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MODULE icethd_pnd
!!======================================================================
!! *** MODULE icethd_pnd ***
!! sea-ice: Melt ponds on top of sea ice
!!======================================================================
!! history : ! 2012 (O. Lecomte) Adaptation from Flocco and Turner
!! ! 2017 (M. Vancoppenolle, O. Lecomte, C. Rousset) Implementation
!! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube]
!!----------------------------------------------------------------------
#if defined key_si3
!!----------------------------------------------------------------------
!! 'key_si3' : SI3 sea-ice model
!!----------------------------------------------------------------------
!! ice_thd_pnd_init : some initialization and namelist read
!! ice_thd_pnd : main calling routine
!!----------------------------------------------------------------------
USE phycst ! physical constants
USE dom_oce ! ocean space and time domain
USE ice ! sea-ice: variables
USE ice1D ! sea-ice: thermodynamics variables
USE icetab ! sea-ice: 1D <==> 2D transformation
USE sbc_ice ! surface energy budget
!
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 timing ! Timing
IMPLICIT NONE
PRIVATE
PUBLIC ice_thd_pnd_init ! routine called by icestp.F90
PUBLIC ice_thd_pnd ! routine called by icestp.F90
INTEGER :: nice_pnd ! choice of the type of pond scheme
! ! associated indices:
INTEGER, PARAMETER :: np_pndNO = 0 ! No pond scheme
INTEGER, PARAMETER :: np_pndCST = 1 ! Constant ice pond scheme
INTEGER, PARAMETER :: np_pndLEV = 2 ! Level ice pond scheme
INTEGER, PARAMETER :: np_pndTOPO = 3 ! Level ice pond scheme
!--------------------------------------------------------------------------
! Diagnostics for pond volume per area
!
! dV/dt = mlt + drn + lid + rnf
! mlt = input from surface melting
! drn = drainage through brine network
! lid = lid growth & melt
! rnf = runoff (water directly removed out of surface melting + overflow)
!
! In topo mode, the pond water lost because it is in the snow is not included in the budget
! In level mode, all terms are incorporated
!
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: diag_dvpn_mlt ! meltwater pond volume input [kg/m2/s]
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: diag_dvpn_drn ! pond volume lost by drainage [-]
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: diag_dvpn_lid ! exchange with lid / refreezing [-]
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: diag_dvpn_rnf ! meltwater pond lost to runoff [-]
REAL(wp), ALLOCATABLE, DIMENSION(:) :: diag_dvpn_mlt_1d ! meltwater pond volume input [-]
REAL(wp), ALLOCATABLE, DIMENSION(:) :: diag_dvpn_drn_1d ! pond volume lost by drainage [-]
REAL(wp), ALLOCATABLE, DIMENSION(:) :: diag_dvpn_lid_1d ! exchange with lid / refreezing [-]
REAL(wp), ALLOCATABLE, DIMENSION(:) :: diag_dvpn_rnf_1d ! meltwater pond lost to runoff [-]
!! * Substitutions
# include "do_loop_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/ICE 4.0 , NEMO Consortium (2018)
!! $Id: icethd_pnd.F90 15244 2021-09-10 09:56:20Z clem $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
SUBROUTINE ice_thd_pnd
!!-------------------------------------------------------------------
!! *** ROUTINE ice_thd_pnd ***
!!
!! ** Purpose : change melt pond fraction and thickness
!!
!! ** Note : Melt ponds affect only radiative transfer for now
!! No heat, no salt.
!! The current diagnostics lacks a contribution from drainage
!!-------------------------------------------------------------------
INTEGER :: ji, jj, jl ! loop indices
!!-------------------------------------------------------------------
ALLOCATE( diag_dvpn_mlt(jpi,jpj), diag_dvpn_lid(jpi,jpj), diag_dvpn_drn(jpi,jpj), diag_dvpn_rnf(jpi,jpj) )
ALLOCATE( diag_dvpn_mlt_1d(jpij), diag_dvpn_lid_1d(jpij), diag_dvpn_drn_1d(jpij), diag_dvpn_rnf_1d(jpij) )
!
diag_dvpn_mlt (:,:) = 0._wp ; diag_dvpn_drn (:,:) = 0._wp
diag_dvpn_lid (:,:) = 0._wp ; diag_dvpn_rnf (:,:) = 0._wp
diag_dvpn_mlt_1d(:) = 0._wp ; diag_dvpn_drn_1d(:) = 0._wp
diag_dvpn_lid_1d(:) = 0._wp ; diag_dvpn_rnf_1d(:) = 0._wp
!-------------------------------------
! Remove ponds where ice has vanished
!-------------------------------------
at_i(:,:) = SUM( a_i, dim=3 )
!
DO jl = 1, jpl
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
IF( v_i(ji,jj,jl) < epsi10 .OR. at_i(ji,jj) < epsi10 ) THEN
wfx_pnd (ji,jj) = wfx_pnd(ji,jj) + ( v_ip(ji,jj,jl) + v_il(ji,jj,jl) ) * rhow * r1_Dt_ice
a_ip (ji,jj,jl) = 0._wp
v_ip (ji,jj,jl) = 0._wp
v_il (ji,jj,jl) = 0._wp
h_ip (ji,jj,jl) = 0._wp
h_il (ji,jj,jl) = 0._wp
a_ip_frac(ji,jj,jl) = 0._wp
ENDIF
END_2D
END DO
!------------------------------
! 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
!------------------------------------
! Select melt pond scheme to be used
!------------------------------------
IF( npti > 0 ) THEN
SELECT CASE ( nice_pnd )
!
CASE (np_pndCST) ; CALL pnd_CST !== Constant melt ponds ==!
!
CASE (np_pndLEV) ; CALL pnd_LEV !== Level ice melt ponds ==!
!
CASE (np_pndTOPO) ; CALL pnd_TOPO !== Topographic melt ponds ==!
!
END SELECT
ENDIF
!------------------------------------
! Diagnostics
!------------------------------------
CALL iom_put( 'dvpn_mlt', diag_dvpn_mlt ) ! input from melting
CALL iom_put( 'dvpn_lid', diag_dvpn_lid ) ! exchanges with lid
CALL iom_put( 'dvpn_drn', diag_dvpn_drn ) ! vertical drainage
CALL iom_put( 'dvpn_rnf', diag_dvpn_rnf ) ! runoff + overflow
!
DEALLOCATE( diag_dvpn_mlt , diag_dvpn_lid , diag_dvpn_drn , diag_dvpn_rnf )
DEALLOCATE( diag_dvpn_mlt_1d, diag_dvpn_lid_1d, diag_dvpn_drn_1d, diag_dvpn_rnf_1d )
END SUBROUTINE ice_thd_pnd
SUBROUTINE pnd_CST
!!-------------------------------------------------------------------
!! *** ROUTINE pnd_CST ***
!!
!! ** Purpose : Compute melt pond evolution
!!
!! ** Method : Melt pond fraction and thickness are prescribed
!! to non-zero values when t_su = 0C
!!
!! ** Tunable parameters : pond fraction (rn_apnd), pond depth (rn_hpnd)
!!
!! ** Note : Coupling with such melt ponds is only radiative
!! Advection, ridging, rafting... are bypassed
!!
!! ** References : Bush, G.W., and Trump, D.J. (2017)
!!-------------------------------------------------------------------
INTEGER :: ji, jl ! loop indices
REAL(wp) :: zdv_pnd ! Amount of water going into the ponds & lids
!!-------------------------------------------------------------------
DO jl = 1, jpl
CALL tab_2d_1d( npti, nptidx(1:npti), a_i_1d (1:npti), a_i (:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), t_su_1d (1:npti), t_su (:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), a_ip_1d (1:npti), a_ip (:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), h_ip_1d (1:npti), h_ip (:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), h_il_1d (1:npti), h_il (:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), wfx_pnd_1d(1:npti), wfx_pnd(:,:) )
DO ji = 1, npti
!
zdv_pnd = ( h_ip_1d(ji) + h_il_1d(ji) ) * a_ip_1d(ji)
!
IF( a_i_1d(ji) >= 0.01_wp .AND. t_su_1d(ji) >= rt0 ) THEN
h_ip_1d(ji) = rn_hpnd
a_ip_1d(ji) = rn_apnd * a_i_1d(ji)
h_il_1d(ji) = 0._wp ! no pond lids whatsoever
ELSE
h_ip_1d(ji) = 0._wp
a_ip_1d(ji) = 0._wp
h_il_1d(ji) = 0._wp
ENDIF
!
v_ip_1d(ji) = h_ip_1d(ji) * a_ip_1d(ji)
v_il_1d(ji) = h_il_1d(ji) * a_ip_1d(ji)
!
zdv_pnd = ( h_ip_1d(ji) + h_il_1d(ji) ) * a_ip_1d(ji) - zdv_pnd
wfx_pnd_1d(ji) = wfx_pnd_1d(ji) - zdv_pnd * rhow * r1_Dt_ice
!
END DO
CALL tab_1d_2d( npti, nptidx(1:npti), a_ip_1d (1:npti), a_ip (:,:,jl) )
CALL tab_1d_2d( npti, nptidx(1:npti), h_ip_1d (1:npti), h_ip (:,:,jl) )
CALL tab_1d_2d( npti, nptidx(1:npti), h_il_1d (1:npti), h_il (:,:,jl) )
CALL tab_1d_2d( npti, nptidx(1:npti), v_ip_1d (1:npti), v_ip (:,:,jl) )
CALL tab_1d_2d( npti, nptidx(1:npti), v_il_1d (1:npti), v_il (:,:,jl) )
CALL tab_1d_2d( npti, nptidx(1:npti), wfx_pnd_1d(1:npti), wfx_pnd(:,:) )
END DO
!
END SUBROUTINE pnd_CST
SUBROUTINE pnd_LEV
!!-------------------------------------------------------------------
!! *** ROUTINE pnd_LEV ***
!!
!! ** Purpose : Compute melt pond evolution
!!
!! ** Method : A fraction of meltwater is accumulated in ponds and sent to ocean when surface is freezing
!! We work with volumes and then redistribute changes into thickness and concentration
!! assuming linear relationship between the two.
!!
!! ** Action : - pond growth: Vp = Vp + dVmelt --- from Holland et al 2012 ---
!! dVmelt = (1-r)/rhow * ( rhoi*dh_i + rhos*dh_s ) * a_i
!! dh_i = meltwater from ice surface melt
!! dh_s = meltwater from snow melt
!! (1-r) = fraction of melt water that is not flushed
!!
!! - limtations: a_ip must not exceed (1-r)*a_i
!! h_ip must not exceed 0.5*h_i
!!
!! - pond shrinking:
!! if lids: Vp = Vp -dH * a_ip
!! dH = lid thickness change. Retrieved from this eq.: --- from Flocco et al 2010 ---
!!
!! rhoi * Lf * dH/dt = ki * MAX(Tp-Tsu,0) / H
!! H = lid thickness
!! Lf = latent heat of fusion
!! Tp = -2C
!!
!! And solved implicitely as:
!! H(t+dt)**2 -H(t) * H(t+dt) -ki * (Tp-Tsu) * dt / (rhoi*Lf) = 0
!!
!! if no lids: Vp = Vp * exp(0.01*MAX(Tp-Tsu,0)/Tp) --- from Holland et al 2012 ---
!!
!! - Flushing: w = -perm/visc * rho_oce * grav * Hp / Hi * flush --- from Flocco et al 2007 ---
!! perm = permability of sea-ice + correction from Hunke et al 2012 (flush)
!! visc = water viscosity
!! Hp = height of top of the pond above sea-level
!! Hi = ice thickness thru which there is flushing
!! flush= correction otherwise flushing is excessive
!!
!! - Corrections: remove melt ponds when lid thickness is 10 times the pond thickness
!!
!! - pond thickness and area is retrieved from pond volume assuming a linear relationship between h_ip and a_ip:
!! a_ip/a_i = a_ip_frac = h_ip / zaspect
!!
!! ** Tunable parameters : rn_apnd_max, rn_apnd_min, rn_pnd_flush
!!
!! ** Note : Mostly stolen from CICE but not only. These are between level-ice ponds and CESM ponds.
!!
!! ** References : Flocco and Feltham (JGR, 2007)
!! Flocco et al (JGR, 2010)
!! Holland et al (J. Clim, 2012)
!! Hunke et al (OM 2012)
!!-------------------------------------------------------------------
REAL(wp), DIMENSION(nlay_i) :: ztmp ! temporary array
!!
REAL(wp), PARAMETER :: zaspect = 0.8_wp ! pond aspect ratio
REAL(wp), PARAMETER :: zTp = -2._wp ! reference temperature
REAL(wp), PARAMETER :: zvisc = 1.79e-3_wp ! water viscosity
!!
REAL(wp) :: zfr_mlt, zdv_mlt, zdv_avail ! fraction and volume of available meltwater retained for melt ponding
REAL(wp) :: zdv_frz, zdv_flush ! Amount of melt pond that freezes, flushes
REAL(wp) :: zdv_pnd ! Amount of water going into the ponds & lids
REAL(wp) :: zhp ! heigh of top of pond lid wrt ssh
REAL(wp) :: zv_ip_max ! max pond volume allowed
REAL(wp) :: zdT ! zTp-t_su
REAL(wp) :: zsbr, ztmelts ! Brine salinity
REAL(wp) :: zperm ! permeability of sea ice
REAL(wp) :: zfac, zdum ! temporary arrays
REAL(wp) :: z1_rhow, z1_aspect, z1_Tp ! inverse
!!
INTEGER :: ji, jk, jl ! loop indices
!!-------------------------------------------------------------------
z1_rhow = 1._wp / rhow
z1_aspect = 1._wp / zaspect
z1_Tp = 1._wp / zTp
CALL tab_2d_1d( npti, nptidx(1:npti), at_i_1d (1:npti), at_i )
CALL tab_2d_1d( npti, nptidx(1:npti), wfx_pnd_1d (1:npti), wfx_pnd )
CALL tab_2d_1d( npti, nptidx(1:npti), diag_dvpn_mlt_1d (1:npti), diag_dvpn_mlt )
CALL tab_2d_1d( npti, nptidx(1:npti), diag_dvpn_drn_1d (1:npti), diag_dvpn_drn )
CALL tab_2d_1d( npti, nptidx(1:npti), diag_dvpn_lid_1d (1:npti), diag_dvpn_lid )
CALL tab_2d_1d( npti, nptidx(1:npti), diag_dvpn_rnf_1d (1:npti), diag_dvpn_rnf )
DO jl = 1, jpl
CALL tab_2d_1d( npti, nptidx(1:npti), a_i_1d (1:npti), a_i (:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), h_i_1d (1:npti), h_i (:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), t_su_1d (1:npti), t_su(:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), a_ip_1d (1:npti), a_ip(:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), h_ip_1d (1:npti), h_ip(:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), h_il_1d (1:npti), h_il(:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), dh_i_sum(1:npti), dh_i_sum_2d(:,:,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), dh_s_mlt(1:npti), dh_s_mlt_2d(:,:,jl) )
DO jk = 1, nlay_i
CALL tab_2d_1d( npti, nptidx(1:npti), sz_i_1d(1:npti,jk), sz_i(:,:,jk,jl) )
CALL tab_2d_1d( npti, nptidx(1:npti), t_i_1d (1:npti,jk), t_i (:,:,jk,jl) )
END DO
!-----------------------
! Melt pond calculations
!-----------------------
DO ji = 1, npti
!
zdv_pnd = ( h_ip_1d(ji) + h_il_1d(ji) ) * a_ip_1d(ji)
! !----------------------------------------------------!
IF( h_i_1d(ji) < rn_himin .OR. a_i_1d(ji) < 0.01_wp ) THEN ! Case ice thickness < rn_himin or tiny ice fraction !
! !----------------------------------------------------!
!--- Remove ponds on thin ice or tiny ice fractions
a_ip_1d(ji) = 0._wp
h_ip_1d(ji) = 0._wp
h_il_1d(ji) = 0._wp
! !--------------------------------!
ELSE ! Case ice thickness >= rn_himin !
! !--------------------------------!
v_ip_1d(ji) = h_ip_1d(ji) * a_ip_1d(ji) ! retrieve volume from thickness
v_il_1d(ji) = h_il_1d(ji) * a_ip_1d(ji)
!
!------------------!
! case ice melting !
!------------------!
!
!--- available meltwater for melt ponding (zdv_avail) ---!
zdv_avail = -( dh_i_sum(ji)*rhoi + dh_s_mlt(ji)*rhos ) * z1_rhow * a_i_1d(ji) ! > 0
zfr_mlt = rn_apnd_min + ( rn_apnd_max - rn_apnd_min ) * at_i_1d(ji) ! = ( 1 - r ) = fraction of melt water that is not flushed
zdv_mlt = MAX( 0._wp, zfr_mlt * zdv_avail ) ! max for roundoff errors?
!
!--- overflow ---!
!
! area driven overflow
! If pond area exceeds zfr_mlt * a_i_1d(ji) then reduce the pond volume
! a_ip_max = zfr_mlt * a_i
! => from zaspect = h_ip / (a_ip / a_i), set v_ip_max as:
zv_ip_max = zfr_mlt**2 * a_i_1d(ji) * zaspect
zdv_mlt = MAX( 0._wp, MIN( zdv_mlt, zv_ip_max - v_ip_1d(ji) ) )
! depth driven overflow
! If pond depth exceeds half the ice thickness then reduce the pond volume
! h_ip_max = 0.5 * h_i
! => from zaspect = h_ip / (a_ip / a_i), set v_ip_max as:
zv_ip_max = z1_aspect * a_i_1d(ji) * 0.25 * h_i_1d(ji) * h_i_1d(ji)
zdv_mlt = MAX( 0._wp, MIN( zdv_mlt, zv_ip_max - v_ip_1d(ji) ) )
!--- Pond growing ---!
v_ip_1d(ji) = v_ip_1d(ji) + zdv_mlt
!
!--- Lid melting ---!
IF( ln_pnd_lids ) v_il_1d(ji) = MAX( 0._wp, v_il_1d(ji) - zdv_mlt ) ! must be bounded by 0
!
!-------------------!
! case ice freezing ! i.e. t_su_1d(ji) < (zTp+rt0)
!-------------------!
!
zdT = MAX( zTp+rt0 - t_su_1d(ji), 0._wp )
!
!--- Pond contraction (due to refreezing) ---!
IF( ln_pnd_lids ) THEN
!
!--- Lid growing and subsequent pond shrinking ---!
zdv_frz = - 0.5_wp * MAX( 0._wp, -v_il_1d(ji) + & ! Flocco 2010 (eq. 5) solved implicitly as aH**2 + bH + c = 0
& SQRT( v_il_1d(ji)**2 + a_ip_1d(ji)**2 * 4._wp * rcnd_i * zdT * rDt_ice / (rLfus * rhow) ) ) ! max for roundoff errors
! Lid growing
v_il_1d(ji) = MAX( 0._wp, v_il_1d(ji) - zdv_frz )
! Pond shrinking
v_ip_1d(ji) = MAX( 0._wp, v_ip_1d(ji) + zdv_frz )
ELSE
zdv_frz = v_ip_1d(ji) * ( EXP( 0.01_wp * zdT * z1_Tp ) - 1._wp ) ! Holland 2012 (eq. 6)
! Pond shrinking
v_ip_1d(ji) = MAX( 0._wp, v_ip_1d(ji) + zdv_frz )
ENDIF
!
!--- Set new pond area and depth ---! assuming linear relation between h_ip and a_ip_frac
! v_ip = h_ip * a_ip
! a_ip/a_i = a_ip_frac = h_ip / zaspect (cf Holland 2012, fitting SHEBA so that knowing v_ip we can distribute it to a_ip and h_ip)
a_ip_1d(ji) = MIN( a_i_1d(ji), SQRT( v_ip_1d(ji) * z1_aspect * a_i_1d(ji) ) ) ! make sure a_ip < a_i
h_ip_1d(ji) = zaspect * a_ip_1d(ji) / a_i_1d(ji)
!
!------------------------------------------------!
! Pond drainage through brine network (flushing) !
!------------------------------------------------!
! height of top of the pond above sea-level
zhp = ( h_i_1d(ji) * ( rho0 - rhoi ) + h_ip_1d(ji) * ( rho0 - rhow * a_ip_1d(ji) / a_i_1d(ji) ) ) * r1_rho0
! Calculate the permeability of the ice (Assur 1958, see Flocco 2010)
DO jk = 1, nlay_i
! MV Assur is inconsistent with SI3
!!zsbr = - 1.2_wp &
!! & - 21.8_wp * ( t_i_1d(ji,jk) - rt0 ) &
!! & - 0.919_wp * ( t_i_1d(ji,jk) - rt0 )**2 &
!! & - 0.0178_wp * ( t_i_1d(ji,jk) - rt0 )**3
!!ztmp(jk) = sz_i_1d(ji,jk) / zsbr
! MV linear expression more consistent & simpler: zsbr = - ( t_i_1d(ji,jk) - rt0 ) / rTmlt
ztmelts = -rTmlt * sz_i_1d(ji,jk)
ztmp(jk) = ztmelts / MIN( ztmelts, t_i_1d(ji,jk) - rt0 )
END DO
zperm = MAX( 0._wp, 3.e-08_wp * MINVAL(ztmp)**3 )
! Do the drainage using Darcy's law
zdv_flush = -zperm * rho0 * grav * zhp * rDt_ice / (zvisc * h_i_1d(ji)) * a_ip_1d(ji) * rn_pnd_flush ! zflush comes from Hunke et al. (2012)
zdv_flush = MAX( zdv_flush, -v_ip_1d(ji) ) ! < 0
v_ip_1d(ji) = v_ip_1d(ji) + zdv_flush
!--- Set new pond area and depth ---! assuming linear relation between h_ip and a_ip_frac
a_ip_1d(ji) = MIN( a_i_1d(ji), SQRT( v_ip_1d(ji) * z1_aspect * a_i_1d(ji) ) ) ! make sure a_ip < a_i
h_ip_1d(ji) = zaspect * a_ip_1d(ji) / a_i_1d(ji)
!--- Corrections and lid thickness ---!
IF( ln_pnd_lids ) THEN
!--- retrieve lid thickness from volume ---!
IF( a_ip_1d(ji) > 0.01_wp ) THEN ; h_il_1d(ji) = v_il_1d(ji) / a_ip_1d(ji)
ELSE ; h_il_1d(ji) = 0._wp
ENDIF
!--- remove ponds if lids are much larger than ponds ---!
IF ( h_il_1d(ji) > h_ip_1d(ji) * 10._wp ) THEN
a_ip_1d(ji) = 0._wp
h_ip_1d(ji) = 0._wp
h_il_1d(ji) = 0._wp
ENDIF
ENDIF
! diagnostics: dvpnd = mlt+rnf+lid+drn
diag_dvpn_mlt_1d(ji) = diag_dvpn_mlt_1d(ji) + rhow * zdv_avail * r1_Dt_ice ! > 0, surface melt input
diag_dvpn_rnf_1d(ji) = diag_dvpn_rnf_1d(ji) + rhow * ( zdv_mlt - zdv_avail ) * r1_Dt_ice ! < 0, runoff
diag_dvpn_lid_1d(ji) = diag_dvpn_lid_1d(ji) + rhow * zdv_frz * r1_Dt_ice ! < 0, shrinking
diag_dvpn_drn_1d(ji) = diag_dvpn_drn_1d(ji) + rhow * zdv_flush * r1_Dt_ice ! < 0, drainage
!
ENDIF
!
v_ip_1d(ji) = h_ip_1d(ji) * a_ip_1d(ji)
v_il_1d(ji) = h_il_1d(ji) * a_ip_1d(ji)
!
zdv_pnd = ( h_ip_1d(ji) + h_il_1d(ji) ) * a_ip_1d(ji) - zdv_pnd
wfx_pnd_1d(ji) = wfx_pnd_1d(ji) - zdv_pnd * rhow * r1_Dt_ice
!
END DO
!--------------------------------------------------------------------
! Retrieve 2D arrays
!--------------------------------------------------------------------
CALL tab_1d_2d( npti, nptidx(1:npti), a_ip_1d(1:npti), a_ip(:,:,jl) )
CALL tab_1d_2d( npti, nptidx(1:npti), h_ip_1d(1:npti), h_ip(:,:,jl) )
CALL tab_1d_2d( npti, nptidx(1:npti), h_il_1d(1:npti), h_il(:,:,jl) )
CALL tab_1d_2d( npti, nptidx(1:npti), v_ip_1d(1:npti), v_ip(:,:,jl) )
CALL tab_1d_2d( npti, nptidx(1:npti), v_il_1d(1:npti), v_il(:,:,jl) )
!
END DO
!
CALL tab_1d_2d( npti, nptidx(1:npti), wfx_pnd_1d(1:npti), wfx_pnd )
!
CALL tab_1d_2d( npti, nptidx(1:npti), diag_dvpn_mlt_1d (1:npti), diag_dvpn_mlt )
CALL tab_1d_2d( npti, nptidx(1:npti), diag_dvpn_drn_1d (1:npti), diag_dvpn_drn )
CALL tab_1d_2d( npti, nptidx(1:npti), diag_dvpn_lid_1d (1:npti), diag_dvpn_lid )
CALL tab_1d_2d( npti, nptidx(1:npti), diag_dvpn_rnf_1d (1:npti), diag_dvpn_rnf )
!
END SUBROUTINE pnd_LEV
SUBROUTINE pnd_TOPO
!!-------------------------------------------------------------------
!! *** ROUTINE pnd_TOPO ***
!!
!! ** Purpose : Compute melt pond evolution based on the ice
!! topography inferred from the ice thickness distribution
!!
!! ** Method : This code is initially based on Flocco and Feltham
!! (2007) and Flocco et al. (2010).
!!
!! - Calculate available pond water base on surface meltwater
!! - Redistribute water as a function of topography, drain water
!! - Exchange water with the lid
!!
!! ** Tunable parameters :
!!
!! ** Note :
!!
!! ** References
!!
!! Flocco, D. and D. L. Feltham, 2007. A continuum model of melt pond
!! evolution on Arctic sea ice. J. Geophys. Res. 112, C08016, doi:
!! 10.1029/2006JC003836.
!!
!! Flocco, D., D. L. Feltham and A. K. Turner, 2010. Incorporation of
!! a physically based melt pond scheme into the sea ice component of a
!! climate model. J. Geophys. Res. 115, C08012,
!! doi: 10.1029/2009JC005568.
!!
!!-------------------------------------------------------------------
REAL(wp), PARAMETER :: & ! shared parameters for topographic melt ponds
zTd = 273._wp , & ! temperature difference for freeze-up (K)
zvp_min = 1.e-4_wp ! minimum pond volume (m)
! local variables
REAL(wp) :: &
zdHui, & ! change in thickness of ice lid (m)
zomega, & ! conduction
zdTice, & ! temperature difference across ice lid (C)
zdvice, & ! change in ice volume (m)
zTavg, & ! mean surface temperature across categories (C)
zfsurf, & ! net heat flux, excluding conduction and transmitted radiation (W/m2)
zTp, & ! pond freezing temperature (C)
zrhoi_L, & ! volumetric latent heat of sea ice (J/m^3)
zfr_mlt, & ! fraction and volume of available meltwater retained for melt ponding
z1_rhow, & ! inverse water density
zv_pnd , & ! volume of meltwater contributing to ponds
zv_mlt ! total amount of meltwater produced
REAL(wp), DIMENSION(jpi,jpj) :: zvolp_ini , & !! total melt pond water available before redistribution and drainage
zvolp , & !! total melt pond water volume
zvolp_res !! remaining melt pond water available after drainage
REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_a_i
INTEGER :: ji, jj, jk, jl ! loop indices
INTEGER :: i_test
! Note
! equivalent for CICE translation
! a_ip -> apond
! a_ip_frac -> apnd
CALL ctl_stop( 'STOP', 'icethd_pnd : topographic melt ponds are still an ongoing work' )
!---------------------------------------------------------------
! Initialise
!---------------------------------------------------------------
! Parameters & constants (move to parameters)
zrhoi_L = rhoi * rLfus ! volumetric latent heat (J/m^3)
zTp = rt0 - 0.15_wp ! pond freezing point, slightly below 0C (ponds are bid saline)
z1_rhow = 1._wp / rhow
! Set required ice variables (hard-coded here for now)
! zfpond(:,:) = 0._wp ! contributing freshwater flux (?)
at_i (:,:) = SUM( a_i (:,:,:), dim=3 ) ! ice fraction
vt_i (:,:) = SUM( v_i (:,:,:), dim=3 ) ! volume per grid area
vt_ip(:,:) = SUM( v_ip(:,:,:), dim=3 ) ! pond volume per grid area
vt_il(:,:) = SUM( v_il(:,:,:), dim=3 ) ! lid volume per grid area
! thickness
WHERE( a_i(:,:,:) > epsi20 ) ; z1_a_i(:,:,:) = 1._wp / a_i(:,:,:)
ELSEWHERE ; z1_a_i(:,:,:) = 0._wp
END WHERE
h_i(:,:,:) = v_i (:,:,:) * z1_a_i(:,:,:)
!---------------------------------------------------------------
! Change 2D to 1D
!---------------------------------------------------------------
! MV
! a less computing-intensive version would have 2D-1D passage here
! use what we have in iceitd.F90 (incremental remapping)
!--------------------------------------------------------------
! Collect total available pond water volume
!--------------------------------------------------------------
! Assuming that meltwater (+rain in principle) runsoff the surface
! Holland et al (2012) suggest that the fraction of runoff decreases with total ice fraction
! I cite her words, they are very talkative
! "grid cells with very little ice cover (and hence more open water area)
! have a higher runoff fraction to rep- resent the greater proximity of ice to open water."
! "This results in the same runoff fraction r for each ice category within a grid cell"
zvolp(:,:) = 0._wp
DO jl = 1, jpl
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
IF ( a_i(ji,jj,jl) > epsi10 ) THEN
!--- Available and contributing meltwater for melt ponding ---!
zv_mlt = - ( dh_i_sum_2d(ji,jj,jl) * rhoi + dh_s_mlt_2d(ji,jj,jl) * rhos ) & ! available volume of surface melt water per grid area
& * z1_rhow * a_i(ji,jj,jl)
! MV -> could move this directly in ice_thd_dh and get an array (ji,jj,jl) for surface melt water volume per grid area
zfr_mlt = rn_apnd_min + ( rn_apnd_max - rn_apnd_min ) * at_i(ji,jj) ! fraction of surface meltwater going to ponds
zv_pnd = zfr_mlt * zv_mlt ! contributing meltwater volume for category jl
diag_dvpn_mlt(ji,jj) = diag_dvpn_mlt(ji,jj) + zv_mlt * r1_Dt_ice ! diags
diag_dvpn_rnf(ji,jj) = diag_dvpn_rnf(ji,jj) + ( 1. - zfr_mlt ) * zv_mlt * r1_Dt_ice
!--- Create possible new ponds
! if pond does not exist, create new pond over full ice area
!IF ( a_ip_frac(ji,jj,jl) < epsi10 ) THEN
IF ( a_ip(ji,jj,jl) < epsi10 ) THEN
a_ip(ji,jj,jl) = a_i(ji,jj,jl)
a_ip_frac(ji,jj,jl) = 1.0_wp ! pond fraction of sea ice (apnd for CICE)
ENDIF
!--- Deepen existing ponds with no change in pond fraction, before redistribution and drainage
v_ip(ji,jj,jl) = v_ip(ji,jj,jl) + zv_pnd ! use pond water to increase thickness
h_ip(ji,jj,jl) = v_ip(ji,jj,jl) / a_ip(ji,jj,jl)
!--- Total available pond water volume (pre-existing + newly produced)j
zvolp(ji,jj) = zvolp(ji,jj) + v_ip(ji,jj,jl)
! zfpond(ji,jj) = zfpond(ji,jj) + zpond * a_ip_frac(ji,jj,jl) ! useless for now
ENDIF ! a_i
END_2D
END DO ! ji
zvolp_ini(:,:) = zvolp(:,:)
!--------------------------------------------------------------
! Redistribute and drain water from ponds
!--------------------------------------------------------------
CALL ice_thd_pnd_area( zvolp, zvolp_res )
!--------------------------------------------------------------
! Melt pond lid growth and melt
!--------------------------------------------------------------
IF( ln_pnd_lids ) THEN
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
IF ( at_i(ji,jj) > 0.01 .AND. hm_i(ji,jj) > rn_himin .AND. zvolp_ini(ji,jj) > zvp_min * at_i(ji,jj) ) THEN
!--------------------------
! Pond lid growth and melt
!--------------------------
! Mean surface temperature
zTavg = 0._wp
DO jl = 1, jpl
zTavg = zTavg + t_su(ji,jj,jl)*a_i(ji,jj,jl)
END DO
zTavg = zTavg / a_i(ji,jj,jl) !!! could get a division by zero here
DO jl = 1, jpl-1
IF ( v_il(ji,jj,jl) > epsi10 ) THEN
!----------------------------------------------------------------
! Lid melting: floating upper ice layer melts in whole or part
!----------------------------------------------------------------
! Use Tsfc for each category
IF ( t_su(ji,jj,jl) > zTp ) THEN
zdvice = MIN( -dh_i_sum_2d(ji,jj,jl)*a_ip(ji,jj,jl), v_il(ji,jj,jl) )
IF ( zdvice > epsi10 ) THEN
v_il (ji,jj,jl) = v_il (ji,jj,jl) - zdvice
v_ip(ji,jj,jl) = v_ip(ji,jj,jl) + zdvice ! MV: not sure i understand dh_i_sum seems counted twice -
! as it is already counted in surface melt
! zvolp(ji,jj) = zvolp(ji,jj) + zdvice ! pointless to calculate total volume (done in icevar)
! zfpond(ji,jj) = fpond(ji,jj) + zdvice ! pointless to follow fw budget (ponds have no fw)
IF ( v_il(ji,jj,jl) < epsi10 .AND. v_ip(ji,jj,jl) > epsi10) THEN
! ice lid melted and category is pond covered
v_ip(ji,jj,jl) = v_ip(ji,jj,jl) + v_il(ji,jj,jl)
! zfpond(ji,jj) = zfpond (ji,jj) + v_il(ji,jj,jl)
v_il(ji,jj,jl) = 0._wp
ENDIF
h_ip(ji,jj,jl) = v_ip(ji,jj,jl) / a_ip(ji,jj,jl) !!! could get a division by zero here
diag_dvpn_lid(ji,jj) = diag_dvpn_lid(ji,jj) + zdvice ! diag
ENDIF
!----------------------------------------------------------------
! Freeze pre-existing lid
!----------------------------------------------------------------
ELSE IF ( v_ip(ji,jj,jl) > epsi10 ) THEN ! Tsfcn(i,j,n) <= Tp
! differential growth of base of surface floating ice layer
zdTice = MAX( - ( t_su(ji,jj,jl) - zTd ) , 0._wp ) ! > 0
zomega = rcnd_i * zdTice / zrhoi_L
zdHui = SQRT( 2._wp * zomega * rDt_ice + ( v_il(ji,jj,jl) / a_i(ji,jj,jl) )**2 ) &
- v_il(ji,jj,jl) / a_i(ji,jj,jl)
zdvice = min( zdHui*a_ip(ji,jj,jl) , v_ip(ji,jj,jl) )
IF ( zdvice > epsi10 ) THEN
v_il (ji,jj,jl) = v_il(ji,jj,jl) + zdvice
v_ip(ji,jj,jl) = v_ip(ji,jj,jl) - zdvice
! zvolp(ji,jj) = zvolp(ji,jj) - zdvice
! zfpond(ji,jj) = zfpond(ji,jj) - zdvice
h_ip(ji,jj,jl) = v_ip(ji,jj,jl) / a_ip(ji,jj,jl)
diag_dvpn_lid(ji,jj) = diag_dvpn_lid(ji,jj) - zdvice ! diag
ENDIF
ENDIF ! Tsfcn(i,j,n)
!----------------------------------------------------------------
! Freeze new lids
!----------------------------------------------------------------
! upper ice layer begins to form
! note: albedo does not change
ELSE ! v_il < epsi10
! thickness of newly formed ice
! the surface temperature of a meltpond is the same as that
! of the ice underneath (0C), and the thermodynamic surface
! flux is the same
!!! we need net surface energy flux, excluding conduction
!!! fsurf is summed over categories in CICE
!!! we have the category-dependent flux, let us use it ?
zfsurf = qns_ice(ji,jj,jl) + qsr_ice(ji,jj,jl)
zdHui = MAX ( -zfsurf * rDt_ice/zrhoi_L , 0._wp )
zdvice = MIN ( zdHui * a_ip(ji,jj,jl) , v_ip(ji,jj,jl) )
IF ( zdvice > epsi10 ) THEN
v_il (ji,jj,jl) = v_il(ji,jj,jl) + zdvice
v_ip(ji,jj,jl) = v_ip(ji,jj,jl) - zdvice
diag_dvpn_lid(ji,jj) = diag_dvpn_lid(ji,jj) - zdvice ! diag
! zvolp(ji,jj) = zvolp(ji,jj) - zdvice
! zfpond(ji,jj) = zfpond(ji,jj) - zdvice
h_ip(ji,jj,jl) = v_ip(ji,jj,jl) / a_ip(ji,jj,jl) ! MV - in principle, this is useless as h_ip is computed in icevar
ENDIF
ENDIF ! v_il
END DO ! jl
ELSE ! remove ponds on thin ice
v_ip(ji,jj,:) = 0._wp
v_il(ji,jj,:) = 0._wp
! zfpond(ji,jj) = zfpond(ji,jj)- zvolp(ji,jj)
! zvolp(ji,jj) = 0._wp
ENDIF
END_2D
ENDIF ! ln_pnd_lids
!---------------------------------------------------------------
! Clean-up variables (probably duplicates what icevar would do)
!---------------------------------------------------------------
! MV comment
! In the ideal world, the lines above should update only v_ip, a_ip, v_il
! icevar should recompute all other variables (if needed at all)
DO jl = 1, jpl
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
! ! zap lids on small ponds
! IF ( a_i(ji,jj,jl) > epsi10 .AND. v_ip(ji,jj,jl) < epsi10 &
! .AND. v_il(ji,jj,jl) > epsi10) THEN
! v_il(ji,jj,jl) = 0._wp ! probably uselesss now since we get zap_small
! ENDIF
! recalculate equivalent pond variables
IF ( a_ip(ji,jj,jl) > epsi10) THEN
h_ip(ji,jj,jl) = v_ip(ji,jj,jl) / a_ip(ji,jj,jl)
a_ip_frac(ji,jj,jl) = a_ip(ji,jj,jl) / a_i(ji,jj,jl) ! MV in principle, useless as computed in icevar
h_il(ji,jj,jl) = v_il(ji,jj,jl) / a_ip(ji,jj,jl) ! MV in principle, useless as computed in icevar
ENDIF
! h_ip(ji,jj,jl) = 0._wp ! MV in principle, useless as computed in icevar
! h_il(ji,jj,jl) = 0._wp ! MV in principle, useless as omputed in icevar
! ENDIF
END_2D
END DO ! jl
END SUBROUTINE pnd_TOPO
SUBROUTINE ice_thd_pnd_area( zvolp , zdvolp )
!!-------------------------------------------------------------------
!! *** ROUTINE ice_thd_pnd_area ***
!!
!! ** Purpose : Given the total volume of available pond water,
!! redistribute and drain water
!!
!! ** Method
!!
!-----------|
! |
! |-----------|
!___________|___________|______________________________________sea-level
! | |
! | |---^--------|
! | | | |
! | | | |-----------| |-------
! | | | alfan | | |
! | | | | |--------------|
! | | | | | |
!---------------------------v-------------------------------------------
! | | ^ | | |
! | | | | |--------------|
! | | | betan | | |
! | | | |-----------| |-------
! | | | |
! | |---v------- |
! | |
! |-----------|
! |
!-----------|
!
!!
!!------------------------------------------------------------------
REAL (wp), DIMENSION(jpi,jpj), INTENT(INOUT) :: &
zvolp, & ! total available pond water
zdvolp ! remaining meltwater after redistribution
INTEGER :: &
ns, &
m_index, &
permflag
REAL (wp), DIMENSION(jpl) :: &
hicen, &
hsnon, &
asnon, &
alfan, &
betan, &
cum_max_vol, &
reduced_aicen
REAL (wp), DIMENSION(0:jpl) :: &
cum_max_vol_tmp
REAL (wp) :: &
hpond, &
drain, &
floe_weight, &
pressure_head, &
hsl_rel, &
deltah, &
perm, &
msno
REAL (wp), parameter :: &
viscosity = 1.79e-3_wp ! kinematic water viscosity in kg/m/s
REAL(wp), PARAMETER :: & ! shared parameters for topographic melt ponds
zvp_min = 1.e-4_wp ! minimum pond volume (m)
INTEGER :: ji, jj, jk, jl ! loop indices
a_ip(:,:,:) = 0._wp
h_ip(:,:,:) = 0._wp
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
IF ( at_i(ji,jj) > 0.01 .AND. hm_i(ji,jj) > rn_himin .AND. zvolp(ji,jj) > zvp_min * at_i(ji,jj) ) THEN
!-------------------------------------------------------------------
! initialize
!-------------------------------------------------------------------
DO jl = 1, jpl
!----------------------------------------
! compute the effective snow fraction
!----------------------------------------
IF (a_i(ji,jj,jl) < epsi10) THEN
hicen(jl) = 0._wp
hsnon(jl) = 0._wp
reduced_aicen(jl) = 0._wp
asnon(jl) = 0._wp !js: in CICE 5.1.2: make sense as the compiler may not initiate the variables
ELSE
hicen(jl) = v_i(ji,jj,jl) / a_i(ji,jj,jl)
hsnon(jl) = v_s(ji,jj,jl) / a_i(ji,jj,jl)
reduced_aicen(jl) = 1._wp ! n=jpl
!js: initial code in NEMO_DEV
!IF (n < jpl) reduced_aicen(jl) = aicen(jl) &
! * (-0.024_wp*hicen(jl) + 0.832_wp)
!js: from CICE 5.1.2: this limit reduced_aicen to 0.2 when hicen is too large
IF (jl < jpl) reduced_aicen(jl) = a_i(ji,jj,jl) &
* max(0.2_wp,(-0.024_wp*hicen(jl) + 0.832_wp))
asnon(jl) = reduced_aicen(jl) ! effective snow fraction (empirical)
! MV should check whether this makes sense to have the same effective snow fraction in here
! OLI: it probably doesn't
END IF
! This choice for alfa and beta ignores hydrostatic equilibium of categories.
! Hydrostatic equilibium of the entire ITD is accounted for below, assuming
! a surface topography implied by alfa=0.6 and beta=0.4, and rigidity across all
! categories. alfa and beta partition the ITD - they are areas not thicknesses!
! Multiplying by hicen, alfan and betan (below) are thus volumes per unit area.
! Here, alfa = 60% of the ice area (and since hice is constant in a category,
! alfan = 60% of the ice volume) in each category lies above the reference line,
! and 40% below. Note: p6 is an arbitrary choice, but alfa+beta=1 is required.
! MV:
! Note that this choice is not in the original FF07 paper and has been adopted in CICE
! No reason why is explained in the doc, but I guess there is a reason. I'll try to investigate, maybe
! Where does that choice come from ? => OLI : Coz' Chuck Norris said so...
alfan(jl) = 0.6 * hicen(jl)
betan(jl) = 0.4 * hicen(jl)
cum_max_vol(jl) = 0._wp
cum_max_vol_tmp(jl) = 0._wp
END DO ! jpl
cum_max_vol_tmp(0) = 0._wp
drain = 0._wp
zdvolp(ji,jj) = 0._wp
!----------------------------------------------------------
! Drain overflow water, update pond fraction and volume
!----------------------------------------------------------
!--------------------------------------------------------------------------
! the maximum amount of water that can be contained up to each ice category
!--------------------------------------------------------------------------
! If melt ponds are too deep to be sustainable given the ITD (OVERFLOW)
! Then the excess volume cum_max_vol(jl) drains out of the system
! It should be added to wfx_pnd_out
DO jl = 1, jpl-1 ! last category can not hold any volume
IF (alfan(jl+1) >= alfan(jl) .AND. alfan(jl+1) > 0._wp ) THEN
! total volume in level including snow
cum_max_vol_tmp(jl) = cum_max_vol_tmp(jl-1) + &
(alfan(jl+1) - alfan(jl)) * sum(reduced_aicen(1:jl))
! subtract snow solid volumes from lower categories in current level
DO ns = 1, jl
cum_max_vol_tmp(jl) = cum_max_vol_tmp(jl) &
- rhos/rhow * & ! free air fraction that can be filled by water
asnon(ns) * & ! effective areal fraction of snow in that category
max(min(hsnon(ns)+alfan(ns)-alfan(jl), alfan(jl+1)-alfan(jl)), 0._wp)
END DO
ELSE ! assume higher categories unoccupied
cum_max_vol_tmp(jl) = cum_max_vol_tmp(jl-1)
END IF
!IF (cum_max_vol_tmp(jl) < z0) THEN
! CALL abort_ice('negative melt pond volume')
!END IF
END DO
cum_max_vol_tmp(jpl) = cum_max_vol_tmp(jpl-1) ! last category holds no volume
cum_max_vol (1:jpl) = cum_max_vol_tmp(1:jpl)
!----------------------------------------------------------------
! is there more meltwater than can be held in the floe?
!----------------------------------------------------------------
IF (zvolp(ji,jj) >= cum_max_vol(jpl)) THEN
drain = zvolp(ji,jj) - cum_max_vol(jpl) + epsi10
zvolp(ji,jj) = zvolp(ji,jj) - drain ! update meltwater volume available
diag_dvpn_rnf(ji,jj) = - drain ! diag - overflow counted in the runoff part (arbitrary choice)
zdvolp(ji,jj) = drain ! this is the drained water
IF (zvolp(ji,jj) < epsi10) THEN
zdvolp(ji,jj) = zdvolp(ji,jj) + zvolp(ji,jj)
zvolp(ji,jj) = 0._wp
END IF
END IF
! height and area corresponding to the remaining volume
! routine leaves zvolp unchanged
CALL ice_thd_pnd_depth(reduced_aicen, asnon, hsnon, alfan, zvolp(ji,jj), cum_max_vol, hpond, m_index)
DO jl = 1, m_index
!h_ip(jl) = hpond - alfan(jl) + alfan(1) ! here oui choulde update
! ! volume instead, no ?
h_ip(ji,jj,jl) = max((hpond - alfan(jl) + alfan(1)), 0._wp) !js: from CICE 5.1.2
a_ip(ji,jj,jl) = reduced_aicen(jl)
! in practise, pond fraction depends on the empirical snow fraction
! so in turn on ice thickness
END DO
!zapond = sum(a_ip(1:m_index)) !js: from CICE 5.1.2; not in Icepack1.1.0-6-gac6195d