C $Header: /u/gcmpack/MITgcm/pkg/gmredi/gmredi_k3d.F,v 1.26 2015/10/30 10:33:24 dfer Exp $ C $Name: $ #include "GMREDI_OPTIONS.h" C !ROUTINE: GMREDI_K3D C !INTERFACE: SUBROUTINE GMREDI_K3D( I iMin, iMax, jMin, jMax, I sigmaX, sigmaY, sigmaR, I bi, bj, myTime, myThid ) C !DESCRIPTION: \bv C *==========================================================* C | SUBROUTINE GMREDI_K3D C | o Calculates the 3D diffusivity as per Bates et al. (2013) C *==========================================================* C \ev IMPLICIT NONE C == Global variables == #include "SIZE.h" #include "EEPARAMS.h" #include "PARAMS.h" #include "GRID.h" #include "DYNVARS.h" #include "FFIELDS.h" #include "GMREDI.h" C !INPUT/OUTPUT PARAMETERS: C == Routine arguments == C bi, bj :: tile indices C myThid :: My Thread Id. number INTEGER iMin,iMax,jMin,jMax _RL sigmaX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL sigmaY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL sigmaR(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) INTEGER bi, bj _RL myTime INTEGER myThid #ifdef GM_K3D C === Functions ==== LOGICAL DIFFERENT_MULTIPLE EXTERNAL DIFFERENT_MULTIPLE C !LOCAL VARIABLES: C == Local variables == INTEGER i,j,k,kk,m,kp1 C update_modes :: Whether to update the eigenmodes LOGICAL update_modes C surfk :: index of the depth of the surface layer C kLow_C :: Local version of the index of deepest wet grid cell on tracer grid C kLow_U :: Local version of the index of deepest wet grid cell on U grid C kLow_V :: Local version of the index of deepest wet grid cell on V grid INTEGER surfk(1-Olx:sNx+Olx,1-Oly:sNy+Oly) INTEGER kLow_C(1-Olx:sNx+Olx,1-Oly:sNy+Oly) INTEGER kLow_U(1-Olx:sNx+Olx,1-Oly:sNy+Oly) INTEGER kLow_V(1-Olx:sNx+Olx,1-Oly:sNy+Oly) C N2loc :: local N**2 C slope :: local slope C Req :: local equatorial deformation radius (m) C deltaH :: local thickness of Eady integration (m) C g_reciprho_sq :: (gravity*recip_rhoConst)**2 C M4loc :: local M**4 C maxDRhoDz :: maximum value of d(rho)/dz (derived from GM_K3D_minN2) C sigx :: local d(rho)/dx C sigy :: local d(rho)/dy C sigz :: local d(rho)/dz C hsurf :: local surface layer depth C small :: a small number (to avoid floating point exceptions) _RL N2loc(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL slope _RL slopeC(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL Req _RL deltaH(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL g_reciprho_sq _RL M4loc(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL M4onN2(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL maxDRhoDz _RL sigx, sigy, sigz _RL hsurf, mskp1 _RL small C dfdy :: gradient of the Coriolis paramater, df/dy, 1/(m*s) C dfdx :: gradient of the Coriolis paramater, df/dx, 1/(m*s) C Rurms :: a local mixing length used in calculation of urms (m) C RRhines :: The Rhines scale (m) C Rmix :: Mixing length C N2 :: Square of the buoyancy frequency (1/s**2) C N2W :: Square of the buoyancy frequency (1/s**2) averaged to west of grid cell C N2S :: Square of the buoyancy frequency (1/s**2) averaged to south of grid cell C N :: Buoyancy frequency, SQRT(N2) C BVint :: The vertical integral of N (m/s) C ubar :: Zonal velocity on a tracer point (m/s) C Ubaro :: Barotropic velocity (m/s) _RL dfdy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL dfdx( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL dummy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL Rurms( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL RRhines(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL Rmix( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL N2( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL N2W( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL N2S( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL N( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL BVint( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL Ubaro( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL ubar( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL tmpU( 1-Olx:sNx+Olx,1-Oly:sNy+Oly ) _RL tmpV( 1-Olx:sNx+Olx,1-Oly:sNy+Oly ) _RL uFldX( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr ) _RL vFldY( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr ) C Rmid :: Rossby radius (m) C KPV :: Diffusivity (m**2/s) C Kdqdx :: diffusivity multiplied by zonal PV gradient C Kdqdy :: diffusivity multiplied by meridional PV gradient C SlopeX :: isopycnal slope in x direction C SlopeY :: isopycnal slope in y direction C dSigmaDx :: sigmaX averaged onto tracer grid C dSigmaDy :: sigmaY averaged onto tracer grid C tfluxX :: thickness flux in x direction C tfluxY :: thickness flux in y direction C fCoriU :: Coriolis parameter averaged to U points C fCoriV :: Coriolis parameter averaged to V points C coriU :: As fCoriU, but limited C coriV :: As fCoriV, but limited C surfkz :: Depth of surface layer (in r units) _RL Rmid(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL KPV(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL Kdqdy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL Kdqdx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL SlopeX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL SlopeY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL dSigmaDx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL dSigmaDy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL tfluxX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL tfluxY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL coriU(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL coriV(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL fCoriU(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL fCoriV(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL surfkz(1-Olx:sNx+Olx,1-Oly:sNy+Oly) C centreX,centreY :: used for calculating averages at centre of cell C numerator,denominator :: of the renormalisation factor C uInt :: column integral of u velocity (sum u*dz) C vInt :: column integral of v velocity (sum v*dz) C KdqdxInt :: column integral of K*dqdx (sum K*dqdx*dz) C KdqdyInt :: column integral of K*dqdy (sum K*dqdy*dz) C uKdqdyInt :: column integral of u*K*dqdy (sum u*K*dqdy*dz) C vKdqdxInt :: column integral of v*K*dqdx (sum v*K*dqdx*dz) C uXiyInt :: column integral of u*Xiy (sum u*Xiy*dz) C vXixInt :: column integral of v*Xix (sum v*Xix*dz) C Renorm :: renormalisation factor at the centre of a cell C RenormU :: renormalisation factor at the western face of a cell C RenormV :: renormalisation factor at the southern face of a cell _RL centreX, centreY _RL numerator, denominator _RL uInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL vInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL KdqdxInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL KdqdyInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL uKdqdyInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL vKdqdxInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL uXiyInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL vXixInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL Renorm(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL RenormU(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL RenormV(1-Olx:sNx+Olx,1-Oly:sNy+Oly) C gradqx :: Potential vorticity gradient in x direction C gradqy :: Potential vorticity gradient in y direction C XimX :: Vertical integral of phi_m*K*gradqx C XimY :: Vertical integral of phi_m*K*gradqy C cDopp :: Quasi-Doppler shifted long Rossby wave speed (m/s) C umc :: ubar-c (m/s) C eady :: Eady growth rate (1/s) C urms :: the rms eddy velocity (m/s) C supp :: The suppression factor C ustar :: The eddy induced velocity in the x direction C vstar :: The eddy induced velocity in the y direction C Xix :: Xi in the x direction (m/s**2) C Xiy :: Xi in the y direction (m/s**2) _RL gradqx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL gradqy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL XimX(GM_K3D_NModes,1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL XimY(GM_K3D_NModes,1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL cDopp(1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL umc( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) _RL eady( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) _RL urms( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) _RL supp( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) _RL ustar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) _RL vstar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) _RL Xix( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) _RL Xiy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) #ifdef GM_K3D_PASSIVE C psistar :: eddy induced streamfunction in the y direction _RL psistar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) #endif C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| C ====================================== C Initialise some variables C ====================================== small = TINY(zeroRL) update_modes=.FALSE. IF ( DIFFERENT_MULTIPLE(GM_K3D_vecFreq,myTime,deltaTClock) ) & update_modes=.TRUE. DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx kLow_C(i,j) = kLowC(i,j,bi,bj) ENDDO ENDDO DO j=1-Oly,sNy+Oly DO i=1-Olx+1,sNx+Olx kLow_U(i,j) = MIN( kLow_C(i,j), kLow_C(i-1,j) ) ENDDO ENDDO DO j=1-Oly+1,sNy+Oly DO i=1-Olx,sNx+Olx kLow_V(i,j) = MIN( kLow_C(i,j), kLow_C(i,j-1) ) ENDDO ENDDO C Dummy values for the edges. This does not affect the results C but avoids problems when solving for the eigenvalues. i=1-Olx DO j=1-Oly,sNy+Oly kLow_U(i,j) = 0 ENDDO j=1-Oly DO i=1-Olx,sNx+Olx kLow_V(i,j) = 0 ENDDO g_reciprho_sq = (gravity*recip_rhoConst)**2 C Gradient of Coriolis DO j=1-Oly+1,sNy+Oly DO i=1-Olx+1,sNx+Olx dfdx(i,j) = ( fCori(i,j,bi,bj)-fCori(i-1,j,bi,bj) ) & *recip_dxC(i,j,bi,bj) dfdy(i,j) = ( fCori(i,j,bi,bj)-fCori(i,j-1,bi,bj) ) & *recip_dyC(i,j,bi,bj) ENDDO ENDDO C Coriolis at U and V points enforcing a minimum value so C that it is defined at the equator DO j=1-Oly,sNy+Oly DO i=1-Olx+1,sNx+Olx C Not limited fCoriU(i,j)= op5*( fCori(i,j,bi,bj)+fCori(i-1,j,bi,bj) ) C Limited so that the inverse is defined at the equator coriU(i,j) = SIGN( MAX( ABS(fCoriU(i,j)),GM_K3D_minCori ), & fCoriU(i,j) ) ENDDO ENDDO DO j=1-Oly+1,sNy+Oly DO i=1-Olx,sNx+Olx C Not limited fCoriV(i,j)= op5*( fCori(i,j,bi,bj)+fCori(i,j-1,bi,bj) ) C Limited so that the inverse is defined at the equator coriV(i,j) = SIGN( MAX( ABS(fCoriV(i,j)),GM_K3D_minCori ), & fCoriV(i,j) ) ENDDO ENDDO C Some dummy values at the edges i=1-Olx DO j=1-Oly,sNy+Oly fCoriU(i,j)= fCori(i,j,bi,bj) coriU(i,j) = SIGN( MAX( ABS(fCori(i,j,bi,bj)),GM_K3D_minCori ), & fCori(i,j,bi,bj) ) ENDDO j=1-Oly DO i=1-Olx,sNx+Olx fCoriV(i,j)= fCori(i,j,bi,bj) coriV(i,j) = SIGN( MAX( ABS(fCori(i,j,bi,bj)),GM_K3D_minCori ), & fCori(i,j,bi,bj) ) ENDDO C Zeroing some cumulative fields DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx eady(i,j) = zeroRL BVint(i,j) = zeroRL Ubaro(i,j) = zeroRL deltaH(i,j) = zeroRL ENDDO ENDDO DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx slopeC(i,j,k)=zeroRL ENDDO ENDDO ENDDO C initialise remaining 2d variables DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx Rurms(i,j)=zeroRL RRhines(i,j)=zeroRL Rmix(i,j)=zeroRL ENDDO ENDDO C initialise remaining 3d variables DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx N2loc(i,j,k)=GM_K3D_minN2 N2W(i,j,k) = GM_K3D_minN2 N2S(i,j,k) = GM_K3D_minN2 M4loc(i,j,k)=zeroRL M4onN2(i,j,k)=zeroRL urms(i,j,k)=zeroRL SlopeX(i,j,k)=zeroRL SlopeY(i,j,k)=zeroRL dSigmaDx(i,j,k)=zeroRL dSigmaDy(i,j,k)=zeroRL gradqx(i,j,k)=zeroRL gradqy(i,j,k)=zeroRL ENDDO ENDDO ENDDO C Find the zonal velocity at the cell centre #ifdef ALLOW_EDDYPSI IF (GM_InMomAsStress) THEN DO k=1,Nr DO i = 1-olx,snx+olx DO j = 1-oly,sny+oly uFldX(i,j,k) = uEulerMean(i,j,k,bi,bj) vFldY(i,j,k) = vEulerMean(i,j,k,bi,bj) ENDDO ENDDO ENDDO ELSE #endif DO k=1,Nr DO i = 1-olx,snx+olx DO j = 1-oly,sny+oly uFldX(i,j,k) = uVel(i,j,k,bi,bj) vFldY(i,j,k) = vVel(i,j,k,bi,bj) ENDDO ENDDO ENDDO #ifdef ALLOW_EDDYPSI ENDIF #endif C The following comes from rotate_uv2en_rl C This code does two things: C 1) go from C grid velocity points to A grid velocity points C 2) go from model grid directions to east/west directions DO k = 1,Nr DO i = 1-Olx,sNx+Olx j=sNy+Oly tmpU(i,j)=zeroRL tmpV(i,j)=zeroRL ENDDO DO j = 1-Oly,sNy+Oly-1 i=sNx+Olx tmpU(i,j)=zeroRL tmpV(i,j)=zeroRL DO i = 1-Olx,sNx+Olx-1 tmpU(i,j) = 0.5 _d 0 & *( uFldX(i+1,j,k) + uFldX(i,j,k) ) tmpV(i,j) = 0.5 _d 0 & *( vFldY(i,j+1,k) + vFldY(i,j,k) ) tmpU(i,j) = tmpU(i,j) * maskC(i,j,k,bi,bj) tmpV(i,j) = tmpV(i,j) * maskC(i,j,k,bi,bj) ENDDO ENDDO C Rotation DO j = 1-oly,sny+oly DO i = 1-olx,snx+olx ubar(i,j,k) = & angleCosC(i,j,bi,bj)*tmpU(i,j) & -angleSinC(i,j,bi,bj)*tmpV(i,j) ENDDO ENDDO ENDDO C Calculate the barotropic velocity by vertically integrating C and the dividing by the depth of the water column C Note that Ubaro is at the C-point. DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx Ubaro(i,j) = Ubaro(i,j) + & drF(k)*hfacC(i,j,k,bi,bj)*ubar(i,j,k) ENDDO ENDDO ENDDO DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx IF (kLow_C(i,j).GT.0) THEN C The minus sign is because r_Low<0 Ubaro(i,j) = -Ubaro(i,j)/r_Low(i,j,bi,bj) ENDIF ENDDO ENDDO C Square of the buoyancy frequency at the top of a grid cell C Enforce a minimum N2 C Mask N2, so it is zero at bottom DO k=2,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx N2(i,j,k) = -gravity*recip_rhoConst*sigmaR(i,j,k) N2(i,j,k) = MAX(N2(i,j,k),GM_K3D_minN2)*maskC(i,j,k,bi,bj) N(i,j,k) = SQRT(N2(i,j,k)) ENDDO ENDDO ENDDO C N2(k=1) is always zero DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx N2(i,j,1) = zeroRL N(i,j,1) = zeroRL ENDDO ENDDO C Calculate the minimum drho/dz maxDRhoDz = -rhoConst*GM_K3D_minN2/gravity C Integrate the buoyancy frequency vertically using the trapezoidal method. C Assume that N(z=-H)=0 DO k=1,Nr kp1 = min(k+1,Nr) mskp1 = oneRL IF ( k.EQ.Nr ) mskp1 = zeroRL DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx BVint(i,j) = BVint(i,j) + hFacC(i,j,k,bi,bj)*drF(k) & *op5*(N(i,j,k)+mskp1*N(i,j,kp1)) ENDDO ENDDO ENDDO C Calculate the eigenvalues and eigenvectors IF (update_modes) THEN CALL GMREDI_CALC_EIGS( I iMin,iMax,jMin,jMax,bi,bj,N2,myThid, I kLow_C, maskC(:,:,:,bi,bj), I hfacC(:,:,:,bi,bj), recip_hfacC(:,:,:,bi,bj), I R_Low(:,:,bi,bj), 1, .TRUE., O Rmid, modesC(:,:,:,:,bi,bj)) C Calculate the Rossby Radius DO j=1-Oly+1,sNy+Oly DO i=1-Olx+1,sNx+Olx Req = SQRT(BVint(i,j)/(2. _d 0*pi*gradf(i,j,bi,bj))) Rdef(i,j,bi,bj) = MIN(Rmid(i,j),Req) ENDDO ENDDO ENDIF C Average dsigma/dx and dsigma/dy onto the centre points DO k=1,Nr DO j=1-Oly,sNy+Oly-1 DO i=1-Olx,sNx+Olx-1 dSigmaDx(i,j,k) = op5*(sigmaX(i,j,k)+sigmaX(i+1,j,k)) dSigmaDy(i,j,k) = op5*(sigmaY(i,j,k)+sigmaY(i,j+1,k)) ENDDO ENDDO ENDDO C =============================== C Calculate the Eady growth rate C =============================== DO k=1,Nr kp1 = min(k+1,Nr) mskp1 = oneRL IF ( k.EQ.Nr ) mskp1 = zeroRL DO j=1-Oly,sNy+Oly-1 DO i=1-Olx,sNx+Olx-1 M4loc(i,j,k) = g_reciprho_sq*( dSigmaDx(i,j,k)**2 & +dSigmaDy(i,j,k)**2 ) N2loc(i,j,k) = op5*(N2(i,j,k)+mskp1*N2(i,j,kp1)) ENDDO ENDDO C The bottom of the grid cell is shallower than the top C integration level, so, advance the depth. IF (-rF(k+1) .LE. GM_K3D_EadyMinDepth) CYCLE C Do not bother going any deeper since the top of the C cell is deeper than the bottom integration level IF (-rF(k).GE.GM_K3D_EadyMaxDepth) EXIT C We are in the integration depth range DO j=1-Oly,sNy+Oly-1 DO i=1-Olx,sNx+Olx-1 IF ( (kLow_C(i,j).GE.k) .AND. & (-hMixLayer(i,j,bi,bj).LE.-rC(k)) ) THEN slopeC(i,j,k) = SQRT(M4loc(i,j,k))/N2loc(i,j,k) C Limit the slope. Note, this is not all the Eady calculations. IF (slopeC(i,j,k).LE.GM_maxSlope) THEN M4onN2(i,j,k) = M4loc(i,j,k)/N2loc(i,j,k) ELSE slopeC(i,j,k) = GM_maxslope M4onN2(i,j,k) = SQRT(M4loc(i,j,k))*GM_maxslope ENDIF eady(i,j) = eady(i,j) & + hfacC(i,j,k,bi,bj)*drF(k)*M4onN2(i,j,k) deltaH(i,j) = deltaH(i,j) + drF(k) ENDIF ENDDO ENDDO ENDDO DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx C If the minimum depth for the integration is deeper than the ocean C bottom OR the mixed layer is deeper than the maximum depth of C integration, we set the Eady growth rate to something small C to avoid floating point exceptions. C Later, these areas will be given a small diffusivity. IF (deltaH(i,j).EQ.zeroRL) THEN eady(i,j) = small C Otherwise, divide over the integration and take the square root C to actually find the Eady growth rate. ELSE eady(i,j) = SQRT(eady(i,j)/deltaH(i,j)) ENDIF ENDDO ENDDO C ====================================== C Calculate the diffusivity C ====================================== DO j=1-Oly+1,sNy+Oly DO i=1-Olx+1,sNx+Olx-1 C Calculate the Visbeck velocity Rurms(i,j) = MIN(Rdef(i,j,bi,bj),GM_K3D_Rmax) urms(i,j,1) = GM_K3D_Lambda*eady(i,j)*Rurms(i,j) C Set the bottom urms to zero k=kLow_C(i,j) IF (k.GT.0) urms(i,j,k) = 0.0 C Calculate the Rhines scale RRhines(i,j) = SQRT(urms(i,j,1)/gradf(i,j,bi,bj)) C Calculate the estimated length scale Rmix(i,j) = MIN(Rdef(i,j,bi,bj), RRhines(i,j)) Rmix(i,j) = MAX(Rmix(i,j),GM_K3D_Rmin) C Calculate the Doppler shifted long Rossby wave speed C Ubaro is at the C-point. cDopp(i,j) = Ubaro(i,j) & - gradf(i,j,bi,bj)*Rdef(i,j,bi,bj)*Rdef(i,j,bi,bj) C Limit the wave speed to the namelist variable GM_K3D_maxC IF (ABS(cDopp(i,j)).GT.GM_K3D_maxC) THEN cDopp(i,j) = MAX(GM_K3D_maxC, cDopp(i,j)) ENDIF ENDDO ENDDO C Project the surface urms to the subsurface using the first baroclinic mode CALL GMREDI_CALC_URMS( I iMin,iMax,jMin,jMax,bi,bj,N2,myThid, U urms) C Calculate the diffusivity (on the mass grid) DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx IF (k.LE.kLow_C(i,j)) THEN IF (deltaH(i,j).EQ.zeroRL) THEN K3D(i,j,k,bi,bj) = GM_K3D_smallK ELSE IF (urms(i,j,k).EQ.0.0) THEN K3D(i,j,k,bi,bj) = GM_K3D_smallK ELSE umc(i,j,k) =ubar(i,j,k) - cDopp(i,j) supp(i,j,k)=1./(1.+GM_K3D_b1*umc(i,j,k)**2/urms(i,j,1)**2) C 2*Rmix gives the diameter K3D(i,j,k,bi,bj) = GM_K3D_gamma*urms(i,j,k) & *2.*Rmix(i,j)*supp(i,j,k) ENDIF C Enforce lower and upper bounds on the diffusivity K3D(i,j,k,bi,bj) = MIN(K3D(i,j,k,bi,bj),GM_maxK3D) K3D(i,j,k,bi,bj) = MAX(K3D(i,j,k,bi,bj),GM_K3D_smallK) ENDIF ENDIF ENDDO ENDDO ENDDO C ====================================== C Find the PV gradient C ====================================== C Calculate the surface layer thickness. C Use hMixLayer (calculated in model/src/calc_oce_mxlayer) C for the mixed layer depth. C Enforce a minimum surface layer depth DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx surfkz(i,j) = MIN(-GM_K3D_surfMinDepth,-hMixLayer(i,j,bi,bj)) surfkz(i,j) = MAX(surfkz(i,j),R_low(i,j,bi,bj)) IF(maskC(i,j,1,bi,bj).EQ.0.0) surfkz(i,j)=0.0 surfk(i,j) = 0 ENDDO ENDDO DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx IF (rF(k).GT.surfkz(i,j) .AND. surfkz(i,j).GE.rF(k+1)) & surfk(i,j) = k ENDDO ENDDO ENDDO C Calculate the isopycnal slope DO j=1-Oly,sNy+Oly-1 DO i=1-Olx,sNx+Olx-1 SlopeX(i,j,1) = zeroRL SlopeY(i,j,1) = zeroRL ENDDO ENDDO DO k=2,Nr DO j=1-Oly+1,sNy+Oly DO i=1-Olx+1,sNx+Olx IF(surfk(i,j).GE.kLowC(i,j,bi,bj)) THEN C If the surface layer is thinner than the water column C the set the slope to zero to avoid problems. SlopeX(i,j,k) = zeroRL SlopeY(i,j,k) = zeroRL ELSE C Calculate the zonal slope at the western cell face (U grid) sigz = MIN( op5*(sigmaR(i,j,k)+sigmaR(i-1,j,k)), maxDRhoDz ) sigx = op5*( sigmaX(i,j,k)+sigmaX(i,j,k-1) ) slope = sigx/sigz IF(ABS(slope).GT.GM_maxSlope) & slope = SIGN(GM_maxSlope,slope) SlopeX(i,j,k)=-maskW(i,j,k-1,bi,bj)*maskW(i,j,k,bi,bj)*slope C Calculate the meridional slope at the southern cell face (V grid) sigz = MIN( op5*(sigmaR(i,j,k)+sigmaR(i,j-1,k)), maxDRhoDz ) sigy = op5*( sigmaY(i,j,k) + sigmaY(i,j,k-1) ) slope = sigy/sigz IF(ABS(slope).GT.GM_maxSlope) & slope = SIGN(GM_maxSlope,slope) SlopeY(i,j,k)=-maskS(i,j,k-1,bi,bj)*maskS(i,j,k,bi,bj)*slope ENDIF ENDDO ENDDO ENDDO C Calculate gradients of PV stretching term and PV diffusivity. C These may be altered later depending on namelist options. C Enforce a zero slope bottom boundary condition for the bottom most cells (k=Nr) k=Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx C Zonal gradient of PV stretching term: at the western cell face tfluxX(i,j,k) = -fCoriU(i,j)*SlopeX(i,j,k) & *recip_drF(k)*recip_hFacW(i,j,k,bi,bj) C Meridional gradient of PV stretching term: at the southern cell face tfluxY(i,j,k) = -fCoriV(i,j)*SlopeY(i,j,k) & *recip_drF(k)*recip_hFacS(i,j,k,bi,bj) C Use the interior diffusivity. Note: if we are using a C constant diffusivity KPV is overwritten later KPV(i,j,k) = K3D(i,j,k,bi,bj) ENDDO ENDDO C Calculate gradients of PV stretching term and PV diffusivity: for other cells (k no smoothing C May only be done with a constant K, otherwise the C integral constraint is violated. DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx Xix(i,j,k) = -maskW(i,j,k,bi,bj)*KPV(i,j,k)*gradqx(i,j,k) Xiy(i,j,k) = -maskS(i,j,k,bi,bj)*KPV(i,j,k)*gradqy(i,j,k) ENDDO ENDDO ENDDO ELSE C Expand K grad(q) in terms of baroclinic modes to smooth C and satisfy the integral constraint C Start with the X direction C ------------------------------ C Calculate the eigenvectors at the West face of a cell IF (update_modes) THEN CALL GMREDI_CALC_EIGS( I iMin,iMax,jMin,jMax,bi,bj,N2W,myThid, I kLow_U,maskW(:,:,:,bi,bj), I hfacW(:,:,:,bi,bj),recip_hfacW(:,:,:,bi,bj), I rLowW(:,:,bi,bj),GM_K3D_NModes,.FALSE., O dummy,modesW(:,:,:,:,bi,bj)) ENDIF C Calculate Xi_m at the west face of a cell DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx DO m=1,GM_K3D_NModes XimX(m,i,j) = zeroRL ENDDO ENDDO ENDDO DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx DO m=1,GM_K3D_NModes Kdqdx(i,j,k) = KPV(i,j,k)*gradqx(i,j,k) XimX(m,i,j) = XimX(m,i,j) & - maskW(i,j,k,bi,bj)*drF(k)*hfacW(i,j,k,bi,bj) & *Kdqdx(i,j,k)*modesW(m,i,j,k,bi,bj) ENDDO ENDDO ENDDO ENDDO C Calculate Xi in the X direction at the west face DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx Xix(i,j,k) = zeroRL ENDDO ENDDO ENDDO DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx DO m=1,GM_K3D_NModes Xix(i,j,k) = Xix(i,j,k) & + maskW(i,j,k,bi,bj)*XimX(m,i,j)*modesW(m,i,j,k,bi,bj) ENDDO ENDDO ENDDO ENDDO C Now the Y direction C ------------------------------ C Calculate the eigenvectors at the West face of a cell IF (update_modes) THEN CALL GMREDI_CALC_EIGS( I iMin,iMax,jMin,jMax,bi,bj,N2S,myThid, I kLow_V,maskS(:,:,:,bi,bj), I hfacS(:,:,:,bi,bj),recip_hfacS(:,:,:,bi,bj), I rLowS(:,:,bi,bj), GM_K3D_NModes, .FALSE., O dummy,modesS(:,:,:,:,bi,bj)) ENDIF DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx DO m=1,GM_K3D_NModes XimY(m,i,j) = zeroRL ENDDO ENDDO ENDDO DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx DO m=1,GM_K3D_NModes Kdqdy(i,j,k) = KPV(i,j,k)*gradqy(i,j,k) XimY(m,i,j) = XimY(m,i,j) & - drF(k)*hfacS(i,j,k,bi,bj) & *Kdqdy(i,j,k)*modesS(m,i,j,k,bi,bj) ENDDO ENDDO ENDDO ENDDO C Calculate Xi for Y direction at the south face DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx Xiy(i,j,k) = zeroRL ENDDO ENDDO ENDDO DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx DO m=1,GM_K3D_NModes Xiy(i,j,k) = Xiy(i,j,k) & + maskS(i,j,k,bi,bj)*XimY(m,i,j)*modesS(m,i,j,k,bi,bj) ENDDO ENDDO ENDDO ENDDO C ENDIF (.NOT. GM_K3D_smooth) ENDIF C Calculate the renormalisation factor DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx uInt(i,j)=zeroRL vInt(i,j)=zeroRL KdqdyInt(i,j)=zeroRL KdqdxInt(i,j)=zeroRL uKdqdyInt(i,j)=zeroRL vKdqdxInt(i,j)=zeroRL uXiyInt(i,j)=zeroRL vXixInt(i,j)=zeroRL Renorm(i,j)=oneRL RenormU(i,j)=oneRL RenormV(i,j)=oneRL ENDDO ENDDO DO k=1,Nr DO j=1-Oly,sNy+Oly-1 DO i=1-Olx,sNx+Olx-1 centreX = op5*(uVel(i,j,k,bi,bj)+uVel(i+1,j,k,bi,bj)) centreY = op5*(Kdqdy(i,j,k) +Kdqdy(i,j+1,k) ) C For the numerator uInt(i,j) = uInt(i,j) & + centreX*hfacC(i,j,k,bi,bj)*drF(k) KdqdyInt(i,j) = KdqdyInt(i,j) & + centreY*hfacC(i,j,k,bi,bj)*drF(k) uKdqdyInt(i,j) = uKdqdyInt(i,j) & + centreX*centreY*hfacC(i,j,k,bi,bj)*drF(k) C For the denominator centreY = op5*(Xiy(i,j,k) + Xiy(i,j+1,k)) uXiyInt(i,j) = uXiyInt(i,j) & + centreX*centreY*hfacC(i,j,k,bi,bj)*drF(k) centreX = op5*(Kdqdx(i,j,k) +Kdqdx(i+1,j,k)) centreY = op5*(vVel(i,j,k,bi,bj)+vVel(i,j+1,k,bi,bj) ) C For the numerator vInt(i,j) = vInt(i,j) & + centreY*hfacC(i,j,k,bi,bj)*drF(k) KdqdxInt(i,j) = KdqdxInt(i,j) & + CentreX*hfacC(i,j,k,bi,bj)*drF(k) vKdqdxInt(i,j) = vKdqdxInt(i,j) & + centreY*centreX*hfacC(i,j,k,bi,bj)*drF(k) C For the denominator centreX = op5*(Xix(i,j,k) + Xix(i+1,j,k)) vXixInt(i,j) = vXixInt(i,j) & + centreY*centreX*hfacC(i,j,k,bi,bj)*drF(k) ENDDO ENDDO ENDDO DO j=1-Oly,sNy+Oly-1 DO i=1-Olx,sNx+Olx-1 IF (kLowC(i,j,bi,bj).GT.0) THEN numerator = & (uKdqdyInt(i,j)-uInt(i,j)*KdqdyInt(i,j)/R_low(i,j,bi,bj)) & -(vKdqdxInt(i,j)-vInt(i,j)*KdqdxInt(i,j)/R_low(i,j,bi,bj)) denominator = uXiyInt(i,j) - vXixInt(i,j) C We can have troubles with floating point exceptions if the denominator C of the renormalisation if the ocean is resting (e.g. intial conditions). C So we make the renormalisation factor one if the denominator is very small C The renormalisation factor is supposed to correct the error in the extraction of C potential energy associated with the truncation of the expansion. Thus, we C enforce a minimum value for the renormalisation factor. C We also enforce a maximum renormalisation factor. IF (denominator.GT.small) THEN Renorm(i,j) = ABS(numerator/denominator) Renorm(i,j) = MAX(Renorm(i,j),GM_K3D_minRenorm) Renorm(i,j) = MIN(Renorm(i,j),GM_K3D_maxRenorm) ENDIF ENDIF ENDDO ENDDO C Now put it back on to the velocity grids DO j=1-Oly+1,sNy+Oly-1 DO i=1-Olx+1,sNx+Olx-1 RenormU(i,j) = op5*(Renorm(i-1,j)+Renorm(i,j)) RenormV(i,j) = op5*(Renorm(i,j-1)+Renorm(i,j)) ENDDO ENDDO C Calculate the eddy induced velocity in the X direction at the west face DO k=1,Nr DO j=1-Oly+1,sNy+Oly DO i=1-Olx+1,sNx+Olx ustar(i,j,k) = -RenormU(i,j)*Xix(i,j,k)/coriU(i,j) ENDDO ENDDO ENDDO C Calculate the eddy induced velocity in the Y direction at the south face DO k=1,Nr DO j=1-Oly+1,sNy+Oly DO i=1-Olx+1,sNx+Olx vstar(i,j,k) = -RenormV(i,j)*Xiy(i,j,k)/coriV(i,j) ENDDO ENDDO ENDDO C ====================================== C Calculate the eddy induced overturning streamfunction C ====================================== #ifdef GM_K3D_PASSIVE k=Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx psistar(i,j,Nr) = -hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) ENDDO ENDDO DO k=Nr-1,1,-1 DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx psistar(i,j,k) = psistar(i,j,k+1) & - hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) ENDDO ENDDO ENDDO #else IF (GM_AdvForm) THEN k=Nr DO j=1-Oly+1,sNy+1 DO i=1-Olx+1,sNx+1 GM_PsiX(i,j,k,bi,bj) = -hfacW(i,j,k,bi,bj)*drF(k)*ustar(i,j,k) GM_PsiY(i,j,k,bi,bj) = -hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) ENDDO ENDDO DO k=Nr-1,1,-1 DO j=1-Oly+1,sNy+1 DO i=1-Olx+1,sNx+1 GM_PsiX(i,j,k,bi,bj) = GM_PsiX(i,j,k+1,bi,bj) & - hfacW(i,j,k,bi,bj)*drF(k)*ustar(i,j,k) GM_PsiY(i,j,k,bi,bj) = GM_PsiY(i,j,k+1,bi,bj) & - hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) ENDDO ENDDO ENDDO ENDIF #endif #ifdef ALLOW_DIAGNOSTICS C Diagnostics IF ( useDiagnostics ) THEN CALL DIAGNOSTICS_FILL(K3D, 'GM_K3D ',0,Nr,1,bi,bj,myThid) CALL DIAGNOSTICS_FILL(KPV, 'GM_KPV ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(urms, 'GM_URMS ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(Rdef, 'GM_RDEF ',0, 1,1,bi,bj,myThid) CALL DIAGNOSTICS_FILL(Rurms, 'GM_RURMS',0, 1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(RRhines,'GM_RRHNS',0, 1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(Rmix, 'GM_RMIX ',0, 1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(supp, 'GM_SUPP ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(Xix, 'GM_Xix ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(Xiy, 'GM_Xiy ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(cDopp, 'GM_C ',0, 1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(Ubaro, 'GM_UBARO',0, 1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(eady, 'GM_EADY ',0, 1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(SlopeX, 'GM_Sx ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(SlopeY, 'GM_Sy ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(tfluxX, 'GM_TFLXX',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(tfluxY, 'GM_TFLXY',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(gradqx, 'GM_dqdx ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(gradqy, 'GM_dqdy ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(Kdqdy, 'GM_Kdqdy',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(Kdqdx, 'GM_Kdqdx',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(surfkz, 'GM_SFLYR',0, 1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(ustar, 'GM_USTAR',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(vstar, 'GM_VSTAR',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(umc, 'GM_UMC ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(ubar, 'GM_UBAR ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(modesC, 'GM_MODEC',0,Nr,1,bi,bj,myThid) CALL DIAGNOSTICS_FILL(M4loc, 'GM_M4 ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(N2loc, 'GM_N2 ',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(M4onN2, 'GM_M4_N2',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(slopeC, 'GM_SLOPE',0,Nr,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(Renorm, 'GM_RENRM',0, 1,2,bi,bj,myThid) #ifdef GM_K3D_PASSIVE CALL DIAGNOSTICS_FILL(psistar,'GM_PSTAR',0,Nr,2,bi,bj,myThid) #endif ENDIF #endif C For the Redi diffusivity, we set K3D to a constant if C GM_K3D_constRedi=.TRUE. IF (GM_K3D_constRedi) THEN DO k=1,Nr DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx K3D(i,j,k,bi,bj) = GM_K3D_constK ENDDO ENDDO ENDDO ENDIF #ifdef ALLOW_DIAGNOSTICS IF ( useDiagnostics ) & CALL DIAGNOSTICS_FILL(K3D, 'GM_K3D_T',0,Nr,1,bi,bj,myThid) #endif #endif /* GM_K3D */ RETURN END