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MODULE icevar
!!======================================================================
!! *** MODULE icevar ***
!! sea-ice: series of functions to transform or compute ice variables
!!======================================================================
!! History : - ! 2006-01 (M. Vancoppenolle) Original code
!! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube]
!!----------------------------------------------------------------------
#if defined key_si3
!!----------------------------------------------------------------------
!! 'key_si3' SI3 sea-ice model
!!----------------------------------------------------------------------
!!
!! There are three sets of variables
!! VGLO : global variables of the model
!! - v_i (jpi,jpj,jpl)
!! - v_s (jpi,jpj,jpl)
!! - a_i (jpi,jpj,jpl)
!! - t_s (jpi,jpj,jpl)
!! - e_i (jpi,jpj,nlay_i,jpl)
!! - e_s (jpi,jpj,nlay_s,jpl)
!! - sv_i(jpi,jpj,jpl)
!! - oa_i(jpi,jpj,jpl)
!! VEQV : equivalent variables sometimes used in the model
!! - h_i(jpi,jpj,jpl)
!! - h_s(jpi,jpj,jpl)
!! - t_i(jpi,jpj,nlay_i,jpl)
!! ...
!! VAGG : aggregate variables, averaged/summed over all
!! thickness categories
!! - vt_i(jpi,jpj)
!! - vt_s(jpi,jpj)
!! - at_i(jpi,jpj)
!! - st_i(jpi,jpj)
!! - et_s(jpi,jpj) total snow heat content
!! - et_i(jpi,jpj) total ice thermal content
!! - sm_i(jpi,jpj) mean ice salinity
!! - tm_i(jpi,jpj) mean ice temperature
!! - tm_s(jpi,jpj) mean snw temperature
!!----------------------------------------------------------------------
!! ice_var_agg : integrate variables over layers and categories
!! ice_var_glo2eqv : transform from VGLO to VEQV
!! ice_var_eqv2glo : transform from VEQV to VGLO
!! ice_var_salprof : salinity profile in the ice
!! ice_var_salprof1d : salinity profile in the ice 1D
!! ice_var_zapsmall : remove very small area and volume
!! ice_var_zapneg : remove negative ice fields
!! ice_var_roundoff : remove negative values arising from roundoff erros
!! ice_var_bv : brine volume
!! ice_var_enthalpy : compute ice and snow enthalpies from temperature
!! ice_var_sshdyn : compute equivalent ssh in lead
!! ice_var_itd : convert N-cat to M-cat
!! ice_var_snwfra : fraction of ice covered by snow
!! ice_var_snwblow : distribute snow fall between ice and ocean
!!----------------------------------------------------------------------
USE dom_oce ! ocean space and time domain
USE phycst ! physical constants (ocean directory)
USE sbc_oce , ONLY : sss_m, ln_ice_embd, nn_fsbc
USE ice ! sea-ice: variables
USE ice1D ! sea-ice: thermodynamics variables
!
USE in_out_manager ! I/O manager
USE lib_mpp ! MPP library
USE lib_fortran ! fortran utilities (glob_sum + no signed zero)
IMPLICIT NONE
PRIVATE
PUBLIC ice_var_agg
PUBLIC ice_var_glo2eqv
PUBLIC ice_var_eqv2glo
PUBLIC ice_var_salprof
PUBLIC ice_var_salprof1d
PUBLIC ice_var_zapsmall
PUBLIC ice_var_zapneg
PUBLIC ice_var_roundoff
PUBLIC ice_var_bv
PUBLIC ice_var_enthalpy
PUBLIC ice_var_sshdyn
PUBLIC ice_var_itd
PUBLIC ice_var_snwfra
PUBLIC ice_var_snwblow
INTERFACE ice_var_itd
MODULE PROCEDURE ice_var_itd_1c1c, ice_var_itd_Nc1c, ice_var_itd_1cMc, ice_var_itd_NcMc
END INTERFACE
!! * Substitutions
# include "do_loop_substitute.h90"
INTERFACE ice_var_snwfra
MODULE PROCEDURE ice_var_snwfra_1d, ice_var_snwfra_2d, ice_var_snwfra_3d
END INTERFACE
INTERFACE ice_var_snwblow
MODULE PROCEDURE ice_var_snwblow_1d, ice_var_snwblow_2d
END INTERFACE
!!----------------------------------------------------------------------
!! NEMO/ICE 4.0 , NEMO Consortium (2018)
!! $Id: icevar.F90 15385 2021-10-15 13:52:48Z clem $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
SUBROUTINE ice_var_agg( kn )
!!-------------------------------------------------------------------
!! *** ROUTINE ice_var_agg ***
!!
!! ** Purpose : aggregates ice-thickness-category variables to
!! all-ice variables, i.e. it turns VGLO into VAGG
!!-------------------------------------------------------------------
INTEGER, INTENT( in ) :: kn ! =1 state variables only
! ! >1 state variables + others
!
INTEGER :: ji, jj, jk, jl ! dummy loop indices
REAL(wp) :: z1_vt_i, z1_vt_s
REAL(wp), DIMENSION(A2D(0)) :: z1_at_i
!!-------------------------------------------------------------------
!
! full arrays: vt_i, vt_s, at_i, vt_ip, vt_il, at_ip
! reduced arrays: the rest
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
vt_i(ji,jj) = SUM( v_i (ji,jj,:) )
vt_s(ji,jj) = SUM( v_s (ji,jj,:) )
at_i(ji,jj) = SUM( a_i (ji,jj,:) )
!
at_ip(ji,jj) = SUM( a_ip(ji,jj,:) ) ! melt ponds
vt_ip(ji,jj) = SUM( v_ip(ji,jj,:) )
vt_il(ji,jj) = SUM( v_il(ji,jj,:) )
!
ato_i(ji,jj) = 1._wp - at_i(ji,jj) ! open water fraction
DO_2D( 0, 0, 0, 0 )
st_i(ji,jj) = SUM( sv_i(ji,jj,:) )
et_s(ji,jj) = SUM( SUM( e_s (ji,jj,:,:), dim=2 ) )
et_i(ji,jj) = SUM( SUM( e_i (ji,jj,:,:), dim=2 ) )
!
!!GS: tm_su always needed by ABL over sea-ice
IF( at_i(ji,jj) <= epsi20 ) THEN
z1_at_i(ji,jj) = 0._wp
tm_su (ji,jj) = rt0
z1_at_i(ji,jj) = 1._wp / at_i(ji,jj)
tm_su (ji,jj) = SUM( t_su(ji,jj,:) * a_i(ji,jj,:) ) * z1_at_i(ji,jj)
!
! The following fields are calculated for diagnostics and outputs only
! ==> Do not use them for other purposes
IF( kn > 1 ) THEN
!
IF( vt_i(ji,jj) > epsi20 ) THEN ; z1_vt_i = 1._wp / vt_i(ji,jj)
ELSE ; z1_vt_i = 0._wp
ENDIF
IF( vt_s(ji,jj) > epsi20 ) THEN ; z1_vt_s = 1._wp / vt_s(ji,jj)
ELSE ; z1_vt_s = 0._wp
ENDIF
! mean ice/snow thickness
hm_i(ji,jj) = vt_i(ji,jj) * z1_at_i(ji,jj)
hm_s(ji,jj) = vt_s(ji,jj) * z1_at_i(ji,jj)
!
! mean temperature (K), salinity and age
tm_si(ji,jj) = SUM( t_si(ji,jj,:) * a_i(ji,jj,:) ) * z1_at_i(ji,jj)
om_i (ji,jj) = SUM( oa_i(ji,jj,:) ) * z1_at_i(ji,jj)
!
tm_i(ji,jj) = 0._wp
tm_s(ji,jj) = 0._wp
DO jl = 1, jpl
DO jk = 1, nlay_i
tm_i(ji,jj) = tm_i(ji,jj) + r1_nlay_i * t_i (ji,jj,jk,jl) * v_i(ji,jj,jl) * z1_vt_i
END DO
DO jk = 1, nlay_s
tm_s(ji,jj) = tm_s(ji,jj) + r1_nlay_s * t_s (ji,jj,jk,jl) * v_s(ji,jj,jl) * z1_vt_s
WHERE( at_i(A2D(0)) <= epsi20 )
tm_si(:,:) = rt0
tm_i (:,:) = rt0
tm_s (:,:) = rt0
END WHERE
!
WHERE( at_ip(A2D(0)) > epsi20 )
hm_ip(:,:) = vt_ip(A2D(0)) / at_ip(A2D(0))
hm_il(:,:) = vt_il(A2D(0)) / at_ip(A2D(0))
ELSEWHERE
hm_ip(:,:) = 0._wp
hm_il(:,:) = 0._wp
END WHERE
!
ENDIF
!
END SUBROUTINE ice_var_agg
SUBROUTINE ice_var_glo2eqv
!!-------------------------------------------------------------------
!! *** ROUTINE ice_var_glo2eqv ***
!!
!! ** Purpose : computes equivalent variables as function of
!! global variables, i.e. it turns VGLO into VEQV
!!-------------------------------------------------------------------
INTEGER :: ji, jj, jk, jl ! dummy loop indices
REAL(wp) :: ze_i ! local scalars
REAL(wp) :: ze_s, ztmelts, zbbb, zccc ! - -
REAL(wp) :: zhmax, z1_zhmax ! - -
REAL(wp) :: zlay_i, zlay_s ! - -
REAL(wp), PARAMETER :: zhl_max = 0.015_wp ! pond lid thickness above which the ponds disappear from the albedo calculation
REAL(wp), PARAMETER :: zhl_min = 0.005_wp ! pond lid thickness below which the full pond area is used in the albedo calculation
REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_a_i, z1_v_i, z1_a_ip
REAL(wp), DIMENSION(A2D(0),jpl) :: za_s_fra
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!!-------------------------------------------------------------------
!!gm Question 2: It is possible to define existence of sea-ice in a common way between
!! ice area and ice volume ?
!! the idea is to be able to define one for all at the begining of this routine
!! a criteria for icy area (i.e. a_i > epsi20 and v_i > epsi20 )
!---------------------------------------------------------------
! Ice thickness, snow thickness, ice salinity, ice age and ponds
!---------------------------------------------------------------
! !--- inverse of the ice area
WHERE( a_i(:,:,:) > epsi20 ) ; z1_a_i(:,:,:) = 1._wp / a_i(:,:,:)
ELSEWHERE ; z1_a_i(:,:,:) = 0._wp
END WHERE
!
WHERE( v_i(:,:,:) > epsi20 ) ; z1_v_i(:,:,:) = 1._wp / v_i(:,:,:)
ELSEWHERE ; z1_v_i(:,:,:) = 0._wp
END WHERE
!
WHERE( a_ip(:,:,:) > epsi20 ) ; z1_a_ip(:,:,:) = 1._wp / a_ip(:,:,:)
ELSEWHERE ; z1_a_ip(:,:,:) = 0._wp
END WHERE
! !--- ice thickness
h_i(:,:,:) = v_i (:,:,:) * z1_a_i(:,:,:)
zhmax = hi_max(jpl)
z1_zhmax = 1._wp / hi_max(jpl)
WHERE( h_i(:,:,jpl) > zhmax ) ! bound h_i by hi_max (i.e. 99 m) with associated update of ice area
h_i (:,:,jpl) = zhmax
a_i (:,:,jpl) = v_i(:,:,jpl) * z1_zhmax
z1_a_i(:,:,jpl) = zhmax * z1_v_i(:,:,jpl)
END WHERE
! !--- snow thickness
h_s(:,:,:) = v_s (:,:,:) * z1_a_i(:,:,:)
! !--- ice age
o_i(:,:,:) = oa_i(:,:,:) * z1_a_i(:,:,:)
! !--- pond and lid thickness
h_ip(:,:,:) = v_ip(:,:,:) * z1_a_ip(:,:,:)
h_il(:,:,:) = v_il(:,:,:) * z1_a_ip(:,:,:)
! !--- melt pond effective area (used for albedo)
a_ip_frac(:,:,:) = a_ip(A2D(0),:) * z1_a_i(A2D(0),:)
WHERE ( h_il(A2D(0),:) <= zhl_min ) ; a_ip_eff(:,:,:) = a_ip_frac(:,:,:) ! lid is very thin. Expose all the pond
ELSEWHERE( h_il(A2D(0),:) >= zhl_max ) ; a_ip_eff(:,:,:) = 0._wp ! lid is very thick. Cover all the pond up with ice and snow
ELSEWHERE ; a_ip_eff(:,:,:) = a_ip_frac(:,:,:) * & ! lid is in between. Expose part of the pond
& ( zhl_max - h_il(A2D(0),:) ) / ( zhl_max - zhl_min )
CALL ice_var_snwfra( h_s(A2D(0),:), za_s_fra(:,:,:) ) ! calculate ice fraction covered by snow
a_ip_eff(:,:,:) = MIN( a_ip_eff(:,:,:), 1._wp - za_s_fra(:,:,:) ) ! make sure (a_ip_eff + a_s_fra) <= 1
!
! !--- salinity (with a minimum value imposed everywhere)
IF( nn_icesal == 2 ) THEN
WHERE( v_i(:,:,:) > epsi20 ) ; s_i(:,:,:) = MAX( rn_simin , MIN( rn_simax, sv_i(:,:,:) * z1_v_i(:,:,:) ) )
ELSEWHERE ; s_i(:,:,:) = rn_simin
END WHERE
ENDIF
CALL ice_var_salprof ! salinity profile
!-------------------
! Ice temperature [K] (with a minimum value (rt0 - 100.))
!-------------------
zlay_i = REAL( nlay_i , wp ) ! number of layers
DO jl = 1, jpl
DO jk = 1, nlay_i
!
ze_i = e_i (ji,jj,jk,jl) * z1_v_i(ji,jj,jl) * zlay_i ! Energy of melting e(S,T) [J.m-3]
ztmelts = - sz_i(ji,jj,jk,jl) * rTmlt ! Ice layer melt temperature [C]
! Conversion q(S,T) -> T (second order equation)
zbbb = ( rcp - rcpi ) * ztmelts + ze_i * r1_rhoi - rLfus
zccc = SQRT( MAX( zbbb * zbbb - 4._wp * rcpi * rLfus * ztmelts , 0._wp) )
t_i(ji,jj,jk,jl) = MAX( -100._wp , MIN( -( zbbb + zccc ) * 0.5_wp * r1_rcpi , ztmelts ) ) + rt0 ! [K] with bounds: -100 < t_i < ztmelts
!
END DO
DO jk = 1, nlay_i
t_i(ji,jj,jk,jl) = rt0
END DO
END DO
!--------------------
! Snow temperature [K] (with a minimum value (rt0 - 100.))
!--------------------
zlay_s = REAL( nlay_s , wp )
DO jk = 1, nlay_s
WHERE( v_s(:,:,:) > epsi20 ) !--- icy area
t_s(:,:,jk,:) = rt0 + MAX( -100._wp , &
& MIN( r1_rcpi * ( -r1_rhos * ( e_s(:,:,jk,:) / v_s(:,:,:) * zlay_s ) + rLfus ) , 0._wp ) )
ELSEWHERE !--- no ice
t_s(:,:,jk,:) = rt0
END WHERE
END DO
!
! integrated values
vt_i (:,:) = SUM( v_i, dim=3 )
vt_s (:,:) = SUM( v_s, dim=3 )
at_i (:,:) = SUM( a_i, dim=3 )
!
END SUBROUTINE ice_var_glo2eqv
SUBROUTINE ice_var_eqv2glo
!!-------------------------------------------------------------------
!! *** ROUTINE ice_var_eqv2glo ***
!!
!! ** Purpose : computes global variables as function of
!! equivalent variables, i.e. it turns VEQV into VGLO
!!-------------------------------------------------------------------
INTEGER :: ji, jj, jl ! dummy loop indices
!!-------------------------------------------------------------------
DO jl = 1, jpl
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
v_i (ji,jj,jl) = h_i (ji,jj,jl) * a_i (ji,jj,jl)
v_s (ji,jj,jl) = h_s (ji,jj,jl) * a_i (ji,jj,jl)
sv_i(ji,jj,jl) = s_i (ji,jj,jl) * v_i (ji,jj,jl)
v_ip(ji,jj,jl) = h_ip(ji,jj,jl) * a_ip(ji,jj,jl)
v_il(ji,jj,jl) = h_il(ji,jj,jl) * a_ip(ji,jj,jl)
END_2D
ENDDO
!
END SUBROUTINE ice_var_eqv2glo
SUBROUTINE ice_var_salprof
!!-------------------------------------------------------------------
!! *** ROUTINE ice_var_salprof ***
!!
!! ** Purpose : computes salinity profile in function of bulk salinity
!!
!! ** Method : If bulk salinity greater than zsi1,
!! the profile is assumed to be constant (S_inf)
!! If bulk salinity lower than zsi0,
!! the profile is linear with 0 at the surface (S_zero)
!! If it is between zsi0 and zsi1, it is a
!! alpha-weighted linear combination of s_inf and s_zero
!!
!! ** References : Vancoppenolle et al., 2007
!!-------------------------------------------------------------------
INTEGER :: ji, jj, jk, jl ! dummy loop index
REAL(wp) :: z1_dS
REAL(wp) :: ztmp1, ztmp2, zs0, zs
REAL(wp) :: z_slope_s, zalpha ! case 2 only
REAL(wp), PARAMETER :: zsi0 = 3.5_wp
REAL(wp), PARAMETER :: zsi1 = 4.5_wp
!!-------------------------------------------------------------------
!!gm Question: Remove the option 3 ? How many years since it last use ?
SELECT CASE ( nn_icesal )
!
! !---------------------------------------!
CASE( 1 ) ! constant salinity in time and space !
! !---------------------------------------!
sz_i(:,:,:,:) = rn_icesal
s_i (:,:,:) = rn_icesal
!
! !---------------------------------------------!
CASE( 2 ) ! time varying salinity with linear profile !
! !---------------------------------------------!
z1_dS = 1._wp / ( zsi1 - zsi0 )
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
DO jl = 1, jpl
IF( h_i(ji,jj,jl) > epsi20 ) THEN ; z_slope_s = 2._wp * s_i(ji,jj,jl) / h_i(ji,jj,jl)
ELSE ; z_slope_s = 0._wp
zalpha = MAX( 0._wp , MIN( ( zsi1 - s_i(ji,jj,jl) ) * z1_dS , 1._wp ) )
! ! force a constant profile when SSS too low (Baltic Sea)
IF( 2._wp * s_i(ji,jj,jl) >= sss_m(ji,jj) ) zalpha = 0._wp
!
! Computation of the profile
DO jk = 1, nlay_i
! ! linear profile with 0 surface value
zs0 = z_slope_s * ( REAL(jk,wp) - 0.5_wp ) * h_i(ji,jj,jl) * r1_nlay_i
zs = zalpha * zs0 + ( 1._wp - zalpha ) * s_i(ji,jj,jl) ! weighting the profile
sz_i(ji,jj,jk,jl) = MIN( rn_simax, MAX( zs, rn_simin ) )
ENDDO
ENDDO
END_2D
!
! !-------------------------------------------!
CASE( 3 ) ! constant salinity with a fix profile ! (Schwarzacher (1959) multiyear salinity profile
! !-------------------------------------------! (mean = 2.30)
!
s_i(:,:,:) = 2.30_wp
!!gm Remark: if we keep the case 3, then compute an store one for all time-step
!! a array S_prof(1:nlay_i) containing the calculation and just do:
! DO jk = 1, nlay_i
! sz_i(:,:,jk,:) = S_prof(jk)
! END DO
!!gm end
DO jl = 1, jpl
DO jk = 1, nlay_i
ztmp1 = ( REAL(jk,wp) - 0.5_wp ) * r1_nlay_i
ztmp2 = 1.6_wp * ( 1._wp - COS( rpi * ztmp1**(0.407_wp/(0.573_wp+ztmp1)) ) )
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
sz_i(ji,jj,jk,jl) = ztmp2
END_2D
END DO
END DO
END SELECT
!
END SUBROUTINE ice_var_salprof
SUBROUTINE ice_var_salprof1d
!!-------------------------------------------------------------------
!! *** ROUTINE ice_var_salprof1d ***
!!
!! ** Purpose : 1d computation of the sea ice salinity profile
!! Works with 1d vectors and is used by thermodynamic modules
!!-------------------------------------------------------------------
INTEGER :: ji, jk ! dummy loop indices
REAL(wp) :: ztmp1, ztmp2, z1_dS ! local scalars
REAL(wp) :: zs, zs0 ! - -
!
REAL(wp), PARAMETER :: zsi0 = 3.5_wp
REAL(wp), PARAMETER :: zsi1 = 4.5_wp
!!-------------------------------------------------------------------
!
SELECT CASE ( nn_icesal )
!
! !---------------------------------------!
CASE( 1 ) ! constant salinity in time and space !
! !---------------------------------------!
sz_i_1d(1:npti,:) = rn_icesal
!
! !---------------------------------------------!
CASE( 2 ) ! time varying salinity with linear profile !
! !---------------------------------------------!
z1_dS = 1._wp / ( zsi1 - zsi0 )
!
DO ji = 1, npti
! ! Slope of the linear profile
IF( h_i_1d(ji) > epsi20 ) THEN ; z_slope_s = 2._wp * s_i_1d(ji) / h_i_1d(ji)
ELSE ; z_slope_s = 0._wp
zalpha = MAX( 0._wp , MIN( ( zsi1 - s_i_1d(ji) ) * z1_dS , 1._wp ) )
! ! force a constant profile when SSS too low (Baltic Sea)
IF( 2._wp * s_i_1d(ji) >= sss_1d(ji) ) zalpha = 0._wp
!
! Computation of the profile
DO jk = 1, nlay_i
zs0 = z_slope_s * ( REAL(jk,wp) - 0.5_wp ) * h_i_1d(ji) * r1_nlay_i
zs = zalpha * zs0 + ( 1._wp - zalpha ) * s_i_1d(ji)
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sz_i_1d(ji,jk) = MIN( rn_simax , MAX( zs , rn_simin ) )
END DO
END DO
!
! !-------------------------------------------!
CASE( 3 ) ! constant salinity with a fix profile ! (Schwarzacher (1959) multiyear salinity profile
! !-------------------------------------------! (mean = 2.30)
!
s_i_1d(1:npti) = 2.30_wp
!
!!gm cf remark in ice_var_salprof routine, CASE( 3 )
DO jk = 1, nlay_i
ztmp1 = ( REAL(jk,wp) - 0.5_wp ) * r1_nlay_i
ztmp2 = 1.6_wp * ( 1._wp - COS( rpi * ztmp1**( 0.407_wp / ( 0.573_wp + ztmp1 ) ) ) )
DO ji = 1, npti
sz_i_1d(ji,jk) = ztmp2
END DO
END DO
!
END SELECT
!
END SUBROUTINE ice_var_salprof1d
SUBROUTINE ice_var_zapsmall
!!-------------------------------------------------------------------
!! *** ROUTINE ice_var_zapsmall ***
!!
!! ** Purpose : Remove too small sea ice areas and correct fluxes
!!-------------------------------------------------------------------
INTEGER :: ji, jj, jl, jk ! dummy loop indices
REAL(wp), DIMENSION(jpi,jpj) :: zswitch
!!-------------------------------------------------------------------
!
DO jl = 1, jpl !== loop over the categories ==!
!
WHERE( a_i(:,:,jl) > epsi10 ) ; h_i(:,:,jl) = v_i(:,:,jl) / a_i(:,:,jl)
ELSEWHERE ; h_i(:,:,jl) = 0._wp
END WHERE
!
WHERE( a_i(:,:,jl) < epsi10 .OR. v_i(:,:,jl) < epsi10 .OR. h_i(:,:,jl) < epsi10 ) ; zswitch(:,:) = 0._wp
ELSEWHERE ; zswitch(:,:) = 1._wp
END WHERE
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!-----------------------------------------------------------------
! Zap ice energy and use ocean heat to melt ice
!-----------------------------------------------------------------
DO jk = 1, nlay_i
! update exchanges with ocean
hfx_res(ji,jj) = hfx_res(ji,jj) - (1._wp - zswitch(ji,jj) ) * e_i(ji,jj,jk,jl) * r1_Dt_ice ! W.m-2 <0
e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) * zswitch(ji,jj)
t_i(ji,jj,jk,jl) = t_i(ji,jj,jk,jl) * zswitch(ji,jj) + rt0 * ( 1._wp - zswitch(ji,jj) )
ENDDO
!
DO jk = 1, nlay_s
! update exchanges with ocean
hfx_res(ji,jj) = hfx_res(ji,jj) - (1._wp - zswitch(ji,jj) ) * e_s(ji,jj,jk,jl) * r1_Dt_ice ! W.m-2 <0
e_s(ji,jj,jk,jl) = e_s(ji,jj,jk,jl) * zswitch(ji,jj)
t_s(ji,jj,jk,jl) = t_s(ji,jj,jk,jl) * zswitch(ji,jj) + rt0 * ( 1._wp - zswitch(ji,jj) )
ENDDO
!
!-----------------------------------------------------------------
! zap ice and snow volume, add water and salt to ocean
!-----------------------------------------------------------------
! update exchanges with ocean
sfx_res(ji,jj) = sfx_res(ji,jj) + ( 1._wp - zswitch(ji,jj) ) * sv_i(ji,jj,jl) * rhoi * r1_Dt_ice
wfx_res(ji,jj) = wfx_res(ji,jj) + ( 1._wp - zswitch(ji,jj) ) * v_i (ji,jj,jl) * rhoi * r1_Dt_ice
wfx_res(ji,jj) = wfx_res(ji,jj) + ( 1._wp - zswitch(ji,jj) ) * v_s (ji,jj,jl) * rhos * r1_Dt_ice
wfx_res(ji,jj) = wfx_res(ji,jj) + ( 1._wp - zswitch(ji,jj) ) * ( v_ip(ji,jj,jl)+v_il(ji,jj,jl) ) * rhow * r1_Dt_ice
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!
a_i (ji,jj,jl) = a_i (ji,jj,jl) * zswitch(ji,jj)
v_i (ji,jj,jl) = v_i (ji,jj,jl) * zswitch(ji,jj)
v_s (ji,jj,jl) = v_s (ji,jj,jl) * zswitch(ji,jj)
t_su (ji,jj,jl) = t_su(ji,jj,jl) * zswitch(ji,jj) + t_bo(ji,jj) * ( 1._wp - zswitch(ji,jj) )
oa_i (ji,jj,jl) = oa_i(ji,jj,jl) * zswitch(ji,jj)
sv_i (ji,jj,jl) = sv_i(ji,jj,jl) * zswitch(ji,jj)
!
h_i (ji,jj,jl) = h_i (ji,jj,jl) * zswitch(ji,jj)
h_s (ji,jj,jl) = h_s (ji,jj,jl) * zswitch(ji,jj)
!
a_ip (ji,jj,jl) = a_ip (ji,jj,jl) * zswitch(ji,jj)
v_ip (ji,jj,jl) = v_ip (ji,jj,jl) * zswitch(ji,jj)
v_il (ji,jj,jl) = v_il (ji,jj,jl) * zswitch(ji,jj)
h_ip (ji,jj,jl) = h_ip (ji,jj,jl) * zswitch(ji,jj)
h_il (ji,jj,jl) = h_il (ji,jj,jl) * zswitch(ji,jj)
!
END_2D
!
END DO
! to be sure that at_i is the sum of a_i(jl)
at_i (:,:) = SUM( a_i (:,:,:), dim=3 )
vt_i (:,:) = SUM( v_i (:,:,:), dim=3 )
!!clem add?
! vt_s (:,:) = SUM( v_s (:,:,:), dim=3 )
! st_i (:,:) = SUM( sv_i(:,:,:), dim=3 )
! et_s(:,:) = SUM( SUM( e_s (:,:,:,:), dim=4 ), dim=3 )
! et_i(:,:) = SUM( SUM( e_i (:,:,:,:), dim=4 ), dim=3 )
!!clem
! open water = 1 if at_i=0
WHERE( at_i(:,:) == 0._wp ) ato_i(:,:) = 1._wp
!
END SUBROUTINE ice_var_zapsmall
SUBROUTINE ice_var_zapneg( pdt, pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pv_il, pe_s, pe_i )
!!-------------------------------------------------------------------
!! *** ROUTINE ice_var_zapneg ***
!!
!! ** Purpose : Remove negative sea ice fields and correct fluxes
!!-------------------------------------------------------------------
REAL(wp) , INTENT(in ) :: pdt ! tracer time-step
REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area
REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume
REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume
REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psv_i ! salt content
REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content
REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration
REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond fraction
REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume
REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_il ! melt pond lid volume
REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content
REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content
!
INTEGER :: ji, jj, jl, jk ! dummy loop indices
REAL(wp) :: z1_dt
!!-------------------------------------------------------------------
!
z1_dt = 1._wp / pdt
!
DO jl = 1, jpl !== loop over the categories ==!
!
! make sure a_i=0 where v_i<=0
WHERE( pv_i(:,:,:) <= 0._wp ) pa_i(:,:,:) = 0._wp
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!----------------------------------------
! zap ice energy and send it to the ocean
!----------------------------------------
DO jk = 1, nlay_i
IF( pe_i(ji,jj,jk,jl) < 0._wp .OR. pa_i(ji,jj,jl) <= 0._wp ) THEN
hfx_res(ji,jj) = hfx_res(ji,jj) - pe_i(ji,jj,jk,jl) * z1_dt ! W.m-2 >0
pe_i(ji,jj,jk,jl) = 0._wp
ENDIF
ENDDO
!
DO jk = 1, nlay_s
IF( pe_s(ji,jj,jk,jl) < 0._wp .OR. pa_i(ji,jj,jl) <= 0._wp ) THEN
hfx_res(ji,jj) = hfx_res(ji,jj) - pe_s(ji,jj,jk,jl) * z1_dt ! W.m-2 <0
pe_s(ji,jj,jk,jl) = 0._wp
ENDIF
ENDDO
!
!-----------------------------------------------------
! zap ice and snow volume, add water and salt to ocean
!-----------------------------------------------------
IF( pv_i(ji,jj,jl) < 0._wp .OR. pa_i(ji,jj,jl) <= 0._wp ) THEN
wfx_res(ji,jj) = wfx_res(ji,jj) + pv_i (ji,jj,jl) * rhoi * z1_dt
pv_i (ji,jj,jl) = 0._wp
ENDIF
IF( pv_s(ji,jj,jl) < 0._wp .OR. pa_i(ji,jj,jl) <= 0._wp ) THEN
wfx_res(ji,jj) = wfx_res(ji,jj) + pv_s (ji,jj,jl) * rhos * z1_dt
pv_s (ji,jj,jl) = 0._wp
ENDIF
IF( psv_i(ji,jj,jl) < 0._wp .OR. pa_i(ji,jj,jl) <= 0._wp .OR. pv_i(ji,jj,jl) <= 0._wp ) THEN
sfx_res(ji,jj) = sfx_res(ji,jj) + psv_i(ji,jj,jl) * rhoi * z1_dt
psv_i (ji,jj,jl) = 0._wp
ENDIF
IF( pv_ip(ji,jj,jl) < 0._wp .OR. pv_il(ji,jj,jl) < 0._wp .OR. pa_ip(ji,jj,jl) <= 0._wp ) THEN
wfx_res(ji,jj) = wfx_res(ji,jj) + pv_il(ji,jj,jl) * rhow * z1_dt
pv_il (ji,jj,jl) = 0._wp
ENDIF
IF( pv_ip(ji,jj,jl) < 0._wp .OR. pa_ip(ji,jj,jl) <= 0._wp ) THEN
wfx_res(ji,jj) = wfx_res(ji,jj) + pv_ip(ji,jj,jl) * rhow * z1_dt
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pv_ip (ji,jj,jl) = 0._wp
ENDIF
END_2D
!
END DO
!
WHERE( pato_i(:,:) < 0._wp ) pato_i(:,:) = 0._wp
WHERE( poa_i (:,:,:) < 0._wp ) poa_i (:,:,:) = 0._wp
WHERE( pa_i (:,:,:) < 0._wp ) pa_i (:,:,:) = 0._wp
WHERE( pa_ip (:,:,:) < 0._wp ) pa_ip (:,:,:) = 0._wp
!
END SUBROUTINE ice_var_zapneg
SUBROUTINE ice_var_roundoff( pa_i, pv_i, pv_s, psv_i, poa_i, pa_ip, pv_ip, pv_il, pe_s, pe_i )
!!-------------------------------------------------------------------
!! *** ROUTINE ice_var_roundoff ***
!!
!! ** Purpose : Remove negative sea ice values arising from roundoff errors
!!-------------------------------------------------------------------
REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pa_i ! ice concentration
REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pv_i ! ice volume
REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pv_s ! snw volume
REAL(wp), DIMENSION(:,:) , INTENT(inout) :: psv_i ! salt content
REAL(wp), DIMENSION(:,:) , INTENT(inout) :: poa_i ! age content
REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pa_ip ! melt pond fraction
REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pv_ip ! melt pond volume
REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pv_il ! melt pond lid volume
REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: pe_s ! snw heat content
REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: pe_i ! ice heat content
!!-------------------------------------------------------------------
!
WHERE( pa_i (1:npti,:) < 0._wp ) pa_i (1:npti,:) = 0._wp ! a_i must be >= 0
WHERE( pv_i (1:npti,:) < 0._wp ) pv_i (1:npti,:) = 0._wp ! v_i must be >= 0
WHERE( pv_s (1:npti,:) < 0._wp ) pv_s (1:npti,:) = 0._wp ! v_s must be >= 0
WHERE( psv_i(1:npti,:) < 0._wp ) psv_i(1:npti,:) = 0._wp ! sv_i must be >= 0
WHERE( poa_i(1:npti,:) < 0._wp ) poa_i(1:npti,:) = 0._wp ! oa_i must be >= 0
WHERE( pe_i (1:npti,:,:) < 0._wp ) pe_i (1:npti,:,:) = 0._wp ! e_i must be >= 0
WHERE( pe_s (1:npti,:,:) < 0._wp ) pe_s (1:npti,:,:) = 0._wp ! e_s must be >= 0
IF( ln_pnd_LEV .OR. ln_pnd_TOPO ) THEN
WHERE( pa_ip(1:npti,:) < 0._wp ) pa_ip(1:npti,:) = 0._wp ! a_ip must be >= 0
WHERE( pv_ip(1:npti,:) < 0._wp ) pv_ip(1:npti,:) = 0._wp ! v_ip must be >= 0
IF( ln_pnd_lids ) THEN
WHERE( pv_il(1:npti,:) < 0._wp .AND. pv_il(1:npti,:) > -epsi10 ) pv_il(1:npti,:) = 0._wp ! v_il must be >= 0
ENDIF
ENDIF
!
END SUBROUTINE ice_var_roundoff
SUBROUTINE ice_var_bv
!!-------------------------------------------------------------------
!! *** ROUTINE ice_var_bv ***
!!
!! ** Purpose : computes mean brine volume (%) in sea ice
!!
!! ** Method : e = - 0.054 * S (ppt) / T (C)
!!
!! References : Vancoppenolle et al., JGR, 2007
!!-------------------------------------------------------------------
INTEGER :: ji, jj, jk, jl ! dummy loop indices
!!-------------------------------------------------------------------
!
bv_i (:,:,:) = 0._wp
DO jl = 1, jpl
DO jk = 1, nlay_i
IF( t_i(ji,jj,jk,jl) < rt0 - epsi10 ) THEN
bv_i(ji,jj,jl) = bv_i(ji,jj,jl) - rTmlt * sz_i(ji,jj,jk,jl) * r1_nlay_i / ( t_i(ji,jj,jk,jl) - rt0 )
ENDIF
ENDDO
ENDDO
IF( vt_i(ji,jj) > epsi20 ) THEN
bvm_i(ji,jj) = SUM( bv_i(ji,jj,:) * v_i(ji,jj,:) ) / vt_i(ji,jj)
ELSE
bvm_i(ji,jj) = 0._wp
ENDIF
END_2D
!
END SUBROUTINE ice_var_bv
SUBROUTINE ice_var_enthalpy
!!-------------------------------------------------------------------
!! *** ROUTINE ice_var_enthalpy ***
!!
!! ** Purpose : Computes sea ice energy of melting q_i (J.m-3) from temperature
!!
!! ** Method : Formula (Bitz and Lipscomb, 1999)
!!-------------------------------------------------------------------
INTEGER :: ji, jk ! dummy loop indices
REAL(wp) :: ztmelts ! local scalar
!!-------------------------------------------------------------------
!
DO ji = 1, npti
DO jk = 1, nlay_i ! Sea ice energy of melting
ztmelts = - rTmlt * sz_i_1d(ji,jk)
t_i_1d(ji,jk) = MIN( t_i_1d(ji,jk), ztmelts + rt0 ) ! Force t_i_1d to be lower than melting point => likely conservation issue
! (sometimes zdf scheme produces abnormally high temperatures)
e_i_1d(ji,jk) = rhoi * ( rcpi * ( ztmelts - ( t_i_1d(ji,jk) - rt0 ) ) &
& + rLfus * ( 1._wp - ztmelts / ( t_i_1d(ji,jk) - rt0 ) ) &
& - rcp * ztmelts )
END DO
DO jk = 1, nlay_s ! Snow energy of melting
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e_s_1d(ji,jk) = rhos * ( rcpi * ( rt0 - t_s_1d(ji,jk) ) + rLfus )
END DO
END DO
!
END SUBROUTINE ice_var_enthalpy
FUNCTION ice_var_sshdyn(pssh, psnwice_mass, psnwice_mass_b)
!!---------------------------------------------------------------------
!! *** ROUTINE ice_var_sshdyn ***
!!
!! ** Purpose : compute the equivalent ssh in lead when sea ice is embedded
!!
!! ** Method : ssh_lead = ssh + (Mice + Msnow) / rho0
!!
!! ** Reference : Jean-Michel Campin, John Marshall, David Ferreira,
!! Sea ice-ocean coupling using a rescaled vertical coordinate z*,
!! Ocean Modelling, Volume 24, Issues 1-2, 2008
!!----------------------------------------------------------------------
!
! input
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pssh !: ssh [m]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psnwice_mass !: mass of snow and ice at current ice time step [Kg/m2]
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psnwice_mass_b !: mass of snow and ice at previous ice time step [Kg/m2]
!
! output
REAL(wp), DIMENSION(jpi,jpj) :: ice_var_sshdyn ! equivalent ssh in lead [m]
!
! temporary
REAL(wp) :: zintn, zintb ! time interpolation weights []
!
! compute ice load used to define the equivalent ssh in lead
IF( ln_ice_embd ) THEN
!
! average interpolation coeff as used in dynspg = (1/nn_fsbc) * {SUM[n/nn_fsbc], n=0,nn_fsbc-1}
! = (1/nn_fsbc)^2 * {SUM[n] , n=0,nn_fsbc-1}
zintn = REAL( nn_fsbc - 1 ) / REAL( nn_fsbc ) * 0.5_wp
!
! average interpolation coeff as used in dynspg = (1/nn_fsbc) * {SUM[1-n/nn_fsbc], n=0,nn_fsbc-1}
! = (1/nn_fsbc)^2 * (nn_fsbc^2 - {SUM[n], n=0,nn_fsbc-1})
zintb = REAL( nn_fsbc + 1 ) / REAL( nn_fsbc ) * 0.5_wp
!
! compute equivalent ssh in lead
ice_var_sshdyn(:,:) = pssh(:,:) + ( zintn * psnwice_mass(:,:) + zintb * psnwice_mass_b(:,:) ) * r1_rho0
!
ELSE
! compute equivalent ssh in lead
ice_var_sshdyn(:,:) = pssh(:,:)
ENDIF
!
END FUNCTION ice_var_sshdyn
!!-------------------------------------------------------------------
!! *** INTERFACE ice_var_itd ***
!!
!! ** Purpose : converting N-cat ice to jpl ice categories
!!-------------------------------------------------------------------
SUBROUTINE ice_var_itd_1c1c( phti, phts, pati , ph_i, ph_s, pa_i, &
& ptmi, ptms, ptmsu, psmi, patip, phtip, phtil, pt_i, pt_s, pt_su, ps_i, pa_ip, ph_ip, ph_il )
!!-------------------------------------------------------------------
!! ** Purpose : converting 1-cat ice to 1 ice category
!!-------------------------------------------------------------------
REAL(wp), DIMENSION(:), INTENT(in) :: phti, phts, pati ! input ice/snow variables
REAL(wp), DIMENSION(:), INTENT(inout) :: ph_i, ph_s, pa_i ! output ice/snow variables
REAL(wp), DIMENSION(:), INTENT(in) :: ptmi, ptms, ptmsu, psmi, patip, phtip, phtil ! input ice/snow temp & sal & ponds
REAL(wp), DIMENSION(:), INTENT(inout) :: pt_i, pt_s, pt_su, ps_i, pa_ip, ph_ip, ph_il ! output ice/snow temp & sal & ponds
!!-------------------------------------------------------------------
! == thickness and concentration == !
ph_i(:) = phti(:)
ph_s(:) = phts(:)
pa_i(:) = pati(:)
!
! == temperature and salinity and ponds == !
pt_i (:) = ptmi (:)
pt_s (:) = ptms (:)
pt_su(:) = ptmsu(:)
ps_i (:) = psmi (:)
pa_ip(:) = patip(:)
ph_ip(:) = phtip(:)
ph_il(:) = phtil(:)
END SUBROUTINE ice_var_itd_1c1c
SUBROUTINE ice_var_itd_Nc1c( phti, phts, pati , ph_i, ph_s, pa_i, &
& ptmi, ptms, ptmsu, psmi, patip, phtip, phtil, pt_i, pt_s, pt_su, ps_i, pa_ip, ph_ip, ph_il )
!!-------------------------------------------------------------------
!! ** Purpose : converting N-cat ice to 1 ice category
!!-------------------------------------------------------------------
REAL(wp), DIMENSION(:,:), INTENT(in) :: phti, phts, pati ! input ice/snow variables
REAL(wp), DIMENSION(:) , INTENT(inout) :: ph_i, ph_s, pa_i ! output ice/snow variables
REAL(wp), DIMENSION(:,:), INTENT(in) :: ptmi, ptms, ptmsu, psmi, patip, phtip, phtil ! input ice/snow temp & sal & ponds
REAL(wp), DIMENSION(:) , INTENT(inout) :: pt_i, pt_s, pt_su, ps_i, pa_ip, ph_ip, ph_il ! output ice/snow temp & sal & ponds
!
REAL(wp), ALLOCATABLE, DIMENSION(:) :: z1_ai, z1_vi, z1_vs
!
INTEGER :: idim
!!-------------------------------------------------------------------
!
idim = SIZE( phti, 1 )
!
! == thickness and concentration == !
ALLOCATE( z1_ai(idim), z1_vi(idim), z1_vs(idim) )
!
pa_i(:) = SUM( pati(:,:), dim=2 )
WHERE( ( pa_i(:) ) /= 0._wp ) ; z1_ai(:) = 1._wp / pa_i(:)
ELSEWHERE ; z1_ai(:) = 0._wp
END WHERE
ph_i(:) = SUM( phti(:,:) * pati(:,:), dim=2 ) * z1_ai(:)
ph_s(:) = SUM( phts(:,:) * pati(:,:), dim=2 ) * z1_ai(:)
!
! == temperature and salinity == !
WHERE( ( pa_i(:) * ph_i(:) ) /= 0._wp ) ; z1_vi(:) = 1._wp / ( pa_i(:) * ph_i(:) )
ELSEWHERE ; z1_vi(:) = 0._wp
END WHERE
WHERE( ( pa_i(:) * ph_s(:) ) /= 0._wp ) ; z1_vs(:) = 1._wp / ( pa_i(:) * ph_s(:) )
ELSEWHERE ; z1_vs(:) = 0._wp
END WHERE
pt_i (:) = SUM( ptmi (:,:) * pati(:,:) * phti(:,:), dim=2 ) * z1_vi(:)
pt_s (:) = SUM( ptms (:,:) * pati(:,:) * phts(:,:), dim=2 ) * z1_vs(:)
pt_su(:) = SUM( ptmsu(:,:) * pati(:,:) , dim=2 ) * z1_ai(:)
ps_i (:) = SUM( psmi (:,:) * pati(:,:) * phti(:,:), dim=2 ) * z1_vi(:)
! == ponds == !
pa_ip(:) = SUM( patip(:,:), dim=2 )
WHERE( pa_ip(:) /= 0._wp )
ph_ip(:) = SUM( phtip(:,:) * patip(:,:), dim=2 ) / pa_ip(:)
ph_il(:) = SUM( phtil(:,:) * patip(:,:), dim=2 ) / pa_ip(:)
ELSEWHERE
ph_ip(:) = 0._wp
ph_il(:) = 0._wp
END WHERE
!
DEALLOCATE( z1_ai, z1_vi, z1_vs )
!
END SUBROUTINE ice_var_itd_Nc1c
SUBROUTINE ice_var_itd_1cMc( phti, phts, pati , ph_i, ph_s, pa_i, &
& ptmi, ptms, ptmsu, psmi, patip, phtip, phtil, pt_i, pt_s, pt_su, ps_i, pa_ip, ph_ip, ph_il )
!!-------------------------------------------------------------------
!!
!! ** Purpose : converting 1-cat ice to jpl ice categories
!!
!!
!! ** Method: ice thickness distribution follows a gamma function from Abraham et al. (2015)
!! it has the property of conserving total concentration and volume
!!
!!
!! ** Arguments : phti: 1-cat ice thickness
!! phts: 1-cat snow depth
!! pati: 1-cat ice concentration
!!
!! ** Output : jpl-cat
!!
!! Abraham, C., Steiner, N., Monahan, A. and Michel, C., 2015.
!! Effects of subgrid‐scale snow thickness variability on radiative transfer in sea ice.
!! Journal of Geophysical Research: Oceans, 120(8), pp.5597-5614
!!-------------------------------------------------------------------
REAL(wp), DIMENSION(:), INTENT(in) :: phti, phts, pati ! input ice/snow variables
REAL(wp), DIMENSION(:,:), INTENT(inout) :: ph_i, ph_s, pa_i ! output ice/snow variables
REAL(wp), DIMENSION(:) , INTENT(in) :: ptmi, ptms, ptmsu, psmi, patip, phtip, phtil ! input ice/snow temp & sal & ponds
REAL(wp), DIMENSION(:,:), INTENT(inout) :: pt_i, pt_s, pt_su, ps_i, pa_ip, ph_ip, ph_il ! output ice/snow temp & sal & ponds
!
REAL(wp), ALLOCATABLE, DIMENSION(:) :: zfra, z1_hti
INTEGER :: ji, jk, jl
INTEGER :: idim
REAL(wp) :: zv, zdh
!!-------------------------------------------------------------------
!
idim = SIZE( phti , 1 )
!
ph_i(1:idim,1:jpl) = 0._wp
ph_s(1:idim,1:jpl) = 0._wp
pa_i(1:idim,1:jpl) = 0._wp
!
ALLOCATE( z1_hti(idim) )
WHERE( phti(:) /= 0._wp ) ; z1_hti(:) = 1._wp / phti(:)
ELSEWHERE ; z1_hti(:) = 0._wp
END WHERE
!
! == thickness and concentration == !
! for categories 1:jpl-1, integrate the gamma function from hi_max(jl-1) to hi_max(jl)
DO jl = 1, jpl-1
DO ji = 1, idim
!
IF( phti(ji) > 0._wp ) THEN
! concentration : integrate ((4A/H^2)xexp(-2x/H))dx from x=hi_max(jl-1) to hi_max(jl)
pa_i(ji,jl) = pati(ji) * z1_hti(ji) * ( ( phti(ji) + 2.*hi_max(jl-1) ) * EXP( -2.*hi_max(jl-1)*z1_hti(ji) ) &
& - ( phti(ji) + 2.*hi_max(jl ) ) * EXP( -2.*hi_max(jl )*z1_hti(ji) ) )
!
! volume : integrate ((4A/H^2)x^2exp(-2x/H))dx from x=hi_max(jl-1) to hi_max(jl)
zv = pati(ji) * z1_hti(ji) * ( ( phti(ji)*phti(ji) + 2.*phti(ji)*hi_max(jl-1) + 2.*hi_max(jl-1)*hi_max(jl-1) ) &
& * EXP( -2.*hi_max(jl-1)*z1_hti(ji) ) &
& - ( phti(ji)*phti(ji) + 2.*phti(ji)*hi_max(jl) + 2.*hi_max(jl)*hi_max(jl) ) &
& * EXP(-2.*hi_max(jl)*z1_hti(ji)) )
! thickness
IF( pa_i(ji,jl) > epsi06 ) THEN
ph_i(ji,jl) = zv / pa_i(ji,jl)
ELSE
ph_i(ji,jl) = 0.
pa_i(ji,jl) = 0.
ENDIF
ENDIF
!
ENDDO
ENDDO
!
! for the last category (jpl), integrate the gamma function from hi_max(jpl-1) to infinity
DO ji = 1, idim
!
IF( phti(ji) > 0._wp ) THEN
! concentration : integrate ((4A/H^2)xexp(-2x/H))dx from x=hi_max(jpl-1) to infinity
pa_i(ji,jpl) = pati(ji) * z1_hti(ji) * ( phti(ji) + 2.*hi_max(jpl-1) ) * EXP( -2.*hi_max(jpl-1)*z1_hti(ji) )
! volume : integrate ((4A/H^2)x^2exp(-2x/H))dx from x=hi_max(jpl-1) to infinity
zv = pati(ji) * z1_hti(ji) * ( phti(ji)*phti(ji) + 2.*phti(ji)*hi_max(jpl-1) + 2.*hi_max(jpl-1)*hi_max(jpl-1) ) &
& * EXP( -2.*hi_max(jpl-1)*z1_hti(ji) )
! thickness
IF( pa_i(ji,jpl) > epsi06 ) THEN
ph_i(ji,jpl) = zv / pa_i(ji,jpl)
else
ph_i(ji,jpl) = 0.
pa_i(ji,jpl) = 0.
ENDIF
ENDIF
!
ENDDO
!
! Add Snow in each category where pa_i is not 0
DO jl = 1, jpl
DO ji = 1, idim
IF( pa_i(ji,jl) > 0._wp ) THEN
ph_s(ji,jl) = ph_i(ji,jl) * phts(ji) * z1_hti(ji)
! In case snow load is in excess that would lead to transformation from snow to ice
! Then, transfer the snow excess into the ice (different from icethd_dh)
zdh = MAX( 0._wp, ( rhos * ph_s(ji,jl) + ( rhoi - rho0 ) * ph_i(ji,jl) ) * r1_rho0 )
! recompute h_i, h_s avoiding out of bounds values
ph_i(ji,jl) = MIN( hi_max(jl), ph_i(ji,jl) + zdh )
ph_s(ji,jl) = MAX( 0._wp, ph_s(ji,jl) - zdh * rhoi * r1_rhos )
ENDIF