn_hls-1))**3 )**pthird * sustke(A2D(nn_hls-1)) / &
& MIN( sla(A2D(nn_hls-1))**( 8.0_wp / 3.0_wp ) + epsln, 0.12_wp )
zsc_vw_1(:,:) = ff_t(A2D(nn_hls-1)) * phml(A2D(nn_hls-1)) * sustke(A2D(nn_hls-1))**3 * &
& MIN( sla(A2D(nn_hls-1))**( 8.0_wp / 3.0_wp ), 0.12_wp ) / &
& ( ( svstr(A2D(nn_hls-1))**3 + 0.5_wp * swstrc(A2D(nn_hls-1))**3 )**( 2.0_wp / 3.0_wp ) + epsln )
ELSEWHERE
zsc_uw_1(:,:) = sustar(A2D(nn_hls-1))**2
zsc_vw_1(:,:) = ff_t(A2D(nn_hls-1)) * phbl(A2D(nn_hls-1)) * sustke(A2D(nn_hls-1))**3 * &
& MIN( sla(A2D(nn_hls-1))**( 8.0_wp / 3.0_wp ), 0.12_wp ) / ( svstr(A2D(nn_hls-1))**2 + epsln )
ENDWHERE
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, MAX( jkm_mld, jkm_bld ) )
IF ( l_conv(ji,jj) ) THEN
IF ( jk <= nmld(ji,jj) ) THEN
zznd_d = gdepw(ji,jj,jk,Kmm) / dstokes(ji,jj)
ghamu(ji,jj,jk) = ghamu(ji,jj,jk) + ( -0.05_wp * EXP( -0.4_wp * zznd_d ) * zsc_uw_1(ji,jj) + &
& 0.00125_wp * EXP( -1.0_wp * zznd_d ) * zsc_uw_2(ji,jj) ) * &
& ( 1.0_wp - EXP( -2.0_wp * zznd_d ) )
ghamv(ji,jj,jk) = ghamv(ji,jj,jk) - 0.65_wp * 0.15_wp * EXP( -1.0_wp * zznd_d ) * &
& ( 1.0_wp - EXP( -2.0_wp * zznd_d ) ) * zsc_vw_1(ji,jj)
END IF
ELSE ! Stable conditions
IF ( jk <= nbld(ji,jj) ) THEN ! Corrected to nbld
zznd_d = gdepw(ji,jj,jk,Kmm) / dstokes(ji,jj)
ghamu(ji,jj,jk) = ghamu(ji,jj,jk) - 0.75_wp * 1.3_wp * EXP( -0.5_wp * zznd_d ) * &
& ( 1.0_wp - EXP( -4.0_wp * zznd_d ) ) * zsc_uw_1(ji,jj)
END IF
END IF
END_3D
!
! Buoyancy term in flux-gradient relationship [note : includes ROI ratio
! (X0.3) and pressure (X0.5)]
! ----------------------------------------------------------------------
WHERE ( l_conv(A2D(nn_hls-1)) )
zsc_wth_1(:,:) = swbav(A2D(nn_hls-1)) * swth0(A2D(nn_hls-1)) * ( 1.0_wp + EXP( 0.2_wp * shol(A2D(nn_hls-1)) ) ) * &
& phml(A2D(nn_hls-1)) / ( svstr(A2D(nn_hls-1))**3 + 0.5_wp * swstrc(A2D(nn_hls-1))**3 + epsln )
zsc_ws_1(:,:) = swbav(A2D(nn_hls-1)) * sws0(A2D(nn_hls-1)) * ( 1.0_wp + EXP( 0.2_wp * shol(A2D(nn_hls-1)) ) ) * &
& phml(A2D(nn_hls-1)) / ( svstr(A2D(nn_hls-1))**3 + 0.5_wp * swstrc(A2D(nn_hls-1))**3 + epsln )
ELSEWHERE
zsc_wth_1(:,:) = 0.0_wp
zsc_ws_1(:,:) = 0.0_wp
ENDWHERE
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, MAX( jkm_mld, jkm_bld ) )
IF ( l_conv(ji,jj) ) THEN
IF ( jk <= nmld(ji,jj) ) THEN
zznd_ml = gdepw(ji,jj,jk,Kmm) / phml(ji,jj)
! Calculate turbulent time scale
zl_c = 0.9_wp * ( 1.0_wp - EXP( -5.0_wp * ( zznd_ml + zznd_ml**3 / 3.0_wp ) ) ) * &
& ( 1.0_wp - EXP( -15.0_wp * ( 1.2_wp - zznd_ml ) ) )
zl_l = 2.0_wp * ( 1.0_wp - EXP( -2.0_wp * ( zznd_ml + zznd_ml**3 / 3.0_wp ) ) ) * &
& ( 1.0_wp - EXP( -8.0_wp * ( 1.15_wp - zznd_ml ) ) ) * ( 1.0_wp + dstokes(ji,jj) / phml (ji,jj) )
zl_eps = zl_l + ( zl_c - zl_l ) / ( 1.0_wp + EXP( -3.0_wp * LOG10( -1.0_wp * shol(ji,jj) ) ) )**( 3.0_wp / 2.0_wp )
! Non-gradient buoyancy terms
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) + 0.3_wp * 0.4_wp * zsc_wth_1(ji,jj) * zl_eps / ( 0.15_wp + zznd_ml )
ghams(ji,jj,jk) = ghams(ji,jj,jk) + 0.3_wp * 0.4_wp * zsc_ws_1(ji,jj) * zl_eps / ( 0.15_wp + zznd_ml )
END IF
ELSE ! Stable conditions
IF ( jk <= nbld(ji,jj) ) THEN
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) + zsc_wth_1(ji,jj)
ghams(ji,jj,jk) = ghams(ji,jj,jk) + zsc_ws_1(ji,jj)
END IF
END IF
END_3D
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( l_conv(ji,jj) .AND. l_pyc(ji,jj) ) THEN
ztau_sc_u(ji,jj) = phml(ji,jj) / ( svstr(ji,jj)**3 + swstrc(ji,jj)**3 )**pthird * &
& ( 1.4_wp - 0.4_wp / ( 1.0_wp + EXP( -3.5_wp * LOG10( -1.0_wp * shol(ji,jj) ) ) )**1.5_wp )
zwth_ent(ji,jj) = -0.003_wp * ( 0.15_wp * svstr(ji,jj)**3 + swstrc(ji,jj)**3 )**pthird * &
& ( 1.0_wp - pdh(ji,jj) / phbl(ji,jj) ) * av_dt_ml(ji,jj)
zws_ent(ji,jj) = -0.003_wp * ( 0.15_wp * svstr(ji,jj)**3 + swstrc(ji,jj)**3 )**pthird * &
& ( 1.0_wp - pdh(ji,jj) / phbl(ji,jj) ) * av_ds_ml(ji,jj)
IF ( dh(ji,jj) < 0.2_wp * hbl(ji,jj) ) THEN
zbuoy_pyc_sc = 2.0_wp * MAX( av_db_ml(ji,jj), 0.0_wp ) / pdh(ji,jj)
zdelta_pyc = ( svstr(ji,jj)**3 + swstrc(ji,jj)**3 )**pthird / &
& SQRT( MAX( zbuoy_pyc_sc, ( svstr(ji,jj)**3 + swstrc(ji,jj)**3 )**p2third / pdh(ji,jj)**2 ) )
zwt_pyc_sc_1(ji,jj) = 0.325_wp * ( zalpha_pyc(ji,jj) * av_dt_ml(ji,jj) / pdh(ji,jj) + pdtdz_bl_ext(ji,jj) ) * &
& zdelta_pyc**2 / pdh(ji,jj)
zws_pyc_sc_1(ji,jj) = 0.325_wp * ( zalpha_pyc(ji,jj) * av_ds_ml(ji,jj) / pdh(ji,jj) + pdsdz_bl_ext(ji,jj) ) * &
& zdelta_pyc**2 / pdh(ji,jj)
zzeta_pyc(ji,jj) = 0.15_wp - 0.175_wp / ( 1.0_wp + EXP( -3.5_wp * LOG10( -1.0_wp * shol(ji,jj) ) ) )
END IF
END IF
END_2D
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jkm_bld )
IF ( l_conv(ji,jj) .AND. l_pyc(ji,jj) .AND. ( jk <= nbld(ji,jj) ) ) THEN
zznd_pyc = -1.0_wp * ( gdepw(ji,jj,jk,Kmm) - phbl(ji,jj) ) / pdh(ji,jj)
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) - &
& 0.045_wp * ( ( zwth_ent(ji,jj) * zdbdz_pyc(ji,jj,jk) ) * ztau_sc_u(ji,jj)**2 ) * &
& MAX( ( 1.75_wp * zznd_pyc -0.15_wp * zznd_pyc**2 - 0.2_wp * zznd_pyc**3 ), 0.0_wp )
ghams(ji,jj,jk) = ghams(ji,jj,jk) - &
& 0.045_wp * ( ( zws_ent(ji,jj) * zdbdz_pyc(ji,jj,jk) ) * ztau_sc_u(ji,jj)**2 ) * &
& MAX( ( 1.75_wp * zznd_pyc -0.15_wp * zznd_pyc**2 - 0.2_wp * zznd_pyc**3 ), 0.0_wp )
IF ( dh(ji,jj) < 0.2_wp * hbl(ji,jj) .AND. nbld(ji,jj) - nmld(ji,jj) > 3 ) THEN
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) + 0.05_wp * zwt_pyc_sc_1(ji,jj) * &
& EXP( -0.25_wp * ( zznd_pyc / zzeta_pyc(ji,jj) )**2 ) * &
& pdh(ji,jj) / ( svstr(ji,jj)**3 + swstrc(ji,jj)**3 )**pthird
ghams(ji,jj,jk) = ghams(ji,jj,jk) + 0.05_wp * zws_pyc_sc_1(ji,jj) * &
& EXP( -0.25_wp * ( zznd_pyc / zzeta_pyc(ji,jj) )**2 ) * &
& pdh(ji,jj) / ( svstr(ji,jj)**3 + swstrc(ji,jj)**3 )**pthird
END IF
END IF ! End of pycnocline
END_3D
!
IF ( ln_dia_osm ) THEN
CALL zdf_osm_iomput( "zwth_ent", tmask(A2D(0),1) * zwth_ent(A2D(0)) ) ! Upward turb. temperature entrainment flux
CALL zdf_osm_iomput( "zws_ent", tmask(A2D(0),1) * zws_ent(A2D(0)) ) ! Upward turb. salinity entrainment flux
END IF
!
zsc_vw_1(:,:) = 0.0_wp
WHERE ( l_conv(A2D(nn_hls-1)) )
zsc_uw_1(:,:) = -1.0_wp * swb0(A2D(nn_hls-1)) * sustar(A2D(nn_hls-1))**2 * phml(A2D(nn_hls-1)) / &
& ( svstr(A2D(nn_hls-1))**3 + 0.5_wp * swstrc(A2D(nn_hls-1))**3 + epsln )
zsc_uw_2(:,:) = swb0(A2D(nn_hls-1)) * sustke(A2D(nn_hls-1)) * phml(A2D(nn_hls-1)) / &
& ( svstr(A2D(nn_hls-1))**3 + 0.5_wp * swstrc(A2D(nn_hls-1))**3 + epsln )**( 2.0_wp / 3.0_wp )
ELSEWHERE
zsc_uw_1(:,:) = 0.0_wp
ENDWHERE
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, MAX( jkm_mld, jkm_bld ) )
IF ( l_conv(ji,jj) ) THEN
IF ( jk <= nmld(ji,jj) ) THEN
zznd_d = gdepw(ji,jj,jk,Kmm) / dstokes(ji,jj)
ghamu(ji,jj,jk) = ghamu(ji,jj,jk) + 0.3_wp * 0.5_wp * &
& ( zsc_uw_1(ji,jj) + 0.125_wp * EXP( -0.5_wp * zznd_d ) * &
& ( 1.0_wp - EXP( -0.5_wp * zznd_d ) ) * zsc_uw_2(ji,jj) )
ghamv(ji,jj,jk) = ghamv(ji,jj,jk) + zsc_vw_1(ji,jj)
END IF
ELSE ! Stable conditions
IF ( jk <= nbld(ji,jj) ) THEN
ghamu(ji,jj,jk) = ghamu(ji,jj,jk) + zsc_uw_1(ji,jj)
ghamv(ji,jj,jk) = ghamv(ji,jj,jk) + zsc_vw_1(ji,jj)
END IF
ENDIF
END_3D
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( l_conv(ji,jj) .AND. l_pyc(ji,jj) ) THEN
IF ( n_ddh(ji,jj) == 0 ) THEN
! Place holding code. Parametrization needs checking for these conditions.
zomega = ( 0.15_wp * swstrl(ji,jj)**3 + swstrc(ji,jj)**3 + 4.75_wp * ( pshear(ji,jj) * phbl(ji,jj) ) )**pthird
zuw_bse(ji,jj) = -0.0035_wp * zomega * ( 1.0_wp - pdh(ji,jj) / phbl(ji,jj) ) * av_du_ml(ji,jj)
zvw_bse(ji,jj) = -0.0075_wp * zomega * ( 1.0_wp - pdh(ji,jj) / phbl(ji,jj) ) * av_dv_ml(ji,jj)
ELSE
zomega = ( 0.15_wp * swstrl(ji,jj)**3 + swstrc(ji,jj)**3 + 4.75_wp * ( pshear(ji,jj) * phbl(ji,jj) ) )**pthird
zuw_bse(ji,jj) = -0.0035_wp * zomega * ( 1.0_wp - pdh(ji,jj) / phbl(ji,jj) ) * av_du_ml(ji,jj)
zvw_bse(ji,jj) = -0.0075_wp * zomega * ( 1.0_wp - pdh(ji,jj) / phbl(ji,jj) ) * av_dv_ml(ji,jj)
ENDIF
zb_cubic(ji,jj) = pdh(ji,jj) / phbl(ji,jj) * suw0(ji,jj) - ( 2.0_wp + pdh(ji,jj) / phml(ji,jj) ) * zuw_bse(ji,jj)
za_cubic(ji,jj) = zuw_bse(ji,jj) - zb_cubic(ji,jj)
zvw_max = 0.7_wp * ff_t(ji,jj) * ( sustke(ji,jj) * dstokes(ji,jj) + 0.7_wp * sustar(ji,jj) * phml(ji,jj) )
zd_cubic(ji,jj) = zvw_max * pdh(ji,jj) / phml(ji,jj) - ( 2.0_wp + pdh(ji,jj) / phml(ji,jj) ) * zvw_bse(ji,jj)
zc_cubic(ji,jj) = zvw_bse(ji,jj) - zd_cubic(ji,jj)
END IF
END_2D
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, jkf_mld, jkm_bld ) ! Need ztau_sc_u to be available. Change to array.
IF ( l_conv(ji,jj) .AND. l_pyc(ji,jj) .AND. ( jk >= nmld(ji,jj) ) .AND. ( jk <= nbld(ji,jj) ) ) THEN
zznd_pyc = -1.0_wp * ( gdepw(ji,jj,jk,Kmm) - phbl(ji,jj) ) / pdh(ji,jj)
ghamu(ji,jj,jk) = ghamu(ji,jj,jk) - 0.045_wp * ( ztau_sc_u(ji,jj)**2 ) * zuw_bse(ji,jj) * &
& ( za_cubic(ji,jj) * zznd_pyc**2 + zb_cubic(ji,jj) * zznd_pyc**3 ) * &
& ( 0.75_wp + 0.25_wp * zznd_pyc )**2 * zdbdz_pyc(ji,jj,jk)
ghamv(ji,jj,jk) = ghamv(ji,jj,jk) - 0.045_wp * ( ztau_sc_u(ji,jj)**2 ) * zvw_bse(ji,jj) * &
& ( zc_cubic(ji,jj) * zznd_pyc**2 + zd_cubic(ji,jj) * zznd_pyc**3 ) * &
& ( 0.75_wp + 0.25_wp * zznd_pyc )**2 * zdbdz_pyc(ji,jj,jk)
END IF ! l_conv .AND. l_pyc
END_3D
!
IF ( ln_dia_osm ) THEN
CALL zdf_osm_iomput( "ghamu_0", wmask(A2D(0),:) * ghamu(A2D(0),:) )
CALL zdf_osm_iomput( "zsc_uw_1_0", tmask(A2D(0),1) * zsc_uw_1(A2D(0)) )
END IF
!
! Transport term in flux-gradient relationship [note : includes ROI ratio
! (X0.3) ]
! -----------------------------------------------------------------------
WHERE ( l_conv(A2D(nn_hls-1)) )
zsc_wth_1(:,:) = swth0(A2D(nn_hls-1)) / ( 1.0_wp - 0.56_wp * EXP( shol(A2D(nn_hls-1)) ) )
zsc_ws_1(:,:) = sws0(A2D(nn_hls-1)) / ( 1.0_wp - 0.56_wp * EXP( shol(A2D(nn_hls-1)) ) )
WHERE ( l_pyc(A2D(nn_hls-1)) ) ! Pycnocline scales
zsc_wth_pyc(:,:) = -0.003_wp * swstrc(A2D(nn_hls-1)) * ( 1.0_wp - pdh(A2D(nn_hls-1)) / phbl(A2D(nn_hls-1)) ) * &
& av_dt_ml(A2D(nn_hls-1))
zsc_ws_pyc(:,:) = -0.003_wp * swstrc(A2D(nn_hls-1)) * ( 1.0_wp - pdh(A2D(nn_hls-1)) / phbl(A2D(nn_hls-1)) ) * &
& av_ds_ml(A2D(nn_hls-1))
END WHERE
ELSEWHERE
zsc_wth_1(:,:) = 2.0_wp * swthav(A2D(nn_hls-1))
zsc_ws_1(:,:) = sws0(A2D(nn_hls-1))
END WHERE
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, MAX( jkm_mld, jkm_bld ) )
IF ( l_conv(ji,jj) ) THEN
IF ( ( jk > 1 ) .AND. ( jk <= nmld(ji,jj) ) ) THEN
zznd_ml = gdepw(ji,jj,jk,Kmm) / phml(ji,jj)
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) + 0.3_wp * zsc_wth_1(ji,jj) * &
& ( -2.0_wp + 2.75_wp * ( ( 1.0_wp + 0.6_wp * zznd_ml**4 ) - &
& EXP( -6.0_wp * zznd_ml ) ) ) * &
& ( 1.0_wp - EXP( -15.0_wp * ( 1.0_wp - zznd_ml ) ) )
ghams(ji,jj,jk) = ghams(ji,jj,jk) + 0.3_wp * zsc_ws_1(ji,jj) * &
& ( -2.0_wp + 2.75_wp * ( ( 1.0_wp + 0.6_wp * zznd_ml**4 ) - &
& EXP( -6.0_wp * zznd_ml ) ) ) * ( 1.0_wp - EXP( -15.0_wp * ( 1.0_wp - zznd_ml ) ) )
END IF
!
! may need to comment out lpyc block
IF ( l_pyc(ji,jj) .AND. ( jk >= nmld(ji,jj) ) .AND. ( jk <= nbld(ji,jj) ) ) THEN ! Pycnocline
zznd_pyc = -1.0_wp * ( gdepw(ji,jj,jk,Kmm) - phbl(ji,jj) ) / pdh(ji,jj)
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) + 4.0_wp * zsc_wth_pyc(ji,jj) * &
& ( 0.48_wp - EXP( -1.5_wp * ( zznd_pyc - 0.3_wp )**2 ) )
ghams(ji,jj,jk) = ghams(ji,jj,jk) + 4.0_wp * zsc_ws_pyc(ji,jj) * &
& ( 0.48_wp - EXP( -1.5_wp * ( zznd_pyc - 0.3_wp )**2 ) )
END IF
ELSE
IF( pdhdt(ji,jj) > 0. ) THEN
IF ( ( jk > 1 ) .AND. ( jk <= nbld(ji,jj) ) ) THEN
zznd_d = gdepw(ji,jj,jk,Kmm) / dstokes(ji,jj)
znd = gdepw(ji,jj,jk,Kmm) / phbl(ji,jj)
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) + 0.3_wp * ( -4.06_wp * EXP( -2.0_wp * zznd_d ) * ( 1.0_wp - EXP( -4.0_wp * zznd_d ) ) + &
7.5_wp * EXP ( -10.0_wp * ( 0.95_wp - znd )**2 ) * ( 1.0_wp - znd ) ) * zsc_wth_1(ji,jj)
ghams(ji,jj,jk) = ghams(ji,jj,jk) + 0.3_wp * ( -4.06_wp * EXP( -2.0_wp * zznd_d ) * ( 1.0_wp - EXP( -4.0_wp * zznd_d ) ) + &
7.5_wp * EXP ( -10.0_wp * ( 0.95_wp - znd )**2 ) * ( 1.0_wp - znd ) ) * zsc_ws_1(ji,jj)
END IF
ENDIF
ENDIF
END_3D
!
WHERE ( l_conv(A2D(nn_hls-1)) )
zsc_uw_1(:,:) = sustar(A2D(nn_hls-1))**2
zsc_vw_1(:,:) = ff_t(A2D(nn_hls-1)) * sustke(A2D(nn_hls-1)) * phml(A2D(nn_hls-1))
ELSEWHERE
zsc_uw_1(:,:) = sustar(A2D(nn_hls-1))**2
zsc_uw_2(:,:) = ( 2.25_wp - 3.0_wp * ( 1.0_wp - EXP( -1.25_wp * 2.0_wp ) ) ) * ( 1.0_wp - EXP( -4.0_wp * 2.0_wp ) ) * &
& zsc_uw_1(:,:)
zsc_vw_1(:,:) = ff_t(A2D(nn_hls-1)) * sustke(A2D(nn_hls-1)) * phbl(A2D(nn_hls-1))
zsc_vw_2(:,:) = -0.11_wp * SIN( 3.14159_wp * ( 2.0_wp + 0.4_wp ) ) * EXP( -1.0_wp * ( 1.5_wp + 2.0_wp )**2 ) * &
& zsc_vw_1(:,:)
ENDWHERE
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, MAX( jkm_mld, jkm_bld ) )
IF ( l_conv(ji,jj) ) THEN
IF ( jk <= nmld(ji,jj) ) THEN
zznd_ml = gdepw(ji,jj,jk,Kmm) / phml(ji,jj)
zznd_d = gdepw(ji,jj,jk,Kmm) / dstokes(ji,jj)
ghamu(ji,jj,jk) = ghamu(ji,jj,jk) + &
& 0.3_wp * ( -2.0_wp + 2.5_wp * ( 1.0_wp + 0.1_wp * zznd_ml**4 ) - EXP( -8.0_wp * zznd_ml ) ) * &
& zsc_uw_1(ji,jj)
ghamv(ji,jj,jk) = ghamv(ji,jj,jk) + &
& 0.3_wp * 0.1_wp * ( EXP( -1.0_wp * zznd_d ) + EXP( -5.0_wp * ( 1.0_wp - zznd_ml ) ) ) * &
& zsc_vw_1(ji,jj)
END IF
ELSE
IF ( jk <= nbld(ji,jj) ) THEN
znd = gdepw(ji,jj,jk,Kmm) / phbl(ji,jj)
zznd_d = gdepw(ji,jj,jk,Kmm) / dstokes(ji,jj)
IF ( zznd_d <= 2.0_wp ) THEN
ghamu(ji,jj,jk) = ghamu(ji,jj,jk) + 0.5_wp * 0.3_wp * &
& ( 2.25_wp - 3.0_wp * ( 1.0_wp - EXP( -1.25_wp * zznd_d ) ) * &
& ( 1.0_wp - EXP( -2.0_wp * zznd_d ) ) ) * zsc_uw_1(ji,jj)
ELSE
ghamu(ji,jj,jk) = ghamu(ji,jj,jk) + 0.5_wp * 0.3_wp * &
& ( 1.0_wp - EXP( -5.0_wp * ( 1.0_wp - znd ) ) ) * zsc_uw_2(ji,jj)
ENDIF
ghamv(ji,jj,jk) = ghamv(ji,jj,jk) + 0.3_wp * 0.15_wp * SIN( 3.14159_wp * ( 0.65_wp * zznd_d ) ) * &
& EXP( -0.25_wp * zznd_d**2 ) * zsc_vw_1(ji,jj)
ghamv(ji,jj,jk) = ghamv(ji,jj,jk) + 0.3_wp * 0.15_wp * EXP( -5.0 * ( 1.0 - znd ) ) * &
& ( 1.0 - EXP( -20.0 * ( 1.0 - znd ) ) ) * zsc_vw_2(ji,jj)
END IF
END IF
END_3D
!
IF ( ln_dia_osm ) THEN
CALL zdf_osm_iomput( "ghamu_f", wmask(A2D(0),:) * ghamu(A2D(0),:) )
CALL zdf_osm_iomput( "ghamv_f", wmask(A2D(0),:) * ghamv(A2D(0),:) )
CALL zdf_osm_iomput( "zsc_uw_1_f", tmask(A2D(0),1) * zsc_uw_1(A2D(0)) )
CALL zdf_osm_iomput( "zsc_vw_1_f", tmask(A2D(0),1) * zsc_vw_1(A2D(0)) )
CALL zdf_osm_iomput( "zsc_uw_2_f", tmask(A2D(0),1) * zsc_uw_2(A2D(0)) )
CALL zdf_osm_iomput( "zsc_vw_2_f", tmask(A2D(0),1) * zsc_vw_2(A2D(0)) )
END IF
!
! Make surface forced velocity non-gradient terms go to zero at the base
! of the mixed layer.
!
! Make surface forced velocity non-gradient terms go to zero at the base
! of the boundary layer.
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jkm_bld )
IF ( ( .NOT. l_conv(ji,jj) ) .AND. ( jk <= nbld(ji,jj) ) ) THEN
znd = -1.0_wp * ( gdepw(ji,jj,jk,Kmm) - phbl(ji,jj) ) / phbl(ji,jj) ! ALMG to think about
IF ( znd >= 0.0_wp ) THEN
ghamu(ji,jj,jk) = ghamu(ji,jj,jk) * ( 1.0_wp - EXP( -10.0_wp * znd**2 ) )
ghamv(ji,jj,jk) = ghamv(ji,jj,jk) * ( 1.0_wp - EXP( -10.0_wp * znd**2 ) )
ELSE
ghamu(ji,jj,jk) = 0.0_wp
ghamv(ji,jj,jk) = 0.0_wp
ENDIF
END IF
END_3D
!
! Pynocline contributions
!
IF ( ln_dia_pyc_scl .OR. ln_dia_pyc_shr ) THEN ! Allocate arrays for output of pycnocline gradient/shear profiles
ALLOCATE( z3ddz_pyc_1(A2D(nn_hls),jpk), z3ddz_pyc_2(A2D(nn_hls),jpk), STAT=istat )
IF ( istat /= 0 ) CALL ctl_stop( 'zdf_osm: failed to allocate temporary arrays' )
z3ddz_pyc_1(:,:,:) = 0.0_wp
z3ddz_pyc_2(:,:,:) = 0.0_wp
END IF
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jkm_bld )
IF ( l_conv (ji,jj) ) THEN
! Unstable conditions. Shouldn;t be needed with no pycnocline code.
! zugrad = 0.7 * av_du_ml(ji,jj) / zdh(ji,jj) + 0.3 * zustar(ji,jj)*zustar(ji,jj) / &
! & ( ( ( zvstr(ji,jj)**3 + 0.5 * zwstrc(ji,jj)**3 )**pthird * zhml(ji,jj) ) * &
! & MIN(zla(ji,jj)**(8.0/3.0) + epsln, 0.12 ))
!Alan is this right?
! zvgrad = ( 0.7 * av_dv_ml(ji,jj) + &
! & 2.0 * ff_t(ji,jj) * zustke(ji,jj) * dstokes(ji,jj) / &
! & ( ( zvstr(ji,jj)**3 + 0.5 * zwstrc(ji,jj)**3 )**pthird + epsln ) &
! & )/ (zdh(ji,jj) + epsln )
! DO jk = 2, nbld(ji,jj) - 1 + ibld_ext
! znd = -( gdepw(ji,jj,jk,Kmm) - zhbl(ji,jj) ) / (zdh(ji,jj) + epsln ) - zzeta_v
! IF ( znd <= 0.0 ) THEN
! zdudz(ji,jj,jk) = 1.25 * zugrad * EXP( 3.0 * znd )
! zdvdz(ji,jj,jk) = 1.25 * zvgrad * EXP( 3.0 * znd )
! ELSE
! zdudz(ji,jj,jk) = 1.25 * zugrad * EXP( -2.0 * znd )
! zdvdz(ji,jj,jk) = 1.25 * zvgrad * EXP( -2.0 * znd )
! ENDIF
! END DO
ELSE ! Stable conditions
IF ( nbld(ji,jj) + kp_ext(ji,jj) < mbkt(ji,jj) ) THEN
! 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 )
ztgrad = av_dt_bl(ji,jj) * ztmp
zsgrad = av_ds_bl(ji,jj) * ztmp
zbgrad = av_db_bl(ji,jj) * ztmp
IF ( jk <= nbld(ji,jj) ) THEN
znd = gdepw(ji,jj,jk,Kmm) * ztmp
zdtdz_pyc = ztgrad * EXP( -15.0_wp * ( znd - 0.9_wp )**2 )
zdsdz_pyc = zsgrad * EXP( -15.0_wp * ( znd - 0.9_wp )**2 )
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) + pdiffut(ji,jj,jk) * zdtdz_pyc
ghams(ji,jj,jk) = ghams(ji,jj,jk) + pdiffut(ji,jj,jk) * zdsdz_pyc
IF ( ln_dia_pyc_scl ) THEN
z3ddz_pyc_1(ji,jj,jk) = zdtdz_pyc
z3ddz_pyc_2(ji,jj,jk) = zdsdz_pyc
END IF
END IF
ELSE ! Slightly stable - 'thin' pycnoline - needed when stable layer begins to form.
ztmp = 1.0_wp / MAX( pdh(ji,jj), epsln )
ztgrad = av_dt_bl(ji,jj) * ztmp
zsgrad = av_ds_bl(ji,jj) * ztmp
zbgrad = av_db_bl(ji,jj) * ztmp
IF ( jk <= nbld(ji,jj) ) THEN
znd = -1.0_wp * ( gdepw(ji,jj,jk,Kmm) - phml(ji,jj) ) * ztmp
zdtdz_pyc = ztgrad * EXP( -1.75_wp * ( znd + 0.75_wp )**2 )
zdsdz_pyc = zsgrad * EXP( -1.75_wp * ( znd + 0.75_wp )**2 )
ghamt(ji,jj,jk) = ghamt(ji,jj,jk) + pdiffut(ji,jj,jk) * zdtdz_pyc
ghams(ji,jj,jk) = ghams(ji,jj,jk) + pdiffut(ji,jj,jk) * zdsdz_pyc
IF ( ln_dia_pyc_scl ) THEN
z3ddz_pyc_1(ji,jj,jk) = zdtdz_pyc
z3ddz_pyc_2(ji,jj,jk) = zdsdz_pyc
END IF
END IF
ENDIF ! IF (shol >=0.5)
ENDIF ! IF (av_db_bl> 0.)
ENDIF ! IF (zdhdt >= 0) zdhdt < 0 not considered since pycnocline profile is zero and profile arrays are
! ! intialized to zero
END IF
END IF
END_3D
IF ( ln_dia_pyc_scl ) THEN ! Output of pycnocline gradient profiles
CALL zdf_osm_iomput( "zdtdz_pyc", wmask(A2D(0),:) * z3ddz_pyc_1(A2D(0),:) )
CALL zdf_osm_iomput( "zdsdz_pyc", wmask(A2D(0),:) * z3ddz_pyc_2(A2D(0),:) )
END IF
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jkm_bld )
IF ( .NOT. l_conv (ji,jj) ) THEN
IF ( nbld(ji,jj) + kp_ext(ji,jj) < mbkt(ji,jj) ) THEN
zugrad = 3.25_wp * av_du_bl(ji,jj) / phbl(ji,jj)
zvgrad = 2.75_wp * av_dv_bl(ji,jj) / phbl(ji,jj)
IF ( jk <= nbld(ji,jj) ) THEN
znd = gdepw(ji,jj,jk,Kmm) / phbl(ji,jj)
IF ( znd < 1.0 ) THEN
zdudz_pyc = zugrad * EXP( -40.0_wp * ( znd - 1.0_wp )**2 )
ELSE
zdudz_pyc = zugrad * EXP( -20.0_wp * ( znd - 1.0_wp )**2 )
ENDIF
zdvdz_pyc = zvgrad * EXP( -20.0_wp * ( znd - 0.85_wp )**2 )
ghamu(ji,jj,jk) = ghamu(ji,jj,jk) + pviscos(ji,jj,jk) * zdudz_pyc
ghamv(ji,jj,jk) = ghamv(ji,jj,jk) + pviscos(ji,jj,jk) * zdvdz_pyc
IF ( ln_dia_pyc_shr ) THEN
z3ddz_pyc_1(ji,jj,jk) = zdudz_pyc
z3ddz_pyc_2(ji,jj,jk) = zdvdz_pyc
END IF
END IF
END IF
END IF
END_3D
IF ( ln_dia_pyc_shr ) THEN ! Output of pycnocline shear profiles
CALL zdf_osm_iomput( "zdudz_pyc", wmask(A2D(0),:) * z3ddz_pyc_1(A2D(0),:) )
CALL zdf_osm_iomput( "zdvdz_pyc", wmask(A2D(0),:) * z3ddz_pyc_2(A2D(0),:) )
END IF
IF ( ln_dia_osm ) THEN
CALL zdf_osm_iomput( "ghamu_b", wmask(A2D(0),:) * ghamu(A2D(0),:) )
CALL zdf_osm_iomput( "ghamv_b", wmask(A2D(0),:) * ghamv(A2D(0),:) )
END IF
IF ( ln_dia_pyc_scl .OR. ln_dia_pyc_shr ) THEN ! Deallocate arrays used for output of pycnocline gradient/shear profiles
DEALLOCATE( z3ddz_pyc_1, z3ddz_pyc_2 )
END IF
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
ghamt(ji,jj,nbld(ji,jj)) = 0.0_wp
ghams(ji,jj,nbld(ji,jj)) = 0.0_wp
ghamu(ji,jj,nbld(ji,jj)) = 0.0_wp
ghamv(ji,jj,nbld(ji,jj)) = 0.0_wp
END_2D
!
IF ( ln_dia_osm ) THEN
CALL zdf_osm_iomput( "ghamu_1", wmask(A2D(0),:) * ghamu(A2D(0),:) )
CALL zdf_osm_iomput( "ghamv_1", wmask(A2D(0),:) * ghamv(A2D(0),:) )
CALL zdf_osm_iomput( "zviscos", wmask(A2D(0),:) * pviscos(A2D(0),:) )
END IF
!
END SUBROUTINE zdf_osm_fgr_terms
SUBROUTINE zdf_osm_zmld_horizontal_gradients( Kmm, pmld, pdtdx, pdtdy, pdsdx, &
& pdsdy, pdbds_mle )
!!----------------------------------------------------------------------
!! *** ROUTINE zdf_osm_zmld_horizontal_gradients ***
!!
!! ** Purpose : Calculates horizontal gradients of buoyancy for use with
!! Fox-Kemper parametrization
!!
!! ** Method :
!!
!! References: Fox-Kemper et al., JPO, 38, 1145-1165, 2008
!! Fox-Kemper and Ferrari, JPO, 38, 1166-1179, 2008
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kmm ! Time-level index
REAL(wp), DIMENSION(A2D(nn_hls)), INTENT( out) :: pmld ! == Estimated FK BLD used for MLE horizontal gradients == !
REAL(wp), DIMENSION(A2D(nn_hls)), INTENT(inout) :: pdtdx ! Horizontal gradient for Fox-Kemper parametrization
REAL(wp), DIMENSION(A2D(nn_hls)), INTENT(inout) :: pdtdy ! Horizontal gradient for Fox-Kemper parametrization
REAL(wp), DIMENSION(A2D(nn_hls)), INTENT(inout) :: pdsdx ! Horizontal gradient for Fox-Kemper parametrization
REAL(wp), DIMENSION(A2D(nn_hls)), INTENT(inout) :: pdsdy ! Horizontal gradient for Fox-Kemper parametrization
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(inout) :: pdbds_mle ! Magnitude of horizontal buoyancy gradient
!!
INTEGER :: ji, jj, jk ! Dummy loop indices
INTEGER, DIMENSION(A2D(nn_hls)) :: jk_mld_prof ! Base level of MLE layer
INTEGER :: ikt, ikmax ! Local integers
REAL(wp) :: zc
REAL(wp) :: zN2_c ! Local buoyancy difference from 10m value
REAL(wp), DIMENSION(A2D(nn_hls)) :: ztm
REAL(wp), DIMENSION(A2D(nn_hls)) :: zsm
REAL(wp), DIMENSION(A2D(nn_hls),jpts) :: ztsm_midu
REAL(wp), DIMENSION(A2D(nn_hls),jpts) :: ztsm_midv
REAL(wp), DIMENSION(A2D(nn_hls),jpts) :: zabu
REAL(wp), DIMENSION(A2D(nn_hls),jpts) :: zabv
REAL(wp), DIMENSION(A2D(nn_hls)) :: zmld_midu
REAL(wp), DIMENSION(A2D(nn_hls)) :: zmld_midv
!!----------------------------------------------------------------------
!
! == MLD used for MLE ==!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
jk_mld_prof(ji,jj) = nlb10 ! Initialization to the number of w ocean point
pmld(ji,jj) = 0.0_wp ! Here hmlp used as a dummy variable, integrating vertically N^2
END_2D
zN2_c = grav * rn_osm_mle_rho_c * r1_rho0 ! Convert density criteria into N^2 criteria
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, nlb10, jpkm1 )
ikt = mbkt(ji,jj)
pmld(ji,jj) = pmld(ji,jj) + MAX( rn2b(ji,jj,jk), 0.0_wp ) * e3w(ji,jj,jk,Kmm)
IF( pmld(ji,jj) < zN2_c ) jk_mld_prof(ji,jj) = MIN( jk , ikt ) + 1 ! Mixed layer level
END_3D
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
jk_mld_prof(ji,jj) = MAX( jk_mld_prof(ji,jj), nbld(ji,jj) ) ! Ensure jk_mld_prof .ge. nbld
pmld(ji,jj) = gdepw(ji,jj,jk_mld_prof(ji,jj),Kmm)
END_2D
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
mld_prof(ji,jj) = jk_mld_prof(ji,jj)
END_2D
!
ikmax = MIN( MAXVAL( jk_mld_prof(A2D(nn_hls)) ), jpkm1 ) ! Max level of the computation
ztm(:,:) = 0.0_wp
zsm(:,:) = 0.0_wp
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, ikmax )
zc = e3t(ji,jj,jk,Kmm) * REAL( MIN( MAX( 0, jk_mld_prof(ji,jj) - jk ), 1 ), KIND=wp ) ! zc being 0 outside the ML
! ! t-points
ztm(ji,jj) = ztm(ji,jj) + zc * ts(ji,jj,jk,jp_tem,Kmm)
zsm(ji,jj) = zsm(ji,jj) + zc * ts(ji,jj,jk,jp_sal,Kmm)
END_3D
! Average temperature and salinity
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
ztm(ji,jj) = ztm(ji,jj) / MAX( e3t(ji,jj,1,Kmm), pmld(ji,jj) )
zsm(ji,jj) = zsm(ji,jj) / MAX( e3t(ji,jj,1,Kmm), pmld(ji,jj) )
END_2D
! Calculate horizontal gradients at u & v points
zmld_midu(:,:) = 0.0_wp
ztsm_midu(:,:,:) = 10.0_wp
DO_2D( nn_hls, nn_hls-1, nn_hls-1, nn_hls-1 )
pdtdx(ji,jj) = ( ztm(ji+1,jj) - ztm(ji,jj) ) * umask(ji,jj,1) / e1u(ji,jj)
pdsdx(ji,jj) = ( zsm(ji+1,jj) - zsm(ji,jj) ) * umask(ji,jj,1) / e1u(ji,jj)
zmld_midu(ji,jj) = 0.25_wp * ( pmld(ji+1,jj) + pmld(ji,jj))
ztsm_midu(ji,jj,jp_tem) = 0.5_wp * ( ztm( ji+1,jj) + ztm( ji,jj) )
ztsm_midu(ji,jj,jp_sal) = 0.5_wp * ( zsm( ji+1,jj) + zsm( ji,jj) )
END_2D
zmld_midv(:,:) = 0.0_wp
ztsm_midv(:,:,:) = 10.0_wp
DO_2D( nn_hls-1, nn_hls-1, nn_hls, nn_hls-1 )
pdtdy(ji,jj) = ( ztm(ji,jj+1) - ztm(ji,jj) ) * vmask(ji,jj,1) / e1v(ji,jj)
pdsdy(ji,jj) = ( zsm(ji,jj+1) - zsm(ji,jj) ) * vmask(ji,jj,1) / e1v(ji,jj)
zmld_midv(ji,jj) = 0.25_wp * ( pmld(ji,jj+1) + pmld( ji,jj) )
ztsm_midv(ji,jj,jp_tem) = 0.5_wp * ( ztm( ji,jj+1) + ztm( ji,jj) )
ztsm_midv(ji,jj,jp_sal) = 0.5_wp * ( zsm( ji,jj+1) + zsm( ji,jj) )
END_2D
CALL eos_rab( ztsm_midu, zmld_midu, zabu, Kmm )
CALL eos_rab( ztsm_midv, zmld_midv, zabv, Kmm )
DO_2D_OVR( nn_hls, nn_hls-1, nn_hls-1, nn_hls-1 )
dbdx_mle(ji,jj) = grav * ( pdtdx(ji,jj) * zabu(ji,jj,jp_tem) - pdsdx(ji,jj) * zabu(ji,jj,jp_sal) )
END_2D
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls, nn_hls-1 )
dbdy_mle(ji,jj) = grav * ( pdtdy(ji,jj) * zabv(ji,jj,jp_tem) - pdsdy(ji,jj) * zabv(ji,jj,jp_sal) )
END_2D
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
pdbds_mle(ji,jj) = SQRT( 0.5_wp * ( dbdx_mle(ji, jj) * dbdx_mle(ji, jj) + dbdy_mle(ji,jj ) * dbdy_mle(ji,jj ) + &
& dbdx_mle(ji-1,jj) * dbdx_mle(ji-1,jj) + dbdy_mle(ji,jj-1) * dbdy_mle(ji,jj-1) ) )
END_2D
!
END SUBROUTINE zdf_osm_zmld_horizontal_gradients
SUBROUTINE zdf_osm_osbl_state_fk( Kmm, pwb_fk, phbl, phmle, pwb_ent, &
& pdbds_mle )
!!---------------------------------------------------------------------
!! *** ROUTINE zdf_osm_osbl_state_fk ***
!!
!! ** Purpose : Determines the state of the OSBL and MLE layer. Info is
!! returned in the logicals l_pyc, l_flux and ldmle. Used
!! with Fox-Kemper scheme.
!! l_pyc :: determines whether pycnocline flux-grad
!! relationship needs to be determined
!! l_flux :: determines whether effects of surface flux
!! extend below the base of the OSBL
!! ldmle :: determines whether the layer with MLE is
!! increasing with time or if base is relaxing
!! towards hbl
!!
!! ** Method :
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kmm ! Time-level index
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(inout) :: pwb_fk
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phmle ! MLE depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pwb_ent ! Buoyancy entrainment flux
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdbds_mle ! Magnitude of horizontal buoyancy gradient
!!
INTEGER :: ji, jj, jk ! Dummy loop indices
REAL(wp), DIMENSION(A2D(nn_hls-1)) :: znd_param
REAL(wp) :: zthermal, zbeta
REAL(wp) :: zbuoy
REAL(wp) :: ztmp
REAL(wp) :: zpe_mle_layer
REAL(wp) :: zpe_mle_ref
REAL(wp) :: zdbdz_mle_int
!!----------------------------------------------------------------------
!
znd_param(:,:) = 0.0_wp
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
ztmp = r1_ft(ji,jj) * MIN( 111.e3_wp , e1u(ji,jj) ) / rn_osm_mle_lf
pwb_fk(ji,jj) = rn_osm_mle_ce * hmle(ji,jj) * hmle(ji,jj) * ztmp * pdbds_mle(ji,jj) * pdbds_mle(ji,jj)
END_2D
!
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
!
IF ( l_conv(ji,jj) ) THEN
IF ( phmle(ji,jj) > 1.2_wp * phbl(ji,jj) ) THEN
av_t_mle(ji,jj) = ( av_t_mle(ji,jj) * phmle(ji,jj) - av_t_bl(ji,jj) * phbl(ji,jj) ) / ( phmle(ji,jj) - phbl(ji,jj) )
av_s_mle(ji,jj) = ( av_s_mle(ji,jj) * phmle(ji,jj) - av_s_bl(ji,jj) * phbl(ji,jj) ) / ( phmle(ji,jj) - phbl(ji,jj) )
av_b_mle(ji,jj) = ( av_b_mle(ji,jj) * phmle(ji,jj) - av_b_bl(ji,jj) * phbl(ji,jj) ) / ( phmle(ji,jj) - phbl(ji,jj) )
zdbdz_mle_int = ( av_b_bl(ji,jj) - ( 2.0_wp * av_b_mle(ji,jj) - av_b_bl(ji,jj) ) ) / ( phmle(ji,jj) - phbl(ji,jj) )
! Calculate potential energies of actual profile and reference profile
zpe_mle_layer = 0.0_wp
zpe_mle_ref = 0.0_wp
zthermal = rab_n(ji,jj,1,jp_tem)
zbeta = rab_n(ji,jj,1,jp_sal)
DO jk = nbld(ji,jj), mld_prof(ji,jj)
zbuoy = grav * ( zthermal * ts(ji,jj,jk,jp_tem,Kmm) - zbeta * ts(ji,jj,jk,jp_sal,Kmm) )
zpe_mle_layer = zpe_mle_layer + zbuoy * gdepw(ji,jj,jk,Kmm) * e3w(ji,jj,jk,Kmm)
zpe_mle_ref = zpe_mle_ref + ( av_b_bl(ji,jj) - zdbdz_mle_int * ( gdepw(ji,jj,jk,Kmm) - phbl(ji,jj) ) ) * &
& gdepw(ji,jj,jk,Kmm) * e3w(ji,jj,jk,Kmm)
END DO
! Non-dimensional parameter to diagnose the presence of thermocline
znd_param(ji,jj) = ( zpe_mle_layer - zpe_mle_ref ) * ABS( ff_t(ji,jj) ) / &
& ( MAX( pwb_fk(ji,jj), 1e-10 ) * phmle(ji,jj) )
END IF
END IF
!
END_2D
!
! Diagnosis
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
!
IF ( l_conv(ji,jj) ) THEN
IF ( -2.0_wp * pwb_fk(ji,jj) / pwb_ent(ji,jj) > 0.5_wp ) THEN
IF ( phmle(ji,jj) > 1.2_wp * phbl(ji,jj) ) THEN ! MLE layer growing
IF ( znd_param (ji,jj) > 100.0_wp ) THEN ! Thermocline present
l_flux(ji,jj) = .FALSE.
l_mle(ji,jj) = .FALSE.
ELSE ! Thermocline not present
l_flux(ji,jj) = .TRUE.
l_mle(ji,jj) = .TRUE.
ENDIF ! znd_param > 100
!
IF ( av_db_bl(ji,jj) < rn_osm_bl_thresh ) THEN
l_pyc(ji,jj) = .FALSE.
ELSE
l_pyc(ji,jj) = .TRUE.
ENDIF
ELSE ! MLE layer restricted to OSBL or just below
IF ( av_db_bl(ji,jj) < rn_osm_bl_thresh ) THEN ! Weak stratification MLE layer can grow
l_pyc(ji,jj) = .FALSE.
l_flux(ji,jj) = .TRUE.
l_mle(ji,jj) = .TRUE.
ELSE ! Strong stratification
l_pyc(ji,jj) = .TRUE.
l_flux(ji,jj) = .FALSE.
l_mle(ji,jj) = .FALSE.
END IF ! av_db_bl < rn_mle_thresh_bl and
END IF ! phmle > 1.2 phbl
ELSE
l_pyc(ji,jj) = .TRUE.
l_flux(ji,jj) = .FALSE.
l_mle(ji,jj) = .FALSE.
IF ( av_db_bl(ji,jj) < rn_osm_bl_thresh ) l_pyc(ji,jj) = .FALSE.
END IF ! -2.0 * pwb_fk(ji,jj) / pwb_ent > 0.5
ELSE ! Stable Boundary Layer
l_pyc(ji,jj) = .FALSE.
l_flux(ji,jj) = .FALSE.
l_mle(ji,jj) = .FALSE.
END IF ! l_conv
!
END_2D
!
END SUBROUTINE zdf_osm_osbl_state_fk
SUBROUTINE zdf_osm_mle_parameters( Kmm, pmld, phmle, pvel_mle, pdiff_mle, &
& pdbds_mle, phbl, pwb0tot )
!!----------------------------------------------------------------------
!! *** ROUTINE zdf_osm_mle_parameters ***
!!
!! ** Purpose : Timesteps the mixed layer eddy depth, hmle and calculates
!! the mixed layer eddy fluxes for buoyancy, heat and
!! salinity.
!!
!! ** Method :
!!
!! References: Fox-Kemper et al., JPO, 38, 1145-1165, 2008
!! Fox-Kemper and Ferrari, JPO, 38, 1166-1179, 2008
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kmm ! Time-level index
REAL(wp), DIMENSION(A2D(nn_hls)), INTENT(in ) :: pmld ! == Estimated FK BLD used for MLE horiz gradients == !
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(inout) :: phmle ! MLE depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(inout) :: pvel_mle ! Velocity scale for dhdt with stable ML and FK
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(inout) :: pdiff_mle ! Extra MLE vertical diff
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pdbds_mle ! Magnitude of horizontal buoyancy gradient
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: phbl ! BL depth
REAL(wp), DIMENSION(A2D(nn_hls-1)), INTENT(in ) :: pwb0tot ! Total surface buoyancy flux including insolation
!!
INTEGER :: ji, jj, jk ! Dummy loop indices
REAL(wp) :: ztmp
REAL(wp) :: zdbdz
REAL(wp) :: zdtdz
REAL(wp) :: zdsdz
REAL(wp) :: zthermal
REAL(wp) :: zbeta
REAL(wp) :: zbuoy
REAL(wp) :: zdb_mle
!!----------------------------------------------------------------------
!
! Calculate vertical buoyancy, heat and salinity fluxes due to MLE
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( l_conv(ji,jj) ) THEN
ztmp = r1_ft(ji,jj) * MIN( 111e3_wp, e1u(ji,jj) ) / rn_osm_mle_lf
! This velocity scale, defined in Fox-Kemper et al (2008), is needed for calculating dhdt
pvel_mle(ji,jj) = pdbds_mle(ji,jj) * ztmp * hmle(ji,jj) * tmask(ji,jj,1)
pdiff_mle(ji,jj) = 5e-4_wp * rn_osm_mle_ce * ztmp * pdbds_mle(ji,jj) * phmle(ji,jj)**2
END IF
END_2D
! Timestep mixed layer eddy depth
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
IF ( l_mle(ji,jj) ) THEN ! MLE layer growing
! Buoyancy gradient at base of MLE layer
zthermal = rab_n(ji,jj,1,jp_tem)
zbeta = rab_n(ji,jj,1,jp_sal)
zbuoy = grav * ( zthermal * ts(ji,jj,mld_prof(ji,jj)+2,jp_tem,Kmm) - &
& zbeta * ts(ji,jj,mld_prof(ji,jj)+2,jp_sal,Kmm) )
zdb_mle = av_b_bl(ji,jj) - zbuoy
! Timestep hmle
hmle(ji,jj) = hmle(ji,jj) + pwb0tot(ji,jj) * rn_Dt / zdb_mle
ELSE
IF ( phmle(ji,jj) > phbl(ji,jj) ) THEN
hmle(ji,jj) = hmle(ji,jj) - ( hmle(ji,jj) - hbl(ji,jj) ) * rn_Dt / rn_osm_mle_tau
ELSE
hmle(ji,jj) = hmle(ji,jj) - 10.0_wp * ( hmle(ji,jj) - hbl(ji,jj) ) * rn_Dt / rn_osm_mle_tau
END IF
END IF
hmle(ji,jj) = MAX( MIN( hmle(ji,jj), ht(ji,jj) ), gdepw(ji,jj,4,Kmm) )
IF ( ln_osm_hmle_limit ) hmle(ji,jj) = MIN( hmle(ji,jj), rn_osm_hmle_limit*hbl(ji,jj) )
hmle(ji,jj) = pmld(ji,jj) ! For now try just set hmle to pmld
END_2D
!
DO_3D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 5, jpkm1 )
IF ( hmle(ji,jj) >= gdepw(ji,jj,jk,Kmm) ) mld_prof(ji,jj) = MIN( mbkt(ji,jj), jk )
END_3D
DO_2D_OVR( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
phmle(ji,jj) = gdepw(ji,jj,mld_prof(ji,jj),Kmm)
END_2D
!
END SUBROUTINE zdf_osm_mle_parameters
SUBROUTINE zdf_osm_init( Kmm )
!!----------------------------------------------------------------------
!! *** ROUTINE zdf_osm_init ***
!!
!! ** Purpose : Initialization of the vertical eddy diffivity and
!! viscosity when using a osm turbulent closure scheme
!!
!! ** Method : Read the namosm namelist and check the parameters
!! called at the first timestep (nit000)
!!
!! ** input : Namlists namzdf_osm and namosm_mle
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in ) :: Kmm ! Time level
!!
INTEGER :: ios ! Local integer
INTEGER :: ji, jj, jk ! Dummy loop indices
REAL(wp) :: z1_t2
!!
REAL(wp), PARAMETER :: pp_large = -1e10_wp
!!
NAMELIST/namzdf_osm/ ln_use_osm_la, rn_osm_la, rn_osm_dstokes, nn_ave, nn_osm_wave, &
& ln_dia_osm, rn_osm_hbl0, rn_zdfosm_adjust_sd, ln_kpprimix, rn_riinfty, &
& rn_difri, ln_convmix, rn_difconv, nn_osm_wave, nn_osm_SD_reduce, &
& ln_osm_mle, rn_osm_hblfrac, rn_osm_bl_thresh, ln_zdfosm_ice_shelter
!! Namelist for Fox-Kemper parametrization
NAMELIST/namosm_mle/ nn_osm_mle, rn_osm_mle_ce, rn_osm_mle_lf, rn_osm_mle_time, rn_osm_mle_lat, &
& rn_osm_mle_rho_c, rn_osm_mle_thresh, rn_osm_mle_tau, ln_osm_hmle_limit, rn_osm_hmle_limit
!!----------------------------------------------------------------------
!
READ ( numnam_ref, namzdf_osm, IOSTAT = ios, ERR = 901)
901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namzdf_osm in reference namelist' )
READ ( numnam_cfg, namzdf_osm, IOSTAT = ios, ERR = 902 )
902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namzdf_osm in configuration namelist' )
IF(lwm) WRITE ( numond, namzdf_osm )
IF(lwp) THEN ! Control print
WRITE(numout,*)
WRITE(numout,*) 'zdf_osm_init : OSMOSIS Parameterisation'
WRITE(numout,*) '~~~~~~~~~~~~'
WRITE(numout,*) ' Namelist namzdf_osm : set osm mixing parameters'
WRITE(numout,*) ' Use rn_osm_la ln_use_osm_la = ', ln_use_osm_la
WRITE(numout,*) ' Use MLE in OBL, i.e. Fox-Kemper param ln_osm_mle = ', ln_osm_mle
WRITE(numout,*) ' Turbulent Langmuir number rn_osm_la = ', rn_osm_la
WRITE(numout,*) ' Stokes drift reduction factor rn_zdfosm_adjust_sd = ', rn_zdfosm_adjust_sd
WRITE(numout,*) ' Initial hbl for 1D runs rn_osm_hbl0 = ', rn_osm_hbl0
WRITE(numout,*) ' Depth scale of Stokes drift rn_osm_dstokes = ', rn_osm_dstokes
WRITE(numout,*) ' Horizontal average flag nn_ave = ', nn_ave
WRITE(numout,*) ' Stokes drift nn_osm_wave = ', nn_osm_wave
SELECT CASE (nn_osm_wave)
CASE(0)
WRITE(numout,*) ' Calculated assuming constant La#=0.3'
CASE(1)
WRITE(numout,*) ' Calculated from Pierson Moskowitz wind-waves'
CASE(2)
WRITE(numout,*) ' Calculated from ECMWF wave fields'
END SELECT
WRITE(numout,*) ' Stokes drift reduction nn_osm_SD_reduce = ', nn_osm_SD_reduce
WRITE(numout,*) ' Fraction of hbl to average SD over/fit'
WRITE(numout,*) ' Exponential with nn_osm_SD_reduce = 1 or 2 rn_osm_hblfrac = ', rn_osm_hblfrac
SELECT CASE (nn_osm_SD_reduce)
CASE(0)
WRITE(numout,*) ' No reduction'
CASE(1)
WRITE(numout,*) ' Average SD over upper rn_osm_hblfrac of BL'
CASE(2)
WRITE(numout,*) ' Fit exponential to slope rn_osm_hblfrac of BL'
END SELECT
WRITE(numout,*) ' Reduce surface SD and depth scale under ice ln_zdfosm_ice_shelter = ', ln_zdfosm_ice_shelter
WRITE(numout,*) ' Output osm diagnostics ln_dia_osm = ', ln_dia_osm
WRITE(numout,*) ' Threshold used to define BL rn_osm_bl_thresh = ', rn_osm_bl_thresh, &
& 'm^2/s'
WRITE(numout,*) ' Use KPP-style shear instability mixing ln_kpprimix = ', ln_kpprimix
WRITE(numout,*) ' Local Richardson Number limit for shear instability rn_riinfty = ', rn_riinfty
WRITE(numout,*) ' Maximum shear diffusivity at Rig = 0 (m2/s) rn_difri = ', rn_difri
WRITE(numout,*) ' Use large mixing below BL when unstable ln_convmix = ', ln_convmix
WRITE(numout,*) ' Diffusivity when unstable below BL (m2/s) rn_difconv = ', rn_difconv
ENDIF
!
! ! Check wave coupling settings !
! ! Further work needed - see ticket #2447 !
IF ( nn_osm_wave == 2 ) THEN
IF (.NOT. ( ln_wave .AND. ln_sdw )) &
& CALL ctl_stop( 'zdf_osm_init : ln_zdfosm and nn_osm_wave=2, ln_wave and ln_sdw must be true' )
END IF
!
! Flags associated with diagnostic output
IF ( ln_dia_osm .AND. ( iom_use("zdudz_pyc") .OR. iom_use("zdvdz_pyc") ) ) ln_dia_pyc_shr = .TRUE.
IF ( ln_dia_osm .AND. ( iom_use("zdtdz_pyc") .OR. iom_use("zdsdz_pyc") .OR. iom_use("zdbdz_pyc" ) ) ) ln_dia_pyc_scl = .TRUE.
!
! Allocate zdfosm arrays
IF( zdf_osm_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'zdf_osm_init : unable to allocate arrays' )
!
IF( ln_osm_mle ) THEN ! Initialise Fox-Kemper parametrization
READ ( numnam_ref, namosm_mle, IOSTAT = ios, ERR = 903)
903 IF( ios /= 0 ) CALL ctl_nam( ios, 'namosm_mle in reference namelist' )
READ ( numnam_cfg, namosm_mle, IOSTAT = ios, ERR = 904 )
904 IF( ios > 0 ) CALL ctl_nam( ios, 'namosm_mle in configuration namelist' )
IF(lwm) WRITE ( numond, namosm_mle )
!
IF(lwp) THEN ! Namelist print
WRITE(numout,*)
WRITE(numout,*) 'zdf_osm_init : initialise mixed layer eddy (MLE)'
WRITE(numout,*) '~~~~~~~~~~~~~'
WRITE(numout,*) ' Namelist namosm_mle : '
WRITE(numout,*) ' MLE type: =0 standard Fox-Kemper ; =1 new formulation nn_osm_mle = ', nn_osm_mle
WRITE(numout,*) ' Magnitude of the MLE (typical value: 0.06 to 0.08) rn_osm_mle_ce = ', rn_osm_mle_ce
WRITE(numout,*) ' Scale of ML front (ML radius of deform.) (nn_osm_mle=0) rn_osm_mle_lf = ', rn_osm_mle_lf, &
& 'm'
WRITE(numout,*) ' Maximum time scale of MLE (nn_osm_mle=0) rn_osm_mle_time = ', &
& rn_osm_mle_time, 's'
WRITE(numout,*) ' Reference latitude (deg) of MLE coef. (nn_osm_mle=1) rn_osm_mle_lat = ', rn_osm_mle_lat, &
& 'deg'
WRITE(numout,*) ' Density difference used to define ML for FK rn_osm_mle_rho_c = ', rn_osm_mle_rho_c
WRITE(numout,*) ' Threshold used to define MLE for FK rn_osm_mle_thresh = ', &
& rn_osm_mle_thresh, 'm^2/s'
WRITE(numout,*) ' Timescale for OSM-FK rn_osm_mle_tau = ', rn_osm_mle_tau, 's'
WRITE(numout,*) ' Switch to limit hmle ln_osm_hmle_limit = ', ln_osm_hmle_limit
WRITE(numout,*) ' hmle limit (fraction of zmld) (ln_osm_hmle_limit = .T.) rn_osm_hmle_limit = ', rn_osm_hmle_limit
END IF
END IF
!
IF(lwp) THEN
WRITE(numout,*)
IF ( ln_osm_mle ) THEN
WRITE(numout,*) ' ==>>> Mixed Layer Eddy induced transport added to OSMOSIS BL calculation'
IF( nn_osm_mle == 0 ) WRITE(numout,*) ' Fox-Kemper et al 2010 formulation'
IF( nn_osm_mle == 1 ) WRITE(numout,*) ' New formulation'
ELSE
WRITE(numout,*) ' ==>>> Mixed Layer induced transport NOT added to OSMOSIS BL calculation'
END IF
END IF
!
IF( ln_osm_mle ) THEN ! MLE initialisation
!
rb_c = grav * rn_osm_mle_rho_c / 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 = ', rn_osm_mle_rho_c, 'kg/m3'
!
IF( nn_osm_mle == 1 ) THEN
rc_f = rn_osm_mle_ce / ( 5e3_wp * 2.0_wp * omega * SIN( rad * rn_osm_mle_lat ) )
END IF
! 1/(f^2+tau^2)^1/2 at t-point (needed in both nn_osm_mle case)
z1_t2 = 2e-5_wp
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
r1_ft(ji,jj) = MIN( 1.0_wp / ( ABS( ff_t(ji,jj)) + epsln ), ABS( ff_t(ji,jj) ) / z1_t2**2 )
END_2D
! z1_t2 = 1._wp / ( rn_osm_mle_time * rn_osm_mle_timeji,jj )
! r1_ft(:,:) = 1._wp / SQRT( ff_t(:,:) * ff_t(:,:) + z1_t2 )
!
END IF
!
CALL osm_rst( nit000, Kmm, 'READ' ) ! Read or initialize hbl, dh, hmle
!
IF ( ln_zdfddm ) THEN
IF(lwp) THEN
WRITE(numout,*)
WRITE(numout,*) ' Double diffusion mixing on temperature and salinity '
WRITE(numout,*) ' CAUTION : done in routine zdfosm, not in routine zdfddm '
END IF
END IF
!
! Set constants not in namelist
! -----------------------------
IF(lwp) THEN
WRITE(numout,*)
END IF
!
dstokes(:,:) = pp_large
IF (nn_osm_wave == 0) THEN
dstokes(:,:) = rn_osm_dstokes
END IF
!
! Horizontal average : initialization of weighting arrays
! -------------------
SELECT CASE ( nn_ave )
CASE ( 0 ) ! no horizontal average
IF(lwp) WRITE(numout,*) ' no horizontal average on avt'
IF(lwp) WRITE(numout,*) ' only in very high horizontal resolution !'
! Weighting mean arrays etmean
! ( 1 1 )
! avt = 1/4 ( 1 1 )
!
etmean(:,:,:) = 0.0_wp
!
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 )
etmean(ji,jj,jk) = tmask(ji,jj,jk) / MAX( 1.0_wp, umask(ji-1,jj, jk) + umask(ji,jj,jk) + &
& vmask(ji, jj-1,jk) + vmask(ji,jj,jk) )
END_3D
CASE ( 1 ) ! horizontal average
IF(lwp) WRITE(numout,*) ' horizontal average on avt'
! Weighting mean arrays etmean
! ( 1/2 1 1/2 )
! avt = 1/8 ( 1 2 1 )
! ( 1/2 1 1/2 )
etmean(:,:,:) = 0.0_wp
!
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 )
etmean(ji,jj,jk) = tmask(ji, jj,jk) / MAX( 1.0_wp, 2.0_wp * tmask(ji,jj,jk) + &
& 0.5_wp * ( tmask(ji-1,jj+1,jk) + tmask(ji-1,jj-1,jk) + &
& tmask(ji+1,jj+1,jk) + tmask(ji+1,jj-1,jk) ) + &
& 1.0_wp * ( tmask(ji-1,jj, jk) + tmask(ji, jj+1,jk) + &
& tmask(ji, jj-1,jk) + tmask(ji+1,jj, jk) ) )
END_3D
CASE DEFAULT
WRITE(ctmp1,*) ' bad flag value for nn_ave = ', nn_ave
CALL ctl_stop( ctmp1 )
END SELECT
!
! Initialization of vertical eddy coef. to the background value
! -------------------------------------------------------------
DO jk = 1, jpk
avt(:,:,jk) = avtb(jk) * tmask(:,:,jk)
END DO
!
! Zero the surface flux for non local term and osm mixed layer depth
! ------------------------------------------------------------------
ghamt(:,:,:) = 0.0_wp
ghams(:,:,:) = 0.0_wp
ghamu(:,:,:) = 0.0_wp
ghamv(:,:,:) = 0.0_wp
!
IF ( ln_dia_osm ) THEN ! Initialise auxiliary arrays for diagnostic output
osmdia2d(:,:) = 0.0_wp
osmdia3d(:,:,:) = 0.0_wp
END IF
!
END SUBROUTINE zdf_osm_init
SUBROUTINE osm_rst( kt, Kmm, cdrw )
!!---------------------------------------------------------------------
!! *** ROUTINE osm_rst ***
!!
!! ** Purpose : Read or write BL fields in restart file
!!
!! ** Method : use of IOM library. If the restart does not contain
!! required fields, they are recomputed from stratification
!!
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt ! Ocean time step index
INTEGER , INTENT(in ) :: Kmm ! Ocean time level index (middle)
CHARACTER(len=*), INTENT(in ) :: cdrw ! "READ"/"WRITE" flag
!!
INTEGER :: id1, id2, id3 ! iom enquiry index
INTEGER :: ji, jj, jk ! Dummy loop indices
INTEGER :: iiki, ikt ! Local integer
REAL(wp) :: zhbf ! Tempory scalars
REAL(wp) :: zN2_c ! Local scalar
REAL(wp) :: rho_c = 0.01_wp ! Density criterion for mixed layer depth
INTEGER, DIMENSION(jpi,jpj) :: imld_rst ! Level of mixed-layer depth (pycnocline top)
!!----------------------------------------------------------------------
!
!!-----------------------------------------------------------------------------
! If READ/WRITE Flag is 'READ', try to get hbl from restart file. If successful then return
!!-----------------------------------------------------------------------------
IF( TRIM(cdrw) == 'READ' .AND. ln_rstart) THEN
id1 = iom_varid( numror, 'wn', ldstop = .FALSE. )
IF( id1 > 0 ) THEN ! 'wn' exists; read
CALL iom_get( numror, jpdom_auto, 'wn', ww )
WRITE(numout,*) ' ===>>>> : wn read from restart file'
ELSE
ww(:,:,:) = 0.0_wp
WRITE(numout,*) ' ===>>>> : wn not in restart file, set to zero initially'
END IF
!
id1 = iom_varid( numror, 'hbl', ldstop = .FALSE. )
id2 = iom_varid( numror, 'dh', ldstop = .FALSE. )
IF( id1 > 0 .AND. id2 > 0 ) THEN ! 'hbl' exists; read and return
CALL iom_get( numror, jpdom_auto, 'hbl', hbl )
CALL iom_get( numror, jpdom_auto, 'dh', dh )
hml(:,:) = hbl(:,:) - dh(:,:) ! Initialise ML depth
WRITE(numout,*) ' ===>>>> : hbl & dh read from restart file'
IF( ln_osm_mle ) THEN
id3 = iom_varid( numror, 'hmle', ldstop = .FALSE. )
IF( id3 > 0 ) THEN
CALL iom_get( numror, jpdom_auto, 'hmle', hmle )
WRITE(numout,*) ' ===>>>> : hmle read from restart file'
ELSE
WRITE(numout,*) ' ===>>>> : hmle not found, set to hbl'
hmle(:,:) = hbl(:,:) ! Initialise MLE depth
END IF
END IF
RETURN
ELSE ! 'hbl' & 'dh' not in restart file, recalculate
WRITE(numout,*) ' ===>>>> : previous run without osmosis scheme, hbl computed from stratification'
END IF
END IF
!
!!-----------------------------------------------------------------------------
! If READ/WRITE Flag is 'WRITE', write hbl into the restart file, then return
!!-----------------------------------------------------------------------------
IF ( TRIM(cdrw) == 'WRITE' ) THEN
IF(lwp) WRITE(numout,*) '---- osm-rst ----'
CALL iom_rstput( kt, nitrst, numrow, 'wn', ww )
CALL iom_rstput( kt, nitrst, numrow, 'hbl', hbl )
CALL iom_rstput( kt, nitrst, numrow, 'dh', dh )
IF ( ln_osm_mle ) THEN
CALL iom_rstput( kt, nitrst, numrow, 'hmle', hmle )
END IF
RETURN
END IF
!
!!-----------------------------------------------------------------------------
! Getting hbl, no restart file with hbl, so calculate from surface stratification
!!-----------------------------------------------------------------------------
IF( lwp ) WRITE(numout,*) ' ===>>>> : calculating hbl computed from stratification'
! w-level of the mixing and mixed layers
CALL eos_rab( ts(:,:,:,:,Kmm), rab_n, Kmm )
CALL bn2( ts(:,:,:,:,Kmm), rab_n, rn2, Kmm )
imld_rst(:,:) = nlb10 ! Initialization to the number of w ocean point
hbl(:,:) = 0.0_wp ! Here hbl used as a dummy variable, integrating vertically N^2
zN2_c = grav * rho_c * r1_rho0 ! Convert density criteria into N^2 criteria
!
hbl(:,:) = 0.0_wp ! Here hbl used as a dummy variable, integrating vertically N^2
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
ikt = mbkt(ji,jj)
hbl(ji,jj) = hbl(ji,jj) + MAX( rn2(ji,jj,jk) , 0.0_wp ) * e3w(ji,jj,jk,Kmm)
IF ( hbl(ji,jj) < zN2_c ) imld_rst(ji,jj) = MIN( jk , ikt ) + 1 ! Mixed layer level
END_3D
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
iiki = MAX( 4, imld_rst(ji,jj) )
hbl(ji,jj) = gdepw(ji,jj,iiki,Kmm ) ! Turbocline depth
dh(ji,jj) = e3t(ji,jj,iiki-1,Kmm ) ! Turbocline depth
hml(ji,jj) = hbl(ji,jj) - dh(ji,jj)
END_2D
!
WRITE(numout,*) ' ===>>>> : hbl computed from stratification'
!
IF( ln_osm_mle ) THEN
hmle(:,:) = hbl(:,:) ! Initialise MLE depth.
WRITE(numout,*) ' ===>>>> : hmle set = to hbl'
END IF
!
ww(:,:,:) = 0.0_wp
WRITE(numout,*) ' ===>>>> : wn not in restart file, set to zero initially'
!
END SUBROUTINE osm_rst
SUBROUTINE tra_osm( kt, Kmm, pts, Krhs )
!!----------------------------------------------------------------------
!! *** ROUTINE tra_osm ***
!!
!! ** Purpose : compute and add to the tracer trend the non-local tracer flux
!!
!! ** Method : ???
!!
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt ! Time step index
INTEGER , INTENT(in ) :: Kmm, Krhs ! Time level indices
REAL(dp), DIMENSION(jpi,jpj,jpk,jpts,jpt), INTENT(inout) :: pts ! Active tracers and RHS of tracer equation
!!
INTEGER :: ji, jj, jk
REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdt, ztrds ! 3D workspace
!!----------------------------------------------------------------------
!
IF ( kt == nit000 ) THEN
IF ( ntile == 0 .OR. ntile == 1 ) THEN ! Do only on the first tile
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'tra_osm : OSM non-local tracer fluxes'
IF(lwp) WRITE(numout,*) '~~~~~~~ '
END IF
END IF
!
IF ( l_trdtra ) THEN ! Save ta and sa trends
ALLOCATE( ztrdt(jpi,jpj,jpk), ztrds(jpi,jpj,jpk) )
ztrdt(:,:,:) = pts(:,:,:,jp_tem,Krhs)
ztrds(:,:,:) = pts(:,:,:,jp_sal,Krhs)
END IF
!
DO_3D( 0, 0, 0, 0, 1, jpkm1 )
pts(ji,jj,jk,jp_tem,Krhs) = pts(ji,jj,jk,jp_tem,Krhs) &
& - ( ghamt(ji,jj,jk ) &
& - ghamt(ji,jj,jk+1) ) /e3t(ji,jj,jk,Kmm)
pts(ji,jj,jk,jp_sal,Krhs) = pts(ji,jj,jk,jp_sal,Krhs) &
& - ( ghams(ji,jj,jk ) &
& - ghams(ji,jj,jk+1) ) / e3t(ji,jj,jk,Kmm)
END_3D
!
IF ( l_trdtra ) THEN ! Save the non-local tracer flux trends for diagnostics
ztrdt(:,:,:) = pts(:,:,:,jp_tem,Krhs) - ztrdt(:,:,:)
ztrds(:,:,:) = pts(:,:,:,jp_sal,Krhs) - ztrds(:,:,:)
CALL trd_tra( kt, Kmm, Krhs, 'TRA', jp_tem, jptra_osm, ztrdt )
CALL trd_tra( kt, Kmm, Krhs, 'TRA', jp_sal, jptra_osm, ztrds )
DEALLOCATE( ztrdt, ztrds )
END IF
!
IF ( sn_cfctl%l_prtctl ) THEN
CALL prt_ctl( tab3d_1=pts(:,:,:,jp_tem,Krhs), clinfo1=' osm - Ta: ', mask1=tmask, &
& tab3d_2=pts(:,:,:,jp_sal,Krhs), clinfo2= ' Sa: ', mask2=tmask, clinfo3='tra' )
END IF
!
END SUBROUTINE tra_osm
SUBROUTINE trc_osm( kt ) ! Dummy routine
!!----------------------------------------------------------------------
!! *** ROUTINE trc_osm ***
!!
!! ** Purpose : compute and add to the passive tracer trend the non-local
!! passive tracer flux
!!
!!
!! ** Method : ???
!!
!!----------------------------------------------------------------------
INTEGER, INTENT(in) :: kt
!!----------------------------------------------------------------------
!
WRITE(*,*) 'trc_osm: Not written yet', kt
!
END SUBROUTINE trc_osm
SUBROUTINE dyn_osm( kt, Kmm, puu, pvv, Krhs )
!!----------------------------------------------------------------------
!! *** ROUTINE dyn_osm ***
!!
!! ** Purpose : compute and add to the velocity trend the non-local flux
!! copied/modified from tra_osm
!!
!! ** Method : ???
!!
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt ! Ocean time step index
INTEGER , INTENT(in ) :: Kmm, Krhs ! Ocean time level indices
REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! Ocean velocities and RHS of momentum equation
!!
INTEGER :: ji, jj, jk ! dummy loop indices
!!----------------------------------------------------------------------
!
IF ( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'dyn_osm : OSM non-local velocity'
IF(lwp) WRITE(numout,*) '~~~~~~~ '
END IF
!
! Code saving tracer trends removed, replace with trdmxl_oce
!
DO_3D( 0, 0, 0, 0, 1, jpkm1 ) ! Add non-local u and v fluxes
puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) - ( ghamu(ji,jj,jk ) - &
& ghamu(ji,jj,jk+1) ) / e3u(ji,jj,jk,Kmm)
pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) - ( ghamv(ji,jj,jk ) - &
& ghamv(ji,jj,jk+1) ) / e3v(ji,jj,jk,Kmm)
END_3D
!
! Code for saving tracer trends removed
!
END SUBROUTINE dyn_osm
SUBROUTINE zdf_osm_iomput_2d( cdname, posmdia2d )
!!----------------------------------------------------------------------
!! *** ROUTINE zdf_osm_iomput_2d ***
!!
!! ** Purpose : Wrapper for subroutine iom_put that accepts 2D arrays
!! with and without halo
!!
!!----------------------------------------------------------------------
CHARACTER(LEN=*), INTENT(in ) :: cdname
REAL(wp), DIMENSION(:,:), INTENT(in ) :: posmdia2d
!!----------------------------------------------------------------------
!
IF ( ln_dia_osm .AND. iom_use( cdname ) ) THEN
IF ( SIZE( posmdia2d, 1 ) == ntei-ntsi+1 .AND. SIZE( posmdia2d, 2 ) == ntej-ntsj+1 ) THEN ! Halo absent
osmdia2d(A2D(0)) = posmdia2d(:,:)
CALL iom_put( cdname, osmdia2d(A2D(nn_hls)) )
ELSE ! Halo present
CALL iom_put( cdname, posmdia2d )
END IF
END IF
!
END SUBROUTINE zdf_osm_iomput_2d
SUBROUTINE zdf_osm_iomput_3d( cdname, posmdia3d )
!!----------------------------------------------------------------------
!! *** ROUTINE zdf_osm_iomput_3d ***
!!
!! ** Purpose : Wrapper for subroutine iom_put that accepts 3D arrays
!! with and without halo
!!
!!----------------------------------------------------------------------
CHARACTER(LEN=*), INTENT(in ) :: cdname
REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: posmdia3d
!!----------------------------------------------------------------------
!
IF ( ln_dia_osm .AND. iom_use( cdname ) ) THEN
IF ( SIZE( posmdia3d, 1 ) == ntei-ntsi+1 .AND. SIZE( posmdia3d, 2 ) == ntej-ntsj+1 ) THEN ! Halo absent
osmdia3d(A2D(0),:) = posmdia3d(:,:,:)
CALL iom_put( cdname, osmdia3d(A2D(nn_hls),:) )
ELSE ! Halo present
CALL iom_put( cdname, posmdia3d )
END IF
END IF
!
END SUBROUTINE zdf_osm_iomput_3d
!!======================================================================
END MODULE zdfosm