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C $Header: /u/gcmpack/MITgcm/pkg/thsice/thsice_solve4temp.F,v 1.8 2006/05/25 18:03:25 jmc Exp $ |
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C $Name: $ |
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|
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#include "THSICE_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: THSICE_SOLVE4TEMP |
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C !INTERFACE: |
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SUBROUTINE THSICE_SOLVE4TEMP( |
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I bi, bj, siLo, siHi, sjLo, sjHi, |
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I iMin,iMax, jMin,jMax, dBugFlag, |
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I useBulkForce, useEXF, |
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I iceMask, hIce, hSnow, tFrz, flxExSW, |
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U flxSW, tSrf, qIc1, qIc2, |
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O tIc1, tIc2, dTsrf, |
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O sHeat, flxCnB, flxAtm, evpAtm, |
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I myTime, myIter, myThid ) |
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | S/R THSICE_SOLVE4TEMP |
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C *==========================================================* |
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C | Solve (implicitly) for sea-ice and surface temperature |
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C *==========================================================* |
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C \ev |
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|
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C ADAPTED FROM: |
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C LANL CICE.v2.0.2 |
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C----------------------------------------------------------------------- |
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C.. thermodynamics (vertical physics) based on M. Winton 3-layer model |
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C.. See Bitz, C. M. and W. H. Lipscomb, 1999: "An energy-conserving |
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C.. thermodynamic sea ice model for climate study." J. Geophys. |
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C.. Res., 104, 15669 - 15677. |
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C.. Winton, M., 1999: "A reformulated three-layer sea ice model." |
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C.. Submitted to J. Atmos. Ocean. Technol. |
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C.. authors Elizabeth C. Hunke and William Lipscomb |
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C.. Fluid Dynamics Group, Los Alamos National Laboratory |
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C----------------------------------------------------------------------- |
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Cc****subroutine thermo_winton(n,fice,fsnow,dqice,dTsfc) |
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C.. Compute temperature change using Winton model with 2 ice layers, of |
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C.. which only the top layer has a variable heat capacity. |
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|
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C !USES: |
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IMPLICIT NONE |
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|
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C == Global variables === |
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#include "EEPARAMS.h" |
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#include "THSICE_SIZE.h" |
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#include "THSICE_PARAMS.h" |
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|
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C !INPUT/OUTPUT PARAMETERS: |
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C == Routine Arguments == |
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C siLo,siHi :: size of input/output array: 1rst dim. lower,higher bounds |
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C sjLo,sjHi :: size of input/output array: 2nd dim. lower,higher bounds |
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C bi,bj :: tile indices |
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C iMin,iMax :: computation domain: 1rst index range |
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C jMin,jMax :: computation domain: 2nd index range |
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C dBugFlag :: allow to print debugging stuff (e.g. on 1 grid point). |
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C useBulkForce:: use surf. fluxes from bulk-forcing external S/R |
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C useEXF :: use surf. fluxes from exf external S/R |
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C--- Input: |
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C iceMask :: sea-ice fractional mask [0-1] |
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C hIce (hi) :: ice height [m] |
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C hSnow (hs) :: snow height [m] |
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C tFrz (Tf) :: sea-water freezing temperature [oC] (function of S) |
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C flxExSW (=) :: surf. heat flux (+=down) except SW, function of surf. temp Ts: |
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C 0: Flx(Ts=0) ; 1: Flx(Ts=Ts^n) ; 2: d.Flx/dTs(Ts=Ts^n) |
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C--- Modified (input&output): |
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C flxSW (netSW) :: net Short-Wave flux (+=down) [W/m2]: input= at surface |
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C (=) :: output= below sea-ice, into the ocean |
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C tSrf (Tsf) :: surface (ice or snow) temperature |
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C qIc1 (qicen) :: ice enthalpy (J/kg), 1rst level |
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C qIc2 (qicen) :: ice enthalpy (J/kg), 2nd level |
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C--- Output |
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C tIc1 (Tice) :: temperature of ice layer 1 [oC] |
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C tIc2 (Tice) :: temperature of ice layer 2 [oC] |
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C dTsrf (dTsf) :: surf. temp adjusment: Ts^n+1 - Ts^n |
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C sHeat(sHeating):: surf heating flux left to melt snow or ice (= Atmos-conduction) |
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C flxCnB (=) :: heat flux conducted through the ice to bottom surface |
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C flxAtm (=) :: net flux of energy from the atmosphere [W/m2] (+=down) |
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C without snow precip. (energy=0 for liquid water at 0.oC) |
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C evpAtm (=) :: evaporation to the atmosphere [kg/m2/s] (>0 if evaporate) |
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C--- Input: |
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C myTime :: current Time of simulation [s] |
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C myIter :: current Iteration number in simulation |
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C myThid :: my Thread Id number |
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INTEGER siLo, siHi, sjLo, sjHi |
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INTEGER bi,bj |
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INTEGER iMin, iMax |
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INTEGER jMin, jMax |
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LOGICAL dBugFlag |
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LOGICAL useBulkForce |
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LOGICAL useEXF |
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_RL iceMask(siLo:siHi,sjLo:sjHi) |
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_RL hIce (siLo:siHi,sjLo:sjHi) |
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_RL hSnow (siLo:siHi,sjLo:sjHi) |
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_RL tFrz (siLo:siHi,sjLo:sjHi) |
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_RL flxExSW(iMin:iMax,jMin:jMax,0:2) |
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_RL flxSW (siLo:siHi,sjLo:sjHi) |
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_RL tSrf (siLo:siHi,sjLo:sjHi) |
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_RL qIc1 (siLo:siHi,sjLo:sjHi) |
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_RL qIc2 (siLo:siHi,sjLo:sjHi) |
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_RL tIc1 (siLo:siHi,sjLo:sjHi) |
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_RL tIc2 (siLo:siHi,sjLo:sjHi) |
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c _RL dTsrf (siLo:siHi,sjLo:sjHi) |
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_RL dTsrf (iMin:iMax,jMin:jMax) |
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_RL sHeat (siLo:siHi,sjLo:sjHi) |
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_RL flxCnB (siLo:siHi,sjLo:sjHi) |
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_RL flxAtm (siLo:siHi,sjLo:sjHi) |
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_RL evpAtm (siLo:siHi,sjLo:sjHi) |
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_RL myTime |
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INTEGER myIter |
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INTEGER myThid |
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CEOP |
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|
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#ifdef ALLOW_THSICE |
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C !LOCAL VARIABLES: |
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C--- local copy of input/output argument list variables (see description above) |
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c _RL flxExcSw(0:2) |
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_RL Tf |
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_RL hi |
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_RL hs |
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_RL netSW |
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_RL Tsf |
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_RL qicen(nlyr) |
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_RL Tice (nlyr) |
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c _RL sHeating |
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c _RL flxCnB |
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_RL dTsf |
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c _RL flxAtm |
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c _RL evpAtm |
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|
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C == Local Variables == |
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INTEGER i,j |
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INTEGER k, iterMax |
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|
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_RL frsnow ! fractional snow cover |
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_RL fswpen ! SW penetrating beneath surface (W m-2) |
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_RL fswdn ! SW absorbed at surface (W m-2) |
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_RL fswint ! SW absorbed in ice (W m-2) |
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_RL fswocn ! SW passed through ice to ocean (W m-2) |
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_RL flxExceptSw ! net surface heat flux, except short-wave (W/m2) |
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C evap :: evaporation over snow/ice [kg/m2/s] (>0 if evaporate) |
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C dEvdT :: derivative of evap. with respect to Tsf [kg/m2/s/K] |
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_RL evap, dEvdT |
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_RL flx0 ! net surf heat flux, from Atmos. to sea-ice (W m-2) |
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_RL fct ! heat conducted to top surface |
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_RL df0dT ! deriv of flx0 wrt Tsf (W m-2 deg-1) |
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_RL k12, k32 ! thermal conductivity terms |
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_RL a10, b10 ! coefficients in quadratic eqn for T1 |
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_RL a1, b1, c1 ! coefficients in quadratic eqn for T1 |
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c _RL Tsf_start ! old value of Tsf |
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_RL dt ! timestep |
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INTEGER iceornot |
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LOGICAL useBlkFlx |
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|
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C- define grid-point location where to print debugging values |
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#include "THSICE_DEBUG.h" |
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|
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1010 FORMAT(A,I3,3F11.6) |
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1020 FORMAT(A,1P4E14.6) |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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|
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useBlkFlx = useEXF .OR. useBulkForce |
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|
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dt = thSIce_deltaT |
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DO j = jMin, jMax |
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DO i = iMin, iMax |
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IF ( iceMask(i,j).GT.0. _d 0) THEN |
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hi = hIce(i,j) |
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hs = hSnow(i,j) |
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Tf = tFrz(i,j) |
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netSW = flxSW(i,j) |
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Tsf = tSrf(i,j) |
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qicen(1)= qIc1(i,j) |
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qicen(2)= qIc2(i,j) |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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#ifdef ALLOW_DBUG_THSICE |
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IF ( dBug(i,j,bi,bj) ) WRITE(6,'(A,2I4,2I2)') |
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& 'ThSI_SOLVE4T: i,j=',i,j,bi,bj |
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#endif |
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IF ( hi.LT.himin ) THEN |
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C If hi < himin, melt the ice. |
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STOP 'THSICE_SOLVE4TEMP: should not enter if hi<himin' |
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ENDIF |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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|
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C fractional snow cover |
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frsnow = 0. _d 0 |
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IF (hs .GT. 0. _d 0) frsnow = 1. _d 0 |
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|
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C Compute SW flux absorbed at surface and penetrating to layer 1. |
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fswpen = netSW * (1. _d 0 - frsnow) * i0 |
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fswocn = fswpen * exp(-ksolar*hi) |
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fswint = fswpen - fswocn |
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|
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fswdn = netSW - fswpen |
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|
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C Compute conductivity terms at layer interfaces. |
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|
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k12 = 4. _d 0*kice*ksnow / (ksnow*hi + 4. _d 0*kice*hs) |
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k32 = 2. _d 0*kice / hi |
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|
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C compute ice temperatures |
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a1 = cpice |
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b1 = qicen(1) + (cpwater-cpice )*Tmlt1 - Lfresh |
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c1 = Lfresh * Tmlt1 |
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Tice(1) = 0.5 _d 0 *(-b1 - SQRT(b1*b1-4. _d 0*a1*c1))/a1 |
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Tice(2) = (Lfresh-qicen(2)) / cpice |
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|
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IF (Tice(1).GT.0. _d 0 .OR. Tice(2).GT.0. _d 0) THEN |
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WRITE (6,*) 'BBerr Tice(1) > 0 = ',Tice(1) |
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WRITE (6,*) 'BBerr Tice(2) > 0 = ',Tice(2) |
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ENDIF |
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#ifdef ALLOW_DBUG_THSICE |
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IF ( dBug(i,j,bi,bj) ) WRITE(6,1010) |
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& 'ThSI_SOLVE4T: k, Ts, Tice=',0,Tsf,Tice |
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#endif |
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|
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C Compute coefficients used in quadratic formula. |
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|
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a10 = rhoi*cpice *hi/(2. _d 0*dt) + |
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& k32 * (4. _d 0*dt*k32 + rhoi*cpice *hi) |
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& / (6. _d 0*dt*k32 + rhoi*cpice *hi) |
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b10 = -hi* |
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& (rhoi*cpice*Tice(1)+rhoi*Lfresh*Tmlt1/Tice(1)) |
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& /(2. _d 0*dt) |
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& - k32 * (4. _d 0*dt*k32*Tf+rhoi*cpice *hi*Tice(2)) |
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& / (6. _d 0*dt*k32 + rhoi*cpice *hi) - fswint |
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c1 = rhoi*Lfresh*hi*Tmlt1 / (2. _d 0*dt) |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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C Compute new surface and internal temperatures; iterate until |
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C Tsfc converges. |
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|
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IF ( useBlkFlx ) THEN |
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iterMax = nitMaxTsf |
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ELSE |
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iterMax = 1 |
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ENDIF |
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dTsf = Terrmax |
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|
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C ----- begin iteration ----- |
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DO k = 1,iterMax |
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IF ( ABS(dTsf).GE.Terrmax ) THEN |
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|
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C Save temperatures at start of iteration. |
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c Tsf_start = Tsf |
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|
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IF ( useBlkFlx ) THEN |
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C Compute top surface flux. |
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IF (hs.GT.3. _d -1) THEN |
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iceornot=2 |
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ELSE |
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iceornot=1 |
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ENDIF |
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IF ( useBulkForce ) THEN |
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CALL THSICE_GET_BULKF( |
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I iceornot, Tsf, |
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O flxExceptSw, df0dT, evap, dEvdT, |
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I i,j,bi,bj,myThid ) |
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ELSEIF ( useEXF ) THEN |
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CALL THSICE_GET_EXF ( |
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I iceornot, Tsf, |
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O flxExceptSw, df0dT, evap, dEvdT, |
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I i,j,bi,bj,myThid ) |
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ENDIF |
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ELSE |
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flxExceptSw = flxExSW(i,j,1) |
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df0dT = flxExSW(i,j,2) |
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ENDIF |
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flx0 = fswdn + flxExceptSw |
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#ifdef ALLOW_DBUG_THSICE |
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IF ( dBug(i,j,bi,bj) ) WRITE(6,1020) |
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& 'ThSI_SOLVE4T: flx0,df0dT,k12,D=', flx0,df0dT,k12,k12-df0dT |
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#endif |
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|
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C Compute new top layer and surface temperatures. |
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C If Tsfc is computed to be > 0 C, fix Tsfc = 0 and recompute T1 |
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C with different coefficients. |
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|
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a1 = a10 - k12*df0dT / (k12-df0dT) |
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b1 = b10 - k12*(flx0-df0dT*Tsf) / (k12-df0dT) |
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Tice(1) = -(b1 + SQRT(b1*b1-4. _d 0*a1*c1))/(2. _d 0*a1) |
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dTsf = (flx0 + k12*(Tice(1)-Tsf)) / (k12-df0dT) |
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Tsf = Tsf + dTsf |
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IF (Tsf .GT. 0. _d 0) THEN |
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#ifdef ALLOW_DBUG_THSICE |
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IF ( dBug(i,j,bi,bj) ) WRITE(6,1010) |
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& 'ThSI_SOLVE4T: k,ts,t1,dTs=', k,Tsf,Tice(1),dTsf |
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#endif |
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a1 = a10 + k12 |
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b1 = b10 ! note b1 = b10 - k12*Tf0 |
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Tice(1) = (-b1 - SQRT(b1*b1-4. _d 0*a1*c1))/(2. _d 0*a1) |
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Tsf = 0. _d 0 |
| 297 |
IF ( useBlkFlx ) THEN |
| 298 |
IF (hs.GT.3. _d -1) THEN |
| 299 |
iceornot=2 |
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ELSE |
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iceornot=1 |
| 302 |
ENDIF |
| 303 |
IF ( useBulkForce ) THEN |
| 304 |
CALL THSICE_GET_BULKF( |
| 305 |
I iceornot, Tsf, |
| 306 |
O flxExceptSw, df0dT, evap, dEvdT, |
| 307 |
I i,j,bi,bj,myThid ) |
| 308 |
ELSEIF ( useEXF ) THEN |
| 309 |
CALL THSICE_GET_EXF ( |
| 310 |
I iceornot, Tsf, |
| 311 |
O flxExceptSw, df0dT, evap, dEvdT, |
| 312 |
I i,j,bi,bj,myThid ) |
| 313 |
ENDIF |
| 314 |
dTsf = 0. _d 0 |
| 315 |
ELSE |
| 316 |
flxExceptSw = flxExSW(i,j,0) |
| 317 |
dTsf = 1000. |
| 318 |
df0dT = 0. |
| 319 |
ENDIF |
| 320 |
flx0 = fswdn + flxExceptSw |
| 321 |
ENDIF |
| 322 |
|
| 323 |
C Check for convergence. If no convergence, then repeat. |
| 324 |
C |
| 325 |
C Convergence test: Make sure Tsfc has converged, within prescribed error. |
| 326 |
C (Energy conservation is guaranteed within machine roundoff, even |
| 327 |
C if Tsfc has not converged.) |
| 328 |
C If no convergence, then repeat. |
| 329 |
|
| 330 |
#ifdef ALLOW_DBUG_THSICE |
| 331 |
IF ( dBug(i,j,bi,bj) ) WRITE(6,1010) |
| 332 |
& 'ThSI_SOLVE4T: k,ts,t1,dTs=', k,Tsf,Tice(1),dTsf |
| 333 |
#endif |
| 334 |
IF ( useBlkFlx .AND. k.EQ.nitMaxTsf |
| 335 |
& .AND. ABS(dTsf).GE.Terrmax ) THEN |
| 336 |
WRITE (6,*) 'BB: thermw conv err ',i,j,bi,bj,dTsf |
| 337 |
WRITE (6,*) 'BB: thermw conv err, iceheight ', hi |
| 338 |
WRITE (6,*) 'BB: thermw conv err: Tsf, flx0', Tsf,flx0 |
| 339 |
IF (Tsf.LT.-70. _d 0) STOP |
| 340 |
ENDIF |
| 341 |
|
| 342 |
100 continue ! surface temperature iteration |
| 343 |
ENDIF |
| 344 |
ENDDO |
| 345 |
150 continue |
| 346 |
C ------ end iteration ------------ |
| 347 |
|
| 348 |
C Compute new bottom layer temperature. |
| 349 |
|
| 350 |
Tice(2) = (2. _d 0*dt*k32*(Tice(1)+2. _d 0*Tf) |
| 351 |
& + rhoi*cpice *hi*Tice(2)) |
| 352 |
& /(6. _d 0*dt*k32 + rhoi*cpice *hi) |
| 353 |
#ifdef ALLOW_DBUG_THSICE |
| 354 |
IF ( dBug(i,j,bi,bj) ) WRITE(6,1010) |
| 355 |
& 'ThSI_SOLVE4T: k, Ts, Tice=',k,Tsf,Tice |
| 356 |
#endif |
| 357 |
|
| 358 |
C Compute final flux values at surfaces. |
| 359 |
|
| 360 |
fct = k12*(Tsf-Tice(1)) |
| 361 |
flxCnB(i,j) = 4. _d 0*kice *(Tice(2)-Tf)/hi |
| 362 |
flx0 = flx0 + df0dT*dTsf |
| 363 |
IF ( useBlkFlx ) THEN |
| 364 |
C-- needs to update also Evap (Tsf changes) since Latent heat has been updated |
| 365 |
evpAtm(i,j) = evap + dEvdT*dTsf |
| 366 |
ELSE |
| 367 |
C- WARNING: Evap & +Evap*Lfresh are missing ! (but only affects Diagnostics) |
| 368 |
evpAtm(i,j) = 0. |
| 369 |
ENDIF |
| 370 |
C- energy flux to Atmos: use net short-wave flux at surf. and |
| 371 |
C use latent heat = Lvap (energy=0 for liq. water at 0.oC) |
| 372 |
flxAtm(i,j) = netSW + flxExceptSw |
| 373 |
& + df0dT*dTsf + evpAtm(i,j)*Lfresh |
| 374 |
C- excess of energy @ surface (used for surface melting): |
| 375 |
sHeat(i,j) = flx0 - fct |
| 376 |
|
| 377 |
C- SW flux at sea-ice base left to the ocean |
| 378 |
flxSW(i,j) = fswocn |
| 379 |
|
| 380 |
#ifdef ALLOW_DBUG_THSICE |
| 381 |
IF ( dBug(i,j,bi,bj) ) WRITE(6,1020) |
| 382 |
& 'ThSI_SOLVE4T: flx0,fct,Dif,flxCnB=', |
| 383 |
& flx0,fct,flx0-fct,flxCnB(i,j) |
| 384 |
#endif |
| 385 |
|
| 386 |
C Compute new enthalpy for each layer. |
| 387 |
|
| 388 |
qicen(1) = -cpwater*Tmlt1 + cpice *(Tmlt1-Tice(1)) |
| 389 |
& + Lfresh*(1. _d 0-Tmlt1/Tice(1)) |
| 390 |
qicen(2) = -cpice *Tice(2) + Lfresh |
| 391 |
|
| 392 |
C Make sure internal ice temperatures do not exceed Tmlt. |
| 393 |
C (This should not happen for reasonable values of i0.) |
| 394 |
|
| 395 |
IF (Tice(1) .GE. Tmlt1) THEN |
| 396 |
WRITE (6,'(A,2I4,2I3,1P2E14.6)') |
| 397 |
& 'BBerr - Bug: IceT(1) > Tmlt',i,j,bi,bj,Tice(1),Tmlt1 |
| 398 |
ENDIF |
| 399 |
IF (Tice(2) .GE. 0. _d 0) THEN |
| 400 |
WRITE (6,'(A,2I4,2I3,1P2E14.6)') |
| 401 |
& 'BBerr - Bug: IceT(2) > 0',i,j,bi,bj,Tice(2) |
| 402 |
ENDIF |
| 403 |
|
| 404 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 405 |
C-- Update Sea-Ice state : |
| 406 |
tSrf(i,j) = Tsf |
| 407 |
tIc1(i,j) = Tice(1) |
| 408 |
tic2(i,j) = Tice(2) |
| 409 |
qIc1(i,j) = qicen(1) |
| 410 |
qIc2(i,j) = qicen(2) |
| 411 |
c dTsrf(i,j) = dTsf |
| 412 |
IF ( .NOT.useBlkFlx ) dTsrf(i,j) = dTsf |
| 413 |
c sHeat(i,j) = sHeating |
| 414 |
c flxCnB(i,j)= flxCnB |
| 415 |
c flxAtm(i,j)= flxAtm |
| 416 |
c evpAtm(i,j)= evpAtm |
| 417 |
#ifdef ALLOW_DBUG_THSICE |
| 418 |
IF ( dBug(i,j,bi,bj) ) THEN |
| 419 |
WRITE(6,1020) 'ThSI_SOLV_4T: Tsf, Tice(1,2), dTsurf=', |
| 420 |
& Tsf, Tice, dTsf |
| 421 |
WRITE(6,1020) 'ThSI_SOLV_4T: sHeat, flxCndBt, Qice =', |
| 422 |
& sHeat(i,j), flxCnB(i,j), qicen |
| 423 |
WRITE(6,1020) 'ThSI_SOLV_4T: flxA, evpA, fxSW_bf,af=', |
| 424 |
& flxAtm(i,j), evpAtm(i,j), netSW, flxSW(i,j) |
| 425 |
ENDIF |
| 426 |
#endif |
| 427 |
ELSE |
| 428 |
IF ( .NOT.useBlkFlx ) dTsrf(i,j) = 0. _d 0 |
| 429 |
ENDIF |
| 430 |
ENDDO |
| 431 |
ENDDO |
| 432 |
#endif /* ALLOW_THSICE */ |
| 433 |
|
| 434 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 435 |
|
| 436 |
RETURN |
| 437 |
END |
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