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C $Header: /u/gcmpack/MITgcm/pkg/seaice/seaice_prepare_ridging.F,v 1.4 2014/05/08 11:29:26 mlosch Exp $ |
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C $Name: $ |
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|
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#include "SEAICE_OPTIONS.h" |
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#ifdef ALLOW_AUTODIFF |
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# include "AUTODIFF_OPTIONS.h" |
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#endif |
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|
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CBOP |
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C !ROUTINE: SEAICE_PREPARE_RIDGING |
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C !INTERFACE: ========================================================== |
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SUBROUTINE SEAICE_PREPARE_RIDGING( |
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#ifdef SEAICE_ITD |
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O hActual, |
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O hrMin, hrMax, hrExp, ridgeRatio, ridgingModeNorm, partFunc, |
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#endif /* SEAICE_ITD */ |
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I iMin, iMax, jMin, jMax, bi, bj, myTime, myIter, myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *===========================================================* |
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C | SUBROUTINE SEAICE_PREPARE_RIDGING |
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C | o compute ridging parameters according to Thorndyke et al |
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C | (1975), Hibler (1980), Bitz et al (2001) or |
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C | Lipscomb et al (2007) |
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C | o this routine is called from s/r seaice_do_ridging and |
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C | from s/r seaice_calc_ice_strength |
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C | |
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C | Martin Losch, Apr. 2014, Martin.Losch@awi.de |
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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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#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_SIZE.h" |
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#include "SEAICE_PARAMS.h" |
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#include "SEAICE.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 !INPUT PARAMETERS: =================================================== |
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C === Routine arguments === |
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C bi, bj :: outer loop counters |
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C myTime :: current time |
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C myIter :: iteration number |
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C myThid :: Thread no. that called this routine. |
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C i/jMin/Max:: loop boundaries |
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_RL myTime |
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INTEGER bi,bj |
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INTEGER myIter |
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INTEGER myThid |
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INTEGER iMin, iMax, jMin, jMax |
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#ifdef SEAICE_ITD |
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C ridgingModeNorm :: norm to ensure convervation (N in Lipscomb et al 2007) |
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C partFunc :: participation function (a_n in Lipscomb et al 2007) |
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C ridgeRatio :: mean ridge thickness/ thickness of ridging ice |
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C hrMin :: min ridge thickness |
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C hrMax :: max ridge thickness (SEAICEredistFunc = 0) |
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C hrExp :: ridge e-folding scale (SEAICEredistFunc = 1) |
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C hActual :: HEFFITD/AREAITD, regularized |
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_RL ridgingModeNorm (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL partFunc (1-OLx:sNx+OLx,1-OLy:sNy+OLy,0:nITD) |
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_RL hrMin (1-OLx:sNx+OLx,1-OLy:sNy+OLy,1:nITD) |
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_RL hrMax (1-OLx:sNx+OLx,1-OLy:sNy+OLy,1:nITD) |
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_RL hrExp (1-OLx:sNx+OLx,1-OLy:sNy+OLy,1:nITD) |
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_RL ridgeRatio (1-OLx:sNx+OLx,1-OLy:sNy+OLy,1:nITD) |
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_RL hActual (1-OLx:sNx+OLx,1-OLy:sNy+OLy,1:nITD) |
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CEndOfInterface |
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|
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C !LOCAL VARIABLES: ==================================================== |
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C === Local variables === |
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C i,j,k :: inner loop counters |
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C |
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INTEGER i, j |
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INTEGER k |
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C variables related to ridging schemes |
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C gSum :: cumulative distribution function G |
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_RL gSum (1-OLx:sNx+OLx,1-OLy:sNy+OLy,-1:nITD) |
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_RL recip_gStar, recip_aStar, tmp |
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C Regularization values squared |
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_RL area_reg_sq, hice_reg_sq |
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CEOP |
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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 regularization constants |
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area_reg_sq = SEAICE_area_reg * SEAICE_area_reg |
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hice_reg_sq = SEAICE_hice_reg * SEAICE_hice_reg |
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DO k=1,nITD |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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hActual(i,j,k) = 0. _d 0 |
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CML IF ( AREAITD(i,j,k,bi,bj) .GT. SEAICE_area_reg ) THEN |
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CML hActual(i,j,k) = HEFFITD(i,j,k,bi,bj)/AREAITD(i,j,k,bi,bj) |
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CML ENDIF |
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IF ( HEFFITD(i,j,k,bi,bj) .GT. 0. _d 0 ) THEN |
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C regularize as in seaice_growth: compute hActual with regularized |
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C AREA and regularize from below with a minimum thickness |
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tmp = HEFFITD(i,j,k,bi,bj) |
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& /SQRT( AREAITD(i,j,k,bi,bj)**2 + area_reg_sq ) |
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hActual(i,j,k) = SQRT(tmp * tmp + hice_reg_sq) |
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ENDIF |
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ENDDO |
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ENDDO |
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ENDDO |
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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 the cumulative thickness distribution function gSum |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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gSum(i,j,-1) = 0. _d 0 |
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gSum(i,j,0) = 0. _d 0 |
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IF ( opnWtrFrac(i,j,bi,bj) .GT. SEAICE_area_floor ) |
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& gSum(i,j,0) = opnWtrFrac(i,j,bi,bj) |
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ENDDO |
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ENDDO |
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DO k = 1, nITD |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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gSum(i,j,k) = gSum(i,j,k-1) |
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IF ( AREAITD(i,j,k,bi,bj) .GT. SEAICE_area_floor ) |
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& gSum(i,j,k) = gSum(i,j,k) + AREAITD(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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C normalize |
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DO k = 0, nITD |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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IF ( gSum(i,j,nITD).NE.0. _d 0 ) |
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& gSum(i,j,k) = gSum(i,j,k) / gSum(i,j,nITD) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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C Compute the participation function |
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C area lost from category n due to ridging/closing |
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C partFunc(n) = -------------------------------------------------- |
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C total area lost due to ridging/closing |
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|
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IF ( SEAICEpartFunc .EQ. 0 ) THEN |
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C Thorndike et al. (1975) discretize b(h) = (2/Gstar) * (1 - G(h)/Gstar) |
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C The expressions for the partition function partFunc are found by |
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C integrating b(h)g(h) between the category boundaries. |
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recip_gStar = 1. _d 0 / SEAICEgStar |
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DO k = 0, nITD |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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partFunc(i,j,k) = 0. _d 0 |
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IF ( gSum(i,j,k) .LT. SEAICEgStar ) THEN |
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partFunc(i,j,k) = |
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& (gSum(i,j,k)-gSum(i,j,k-1)) * recip_gStar |
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& *( 2. _d 0 - (gSum(i,j,k-1)+gSum(i,j,k))*recip_gStar) |
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ELSEIF ( gSum(i,j,k-1) .LT. SEAICEgStar |
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& .AND. gSum(i,j,k) .GE. SEAICEgStar ) THEN |
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partFunc(i,j,k) = |
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& (SEAICEgStar-gSum(i,j,k-1)) * recip_gStar |
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& *( 2. _d 0 - (gSum(i,j,k-1)+SEAICEgStar)*recip_gStar) |
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ENDIF |
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ENDDO |
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ENDDO |
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ENDDO |
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ELSEIF ( SEAICEpartFunc .EQ. 1 ) THEN |
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C Lipscomb et al. (2007) discretize b(h) = exp(-G(h)/astar) into |
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C partFunc(n) = [exp(-G(n-1)/astar - exp(-G(n)/astar] / [1-exp(-1/astar)]. |
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C The expression is found by integrating b(h)g(h) between the category |
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C boundaries. |
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recip_astar = 1. _d 0 / SEAICEaStar |
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tmp = 1. _d 0 / ( 1. _d 0 - EXP( -recip_astar ) ) |
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C abuse gSum as a work array |
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k = -1 |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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gSum(i,j,k) = EXP(-gSum(i,j,k)*recip_astar) * tmp |
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ENDDO |
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ENDDO |
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DO k = 0, nITD |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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gSum(i,j,k) = EXP(-gSum(i,j,k)*recip_astar) * tmp |
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partFunc(i,j,k) = gSum(i,j,k-1) - gSum(i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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ELSE |
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STOP 'Ooops: SEAICEpartFunc > 1 not implemented' |
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ENDIF |
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|
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C Compute variables of ITD of ridged ice |
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C ridgeRatio :: mean ridge thickness/ thickness of ridging ice |
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C hrMin :: min ridge thickness |
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C hrMax :: max ridge thickness (SEAICEredistFunc = 0) |
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C hrExp :: ridge e-folding scale (SEAICEredistFunc = 1) |
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DO k = 1, nITD |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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hrMin(i,j,k) = 0. _d 0 |
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hrMax(i,j,k) = 0. _d 0 |
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hrExp(i,j,k) = 0. _d 0 |
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C avoid divisions by zero |
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ridgeRatio(i,j,k) = 1. _d 0 |
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ENDDO |
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ENDDO |
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ENDDO |
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IF ( SEAICEredistFunc .EQ. 0 ) THEN |
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C Assume ridged ice is uniformly distributed between hrmin and hrmax. |
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C (Hibler, 1980) |
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DO k = 1, nITD |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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IF ( hActual(i,j,k) .GT. 0. _d 0 ) THEN |
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C This is the original Hibler (1980) scheme: |
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hrMin(i,j,k) = 2. _d 0 * hActual(i,j,k) |
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hrMax(i,j,k) = 2. _d 0 * SQRT(hActual(i,j,k)*SEAICEhStar) |
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C CICE does this in addition, so that thick ridging ice is not required |
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C to raft: |
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hrMin(i,j,k) = MIN(hrMin(i,j,k),hActual(i,j,k)+SEAICEmaxRaft) |
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hrMax(i,j,k) = MAX(hrMax(i,j,k),hrMin(i,j,k)+SEAICE_hice_reg) |
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C |
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ridgeRatio(i,j,k) = |
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& 0.5 _d 0 * (hrMax(i,j,k)+hrMin(i,j,k))/hActual(i,j,k) |
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ENDIF |
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ENDDO |
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ENDDO |
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ENDDO |
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ELSEIF ( SEAICEredistFunc .EQ. 1 ) THEN |
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C Follow Lipscomb et al. (2007) and model ridge ITD as an exponentially |
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C decaying function |
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DO k = 1, nITD |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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IF ( hActual(i,j,k) .GT. 0. _d 0 ) THEN |
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C regularization is only required in this case but already done above |
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CML tmp = MAX(hActual(i,j,k), SEAICE_hice_reg) |
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tmp = hActual(i,j,k) |
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hrMin(i,j,k) = MIN(2.D0 * tmp, tmp+SEAICEmaxRaft) |
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hrExp(i,j,k) = SEAICEmuRidging*SQRT(tmp) |
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C arent we missing a factor 0.5 here? |
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ridgeRatio(i,j,k)=(hrMin(i,j,k)+hrExp(i,j,k))/tmp |
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ENDIF |
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ENDDO |
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ENDDO |
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ENDDO |
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ELSE |
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STOP 'Ooops: SEAICEredistFunc > 1 not implemented' |
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ENDIF |
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|
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C Compute the norm of the ridging mode N (in Lipscomp et al 2007) |
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C or omega (in Bitz et al 2001): |
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C rigdingModeNorm = net ice area removed / total area participating. |
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C For instance, if a unit area of ice with thickness = 1 participates in |
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C ridging to form a ridge with a = 1/3 and thickness = 3, then |
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C rigdingModeNorm = 1 - 1/3 = 2/3. |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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ridgingModeNorm(i,j) = partFunc(i,j,0) |
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ENDDO |
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ENDDO |
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DO k = 1, nITD |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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partFunc(i,j,k) = partFunc(i,j,k) * heffM(i,j,bi,bj) |
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ridgingModeNorm(i,j) = ridgingModeNorm(i,j) |
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& + partFunc(i,j,k)*( 1. _d 0 - 1. _d 0/ridgeRatio(i,j,k) ) |
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ENDDO |
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ENDDO |
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ENDDO |
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C avoid division by zero |
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DO j=jMin,jMax |
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DO i=iMin,iMax |
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IF ( ridgingModeNorm(i,j) .LE. 0. _d 0 ) |
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& ridgingModeNorm(i,j) = 1. _d 0 |
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ENDDO |
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ENDDO |
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|
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#endif /* SEAICE_ITD */ |
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|
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RETURN |
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END |
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