| 1 |
C $Header: /u/gcmpack/MITgcm/pkg/gmredi/gmredi_calc_eigs.F,v 1.2 2013/06/22 14:44:54 jmc Exp $ |
| 2 |
C $Name: $ |
| 3 |
|
| 4 |
#include "GMREDI_OPTIONS.h" |
| 5 |
|
| 6 |
C !ROUTINE: EIGENVAL |
| 7 |
C !INTERFACE: |
| 8 |
SUBROUTINE GMREDI_CALC_EIGS( |
| 9 |
I iMin, iMax, jMin, jMax, |
| 10 |
I bi, bj, N2, myThid, kLow, |
| 11 |
I mask, hfac, recip_hfac, |
| 12 |
I rlow, nmodes, writediag, |
| 13 |
O Rmid, vec) |
| 14 |
|
| 15 |
C !DESCRIPTION: \bv |
| 16 |
C *==========================================================* |
| 17 |
C | SUBROUTINE GMREDI_CALC_URMS |
| 18 |
C | o Calculate the vertical structure of the rms eddy |
| 19 |
C | velocity based on baroclinic modal decomposition |
| 20 |
C *==========================================================* |
| 21 |
C \ev |
| 22 |
|
| 23 |
IMPLICIT NONE |
| 24 |
|
| 25 |
C == Global variables == |
| 26 |
#include "SIZE.h" |
| 27 |
#include "GRID.h" |
| 28 |
#include "EEPARAMS.h" |
| 29 |
#include "PARAMS.h" |
| 30 |
#include "GMREDI.h" |
| 31 |
|
| 32 |
C !INPUT/OUTPUT PARAMETERS: |
| 33 |
C == Routine arguments == |
| 34 |
C bi, bj :: tile indices |
| 35 |
LOGICAL writediag |
| 36 |
INTEGER iMin,iMax,jMin,jMax |
| 37 |
INTEGER bi, bj |
| 38 |
INTEGER myThid |
| 39 |
INTEGER nmodes |
| 40 |
INTEGER kLow(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 41 |
_RL mask(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 42 |
_RL hfac(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 43 |
_RL recip_hfac(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 44 |
_RL rlow(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 45 |
_RL N2( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 46 |
_RL Rmid(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 47 |
_RL vec(nmodes,1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 48 |
|
| 49 |
#ifdef GM_K3D |
| 50 |
C !LOCAL VARIABLES: |
| 51 |
C == Local variables == |
| 52 |
INTEGER i,j,k,kk,m |
| 53 |
# ifdef use_lapack |
| 54 |
C info :: error code from LAPACK |
| 55 |
C idx :: index used for sorting the eigenvalues |
| 56 |
C a3d :: lower diagonal of eigenvalue problem |
| 57 |
C b3d :: diagonal of eigenvalue problem |
| 58 |
C c3d :: upper diagonal of eigenvalue problem |
| 59 |
C val :: Eigenvalue (wavenumber) of the first baroclinic mode |
| 60 |
C eigR :: Real component of all the eigenvalues in a water column |
| 61 |
C eigI :: Imaginary component of all the eigenvalues in a water column |
| 62 |
C vecs :: All the eigenvectors of a water column |
| 63 |
C dummy :: Redundant variable for calling lapack |
| 64 |
C work :: Work array for lapack |
| 65 |
C array :: Array containing the matrix with a,b,c |
| 66 |
C eigval :: Vector containing the eigenvalues |
| 67 |
INTEGER info |
| 68 |
INTEGER idx |
| 69 |
_RL a3d( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 70 |
_RL b3d( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 71 |
_RL c3d( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 72 |
_RL val( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 73 |
_RL eigR(Nr),eigI(Nr),vecs(Nr,Nr),dummy(1,Nr),work(Nr*Nr) |
| 74 |
_RL array(Nr,Nr) |
| 75 |
_RL eigval(0:nmodes) |
| 76 |
# else |
| 77 |
C drNr :: distance from bottom of cell to cell centre at Nr |
| 78 |
C BuoyFreq :: buoyancy frequency, SQRT(N2) |
| 79 |
C intN :: Vertical integral of BuoyFreq to each grid cell centre |
| 80 |
C intN0 :: Vertical integral of BuoyFreq to z=0 |
| 81 |
C c1 :: intN0/pi |
| 82 |
C nEigs :: number of eigenvalues/vectors to calculate |
| 83 |
_RL drNr |
| 84 |
_RL BuoyFreq(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr+1) |
| 85 |
_RL intN(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
| 86 |
_RL intN0(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 87 |
_RL c1(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 88 |
INTEGER nEigs(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 89 |
# endif |
| 90 |
C small :: a small number (used to avoid floating point exceptions) |
| 91 |
C vecint :: vertical integral of eigenvector and/or square of eigenvector |
| 92 |
C fCori2 :: square of the Coriolis parameter |
| 93 |
_RL small |
| 94 |
_RL vecint(nmodes,1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 95 |
_RL fCori2(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
| 96 |
CHARACTER*(MAX_LEN_MBUF) msgBuf |
| 97 |
|
| 98 |
small = TINY(zeroRL) |
| 99 |
|
| 100 |
C Square of the Coriolis parameter |
| 101 |
DO i=1-OLx,sNx+OLx |
| 102 |
DO j=1-OLy,sNy+OLy |
| 103 |
fCori2(i,j) = fCori(i,j,bi,bj)*fCori(i,j,bi,bj) |
| 104 |
ENDDO |
| 105 |
ENDDO |
| 106 |
|
| 107 |
DO k=1,Nr |
| 108 |
DO j=1-Oly,sNy+Oly |
| 109 |
DO i=1-Olx,sNx+Olx |
| 110 |
DO m=1,nmodes |
| 111 |
vec(m,i,j,k) = zeroRL |
| 112 |
ENDDO |
| 113 |
ENDDO |
| 114 |
ENDDO |
| 115 |
ENDDO |
| 116 |
|
| 117 |
# ifdef use_lapack |
| 118 |
C Calculate the tridiagonal operator matrix for |
| 119 |
C f^2 d/dz 1/N^2 d/dz |
| 120 |
C a3d is the lower off-diagonal, b3d is the diagonal |
| 121 |
C and c3d is the upper off-diagonal |
| 122 |
DO k=1,Nr |
| 123 |
DO j=1-OLy,sNy+OLy |
| 124 |
DO i=1-OLx,sNx+OLx |
| 125 |
IF (kLow(i,j) .GT. 0) THEN |
| 126 |
IF (k.EQ.1) THEN |
| 127 |
a3d(i,j,k) = zeroRL |
| 128 |
c3d(i,j,k) = fCori2(i,j)*recip_hFac(i,j,k) |
| 129 |
& *recip_drC(k+1)*recip_drF(k)/N2(i,j,k+1) |
| 130 |
b3d(i,j,k) = -c3d(i,j,k) |
| 131 |
|
| 132 |
ELSEIF (k.LT.kLow(i,j)) THEN |
| 133 |
a3d(i,j,k) = fCori2(i,j)*recip_hFac(i,j,k) |
| 134 |
& *recip_drF(k)*recip_drC(k)/N2(i,j,k) |
| 135 |
c3d(i,j,k) = fCori2(i,j)*recip_hFac(i,j,k) |
| 136 |
& *recip_drF(k)*recip_drC(k+1)/N2(i,j,k+1) |
| 137 |
b3d(i,j,k) = -a3d(i,j,k)-c3d(i,j,k) |
| 138 |
|
| 139 |
ELSEIF (k.EQ.kLow(i,j)) THEN |
| 140 |
a3d(i,j,k) = fCori2(i,j)*recip_hFac(i,j,k) |
| 141 |
& *recip_drF(k)*recip_drC(k)/N2(i,j,k) |
| 142 |
c3d(i,j,k) = zeroRL |
| 143 |
b3d(i,j,k) = -a3d(i,j,k) |
| 144 |
|
| 145 |
ELSE |
| 146 |
a3d(i,j,k) = zeroRL |
| 147 |
b3d(i,j,k) = zeroRL |
| 148 |
c3d(i,j,k) = zeroRL |
| 149 |
ENDIF |
| 150 |
|
| 151 |
ELSE |
| 152 |
a3d(i,j,k) = zeroRL |
| 153 |
b3d(i,j,k) = zeroRL |
| 154 |
c3d(i,j,k) = zeroRL |
| 155 |
ENDIF |
| 156 |
ENDDO |
| 157 |
ENDDO |
| 158 |
ENDDO |
| 159 |
|
| 160 |
DO j=1-Oly,sNy+Oly |
| 161 |
DO i=1-Olx,sNx+Olx |
| 162 |
IF (kLow(i,j).GT.0) THEN |
| 163 |
DO kk=1,Nr |
| 164 |
DO k=1,Nr |
| 165 |
array(k,kk) = zeroRL |
| 166 |
ENDDO |
| 167 |
ENDDO |
| 168 |
|
| 169 |
k=1 |
| 170 |
array(k,k) = b3d(i,j,k) |
| 171 |
array(k,k+1) = c3d(i,j,k) |
| 172 |
DO k=2,Nr-1 |
| 173 |
array(k,k-1) = a3d(i,j,k) |
| 174 |
array(k,k) = b3d(i,j,k) |
| 175 |
array(k,k+1) = c3d(i,j,k) |
| 176 |
ENDDO |
| 177 |
k=Nr |
| 178 |
array(k,k-1) = a3d(i,j,k) |
| 179 |
array(k,k) = b3d(i,j,k) |
| 180 |
|
| 181 |
CALL DGEEV('N','V',Nr,array,Nr,eigR,eigI,dummy,1, |
| 182 |
& vecs,Nr,work,Nr*Nr,info) |
| 183 |
IF( info.LT.0 ) THEN |
| 184 |
WRITE(msgBuf,'(A,x,2(A1,I2),A1,x,A,I4)') |
| 185 |
& 'GMREDI_CALC_EIGS problem with arguments for DGEEV at', |
| 186 |
& '(',i,',',j,')', 'error code =',info |
| 187 |
CALL PRINT_ERROR( msgBuf , myThid ) |
| 188 |
|
| 189 |
ELSEIF(info.GT.0 ) THEN |
| 190 |
WRITE(msgBuf,'(A,x,2(A1,I2),A1,x,A,I4)') |
| 191 |
& 'GMREDI_CALC_EIGS problems with eigensolver DGEEV at', |
| 192 |
& '(',i,',',j,')', 'error code =',info |
| 193 |
CALL PRINT_ERROR( msgBuf , myThid ) |
| 194 |
|
| 195 |
ENDIF |
| 196 |
|
| 197 |
C Find the second largest eigenvalue (the Rossby radius) |
| 198 |
C and the first M baroclinic modes (eigenvectors) |
| 199 |
DO m=0,nmodes |
| 200 |
eigval(m) = -HUGE(zeroRL) |
| 201 |
ENDDO |
| 202 |
|
| 203 |
DO k=1,kLow(i,j) |
| 204 |
eigval(0) = MAX(eigval(0),eigR(k)) |
| 205 |
ENDDO |
| 206 |
DO m=1,MIN(nmodes,klow(i,j)) |
| 207 |
DO k=1,kLow(i,j) |
| 208 |
IF (eigR(k).LT.eigval(m-1)) THEN |
| 209 |
eigval(m) = MAX(eigval(m),eigR(k)) |
| 210 |
IF (eigval(m).EQ.eigR(k)) idx=k |
| 211 |
ENDIF |
| 212 |
ENDDO |
| 213 |
IF(vecs(1,idx).LT.zeroRL) THEN |
| 214 |
DO k=1,Nr |
| 215 |
vec(m,i,j,k) = -vecs(k,idx) |
| 216 |
ENDDO |
| 217 |
ELSE |
| 218 |
DO k=1,Nr |
| 219 |
vec(m,i,j,k) = vecs(k,idx) |
| 220 |
ENDDO |
| 221 |
ENDIF |
| 222 |
ENDDO |
| 223 |
val(i,j) = eigval(1) |
| 224 |
ELSE |
| 225 |
val(i,j)=zeroRL |
| 226 |
DO k=1,Nr |
| 227 |
DO m=1,nmodes |
| 228 |
vec(m,i,j,k)=zeroRL |
| 229 |
ENDDO |
| 230 |
ENDDO |
| 231 |
|
| 232 |
ENDIF |
| 233 |
ENDDO |
| 234 |
ENDDO |
| 235 |
|
| 236 |
DO k=1,Nr |
| 237 |
DO j=1-Oly,sNy+Oly |
| 238 |
DO i=1-Olx,sNx+Olx |
| 239 |
IF (kLow(i,j).GT.2 .AND. val(i,j).NE.zeroRL) THEN |
| 240 |
Rmid(i,j) = 1.0/(SQRT(ABS(val(i,j)))+small) |
| 241 |
ELSE |
| 242 |
Rmid(i,j) = zeroRL |
| 243 |
ENDIF |
| 244 |
ENDDO |
| 245 |
ENDDO |
| 246 |
ENDDO |
| 247 |
|
| 248 |
# else |
| 249 |
DO k=1,Nr |
| 250 |
DO j=1-Oly,sNy+Oly |
| 251 |
DO i=1-Olx,sNx+Olx |
| 252 |
BuoyFreq(i,j,k) = mask(i,j,k)*SQRT(N2(i,j,k)) |
| 253 |
ENDDO |
| 254 |
ENDDO |
| 255 |
ENDDO |
| 256 |
k=Nr+1 |
| 257 |
DO j=1-Oly,sNy+Oly |
| 258 |
DO i=1-Olx,sNx+Olx |
| 259 |
BuoyFreq(i,j,k) = zeroRL |
| 260 |
ENDDO |
| 261 |
ENDDO |
| 262 |
|
| 263 |
C integrate N using something like Simpson's rule (but not quite) |
| 264 |
C drC*( (N(k+1)+N(k+2))/2 + (N(k)+N(k+1))/2 )/2 |
| 265 |
C when k=Nr, say that N(k+2)=0 and N(k+1)=0 |
| 266 |
k=Nr |
| 267 |
C drNr is like drC(Nr+1)/2 |
| 268 |
drNr = rC(Nr)-rF(Nr+1) |
| 269 |
DO j=1-Oly,sNy+Oly |
| 270 |
DO i=1-Olx,sNx+Olx |
| 271 |
intN(i,j,k) = op5*BuoyFreq(i,j,k)*drNr |
| 272 |
ENDDO |
| 273 |
ENDDO |
| 274 |
DO k=Nr-1,1,-1 |
| 275 |
DO j=1-Oly,sNy+Oly |
| 276 |
DO i=1-Olx,sNx+Olx |
| 277 |
intN(i,j,k) = intN(i,j,k+1) |
| 278 |
& + drC(k)*( op25*BuoyFreq(i,j,k+2) + op5*BuoyFreq(i,j,k) |
| 279 |
& + op25*BuoyFreq(i,j,k+1) ) |
| 280 |
ENDDO |
| 281 |
ENDDO |
| 282 |
ENDDO |
| 283 |
|
| 284 |
C intN integrates to z=rC(1). We want to integrate to z=0. |
| 285 |
C Assume that N(0)=0 and N(1)=0. |
| 286 |
C drC(1) is like half a grid cell. |
| 287 |
DO j=1-Oly,sNy+Oly |
| 288 |
DO i=1-Olx,sNx+Olx |
| 289 |
intN0(i,j) = intN(i,j,1) |
| 290 |
& + drC(1)*op5*BuoyFreq(i,j,2) |
| 291 |
ENDDO |
| 292 |
ENDDO |
| 293 |
|
| 294 |
DO j=1-Oly,sNy+Oly |
| 295 |
DO i=1-Olx,sNx+Olx |
| 296 |
c1(i,j) = intN0(i,j)/pi |
| 297 |
Rmid(i,j) = c1(i,j)/ABS(fCori(i,j,bi,bj)) |
| 298 |
ENDDO |
| 299 |
ENDDO |
| 300 |
|
| 301 |
DO j=1-Oly,sNy+Oly |
| 302 |
DO i=1-Olx,sNx+Olx |
| 303 |
nEigs(i,j) = MIN(klow(i,j),nmodes) |
| 304 |
ENDDO |
| 305 |
ENDDO |
| 306 |
DO k=1,Nr |
| 307 |
DO j=1-Oly,sNy+Oly |
| 308 |
DO i=1-Olx,sNx+Olx |
| 309 |
IF (mask(i,j,k).NE.0.0) THEN |
| 310 |
DO m=1,nEigs(i,j) |
| 311 |
vec(m,i,j,k) = -COS(intN(i,j,k)/(m*c1(i,j))) |
| 312 |
ENDDO |
| 313 |
ENDIF |
| 314 |
ENDDO |
| 315 |
ENDDO |
| 316 |
ENDDO |
| 317 |
|
| 318 |
C The WKB approximation for the baroclinic mode does not always |
| 319 |
C integrate to zero so we adjust it. |
| 320 |
DO j=1-Oly,sNy+Oly |
| 321 |
DO i=1-Olx,sNx+Olx |
| 322 |
DO m=1,nEigs(i,j) |
| 323 |
vecint(m,i,j) = zeroRL |
| 324 |
ENDDO |
| 325 |
ENDDO |
| 326 |
ENDDO |
| 327 |
DO k=1,Nr |
| 328 |
DO j=1-Oly,sNy+Oly |
| 329 |
DO i=1-Olx,sNx+Olx |
| 330 |
DO m=1,nEigs(i,j) |
| 331 |
vecint(m,i,j) = vecint(m,i,j) + hfac(i,j,k)*vec(m,i,j,k)*drF(k) |
| 332 |
ENDDO |
| 333 |
ENDDO |
| 334 |
ENDDO |
| 335 |
ENDDO |
| 336 |
DO j=1-Oly,sNy+Oly |
| 337 |
DO i=1-Olx,sNx+Olx |
| 338 |
DO m=1,nEigs(i,j) |
| 339 |
vecint(m,i,j) = vecint(m,i,j)/(-rlow(i,j)+small) |
| 340 |
ENDDO |
| 341 |
ENDDO |
| 342 |
ENDDO |
| 343 |
DO k=1,Nr |
| 344 |
DO j=1-Oly,sNy+Oly |
| 345 |
DO i=1-Olx,sNx+Olx |
| 346 |
DO m=1,nEigs(i,j) |
| 347 |
vec(m,i,j,k) = vec(m,i,j,k) - vecint(m,i,j) |
| 348 |
ENDDO |
| 349 |
ENDDO |
| 350 |
ENDDO |
| 351 |
ENDDO |
| 352 |
# endif |
| 353 |
|
| 354 |
C Normalise the eigenvectors |
| 355 |
DO j=1-Oly,sNy+Oly |
| 356 |
DO i=1-Olx,sNx+Olx |
| 357 |
DO m=1,nmodes |
| 358 |
vecint(m,i,j) = zeroRL |
| 359 |
ENDDO |
| 360 |
ENDDO |
| 361 |
ENDDO |
| 362 |
|
| 363 |
DO k=1,Nr |
| 364 |
DO j=1-Oly,sNy+Oly |
| 365 |
DO i=1-Olx,sNx+Olx |
| 366 |
DO m=1,nmodes |
| 367 |
vecint(m,i,j) = vecint(m,i,j) + |
| 368 |
& mask(i,j,k)*drF(k)*hfac(i,j,k) |
| 369 |
& *vec(m,i,j,k)*vec(m,i,j,k) |
| 370 |
ENDDO |
| 371 |
ENDDO |
| 372 |
ENDDO |
| 373 |
ENDDO |
| 374 |
|
| 375 |
DO j=1-Oly,sNy+Oly |
| 376 |
DO i=1-Olx,sNx+Olx |
| 377 |
DO m=1,nmodes |
| 378 |
vecint(m,i,j) = SQRT(vecint(m,i,j)) |
| 379 |
ENDDO |
| 380 |
ENDDO |
| 381 |
ENDDO |
| 382 |
|
| 383 |
DO k=1,Nr |
| 384 |
DO j=1-Oly,sNy+Oly |
| 385 |
DO i=1-Olx,sNx+Olx |
| 386 |
DO m=1,nmodes |
| 387 |
vec(m,i,j,k) = vec(m,i,j,k)/(vecint(m,i,j)+small) |
| 388 |
ENDDO |
| 389 |
ENDDO |
| 390 |
ENDDO |
| 391 |
ENDDO |
| 392 |
|
| 393 |
# ifdef ALLOW_DIAGNOSTICS |
| 394 |
C Diagnostics |
| 395 |
IF ( useDiagnostics.AND.writediag ) THEN |
| 396 |
# ifdef use_lapack |
| 397 |
CALL DIAGNOSTICS_FILL(a3d, 'GM_A3D ',0,Nr,0,1,1,myThid) |
| 398 |
CALL DIAGNOSTICS_FILL(b3d, 'GM_B3D ',0,Nr,0,1,1,myThid) |
| 399 |
CALL DIAGNOSTICS_FILL(c3d, 'GM_C3D ',0,Nr,0,1,1,myThid) |
| 400 |
# endif |
| 401 |
ENDIF |
| 402 |
# endif |
| 403 |
|
| 404 |
#endif /* GM_K3D */ |
| 405 |
|
| 406 |
RETURN |
| 407 |
END |
Parent Directory
| 
Revision Log
| 
Revision Graph