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C $Header: /u/gcmpack/MITgcm/pkg/thsice/thsice_calc_thickn.F,v 1.2 2004/04/18 22:19:37 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_CALC_THICKN |
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C !INTERFACE: |
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SUBROUTINE THSICE_CALC_THICKN( |
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I frzmlt, Tf, oceTs, oceV2s, snowPr, |
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I sHeating, flxCnB, evpAtm, |
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U compact, hi, hs, Tsf, qicen, qleft, |
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O fresh, fsalt, Fbot, |
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I dBugFlag, myThid ) |
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | S/R THSICE_CALC_THICKN |
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C | o Calculate ice & snow thickness changes |
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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 "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 frzmlt :: ocean mixed-layer freezing/melting potential [W/m2] |
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C Tf :: sea-water freezing temperature [oC] (function of S) |
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C oceTs :: surface level oceanic temperature [oC] |
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C oceV2s :: square of ocean surface-level velocity [m2/s2] |
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C snowPr :: snow precipitation [kg/m2/s] |
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C 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 evpAtm :: evaporation to the atmosphere [kg/m2/s] (>0 if evaporate) |
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C compact :: fraction of grid area covered in ice |
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C hi :: ice height |
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C hs :: snow height |
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C Tsf :: surface (ice or snow) temperature |
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C qicen :: ice enthalpy (J m-3) |
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C qleft :: net heat flux to ocean [W/m2] (> 0 downward) |
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C fresh :: Total fresh water flux to ocean [kg/m2/s] (> 0 downward) |
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C fsalt :: salt flux to ocean [g/m2/s] (> 0 downward) |
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C Fbot :: oceanic heat flux used to melt/form ice [W/m2] |
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C dBugFlag :: allow to print debugging stuff (e.g. on 1 grid point). |
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C myThid :: Thread no. that called this routine. |
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_RL frzmlt |
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_RL Tf |
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_RL oceTs, oceV2s, snowPr |
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_RL sHeating |
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_RL flxCnB |
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_RL evpAtm |
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_RL compact |
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_RL hi |
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_RL hs |
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_RL Tsf |
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_RL qicen(nlyr) |
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|
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_RL qleft |
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_RL fresh |
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_RL fsalt |
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_RL Fbot |
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LOGICAL dBugFlag |
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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 |
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|
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_RL rnlyr ! maximum number of ice layers (real value) |
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C evap :: evaporation over snow/ice [kg/m2/s] (>0 if evaporate) |
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_RL evap |
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_RL etop ! energy for top melting (J m-2) |
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_RL ebot ! energy for bottom melting (J m-2) |
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_RL etope ! energy (from top) for lateral melting (J m-2) |
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_RL ebote ! energy (from bottom) for lateral melting (J m-2) |
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_RL extend ! total energy for lateral melting (J m-2) |
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_RL hnew(nlyr) ! new ice layer thickness (m) |
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_RL hlyr ! individual ice layer thickness (m) |
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_RL dhi ! change in ice thickness |
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_RL dhs ! change in snow thickness |
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_RL rq ! rho * q for a layer |
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_RL rqh ! rho * q * h for a layer |
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_RL qbot ! q for new ice at bottom surf (J m-3) |
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_RL dt ! timestep |
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_RL esurp ! surplus energy from melting (J m-2) |
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_RL mwater0 ! fresh water mass gained/lost (kg/m^2) |
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_RL msalt0 ! salt gained/lost (kg/m^2) |
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_RL freshe ! fresh water gain from extension melting |
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_RL salte ! salt gained from extension melting |
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|
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_RL ustar, cpchr |
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|
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_RL chi, chs |
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_RL frace, rs, hq |
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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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rnlyr = nlyr |
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dt = thSIce_deltaT |
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dBug = .FALSE. |
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c dBug = dBugFlag |
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|
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C initialize energies |
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esurp = 0. _d 0 |
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|
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evap = evpAtm |
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|
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C...................................................................... |
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C.. Compute growth and/or melting at the top and bottom surfaces....... |
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C...................................................................... |
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|
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if (frzmlt.ge. 0. _d 0) then |
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C !----------------------------------------------------------------- |
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C ! freezing conditions |
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C !----------------------------------------------------------------- |
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C if higher than hihig, use all frzmlt energy to grow extra ice |
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if (hi.gt.hihig.and. compact.le.iceMaskmax) then |
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Fbot=0. _d 0 |
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else |
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Fbot=frzmlt |
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endif |
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else |
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C !----------------------------------------------------------------- |
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C ! melting conditions |
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C !----------------------------------------------------------------- |
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ustar = 5. _d -2 !for no currents |
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C frictional velocity between ice and water |
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ustar = sqrt(0.00536 _d 0*oceV2s) |
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ustar=max(5. _d -3,ustar) |
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cpchr =cpwater*rhosw*transcoef |
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Fbot = cpchr*(Tf-oceTs)*ustar ! < 0 |
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Fbot = max(Fbot,frzmlt) ! frzmlt < Fbot < 0 |
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Fbot = min(Fbot,0. _d 0) |
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endif |
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|
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C mass of fresh water and salt initially present in ice |
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mwater0 = rhos*hs + rhoi*hi |
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msalt0 = rhoi*hi*saltice |
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|
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IF (dBug) WRITE(6,1020) 'ThSI_CALC_TH: evpAtm, frzmlt, Fbot =', |
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& evpAtm, frzmlt, Fbot |
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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 Compute energy available for melting/growth. |
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|
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if (hi.lt.himin0) then |
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C below a certain height, all energy goes to changing ice extent |
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frace=1. _d 0 |
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else |
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frace=frac_energy |
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endif |
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if (hi.gt.hihig) then |
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C above certain height only melt from top |
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frace=0. _d 0 |
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else |
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frace=frac_energy |
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endif |
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C force this when no ice fractionation |
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if (frac_energy.eq.0. _d 0) frace=0. _d 0 |
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|
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c if (Tsf .eq. 0. _d 0 .and. sHeating.gt.0. _d 0) then |
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if ( sHeating.gt.0. _d 0 ) then |
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etop = (1. _d 0-frace)*sHeating * dt |
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etope = frace*sHeating * dt |
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else |
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etop = 0. _d 0 |
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etope = 0. _d 0 |
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C jmc: found few cases where Tsf=0 & sHeating < 0 : add this line to conserv energy: |
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esurp = sHeating * dt |
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endif |
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C-- flux at the base of sea-ice: |
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C conduction H.flx= flxCnB (+ =down); oceanic turbulent H.flx= Fbot (+ =down). |
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C- ==> energy available(+ => melt)= (flxCnB-Fbot)*dt |
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c if (frzmlt.lt.0. _d 0) then |
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c ebot = (1. _d 0-frace)*(flxCnB-Fbot) * dt |
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c ebote = frace*(flxCnB-Fbot) * dt |
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c else |
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c ebot = (flxCnB-Fbot) * dt |
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c ebote = 0. _d 0 |
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c endif |
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C- original formulation(above): Loose energy when flxCnB < Fbot < 0 |
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ebot = (flxCnB-Fbot) * dt |
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if (ebot.gt.0. _d 0) then |
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ebote = frace*ebot |
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ebot = ebot-ebote |
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else |
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ebote = 0. _d 0 |
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endif |
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IF (dBug) WRITE(6,1020) 'ThSI_CALC_TH: etop,etope,ebot,ebote=', |
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& etop,etope,ebot,ebote |
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|
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C Initialize layer thicknesses. |
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C Make sure internal ice temperatures do not exceed Tmlt. |
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C If they do, then eliminate the layer. (Dont think this will happen |
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C for reasonable values of i0.) |
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|
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hlyr = hi / rnlyr |
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do k = 1, nlyr |
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hnew(k) = hlyr |
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enddo |
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|
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C Top melt: snow, then ice. |
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|
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if (etop .gt. 0. _d 0) then |
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if (hs. gt. 0. _d 0) then |
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rq = rhos * qsnow |
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rqh = rq * hs |
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if (etop .lt. rqh) then |
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hs = hs - etop/rq |
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etop = 0. _d 0 |
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else |
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etop = etop - rqh |
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hs = 0. _d 0 |
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endif |
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endif |
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|
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do k = 1, nlyr |
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if (etop .gt. 0. _d 0) then |
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rq = rhoi * qicen(k) |
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rqh = rq * hnew(k) |
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if (etop .lt. rqh) then |
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hnew(k) = hnew(k) - etop / rq |
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etop = 0. _d 0 |
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else |
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etop = etop - rqh |
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hnew(k) = 0. _d 0 |
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endif |
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endif |
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enddo |
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else |
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etop=0. _d 0 |
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endif |
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C If ice is gone and melting energy remains |
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c if (etop .gt. 0. _d 0) then |
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c write (6,*) 'QQ All ice melts from top ', i,j |
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c hi=0. _d 0 |
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c go to 200 |
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c endif |
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|
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|
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C Bottom melt/growth. |
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|
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if (ebot .lt. 0. _d 0) then |
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C Compute enthalpy of new ice growing at bottom surface. |
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qbot = -cpice *Tf + Lfresh |
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dhi = -ebot / (qbot * rhoi) |
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ebot = 0. _d 0 |
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k = nlyr |
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qicen(k) = (hnew(k)*qicen(k)+dhi*qbot) / (hnew(k)+dhi) |
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hnew(k) = hnew(k) + dhi |
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else |
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do k = nlyr, 1, -1 |
| 278 |
if (ebot.gt.0. _d 0 .and. hnew(k).gt.0. _d 0) then |
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rq = rhoi * qicen(k) |
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rqh = rq * hnew(k) |
| 281 |
if (ebot .lt. rqh) then |
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hnew(k) = hnew(k) - ebot / rq |
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ebot = 0. _d 0 |
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else |
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ebot = ebot - rqh |
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hnew(k) = 0. _d 0 |
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endif |
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endif |
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enddo |
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|
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C If ice melts completely and snow is left, remove the snow with |
| 292 |
C energy from the mixed layer |
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|
| 294 |
if (ebot.gt.0. _d 0 .and. hs.gt.0. _d 0) then |
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rq = rhos * qsnow |
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rqh = rq * hs |
| 297 |
if (ebot .lt. rqh) then |
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hs = hs - ebot / rq |
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ebot = 0. _d 0 |
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else |
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ebot = ebot - rqh |
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hs = 0. _d 0 |
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endif |
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endif |
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c if (ebot .gt. 0. _d 0) then |
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c IF (dBug) WRITE(6,*) 'All ice (& snow) melts from bottom' |
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c hi=0. _d 0 |
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c go to 200 |
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c endif |
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endif |
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|
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C Compute new total ice thickness. |
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hi = 0. _d 0 |
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do k = 1, nlyr |
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hi = hi + hnew(k) |
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enddo |
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IF (dBug) WRITE(6,1020) 'ThSI_CALC_TH: etop, ebot, hi, hs =', |
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& etop, ebot, hi, hs |
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|
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C If hi < himin, melt the ice. |
| 321 |
if ( hi.lt.himin .AND. (hi+hs).gt.0. _d 0 ) then |
| 322 |
esurp = esurp - rhos*qsnow*hs |
| 323 |
do k = 1, nlyr |
| 324 |
esurp = esurp - rhoi*qicen(k)*hnew(k) |
| 325 |
enddo |
| 326 |
hi = 0. _d 0 |
| 327 |
hs = 0. _d 0 |
| 328 |
Tsf=0. _d 0 |
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compact = 0. _d 0 |
| 330 |
do k = 1, nlyr |
| 331 |
qicen(k) = 0. _d 0 |
| 332 |
enddo |
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IF (dBug) WRITE(6,1020) 'ThSI_CALC_TH: -1 : esurp=',esurp |
| 334 |
endif |
| 335 |
|
| 336 |
C-- do a mass-budget of sea-ice to compute "fresh" = the fresh-water flux |
| 337 |
C that is returned to the ocean ; needs to be done before snow/evap |
| 338 |
fresh = (mwater0 - (rhos*hs + rhoi*hi))/dt |
| 339 |
|
| 340 |
C- note : was not supposed to modify snowPr in THSICE_CALC_TH ; |
| 341 |
C but to reproduce old results, reset to zero if Tsf >= 0 |
| 342 |
c IF ( Tsf.ge.0. _d 0 ) snowPr = 0. |
| 343 |
|
| 344 |
IF ( hi .LE. 0. _d 0 ) THEN |
| 345 |
C- return snow to the ocean (account for Latent heat of freezing) |
| 346 |
fresh = fresh + snowPr |
| 347 |
qleft = qleft - snowPr*Lfresh |
| 348 |
GOTO 200 |
| 349 |
ENDIF |
| 350 |
|
| 351 |
C Let it snow |
| 352 |
|
| 353 |
hs = hs + dt*snowPr/rhos |
| 354 |
|
| 355 |
C If ice evap is used to sublimate surface snow/ice or |
| 356 |
C if no ice pass on to ocean |
| 357 |
if (hs.gt.0. _d 0) then |
| 358 |
if (evap/rhos *dt.gt.hs) then |
| 359 |
evap=evap-hs*rhos/dt |
| 360 |
hs=0. _d 0 |
| 361 |
else |
| 362 |
hs = hs - evap/rhos *dt |
| 363 |
evap=0. _d 0 |
| 364 |
endif |
| 365 |
endif |
| 366 |
if (hi.gt.0. _d 0.and.evap.gt.0. _d 0) then |
| 367 |
do k = 1, nlyr |
| 368 |
if (evap .gt. 0. _d 0) then |
| 369 |
C-- original scheme, does not care about ice temp. |
| 370 |
C- this can produce small error (< 1.W/m2) in the Energy budget |
| 371 |
c if (evap/rhoi *dt.gt.hnew(k)) then |
| 372 |
c evap=evap-hnew(k)*rhoi/dt |
| 373 |
c hnew(k)=0. _d 0 |
| 374 |
c else |
| 375 |
c hnew(k) = hnew(k) - evap/rhoi *dt |
| 376 |
c evap=0. _d 0 |
| 377 |
c endif |
| 378 |
C-- modified scheme. taking into account Ice enthalpy |
| 379 |
dhi = evap/rhoi*dt |
| 380 |
if (dhi.ge.hnew(k)) then |
| 381 |
evap=evap-hnew(k)*rhoi/dt |
| 382 |
esurp = esurp - hnew(k)*rhoi*(qicen(k)-Lfresh) |
| 383 |
hnew(k)=0. _d 0 |
| 384 |
else |
| 385 |
hq = hnew(k)*qicen(k)-dhi*Lfresh |
| 386 |
hnew(k) = hnew(k) - dhi |
| 387 |
qicen(k)=hq/hnew(k) |
| 388 |
evap=0. _d 0 |
| 389 |
endif |
| 390 |
C------- |
| 391 |
endif |
| 392 |
enddo |
| 393 |
endif |
| 394 |
c if (evap .gt. 0. _d 0) then |
| 395 |
c write (6,*) 'BB All ice sublimates', i,j |
| 396 |
c hi=0. _d 0 |
| 397 |
c go to 200 |
| 398 |
c endif |
| 399 |
|
| 400 |
C Compute new total ice thickness. |
| 401 |
|
| 402 |
hi = 0. _d 0 |
| 403 |
do k = 1, nlyr |
| 404 |
hi = hi + hnew(k) |
| 405 |
enddo |
| 406 |
|
| 407 |
C If hi < himin, melt the ice. |
| 408 |
if ( hi.gt.0. _d 0 .AND. hi.lt.himin ) then |
| 409 |
fresh = fresh + (rhos*hs + rhoi*hi)/dt |
| 410 |
esurp = esurp - rhos*qsnow*hs |
| 411 |
do k = 1, nlyr |
| 412 |
esurp = esurp - rhoi*qicen(k)*hnew(k) |
| 413 |
enddo |
| 414 |
hi = 0. _d 0 |
| 415 |
hs = 0. _d 0 |
| 416 |
Tsf=0. _d 0 |
| 417 |
compact = 0. _d 0 |
| 418 |
do k = 1, nlyr |
| 419 |
qicen(k) = 0. _d 0 |
| 420 |
enddo |
| 421 |
IF (dBug) WRITE(6,1020) 'ThSI_CALC_TH: -2 : esurp,fresh=', |
| 422 |
& esurp, fresh |
| 423 |
endif |
| 424 |
IF ( hi .le. 0. _d 0 ) GOTO 200 |
| 425 |
|
| 426 |
C If there is enough snow to lower the ice/snow interface below |
| 427 |
C freeboard, convert enough snow to ice to bring the interface back |
| 428 |
C to sea-level. Adjust enthalpy of top ice layer accordingly. |
| 429 |
|
| 430 |
if ( hs .gt. hi*rhoiw/rhos ) then |
| 431 |
cBB write (6,*) 'Freeboard adjusts' |
| 432 |
dhi = (hs * rhos - hi * rhoiw) / rhosw |
| 433 |
dhs = dhi * rhoi / rhos |
| 434 |
rqh = rhoi*qicen(1)*hnew(1) + rhos*qsnow*dhs |
| 435 |
hnew(1) = hnew(1) + dhi |
| 436 |
qicen(1) = rqh / (rhoi*hnew(1)) |
| 437 |
hi = hi + dhi |
| 438 |
hs = hs - dhs |
| 439 |
end if |
| 440 |
|
| 441 |
|
| 442 |
C limit ice height |
| 443 |
C- NOTE: this part does not conserve Energy ; |
| 444 |
C but surplus of fresh water and salt are taken into account. |
| 445 |
if (hi.gt.hiMax) then |
| 446 |
cBB print*,'BBerr, hi>hiMax',i,j,hi |
| 447 |
chi=hi-hiMax |
| 448 |
do k=1,nlyr |
| 449 |
hnew(k)=hnew(k)-chi/2. _d 0 |
| 450 |
enddo |
| 451 |
fresh = fresh + chi*rhoi/dt |
| 452 |
endif |
| 453 |
if (hs.gt.hsMax) then |
| 454 |
c print*,'BBerr, hs>hsMax',i,j,hs |
| 455 |
chs=hs-hsMax |
| 456 |
hs=hsMax |
| 457 |
fresh = fresh + chs*rhos/dt |
| 458 |
endif |
| 459 |
|
| 460 |
C Compute new total ice thickness. |
| 461 |
|
| 462 |
hi = 0. _d 0 |
| 463 |
do k = 1, nlyr |
| 464 |
hi = hi + hnew(k) |
| 465 |
enddo |
| 466 |
|
| 467 |
IF (dBug) WRITE(6,1020) 'ThSI_CALC_TH: b-Winton: hnew, qice =', |
| 468 |
& hnew, qicen |
| 469 |
|
| 470 |
hlyr = hi/rnlyr |
| 471 |
CALL THSICE_RESHAPE_LAYERS( |
| 472 |
U qicen, |
| 473 |
I hlyr, hnew, myThid ) |
| 474 |
|
| 475 |
IF (dBug) WRITE(6,1020) 'ThSI_CALC_TH: compact,hi, qtot, hs =', |
| 476 |
& compact,hi,(qicen(1)+qicen(2))*0.5, hs |
| 477 |
|
| 478 |
200 continue |
| 479 |
|
| 480 |
C- Compute surplus energy left over from melting. |
| 481 |
|
| 482 |
if (hi.le.0. _d 0) compact=0. _d 0 |
| 483 |
|
| 484 |
C.. heat fluxes left over for ocean |
| 485 |
qleft = qleft + (Fbot+(esurp+etop+ebot)/dt) |
| 486 |
IF(dBug) WRITE(6,1020)'ThSI_CALC_TH: [esurp,etop+ebot]/dt =' |
| 487 |
& ,esurp/dt,etop/dt,ebot/dt |
| 488 |
|
| 489 |
C-- Evaporation left to the ocean : |
| 490 |
fresh = fresh - evap |
| 491 |
C- Correct Atmos. fluxes for this different latent heat: |
| 492 |
C evap was computed over freezing surf.(Tsf<0), latent heat = Lvap+Lfresh |
| 493 |
C but should be Lvap only for the fraction "evap" that is left to the ocean. |
| 494 |
qleft = qleft + evap*Lfresh |
| 495 |
|
| 496 |
C fresh and salt fluxes |
| 497 |
c fresh = (mwater0 - (rhos*(hs) + rhoi*(hi)))/dt-evap |
| 498 |
c fsalt = (msalt0 - rhoi*hi*saltice)/35. _d 0/dt ! for same units as fresh |
| 499 |
C note (jmc): fresh is computed from a sea-ice mass budget that already |
| 500 |
C contains, at this point, snow & evaporation (of snow & ice) |
| 501 |
C but are not meant to be part of ice/ocean fresh-water flux. |
| 502 |
C fix: a) like below or b) by making the budget before snow/evap is added |
| 503 |
c fresh = (mwater0 - (rhos*(hs) + rhoi*(hi)))/dt |
| 504 |
c & + snow(i,j,bi,bj)*rhos - evpAtm |
| 505 |
fsalt = (msalt0 - rhoi*hi*saltice)/dt |
| 506 |
|
| 507 |
IF (dBug) WRITE(6,1020)'ThSI_CALC_TH:dH2O,Ev[kg],fresh,fsalt', |
| 508 |
& (mwater0-(rhos*hs+rhoi*hi))/dt,evap,fresh,fsalt |
| 509 |
IF (dBug) WRITE(6,1020)'ThSI_CALC_TH: Qleft,Fbot,extend/dt =', |
| 510 |
& Qleft,Fbot,(etope+ebote)/dt |
| 511 |
|
| 512 |
C-- note: at this point, compact has not been changed (unless reset to zero) |
| 513 |
C and it can only be reduced by lateral melting in the following part: |
| 514 |
|
| 515 |
C calculate extent changes |
| 516 |
extend=etope+ebote |
| 517 |
if (compact.gt.0. _d 0.and.extend.gt.0. _d 0) then |
| 518 |
rq = rhoi * 0.5 _d 0*(qicen(1)+qicen(2)) |
| 519 |
rs = rhos * qsnow |
| 520 |
rqh = rq * hi + rs * hs |
| 521 |
freshe=(rhos*hs+rhoi*hi)/dt |
| 522 |
salte=(rhoi*hi*saltice)/dt |
| 523 |
if (extend .lt. rqh) then |
| 524 |
compact=(1. _d 0-extend/rqh)*compact |
| 525 |
fresh=fresh+extend/rqh*freshe |
| 526 |
fsalt=fsalt+extend/rqh*salte |
| 527 |
else |
| 528 |
compact=0. _d 0 |
| 529 |
hi=0. _d 0 |
| 530 |
hs=0. _d 0 |
| 531 |
qleft=qleft+(extend-rqh)/dt |
| 532 |
fresh=fresh+freshe |
| 533 |
fsalt=fsalt+salte |
| 534 |
endif |
| 535 |
elseif (extend.gt.0. _d 0) then |
| 536 |
qleft=qleft+extend/dt |
| 537 |
endif |
| 538 |
|
| 539 |
#endif /* ALLOW_THSICE */ |
| 540 |
|
| 541 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 542 |
|
| 543 |
RETURN |
| 544 |
END |
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