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C $Header: /u/gcmpack/MITgcm/pkg/seaice/seaice_evp.F,v 1.13 2007/06/06 14:26:32 mlosch Exp $ |
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C $Name: $ |
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|
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#include "SEAICE_OPTIONS.h" |
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|
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CStartOfInterface |
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SUBROUTINE SEAICE_EVP( myTime, myIter, myThid ) |
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C /==========================================================\ |
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C | SUBROUTINE SEAICE_EVP | |
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C | o Ice dynamics using an EVP solver following | |
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C | E. C. Hunke and J. K. Dukowicz. An | |
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C | Elastic-Viscous-Plastic Model for Sea Ice Dynamics, | |
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C | J. Phys. Oceanogr., 27, 1849-1867 (1997). | |
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C |==========================================================| |
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C | written by Martin Losch, March 2006 | |
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C \==========================================================/ |
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IMPLICIT NONE |
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|
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C === Global variables === |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "GRID.h" |
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#include "SEAICE.h" |
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#include "SEAICE_PARAMS.h" |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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# include "tamc.h" |
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#endif |
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|
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C === Routine arguments === |
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C myTime - Simulation time |
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C myIter - Simulation timestep number |
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C myThid - Thread no. that called this routine. |
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_RL myTime |
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INTEGER myIter |
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INTEGER myThid |
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CEndOfInterface |
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|
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#if ( defined (SEAICE_CGRID) && \ |
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defined (SEAICE_ALLOW_EVP) && \ |
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defined (SEAICE_ALLOW_DYNAMICS) ) |
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|
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C === Local variables === |
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C i,j,bi,bj - Loop counters |
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C nEVPstep - number of timesteps within the EVP solver |
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C iEVPstep - Loop counter |
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C SIN/COSWAT - sine/cosine of turning angle |
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C recip_evp_tau - inverse of EVP relaxation/damping timescale |
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C ecc2 - eccentricity squared |
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C e11,e12,e22 - components of strain rate tensor |
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C seaice_div - divergence strain rates at C-points times P |
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C /divided by Delta minus 1 |
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C seaice_tension- tension strain rates at C-points times P |
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C /divided by Delta |
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C seaice_shear - shear strain rates, defined at Z-points times P |
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C /divided by Delta |
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C sig11, sig22 - sum and difference of diagonal terms of stress tensor |
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|
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INTEGER i, j, bi, bj |
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INTEGER nEVPstep, iEVPstep |
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INTEGER ikeyloc |
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#ifndef ALLOW_AUTODIFF_TAMC |
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integer nEVPstepMax |
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#endif |
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|
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_RL SINWAT, COSWAT |
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_RL TEMPVAR, ecc2, recip_ecc2, recip_evp_tau |
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|
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_RL e11 (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL e22 (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL e12 (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL seaice_div (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL seaice_tension(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL seaice_shear (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sig11 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sig22 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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C auxilliary variables |
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_RL e11C, e22C, e12C, deltaC, deltaCreg, pressC, zetaC |
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_RL e11Z, e22Z, e12Z, deltaZ, deltaZreg, pressZ, zetaZ |
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_RL denom1, denom2, fac |
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|
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C-- introduce turning angles |
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SINWAT=SIN(SEAICE_waterTurnAngle*deg2rad) |
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COSWAT=COS(SEAICE_waterTurnAngle*deg2rad) |
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|
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C abbreviation eccentricity squared |
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ecc2=SEAICE_eccen**2 |
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recip_ecc2 = 0. _d 0 |
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IF ( ecc2 .NE. 0. _d 0 ) recip_ecc2=ONE/ecc2 |
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C determine number of interal time steps |
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nEVPstep = INT(SEAICE_deltaTdyn/SEAICE_deltaTevp) |
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C inverse relaxation/damping time scale |
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recip_evp_tau = 0. _d 0 |
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IF ( SEAICE_evpTauRelax .GT. 0. _d 0 ) |
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& recip_evp_tau=1. _d 0/SEAICE_evpTauRelax |
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denom1 = 1. _d 0 |
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& / (1. _d 0 + 0.5 _d 0 *SEAICE_deltaTevp*recip_evp_tau) |
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denom2 = 1. _d 0 |
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& / (1. _d 0 + 0.5 _d 0 *SEAICE_deltaTevp*recip_evp_tau*ecc2) |
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#ifndef ALLOW_AUTODIFF_TAMC |
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nEVPstepMax = nEVPstep |
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#endif |
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|
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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C save last external time step (useless, but consistent with |
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C VP-solver) |
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uIce (I,J,2,bi,bj) = uIce(I,J,1,bi,bj) |
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vIce (I,J,2,bi,bj) = vIce(I,J,1,bi,bj) |
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C use u/vIceC as work arrays: copy previous time step to u/vIceC |
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uIceC(I,J,bi,bj) = uIce(I,J,1,bi,bj) |
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vIceC(I,J,bi,bj) = vIce(I,J,1,bi,bj) |
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c initialise strain rates |
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e11 (I,J,bi,bj) = 0. _d 0 |
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e22 (I,J,bi,bj) = 0. _d 0 |
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e12 (I,J,bi,bj) = 0. _d 0 |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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C damping constraint (Hunke, J.Comp.Phys.,2001) |
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IF ( SEAICE_evpDampC .GT. 0. _d 0 ) THEN |
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fac = HALF * SEAICE_evpDampC * SEAICE_evpTauRelax |
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& /SEAICE_deltaTevp**2 |
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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zMax (I,J,bi,bj) = _rA(I,J,bi,bj) * fac |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDIF |
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C |
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C start of the main time loop |
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DO iEVPstep = 1, nEVPstepMax |
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IF (iEVPstep.LE.nEVPstep) THEN |
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C |
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#ifdef ALLOW_AUTODIFF_TAMC |
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ikeyloc = iEVPstep + |
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& (ikey_dynamics-1)*nEVPstepMax |
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CADJ STORE uicec = comlev1_evp, |
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CADJ & key = ikeyloc, byte = isbyte |
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CADJ STORE vicec = comlev1_evp, |
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CADJ & key = ikeyloc, byte = isbyte |
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CADJ STORE seaice_sigma1 = comlev1_evp, |
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CADJ & key = ikeyloc, byte = isbyte |
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CADJ STORE seaice_sigma2 = comlev1_evp, |
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CADJ & key = ikeyloc, byte = isbyte |
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CADJ STORE seaice_sigma12 = comlev1_evp, |
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CADJ & key = ikeyloc, byte = isbyte |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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C |
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C first calculate strain rates and bulk moduli/viscosities |
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C |
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CALL SEAICE_CALC_STRAINRATES( |
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I uIceC, vIceC, |
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O e11, e22, e12, |
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I myThid ) |
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|
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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seaice_div (I,J) = 0. _d 0 |
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seaice_tension(I,J) = 0. _d 0 |
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seaice_shear (I,J) = 0. _d 0 |
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ENDDO |
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ENDDO |
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DO j=0,sNy+1 |
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DO i=0,sNx+1 |
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C average strain rates to Z and C points |
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e11C = e11(i,j,bi,bj) |
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e22C = e22(i,j,bi,bj) |
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e12C = 0.25 _d 0 |
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& * ( e12(I,J ,bi,bj) + e12(I+1,J ,bi,bj) |
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& + e12(I,J+1,bi,bj) + e12(I+1,J+1,bi,bj) ) |
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e11Z = 0.25 _d 0 |
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& * ( e11(I,J ,bi,bj) + e11(I-1,J ,bi,bj) |
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& + e11(I,J-1,bi,bj) + e11(I-1,J-1,bi,bj) ) |
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e22Z = 0.25 _d 0 |
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& * ( e22(I,J ,bi,bj) + e22(I-1,J ,bi,bj) |
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& + e22(I,J-1,bi,bj) + e22(I-1,J-1,bi,bj) ) |
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e12Z = e12(i,j,bi,bj) |
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deltaC = (e11C**2+e22C**2)*(ONE+recip_ecc2) |
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& + 4. _d 0*recip_ecc2*e12C**2 |
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& + 2. _d 0*e11C*e22C*(ONE-recip_ecc2) |
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deltaCreg = SQRT(MAX(deltaC,SEAICE_EPS_SQ)) |
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deltaZ = (e11Z**2+e22Z**2)*(ONE+recip_ecc2) |
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& + 4. _d 0*recip_ecc2*e12Z**2 |
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& + 2. _d 0*e11Z*e22Z*(ONE-recip_ecc2) |
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deltaZreg = SQRT(MAX(deltaZ,SEAICE_EPS_SQ)) |
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#ifdef ALLOW_AUTODIFF_TAMC |
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C avoid sqrt of 0 |
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IF ( deltaC .GT. 0. _d 0 ) deltaC = SQRT(deltaC) |
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IF ( deltaZ .GT. 0. _d 0 ) deltaZ = SQRT(deltaZ) |
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#else |
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deltaC = SQRT(deltaC) |
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deltaZ = SQRT(deltaZ) |
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#endif /* ALLOW_AUTODIFF_TAMC */ |
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C modify pressure (copied from seaice_calc_viscosities) |
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zetaC = HALF*press0(I,J,bi,bj)/deltaCreg |
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zetaC = MIN(zMax(I,J,bi,bj),zetaC) |
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zetaC = MAX(zMin(I,J,bi,bj),zetaC) |
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CML zetaC = zetaC*hEffM(I,J,bi,bj) |
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pressZ = (deltaZ/deltaZreg) * 0.25 _d 0 |
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& * ( PRESS0(I,J ,bi,bj) + PRESS0(I-1,J ,bi,bj) |
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& + PRESS0(I,J-1,bi,bj) + PRESS0(I-1,J-1,bi,bj) ) |
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zetaZ = HALF/deltaZreg * pressZ |
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zetaZ = MIN(zMax(I,J,bi,bj),zetaZ) |
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zetaZ = MAX(zMin(I,J,bi,bj),zetaZ) |
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pressC = TWO*zetaC*deltaC |
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C Calculate the RHS of the stress equations. Do this now in order to |
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C avoid multiple divisions by Delta |
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C P * ( D_d/Delta - 1 ) = 2*zeta*D_d - P = 2*zeta*D_d - 2*zeta*Delta |
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C P * ( D_t/Delta ) = 2*zeta*D_t |
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C P * ( D_s/Delta ) = 2*zeta*D_s |
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seaice_div (I,J) = ( |
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& 2. _d 0 *zetaC*(e11C+e22C) - pressC |
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& ) *hEffM(I,J,bi,bj) |
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seaice_tension(I,J) = 2. _d 0*zetaC*(e11C-e22C) |
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& *hEffM(I,J,bi,bj) |
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seaice_shear (I,J) = 2. _d 0*zetaZ*2. _d 0*e12Z |
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ENDDO |
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ENDDO |
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C |
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C first step stress equations |
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C |
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DO j=0,sNy |
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DO i=0,sNx |
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C sigma1 and sigma2 are computed on C points |
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seaice_sigma1 (I,J,bi,bj) = ( seaice_sigma1 (I,J,bi,bj) |
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& + SEAICE_deltaTevp * 0.5 _d 0 * recip_evp_tau |
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& * seaice_div(I,J) |
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& ) * denom1 |
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& *hEffM(I,J,bi,bj) |
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seaice_sigma2 (I,J,bi,bj) = ( seaice_sigma2 (I,J,bi,bj) |
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& + SEAICE_deltaTevp * 0.5 _d 0 * recip_evp_tau |
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& * seaice_tension(I,J) |
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& ) * denom2 |
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& *hEffM(I,J,bi,bj) |
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C recover sigma11 and sigma22 |
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sig11(I,J) = 0.5 _d 0 * |
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& ( seaice_sigma1(I,J,bi,bj)+seaice_sigma2(I,J,bi,bj) ) |
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sig22(I,J) = 0.5 _d 0 * |
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& ( seaice_sigma1(I,J,bi,bj)-seaice_sigma2(I,J,bi,bj) ) |
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ENDDO |
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ENDDO |
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|
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C sigma12 is computed on Z points |
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DO j=1,sNy+1 |
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DO i=1,sNx+1 |
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seaice_sigma12(I,J,bi,bj) = ( seaice_sigma12(I,J,bi,bj) |
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& + SEAICE_deltaTevp * 0.25 _d 0 * recip_evp_tau * |
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& seaice_shear(I,J) |
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& ) * denom2 |
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ENDDO |
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ENDDO |
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C |
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C compute divergence of stress tensor |
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C |
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DO J=1,sNy |
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DO I=1,sNx |
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stressDivergenceX(I,J,bi,bj) = |
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& ( sig11(I ,J ) * _dyF(I ,J,bi,bj) |
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& - sig11(I-1,J ) * _dyF(I-1,J,bi,bj) |
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& + seaice_sigma12(I,J+1,bi,bj) * _dxV(I,J+1,bi,bj) |
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& - seaice_sigma12(I,J ,bi,bj) * _dxV(I,J ,bi,bj) |
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& ) * recip_rAw(I,J,bi,bj) |
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& - |
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& ( seaice_sigma12(I,J ,bi,bj) |
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& + seaice_sigma12(I,J+1,bi,bj) ) |
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& * _tanPhiAtU(I,J,bi,bj) * recip_rSphere |
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& + |
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& ( sig22(I,J) + sig22(I-1,J) ) * 0.5 _d 0 |
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& * _tanPhiAtU(I,J,bi,bj) * recip_rSphere |
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C one metric term missing for general curvilinear coordinates |
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stressDivergenceY(I,J,bi,bj) = |
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& ( sig22(I,J ) * _dxF(I,J ,bi,bj) |
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& - sig22(I,J-1) * _dxF(I,J-1,bi,bj) |
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& + seaice_sigma12(I+1,J,bi,bj) * _dyU(I+1,J,bi,bj) |
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& - seaice_sigma12(I ,J,bi,bj) * _dyU(I ,J,bi,bj) |
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& ) * recip_rAs(I,J,bi,bj) |
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& - |
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& ( sig22(I,J) + sig22(I,J-1) ) * 0.5 _d 0 |
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& * _tanPhiAtV(I,J,bi,bj) * recip_rSphere |
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C two metric terms missing for general curvilinear coordinates |
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ENDDO |
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ENDDO |
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|
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C |
| 296 |
C set up rhs for stepping the velocity field |
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C |
| 298 |
DO J=0,sNy |
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DO I=0,sNx |
| 300 |
C set up non-linear water drag, forcex, forcey |
| 301 |
TEMPVAR = QUART*( |
| 302 |
& ( uIceC(I ,J,bi,bj)-GWATX(I ,J,bi,bj) |
| 303 |
& + uIceC(I+1,J,bi,bj)-GWATX(I+1,J,bi,bj))**2 |
| 304 |
& +(vIceC(I,J ,bi,bj)-GWATY(I,J ,bi,bj) |
| 305 |
& + vIceC(I,J+1,bi,bj)-GWATY(I,J+1,bi,bj))**2) |
| 306 |
IF ( TEMPVAR .LE. (QUART/SEAICE_waterDrag)**2 ) THEN |
| 307 |
DWATN(I,J,bi,bj)=QUART |
| 308 |
ELSE |
| 309 |
DWATN(I,J,bi,bj)=SEAICE_waterDrag*SQRT(TEMPVAR) |
| 310 |
ENDIF |
| 311 |
DWATN(I,J,bi,bj) = DWATN(I,J,bi,bj) * HEFFM(I,J,bi,bj) |
| 312 |
C set up symmetric drag |
| 313 |
DRAGS(I,J,bi,bj) = DWATN(I,J,bi,bj)*COSWAT |
| 314 |
ENDDO |
| 315 |
ENDDO |
| 316 |
|
| 317 |
DO j=1,sNy |
| 318 |
DO i=1,sNx |
| 319 |
C set up anti symmetric drag force and add in ice ocean stress |
| 320 |
C ( remember to average to correct velocity points ) |
| 321 |
FORCEX(I,J,bi,bj)=FORCEX0(I,J,bi,bj)+ |
| 322 |
& 0.5 _d 0 * ( DWATN(I,J,bi,bj)+DWATN(I-1,J,bi,bj) ) * |
| 323 |
& COSWAT * GWATX(I,J,bi,bj) |
| 324 |
& - SIGN(SINWAT, _fCori(I,J,bi,bj))* 0.5 _d 0 * |
| 325 |
& ( DWATN(I ,J,bi,bj) * |
| 326 |
& 0.5 _d 0 * (GWATY(I ,J ,bi,bj)-vIceC(I ,J ,bi,bj) |
| 327 |
& +GWATY(I ,J+1,bi,bj)-vIceC(I ,J+1,bi,bj)) |
| 328 |
& + DWATN(I-1,J,bi,bj) * |
| 329 |
& 0.5 _d 0 * (GWATY(I-1,J ,bi,bj)-vIceC(I-1,J ,bi,bj) |
| 330 |
& +GWATY(I-1,J+1,bi,bj)-vIceC(I-1,J+1,bi,bj)) |
| 331 |
& ) |
| 332 |
FORCEY(I,J,bi,bj)=FORCEY0(I,J,bi,bj)+ |
| 333 |
& 0.5 _d 0 * ( DWATN(I,J,bi,bj)+DWATN(I,J-1,bi,bj) ) * |
| 334 |
& COSWAT * GWATY(I,J,bi,bj) |
| 335 |
& + SIGN(SINWAT, _fCori(I,J,bi,bj)) * 0.5 _d 0 * |
| 336 |
& ( DWATN(I,J ,bi,bj) * |
| 337 |
& 0.5 _d 0 * (GWATX(I ,J ,bi,bj)-uIceC(I ,J ,bi,bj) |
| 338 |
& +GWATX(I+1,J ,bi,bj)-uIceC(I+1,J ,bi,bj)) |
| 339 |
& + DWATN(I,J-1,bi,bj) * |
| 340 |
& 0.5 _d 0 * (GWATX(I ,J-1,bi,bj)-uIceC(I ,J-1,bi,bj) |
| 341 |
& +GWATX(I+1,J-1,bi,bj)-uIceC(I+1,J-1,bi,bj)) |
| 342 |
& ) |
| 343 |
C coriols terms |
| 344 |
FORCEX(I,J,bi,bj)=FORCEX(I,J,bi,bj) + 0.5 _d 0*( |
| 345 |
& seaiceMassC(I ,J,bi,bj) * _fCori(I ,J,bi,bj) |
| 346 |
& * 0.5 _d 0*( vIceC(I ,J,bi,bj)+vIceC(I ,J+1,bi,bj) ) |
| 347 |
& + seaiceMassC(I-1,J,bi,bj) * _fCori(I-1,J,bi,bj) |
| 348 |
& * 0.5 _d 0*( vIceC(I-1,J,bi,bj)+vIceC(I-1,J+1,bi,bj) ) |
| 349 |
& ) |
| 350 |
FORCEY(I,J,bi,bj)=FORCEY(I,J,bi,bj) - 0.5 _d 0*( |
| 351 |
& seaiceMassC(I,J ,bi,bj) * _fCori(I,J ,bi,bj) |
| 352 |
& * 0.5 _d 0*( uIceC(I,J ,bi,bj)+uIceC(I+1, J,bi,bj) ) |
| 353 |
& + seaiceMassC(I,J-1,bi,bj) * _fCori(I,J-1,bi,bj) |
| 354 |
& * 0.5 _d 0*( uIceC(I,J-1,bi,bj)+uIceC(I+1,J-1,bi,bj) ) |
| 355 |
& ) |
| 356 |
ENDDO |
| 357 |
ENDDO |
| 358 |
C |
| 359 |
C step momentum equations with ice-ocean stress term treated implicitly |
| 360 |
C |
| 361 |
DO J=1,sNy |
| 362 |
DO I=1,sNx |
| 363 |
uIceC(I,J,bi,bj) = seaiceMaskU(I,J,bi,bj) * |
| 364 |
& ( seaiceMassU(I,J,bi,bj)/SEAICE_deltaTevp |
| 365 |
& * uIceC(I,J,bi,bj) |
| 366 |
& + FORCEX(I,J,bi,bj) |
| 367 |
& + stressDivergenceX(I,J,bi,bj) ) |
| 368 |
& /( 1. _d 0 - seaiceMaskU(I,J,bi,bj) |
| 369 |
& + seaiceMassU(I,J,bi,bj)/SEAICE_deltaTevp |
| 370 |
& + 0.5 _d 0*( DRAGS(I,J,bi,bj) + DRAGS(I-1,J,bi,bj) ) ) |
| 371 |
vIceC(I,J,bi,bj) = seaiceMaskV(I,J,bi,bj) * |
| 372 |
& ( seaiceMassV(I,J,bi,bj)/SEAICE_deltaTevp |
| 373 |
& * vIceC(I,J,bi,bj) |
| 374 |
& + FORCEY(I,J,bi,bj) |
| 375 |
& + stressDivergenceY(I,J,bi,bj) ) |
| 376 |
& /( 1. _d 0 - seaiceMaskV(I,J,bi,bj) |
| 377 |
& + seaiceMassV(I,J,bi,bj)/SEAICE_deltaTevp |
| 378 |
& + 0.5 _d 0*( DRAGS(I,J,bi,bj) + DRAGS(I,J-1,bi,bj) ) ) |
| 379 |
ENDDO |
| 380 |
ENDDO |
| 381 |
ENDDO |
| 382 |
ENDDO |
| 383 |
|
| 384 |
CALL EXCH_UV_XY_RL(uIceC,vIceC,.TRUE.,myThid) |
| 385 |
|
| 386 |
ENDIF |
| 387 |
C end of the main time loop |
| 388 |
ENDDO |
| 389 |
|
| 390 |
C Copy work arrays and apply masks |
| 391 |
DO bj=myByLo(myThid),myByHi(myThid) |
| 392 |
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 393 |
DO J=1-Oly,sNy+Oly |
| 394 |
DO I=1-Olx,sNx+Olx |
| 395 |
uIce(I,J,1,bi,bj)=uIceC(I,J,bi,bj)* _maskW(I,J,1,bi,bj) |
| 396 |
vIce(I,J,1,bi,bj)=vIceC(I,J,bi,bj)* _maskS(I,J,1,bi,bj) |
| 397 |
END DO |
| 398 |
END DO |
| 399 |
ENDDO |
| 400 |
ENDDO |
| 401 |
|
| 402 |
#endif /* SEAICE_ALLOW_DYNAMICS and SEAICE_CGRID and SEAICE_ALLOW_EVP */ |
| 403 |
|
| 404 |
RETURN |
| 405 |
END |
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