| 1 |
C $Header: /u/gcmpack/MITgcm/pkg/gmredi/gmredi_k3d.F,v 1.13 2013/10/21 18:46:05 m_bates Exp $ |
| 2 |
C $Name: $ |
| 3 |
#include "CPP_OPTIONS.h" |
| 4 |
#include "GMREDI_OPTIONS.h" |
| 5 |
|
| 6 |
C !ROUTINE: GMREDI_K3D |
| 7 |
C !INTERFACE: |
| 8 |
SUBROUTINE GMREDI_K3D( |
| 9 |
I iMin, iMax, jMin, jMax, |
| 10 |
I sigmaX, sigmaY, sigmaR, |
| 11 |
I bi, bj, myTime, myThid ) |
| 12 |
|
| 13 |
C !DESCRIPTION: \bv |
| 14 |
C *==========================================================* |
| 15 |
C | SUBROUTINE GMREDI_K3D |
| 16 |
C | o Calculates the 3D diffusivity as per Bates et al. (2013) |
| 17 |
C *==========================================================* |
| 18 |
C \ev |
| 19 |
|
| 20 |
IMPLICIT NONE |
| 21 |
|
| 22 |
C == Global variables == |
| 23 |
#include "SIZE.h" |
| 24 |
#include "GRID.h" |
| 25 |
#include "DYNVARS.h" |
| 26 |
#include "EEPARAMS.h" |
| 27 |
#include "PARAMS.h" |
| 28 |
#include "GMREDI.h" |
| 29 |
|
| 30 |
C !INPUT/OUTPUT PARAMETERS: |
| 31 |
C == Routine arguments == |
| 32 |
C bi, bj :: tile indices |
| 33 |
C myThid :: My Thread Id. number |
| 34 |
|
| 35 |
INTEGER iMin,iMax,jMin,jMax |
| 36 |
_RL sigmaX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 37 |
_RL sigmaY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 38 |
_RL sigmaR(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 39 |
INTEGER bi, bj |
| 40 |
_RL myTime |
| 41 |
INTEGER myThid |
| 42 |
|
| 43 |
#ifdef GM_K3D |
| 44 |
|
| 45 |
C === Functions ==== |
| 46 |
LOGICAL DIFFERENT_MULTIPLE |
| 47 |
EXTERNAL DIFFERENT_MULTIPLE |
| 48 |
|
| 49 |
C !LOCAL VARIABLES: |
| 50 |
C == Local variables == |
| 51 |
INTEGER i,j,k,kk,m |
| 52 |
|
| 53 |
C update_modes :: Whether to update the eigenmodes |
| 54 |
LOGICAL update_modes |
| 55 |
|
| 56 |
C surfk :: index of the depth of the surface layer |
| 57 |
C kLow_C :: Local version of the index of deepest wet grid cell on tracer grid |
| 58 |
C kLow_U :: Local version of the index of deepest wet grid cell on U grid |
| 59 |
C kLow_V :: Local version of the index of deepest wet grid cell on V grid |
| 60 |
INTEGER surfk(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 61 |
INTEGER kLow_C(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 62 |
INTEGER kLow_U(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 63 |
INTEGER kLow_V(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 64 |
|
| 65 |
C N2loc :: local N**2 |
| 66 |
C slope :: local slope |
| 67 |
C Req :: local equatorial deformation radius (m) |
| 68 |
C deltaH :: local thickness of Eady integration (m) |
| 69 |
C g_reciprho_sq :: (gravity*recip_rhoConst)**2 |
| 70 |
C M4loc :: local M**4 |
| 71 |
C maxDRhoDz :: maximum value of d(rho)/dz (derived from GM_K3D_minN2) |
| 72 |
C sigx :: local d(rho)/dx |
| 73 |
C sigy :: local d(rho)/dy |
| 74 |
C sigz :: local d(rho)/dz |
| 75 |
C hsurf :: local surface layer depth |
| 76 |
C small :: a small number (to avoid floating point exceptions) |
| 77 |
_RL N2loc(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 78 |
_RL slope |
| 79 |
_RL slopeC(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 80 |
_RL Req |
| 81 |
_RL deltaH(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 82 |
_RL g_reciprho_sq |
| 83 |
_RL M4loc(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 84 |
_RL M4onN2(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 85 |
_RL maxDRhoDz |
| 86 |
_RL sigx, sigy, sigz |
| 87 |
_RL hsurf |
| 88 |
_RL small |
| 89 |
|
| 90 |
C dfdy :: gradient of the Coriolis paramter, df/dy, 1/(m*s) |
| 91 |
C dfdx :: gradient of the Coriolis paramter, df/dx, 1/(m*s) |
| 92 |
C gradf :: gradient of the Coriolis paramter at a cell centre, 1/(m*s) |
| 93 |
C Rurms :: a local mixing length used in calculation of urms (m) |
| 94 |
C RRhines :: The Rhines scale (m) |
| 95 |
C Rmix :: Mixing length |
| 96 |
C N2 :: Square of the buoyancy frequency (1/s**2) |
| 97 |
C N2W :: Square of the buoyancy frequency (1/s**2) averaged to west of grid cell |
| 98 |
C N2S :: Square of the buoyancy frequency (1/s**2) averaged to south of grid cell |
| 99 |
C N :: Buoyancy frequency, SQRT(N2) |
| 100 |
C BVint :: The vertical integral of N (m/s) |
| 101 |
C ubar :: Zonal velocity on a tracer point (m/s) |
| 102 |
C vbar :: Meridional velocity on a tracer point (m/s) |
| 103 |
C Ubaro :: Barotropic velocity (m/s) |
| 104 |
_RL dfdy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 105 |
_RL dfdx( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 106 |
_RL gradf( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 107 |
_RL dummy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 108 |
_RL Rurms( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 109 |
_RL RRhines(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 110 |
_RL Rmix( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 111 |
_RL N2( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 112 |
_RL N2W( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 113 |
_RL N2S( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 114 |
_RL N( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 115 |
_RL BVint( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 116 |
_RL Ubaro( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 117 |
_RL ubar( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy) |
| 118 |
_RL vbar( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy) |
| 119 |
|
| 120 |
C Rmid :: Rossby radius (m) |
| 121 |
C KPV :: Diffusivity (m**2/s) |
| 122 |
C Kdqdx :: diffusivity multiplied by zonal PV gradient |
| 123 |
C Kdqdy :: diffusivity multiplied by meridional PV gradient |
| 124 |
C SlopeX :: isopycnal slope in x direction |
| 125 |
C SlopeY :: isopycnal slope in y direction |
| 126 |
C dSigmaDx :: sigmaX averaged onto tracer grid |
| 127 |
C dSigmaDy :: sigmaY averaged onto tracer grid |
| 128 |
C tfluxX :: thickness flux in x direction |
| 129 |
C tfluxY :: thickness flux in y direction |
| 130 |
C fCoriU :: Coriolis parameter averaged to U points |
| 131 |
C fCoriV :: Coriolis parameter averaged to V points |
| 132 |
C cori :: Coriolis parameter forced to be finite near the equator |
| 133 |
C coriU :: As for cori, but, at U point |
| 134 |
C coriV :: As for cori, but, at V point |
| 135 |
C surfkz :: Depth of surface layer (in r units) |
| 136 |
_RL Rmid(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 137 |
_RL KPV(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 138 |
_RL Kdqdy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 139 |
_RL Kdqdx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 140 |
_RL SlopeX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 141 |
_RL SlopeY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 142 |
_RL dSigmaDx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 143 |
_RL dSigmaDy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 144 |
_RL tfluxX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 145 |
_RL tfluxY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 146 |
_RL cori(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 147 |
_RL coriU(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 148 |
_RL coriV(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 149 |
_RL fCoriU(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 150 |
_RL fCoriV(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 151 |
_RL surfkz(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 152 |
|
| 153 |
C gradqx :: Potential vorticity gradient in x direction |
| 154 |
C gradqy :: Potential vorticity gradient in y direction |
| 155 |
C XimX :: Vertical integral of phi_m*K*gradqx |
| 156 |
C XimY :: Vertical integral of phi_m*K*gradqy |
| 157 |
C cDopp :: Quasi-Doppler shifted long Rossby wave speed (m/s) |
| 158 |
C umc :: ubar-c (m/s) |
| 159 |
C eady :: Eady growth rate (1/s) |
| 160 |
C urms :: the rms eddy velocity (m/s) |
| 161 |
C supp :: The suppression factor |
| 162 |
C ustar :: The eddy induced velocity in the x direction |
| 163 |
C vstar :: The eddy induced velocity in the y direction |
| 164 |
C Xix :: Xi in the x direction (m/s**2) |
| 165 |
C Xiy :: Xi in the y direction (m/s**2) |
| 166 |
_RL gradqx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 167 |
_RL gradqy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 168 |
_RL XimX(GM_K3D_NModes,1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 169 |
_RL XimY(GM_K3D_NModes,1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 170 |
_RL cDopp(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 171 |
_RL umc( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
| 172 |
_RL eady( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 173 |
_RL urms( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
| 174 |
_RL supp( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
| 175 |
_RL ustar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
| 176 |
_RL vstar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
| 177 |
_RL Xix( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 178 |
_RL Xiy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 179 |
#ifdef GM_K3D_PASSIVE |
| 180 |
C psistar :: eddy induced streamfunction in the y direction |
| 181 |
_RL psistar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
| 182 |
#endif |
| 183 |
|
| 184 |
|
| 185 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 186 |
|
| 187 |
C ====================================== |
| 188 |
C Initialise some variables |
| 189 |
C ====================================== |
| 190 |
small = TINY(zeroRL) |
| 191 |
update_modes=.FALSE. |
| 192 |
IF ( DIFFERENT_MULTIPLE(GM_K3D_vecFreq,myTime,deltaTClock) ) |
| 193 |
& update_modes=.TRUE. |
| 194 |
|
| 195 |
DO j=1-Oly,sNy+Oly |
| 196 |
DO i=1-Olx,sNx+Olx |
| 197 |
kLow_C(i,j) = kLowC(i,j,bi,bj) |
| 198 |
ENDDO |
| 199 |
ENDDO |
| 200 |
DO j=1-Oly,sNy+Oly |
| 201 |
DO i=1-Olx+1,sNx+Olx |
| 202 |
kLow_U(i,j) = MIN( kLow_C(i,j), kLow_C(i-1,j) ) |
| 203 |
ENDDO |
| 204 |
ENDDO |
| 205 |
DO j=1-Oly+1,sNy+Oly |
| 206 |
DO i=1-Olx,sNx+Olx |
| 207 |
kLow_V(i,j) = MIN( kLow_C(i,j), kLow_C(i,j-1) ) |
| 208 |
ENDDO |
| 209 |
ENDDO |
| 210 |
|
| 211 |
C Dummy values for the edges |
| 212 |
C This avoids weirdness in gmredi_calc_eigs |
| 213 |
i=1-Olx |
| 214 |
DO j=1-Oly,sNy+Oly |
| 215 |
kLow_U(i,j) = kLow_C(i,j) |
| 216 |
ENDDO |
| 217 |
j=1-Oly |
| 218 |
DO i=1-Olx,sNx+Olx |
| 219 |
kLow_V(i,j) = kLow_C(i,j) |
| 220 |
ENDDO |
| 221 |
|
| 222 |
g_reciprho_sq = (gravity*recip_rhoConst)**2 |
| 223 |
C Gradient of Coriolis |
| 224 |
DO j=1-Oly+1,sNy+Oly |
| 225 |
DO i=1-Olx+1,sNx+Olx |
| 226 |
dfdx(i,j) = ( fCori(i,j,bi,bj)-fCori(i-1,j,bi,bj) ) |
| 227 |
& *recip_dxC(i,j,bi,bj) |
| 228 |
dfdy(i,j) = ( fCori(i,j,bi,bj)-fCori(i,j-1,bi,bj) ) |
| 229 |
& *recip_dyC(i,j,bi,bj) |
| 230 |
ENDDO |
| 231 |
ENDDO |
| 232 |
|
| 233 |
C Coriolis at C points enforcing a minimum value so |
| 234 |
C that it is defined at the equator |
| 235 |
DO j=1-Oly,sNy+Oly |
| 236 |
DO i=1-Olx,sNx+Olx |
| 237 |
cori(i,j) = SIGN( MAX( ABS(fCori(i,j,bi,bj)),GM_K3D_minCori ), |
| 238 |
& fCori(i,j,bi,bj) ) |
| 239 |
ENDDO |
| 240 |
ENDDO |
| 241 |
C Coriolis at U and V points |
| 242 |
DO j=1-Oly+1,sNy+Oly |
| 243 |
DO i=1-Olx+1,sNx+Olx |
| 244 |
C Limited so that the inverse is defined at the equator |
| 245 |
coriU(i,j) = op5*( cori(i,j)+cori(i-1,j) ) |
| 246 |
coriU(i,j) = SIGN( MAX( ABS(coriU(i,j)),GM_K3D_minCori ), |
| 247 |
& coriU(i,j) ) |
| 248 |
|
| 249 |
coriV(i,j) = op5*( cori(i,j)+cori(i,j-1) ) |
| 250 |
coriV(i,j) = SIGN( MAX( ABS(coriV(i,j)),GM_K3D_minCori ), |
| 251 |
& coriV(i,j) ) |
| 252 |
|
| 253 |
C Not limited |
| 254 |
fCoriU(i,j) = op5*( fCori(i,j,bi,bj)+fCori(i-1,j,bi,bj) ) |
| 255 |
fCoriV(i,j) = op5*( fCori(i,j,bi,bj)+fCori(i,j-1,bi,bj) ) |
| 256 |
ENDDO |
| 257 |
ENDDO |
| 258 |
DO j=1-Oly,sNy+Oly |
| 259 |
DO i=1-Olx,sNx+Olx |
| 260 |
gradf(i,j) = recip_rSphere*fCoriCos(i,j,bi,bj) |
| 261 |
ENDDO |
| 262 |
ENDDO |
| 263 |
|
| 264 |
C Zeroing some cumulative fields |
| 265 |
DO j=1-Oly,sNy+Oly |
| 266 |
DO i=1-Olx,sNx+Olx |
| 267 |
eady(i,j) = zeroRL |
| 268 |
BVint(i,j) = zeroRL |
| 269 |
Ubaro(i,j) = zeroRL |
| 270 |
deltaH(i,j) = zeroRL |
| 271 |
ENDDO |
| 272 |
ENDDO |
| 273 |
DO k=1,Nr |
| 274 |
DO j=1-Oly,sNy+Oly |
| 275 |
DO i=1-Olx,sNx+Olx |
| 276 |
slopeC(i,j,k)=zeroRL |
| 277 |
ENDDO |
| 278 |
ENDDO |
| 279 |
ENDDO |
| 280 |
|
| 281 |
C Find the zonal velocity at the cell centre |
| 282 |
C The logicals here are, in order: 1/ go from grid to north/east directions |
| 283 |
C 2/ go from C to A grid and 3/ apply the mask |
| 284 |
#ifdef ALLOW_EDDYPSI |
| 285 |
IF (GM_InMomAsStress) THEN |
| 286 |
CALL rotate_uv2en_rl(uMean, vMean, ubar, vbar, .TRUE., .TRUE., |
| 287 |
& .TRUE.,Nr,mythid) |
| 288 |
ELSE |
| 289 |
#endif |
| 290 |
CALL rotate_uv2en_rl(uVel, vVel, ubar, vbar, .TRUE., .TRUE., |
| 291 |
& .TRUE.,Nr,mythid) |
| 292 |
#ifdef ALLOW_EDDYPSI |
| 293 |
ENDIF |
| 294 |
#endif |
| 295 |
|
| 296 |
C Square of the buoyancy frequency at the top of a grid cell |
| 297 |
DO k=2,Nr |
| 298 |
DO j=1-Oly,sNy+Oly |
| 299 |
DO i=1-Olx,sNx+Olx |
| 300 |
N2(i,j,k) = -gravity*recip_rhoConst*sigmaR(i,j,k) |
| 301 |
ENDDO |
| 302 |
ENDDO |
| 303 |
ENDDO |
| 304 |
C N2(k=1) is always zero |
| 305 |
k=1 |
| 306 |
DO j=1-Oly,sNy+Oly |
| 307 |
DO i=1-Olx,sNx+Olx |
| 308 |
N2(i,j,k) = 0.0 |
| 309 |
N(i,j,k) = 0.0 |
| 310 |
ENDDO |
| 311 |
ENDDO |
| 312 |
C Enforce a minimum N2 |
| 313 |
DO k=2,Nr |
| 314 |
DO j=1-Oly,sNy+Oly |
| 315 |
DO i=1-Olx,sNx+Olx |
| 316 |
IF (N2(i,j,k).LT.GM_K3D_minN2) N2(i,j,k)=GM_K3D_minN2 |
| 317 |
N(i,j,k) = SQRT(N2(i,j,k)) |
| 318 |
ENDDO |
| 319 |
ENDDO |
| 320 |
ENDDO |
| 321 |
C Calculate the minimum drho/dz |
| 322 |
maxDRhoDz = -rhoConst*GM_K3D_minN2/gravity |
| 323 |
|
| 324 |
C Calculate the barotropic velocity by vertically integrating |
| 325 |
C and the dividing by the depth of the water column |
| 326 |
C Note that Ubaro is on the U grid. |
| 327 |
DO k=1,Nr |
| 328 |
DO j=1-Oly,sNy+Oly |
| 329 |
DO i=1-Olx,sNx+Olx |
| 330 |
Ubaro(i,j) = Ubaro(i,j) + |
| 331 |
& maskW(i,j,k,bi,bj)*drF(k)*hfacC(i,j,k,bi,bj) |
| 332 |
& *ubar(i,j,k,bi,bj) |
| 333 |
ENDDO |
| 334 |
ENDDO |
| 335 |
ENDDO |
| 336 |
DO j=1-Oly,sNy+Oly |
| 337 |
DO i=1-Olx,sNx+Olx |
| 338 |
IF (kLow_C(i,j).GT.0) THEN |
| 339 |
C The minus sign is because r_Low<0 |
| 340 |
Ubaro(i,j) = -Ubaro(i,j)/r_Low(i,j,bi,bj) |
| 341 |
ENDIF |
| 342 |
ENDDO |
| 343 |
ENDDO |
| 344 |
|
| 345 |
C Integrate the buoyancy frequency vertically using the trapezoidal method. |
| 346 |
DO k=1,Nr |
| 347 |
DO j=1-Oly,sNy+Oly |
| 348 |
DO i=1-Olx,sNx+Olx |
| 349 |
IF (k.LT.kLow_C(i,j)) THEN |
| 350 |
BVint(i,j) = BVint(i,j) + hFacC(i,j,k,bi,bj)*drF(k) |
| 351 |
& *(N(i,j,k)+N(i,j,k+1)) |
| 352 |
ELSEIF (k.EQ.kLow_C(i,j)) THEN |
| 353 |
C Assume that N(z=-H)=0 |
| 354 |
BVint(i,j) = BVint(i,j) + hFacC(i,j,k,bi,bj)*drF(k)*N(i,j,k) |
| 355 |
ENDIF |
| 356 |
ENDDO |
| 357 |
ENDDO |
| 358 |
ENDDO |
| 359 |
DO j=1-Oly,sNy+Oly |
| 360 |
DO i=1-Olx,sNx+Olx |
| 361 |
BVint(i,j) = op5*BVint(i,j) |
| 362 |
ENDDO |
| 363 |
ENDDO |
| 364 |
|
| 365 |
C Calculate the eigenvalues and eigenvectors |
| 366 |
IF (update_modes) THEN |
| 367 |
CALL GMREDI_CALC_EIGS( |
| 368 |
I iMin,iMax,jMin,jMax,bi,bj,N2,myThid, |
| 369 |
I kLow_C, maskC(:,:,:,bi,bj), |
| 370 |
I hfacC(:,:,:,bi,bj), recip_hfacC(:,:,:,bi,bj), |
| 371 |
I R_Low(:,:,bi,bj), 1, .TRUE., |
| 372 |
O Rmid, modesC(:,:,:,:,bi,bj)) |
| 373 |
|
| 374 |
C Calculate the Rossby Radius |
| 375 |
DO j=1-Oly+1,sNy+Oly |
| 376 |
DO i=1-Olx+1,sNx+Olx |
| 377 |
Req = SQRT(BVint(i,j)/(2*pi*gradf(i,j))) |
| 378 |
Rdef(i,j,bi,bj) = MIN(Rmid(i,j),Req) |
| 379 |
ENDDO |
| 380 |
ENDDO |
| 381 |
ENDIF |
| 382 |
|
| 383 |
C Average dsigma/dx and dsigma/dy onto the centre points |
| 384 |
|
| 385 |
DO k=1,Nr |
| 386 |
DO j=1-Oly,sNy+Oly-1 |
| 387 |
DO i=1-Olx,sNx+Olx-1 |
| 388 |
dSigmaDx(i,j,k) = op5*(sigmaX(i,j,k)+sigmaX(i+1,j,k)) |
| 389 |
dSigmaDy(i,j,k) = op5*(sigmaY(i,j,k)+sigmaY(i,j+1,k)) |
| 390 |
ENDDO |
| 391 |
ENDDO |
| 392 |
ENDDO |
| 393 |
|
| 394 |
C =============================== |
| 395 |
C Calculate the Eady growth rate |
| 396 |
C =============================== |
| 397 |
DO k=1,Nr |
| 398 |
|
| 399 |
DO j=1-Oly,sNy+Oly-1 |
| 400 |
DO i=1-Olx,sNx+Olx-1 |
| 401 |
M4loc(i,j,k) = g_reciprho_sq*( dSigmaDx(i,j,k)**2 |
| 402 |
& +dSigmaDy(i,j,k)**2 ) |
| 403 |
IF (k.NE.kLow_C(i,j)) THEN |
| 404 |
N2loc(i,j,k) = op5*(N2(i,j,k)+N2(i,j,k+1)) |
| 405 |
ELSE |
| 406 |
N2loc(i,j,k) = op5*N2(i,j,k) |
| 407 |
ENDIF |
| 408 |
ENDDO |
| 409 |
ENDDO |
| 410 |
C The bottom of the grid cell is shallower than the top |
| 411 |
C integration level, so, advance the depth. |
| 412 |
IF (-rF(k+1) .LE. GM_K3D_EadyMinDepth) CYCLE |
| 413 |
|
| 414 |
C Do not bother going any deeper since the top of the |
| 415 |
C cell is deeper than the bottom integration level |
| 416 |
IF (-rF(k).GE.GM_K3D_EadyMaxDepth) EXIT |
| 417 |
|
| 418 |
C We are in the integration depth range |
| 419 |
DO j=1-Oly,sNy+Oly-1 |
| 420 |
DO i=1-Olx,sNx+Olx-1 |
| 421 |
IF ( (kLow_C(i,j).GE.k) .AND. |
| 422 |
& (-hMixLayer(i,j,bi,bj).LE.-rC(k)) ) THEN |
| 423 |
|
| 424 |
slopeC(i,j,k) = SQRT(M4loc(i,j,k))/N2loc(i,j,k) |
| 425 |
C Limit the slope. Note, this is not all the Eady calculations. |
| 426 |
IF (slopeC(i,j,k).LE.GM_maxSlope) THEN |
| 427 |
M4onN2(i,j,k) = M4loc(i,j,k)/N2loc(i,j,k) |
| 428 |
ELSE |
| 429 |
slopeC(i,j,k) = GM_maxslope |
| 430 |
M4onN2(i,j,k) = SQRT(M4loc(i,j,k))*GM_maxslope |
| 431 |
ENDIF |
| 432 |
eady(i,j) = eady(i,j) |
| 433 |
& + hfacC(i,j,k,bi,bj)*drF(k)*M4onN2(i,j,k) |
| 434 |
deltaH(i,j) = deltaH(i,j) + drF(k) |
| 435 |
ENDIF |
| 436 |
ENDDO |
| 437 |
ENDDO |
| 438 |
ENDDO |
| 439 |
|
| 440 |
DO j=1-Oly,sNy+Oly |
| 441 |
DO i=1-Olx,sNx+Olx |
| 442 |
C If the minimum depth for the integration is deeper than the ocean |
| 443 |
C bottom OR the mixed layer is deeper than the maximum depth of |
| 444 |
C integration, we set the Eady growth rate to something small |
| 445 |
C to avoid floating point exceptions. |
| 446 |
C Later, these areas will be given a small diffusivity. |
| 447 |
IF (deltaH(i,j).EQ.zeroRL) THEN |
| 448 |
eady(i,j) = small |
| 449 |
|
| 450 |
C Otherwise, divide over the integration and take the square root |
| 451 |
C to actually find the Eady growth rate. |
| 452 |
ELSE |
| 453 |
eady(i,j) = SQRT(eady(i,j)/deltaH(i,j)) |
| 454 |
|
| 455 |
ENDIF |
| 456 |
|
| 457 |
ENDDO |
| 458 |
ENDDO |
| 459 |
|
| 460 |
C ====================================== |
| 461 |
C Calculate the diffusivity |
| 462 |
C ====================================== |
| 463 |
DO j=1-Oly+1,sNy+Oly |
| 464 |
DO i=1-Olx+1,sNx+Olx-1 |
| 465 |
C Calculate the Visbeck velocity |
| 466 |
Rurms(i,j) = MIN(Rdef(i,j,bi,bj),GM_K3D_Rmax) |
| 467 |
urms(i,j,1) = GM_K3D_Lambda*eady(i,j)*Rurms(i,j) |
| 468 |
C Set the bottom urms to zero |
| 469 |
k=kLow_C(i,j) |
| 470 |
IF (k.GT.0) urms(i,j,k) = 0.0 |
| 471 |
|
| 472 |
C Calculate the Rhines scale |
| 473 |
RRhines(i,j) = SQRT(urms(i,j,1)/gradf(i,j)) |
| 474 |
|
| 475 |
C Calculate the estimated length scale |
| 476 |
Rmix(i,j) = MIN(Rdef(i,j,bi,bj), RRhines(i,j)) |
| 477 |
Rmix(i,j) = MAX(Rmix(i,j),GM_K3D_Rmin) |
| 478 |
|
| 479 |
C Calculate the Doppler shifted long Rossby wave speed |
| 480 |
C Ubaro is on the U grid so we must average onto the M grid. |
| 481 |
cDopp(i,j) = op5*( Ubaro(i,j)+Ubaro(i+1,j) ) |
| 482 |
& - gradf(i,j)*Rdef(i,j,bi,bj)*Rdef(i,j,bi,bj) |
| 483 |
C Limit the wave speed to the namelist variable GM_K3D_maxC |
| 484 |
IF (ABS(cDopp(i,j)).GT.GM_K3D_maxC) THEN |
| 485 |
cDopp(i,j) = MAX(GM_K3D_maxC, cDopp(i,j)) |
| 486 |
ENDIF |
| 487 |
|
| 488 |
ENDDO |
| 489 |
ENDDO |
| 490 |
|
| 491 |
C Project the surface urms to the subsurface using the first baroclinic mode |
| 492 |
CALL GMREDI_CALC_URMS( |
| 493 |
I iMin,iMax,jMin,jMax,bi,bj,N2,myThid, |
| 494 |
U urms) |
| 495 |
|
| 496 |
C Calculate the diffusivity (on the mass grid) |
| 497 |
DO k=1,Nr |
| 498 |
DO j=1-Oly,sNy+Oly |
| 499 |
DO i=1-Olx,sNx+Olx |
| 500 |
IF (k.LE.kLow_C(i,j)) THEN |
| 501 |
IF (deltaH(i,j).EQ.zeroRL) THEN |
| 502 |
K3D(i,j,k,bi,bj) = GM_K3D_smallK |
| 503 |
ELSE |
| 504 |
IF (urms(i,j,k).EQ.0.0) THEN |
| 505 |
K3D(i,j,k,bi,bj) = GM_K3D_smallK |
| 506 |
ELSE |
| 507 |
umc(i,j,k) =ubar(i,j,k,bi,bj) - cDopp(i,j) |
| 508 |
supp(i,j,k)=1/(1+GM_K3D_b1*umc(i,j,k)**2/urms(i,j,1)**2) |
| 509 |
C 2*Rmix gives the diameter |
| 510 |
K3D(i,j,k,bi,bj) = GM_K3D_gamma*urms(i,j,k) |
| 511 |
& *2*Rmix(i,j)*supp(i,j,k) |
| 512 |
ENDIF |
| 513 |
|
| 514 |
C Enforce lower and upper bounds on the diffusivity |
| 515 |
IF (K3D(i,j,k,bi,bj).LT.GM_K3D_smallK) |
| 516 |
& K3D(i,j,k,bi,bj) = GM_K3D_smallK |
| 517 |
IF (K3D(i,j,k,bi,bj).GT.GM_maxK3D) |
| 518 |
& K3D(i,j,k,bi,bj) = GM_maxK3D |
| 519 |
ENDIF |
| 520 |
ENDIF |
| 521 |
ENDDO |
| 522 |
ENDDO |
| 523 |
ENDDO |
| 524 |
|
| 525 |
C ====================================== |
| 526 |
C Find the PV gradient |
| 527 |
C ====================================== |
| 528 |
C Calculate the surface layer thickness. |
| 529 |
C Use hMixLayer (calculated in model/src/calc_oce_mxlayer) |
| 530 |
C for the mixed layer depth. |
| 531 |
|
| 532 |
C Enforce a minimum surface layer depth |
| 533 |
DO j=1-Oly,sNy+Oly |
| 534 |
DO i=1-Olx,sNx+Olx |
| 535 |
surfkz(i,j) = MIN(-GM_K3D_surfMinDepth,-hMixLayer(i,j,bi,bj)) |
| 536 |
surfkz(i,j) = MAX(surfkz(i,j),R_low(i,j,bi,bj)) |
| 537 |
IF(maskC(i,j,1,bi,bj).EQ.0.0) surfkz(i,j)=0.0 |
| 538 |
surfk(i,j) = 0 |
| 539 |
ENDDO |
| 540 |
ENDDO |
| 541 |
DO k=1,Nr |
| 542 |
DO j=1-Oly,sNy+Oly |
| 543 |
DO i=1-Olx,sNx+Olx |
| 544 |
IF (rF(k).GT.surfkz(i,j) .AND. surfkz(i,j).GE.rF(k+1)) |
| 545 |
& surfk(i,j) = k |
| 546 |
ENDDO |
| 547 |
ENDDO |
| 548 |
ENDDO |
| 549 |
|
| 550 |
C Calculate the isopycnal slope |
| 551 |
DO j=1-Oly,sNy+Oly-1 |
| 552 |
DO i=1-Olx,sNx+Olx-1 |
| 553 |
SlopeX(i,j,1) = zeroRL |
| 554 |
SlopeY(i,j,1) = zeroRL |
| 555 |
ENDDO |
| 556 |
ENDDO |
| 557 |
DO k=2,Nr |
| 558 |
DO j=1-Oly+1,sNy+Oly |
| 559 |
DO i=1-Olx+1,sNx+Olx |
| 560 |
IF(surfk(i,j).GE.kLowC(i,j,bi,bj)) THEN |
| 561 |
C If the surface layer is thinner than the water column |
| 562 |
C the set the slope to zero to avoid problems. |
| 563 |
SlopeX(i,j,k) = zeroRL |
| 564 |
SlopeY(i,j,k) = zeroRL |
| 565 |
|
| 566 |
ELSE |
| 567 |
C Calculate the zonal slope at the western cell face (U grid) |
| 568 |
sigz = MIN( op5*(sigmaR(i,j,k)+sigmaR(i-1,j,k)), maxDRhoDz ) |
| 569 |
sigx = op5*( sigmaX(i,j,k)+sigmaX(i,j,k-1) ) |
| 570 |
slope = sigx/sigz |
| 571 |
IF(ABS(slope).GT.GM_maxSlope) |
| 572 |
& slope = SIGN(GM_maxSlope,slope) |
| 573 |
SlopeX(i,j,k)=-maskW(i,j,k-1,bi,bj)*maskW(i,j,k,bi,bj)*slope |
| 574 |
|
| 575 |
C Calculate the meridional slope at the southern cell face (V grid) |
| 576 |
sigz = MIN( op5*(sigmaR(i,j,k)+sigmaR(i,j-1,k)), maxDRhoDz ) |
| 577 |
sigy = op5*( sigmaY(i,j,k) + sigmaY(i,j,k-1) ) |
| 578 |
slope = sigy/sigz |
| 579 |
IF(ABS(slope).GT.GM_maxSlope) |
| 580 |
& slope = SIGN(GM_maxSlope,slope) |
| 581 |
SlopeY(i,j,k)=-maskS(i,j,k-1,bi,bj)*maskS(i,j,k,bi,bj)*slope |
| 582 |
ENDIF |
| 583 |
ENDDO |
| 584 |
ENDDO |
| 585 |
ENDDO |
| 586 |
|
| 587 |
C Calculate the thickness flux and diffusivity. These may be altered later |
| 588 |
C depending on namelist options. |
| 589 |
C Enforce a zero slope bottom boundary condition for the bottom most cells (k=Nr) |
| 590 |
k=Nr |
| 591 |
DO j=1-Oly,sNy+Oly |
| 592 |
DO i=1-Olx,sNx+Olx |
| 593 |
C Zonal thickness flux at the western cell face |
| 594 |
tfluxX(i,j,k) = -fCoriU(i,j)*SlopeX(i,j,k) |
| 595 |
& *recip_drF(k)*recip_hFacW(i,j,k,bi,bj) |
| 596 |
C Meridional thickness flux at the southern cell face |
| 597 |
tfluxY(i,j,k) = -fCoriV(i,j)*SlopeY(i,j,k) |
| 598 |
& *recip_drF(k)*recip_hFacS(i,j,k,bi,bj) |
| 599 |
|
| 600 |
C Use the interior diffusivity. Note: if we are using a |
| 601 |
C constant diffusivity KPV is overwritten later |
| 602 |
KPV(i,j,k) = K3D(i,j,k,bi,bj) |
| 603 |
|
| 604 |
ENDDO |
| 605 |
ENDDO |
| 606 |
|
| 607 |
C Calculate the thickness flux and diffusivity and for other cells (k<Nr) |
| 608 |
DO k=Nr-1,1,-1 |
| 609 |
DO j=1-Oly,sNy+Oly |
| 610 |
DO i=1-Olx,sNx+Olx |
| 611 |
C Zonal thickness flux at the western cell face |
| 612 |
tfluxX(i,j,k)=-fCoriU(i,j)*(SlopeX(i,j,k)-SlopeX(i,j,k+1)) |
| 613 |
& *recip_drF(k)*recip_hFacW(i,j,k,bi,bj) |
| 614 |
& *maskW(i,j,k,bi,bj) |
| 615 |
|
| 616 |
C Meridional thickness flux at the southern cell face |
| 617 |
tfluxY(i,j,k)=-fCoriV(i,j)*(SlopeY(i,j,k)-SlopeY(i,j,k+1)) |
| 618 |
& *recip_drF(k)*recip_hFacS(i,j,k,bi,bj) |
| 619 |
& *maskS(i,j,k,bi,bj) |
| 620 |
|
| 621 |
C Use the interior diffusivity. Note: if we are using a |
| 622 |
C constant diffusivity KPV is overwritten later |
| 623 |
KPV(i,j,k) = K3D(i,j,k,bi,bj) |
| 624 |
ENDDO |
| 625 |
ENDDO |
| 626 |
ENDDO |
| 627 |
|
| 628 |
|
| 629 |
C Special treatment for the surface layer (if necessary), which overwrites |
| 630 |
C values in the previous loops. |
| 631 |
IF (GM_K3D_ThickSheet .OR. GM_K3D_surfK) THEN |
| 632 |
DO k=Nr-1,1,-1 |
| 633 |
DO j=1-Oly,sNy+Oly |
| 634 |
DO i=1-Olx,sNx+Olx |
| 635 |
IF(k.LE.surfk(i,j)) THEN |
| 636 |
C We are in the surface layer. Change the thickness flux |
| 637 |
C and diffusivity as necessary. |
| 638 |
|
| 639 |
IF (GM_K3D_ThickSheet) THEN |
| 640 |
C We are in the surface layer, so set the thickness flux |
| 641 |
C based on the average slope over the surface layer |
| 642 |
C If we are on the edge of a "cliff" the surface layer at the |
| 643 |
C centre of the grid point could be deeper than the U or V point. |
| 644 |
C So, we ensure that we always take a sensible slope. |
| 645 |
IF(kLow_U(i,j).LT.surfk(i,j)) THEN |
| 646 |
kk=kLow_U(i,j) |
| 647 |
hsurf = -rLowW(i,j,bi,bj) |
| 648 |
ELSE |
| 649 |
kk=surfk(i,j) |
| 650 |
hsurf = -surfkz(i,j) |
| 651 |
ENDIF |
| 652 |
IF(kk.GT.0) THEN |
| 653 |
IF(kk.EQ.Nr) THEN |
| 654 |
tfluxX(i,j,k) = -fCoriU(i,j)*maskW(i,j,k,bi,bj) |
| 655 |
& *SlopeX(i,j,kk)/hsurf |
| 656 |
ELSE |
| 657 |
tfluxX(i,j,k) = -fCoriU(i,j)*maskW(i,j,k,bi,bj) |
| 658 |
& *( SlopeX(i,j,kk)-SlopeX(i,j,kk+1) )/hsurf |
| 659 |
ENDIF |
| 660 |
ELSE |
| 661 |
tfluxX(i,j,k) = zeroRL |
| 662 |
ENDIF |
| 663 |
|
| 664 |
IF(kLow_V(i,j).LT.surfk(i,j)) THEN |
| 665 |
kk=kLow_V(i,j) |
| 666 |
hsurf = -rLowS(i,j,bi,bj) |
| 667 |
ELSE |
| 668 |
kk=surfk(i,j) |
| 669 |
hsurf = -surfkz(i,j) |
| 670 |
ENDIF |
| 671 |
IF(kk.GT.0) THEN |
| 672 |
IF(kk.EQ.Nr) THEN |
| 673 |
tfluxY(i,j,k) = -fCoriV(i,j)*maskS(i,j,k,bi,bj) |
| 674 |
& *SlopeY(i,j,kk)/hsurf |
| 675 |
ELSE |
| 676 |
tfluxY(i,j,k) = -fCoriV(i,j)*maskS(i,j,k,bi,bj) |
| 677 |
& *( SlopeY(i,j,kk)-SlopeY(i,j,kk+1) )/hsurf |
| 678 |
ENDIF |
| 679 |
ELSE |
| 680 |
tfluxY(i,j,k) = zeroRL |
| 681 |
ENDIF |
| 682 |
ENDIF |
| 683 |
|
| 684 |
IF (GM_K3D_surfK) THEN |
| 685 |
C Use a constant K in the surface layer. |
| 686 |
KPV(i,j,k) = GM_K3D_constK |
| 687 |
ENDIF |
| 688 |
ENDIF |
| 689 |
ENDDO |
| 690 |
ENDDO |
| 691 |
ENDDO |
| 692 |
ENDIF |
| 693 |
|
| 694 |
C Calculate gradq |
| 695 |
IF (GM_K3D_likeGM .OR. GM_K3D_beta_eq_0) THEN |
| 696 |
C Ignore beta in the calculation of grad(q) |
| 697 |
DO k=1,Nr |
| 698 |
DO j=1-Oly+1,sNy+Oly |
| 699 |
DO i=1-Olx+1,sNx+Olx |
| 700 |
gradqx(i,j,k) = maskW(i,j,k,bi,bj)*tfluxX(i,j,k) |
| 701 |
gradqy(i,j,k) = maskS(i,j,k,bi,bj)*tfluxY(i,j,k) |
| 702 |
ENDDO |
| 703 |
ENDDO |
| 704 |
ENDDO |
| 705 |
|
| 706 |
ELSE |
| 707 |
C Do not ignore beta |
| 708 |
DO k=1,Nr |
| 709 |
DO j=1-Oly+1,sNy+Oly |
| 710 |
DO i=1-Olx+1,sNx+Olx |
| 711 |
gradqx(i,j,k) = maskW(i,j,k,bi,bj)*(dfdx(i,j)+tfluxX(i,j,k)) |
| 712 |
gradqy(i,j,k) = maskS(i,j,k,bi,bj)*(dfdy(i,j)+tfluxY(i,j,k)) |
| 713 |
ENDDO |
| 714 |
ENDDO |
| 715 |
ENDDO |
| 716 |
ENDIF |
| 717 |
|
| 718 |
C ====================================== |
| 719 |
C Find Xi and the eddy induced velocities |
| 720 |
C ====================================== |
| 721 |
C Find the buoyancy frequency at the west and south faces of a cell |
| 722 |
C This is necessary to find the eigenvectors at those points |
| 723 |
DO k=1,Nr |
| 724 |
DO j=1-Oly+1,sNy+Oly |
| 725 |
DO i=1-Olx+1,sNx+Olx |
| 726 |
N2W(i,j,k) = maskW(i,j,k,bi,bj) |
| 727 |
& *( N2(i,j,k)+N2(i-1,j,k) ) |
| 728 |
N2S(i,j,k) = maskS(i,j,k,bi,bj) |
| 729 |
& *( N2(i,j,k)+N2(i,j-1,k) ) |
| 730 |
ENDDO |
| 731 |
ENDDO |
| 732 |
C This fudge is necessary to avoid division by zero in gmredi_calc_eigs. |
| 733 |
C It does not affect the end result since it is in the overlap region. |
| 734 |
j=1-Oly |
| 735 |
DO i=1-Olx,sNx+Olx |
| 736 |
N2W(i,j,k) = GM_K3D_minN2 |
| 737 |
N2S(i,j,k) = GM_K3D_minN2 |
| 738 |
ENDDO |
| 739 |
i=1-Olx |
| 740 |
DO j=1-Oly,sNy+Oly |
| 741 |
N2W(i,j,k) = GM_K3D_minN2 |
| 742 |
N2S(i,j,k) = GM_K3D_minN2 |
| 743 |
ENDDO |
| 744 |
ENDDO |
| 745 |
|
| 746 |
C If GM_K3D_likeGM=.TRUE., the diffusivity for the eddy transport is |
| 747 |
C set to a constant equal to GM_K3D_constK. |
| 748 |
C If the diffusivity is constant the method here is the same as GM. |
| 749 |
C If GM_K3D_constRedi=.TRUE. K3D will be set equal to GM_K3D_constK later. |
| 750 |
IF(GM_K3D_likeGM) THEN |
| 751 |
DO k=1,Nr |
| 752 |
DO j=1-Oly,sNy+Oly |
| 753 |
DO i=1-Olx,sNx+Olx |
| 754 |
KPV(i,j,k) = GM_K3D_constK |
| 755 |
ENDDO |
| 756 |
ENDDO |
| 757 |
ENDDO |
| 758 |
ENDIF |
| 759 |
|
| 760 |
IF (.NOT. GM_K3D_smooth) THEN |
| 761 |
C Do not expand K grad(q) => no smoothing |
| 762 |
C May only be done with a constant K, otherwise the |
| 763 |
C integral constraint is violated. |
| 764 |
DO k=1,Nr |
| 765 |
DO j=1-Oly,sNy+Oly |
| 766 |
DO i=1-Olx,sNx+Olx |
| 767 |
Xix(i,j,k) = -maskW(i,j,k,bi,bj)*KPV(i,j,k)*gradqx(i,j,k) |
| 768 |
Xiy(i,j,k) = -maskS(i,j,k,bi,bj)*KPV(i,j,k)*gradqy(i,j,k) |
| 769 |
ENDDO |
| 770 |
ENDDO |
| 771 |
ENDDO |
| 772 |
|
| 773 |
ELSE |
| 774 |
C Expand K grad(q) in terms of baroclinic modes to smooth |
| 775 |
C and satisfy the integral constraint |
| 776 |
|
| 777 |
C Start with the X direction |
| 778 |
C ------------------------------ |
| 779 |
C Calculate the eigenvectors at the West face of a cell |
| 780 |
IF (update_modes) THEN |
| 781 |
CALL GMREDI_CALC_EIGS( |
| 782 |
I iMin,iMax,jMin,jMax,bi,bj,N2W,myThid, |
| 783 |
I kLow_U,maskW(:,:,:,bi,bj), |
| 784 |
I hfacW(:,:,:,bi,bj),recip_hfacW(:,:,:,bi,bj), |
| 785 |
I rLowW(:,:,bi,bj),GM_K3D_NModes,.FALSE., |
| 786 |
O dummy,modesW(:,:,:,:,bi,bj)) |
| 787 |
ENDIF |
| 788 |
|
| 789 |
C Calculate Xi_m at the west face of a cell |
| 790 |
DO j=1-Oly,sNy+Oly |
| 791 |
DO i=1-Olx,sNx+Olx |
| 792 |
DO m=1,GM_K3D_NModes |
| 793 |
XimX(m,i,j) = zeroRL |
| 794 |
ENDDO |
| 795 |
ENDDO |
| 796 |
ENDDO |
| 797 |
DO k=1,Nr |
| 798 |
DO j=1-Oly,sNy+Oly |
| 799 |
DO i=1-Olx,sNx+Olx |
| 800 |
DO m=1,GM_K3D_NModes |
| 801 |
Kdqdx(i,j,k) = KPV(i,j,k)*gradqx(i,j,k) |
| 802 |
XimX(m,i,j) = XimX(m,i,j) |
| 803 |
& - maskW(i,j,k,bi,bj)*drF(k)*hfacW(i,j,k,bi,bj) |
| 804 |
& *Kdqdx(i,j,k)*modesW(m,i,j,k,bi,bj) |
| 805 |
ENDDO |
| 806 |
ENDDO |
| 807 |
ENDDO |
| 808 |
ENDDO |
| 809 |
|
| 810 |
C Calculate Xi in the X direction at the west face |
| 811 |
DO k=1,Nr |
| 812 |
DO j=1-Oly,sNy+Oly |
| 813 |
DO i=1-Olx,sNx+Olx |
| 814 |
Xix(i,j,k) = zeroRL |
| 815 |
ENDDO |
| 816 |
ENDDO |
| 817 |
ENDDO |
| 818 |
DO k=1,Nr |
| 819 |
DO j=1-Oly,sNy+Oly |
| 820 |
DO i=1-Olx,sNx+Olx |
| 821 |
DO m=1,GM_K3D_NModes |
| 822 |
Xix(i,j,k) = Xix(i,j,k) |
| 823 |
& + maskW(i,j,k,bi,bj)*XimX(m,i,j)*modesW(m,i,j,k,bi,bj) |
| 824 |
ENDDO |
| 825 |
ENDDO |
| 826 |
ENDDO |
| 827 |
ENDDO |
| 828 |
|
| 829 |
C Now the Y direction |
| 830 |
C ------------------------------ |
| 831 |
C Calculate the eigenvectors at the West face of a cell |
| 832 |
IF (update_modes) THEN |
| 833 |
CALL GMREDI_CALC_EIGS( |
| 834 |
I iMin,iMax,jMin,jMax,bi,bj,N2S,myThid, |
| 835 |
I kLow_V,maskS(:,:,:,bi,bj), |
| 836 |
I hfacS(:,:,:,bi,bj),recip_hfacS(:,:,:,bi,bj), |
| 837 |
I rLowS(:,:,bi,bj), GM_K3D_NModes, .FALSE., |
| 838 |
O dummy,modesS(:,:,:,:,bi,bj)) |
| 839 |
ENDIF |
| 840 |
|
| 841 |
DO j=1-Oly,sNy+Oly |
| 842 |
DO i=1-Olx,sNx+Olx |
| 843 |
DO m=1,GM_K3D_NModes |
| 844 |
XimY(m,i,j) = zeroRL |
| 845 |
ENDDO |
| 846 |
ENDDO |
| 847 |
ENDDO |
| 848 |
DO k=1,Nr |
| 849 |
DO j=1-Oly,sNy+Oly |
| 850 |
DO i=1-Olx,sNx+Olx |
| 851 |
DO m=1,GM_K3D_NModes |
| 852 |
Kdqdy(i,j,k) = KPV(i,j,k)*gradqy(i,j,k) |
| 853 |
XimY(m,i,j) = XimY(m,i,j) |
| 854 |
& - drF(k)*hfacS(i,j,k,bi,bj) |
| 855 |
& *Kdqdy(i,j,k)*modesS(m,i,j,k,bi,bj) |
| 856 |
ENDDO |
| 857 |
ENDDO |
| 858 |
ENDDO |
| 859 |
ENDDO |
| 860 |
|
| 861 |
C Calculate Xi for Y direction at the south face |
| 862 |
DO k=1,Nr |
| 863 |
DO j=1-Oly,sNy+Oly |
| 864 |
DO i=1-Olx,sNx+Olx |
| 865 |
Xiy(i,j,k) = zeroRL |
| 866 |
ENDDO |
| 867 |
ENDDO |
| 868 |
ENDDO |
| 869 |
DO k=1,Nr |
| 870 |
DO j=1-Oly,sNy+Oly |
| 871 |
DO i=1-Olx,sNx+Olx |
| 872 |
DO m=1,GM_K3D_NModes |
| 873 |
Xiy(i,j,k) = Xiy(i,j,k) |
| 874 |
& + maskS(i,j,k,bi,bj)*XimY(m,i,j)*modesS(m,i,j,k,bi,bj) |
| 875 |
ENDDO |
| 876 |
ENDDO |
| 877 |
ENDDO |
| 878 |
ENDDO |
| 879 |
|
| 880 |
C ENDIF (.NOT. GM_K3D_smooth) |
| 881 |
ENDIF |
| 882 |
|
| 883 |
|
| 884 |
C Calculate the eddy induced velocity in the X direction at the west face |
| 885 |
DO k=1,Nr |
| 886 |
DO j=1-Oly+1,sNy+Oly |
| 887 |
DO i=1-Olx+1,sNx+Olx |
| 888 |
ustar(i,j,k) = -Xix(i,j,k)/coriU(i,j) |
| 889 |
ENDDO |
| 890 |
ENDDO |
| 891 |
ENDDO |
| 892 |
|
| 893 |
C Calculate the eddy induced velocity in the Y direction at the south face |
| 894 |
DO k=1,Nr |
| 895 |
DO j=1-Oly+1,sNy+Oly |
| 896 |
DO i=1-Olx+1,sNx+Olx |
| 897 |
vstar(i,j,k) = -Xiy(i,j,k)/coriV(i,j) |
| 898 |
ENDDO |
| 899 |
ENDDO |
| 900 |
ENDDO |
| 901 |
|
| 902 |
C ====================================== |
| 903 |
C Calculate the eddy induced overturning streamfunction |
| 904 |
C ====================================== |
| 905 |
#ifdef GM_K3D_PASSIVE |
| 906 |
k=Nr |
| 907 |
DO j=1-Oly,sNy+Oly |
| 908 |
DO i=1-Olx,sNx+Olx |
| 909 |
psistar(i,j,Nr) = -hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
| 910 |
ENDDO |
| 911 |
ENDDO |
| 912 |
DO k=Nr-1,1,-1 |
| 913 |
DO j=1-Oly,sNy+Oly |
| 914 |
DO i=1-Olx,sNx+Olx |
| 915 |
psistar(i,j,k) = psistar(i,j,k+1) |
| 916 |
& - hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
| 917 |
ENDDO |
| 918 |
ENDDO |
| 919 |
ENDDO |
| 920 |
|
| 921 |
#else |
| 922 |
|
| 923 |
IF (GM_AdvForm) THEN |
| 924 |
k=Nr |
| 925 |
DO j=1-Oly+1,sNy+1 |
| 926 |
DO i=1-Olx+1,sNx+1 |
| 927 |
GM_PsiX(i,j,k,bi,bj) = -hfacW(i,j,k,bi,bj)*drF(k)*ustar(i,j,k) |
| 928 |
GM_PsiY(i,j,k,bi,bj) = -hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
| 929 |
ENDDO |
| 930 |
ENDDO |
| 931 |
DO k=Nr-1,1,-1 |
| 932 |
DO j=1-Oly+1,sNy+1 |
| 933 |
DO i=1-Olx+1,sNx+1 |
| 934 |
GM_PsiX(i,j,k,bi,bj) = GM_PsiX(i,j,k+1,bi,bj) |
| 935 |
& - hfacW(i,j,k,bi,bj)*drF(k)*ustar(i,j,k) |
| 936 |
GM_PsiY(i,j,k,bi,bj) = GM_PsiY(i,j,k+1,bi,bj) |
| 937 |
& - hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
| 938 |
ENDDO |
| 939 |
ENDDO |
| 940 |
ENDDO |
| 941 |
|
| 942 |
ENDIF |
| 943 |
#endif |
| 944 |
|
| 945 |
#ifdef ALLOW_DIAGNOSTICS |
| 946 |
C Diagnostics |
| 947 |
IF ( useDiagnostics ) THEN |
| 948 |
CALL DIAGNOSTICS_FILL(K3D, 'GM_K3D ',0,Nr,0,1,1,myThid) |
| 949 |
CALL DIAGNOSTICS_FILL(KPV, 'GM_KPV ',0,Nr,0,1,1,myThid) |
| 950 |
CALL DIAGNOSTICS_FILL(urms, 'GM_URMS ',0,Nr,0,1,1,myThid) |
| 951 |
CALL DIAGNOSTICS_FILL(Rdef, 'GM_RDEF ',0, 1,0,1,1,myThid) |
| 952 |
CALL DIAGNOSTICS_FILL(Rurms, 'GM_RURMS',0, 1,0,1,1,myThid) |
| 953 |
CALL DIAGNOSTICS_FILL(RRhines,'GM_RRHNS',0, 1,0,1,1,myThid) |
| 954 |
CALL DIAGNOSTICS_FILL(Rmix, 'GM_RMIX ',0, 1,0,1,1,myThid) |
| 955 |
CALL DIAGNOSTICS_FILL(supp, 'GM_SUPP ',0,Nr,0,1,1,myThid) |
| 956 |
CALL DIAGNOSTICS_FILL(Xix, 'GM_Xix ',0,Nr,0,1,1,myThid) |
| 957 |
CALL DIAGNOSTICS_FILL(Xiy, 'GM_Xiy ',0,Nr,0,1,1,myThid) |
| 958 |
CALL DIAGNOSTICS_FILL(cDopp, 'GM_C ',0, 1,0,1,1,myThid) |
| 959 |
CALL DIAGNOSTICS_FILL(Ubaro, 'GM_UBARO',0, 1,0,1,1,myThid) |
| 960 |
CALL DIAGNOSTICS_FILL(eady, 'GM_EADY ',0, 1,0,1,1,myThid) |
| 961 |
CALL DIAGNOSTICS_FILL(SlopeX, 'GM_Sx ',0,Nr,0,1,1,myThid) |
| 962 |
CALL DIAGNOSTICS_FILL(SlopeY, 'GM_Sy ',0,Nr,0,1,1,myThid) |
| 963 |
CALL DIAGNOSTICS_FILL(tfluxX, 'GM_TFLXX',0,Nr,0,1,1,myThid) |
| 964 |
CALL DIAGNOSTICS_FILL(tfluxY, 'GM_TFLXY',0,Nr,0,1,1,myThid) |
| 965 |
CALL DIAGNOSTICS_FILL(gradqx, 'GM_dqdx ',0,Nr,0,1,1,myThid) |
| 966 |
CALL DIAGNOSTICS_FILL(gradqy, 'GM_dqdy ',0,Nr,0,1,1,myThid) |
| 967 |
CALL DIAGNOSTICS_FILL(Kdqdy, 'GM_Kdqdy',0,Nr,0,1,1,myThid) |
| 968 |
CALL DIAGNOSTICS_FILL(Kdqdx, 'GM_Kdqdx',0,Nr,0,1,1,myThid) |
| 969 |
CALL DIAGNOSTICS_FILL(surfkz, 'GM_SFLYR',0, 1,0,1,1,myThid) |
| 970 |
CALL DIAGNOSTICS_FILL(ustar, 'GM_USTAR',0,Nr,0,1,1,myThid) |
| 971 |
CALL DIAGNOSTICS_FILL(vstar, 'GM_VSTAR',0,Nr,0,1,1,myThid) |
| 972 |
CALL DIAGNOSTICS_FILL(umc, 'GM_UMC ',0,Nr,0,1,1,myThid) |
| 973 |
CALL DIAGNOSTICS_FILL(ubar, 'GM_UBAR ',0,Nr,0,1,1,myThid) |
| 974 |
CALL DIAGNOSTICS_FILL(modesC(1,:,:,:,bi,bj), |
| 975 |
& 'GM_MODEC',0,Nr,0,1,1,myThid) |
| 976 |
CALL DIAGNOSTICS_FILL(M4loc, 'GM_M4 ',0,Nr,0,1,1,myThid) |
| 977 |
CALL DIAGNOSTICS_FILL(N2loc, 'GM_N2 ',0,Nr,0,1,1,myThid) |
| 978 |
CALL DIAGNOSTICS_FILL(M4onN2, 'GM_M4_N2',0,Nr,0,1,1,myThid) |
| 979 |
CALL DIAGNOSTICS_FILL(slopeC, 'GM_SLOPE',0,Nr,0,1,1,myThid) |
| 980 |
|
| 981 |
ENDIF |
| 982 |
#endif |
| 983 |
|
| 984 |
C For the Redi diffusivity, we set K3D to a constant if |
| 985 |
C GM_K3D_constRedi=.TRUE. |
| 986 |
IF (GM_K3D_constRedi) THEN |
| 987 |
DO k=1,Nr |
| 988 |
DO j=1-Oly,sNy+Oly |
| 989 |
DO i=1-Olx,sNx+Olx |
| 990 |
K3D(i,j,k,bi,bj) = GM_K3D_constK |
| 991 |
ENDDO |
| 992 |
ENDDO |
| 993 |
ENDDO |
| 994 |
ENDIF |
| 995 |
|
| 996 |
#ifdef ALLOW_DIAGNOSTICS |
| 997 |
IF ( useDiagnostics ) |
| 998 |
& CALL DIAGNOSTICS_FILL(K3D, 'GM_K3D_T',0,Nr,0,1,1,myThid) |
| 999 |
#endif |
| 1000 |
|
| 1001 |
#endif /* GM_K3D */ |
| 1002 |
RETURN |
| 1003 |
END |
Parent Directory
| 
Revision Log
| 
Revision Graph