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!------------------------------------------------------------------------
! Drainage through brine network (permeability)
!------------------------------------------------------------------------
!!! drainage due to ice permeability - Darcy's law
! sea water level
msno = 0._wp
DO jl = 1 , jpl
msno = msno + v_s(ji,jj,jl) * rhos
END DO
floe_weight = ( msno + rhoi*vt_i(ji,jj) + rho0*zvolp(ji,jj) ) / at_i(ji,jj)
hsl_rel = floe_weight / rho0 &
- ( ( sum(betan(:)*a_i(ji,jj,:)) / at_i(ji,jj) ) + alfan(1) )
deltah = hpond - hsl_rel
pressure_head = grav * rho0 * max(deltah, 0._wp)
! drain if ice is permeable
permflag = 0
IF (pressure_head > 0._wp) THEN
DO jl = 1, jpl-1
IF ( hicen(jl) /= 0._wp ) THEN
!IF (hicen(jl) > 0._wp) THEN !js: from CICE 5.1.2
perm = 0._wp ! MV ugly dummy patch
CALL ice_thd_pnd_perm(t_i(ji,jj,:,jl), sz_i(ji,jj,:,jl), perm) ! bof
IF (perm > 0._wp) permflag = 1
drain = perm*a_ip(ji,jj,jl)*pressure_head*rDt_ice / &
(viscosity*hicen(jl))
zdvolp(ji,jj) = zdvolp(ji,jj) + min(drain, zvolp(ji,jj))
zvolp(ji,jj) = max(zvolp(ji,jj) - drain, 0._wp)
diag_dvpn_drn(ji,jj) = - drain ! diag (could be better coded)
IF (zvolp(ji,jj) < epsi10) THEN
zdvolp(ji,jj) = zdvolp(ji,jj) + zvolp(ji,jj)
zvolp(ji,jj) = 0._wp
END IF
END IF
END DO
! adjust melt pond dimensions
IF (permflag > 0) THEN
! recompute pond depth
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(ji,jj,jl) = hpond - alfan(jl) + alfan(1)
a_ip(ji,jj,jl) = reduced_aicen(jl)
END DO
!zapond = sum(a_ip(1:m_index)) !js: from CICE 5.1.2; not in Icepack1.1.0-6-gac6195d
END IF
END IF ! pressure_head
!-------------------------------
! remove water from the snow
!-------------------------------
!------------------------------------------------------------------------
! total melt pond volume in category does not include snow volume
! snow in melt ponds is not melted
!------------------------------------------------------------------------
! MV here, it seems that we remove some meltwater from the ponds, but I can't really tell
! how much, so I did not diagnose it
! so if there is a problem here, nobody is going to see it...
! Calculate pond volume for lower categories
DO jl = 1,m_index-1
v_ip(ji,jj,jl) = a_ip(ji,jj,jl) * h_ip(ji,jj,jl) & ! what is not in the snow
- (rhos/rhow) * asnon(jl) * min(hsnon(jl), h_ip(ji,jj,jl))
END DO
! Calculate pond volume for highest category = remaining pond volume
! The following is completely unclear to Martin at least
! Could we redefine properly and recode in a more readable way ?
! m_index = last category with melt pond
IF (m_index == 1) v_ip(ji,jj,m_index) = zvolp(ji,jj) ! volume of mw in 1st category is the total volume of melt water
IF (m_index > 1) THEN
IF (zvolp(ji,jj) > sum( v_ip(ji,jj,1:m_index-1))) THEN
v_ip(ji,jj,m_index) = zvolp(ji,jj) - sum(v_ip(ji,jj,1:m_index-1))
ELSE
v_ip(ji,jj,m_index) = 0._wp
h_ip(ji,jj,m_index) = 0._wp
a_ip(ji,jj,m_index) = 0._wp
! If remaining pond volume is negative reduce pond volume of
! lower category
IF ( zvolp(ji,jj) + epsi10 < SUM(v_ip(ji,jj,1:m_index-1))) &
v_ip(ji,jj,m_index-1) = v_ip(ji,jj,m_index-1) - sum(v_ip(ji,jj,1:m_index-1)) + zvolp(ji,jj)
END IF
END IF
DO jl = 1,m_index
IF (a_ip(ji,jj,jl) > epsi10) THEN
h_ip(ji,jj,jl) = v_ip(ji,jj,jl) / a_ip(ji,jj,jl)
ELSE
zdvolp(ji,jj) = zdvolp(ji,jj) + v_ip(ji,jj,jl)
h_ip(ji,jj,jl) = 0._wp
v_ip(ji,jj,jl) = 0._wp
a_ip(ji,jj,jl) = 0._wp
END IF
END DO
DO jl = m_index+1, jpl
h_ip(ji,jj,jl) = 0._wp
a_ip(ji,jj,jl) = 0._wp
v_ip(ji,jj,jl) = 0._wp
END DO
ENDIF
END_2D
END SUBROUTINE ice_thd_pnd_area
SUBROUTINE ice_thd_pnd_depth(aicen, asnon, hsnon, alfan, zvolp, cum_max_vol, hpond, m_index)
!!-------------------------------------------------------------------
!! *** ROUTINE ice_thd_pnd_depth ***
!!
!! ** Purpose : Compute melt pond depth
!!-------------------------------------------------------------------
REAL (wp), DIMENSION(jpl), INTENT(IN) :: &
aicen, &
asnon, &
hsnon, &
alfan, &
cum_max_vol
REAL (wp), INTENT(IN) :: &
zvolp
REAL (wp), INTENT(OUT) :: &
hpond
INTEGER, INTENT(OUT) :: &
m_index
INTEGER :: n, ns
REAL (wp), DIMENSION(0:jpl+1) :: &
hitl, &
aicetl
REAL (wp) :: &
rem_vol, &
area, &
vol, &
tmp, &
z0 = 0.0_wp
!----------------------------------------------------------------
! hpond is zero if zvolp is zero - have we fully drained?
!----------------------------------------------------------------
IF (zvolp < epsi10) THEN
hpond = z0
m_index = 0
ELSE
!----------------------------------------------------------------
! Calculate the category where water fills up to
!----------------------------------------------------------------
!----------|
! |
! |
! |----------| -- --
!__________|__________|_________________________________________ ^
! | | rem_vol ^ | Semi-filled
! | |----------|-- -- -- - ---|-- ---- -- -- --v layer
! | | | |
! | | | |hpond
! | | |----------| | |-------
! | | | | | |
! | | | |---v-----|
! | | m_index | | |
!-------------------------------------------------------------
m_index = 0 ! 1:m_index categories have water in them
DO n = 1, jpl
IF (zvolp <= cum_max_vol(n)) THEN
m_index = n
IF (n == 1) THEN
rem_vol = zvolp
ELSE
rem_vol = zvolp - cum_max_vol(n-1)
END IF
exit ! to break out of the loop
END IF
END DO
m_index = min(jpl-1, m_index)
!----------------------------------------------------------------
! semi-filled layer may have m_index different snow in it
!----------------------------------------------------------------
!----------------------------------------------------------- ^
! | alfan(m_index+1)
! |
!hitl(3)--> |----------| |
!hitl(2)--> |------------| * * * * *| |
!hitl(1)--> |----------|* * * * * * |* * * * * | |
!hitl(0)-->------------------------------------------------- | ^
! various snow from lower categories | |alfa(m_index)
! hitl - heights of the snow layers from thinner and current categories
! aicetl - area of each snow depth in this layer
hitl(:) = z0
aicetl(:) = z0
DO n = 1, m_index
hitl(n) = max(min(hsnon(n) + alfan(n) - alfan(m_index), &
alfan(m_index+1) - alfan(m_index)), z0)
aicetl(n) = asnon(n)
aicetl(0) = aicetl(0) + (aicen(n) - asnon(n))
END DO
hitl(m_index+1) = alfan(m_index+1) - alfan(m_index)
aicetl(m_index+1) = z0
!----------------------------------------------------------------
! reorder array according to hitl
! snow heights not necessarily in height order
!----------------------------------------------------------------
DO ns = 1, m_index+1
DO n = 0, m_index - ns + 1
IF (hitl(n) > hitl(n+1)) THEN ! swap order
tmp = hitl(n)
hitl(n) = hitl(n+1)
hitl(n+1) = tmp
tmp = aicetl(n)
aicetl(n) = aicetl(n+1)
aicetl(n+1) = tmp
END IF
END DO
END DO
!----------------------------------------------------------------
! divide semi-filled layer into set of sublayers each vertically homogenous
!----------------------------------------------------------------
!hitl(3)----------------------------------------------------------------
! | * * * * * * * *
! |* * * * * * * * *
!hitl(2)----------------------------------------------------------------
! | * * * * * * * * | * * * * * * * *
! |* * * * * * * * * |* * * * * * * * *
!hitl(1)----------------------------------------------------------------
! | * * * * * * * * | * * * * * * * * | * * * * * * * *
! |* * * * * * * * * |* * * * * * * * * |* * * * * * * * *
!hitl(0)----------------------------------------------------------------
! aicetl(0) aicetl(1) aicetl(2) aicetl(3)
! move up over layers incrementing volume
DO n = 1, m_index+1
area = sum(aicetl(:)) - & ! total area of sub-layer
(rhos/rho0) * sum(aicetl(n:jpl+1)) ! area of sub-layer occupied by snow
vol = (hitl(n) - hitl(n-1)) * area ! thickness of sub-layer times area
IF (vol >= rem_vol) THEN ! have reached the sub-layer with the depth within
hpond = rem_vol / area + hitl(n-1) + alfan(m_index) - alfan(1)
exit
ELSE ! still in sub-layer below the sub-layer with the depth
rem_vol = rem_vol - vol
END IF
END DO
END IF
END SUBROUTINE ice_thd_pnd_depth
SUBROUTINE ice_thd_pnd_perm(ticen, salin, perm)
!!-------------------------------------------------------------------
!! *** ROUTINE ice_thd_pnd_perm ***
!!
!! ** Purpose : Determine the liquid fraction of brine in the ice
!! and its permeability
!!-------------------------------------------------------------------
REAL (wp), DIMENSION(nlay_i), INTENT(IN) :: &
ticen, & ! internal ice temperature (K)
salin ! salinity (ppt) !js: ppt according to cice
REAL (wp), INTENT(OUT) :: &
perm ! permeability
REAL (wp) :: &
Sbr ! brine salinity
REAL (wp), DIMENSION(nlay_i) :: &
Tin, & ! ice temperature
phi ! liquid fraction
INTEGER :: k
!-----------------------------------------------------------------
! Compute ice temperatures from enthalpies using quadratic formula
!-----------------------------------------------------------------
DO k = 1,nlay_i
Tin(k) = ticen(k) - rt0 !js: from K to degC
END DO
!-----------------------------------------------------------------
! brine salinity and liquid fraction
!-----------------------------------------------------------------
DO k = 1, nlay_i
Sbr = - Tin(k) / rTmlt ! Consistent expression with SI3 (linear liquidus)
! Best expression to date is that one (Vancoppenolle et al JGR 2019)
! Sbr = - 18.7 * Tin(k) - 0.519 * Tin(k)**2 - 0.00535 * Tin(k) **3
phi(k) = salin(k) / Sbr
END DO
!-----------------------------------------------------------------
! permeability
!-----------------------------------------------------------------
perm = 3.0e-08_wp * (minval(phi))**3 ! Golden et al. (2007)
END SUBROUTINE ice_thd_pnd_perm
SUBROUTINE ice_thd_pnd_init
!!-------------------------------------------------------------------
!! *** ROUTINE ice_thd_pnd_init ***
!!
!! ** Purpose : Physical constants and parameters linked to melt ponds
!! over sea ice
!!
!! ** Method : Read the namthd_pnd namelist and check the melt pond
!! parameter values called at the first timestep (nit000)
!!
!! ** input : Namelist namthd_pnd
!!-------------------------------------------------------------------
INTEGER :: ios, ioptio ! Local integer
!!
NAMELIST/namthd_pnd/ ln_pnd, ln_pnd_LEV , rn_apnd_min, rn_apnd_max, rn_pnd_flush, &
& ln_pnd_CST , rn_apnd, rn_hpnd, &
& ln_pnd_TOPO, &
& ln_pnd_lids, ln_pnd_alb
!!-------------------------------------------------------------------
!
READ ( numnam_ice_ref, namthd_pnd, IOSTAT = ios, ERR = 901)
901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namthd_pnd in reference namelist' )
READ ( numnam_ice_cfg, namthd_pnd, IOSTAT = ios, ERR = 902 )
902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namthd_pnd in configuration namelist' )
IF(lwm) WRITE ( numoni, namthd_pnd )
!
IF(lwp) THEN ! control print
WRITE(numout,*)
WRITE(numout,*) 'ice_thd_pnd_init: ice parameters for melt ponds'
WRITE(numout,*) '~~~~~~~~~~~~~~~~'
WRITE(numout,*) ' Namelist namicethd_pnd:'
WRITE(numout,*) ' Melt ponds activated or not ln_pnd = ', ln_pnd
WRITE(numout,*) ' Topographic melt pond scheme ln_pnd_TOPO = ', ln_pnd_TOPO
WRITE(numout,*) ' Level ice melt pond scheme ln_pnd_LEV = ', ln_pnd_LEV
WRITE(numout,*) ' Minimum ice fraction that contributes to melt ponds rn_apnd_min = ', rn_apnd_min
WRITE(numout,*) ' Maximum ice fraction that contributes to melt ponds rn_apnd_max = ', rn_apnd_max
WRITE(numout,*) ' Pond flushing efficiency rn_pnd_flush = ', rn_pnd_flush
WRITE(numout,*) ' Constant ice melt pond scheme ln_pnd_CST = ', ln_pnd_CST
WRITE(numout,*) ' Prescribed pond fraction rn_apnd = ', rn_apnd
WRITE(numout,*) ' Prescribed pond depth rn_hpnd = ', rn_hpnd
WRITE(numout,*) ' Frozen lids on top of melt ponds ln_pnd_lids = ', ln_pnd_lids
WRITE(numout,*) ' Melt ponds affect albedo or not ln_pnd_alb = ', ln_pnd_alb
ENDIF
!
! !== set the choice of ice pond scheme ==!
ioptio = 0
IF( .NOT.ln_pnd ) THEN ; ioptio = ioptio + 1 ; nice_pnd = np_pndNO ; ENDIF
IF( ln_pnd_CST ) THEN ; ioptio = ioptio + 1 ; nice_pnd = np_pndCST ; ENDIF
IF( ln_pnd_LEV ) THEN ; ioptio = ioptio + 1 ; nice_pnd = np_pndLEV ; ENDIF
IF( ln_pnd_TOPO ) THEN ; ioptio = ioptio + 1 ; nice_pnd = np_pndTOPO ; ENDIF
IF( ioptio /= 1 ) &
& CALL ctl_stop( 'ice_thd_pnd_init: choose either none (ln_pnd=F) or only one pond scheme (ln_pnd_LEV, ln_pnd_CST or ln_pnd_TOPO)' )
!
SELECT CASE( nice_pnd )
CASE( np_pndNO )
IF( ln_pnd_alb ) THEN ; ln_pnd_alb = .FALSE. ; CALL ctl_warn( 'ln_pnd_alb=false when no ponds' ) ; ENDIF
IF( ln_pnd_lids ) THEN ; ln_pnd_lids = .FALSE. ; CALL ctl_warn( 'ln_pnd_lids=false when no ponds' ) ; ENDIF
CASE( np_pndCST )
IF( ln_pnd_lids ) THEN ; ln_pnd_lids = .FALSE. ; CALL ctl_warn( 'ln_pnd_lids=false when constant ponds' ) ; ENDIF
END SELECT
!
END SUBROUTINE ice_thd_pnd_init
#else
!!----------------------------------------------------------------------
!! Default option Empty module NO SI3 sea-ice model
!!----------------------------------------------------------------------
#endif
!!======================================================================
END MODULE icethd_pnd