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C $Header: /u/gcmpack/MITgcm/pkg/gmredi/gmredi_k3d.F,v 1.18 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: GMREDI_K3D |
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C !INTERFACE: |
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SUBROUTINE GMREDI_K3D( |
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I iMin, iMax, jMin, jMax, |
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I sigmaX, sigmaY, sigmaR, |
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I bi, bj, myTime, myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE GMREDI_K3D |
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C | o Calculates the 3D diffusivity as per Bates et al. (2013) |
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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 "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "GRID.h" |
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#include "DYNVARS.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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C myThid :: My Thread Id. number |
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|
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INTEGER iMin,iMax,jMin,jMax |
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_RL sigmaX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL sigmaY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL sigmaR(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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INTEGER bi, bj |
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_RL myTime |
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INTEGER myThid |
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|
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#ifdef GM_K3D |
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|
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C === Functions ==== |
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LOGICAL DIFFERENT_MULTIPLE |
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EXTERNAL DIFFERENT_MULTIPLE |
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|
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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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|
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C update_modes :: Whether to update the eigenmodes |
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LOGICAL update_modes |
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|
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C surfk :: index of the depth of the surface layer |
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C kLow_C :: Local version of the index of deepest wet grid cell on tracer grid |
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C kLow_U :: Local version of the index of deepest wet grid cell on U grid |
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C kLow_V :: Local version of the index of deepest wet grid cell on V grid |
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INTEGER surfk(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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INTEGER kLow_C(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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INTEGER kLow_U(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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INTEGER kLow_V(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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|
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C N2loc :: local N**2 |
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C slope :: local slope |
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C Req :: local equatorial deformation radius (m) |
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C deltaH :: local thickness of Eady integration (m) |
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C g_reciprho_sq :: (gravity*recip_rhoConst)**2 |
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C M4loc :: local M**4 |
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C maxDRhoDz :: maximum value of d(rho)/dz (derived from GM_K3D_minN2) |
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C sigx :: local d(rho)/dx |
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C sigy :: local d(rho)/dy |
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C sigz :: local d(rho)/dz |
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C hsurf :: local surface layer depth |
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C small :: a small number (to avoid floating point exceptions) |
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_RL N2loc(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL slope |
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_RL slopeC(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL Req |
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_RL deltaH(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL g_reciprho_sq |
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_RL M4loc(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL M4onN2(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL maxDRhoDz |
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_RL sigx, sigy, sigz |
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_RL hsurf |
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_RL small |
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|
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C dfdy :: gradient of the Coriolis paramter, df/dy, 1/(m*s) |
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C dfdx :: gradient of the Coriolis paramter, df/dx, 1/(m*s) |
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C gradf :: gradient of the Coriolis paramter at a cell centre, 1/(m*s) |
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C Rurms :: a local mixing length used in calculation of urms (m) |
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C RRhines :: The Rhines scale (m) |
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C Rmix :: Mixing length |
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C N2 :: Square of the buoyancy frequency (1/s**2) |
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C N2W :: Square of the buoyancy frequency (1/s**2) averaged to west of grid cell |
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C N2S :: Square of the buoyancy frequency (1/s**2) averaged to south of grid cell |
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C N :: Buoyancy frequency, SQRT(N2) |
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C BVint :: The vertical integral of N (m/s) |
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C ubar :: Zonal velocity on a tracer point (m/s) |
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C vbar :: Meridional velocity on a tracer point (m/s) |
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C Ubaro :: Barotropic velocity (m/s) |
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_RL dfdy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL dfdx( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL gradf( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL dummy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL Rurms( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL RRhines(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL Rmix( 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 N2W( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL N2S( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL N( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL BVint( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL Ubaro( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL ubar( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy) |
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_RL vbar( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy) |
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|
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C Rmid :: Rossby radius (m) |
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C KPV :: Diffusivity (m**2/s) |
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C Kdqdx :: diffusivity multiplied by zonal PV gradient |
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C Kdqdy :: diffusivity multiplied by meridional PV gradient |
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C SlopeX :: isopycnal slope in x direction |
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C SlopeY :: isopycnal slope in y direction |
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C dSigmaDx :: sigmaX averaged onto tracer grid |
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C dSigmaDy :: sigmaY averaged onto tracer grid |
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C tfluxX :: thickness flux in x direction |
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C tfluxY :: thickness flux in y direction |
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C fCoriU :: Coriolis parameter averaged to U points |
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C fCoriV :: Coriolis parameter averaged to V points |
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C cori :: Coriolis parameter forced to be finite near the equator |
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C coriU :: As for cori, but, at U point |
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C coriV :: As for cori, but, at V point |
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C surfkz :: Depth of surface layer (in r units) |
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_RL Rmid(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL KPV(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL Kdqdy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL Kdqdx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL SlopeX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL SlopeY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL dSigmaDx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL dSigmaDy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL tfluxX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL tfluxY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL cori(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL coriU(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL coriV(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL fCoriU(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL fCoriV(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL surfkz(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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|
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C centreX,centreY :: used for calculating averages at centre of cell |
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C numerator,denominator :: of the renormalisation factor |
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C uInt :: column integral of u velocity (sum u*dz) |
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C vInt :: column integral of v velocity (sum v*dz) |
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C KdqdxInt :: column integral of K*dqdx (sum K*dqdx*dz) |
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C KdqdyInt :: column integral of K*dqdy (sum K*dqdy*dz) |
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C uKdqdyInt :: column integral of u*K*dqdy (sum u*K*dqdy*dz) |
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C vKdqdxInt :: column integral of v*K*dqdx (sum v*K*dqdx*dz) |
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C uXiyInt :: column integral of u*Xiy (sum u*Xiy*dz) |
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C vXixInt :: column integral of v*Xix (sum v*Xix*dz) |
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C Renorm :: renormalisation factor at the centre of a cell |
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C RenormU :: renormalisation factor at the western face of a cell |
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C RenormV :: renormalisation factor at the southern face of a cell |
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_RL centreX, centreY |
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_RL numerator, denominator |
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_RL uInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL vInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL KdqdxInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL KdqdyInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL uKdqdyInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL vKdqdxInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL uXiyInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL vXixInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL Renorm(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL RenormU(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL RenormV(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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|
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C gradqx :: Potential vorticity gradient in x direction |
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C gradqy :: Potential vorticity gradient in y direction |
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C XimX :: Vertical integral of phi_m*K*gradqx |
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C XimY :: Vertical integral of phi_m*K*gradqy |
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C cDopp :: Quasi-Doppler shifted long Rossby wave speed (m/s) |
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C umc :: ubar-c (m/s) |
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C eady :: Eady growth rate (1/s) |
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C urms :: the rms eddy velocity (m/s) |
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C supp :: The suppression factor |
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C ustar :: The eddy induced velocity in the x direction |
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C vstar :: The eddy induced velocity in the y direction |
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C Xix :: Xi in the x direction (m/s**2) |
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C Xiy :: Xi in the y direction (m/s**2) |
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_RL gradqx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL gradqy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL XimX(GM_K3D_NModes,1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL XimY(GM_K3D_NModes,1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL cDopp(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL umc( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
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_RL eady( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
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_RL urms( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
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_RL supp( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
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_RL ustar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
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_RL vstar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
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_RL Xix( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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_RL Xiy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
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#ifdef GM_K3D_PASSIVE |
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C psistar :: eddy induced streamfunction in the y direction |
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_RL psistar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
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#endif |
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|
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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 ====================================== |
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C Initialise some variables |
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C ====================================== |
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small = TINY(zeroRL) |
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update_modes=.FALSE. |
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IF ( DIFFERENT_MULTIPLE(GM_K3D_vecFreq,myTime,deltaTClock) ) |
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& update_modes=.TRUE. |
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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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kLow_C(i,j) = kLowC(i,j,bi,bj) |
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ENDDO |
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ENDDO |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx+1,sNx+Olx |
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kLow_U(i,j) = MIN( kLow_C(i,j), kLow_C(i-1,j) ) |
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ENDDO |
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ENDDO |
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DO j=1-Oly+1,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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kLow_V(i,j) = MIN( kLow_C(i,j), kLow_C(i,j-1) ) |
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ENDDO |
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ENDDO |
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|
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C Dummy values for the edges. This does not affect the results |
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C but avoids problems when solving for the eigenvalues. |
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i=1-Olx |
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DO j=1-Oly,sNy+Oly |
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kLow_U(i,j) = 0 |
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ENDDO |
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j=1-Oly |
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DO i=1-Olx,sNx+Olx |
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kLow_V(i,j) = 0 |
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ENDDO |
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|
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g_reciprho_sq = (gravity*recip_rhoConst)**2 |
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C Gradient of Coriolis |
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DO j=1-Oly+1,sNy+Oly |
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DO i=1-Olx+1,sNx+Olx |
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dfdx(i,j) = ( fCori(i,j,bi,bj)-fCori(i-1,j,bi,bj) ) |
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& *recip_dxC(i,j,bi,bj) |
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dfdy(i,j) = ( fCori(i,j,bi,bj)-fCori(i,j-1,bi,bj) ) |
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& *recip_dyC(i,j,bi,bj) |
| 257 |
ENDDO |
| 258 |
ENDDO |
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|
| 260 |
C Coriolis at C points enforcing a minimum value so |
| 261 |
C that it is defined at the equator |
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DO j=1-Oly,sNy+Oly |
| 263 |
DO i=1-Olx,sNx+Olx |
| 264 |
cori(i,j) = SIGN( MAX( ABS(fCori(i,j,bi,bj)),GM_K3D_minCori ), |
| 265 |
& fCori(i,j,bi,bj) ) |
| 266 |
ENDDO |
| 267 |
ENDDO |
| 268 |
C Coriolis at U and V points |
| 269 |
DO j=1-Oly,sNy+Oly |
| 270 |
DO i=1-Olx+1,sNx+Olx |
| 271 |
C Limited so that the inverse is defined at the equator |
| 272 |
coriU(i,j) = op5*( cori(i,j)+cori(i-1,j) ) |
| 273 |
coriU(i,j) = SIGN( MAX( ABS(coriU(i,j)),GM_K3D_minCori ), |
| 274 |
& coriU(i,j) ) |
| 275 |
|
| 276 |
C Not limited |
| 277 |
fCoriU(i,j) = op5*( fCori(i,j,bi,bj)+fCori(i-1,j,bi,bj) ) |
| 278 |
ENDDO |
| 279 |
ENDDO |
| 280 |
DO j=1-Oly+1,sNy+Oly |
| 281 |
DO i=1-Olx,sNx+Olx |
| 282 |
C Limited so that the inverse is defined at the equator |
| 283 |
coriV(i,j) = op5*( cori(i,j)+cori(i,j-1) ) |
| 284 |
coriV(i,j) = SIGN( MAX( ABS(coriV(i,j)),GM_K3D_minCori ), |
| 285 |
& coriV(i,j) ) |
| 286 |
|
| 287 |
C Not limited |
| 288 |
fCoriV(i,j) = op5*( fCori(i,j,bi,bj)+fCori(i,j-1,bi,bj) ) |
| 289 |
ENDDO |
| 290 |
ENDDO |
| 291 |
DO j=1-Oly,sNy+Oly |
| 292 |
DO i=1-Olx,sNx+Olx |
| 293 |
gradf(i,j) = recip_rSphere*fCoriCos(i,j,bi,bj) |
| 294 |
ENDDO |
| 295 |
ENDDO |
| 296 |
C Some dummy values at the edges |
| 297 |
i=1-Olx |
| 298 |
DO j=1-Oly,sNy+Oly |
| 299 |
coriU(i,j)=cori(i,j) |
| 300 |
fCoriU(i,j)=fCori(i,j,bi,bj) |
| 301 |
ENDDO |
| 302 |
j=1-Oly |
| 303 |
DO i=1-Olx,sNx+Olx |
| 304 |
coriV(i,j)=cori(i,j) |
| 305 |
fCoriV(i,j)=fCori(i,j,bi,bj) |
| 306 |
ENDDO |
| 307 |
|
| 308 |
C Zeroing some cumulative fields |
| 309 |
DO j=1-Oly,sNy+Oly |
| 310 |
DO i=1-Olx,sNx+Olx |
| 311 |
eady(i,j) = zeroRL |
| 312 |
BVint(i,j) = zeroRL |
| 313 |
Ubaro(i,j) = zeroRL |
| 314 |
deltaH(i,j) = zeroRL |
| 315 |
ENDDO |
| 316 |
ENDDO |
| 317 |
DO k=1,Nr |
| 318 |
DO j=1-Oly,sNy+Oly |
| 319 |
DO i=1-Olx,sNx+Olx |
| 320 |
slopeC(i,j,k)=zeroRL |
| 321 |
ENDDO |
| 322 |
ENDDO |
| 323 |
ENDDO |
| 324 |
|
| 325 |
C initialise remaining 2d variables |
| 326 |
DO j=1-Oly,sNy+Oly |
| 327 |
DO i=1-Olx,sNx+Olx |
| 328 |
dfdy(i,j)=zeroRL |
| 329 |
dfdy(i,j)=zeroRL |
| 330 |
Rurms(i,j)=zeroRL |
| 331 |
RRhines(i,j)=zeroRL |
| 332 |
Rmix(i,j)=zeroRL |
| 333 |
ENDDO |
| 334 |
ENDDO |
| 335 |
C initialise remaining 3d variables |
| 336 |
DO k=1,Nr |
| 337 |
DO j=1-Oly,sNy+Oly |
| 338 |
DO i=1-Olx,sNx+Olx |
| 339 |
N2loc(i,j,k)=GM_K3D_minN2 |
| 340 |
N2W(i,j,k) = GM_K3D_minN2 |
| 341 |
N2S(i,j,k) = GM_K3D_minN2 |
| 342 |
M4loc(i,j,k)=zeroRL |
| 343 |
M4onN2(i,j,k)=zeroRL |
| 344 |
urms(i,j,k)=zeroRL |
| 345 |
SlopeX(i,j,k)=zeroRL |
| 346 |
SlopeY(i,j,k)=zeroRL |
| 347 |
dSigmaDx(i,j,k)=zeroRL |
| 348 |
dSigmaDy(i,j,k)=zeroRL |
| 349 |
gradqx(i,j,k)=zeroRL |
| 350 |
gradqy(i,j,k)=zeroRL |
| 351 |
ENDDO |
| 352 |
ENDDO |
| 353 |
ENDDO |
| 354 |
|
| 355 |
C Find the zonal velocity at the cell centre |
| 356 |
C The logicals here are, in order: 1/ go from grid to north/east directions |
| 357 |
C 2/ go from C to A grid and 3/ apply the mask |
| 358 |
#ifdef ALLOW_EDDYPSI |
| 359 |
IF (GM_InMomAsStress) THEN |
| 360 |
CALL rotate_uv2en_rl(uMean, vMean, ubar, vbar, .TRUE., .TRUE., |
| 361 |
& .TRUE.,Nr,mythid) |
| 362 |
ELSE |
| 363 |
#endif |
| 364 |
CALL rotate_uv2en_rl(uVel, vVel, ubar, vbar, .TRUE., .TRUE., |
| 365 |
& .TRUE.,Nr,mythid) |
| 366 |
#ifdef ALLOW_EDDYPSI |
| 367 |
ENDIF |
| 368 |
#endif |
| 369 |
|
| 370 |
C Square of the buoyancy frequency at the top of a grid cell |
| 371 |
DO k=2,Nr |
| 372 |
DO j=1-Oly,sNy+Oly |
| 373 |
DO i=1-Olx,sNx+Olx |
| 374 |
N2(i,j,k) = -gravity*recip_rhoConst*sigmaR(i,j,k) |
| 375 |
ENDDO |
| 376 |
ENDDO |
| 377 |
ENDDO |
| 378 |
C N2(k=1) is always zero |
| 379 |
k=1 |
| 380 |
DO j=1-Oly,sNy+Oly |
| 381 |
DO i=1-Olx,sNx+Olx |
| 382 |
N2(i,j,k) = zeroRL |
| 383 |
N(i,j,k) = zeroRL |
| 384 |
ENDDO |
| 385 |
ENDDO |
| 386 |
C Enforce a minimum N2 |
| 387 |
DO k=2,Nr |
| 388 |
DO j=1-Oly,sNy+Oly |
| 389 |
DO i=1-Olx,sNx+Olx |
| 390 |
IF (N2(i,j,k).LT.GM_K3D_minN2) N2(i,j,k)=GM_K3D_minN2 |
| 391 |
N(i,j,k) = SQRT(N2(i,j,k)) |
| 392 |
ENDDO |
| 393 |
ENDDO |
| 394 |
ENDDO |
| 395 |
C Calculate the minimum drho/dz |
| 396 |
maxDRhoDz = -rhoConst*GM_K3D_minN2/gravity |
| 397 |
|
| 398 |
C Calculate the barotropic velocity by vertically integrating |
| 399 |
C and the dividing by the depth of the water column |
| 400 |
C Note that Ubaro is on the U grid. |
| 401 |
DO k=1,Nr |
| 402 |
DO j=1-Oly,sNy+Oly |
| 403 |
DO i=1-Olx,sNx+Olx |
| 404 |
Ubaro(i,j) = Ubaro(i,j) + |
| 405 |
& maskW(i,j,k,bi,bj)*drF(k)*hfacC(i,j,k,bi,bj) |
| 406 |
& *ubar(i,j,k,bi,bj) |
| 407 |
ENDDO |
| 408 |
ENDDO |
| 409 |
ENDDO |
| 410 |
DO j=1-Oly,sNy+Oly |
| 411 |
DO i=1-Olx,sNx+Olx |
| 412 |
IF (kLow_C(i,j).GT.0) THEN |
| 413 |
C The minus sign is because r_Low<0 |
| 414 |
Ubaro(i,j) = -Ubaro(i,j)/r_Low(i,j,bi,bj) |
| 415 |
ENDIF |
| 416 |
ENDDO |
| 417 |
ENDDO |
| 418 |
|
| 419 |
C Integrate the buoyancy frequency vertically using the trapezoidal method. |
| 420 |
DO k=1,Nr |
| 421 |
DO j=1-Oly,sNy+Oly |
| 422 |
DO i=1-Olx,sNx+Olx |
| 423 |
IF (k.LT.kLow_C(i,j)) THEN |
| 424 |
BVint(i,j) = BVint(i,j) + hFacC(i,j,k,bi,bj)*drF(k) |
| 425 |
& *(N(i,j,k)+N(i,j,k+1)) |
| 426 |
ELSEIF (k.EQ.kLow_C(i,j)) THEN |
| 427 |
C Assume that N(z=-H)=0 |
| 428 |
BVint(i,j) = BVint(i,j) + hFacC(i,j,k,bi,bj)*drF(k)*N(i,j,k) |
| 429 |
ENDIF |
| 430 |
ENDDO |
| 431 |
ENDDO |
| 432 |
ENDDO |
| 433 |
DO j=1-Oly,sNy+Oly |
| 434 |
DO i=1-Olx,sNx+Olx |
| 435 |
BVint(i,j) = op5*BVint(i,j) |
| 436 |
ENDDO |
| 437 |
ENDDO |
| 438 |
|
| 439 |
C Calculate the eigenvalues and eigenvectors |
| 440 |
IF (update_modes) THEN |
| 441 |
CALL GMREDI_CALC_EIGS( |
| 442 |
I iMin,iMax,jMin,jMax,bi,bj,N2,myThid, |
| 443 |
I kLow_C, maskC(:,:,:,bi,bj), |
| 444 |
I hfacC(:,:,:,bi,bj), recip_hfacC(:,:,:,bi,bj), |
| 445 |
I R_Low(:,:,bi,bj), 1, .TRUE., |
| 446 |
O Rmid, modesC(:,:,:,:,bi,bj)) |
| 447 |
|
| 448 |
C Calculate the Rossby Radius |
| 449 |
DO j=1-Oly+1,sNy+Oly |
| 450 |
DO i=1-Olx+1,sNx+Olx |
| 451 |
Req = SQRT(BVint(i,j)/(2*pi*gradf(i,j))) |
| 452 |
Rdef(i,j,bi,bj) = MIN(Rmid(i,j),Req) |
| 453 |
ENDDO |
| 454 |
ENDDO |
| 455 |
ENDIF |
| 456 |
|
| 457 |
C Average dsigma/dx and dsigma/dy onto the centre points |
| 458 |
|
| 459 |
DO k=1,Nr |
| 460 |
DO j=1-Oly,sNy+Oly-1 |
| 461 |
DO i=1-Olx,sNx+Olx-1 |
| 462 |
dSigmaDx(i,j,k) = op5*(sigmaX(i,j,k)+sigmaX(i+1,j,k)) |
| 463 |
dSigmaDy(i,j,k) = op5*(sigmaY(i,j,k)+sigmaY(i,j+1,k)) |
| 464 |
ENDDO |
| 465 |
ENDDO |
| 466 |
ENDDO |
| 467 |
|
| 468 |
C =============================== |
| 469 |
C Calculate the Eady growth rate |
| 470 |
C =============================== |
| 471 |
DO k=1,Nr |
| 472 |
|
| 473 |
DO j=1-Oly,sNy+Oly-1 |
| 474 |
DO i=1-Olx,sNx+Olx-1 |
| 475 |
M4loc(i,j,k) = g_reciprho_sq*( dSigmaDx(i,j,k)**2 |
| 476 |
& +dSigmaDy(i,j,k)**2 ) |
| 477 |
IF (k.NE.kLow_C(i,j)) THEN |
| 478 |
N2loc(i,j,k) = op5*(N2(i,j,k)+N2(i,j,k+1)) |
| 479 |
ELSE |
| 480 |
N2loc(i,j,k) = op5*N2(i,j,k) |
| 481 |
ENDIF |
| 482 |
ENDDO |
| 483 |
ENDDO |
| 484 |
C The bottom of the grid cell is shallower than the top |
| 485 |
C integration level, so, advance the depth. |
| 486 |
IF (-rF(k+1) .LE. GM_K3D_EadyMinDepth) CYCLE |
| 487 |
|
| 488 |
C Do not bother going any deeper since the top of the |
| 489 |
C cell is deeper than the bottom integration level |
| 490 |
IF (-rF(k).GE.GM_K3D_EadyMaxDepth) EXIT |
| 491 |
|
| 492 |
C We are in the integration depth range |
| 493 |
DO j=1-Oly,sNy+Oly-1 |
| 494 |
DO i=1-Olx,sNx+Olx-1 |
| 495 |
IF ( (kLow_C(i,j).GE.k) .AND. |
| 496 |
& (-hMixLayer(i,j,bi,bj).LE.-rC(k)) ) THEN |
| 497 |
|
| 498 |
slopeC(i,j,k) = SQRT(M4loc(i,j,k))/N2loc(i,j,k) |
| 499 |
C Limit the slope. Note, this is not all the Eady calculations. |
| 500 |
IF (slopeC(i,j,k).LE.GM_maxSlope) THEN |
| 501 |
M4onN2(i,j,k) = M4loc(i,j,k)/N2loc(i,j,k) |
| 502 |
ELSE |
| 503 |
slopeC(i,j,k) = GM_maxslope |
| 504 |
M4onN2(i,j,k) = SQRT(M4loc(i,j,k))*GM_maxslope |
| 505 |
ENDIF |
| 506 |
eady(i,j) = eady(i,j) |
| 507 |
& + hfacC(i,j,k,bi,bj)*drF(k)*M4onN2(i,j,k) |
| 508 |
deltaH(i,j) = deltaH(i,j) + drF(k) |
| 509 |
ENDIF |
| 510 |
ENDDO |
| 511 |
ENDDO |
| 512 |
ENDDO |
| 513 |
|
| 514 |
DO j=1-Oly,sNy+Oly |
| 515 |
DO i=1-Olx,sNx+Olx |
| 516 |
C If the minimum depth for the integration is deeper than the ocean |
| 517 |
C bottom OR the mixed layer is deeper than the maximum depth of |
| 518 |
C integration, we set the Eady growth rate to something small |
| 519 |
C to avoid floating point exceptions. |
| 520 |
C Later, these areas will be given a small diffusivity. |
| 521 |
IF (deltaH(i,j).EQ.zeroRL) THEN |
| 522 |
eady(i,j) = small |
| 523 |
|
| 524 |
C Otherwise, divide over the integration and take the square root |
| 525 |
C to actually find the Eady growth rate. |
| 526 |
ELSE |
| 527 |
eady(i,j) = SQRT(eady(i,j)/deltaH(i,j)) |
| 528 |
|
| 529 |
ENDIF |
| 530 |
|
| 531 |
ENDDO |
| 532 |
ENDDO |
| 533 |
|
| 534 |
C ====================================== |
| 535 |
C Calculate the diffusivity |
| 536 |
C ====================================== |
| 537 |
DO j=1-Oly+1,sNy+Oly |
| 538 |
DO i=1-Olx+1,sNx+Olx-1 |
| 539 |
C Calculate the Visbeck velocity |
| 540 |
Rurms(i,j) = MIN(Rdef(i,j,bi,bj),GM_K3D_Rmax) |
| 541 |
urms(i,j,1) = GM_K3D_Lambda*eady(i,j)*Rurms(i,j) |
| 542 |
C Set the bottom urms to zero |
| 543 |
k=kLow_C(i,j) |
| 544 |
IF (k.GT.0) urms(i,j,k) = 0.0 |
| 545 |
|
| 546 |
C Calculate the Rhines scale |
| 547 |
RRhines(i,j) = SQRT(urms(i,j,1)/gradf(i,j)) |
| 548 |
|
| 549 |
C Calculate the estimated length scale |
| 550 |
Rmix(i,j) = MIN(Rdef(i,j,bi,bj), RRhines(i,j)) |
| 551 |
Rmix(i,j) = MAX(Rmix(i,j),GM_K3D_Rmin) |
| 552 |
|
| 553 |
C Calculate the Doppler shifted long Rossby wave speed |
| 554 |
C Ubaro is on the U grid so we must average onto the M grid. |
| 555 |
cDopp(i,j) = op5*( Ubaro(i,j)+Ubaro(i+1,j) ) |
| 556 |
& - gradf(i,j)*Rdef(i,j,bi,bj)*Rdef(i,j,bi,bj) |
| 557 |
C Limit the wave speed to the namelist variable GM_K3D_maxC |
| 558 |
IF (ABS(cDopp(i,j)).GT.GM_K3D_maxC) THEN |
| 559 |
cDopp(i,j) = MAX(GM_K3D_maxC, cDopp(i,j)) |
| 560 |
ENDIF |
| 561 |
|
| 562 |
ENDDO |
| 563 |
ENDDO |
| 564 |
|
| 565 |
C Project the surface urms to the subsurface using the first baroclinic mode |
| 566 |
CALL GMREDI_CALC_URMS( |
| 567 |
I iMin,iMax,jMin,jMax,bi,bj,N2,myThid, |
| 568 |
U urms) |
| 569 |
|
| 570 |
C Calculate the diffusivity (on the mass grid) |
| 571 |
DO k=1,Nr |
| 572 |
DO j=1-Oly,sNy+Oly |
| 573 |
DO i=1-Olx,sNx+Olx |
| 574 |
IF (k.LE.kLow_C(i,j)) THEN |
| 575 |
IF (deltaH(i,j).EQ.zeroRL) THEN |
| 576 |
K3D(i,j,k,bi,bj) = GM_K3D_smallK |
| 577 |
ELSE |
| 578 |
IF (urms(i,j,k).EQ.0.0) THEN |
| 579 |
K3D(i,j,k,bi,bj) = GM_K3D_smallK |
| 580 |
ELSE |
| 581 |
umc(i,j,k) =ubar(i,j,k,bi,bj) - cDopp(i,j) |
| 582 |
supp(i,j,k)=1/(1+GM_K3D_b1*umc(i,j,k)**2/urms(i,j,1)**2) |
| 583 |
C 2*Rmix gives the diameter |
| 584 |
K3D(i,j,k,bi,bj) = GM_K3D_gamma*urms(i,j,k) |
| 585 |
& *2*Rmix(i,j)*supp(i,j,k) |
| 586 |
ENDIF |
| 587 |
|
| 588 |
C Enforce lower and upper bounds on the diffusivity |
| 589 |
IF (K3D(i,j,k,bi,bj).LT.GM_K3D_smallK) |
| 590 |
& K3D(i,j,k,bi,bj) = GM_K3D_smallK |
| 591 |
IF (K3D(i,j,k,bi,bj).GT.GM_maxK3D) |
| 592 |
& K3D(i,j,k,bi,bj) = GM_maxK3D |
| 593 |
ENDIF |
| 594 |
ENDIF |
| 595 |
ENDDO |
| 596 |
ENDDO |
| 597 |
ENDDO |
| 598 |
|
| 599 |
C ====================================== |
| 600 |
C Find the PV gradient |
| 601 |
C ====================================== |
| 602 |
C Calculate the surface layer thickness. |
| 603 |
C Use hMixLayer (calculated in model/src/calc_oce_mxlayer) |
| 604 |
C for the mixed layer depth. |
| 605 |
|
| 606 |
C Enforce a minimum surface layer depth |
| 607 |
DO j=1-Oly,sNy+Oly |
| 608 |
DO i=1-Olx,sNx+Olx |
| 609 |
surfkz(i,j) = MIN(-GM_K3D_surfMinDepth,-hMixLayer(i,j,bi,bj)) |
| 610 |
surfkz(i,j) = MAX(surfkz(i,j),R_low(i,j,bi,bj)) |
| 611 |
IF(maskC(i,j,1,bi,bj).EQ.0.0) surfkz(i,j)=0.0 |
| 612 |
surfk(i,j) = 0 |
| 613 |
ENDDO |
| 614 |
ENDDO |
| 615 |
DO k=1,Nr |
| 616 |
DO j=1-Oly,sNy+Oly |
| 617 |
DO i=1-Olx,sNx+Olx |
| 618 |
IF (rF(k).GT.surfkz(i,j) .AND. surfkz(i,j).GE.rF(k+1)) |
| 619 |
& surfk(i,j) = k |
| 620 |
ENDDO |
| 621 |
ENDDO |
| 622 |
ENDDO |
| 623 |
|
| 624 |
C Calculate the isopycnal slope |
| 625 |
DO j=1-Oly,sNy+Oly-1 |
| 626 |
DO i=1-Olx,sNx+Olx-1 |
| 627 |
SlopeX(i,j,1) = zeroRL |
| 628 |
SlopeY(i,j,1) = zeroRL |
| 629 |
ENDDO |
| 630 |
ENDDO |
| 631 |
DO k=2,Nr |
| 632 |
DO j=1-Oly+1,sNy+Oly |
| 633 |
DO i=1-Olx+1,sNx+Olx |
| 634 |
IF(surfk(i,j).GE.kLowC(i,j,bi,bj)) THEN |
| 635 |
C If the surface layer is thinner than the water column |
| 636 |
C the set the slope to zero to avoid problems. |
| 637 |
SlopeX(i,j,k) = zeroRL |
| 638 |
SlopeY(i,j,k) = zeroRL |
| 639 |
|
| 640 |
ELSE |
| 641 |
C Calculate the zonal slope at the western cell face (U grid) |
| 642 |
sigz = MIN( op5*(sigmaR(i,j,k)+sigmaR(i-1,j,k)), maxDRhoDz ) |
| 643 |
sigx = op5*( sigmaX(i,j,k)+sigmaX(i,j,k-1) ) |
| 644 |
slope = sigx/sigz |
| 645 |
IF(ABS(slope).GT.GM_maxSlope) |
| 646 |
& slope = SIGN(GM_maxSlope,slope) |
| 647 |
SlopeX(i,j,k)=-maskW(i,j,k-1,bi,bj)*maskW(i,j,k,bi,bj)*slope |
| 648 |
|
| 649 |
C Calculate the meridional slope at the southern cell face (V grid) |
| 650 |
sigz = MIN( op5*(sigmaR(i,j,k)+sigmaR(i,j-1,k)), maxDRhoDz ) |
| 651 |
sigy = op5*( sigmaY(i,j,k) + sigmaY(i,j,k-1) ) |
| 652 |
slope = sigy/sigz |
| 653 |
IF(ABS(slope).GT.GM_maxSlope) |
| 654 |
& slope = SIGN(GM_maxSlope,slope) |
| 655 |
SlopeY(i,j,k)=-maskS(i,j,k-1,bi,bj)*maskS(i,j,k,bi,bj)*slope |
| 656 |
ENDIF |
| 657 |
ENDDO |
| 658 |
ENDDO |
| 659 |
ENDDO |
| 660 |
|
| 661 |
C Calculate the thickness flux and diffusivity. These may be altered later |
| 662 |
C depending on namelist options. |
| 663 |
C Enforce a zero slope bottom boundary condition for the bottom most cells (k=Nr) |
| 664 |
k=Nr |
| 665 |
DO j=1-Oly,sNy+Oly |
| 666 |
DO i=1-Olx,sNx+Olx |
| 667 |
C Zonal thickness flux at the western cell face |
| 668 |
tfluxX(i,j,k) = -fCoriU(i,j)*SlopeX(i,j,k) |
| 669 |
& *recip_drF(k)*recip_hFacW(i,j,k,bi,bj) |
| 670 |
C Meridional thickness flux at the southern cell face |
| 671 |
tfluxY(i,j,k) = -fCoriV(i,j)*SlopeY(i,j,k) |
| 672 |
& *recip_drF(k)*recip_hFacS(i,j,k,bi,bj) |
| 673 |
|
| 674 |
C Use the interior diffusivity. Note: if we are using a |
| 675 |
C constant diffusivity KPV is overwritten later |
| 676 |
KPV(i,j,k) = K3D(i,j,k,bi,bj) |
| 677 |
|
| 678 |
ENDDO |
| 679 |
ENDDO |
| 680 |
|
| 681 |
C Calculate the thickness flux and diffusivity and for other cells (k<Nr) |
| 682 |
DO k=Nr-1,1,-1 |
| 683 |
DO j=1-Oly,sNy+Oly |
| 684 |
DO i=1-Olx,sNx+Olx |
| 685 |
C Zonal thickness flux at the western cell face |
| 686 |
tfluxX(i,j,k)=-fCoriU(i,j)*(SlopeX(i,j,k)-SlopeX(i,j,k+1)) |
| 687 |
& *recip_drF(k)*recip_hFacW(i,j,k,bi,bj) |
| 688 |
& *maskW(i,j,k,bi,bj) |
| 689 |
|
| 690 |
C Meridional thickness flux at the southern cell face |
| 691 |
tfluxY(i,j,k)=-fCoriV(i,j)*(SlopeY(i,j,k)-SlopeY(i,j,k+1)) |
| 692 |
& *recip_drF(k)*recip_hFacS(i,j,k,bi,bj) |
| 693 |
& *maskS(i,j,k,bi,bj) |
| 694 |
|
| 695 |
C Use the interior diffusivity. Note: if we are using a |
| 696 |
C constant diffusivity KPV is overwritten later |
| 697 |
KPV(i,j,k) = K3D(i,j,k,bi,bj) |
| 698 |
ENDDO |
| 699 |
ENDDO |
| 700 |
ENDDO |
| 701 |
|
| 702 |
|
| 703 |
C Special treatment for the surface layer (if necessary), which overwrites |
| 704 |
C values in the previous loops. |
| 705 |
IF (GM_K3D_ThickSheet .OR. GM_K3D_surfK) THEN |
| 706 |
DO k=Nr-1,1,-1 |
| 707 |
DO j=1-Oly,sNy+Oly |
| 708 |
DO i=1-Olx,sNx+Olx |
| 709 |
IF(k.LE.surfk(i,j)) THEN |
| 710 |
C We are in the surface layer. Change the thickness flux |
| 711 |
C and diffusivity as necessary. |
| 712 |
|
| 713 |
IF (GM_K3D_ThickSheet) THEN |
| 714 |
C We are in the surface layer, so set the thickness flux |
| 715 |
C based on the average slope over the surface layer |
| 716 |
C If we are on the edge of a "cliff" the surface layer at the |
| 717 |
C centre of the grid point could be deeper than the U or V point. |
| 718 |
C So, we ensure that we always take a sensible slope. |
| 719 |
IF(kLow_U(i,j).LT.surfk(i,j)) THEN |
| 720 |
kk=kLow_U(i,j) |
| 721 |
hsurf = -rLowW(i,j,bi,bj) |
| 722 |
ELSE |
| 723 |
kk=surfk(i,j) |
| 724 |
hsurf = -surfkz(i,j) |
| 725 |
ENDIF |
| 726 |
IF(kk.GT.0) THEN |
| 727 |
IF(kk.EQ.Nr) THEN |
| 728 |
tfluxX(i,j,k) = -fCoriU(i,j)*maskW(i,j,k,bi,bj) |
| 729 |
& *SlopeX(i,j,kk)/hsurf |
| 730 |
ELSE |
| 731 |
tfluxX(i,j,k) = -fCoriU(i,j)*maskW(i,j,k,bi,bj) |
| 732 |
& *( SlopeX(i,j,kk)-SlopeX(i,j,kk+1) )/hsurf |
| 733 |
ENDIF |
| 734 |
ELSE |
| 735 |
tfluxX(i,j,k) = zeroRL |
| 736 |
ENDIF |
| 737 |
|
| 738 |
IF(kLow_V(i,j).LT.surfk(i,j)) THEN |
| 739 |
kk=kLow_V(i,j) |
| 740 |
hsurf = -rLowS(i,j,bi,bj) |
| 741 |
ELSE |
| 742 |
kk=surfk(i,j) |
| 743 |
hsurf = -surfkz(i,j) |
| 744 |
ENDIF |
| 745 |
IF(kk.GT.0) THEN |
| 746 |
IF(kk.EQ.Nr) THEN |
| 747 |
tfluxY(i,j,k) = -fCoriV(i,j)*maskS(i,j,k,bi,bj) |
| 748 |
& *SlopeY(i,j,kk)/hsurf |
| 749 |
ELSE |
| 750 |
tfluxY(i,j,k) = -fCoriV(i,j)*maskS(i,j,k,bi,bj) |
| 751 |
& *( SlopeY(i,j,kk)-SlopeY(i,j,kk+1) )/hsurf |
| 752 |
ENDIF |
| 753 |
ELSE |
| 754 |
tfluxY(i,j,k) = zeroRL |
| 755 |
ENDIF |
| 756 |
ENDIF |
| 757 |
|
| 758 |
IF (GM_K3D_surfK) THEN |
| 759 |
C Use a constant K in the surface layer. |
| 760 |
KPV(i,j,k) = GM_K3D_constK |
| 761 |
ENDIF |
| 762 |
ENDIF |
| 763 |
ENDDO |
| 764 |
ENDDO |
| 765 |
ENDDO |
| 766 |
ENDIF |
| 767 |
|
| 768 |
C Calculate gradq |
| 769 |
IF (GM_K3D_likeGM .OR. GM_K3D_beta_eq_0) THEN |
| 770 |
C Ignore beta in the calculation of grad(q) |
| 771 |
DO k=1,Nr |
| 772 |
DO j=1-Oly+1,sNy+Oly |
| 773 |
DO i=1-Olx+1,sNx+Olx |
| 774 |
gradqx(i,j,k) = maskW(i,j,k,bi,bj)*tfluxX(i,j,k) |
| 775 |
gradqy(i,j,k) = maskS(i,j,k,bi,bj)*tfluxY(i,j,k) |
| 776 |
ENDDO |
| 777 |
ENDDO |
| 778 |
ENDDO |
| 779 |
|
| 780 |
ELSE |
| 781 |
C Do not ignore beta |
| 782 |
DO k=1,Nr |
| 783 |
DO j=1-Oly+1,sNy+Oly |
| 784 |
DO i=1-Olx+1,sNx+Olx |
| 785 |
gradqx(i,j,k) = maskW(i,j,k,bi,bj)*(dfdx(i,j)+tfluxX(i,j,k)) |
| 786 |
gradqy(i,j,k) = maskS(i,j,k,bi,bj)*(dfdy(i,j)+tfluxY(i,j,k)) |
| 787 |
ENDDO |
| 788 |
ENDDO |
| 789 |
ENDDO |
| 790 |
ENDIF |
| 791 |
|
| 792 |
C ====================================== |
| 793 |
C Find Xi and the eddy induced velocities |
| 794 |
C ====================================== |
| 795 |
C Find the buoyancy frequency at the west and south faces of a cell |
| 796 |
C This is necessary to find the eigenvectors at those points |
| 797 |
DO k=1,Nr |
| 798 |
DO j=1-Oly+1,sNy+Oly |
| 799 |
DO i=1-Olx+1,sNx+Olx |
| 800 |
N2W(i,j,k) = maskW(i,j,k,bi,bj) |
| 801 |
& *( N2(i,j,k)+N2(i-1,j,k) ) |
| 802 |
N2S(i,j,k) = maskS(i,j,k,bi,bj) |
| 803 |
& *( N2(i,j,k)+N2(i,j-1,k) ) |
| 804 |
ENDDO |
| 805 |
ENDDO |
| 806 |
ENDDO |
| 807 |
|
| 808 |
C If GM_K3D_likeGM=.TRUE., the diffusivity for the eddy transport is |
| 809 |
C set to a constant equal to GM_K3D_constK. |
| 810 |
C If the diffusivity is constant the method here is the same as GM. |
| 811 |
C If GM_K3D_constRedi=.TRUE. K3D will be set equal to GM_K3D_constK later. |
| 812 |
IF(GM_K3D_likeGM) THEN |
| 813 |
DO k=1,Nr |
| 814 |
DO j=1-Oly,sNy+Oly |
| 815 |
DO i=1-Olx,sNx+Olx |
| 816 |
KPV(i,j,k) = GM_K3D_constK |
| 817 |
ENDDO |
| 818 |
ENDDO |
| 819 |
ENDDO |
| 820 |
ENDIF |
| 821 |
|
| 822 |
IF (.NOT. GM_K3D_smooth) THEN |
| 823 |
C Do not expand K grad(q) => no smoothing |
| 824 |
C May only be done with a constant K, otherwise the |
| 825 |
C integral constraint is violated. |
| 826 |
DO k=1,Nr |
| 827 |
DO j=1-Oly,sNy+Oly |
| 828 |
DO i=1-Olx,sNx+Olx |
| 829 |
Xix(i,j,k) = -maskW(i,j,k,bi,bj)*KPV(i,j,k)*gradqx(i,j,k) |
| 830 |
Xiy(i,j,k) = -maskS(i,j,k,bi,bj)*KPV(i,j,k)*gradqy(i,j,k) |
| 831 |
ENDDO |
| 832 |
ENDDO |
| 833 |
ENDDO |
| 834 |
|
| 835 |
ELSE |
| 836 |
C Expand K grad(q) in terms of baroclinic modes to smooth |
| 837 |
C and satisfy the integral constraint |
| 838 |
|
| 839 |
C Start with the X direction |
| 840 |
C ------------------------------ |
| 841 |
C Calculate the eigenvectors at the West face of a cell |
| 842 |
IF (update_modes) THEN |
| 843 |
CALL GMREDI_CALC_EIGS( |
| 844 |
I iMin,iMax,jMin,jMax,bi,bj,N2W,myThid, |
| 845 |
I kLow_U,maskW(:,:,:,bi,bj), |
| 846 |
I hfacW(:,:,:,bi,bj),recip_hfacW(:,:,:,bi,bj), |
| 847 |
I rLowW(:,:,bi,bj),GM_K3D_NModes,.FALSE., |
| 848 |
O dummy,modesW(:,:,:,:,bi,bj)) |
| 849 |
ENDIF |
| 850 |
|
| 851 |
C Calculate Xi_m at the west face of a cell |
| 852 |
DO j=1-Oly,sNy+Oly |
| 853 |
DO i=1-Olx,sNx+Olx |
| 854 |
DO m=1,GM_K3D_NModes |
| 855 |
XimX(m,i,j) = zeroRL |
| 856 |
ENDDO |
| 857 |
ENDDO |
| 858 |
ENDDO |
| 859 |
DO k=1,Nr |
| 860 |
DO j=1-Oly,sNy+Oly |
| 861 |
DO i=1-Olx,sNx+Olx |
| 862 |
DO m=1,GM_K3D_NModes |
| 863 |
Kdqdx(i,j,k) = KPV(i,j,k)*gradqx(i,j,k) |
| 864 |
XimX(m,i,j) = XimX(m,i,j) |
| 865 |
& - maskW(i,j,k,bi,bj)*drF(k)*hfacW(i,j,k,bi,bj) |
| 866 |
& *Kdqdx(i,j,k)*modesW(m,i,j,k,bi,bj) |
| 867 |
ENDDO |
| 868 |
ENDDO |
| 869 |
ENDDO |
| 870 |
ENDDO |
| 871 |
|
| 872 |
C Calculate Xi in the X direction at the west face |
| 873 |
DO k=1,Nr |
| 874 |
DO j=1-Oly,sNy+Oly |
| 875 |
DO i=1-Olx,sNx+Olx |
| 876 |
Xix(i,j,k) = zeroRL |
| 877 |
ENDDO |
| 878 |
ENDDO |
| 879 |
ENDDO |
| 880 |
DO k=1,Nr |
| 881 |
DO j=1-Oly,sNy+Oly |
| 882 |
DO i=1-Olx,sNx+Olx |
| 883 |
DO m=1,GM_K3D_NModes |
| 884 |
Xix(i,j,k) = Xix(i,j,k) |
| 885 |
& + maskW(i,j,k,bi,bj)*XimX(m,i,j)*modesW(m,i,j,k,bi,bj) |
| 886 |
ENDDO |
| 887 |
ENDDO |
| 888 |
ENDDO |
| 889 |
ENDDO |
| 890 |
|
| 891 |
C Now the Y direction |
| 892 |
C ------------------------------ |
| 893 |
C Calculate the eigenvectors at the West face of a cell |
| 894 |
IF (update_modes) THEN |
| 895 |
CALL GMREDI_CALC_EIGS( |
| 896 |
I iMin,iMax,jMin,jMax,bi,bj,N2S,myThid, |
| 897 |
I kLow_V,maskS(:,:,:,bi,bj), |
| 898 |
I hfacS(:,:,:,bi,bj),recip_hfacS(:,:,:,bi,bj), |
| 899 |
I rLowS(:,:,bi,bj), GM_K3D_NModes, .FALSE., |
| 900 |
O dummy,modesS(:,:,:,:,bi,bj)) |
| 901 |
ENDIF |
| 902 |
|
| 903 |
DO j=1-Oly,sNy+Oly |
| 904 |
DO i=1-Olx,sNx+Olx |
| 905 |
DO m=1,GM_K3D_NModes |
| 906 |
XimY(m,i,j) = zeroRL |
| 907 |
ENDDO |
| 908 |
ENDDO |
| 909 |
ENDDO |
| 910 |
DO k=1,Nr |
| 911 |
DO j=1-Oly,sNy+Oly |
| 912 |
DO i=1-Olx,sNx+Olx |
| 913 |
DO m=1,GM_K3D_NModes |
| 914 |
Kdqdy(i,j,k) = KPV(i,j,k)*gradqy(i,j,k) |
| 915 |
XimY(m,i,j) = XimY(m,i,j) |
| 916 |
& - drF(k)*hfacS(i,j,k,bi,bj) |
| 917 |
& *Kdqdy(i,j,k)*modesS(m,i,j,k,bi,bj) |
| 918 |
ENDDO |
| 919 |
ENDDO |
| 920 |
ENDDO |
| 921 |
ENDDO |
| 922 |
|
| 923 |
C Calculate Xi for Y direction at the south face |
| 924 |
DO k=1,Nr |
| 925 |
DO j=1-Oly,sNy+Oly |
| 926 |
DO i=1-Olx,sNx+Olx |
| 927 |
Xiy(i,j,k) = zeroRL |
| 928 |
ENDDO |
| 929 |
ENDDO |
| 930 |
ENDDO |
| 931 |
DO k=1,Nr |
| 932 |
DO j=1-Oly,sNy+Oly |
| 933 |
DO i=1-Olx,sNx+Olx |
| 934 |
DO m=1,GM_K3D_NModes |
| 935 |
Xiy(i,j,k) = Xiy(i,j,k) |
| 936 |
& + maskS(i,j,k,bi,bj)*XimY(m,i,j)*modesS(m,i,j,k,bi,bj) |
| 937 |
ENDDO |
| 938 |
ENDDO |
| 939 |
ENDDO |
| 940 |
ENDDO |
| 941 |
|
| 942 |
C ENDIF (.NOT. GM_K3D_smooth) |
| 943 |
ENDIF |
| 944 |
|
| 945 |
|
| 946 |
C Calculate the renormalisation factor |
| 947 |
DO j=1-Oly,sNy+Oly |
| 948 |
DO i=1-Olx,sNx+Olx |
| 949 |
uInt(i,j)=zeroRL |
| 950 |
vInt(i,j)=zeroRL |
| 951 |
KdqdyInt(i,j)=zeroRL |
| 952 |
KdqdxInt(i,j)=zeroRL |
| 953 |
uKdqdyInt(i,j)=zeroRL |
| 954 |
vKdqdxInt(i,j)=zeroRL |
| 955 |
uXiyInt(i,j)=zeroRL |
| 956 |
vXixInt(i,j)=zeroRL |
| 957 |
Renorm(i,j)=oneRL |
| 958 |
RenormU(i,j)=oneRL |
| 959 |
RenormV(i,j)=oneRL |
| 960 |
ENDDO |
| 961 |
ENDDO |
| 962 |
DO k=1,Nr |
| 963 |
DO j=1-Oly,sNy+Oly-1 |
| 964 |
DO i=1-Olx,sNx+Olx-1 |
| 965 |
centreX = op5*(uVel(i,j,k,bi,bj)+uVel(i+1,j,k,bi,bj)) |
| 966 |
centreY = op5*(Kdqdy(i,j,k) +Kdqdy(i,j+1,k) ) |
| 967 |
C For the numerator |
| 968 |
uInt(i,j) = uInt(i,j) |
| 969 |
& + centreX*hfacC(i,j,k,bi,bj)*drF(k) |
| 970 |
KdqdyInt(i,j) = KdqdyInt(i,j) |
| 971 |
& + centreY*hfacC(i,j,k,bi,bj)*drF(k) |
| 972 |
uKdqdyInt(i,j) = uKdqdyInt(i,j) |
| 973 |
& + centreX*centreY*hfacC(i,j,k,bi,bj)*drF(k) |
| 974 |
C For the denominator |
| 975 |
centreY = op5*(Xiy(i,j,k) + Xiy(i,j+1,k)) |
| 976 |
uXiyInt(i,j) = uXiyInt(i,j) |
| 977 |
& + centreX*centreY*hfacC(i,j,k,bi,bj)*drF(k) |
| 978 |
|
| 979 |
centreX = op5*(Kdqdx(i,j,k) +Kdqdx(i+1,j,k)) |
| 980 |
centreY = op5*(vVel(i,j,k,bi,bj)+vVel(i,j+1,k,bi,bj) ) |
| 981 |
C For the numerator |
| 982 |
vInt(i,j) = vInt(i,j) |
| 983 |
& + centreY*hfacC(i,j,k,bi,bj)*drF(k) |
| 984 |
KdqdxInt(i,j) = KdqdxInt(i,j) |
| 985 |
& + CentreX*hfacC(i,j,k,bi,bj)*drF(k) |
| 986 |
vKdqdxInt(i,j) = vKdqdxInt(i,j) |
| 987 |
& + centreY*centreX*hfacC(i,j,k,bi,bj)*drF(k) |
| 988 |
C For the denominator |
| 989 |
centreX = op5*(Xix(i,j,k) + Xix(i+1,j,k)) |
| 990 |
vXixInt(i,j) = vXixInt(i,j) |
| 991 |
& + centreY*centreX*hfacC(i,j,k,bi,bj)*drF(k) |
| 992 |
|
| 993 |
ENDDO |
| 994 |
ENDDO |
| 995 |
ENDDO |
| 996 |
|
| 997 |
DO j=1-Oly,sNy+Oly-1 |
| 998 |
DO i=1-Olx,sNx+Olx-1 |
| 999 |
IF (kLowC(i,j,bi,bj).GT.0) THEN |
| 1000 |
numerator = |
| 1001 |
& (uKdqdyInt(i,j)-uInt(i,j)*KdqdyInt(i,j)/R_low(i,j,bi,bj)) |
| 1002 |
& -(vKdqdxInt(i,j)-vInt(i,j)*KdqdxInt(i,j)/R_low(i,j,bi,bj)) |
| 1003 |
denominator = uXiyInt(i,j) - vXixInt(i,j) |
| 1004 |
C We can have troubles with floating point exceptions if the denominator |
| 1005 |
C of the renormalisation if the ocean is resting (e.g. intial conditions). |
| 1006 |
C So we make the renormalisation factor one if the denominator is very small |
| 1007 |
C The renormalisation factor is supposed to correct the error in the extraction of |
| 1008 |
C potential energy associated with the truncation of the expansion. Thus, we |
| 1009 |
C enforce a minimum value for the renormalisation factor. |
| 1010 |
C We also enforce a maximum renormalisation factor. |
| 1011 |
IF (denominator.GT.small) THEN |
| 1012 |
Renorm(i,j) = ABS(numerator/denominator) |
| 1013 |
Renorm(i,j) = MAX(Renorm(i,j),GM_K3D_minRenorm) |
| 1014 |
Renorm(i,j) = MIN(Renorm(i,j),GM_K3D_maxRenorm) |
| 1015 |
ENDIF |
| 1016 |
ENDIF |
| 1017 |
ENDDO |
| 1018 |
ENDDO |
| 1019 |
C Now put it back on to the velocity grids |
| 1020 |
DO j=1-Oly+1,sNy+Oly-1 |
| 1021 |
DO i=1-Olx+1,sNx+Olx-1 |
| 1022 |
RenormU(i,j) = op5*(Renorm(i-1,j)+Renorm(i,j)) |
| 1023 |
RenormV(i,j) = op5*(Renorm(i,j-1)+Renorm(i,j)) |
| 1024 |
ENDDO |
| 1025 |
ENDDO |
| 1026 |
|
| 1027 |
C Calculate the eddy induced velocity in the X direction at the west face |
| 1028 |
DO k=1,Nr |
| 1029 |
DO j=1-Oly+1,sNy+Oly |
| 1030 |
DO i=1-Olx+1,sNx+Olx |
| 1031 |
ustar(i,j,k) = -RenormU(i,j)*Xix(i,j,k)/coriU(i,j) |
| 1032 |
ENDDO |
| 1033 |
ENDDO |
| 1034 |
ENDDO |
| 1035 |
|
| 1036 |
C Calculate the eddy induced velocity in the Y direction at the south face |
| 1037 |
DO k=1,Nr |
| 1038 |
DO j=1-Oly+1,sNy+Oly |
| 1039 |
DO i=1-Olx+1,sNx+Olx |
| 1040 |
vstar(i,j,k) = -RenormV(i,j)*Xiy(i,j,k)/coriV(i,j) |
| 1041 |
ENDDO |
| 1042 |
ENDDO |
| 1043 |
ENDDO |
| 1044 |
|
| 1045 |
C ====================================== |
| 1046 |
C Calculate the eddy induced overturning streamfunction |
| 1047 |
C ====================================== |
| 1048 |
#ifdef GM_K3D_PASSIVE |
| 1049 |
k=Nr |
| 1050 |
DO j=1-Oly,sNy+Oly |
| 1051 |
DO i=1-Olx,sNx+Olx |
| 1052 |
psistar(i,j,Nr) = -hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
| 1053 |
ENDDO |
| 1054 |
ENDDO |
| 1055 |
DO k=Nr-1,1,-1 |
| 1056 |
DO j=1-Oly,sNy+Oly |
| 1057 |
DO i=1-Olx,sNx+Olx |
| 1058 |
psistar(i,j,k) = psistar(i,j,k+1) |
| 1059 |
& - hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
| 1060 |
ENDDO |
| 1061 |
ENDDO |
| 1062 |
ENDDO |
| 1063 |
|
| 1064 |
#else |
| 1065 |
|
| 1066 |
IF (GM_AdvForm) THEN |
| 1067 |
k=Nr |
| 1068 |
DO j=1-Oly+1,sNy+1 |
| 1069 |
DO i=1-Olx+1,sNx+1 |
| 1070 |
GM_PsiX(i,j,k,bi,bj) = -hfacW(i,j,k,bi,bj)*drF(k)*ustar(i,j,k) |
| 1071 |
GM_PsiY(i,j,k,bi,bj) = -hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
| 1072 |
ENDDO |
| 1073 |
ENDDO |
| 1074 |
DO k=Nr-1,1,-1 |
| 1075 |
DO j=1-Oly+1,sNy+1 |
| 1076 |
DO i=1-Olx+1,sNx+1 |
| 1077 |
GM_PsiX(i,j,k,bi,bj) = GM_PsiX(i,j,k+1,bi,bj) |
| 1078 |
& - hfacW(i,j,k,bi,bj)*drF(k)*ustar(i,j,k) |
| 1079 |
GM_PsiY(i,j,k,bi,bj) = GM_PsiY(i,j,k+1,bi,bj) |
| 1080 |
& - hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
| 1081 |
ENDDO |
| 1082 |
ENDDO |
| 1083 |
ENDDO |
| 1084 |
|
| 1085 |
ENDIF |
| 1086 |
#endif |
| 1087 |
|
| 1088 |
#ifdef ALLOW_DIAGNOSTICS |
| 1089 |
C Diagnostics |
| 1090 |
IF ( useDiagnostics ) THEN |
| 1091 |
CALL DIAGNOSTICS_FILL(K3D, 'GM_K3D ',0,Nr,0,1,1,myThid) |
| 1092 |
CALL DIAGNOSTICS_FILL(KPV, 'GM_KPV ',0,Nr,0,1,1,myThid) |
| 1093 |
CALL DIAGNOSTICS_FILL(urms, 'GM_URMS ',0,Nr,0,1,1,myThid) |
| 1094 |
CALL DIAGNOSTICS_FILL(Rdef, 'GM_RDEF ',0, 1,0,1,1,myThid) |
| 1095 |
CALL DIAGNOSTICS_FILL(Rurms, 'GM_RURMS',0, 1,0,1,1,myThid) |
| 1096 |
CALL DIAGNOSTICS_FILL(RRhines,'GM_RRHNS',0, 1,0,1,1,myThid) |
| 1097 |
CALL DIAGNOSTICS_FILL(Rmix, 'GM_RMIX ',0, 1,0,1,1,myThid) |
| 1098 |
CALL DIAGNOSTICS_FILL(supp, 'GM_SUPP ',0,Nr,0,1,1,myThid) |
| 1099 |
CALL DIAGNOSTICS_FILL(Xix, 'GM_Xix ',0,Nr,0,1,1,myThid) |
| 1100 |
CALL DIAGNOSTICS_FILL(Xiy, 'GM_Xiy ',0,Nr,0,1,1,myThid) |
| 1101 |
CALL DIAGNOSTICS_FILL(cDopp, 'GM_C ',0, 1,0,1,1,myThid) |
| 1102 |
CALL DIAGNOSTICS_FILL(Ubaro, 'GM_UBARO',0, 1,0,1,1,myThid) |
| 1103 |
CALL DIAGNOSTICS_FILL(eady, 'GM_EADY ',0, 1,0,1,1,myThid) |
| 1104 |
CALL DIAGNOSTICS_FILL(SlopeX, 'GM_Sx ',0,Nr,0,1,1,myThid) |
| 1105 |
CALL DIAGNOSTICS_FILL(SlopeY, 'GM_Sy ',0,Nr,0,1,1,myThid) |
| 1106 |
CALL DIAGNOSTICS_FILL(tfluxX, 'GM_TFLXX',0,Nr,0,1,1,myThid) |
| 1107 |
CALL DIAGNOSTICS_FILL(tfluxY, 'GM_TFLXY',0,Nr,0,1,1,myThid) |
| 1108 |
CALL DIAGNOSTICS_FILL(gradqx, 'GM_dqdx ',0,Nr,0,1,1,myThid) |
| 1109 |
CALL DIAGNOSTICS_FILL(gradqy, 'GM_dqdy ',0,Nr,0,1,1,myThid) |
| 1110 |
CALL DIAGNOSTICS_FILL(Kdqdy, 'GM_Kdqdy',0,Nr,0,1,1,myThid) |
| 1111 |
CALL DIAGNOSTICS_FILL(Kdqdx, 'GM_Kdqdx',0,Nr,0,1,1,myThid) |
| 1112 |
CALL DIAGNOSTICS_FILL(surfkz, 'GM_SFLYR',0, 1,0,1,1,myThid) |
| 1113 |
CALL DIAGNOSTICS_FILL(ustar, 'GM_USTAR',0,Nr,0,1,1,myThid) |
| 1114 |
CALL DIAGNOSTICS_FILL(vstar, 'GM_VSTAR',0,Nr,0,1,1,myThid) |
| 1115 |
CALL DIAGNOSTICS_FILL(umc, 'GM_UMC ',0,Nr,0,1,1,myThid) |
| 1116 |
CALL DIAGNOSTICS_FILL(ubar, 'GM_UBAR ',0,Nr,0,1,1,myThid) |
| 1117 |
CALL DIAGNOSTICS_FILL(modesC(1,:,:,:,bi,bj), |
| 1118 |
& 'GM_MODEC',0,Nr,0,1,1,myThid) |
| 1119 |
CALL DIAGNOSTICS_FILL(M4loc, 'GM_M4 ',0,Nr,0,1,1,myThid) |
| 1120 |
CALL DIAGNOSTICS_FILL(N2loc, 'GM_N2 ',0,Nr,0,1,1,myThid) |
| 1121 |
CALL DIAGNOSTICS_FILL(M4onN2, 'GM_M4_N2',0,Nr,0,1,1,myThid) |
| 1122 |
CALL DIAGNOSTICS_FILL(slopeC, 'GM_SLOPE',0,Nr,0,1,1,myThid) |
| 1123 |
CALL DIAGNOSTICS_FILL(Renorm, 'GM_RENRM',0, 1,0,1,1,myThid) |
| 1124 |
|
| 1125 |
ENDIF |
| 1126 |
#endif |
| 1127 |
|
| 1128 |
C For the Redi diffusivity, we set K3D to a constant if |
| 1129 |
C GM_K3D_constRedi=.TRUE. |
| 1130 |
IF (GM_K3D_constRedi) THEN |
| 1131 |
DO k=1,Nr |
| 1132 |
DO j=1-Oly,sNy+Oly |
| 1133 |
DO i=1-Olx,sNx+Olx |
| 1134 |
K3D(i,j,k,bi,bj) = GM_K3D_constK |
| 1135 |
ENDDO |
| 1136 |
ENDDO |
| 1137 |
ENDDO |
| 1138 |
ENDIF |
| 1139 |
|
| 1140 |
#ifdef ALLOW_DIAGNOSTICS |
| 1141 |
IF ( useDiagnostics ) |
| 1142 |
& CALL DIAGNOSTICS_FILL(K3D, 'GM_K3D_T',0,Nr,0,1,1,myThid) |
| 1143 |
#endif |
| 1144 |
|
| 1145 |
#endif /* GM_K3D */ |
| 1146 |
RETURN |
| 1147 |
END |
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