1 |
C $Header: /u/gcmpack/MITgcm/pkg/gmredi/gmredi_k3d.F,v 1.21 2015/02/22 01:52:18 m_bates Exp $ |
2 |
C $Name: $ |
3 |
|
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 "EEPARAMS.h" |
25 |
#include "PARAMS.h" |
26 |
#include "GRID.h" |
27 |
#include "DYNVARS.h" |
28 |
#include "FFIELDS.h" |
29 |
#include "GMREDI.h" |
30 |
|
31 |
C !INPUT/OUTPUT PARAMETERS: |
32 |
C == Routine arguments == |
33 |
C bi, bj :: tile indices |
34 |
C myThid :: My Thread Id. number |
35 |
|
36 |
INTEGER iMin,iMax,jMin,jMax |
37 |
_RL sigmaX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
38 |
_RL sigmaY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
39 |
_RL sigmaR(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
40 |
INTEGER bi, bj |
41 |
_RL myTime |
42 |
INTEGER myThid |
43 |
|
44 |
#ifdef GM_K3D |
45 |
|
46 |
C === Functions ==== |
47 |
LOGICAL DIFFERENT_MULTIPLE |
48 |
EXTERNAL DIFFERENT_MULTIPLE |
49 |
|
50 |
C !LOCAL VARIABLES: |
51 |
C == Local variables == |
52 |
INTEGER i,j,k,kk,m,kp1 |
53 |
|
54 |
C update_modes :: Whether to update the eigenmodes |
55 |
LOGICAL update_modes |
56 |
|
57 |
C surfk :: index of the depth of the surface layer |
58 |
C kLow_C :: Local version of the index of deepest wet grid cell on tracer grid |
59 |
C kLow_U :: Local version of the index of deepest wet grid cell on U grid |
60 |
C kLow_V :: Local version of the index of deepest wet grid cell on V grid |
61 |
INTEGER surfk(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
62 |
INTEGER kLow_C(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
63 |
INTEGER kLow_U(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
64 |
INTEGER kLow_V(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
65 |
|
66 |
C N2loc :: local N**2 |
67 |
C slope :: local slope |
68 |
C Req :: local equatorial deformation radius (m) |
69 |
C deltaH :: local thickness of Eady integration (m) |
70 |
C g_reciprho_sq :: (gravity*recip_rhoConst)**2 |
71 |
C M4loc :: local M**4 |
72 |
C maxDRhoDz :: maximum value of d(rho)/dz (derived from GM_K3D_minN2) |
73 |
C sigx :: local d(rho)/dx |
74 |
C sigy :: local d(rho)/dy |
75 |
C sigz :: local d(rho)/dz |
76 |
C hsurf :: local surface layer depth |
77 |
C small :: a small number (to avoid floating point exceptions) |
78 |
_RL N2loc(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
79 |
_RL slope |
80 |
_RL slopeC(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
81 |
_RL Req |
82 |
_RL deltaH(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
83 |
_RL g_reciprho_sq |
84 |
_RL M4loc(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
85 |
_RL M4onN2(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
86 |
_RL maxDRhoDz |
87 |
_RL sigx, sigy, sigz |
88 |
_RL hsurf, mskp1 |
89 |
_RL small |
90 |
|
91 |
C dfdy :: gradient of the Coriolis paramater, df/dy, 1/(m*s) |
92 |
C dfdx :: gradient of the Coriolis paramater, df/dx, 1/(m*s) |
93 |
C gradf :: gradient of the Coriolis paramater at a cell centre, 1/(m*s) |
94 |
C Rurms :: a local mixing length used in calculation of urms (m) |
95 |
C RRhines :: The Rhines scale (m) |
96 |
C Rmix :: Mixing length |
97 |
C N2 :: Square of the buoyancy frequency (1/s**2) |
98 |
C N2W :: Square of the buoyancy frequency (1/s**2) averaged to west of grid cell |
99 |
C N2S :: Square of the buoyancy frequency (1/s**2) averaged to south of grid cell |
100 |
C N :: Buoyancy frequency, SQRT(N2) |
101 |
C BVint :: The vertical integral of N (m/s) |
102 |
C ubar :: Zonal velocity on a tracer point (m/s) |
103 |
C vbar :: Meridional velocity on a tracer point (m/s) |
104 |
C Ubaro :: Barotropic velocity (m/s) |
105 |
_RL dfdy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
106 |
_RL dfdx( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
107 |
_RL gradf( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
108 |
_RL dummy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
109 |
_RL Rurms( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
110 |
_RL RRhines(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
111 |
_RL Rmix( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
112 |
_RL N2( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
113 |
_RL N2W( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
114 |
_RL N2S( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
115 |
_RL N( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
116 |
_RL BVint( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
117 |
_RL Ubaro( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
118 |
_RL ubar( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
119 |
|
120 |
_RL tmpU( 1-Olx:sNx+Olx,1-Oly:sNy+Oly ) |
121 |
_RL tmpV( 1-Olx:sNx+Olx,1-Oly:sNy+Oly ) |
122 |
_RL uFldX( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr ) |
123 |
_RL vFldY( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr ) |
124 |
|
125 |
C Rmid :: Rossby radius (m) |
126 |
C KPV :: Diffusivity (m**2/s) |
127 |
C Kdqdx :: diffusivity multiplied by zonal PV gradient |
128 |
C Kdqdy :: diffusivity multiplied by meridional PV gradient |
129 |
C SlopeX :: isopycnal slope in x direction |
130 |
C SlopeY :: isopycnal slope in y direction |
131 |
C dSigmaDx :: sigmaX averaged onto tracer grid |
132 |
C dSigmaDy :: sigmaY averaged onto tracer grid |
133 |
C tfluxX :: thickness flux in x direction |
134 |
C tfluxY :: thickness flux in y direction |
135 |
C fCoriU :: Coriolis parameter averaged to U points |
136 |
C fCoriV :: Coriolis parameter averaged to V points |
137 |
C cori :: Coriolis parameter forced to be finite near the equator |
138 |
C coriU :: As for cori, but, at U point |
139 |
C coriV :: As for cori, but, at V point |
140 |
C surfkz :: Depth of surface layer (in r units) |
141 |
_RL Rmid(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
142 |
_RL KPV(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
143 |
_RL Kdqdy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
144 |
_RL Kdqdx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
145 |
_RL SlopeX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
146 |
_RL SlopeY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
147 |
_RL dSigmaDx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
148 |
_RL dSigmaDy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
149 |
_RL tfluxX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
150 |
_RL tfluxY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
151 |
_RL cori(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
152 |
_RL coriU(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
153 |
_RL coriV(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
154 |
_RL fCoriU(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
155 |
_RL fCoriV(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
156 |
_RL surfkz(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
157 |
|
158 |
C centreX,centreY :: used for calculating averages at centre of cell |
159 |
C numerator,denominator :: of the renormalisation factor |
160 |
C uInt :: column integral of u velocity (sum u*dz) |
161 |
C vInt :: column integral of v velocity (sum v*dz) |
162 |
C KdqdxInt :: column integral of K*dqdx (sum K*dqdx*dz) |
163 |
C KdqdyInt :: column integral of K*dqdy (sum K*dqdy*dz) |
164 |
C uKdqdyInt :: column integral of u*K*dqdy (sum u*K*dqdy*dz) |
165 |
C vKdqdxInt :: column integral of v*K*dqdx (sum v*K*dqdx*dz) |
166 |
C uXiyInt :: column integral of u*Xiy (sum u*Xiy*dz) |
167 |
C vXixInt :: column integral of v*Xix (sum v*Xix*dz) |
168 |
C Renorm :: renormalisation factor at the centre of a cell |
169 |
C RenormU :: renormalisation factor at the western face of a cell |
170 |
C RenormV :: renormalisation factor at the southern face of a cell |
171 |
_RL centreX, centreY |
172 |
_RL numerator, denominator |
173 |
_RL uInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
174 |
_RL vInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
175 |
_RL KdqdxInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
176 |
_RL KdqdyInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
177 |
_RL uKdqdyInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
178 |
_RL vKdqdxInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
179 |
_RL uXiyInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
180 |
_RL vXixInt(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
181 |
_RL Renorm(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
182 |
_RL RenormU(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
183 |
_RL RenormV(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
184 |
|
185 |
C gradqx :: Potential vorticity gradient in x direction |
186 |
C gradqy :: Potential vorticity gradient in y direction |
187 |
C XimX :: Vertical integral of phi_m*K*gradqx |
188 |
C XimY :: Vertical integral of phi_m*K*gradqy |
189 |
C cDopp :: Quasi-Doppler shifted long Rossby wave speed (m/s) |
190 |
C umc :: ubar-c (m/s) |
191 |
C eady :: Eady growth rate (1/s) |
192 |
C urms :: the rms eddy velocity (m/s) |
193 |
C supp :: The suppression factor |
194 |
C ustar :: The eddy induced velocity in the x direction |
195 |
C vstar :: The eddy induced velocity in the y direction |
196 |
C Xix :: Xi in the x direction (m/s**2) |
197 |
C Xiy :: Xi in the y direction (m/s**2) |
198 |
_RL gradqx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
199 |
_RL gradqy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
200 |
_RL XimX(GM_K3D_NModes,1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
201 |
_RL XimY(GM_K3D_NModes,1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
202 |
_RL cDopp(1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
203 |
_RL umc( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
204 |
_RL eady( 1-Olx:sNx+Olx,1-Oly:sNy+Oly) |
205 |
_RL urms( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
206 |
_RL supp( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
207 |
_RL ustar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
208 |
_RL vstar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
209 |
_RL Xix( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
210 |
_RL Xiy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr) |
211 |
#ifdef GM_K3D_PASSIVE |
212 |
C psistar :: eddy induced streamfunction in the y direction |
213 |
_RL psistar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr) |
214 |
#endif |
215 |
|
216 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
217 |
|
218 |
C ====================================== |
219 |
C Initialise some variables |
220 |
C ====================================== |
221 |
small = TINY(zeroRL) |
222 |
update_modes=.FALSE. |
223 |
IF ( DIFFERENT_MULTIPLE(GM_K3D_vecFreq,myTime,deltaTClock) ) |
224 |
& update_modes=.TRUE. |
225 |
|
226 |
DO j=1-Oly,sNy+Oly |
227 |
DO i=1-Olx,sNx+Olx |
228 |
kLow_C(i,j) = kLowC(i,j,bi,bj) |
229 |
ENDDO |
230 |
ENDDO |
231 |
DO j=1-Oly,sNy+Oly |
232 |
DO i=1-Olx+1,sNx+Olx |
233 |
kLow_U(i,j) = MIN( kLow_C(i,j), kLow_C(i-1,j) ) |
234 |
ENDDO |
235 |
ENDDO |
236 |
DO j=1-Oly+1,sNy+Oly |
237 |
DO i=1-Olx,sNx+Olx |
238 |
kLow_V(i,j) = MIN( kLow_C(i,j), kLow_C(i,j-1) ) |
239 |
ENDDO |
240 |
ENDDO |
241 |
|
242 |
C Dummy values for the edges. This does not affect the results |
243 |
C but avoids problems when solving for the eigenvalues. |
244 |
i=1-Olx |
245 |
DO j=1-Oly,sNy+Oly |
246 |
kLow_U(i,j) = 0 |
247 |
ENDDO |
248 |
j=1-Oly |
249 |
DO i=1-Olx,sNx+Olx |
250 |
kLow_V(i,j) = 0 |
251 |
ENDDO |
252 |
|
253 |
g_reciprho_sq = (gravity*recip_rhoConst)**2 |
254 |
C Gradient of Coriolis |
255 |
DO j=1-Oly+1,sNy+Oly |
256 |
DO i=1-Olx+1,sNx+Olx |
257 |
dfdx(i,j) = ( fCori(i,j,bi,bj)-fCori(i-1,j,bi,bj) ) |
258 |
& *recip_dxC(i,j,bi,bj) |
259 |
dfdy(i,j) = ( fCori(i,j,bi,bj)-fCori(i,j-1,bi,bj) ) |
260 |
& *recip_dyC(i,j,bi,bj) |
261 |
ENDDO |
262 |
ENDDO |
263 |
|
264 |
C Coriolis at C points enforcing a minimum value so |
265 |
C that it is defined at the equator |
266 |
DO j=1-Oly,sNy+Oly |
267 |
DO i=1-Olx,sNx+Olx |
268 |
cori(i,j) = SIGN( MAX( ABS(fCori(i,j,bi,bj)),GM_K3D_minCori ), |
269 |
& fCori(i,j,bi,bj) ) |
270 |
ENDDO |
271 |
ENDDO |
272 |
C Coriolis at U and V points |
273 |
DO j=1-Oly,sNy+Oly |
274 |
DO i=1-Olx+1,sNx+Olx |
275 |
C Limited so that the inverse is defined at the equator |
276 |
coriU(i,j) = op5*( cori(i,j)+cori(i-1,j) ) |
277 |
coriU(i,j) = SIGN( MAX( ABS(coriU(i,j)),GM_K3D_minCori ), |
278 |
& coriU(i,j) ) |
279 |
|
280 |
C Not limited |
281 |
fCoriU(i,j) = op5*( fCori(i,j,bi,bj)+fCori(i-1,j,bi,bj) ) |
282 |
ENDDO |
283 |
ENDDO |
284 |
DO j=1-Oly+1,sNy+Oly |
285 |
DO i=1-Olx,sNx+Olx |
286 |
C Limited so that the inverse is defined at the equator |
287 |
coriV(i,j) = op5*( cori(i,j)+cori(i,j-1) ) |
288 |
coriV(i,j) = SIGN( MAX( ABS(coriV(i,j)),GM_K3D_minCori ), |
289 |
& coriV(i,j) ) |
290 |
|
291 |
C Not limited |
292 |
fCoriV(i,j) = op5*( fCori(i,j,bi,bj)+fCori(i,j-1,bi,bj) ) |
293 |
ENDDO |
294 |
ENDDO |
295 |
C Computing beta |
296 |
IF ( selectCoriMap.EQ.1 ) THEN |
297 |
DO j=1-Oly,sNy+Oly |
298 |
DO i=1-Olx,sNx+Olx |
299 |
gradf(i,j) = beta |
300 |
ENDDO |
301 |
ENDDO |
302 |
ELSEIF ( selectCoriMap.EQ.2 ) THEN |
303 |
DO j=1-Oly,sNy+Oly |
304 |
DO i=1-Olx,sNx+Olx |
305 |
gradf(i,j) = recip_rSphere*fCoriCos(i,j,bi,bj) |
306 |
ENDDO |
307 |
ENDDO |
308 |
ENDIF |
309 |
C Some dummy values at the edges |
310 |
i=1-Olx |
311 |
DO j=1-Oly,sNy+Oly |
312 |
coriU(i,j)=cori(i,j) |
313 |
fCoriU(i,j)=fCori(i,j,bi,bj) |
314 |
ENDDO |
315 |
j=1-Oly |
316 |
DO i=1-Olx,sNx+Olx |
317 |
coriV(i,j)=cori(i,j) |
318 |
fCoriV(i,j)=fCori(i,j,bi,bj) |
319 |
ENDDO |
320 |
|
321 |
C Zeroing some cumulative fields |
322 |
DO j=1-Oly,sNy+Oly |
323 |
DO i=1-Olx,sNx+Olx |
324 |
eady(i,j) = zeroRL |
325 |
BVint(i,j) = zeroRL |
326 |
Ubaro(i,j) = zeroRL |
327 |
deltaH(i,j) = zeroRL |
328 |
ENDDO |
329 |
ENDDO |
330 |
DO k=1,Nr |
331 |
DO j=1-Oly,sNy+Oly |
332 |
DO i=1-Olx,sNx+Olx |
333 |
slopeC(i,j,k)=zeroRL |
334 |
ENDDO |
335 |
ENDDO |
336 |
ENDDO |
337 |
|
338 |
C initialise remaining 2d variables |
339 |
DO j=1-Oly,sNy+Oly |
340 |
DO i=1-Olx,sNx+Olx |
341 |
dfdy(i,j)=zeroRL |
342 |
dfdy(i,j)=zeroRL |
343 |
Rurms(i,j)=zeroRL |
344 |
RRhines(i,j)=zeroRL |
345 |
Rmix(i,j)=zeroRL |
346 |
ENDDO |
347 |
ENDDO |
348 |
C initialise remaining 3d variables |
349 |
DO k=1,Nr |
350 |
DO j=1-Oly,sNy+Oly |
351 |
DO i=1-Olx,sNx+Olx |
352 |
N2loc(i,j,k)=GM_K3D_minN2 |
353 |
N2W(i,j,k) = GM_K3D_minN2 |
354 |
N2S(i,j,k) = GM_K3D_minN2 |
355 |
M4loc(i,j,k)=zeroRL |
356 |
M4onN2(i,j,k)=zeroRL |
357 |
urms(i,j,k)=zeroRL |
358 |
SlopeX(i,j,k)=zeroRL |
359 |
SlopeY(i,j,k)=zeroRL |
360 |
dSigmaDx(i,j,k)=zeroRL |
361 |
dSigmaDy(i,j,k)=zeroRL |
362 |
gradqx(i,j,k)=zeroRL |
363 |
gradqy(i,j,k)=zeroRL |
364 |
ENDDO |
365 |
ENDDO |
366 |
ENDDO |
367 |
|
368 |
C Find the zonal velocity at the cell centre |
369 |
#ifdef ALLOW_EDDYPSI |
370 |
IF (GM_InMomAsStress) THEN |
371 |
DO k=1,Nr |
372 |
DO i = 1-olx,snx+olx |
373 |
DO j = 1-oly,sny+oly |
374 |
uFldX(i,j,k) = uEulerMean(i,j,k,bi,bj) |
375 |
vFldY(i,j,k) = vEulerMean(i,j,k,bi,bj) |
376 |
ENDDO |
377 |
ENDDO |
378 |
ENDDO |
379 |
ELSE |
380 |
#endif |
381 |
DO k=1,Nr |
382 |
DO i = 1-olx,snx+olx |
383 |
DO j = 1-oly,sny+oly |
384 |
uFldX(i,j,k) = uVel(i,j,k,bi,bj) |
385 |
vFldY(i,j,k) = vVel(i,j,k,bi,bj) |
386 |
ENDDO |
387 |
ENDDO |
388 |
ENDDO |
389 |
#ifdef ALLOW_EDDYPSI |
390 |
ENDIF |
391 |
#endif |
392 |
|
393 |
C The following comes from rotate_uv2en_rl |
394 |
C This code does two things: |
395 |
C 1) go from C grid velocity points to A grid velocity points |
396 |
C 2) go from model grid directions to east/west directions |
397 |
DO k = 1,Nr |
398 |
|
399 |
DO i = 1-Olx,sNx+Olx |
400 |
j=sNy+Oly |
401 |
tmpU(i,j)=zeroRL |
402 |
tmpV(i,j)=zeroRL |
403 |
ENDDO |
404 |
DO j = 1-Oly,sNy+Oly-1 |
405 |
i=sNx+Olx |
406 |
tmpU(i,j)=zeroRL |
407 |
tmpV(i,j)=zeroRL |
408 |
DO i = 1-Olx,sNx+Olx-1 |
409 |
tmpU(i,j) = 0.5 _d 0 |
410 |
& *( uFldX(i+1,j,k) + uFldX(i,j,k) ) |
411 |
tmpV(i,j) = 0.5 _d 0 |
412 |
& *( vFldY(i,j+1,k) + vFldY(i,j,k) ) |
413 |
|
414 |
tmpU(i,j) = tmpU(i,j) * maskC(i,j,k,bi,bj) |
415 |
tmpV(i,j) = tmpV(i,j) * maskC(i,j,k,bi,bj) |
416 |
ENDDO |
417 |
ENDDO |
418 |
|
419 |
DO j = 1-oly,sny+oly |
420 |
DO i = 1-olx,snx+olx |
421 |
ENDDO |
422 |
ENDDO |
423 |
|
424 |
C rotation |
425 |
DO j = 1-oly,sny+oly |
426 |
DO i = 1-olx,snx+olx |
427 |
ubar(i,j,k) = |
428 |
& angleCosC(i,j,bi,bj)*tmpU(i,j) |
429 |
& -angleSinC(i,j,bi,bj)*tmpV(i,j) |
430 |
ENDDO |
431 |
ENDDO |
432 |
ENDDO |
433 |
|
434 |
C Square of the buoyancy frequency at the top of a grid cell |
435 |
C Enforce a minimum N2 |
436 |
C Mask N2, so it is zero at bottom |
437 |
DO k=2,Nr |
438 |
DO j=1-Oly,sNy+Oly |
439 |
DO i=1-Olx,sNx+Olx |
440 |
N2(i,j,k) = -gravity*recip_rhoConst*sigmaR(i,j,k) |
441 |
N2(i,j,k) = MAX(N2(i,j,k),GM_K3D_minN2)*maskC(i,j,k,bi,bj) |
442 |
N(i,j,k) = SQRT(N2(i,j,k)) |
443 |
ENDDO |
444 |
ENDDO |
445 |
ENDDO |
446 |
C N2(k=1) is always zero |
447 |
DO j=1-Oly,sNy+Oly |
448 |
DO i=1-Olx,sNx+Olx |
449 |
N2(i,j,1) = zeroRL |
450 |
N(i,j,1) = zeroRL |
451 |
ENDDO |
452 |
ENDDO |
453 |
C Calculate the minimum drho/dz |
454 |
maxDRhoDz = -rhoConst*GM_K3D_minN2/gravity |
455 |
|
456 |
C Calculate the barotropic velocity by vertically integrating |
457 |
C and the dividing by the depth of the water column |
458 |
C Note that Ubaro is at the C-point. |
459 |
DO k=1,Nr |
460 |
DO j=1-Oly,sNy+Oly |
461 |
DO i=1-Olx,sNx+Olx |
462 |
Ubaro(i,j) = Ubaro(i,j) + |
463 |
& drF(k)*hfacC(i,j,k,bi,bj)*ubar(i,j,k) |
464 |
ENDDO |
465 |
ENDDO |
466 |
ENDDO |
467 |
DO j=1-Oly,sNy+Oly |
468 |
DO i=1-Olx,sNx+Olx |
469 |
IF (kLow_C(i,j).GT.0) THEN |
470 |
C The minus sign is because r_Low<0 |
471 |
Ubaro(i,j) = -Ubaro(i,j)/r_Low(i,j,bi,bj) |
472 |
ENDIF |
473 |
ENDDO |
474 |
ENDDO |
475 |
|
476 |
C Integrate the buoyancy frequency vertically using the trapezoidal method. |
477 |
C Assume that N(z=-H)=0 |
478 |
DO k=1,Nr |
479 |
kp1 = min(k+1,Nr) |
480 |
mskp1 = oneRL |
481 |
IF ( k.EQ.Nr ) mskp1 = zeroRL |
482 |
DO j=1-Oly,sNy+Oly |
483 |
DO i=1-Olx,sNx+Olx |
484 |
BVint(i,j) = BVint(i,j) + hFacC(i,j,k,bi,bj)*drF(k) |
485 |
& *op5*(N(i,j,k)+mskp1*N(i,j,kp1)) |
486 |
ENDDO |
487 |
ENDDO |
488 |
ENDDO |
489 |
|
490 |
C Calculate the eigenvalues and eigenvectors |
491 |
IF (update_modes) THEN |
492 |
CALL GMREDI_CALC_EIGS( |
493 |
I iMin,iMax,jMin,jMax,bi,bj,N2,myThid, |
494 |
I kLow_C, maskC(:,:,:,bi,bj), |
495 |
I hfacC(:,:,:,bi,bj), recip_hfacC(:,:,:,bi,bj), |
496 |
I R_Low(:,:,bi,bj), 1, .TRUE., |
497 |
O Rmid, modesC(:,:,:,:,bi,bj)) |
498 |
|
499 |
C Calculate the Rossby Radius |
500 |
DO j=1-Oly+1,sNy+Oly |
501 |
DO i=1-Olx+1,sNx+Olx |
502 |
Req = SQRT(BVint(i,j)/(2*pi*gradf(i,j))) |
503 |
Rdef(i,j,bi,bj) = MIN(Rmid(i,j),Req) |
504 |
ENDDO |
505 |
ENDDO |
506 |
ENDIF |
507 |
|
508 |
C Average dsigma/dx and dsigma/dy onto the centre points |
509 |
|
510 |
DO k=1,Nr |
511 |
DO j=1-Oly,sNy+Oly-1 |
512 |
DO i=1-Olx,sNx+Olx-1 |
513 |
dSigmaDx(i,j,k) = op5*(sigmaX(i,j,k)+sigmaX(i+1,j,k)) |
514 |
dSigmaDy(i,j,k) = op5*(sigmaY(i,j,k)+sigmaY(i,j+1,k)) |
515 |
ENDDO |
516 |
ENDDO |
517 |
ENDDO |
518 |
|
519 |
C =============================== |
520 |
C Calculate the Eady growth rate |
521 |
C =============================== |
522 |
DO k=1,Nr |
523 |
|
524 |
kp1 = min(k+1,Nr) |
525 |
mskp1 = oneRL |
526 |
IF ( k.EQ.Nr ) mskp1 = zeroRL |
527 |
|
528 |
DO j=1-Oly,sNy+Oly-1 |
529 |
DO i=1-Olx,sNx+Olx-1 |
530 |
M4loc(i,j,k) = g_reciprho_sq*( dSigmaDx(i,j,k)**2 |
531 |
& +dSigmaDy(i,j,k)**2 ) |
532 |
N2loc(i,j,k) = op5*(N2(i,j,k)+mskp1*N2(i,j,kp1)) |
533 |
ENDDO |
534 |
ENDDO |
535 |
C The bottom of the grid cell is shallower than the top |
536 |
C integration level, so, advance the depth. |
537 |
IF (-rF(k+1) .LE. GM_K3D_EadyMinDepth) CYCLE |
538 |
|
539 |
C Do not bother going any deeper since the top of the |
540 |
C cell is deeper than the bottom integration level |
541 |
IF (-rF(k).GE.GM_K3D_EadyMaxDepth) EXIT |
542 |
|
543 |
C We are in the integration depth range |
544 |
DO j=1-Oly,sNy+Oly-1 |
545 |
DO i=1-Olx,sNx+Olx-1 |
546 |
IF ( (kLow_C(i,j).GE.k) .AND. |
547 |
& (-hMixLayer(i,j,bi,bj).LE.-rC(k)) ) THEN |
548 |
|
549 |
slopeC(i,j,k) = SQRT(M4loc(i,j,k))/N2loc(i,j,k) |
550 |
C Limit the slope. Note, this is not all the Eady calculations. |
551 |
IF (slopeC(i,j,k).LE.GM_maxSlope) THEN |
552 |
M4onN2(i,j,k) = M4loc(i,j,k)/N2loc(i,j,k) |
553 |
ELSE |
554 |
slopeC(i,j,k) = GM_maxslope |
555 |
M4onN2(i,j,k) = SQRT(M4loc(i,j,k))*GM_maxslope |
556 |
ENDIF |
557 |
eady(i,j) = eady(i,j) |
558 |
& + hfacC(i,j,k,bi,bj)*drF(k)*M4onN2(i,j,k) |
559 |
deltaH(i,j) = deltaH(i,j) + drF(k) |
560 |
ENDIF |
561 |
ENDDO |
562 |
ENDDO |
563 |
ENDDO |
564 |
|
565 |
DO j=1-Oly,sNy+Oly |
566 |
DO i=1-Olx,sNx+Olx |
567 |
C If the minimum depth for the integration is deeper than the ocean |
568 |
C bottom OR the mixed layer is deeper than the maximum depth of |
569 |
C integration, we set the Eady growth rate to something small |
570 |
C to avoid floating point exceptions. |
571 |
C Later, these areas will be given a small diffusivity. |
572 |
IF (deltaH(i,j).EQ.zeroRL) THEN |
573 |
eady(i,j) = small |
574 |
|
575 |
C Otherwise, divide over the integration and take the square root |
576 |
C to actually find the Eady growth rate. |
577 |
ELSE |
578 |
eady(i,j) = SQRT(eady(i,j)/deltaH(i,j)) |
579 |
|
580 |
ENDIF |
581 |
|
582 |
ENDDO |
583 |
ENDDO |
584 |
|
585 |
C ====================================== |
586 |
C Calculate the diffusivity |
587 |
C ====================================== |
588 |
DO j=1-Oly+1,sNy+Oly |
589 |
DO i=1-Olx+1,sNx+Olx-1 |
590 |
C Calculate the Visbeck velocity |
591 |
Rurms(i,j) = MIN(Rdef(i,j,bi,bj),GM_K3D_Rmax) |
592 |
urms(i,j,1) = GM_K3D_Lambda*eady(i,j)*Rurms(i,j) |
593 |
C Set the bottom urms to zero |
594 |
k=kLow_C(i,j) |
595 |
IF (k.GT.0) urms(i,j,k) = 0.0 |
596 |
|
597 |
C Calculate the Rhines scale |
598 |
RRhines(i,j) = SQRT(urms(i,j,1)/gradf(i,j)) |
599 |
|
600 |
C Calculate the estimated length scale |
601 |
Rmix(i,j) = MIN(Rdef(i,j,bi,bj), RRhines(i,j)) |
602 |
Rmix(i,j) = MAX(Rmix(i,j),GM_K3D_Rmin) |
603 |
|
604 |
C Calculate the Doppler shifted long Rossby wave speed |
605 |
C Ubaro is at the C-point. |
606 |
cDopp(i,j) = Ubaro(i,j) |
607 |
& - gradf(i,j)*Rdef(i,j,bi,bj)*Rdef(i,j,bi,bj) |
608 |
C Limit the wave speed to the namelist variable GM_K3D_maxC |
609 |
IF (ABS(cDopp(i,j)).GT.GM_K3D_maxC) THEN |
610 |
cDopp(i,j) = MAX(GM_K3D_maxC, cDopp(i,j)) |
611 |
ENDIF |
612 |
|
613 |
ENDDO |
614 |
ENDDO |
615 |
|
616 |
C Project the surface urms to the subsurface using the first baroclinic mode |
617 |
CALL GMREDI_CALC_URMS( |
618 |
I iMin,iMax,jMin,jMax,bi,bj,N2,myThid, |
619 |
U urms) |
620 |
|
621 |
C Calculate the diffusivity (on the mass grid) |
622 |
DO k=1,Nr |
623 |
DO j=1-Oly,sNy+Oly |
624 |
DO i=1-Olx,sNx+Olx |
625 |
IF (k.LE.kLow_C(i,j)) THEN |
626 |
IF (deltaH(i,j).EQ.zeroRL) THEN |
627 |
K3D(i,j,k,bi,bj) = GM_K3D_smallK |
628 |
ELSE |
629 |
IF (urms(i,j,k).EQ.0.0) THEN |
630 |
K3D(i,j,k,bi,bj) = GM_K3D_smallK |
631 |
ELSE |
632 |
umc(i,j,k) =ubar(i,j,k) - cDopp(i,j) |
633 |
supp(i,j,k)=1./(1.+GM_K3D_b1*umc(i,j,k)**2/urms(i,j,1)**2) |
634 |
C 2*Rmix gives the diameter |
635 |
K3D(i,j,k,bi,bj) = GM_K3D_gamma*urms(i,j,k) |
636 |
& *2.*Rmix(i,j)*supp(i,j,k) |
637 |
ENDIF |
638 |
|
639 |
C Enforce lower and upper bounds on the diffusivity |
640 |
K3D(i,j,k,bi,bj) = MIN(K3D(i,j,k,bi,bj),GM_maxK3D) |
641 |
K3D(i,j,k,bi,bj) = MAX(K3D(i,j,k,bi,bj),GM_K3D_smallK) |
642 |
ENDIF |
643 |
ENDIF |
644 |
ENDDO |
645 |
ENDDO |
646 |
ENDDO |
647 |
|
648 |
C ====================================== |
649 |
C Find the PV gradient |
650 |
C ====================================== |
651 |
C Calculate the surface layer thickness. |
652 |
C Use hMixLayer (calculated in model/src/calc_oce_mxlayer) |
653 |
C for the mixed layer depth. |
654 |
|
655 |
C Enforce a minimum surface layer depth |
656 |
DO j=1-Oly,sNy+Oly |
657 |
DO i=1-Olx,sNx+Olx |
658 |
surfkz(i,j) = MIN(-GM_K3D_surfMinDepth,-hMixLayer(i,j,bi,bj)) |
659 |
surfkz(i,j) = MAX(surfkz(i,j),R_low(i,j,bi,bj)) |
660 |
IF(maskC(i,j,1,bi,bj).EQ.0.0) surfkz(i,j)=0.0 |
661 |
surfk(i,j) = 0 |
662 |
ENDDO |
663 |
ENDDO |
664 |
DO k=1,Nr |
665 |
DO j=1-Oly,sNy+Oly |
666 |
DO i=1-Olx,sNx+Olx |
667 |
IF (rF(k).GT.surfkz(i,j) .AND. surfkz(i,j).GE.rF(k+1)) |
668 |
& surfk(i,j) = k |
669 |
ENDDO |
670 |
ENDDO |
671 |
ENDDO |
672 |
|
673 |
C Calculate the isopycnal slope |
674 |
DO j=1-Oly,sNy+Oly-1 |
675 |
DO i=1-Olx,sNx+Olx-1 |
676 |
SlopeX(i,j,1) = zeroRL |
677 |
SlopeY(i,j,1) = zeroRL |
678 |
ENDDO |
679 |
ENDDO |
680 |
DO k=2,Nr |
681 |
DO j=1-Oly+1,sNy+Oly |
682 |
DO i=1-Olx+1,sNx+Olx |
683 |
IF(surfk(i,j).GE.kLowC(i,j,bi,bj)) THEN |
684 |
C If the surface layer is thinner than the water column |
685 |
C the set the slope to zero to avoid problems. |
686 |
SlopeX(i,j,k) = zeroRL |
687 |
SlopeY(i,j,k) = zeroRL |
688 |
|
689 |
ELSE |
690 |
C Calculate the zonal slope at the western cell face (U grid) |
691 |
sigz = MIN( op5*(sigmaR(i,j,k)+sigmaR(i-1,j,k)), maxDRhoDz ) |
692 |
sigx = op5*( sigmaX(i,j,k)+sigmaX(i,j,k-1) ) |
693 |
slope = sigx/sigz |
694 |
IF(ABS(slope).GT.GM_maxSlope) |
695 |
& slope = SIGN(GM_maxSlope,slope) |
696 |
SlopeX(i,j,k)=-maskW(i,j,k-1,bi,bj)*maskW(i,j,k,bi,bj)*slope |
697 |
|
698 |
C Calculate the meridional slope at the southern cell face (V grid) |
699 |
sigz = MIN( op5*(sigmaR(i,j,k)+sigmaR(i,j-1,k)), maxDRhoDz ) |
700 |
sigy = op5*( sigmaY(i,j,k) + sigmaY(i,j,k-1) ) |
701 |
slope = sigy/sigz |
702 |
IF(ABS(slope).GT.GM_maxSlope) |
703 |
& slope = SIGN(GM_maxSlope,slope) |
704 |
SlopeY(i,j,k)=-maskS(i,j,k-1,bi,bj)*maskS(i,j,k,bi,bj)*slope |
705 |
ENDIF |
706 |
ENDDO |
707 |
ENDDO |
708 |
ENDDO |
709 |
|
710 |
C Calculate the thickness flux and diffusivity. These may be altered later |
711 |
C depending on namelist options. |
712 |
C Enforce a zero slope bottom boundary condition for the bottom most cells (k=Nr) |
713 |
k=Nr |
714 |
DO j=1-Oly,sNy+Oly |
715 |
DO i=1-Olx,sNx+Olx |
716 |
C Zonal thickness flux at the western cell face |
717 |
tfluxX(i,j,k) = -fCoriU(i,j)*SlopeX(i,j,k) |
718 |
& *recip_drF(k)*recip_hFacW(i,j,k,bi,bj) |
719 |
C Meridional thickness flux at the southern cell face |
720 |
tfluxY(i,j,k) = -fCoriV(i,j)*SlopeY(i,j,k) |
721 |
& *recip_drF(k)*recip_hFacS(i,j,k,bi,bj) |
722 |
|
723 |
C Use the interior diffusivity. Note: if we are using a |
724 |
C constant diffusivity KPV is overwritten later |
725 |
KPV(i,j,k) = K3D(i,j,k,bi,bj) |
726 |
|
727 |
ENDDO |
728 |
ENDDO |
729 |
|
730 |
C Calculate the thickness flux and diffusivity and for other cells (k<Nr) |
731 |
DO k=Nr-1,1,-1 |
732 |
DO j=1-Oly,sNy+Oly |
733 |
DO i=1-Olx,sNx+Olx |
734 |
C Zonal thickness flux at the western cell face |
735 |
tfluxX(i,j,k)=-fCoriU(i,j)*(SlopeX(i,j,k)-SlopeX(i,j,k+1)) |
736 |
& *recip_drF(k)*recip_hFacW(i,j,k,bi,bj) |
737 |
& *maskW(i,j,k,bi,bj) |
738 |
|
739 |
C Meridional thickness flux at the southern cell face |
740 |
tfluxY(i,j,k)=-fCoriV(i,j)*(SlopeY(i,j,k)-SlopeY(i,j,k+1)) |
741 |
& *recip_drF(k)*recip_hFacS(i,j,k,bi,bj) |
742 |
& *maskS(i,j,k,bi,bj) |
743 |
|
744 |
C Use the interior diffusivity. Note: if we are using a |
745 |
C constant diffusivity KPV is overwritten later |
746 |
KPV(i,j,k) = K3D(i,j,k,bi,bj) |
747 |
ENDDO |
748 |
ENDDO |
749 |
ENDDO |
750 |
|
751 |
C Special treatment for the surface layer (if necessary), which overwrites |
752 |
C values in the previous loops. |
753 |
IF (GM_K3D_ThickSheet .OR. GM_K3D_surfK) THEN |
754 |
DO k=Nr-1,1,-1 |
755 |
DO j=1-Oly,sNy+Oly |
756 |
DO i=1-Olx,sNx+Olx |
757 |
IF(k.LE.surfk(i,j)) THEN |
758 |
C We are in the surface layer. Change the thickness flux |
759 |
C and diffusivity as necessary. |
760 |
|
761 |
IF (GM_K3D_ThickSheet) THEN |
762 |
C We are in the surface layer, so set the thickness flux |
763 |
C based on the average slope over the surface layer |
764 |
C If we are on the edge of a "cliff" the surface layer at the |
765 |
C centre of the grid point could be deeper than the U or V point. |
766 |
C So, we ensure that we always take a sensible slope. |
767 |
IF(kLow_U(i,j).LT.surfk(i,j)) THEN |
768 |
kk=kLow_U(i,j) |
769 |
hsurf = -rLowW(i,j,bi,bj) |
770 |
ELSE |
771 |
kk=surfk(i,j) |
772 |
hsurf = -surfkz(i,j) |
773 |
ENDIF |
774 |
IF(kk.GT.0) THEN |
775 |
IF(kk.EQ.Nr) THEN |
776 |
tfluxX(i,j,k) = -fCoriU(i,j)*maskW(i,j,k,bi,bj) |
777 |
& *SlopeX(i,j,kk)/hsurf |
778 |
ELSE |
779 |
tfluxX(i,j,k) = -fCoriU(i,j)*maskW(i,j,k,bi,bj) |
780 |
& *( SlopeX(i,j,kk)-SlopeX(i,j,kk+1) )/hsurf |
781 |
ENDIF |
782 |
ELSE |
783 |
tfluxX(i,j,k) = zeroRL |
784 |
ENDIF |
785 |
|
786 |
IF(kLow_V(i,j).LT.surfk(i,j)) THEN |
787 |
kk=kLow_V(i,j) |
788 |
hsurf = -rLowS(i,j,bi,bj) |
789 |
ELSE |
790 |
kk=surfk(i,j) |
791 |
hsurf = -surfkz(i,j) |
792 |
ENDIF |
793 |
IF(kk.GT.0) THEN |
794 |
IF(kk.EQ.Nr) THEN |
795 |
tfluxY(i,j,k) = -fCoriV(i,j)*maskS(i,j,k,bi,bj) |
796 |
& *SlopeY(i,j,kk)/hsurf |
797 |
ELSE |
798 |
tfluxY(i,j,k) = -fCoriV(i,j)*maskS(i,j,k,bi,bj) |
799 |
& *( SlopeY(i,j,kk)-SlopeY(i,j,kk+1) )/hsurf |
800 |
ENDIF |
801 |
ELSE |
802 |
tfluxY(i,j,k) = zeroRL |
803 |
ENDIF |
804 |
ENDIF |
805 |
|
806 |
IF (GM_K3D_surfK) THEN |
807 |
C Use a constant K in the surface layer. |
808 |
KPV(i,j,k) = GM_K3D_constK |
809 |
ENDIF |
810 |
ENDIF |
811 |
ENDDO |
812 |
ENDDO |
813 |
ENDDO |
814 |
ENDIF |
815 |
|
816 |
C Calculate gradq |
817 |
IF (GM_K3D_beta_eq_0) THEN |
818 |
C Ignore beta in the calculation of grad(q) |
819 |
DO k=1,Nr |
820 |
DO j=1-Oly+1,sNy+Oly |
821 |
DO i=1-Olx+1,sNx+Olx |
822 |
gradqx(i,j,k) = maskW(i,j,k,bi,bj)*tfluxX(i,j,k) |
823 |
gradqy(i,j,k) = maskS(i,j,k,bi,bj)*tfluxY(i,j,k) |
824 |
ENDDO |
825 |
ENDDO |
826 |
ENDDO |
827 |
|
828 |
ELSE |
829 |
C Do not ignore beta |
830 |
DO k=1,Nr |
831 |
DO j=1-Oly+1,sNy+Oly |
832 |
DO i=1-Olx+1,sNx+Olx |
833 |
gradqx(i,j,k) = maskW(i,j,k,bi,bj)*(dfdx(i,j)+tfluxX(i,j,k)) |
834 |
gradqy(i,j,k) = maskS(i,j,k,bi,bj)*(dfdy(i,j)+tfluxY(i,j,k)) |
835 |
ENDDO |
836 |
ENDDO |
837 |
ENDDO |
838 |
ENDIF |
839 |
|
840 |
C ====================================== |
841 |
C Find Xi and the eddy induced velocities |
842 |
C ====================================== |
843 |
C Find the buoyancy frequency at the west and south faces of a cell |
844 |
C This is necessary to find the eigenvectors at those points |
845 |
DO k=1,Nr |
846 |
DO j=1-Oly+1,sNy+Oly |
847 |
DO i=1-Olx+1,sNx+Olx |
848 |
N2W(i,j,k) = maskW(i,j,k,bi,bj) |
849 |
& *( N2(i,j,k)+N2(i-1,j,k) ) |
850 |
N2S(i,j,k) = maskS(i,j,k,bi,bj) |
851 |
& *( N2(i,j,k)+N2(i,j-1,k) ) |
852 |
ENDDO |
853 |
ENDDO |
854 |
ENDDO |
855 |
|
856 |
C If GM_K3D_use_constK=.TRUE., the diffusivity for the eddy transport is |
857 |
C set to a constant equal to GM_K3D_constK. |
858 |
C If the diffusivity is constant the method here is the same as GM. |
859 |
C If GM_K3D_constRedi=.TRUE. K3D will be set equal to GM_K3D_constK later. |
860 |
IF(GM_K3D_use_constK) THEN |
861 |
DO k=1,Nr |
862 |
DO j=1-Oly,sNy+Oly |
863 |
DO i=1-Olx,sNx+Olx |
864 |
KPV(i,j,k) = GM_K3D_constK |
865 |
ENDDO |
866 |
ENDDO |
867 |
ENDDO |
868 |
ENDIF |
869 |
|
870 |
IF (.NOT. GM_K3D_smooth) THEN |
871 |
C Do not expand K grad(q) => no smoothing |
872 |
C May only be done with a constant K, otherwise the |
873 |
C integral constraint is violated. |
874 |
DO k=1,Nr |
875 |
DO j=1-Oly,sNy+Oly |
876 |
DO i=1-Olx,sNx+Olx |
877 |
Xix(i,j,k) = -maskW(i,j,k,bi,bj)*KPV(i,j,k)*gradqx(i,j,k) |
878 |
Xiy(i,j,k) = -maskS(i,j,k,bi,bj)*KPV(i,j,k)*gradqy(i,j,k) |
879 |
ENDDO |
880 |
ENDDO |
881 |
ENDDO |
882 |
|
883 |
ELSE |
884 |
C Expand K grad(q) in terms of baroclinic modes to smooth |
885 |
C and satisfy the integral constraint |
886 |
|
887 |
C Start with the X direction |
888 |
C ------------------------------ |
889 |
C Calculate the eigenvectors at the West face of a cell |
890 |
IF (update_modes) THEN |
891 |
CALL GMREDI_CALC_EIGS( |
892 |
I iMin,iMax,jMin,jMax,bi,bj,N2W,myThid, |
893 |
I kLow_U,maskW(:,:,:,bi,bj), |
894 |
I hfacW(:,:,:,bi,bj),recip_hfacW(:,:,:,bi,bj), |
895 |
I rLowW(:,:,bi,bj),GM_K3D_NModes,.FALSE., |
896 |
O dummy,modesW(:,:,:,:,bi,bj)) |
897 |
ENDIF |
898 |
|
899 |
C Calculate Xi_m at the west face of a cell |
900 |
DO j=1-Oly,sNy+Oly |
901 |
DO i=1-Olx,sNx+Olx |
902 |
DO m=1,GM_K3D_NModes |
903 |
XimX(m,i,j) = zeroRL |
904 |
ENDDO |
905 |
ENDDO |
906 |
ENDDO |
907 |
DO k=1,Nr |
908 |
DO j=1-Oly,sNy+Oly |
909 |
DO i=1-Olx,sNx+Olx |
910 |
DO m=1,GM_K3D_NModes |
911 |
Kdqdx(i,j,k) = KPV(i,j,k)*gradqx(i,j,k) |
912 |
XimX(m,i,j) = XimX(m,i,j) |
913 |
& - maskW(i,j,k,bi,bj)*drF(k)*hfacW(i,j,k,bi,bj) |
914 |
& *Kdqdx(i,j,k)*modesW(m,i,j,k,bi,bj) |
915 |
ENDDO |
916 |
ENDDO |
917 |
ENDDO |
918 |
ENDDO |
919 |
|
920 |
C Calculate Xi in the X direction at the west face |
921 |
DO k=1,Nr |
922 |
DO j=1-Oly,sNy+Oly |
923 |
DO i=1-Olx,sNx+Olx |
924 |
Xix(i,j,k) = zeroRL |
925 |
ENDDO |
926 |
ENDDO |
927 |
ENDDO |
928 |
DO k=1,Nr |
929 |
DO j=1-Oly,sNy+Oly |
930 |
DO i=1-Olx,sNx+Olx |
931 |
DO m=1,GM_K3D_NModes |
932 |
Xix(i,j,k) = Xix(i,j,k) |
933 |
& + maskW(i,j,k,bi,bj)*XimX(m,i,j)*modesW(m,i,j,k,bi,bj) |
934 |
ENDDO |
935 |
ENDDO |
936 |
ENDDO |
937 |
ENDDO |
938 |
|
939 |
C Now the Y direction |
940 |
C ------------------------------ |
941 |
C Calculate the eigenvectors at the West face of a cell |
942 |
IF (update_modes) THEN |
943 |
CALL GMREDI_CALC_EIGS( |
944 |
I iMin,iMax,jMin,jMax,bi,bj,N2S,myThid, |
945 |
I kLow_V,maskS(:,:,:,bi,bj), |
946 |
I hfacS(:,:,:,bi,bj),recip_hfacS(:,:,:,bi,bj), |
947 |
I rLowS(:,:,bi,bj), GM_K3D_NModes, .FALSE., |
948 |
O dummy,modesS(:,:,:,:,bi,bj)) |
949 |
ENDIF |
950 |
|
951 |
DO j=1-Oly,sNy+Oly |
952 |
DO i=1-Olx,sNx+Olx |
953 |
DO m=1,GM_K3D_NModes |
954 |
XimY(m,i,j) = zeroRL |
955 |
ENDDO |
956 |
ENDDO |
957 |
ENDDO |
958 |
DO k=1,Nr |
959 |
DO j=1-Oly,sNy+Oly |
960 |
DO i=1-Olx,sNx+Olx |
961 |
DO m=1,GM_K3D_NModes |
962 |
Kdqdy(i,j,k) = KPV(i,j,k)*gradqy(i,j,k) |
963 |
XimY(m,i,j) = XimY(m,i,j) |
964 |
& - drF(k)*hfacS(i,j,k,bi,bj) |
965 |
& *Kdqdy(i,j,k)*modesS(m,i,j,k,bi,bj) |
966 |
ENDDO |
967 |
ENDDO |
968 |
ENDDO |
969 |
ENDDO |
970 |
|
971 |
C Calculate Xi for Y direction at the south face |
972 |
DO k=1,Nr |
973 |
DO j=1-Oly,sNy+Oly |
974 |
DO i=1-Olx,sNx+Olx |
975 |
Xiy(i,j,k) = zeroRL |
976 |
ENDDO |
977 |
ENDDO |
978 |
ENDDO |
979 |
DO k=1,Nr |
980 |
DO j=1-Oly,sNy+Oly |
981 |
DO i=1-Olx,sNx+Olx |
982 |
DO m=1,GM_K3D_NModes |
983 |
Xiy(i,j,k) = Xiy(i,j,k) |
984 |
& + maskS(i,j,k,bi,bj)*XimY(m,i,j)*modesS(m,i,j,k,bi,bj) |
985 |
ENDDO |
986 |
ENDDO |
987 |
ENDDO |
988 |
ENDDO |
989 |
|
990 |
C ENDIF (.NOT. GM_K3D_smooth) |
991 |
ENDIF |
992 |
|
993 |
C Calculate the renormalisation factor |
994 |
DO j=1-Oly,sNy+Oly |
995 |
DO i=1-Olx,sNx+Olx |
996 |
uInt(i,j)=zeroRL |
997 |
vInt(i,j)=zeroRL |
998 |
KdqdyInt(i,j)=zeroRL |
999 |
KdqdxInt(i,j)=zeroRL |
1000 |
uKdqdyInt(i,j)=zeroRL |
1001 |
vKdqdxInt(i,j)=zeroRL |
1002 |
uXiyInt(i,j)=zeroRL |
1003 |
vXixInt(i,j)=zeroRL |
1004 |
Renorm(i,j)=oneRL |
1005 |
RenormU(i,j)=oneRL |
1006 |
RenormV(i,j)=oneRL |
1007 |
ENDDO |
1008 |
ENDDO |
1009 |
DO k=1,Nr |
1010 |
DO j=1-Oly,sNy+Oly-1 |
1011 |
DO i=1-Olx,sNx+Olx-1 |
1012 |
centreX = op5*(uVel(i,j,k,bi,bj)+uVel(i+1,j,k,bi,bj)) |
1013 |
centreY = op5*(Kdqdy(i,j,k) +Kdqdy(i,j+1,k) ) |
1014 |
C For the numerator |
1015 |
uInt(i,j) = uInt(i,j) |
1016 |
& + centreX*hfacC(i,j,k,bi,bj)*drF(k) |
1017 |
KdqdyInt(i,j) = KdqdyInt(i,j) |
1018 |
& + centreY*hfacC(i,j,k,bi,bj)*drF(k) |
1019 |
uKdqdyInt(i,j) = uKdqdyInt(i,j) |
1020 |
& + centreX*centreY*hfacC(i,j,k,bi,bj)*drF(k) |
1021 |
C For the denominator |
1022 |
centreY = op5*(Xiy(i,j,k) + Xiy(i,j+1,k)) |
1023 |
uXiyInt(i,j) = uXiyInt(i,j) |
1024 |
& + centreX*centreY*hfacC(i,j,k,bi,bj)*drF(k) |
1025 |
|
1026 |
centreX = op5*(Kdqdx(i,j,k) +Kdqdx(i+1,j,k)) |
1027 |
centreY = op5*(vVel(i,j,k,bi,bj)+vVel(i,j+1,k,bi,bj) ) |
1028 |
C For the numerator |
1029 |
vInt(i,j) = vInt(i,j) |
1030 |
& + centreY*hfacC(i,j,k,bi,bj)*drF(k) |
1031 |
KdqdxInt(i,j) = KdqdxInt(i,j) |
1032 |
& + CentreX*hfacC(i,j,k,bi,bj)*drF(k) |
1033 |
vKdqdxInt(i,j) = vKdqdxInt(i,j) |
1034 |
& + centreY*centreX*hfacC(i,j,k,bi,bj)*drF(k) |
1035 |
C For the denominator |
1036 |
centreX = op5*(Xix(i,j,k) + Xix(i+1,j,k)) |
1037 |
vXixInt(i,j) = vXixInt(i,j) |
1038 |
& + centreY*centreX*hfacC(i,j,k,bi,bj)*drF(k) |
1039 |
|
1040 |
ENDDO |
1041 |
ENDDO |
1042 |
ENDDO |
1043 |
|
1044 |
DO j=1-Oly,sNy+Oly-1 |
1045 |
DO i=1-Olx,sNx+Olx-1 |
1046 |
IF (kLowC(i,j,bi,bj).GT.0) THEN |
1047 |
numerator = |
1048 |
& (uKdqdyInt(i,j)-uInt(i,j)*KdqdyInt(i,j)/R_low(i,j,bi,bj)) |
1049 |
& -(vKdqdxInt(i,j)-vInt(i,j)*KdqdxInt(i,j)/R_low(i,j,bi,bj)) |
1050 |
denominator = uXiyInt(i,j) - vXixInt(i,j) |
1051 |
C We can have troubles with floating point exceptions if the denominator |
1052 |
C of the renormalisation if the ocean is resting (e.g. intial conditions). |
1053 |
C So we make the renormalisation factor one if the denominator is very small |
1054 |
C The renormalisation factor is supposed to correct the error in the extraction of |
1055 |
C potential energy associated with the truncation of the expansion. Thus, we |
1056 |
C enforce a minimum value for the renormalisation factor. |
1057 |
C We also enforce a maximum renormalisation factor. |
1058 |
IF (denominator.GT.small) THEN |
1059 |
Renorm(i,j) = ABS(numerator/denominator) |
1060 |
Renorm(i,j) = MAX(Renorm(i,j),GM_K3D_minRenorm) |
1061 |
Renorm(i,j) = MIN(Renorm(i,j),GM_K3D_maxRenorm) |
1062 |
ENDIF |
1063 |
ENDIF |
1064 |
ENDDO |
1065 |
ENDDO |
1066 |
C Now put it back on to the velocity grids |
1067 |
DO j=1-Oly+1,sNy+Oly-1 |
1068 |
DO i=1-Olx+1,sNx+Olx-1 |
1069 |
RenormU(i,j) = op5*(Renorm(i-1,j)+Renorm(i,j)) |
1070 |
RenormV(i,j) = op5*(Renorm(i,j-1)+Renorm(i,j)) |
1071 |
ENDDO |
1072 |
ENDDO |
1073 |
|
1074 |
C Calculate the eddy induced velocity in the X direction at the west face |
1075 |
DO k=1,Nr |
1076 |
DO j=1-Oly+1,sNy+Oly |
1077 |
DO i=1-Olx+1,sNx+Olx |
1078 |
ustar(i,j,k) = -RenormU(i,j)*Xix(i,j,k)/coriU(i,j) |
1079 |
ENDDO |
1080 |
ENDDO |
1081 |
ENDDO |
1082 |
|
1083 |
C Calculate the eddy induced velocity in the Y direction at the south face |
1084 |
DO k=1,Nr |
1085 |
DO j=1-Oly+1,sNy+Oly |
1086 |
DO i=1-Olx+1,sNx+Olx |
1087 |
vstar(i,j,k) = -RenormV(i,j)*Xiy(i,j,k)/coriV(i,j) |
1088 |
ENDDO |
1089 |
ENDDO |
1090 |
ENDDO |
1091 |
|
1092 |
C ====================================== |
1093 |
C Calculate the eddy induced overturning streamfunction |
1094 |
C ====================================== |
1095 |
#ifdef GM_K3D_PASSIVE |
1096 |
k=Nr |
1097 |
DO j=1-Oly,sNy+Oly |
1098 |
DO i=1-Olx,sNx+Olx |
1099 |
psistar(i,j,Nr) = -hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
1100 |
ENDDO |
1101 |
ENDDO |
1102 |
DO k=Nr-1,1,-1 |
1103 |
DO j=1-Oly,sNy+Oly |
1104 |
DO i=1-Olx,sNx+Olx |
1105 |
psistar(i,j,k) = psistar(i,j,k+1) |
1106 |
& - hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
1107 |
ENDDO |
1108 |
ENDDO |
1109 |
ENDDO |
1110 |
|
1111 |
#else |
1112 |
|
1113 |
IF (GM_AdvForm) THEN |
1114 |
k=Nr |
1115 |
DO j=1-Oly+1,sNy+1 |
1116 |
DO i=1-Olx+1,sNx+1 |
1117 |
GM_PsiX(i,j,k,bi,bj) = -hfacW(i,j,k,bi,bj)*drF(k)*ustar(i,j,k) |
1118 |
GM_PsiY(i,j,k,bi,bj) = -hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
1119 |
ENDDO |
1120 |
ENDDO |
1121 |
DO k=Nr-1,1,-1 |
1122 |
DO j=1-Oly+1,sNy+1 |
1123 |
DO i=1-Olx+1,sNx+1 |
1124 |
GM_PsiX(i,j,k,bi,bj) = GM_PsiX(i,j,k+1,bi,bj) |
1125 |
& - hfacW(i,j,k,bi,bj)*drF(k)*ustar(i,j,k) |
1126 |
GM_PsiY(i,j,k,bi,bj) = GM_PsiY(i,j,k+1,bi,bj) |
1127 |
& - hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k) |
1128 |
ENDDO |
1129 |
ENDDO |
1130 |
ENDDO |
1131 |
|
1132 |
ENDIF |
1133 |
#endif |
1134 |
|
1135 |
#ifdef ALLOW_DIAGNOSTICS |
1136 |
C Diagnostics |
1137 |
IF ( useDiagnostics ) THEN |
1138 |
CALL DIAGNOSTICS_FILL(K3D, 'GM_K3D ',0,Nr,1,bi,bj,myThid) |
1139 |
CALL DIAGNOSTICS_FILL(KPV, 'GM_KPV ',0,Nr,2,bi,bj,myThid) |
1140 |
CALL DIAGNOSTICS_FILL(urms, 'GM_URMS ',0,Nr,2,bi,bj,myThid) |
1141 |
CALL DIAGNOSTICS_FILL(Rdef, 'GM_RDEF ',0, 1,1,bi,bj,myThid) |
1142 |
CALL DIAGNOSTICS_FILL(Rurms, 'GM_RURMS',0, 1,2,bi,bj,myThid) |
1143 |
CALL DIAGNOSTICS_FILL(RRhines,'GM_RRHNS',0, 1,2,bi,bj,myThid) |
1144 |
CALL DIAGNOSTICS_FILL(Rmix, 'GM_RMIX ',0, 1,2,bi,bj,myThid) |
1145 |
CALL DIAGNOSTICS_FILL(supp, 'GM_SUPP ',0,Nr,2,bi,bj,myThid) |
1146 |
CALL DIAGNOSTICS_FILL(Xix, 'GM_Xix ',0,Nr,2,bi,bj,myThid) |
1147 |
CALL DIAGNOSTICS_FILL(Xiy, 'GM_Xiy ',0,Nr,2,bi,bj,myThid) |
1148 |
CALL DIAGNOSTICS_FILL(cDopp, 'GM_C ',0, 1,2,bi,bj,myThid) |
1149 |
CALL DIAGNOSTICS_FILL(Ubaro, 'GM_UBARO',0, 1,2,bi,bj,myThid) |
1150 |
CALL DIAGNOSTICS_FILL(eady, 'GM_EADY ',0, 1,2,bi,bj,myThid) |
1151 |
CALL DIAGNOSTICS_FILL(SlopeX, 'GM_Sx ',0,Nr,2,bi,bj,myThid) |
1152 |
CALL DIAGNOSTICS_FILL(SlopeY, 'GM_Sy ',0,Nr,2,bi,bj,myThid) |
1153 |
CALL DIAGNOSTICS_FILL(tfluxX, 'GM_TFLXX',0,Nr,2,bi,bj,myThid) |
1154 |
CALL DIAGNOSTICS_FILL(tfluxY, 'GM_TFLXY',0,Nr,2,bi,bj,myThid) |
1155 |
CALL DIAGNOSTICS_FILL(gradqx, 'GM_dqdx ',0,Nr,2,bi,bj,myThid) |
1156 |
CALL DIAGNOSTICS_FILL(gradqy, 'GM_dqdy ',0,Nr,2,bi,bj,myThid) |
1157 |
CALL DIAGNOSTICS_FILL(Kdqdy, 'GM_Kdqdy',0,Nr,2,bi,bj,myThid) |
1158 |
CALL DIAGNOSTICS_FILL(Kdqdx, 'GM_Kdqdx',0,Nr,2,bi,bj,myThid) |
1159 |
CALL DIAGNOSTICS_FILL(surfkz, 'GM_SFLYR',0, 1,2,bi,bj,myThid) |
1160 |
CALL DIAGNOSTICS_FILL(ustar, 'GM_USTAR',0,Nr,2,bi,bj,myThid) |
1161 |
CALL DIAGNOSTICS_FILL(vstar, 'GM_VSTAR',0,Nr,2,bi,bj,myThid) |
1162 |
CALL DIAGNOSTICS_FILL(umc, 'GM_UMC ',0,Nr,2,bi,bj,myThid) |
1163 |
CALL DIAGNOSTICS_FILL(ubar, 'GM_UBAR ',0,Nr,2,bi,bj,myThid) |
1164 |
CALL DIAGNOSTICS_FILL(modesC, 'GM_MODEC',0,Nr,1,bi,bj,myThid) |
1165 |
CALL DIAGNOSTICS_FILL(M4loc, 'GM_M4 ',0,Nr,2,bi,bj,myThid) |
1166 |
CALL DIAGNOSTICS_FILL(N2loc, 'GM_N2 ',0,Nr,2,bi,bj,myThid) |
1167 |
CALL DIAGNOSTICS_FILL(M4onN2, 'GM_M4_N2',0,Nr,2,bi,bj,myThid) |
1168 |
CALL DIAGNOSTICS_FILL(slopeC, 'GM_SLOPE',0,Nr,2,bi,bj,myThid) |
1169 |
CALL DIAGNOSTICS_FILL(Renorm, 'GM_RENRM',0, 1,2,bi,bj,myThid) |
1170 |
#ifdef GM_K3D_PASSIVE |
1171 |
CALL DIAGNOSTICS_FILL(psistar,'GM_PSTAR',0,Nr,2,bi,bj,myThid) |
1172 |
#endif |
1173 |
ENDIF |
1174 |
#endif |
1175 |
|
1176 |
C For the Redi diffusivity, we set K3D to a constant if |
1177 |
C GM_K3D_constRedi=.TRUE. |
1178 |
IF (GM_K3D_constRedi) THEN |
1179 |
DO k=1,Nr |
1180 |
DO j=1-Oly,sNy+Oly |
1181 |
DO i=1-Olx,sNx+Olx |
1182 |
K3D(i,j,k,bi,bj) = GM_K3D_constK |
1183 |
ENDDO |
1184 |
ENDDO |
1185 |
ENDDO |
1186 |
ENDIF |
1187 |
|
1188 |
#ifdef ALLOW_DIAGNOSTICS |
1189 |
IF ( useDiagnostics ) |
1190 |
& CALL DIAGNOSTICS_FILL(K3D, 'GM_K3D_T',0,Nr,1,bi,bj,myThid) |
1191 |
#endif |
1192 |
|
1193 |
#endif /* GM_K3D */ |
1194 |
RETURN |
1195 |
END |