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C $Header: /u/gcmpack/MITgcm/pkg/thsice/thsice_solve4temp.F,v 1.5 2004/12/17 03:44:52 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 useBlkFlx, flxExcSw, Tf, hi, hs, |
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U flxSW, Tsf, qicen, |
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O Tice, sHeating, flxCnB, |
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O dTsf, flxAtm, evpAtm, |
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I i,j,bi,bj, 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 !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 useBlkFlx :: use surf. fluxes from bulk-forcing external S/R |
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C flxExcSw :: 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 Tf :: freezing temperature (oC) of local sea-water |
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C hi :: ice height |
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C hs :: snow height |
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C flxSW :: net Short-Wave flux (+=down) [W/m2]: input= at surface |
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C :: output= at the sea-ice base to the ocean |
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C Tsf :: surface (ice or snow) temperature |
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C qicen :: ice enthalpy (J/kg) |
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C Tice :: internal ice temperatures |
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C sHeating :: surf heating 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 dTsf :: surf. temp adjusment: Ts^n+1 - Ts^n |
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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 i,j,bi,bj :: indices of current grid point |
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C myThid :: Thread no. that called this routine. |
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LOGICAL useBlkFlx |
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_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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|
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_RL flxSW |
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_RL Tsf |
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_RL qicen(nlyr) |
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|
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_RL Tice (nlyr) |
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_RL sHeating |
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_RL flxCnB |
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_RL dTsf |
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_RL flxAtm |
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_RL evpAtm |
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INTEGER i,j, bi,bj |
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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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|
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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 == Local Variables == |
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INTEGER k, iterMax |
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|
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_RL frsnow ! fractional snow cover |
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|
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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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|
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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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|
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_RL df0dT ! deriv of flx0 wrt Tsf (W m-2 deg-1) |
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|
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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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|
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_RL dt ! timestep |
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|
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INTEGER iceornot |
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LOGICAL dBug |
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|
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1010 FORMAT(A,I3,3F8.3) |
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1020 FORMAT(A,1P4E11.3) |
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|
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dt = thSIce_deltaT |
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dBug = .FALSE. |
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c dBug = ( bi.EQ.3 .AND. i.EQ.15 .AND. j.EQ.11 ) |
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c dBug = ( bi.EQ.6 .AND. i.EQ.18 .AND. j.EQ.10 ) |
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IF (dBug) WRITE(6,'(A,2I4,2I2)') 'ThSI_SOLVE4T: i,j=',i,j,bi,bj |
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|
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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 = flxSW * (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 = flxSW - 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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IF (dBug) WRITE(6,1010) 'ThSI_SOLVE4T: k, Ts, Tice=',0,Tsf,Tice |
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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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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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flx0 = fswdn + flxExceptSw |
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ELSE |
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flx0 = fswdn + flxExcSw(1) |
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df0dT = flxExcSw(2) |
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ENDIF |
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IF ( dBug ) WRITE(6,1020) 'ThSI_SOLVE4T: flx0,df0dT,k12,D=', |
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& flx0,df0dT,k12,k12-df0dT |
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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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IF(dBug) WRITE(6,1010) 'ThSI_SOLVE4T: k,ts,t1,dTs=', |
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& k,Tsf,Tice(1),dTsf |
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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 |
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IF ( useBlkFlx ) THEN |
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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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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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flx0 = fswdn + flxExceptSw |
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dTsf = 0. _d 0 |
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ELSE |
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flx0 = fswdn + flxExcSw(0) |
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dTsf = 1000. |
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df0dT = 0. |
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ENDIF |
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ENDIF |
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|
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C Check for convergence. If no convergence, then repeat. |
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C |
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C Convergence test: Make sure Tsfc has converged, within prescribed error. |
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C (Energy conservation is guaranteed within machine roundoff, even |
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C if Tsfc has not converged.) |
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C If no convergence, then repeat. |
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|
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IF ( dBug ) WRITE(6,1010) 'ThSI_SOLVE4T: k,ts,t1,dTs=', |
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& k,Tsf,Tice(1),dTsf |
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IF ( useBlkFlx .AND. k.EQ.nitMaxTsf |
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& .AND. ABS(dTsf).GE.Terrmax ) THEN |
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WRITE (6,*) 'BB: thermw conv err ',i,j,bi,bj,dTsf |
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WRITE (6,*) 'BB: thermw conv err, iceheight ', hi |
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WRITE (6,*) 'BB: thermw conv err: Tsf, flx0', Tsf,flx0 |
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IF (Tsf.LT.-70. _d 0) STOP |
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ENDIF |
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|
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100 continue ! surface temperature iteration |
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ENDIF |
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ENDDO |
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150 continue |
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C ------ end iteration ------------ |
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|
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C Compute new bottom layer temperature. |
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|
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Tice(2) = (2. _d 0*dt*k32*(Tice(1)+2. _d 0*Tf) |
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& + rhoi*cpice *hi*Tice(2)) |
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& /(6. _d 0*dt*k32 + rhoi*cpice *hi) |
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IF (dBug) WRITE(6,1010) 'ThSI_SOLVE4T: k, Ts, Tice=',k,Tsf,Tice |
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|
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|
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C Compute final flux values at surfaces. |
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|
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fct = k12*(Tsf-Tice(1)) |
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flxCnB = 4. _d 0*kice *(Tice(2)-Tf)/hi |
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flx0 = flx0 + df0dT*dTsf |
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IF ( useBlkFlx ) THEN |
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evpAtm = evap |
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C-- needs to update also Evap (Tsf changes) since Latent heat has been updated |
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evpAtm = evap + dEvdT*dTsf |
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C- energy flux to Atmos: use net short-wave flux at surf. and |
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C use latent heat = Lvap (energy=0 for liq. water at 0.oC) |
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flxAtm = flxSW + flxExceptSw + df0dT*dTsf |
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& + evpAtm*Lfresh |
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ELSE |
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flxAtm = 0. |
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evpAtm = 0. |
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ENDIF |
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sHeating = flx0 - fct |
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|
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C- SW flux at sea-ice base left to the ocean |
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flxSW = fswocn |
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|
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IF (dBug) WRITE(6,1020) 'ThSI_SOLVE4T: flx0,fct,Dif,flxCnB=', |
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& flx0,fct,flx0-fct,flxCnB |
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|
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C Compute new enthalpy for each layer. |
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|
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qicen(1) = -cpwater*Tmlt1 + cpice *(Tmlt1-Tice(1)) + |
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& Lfresh*(1. _d 0-Tmlt1/Tice(1)) |
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qicen(2) = -cpice *Tice(2) + Lfresh |
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|
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C Make sure internal ice temperatures do not exceed Tmlt. |
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C (This should not happen for reasonable values of i0.) |
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|
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IF (Tice(1) .GE. Tmlt1) then |
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WRITE (6,'(A,2I4,2I3,1P2E14.6)') |
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& 'BBerr - Bug: IceT(1) > Tmlt',i,j,bi,bj,Tice(1),Tmlt1 |
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ENDIF |
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IF (Tice(2) .GE. 0. _d 0) THEN |
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WRITE (6,'(A,2I4,2I3,1P2E14.6)') |
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& 'BBerr - Bug: IceT(2) > 0',i,j,bi,bj,Tice(2) |
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ENDIF |
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|
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#endif /* ALLOW_THSICE */ |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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|
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RETURN |
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END |
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