MODULE icedyn_rdgrft
!!======================================================================
!! *** MODULE icedyn_rdgrft ***
!! sea-ice : Mechanical impact on ice thickness distribution
!!======================================================================
!! History : ! 2006-02 (M. Vancoppenolle) Original code
!! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube]
!!----------------------------------------------------------------------
#if defined key_si3
!!----------------------------------------------------------------------
!! 'key_si3' SI3 sea-ice model
!!----------------------------------------------------------------------
!! ice_dyn_rdgrft : ridging/rafting of sea ice
!! ice_dyn_rdgrft_init : initialization of ridging/rafting of sea ice
!! ice_strength : ice strength calculation
!!----------------------------------------------------------------------
USE dom_oce ! ocean domain
USE phycst ! physical constants (ocean directory)
USE sbc_oce , ONLY : sss_m, sst_m ! surface boundary condition: ocean fields
USE ice1D ! sea-ice: thermodynamics
USE ice ! sea-ice: variables
USE icetab ! sea-ice: 1D <==> 2D transformation
USE icevar ! sea-ice: operations
USE icectl ! sea-ice: control prints
!
USE in_out_manager ! I/O manager
USE iom ! I/O manager library
USE lib_mpp ! MPP library
USE lib_fortran ! fortran utilities (glob_sum + no signed zero)
USE lbclnk ! lateral boundary conditions (or mpp links)
USE timing ! Timing
IMPLICIT NONE
PRIVATE
PUBLIC ice_dyn_rdgrft ! called by icestp
PUBLIC ice_dyn_rdgrft_init ! called by icedyn
PUBLIC ice_strength ! called by icedyn_rhg_evp
INTEGER :: nice_str ! choice of the type of strength
! ! associated indices:
INTEGER, PARAMETER :: np_strh79 = 1 ! Hibler 79
INTEGER, PARAMETER :: np_strr75 = 2 ! Rothrock 75
INTEGER, PARAMETER :: np_strcst = 3 ! Constant value
! Variables shared among ridging subroutines
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:) :: closing_net ! net rate at which area is removed (1/s)
! ! (ridging ice area - area of new ridges) / dt
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:) :: opning ! rate of opening due to divergence/shear
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:) :: closing_gross ! rate at which area removed, not counting area of new ridges
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: apartf ! participation function; fraction of ridging/closing associated w/ category n
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: hrmin ! minimum ridge thickness
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: hrmax ! maximum ridge thickness
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: hrexp ! e-folding ridge thickness
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: hraft ! thickness of rafted ice
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: hi_hrdg ! thickness of ridging ice / mean ridge thickness
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: aridge ! participating ice ridging
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: araft ! participating ice rafting
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ze_i_2d
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ze_s_2d
!
REAL(wp), PARAMETER :: hrdg_hi_min = 1.1_wp ! min ridge thickness multiplier: min(hrdg/hi)
REAL(wp), PARAMETER :: hi_hrft = 0.5_wp ! rafting multiplier: (hi/hraft)
!
! ** namelist (namdyn_rdgrft) **
LOGICAL :: ln_str_R75 ! ice strength parameterization: Rothrock 75
REAL(wp) :: rn_pe_rdg ! coef accounting for frictional dissipation
LOGICAL :: ln_str_CST ! ice strength parameterization: Constant
REAL(wp) :: rn_str ! constant value of ice strength
LOGICAL :: ln_str_smooth ! ice strength spatial smoothing
LOGICAL :: ln_distf_lin ! redistribution of ridged ice: linear (Hibler, 1980)
LOGICAL :: ln_distf_exp ! redistribution of ridged ice: exponential (Lipscomb et al., 2007)
REAL(wp) :: rn_murdg ! gives e-folding scale of ridged ice (m^.5)
REAL(wp) :: rn_csrdg ! fraction of shearing energy contributing to ridging
LOGICAL :: ln_partf_lin ! participation function: linear (Thorndike et al., 1975)
REAL(wp) :: rn_gstar ! fractional area of young ice contributing to ridging
LOGICAL :: ln_partf_exp ! participation function: exponential (Lipscomb et al., 2007)
REAL(wp) :: rn_astar ! equivalent of G* for an exponential participation function
LOGICAL :: ln_ridging ! ridging of ice or not
REAL(wp) :: rn_hstar ! thickness that determines the maximal thickness of ridged ice
REAL(wp) :: rn_porordg ! initial porosity of ridges (0.3 regular value)
REAL(wp) :: rn_fsnwrdg ! fractional snow loss to the ocean during ridging
REAL(wp) :: rn_fpndrdg ! fractional pond loss to the ocean during ridging
LOGICAL :: ln_rafting ! rafting of ice or not
REAL(wp) :: rn_hraft ! threshold thickness (m) for rafting / ridging
REAL(wp) :: rn_craft ! coefficient for smoothness of the hyperbolic tangent in rafting
REAL(wp) :: rn_fsnwrft ! fractional snow loss to the ocean during rafting
REAL(wp) :: rn_fpndrft ! fractional pond loss to the ocean during rafting
!
!! * Substitutions
# include "do_loop_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/ICE 4.0 , NEMO Consortium (2018)
!! $Id: icedyn_rdgrft.F90 15549 2021-11-28 20:00:36Z clem $
!! Software governed by the CeCILL licence (./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
INTEGER FUNCTION ice_dyn_rdgrft_alloc()
!!-------------------------------------------------------------------
!! *** ROUTINE ice_dyn_rdgrft_alloc ***
!!-------------------------------------------------------------------
ALLOCATE( closing_net(jpij) , opning(jpij) , closing_gross(jpij), &
& apartf(jpij,0:jpl), hrmin (jpij,jpl), hraft(jpij,jpl) , aridge(jpij,jpl), &
& hrmax (jpij,jpl) , hrexp (jpij,jpl), hi_hrdg(jpij,jpl) , araft(jpij,jpl) , &
& ze_i_2d(jpij,nlay_i,jpl), ze_s_2d(jpij,nlay_s,jpl), STAT=ice_dyn_rdgrft_alloc )
CALL mpp_sum ( 'icedyn_rdgrft', ice_dyn_rdgrft_alloc )
IF( ice_dyn_rdgrft_alloc /= 0 ) CALL ctl_stop( 'STOP', 'ice_dyn_rdgrft_alloc: failed to allocate arrays' )
!
END FUNCTION ice_dyn_rdgrft_alloc
SUBROUTINE ice_dyn_rdgrft( kt )
!!-------------------------------------------------------------------
!! *** ROUTINE ice_dyn_rdgrft ***
!!
!! ** Purpose : computes the mechanical redistribution of ice thickness
!!
!! ** Method : Steps :
!! 0) Identify grid cells with ice
!! 1) Calculate closing rate, divergence and opening
!! 2) Identify grid cells with ridging
!! 3) Start ridging iterations
!! - prep = ridged and rafted ice + closing_gross
!! - shift = move ice from one category to another
!!
!! ** Details
!! step1: The net rate of closing is due to convergence and shear, based on Flato and Hibler (1995).
!! The energy dissipation rate is equal to the net closing rate times the ice strength.
!!
!! step3: The gross closing rate is equal to the first two terms (open
!! water closing and thin ice ridging) without the third term
!! (thick, newly ridged ice).
!!
!! References : Flato, G. M., and W. D. Hibler III, 1995, JGR, 100, 18,611-18,626.
!! Hibler, W. D. III, 1980, MWR, 108, 1943-1973, 1980.
!! Rothrock, D. A., 1975: JGR, 80, 4514-4519.
!! Thorndike et al., 1975, JGR, 80, 4501-4513.
!! Bitz et al., JGR, 2001
!! Amundrud and Melling, JGR 2005
!! Babko et al., JGR 2002
!!
!! This routine is based on CICE code and authors William H. Lipscomb,
!! and Elizabeth C. Hunke, LANL are gratefully acknowledged
!!-------------------------------------------------------------------
INTEGER, INTENT(in) :: kt ! number of iteration
!!
INTEGER :: ji, jj, jk, jl ! dummy loop index
INTEGER :: iter, iterate_ridging ! local integer
INTEGER :: ipti ! local integer
REAL(wp) :: zfac ! local scalar
INTEGER , DIMENSION(jpij) :: iptidx ! compute ridge/raft or not
REAL(wp), DIMENSION(jpij) :: zdivu, zdelt ! 1D divu_i & delta_i
REAL(wp), DIMENSION(jpij) :: zconv ! 1D rdg_conv (if EAP rheology)
!
INTEGER, PARAMETER :: jp_itermax = 20
!!-------------------------------------------------------------------
! controls
IF( ln_timing ) CALL timing_start('icedyn_rdgrft') ! timing
IF( ln_icediachk ) CALL ice_cons_hsm(0, 'icedyn_rdgrft', rdiag_v, rdiag_s, rdiag_t, rdiag_fv, rdiag_fs, rdiag_ft) ! conservation
IF( ln_icediachk ) CALL ice_cons2D (0, 'icedyn_rdgrft', diag_v, diag_s, diag_t, diag_fv, diag_fs, diag_ft) ! conservation
IF( kt == nit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*)'ice_dyn_rdgrft: ice ridging and rafting'
IF(lwp) WRITE(numout,*)'~~~~~~~~~~~~~~'
ENDIF
!--------------------------------
! 0) Identify grid cells with ice
!--------------------------------
at_i(:,:) = SUM( a_i, dim=3 )
!
npti = 0 ; nptidx(:) = 0
ipti = 0 ; iptidx(:) = 0
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
IF ( at_i(ji,jj) > epsi10 ) THEN
npti = npti + 1
nptidx( npti ) = (jj - 1) * jpi + ji
ENDIF
END_2D
!--------------------------------------------------------
! 1) Dynamical inputs (closing rate, divergence, opening)
!--------------------------------------------------------
IF( npti > 0 ) THEN
! just needed here
CALL tab_2d_1d( npti, nptidx(1:npti), zdelt (1:npti) , delta_i )
CALL tab_2d_1d( npti, nptidx(1:npti), zconv (1:npti) , rdg_conv )
! needed here and in the iteration loop
CALL tab_2d_1d( npti, nptidx(1:npti), zdivu (1:npti) , divu_i) ! zdivu is used as a work array here (no change in divu_i)
CALL tab_3d_2d( npti, nptidx(1:npti), a_i_2d (1:npti,1:jpl), a_i )
CALL tab_3d_2d( npti, nptidx(1:npti), v_i_2d (1:npti,1:jpl), v_i )
CALL tab_2d_1d( npti, nptidx(1:npti), ato_i_1d(1:npti) , ato_i )
DO ji = 1, npti
! closing_net = rate at which open water area is removed + ice area removed by ridging
! - ice area added in new ridges
IF( ln_rhg_EVP .OR. ln_rhg_VP ) &
& closing_net(ji) = rn_csrdg * 0.5_wp * ( zdelt(ji) - ABS( zdivu(ji) ) ) - MIN( zdivu(ji), 0._wp )
IF( ln_rhg_EAP ) closing_net(ji) = zconv(ji)
!
IF( zdivu(ji) < 0._wp ) closing_net(ji) = MAX( closing_net(ji), -zdivu(ji) ) ! make sure the closing rate is large enough
! ! to give asum = 1.0 after ridging
! Opening rate (non-negative) that will give asum = 1.0 after ridging.
opning(ji) = closing_net(ji) + zdivu(ji)
END DO
!
!------------------------------------
! 2) Identify grid cells with ridging
!------------------------------------
CALL rdgrft_prep( a_i_2d, v_i_2d, ato_i_1d, closing_net )
DO ji = 1, npti
IF( SUM( apartf(ji,1:jpl) ) > 0._wp .AND. closing_gross(ji) > 0._wp ) THEN
ipti = ipti + 1
iptidx (ipti) = nptidx (ji)
! adjust to new indices
a_i_2d (ipti,:) = a_i_2d (ji,:)
v_i_2d (ipti,:) = v_i_2d (ji,:)
ato_i_1d (ipti) = ato_i_1d (ji)
closing_net(ipti) = closing_net(ji)
zdivu (ipti) = zdivu (ji)
opning (ipti) = opning (ji)
ENDIF
END DO
ENDIF
! grid cells with ridging
nptidx(:) = iptidx(:)
npti = ipti
!-----------------
! 3) Start ridging
!-----------------
IF( npti > 0 ) THEN
CALL ice_dyn_1d2d( 1 ) ! --- Move to 1D arrays --- !
iter = 1
iterate_ridging = 1
! !----------------------!
DO WHILE( iterate_ridging > 0 .AND. iter < jp_itermax ) ! ridging iterations !
! !----------------------!
! Calculate participation function (apartf)
! and transfer function
! and closing_gross (+correction on opening)
CALL rdgrft_prep( a_i_2d, v_i_2d, ato_i_1d, closing_net )
! Redistribute area, volume, and energy between categories
CALL rdgrft_shift
! Do we keep on iterating?
!-------------------------
! Check whether a_i + ato_i = 0
! If not, because the closing and opening rates were reduced above, ridge again with new rates
iterate_ridging = 0
DO ji = 1, npti
zfac = 1._wp - ( ato_i_1d(ji) + SUM( a_i_2d(ji,:) ) )
IF( ABS( zfac ) < epsi10 ) THEN
closing_net(ji) = 0._wp
opning (ji) = 0._wp
ato_i_1d (ji) = MAX( 0._wp, 1._wp - SUM( a_i_2d(ji,:) ) )
ELSE
iterate_ridging = 1
zdivu (ji) = zfac * r1_Dt_ice
closing_net(ji) = MAX( 0._wp, -zdivu(ji) )
opning (ji) = MAX( 0._wp, zdivu(ji) )
ENDIF
END DO
!
iter = iter + 1
IF( iter > jp_itermax ) CALL ctl_stop( 'STOP', 'icedyn_rdgrft: non-converging ridging scheme' )
!
END DO
CALL ice_dyn_1d2d( 2 ) ! --- Move to 2D arrays --- !
ENDIF
CALL ice_var_agg( 1 )
! controls
IF( sn_cfctl%l_prtctl ) CALL ice_prt3D('icedyn_rdgrft') ! prints
IF( ln_icectl ) CALL ice_prt (kt, iiceprt, jiceprt,-1, ' - ice dyn rdgrft - ') ! prints
IF( ln_icediachk ) CALL ice_cons_hsm(1, 'icedyn_rdgrft', rdiag_v, rdiag_s, rdiag_t, rdiag_fv, rdiag_fs, rdiag_ft) ! conservation
IF( ln_icediachk ) CALL ice_cons2D (1, 'icedyn_rdgrft', diag_v, diag_s, diag_t, diag_fv, diag_fs, diag_ft) ! conservation
IF( ln_timing ) CALL timing_stop ('icedyn_rdgrft') ! timing
!
END SUBROUTINE ice_dyn_rdgrft
SUBROUTINE rdgrft_prep( pa_i, pv_i, pato_i, pclosing_net )
!!-------------------------------------------------------------------
!! *** ROUTINE rdgrft_prep ***
!!
!! ** Purpose : preparation for ridging calculations
!!
!! ** Method : Compute the thickness distribution of the ice and open water
!! participating in ridging and of the resulting ridges.
!!-------------------------------------------------------------------
REAL(wp), DIMENSION(:,:), INTENT(in) :: pa_i, pv_i
REAL(wp), DIMENSION(:) , INTENT(in) :: pato_i
REAL(wp), DIMENSION(:) , INTENT(in), OPTIONAL :: pclosing_net
!!
INTEGER :: ji, jl ! dummy loop indices
REAL(wp) :: z1_gstar, z1_astar, zhmean, zfac ! local scalar
REAL(wp), DIMENSION(jpij) :: zasum, z1_asum, zaksum ! sum of a_i+ato_i and reverse
REAL(wp), DIMENSION(jpij,jpl) :: zhi ! ice thickness
REAL(wp), DIMENSION(jpij,-1:jpl) :: zGsum ! zGsum(n) = sum of areas in categories 0 to n
!--------------------------------------------------------------------
z1_gstar = 1._wp / rn_gstar
z1_astar = 1._wp / rn_astar
! ! Ice thickness needed for rafting
! In single precision there were floating point invalids due a sqrt of zhi which happens to have negative values
! To solve that an extra check about the value of pv_i was added.
! Although adding this condition is safe, the double definition (one for single other for double) has been kept to preserve the results of the sette test.
#if defined key_single
WHERE( pa_i(1:npti,:) > epsi10 .and. pv_i(1:npti,:) > epsi10 ) ; zhi(1:npti,:) = pv_i(1:npti,:) / pa_i(1:npti,:)
#else
WHERE( pa_i(1:npti,:) > epsi10 ) ; zhi(1:npti,:) = pv_i(1:npti,:) / pa_i(1:npti,:)
#endif
ELSEWHERE ; zhi(1:npti,:) = 0._wp
END WHERE
! 1) Participation function (apartf): a(h) = b(h).g(h)
!-----------------------------------------------------------------
! Compute the participation function = total area lost due to ridging/closing
! This is analogous to
! a(h) = b(h)g(h) as defined in Thorndike et al. (1975).
! assuming b(h) = (2/Gstar) * (1 - G(h)/Gstar).
!
! apartf = integrating b(h)g(h) between the category boundaries
! apartf is always >= 0 and SUM(apartf(0:jpl))=1
!-----------------------------------------------------------------
!
! Compute total area of ice plus open water.
! This is in general not equal to one because of divergence during transport
zasum(1:npti) = pato_i(1:npti) + SUM( pa_i(1:npti,:), dim=2 )
!
WHERE( zasum(1:npti) > epsi10 ) ; z1_asum(1:npti) = 1._wp / zasum(1:npti)
ELSEWHERE ; z1_asum(1:npti) = 0._wp
END WHERE
!
! Compute cumulative thickness distribution function
! Compute the cumulative thickness distribution function zGsum,
! where zGsum(n) is the fractional area in categories 0 to n.
! initial value (in h = 0) = open water area
zGsum(1:npti,-1) = 0._wp
zGsum(1:npti,0 ) = pato_i(1:npti) * z1_asum(1:npti)
DO jl = 1, jpl
zGsum(1:npti,jl) = ( pato_i(1:npti) + SUM( pa_i(1:npti,1:jl), dim=2 ) ) * z1_asum(1:npti) ! sum(1:jl) is correct (and not jpl)
END DO
!
IF( ln_partf_lin ) THEN !--- Linear formulation (Thorndike et al., 1975)
DO jl = 0, jpl
DO ji = 1, npti
IF ( zGsum(ji,jl) < rn_gstar ) THEN
apartf(ji,jl) = z1_gstar * ( zGsum(ji,jl) - zGsum(ji,jl-1) ) * &
& ( 2._wp - ( zGsum(ji,jl-1) + zGsum(ji,jl) ) * z1_gstar )
ELSEIF( zGsum(ji,jl-1) < rn_gstar ) THEN
apartf(ji,jl) = z1_gstar * ( rn_gstar - zGsum(ji,jl-1) ) * &
& ( 2._wp - ( zGsum(ji,jl-1) + rn_gstar ) * z1_gstar )
ELSE
apartf(ji,jl) = 0._wp
ENDIF
END DO
END DO
!
ELSEIF( ln_partf_exp ) THEN !--- Exponential, more stable formulation (Lipscomb et al., 2007)
!
zfac = 1._wp / ( 1._wp - EXP(-z1_astar) )
DO jl = -1, jpl
DO ji = 1, npti
zGsum(ji,jl) = EXP( -zGsum(ji,jl) * z1_astar ) * zfac
END DO
END DO
DO jl = 0, jpl
DO ji = 1, npti
apartf(ji,jl) = zGsum(ji,jl-1) - zGsum(ji,jl)
END DO
END DO
!
ENDIF
! !--- Ridging and rafting participation concentrations
IF( ln_rafting .AND. ln_ridging ) THEN !- ridging & rafting
DO jl = 1, jpl
DO ji = 1, npti
aridge(ji,jl) = ( 1._wp + TANH ( rn_craft * ( zhi(ji,jl) - rn_hraft ) ) ) * 0.5_wp * apartf(ji,jl)
araft (ji,jl) = apartf(ji,jl) - aridge(ji,jl)
END DO
END DO
ELSEIF( ln_ridging .AND. .NOT. ln_rafting ) THEN !- ridging alone
DO jl = 1, jpl
DO ji = 1, npti
aridge(ji,jl) = apartf(ji,jl)
araft (ji,jl) = 0._wp
END DO
END DO
ELSEIF( ln_rafting .AND. .NOT. ln_ridging ) THEN !- rafting alone
DO jl = 1, jpl
DO ji = 1, npti
aridge(ji,jl) = 0._wp
araft (ji,jl) = apartf(ji,jl)
END DO
END DO
ELSE !- no ridging & no rafting
DO jl = 1, jpl
DO ji = 1, npti
aridge(ji,jl) = 0._wp
araft (ji,jl) = 0._wp
END DO
END DO
ENDIF
! 2) Transfer function
!-----------------------------------------------------------------
! If assuming ridged ice is uniformly distributed between hrmin and
! hrmax (ln_distf_lin):
!
! Compute max and min ridged ice thickness for each ridging category.
!
! This parameterization is a modified version of Hibler (1980).
! The mean ridging thickness, zhmean, is proportional to hi^(0.5)
! and for very thick ridging ice must be >= hrdg_hi_min*hi
!
! The minimum ridging thickness, hrmin, is equal to 2*hi
! (i.e., rafting) and for very thick ridging ice is
! constrained by hrmin <= (zhmean + hi)/2.
!
! The maximum ridging thickness, hrmax, is determined by zhmean and hrmin.
!
! These modifications have the effect of reducing the ice strength
! (relative to the Hibler formulation) when very thick ice is ridging.
!
!-----------------------------------------------------------------
! If assuming ridged ice ITD is a negative exponential
! (ln_distf_exp) and following CICE implementation:
!
! g(h) ~ exp[-(h-hrmin)/hrexp], h >= hrmin
!
! where hrmin is the minimum thickness of ridging ice and
! hrexp is the e-folding thickness.
!
! Here, assume as above that hrmin = min(2*hi, hi+maxraft).
! That is, the minimum ridge thickness results from rafting,
! unless the ice is thicker than maxraft.
!
! Also, assume that hrexp = mu_rdg*sqrt(hi).
! The parameter mu_rdg is tuned to give e-folding scales mostly
! in the range 2-4 m as observed by upward-looking sonar.
!
! Values of mu_rdg in the right column give ice strengths
! roughly equal to values of Hstar in the left column
! (within ~10 kN/m for typical ITDs):
!
! Hstar mu_rdg
!
! 25 3.0
! 50 4.0
! 75 5.0
! 100 6.0
!
! zaksum = net area removed/ total area participating
! where total area participating = area of ice that ridges
! net area removed = total area participating - area of new ridges
!-----------------------------------------------------------------
zfac = 1._wp / hi_hrft
zaksum(1:npti) = apartf(1:npti,0)
!
DO jl = 1, jpl
DO ji = 1, npti
IF ( apartf(ji,jl) > 0._wp ) THEN
zhmean = MAX( SQRT( rn_hstar * zhi(ji,jl) ), zhi(ji,jl) * hrdg_hi_min )
hrmin (ji,jl) = MIN( 2._wp * zhi(ji,jl), 0.5_wp * ( zhmean + zhi(ji,jl) ) )
hraft (ji,jl) = zhi(ji,jl) * zfac
!
IF( ln_distf_lin ) THEN
hrmax (ji,jl) = 2._wp * zhmean - hrmin(ji,jl)
hi_hrdg(ji,jl) = zhi(ji,jl) / MAX( zhmean, epsi20 )
ELSEIF( ln_distf_exp ) THEN
hrexp (ji,jl) = rn_murdg * SQRT( zhi(ji,jl) )
hi_hrdg(ji,jl) = zhi(ji,jl) / ( hrmin(ji,jl) + hrexp(ji,jl) )
!!clem: set a mini for zhi??
ENDIF
!
! Normalization factor : zaksum, ensures mass conservation
zaksum(ji) = zaksum(ji) + aridge(ji,jl) * ( 1._wp - hi_hrdg(ji,jl) ) &
& + araft (ji,jl) * ( 1._wp - hi_hrft )
ELSE
hrmin (ji,jl) = 0._wp
hrmax (ji,jl) = 0._wp
hrexp (ji,jl) = 0._wp
hraft (ji,jl) = 0._wp
hi_hrdg(ji,jl) = 1._wp
!!clem zaksum(ji,jl) = 0._wp
ENDIF
END DO
END DO
!
IF( PRESENT( pclosing_net ) ) THEN
!
! 3) closing_gross
!-----------------
! Based on the ITD of ridging and ridged ice, convert the net closing rate to a gross closing rate.
! NOTE: 0 < aksum <= 1
WHERE( zaksum(1:npti) > epsi10 ) ; closing_gross(1:npti) = pclosing_net(1:npti) / zaksum(1:npti)
ELSEWHERE ; closing_gross(1:npti) = 0._wp
END WHERE
! correction to closing rate if excessive ice removal
!----------------------------------------------------
! Reduce the closing rate if more than 100% of any ice category would be removed
! Reduce the opening rate in proportion
DO jl = 1, jpl
DO ji = 1, npti
zfac = apartf(ji,jl) * closing_gross(ji) * rDt_ice
IF( zfac > pa_i(ji,jl) .AND. apartf(ji,jl) /= 0._wp ) THEN
closing_gross(ji) = pa_i(ji,jl) / apartf(ji,jl) * r1_Dt_ice
ENDIF
END DO
END DO
! 4) correction to opening if excessive open water removal
!---------------------------------------------------------
! Reduce the closing rate if more than 100% of the open water would be removed
! Reduce the opening rate in proportion
DO ji = 1, npti
zfac = pato_i(ji) + ( opning(ji) - apartf(ji,0) * closing_gross(ji) ) * rDt_ice
IF( zfac < 0._wp ) THEN ! would lead to negative ato_i
opning(ji) = apartf(ji,0) * closing_gross(ji) - pato_i(ji) * r1_Dt_ice
ELSEIF( zfac > zasum(ji) ) THEN ! would lead to ato_i > asum
opning(ji) = apartf(ji,0) * closing_gross(ji) + ( zasum(ji) - pato_i(ji) ) * r1_Dt_ice
ENDIF
END DO
!
ENDIF
!
END SUBROUTINE rdgrft_prep
SUBROUTINE rdgrft_shift
!!-------------------------------------------------------------------
!! *** ROUTINE rdgrft_shift ***
!!
!! ** Purpose : shift ridging ice among thickness categories of ice thickness
!!
!! ** Method : Remove area, volume, and energy from each ridging category
!! and add to thicker ice categories.
!!-------------------------------------------------------------------
!
INTEGER :: ji, jj, jl, jl1, jl2, jk ! dummy loop indices
REAL(wp) :: hL, hR, farea ! left and right limits of integration and new area going to jl2
REAL(wp) :: expL, expR ! exponentials involving hL, hR
REAL(wp) :: vsw ! vol of water trapped into ridges
REAL(wp) :: afrdg, afrft ! fraction of category area ridged/rafted
REAL(wp) :: airdg1, oirdg1, aprdg1, virdg1, sirdg1
REAL(wp) :: airft1, oirft1, aprft1
REAL(wp), DIMENSION(jpij) :: airdg2, oirdg2, aprdg2, virdg2, sirdg2, vsrdg, vprdg, vlrdg ! area etc of new ridges
REAL(wp), DIMENSION(jpij) :: airft2, oirft2, aprft2, virft , sirft , vsrft, vprft, vlrft ! area etc of rafted ice
!
REAL(wp), DIMENSION(jpij) :: ersw ! enth of water trapped into ridges
REAL(wp), DIMENSION(jpij) :: zswitch, fvol ! new ridge volume going to jl2
REAL(wp), DIMENSION(jpij) :: z1_ai ! 1 / a
REAL(wp), DIMENSION(jpij) :: zvti ! sum(v_i)
!
REAL(wp), DIMENSION(jpij,nlay_s) :: esrft ! snow energy of rafting ice
REAL(wp), DIMENSION(jpij,nlay_i) :: eirft ! ice energy of rafting ice
REAL(wp), DIMENSION(jpij,nlay_s) :: esrdg ! enth*volume of new ridges
REAL(wp), DIMENSION(jpij,nlay_i) :: eirdg ! enth*volume of new ridges
!
INTEGER , DIMENSION(jpij) :: itest_rdg, itest_rft ! test for conservation
LOGICAL , DIMENSION(jpij) :: ll_shift ! logical for doing calculation or not
!!-------------------------------------------------------------------
!
zvti(1:npti) = SUM( v_i_2d(1:npti,:), dim=2 ) ! total ice volume
!
! 1) Change in open water area due to closing and opening
!--------------------------------------------------------
DO ji = 1, npti
ato_i_1d(ji) = MAX( 0._wp, ato_i_1d(ji) + ( opning(ji) - apartf(ji,0) * closing_gross(ji) ) * rDt_ice )
END DO
! 2) compute categories in which ice is removed (jl1)
!----------------------------------------------------
DO jl1 = 1, jpl
IF( nn_icesal /= 2 ) THEN
CALL tab_2d_1d( npti, nptidx(1:npti), s_i_1d(1:npti), s_i(:,:,jl1) )
ENDIF
DO ji = 1, npti
! set logical to true when ridging
IF( apartf(ji,jl1) > 0._wp .AND. closing_gross(ji) > 0._wp ) THEN ; ll_shift(ji) = .TRUE.
ELSE ; ll_shift(ji) = .FALSE.
ENDIF
IF( ll_shift(ji) ) THEN ! only if ice is ridging
IF( a_i_2d(ji,jl1) > epsi10 ) THEN ; z1_ai(ji) = 1._wp / a_i_2d(ji,jl1)
ELSE ; z1_ai(ji) = 0._wp
ENDIF
! area of ridging / rafting ice (airdg1) and of new ridge (airdg2)
airdg1 = aridge(ji,jl1) * closing_gross(ji) * rDt_ice
airft1 = araft (ji,jl1) * closing_gross(ji) * rDt_ice
airdg2(ji) = airdg1 * hi_hrdg(ji,jl1)
airft2(ji) = airft1 * hi_hrft
! ridging /rafting fractions
afrdg = airdg1 * z1_ai(ji)
afrft = airft1 * z1_ai(ji)
! volume and enthalpy (J/m2, >0) of seawater trapped into ridges
IF ( zvti(ji) <= 10. ) THEN ; vsw = v_i_2d(ji,jl1) * afrdg * rn_porordg ! v <= 10m then porosity = rn_porordg
ELSEIF( zvti(ji) >= 20. ) THEN ; vsw = 0._wp ! v >= 20m then porosity = 0
ELSE ; vsw = v_i_2d(ji,jl1) * afrdg * rn_porordg * MAX( 0._wp, 2._wp - 0.1_wp * zvti(ji) ) ! v > 10m and v < 20m then porosity = linear transition to 0
ENDIF
ersw(ji) = -rhoi * vsw * rcp * sst_1d(ji) ! clem: if sst>0, then ersw <0 (is that possible?)
! volume etc of ridging / rafting ice and new ridges (vi, vs, sm, oi, es, ei)
virdg1 = v_i_2d (ji,jl1) * afrdg
virdg2(ji) = v_i_2d (ji,jl1) * afrdg + vsw
vsrdg(ji) = v_s_2d (ji,jl1) * afrdg
sirdg1 = sv_i_2d(ji,jl1) * afrdg
sirdg2(ji) = sv_i_2d(ji,jl1) * afrdg + vsw * sss_1d(ji)
oirdg1 = oa_i_2d(ji,jl1) * afrdg
oirdg2(ji) = oa_i_2d(ji,jl1) * afrdg * hi_hrdg(ji,jl1)
virft(ji) = v_i_2d (ji,jl1) * afrft
vsrft(ji) = v_s_2d (ji,jl1) * afrft
sirft(ji) = sv_i_2d(ji,jl1) * afrft
oirft1 = oa_i_2d(ji,jl1) * afrft
oirft2(ji) = oa_i_2d(ji,jl1) * afrft * hi_hrft
IF ( ln_pnd_LEV .OR. ln_pnd_TOPO ) THEN
aprdg1 = a_ip_2d(ji,jl1) * afrdg
aprdg2(ji) = a_ip_2d(ji,jl1) * afrdg * hi_hrdg(ji,jl1)
vprdg (ji) = v_ip_2d(ji,jl1) * afrdg
aprft1 = a_ip_2d(ji,jl1) * afrft
aprft2(ji) = a_ip_2d(ji,jl1) * afrft * hi_hrft
vprft (ji) = v_ip_2d(ji,jl1) * afrft
IF ( ln_pnd_lids ) THEN
vlrdg (ji) = v_il_2d(ji,jl1) * afrdg
vlrft (ji) = v_il_2d(ji,jl1) * afrft
ENDIF
ENDIF
! Ice-ocean exchanges associated with ice porosity
wfx_dyn_1d(ji) = wfx_dyn_1d(ji) - vsw * rhoi * r1_Dt_ice ! increase in ice volume due to seawater frozen in voids
sfx_dyn_1d(ji) = sfx_dyn_1d(ji) - vsw * sss_1d(ji) * rhoi * r1_Dt_ice
hfx_dyn_1d(ji) = hfx_dyn_1d(ji) + ersw(ji) * r1_Dt_ice ! > 0 [W.m-2]
! Put the snow lost by ridging into the ocean
! Note that esrdg > 0; the ocean must cool to melt snow. If the ocean temp = Tf already, new ice must grow.
wfx_snw_dyn_1d(ji) = wfx_snw_dyn_1d(ji) + ( rhos * vsrdg(ji) * ( 1._wp - rn_fsnwrdg ) & ! fresh water source for ocean
& + rhos * vsrft(ji) * ( 1._wp - rn_fsnwrft ) ) * r1_Dt_ice
! virtual salt flux to keep salinity constant
IF( nn_icesal /= 2 ) THEN
sirdg2(ji) = sirdg2(ji) - vsw * ( sss_1d(ji) - s_i_1d(ji) ) ! ridge salinity = s_i
sfx_bri_1d(ji) = sfx_bri_1d(ji) + sss_1d(ji) * vsw * rhoi * r1_Dt_ice & ! put back sss_m into the ocean
& - s_i_1d(ji) * vsw * rhoi * r1_Dt_ice ! and get s_i from the ocean
ENDIF
! Remove area, volume of new ridge to each category jl1
!------------------------------------------------------
a_i_2d (ji,jl1) = a_i_2d (ji,jl1) - airdg1 - airft1
v_i_2d (ji,jl1) = v_i_2d (ji,jl1) - virdg1 - virft(ji)
v_s_2d (ji,jl1) = v_s_2d (ji,jl1) - vsrdg(ji) - vsrft(ji)
sv_i_2d(ji,jl1) = sv_i_2d(ji,jl1) - sirdg1 - sirft(ji)
oa_i_2d(ji,jl1) = oa_i_2d(ji,jl1) - oirdg1 - oirft1
IF ( ln_pnd_LEV .OR. ln_pnd_TOPO ) THEN
a_ip_2d(ji,jl1) = a_ip_2d(ji,jl1) - aprdg1 - aprft1
v_ip_2d(ji,jl1) = v_ip_2d(ji,jl1) - vprdg(ji) - vprft(ji)
IF ( ln_pnd_lids ) THEN
v_il_2d(ji,jl1) = v_il_2d(ji,jl1) - vlrdg(ji) - vlrft(ji)
ENDIF
ENDIF
ENDIF
END DO ! ji
! special loop for e_s because of layers jk
DO jk = 1, nlay_s
DO ji = 1, npti
IF( ll_shift(ji) ) THEN
! Compute ridging /rafting fractions
afrdg = aridge(ji,jl1) * closing_gross(ji) * rDt_ice * z1_ai(ji)
afrft = araft (ji,jl1) * closing_gross(ji) * rDt_ice * z1_ai(ji)
! Compute ridging /rafting ice and new ridges for es
esrdg(ji,jk) = ze_s_2d (ji,jk,jl1) * afrdg
esrft(ji,jk) = ze_s_2d (ji,jk,jl1) * afrft
! Put the snow lost by ridging into the ocean
hfx_dyn_1d(ji) = hfx_dyn_1d(ji) + ( - esrdg(ji,jk) * ( 1._wp - rn_fsnwrdg ) & ! heat sink for ocean (<0, W.m-2)
& - esrft(ji,jk) * ( 1._wp - rn_fsnwrft ) ) * r1_Dt_ice
!
! Remove energy of new ridge to each category jl1
!-------------------------------------------------
ze_s_2d(ji,jk,jl1) = ze_s_2d(ji,jk,jl1) * ( 1._wp - afrdg - afrft )
ENDIF
END DO
END DO
! special loop for e_i because of layers jk
DO jk = 1, nlay_i
DO ji = 1, npti
IF( ll_shift(ji) ) THEN
! Compute ridging /rafting fractions
afrdg = aridge(ji,jl1) * closing_gross(ji) * rDt_ice * z1_ai(ji)
afrft = araft (ji,jl1) * closing_gross(ji) * rDt_ice * z1_ai(ji)
! Compute ridging ice and new ridges for ei
eirdg(ji,jk) = ze_i_2d (ji,jk,jl1) * afrdg + ersw(ji) * r1_nlay_i
eirft(ji,jk) = ze_i_2d (ji,jk,jl1) * afrft
!
! Remove energy of new ridge to each category jl1
!-------------------------------------------------
ze_i_2d(ji,jk,jl1) = ze_i_2d(ji,jk,jl1) * ( 1._wp - afrdg - afrft )
ENDIF
END DO
END DO
! 3) compute categories in which ice is added (jl2)
!--------------------------------------------------
itest_rdg(1:npti) = 0
itest_rft(1:npti) = 0
DO jl2 = 1, jpl
!
DO ji = 1, npti
IF( ll_shift(ji) ) THEN
! Compute the fraction of ridged ice area and volume going to thickness category jl2
IF( ln_distf_lin ) THEN ! Hibler (1980) linear formulation
!
IF( hrmin(ji,jl1) <= hi_max(jl2) .AND. hrmax(ji,jl1) > hi_max(jl2-1) ) THEN
hL = MAX( hrmin(ji,jl1), hi_max(jl2-1) )
hR = MIN( hrmax(ji,jl1), hi_max(jl2) )
farea = ( hR - hL ) / ( hrmax(ji,jl1) - hrmin(ji,jl1) )
fvol(ji) = ( hR * hR - hL * hL ) / ( hrmax(ji,jl1) * hrmax(ji,jl1) - hrmin(ji,jl1) * hrmin(ji,jl1) )
!
itest_rdg(ji) = 1 ! test for conservation
ELSE
farea = 0._wp
fvol(ji) = 0._wp
ENDIF
!
ELSEIF( ln_distf_exp ) THEN ! Lipscomb et al. (2007) exponential formulation
!
IF( jl2 < jpl ) THEN
!
IF( hrmin(ji,jl1) <= hi_max(jl2) ) THEN
hL = MAX( hrmin(ji,jl1), hi_max(jl2-1) )
hR = hi_max(jl2)
expL = EXP( -( hL - hrmin(ji,jl1) ) / hrexp(ji,jl1) )
expR = EXP( -( hR - hrmin(ji,jl1) ) / hrexp(ji,jl1) )
farea = expL - expR
fvol(ji) = ( ( hL + hrexp(ji,jl1) ) * expL &
- ( hR + hrexp(ji,jl1) ) * expR ) / ( hrmin(ji,jl1) + hrexp(ji,jl1) )
ELSE
farea = 0._wp
fvol(ji) = 0._wp
END IF
!
ELSE ! jl2 = jpl
!
hL = MAX( hrmin(ji,jl1), hi_max(jl2-1) )
expL = EXP(-( hL - hrmin(ji,jl1) ) / hrexp(ji,jl1) )
farea = expL
fvol(ji) = ( hL + hrexp(ji,jl1) ) * expL / ( hrmin(ji,jl1) + hrexp(ji,jl1) )
!
END IF ! jl2 < jpl
!
itest_rdg(ji) = 1 ! test for conservation => clem: I am not sure about that
!
END IF ! ridge redistribution
! Compute the fraction of rafted ice area and volume going to thickness category jl2
IF( hraft(ji,jl1) <= hi_max(jl2) .AND. hraft(ji,jl1) > hi_max(jl2-1) ) THEN
zswitch(ji) = 1._wp
!
itest_rft(ji) = 1 ! test for conservation
ELSE
zswitch(ji) = 0._wp
ENDIF
!
! Patch to ensure perfect conservation if ice thickness goes mad
! Sometimes thickness is larger than hi_max(jpl) because of advection scheme (for very small areas)
! Then ice volume is removed from one category but the ridging/rafting scheme
! does not know where to move it, leading to a conservation issue.
IF( itest_rdg(ji) == 0 .AND. jl2 == jpl ) THEN ; farea = 1._wp ; fvol(ji) = 1._wp ; ENDIF
IF( itest_rft(ji) == 0 .AND. jl2 == jpl ) zswitch(ji) = 1._wp
!
! Add area, volume of new ridge to category jl2
!----------------------------------------------
a_i_2d (ji,jl2) = a_i_2d (ji,jl2) + ( airdg2(ji) * farea + airft2(ji) * zswitch(ji) )
oa_i_2d(ji,jl2) = oa_i_2d(ji,jl2) + ( oirdg2(ji) * farea + oirft2(ji) * zswitch(ji) )
v_i_2d (ji,jl2) = v_i_2d (ji,jl2) + ( virdg2(ji) * fvol(ji) + virft (ji) * zswitch(ji) )
sv_i_2d(ji,jl2) = sv_i_2d(ji,jl2) + ( sirdg2(ji) * fvol(ji) + sirft (ji) * zswitch(ji) )
v_s_2d (ji,jl2) = v_s_2d (ji,jl2) + ( vsrdg (ji) * rn_fsnwrdg * fvol(ji) + &
& vsrft (ji) * rn_fsnwrft * zswitch(ji) )
IF ( ln_pnd_LEV .OR. ln_pnd_TOPO ) THEN
v_ip_2d (ji,jl2) = v_ip_2d(ji,jl2) + ( vprdg (ji) * rn_fpndrdg * fvol (ji) &
& + vprft (ji) * rn_fpndrft * zswitch(ji) )
a_ip_2d (ji,jl2) = a_ip_2d(ji,jl2) + ( aprdg2(ji) * rn_fpndrdg * farea &
& + aprft2(ji) * rn_fpndrft * zswitch(ji) )
IF ( ln_pnd_lids ) THEN
v_il_2d (ji,jl2) = v_il_2d(ji,jl2) + ( vlrdg(ji) * rn_fpndrdg * fvol (ji) &
& + vlrft(ji) * rn_fpndrft * zswitch(ji) )
ENDIF
ENDIF
ENDIF
END DO
! Add snow energy of new ridge to category jl2
!---------------------------------------------
DO jk = 1, nlay_s
DO ji = 1, npti
IF( ll_shift(ji) ) &
& ze_s_2d(ji,jk,jl2) = ze_s_2d(ji,jk,jl2) + ( esrdg(ji,jk) * rn_fsnwrdg * fvol(ji) + &
& esrft(ji,jk) * rn_fsnwrft * zswitch(ji) )
END DO
END DO
! Add ice energy of new ridge to category jl2
!--------------------------------------------
DO jk = 1, nlay_i
DO ji = 1, npti
IF( ll_shift(ji) ) &
& ze_i_2d(ji,jk,jl2) = ze_i_2d(ji,jk,jl2) + eirdg(ji,jk) * fvol(ji) + eirft(ji,jk) * zswitch(ji)
END DO
END DO
!
END DO ! jl2
!
END DO ! jl1
!
! roundoff errors
!----------------
! In case ridging/rafting lead to very small negative values (sometimes it happens)
CALL ice_var_roundoff( a_i_2d, v_i_2d, v_s_2d, sv_i_2d, oa_i_2d, a_ip_2d, v_ip_2d, v_il_2d, ze_s_2d, ze_i_2d )
!
END SUBROUTINE rdgrft_shift
SUBROUTINE ice_strength
!!----------------------------------------------------------------------
!! *** ROUTINE ice_strength ***
!!
!! ** Purpose : computes ice strength used in dynamics routines of ice thickness
!!
!! ** Method : Compute the strength of the ice pack, defined as the energy (J m-2)
!! dissipated per unit area removed from the ice pack under compression,
!! and assumed proportional to the change in potential energy caused
!! by ridging. Note that ice strength using Hibler's formulation must be
!! smoothed.
!!----------------------------------------------------------------------
INTEGER :: ji, jj, jl ! dummy loop indices
REAL(wp) :: z1_3 ! local scalars
REAL(wp), DIMENSION(jpi,jpj) :: zmsk, zworka ! temporary array used here
!!
LOGICAL :: ln_str_R75
REAL(wp) :: zhi, zcp
REAL(wp) :: h2rdg ! mean value of h^2 for new ridge
REAL(wp), PARAMETER :: zmax_strength = 200.e3_wp ! Richter-Menge and Elder (1998) estimate maximum in Beaufort Sea in wintertime of the order 150 kN/m
REAL(wp), DIMENSION(jpij) :: zstrength, zaksum ! strength in 1D
!!----------------------------------------------------------------------
! prepare the mask
at_i(:,:) = SUM( a_i, dim=3 )
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zmsk(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi10 ) ) ! 1 if ice , 0 if no ice
END_2D
!
SELECT CASE( nice_str ) !--- Set which ice strength is chosen
CASE ( np_strr75 ) !== Rothrock(1975)'s method ==!
! this should be defined once for all at the 1st time step
zcp = 0.5_wp * grav * (rho0-rhoi) * rhoi * r1_rho0 ! proport const for PE
!
strength(:,:) = 0._wp
!
! Identify grid cells with ice
npti = 0 ; nptidx(:) = 0
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
IF ( at_i(ji,jj) > epsi10 ) THEN
npti = npti + 1
nptidx( npti ) = (jj - 1) * jpi + ji
ENDIF
END_2D
IF( npti > 0 ) THEN
CALL tab_3d_2d( npti, nptidx(1:npti), a_i_2d (1:npti,1:jpl), a_i )
CALL tab_3d_2d( npti, nptidx(1:npti), v_i_2d (1:npti,1:jpl), v_i )
CALL tab_2d_1d( npti, nptidx(1:npti), ato_i_1d(1:npti) , ato_i )
CALL tab_2d_1d( npti, nptidx(1:npti), zstrength(1:npti) , strength )
CALL rdgrft_prep( a_i_2d, v_i_2d, ato_i_1d )
!
zaksum(1:npti) = apartf(1:npti,0) !clem: aksum should be defined in the header => local to module
DO jl = 1, jpl
DO ji = 1, npti
IF ( apartf(ji,jl) > 0._wp ) THEN
zaksum(ji) = zaksum(ji) + aridge(ji,jl) * ( 1._wp - hi_hrdg(ji,jl) ) &
& + araft (ji,jl) * ( 1._wp - hi_hrft )
ENDIF
END DO
END DO
!
z1_3 = 1._wp / 3._wp
DO jl = 1, jpl
DO ji = 1, npti
!
IF( apartf(ji,jl) > 0._wp ) THEN
!
IF( ln_distf_lin ) THEN ! Uniform redistribution of ridged ice
h2rdg = z1_3 * ( hrmax(ji,jl) * hrmax(ji,jl) + & ! (a**3-b**3)/(a-b) = a*a+ab+b*b
& hrmin(ji,jl) * hrmin(ji,jl) + &
& hrmax(ji,jl) * hrmin(ji,jl) )
!
ELSEIF( ln_distf_exp ) THEN ! Exponential redistribution of ridged ice
h2rdg = hrmin(ji,jl) * hrmin(ji,jl) &
& + 2._wp * hrmin(ji,jl) * hrexp(ji,jl) &
& + 2._wp * hrexp(ji,jl) * hrexp(ji,jl)
END IF
!
IF( a_i_2d(ji,jl) > epsi10 ) THEN ; zhi = v_i_2d(ji,jl) / a_i_2d(ji,jl)
ELSE ; zhi = 0._wp
ENDIF
!!$ zstrength(ji) = zstrength(ji) - apartf(ji,jl) * zhi * zhi ! PE loss from deforming ice
!!$ zstrength(ji) = zstrength(ji) + 2._wp * araft (ji,jl) * zhi * zhi ! PE gain from rafting ice
!!$ zstrength(ji) = zstrength(ji) + aridge(ji,jl) * hi_hrdg(ji,jl) * z1_3 * & ! PE gain from ridging ice
!!$ & ( hrmax(ji,jl) * hrmax(ji,jl) + & ! (a**3-b**3)/(a-b) = a*a+ab+b*b
!!$ & hrmin(ji,jl) * hrmin(ji,jl) + &
!!$ & hrmax(ji,jl) * hrmin(ji,jl) )
zstrength(ji) = zstrength(ji) - apartf(ji,jl) * zhi * zhi ! PE loss
zstrength(ji) = zstrength(ji) + 2._wp * araft(ji,jl) * zhi * zhi ! PE gain (rafting)
zstrength(ji) = zstrength(ji) + aridge(ji,jl) * h2rdg * hi_hrdg(ji,jl) ! PE gain (ridging)
ENDIF
!
END DO
END DO
!
zstrength(1:npti) = rn_pe_rdg * zcp * zstrength(1:npti) / zaksum(1:npti)
!
! Enforce a maximum for strength
! Richter-Menge and Elder (1998) estimate maximum in Beaufort Sea in wintertime of the order 150 kN/m
WHERE( zstrength(1:npti) > zmax_strength ) ; zstrength(1:npti) = zmax_strength
ENDWHERE
!
CALL tab_1d_2d( npti, nptidx(1:npti), zstrength(1:npti), strength )
!
ENDIF
!
CASE ( np_strh79 ) !== Hibler(1979)'s method ==!
strength(:,:) = rn_pstar * SUM( v_i(:,:,:), dim=3 ) * EXP( -rn_crhg * ( 1._wp - at_i(:,:) ) ) * zmsk(:,:)
!
CASE ( np_strcst ) !== Constant strength ==!
strength(:,:) = rn_str * zmsk(:,:)
!
END SELECT
!
IF( ln_str_smooth ) THEN !--- Spatial smoothing
DO_2D( 0, 0, 0, 0 )
IF ( SUM( a_i(ji,jj,:) ) > 0._wp ) THEN
zworka(ji,jj) = ( 4._wp * strength(ji,jj) &
& + strength(ji-1,jj) * tmask(ji-1,jj,1) + strength(ji+1,jj) * tmask(ji+1,jj,1) &
& + strength(ji,jj-1) * tmask(ji,jj-1,1) + strength(ji,jj+1) * tmask(ji,jj+1,1) &
& ) / ( 4._wp + tmask(ji-1,jj,1) + tmask(ji+1,jj,1) + tmask(ji,jj-1,1) + tmask(ji,jj+1,1) )
ELSE
zworka(ji,jj) = 0._wp
ENDIF
END_2D
DO_2D( 0, 0, 0, 0 )
strength(ji,jj) = zworka(ji,jj) * zmsk(ji,jj)
END_2D
CALL lbc_lnk( 'icedyn_rdgrft', strength, 'T', 1.0_wp )
!
ENDIF
!
END SUBROUTINE ice_strength
SUBROUTINE ice_dyn_1d2d( kn )
!!-----------------------------------------------------------------------
!! *** ROUTINE ice_dyn_1d2d ***
!!
!! ** Purpose : move arrays between 1d <=> 2d forms and
!! between 2d <=> 3d forms
!!-----------------------------------------------------------------------
INTEGER, INTENT(in) :: kn ! 1= from 2D/3D to 1D/2D
! 2= from 1D/2D to 2D/3D
!
INTEGER :: jl, jk ! dummy loop indices
!!-----------------------------------------------------------------------
!
SELECT CASE( kn )
! !---------------------------!
CASE( 1 ) !== from 2D/3D to 1D/2D ==!
! !---------------------------!
! fields used but not modified
CALL tab_2d_1d( npti, nptidx(1:npti), sss_1d(1:npti), sss_m(:,:) )
CALL tab_2d_1d( npti, nptidx(1:npti), sst_1d(1:npti), sst_m(:,:) )
CALL tab_3d_2d( npti, nptidx(1:npti), v_s_2d (1:npti,1:jpl), v_s (:,:,:) )
CALL tab_3d_2d( npti, nptidx(1:npti), sv_i_2d(1:npti,1:jpl), sv_i(:,:,:) )
CALL tab_3d_2d( npti, nptidx(1:npti), oa_i_2d(1:npti,1:jpl), oa_i(:,:,:) )
CALL tab_3d_2d( npti, nptidx(1:npti), a_ip_2d(1:npti,1:jpl), a_ip(:,:,:) )
CALL tab_3d_2d( npti, nptidx(1:npti), v_ip_2d(1:npti,1:jpl), v_ip(:,:,:) )
CALL tab_3d_2d( npti, nptidx(1:npti), v_il_2d(1:npti,1:jpl), v_il(:,:,:) )
DO jl = 1, jpl
DO jk = 1, nlay_s
CALL tab_2d_1d( npti, nptidx(1:npti), ze_s_2d(1:npti,jk,jl), e_s(:,:,jk,jl) )
END DO
DO jk = 1, nlay_i
CALL tab_2d_1d( npti, nptidx(1:npti), ze_i_2d(1:npti,jk,jl), e_i(:,:,jk,jl) )
END DO
END DO
CALL tab_2d_1d( npti, nptidx(1:npti), sfx_dyn_1d (1:npti), sfx_dyn (:,:) )
CALL tab_2d_1d( npti, nptidx(1:npti), sfx_bri_1d (1:npti), sfx_bri (:,:) )
CALL tab_2d_1d( npti, nptidx(1:npti), wfx_dyn_1d (1:npti), wfx_dyn (:,:) )
CALL tab_2d_1d( npti, nptidx(1:npti), hfx_dyn_1d (1:npti), hfx_dyn (:,:) )
CALL tab_2d_1d( npti, nptidx(1:npti), wfx_snw_dyn_1d(1:npti), wfx_snw_dyn(:,:) )
CALL tab_2d_1d( npti, nptidx(1:npti), wfx_pnd_1d (1:npti), wfx_pnd (:,:) )
!
! !---------------------------!
CASE( 2 ) !== from 1D/2D to 2D/3D ==!
! !---------------------------!
CALL tab_1d_2d( npti, nptidx(1:npti), ato_i_1d(1:npti), ato_i(:,:) )
CALL tab_2d_3d( npti, nptidx(1:npti), a_i_2d (1:npti,1:jpl), a_i (:,:,:) )
CALL tab_2d_3d( npti, nptidx(1:npti), v_i_2d (1:npti,1:jpl), v_i (:,:,:) )
CALL tab_2d_3d( npti, nptidx(1:npti), v_s_2d (1:npti,1:jpl), v_s (:,:,:) )
CALL tab_2d_3d( npti, nptidx(1:npti), sv_i_2d(1:npti,1:jpl), sv_i(:,:,:) )
CALL tab_2d_3d( npti, nptidx(1:npti), oa_i_2d(1:npti,1:jpl), oa_i(:,:,:) )
CALL tab_2d_3d( npti, nptidx(1:npti), a_ip_2d(1:npti,1:jpl), a_ip(:,:,:) )
CALL tab_2d_3d( npti, nptidx(1:npti), v_ip_2d(1:npti,1:jpl), v_ip(:,:,:) )
CALL tab_2d_3d( npti, nptidx(1:npti), v_il_2d(1:npti,1:jpl), v_il(:,:,:) )
DO jl = 1, jpl
DO jk = 1, nlay_s
CALL tab_1d_2d( npti, nptidx(1:npti), ze_s_2d(1:npti,jk,jl), e_s(:,:,jk,jl) )
END DO
DO jk = 1, nlay_i
CALL tab_1d_2d( npti, nptidx(1:npti), ze_i_2d(1:npti,jk,jl), e_i(:,:,jk,jl) )
END DO
END DO
CALL tab_1d_2d( npti, nptidx(1:npti), sfx_dyn_1d (1:npti), sfx_dyn (:,:) )
CALL tab_1d_2d( npti, nptidx(1:npti), sfx_bri_1d (1:npti), sfx_bri (:,:) )
CALL tab_1d_2d( npti, nptidx(1:npti), wfx_dyn_1d (1:npti), wfx_dyn (:,:) )
CALL tab_1d_2d( npti, nptidx(1:npti), hfx_dyn_1d (1:npti), hfx_dyn (:,:) )
CALL tab_1d_2d( npti, nptidx(1:npti), wfx_snw_dyn_1d(1:npti), wfx_snw_dyn(:,:) )
CALL tab_1d_2d( npti, nptidx(1:npti), wfx_pnd_1d (1:npti), wfx_pnd (:,:) )
!
END SELECT
!
END SUBROUTINE ice_dyn_1d2d
SUBROUTINE ice_dyn_rdgrft_init
!!-------------------------------------------------------------------
!! *** ROUTINE ice_dyn_rdgrft_init ***
!!
!! ** Purpose : Physical constants and parameters linked
!! to the mechanical ice redistribution
!!
!! ** Method : Read the namdyn_rdgrft namelist
!! and check the parameters values
!! called at the first timestep (nit000)
!!
!! ** input : Namelist namdyn_rdgrft
!!-------------------------------------------------------------------
INTEGER :: ios, ioptio ! Local integer output status for namelist read
!!
NAMELIST/namdyn_rdgrft/ ln_str_H79, rn_pstar, rn_crhg, ln_str_R75, rn_pe_rdg, ln_str_CST, rn_str, ln_str_smooth, &
& ln_distf_lin, ln_distf_exp, rn_murdg, rn_csrdg, &
& ln_partf_lin, rn_gstar, ln_partf_exp, rn_astar, &
& ln_ridging, rn_hstar, rn_porordg, rn_fsnwrdg, rn_fpndrdg, &
& ln_rafting, rn_hraft, rn_craft , rn_fsnwrft, rn_fpndrft
!!-------------------------------------------------------------------
!
READ ( numnam_ice_ref, namdyn_rdgrft, IOSTAT = ios, ERR = 901)
901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_rdgrft in reference namelist' )
READ ( numnam_ice_cfg, namdyn_rdgrft, IOSTAT = ios, ERR = 902 )
902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_rdgrft in configuration namelist' )
IF(lwm) WRITE ( numoni, namdyn_rdgrft )
!
IF (lwp) THEN ! control print
WRITE(numout,*)
WRITE(numout,*) 'ice_dyn_rdgrft_init: ice parameters for ridging/rafting '
WRITE(numout,*) '~~~~~~~~~~~~~~~~~~'
WRITE(numout,*) ' Namelist namdyn_rdgrft:'
WRITE(numout,*) ' ice strength parameterization Hibler (1979) ln_str_H79 = ', ln_str_H79
WRITE(numout,*) ' 1st bulk-rheology parameter rn_pstar = ', rn_pstar
WRITE(numout,*) ' 2nd bulk-rhelogy parameter rn_crhg = ', rn_crhg
WRITE(numout,*) ' ice strength parameterization Rothrock (1975) ln_str_R75 = ', ln_str_R75
WRITE(numout,*) ' coef accounting for frictional dissipation rn_pe_rdg = ', rn_pe_rdg
WRITE(numout,*) ' ice strength parameterization Constant ln_str_CST = ', ln_str_CST
WRITE(numout,*) ' ice strength value rn_str = ', rn_str
WRITE(numout,*) ' spatial smoothing of the strength ln_str_smooth= ', ln_str_smooth
WRITE(numout,*) ' redistribution of ridged ice: linear (Hibler 1980) ln_distf_lin = ', ln_distf_lin
WRITE(numout,*) ' redistribution of ridged ice: exponential(Lipscomb 2007) ln_distf_exp = ', ln_distf_exp
WRITE(numout,*) ' e-folding scale of ridged ice rn_murdg = ', rn_murdg
WRITE(numout,*) ' Fraction of shear energy contributing to ridging rn_csrdg = ', rn_csrdg
WRITE(numout,*) ' linear ridging participation function ln_partf_lin = ', ln_partf_lin
WRITE(numout,*) ' Fraction of ice coverage contributing to ridging rn_gstar = ', rn_gstar
WRITE(numout,*) ' Exponential ridging participation function ln_partf_exp = ', ln_partf_exp
WRITE(numout,*) ' Equivalent to G* for an exponential function rn_astar = ', rn_astar
WRITE(numout,*) ' Ridging of ice sheets or not ln_ridging = ', ln_ridging
WRITE(numout,*) ' max ridged ice thickness rn_hstar = ', rn_hstar
WRITE(numout,*) ' Initial porosity of ridges rn_porordg = ', rn_porordg
WRITE(numout,*) ' Fraction of snow volume conserved during ridging rn_fsnwrdg = ', rn_fsnwrdg
WRITE(numout,*) ' Fraction of pond volume conserved during ridging rn_fpndrdg = ', rn_fpndrdg
WRITE(numout,*) ' Rafting of ice sheets or not ln_rafting = ', ln_rafting
WRITE(numout,*) ' Parmeter thickness (threshold between ridge-raft) rn_hraft = ', rn_hraft
WRITE(numout,*) ' Rafting hyperbolic tangent coefficient rn_craft = ', rn_craft
WRITE(numout,*) ' Fraction of snow volume conserved during rafting rn_fsnwrft = ', rn_fsnwrft
WRITE(numout,*) ' Fraction of pond volume conserved during rafting rn_fpndrft = ', rn_fpndrft
ENDIF
!
ioptio = 0
IF( ln_str_H79 ) THEN ; ioptio = ioptio + 1 ; nice_str = np_strh79 ; ENDIF
IF( ln_str_R75 ) THEN ; ioptio = ioptio + 1 ; nice_str = np_strr75 ; ENDIF
IF( ln_str_CST ) THEN ; ioptio = ioptio + 1 ; nice_str = np_strcst ; ENDIF
IF( ioptio /= 1 ) CALL ctl_stop( 'ice_dyn_rdgrft_init: one and only one ice strength option has to be defined ' )
!
IF ( ( ln_str_H79 .AND. ln_str_R75 ) .OR. ( .NOT.ln_str_H79 .AND. .NOT.ln_str_R75 ) ) THEN
CALL ctl_stop( 'ice_dyn_rdgrft_init: choose one and only one ice strength formulation (ln_str_H79 or ln_str_R75)' )
ENDIF
!
IF ( ( ln_distf_lin .AND. ln_distf_exp ) .OR. ( .NOT.ln_distf_lin .AND. .NOT.ln_distf_exp ) ) THEN
CALL ctl_stop( 'ice_dyn_rdgrft_init: choose one and only one redistribution function (ln_distf_lin or ln_distf_exp)' )
ENDIF
!
IF ( ( ln_partf_lin .AND. ln_partf_exp ) .OR. ( .NOT.ln_partf_lin .AND. .NOT.ln_partf_exp ) ) THEN
CALL ctl_stop( 'ice_dyn_rdgrft_init: choose one and only one participation function (ln_partf_lin or ln_partf_exp)' )
ENDIF
!
IF( .NOT. ln_icethd ) THEN
rn_porordg = 0._wp
rn_fsnwrdg = 1._wp ; rn_fsnwrft = 1._wp
rn_fpndrdg = 1._wp ; rn_fpndrft = 1._wp
IF( lwp ) THEN
WRITE(numout,*) ' ==> only ice dynamics is activated, thus some parameters must be changed'
WRITE(numout,*) ' rn_porordg = ', rn_porordg
WRITE(numout,*) ' rn_fsnwrdg = ', rn_fsnwrdg
WRITE(numout,*) ' rn_fpndrdg = ', rn_fpndrdg
WRITE(numout,*) ' rn_fsnwrft = ', rn_fsnwrft
WRITE(numout,*) ' rn_fpndrft = ', rn_fpndrft
ENDIF
ENDIF
! ! allocate arrays
IF( ice_dyn_rdgrft_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'ice_dyn_rdgrft_init: unable to allocate arrays' )
!
END SUBROUTINE ice_dyn_rdgrft_init
#else
!!----------------------------------------------------------------------
!! Default option Empty module NO SI3 sea-ice model
!!----------------------------------------------------------------------
#endif
!!======================================================================
END MODULE icedyn_rdgrft