/[MITgcm]/MITgcm/pkg/gmredi/gmredi_k3d.F
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Revision 1.5 - (hide annotations) (download)
Thu Aug 8 22:39:36 2013 UTC (10 years, 10 months ago) by m_bates
Branch: MAIN
CVS Tags: checkpoint64m
Changes since 1.4: +3 -3 lines 
Namelist option to ignore beta in the calculation of grad(q) for GM_K3D
1 m_bates 1.5 C $Header: /u/gcmpack/MITgcm/pkg/gmredi/gmredi_k3d.F,v 1.4 2013/07/11 14:33:23 m_bates Exp $
2 m_bates 1.1 C $Name: $
3     #include "GMREDI_OPTIONS.h"
4    
5     C !ROUTINE: GMREDI_K3D
6     C !INTERFACE:
7     SUBROUTINE GMREDI_K3D(
8     I iMin, iMax, jMin, jMax,
9     I sigmaX, sigmaY, sigmaR,
10 m_bates 1.4 I bi, bj, myTime, myThid )
11 m_bates 1.1
12     C !DESCRIPTION: \bv
13     C *==========================================================*
14     C | SUBROUTINE GMREDI_K3D
15     C | o Calculates the 3D diffusivity as per Bates et al. (2013)
16     C *==========================================================*
17     C \ev
18    
19     IMPLICIT NONE
20    
21     C == Global variables ==
22     #include "SIZE.h"
23     #include "GRID.h"
24     #include "DYNVARS.h"
25     #include "EEPARAMS.h"
26     #include "PARAMS.h"
27     #include "GMREDI.h"
28    
29     C !INPUT/OUTPUT PARAMETERS:
30     C == Routine arguments ==
31     C bi, bj :: tile indices
32     C myThid :: My Thread Id. number
33    
34     INTEGER iMin,iMax,jMin,jMax
35     _RL sigmaX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
36     _RL sigmaY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
37     _RL sigmaR(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
38     INTEGER bi, bj
39 m_bates 1.4 _RL myTime
40 m_bates 1.1 INTEGER myThid
41    
42     #ifdef GM_K3D
43    
44 m_bates 1.4 C === Functions ====
45     LOGICAL DIFFERENT_MULTIPLE
46     EXTERNAL DIFFERENT_MULTIPLE
47    
48 m_bates 1.1 C !LOCAL VARIABLES:
49     C == Local variables ==
50 m_bates 1.4 INTEGER i,j,k,kk,m
51    
52     C update_modes :: Whether to update the eigenmodes
53     LOGICAL update_modes
54    
55     C surfk :: index of the depth of the surface layer
56     C kLow_C :: Local version of the index of deepest wet grid cell on tracer grid
57     C kLow_U :: Local version of the index of deepest wet grid cell on U grid
58     C kLow_V :: Local version of the index of deepest wet grid cell on V grid
59 m_bates 1.1 INTEGER surfk(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
60     INTEGER kLow_C(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
61     INTEGER kLow_U(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
62     INTEGER kLow_V(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
63 m_bates 1.4
64     C N2loc :: local N**2
65     C slope :: local slope
66     C Req :: local equatorial deformation radius (m)
67     C Rurms :: a local mixing length used in calculation of urms (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 m_bates 1.1 _RL N2loc
78     _RL slope
79 m_bates 1.4 _RL Req
80     _RL Rurms
81 m_bates 1.1 _RL deltaH
82     _RL g_reciprho_sq
83     _RL M4loc
84     _RL maxDRhoDz
85     _RL sigx, sigy, sigz
86     _RL hsurf
87     _RL small
88 m_bates 1.4
89     C dfdy :: gradient of the Coriolis paramter, df/dy, 1/(m*s)
90     C dfdx :: gradient of the Coriolis paramter, df/dx, 1/(m*s)
91     C gradf :: total gradient of the Coriolis paramter, SQRT(df/dx**2+df/dy**2), 1/(m*s)
92     C RRhines :: The Rhines scale (m)
93     C Rmix :: Mixing length
94     C N2 :: Square of the buoyancy frequency (1/s**2)
95     C N2W :: Square of the buoyancy frequency (1/s**2) averaged to west of grid cell
96     C N2S :: Square of the buoyancy frequency (1/s**2) averaged to south of grid cell
97     C N :: Buoyancy frequency, SQRT(N2)
98     C BVint :: The vertical integral of N (m/s)
99     C ubar :: Zonal velocity on a tracer point (m/s)
100     C vbar :: Meridional velocity on a tracer point (m/s)
101     C Ubaro :: Barotropic velocity (m/s)
102     _RL dfdy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly)
103     _RL dfdx( 1-Olx:sNx+Olx,1-Oly:sNy+Oly)
104     _RL gradf( 1-Olx:sNx+Olx,1-Oly:sNy+Oly)
105     _RL dummy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly)
106     _RL RRhines(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
107     _RL Rmix( 1-Olx:sNx+Olx,1-Oly:sNy+Oly)
108     _RL N2( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
109     _RL N2W( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
110     _RL N2S( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
111     _RL N( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
112     _RL BVint( 1-Olx:sNx+Olx,1-Oly:sNy+Oly)
113     _RL Ubaro( 1-Olx:sNx+Olx,1-Oly:sNy+Oly)
114     _RL ubar( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
115     _RL vbar( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr,nSx,nSy)
116    
117     C Rmid :: Rossby radius (m)
118     C KPV :: Diffusivity (m**2/s)
119     C SlopeX :: isopycnal slope in x direction
120     C SlopeY :: isopycnal slope in y direction
121     C dSigmaDx :: sigmaX averaged onto tracer grid
122     C dSigmaDy :: sigmaY averaged onto tracer grid
123     C tfluxX :: thickness flux in x direction
124     C tfluxY :: thickness flux in y direction
125     C fCoriU :: Coriolis parameter averaged to U points
126     C fCoriV :: Coriolis parameter averaged to V points
127     C cori :: Coriolis parameter forced to be finite near the equator
128     C coriU :: As for cori, but, at U point
129     C coriV :: As for cori, but, at V point
130     C surfkz :: Depth of surface layer (in r units)
131     _RL Rmid(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
132 m_bates 1.3 _RL KPV(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
133 m_bates 1.1 _RL SlopeX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
134     _RL SlopeY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
135     _RL dSigmaDx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
136     _RL dSigmaDy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
137     _RL tfluxX(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
138     _RL tfluxY(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
139     _RL cori(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
140     _RL coriU(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
141     _RL coriV(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
142     _RL fCoriU(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
143     _RL fCoriV(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
144     _RL surfkz(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
145 m_bates 1.4
146     C gradqx :: Potential vorticity gradient in x direction
147     C gradqy :: Potential vorticity gradient in y direction
148     C XimX :: Vertical integral of phi_m*K*gradqx
149     C XimY :: Vertical integral of phi_m*K*gradqy
150     C cDopp :: Quasi-Doppler shifted long Rossby wave speed (m/s)
151     C umc :: ubar-c (m/s)
152     C eady :: Eady growth rate (1/s)
153     C urms :: the rms eddy velocity (m/s)
154     C supp :: The suppression factor
155     C ustar :: The eddy induced velocity in the x direction
156     C vstar :: The eddy induced velocity in the y direction
157     C Xix :: Xi in the x direction (m/s**2)
158     C Xiy :: Xi in the y direction (m/s**2)
159 m_bates 1.1 _RL gradqx(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
160     _RL gradqy(1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
161     _RL XimX(GM_K3D_NModes,1-Olx:sNx+Olx,1-Oly:sNy+Oly)
162     _RL XimY(GM_K3D_NModes,1-Olx:sNx+Olx,1-Oly:sNy+Oly)
163 m_bates 1.4 _RL cDopp(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
164 m_bates 1.1 _RL umc( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr)
165     _RL eady( 1-Olx:sNx+Olx,1-Oly:sNy+Oly)
166     _RL urms( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr)
167     _RL supp( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr)
168     _RL ustar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr)
169     _RL vstar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr)
170     _RL Xix( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
171     _RL Xiy( 1-Olx:sNx+Olx,1-Oly:sNy+Oly,Nr)
172 m_bates 1.4 #ifdef GM_K3D_PASSIVE
173     C psistar :: eddy induced streamfunction in the y direction
174 m_bates 1.1 _RL psistar(1-Olx:sNx+Olx,1-Oly:sNy+Oly,1:Nr)
175 m_bates 1.4 #endif
176 m_bates 1.1
177    
178     C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
179    
180     C ======================================
181     C Initialise some variables
182     C ======================================
183     small = TINY(zeroRL)
184 m_bates 1.4 update_modes=.FALSE.
185     IF ( DIFFERENT_MULTIPLE(GM_K3D_vecFreq,myTime,deltaTClock) )
186     & update_modes=.TRUE.
187    
188 m_bates 1.1 DO j=1-Oly,sNy+Oly
189     DO i=1-Olx,sNx+Olx
190     kLow_C(i,j) = kLowC(i,j,bi,bj)
191     ENDDO
192     ENDDO
193     DO j=1-Oly,sNy+Oly
194     DO i=1-Olx+1,sNx+Olx
195     kLow_U(i,j) = MIN( kLow_C(i,j), kLow_C(i-1,j) )
196     ENDDO
197     ENDDO
198     DO j=1-Oly+1,sNy+Oly
199     DO i=1-Olx,sNx+Olx
200     kLow_V(i,j) = MIN( kLow_C(i,j), kLow_C(i,j-1) )
201     ENDDO
202     ENDDO
203    
204     C Dummy values for the edges
205     C This avoids weirdness in gmredi_calc_eigs
206     i=1-Olx
207     DO j=1-Oly,sNy+Oly
208     kLow_U(i,j) = kLow_C(i,j)
209     ENDDO
210     j=1-Oly
211     DO i=1-Olx,sNx+Olx
212     kLow_V(i,j) = kLow_C(i,j)
213     ENDDO
214    
215     g_reciprho_sq = (gravity*recip_rhoConst)**2
216     C Gradient of Coriolis
217     DO j=1-Oly+1,sNy+Oly
218     DO i=1-Olx+1,sNx+Olx
219     dfdx(i,j) = ( fCori(i,j,bi,bj)-fCori(i-1,j,bi,bj) )
220     & *recip_dxC(i,j,bi,bj)
221     dfdy(i,j) = ( fCori(i,j,bi,bj)-fCori(i,j-1,bi,bj) )
222     & *recip_dyC(i,j,bi,bj)
223     ENDDO
224     ENDDO
225    
226     C Coriolis at C points enforcing a minimum value so
227     C that it is defined at the equator
228     DO j=1-Oly,sNy+Oly
229     DO i=1-Olx,sNx+Olx
230     cori(i,j) = SIGN( MAX( ABS(fCori(i,j,bi,bj)),GM_K3D_minCori ),
231     & fCori(i,j,bi,bj) )
232     ENDDO
233     ENDDO
234     C Coriolis at U and V points
235     DO j=1-Oly+1,sNy+Oly
236     DO i=1-Olx+1,sNx+Olx
237     C Limited so that the inverse is defined at the equator
238     coriU(i,j) = op5*( cori(i,j)+cori(i-1,j) )
239     coriU(i,j) = SIGN( MAX( ABS(coriU(i,j)),GM_K3D_minCori ),
240     & coriU(i,j) )
241    
242     coriV(i,j) = op5*( cori(i,j)+cori(i,j-1) )
243     coriV(i,j) = SIGN( MAX( ABS(coriV(i,j)),GM_K3D_minCori ),
244     & coriV(i,j) )
245    
246     C Not limited
247     fCoriU(i,j) = op5*( fCori(i,j,bi,bj)+fCori(i-1,j,bi,bj) )
248     fCoriV(i,j) = op5*( fCori(i,j,bi,bj)+fCori(i,j-1,bi,bj) )
249     ENDDO
250     ENDDO
251     DO j=1-Oly,sNy+Oly
252     DO i=1-Olx,sNx+Olx
253     gradf(i,j) = SQRT( dfdx(i,j)**2 + dfdy(i,j)**2 )
254     ENDDO
255     ENDDO
256    
257     C Zeroing some cumulative fields
258     DO j=1-Oly,sNy+Oly
259     DO i=1-Olx,sNx+Olx
260     eady(i,j) = zeroRL
261     BVint(i,j) = zeroRL
262     Ubaro(i,j) = zeroRL
263     ENDDO
264     ENDDO
265    
266     C Find the zonal velocity at the cell centre
267     C The logicals here are, in order: 1/ go from grid to north/east directions
268     C 2/ go from C to A grid and 3/ apply the mask
269     CALL rotate_uv2en_rl(uVel, vVel, ubar, vbar, .TRUE., .TRUE.,
270     & .TRUE.,Nr,mythid)
271    
272     C Square of the buoyancy frequency at the top of a grid cell
273     DO k=2,Nr
274     DO j=1-Oly,sNy+Oly
275     DO i=1-Olx,sNx+Olx
276     N2(i,j,k) = -gravity*recip_rhoConst*sigmaR(i,j,k)
277     ENDDO
278     ENDDO
279     ENDDO
280     C N2(k=1) is always zero
281     k=1
282     DO j=1-Oly,sNy+Oly
283     DO i=1-Olx,sNx+Olx
284     N2(i,j,k) = 0.0
285     N(i,j,k) = 0.0
286     ENDDO
287     ENDDO
288     C Enforce a minimum N2
289     DO k=2,Nr
290     DO j=1-Oly,sNy+Oly
291     DO i=1-Olx,sNx+Olx
292     IF (N2(i,j,k).LT.GM_K3D_minN2) N2(i,j,k)=GM_K3D_minN2
293     N(i,j,k) = SQRT(N2(i,j,k))
294     ENDDO
295     ENDDO
296     ENDDO
297     C Calculate the minimum drho/dz
298     maxDRhoDz = -rhoConst*GM_K3D_minN2/gravity
299    
300     C Calculate the barotropic velocity by vertically integrating
301     C and the dividing by the depth of the water column
302     C Note that Ubaro is on the U grid.
303     DO k=1,Nr
304     DO j=1-Oly,sNy+Oly
305     DO i=1-Olx,sNx+Olx
306     Ubaro(i,j) = Ubaro(i,j) +
307     & maskW(i,j,k,bi,bj)*drF(k)*hfacC(i,j,k,bi,bj)
308     & *ubar(i,j,k,bi,bj)
309     ENDDO
310     ENDDO
311     ENDDO
312     DO j=1-Oly,sNy+Oly
313     DO i=1-Olx,sNx+Olx
314     IF (kLow_C(i,j).GT.0) THEN
315     C The minus sign is because r_Low<0
316     Ubaro(i,j) = -Ubaro(i,j)/r_Low(i,j,bi,bj)
317     ENDIF
318     ENDDO
319     ENDDO
320    
321     C Integrate the buoyancy frequency vertically using the trapezoidal method.
322     DO k=1,Nr
323     DO j=1-Oly,sNy+Oly
324     DO i=1-Olx,sNx+Olx
325     IF (k.LT.kLow_C(i,j)) THEN
326     BVint(i,j) = BVint(i,j) + hFacC(i,j,k,bi,bj)*drF(k)
327     & *(N(i,j,k)+N(i,j,k+1))
328     ELSEIF (k.EQ.kLow_C(i,j)) THEN
329     C Assume that N(z=-H)=0
330     BVint(i,j) = BVint(i,j) + hFacC(i,j,k,bi,bj)*drF(k)*N(i,j,k)
331     ENDIF
332     ENDDO
333     ENDDO
334     ENDDO
335     DO j=1-Oly,sNy+Oly
336     DO i=1-Olx,sNx+Olx
337     BVint(i,j) = op5*BVint(i,j)
338     ENDDO
339     ENDDO
340    
341     C Calculate the eigenvalues and eigenvectors
342 m_bates 1.4 IF (update_modes) THEN
343     CALL GMREDI_CALC_EIGS(
344     I iMin,iMax,jMin,jMax,bi,bj,N2,myThid,
345     I kLow_C, maskC(:,:,:,bi,bj),
346     I hfacC(:,:,:,bi,bj), recip_hfacC(:,:,:,bi,bj),
347     I R_Low(:,:,bi,bj), 1, .TRUE.,
348     O Rmid, modesC(:,:,:,:,bi,bj))
349    
350     C Calculate the Rossby Radius
351     DO j=1-Oly+1,sNy+Oly
352     DO i=1-Olx+1,sNx+Olx
353     Req = SQRT(BVint(i,j)/(2*pi*gradf(i,j)))
354     Rdef(i,j,bi,bj) = MIN(Rmid(i,j),Req)
355     ENDDO
356     ENDDO
357     ENDIF
358 m_bates 1.1
359     C Average dsigma/dx and dsigma/dy onto the centre points
360    
361     DO k=1,Nr
362     DO j=1-Oly,sNy+Oly-1
363     DO i=1-Olx,sNx+Olx-1
364     dSigmaDx(i,j,k) = op5*(sigmaX(i,j,k)+sigmaX(i+1,j,k))
365     dSigmaDy(i,j,k) = op5*(sigmaY(i,j,k)+sigmaY(i,j+1,k))
366     ENDDO
367     ENDDO
368     ENDDO
369    
370     C ===============================
371     C Calculate the Eady growth rate
372     C ===============================
373     DO k=1,Nr
374    
375     C The bottom of the grid cell is shallower than the top
376     C integration level, so, advance the depth.
377     IF (-rF(k+1).LE. GM_K3D_EadyMinDepth) CYCLE
378    
379     C Don't bother going any deeper since the top of the
380     C cell is deeper than the bottom integration level
381     IF (-rF(k).GE.GM_K3D_EadyMaxDepth) EXIT
382    
383     C We are in the integration depth range
384     DO j=1-Oly,sNy+Oly-1
385     DO i=1-Olx,sNx+Olx-1
386     IF (kLow_C(i,j).GE.k) THEN
387     IF (k.NE.kLow_C(i,j)) THEN
388     N2loc = op5*(N2(i,j,k)+N2(i,j,k+1))
389     ELSE
390     N2loc = op5*N2(i,j,k)
391     ENDIF
392     M4loc = g_reciprho_sq*( dSigmaDx(i,j,k)**2
393     & +dSigmaDy(i,j,k)**2 )
394     slope = SQRT(SQRT(M4loc)/N2loc)
395    
396     C Limit the slope. Note, this is not all the Eady calculations.
397     IF (slope.LE.GM_K3D_maxSlope) THEN
398     eady(i,j) = eady(i,j)
399     & + hfacC(i,j,k,bi,bj)*drF(k)*M4loc/(N2loc)
400     ELSE
401     eady(i,j) = eady(i,j)
402     & + hfacC(i,j,k,bi,bj)*drF(k)*SQRT(M4loc)
403     & *GM_K3D_maxSlope*GM_K3D_maxSlope
404     ENDIF
405     ENDIF
406     ENDDO
407     ENDDO
408     ENDDO
409    
410     DO j=1-Oly,sNy+Oly
411     DO i=1-Olx,sNx+Olx
412     C If the minimum depth for the integration is deeper than ocean
413     C bottom then give the eady growth rate a dummy, non-zero value
414     C to avoid floating point exceptions. These points are taken care
415     C of by setting K3D=GM_K3D_smallK later.
416     IF (kLow_C(i,j).NE.0
417     & .AND. -r_Low(i,j,bi,bj).LT.GM_K3D_EadyMinDepth) THEN
418     eady(i,j) = small
419    
420     C Otherwise, multiply eady by the various constants to get the
421     C growth rate.
422     ELSE
423     deltaH = MIN(-r_low(i,j,bi,bj),GM_K3D_EadyMaxDepth)
424     deltaH = deltaH - GM_K3D_EadyMinDepth
425     eady(i,j) = SQRT(eady(i,j)/deltaH)
426    
427     ENDIF
428    
429     ENDDO
430     ENDDO
431    
432     C ======================================
433     C Calculate the diffusivity
434     C ======================================
435     DO j=1-Oly+1,sNy+Oly
436     DO i=1-Olx+1,sNx+Olx-1
437     C Calculate the Visbeck velocity
438 m_bates 1.4 Rurms = MIN(Rdef(i,j,bi,bj),GM_K3D_maxLurms)
439     urms(i,j,1) = GM_K3D_Lambda*eady(i,j)*Rurms
440 m_bates 1.1 C Set the bottom urms to zero
441     k=kLow_C(i,j)
442     IF (k.GT.0) urms(i,j,k) = 0.0
443    
444     C Calculate the Rhines scale
445     RRhines(i,j) = SQRT(urms(i,j,1)/gradf(i,j))
446    
447     C Calculate the estimated length scale
448 m_bates 1.4 Rmix(i,j) = MIN(Rdef(i,j,bi,bj), RRhines(i,j))
449 m_bates 1.1
450     C Calculate the Doppler shifted long Rossby wave speed
451     C Ubaro is on the U grid so we must average onto the M grid.
452     cDopp(i,j) = op5*( Ubaro(i,j)+Ubaro(i+1,j) )
453 m_bates 1.4 & - gradf(i,j)*Rdef(i,j,bi,bj)*Rdef(i,j,bi,bj)
454 m_bates 1.1 C Limit the wave speed to the namelist variable GM_K3D_maxC
455     IF (ABS(cDopp(i,j)).GT.GM_K3D_maxC) THEN
456     cDopp(i,j) = MAX(GM_K3D_maxC, cDopp(i,j))
457     ENDIF
458    
459     ENDDO
460     ENDDO
461    
462     C Project the surface urms to the subsurface using the first baroclinic mode
463 m_bates 1.4 CALL GMREDI_CALC_URMS(
464     I iMin,iMax,jMin,jMax,bi,bj,N2,myThid,
465     U urms)
466 m_bates 1.1
467     C Calculate the diffusivity (on the mass grid)
468     DO k=1,Nr
469     DO j=1-Oly,sNy+Oly
470     DO i=1-Olx,sNx+Olx
471     IF (k.LE.kLow_C(i,j)) THEN
472     IF (-r_Low(i,j,bi,bj).LT.GM_K3D_EadyMinDepth) THEN
473     K3D(i,j,k,bi,bj) = GM_K3D_smallK
474     ELSE
475     IF (urms(i,j,k).EQ.0.0) THEN
476     K3D(i,j,k,bi,bj) = GM_K3D_smallK
477     ELSE
478     umc(i,j,k) = ubar(i,j,k,bi,bj) - cDopp(i,j)
479     supp(i,j,k) = 1/( 1 + 4*umc(i,j,k)**2/urms(i,j,1)**2 )
480     K3D(i,j,k,bi,bj) = GM_K3D_gamma*urms(i,j,k)
481     & *Rmix(i,j)*supp(i,j,k)
482     ENDIF
483    
484     C Enforce lower and upper bounds on the diffusivity
485     IF (K3D(i,j,k,bi,bj).LT.GM_K3D_smallK)
486     & K3D(i,j,k,bi,bj) = GM_K3D_smallK
487     IF (K3D(i,j,k,bi,bj).GT.GM_maxK3D)
488     & K3D(i,j,k,bi,bj) = GM_maxK3D
489     ENDIF
490     ENDIF
491     ENDDO
492     ENDDO
493     ENDDO
494    
495     C ======================================
496     C Find the PV gradient
497     C ======================================
498 m_bates 1.3 C Calculate the surface layer thickness.
499     C Use hMixLayer (calculated in model/src/calc_oce_mxlayer)
500     C for the mixed layer depth.
501 m_bates 1.1
502 m_bates 1.3 C Enforce a minimum surface layer depth
503 m_bates 1.1 DO j=1-Oly,sNy+Oly
504     DO i=1-Olx,sNx+Olx
505 m_bates 1.3 surfkz(i,j) = MIN(-GM_K3D_surfMinDepth,-hMixLayer(i,j,bi,bj))
506     surfkz(i,j) = MAX(surfkz(i,j),R_low(i,j,bi,bj))
507     IF(maskC(i,j,1,bi,bj).EQ.0.0) surfkz(i,j)=0.0
508     surfk(i,j) = 0
509 m_bates 1.1 ENDDO
510     ENDDO
511 m_bates 1.4 DO k=1,Nr
512 m_bates 1.1 DO j=1-Oly,sNy+Oly
513     DO i=1-Olx,sNx+Olx
514 m_bates 1.3 IF (rF(k).GT.surfkz(i,j) .AND. surfkz(i,j).GE.rF(k+1))
515     & surfk(i,j) = k
516 m_bates 1.1 ENDDO
517     ENDDO
518     ENDDO
519 m_bates 1.3
520 m_bates 1.1 C Calculate the isopycnal slope
521     DO j=1-Oly,sNy+Oly-1
522     DO i=1-Olx,sNx+Olx-1
523     SlopeX(i,j,1) = zeroRL
524     SlopeY(i,j,1) = zeroRL
525     ENDDO
526     ENDDO
527     DO k=2,Nr
528     DO j=1-Oly+1,sNy+Oly
529     DO i=1-Olx+1,sNx+Olx
530     IF(surfk(i,j).GE.kLowC(i,j,bi,bj)) THEN
531     C If the surface layer is thinner than the water column
532     C the set the slope to zero to avoid problems.
533     SlopeX(i,j,k) = zeroRL
534     SlopeY(i,j,k) = zeroRL
535    
536     ELSE
537     C Calculate the zonal slope at the western cell face (U grid)
538 m_bates 1.4 sigz = MIN( op5*(sigmaR(i,j,k)+sigmaR(i-1,j,k)), maxDRhoDz )
539 m_bates 1.1 sigx = op5*( sigmaX(i,j,k)+sigmaX(i,j,k-1) )
540     slope = sigx/sigz
541     C IF(ABS(slope).GT.GM_K3D_maxSlope)
542     C & slope = SIGN(GM_K3D_maxSlope,slope)
543     IF(ABS(slope).GT.GM_maxSlope)
544     & slope = SIGN(GM_maxSlope,slope)
545     SlopeX(i,j,k)=-maskW(i,j,k-1,bi,bj)*maskW(i,j,k,bi,bj)*slope
546    
547     C Calculate the meridional slope at the southern cell face (V grid)
548 m_bates 1.4 sigz = MIN( op5*(sigmaR(i,j,k)+sigmaR(i,j-1,k)), maxDRhoDz )
549 m_bates 1.1 sigy = op5*( sigmaY(i,j,k) + sigmaY(i,j,k-1) )
550     slope = sigy/sigz
551     C IF(ABS(slope).GT.GM_K3D_maxSlope)
552     C & slope = SIGN(GM_K3D_maxSlope,slope)
553     IF(ABS(slope).GT.GM_maxSlope)
554     & slope = SIGN(GM_maxSlope,slope)
555     SlopeY(i,j,k)=-maskS(i,j,k-1,bi,bj)*maskS(i,j,k,bi,bj)*slope
556     ENDIF
557     ENDDO
558     ENDDO
559     ENDDO
560    
561     C Calculate the thickness flux
562     C Enforce a zero slope bottom boundary condition for the bottom most cells (k=Nr)
563     k=Nr
564     DO j=1-Oly,sNy+Oly
565     DO i=1-Olx,sNx+Olx
566     C Zonal thickness flux at the western cell face
567     tfluxX(i,j,k) = -fCoriU(i,j)*SlopeX(i,j,k)
568     & *recip_drF(k)*recip_hFacW(i,j,k,bi,bj)
569     C Meridional thickness flux at the southern cell face
570     tfluxY(i,j,k) = -fCoriV(i,j)*SlopeY(i,j,k)
571     & *recip_drF(k)*recip_hFacS(i,j,k,bi,bj)
572     ENDDO
573     ENDDO
574    
575     C Calculate the thickness flux for other cells (k<Nr)
576     C SlopeX and SlopeY are zero in dry cells, so, the bottom boundary
577     C condition that the slope is zero is taken care of.
578     C We still need to give special treatment for the surface layer however.
579     DO k=Nr-1,1,-1
580     DO j=1-Oly,sNy+Oly-1
581     DO i=1-Olx,sNx+Olx-1
582 m_bates 1.3 IF(k.LE.surfk(i,j) .AND. .NOT. GM_K3D_likeGM) THEN
583 m_bates 1.1 C We are in the surface layer, so set the thickness flux
584     C based on the average slope over the surface layer
585     C If we are on the edge of a "cliff" the surface layer at the
586     C centre of the grid point could be deeper than the U or V point.
587     C So, we ensure that we always take a sensible slope.
588     IF(kLow_U(i,j).LT.surfk(i,j)) THEN
589     kk=kLow_U(i,j)
590     hsurf = -rLowW(i,j,bi,bj)
591     ELSE
592     kk=surfk(i,j)
593     hsurf = -surfkz(i,j)
594     ENDIF
595     IF(kk.GT.0) THEN
596 m_bates 1.4 IF(kk.EQ.Nr) THEN
597     tfluxX(i,j,k) = -fCoriU(i,j)*maskW(i,j,k,bi,bj)
598     & *SlopeX(i,j,kk)/hsurf
599     ELSE
600     tfluxX(i,j,k) = -fCoriU(i,j)*maskW(i,j,k,bi,bj)
601     & *( SlopeX(i,j,kk)-SlopeX(i,j,kk+1) )/hsurf
602     ENDIF
603 m_bates 1.1 ELSE
604     tfluxX(i,j,k) = zeroRL
605     ENDIF
606    
607     IF(kLow_V(i,j).LT.surfk(i,j)) THEN
608     kk=kLow_V(i,j)
609     hsurf = -rLowS(i,j,bi,bj)
610     ELSE
611     kk=surfk(i,j)
612     hsurf = -surfkz(i,j)
613     ENDIF
614     IF(kk.GT.0) THEN
615 m_bates 1.4 IF(kk.EQ.Nr) THEN
616     tfluxY(i,j,k) = -fCoriV(i,j)*maskS(i,j,k,bi,bj)
617     & *SlopeY(i,j,kk)/hsurf
618     ELSE
619     tfluxY(i,j,k) = -fCoriV(i,j)*maskS(i,j,k,bi,bj)
620     & *( SlopeY(i,j,kk)-SlopeY(i,j,kk+1) )/hsurf
621     ENDIF
622 m_bates 1.1 ELSE
623     tfluxY(i,j,k) = zeroRL
624     ENDIF
625    
626     ELSE
627     C We are not in the surface layer, so calculate the thickness
628     C flux based on the local isopyncal slope
629    
630     C Zonal thickness flux at the western cell face
631     tfluxX(i,j,k)=-fCoriU(i,j)*(SlopeX(i,j,k)-SlopeX(i,j,k+1))
632     & *recip_drF(k)*recip_hFacW(i,j,k,bi,bj)
633     & *maskW(i,j,k,bi,bj)
634    
635     C Meridional thickness flux at the southern cell face
636     tfluxY(i,j,k)=-fCoriV(i,j)*(SlopeY(i,j,k)-SlopeY(i,j,k+1))
637     & *recip_drF(k)*recip_hFacS(i,j,k,bi,bj)
638     & *maskS(i,j,k,bi,bj)
639     ENDIF
640     ENDDO
641     ENDDO
642     ENDDO
643    
644     C Calculate gradq
645 m_bates 1.5 IF (GM_K3D_likeGM .OR. GM_K3D_beta_eq_0) THEN
646     C Ignore beta in the calculation of grad(q)
647 m_bates 1.2 DO k=1,Nr
648     DO j=1-Oly+1,sNy+Oly
649     DO i=1-Olx+1,sNx+Olx
650     gradqx(i,j,k) = maskW(i,j,k,bi,bj)*tfluxX(i,j,k)
651     gradqy(i,j,k) = maskS(i,j,k,bi,bj)*tfluxY(i,j,k)
652     ENDDO
653     ENDDO
654     ENDDO
655    
656     ELSE
657     C Do not ignore beta
658     DO k=1,Nr
659     DO j=1-Oly+1,sNy+Oly
660     DO i=1-Olx+1,sNx+Olx
661     gradqx(i,j,k) = maskW(i,j,k,bi,bj)*(dfdx(i,j)+tfluxX(i,j,k))
662     gradqy(i,j,k) = maskS(i,j,k,bi,bj)*(dfdy(i,j)+tfluxY(i,j,k))
663     ENDDO
664     ENDDO
665 m_bates 1.1 ENDDO
666 m_bates 1.2 ENDIF
667 m_bates 1.1
668     C ======================================
669     C Find Xi and the eddy induced velocities
670     C ======================================
671     C Find the buoyancy frequency at the west and south faces of a cell
672     C This is necessary to find the eigenvectors at those points
673     DO k=1,Nr
674     DO j=1-Oly+1,sNy+Oly
675     DO i=1-Olx+1,sNx+Olx
676     N2W(i,j,k) = maskW(i,j,k,bi,bj)
677     & *( N2(i,j,k)+N2(i-1,j,k) )
678     N2S(i,j,k) = maskS(i,j,k,bi,bj)
679     & *( N2(i,j,k)+N2(i,j-1,k) )
680     ENDDO
681     ENDDO
682     C This fudge is necessary to avoid division by zero in gmredi_calc_eigs.
683     C It does not affect the end result since it's in the overlap region.
684     j=1-Oly
685     DO i=1-Olx,sNx+Olx
686     N2W(i,j,k) = GM_K3D_minN2
687     N2S(i,j,k) = GM_K3D_minN2
688     ENDDO
689     i=1-Olx
690     DO j=1-Oly,sNy+Oly
691     N2W(i,j,k) = GM_K3D_minN2
692     N2S(i,j,k) = GM_K3D_minN2
693     ENDDO
694     ENDDO
695    
696 m_bates 1.2 IF(GM_K3D_likeGM) THEN
697 m_bates 1.3 DO k=1,Nr
698     DO j=1-Oly,sNy+Oly
699     DO i=1-Olx,sNx+Olx
700     KPV(i,j,k) = GM_K3D_constK
701     ENDDO
702 m_bates 1.2 ENDDO
703     ENDDO
704 m_bates 1.3 ELSE
705 m_bates 1.2 DO k=1,Nr
706     DO j=1-Oly,sNy+Oly
707     DO i=1-Olx,sNx+Olx
708 m_bates 1.3 KPV(i,j,k) = K3D(i,j,k,bi,bj)
709 m_bates 1.2 ENDDO
710     ENDDO
711     ENDDO
712 m_bates 1.3 ENDIF
713 m_bates 1.2
714 m_bates 1.3 IF (.NOT. GM_K3D_smooth) THEN
715     C Do not expand K grad(q) => no smoothing
716     C May only be done with a constant K, otherwise the
717     C integral constraint is violated.
718 m_bates 1.2 DO k=1,Nr
719     DO j=1-Oly,sNy+Oly
720     DO i=1-Olx,sNx+Olx
721 m_bates 1.3 Xix(i,j,k) = -maskW(i,j,k,bi,bj)*KPV(i,j,k)*gradqx(i,j,k)
722     Xiy(i,j,k) = -maskS(i,j,k,bi,bj)*KPV(i,j,k)*gradqy(i,j,k)
723 m_bates 1.2 ENDDO
724     ENDDO
725     ENDDO
726    
727     ELSE
728 m_bates 1.3 C Expand K grad(q) in terms of baroclinic modes to smooth
729     C and satisfy the integral constraint
730 m_bates 1.2
731 m_bates 1.1 C Start with the X direction
732     C ------------------------------
733     C Calculate the eigenvectors at the West face of a cell
734 m_bates 1.4 IF (update_modes) THEN
735     CALL GMREDI_CALC_EIGS(
736     I iMin,iMax,jMin,jMax,bi,bj,N2W,myThid,
737     I kLow_U,maskW(:,:,:,bi,bj),
738     I hfacW(:,:,:,bi,bj),recip_hfacW(:,:,:,bi,bj),
739     I rLowW(:,:,bi,bj),GM_K3D_NModes,.FALSE.,
740     O dummy,modesW(:,:,:,:,bi,bj))
741     ENDIF
742 m_bates 1.1
743     C Calculate Xi_m at the west face of a cell
744     DO j=1-Oly,sNy+Oly
745     DO i=1-Olx,sNx+Olx
746     DO m=1,GM_K3D_NModes
747     XimX(m,i,j) = zeroRL
748     ENDDO
749     ENDDO
750     ENDDO
751     DO k=1,Nr
752     DO j=1-Oly,sNy+Oly
753     DO i=1-Olx,sNx+Olx
754     DO m=1,GM_K3D_NModes
755     XimX(m,i,j) = XimX(m,i,j)
756     & - maskW(i,j,k,bi,bj)*drF(k)*hfacW(i,j,k,bi,bj)
757 m_bates 1.4 & *KPV(i,j,k)*gradqx(i,j,k)*modesW(m,i,j,k,bi,bj)
758 m_bates 1.1 ENDDO
759     ENDDO
760     ENDDO
761     ENDDO
762    
763     C Calculate Xi in the X direction at the west face
764     DO k=1,Nr
765     DO j=1-Oly,sNy+Oly
766     DO i=1-Olx,sNx+Olx
767     Xix(i,j,k) = zeroRL
768     ENDDO
769     ENDDO
770     ENDDO
771     DO k=1,Nr
772     DO j=1-Oly,sNy+Oly
773     DO i=1-Olx,sNx+Olx
774     DO m=1,GM_K3D_NModes
775     Xix(i,j,k) = Xix(i,j,k)
776 m_bates 1.4 & + maskW(i,j,k,bi,bj)*XimX(m,i,j)*modesW(m,i,j,k,bi,bj)
777 m_bates 1.1 ENDDO
778     ENDDO
779     ENDDO
780     ENDDO
781    
782     C Now the Y direction
783     C ------------------------------
784     C Calculate the eigenvectors at the West face of a cell
785 m_bates 1.4 IF (update_modes) THEN
786     CALL GMREDI_CALC_EIGS(
787     I iMin,iMax,jMin,jMax,bi,bj,N2S,myThid,
788     I kLow_V,maskS(:,:,:,bi,bj),
789     I hfacS(:,:,:,bi,bj),recip_hfacS(:,:,:,bi,bj),
790     I rLowS(:,:,bi,bj), GM_K3D_NModes, .FALSE.,
791     O dummy,modesS(:,:,:,:,bi,bj))
792     ENDIF
793    
794 m_bates 1.1 DO j=1-Oly,sNy+Oly
795     DO i=1-Olx,sNx+Olx
796     DO m=1,GM_K3D_NModes
797     XimY(m,i,j) = zeroRL
798     ENDDO
799     ENDDO
800     ENDDO
801     DO k=1,Nr
802     DO j=1-Oly,sNy+Oly
803     DO i=1-Olx,sNx+Olx
804     DO m=1,GM_K3D_NModes
805 m_bates 1.3 XimY(m,i,j) = XimY(m,i,j)
806     & - drF(k)*hfacS(i,j,k,bi,bj)
807 m_bates 1.4 & *KPV(i,j,k)*gradqy(i,j,k)*modesS(m,i,j,k,bi,bj)
808 m_bates 1.1 ENDDO
809     ENDDO
810     ENDDO
811     ENDDO
812    
813     C Calculate Xi for Y direction at the south face
814     DO k=1,Nr
815     DO j=1-Oly,sNy+Oly
816     DO i=1-Olx,sNx+Olx
817     Xiy(i,j,k) = zeroRL
818     ENDDO
819     ENDDO
820     ENDDO
821     DO k=1,Nr
822     DO j=1-Oly,sNy+Oly
823     DO i=1-Olx,sNx+Olx
824     DO m=1,GM_K3D_NModes
825     Xiy(i,j,k) = Xiy(i,j,k)
826 m_bates 1.4 & + maskS(i,j,k,bi,bj)*XimY(m,i,j)*modesS(m,i,j,k,bi,bj)
827 m_bates 1.1 ENDDO
828     ENDDO
829     ENDDO
830     ENDDO
831    
832 m_bates 1.3 C ENDIF GM_K3D_likeGM
833 m_bates 1.1 ENDIF
834    
835    
836     C Calculate the eddy induced velocity in the X direction at the west face
837     DO k=1,Nr
838     DO j=1-Oly+1,sNy+Oly
839     DO i=1-Olx+1,sNx+Olx
840     ustar(i,j,k) = -Xix(i,j,k)/coriU(i,j)
841     ENDDO
842     ENDDO
843     ENDDO
844    
845     C Calculate the eddy induced velocity in the Y direction at the south face
846     DO k=1,Nr
847     DO j=1-Oly+1,sNy+Oly
848     DO i=1-Olx+1,sNx+Olx
849     vstar(i,j,k) = -Xiy(i,j,k)/coriV(i,j)
850     ENDDO
851     ENDDO
852     ENDDO
853    
854     C ======================================
855     C Calculate the eddy induced overturning streamfunction
856     C ======================================
857     #ifdef GM_K3D_PASSIVE
858     k=Nr
859     DO j=1-Oly,sNy+Oly
860     DO i=1-Olx,sNx+Olx
861     psistar(i,j,Nr) = -hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k)
862     ENDDO
863     ENDDO
864     DO k=Nr-1,1,-1
865     DO j=1-Oly,sNy+Oly
866     DO i=1-Olx,sNx+Olx
867     psistar(i,j,k) = psistar(i,j,k+1)
868     & - hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k)
869     ENDDO
870     ENDDO
871     ENDDO
872    
873     #else
874    
875     IF (GM_AdvForm) THEN
876     k=Nr
877     DO j=1-Oly+1,sNy+1
878     DO i=1-Olx+1,sNx+1
879     GM_PsiX(i,j,k,bi,bj) = -hfacW(i,j,k,bi,bj)*drF(k)*ustar(i,j,k)
880     GM_PsiY(i,j,k,bi,bj) = -hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k)
881     ENDDO
882     ENDDO
883     DO k=Nr-1,1,-1
884     DO j=1-Oly+1,sNy+1
885     DO i=1-Olx+1,sNx+1
886     GM_PsiX(i,j,k,bi,bj) = GM_PsiX(i,j,k+1,bi,bj)
887     & - hfacW(i,j,k,bi,bj)*drF(k)*ustar(i,j,k)
888     GM_PsiY(i,j,k,bi,bj) = GM_PsiY(i,j,k+1,bi,bj)
889     & - hfacS(i,j,k,bi,bj)*drF(k)*vstar(i,j,k)
890     ENDDO
891     ENDDO
892     ENDDO
893    
894     ENDIF
895     #endif
896    
897     #ifdef ALLOW_DIAGNOSTICS
898     C Diagnostics
899     IF ( useDiagnostics ) THEN
900     CALL DIAGNOSTICS_FILL(K3D, 'GM_K3D ',0,Nr,0,1,1,myThid)
901     CALL DIAGNOSTICS_FILL(urms, 'GM_URMS ',0,Nr,0,1,1,myThid)
902     CALL DIAGNOSTICS_FILL(Rdef, 'GM_RDEF ',0, 1,0,1,1,myThid)
903     CALL DIAGNOSTICS_FILL(RRhines,'GM_LRHNS',0, 1,0,1,1,myThid)
904     CALL DIAGNOSTICS_FILL(Rmix, 'GM_RMIX ',0, 1,0,1,1,myThid)
905     CALL DIAGNOSTICS_FILL(supp, 'GM_SUPP ',0,Nr,0,1,1,myThid)
906     CALL DIAGNOSTICS_FILL(Xix, 'GM_Xix ',0,Nr,0,1,1,myThid)
907     CALL DIAGNOSTICS_FILL(Xiy, 'GM_Xiy ',0,Nr,0,1,1,myThid)
908     CALL DIAGNOSTICS_FILL(cDopp, 'GM_C ',0, 1,0,1,1,myThid)
909     CALL DIAGNOSTICS_FILL(Ubaro, 'GM_UBARO',0, 1,0,1,1,myThid)
910     CALL DIAGNOSTICS_FILL(eady, 'GM_EADY ',0, 1,0,1,1,myThid)
911     CALL DIAGNOSTICS_FILL(SlopeX, 'GM_Sx ',0,Nr,0,1,1,myThid)
912     CALL DIAGNOSTICS_FILL(SlopeY, 'GM_Sy ',0,Nr,0,1,1,myThid)
913     CALL DIAGNOSTICS_FILL(tfluxX, 'GM_TFLXX',0,Nr,0,1,1,myThid)
914     CALL DIAGNOSTICS_FILL(tfluxY, 'GM_TFLXY',0,Nr,0,1,1,myThid)
915     CALL DIAGNOSTICS_FILL(gradqx, 'GM_dqdx ',0,Nr,0,1,1,myThid)
916     CALL DIAGNOSTICS_FILL(gradqy, 'GM_dqdy ',0,Nr,0,1,1,myThid)
917     CALL DIAGNOSTICS_FILL(surfkz, 'GM_SFLYR',0, 1,0,1,1,myThid)
918     CALL DIAGNOSTICS_FILL(ustar, 'GM_USTAR',0,Nr,0,1,1,myThid)
919     CALL DIAGNOSTICS_FILL(vstar, 'GM_VSTAR',0,Nr,0,1,1,myThid)
920     CALL DIAGNOSTICS_FILL(umc, 'GM_UMC ',0,Nr,0,1,1,myThid)
921     CALL DIAGNOSTICS_FILL(ubar, 'GM_UBAR ',0,Nr,0,1,1,myThid)
922 m_bates 1.4 CALL DIAGNOSTICS_FILL(modesC(1,:,:,:,bi,bj),
923     & 'GM_MODEC',0,Nr,0,1,1,myThid)
924 m_bates 1.1 ENDIF
925     #endif
926    
927     #endif /* GM_K3D */
928     RETURN
929     END
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