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SUBROUTINE ultimate_y( kloop, pamsk, kn_umx, pdt, pt, pv, pt_v, pfv_ho )
!!---------------------------------------------------------------------
!! *** ROUTINE ultimate_y ***
!!
!! ** Purpose : compute tracer at v-points
!!
!! ** Method : ...
!!
!! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74.
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kloop ! either 0 or nn_hls depending on the order of the call
REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0)
INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2)
REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pv ! ice j-velocity component
REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields
REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_v ! tracer at v-point
REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfv_ho ! high order flux
!
INTEGER :: ji, jj, jl ! dummy loop indices
REAL(wp) :: zcv, zdy2, zdy4 ! - -
REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztv1, ztv2, ztv3, ztv4
!!----------------------------------------------------------------------
!
! !-- Laplacian in j-direction --!
DO jl = 1, jpl
DO_2D( kloop, kloop, nn_hls, nn_hls-1 ) ! First derivative (gradient)
ztv1(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1)
END_2D
DO_2D( kloop, kloop, nn_hls-1, nn_hls-1 ) ! Second derivative (Laplacian)
ztv2(ji,jj,jl) = ( ztv1(ji,jj,jl) - ztv1(ji,jj-1,jl) ) * r1_e2t(ji,jj)
END_2D
END DO
IF( nn_hls == 1 ) CALL lbc_lnk( 'icedyn_adv_umx', ztv2, 'T', 1.0_wp )
!
! !-- BiLaplacian in j-direction --!
DO jl = 1, jpl
DO_2D( kloop, kloop, 1, 0 ) ! Third derivative
ztv3(ji,jj,jl) = ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1)
END_2D
DO_2D( kloop, kloop, 0, 0 ) ! Fourth derivative
ztv4(ji,jj,jl) = ( ztv3(ji,jj,jl) - ztv3(ji,jj-1,jl) ) * r1_e2t(ji,jj)
END_2D
END DO
!
!
SELECT CASE (kn_umx )
!
CASE( 1 ) !== 1st order central TIM ==! (Eq. 21)
DO jl = 1, jpl
DO_2D( kloop, kloop, 1, 0 )
pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) &
& - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) )
END_2D
END DO
!
CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23)
DO jl = 1, jpl
DO_2D( kloop, kloop, 1, 0 )
zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj)
pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) &
& - zcv * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) )
END_2D
END DO
!
CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24)
DO jl = 1, jpl
DO_2D( kloop, kloop, 1, 0 )
zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj)
zdy2 = e2v(ji,jj) * e2v(ji,jj)
!!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj)
pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) &
& - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) &
Clement Rousset
committed
& + r1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) &
& - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) )
END_2D
END DO
!
CASE( 4 ) !== 4th order central TIM ==! (Eq. 27)
DO jl = 1, jpl
DO_2D( kloop, kloop, 1, 0 )
zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj)
zdy2 = e2v(ji,jj) * e2v(ji,jj)
!!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj)
pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) &
& - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) &
Clement Rousset
committed
& + r1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) &
& - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) )
END_2D
END DO
!
CASE( 5 ) !== 5th order central TIM ==! (Eq. 29)
!
CALL lbc_lnk( 'icedyn_adv_umx', ztv4, 'T', 1.0_wp )
!
DO jl = 1, jpl
DO_2D( kloop, kloop, 1, 0 )
zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj)
zdy2 = e2v(ji,jj) * e2v(ji,jj)
!!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj)
zdy4 = zdy2 * zdy2
pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) &
& - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) &
Clement Rousset
committed
& + r1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) &
& - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) &
Clement Rousset
committed
& + r1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1,jl) + ztv4(ji,jj,jl) &
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& - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1,jl) - ztv4(ji,jj,jl) ) ) )
END_2D
END DO
!
END SELECT
!
! if pt at v-point is negative then use the upstream value
! this should not be necessary if a proper sea-ice mask is set in Ultimate
! to degrade the order of the scheme when necessary (for ex. at the ice edge)
IF( ll_neg ) THEN
DO jl = 1, jpl
DO_2D( kloop, kloop, 1, 0 )
IF( pt_v(ji,jj,jl) < 0._wp .OR. ( jmsk_small(ji,jj,jl) == 0 .AND. pamsk == 0. ) ) THEN
pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1,jl) + pt(ji,jj,jl) ) &
& - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) )
ENDIF
END_2D
END DO
ENDIF
! !-- High order flux in j-direction --!
DO jl = 1, jpl
DO_2D( 0, 0, 1, 0 )
pfv_ho(ji,jj,jl) = pv(ji,jj) * pt_v(ji,jj,jl)
END_2D
END DO
!
END SUBROUTINE ultimate_y
SUBROUTINE nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho )
!!---------------------------------------------------------------------
!! *** ROUTINE nonosc_ice ***
!!
!! ** Purpose : compute monotonic tracer fluxes from the upstream
!! scheme and the before field by a non-oscillatory algorithm
!!
!! ** Method : ...
!!----------------------------------------------------------------------
REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0)
REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2
REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice j-velocity => v*e1
REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt, pt_ups ! before field & upstream guess of after field
REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups, pfu_ups ! upstream flux
REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho, pfu_ho ! monotonic flux
!
INTEGER :: ji, jj, jl ! dummy loop indices
REAL(wp) :: zpos, zneg, zbig, zup, zdo, z1_dt ! local scalars
REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zcoef, zzt ! - -
REAL(wp), DIMENSION(jpi,jpj ) :: zbup, zbdo
REAL(wp), DIMENSION(jpi,jpj,jpl) :: zbetup, zbetdo, zti_ups, ztj_ups
!!----------------------------------------------------------------------
zbig = 1.e+40_wp
! antidiffusive flux : high order minus low order
! --------------------------------------------------
DO jl = 1, jpl
DO_2D( 1, 0, 0, 0 )
pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl)
END_2D
DO_2D( 0, 0, 1, 0 )
pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl)
END_2D
END DO
! extreme case where pfu_ho has to be zero
! ----------------------------------------
! pfu_ho
! * --->
! | | * | |
! | | | * |
! | | | | *
! t_ups : i-1 i i+1 i+2
IF( ll_prelim ) THEN
DO jl = 1, jpl
DO_2D( 0, 0, 0, 0 )
zti_ups(ji,jj,jl)= pt_ups(ji+1,jj ,jl)
ztj_ups(ji,jj,jl)= pt_ups(ji ,jj+1,jl)
END_2D
END DO
CALL lbc_lnk( 'icedyn_adv_umx', zti_ups, 'T', 1.0_wp, ztj_ups, 'T', 1.0_wp )
DO jl = 1, jpl
DO_2D( 0, 0, 0, 0 )
IF ( pfu_ho(ji,jj,jl) * ( pt_ups(ji+1,jj ,jl) - pt_ups(ji,jj,jl) ) <= 0._wp .AND. &
& pfv_ho(ji,jj,jl) * ( pt_ups(ji ,jj+1,jl) - pt_ups(ji,jj,jl) ) <= 0._wp ) THEN
!
IF( pfu_ho(ji,jj,jl) * ( zti_ups(ji+1,jj ,jl) - zti_ups(ji,jj,jl) ) <= 0._wp .AND. &
& pfv_ho(ji,jj,jl) * ( ztj_ups(ji ,jj+1,jl) - ztj_ups(ji,jj,jl) ) <= 0._wp ) THEN
pfu_ho(ji,jj,jl)=0._wp
pfv_ho(ji,jj,jl)=0._wp
ENDIF
!
IF( pfu_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji-1,jj ,jl) ) <= 0._wp .AND. &
& pfv_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji ,jj-1,jl) ) <= 0._wp ) THEN
pfu_ho(ji,jj,jl)=0._wp
pfv_ho(ji,jj,jl)=0._wp
ENDIF
!
ENDIF
END_2D
END DO
CALL lbc_lnk( 'icedyn_adv_umx', pfu_ho, 'U', -1.0_wp, pfv_ho, 'V', -1.0_wp ) ! lateral boundary cond.
ENDIF
! Search local extrema
! --------------------
! max/min of pt & pt_ups with large negative/positive value (-/+zbig) outside ice cover
z1_dt = 1._wp / pdt
DO jl = 1, jpl
DO_2D( 1, 1, 1, 1 )
IF ( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN
zbup(ji,jj) = -zbig
zbdo(ji,jj) = zbig
ELSEIF( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) > 0._wp ) THEN
zbup(ji,jj) = pt_ups(ji,jj,jl)
zbdo(ji,jj) = pt_ups(ji,jj,jl)
ELSEIF( pt(ji,jj,jl) > 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN
zbup(ji,jj) = pt(ji,jj,jl)
zbdo(ji,jj) = pt(ji,jj,jl)
ELSE
zbup(ji,jj) = MAX( pt(ji,jj,jl) , pt_ups(ji,jj,jl) )
zbdo(ji,jj) = MIN( pt(ji,jj,jl) , pt_ups(ji,jj,jl) )
ENDIF
END_2D
DO_2D( 0, 0, 0, 0 )
!
zup = MAX( zbup(ji,jj), zbup(ji-1,jj), zbup(ji+1,jj), zbup(ji,jj-1), zbup(ji,jj+1) ) ! search max/min in neighbourhood
zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj), zbdo(ji+1,jj), zbdo(ji,jj-1), zbdo(ji,jj+1) )
!
zpos = MAX( 0._wp, pfu_ho(ji-1,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji ,jj ,jl) ) & ! positive/negative part of the flux
& + MAX( 0._wp, pfv_ho(ji ,jj-1,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj ,jl) )
zneg = MAX( 0._wp, pfu_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji-1,jj ,jl) ) &
& + MAX( 0._wp, pfv_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj-1,jl) )
!
zpos = zpos - (pt(ji,jj,jl) * MIN( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MIN( 0., pv(ji,jj) - pv(ji,jj-1) ) &
& ) * ( 1. - pamsk )
zneg = zneg + (pt(ji,jj,jl) * MAX( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MAX( 0., pv(ji,jj) - pv(ji,jj-1) ) &
& ) * ( 1. - pamsk )
!
! ! up & down beta terms
! clem: zbetup and zbetdo must be 0 for zpos>1.e-10 & zneg>1.e-10 (do not put 0 instead of 1.e-10 !!!)
IF( zpos > epsi10 ) THEN ; zbetup(ji,jj,jl) = MAX( 0._wp, zup - pt_ups(ji,jj,jl) ) / zpos * e1e2t(ji,jj) * z1_dt
ELSE ; zbetup(ji,jj,jl) = 0._wp ! zbig
ENDIF
!
IF( zneg > epsi10 ) THEN ; zbetdo(ji,jj,jl) = MAX( 0._wp, pt_ups(ji,jj,jl) - zdo ) / zneg * e1e2t(ji,jj) * z1_dt
ELSE ; zbetdo(ji,jj,jl) = 0._wp ! zbig
ENDIF
!
! if all the points are outside ice cover
IF( zup == -zbig ) zbetup(ji,jj,jl) = 0._wp ! zbig
IF( zdo == zbig ) zbetdo(ji,jj,jl) = 0._wp ! zbig
!
END_2D
END DO
CALL lbc_lnk( 'icedyn_adv_umx', zbetup, 'T', 1.0_wp, zbetdo, 'T', 1.0_wp ) ! lateral boundary cond. (unchanged sign)
! monotonic flux in the y direction
! ---------------------------------
DO jl = 1, jpl
DO_2D( 1, 0, 0, 0 )
zau = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji+1,jj,jl) )
zbu = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji+1,jj,jl) )
zcu = 0.5_wp + SIGN( 0.5_wp , pfu_ho(ji,jj,jl) )
!
zcoef = ( zcu * zau + ( 1._wp - zcu ) * zbu )
!
pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) * zcoef + pfu_ups(ji,jj,jl)
!
END_2D
DO_2D( 0, 0, 1, 0 )
zav = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji,jj+1,jl) )
zbv = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji,jj+1,jl) )
zcv = 0.5_wp + SIGN( 0.5_wp , pfv_ho(ji,jj,jl) )
!
zcoef = ( zcv * zav + ( 1._wp - zcv ) * zbv )
!
pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) * zcoef + pfv_ups(ji,jj,jl)
!
END_2D
END DO
!
END SUBROUTINE nonosc_ice
SUBROUTINE limiter_x( pdt, pu, pt, pfu_ups, pfu_ho )
!!---------------------------------------------------------------------
!! *** ROUTINE limiter_x ***
!!
!! ** Purpose : compute flux limiter
!!----------------------------------------------------------------------
REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
REAL(wp), DIMENSION(:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2
REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pt ! ice tracer
REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pfu_ups ! upstream flux
REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: pfu_ho ! high order flux
!
REAL(wp) :: Cr, Rjm, Rj, Rjp, uCFL, zpsi, zh3, zlimiter, Rr
INTEGER :: ji, jj, jl ! dummy loop indices
REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpx ! tracer slopes
!!----------------------------------------------------------------------
!
DO jl = 1, jpl
DO_2D( nn_hls, nn_hls-1, 0, 0 )
zslpx(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * umask(ji,jj,1)
END_2D
END DO
IF( nn_hls == 1 ) CALL lbc_lnk( 'icedyn_adv_umx', zslpx, 'U', -1.0_wp) ! lateral boundary cond.
DO jl = 1, jpl
DO_2D( nn_hls-1, 0, 0, 0 )
uCFL = pdt * ABS( pu(ji,jj) ) * r1_e1e2t(ji,jj)
Rjm = zslpx(ji-1,jj,jl)
Rj = zslpx(ji ,jj,jl)
Rjp = zslpx(ji+1,jj,jl)
IF( np_limiter == 3 ) THEN
IF( pu(ji,jj) > 0. ) THEN ; Rr = Rjm
ELSE ; Rr = Rjp
ENDIF
zh3 = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl)
IF( Rj > 0. ) THEN
zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pu(ji,jj)), &
& MIN( 2. * Rr * 0.5 * ABS(pu(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) )
ELSE
zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pu(ji,jj)), &
& MIN(-2. * Rr * 0.5 * ABS(pu(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) )
ENDIF
pfu_ho(ji,jj,jl) = pfu_ups(ji,jj,jl) + zlimiter
ELSEIF( np_limiter == 2 ) THEN
IF( Rj /= 0. ) THEN
IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj
ELSE ; Cr = Rjp / Rj
ENDIF
ELSE
Cr = 0.
ENDIF
! -- superbee --
zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) )
! -- van albada 2 --
!!zpsi = 2.*Cr / (Cr*Cr+1.)
! -- sweby (with beta=1) --
!!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) )
! -- van Leer --
!!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) )
! -- ospre --
!!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. )
! -- koren --
!!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) )
! -- charm --
!IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) )
!ELSE ; zpsi = 0.
!ENDIF
! -- van albada 1 --
!!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1)
! -- smart --
!!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) )
! -- umist --
!!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) )
! high order flux corrected by the limiter
pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - ABS( pu(ji,jj) ) * ( (1.-zpsi) + uCFL*zpsi ) * Rj * 0.5
ENDIF
END_2D
END DO
IF( nn_hls == 1 ) CALL lbc_lnk( 'icedyn_adv_umx', pfu_ho, 'U', -1.0_wp) ! lateral boundary cond.
!
END SUBROUTINE limiter_x
SUBROUTINE limiter_y( pdt, pv, pt, pfv_ups, pfv_ho )
!!---------------------------------------------------------------------
!! *** ROUTINE limiter_y ***
!!
!! ** Purpose : compute flux limiter
!!----------------------------------------------------------------------
REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice i-velocity => u*e2
REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt ! ice tracer
REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups ! upstream flux
REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho ! high order flux
!
REAL(wp) :: Cr, Rjm, Rj, Rjp, vCFL, zpsi, zh3, zlimiter, Rr
INTEGER :: ji, jj, jl ! dummy loop indices
REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpy ! tracer slopes
!!----------------------------------------------------------------------
!
DO jl = 1, jpl
DO_2D( 0, 0, nn_hls, nn_hls-1 )
zslpy(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * vmask(ji,jj,1)
END_2D
END DO
IF( nn_hls == 1 ) CALL lbc_lnk( 'icedyn_adv_umx', zslpy, 'V', -1.0_wp) ! lateral boundary cond.
DO jl = 1, jpl
DO_2D( 0, 0, nn_hls-1, 0 )
vCFL = pdt * ABS( pv(ji,jj) ) * r1_e1e2t(ji,jj)
Rjm = zslpy(ji,jj-1,jl)
Rj = zslpy(ji,jj ,jl)
Rjp = zslpy(ji,jj+1,jl)
IF( np_limiter == 3 ) THEN
IF( pv(ji,jj) > 0. ) THEN ; Rr = Rjm
ELSE ; Rr = Rjp
ENDIF
zh3 = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl)
IF( Rj > 0. ) THEN
zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pv(ji,jj)), &
& MIN( 2. * Rr * 0.5 * ABS(pv(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) )
ELSE
zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pv(ji,jj)), &
& MIN(-2. * Rr * 0.5 * ABS(pv(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) )
ENDIF
pfv_ho(ji,jj,jl) = pfv_ups(ji,jj,jl) + zlimiter
ELSEIF( np_limiter == 2 ) THEN
IF( Rj /= 0. ) THEN
IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj
ELSE ; Cr = Rjp / Rj
ENDIF
ELSE
Cr = 0.
ENDIF
! -- superbee --
zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) )
! -- van albada 2 --
!!zpsi = 2.*Cr / (Cr*Cr+1.)
! -- sweby (with beta=1) --
!!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) )
! -- van Leer --
!!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) )
! -- ospre --
!!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. )
! -- koren --
!!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) )
! -- charm --
!IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) )
!ELSE ; zpsi = 0.
!ENDIF
! -- van albada 1 --
!!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1)
! -- smart --
!!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) )
! -- umist --
!!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) )
! high order flux corrected by the limiter
pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - ABS( pv(ji,jj) ) * ( (1.-zpsi) + vCFL*zpsi ) * Rj * 0.5
ENDIF
END_2D
END DO
IF( nn_hls == 1 ) CALL lbc_lnk( 'icedyn_adv_umx', pfv_ho, 'V', -1.0_wp) ! lateral boundary cond.
!
END SUBROUTINE limiter_y
SUBROUTINE Hbig( pdt, phi_max, phs_max, phip_max, psi_max, pes_max, pei_max, &
& pv_i, pv_s, pa_i, pa_ip, pv_ip, psv_i, pe_s, pe_i )
!!-------------------------------------------------------------------
!! *** ROUTINE Hbig ***
!!
!! ** Purpose : Thickness correction in case advection scheme creates
!! abnormally tick ice or snow
!!
!! ** Method : 1- check whether ice thickness is larger than the surrounding 9-points
!! (before advection) and reduce it by adapting ice concentration
!! 2- check whether snow thickness is larger than the surrounding 9-points
!! (before advection) and reduce it by sending the excess in the ocean
!!
!! ** input : Max thickness of the surrounding 9-points
!!-------------------------------------------------------------------
REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: phi_max, phs_max, phip_max, psi_max ! max ice thick from surrounding 9-pts
REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pes_max
REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pei_max
REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, pa_i, pa_ip, pv_ip, psv_i
REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s
REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i
!
INTEGER :: ji, jj, jk, jl ! dummy loop indices
REAL(wp) :: z1_dt, zhip, zhi, zhs, zsi, zes, zei, zfra
!!-------------------------------------------------------------------
!
z1_dt = 1._wp / pdt
!
DO jl = 1, jpl
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
IF ( pv_i(ji,jj,jl) > 0._wp ) THEN
!
! ! -- check h_ip -- !
! if h_ip is larger than the surrounding 9 pts => reduce h_ip and increase a_ip
IF( ( ln_pnd_LEV .OR. ln_pnd_TOPO ) .AND. pv_ip(ji,jj,jl) > 0._wp ) THEN
zhip = pv_ip(ji,jj,jl) / MAX( epsi20, pa_ip(ji,jj,jl) )
IF( zhip > phip_max(ji,jj,jl) .AND. pa_ip(ji,jj,jl) < 0.15 ) THEN
pa_ip(ji,jj,jl) = pv_ip(ji,jj,jl) / phip_max(ji,jj,jl)
ENDIF
ENDIF
!
! ! -- check h_i -- !
! if h_i is larger than the surrounding 9 pts => reduce h_i and increase a_i
zhi = pv_i(ji,jj,jl) / pa_i(ji,jj,jl)
IF( zhi > phi_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN
pa_i(ji,jj,jl) = pv_i(ji,jj,jl) / MIN( phi_max(ji,jj,jl), hi_max(jpl) ) !-- bound h_i to hi_max (99 m)
ENDIF
!
! ! -- check h_s -- !
! if h_s is larger than the surrounding 9 pts => put the snow excess in the ocean
zhs = pv_s(ji,jj,jl) / pa_i(ji,jj,jl)
IF( pv_s(ji,jj,jl) > 0._wp .AND. zhs > phs_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN
zfra = phs_max(ji,jj,jl) / MAX( zhs, epsi20 )
!
wfx_res(ji,jj) = wfx_res(ji,jj) + ( pv_s(ji,jj,jl) - pa_i(ji,jj,jl) * phs_max(ji,jj,jl) ) * rhos * z1_dt
hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0
!
pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra
pv_s(ji,jj,jl) = pa_i(ji,jj,jl) * phs_max(ji,jj,jl)
ENDIF
!
! ! -- check s_i -- !
! if s_i is larger than the surrounding 9 pts => put salt excess in the ocean
zsi = psv_i(ji,jj,jl) / pv_i(ji,jj,jl)
IF( zsi > psi_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN
zfra = psi_max(ji,jj,jl) / zsi
sfx_res(ji,jj) = sfx_res(ji,jj) + psv_i(ji,jj,jl) * ( 1._wp - zfra ) * rhoi * z1_dt
psv_i(ji,jj,jl) = psv_i(ji,jj,jl) * zfra
ENDIF
!
ENDIF
END_2D
END DO
!
! ! -- check e_i/v_i -- !
DO jl = 1, jpl
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, nlay_i )
IF ( pv_i(ji,jj,jl) > 0._wp ) THEN
! if e_i/v_i is larger than the surrounding 9 pts => put the heat excess in the ocean
zei = pe_i(ji,jj,jk,jl) / pv_i(ji,jj,jl)
IF( zei > pei_max(ji,jj,jk,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN
zfra = pei_max(ji,jj,jk,jl) / zei
hfx_res(ji,jj) = hfx_res(ji,jj) - pe_i(ji,jj,jk,jl) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0
pe_i(ji,jj,jk,jl) = pe_i(ji,jj,jk,jl) * zfra
ENDIF
ENDIF
END_3D
END DO
! ! -- check e_s/v_s -- !
DO jl = 1, jpl
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, nlay_s )
IF ( pv_s(ji,jj,jl) > 0._wp ) THEN
! if e_s/v_s is larger than the surrounding 9 pts => put the heat excess in the ocean
zes = pe_s(ji,jj,jk,jl) / pv_s(ji,jj,jl)
IF( zes > pes_max(ji,jj,jk,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN
zfra = pes_max(ji,jj,jk,jl) / zes
hfx_res(ji,jj) = hfx_res(ji,jj) - pe_s(ji,jj,jk,jl) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0
pe_s(ji,jj,jk,jl) = pe_s(ji,jj,jk,jl) * zfra
ENDIF
ENDIF
END_3D
END DO
!
END SUBROUTINE Hbig
SUBROUTINE Hsnow( pdt, pv_i, pv_s, pa_i, pa_ip, pe_s )
!!-------------------------------------------------------------------
!! *** ROUTINE Hsnow ***
!!
!! ** Purpose : 1- Check snow load after advection
!! 2- Correct pond concentration to avoid a_ip > a_i
!!
!! ** Method : If snow load makes snow-ice interface to deplet below the ocean surface
!! then put the snow excess in the ocean
!!
!! ** Notes : This correction is crucial because of the call to routine icecor afterwards
!! which imposes a mini of ice thick. (rn_himin). This imposed mini can artificially
!! make the snow very thick (if concentration decreases drastically)
!! This behavior has been seen in Ultimate-Macho and supposedly it can also be true for Prather
!!-------------------------------------------------------------------
REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, pa_i, pa_ip
REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s
!
INTEGER :: ji, jj, jl ! dummy loop indices
REAL(wp) :: z1_dt, zvs_excess, zfra
!!-------------------------------------------------------------------
!
z1_dt = 1._wp / pdt
!
! -- check snow load -- !
DO jl = 1, jpl
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
IF ( pv_i(ji,jj,jl) > 0._wp ) THEN
!
zvs_excess = MAX( 0._wp, pv_s(ji,jj,jl) - pv_i(ji,jj,jl) * (rho0-rhoi) * r1_rhos )
!
IF( zvs_excess > 0._wp ) THEN ! snow-ice interface deplets below the ocean surface
! put snow excess in the ocean
zfra = ( pv_s(ji,jj,jl) - zvs_excess ) / MAX( pv_s(ji,jj,jl), epsi20 )
wfx_res(ji,jj) = wfx_res(ji,jj) + zvs_excess * rhos * z1_dt
hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0
! correct snow volume and heat content
pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra
pv_s(ji,jj,jl) = pv_s(ji,jj,jl) - zvs_excess
ENDIF
!
ENDIF
END_2D
END DO
!
!-- correct pond concentration to avoid a_ip > a_i -- !
WHERE( pa_ip(:,:,:) > pa_i(:,:,:) ) pa_ip(:,:,:) = pa_i(:,:,:)
!
END SUBROUTINE Hsnow
SUBROUTINE icemax3D( pice , pmax )
!!---------------------------------------------------------------------
!! *** ROUTINE icemax3D ***
!! ** Purpose : compute the max of the 9 points around
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pice ! input
REAL(wp), DIMENSION(:,:,:), INTENT(out) :: pmax ! output
!
REAL(wp), DIMENSION(Nis0:Nie0) :: zmax1, zmax2
REAL(wp) :: zmax3
INTEGER :: ji, jj, jl ! dummy loop indices
!!----------------------------------------------------------------------
! basic version: get the max of epsi20 + 9 neighbours
!!$ DO jl = 1, jpl
!!$ DO_2D( 0, 0, 0, 0 )
!!$ pmax(ji,jj,jl) = MAX( epsi20, pice(ji-1,jj-1,jl), pice(ji,jj-1,jl), pice(ji+1,jj-1,jl), &
!!$ & pice(ji-1,jj ,jl), pice(ji,jj ,jl), pice(ji+1,jj ,jl), &
!!$ & pice(ji-1,jj+1,jl), pice(ji,jj+1,jl), pice(ji+1,jj+1,jl) )
!!$ END_2D
!!$ END DO
! optimized version : does a little bit more than 2 max of epsi20 + 3 neighbours
DO jl = 1, jpl
DO ji = Nis0, Nie0
zmax1(ji) = MAX( epsi20, pice(ji,Njs0-1,jl), pice(ji-1,Njs0-1,jl), pice(ji+1,Njs0-1,jl) )
zmax2(ji) = MAX( epsi20, pice(ji,Njs0 ,jl), pice(ji-1,Njs0 ,jl), pice(ji+1,Njs0 ,jl) )
END DO
DO_2D( 0, 0, 0, 0 )
zmax3 = MAX( epsi20, pice(ji,jj+1,jl), pice(ji-1,jj+1,jl), pice(ji+1,jj+1,jl) )
pmax(ji,jj,jl) = MAX( epsi20, zmax1(ji), zmax2(ji), zmax3 )
zmax1(ji) = zmax2(ji)
zmax2(ji) = zmax3
END_2D
END DO
END SUBROUTINE icemax3D
SUBROUTINE icemax4D( pice , pmax )
!!---------------------------------------------------------------------
!! *** ROUTINE icemax4D ***
!! ** Purpose : compute the max of the 9 points around
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pice ! input
REAL(wp), DIMENSION(:,:,:,:), INTENT(out) :: pmax ! output
!
REAL(wp), DIMENSION(Nis0:Nie0) :: zmax1, zmax2
REAL(wp) :: zmax3
INTEGER :: jlay, ji, jj, jk, jl ! dummy loop indices
!!----------------------------------------------------------------------
jlay = SIZE( pice , 3 ) ! size of input arrays
! basic version: get the max of epsi20 + 9 neighbours
!!$ DO jl = 1, jpl
!!$ DO jk = 1, jlay
!!$ DO_2D( 0, 0, 0, 0 )
!!$ pmax(ji,jj,jk,jl) = MAX( epsi20, pice(ji-1,jj-1,jk,jl), pice(ji,jj-1,jk,jl), pice(ji+1,jj-1,jk,jl), &
!!$ & pice(ji-1,jj ,jk,jl), pice(ji,jj ,jk,jl), pice(ji+1,jj ,jk,jl), &
!!$ & pice(ji-1,jj+1,jk,jl), pice(ji,jj+1,jk,jl), pice(ji+1,jj+1,jk,jl) )
!!$ END_2D
!!$ END DO
!!$ END DO
! optimized version : does a little bit more than 2 max of epsi20 + 3 neighbours
DO jl = 1, jpl
DO jk = 1, jlay
DO ji = Nis0, Nie0
zmax1(ji) = MAX( epsi20, pice(ji,Njs0-1,jk,jl), pice(ji-1,Njs0-1,jk,jl), pice(ji+1,Njs0-1,jk,jl) )
zmax2(ji) = MAX( epsi20, pice(ji,Njs0 ,jk,jl), pice(ji-1,Njs0 ,jk,jl), pice(ji+1,Njs0 ,jk,jl) )
END DO
DO_2D( 0, 0, 0, 0 )
zmax3 = MAX( epsi20, pice(ji,jj+1,jk,jl), pice(ji-1,jj+1,jk,jl), pice(ji+1,jj+1,jk,jl) )
pmax(ji,jj,jk,jl) = MAX( epsi20, zmax1(ji), zmax2(ji), zmax3 )
zmax1(ji) = zmax2(ji)
zmax2(ji) = zmax3
END_2D
END DO
END DO
END SUBROUTINE icemax4D
#else
!!----------------------------------------------------------------------
!! Default option Dummy module NO SI3 sea-ice model
!!----------------------------------------------------------------------
#endif
!!======================================================================
END MODULE icedyn_adv_umx