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icloan.F
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#if defined(ROW_LAND)
#define SEA_P .true.
#define SEA_U .true.
#define SEA_V .true.
#elif defined(ROW_ALLSEA)
#define SEA_P allip(j).or.ip(i,j).ne.0
#define SEA_U alliu(j).or.iu(i,j).ne.0
#define SEA_V alliv(j).or.iv(i,j).ne.0
#else
#define SEA_P ip(i,j).ne.0
#define SEA_U iu(i,j).ne.0
#define SEA_V iv(i,j).ne.0
#endif
subroutine icloan(m,n)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
c
integer m,n
c
c --- 'energy loan' ice model. no advection, no dynamics. ice amount
c --- represents energy 'loaned' to water column to prevent wintertime
c --- cooling below freezing level. loan is paid back in summer.
c
c --- modified version for ice-ocean "coupling".
c --- freeze/melt energy from relaxation to the freezing temperature.
c --- the atmosphere/ice surface exchange is applied to the ocean
c --- (previously done in thermf).
c
integer i,j
real tfrz,tsur,tmxl,smxl,hfrz,paybak,borrow,hice,thkimx,t2f
real radfl,tdif,wind,airt,pair,rair,snsibl,emnp,dtrmui
real thkimxy(jdm)
c
c --- hice = actual ice thickness (m), local variable
c
c --- thkice = average ice thickness, i.e. hice x covice (m)
c --- covice = ice coverage, i.e. cell fraction (0.0 to 1.0)
c --- temice = ice surface temperature (degC)
c --- flxice = cell average heat flux under ice (W/m^2)
c --- fswice = cell average swv flux under ice (W/m^2)
c --- sflice = cell average salt flux under ice
c
c --- icefrq = e-folding time scale back to tfrz (no. time steps)
c --- thkfrz = maximum thickness of near-surface freezing zone (m)
c --- tfrz_0 = ice melting point (degC) at S=0psu
c --- tfrz_s = gradient of ice melting point (degC/psu)
c --- ticegr = vertical temperature gradient inside ice (deg/m)
c --- (0.0 to get ice surface temp. from atmos. surtmp)
c --- hicemn = minimum ice thickness (m)
c --- hicemx = maximum ice thickness (m)
c
real tfrz_n,ticemn,ticemx,salice,rhoice,fusion,meltmx
parameter (tfrz_n= -1.79, ! nominal ice melting point (degC)
& ticemn=-50.0, ! minimum ice surface temperature (degC)
& ticemx= 0.0, ! maximum ice surface temperature (degC)
& salice= 4.0, ! salinity of ice (psu) - same as CICE
& rhoice=917.0, ! density of ice (kg/m**3)
& fusion=334.e3, ! latent heat of fusion (J/kg)
& meltmx= 33.e-7)! max. ice melting rate (m/sec), 0.285 m/day
c
real fluxmx !max. ice melting flux (W/m^2)
parameter (fluxmx=meltmx*fusion*rhoice) !~1000 W/m^2 - like CICE
c
real csice,csubp,pairc,rgas,tzero
parameter (csice =0.0006, !ice-air sensible exchange coefficient
& csubp =1005.7, !specific heat of air (j/kg/deg)
& pairc=1013.0*100.0, !air pressure (mb) * 100
& rgas =287.1, !gas constant (j/kg/k)
& tzero=273.16) !celsius to kelvin temperature offset
c
* include 'stmt_fns.h'
c
dtrmui = delt1/(1.0*86400.0) !dt*1/1days
c
c --- energy loan: add extra energy to the ocean to keep SST from dropping
c --- below tfrz in winter. return this borrowed energy to the 'energy bank'
c --- in summer.
c
c --- salt loan: analogous to energy loan.
c
!$OMP PARALLEL DO PRIVATE(j,i,
!$OMP& t2f,hfrz,smxl,tmxl,tfrz,borrow,paybak)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1,jj
thkimxy(j)=0.0 !simplifies OpenMP parallelization
do i=1,ii
if (SEA_P) then
if (ishlf(i,j).eq.0) then !under an ice shelf
flxice(i,j)=0.0
sflice(i,j)=0.0
thkice(i,j)=hicemx
util1(i,j)=0.0
else !standard ocean point
c --- relax to tfrz with e-folding time of icefrq time steps
c --- assuming the effective surface layer thickness (hfrz)
c --- is at most thkfrz meters
c --- multiply by dpbl(i,j)/hfrz to get the actual e-folding time
c --- icefrq==1 is "Instant Relaxation" and an e-folding time
c --- of 30 days is consistent with the "Drag Law" approach
c --- D.M. Holland (1998) On the Parameterization of Basal
c --- Heat Flux for Sea-ice Modelling; Geophysica 34 pp 1-21
c --- when coupling, icefrq must be at least the coupling interval
c
hfrz = min( thkfrz*onem, dpbl(i,j) )
t2f = (spcifh*hfrz)/(baclin*icefrq*g)
smxl = saln(i,j,1,n)
tmxl = temp(i,j,1,n)
tfrz = tfrz_0 + smxl*tfrz_s !salinity dependent freezing point
borrow = (tfrz-tmxl)*t2f !W/m^2 into ocean
c
c --- limit heat flux range (for both forming and melting ice)
borrow=max( -fluxmx, min( fluxmx, borrow ) )
c
cdiag if (i.eq.itest .and. j.eq.jtest) then
cdiag write (lp,'(i9,2i5,a,5f9.3)')
cdiag& nstep,i+i0,j+j0,' t,tfrz,flx,hfrz,cov:',
cdiag& tmxl,tfrz,borrow,hfrz*qonem,covice(i,j)
cdiag endif
c
if (tmxl.lt.tfrz) then
c
c --- add energy to move tmxl towards tfrz (only if tmxl < tfrz)
c --- include some dependance on sea ice coverage
c
flxice(i,j)=borrow*max(covice(i,j),0.1)
thkice(i,j)=thkice(i,j)+flxice(i,j)*
& (delt1/(fusion*rhoice))
c --- brine rejection as ice forms, must be a positive or zero flux
c--- salt flux (psu m/s kg/m**3) cell average into ocean
sflice(i,j)= +flxice(i,j)*
& max(smxl-salice,0.0)*(1.0/fusion)
elseif (thkice(i,j).gt.0.0) then !tmxl > tfrz
c
c --- ice, so return the borrowed amount whenever tmxl > tfrz
c --- only over the fraction of the cell where ice exists
c
paybak=min( -borrow*covice(i,j),
& thkice(i,j)*(fusion*rhoice/delt1) )
flxice(i,j)= -paybak
thkice(i,j)=thkice(i,j)-paybak*(delt1/(fusion*rhoice))
c --- brine recovery from melting ice, usually a negative flux
c--- salt flux (psu m/s kg/m**3) cell average into ocean
sflice(i,j)= -paybak*(smxl-salice)*(1.0/fusion)
else !tmxl > tfrz & thkice(i,j) == 0.0
c
c --- no ice.
c
flxice(i,j)=0.0
sflice(i,j)=0.0
c
if (icmflg.eq.2) then
c
c --- add extra cooling under the ice mask (tsur<=tfrz_n)
c --- don't allow a new tsur maximum, to preserve sea ice
c
if (natm.eq.2) then
tsur = min( max( surtmp(i,j,l0), surtmp(i,j,l1) ),
& surtmp(i,j,l0)*w0+surtmp(i,j,l1)*w1 )
elseif (yrflag.lt.2) then
tsur = min( max( surtmp(i,j,l0), surtmp(i,j,l1),
& surtmp(i,j,l2), surtmp(i,j,l3) ),
& surtmp(i,j,l0)*w0+surtmp(i,j,l1)*w1+
& surtmp(i,j,l2)*w2+surtmp(i,j,l3)*w3 )
else
tsur = min( max( surtmp(i,j,l0), surtmp(i,j,l1) ),
& surtmp(i,j,l0)*w0+surtmp(i,j,l1)*w1 )
endif
if (tsur.le.tfrz_n) then
surflx(i,j)=surflx(i,j)+borrow*covice(i,j)
endif
endif !icmflg.eq.2
endif
c
util1(i,j)=max(thkice(i,j)-hicemx,0.0) !icex = ice exceeding hicemx
thkimxy(j)=max(thkimxy(j),thkice(i,j))
endif !ishlf:else
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
c
thkimx=maxval(thkimxy(1:jj))
call xcmaxr(thkimx)
c
c --- spread out portion of ice thicker than hicemx
if (thkimx.gt.hicemx) then
call psmooth(util1, 0,0, ishlf, util2) !smooth icex
endif
c
!$OMP PARALLEL DO PRIVATE(j,i,hice,smxl,tfrz,
!$OMP& radfl,tdif,wind,airt,rair,snsibl,emnp)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1,ii
if (SEA_P) then
if (ishlf(i,j).eq.0) then !under an ice shelf
thkice(i,j)=hicemx
covice(i,j)=1.0
fswice(i,j)=0.0
temice(i,j)=ticemn
else !standard ocean point
thkice(i,j)=util1(i,j)+min(thkice(i,j),hicemx) !icex_sm+rest
c
c --- compute fractional ice coverage for energy flux calculation
if (thkice(i,j).lt.1.e-5*hicemn) then
covice(i,j)=0.0
else
covice(i,j)=min(1.0,thkice(i,j)*(1.0/hicemn))
hice=thkice(i,j)/covice(i,j) !minimum of hicemn
end if
c
if (icmflg.eq.3) then
c --- relax to sea ice concentration from coupler
c --- ice thickness is therefore always then 0 and hicemn
covice(i,j)=covice(i,j)+dtrmui*(si_c(i,j)-covice(i,j))
thkice(i,j)=covice(i,j)*hicemn
hice=hicemn
endif
c
c --- compute ice surface temperature
if (covice(i,j).eq.0.0) then
temice(i,j)=ticemx
elseif (icmflg.eq.3 .and. si_c(i,j).gt.0.0) then !from coupler
temice(i,j)=max( ticemn, min( ticemx, si_t(i,j) ) )
elseif (ticegr.eq.0.0) then !use surtmp
if (natm.eq.2) then
temice(i,j)=max( ticemn,
& min( ticemx,
& surtmp(i,j,l0)*w0+
& surtmp(i,j,l1)*w1 ) )
else
temice(i,j)=max( ticemn,
& min( ticemx,
& surtmp(i,j,l0)*w0+
& surtmp(i,j,l1)*w1+
& surtmp(i,j,l2)*w2+
& surtmp(i,j,l3)*w3 ) )
endif !natm
else
temice(i,j)=max( ticemn, ticemx-ticegr*hice )
endif
c
c --- atmosphere to ice surface exchange is applied to the ocean,
c --- i.e. use the "energy-loan" approach.
c --- don't apply to the ocean when coupling, because it has
c --- already been applied to the ice.
c
if (icmflg.ne.3 .and. covice(i,j).gt.0.0) then
c --- net radiative thermal flux (w/m**2) +ve into ocean/ice
c --- radflx's Qsw includes the atmos. model's surface albedo,
c --- i.e. it already allows for ice&snow where it is observed.
if (natm.eq.2) then
radfl=radflx(i,j,l0)*w0+radflx(i,j,l1)*w1
else
radfl=radflx(i,j,l0)*w0+radflx(i,j,l1)*w1
& +radflx(i,j,l2)*w2+radflx(i,j,l3)*w3
endif !natm
if (lwflag.gt.1) then
c --- longwave correction to radfl (Qsw+Qlw).
c --- this will be ~zero for ticegr==0.0 (temice=surtmp)
if (natm.eq.2) then
tdif = temice(i,j) -
& ( surtmp(i,j,l0)*w0+surtmp(i,j,l1)*w1 )
else
tdif = temice(i,j) -
& ( surtmp(i,j,l0)*w0+surtmp(i,j,l1)*w1
& +surtmp(i,j,l2)*w2+surtmp(i,j,l3)*w3 )
endif !natm
!correction is blackbody radiation from tdif at temice
radfl = radfl - (4.506+0.0554*temice(i,j)) * tdif
endif
if (flxflg.ne.3) then
if (natm.eq.2) then
c --- wind speed (m/s)
wind=wndspd(i,j,l0)*w0+wndspd(i,j,l1)*w1
c --- air temperature (C)
airt=airtmp(i,j,l0)*w0+airtmp(i,j,l1)*w1
else
c --- wind speed (m/s)
wind=wndspd(i,j,l0)*w0+wndspd(i,j,l1)*w1
& +wndspd(i,j,l2)*w2+wndspd(i,j,l3)*w3
c --- air temperature (C)
airt=airtmp(i,j,l0)*w0+airtmp(i,j,l1)*w1
& +airtmp(i,j,l2)*w2+airtmp(i,j,l3)*w3
endif !natm
if (mslprf .or. flxflg.eq.6) then
if (natm.eq.2) then
pair=mslprs(i,j,l0)*w0+mslprs(i,j,l1)*w1
& +prsbas
else
pair=mslprs(i,j,l0)*w0+mslprs(i,j,l1)*w1
& +mslprs(i,j,l2)*w2+mslprs(i,j,l3)*w3
& +prsbas
endif !natm
else
pair=pairc
endif
rair = pair/(rgas*(tzero+airt))
snsibl = csubp*rair*wind*csice*(temice(i,j)-airt)
else
snsibl = 0.0 !already in total flux (i.e. in radfl)
endif
flxice(i,j) = flxice(i,j) +
& covice(i,j)*(radfl - snsibl) !no evap
c
c --- add a time-invarient net heat flux offset
if (flxoff) then
flxice(i,j) = flxice(i,j) + covice(i,j)*offlux(i,j)
endif
c
c --- emnp = evaporation minus precipitation (m/sec) into atmos.
c --- no evap (sublimation) over ice, all precip enters ocean
if (pcipf) then
if (natm.eq.2) then
emnp = -( precip(i,j,l0)*w0+precip(i,j,l1)*w1)
else
emnp = -( precip(i,j,l0)*w0+precip(i,j,l1)*w1
& +precip(i,j,l2)*w2+precip(i,j,l3)*w3)
endif !natm
else
emnp = 0.0
endif
if (priver) then
emnp = emnp - ( rivers(i,j,lr0)*wr0+rivers(i,j,lr1)*wr1
& +rivers(i,j,lr2)*wr2+rivers(i,j,lr3)*wr3)
endif
c --- sflice = salt flux (10**-3 kg/m**2/sec) into ocean under ice
sflice(i,j) = sflice(i,j) +
& covice(i,j)*emnp*(saln(i,j,1,n)*qthref)
endif !covice
c
fswice(i,j) = 0.0 !no penetrating Qsw under ice
endif !ishlf:else
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
c
return
end subroutine icloan
c
c
c> Revision history
c>
c> June 2000 - conversion to SI units
c> July 2000 - switched sign convention for vertical fluxes (now >0 if down)
c> May 2003 - added option to impose an ice mask
c> June 2003 - added 8 time step e-folding time scale
c> June 2003 - limited rate of ice formation
c> June 2003 - replaced constant saldif with smxl-salice
c> Mar. 2005 - freezing point linearly dependent on salinity
c> Mar. 2005 - ice surface temperature optionally from surtmp
c> Jun. 2006 - modified version for ice-ocean "coupling"
c> Nov. 2011 - don't apply atmosphere to ice surface exchange when "coupling"
c> May 2012 - limit brine rejection to be a non-negative salt flux
c> July 2012 - flxice and sflice now correctly represent cell average under ice
c> Nov. 2012 - weaker dependance on covice when freezing
c> Jan. 2014 - added natm
c> Apr. 2014 - added pair for time varying msl pressure (mslprf)
c> Apr. 2014 - added ice shelf logic (ishlf)
c> May 2014 - use land/sea masks (e.g. ip) to skip land