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C $Header: /u/gcmpack/MITgcm/pkg/gmredi/gmredi_calc_eigs.F,v 1.1 2013/06/21 17:23:31 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 writediag, |
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O Kdef, 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 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 N2( 1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL Kdef(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vec(GM_K3D_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,info |
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_RL small |
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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 vecint(GM_K3D_NModes,1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL val( 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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_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:GM_K3D_NModes) |
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INTEGER idx |
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#ifdef ALLOW_DIAGNOSTICS |
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_RL vec_diag(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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#endif |
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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,GM_K3D_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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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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IF (k+1.GT.Nr) THEN |
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PRINT '(a4,x,3(a1,i2),a1,3(x,i2))', 'kp1:', |
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& '(',i,',',j,',',k,')', |
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& kLow(i,j), k+1, Nr |
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ENDIF |
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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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IF (k.GT.Nr) THEN |
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PRINT '(a4,x,3(a1,i2),a1,3(x,i2))', 'k :', |
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& '(',i,',',j,',',k,')', |
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& kLow(i,j), k, Nr |
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ENDIF |
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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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#ifdef use_lapack |
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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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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,GM_K3D_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(GM_K3D_NModes,klow(i,j)) |
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C DO m=1,GM_K3D_NModes |
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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,GM_K3D_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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C Normalise the eigenvectors |
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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,GM_K3D_NModes |
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vecint(m,i,j) = zeroRL |
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ENDDO |
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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,GM_K3D_NModes |
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vecint(m,i,j) = vecint(m,i,j) + |
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& mask(i,j,k)*drF(k)*hfac(i,j,k) |
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& *vec(m,i,j,k)*vec(m,i,j,k) |
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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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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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DO m=1,GM_K3D_NModes |
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vecint(m,i,j) = SQRT(vecint(m,i,j)) |
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ENDDO |
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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,GM_K3D_NModes |
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vec(m,i,j,k) = vec(m,i,j,k)/(vecint(m,i,j)+small) |
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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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#else |
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C CALL EIGENVAL(a3d,b3d,c3d,bi,bj,val) |
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C CALL EIGENVEC(a3d,b3d,c3d,val,1,bi,bj,vec) |
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#endif |
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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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IF (kLow(i,j).GT.2 .AND. val(i,j).NE.zeroRL) THEN |
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Kdef(i,j) = SQRT(ABS(val(i,j))) |
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ELSE |
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Kdef(i,j) = 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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#ifdef ALLOW_DIAGNOSTICS |
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C Diagnostics |
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IF ( useDiagnostics.AND.writediag ) THEN |
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CALL DIAGNOSTICS_FILL(a3d, 'GM_A3D ',0,Nr,0,1,1,myThid) |
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CALL DIAGNOSTICS_FILL(b3d, 'GM_B3D ',0,Nr,0,1,1,myThid) |
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CALL DIAGNOSTICS_FILL(c3d, 'GM_C3D ',0,Nr,0,1,1,myThid) |
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CALL DIAGNOSTICS_FILL(val, 'GM_VAL ',0, 1,0,1,1,myThid) |
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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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vec_diag(i,j,k) = vec(1,i,j,k) |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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CALL DIAGNOSTICS_FILL(vec_diag, 'GM_VEC ',0,Nr,0,1,1,myThid) |
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ENDIF |
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#endif |
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|
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#endif /* GM_K3D */ |
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|
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RETURN |
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END |
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