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C $Header: /u/gcmpack/MITgcm/pkg/gmredi/gmredi_calc_eigs.F,v 1.6 2014/05/20 11:42:28 m_bates Exp $ |
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C $Name: $ |
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|
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#include "GMREDI_OPTIONS.h" |
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|
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C !ROUTINE: EIGENVAL |
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C !INTERFACE: |
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SUBROUTINE GMREDI_CALC_EIGS( |
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I iMin, iMax, jMin, jMax, |
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I bi, bj, N2, myThid, kLow, |
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I mask, hfac, recip_hfac, |
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I rlow, nmodes, writediag, |
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O Rmid, vec) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE GMREDI_CALC_URMS |
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C | o Calculate the vertical structure of the rms eddy |
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C | velocity based on baroclinic modal decomposition |
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C *==========================================================* |
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C \ev |
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|
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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 "GRID.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "GMREDI.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 bi, bj :: tile indices |
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LOGICAL writediag |
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INTEGER iMin,iMax,jMin,jMax |
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INTEGER bi, bj |
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INTEGER myThid |
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INTEGER nmodes |
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INTEGER kLow(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL mask(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL hfac(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL recip_hfac(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL rlow(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL N2( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL Rmid(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL vec(nmodes,1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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|
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#ifdef GM_K3D |
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C !LOCAL VARIABLES: |
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C == Local variables == |
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INTEGER i,j,k,kk,m |
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# ifdef HAVE_LAPACK |
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C info :: error code from LAPACK |
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C idx :: index used for sorting the eigenvalues |
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C a3d :: lower diagonal of eigenvalue problem |
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C b3d :: diagonal of eigenvalue problem |
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C c3d :: upper diagonal of eigenvalue problem |
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C val :: Eigenvalue (wavenumber) of the first baroclinic mode |
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C eigR :: Real component of all the eigenvalues in a water column |
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C eigI :: Imaginary component of all the eigenvalues in a water column |
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C vecs :: All the eigenvectors of a water column |
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C dummy :: Redundant variable for calling lapack |
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C work :: Work array for lapack |
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C array :: Array containing the matrix with a,b,c |
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C eigval :: Vector containing the eigenvalues |
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INTEGER info |
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INTEGER idx |
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_RL a3d( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL b3d( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL c3d( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL val( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL eigR(Nr),eigI(Nr),vecs(Nr,Nr),dummy(1,Nr),work(Nr*Nr) |
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_RL array(Nr,Nr) |
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_RL eigval(0:nmodes) |
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# else |
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C drNr :: distance from bottom of cell to cell centre at Nr |
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C BuoyFreq :: buoyancy frequency, SQRT(N2) |
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C intN :: Vertical integral of BuoyFreq to each grid cell centre |
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C intN0 :: Vertical integral of BuoyFreq to z=0 |
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C c1 :: intN0/pi |
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C nEigs :: number of eigenvalues/vectors to calculate |
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_RL drNr |
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_RL BuoyFreq(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr+1) |
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_RL intN(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL intN0(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL c1(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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INTEGER nEigs(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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# endif |
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C small :: a small number (used to avoid floating point exceptions) |
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C vecint :: vertical integral of eigenvector and/or square of eigenvector |
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C fCori2 :: square of the Coriolis parameter |
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_RL small |
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_RL vecint(nmodes,1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL fCori2(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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CHARACTER*(MAX_LEN_MBUF) msgBuf |
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|
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small = TINY(zeroRL) |
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|
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C Square of the Coriolis parameter |
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DO i=1-OLx,sNx+OLx |
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DO j=1-OLy,sNy+OLy |
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fCori2(i,j) = fCori(i,j,bi,bj)*fCori(i,j,bi,bj) |
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ENDDO |
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ENDDO |
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|
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DO k=1,Nr |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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DO m=1,nmodes |
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vec(m,i,j,k) = zeroRL |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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# ifdef HAVE_LAPACK |
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C Calculate the tridiagonal operator matrix for |
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C f^2 d/dz 1/N^2 d/dz |
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C a3d is the lower off-diagonal, b3d is the diagonal |
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C and c3d is the upper off-diagonal |
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DO k=1,Nr |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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IF (kLow(i,j) .GT. 0) THEN |
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IF (k.EQ.1) THEN |
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a3d(i,j,k) = zeroRL |
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c3d(i,j,k) = fCori2(i,j)*recip_hFac(i,j,k) |
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& *recip_drC(k+1)*recip_drF(k)/N2(i,j,k+1) |
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b3d(i,j,k) = -c3d(i,j,k) |
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|
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ELSEIF (k.LT.kLow(i,j)) THEN |
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a3d(i,j,k) = fCori2(i,j)*recip_hFac(i,j,k) |
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& *recip_drF(k)*recip_drC(k)/N2(i,j,k) |
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c3d(i,j,k) = fCori2(i,j)*recip_hFac(i,j,k) |
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& *recip_drF(k)*recip_drC(k+1)/N2(i,j,k+1) |
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b3d(i,j,k) = -a3d(i,j,k)-c3d(i,j,k) |
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|
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ELSEIF (k.EQ.kLow(i,j)) THEN |
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a3d(i,j,k) = fCori2(i,j)*recip_hFac(i,j,k) |
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& *recip_drF(k)*recip_drC(k)/N2(i,j,k) |
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c3d(i,j,k) = zeroRL |
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b3d(i,j,k) = -a3d(i,j,k) |
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|
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ELSE |
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a3d(i,j,k) = zeroRL |
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b3d(i,j,k) = zeroRL |
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c3d(i,j,k) = zeroRL |
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ENDIF |
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|
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ELSE |
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a3d(i,j,k) = zeroRL |
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b3d(i,j,k) = zeroRL |
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c3d(i,j,k) = zeroRL |
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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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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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IF (kLow(i,j).GT.0) THEN |
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DO kk=1,Nr |
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DO k=1,Nr |
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array(k,kk) = zeroRL |
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ENDDO |
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ENDDO |
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|
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k=1 |
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array(k,k) = b3d(i,j,k) |
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array(k,k+1) = c3d(i,j,k) |
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DO k=2,Nr-1 |
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array(k,k-1) = a3d(i,j,k) |
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array(k,k) = b3d(i,j,k) |
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array(k,k+1) = c3d(i,j,k) |
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ENDDO |
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k=Nr |
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array(k,k-1) = a3d(i,j,k) |
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array(k,k) = b3d(i,j,k) |
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|
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CALL DGEEV('N','V',Nr,array,Nr,eigR,eigI,dummy,1, |
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& vecs,Nr,work,Nr*Nr,info) |
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IF( info.LT.0 ) THEN |
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WRITE(msgBuf,'(A,x,2(A1,I2),A1,x,A,I4)') |
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& 'GMREDI_CALC_EIGS problem with arguments for DGEEV at', |
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& '(',i,',',j,')', 'error code =',info |
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CALL PRINT_ERROR( msgBuf , myThid ) |
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|
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ELSEIF(info.GT.0 ) THEN |
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WRITE(msgBuf,'(A,x,2(A1,I2),A1,x,A,I4)') |
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& 'GMREDI_CALC_EIGS problems with eigensolver DGEEV at', |
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& '(',i,',',j,')', 'error code =',info |
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CALL PRINT_ERROR( msgBuf , myThid ) |
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|
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ENDIF |
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|
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C Find the second largest eigenvalue (the Rossby radius) |
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C and the first M baroclinic modes (eigenvectors) |
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DO m=0,nmodes |
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eigval(m) = -HUGE(zeroRL) |
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ENDDO |
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|
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DO k=1,kLow(i,j) |
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eigval(0) = MAX(eigval(0),eigR(k)) |
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ENDDO |
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DO m=1,MIN(nmodes,klow(i,j)-1) |
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DO k=1,kLow(i,j) |
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IF (eigR(k).LT.eigval(m-1)) THEN |
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eigval(m) = MAX(eigval(m),eigR(k)) |
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IF (eigval(m).EQ.eigR(k)) idx=k |
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ENDIF |
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ENDDO |
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IF(vecs(1,idx).LT.zeroRL) THEN |
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DO k=1,Nr |
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vec(m,i,j,k) = -vecs(k,idx) |
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ENDDO |
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ELSE |
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DO k=1,Nr |
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vec(m,i,j,k) = vecs(k,idx) |
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ENDDO |
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ENDIF |
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ENDDO |
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val(i,j) = eigval(1) |
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ELSE |
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val(i,j)=zeroRL |
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DO k=1,Nr |
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DO m=1,nmodes |
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vec(m,i,j,k)=zeroRL |
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ENDDO |
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ENDDO |
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|
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ENDIF |
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ENDDO |
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ENDDO |
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|
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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IF (kLow(i,j).GT.2 .AND. val(i,j).NE.zeroRL) THEN |
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Rmid(i,j) = 1.0/(SQRT(ABS(val(i,j)))+small) |
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ELSE |
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Rmid(i,j) = zeroRL |
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ENDIF |
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ENDDO |
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ENDDO |
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|
| 246 |
# else |
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DO k=1,Nr |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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BuoyFreq(i,j,k) = mask(i,j,k)*SQRT(N2(i,j,k)) |
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ENDDO |
| 252 |
ENDDO |
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ENDDO |
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k=Nr+1 |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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BuoyFreq(i,j,k) = zeroRL |
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ENDDO |
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ENDDO |
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|
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C integrate N using something like Simpson s rule (but not quite) |
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C drC*( (N(k+1)+N(k+2))/2 + (N(k)+N(k+1))/2 )/2 |
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C when k=Nr, say that N(k+2)=0 and N(k+1)=0 |
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k=Nr |
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C drNr is like drC(Nr+1)/2 |
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drNr = rC(Nr)-rF(Nr+1) |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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intN(i,j,k) = op5*BuoyFreq(i,j,k)*drNr |
| 270 |
ENDDO |
| 271 |
ENDDO |
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DO k=Nr-1,1,-1 |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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intN(i,j,k) = intN(i,j,k+1) |
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& + drC(k)*( op25*BuoyFreq(i,j,k+2) + op5*BuoyFreq(i,j,k) |
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& + op25*BuoyFreq(i,j,k+1) ) |
| 278 |
ENDDO |
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ENDDO |
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ENDDO |
| 281 |
|
| 282 |
C intN integrates to z=rC(1). We want to integrate to z=0. |
| 283 |
C Assume that N(0)=0 and N(1)=0. |
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C drC(1) is like half a grid cell. |
| 285 |
DO j=1-Oly,sNy+Oly |
| 286 |
DO i=1-Olx,sNx+Olx |
| 287 |
intN0(i,j) = intN(i,j,1) |
| 288 |
& + drC(1)*op5*BuoyFreq(i,j,2) |
| 289 |
ENDDO |
| 290 |
ENDDO |
| 291 |
|
| 292 |
DO j=1-Oly,sNy+Oly |
| 293 |
DO i=1-Olx,sNx+Olx |
| 294 |
c1(i,j) = intN0(i,j)/pi |
| 295 |
Rmid(i,j) = c1(i,j)/ABS(fCori(i,j,bi,bj)) |
| 296 |
ENDDO |
| 297 |
ENDDO |
| 298 |
|
| 299 |
DO j=1-Oly,sNy+Oly |
| 300 |
DO i=1-Olx,sNx+Olx |
| 301 |
nEigs(i,j) = MIN(klow(i,j),nmodes) |
| 302 |
ENDDO |
| 303 |
ENDDO |
| 304 |
DO k=1,Nr |
| 305 |
DO j=1-Oly,sNy+Oly |
| 306 |
DO i=1-Olx,sNx+Olx |
| 307 |
IF (mask(i,j,k).NE.0.0) THEN |
| 308 |
DO m=1,nEigs(i,j) |
| 309 |
vec(m,i,j,k) = -COS(intN(i,j,k)/(m*c1(i,j))) |
| 310 |
ENDDO |
| 311 |
ENDIF |
| 312 |
ENDDO |
| 313 |
ENDDO |
| 314 |
ENDDO |
| 315 |
|
| 316 |
C The WKB approximation for the baroclinic mode does not always |
| 317 |
C integrate to zero so we adjust it. |
| 318 |
DO j=1-Oly,sNy+Oly |
| 319 |
DO i=1-Olx,sNx+Olx |
| 320 |
DO m=1,nEigs(i,j) |
| 321 |
vecint(m,i,j) = zeroRL |
| 322 |
ENDDO |
| 323 |
ENDDO |
| 324 |
ENDDO |
| 325 |
DO k=1,Nr |
| 326 |
DO j=1-Oly,sNy+Oly |
| 327 |
DO i=1-Olx,sNx+Olx |
| 328 |
DO m=1,nEigs(i,j) |
| 329 |
vecint(m,i,j) = vecint(m,i,j) + hfac(i,j,k)*vec(m,i,j,k)*drF(k) |
| 330 |
ENDDO |
| 331 |
ENDDO |
| 332 |
ENDDO |
| 333 |
ENDDO |
| 334 |
DO j=1-Oly,sNy+Oly |
| 335 |
DO i=1-Olx,sNx+Olx |
| 336 |
DO m=1,nEigs(i,j) |
| 337 |
vecint(m,i,j) = vecint(m,i,j)/(-rlow(i,j)+small) |
| 338 |
ENDDO |
| 339 |
ENDDO |
| 340 |
ENDDO |
| 341 |
DO k=1,Nr |
| 342 |
DO j=1-Oly,sNy+Oly |
| 343 |
DO i=1-Olx,sNx+Olx |
| 344 |
DO m=1,nEigs(i,j) |
| 345 |
vec(m,i,j,k) = vec(m,i,j,k) - vecint(m,i,j) |
| 346 |
ENDDO |
| 347 |
ENDDO |
| 348 |
ENDDO |
| 349 |
ENDDO |
| 350 |
# endif |
| 351 |
|
| 352 |
C Normalise the eigenvectors |
| 353 |
DO j=1-Oly,sNy+Oly |
| 354 |
DO i=1-Olx,sNx+Olx |
| 355 |
DO m=1,nmodes |
| 356 |
vecint(m,i,j) = zeroRL |
| 357 |
ENDDO |
| 358 |
ENDDO |
| 359 |
ENDDO |
| 360 |
|
| 361 |
DO k=1,Nr |
| 362 |
DO j=1-Oly,sNy+Oly |
| 363 |
DO i=1-Olx,sNx+Olx |
| 364 |
DO m=1,nmodes |
| 365 |
vecint(m,i,j) = vecint(m,i,j) + |
| 366 |
& mask(i,j,k)*drF(k)*hfac(i,j,k) |
| 367 |
& *vec(m,i,j,k)*vec(m,i,j,k) |
| 368 |
ENDDO |
| 369 |
ENDDO |
| 370 |
ENDDO |
| 371 |
ENDDO |
| 372 |
|
| 373 |
DO j=1-Oly,sNy+Oly |
| 374 |
DO i=1-Olx,sNx+Olx |
| 375 |
DO m=1,nmodes |
| 376 |
vecint(m,i,j) = SQRT(vecint(m,i,j)) |
| 377 |
ENDDO |
| 378 |
ENDDO |
| 379 |
ENDDO |
| 380 |
|
| 381 |
DO k=1,Nr |
| 382 |
DO j=1-Oly,sNy+Oly |
| 383 |
DO i=1-Olx,sNx+Olx |
| 384 |
DO m=1,nmodes |
| 385 |
vec(m,i,j,k) = vec(m,i,j,k)/(vecint(m,i,j)+small) |
| 386 |
ENDDO |
| 387 |
ENDDO |
| 388 |
ENDDO |
| 389 |
ENDDO |
| 390 |
|
| 391 |
# ifdef ALLOW_DIAGNOSTICS |
| 392 |
C Diagnostics |
| 393 |
IF ( useDiagnostics.AND.writediag ) THEN |
| 394 |
# ifdef HAVE_LAPACK |
| 395 |
CALL DIAGNOSTICS_FILL(a3d, 'GM_A3D ',0,Nr,0,1,1,myThid) |
| 396 |
CALL DIAGNOSTICS_FILL(b3d, 'GM_B3D ',0,Nr,0,1,1,myThid) |
| 397 |
CALL DIAGNOSTICS_FILL(c3d, 'GM_C3D ',0,Nr,0,1,1,myThid) |
| 398 |
# endif |
| 399 |
ENDIF |
| 400 |
# endif |
| 401 |
|
| 402 |
#endif /* GM_K3D */ |
| 403 |
|
| 404 |
RETURN |
| 405 |
END |
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