1 |
C $Header: /u/ralf/cvs/MITgcmUV/pkg/kpp/kpp_routines.F,v 1.4 2000/11/13 16:37:02 heimbach Exp $ |
2 |
|
3 |
#include "KPP_OPTIONS.h" |
4 |
|
5 |
C-- File kpp_routines.F: subroutines needed to implement |
6 |
C-- KPP vertical mixing scheme |
7 |
C-- Contents |
8 |
C-- o KPPMIX - Main driver and interface routine. |
9 |
C-- o BLDEPTH - Determine oceanic planetary boundary layer depth. |
10 |
C-- o WSCALE - Compute turbulent velocity scales. |
11 |
C-- o RI_IWMIX - Compute interior viscosity diffusivity coefficients. |
12 |
C-- o Z121 - Apply 121 vertical smoothing. |
13 |
C-- o KPP_SMOOTH_HORIZ - Apply horizontal smoothing to KPP array. |
14 |
C-- o SMOOTH_HORIZ - Apply horizontal smoothing to global array. |
15 |
C-- o BLMIX - Boundary layer mixing coefficients. |
16 |
C-- o ENHANCE - Enhance diffusivity at boundary layer interface. |
17 |
C-- o STATEKPP - Compute buoyancy-related input arrays. |
18 |
|
19 |
c*********************************************************************** |
20 |
|
21 |
SUBROUTINE KPPMIX ( |
22 |
I mytime, mythid |
23 |
I , kmtj, shsq, dvsq, ustar |
24 |
I , bo, bosol, dbloc, Ritop, coriol |
25 |
I , ikey |
26 |
O , diffus |
27 |
U , ghat |
28 |
O , hbl ) |
29 |
|
30 |
c----------------------------------------------------------------------- |
31 |
c |
32 |
c Main driver subroutine for kpp vertical mixing scheme and |
33 |
c interface to greater ocean model |
34 |
c |
35 |
c written by: bill large, june 6, 1994 |
36 |
c modified by: jan morzel, june 30, 1994 |
37 |
c bill large, august 11, 1994 |
38 |
c bill large, january 25, 1995 : "dVsq" and 1d code |
39 |
c detlef stammer, august 1997 : for use with MIT GCM Classic |
40 |
c d. menemenlis, june 1998 : for use with MIT GCM UV |
41 |
c |
42 |
c----------------------------------------------------------------------- |
43 |
|
44 |
IMPLICIT NONE |
45 |
|
46 |
#include "SIZE.h" |
47 |
#include "EEPARAMS.h" |
48 |
#include "PARAMS.h" |
49 |
#include "DYNVARS.h" |
50 |
#include "FFIELDS.h" |
51 |
#include "KPP_PARAMS.h" |
52 |
|
53 |
c input |
54 |
c myTime - current time in simulation |
55 |
c myThid - thread number for this instance of the routine |
56 |
c kmtj (imt) - number of vertical layers on this row |
57 |
c shsq (imt,Nr) - (local velocity shear)^2 ((m/s)^2) |
58 |
c dvsq (imt,Nr) - (velocity shear re sfc)^2 ((m/s)^2) |
59 |
c ustar (imt) - surface friction velocity (m/s) |
60 |
c bo (imt) - surface turbulent buoy. forcing (m^2/s^3) |
61 |
c bosol (imt) - radiative buoyancy forcing (m^2/s^3) |
62 |
c dbloc (imt,Nr) - local delta buoyancy across interfaces (m/s^2) |
63 |
c dblocSm(imt,Nr) - horizontally smoothed dbloc (m/s^2) |
64 |
c stored in ghat to save space |
65 |
c Ritop (imt,Nr) - numerator of bulk Richardson Number |
66 |
c (zref-z) * delta buoyancy w.r.t. surface ((m/s)^2) |
67 |
c coriol (imt) - Coriolis parameter (1/s) |
68 |
c note: there is a conversion from 2-D to 1-D for input output variables, |
69 |
c e.g., hbl(sNx,sNy) -> hbl(imt), |
70 |
c where hbl(i,j) -> hbl((j-1)*sNx+i) |
71 |
|
72 |
_RL mytime |
73 |
integer mythid |
74 |
integer kmtj (imt ) |
75 |
_KPP_RL shsq (imt,Nr) |
76 |
_KPP_RL dvsq (imt,Nr) |
77 |
_KPP_RL ustar (imt ) |
78 |
_KPP_RL bo (imt ) |
79 |
_KPP_RL bosol (imt ) |
80 |
_KPP_RL dbloc (imt,Nr) |
81 |
_KPP_RL Ritop (imt,Nr) |
82 |
_KPP_RL coriol(imt ) |
83 |
|
84 |
integer ikey |
85 |
|
86 |
c output |
87 |
c diffus (imt,1) - vertical viscosity coefficient (m^2/s) |
88 |
c diffus (imt,2) - vertical scalar diffusivity (m^2/s) |
89 |
c diffus (imt,3) - vertical temperature diffusivity (m^2/s) |
90 |
c ghat (imt) - nonlocal transport coefficient (s/m^2) |
91 |
c hbl (imt) - mixing layer depth (m) |
92 |
|
93 |
_KPP_RL diffus(imt,0:Nrp1,mdiff) |
94 |
_KPP_RL ghat (imt,Nr) |
95 |
_KPP_RL hbl (imt) |
96 |
|
97 |
#ifdef ALLOW_KPP |
98 |
|
99 |
c local |
100 |
c kbl (imt ) - index of first grid level below hbl |
101 |
c bfsfc (imt ) - surface buoyancy forcing (m^2/s^3) |
102 |
c casea (imt ) - 1 in case A; 0 in case B |
103 |
c stable (imt ) - 1 in stable forcing; 0 if unstable |
104 |
c dkm1 (imt, mdiff) - boundary layer diffusivity at kbl-1 level |
105 |
c blmc (imt,Nr,mdiff) - boundary layer mixing coefficients |
106 |
c sigma (imt ) - normalized depth (d / hbl) |
107 |
c Rib (imt,Nr ) - bulk Richardson number |
108 |
|
109 |
integer kbl (imt ) |
110 |
_KPP_RL bfsfc (imt ) |
111 |
_KPP_RL casea (imt ) |
112 |
_KPP_RL stable(imt ) |
113 |
_KPP_RL dkm1 (imt, mdiff) |
114 |
_KPP_RL blmc (imt,Nr,mdiff) |
115 |
_KPP_RL sigma (imt ) |
116 |
_KPP_RL Rib (imt,Nr ) |
117 |
|
118 |
integer i, k, md |
119 |
|
120 |
c----------------------------------------------------------------------- |
121 |
c compute interior mixing coefficients everywhere, due to constant |
122 |
c internal wave activity, static instability, and local shear |
123 |
c instability. |
124 |
c (ghat is temporary storage for horizontally smoothed dbloc) |
125 |
c----------------------------------------------------------------------- |
126 |
|
127 |
CADJ STORE ghat = comlev1_kpp, key = ikey |
128 |
|
129 |
call Ri_iwmix ( |
130 |
I kmtj, shsq, dbloc, ghat |
131 |
I , ikey |
132 |
O , diffus ) |
133 |
|
134 |
c----------------------------------------------------------------------- |
135 |
c set seafloor values to zero and fill extra "Nrp1" coefficients |
136 |
c for blmix |
137 |
c----------------------------------------------------------------------- |
138 |
|
139 |
do md = 1, mdiff |
140 |
do i = 1,imt |
141 |
do k=kmtj(i),Nrp1 |
142 |
diffus(i,k,md) = 0.0 |
143 |
end do |
144 |
end do |
145 |
end do |
146 |
|
147 |
c----------------------------------------------------------------------- |
148 |
c compute boundary layer mixing coefficients: |
149 |
c |
150 |
c diagnose the new boundary layer depth |
151 |
c----------------------------------------------------------------------- |
152 |
|
153 |
call bldepth ( |
154 |
I mytime, mythid |
155 |
I , kmtj |
156 |
I , dvsq, dbloc, Ritop, ustar, bo, bosol, coriol |
157 |
I , ikey |
158 |
O , hbl, bfsfc, stable, casea, kbl, Rib, sigma |
159 |
& ) |
160 |
|
161 |
CADJ STORE hbl,bfsfc,stable,casea,kbl = comlev1_kpp, key = ikey |
162 |
|
163 |
c----------------------------------------------------------------------- |
164 |
c compute boundary layer diffusivities |
165 |
c----------------------------------------------------------------------- |
166 |
|
167 |
call blmix ( |
168 |
I ustar, bfsfc, hbl, stable, casea, diffus, kbl |
169 |
O , dkm1, blmc, ghat, sigma, ikey |
170 |
& ) |
171 |
|
172 |
CADJ STORE dkm1,blmc,ghat = comlev1_kpp, key = ikey |
173 |
|
174 |
c----------------------------------------------------------------------- |
175 |
c enhance diffusivity at interface kbl - 1 |
176 |
c----------------------------------------------------------------------- |
177 |
|
178 |
call enhance ( |
179 |
I dkm1, hbl, kbl, diffus, casea |
180 |
U , ghat |
181 |
O , blmc ) |
182 |
|
183 |
c----------------------------------------------------------------------- |
184 |
c combine interior and boundary layer coefficients and nonlocal term |
185 |
c----------------------------------------------------------------------- |
186 |
|
187 |
do k = 1, Nr |
188 |
do i = 1, imt |
189 |
if (k .lt. kbl(i)) then |
190 |
do md = 1, mdiff |
191 |
diffus(i,k,md) = blmc(i,k,md) |
192 |
end do |
193 |
else |
194 |
ghat(i,k) = 0. |
195 |
endif |
196 |
end do |
197 |
end do |
198 |
|
199 |
#endif /* ALLOW_KPP */ |
200 |
|
201 |
return |
202 |
end |
203 |
|
204 |
c************************************************************************* |
205 |
|
206 |
subroutine bldepth ( |
207 |
I mytime, mythid |
208 |
I , kmtj |
209 |
I , dvsq, dbloc, Ritop, ustar, bo, bosol, coriol |
210 |
I , ikey |
211 |
O , hbl, bfsfc, stable, casea, kbl, Rib, sigma |
212 |
& ) |
213 |
|
214 |
c the oceanic planetary boundary layer depth, hbl, is determined as |
215 |
c the shallowest depth where the bulk Richardson number is |
216 |
c equal to the critical value, Ricr. |
217 |
c |
218 |
c bulk Richardson numbers are evaluated by computing velocity and |
219 |
c buoyancy differences between values at zgrid(kl) < 0 and surface |
220 |
c reference values. |
221 |
c in this configuration, the reference values are equal to the |
222 |
c values in the surface layer. |
223 |
c when using a very fine vertical grid, these values should be |
224 |
c computed as the vertical average of velocity and buoyancy from |
225 |
c the surface down to epsilon*zgrid(kl). |
226 |
c |
227 |
c when the bulk Richardson number at k exceeds Ricr, hbl is |
228 |
c linearly interpolated between grid levels zgrid(k) and zgrid(k-1). |
229 |
c |
230 |
c The water column and the surface forcing are diagnosed for |
231 |
c stable/ustable forcing conditions, and where hbl is relative |
232 |
c to grid points (caseA), so that conditional branches can be |
233 |
c avoided in later subroutines. |
234 |
c |
235 |
IMPLICIT NONE |
236 |
|
237 |
#include "SIZE.h" |
238 |
#include "EEPARAMS.h" |
239 |
#include "PARAMS.h" |
240 |
#include "KPP_PARAMS.h" |
241 |
#include "FFIELDS.h" |
242 |
|
243 |
c input |
244 |
c------ |
245 |
c myTime : current time in simulation |
246 |
c myThid : thread number for this instance of the routine |
247 |
c kmtj : number of vertical layers |
248 |
c dvsq : (velocity shear re sfc)^2 ((m/s)^2) |
249 |
c dbloc : local delta buoyancy across interfaces (m/s^2) |
250 |
c Ritop : numerator of bulk Richardson Number |
251 |
c =(z-zref)*dbsfc, where dbsfc=delta |
252 |
c buoyancy with respect to surface ((m/s)^2) |
253 |
c ustar : surface friction velocity (m/s) |
254 |
c bo : surface turbulent buoyancy forcing (m^2/s^3) |
255 |
c bosol : radiative buoyancy forcing (m^2/s^3) |
256 |
c coriol : Coriolis parameter (1/s) |
257 |
_RL mytime |
258 |
integer mythid |
259 |
integer kmtj(imt) |
260 |
_KPP_RL dvsq (imt,Nr) |
261 |
_KPP_RL dbloc (imt,Nr) |
262 |
_KPP_RL Ritop (imt,Nr) |
263 |
_KPP_RL ustar (imt) |
264 |
_KPP_RL bo (imt) |
265 |
_KPP_RL bosol (imt) |
266 |
_KPP_RL coriol(imt) |
267 |
integer ikey |
268 |
|
269 |
c output |
270 |
c-------- |
271 |
c hbl : boundary layer depth (m) |
272 |
c bfsfc : Bo+radiation absorbed to d=hbf*hbl (m^2/s^3) |
273 |
c stable : =1 in stable forcing; =0 unstable |
274 |
c casea : =1 in case A, =0 in case B |
275 |
c kbl : -1 of first grid level below hbl |
276 |
c Rib : Bulk Richardson number |
277 |
c sigma : normalized depth (d/hbl) |
278 |
_KPP_RL hbl (imt) |
279 |
_KPP_RL bfsfc (imt) |
280 |
_KPP_RL stable(imt) |
281 |
_KPP_RL casea (imt) |
282 |
integer kbl (imt) |
283 |
_KPP_RL Rib (imt,Nr) |
284 |
_KPP_RL sigma (imt) |
285 |
|
286 |
#ifdef ALLOW_KPP |
287 |
|
288 |
c local |
289 |
c------- |
290 |
c wm, ws : turbulent velocity scales (m/s) |
291 |
_KPP_RL wm(imt), ws(imt) |
292 |
_RL worka(imt) |
293 |
|
294 |
_KPP_RL bvsq, vtsq, hekman, hmonob, hlimit, tempVar1, tempVar2 |
295 |
integer i, kl |
296 |
|
297 |
_KPP_RL p5 , eins |
298 |
parameter ( p5=0.5, eins=1.0 ) |
299 |
_RL minusone |
300 |
parameter ( minusone=-1.0 ) |
301 |
|
302 |
c find bulk Richardson number at every grid level until > Ricr |
303 |
c |
304 |
c note: the reference depth is -epsilon/2.*zgrid(k), but the reference |
305 |
c u,v,t,s values are simply the surface layer values, |
306 |
c and not the averaged values from 0 to 2*ref.depth, |
307 |
c which is necessary for very fine grids(top layer < 2m thickness) |
308 |
c note: max values when Ricr never satisfied are |
309 |
c kbl(i)=kmtj(i) and hbl(i)=-zgrid(kmtj(i)) |
310 |
|
311 |
c initialize hbl and kbl to bottomed out values |
312 |
|
313 |
do i = 1, imt |
314 |
Rib(i,1) = 0.0 |
315 |
kbl(i) = max(kmtj(i),1) |
316 |
hbl(i) = -zgrid(kbl(i)) |
317 |
end do |
318 |
|
319 |
do kl = 2, Nr |
320 |
|
321 |
c compute bfsfc = sw fraction at hbf * zgrid |
322 |
|
323 |
do i = 1, imt |
324 |
worka(i) = zgrid(kl) |
325 |
end do |
326 |
call SWFRAC( |
327 |
I imt, hbf, |
328 |
I mytime, mythid, |
329 |
U worka ) |
330 |
|
331 |
do i = 1, imt |
332 |
|
333 |
c use caseA as temporary array |
334 |
|
335 |
casea(i) = -zgrid(kl) |
336 |
|
337 |
c compute bfsfc= Bo + radiative contribution down to hbf * hbl |
338 |
|
339 |
bfsfc(i) = bo(i) + bosol(i)*(1. - worka(i)) |
340 |
stable(i) = p5 + sign(p5,bfsfc(i)) |
341 |
sigma(i) = stable(i) + (1. - stable(i)) * epsilon |
342 |
|
343 |
end do |
344 |
|
345 |
c----------------------------------------------------------------------- |
346 |
c compute velocity scales at sigma, for hbl= caseA = -zgrid(kl) |
347 |
c----------------------------------------------------------------------- |
348 |
|
349 |
call wscale ( |
350 |
I sigma, casea, ustar, bfsfc, |
351 |
O wm, ws ) |
352 |
|
353 |
do i = 1, imt |
354 |
|
355 |
c----------------------------------------------------------------------- |
356 |
c compute the turbulent shear contribution to Rib |
357 |
c----------------------------------------------------------------------- |
358 |
|
359 |
bvsq = p5 * |
360 |
1 ( dbloc(i,kl-1) / (zgrid(kl-1)-zgrid(kl ))+ |
361 |
2 dbloc(i,kl ) / (zgrid(kl )-zgrid(kl+1))) |
362 |
|
363 |
if (bvsq .eq. 0.) then |
364 |
vtsq = 0.0 |
365 |
else |
366 |
vtsq = -zgrid(kl) * ws(i) * sqrt(abs(bvsq)) * Vtc |
367 |
endif |
368 |
|
369 |
c compute bulk Richardson number at new level |
370 |
c note: Ritop needs to be zero on land and ocean bottom |
371 |
c points so that the following if statement gets triggered |
372 |
c correctly; otherwise, hbl might get set to (big) negative |
373 |
c values, that might exceed the limit for the "exp" function |
374 |
c in "SWFRAC" |
375 |
|
376 |
c |
377 |
c rg: assignment to double precision variable to avoid overflow |
378 |
c ph: test for zero nominator |
379 |
c |
380 |
|
381 |
tempVar1 = dvsq(i,kl) + vtsq |
382 |
tempVar2 = max(tempVar1, phepsi) |
383 |
Rib(i,kl) = Ritop(i,kl) / tempVar2 |
384 |
|
385 |
end do |
386 |
end do |
387 |
|
388 |
do kl = 2, Nr |
389 |
do i = 1, imt |
390 |
if (kbl(i).eq.kmtj(i) .and. Rib(i,kl).gt.Ricr) kbl(i) = kl |
391 |
end do |
392 |
end do |
393 |
|
394 |
CADJ store kbl = comlev1_kpp |
395 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
396 |
|
397 |
do i = 1, imt |
398 |
kl = kbl(i) |
399 |
c linearly interpolate to find hbl where Rib = Ricr |
400 |
if (kl.gt.1 .and. kl.lt.kmtj(i)) then |
401 |
tempVar1 = (Rib(i,kl)-Rib(i,kl-1)) |
402 |
hbl(i) = -zgrid(kl-1) + (zgrid(kl-1)-zgrid(kl)) * |
403 |
1 (Ricr - Rib(i,kl-1)) / tempVar1 |
404 |
endif |
405 |
end do |
406 |
|
407 |
CADJ store hbl = comlev1_kpp |
408 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
409 |
|
410 |
c----------------------------------------------------------------------- |
411 |
c find stability and buoyancy forcing for boundary layer |
412 |
c----------------------------------------------------------------------- |
413 |
|
414 |
do i = 1, imt |
415 |
worka(i) = hbl(i) |
416 |
end do |
417 |
call SWFRAC( |
418 |
I imt, minusone, |
419 |
I mytime, mythid, |
420 |
U worka ) |
421 |
|
422 |
do i = 1, imt |
423 |
bfsfc(i) = bo(i) + bosol(i) * (1. - worka(i)) |
424 |
end do |
425 |
CADJ store bfsfc = comlev1_kpp |
426 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
427 |
|
428 |
c-- ensure bfsfc is never 0 |
429 |
do i = 1, imt |
430 |
stable(i) = p5 + sign( p5, bfsfc(i) ) |
431 |
bfsfc(i) = sign(eins,bfsfc(i))*max(phepsi,abs(bfsfc(i))) |
432 |
end do |
433 |
|
434 |
CADJ store bfsfc = comlev1_kpp |
435 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
436 |
|
437 |
c----------------------------------------------------------------------- |
438 |
c check hbl limits for hekman or hmonob |
439 |
c ph: test for zero nominator |
440 |
c----------------------------------------------------------------------- |
441 |
|
442 |
do i = 1, imt |
443 |
if (bfsfc(i) .gt. 0.0) then |
444 |
hekman = cekman * ustar(i) / max(abs(Coriol(i)),phepsi) |
445 |
hmonob = cmonob * ustar(i)*ustar(i)*ustar(i) |
446 |
& / vonk / bfsfc(i) |
447 |
hlimit = stable(i) * min(hekman,hmonob) |
448 |
& + (stable(i)-1.) * zgrid(Nr) |
449 |
hbl(i) = min(hbl(i),hlimit) |
450 |
end if |
451 |
end do |
452 |
CADJ store hbl = comlev1_kpp |
453 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
454 |
|
455 |
do i = 1, imt |
456 |
hbl(i) = max(hbl(i),minKPPhbl) |
457 |
kbl(i) = kmtj(i) |
458 |
end do |
459 |
|
460 |
CADJ store hbl = comlev1_kpp |
461 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
462 |
|
463 |
c----------------------------------------------------------------------- |
464 |
c find new kbl |
465 |
c----------------------------------------------------------------------- |
466 |
|
467 |
do kl = 2, Nr |
468 |
do i = 1, imt |
469 |
if ( kbl(i).eq.kmtj(i) .and. (-zgrid(kl)).gt.hbl(i) ) then |
470 |
kbl(i) = kl |
471 |
endif |
472 |
end do |
473 |
end do |
474 |
|
475 |
c----------------------------------------------------------------------- |
476 |
c find stability and buoyancy forcing for final hbl values |
477 |
c----------------------------------------------------------------------- |
478 |
|
479 |
do i = 1, imt |
480 |
worka(i) = hbl(i) |
481 |
end do |
482 |
call SWFRAC( |
483 |
I imt, minusone, |
484 |
I mytime, mythid, |
485 |
U worka ) |
486 |
|
487 |
do i = 1, imt |
488 |
bfsfc(i) = bo(i) + bosol(i) * (1. - worka(i)) |
489 |
end do |
490 |
CADJ store bfsfc = comlev1_kpp |
491 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
492 |
|
493 |
c-- ensures bfsfc is never 0 |
494 |
do i = 1, imt |
495 |
stable(i) = p5 + sign( p5, bfsfc(i) ) |
496 |
bfsfc(i) = sign(eins,bfsfc(i))*max(phepsi,abs(bfsfc(i))) |
497 |
end do |
498 |
|
499 |
c----------------------------------------------------------------------- |
500 |
c determine caseA and caseB |
501 |
c----------------------------------------------------------------------- |
502 |
|
503 |
do i = 1, imt |
504 |
casea(i) = p5 + |
505 |
1 sign(p5, -zgrid(kbl(i)) - p5*hwide(kbl(i)) - hbl(i)) |
506 |
end do |
507 |
|
508 |
#endif /* ALLOW_KPP */ |
509 |
|
510 |
return |
511 |
end |
512 |
|
513 |
c************************************************************************* |
514 |
|
515 |
subroutine wscale ( |
516 |
I sigma, hbl, ustar, bfsfc, |
517 |
O wm, ws ) |
518 |
|
519 |
c compute turbulent velocity scales. |
520 |
c use a 2D-lookup table for wm and ws as functions of ustar and |
521 |
c zetahat (=vonk*sigma*hbl*bfsfc). |
522 |
c |
523 |
c note: the lookup table is only used for unstable conditions |
524 |
c (zehat.le.0), in the stable domain wm (=ws) gets computed |
525 |
c directly. |
526 |
c |
527 |
IMPLICIT NONE |
528 |
|
529 |
#include "SIZE.h" |
530 |
#include "KPP_PARAMS.h" |
531 |
|
532 |
c input |
533 |
c------ |
534 |
c sigma : normalized depth (d/hbl) |
535 |
c hbl : boundary layer depth (m) |
536 |
c ustar : surface friction velocity (m/s) |
537 |
c bfsfc : total surface buoyancy flux (m^2/s^3) |
538 |
_KPP_RL sigma(imt) |
539 |
_KPP_RL hbl (imt) |
540 |
_KPP_RL ustar(imt) |
541 |
_KPP_RL bfsfc(imt) |
542 |
|
543 |
c output |
544 |
c-------- |
545 |
c wm, ws : turbulent velocity scales at sigma |
546 |
_KPP_RL wm(imt), ws(imt) |
547 |
|
548 |
#ifdef ALLOW_KPP |
549 |
|
550 |
c local |
551 |
c------ |
552 |
c zehat : = zeta * ustar**3 |
553 |
_KPP_RL zehat |
554 |
|
555 |
integer iz, izp1, ju, i, jup1 |
556 |
_KPP_RL udiff, zdiff, zfrac, ufrac, fzfrac, wam |
557 |
_KPP_RL wbm, was, wbs, u3, tempVar |
558 |
|
559 |
c----------------------------------------------------------------------- |
560 |
c use lookup table for zehat < zmax only; otherwise use |
561 |
c stable formulae |
562 |
c----------------------------------------------------------------------- |
563 |
|
564 |
do i = 1, imt |
565 |
zehat = vonk*sigma(i)*hbl(i)*bfsfc(i) |
566 |
|
567 |
if (zehat .le. zmax) then |
568 |
|
569 |
zdiff = zehat - zmin |
570 |
iz = int( zdiff / deltaz ) |
571 |
iz = min( iz, nni ) |
572 |
iz = max( iz, 0 ) |
573 |
izp1 = iz + 1 |
574 |
|
575 |
udiff = ustar(i) - umin |
576 |
ju = int( udiff / deltau ) |
577 |
ju = min( ju, nnj ) |
578 |
ju = max( ju, 0 ) |
579 |
jup1 = ju + 1 |
580 |
|
581 |
zfrac = zdiff / deltaz - float(iz) |
582 |
ufrac = udiff / deltau - float(ju) |
583 |
|
584 |
fzfrac= 1. - zfrac |
585 |
wam = fzfrac * wmt(iz,jup1) + zfrac * wmt(izp1,jup1) |
586 |
wbm = fzfrac * wmt(iz,ju ) + zfrac * wmt(izp1,ju ) |
587 |
wm(i) = (1.-ufrac) * wbm + ufrac * wam |
588 |
|
589 |
was = fzfrac * wst(iz,jup1) + zfrac * wst(izp1,jup1) |
590 |
wbs = fzfrac * wst(iz,ju ) + zfrac * wst(izp1,ju ) |
591 |
ws(i) = (1.-ufrac) * wbs + ufrac * was |
592 |
|
593 |
else |
594 |
|
595 |
u3 = ustar(i) * ustar(i) * ustar(i) |
596 |
tempVar = u3 + conc1 * zehat |
597 |
wm(i) = vonk * ustar(i) * u3 / tempVar |
598 |
ws(i) = wm(i) |
599 |
|
600 |
endif |
601 |
|
602 |
end do |
603 |
|
604 |
#endif /* ALLOW_KPP */ |
605 |
|
606 |
return |
607 |
end |
608 |
|
609 |
c************************************************************************* |
610 |
|
611 |
subroutine Ri_iwmix ( |
612 |
I kmtj, shsq, dbloc, dblocSm |
613 |
I , ikey |
614 |
O , diffus ) |
615 |
|
616 |
c compute interior viscosity diffusivity coefficients due |
617 |
c to shear instability (dependent on a local Richardson number), |
618 |
c to background internal wave activity, and |
619 |
c to static instability (local Richardson number < 0). |
620 |
|
621 |
IMPLICIT NONE |
622 |
|
623 |
#include "SIZE.h" |
624 |
#include "EEPARAMS.h" |
625 |
#include "PARAMS.h" |
626 |
#include "KPP_PARAMS.h" |
627 |
|
628 |
c input |
629 |
c kmtj (imt) number of vertical layers on this row |
630 |
c shsq (imt,Nr) (local velocity shear)^2 ((m/s)^2) |
631 |
c dbloc (imt,Nr) local delta buoyancy (m/s^2) |
632 |
c dblocSm(imt,Nr) horizontally smoothed dbloc (m/s^2) |
633 |
integer kmtj (imt) |
634 |
_KPP_RL shsq (imt,Nr) |
635 |
_KPP_RL dbloc (imt,Nr) |
636 |
_KPP_RL dblocSm(imt,Nr) |
637 |
integer ikey |
638 |
|
639 |
c output |
640 |
c diffus(imt,0:Nrp1,1) vertical viscosivity coefficient (m^2/s) |
641 |
c diffus(imt,0:Nrp1,2) vertical scalar diffusivity (m^2/s) |
642 |
c diffus(imt,0:Nrp1,3) vertical temperature diffusivity (m^2/s) |
643 |
_KPP_RL diffus(imt,0:Nrp1,3) |
644 |
|
645 |
#ifdef ALLOW_KPP |
646 |
|
647 |
c local variables |
648 |
c Rig local Richardson number |
649 |
c fRi, fcon function of Rig |
650 |
_KPP_RL Rig |
651 |
_KPP_RL fRi, fcon |
652 |
_KPP_RL ratio |
653 |
integer i, ki, mr |
654 |
_KPP_RL c1, c0 |
655 |
|
656 |
#ifdef ALLOW_KPP_VERTICALLY_SMOOTH |
657 |
CADJ INIT kpp_ri_tape_mr = common, 1 |
658 |
#endif |
659 |
|
660 |
c constants |
661 |
c1 = 1.0 |
662 |
c0 = 0.0 |
663 |
|
664 |
c----------------------------------------------------------------------- |
665 |
c compute interior gradient Ri at all interfaces ki=1,Nr, (not surface) |
666 |
c use diffus(*,*,1) as temporary storage of Ri to be smoothed |
667 |
c use diffus(*,*,2) as temporary storage for Brunt-Vaisala squared |
668 |
c set values at bottom and below to nearest value above bottom |
669 |
#ifdef ALLOW_AUTODIFF_TAMC |
670 |
C break data flow dependence on diffus |
671 |
diffus(1,1,1) = 0.0 |
672 |
#endif |
673 |
|
674 |
do ki = 1, Nr |
675 |
do i = 1, imt |
676 |
if (kmtj(i) .EQ. 0 ) then |
677 |
diffus(i,ki,1) = 0. |
678 |
diffus(i,ki,2) = 0. |
679 |
elseif (ki .GE. kmtj(i)) then |
680 |
diffus(i,ki,1) = diffus(i,ki-1,1) |
681 |
diffus(i,ki,2) = diffus(i,ki-1,2) |
682 |
else |
683 |
diffus(i,ki,1) = dblocSm(i,ki) * (zgrid(ki)-zgrid(ki+1)) |
684 |
& / max( Shsq(i,ki), phepsi ) |
685 |
diffus(i,ki,2) = dbloc(i,ki) / (zgrid(ki)-zgrid(ki+1)) |
686 |
endif |
687 |
end do |
688 |
end do |
689 |
|
690 |
c----------------------------------------------------------------------- |
691 |
c vertically smooth Ri |
692 |
#ifdef ALLOW_KPP_VERTICALLY_SMOOTH |
693 |
do mr = 1, num_v_smooth_Ri |
694 |
|
695 |
CADJ store diffus(:,:,1) = kpp_ri_tape_mr |
696 |
CADJ & , key=mr, shape=(/ (sNx+2*OLx)*(sNy+2*OLy),Nr+2 /) |
697 |
|
698 |
call z121 ( |
699 |
U diffus(1,0,1)) |
700 |
end do |
701 |
#endif |
702 |
|
703 |
c----------------------------------------------------------------------- |
704 |
c after smoothing loop |
705 |
|
706 |
do ki = 1, Nr |
707 |
do i = 1, imt |
708 |
|
709 |
c evaluate f of Brunt-Vaisala squared for convection, store in fcon |
710 |
|
711 |
Rig = max ( diffus(i,ki,2) , BVSQcon ) |
712 |
ratio = min ( (BVSQcon - Rig) / BVSQcon, c1 ) |
713 |
fcon = c1 - ratio * ratio |
714 |
fcon = fcon * fcon * fcon |
715 |
|
716 |
c evaluate f of smooth Ri for shear instability, store in fRi |
717 |
|
718 |
Rig = max ( diffus(i,ki,1), c0 ) |
719 |
ratio = min ( Rig / Riinfty , c1 ) |
720 |
fRi = c1 - ratio * ratio |
721 |
fRi = fRi * fRi * fRi |
722 |
|
723 |
c ---------------------------------------------------------------------- |
724 |
c evaluate diffusivities and viscosity |
725 |
c mixing due to internal waves, and shear and static instability |
726 |
|
727 |
diffus(i,ki,1) = viscAr + fcon * difmcon + fRi * difm0 |
728 |
diffus(i,ki,2) = diffKrS + fcon * difscon + fRi * difs0 |
729 |
diffus(i,ki,3) = diffKrT + fcon * difscon + fRi * difs0 |
730 |
|
731 |
end do |
732 |
end do |
733 |
|
734 |
c ------------------------------------------------------------------------ |
735 |
c set surface values to 0.0 |
736 |
|
737 |
do i = 1, imt |
738 |
diffus(i,0,1) = c0 |
739 |
diffus(i,0,2) = c0 |
740 |
diffus(i,0,3) = c0 |
741 |
end do |
742 |
|
743 |
#endif /* ALLOW_KPP */ |
744 |
|
745 |
return |
746 |
end |
747 |
|
748 |
c************************************************************************* |
749 |
|
750 |
subroutine z121 ( |
751 |
U v ) |
752 |
|
753 |
c Apply 121 smoothing in k to 2-d array V(i,k=1,Nr) |
754 |
c top (0) value is used as a dummy |
755 |
c bottom (Nrp1) value is set to input value from above. |
756 |
|
757 |
c Note that it is important to exclude from the smoothing any points |
758 |
c that are outside the range of the K(Ri) scheme, ie. >0.8, or <0.0. |
759 |
c Otherwise, there is interference with other physics, especially |
760 |
c penetrative convection. |
761 |
|
762 |
IMPLICIT NONE |
763 |
#include "SIZE.h" |
764 |
#include "KPP_PARAMS.h" |
765 |
|
766 |
c input/output |
767 |
c------------- |
768 |
c v : 2-D array to be smoothed in Nrp1 direction |
769 |
_KPP_RL v(imt,0:Nrp1) |
770 |
|
771 |
#ifdef ALLOW_KPP |
772 |
|
773 |
c local |
774 |
_KPP_RL zwork, zflag |
775 |
_KPP_RL KRi_range(1:Nrp1) |
776 |
integer i, k, km1, kp1 |
777 |
|
778 |
_KPP_RL p0 , p25 , p5 , p2 |
779 |
parameter ( p0 = 0.0, p25 = 0.25, p5 = 0.5, p2 = 2.0 ) |
780 |
|
781 |
KRi_range(Nrp1) = p0 |
782 |
|
783 |
#ifdef ALLOW_AUTODIFF_TAMC |
784 |
C-- dummy assignment to end declaration part for TAMC |
785 |
i = 0 |
786 |
|
787 |
C-- HPF directive to help TAMC |
788 |
CHPF$ INDEPENDENT |
789 |
CADJ INIT z121tape = common, Nr |
790 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
791 |
|
792 |
do i = 1, imt |
793 |
|
794 |
k = 1 |
795 |
CADJ STORE v(i,k) = z121tape |
796 |
v(i,Nrp1) = v(i,Nr) |
797 |
|
798 |
do k = 1, Nr |
799 |
KRi_range(k) = p5 + SIGN(p5,v(i,k)) |
800 |
KRi_range(k) = KRi_range(k) * |
801 |
& ( p5 + SIGN(p5,(Riinfty-v(i,k))) ) |
802 |
end do |
803 |
|
804 |
zwork = KRi_range(1) * v(i,1) |
805 |
v(i,1) = p2 * v(i,1) + |
806 |
& KRi_range(1) * KRi_range(2) * v(i,2) |
807 |
zflag = p2 + KRi_range(1) * KRi_range(2) |
808 |
v(i,1) = v(i,1) / zflag |
809 |
|
810 |
do k = 2, Nr |
811 |
CADJ STORE v(i,k), zwork = z121tape |
812 |
km1 = k - 1 |
813 |
kp1 = k + 1 |
814 |
zflag = v(i,k) |
815 |
v(i,k) = p2 * v(i,k) + |
816 |
& KRi_range(k) * KRi_range(kp1) * v(i,kp1) + |
817 |
& KRi_range(k) * zwork |
818 |
zwork = KRi_range(k) * zflag |
819 |
zflag = p2 + KRi_range(k)*(KRi_range(kp1)+KRi_range(km1)) |
820 |
v(i,k) = v(i,k) / zflag |
821 |
end do |
822 |
|
823 |
end do |
824 |
|
825 |
#endif /* ALLOW_KPP */ |
826 |
|
827 |
return |
828 |
end |
829 |
|
830 |
c************************************************************************* |
831 |
|
832 |
subroutine kpp_smooth_horiz ( |
833 |
I k, bi, bj, |
834 |
U fld ) |
835 |
|
836 |
c Apply horizontal smoothing to KPP array |
837 |
|
838 |
IMPLICIT NONE |
839 |
#include "SIZE.h" |
840 |
#include "KPP_PARAMS.h" |
841 |
|
842 |
c input |
843 |
c bi, bj : array indices |
844 |
c k : vertical index used for masking |
845 |
integer k, bi, bj |
846 |
|
847 |
c input/output |
848 |
c fld : 2-D array to be smoothed |
849 |
_KPP_RL fld( ibot:itop, jbot:jtop ) |
850 |
|
851 |
#ifdef ALLOW_KPP |
852 |
|
853 |
c local |
854 |
integer i, j, im1, ip1, jm1, jp1 |
855 |
_KPP_RL tempVar |
856 |
_KPP_RL fld_tmp( ibot:itop, jbot:jtop ) |
857 |
|
858 |
integer imin , imax , jmin , jmax |
859 |
parameter( imin=ibot+1, imax=itop-1, jmin=jbot+1, jmax=jtop-1 ) |
860 |
|
861 |
_KPP_RL p0 , p5 , p25 , p125 , p0625 |
862 |
parameter( p0=0.0, p5=0.5, p25=0.25, p125=0.125, p0625=0.0625 ) |
863 |
|
864 |
DO j = jmin, jmax |
865 |
jm1 = j-1 |
866 |
jp1 = j+1 |
867 |
DO i = imin, imax |
868 |
im1 = i-1 |
869 |
ip1 = i+1 |
870 |
tempVar = |
871 |
& p25 * pMask(i ,j ,k,bi,bj) + |
872 |
& p125 * ( pMask(im1,j ,k,bi,bj) + |
873 |
& pMask(ip1,j ,k,bi,bj) + |
874 |
& pMask(i ,jm1,k,bi,bj) + |
875 |
& pMask(i ,jp1,k,bi,bj) ) + |
876 |
& p0625 * ( pMask(im1,jm1,k,bi,bj) + |
877 |
& pMask(im1,jp1,k,bi,bj) + |
878 |
& pMask(ip1,jm1,k,bi,bj) + |
879 |
& pMask(ip1,jp1,k,bi,bj) ) |
880 |
IF ( tempVar .GE. p25 ) THEN |
881 |
fld_tmp(i,j) = ( |
882 |
& p25 * fld(i ,j )*pMask(i ,j ,k,bi,bj) + |
883 |
& p125 *(fld(im1,j )*pMask(im1,j ,k,bi,bj) + |
884 |
& fld(ip1,j )*pMask(ip1,j ,k,bi,bj) + |
885 |
& fld(i ,jm1)*pMask(i ,jm1,k,bi,bj) + |
886 |
& fld(i ,jp1)*pMask(i ,jp1,k,bi,bj))+ |
887 |
& p0625*(fld(im1,jm1)*pMask(im1,jm1,k,bi,bj) + |
888 |
& fld(im1,jp1)*pMask(im1,jp1,k,bi,bj) + |
889 |
& fld(ip1,jm1)*pMask(ip1,jm1,k,bi,bj) + |
890 |
& fld(ip1,jp1)*pMask(ip1,jp1,k,bi,bj))) |
891 |
& / tempVar |
892 |
ELSE |
893 |
fld_tmp(i,j) = fld(i,j) |
894 |
ENDIF |
895 |
ENDDO |
896 |
ENDDO |
897 |
|
898 |
c transfer smoothed field to output array |
899 |
DO j = jmin, jmax |
900 |
DO i = imin, imax |
901 |
fld(i,j) = fld_tmp(i,j) |
902 |
ENDDO |
903 |
ENDDO |
904 |
|
905 |
#endif /* ALLOW_KPP */ |
906 |
|
907 |
return |
908 |
end |
909 |
|
910 |
c************************************************************************* |
911 |
|
912 |
subroutine smooth_horiz ( |
913 |
I k, bi, bj, |
914 |
U fld ) |
915 |
|
916 |
c Apply horizontal smoothing to global _RL 2-D array |
917 |
|
918 |
IMPLICIT NONE |
919 |
#include "SIZE.h" |
920 |
#include "KPP_PARAMS.h" |
921 |
|
922 |
c input |
923 |
c bi, bj : array indices |
924 |
c k : vertical index used for masking |
925 |
integer k, bi, bj |
926 |
|
927 |
c input/output |
928 |
c fld : 2-D array to be smoothed |
929 |
_RL fld( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
930 |
|
931 |
#ifdef ALLOW_KPP |
932 |
|
933 |
c local |
934 |
integer i, j, im1, ip1, jm1, jp1 |
935 |
_RL tempVar |
936 |
_RL fld_tmp( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
937 |
|
938 |
integer imin , imax , jmin , jmax |
939 |
parameter(imin=2-OLx, imax=sNx+OLx-1, jmin=2-OLy, jmax=sNy+OLy-1) |
940 |
|
941 |
_RL p0 , p5 , p25 , p125 , p0625 |
942 |
parameter( p0=0.0, p5=0.5, p25=0.25, p125=0.125, p0625=0.0625 ) |
943 |
|
944 |
DO j = jmin, jmax |
945 |
jm1 = j-1 |
946 |
jp1 = j+1 |
947 |
DO i = imin, imax |
948 |
im1 = i-1 |
949 |
ip1 = i+1 |
950 |
tempVar = |
951 |
& p25 * pMask(i ,j ,k,bi,bj) + |
952 |
& p125 * ( pMask(im1,j ,k,bi,bj) + |
953 |
& pMask(ip1,j ,k,bi,bj) + |
954 |
& pMask(i ,jm1,k,bi,bj) + |
955 |
& pMask(i ,jp1,k,bi,bj) ) + |
956 |
& p0625 * ( pMask(im1,jm1,k,bi,bj) + |
957 |
& pMask(im1,jp1,k,bi,bj) + |
958 |
& pMask(ip1,jm1,k,bi,bj) + |
959 |
& pMask(ip1,jp1,k,bi,bj) ) |
960 |
IF ( tempVar .GE. p25 ) THEN |
961 |
fld_tmp(i,j) = ( |
962 |
& p25 * fld(i ,j )*pMask(i ,j ,k,bi,bj) + |
963 |
& p125 *(fld(im1,j )*pMask(im1,j ,k,bi,bj) + |
964 |
& fld(ip1,j )*pMask(ip1,j ,k,bi,bj) + |
965 |
& fld(i ,jm1)*pMask(i ,jm1,k,bi,bj) + |
966 |
& fld(i ,jp1)*pMask(i ,jp1,k,bi,bj))+ |
967 |
& p0625*(fld(im1,jm1)*pMask(im1,jm1,k,bi,bj) + |
968 |
& fld(im1,jp1)*pMask(im1,jp1,k,bi,bj) + |
969 |
& fld(ip1,jm1)*pMask(ip1,jm1,k,bi,bj) + |
970 |
& fld(ip1,jp1)*pMask(ip1,jp1,k,bi,bj))) |
971 |
& / tempVar |
972 |
ELSE |
973 |
fld_tmp(i,j) = fld(i,j) |
974 |
ENDIF |
975 |
ENDDO |
976 |
ENDDO |
977 |
|
978 |
c transfer smoothed field to output array |
979 |
DO j = jmin, jmax |
980 |
DO i = imin, imax |
981 |
fld(i,j) = fld_tmp(i,j) |
982 |
ENDDO |
983 |
ENDDO |
984 |
|
985 |
#endif /* ALLOW_KPP */ |
986 |
|
987 |
return |
988 |
end |
989 |
|
990 |
c************************************************************************* |
991 |
|
992 |
subroutine blmix ( |
993 |
I ustar, bfsfc, hbl, stable, casea, diffus, kbl |
994 |
O , dkm1, blmc, ghat, sigma, ikey |
995 |
& ) |
996 |
|
997 |
c mixing coefficients within boundary layer depend on surface |
998 |
c forcing and the magnitude and gradient of interior mixing below |
999 |
c the boundary layer ("matching"). |
1000 |
c |
1001 |
c caution: if mixing bottoms out at hbl = -zgrid(Nr) then |
1002 |
c fictitious layer at Nrp1 is needed with small but finite width |
1003 |
c hwide(Nrp1) (eg. epsln = 1.e-20). |
1004 |
c |
1005 |
IMPLICIT NONE |
1006 |
|
1007 |
#include "SIZE.h" |
1008 |
#include "KPP_PARAMS.h" |
1009 |
|
1010 |
c input |
1011 |
c ustar (imt) surface friction velocity (m/s) |
1012 |
c bfsfc (imt) surface buoyancy forcing (m^2/s^3) |
1013 |
c hbl (imt) boundary layer depth (m) |
1014 |
c stable(imt) = 1 in stable forcing |
1015 |
c casea (imt) = 1 in case A |
1016 |
c diffus(imt,0:Nrp1,mdiff) vertical diffusivities (m^2/s) |
1017 |
c kbl(imt) -1 of first grid level below hbl |
1018 |
_KPP_RL ustar (imt) |
1019 |
_KPP_RL bfsfc (imt) |
1020 |
_KPP_RL hbl (imt) |
1021 |
_KPP_RL stable(imt) |
1022 |
_KPP_RL casea (imt) |
1023 |
_KPP_RL diffus(imt,0:Nrp1,mdiff) |
1024 |
integer kbl(imt) |
1025 |
|
1026 |
c output |
1027 |
c dkm1 (imt,mdiff) boundary layer difs at kbl-1 level |
1028 |
c blmc (imt,Nr,mdiff) boundary layer mixing coefficients (m^2/s) |
1029 |
c ghat (imt,Nr) nonlocal scalar transport |
1030 |
c sigma(imt) normalized depth (d / hbl) |
1031 |
_KPP_RL dkm1 (imt,mdiff) |
1032 |
_KPP_RL blmc (imt,Nr,mdiff) |
1033 |
_KPP_RL ghat (imt,Nr) |
1034 |
_KPP_RL sigma(imt) |
1035 |
integer ikey |
1036 |
|
1037 |
#ifdef ALLOW_KPP |
1038 |
|
1039 |
c local |
1040 |
c gat1*(imt) shape function at sigma = 1 |
1041 |
c dat1*(imt) derivative of shape function at sigma = 1 |
1042 |
c ws(imt), wm(imt) turbulent velocity scales (m/s) |
1043 |
_KPP_RL gat1m(imt), gat1s(imt), gat1t(imt) |
1044 |
_KPP_RL dat1m(imt), dat1s(imt), dat1t(imt) |
1045 |
_KPP_RL ws(imt), wm(imt) |
1046 |
integer i, kn, ki |
1047 |
_KPP_RL R, dvdzup, dvdzdn, viscp |
1048 |
_KPP_RL difsp, diftp, visch, difsh, difth |
1049 |
_KPP_RL f1, sig, a1, a2, a3, delhat |
1050 |
_KPP_RL Gm, Gs, Gt |
1051 |
_KPP_RL tempVar |
1052 |
|
1053 |
_KPP_RL p0 , eins |
1054 |
parameter (p0=0.0, eins=1.0) |
1055 |
|
1056 |
c----------------------------------------------------------------------- |
1057 |
c compute velocity scales at hbl |
1058 |
c----------------------------------------------------------------------- |
1059 |
|
1060 |
do i = 1, imt |
1061 |
sigma(i) = stable(i) * 1.0 + (1. - stable(i)) * epsilon |
1062 |
end do |
1063 |
|
1064 |
call wscale ( |
1065 |
I sigma, hbl, ustar, bfsfc, |
1066 |
O wm, ws ) |
1067 |
|
1068 |
do i = 1, imt |
1069 |
wm(i) = sign(eins,wm(i))*max(phepsi,abs(wm(i))) |
1070 |
ws(i) = sign(eins,ws(i))*max(phepsi,abs(ws(i))) |
1071 |
end do |
1072 |
CADJ STORE wm = comlev1_kpp, key = ikey |
1073 |
CADJ STORE ws = comlev1_kpp, key = ikey |
1074 |
|
1075 |
do i = 1, imt |
1076 |
|
1077 |
kn = int(caseA(i)+phepsi) *(kbl(i) -1) + |
1078 |
$ (1 - int(caseA(i)+phepsi)) * kbl(i) |
1079 |
|
1080 |
c----------------------------------------------------------------------- |
1081 |
c find the interior viscosities and derivatives at hbl(i) |
1082 |
c----------------------------------------------------------------------- |
1083 |
|
1084 |
delhat = 0.5*hwide(kn) - zgrid(kn) - hbl(i) |
1085 |
R = 1.0 - delhat / hwide(kn) |
1086 |
dvdzup = (diffus(i,kn-1,1) - diffus(i,kn ,1)) / hwide(kn) |
1087 |
dvdzdn = (diffus(i,kn ,1) - diffus(i,kn+1,1)) / hwide(kn+1) |
1088 |
viscp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
1089 |
1 R * (dvdzdn + abs(dvdzdn)) ) |
1090 |
|
1091 |
dvdzup = (diffus(i,kn-1,2) - diffus(i,kn ,2)) / hwide(kn) |
1092 |
dvdzdn = (diffus(i,kn ,2) - diffus(i,kn+1,2)) / hwide(kn+1) |
1093 |
difsp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
1094 |
1 R * (dvdzdn + abs(dvdzdn)) ) |
1095 |
|
1096 |
dvdzup = (diffus(i,kn-1,3) - diffus(i,kn ,3)) / hwide(kn) |
1097 |
dvdzdn = (diffus(i,kn ,3) - diffus(i,kn+1,3)) / hwide(kn+1) |
1098 |
diftp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
1099 |
1 R * (dvdzdn + abs(dvdzdn)) ) |
1100 |
|
1101 |
visch = diffus(i,kn,1) + viscp * delhat |
1102 |
difsh = diffus(i,kn,2) + difsp * delhat |
1103 |
difth = diffus(i,kn,3) + diftp * delhat |
1104 |
|
1105 |
f1 = stable(i) * conc1 * bfsfc(i) / |
1106 |
& max(ustar(i)**4,phepsi) |
1107 |
gat1m(i) = visch / hbl(i) / wm(i) |
1108 |
dat1m(i) = -viscp / wm(i) + f1 * visch |
1109 |
dat1m(i) = min(dat1m(i),p0) |
1110 |
|
1111 |
gat1s(i) = difsh / hbl(i) / ws(i) |
1112 |
dat1s(i) = -difsp / ws(i) + f1 * difsh |
1113 |
dat1s(i) = min(dat1s(i),p0) |
1114 |
|
1115 |
gat1t(i) = difth / hbl(i) / ws(i) |
1116 |
dat1t(i) = -diftp / ws(i) + f1 * difth |
1117 |
dat1t(i) = min(dat1t(i),p0) |
1118 |
|
1119 |
end do |
1120 |
|
1121 |
do ki = 1, Nr |
1122 |
|
1123 |
c----------------------------------------------------------------------- |
1124 |
c compute turbulent velocity scales on the interfaces |
1125 |
c----------------------------------------------------------------------- |
1126 |
|
1127 |
do i = 1, imt |
1128 |
sig = (-zgrid(ki) + 0.5 * hwide(ki)) / hbl(i) |
1129 |
sigma(i) = stable(i)*sig + (1.-stable(i))*min(sig,epsilon) |
1130 |
end do |
1131 |
call wscale ( |
1132 |
I sigma, hbl, ustar, bfsfc, |
1133 |
O wm, ws ) |
1134 |
|
1135 |
c----------------------------------------------------------------------- |
1136 |
c compute the dimensionless shape functions at the interfaces |
1137 |
c----------------------------------------------------------------------- |
1138 |
|
1139 |
do i = 1, imt |
1140 |
sig = (-zgrid(ki) + 0.5 * hwide(ki)) / hbl(i) |
1141 |
a1 = sig - 2. |
1142 |
a2 = 3. - 2. * sig |
1143 |
a3 = sig - 1. |
1144 |
|
1145 |
Gm = a1 + a2 * gat1m(i) + a3 * dat1m(i) |
1146 |
Gs = a1 + a2 * gat1s(i) + a3 * dat1s(i) |
1147 |
Gt = a1 + a2 * gat1t(i) + a3 * dat1t(i) |
1148 |
|
1149 |
c----------------------------------------------------------------------- |
1150 |
c compute boundary layer diffusivities at the interfaces |
1151 |
c----------------------------------------------------------------------- |
1152 |
|
1153 |
blmc(i,ki,1) = hbl(i) * wm(i) * sig * (1. + sig * Gm) |
1154 |
blmc(i,ki,2) = hbl(i) * ws(i) * sig * (1. + sig * Gs) |
1155 |
blmc(i,ki,3) = hbl(i) * ws(i) * sig * (1. + sig * Gt) |
1156 |
|
1157 |
c----------------------------------------------------------------------- |
1158 |
c nonlocal transport term = ghat * <ws>o |
1159 |
c----------------------------------------------------------------------- |
1160 |
|
1161 |
tempVar = ws(i) * hbl(i) |
1162 |
ghat(i,ki) = (1.-stable(i)) * cg / max(phepsi,tempVar) |
1163 |
|
1164 |
end do |
1165 |
end do |
1166 |
|
1167 |
c----------------------------------------------------------------------- |
1168 |
c find diffusivities at kbl-1 grid level |
1169 |
c----------------------------------------------------------------------- |
1170 |
|
1171 |
do i = 1, imt |
1172 |
sig = -zgrid(kbl(i)-1) / hbl(i) |
1173 |
sigma(i) = stable(i) * sig |
1174 |
& + (1. - stable(i)) * min(sig,epsilon) |
1175 |
end do |
1176 |
|
1177 |
call wscale ( |
1178 |
I sigma, hbl, ustar, bfsfc, |
1179 |
O wm, ws ) |
1180 |
|
1181 |
do i = 1, imt |
1182 |
sig = -zgrid(kbl(i)-1) / hbl(i) |
1183 |
a1 = sig - 2. |
1184 |
a2 = 3. - 2. * sig |
1185 |
a3 = sig - 1. |
1186 |
Gm = a1 + a2 * gat1m(i) + a3 * dat1m(i) |
1187 |
Gs = a1 + a2 * gat1s(i) + a3 * dat1s(i) |
1188 |
Gt = a1 + a2 * gat1t(i) + a3 * dat1t(i) |
1189 |
dkm1(i,1) = hbl(i) * wm(i) * sig * (1. + sig * Gm) |
1190 |
dkm1(i,2) = hbl(i) * ws(i) * sig * (1. + sig * Gs) |
1191 |
dkm1(i,3) = hbl(i) * ws(i) * sig * (1. + sig * Gt) |
1192 |
end do |
1193 |
|
1194 |
#endif /* ALLOW_KPP */ |
1195 |
|
1196 |
return |
1197 |
end |
1198 |
|
1199 |
c************************************************************************* |
1200 |
|
1201 |
subroutine enhance ( |
1202 |
I dkm1, hbl, kbl, diffus, casea |
1203 |
U , ghat |
1204 |
O , blmc |
1205 |
& ) |
1206 |
|
1207 |
c enhance the diffusivity at the kbl-.5 interface |
1208 |
|
1209 |
IMPLICIT NONE |
1210 |
|
1211 |
#include "SIZE.h" |
1212 |
#include "KPP_PARAMS.h" |
1213 |
|
1214 |
c input |
1215 |
c dkm1(imt,mdiff) bl diffusivity at kbl-1 grid level |
1216 |
c hbl(imt) boundary layer depth (m) |
1217 |
c kbl(imt) grid above hbl |
1218 |
c diffus(imt,0:Nrp1,mdiff) vertical diffusivities (m^2/s) |
1219 |
c casea(imt) = 1 in caseA, = 0 in case B |
1220 |
_KPP_RL dkm1 (imt,mdiff) |
1221 |
_KPP_RL hbl (imt) |
1222 |
integer kbl (imt) |
1223 |
_KPP_RL diffus(imt,0:Nrp1,mdiff) |
1224 |
_KPP_RL casea (imt) |
1225 |
|
1226 |
c input/output |
1227 |
c nonlocal transport, modified ghat at kbl(i)-1 interface (s/m**2) |
1228 |
_KPP_RL ghat (imt,Nr) |
1229 |
|
1230 |
c output |
1231 |
c enhanced bound. layer mixing coeff. |
1232 |
_KPP_RL blmc (imt,Nr,mdiff) |
1233 |
|
1234 |
#ifdef ALLOW_KPP |
1235 |
|
1236 |
c local |
1237 |
c fraction hbl lies beteen zgrid neighbors |
1238 |
_KPP_RL delta |
1239 |
integer ki, i, md |
1240 |
_KPP_RL dkmp5, dstar |
1241 |
|
1242 |
do i = 1, imt |
1243 |
ki = kbl(i)-1 |
1244 |
if ((ki .ge. 1) .and. (ki .lt. Nr)) then |
1245 |
delta = (hbl(i) + zgrid(ki)) / (zgrid(ki) - zgrid(ki+1)) |
1246 |
do md = 1, mdiff |
1247 |
dkmp5 = casea(i) * diffus(i,ki,md) + |
1248 |
1 (1.- casea(i)) * blmc (i,ki,md) |
1249 |
dstar = (1.- delta)**2 * dkm1(i,md) |
1250 |
& + delta**2 * dkmp5 |
1251 |
blmc(i,ki,md) = (1.- delta)*diffus(i,ki,md) |
1252 |
& + delta*dstar |
1253 |
end do |
1254 |
ghat(i,ki) = (1.- casea(i)) * ghat(i,ki) |
1255 |
endif |
1256 |
end do |
1257 |
|
1258 |
#endif /* ALLOW_KPP */ |
1259 |
|
1260 |
return |
1261 |
end |
1262 |
|
1263 |
c************************************************************************* |
1264 |
|
1265 |
SUBROUTINE STATEKPP ( |
1266 |
I bi, bj, myThid, |
1267 |
O RHO1, DBLOC, DBSFC, TTALPHA, SSBETA) |
1268 |
c |
1269 |
c----------------------------------------------------------------------- |
1270 |
c "statekpp" computes all necessary input arrays |
1271 |
c for the kpp mixing scheme |
1272 |
c |
1273 |
c input: |
1274 |
c bi, bj = array indices on which to apply calculations |
1275 |
c |
1276 |
c output: |
1277 |
c rho1 = potential density of surface layer (kg/m^3) |
1278 |
c dbloc = local buoyancy gradient at Nr interfaces |
1279 |
c g/rho{k+1,k+1} * [ drho{k,k+1}-drho{k+1,k+1} ] (m/s^2) |
1280 |
c dbsfc = buoyancy difference with respect to the surface |
1281 |
c g * [ drho{1,k}/rho{1,k} - drho{k,k}/rho{k,k} ] (m/s^2) |
1282 |
c ttalpha= thermal expansion coefficient without 1/rho factor |
1283 |
c d(rho) / d(potential temperature) (kg/m^3/C) |
1284 |
c ssbeta = salt expansion coefficient without 1/rho factor |
1285 |
c d(rho) / d(salinity) (kg/m^3/PSU) |
1286 |
c |
1287 |
c see also subroutines find_rho.F find_alpha.F find_beta.F |
1288 |
c |
1289 |
c written by: jan morzel, feb. 10, 1995 (converted from "sigma" version) |
1290 |
c modified by: d. menemenlis, june 1998 : for use with MIT GCM UV |
1291 |
c |
1292 |
c----------------------------------------------------------------------- |
1293 |
|
1294 |
IMPLICIT NONE |
1295 |
|
1296 |
#include "SIZE.h" |
1297 |
#include "EEPARAMS.h" |
1298 |
#include "PARAMS.h" |
1299 |
#include "KPP_PARAMS.h" |
1300 |
|
1301 |
c-------------- Routine arguments ----------------------------------------- |
1302 |
INTEGER bi, bj, myThid |
1303 |
_KPP_RL RHO1 ( ibot:itop, jbot:jtop ) |
1304 |
_KPP_RL DBLOC ( ibot:itop, jbot:jtop, Nr ) |
1305 |
_KPP_RL DBSFC ( ibot:itop, jbot:jtop, Nr ) |
1306 |
_KPP_RL TTALPHA( ibot:itop, jbot:jtop, Nrp1 ) |
1307 |
_KPP_RL SSBETA ( ibot:itop, jbot:jtop, Nrp1 ) |
1308 |
|
1309 |
#ifdef ALLOW_KPP |
1310 |
|
1311 |
c-------------------------------------------------------------------------- |
1312 |
c |
1313 |
c local arrays: |
1314 |
c |
1315 |
c rhok - density of t(k ) & s(k ) at depth k |
1316 |
c rhokm1 - density of t(k-1) & s(k-1) at depth k |
1317 |
c rho1k - density of t(1 ) & s(1 ) at depth k |
1318 |
c work1, work2 - work arrays for holding horizontal slabs |
1319 |
|
1320 |
_RL RHOK (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1321 |
_RL RHOKM1(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1322 |
_RL RHO1K (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1323 |
_RL WORK1 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1324 |
_RL WORK2 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1325 |
_RL WORK3 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1326 |
INTEGER I, J, K |
1327 |
|
1328 |
c calculate density, alpha, beta in surface layer, and set dbsfc to zero |
1329 |
|
1330 |
call FIND_RHO( |
1331 |
I bi, bj, ibot, itop, jbot, jtop, 1, 1, eosType, |
1332 |
O WORK1, |
1333 |
I myThid ) |
1334 |
|
1335 |
call FIND_ALPHA( |
1336 |
I bi, bj, ibot, itop, jbot, jtop, 1, 1, eosType, |
1337 |
O WORK2 ) |
1338 |
|
1339 |
call FIND_BETA( |
1340 |
I bi, bj, ibot, itop, jbot, jtop, 1, 1, eosType, |
1341 |
O WORK3 ) |
1342 |
|
1343 |
DO J = jbot, jtop |
1344 |
DO I = ibot, itop |
1345 |
RHO1(I,J) = WORK1(I,J) + rhonil |
1346 |
TTALPHA(I,J,1) = WORK2(I,J) |
1347 |
SSBETA(I,J,1) = WORK3(I,J) |
1348 |
DBSFC(I,J,1) = 0. |
1349 |
END DO |
1350 |
END DO |
1351 |
|
1352 |
c calculate alpha, beta, and gradients in interior layers |
1353 |
|
1354 |
CHPF$ INDEPENDENT, NEW (RHOK,RHOKM1,RHO1K,WORK1,WORK2) |
1355 |
DO K = 2, Nr |
1356 |
|
1357 |
call FIND_RHO( |
1358 |
I bi, bj, ibot, itop, jbot, jtop, K, K, eosType, |
1359 |
O RHOK, |
1360 |
I myThid ) |
1361 |
|
1362 |
call FIND_RHO( |
1363 |
I bi, bj, ibot, itop, jbot, jtop, K-1, K, eosType, |
1364 |
O RHOKM1, |
1365 |
I myThid ) |
1366 |
|
1367 |
call FIND_RHO( |
1368 |
I bi, bj, ibot, itop, jbot, jtop, 1, K, eosType, |
1369 |
O RHO1K, |
1370 |
I myThid ) |
1371 |
|
1372 |
call FIND_ALPHA( |
1373 |
I bi, bj, ibot, itop, jbot, jtop, K, K, eosType, |
1374 |
O WORK1 ) |
1375 |
|
1376 |
call FIND_BETA( |
1377 |
I bi, bj, ibot, itop, jbot, jtop, K, K, eosType, |
1378 |
O WORK2 ) |
1379 |
|
1380 |
DO J = jbot, jtop |
1381 |
DO I = ibot, itop |
1382 |
TTALPHA(I,J,K) = WORK1 (I,J) |
1383 |
SSBETA(I,J,K) = WORK2 (I,J) |
1384 |
DBLOC(I,J,K-1) = gravity * (RHOK(I,J) - RHOKM1(I,J)) / |
1385 |
& (RHOK(I,J) + rhonil) |
1386 |
DBSFC(I,J,K) = gravity * (RHOK(I,J) - RHO1K (I,J)) / |
1387 |
& (RHOK(I,J) + rhonil) |
1388 |
END DO |
1389 |
END DO |
1390 |
|
1391 |
END DO |
1392 |
|
1393 |
c compute arrays for K = Nrp1 |
1394 |
DO J = jbot, jtop |
1395 |
DO I = ibot, itop |
1396 |
TTALPHA(I,J,Nrp1) = TTALPHA(I,J,Nr) |
1397 |
SSBETA(I,J,Nrp1) = SSBETA(I,J,Nr) |
1398 |
DBLOC(I,J,Nr) = 0. |
1399 |
END DO |
1400 |
END DO |
1401 |
|
1402 |
#endif /* ALLOW_KPP */ |
1403 |
|
1404 |
RETURN |
1405 |
END |