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MODULE ablmod
!!======================================================================
!! *** MODULE ablmod ***
!! Surface module : ABL computation to provide atmospheric data
!! for surface fluxes computation
!!======================================================================
!! History : 3.6 ! 2019-03 (F. Lemarié & G. Samson) Original code
!!----------------------------------------------------------------------
!!----------------------------------------------------------------------
!! abl_stp : ABL single column model
!! abl_zdf_tke : atmospheric vertical closure
!!----------------------------------------------------------------------
USE abl ! ABL dynamics and tracers
USE par_abl ! ABL constants
USE phycst ! physical constants
USE dom_oce, ONLY : tmask
USE sbc_oce, ONLY : ght_abl, ghw_abl, e3t_abl, e3w_abl, jpka, jpkam1, rhoa
USE sbcblk ! use rn_efac
USE sbc_phy ! Catalog of functions for physical/meteorological parameters in the marine boundary layer
!
USE prtctl ! Print control (prt_ctl routine)
USE iom ! IOM library
USE in_out_manager ! I/O manager
USE lib_mpp ! MPP library
USE timing ! Timing
IMPLICIT NONE
PUBLIC abl_stp ! called by sbcabl.F90
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ustar2, zrough
!! * Substitutions
# include "do_loop_substitute.h90"
CONTAINS
!===================================================================================================
SUBROUTINE abl_stp( kt, psst, pssu, pssv, pssq, & ! in
& pu_dta, pv_dta, pt_dta, pq_dta, &
& pslp_dta, pgu_dta, pgv_dta, &
& pcd_du, psen, pevp, plat, & ! in/out
& pwndm, ptaui, ptauj, ptaum &
#if defined key_si3
& , ptm_su, pssu_ice, pssv_ice &
& , pssq_ice, pcd_du_ice, psen_ice &
& , pevp_ice, pwndm_ice, pfrac_oce &
& , ptaui_ice, ptauj_ice &
#endif
& )
!---------------------------------------------------------------------------------------------------
!!---------------------------------------------------------------------
!! *** ROUTINE abl_stp ***
!!
!! ** Purpose : Time-integration of the ABL model
!!
!! ** Method : Compute atmospheric variables : vertical turbulence
!! + Coriolis term + newtonian relaxation
!!
!! ** Action : - Advance TKE to time n+1 and compute Avm_abl, Avt_abl, PBLh
!! - Advance tracers to time n+1 (Euler backward scheme)
!! - Compute Coriolis term with forward-backward scheme (possibly with geostrophic guide)
!! - Advance u,v to time n+1 (Euler backward scheme)
!! - Apply newtonian relaxation on the dynamics and the tracers
!! - Finalize flux computation in psen, pevp, pwndm, ptaui, ptauj, ptaum
!!
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt ! time step index
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: psst ! sea-surface temperature [Celsius]
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssu ! sea-surface u (U-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssv ! sea-surface v (V-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssq ! sea-surface humidity
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pu_dta ! large-scale windi
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pv_dta ! large-scale windj
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pgu_dta ! large-scale hpgi
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pgv_dta ! large-scale hpgj
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pt_dta ! large-scale pot. temp.
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pq_dta ! large-scale humidity
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pslp_dta ! sea-level pressure
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pcd_du ! Cd x Du (T-point)
REAL(wp) , INTENT(inout), DIMENSION(:,: ) :: psen ! Ch x Du
REAL(wp) , INTENT(inout), DIMENSION(:,: ) :: pevp ! Ce x Du
REAL(wp) , INTENT(inout), DIMENSION(:,: ) :: pwndm ! ||uwnd||
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: plat ! latent heat flux
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: ptaui ! taux
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: ptauj ! tauy
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: ptaum ! ||tau||
!
#if defined key_si3
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: ptm_su ! ice-surface temperature [K]
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssu_ice ! ice-surface u (U-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssv_ice ! ice-surface v (V-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssq_ice ! ice-surface humidity
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pcd_du_ice ! Cd x Du over ice (T-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: psen_ice ! Ch x Du over ice (T-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pevp_ice ! Ce x Du over ice (T-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pwndm_ice ! ||uwnd - uice||
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pfrac_oce ! ocean fraction
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: ptaui_ice ! ice-surface taux stress (U-point)
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: ptauj_ice ! ice-surface tauy stress (V-point)
#endif
!
REAL(wp), DIMENSION(1:jpi,1:jpj ) :: zwnd_i, zwnd_j
REAL(wp), DIMENSION(1:jpi ,2:jpka) :: zCF
!
REAL(wp), DIMENSION(1:jpi ,1:jpka) :: z_elem_a
REAL(wp), DIMENSION(1:jpi ,1:jpka) :: z_elem_b
REAL(wp), DIMENSION(1:jpi ,1:jpka) :: z_elem_c
!
INTEGER :: ji, jj, jk, jtra, jbak ! dummy loop indices
REAL(wp) :: zztmp, zcff, ztemp, zhumi, zcff1, zztmp1, zztmp2
REAL(wp) :: zcff2, zfcor, zmsk, zsig, zcffu, zcffv, zzice,zzoce
LOGICAL :: SemiImp_Cor = .TRUE.
!
!!---------------------------------------------------------------------
!
IF(lwp .AND. kt == nit000) THEN ! control print
WRITE(numout,*)
WRITE(numout,*) 'abl_stp : ABL time stepping'
WRITE(numout,*) '~~~~~~'
ENDIF
!
IF( kt == nit000 ) ALLOCATE ( ustar2( 1:jpi, 1:jpj ) )
IF( kt == nit000 ) ALLOCATE ( zrough( 1:jpi, 1:jpj ) )
!! Compute ustar squared as Cd || Uatm-Uoce ||^2
!! needed for surface boundary condition of TKE
!! pwndm contains | U10m - U_oce | (see blk_oce_1 in sbcblk)
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zzoce = pCd_du (ji,jj) * pwndm (ji,jj)
#if defined key_si3
zzice = pCd_du_ice(ji,jj) * pwndm_ice(ji,jj)
ustar2(ji,jj) = zzoce * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * zzice
#else
ustar2(ji,jj) = zzoce
#endif
!#LB: sorry Cdn_oce is gone:
!zrough(ji,jj) = ght_abl(2) * EXP( - vkarmn / SQRT( MAX( Cdn_oce(ji,jj), 1.e-4 ) ) ) !<-- recover the value of z0 from Cdn_oce
END_2D
zrough(:,:) = z0_from_Cd( ght_abl(2), pCd_du(:,:) / MAX( pwndm(:,:), 0.5_wp ) ) ! #LB: z0_from_Cd is define in sbc_phy.F90...
!
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 1 *** Advance TKE to time n+1 and compute Avm_abl, Avt_abl, PBLh
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
CALL abl_zdf_tke( ) !--> Avm_abl, Avt_abl, pblh defined on (1,jpi) x (1,jpj)
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 2 *** Advance tracers to time n+1
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!-------------
DO jj = 1, jpj ! outer loop !--> tq_abl computed on (1:jpi) x (1:jpj)
!-------------
! Compute matrix elements for interior points
DO jk = 3, jpkam1
DO ji = 1, jpi ! vector opt.
z_elem_a( ji, jk ) = - rDt_abl * Avt_abl( ji, jj, jk-1 ) / e3w_abl( jk-1 ) ! lower-diagonal
z_elem_c( ji, jk ) = - rDt_abl * Avt_abl( ji, jj, jk ) / e3w_abl( jk ) ! upper-diagonal
z_elem_b( ji, jk ) = e3t_abl(jk) - z_elem_a( ji, jk ) - z_elem_c( ji, jk ) ! diagonal
END DO
END DO
! Boundary conditions
DO ji = 1, jpi ! vector opt.
! Neumann at the bottom
z_elem_a( ji, 2 ) = 0._wp
z_elem_c( ji, 2 ) = - rDt_abl * Avt_abl( ji, jj, 2 ) / e3w_abl( 2 )
! Homogeneous Neumann at the top
z_elem_a( ji, jpka ) = - rDt_abl * Avt_abl( ji, jj, jpka ) / e3w_abl( jpka )
z_elem_c( ji, jpka ) = 0._wp
z_elem_b( ji, jpka ) = e3t_abl( jpka ) - z_elem_a( ji, jpka )
END DO
DO jtra = 1,jptq ! loop on active tracers
DO jk = 3, jpkam1
!DO ji = 2, jpim1
DO ji = 1,jpi !!GS: to be checked if needed
tq_abl( ji, jj, jk, nt_a, jtra ) = e3t_abl(jk) * tq_abl( ji, jj, jk, nt_n, jtra ) ! initialize right-hand-side
END DO
END DO
IF(jtra == jp_ta) THEN
DO ji = 1,jpi ! surface boundary condition for temperature
zztmp1 = psen(ji, jj)
zztmp2 = psen(ji, jj) * ( psst(ji, jj) + rt0 )
#if defined key_si3
zztmp1 = zztmp1 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * psen_ice(ji,jj)
zztmp2 = zztmp2 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * psen_ice(ji,jj) * ptm_su(ji,jj)
#endif
z_elem_b( ji, 2 ) = e3t_abl( 2 ) - z_elem_c( ji, 2 ) + rDt_abl * zztmp1
tq_abl ( ji, jj, 2, nt_a, jtra ) = e3t_abl( 2 ) * tq_abl ( ji, jj, 2, nt_n, jtra ) + rDt_abl * zztmp2
tq_abl ( ji, jj, jpka, nt_a, jtra ) = e3t_abl( jpka ) * tq_abl ( ji, jj, jpka, nt_n, jtra )
END DO
ELSE ! jp_qa
DO ji = 1,jpi ! surface boundary condition for humidity
zztmp1 = pevp(ji, jj)
zztmp2 = pevp(ji, jj) * pssq(ji, jj)
#if defined key_si3
zztmp1 = zztmp1 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pevp_ice(ji,jj)
zztmp2 = zztmp2 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pevp_ice(ji, jj) * pssq_ice(ji, jj)
#endif
z_elem_b( ji, 2 ) = e3t_abl( 2 ) - z_elem_c( ji, 2 ) + rDt_abl * zztmp1
tq_abl ( ji, jj, 2 , nt_a, jtra ) = e3t_abl( 2 ) * tq_abl ( ji, jj, 2, nt_n, jtra ) + rDt_abl * zztmp2
tq_abl ( ji, jj, jpka, nt_a, jtra ) = e3t_abl( jpka ) * tq_abl ( ji, jj, jpka, nt_n, jtra )
END DO
END IF
!!
!! Matrix inversion
!! ----------------------------------------------------------
DO ji = 1,jpi
zcff = 1._wp / z_elem_b( ji, 2 )
zCF ( ji, 2 ) = - zcff * z_elem_c( ji, 2 )
tq_abl( ji, jj, 2, nt_a, jtra ) = zcff * tq_abl( ji, jj, 2, nt_a, jtra )
END DO
DO jk = 3, jpka
DO ji = 1,jpi
zcff = 1._wp / ( z_elem_b( ji, jk ) + z_elem_a( ji, jk ) * zCF( ji, jk-1 ) )
zCF(ji,jk) = - zcff * z_elem_c( ji, jk )
tq_abl(ji,jj,jk,nt_a,jtra) = zcff * ( tq_abl(ji,jj,jk ,nt_a,jtra) &
& - z_elem_a(ji, jk) * tq_abl(ji,jj,jk-1,nt_a,jtra) )
END DO
END DO
!!FL at this point we could check positivity of tq_abl(:,:,:,nt_a,jp_qa) ... test to do ...
DO jk = jpkam1,2,-1
DO ji = 1,jpi
tq_abl(ji,jj,jk,nt_a,jtra) = tq_abl(ji,jj,jk,nt_a,jtra) + &
& zCF(ji,jk) * tq_abl(ji,jj,jk+1,nt_a,jtra)
END DO
END DO
END DO !<-- loop on tracers
!!
!-------------
END DO ! end outer loop
!-------------
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 3 *** Compute Coriolis term with geostrophic guide
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
IF( SemiImp_Cor ) THEN
!-------------
DO jk = 2, jpka ! outer loop
!-------------
!
! Advance u_abl & v_abl to time n+1
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zcff = ( fft_abl(ji,jj) * rDt_abl )*( fft_abl(ji,jj) * rDt_abl ) ! (f dt)**2
u_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) *( &
& (1._wp-gamma_Cor*(1._wp-gamma_Cor)*zcff) * u_abl( ji, jj, jk, nt_n ) &
& + rDt_abl * fft_abl(ji, jj) * v_abl( ji, jj, jk, nt_n ) ) &
& / (1._wp + gamma_Cor*gamma_Cor*zcff)
v_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) *( &
& (1._wp-gamma_Cor*(1._wp-gamma_Cor)*zcff) * v_abl( ji, jj, jk, nt_n ) &
& - rDt_abl * fft_abl(ji, jj) * u_abl( ji, jj, jk, nt_n ) ) &
& / (1._wp + gamma_Cor*gamma_Cor*zcff)
END_2D
!
!-------------
END DO ! end outer loop !<-- u_abl and v_abl are properly updated on (1:jpi) x (1:jpj)
!-------------
!
IF( ln_geos_winds ) THEN
DO jj = 1, jpj ! outer loop
DO jk = 1, jpka
DO ji = 1, jpi
u_abl( ji, jj, jk, nt_a ) = u_abl( ji, jj, jk, nt_a ) &
& - rDt_abl * e3t_abl(jk) * fft_abl(ji , jj) * pgv_dta(ji ,jj ,jk)
v_abl( ji, jj, jk, nt_a ) = v_abl( ji, jj, jk, nt_a ) &
& + rDt_abl * e3t_abl(jk) * fft_abl(ji, jj ) * pgu_dta(ji ,jj ,jk)
END DO
END DO
END DO
END IF
!
IF( ln_hpgls_frc ) THEN
DO jj = 1, jpj ! outer loop
DO jk = 1, jpka
DO ji = 1, jpi
u_abl( ji, jj, jk, nt_a ) = u_abl( ji, jj, jk, nt_a ) - rDt_abl * e3t_abl(jk) * pgu_dta(ji,jj,jk)
v_abl( ji, jj, jk, nt_a ) = v_abl( ji, jj, jk, nt_a ) - rDt_abl * e3t_abl(jk) * pgv_dta(ji,jj,jk)
ENDDO
ENDDO
ENDDO
END IF
ELSE ! SemiImp_Cor = .FALSE.
IF( ln_geos_winds ) THEN
!-------------
DO jk = 2, jpka ! outer loop
!-------------
!
IF( MOD( kt, 2 ) == 0 ) then
! Advance u_abl & v_abl to time n+1
DO jj = 1, jpj
DO ji = 1, jpi
zcff = fft_abl(ji,jj) * ( v_abl ( ji , jj , jk, nt_n ) - pgv_dta(ji ,jj ,jk) )
u_abl( ji, jj, jk, nt_a ) = u_abl( ji, jj, jk, nt_n ) + rDt_abl * zcff
zcff = fft_abl(ji,jj) * ( u_abl ( ji , jj , jk, nt_a ) - pgu_dta(ji ,jj ,jk) )
v_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) *( v_abl( ji, jj, jk, nt_n ) - rDt_abl * zcff )
u_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) * u_abl( ji, jj, jk, nt_a )
END DO
END DO
ELSE
DO jj = 1, jpj
DO ji = 1, jpi
zcff = fft_abl(ji,jj) * ( u_abl ( ji , jj , jk, nt_n ) - pgu_dta(ji ,jj ,jk) )
v_abl( ji, jj, jk, nt_a ) = v_abl( ji, jj, jk, nt_n ) - rDt_abl * zcff
zcff = fft_abl(ji,jj) * ( v_abl ( ji , jj , jk, nt_a ) - pgv_dta(ji ,jj ,jk) )
u_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) *( u_abl( ji, jj, jk, nt_n ) + rDt_abl * zcff )
v_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) * v_abl( ji, jj, jk, nt_a )
END DO
END DO
END IF
!
!-------------
END DO ! end outer loop !<-- u_abl and v_abl are properly updated on (1:jpi) x (1:jpj)
!-------------
ENDIF ! ln_geos_winds
ENDIF ! SemiImp_Cor
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 4 *** Advance u,v to time n+1
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!
! Vertical diffusion for u_abl
!-------------
DO jj = 1, jpj ! outer loop
!-------------
DO jk = 3, jpkam1
DO ji = 1, jpi
z_elem_a( ji, jk ) = - rDt_abl * Avm_abl( ji, jj, jk-1 ) / e3w_abl( jk-1 ) ! lower-diagonal
z_elem_c( ji, jk ) = - rDt_abl * Avm_abl( ji, jj, jk ) / e3w_abl( jk ) ! upper-diagonal
z_elem_b( ji, jk ) = e3t_abl(jk) - z_elem_a( ji, jk ) - z_elem_c( ji, jk ) ! diagonal
END DO
END DO
DO ji = 2, jpi ! boundary conditions (Avm_abl and pcd_du must be available at ji=jpi)
!++ Surface boundary condition
z_elem_a( ji, 2 ) = 0._wp
z_elem_c( ji, 2 ) = - rDt_abl * Avm_abl( ji, jj, 2 ) / e3w_abl( 2 )
!
zztmp1 = pcd_du(ji, jj)
zztmp2 = 0.5_wp * pcd_du(ji, jj) * ( pssu(ji-1, jj) + pssu(ji,jj) )
#if defined key_si3
zztmp1 = zztmp1 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pcd_du_ice(ji, jj)
zzice = 0.5_wp * ( pssu_ice(ji-1, jj) + pssu_ice(ji, jj) )
zztmp2 = zztmp2 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pcd_du_ice(ji, jj) * zzice
#endif
z_elem_b( ji, 2 ) = e3t_abl( 2 ) - z_elem_c( ji, 2 ) + rDt_abl * zztmp1
u_abl( ji, jj, 2, nt_a ) = u_abl( ji, jj, 2, nt_a ) + rDt_abl * zztmp2
! idealized test cases only
!IF( ln_topbc_neumann ) THEN
! !++ Top Neumann B.C.
! z_elem_a( ji, jpka ) = - rDt_abl * Avm_abl( ji, jj, jpka ) / e3w_abl( jpka )
! z_elem_c( ji, jpka ) = 0._wp
! z_elem_b( ji, jpka ) = e3t_abl( jpka ) - z_elem_a( ji, jpka )
! !u_abl ( ji, jj, jpka, nt_a ) = e3t_abl( jpka ) * u_abl ( ji, jj, jpka, nt_a )
!ELSE
!++ Top Dirichlet B.C.
z_elem_a( ji, jpka ) = 0._wp
z_elem_c( ji, jpka ) = 0._wp
z_elem_b( ji, jpka ) = e3t_abl( jpka )
u_abl ( ji, jj, jpka, nt_a ) = e3t_abl( jpka ) * pu_dta(ji,jj,jk)
!ENDIF
END DO
!!
!! Matrix inversion
!! ----------------------------------------------------------
!DO ji = 2, jpi
DO ji = 1, jpi !!GS: TBI
zcff = 1._wp / z_elem_b( ji, 2 )
zCF (ji, 2 ) = - zcff * z_elem_c( ji, 2 )
u_abl (ji,jj,2,nt_a) = zcff * u_abl(ji,jj,2,nt_a)
END DO
DO jk = 3, jpka
DO ji = 2, jpi
zcff = 1._wp / ( z_elem_b( ji, jk ) + z_elem_a( ji, jk ) * zCF (ji, jk-1 ) )
zCF(ji,jk) = - zcff * z_elem_c( ji, jk )
u_abl(ji,jj,jk,nt_a) = zcff * ( u_abl(ji,jj,jk ,nt_a) &
& - z_elem_a(ji, jk) * u_abl(ji,jj,jk-1,nt_a) )
END DO
END DO
DO jk = jpkam1,2,-1
DO ji = 2, jpi
u_abl(ji,jj,jk,nt_a) = u_abl(ji,jj,jk,nt_a) + zCF(ji,jk) * u_abl(ji,jj,jk+1,nt_a)
END DO
END DO
!-------------
END DO ! end outer loop
!-------------
!
! Vertical diffusion for v_abl
!-------------
DO jj = 2, jpj ! outer loop
!-------------
!
DO jk = 3, jpkam1
DO ji = 1, jpi
z_elem_a( ji, jk ) = -rDt_abl * Avm_abl( ji, jj, jk-1 ) / e3w_abl( jk-1 ) ! lower-diagonal
z_elem_c( ji, jk ) = -rDt_abl * Avm_abl( ji, jj, jk ) / e3w_abl( jk ) ! upper-diagonal
z_elem_b( ji, jk ) = e3t_abl(jk) - z_elem_a( ji, jk ) - z_elem_c( ji, jk ) ! diagonal
END DO
END DO
DO ji = 1, jpi ! boundary conditions (Avm_abl and pcd_du must be available at jj=jpj)
!++ Surface boundary condition
z_elem_a( ji, 2 ) = 0._wp
z_elem_c( ji, 2 ) = - rDt_abl * Avm_abl( ji, jj, 2 ) / e3w_abl( 2 )
!
zztmp1 = pcd_du(ji, jj)
zztmp2 = 0.5_wp * pcd_du(ji, jj) * ( pssv(ji, jj) + pssv(ji, jj-1) )
#if defined key_si3
zztmp1 = zztmp1 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pcd_du_ice(ji, jj)
zzice = 0.5_wp * ( pssv_ice(ji, jj) + pssv_ice(ji, jj-1) )
zztmp2 = zztmp2 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pcd_du_ice(ji, jj) * zzice
#endif
z_elem_b( ji, 2 ) = e3t_abl( 2 ) - z_elem_c( ji, 2 ) + rDt_abl * zztmp1
v_abl( ji, jj, 2, nt_a ) = v_abl( ji, jj, 2, nt_a ) + rDt_abl * zztmp2
! idealized test cases only
!IF( ln_topbc_neumann ) THEN
! !++ Top Neumann B.C.
! z_elem_a( ji, jpka ) = - rDt_abl * Avm_abl( ji, jj, jpka ) / e3w_abl( jpka )
! z_elem_c( ji, jpka ) = 0._wp
! z_elem_b( ji, jpka ) = e3t_abl( jpka ) - z_elem_a( ji, jpka )
! !v_abl ( ji, jj, jpka, nt_a ) = e3t_abl( jpka ) * v_abl ( ji, jj, jpka, nt_a )
!ELSE
!++ Top Dirichlet B.C.
z_elem_a( ji, jpka ) = 0._wp
z_elem_c( ji, jpka ) = 0._wp
z_elem_b( ji, jpka ) = e3t_abl( jpka )
v_abl ( ji, jj, jpka, nt_a ) = e3t_abl( jpka ) * pv_dta(ji,jj,jk)
!ENDIF
END DO
!!
!! Matrix inversion
!! ----------------------------------------------------------
DO ji = 1, jpi
zcff = 1._wp / z_elem_b( ji, 2 )
zCF (ji, 2 ) = - zcff * z_elem_c( ji, 2 )
v_abl (ji,jj,2,nt_a) = zcff * v_abl ( ji, jj, 2, nt_a )
END DO
DO jk = 3, jpka
DO ji = 1, jpi
zcff = 1._wp / ( z_elem_b( ji, jk ) + z_elem_a( ji, jk ) * zCF (ji, jk-1 ) )
zCF(ji,jk) = - zcff * z_elem_c( ji, jk )
v_abl(ji,jj,jk,nt_a) = zcff * ( v_abl(ji,jj,jk ,nt_a) &
& - z_elem_a(ji, jk) * v_abl(ji,jj,jk-1,nt_a) )
END DO
END DO
DO jk = jpkam1,2,-1
DO ji = 1, jpi
v_abl(ji,jj,jk,nt_a) = v_abl(ji,jj,jk,nt_a) + zCF(ji,jk) * v_abl(ji,jj,jk+1,nt_a)
END DO
END DO
!
!-------------
END DO ! end outer loop
!-------------
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 5 *** Apply nudging on the dynamics and the tracers
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
IF( nn_dyn_restore > 0 ) THEN
!-------------
DO jk = 2, jpka ! outer loop
!-------------
DO_2D( nn_hls-1, nn_hls, nn_hls-1, nn_hls )
zcff1 = pblh( ji, jj )
zsig = ght_abl(jk) / MAX( jp_pblh_min, MIN( jp_pblh_max, zcff1 ) )
zsig = MIN( jp_bmax , MAX( zsig, jp_bmin) )
zmsk = msk_abl(ji,jj)
zcff2 = jp_alp3_dyn * zsig**3 + jp_alp2_dyn * zsig**2 &
& + jp_alp1_dyn * zsig + jp_alp0_dyn
zcff = (1._wp-zmsk) + zmsk * zcff2 * rn_Dt ! zcff = 1 for masked points
! rn_Dt = rDt_abl / nn_fsbc
zcff = zcff * rest_eq(ji,jj)
u_abl( ji, jj, jk, nt_a ) = (1._wp - zcff ) * u_abl( ji, jj, jk, nt_a ) &
& + zcff * pu_dta( ji, jj, jk )
v_abl( ji, jj, jk, nt_a ) = (1._wp - zcff ) * v_abl( ji, jj, jk, nt_a ) &
& + zcff * pv_dta( ji, jj, jk )
END_2D
!-------------
END DO ! end outer loop
!-------------
END IF
!-------------
DO jk = 2, jpka ! outer loop
!-------------
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zcff1 = pblh( ji, jj )
zsig = ght_abl(jk) / MAX( jp_pblh_min, MIN( jp_pblh_max, zcff1 ) )
zsig = MIN( jp_bmax , MAX( zsig, jp_bmin) )
zmsk = msk_abl(ji,jj)
zcff2 = jp_alp3_tra * zsig**3 + jp_alp2_tra * zsig**2 &
& + jp_alp1_tra * zsig + jp_alp0_tra
zcff = (1._wp-zmsk) + zmsk * zcff2 * rn_Dt ! zcff = 1 for masked points
! rn_Dt = rDt_abl / nn_fsbc
tq_abl( ji, jj, jk, nt_a, jp_ta ) = (1._wp - zcff ) * tq_abl( ji, jj, jk, nt_a, jp_ta ) &
& + zcff * pt_dta( ji, jj, jk )
tq_abl( ji, jj, jk, nt_a, jp_qa ) = (1._wp - zcff ) * tq_abl( ji, jj, jk, nt_a, jp_qa ) &
& + zcff * pq_dta( ji, jj, jk )
END_2D
!-------------
END DO ! end outer loop
!-------------
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 6 *** MPI exchanges & IOM outputs
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!
CALL lbc_lnk( 'ablmod', u_abl(:,:,:,nt_a ), 'T', -1._wp, v_abl(:,:,:,nt_a) , 'T', -1._wp )
CALL lbc_lnk( 'ablmod', tq_abl(:,:,:,nt_a,jp_ta), 'T', 1._wp , tq_abl(:,:,:,nt_a,jp_qa), 'T', 1._wp , kfillmode = jpfillnothing ) ! ++++ this should not be needed...
!
#if defined key_xios
! 2D & first ABL level
IF ( iom_use("pblh" ) ) CALL iom_put ( "pblh", pblh(:,: ) )
IF ( iom_use("uz1_abl") ) CALL iom_put ( "uz1_abl", u_abl(:,:,2,nt_a ) )
IF ( iom_use("vz1_abl") ) CALL iom_put ( "vz1_abl", v_abl(:,:,2,nt_a ) )
IF ( iom_use("tz1_abl") ) CALL iom_put ( "tz1_abl", tq_abl(:,:,2,nt_a,jp_ta) )
IF ( iom_use("qz1_abl") ) CALL iom_put ( "qz1_abl", tq_abl(:,:,2,nt_a,jp_qa) )
IF ( iom_use("uz1_dta") ) CALL iom_put ( "uz1_dta", pu_dta(:,:,2 ) )
IF ( iom_use("vz1_dta") ) CALL iom_put ( "vz1_dta", pv_dta(:,:,2 ) )
IF ( iom_use("tz1_dta") ) CALL iom_put ( "tz1_dta", pt_dta(:,:,2 ) )
IF ( iom_use("qz1_dta") ) CALL iom_put ( "qz1_dta", pq_dta(:,:,2 ) )
! debug 2D
IF( ln_geos_winds ) THEN
IF ( iom_use("uz1_geo") ) CALL iom_put ( "uz1_geo", pgu_dta(:,:,2) )
IF ( iom_use("vz1_geo") ) CALL iom_put ( "vz1_geo", pgv_dta(:,:,2) )
END IF
IF( ln_hpgls_frc ) THEN
IF ( iom_use("uz1_geo") ) CALL iom_put ( "uz1_geo", pgu_dta(:,:,2)/MAX(fft_abl(:,:),2.5e-5_wp) )
IF ( iom_use("vz1_geo") ) CALL iom_put ( "vz1_geo", -pgv_dta(:,:,2)/MAX(fft_abl(:,:),2.5e-5_wp) )
END IF
! 3D (all ABL levels)
IF ( iom_use("u_abl" ) ) CALL iom_put ( "u_abl" , u_abl(:,:,2:jpka,nt_a ) )
IF ( iom_use("v_abl" ) ) CALL iom_put ( "v_abl" , v_abl(:,:,2:jpka,nt_a ) )
IF ( iom_use("t_abl" ) ) CALL iom_put ( "t_abl" , tq_abl(:,:,2:jpka,nt_a,jp_ta) )
IF ( iom_use("q_abl" ) ) CALL iom_put ( "q_abl" , tq_abl(:,:,2:jpka,nt_a,jp_qa) )
IF ( iom_use("tke_abl" ) ) CALL iom_put ( "tke_abl" , tke_abl(:,:,2:jpka,nt_a ) )
IF ( iom_use("avm_abl" ) ) CALL iom_put ( "avm_abl" , avm_abl(:,:,2:jpka ) )
IF ( iom_use("avt_abl" ) ) CALL iom_put ( "avt_abl" , avt_abl(:,:,2:jpka ) )
IF ( iom_use("mxlm_abl") ) CALL iom_put ( "mxlm_abl", mxlm_abl(:,:,2:jpka ) )
IF ( iom_use("mxld_abl") ) CALL iom_put ( "mxld_abl", mxld_abl(:,:,2:jpka ) )
! debug 3D
IF ( iom_use("u_dta") ) CALL iom_put ( "u_dta", pu_dta(:,:,2:jpka) )
IF ( iom_use("v_dta") ) CALL iom_put ( "v_dta", pv_dta(:,:,2:jpka) )
IF ( iom_use("t_dta") ) CALL iom_put ( "t_dta", pt_dta(:,:,2:jpka) )
IF ( iom_use("q_dta") ) CALL iom_put ( "q_dta", pq_dta(:,:,2:jpka) )
IF( ln_geos_winds ) THEN
IF ( iom_use("u_geo") ) CALL iom_put ( "u_geo", pgu_dta(:,:,2:jpka) )
IF ( iom_use("v_geo") ) CALL iom_put ( "v_geo", pgv_dta(:,:,2:jpka) )
END IF
IF( ln_hpgls_frc ) THEN
IF ( iom_use("u_geo") ) CALL iom_put ( "u_geo", pgu_dta(:,:,2:jpka)/MAX( RESHAPE( fft_abl(:,:), (/jpi,jpj,jpka-1/), fft_abl(:,:)), 2.5e-5_wp) )
IF ( iom_use("v_geo") ) CALL iom_put ( "v_geo", -pgv_dta(:,:,2:jpka)/MAX( RESHAPE( fft_abl(:,:), (/jpi,jpj,jpka-1/), fft_abl(:,:)), 2.5e-5_wp) )
END IF
#endif
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 7 *** Finalize flux computation
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
ztemp = tq_abl( ji, jj, 2, nt_a, jp_ta )
zhumi = tq_abl( ji, jj, 2, nt_a, jp_qa )
zcff = rho_air( ztemp, zhumi, pslp_dta( ji, jj ) )
psen( ji, jj ) = - cp_air(zhumi) * zcff * psen(ji,jj) * ( psst(ji,jj) + rt0 - ztemp ) !GS: negative sign to respect aerobulk convention
pevp( ji, jj ) = rn_efac*MAX( 0._wp, zcff * pevp(ji,jj) * ( pssq(ji,jj) - zhumi ) )
plat( ji, jj ) = - L_vap( psst(ji,jj) ) * pevp( ji, jj )
rhoa( ji, jj ) = zcff
END_2D
DO_2D( nn_hls-1, nn_hls, nn_hls-1, nn_hls )
zwnd_i(ji,jj) = u_abl(ji ,jj,2,nt_a) - 0.5_wp * ( pssu(ji ,jj) + pssu(ji-1,jj) )
zwnd_j(ji,jj) = v_abl(ji,jj ,2,nt_a) - 0.5_wp * ( pssv(ji,jj ) + pssv(ji,jj-1) )
END_2D
!
CALL lbc_lnk( 'ablmod', zwnd_i(:,:) , 'T', -1.0_wp, zwnd_j(:,:) , 'T', -1.0_wp )
!
! ... scalar wind ( = | U10m - U_oce | ) at T-point (masked)
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zcff = SQRT( zwnd_i(ji,jj) * zwnd_i(ji,jj) &
& + zwnd_j(ji,jj) * zwnd_j(ji,jj) ) ! * msk_abl(ji,jj)
zztmp = rhoa(ji,jj) * pcd_du(ji,jj)
pwndm (ji,jj) = zcff
ptaum (ji,jj) = zztmp * zcff
zwnd_i(ji,jj) = zztmp * zwnd_i(ji,jj)
zwnd_j(ji,jj) = zztmp * zwnd_j(ji,jj)
END_2D
! ... utau, vtau at U- and V_points, resp.
! Note the use of 0.5*(2-umask) in order to unmask the stress along coastlines
! Note the use of MAX(tmask(i,j),tmask(i+1,j) is to mask tau over ice shelves
DO_2D( 0, 0, 0, 0 )
zcff = 0.5_wp * ( 2._wp - msk_abl(ji,jj)*msk_abl(ji+1,jj) )
zztmp = MAX(msk_abl(ji,jj),msk_abl(ji+1,jj))
ptaui(ji,jj) = zcff * zztmp * ( zwnd_i(ji,jj) + zwnd_i(ji+1,jj ) )
zcff = 0.5_wp * ( 2._wp - msk_abl(ji,jj)*msk_abl(ji,jj+1) )
zztmp = MAX(msk_abl(ji,jj),msk_abl(ji,jj+1))
ptauj(ji,jj) = zcff * zztmp * ( zwnd_j(ji,jj) + zwnd_j(ji ,jj+1) )
END_2D
!
CALL lbc_lnk( 'ablmod', ptaui(:,:), 'U', -1.0_wp, ptauj(:,:), 'V', -1.0_wp )
CALL iom_put( "taum_oce", ptaum )
IF(sn_cfctl%l_prtctl) THEN
CALL prt_ctl( tab2d_1=ptaui , clinfo1=' abl_stp: utau : ', mask1=umask, &
& tab2d_2=ptauj , clinfo2=' vtau : ', mask2=vmask )
CALL prt_ctl( tab2d_1=pwndm , clinfo1=' abl_stp: wndm : ' )
ENDIF
#if defined key_si3
! ------------------------------------------------------------ !
! Wind stress relative to the moving ice ( U10m - U_ice ) !
! ------------------------------------------------------------ !
DO_2D( 0, 0, 0, 0 )
ptaui_ice(ji,jj) = 0.5_wp * ( rhoa(ji+1,jj) * pCd_du_ice(ji+1,jj) + rhoa(ji,jj) * pCd_du_ice(ji,jj) ) &
& * ( 0.5_wp * ( u_abl(ji+1,jj,2,nt_a) + u_abl(ji,jj,2,nt_a) ) - pssu_ice(ji,jj) )
ptauj_ice(ji,jj) = 0.5_wp * ( rhoa(ji,jj+1) * pCd_du_ice(ji,jj+1) + rhoa(ji,jj) * pCd_du_ice(ji,jj) ) &
& * ( 0.5_wp * ( v_abl(ji,jj+1,2,nt_a) + v_abl(ji,jj,2,nt_a) ) - pssv_ice(ji,jj) )
END_2D
CALL lbc_lnk( 'ablmod', ptaui_ice, 'U', -1.0_wp, ptauj_ice, 'V', -1.0_wp )
!
IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=ptaui_ice , clinfo1=' abl_stp: putaui : ' &
& , tab2d_2=ptauj_ice , clinfo2=' pvtaui : ' )
! ------------------------------------------------------------ !
! Wind stress relative to the moving ice ( U10m - U_ice ) !
! ------------------------------------------------------------ !
DO_2D( 0, 0, 0, 0 )
zztmp1 = 0.5_wp * ( u_abl(ji+1,jj ,2,nt_a) + u_abl(ji,jj,2,nt_a) )
zztmp2 = 0.5_wp * ( v_abl(ji ,jj+1,2,nt_a) + v_abl(ji,jj,2,nt_a) )
ptaui_ice(ji,jj) = 0.5_wp * ( rhoa(ji+1,jj) * pCd_du_ice(ji+1,jj) &
& + rhoa(ji ,jj) * pCd_du_ice(ji ,jj) ) &
& * ( zztmp1 - pssu_ice(ji,jj) )
ptauj_ice(ji,jj) = 0.5_wp * ( rhoa(ji,jj+1) * pCd_du_ice(ji,jj+1) &
& + rhoa(ji,jj ) * pCd_du_ice(ji,jj ) ) &
& * ( zztmp2 - pssv_ice(ji,jj) )
END_2D
CALL lbc_lnk( 'ablmod', ptaui_ice, 'U', -1.0_wp, ptauj_ice,'V', -1.0_wp )
!
IF(sn_cfctl%l_prtctl) THEN
CALL prt_ctl( tab2d_1=ptaui_ice , clinfo1=' abl_stp: utau_ice : ', mask1=umask, &
& tab2d_2=ptauj_ice , clinfo2=' vtau_ice : ', mask2=vmask )
END IF
#endif
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 8 *** Swap time indices for the next timestep
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
nt_n = 1 + MOD( nt_n, 2)
nt_a = 1 + MOD( nt_a, 2)
!
!---------------------------------------------------------------------------------------------------
END SUBROUTINE abl_stp
!===================================================================================================
!===================================================================================================
SUBROUTINE abl_zdf_tke( )
!---------------------------------------------------------------------------------------------------
!!----------------------------------------------------------------------
!! *** ROUTINE abl_zdf_tke ***
!!
!! ** Purpose : Time-step Turbulente Kinetic Energy (TKE) equation
!!
!! ** Method : - source term due to shear
!! - source term due to stratification
!! - resolution of the TKE equation by inverting
!! a tridiagonal linear system
!!
!! ** Action : - en : now turbulent kinetic energy)
!! - avmu, avmv : production of TKE by shear at u and v-points
!! (= Kz dz[Ub] * dz[Un] )
!! ---------------------------------------------------------------------
INTEGER :: ji, jj, jk, tind, jbak, jkup, jkdwn
INTEGER, DIMENSION(1:jpi ) :: ikbl
REAL(wp) :: zcff, zcff2, ztken, zesrf, zetop, ziRic, ztv
REAL(wp) :: zdU , zdV , zcff1, zshear, zbuoy, zsig, zustar2
REAL(wp) :: zdU2, zdV2, zbuoy1, zbuoy2 ! zbuoy for BL89
REAL(wp) :: zwndi, zwndj
REAL(wp), DIMENSION(1:jpi, 1:jpka) :: zsh2
REAL(wp), DIMENSION(1:jpi,1:jpj,1:jpka) :: zbn2
REAL(wp), DIMENSION(1:jpi,1:jpka ) :: zFC, zRH, zCF
REAL(wp), DIMENSION(1:jpi,1:jpka ) :: z_elem_a
REAL(wp), DIMENSION(1:jpi,1:jpka ) :: z_elem_b
REAL(wp), DIMENSION(1:jpi,1:jpka ) :: z_elem_c
LOGICAL :: ln_Patankar = .FALSE.
LOGICAL :: ln_dumpvar = .FALSE.
LOGICAL , DIMENSION(1:jpi ) :: ln_foundl
!
tind = nt_n
ziRic = 1._wp / rn_Ric
! if tind = nt_a it is required to apply lbc_lnk on u_abl(nt_a) and v_abl(nt_a)
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! Advance TKE equation to time n+1
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!-------------
DO jj = 1, jpj ! outer loop
!-------------
!
! Compute vertical shear
DO jk = 2, jpkam1
DO ji = 1, jpi
zcff = 1.0_wp / e3w_abl( jk )**2
zdU = zcff* Avm_abl(ji,jj,jk) * (u_abl( ji, jj, jk+1, tind)-u_abl( ji, jj, jk , tind) )**2
zdV = zcff* Avm_abl(ji,jj,jk) * (v_abl( ji, jj, jk+1, tind)-v_abl( ji, jj, jk , tind) )**2
zsh2(ji,jk) = zdU+zdV !<-- zsh2 = Km ( ( du/dz )^2 + ( dv/dz )^2 )
END DO
END DO
!
! Compute brunt-vaisala frequency
DO jk = 2, jpkam1
DO ji = 1,jpi
zcff = grav * itvref / e3w_abl( jk )
zcff1 = tq_abl( ji, jj, jk+1, tind, jp_ta) - tq_abl( ji, jj, jk , tind, jp_ta)
zcff2 = tq_abl( ji, jj, jk+1, tind, jp_ta) * tq_abl( ji, jj, jk+1, tind, jp_qa) &
& - tq_abl( ji, jj, jk , tind, jp_ta) * tq_abl( ji, jj, jk , tind, jp_qa)
zbn2(ji,jj,jk) = zcff * ( zcff1 + rctv0 * zcff2 ) !<-- zbn2 defined on (2,jpi)
END DO
END DO
!
! Terms for the tridiagonal problem
DO jk = 2, jpkam1
DO ji = 1, jpi
zshear = zsh2( ji, jk ) ! zsh2 is already multiplied by Avm_abl at this point
zsh2(ji,jk) = zsh2( ji, jk ) / Avm_abl( ji, jj, jk ) ! reformulate zsh2 as a 'true' vertical shear for PBLH computation
zbuoy = - Avt_abl( ji, jj, jk ) * zbn2( ji, jj, jk )
z_elem_a( ji, jk ) = - 0.5_wp * rDt_abl * rn_Sch * ( Avm_abl( ji, jj, jk ) + Avm_abl( ji, jj, jk-1 ) ) / e3t_abl( jk ) ! lower-diagonal
z_elem_c( ji, jk ) = - 0.5_wp * rDt_abl * rn_Sch * ( Avm_abl( ji, jj, jk ) + Avm_abl( ji, jj, jk+1 ) ) / e3t_abl( jk+1 ) ! upper-diagonal
IF( (zbuoy + zshear) .gt. 0.) THEN ! Patankar trick to avoid negative values of TKE
z_elem_b( ji, jk ) = e3w_abl(jk) - z_elem_a( ji, jk ) - z_elem_c( ji, jk ) &
& + e3w_abl(jk) * rDt_abl * rn_Ceps * sqrt(tke_abl( ji, jj, jk, nt_n )) / mxld_abl(ji,jj,jk) ! diagonal
tke_abl( ji, jj, jk, nt_a ) = e3w_abl(jk) * ( tke_abl( ji, jj, jk, nt_n ) + rDt_abl * ( zbuoy + zshear ) ) ! right-hand-side
ELSE
z_elem_b( ji, jk ) = e3w_abl(jk) - z_elem_a( ji, jk ) - z_elem_c( ji, jk ) &
& + e3w_abl(jk) * rDt_abl * rn_Ceps * sqrt(tke_abl( ji, jj, jk, nt_n )) / mxld_abl(ji,jj,jk) & ! diagonal
& - e3w_abl(jk) * rDt_abl * zbuoy
tke_abl( ji, jj, jk, nt_a ) = e3w_abl(jk) * ( tke_abl( ji, jj, jk, nt_n ) + rDt_abl * zshear ) ! right-hand-side
END IF
END DO
END DO
DO ji = 1,jpi ! vector opt.
zesrf = MAX( rn_Esfc * ustar2(ji,jj), tke_min )
zetop = tke_min
z_elem_a ( ji, 1 ) = 0._wp
z_elem_c ( ji, 1 ) = 0._wp
z_elem_b ( ji, 1 ) = 1._wp
tke_abl ( ji, jj, 1, nt_a ) = zesrf
!++ Top Neumann B.C.
!z_elem_a ( ji, jpka ) = - 0.5 * rDt_abl * rn_Sch * (Avm_abl(ji,jj, jpka-1 )+Avm_abl(ji,jj, jpka )) / e3t_abl( jpka )
!z_elem_c ( ji, jpka ) = 0._wp
!z_elem_b ( ji, jpka ) = e3w_abl(jpka) - z_elem_a(ji, jpka )
!tke_abl ( ji, jj, jpka, nt_a ) = e3w_abl(jpka) * tke_abl( ji,jj, jpka, nt_n )
!++ Top Dirichlet B.C.
z_elem_a ( ji, jpka ) = 0._wp
z_elem_c ( ji, jpka ) = 0._wp
z_elem_b ( ji, jpka ) = 1._wp
tke_abl ( ji, jj, jpka, nt_a ) = zetop
zbn2 ( ji, jj, 1 ) = zbn2 ( ji, jj, 2 )
zsh2 ( ji, 1 ) = zsh2 ( ji, 2 )
zbn2 ( ji, jj, jpka ) = zbn2 ( ji, jj, jpkam1 )
zsh2 ( ji, jpka ) = zsh2 ( ji , jpkam1 )
END DO
!!
!! Matrix inversion
!! ----------------------------------------------------------
DO ji = 1,jpi
zcff = 1._wp / z_elem_b( ji, 1 )
zCF (ji, 1 ) = - zcff * z_elem_c( ji, 1 )
tke_abl(ji,jj,1,nt_a) = zcff * tke_abl ( ji, jj, 1, nt_a )
END DO
DO jk = 2, jpka
DO ji = 1,jpi
zcff = 1._wp / ( z_elem_b( ji, jk ) + z_elem_a( ji, jk ) * zCF(ji, jk-1 ) )
zCF(ji,jk) = - zcff * z_elem_c( ji, jk )
tke_abl(ji,jj,jk,nt_a) = zcff * ( tke_abl(ji,jj,jk ,nt_a) &
& - z_elem_a(ji, jk) * tke_abl(ji,jj,jk-1,nt_a) )
END DO
END DO
DO jk = jpkam1,1,-1
DO ji = 1,jpi
tke_abl(ji,jj,jk,nt_a) = tke_abl(ji,jj,jk,nt_a) + zCF(ji,jk) * tke_abl(ji,jj,jk+1,nt_a)
END DO
END DO
!!FL should not be needed because of Patankar procedure
tke_abl(2:jpi,jj,1:jpka,nt_a) = MAX( tke_abl(2:jpi,jj,1:jpka,nt_a), tke_min )
!!
!! Diagnose PBL height
!! ----------------------------------------------------------
!
! arrays zRH, zFC and zCF are available at this point
! and zFC(:, 1 ) = 0.
! diagnose PBL height based on zsh2 and zbn2
zFC ( : ,1) = 0._wp
ikbl( 1:jpi ) = 0
DO jk = 2,jpka
DO ji = 1, jpi
zcff = ghw_abl( jk-1 )
zcff1 = zcff / ( zcff + rn_epssfc * pblh ( ji, jj ) )
zcff = ghw_abl( jk )
zcff2 = zcff / ( zcff + rn_epssfc * pblh ( ji, jj ) )
zFC( ji, jk ) = zFC( ji, jk-1) + 0.5_wp * e3t_abl( jk )*( &
zcff2 * ( zsh2( ji, jk ) - ziRic * zbn2( ji, jj, jk ) &
- rn_Cek * ( fft_abl( ji, jj ) * fft_abl( ji, jj ) ) ) &
+ zcff1 * ( zsh2( ji, jk-1) - ziRic * zbn2( ji, jj, jk-1 ) &
- rn_Cek * ( fft_abl( ji, jj ) * fft_abl( ji, jj ) ) ) &
& )
IF( ikbl(ji) == 0 .and. zFC( ji, jk ).lt.0._wp ) ikbl(ji)=jk
END DO
END DO
!
! finalize the computation of the PBL height
DO ji = 1, jpi
jk = ikbl(ji)
IF( jk > 2 ) THEN ! linear interpolation to get subgrid value of pblh
pblh( ji, jj ) = ( ghw_abl( jk-1 ) * zFC( ji, jk ) &
& - ghw_abl( jk ) * zFC( ji, jk-1 ) &
& ) / ( zFC( ji, jk ) - zFC( ji, jk-1 ) )
ELSE IF( jk==2 ) THEN
pblh( ji, jj ) = ghw_abl(2 )
ELSE
pblh( ji, jj ) = ghw_abl(jpka)
END IF
END DO
!-------------
END DO
!-------------
!
! Optional : could add pblh smoothing if pblh is noisy horizontally ...
IF(ln_smth_pblh) THEN
CALL lbc_lnk( 'ablmod', pblh, 'T', 1.0_wp) !, kfillmode = jpfillnothing)
CALL smooth_pblh( pblh, msk_abl )
CALL lbc_lnk( 'ablmod', pblh, 'T', 1.0_wp) !, kfillmode = jpfillnothing)
ENDIF
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! Diagnostic mixing length computation
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!
SELECT CASE ( nn_amxl )
!
CASE ( 0 ) ! Deardroff 80 length-scale bounded by the distance to surface and bottom
# define zlup zRH
# define zldw zFC
DO jj = 1, jpj ! outer loop
!
DO ji = 1, jpi
mxld_abl( ji, jj, 1 ) = mxl_min
mxld_abl( ji, jj, jpka ) = mxl_min
mxlm_abl( ji, jj, 1 ) = mxl_min
mxlm_abl( ji, jj, jpka ) = mxl_min
zldw ( ji, 1 ) = zrough(ji,jj) * rn_Lsfc
zlup ( ji, jpka ) = mxl_min
END DO
!
DO jk = 2, jpkam1
DO ji = 1, jpi
zbuoy = MAX( zbn2(ji, jj, jk), rsmall )
mxlm_abl( ji, jj, jk ) = MAX( mxl_min, &
& SQRT( 2._wp * tke_abl( ji, jj, jk, nt_a ) / zbuoy ) )
END DO
END DO
!
! Limit mxl
DO jk = jpkam1,1,-1
DO ji = 1, jpi
zlup(ji,jk) = MIN( zlup(ji,jk+1) + (ghw_abl(jk+1)-ghw_abl(jk)) , mxlm_abl(ji, jj, jk) )
END DO
END DO
!
DO jk = 2, jpka
DO ji = 1, jpi
zldw(ji,jk) = MIN( zldw(ji,jk-1) + (ghw_abl(jk)-ghw_abl(jk-1)) , mxlm_abl(ji, jj, jk) )
END DO
END DO
!
! DO jk = 1, jpka
! DO ji = 1, jpi
! mxlm_abl( ji, jj, jk ) = SQRT( zldw( ji, jk ) * zlup( ji, jk ) )
! mxld_abl( ji, jj, jk ) = MIN ( zldw( ji, jk ), zlup( ji, jk ) )
! END DO
! END DO
!
DO jk = 1, jpka
DO ji = 1, jpi
! zcff = 2.*SQRT(2.)*( zldw( ji, jk )**(-2._wp/3._wp) + zlup( ji, jk )**(-2._wp/3._wp) )**(-3._wp/2._wp)
zcff = SQRT( zldw( ji, jk ) * zlup( ji, jk ) )
mxlm_abl( ji, jj, jk ) = MAX( zcff, mxl_min )
mxld_abl( ji, jj, jk ) = MAX( MIN( zldw( ji, jk ), zlup( ji, jk ) ), mxl_min )
END DO
END DO
!
END DO
# undef zlup
# undef zldw
!
!
CASE ( 1 ) ! Modified Deardroff 80 length-scale bounded by the distance to surface and bottom
# define zlup zRH
# define zldw zFC
DO jj = 1, jpj ! outer loop
!
DO jk = 2, jpkam1
DO ji = 1,jpi
zcff = 1.0_wp / e3w_abl( jk )**2
zdU = zcff* (u_abl( ji, jj, jk+1, tind)-u_abl( ji, jj, jk , tind) )**2
zdV = zcff* (v_abl( ji, jj, jk+1, tind)-v_abl( ji, jj, jk , tind) )**2
zsh2(ji,jk) = SQRT(zdU+zdV) !<-- zsh2 = SQRT ( ( du/dz )^2 + ( dv/dz )^2 )
ENDDO
ENDDO
!
DO ji = 1, jpi
zcff = zrough(ji,jj) * rn_Lsfc
mxld_abl ( ji, jj, 1 ) = zcff
mxld_abl ( ji, jj, jpka ) = mxl_min
mxlm_abl ( ji, jj, 1 ) = zcff
mxlm_abl ( ji, jj, jpka ) = mxl_min
zldw ( ji, 1 ) = zcff
zlup ( ji, jpka ) = mxl_min
END DO
!
DO jk = 2, jpkam1
DO ji = 1, jpi
zbuoy = MAX( zbn2(ji, jj, jk), rsmall )
zcff = 2.0_wp*SQRT(tke_abl( ji, jj, jk, nt_a )) / ( rn_Rod*zsh2(ji,jk) &
& + SQRT(rn_Rod*rn_Rod*zsh2(ji,jk)*zsh2(ji,jk)+2.0_wp*zbuoy ) )
mxlm_abl( ji, jj, jk ) = MAX( mxl_min, zcff )
END DO
END DO
!
! Limit mxl
DO jk = jpkam1,1,-1
DO ji = 1, jpi
zlup(ji,jk) = MIN( zlup(ji,jk+1) + (ghw_abl(jk+1)-ghw_abl(jk)) , mxlm_abl(ji, jj, jk) )
END DO
END DO
!
DO jk = 2, jpka
DO ji = 1, jpi
zldw(ji,jk) = MIN( zldw(ji,jk-1) + (ghw_abl(jk)-ghw_abl(jk-1)) , mxlm_abl(ji, jj, jk) )
END DO
END DO
!
DO jk = 1, jpka
DO ji = 1, jpi
!mxlm_abl( ji, jj, jk ) = SQRT( zldw( ji, jk ) * zlup( ji, jk ) )
!zcff = 2.*SQRT(2.)*( zldw( ji, jk )**(-2._wp/3._wp) + zlup( ji, jk )**(-2._wp/3._wp) )**(-3._wp/2._wp)
zcff = SQRT( zldw( ji, jk ) * zlup( ji, jk ) )
mxlm_abl( ji, jj, jk ) = MAX( zcff, mxl_min )
!mxld_abl( ji, jj, jk ) = MIN( zldw( ji, jk ), zlup( ji, jk ) )
mxld_abl( ji, jj, jk ) = MAX( MIN( zldw( ji, jk ), zlup( ji, jk ) ), mxl_min )
END DO
END DO
!
END DO
# undef zlup
# undef zldw
!
CASE ( 2 ) ! Bougeault & Lacarrere 89 length-scale