-
Notifications
You must be signed in to change notification settings - Fork 23
/
diapfl.F90
1405 lines (1404 loc) · 46.1 KB
/
diapfl.F90
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
#if defined(ROW_LAND)
#define SEA_P .true.
#define SEA_U .true.
#define SEA_V .true.
#elif defined(ROW_ALLSEA)
#define SEA_P allip(j).or.ip(i,j).ne.0
#define SEA_U alliu(j).or.iu(i,j).ne.0
#define SEA_V alliv(j).or.iv(i,j).ne.0
#else
#define SEA_P ip(i,j).ne.0
#define SEA_U iu(i,j).ne.0
#define SEA_V iv(i,j).ne.0
#endif
subroutine diapf1(m,n)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
! --- KPP-style implicit interior diapycnal mixing
implicit none
!
integer m,n
!
! --------------------
! --- diapycnal mixing
! --------------------
!
! --- interior diapycnal mixing due to three processes:
! --- shear instability
! --- double diffusion
! --- background internal waves
!
! --- this is essentially the k-profile-parameterization (kpp) mixing model
! --- (mxkpp.f) with all surface boundary layer processes removed
!
! --- uses the same tri-diagonal matrix solution of vertical diffusion
! --- equation as mxkpp.f
!
integer j
!
if (mod(nstep, mixfrq).ne.0 .and. &
mod(nstep+1,mixfrq).ne.0 ) then
return ! diapycnal mixing only every mixfrq,mixfrq+1 time steps
endif
!
call xctilr(u(1-nbdy,1-nbdy,1,n),1,kk, 1,1, halo_uv)
call xctilr(v(1-nbdy,1-nbdy,1,n),1,kk, 1,1, halo_vv)
call xctilr(p(1-nbdy,1-nbdy,2 ),1,kk, 1,1, halo_ps)
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call diapf1aj(m,n, j)
enddo
!$OMP END PARALLEL DO
!
! --- momentum mixing
!
call xctilr(vcty(1-nbdy,1-nbdy,2),1,kk, 1,1, halo_ps)
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call diapf1bj(m,n, j)
enddo
!$OMP END PARALLEL DO
!
return
end
subroutine diapf1aj(m,n, j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n, j
integer i
!
do i=1,ii
if (SEA_P) then
call diapf1aij(m,n, i,j)
endif !ip
enddo !i
!
return
end
subroutine diapf1bj(m,n, j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n, j
integer i
!
do i=1,ii
if (SEA_U) then
call diapf1uij(m,n, i,j)
endif !iu
if (SEA_V) then
call diapf1vij(m,n, i,j)
endif !iv
enddo !i
!
return
end
subroutine diapf1aij(m,n, i,j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
#if defined(STOKES)
use mod_stokes ! HYCOM Stokes drift
#endif
!
! --- hycom version 1.0
! --- KPP-style implicit interior diapycnal mixing
implicit none
!
integer m,n, i,j
!
! -----------------------------------------------
! --- diapycnal mixing, single i,j point (part A)
! -----------------------------------------------
!
! --- interior diapycnal mixing due to three processes:
! --- shear instability
! --- double diffusion
! --- background internal waves
!
! --- this is essentially the k-profile-parameterization (kpp) mixing model
! --- (mxkpp.f) with all surface boundary layer processes removed
!
! --- uses the same tri-diagonal matrix solution of vertical diffusion
! --- equation as mxkpp.f
!
! local variables for kpp mixing
real shsq(kdm+1) ! velocity shear squared
real alfadt(kdm+1) ! t contribution to density jump
real betads(kdm+1) ! s contribution to density jump
real dbloc(kdm+1) ! buoyancy jump across interface
real hwide(kdm) ! layer thicknesses in m
real rrho ! double diffusion parameter
real diffdd ! double diffusion diffusivity scale
real prandtl ! prandtl number
real rigr ! local richardson number
real fri ! function of Rig for KPP shear instability
real dflsiw ! wave diffusivity
real dflmiw ! wave viscosity
real dflbot(kdm+1) ! bottom intensified background viscosity
!
! --- local 1-d arrays for matrix inversion
real t1do(kdm+1),t1dn(kdm+1),s1do(kdm+1),s1dn(kdm+1), &
tr1do(kdm+1,mxtrcr),tr1dn(kdm+1,mxtrcr), &
difft(kdm+1),diffs(kdm+1),difftr(kdm+1), &
zm(kdm+1),hm(kdm),dzb(kdm)
!
! --- tridiagonal matrix solution arrays
real tri(kdm,0:1) ! dt/dz/dz factors in trid. matrix
real tcu(kdm), & ! upper coeff for (k-1) on k line of trid.matrix
tcc(kdm), & ! central ... (k ) ..
tcl(kdm), & ! lower ..... (k-1) ..
rhs(kdm) ! right-hand-side terms
!
real ratio,froglp,q,wq,wt,wz0,wz1,wz2
integer k,k1,ka,kmask,ktr,nlayer,mixflg
real riv_input
!
real, parameter :: difriv = 50.0e-4 !river diffusion
!
# include "stmt_fns.h"
froglp=.5*max(2,mixfrq)
!
! --- internal wave diffusion/viscosity
dflsiw = diws(i,j)
dflmiw = diwm(i,j)
!
! --- locate lowest substantial mass-containing layer. avoid near-zero
! --- thickness layers near the bottom
klist(i,j)=0
kmask=0
!
do k=1,kk
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
if (dp(i,j,k,n).lt.onemm) kmask=1
if (p(i,j,k).lt.p(i,j,kk+1)-onem.and.kmask.eq.0) klist(i,j)=k
enddo
!
! --- dflbot (Prandtl number of one, i.e. diffusion = viscosity)
if (botdiw) then
! --- diffusion coefficent profile is: K = Kb / (1 + h/h0)**2
! --- where diwbot = Kb; diwqh0 = 1/h0 (input as h0, see forfun.f)
! --- Decloedt T. and D.S. Luther, 2009: On a Simple Empirical
! --- Parameterization of Topography-Catalyzed Diapycnal Mixing
! --- in the Abyssal Ocean. JPO, 40, pp 487-508.
! --- use Simpson's rule to estimate the average K across each layer
wz0 = 1.0 / (1.0 + (p(i,j,kk+1)- p(i,j,1) )*diwqh0(i,j))**2
wz1 = 1.0 / (1.0 + (p(i,j,kk+1)-0.5*(p(i,j,1)+ &
p(i,j,2) ))*diwqh0(i,j))**2
wz2 = 1.0 / (1.0 + (p(i,j,kk+1)- p(i,j,2) )*diwqh0(i,j))**2
wq = wz0 + wz2 + 4.0*wz1 !6 times the average value over layer 1
do k= 2,kk
wt = wq
wz0 = wz2
wz1 = 1.0 / (1.0 + (p(i,j,kk+1) - &
0.5*(p(i,j,k) + &
p(i,j,k+1) ))*diwqh0(i,j))**2
wz2 = 1.0 / (1.0 + (p(i,j,kk+1) - &
p(i,j,k+1) )*diwqh0(i,j))**2
wq = wz0 + wz2 + 4.0*wz1 !6 times the average value over layer k
dflbot(k) = (0.5/6.0)*(wt+wq)*diwbot(i,j)
enddo
dflbot(kk+1) = dflbot(kk)
else
do k= 2,kk+1
dflbot(k) = 0.0
enddo
endif !botdiw
!
! --- calculate vertical grid and layer widths
do k=1,kk
if (k.eq.1) then
hwide(k)=dp(i,j,k,n)*qonem
zgrid(i,j,k)=-.5*hwide(k)
elseif (k.lt.klist(i,j)) then
hwide(k)=dp(i,j,k,n)*qonem
zgrid(i,j,k)=zgrid(i,j,k-1)-.5*(hwide(k-1)+hwide(k))
elseif (k.eq.klist(i,j)) then
hwide(k)=dp(i,j,k,n)*qonem
zgrid(i,j,k)=zgrid(i,j,k-1)-.5*(hwide(k-1)+hwide(k))
zgrid(i,j,k+1)=zgrid(i,j,k)-.5*hwide(k)
else
hwide(k)=0.
endif
enddo
!
! --- calculate interface variables required to estimate interior diffusivities
do k=1,kk
k1= k+1
ka=min(k+1,kk)
if (k.le.klist(i,j)) then
#if defined(STOKES)
!DAN==========================================================================
!DAN U and V Stokes Drift Layer Average Velocities addes to Shear calculation
!DAN
shsq(k1)=(u(i,j,k, n)+u(i+1,j,k, n)+usd(i,j,k)+usd(i+1,j,k)- &
u(i,j,ka,n)-usd(i+1,j,ka)-u(i,j,ka,n)-usd(i+1,j,ka))**2+ &
(v(i,j,k, n)+v(i,j+1,k, n)+vsd(i,j,k)+vsd(i,j+1,k)- &
v(i,j,ka,n)-v(i,j+1,ka,n)-vsd(i,j,ka)-vsd(i,j+1,ka))**2
#else
shsq( k1)=(u(i,j,k, n)+u(i+1,j,k, n)- &
u(i,j,ka,n)-u(i+1,j,ka,n))**2+ &
(v(i,j,k, n)+v(i,j+1,k, n)- &
v(i,j,ka,n)-v(i,j+1,ka,n))**2
#endif
if (locsig) then
alfadt(k1)=dsiglocdt(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,ka,n) ), &
ahalf*(saln(i,j,k, n)+ &
saln(i,j,ka,n) ),p(i,j,k1))* &
(temp(i,j,k ,n)- &
temp(i,j,ka,n) )
betads(k1)=dsiglocds(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,ka,n) ), &
ahalf*(saln(i,j,k, n)+ &
saln(i,j,ka,n) ),p(i,j,k1))* &
(saln(i,j,k ,n)- &
saln(i,j,ka,n) )
else
alfadt(k1)=dsigdt(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,ka,n) ), &
ahalf*(saln(i,j,k, n)+ &
saln(i,j,ka,n) ) )* &
(temp(i,j,k ,n)- &
temp(i,j,ka,n) )
betads(k1)=dsigds(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,ka,n) ), &
ahalf*(saln(i,j,k, n)+ &
saln(i,j,ka,n) ) )* &
(saln(i,j,k ,n)- &
saln(i,j,ka,n) )
endif
dbloc(k1)=-g*svref*(alfadt(k1)+betads(k1))
endif
enddo
!
! --- determine interior diffusivity profiles throughout the water column
! --- limit mixing to the stratified interior of the ocean
!
do k=1,kk+1
vcty(i,j,k)=0.
dift(i,j,k)=0.
difs(i,j,k)=0.
enddo
!
! --- shear instability plus background internal wave contributions
do k=2,kk+1
if (k-1.le.klist(i,j) .and. p(i,j,k).gt.dpmixl(i,j,n)) then
if (shinst) then
q =zgrid(i,j,k-1)-zgrid(i,j,k) !0.5*(hwide(k-1)+hwide(k))
rigr=max(0.0,dbloc(k)*q/(shsq(k)+epsil))
ratio=min(rigr*qrinfy,1.0)
fri=(1.0-ratio*ratio)
fri=fri*fri*fri
vcty(i,j,k)=difm0*fri+dflmiw+dflbot(k)
difs(i,j,k)=difs0*fri+dflsiw+dflbot(k)
dift(i,j,k)=difs(i,j,k)
else
vcty(i,j,k)=dflmiw+dflbot(k)
difs(i,j,k)=dflsiw+dflbot(k)
dift(i,j,k)=dflsiw+dflbot(k)
endif
endif
enddo
!
! --- double-diffusion (salt fingering and diffusive convection)
if (dbdiff) then
do k=2,kk+1
if (k-1.le.klist(i,j) .and. p(i,j,k).gt.dpmixl(i,j,n)) then
!
! --- salt fingering case
if (-alfadt(k).gt.betads(k) .and. betads(k).gt.0.) then
rrho= min(-alfadt(k)/betads(k),rrho0)
diffdd=1.-((rrho-1.)/(rrho0-1.))**2
diffdd=dsfmax*diffdd*diffdd*diffdd
dift(i,j,k)=dift(i,j,k)+0.7*diffdd
difs(i,j,k)=difs(i,j,k)+diffdd
!
! --- diffusive convection case
elseif (alfadt(k).gt.0.0 .and. betads(k).lt.0.0 .and. &
-alfadt(k).gt.betads(k)) then
rrho=-alfadt(k)/betads(k)
diffdd=1.5e-6*9.*.101*exp(4.6*exp(-.54*(1./rrho-1.)))
prandtl=.15*rrho
if (rrho.gt..5) prandtl=(1.85-.85/rrho)*rrho
dift(i,j,k)=dift(i,j,k)+diffdd
difs(i,j,k)=difs(i,j,k)+prandtl*diffdd
endif
endif
enddo
endif
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,101) &
!diag (nstep,i+i0,j+i0,k, &
!diag hwide(k),1.e4*vcty(i,j,k),1.e4*dift(i,j,k), &
!diag 1.e4*difs(i,j,k),k=1,kk+1)
!
! --- perform the vertical mixing at p points
!
mixflg=0
do k=1,klist(i,j)
if (dift(i,j,k+1).gt.0. .or. &
difs(i,j,k+1).gt.0.) mixflg=mixflg+1
difft( k+1)=froglp*dift(i,j,k+1)
diffs( k+1)=froglp*difs(i,j,k+1)
difftr(k+1)=froglp*difs(i,j,k+1)
t1do(k)=temp(i,j,k,n)
s1do(k)=saln(i,j,k,n)
do ktr= 1,ntracr
tr1do(k,ktr)=tracer(i,j,k,n,ktr)
enddo
hm(k)=hwide(k)
zm(k)=zgrid(i,j,k)
enddo
!
if (mixflg.le.1) return
nlayer=klist(i,j)
k=nlayer+1
ka=min(k,kk)
difft( k)=0.
diffs( k)=0.
difftr(k)=0.
t1do(k)=temp(i,j,ka,n)
s1do(k)=saln(i,j,ka,n)
do ktr= 1,ntracr
tr1do(k,ktr)=tracer(i,j,ka,n,ktr)
enddo
zm(k)=zgrid(i,j,k)
!
! --- do rivers here because difs is also used for tracers.
if(cpl_orivers.and.cpl_irivers) then
riv_input = imp_orivers(i,j,1)+imp_irivers(i,j,1)
else
riv_input = rivers(i,j,1)
endif
if (thkriv.gt.0.0 .and. riv_input.ne.0.0) then
do k=1,nlayer
if (-zm(k)+0.5*hm(k).lt.thkriv) then !interface<thkriv
diffs(k+1) = max(diffs(k+1),froglp*difriv)
endif
enddo !k
endif !river
!
! --- compute factors for coefficients of tridiagonal matrix elements.
! tri(k=1:NZ,0) : dt/hwide(k)/ dzb(k-1)=z(k-1)-z(k)=dzabove)
! tri(k=1:NZ,1) : dt/hwide(k)/(dzb(k )=z(k)-z(k+1)=dzbelow)
!
do k=1,nlayer
dzb(k)=zm(k)-zm(k+1)
enddo
!
tri(1,1)=delt1/(hm(1)*dzb(1))
tri(1,0)=0.
do k=2,nlayer
tri(k,1)=delt1/(hm(k)*dzb(k))
tri(k,0)=delt1/(hm(k)*dzb(k-1))
enddo
!
! --- solve the diffusion equation
!
! --- t solution
call tridcof(difft,tri,nlayer,tcu,tcc,tcl)
do k=1,nlayer
rhs(k)=t1do(k)
enddo
call tridmat(tcu,tcc,tcl,nlayer,hm,rhs,t1do,t1dn,difft, i,j)
if ( tofset.eq.0.0 .or. &
(mod(nstep ,tsofrq).ne.0 .and. &
mod(nstep+1,tsofrq).ne.0 ) ) then
do k=1,nlayer
temp(i,j,k,n)=t1dn(k)
enddo
else !include tofset drift correction
do k=1,nlayer
temp(i,j,k,n)=t1dn(k) + baclin*max(2,tsofrq)*tofset
enddo
endif !without:with tofset
!
! --- t-like tracer solution
do ktr= 1,ntracr
if (trcflg(ktr).eq.2) then
do k=1,nlayer
rhs(k)=tr1do(k,ktr)
enddo
call tridmat(tcu,tcc,tcl,nlayer,hm,rhs,tr1do,tr1dn,difft, i,j)
do k=1,nlayer
tracer(i,j,k,n,ktr)=tr1dn(k,ktr)
enddo
endif
enddo !ktr
!
! --- s solution and th3d reset
call tridcof(diffs,tri,nlayer,tcu,tcc,tcl)
do k=1,nlayer
rhs(k)=s1do(k)
enddo
call tridmat(tcu,tcc,tcl,nlayer,hm,rhs,s1do,s1dn,diffs, i,j)
if ( sofset.eq.0.0 .or. &
(mod(nstep ,tsofrq).ne.0 .and. &
mod(nstep+1,tsofrq).ne.0 ) ) then
do k=1,nlayer
saln(i,j,k,n)=s1dn(k)
th3d(i,j,k,n)=sig(temp(i,j,k,n),saln(i,j,k,n))-thbase
enddo
else !include sofset drift correction
do k=1,nlayer
saln(i,j,k,n)=s1dn(k) + baclin*max(2,tsofrq)*sofset
th3d(i,j,k,n)=sig(temp(i,j,k,n),saln(i,j,k,n))-thbase
enddo
endif !without:with sofset
!
! --- standard tracer solution
if (ntracr.gt.0) then
call tridcof(difftr,tri,nlayer,tcu,tcc,tcl)
endif
do ktr= 1,ntracr
if (trcflg(ktr).ne.2) then
do k=1,nlayer
rhs(k)=tr1do(k,ktr)
enddo
call tridmat(tcu,tcc,tcl,nlayer, &
hm,rhs,tr1do(1,ktr),tr1dn(1,ktr),difftr, i,j)
do k=1,nlayer
tracer(i,j,k,n,ktr)=tr1dn(k,ktr)
enddo
endif
enddo !ktr
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,102) &
!diag (nstep,i+i0,j+j0,k, &
!diag difft(k),t1do(k),t1dn(k),t1dn(k)-t1do(k), &
!diag diffs(k),s1do(k),s1dn(k),s1dn(k)-s1do(k),k=1,nlayer)
!
return
!
101 format(25x,' thick viscty t diff s diff ' &
/(i9,2i5,i3,2x,4f10.2))
102 format(25x, &
' diff t t old t new t chng diff s s old s new s chng' &
/(i9,2i5,i3,1x,8f8.3))
end
subroutine diapf1uij(m,n, i,j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
! --- KPP-style implicit interior diapycnal mixing
implicit none
!
integer m,n, i,j
!
! -----------------------------------------------------------------
! --- diapycnal mixing, single i,j point, momentum at u grid points
! -----------------------------------------------------------------
!
! --- local 1-d arrays for matrix inversion
real u1do(kdm+1),u1dn(kdm+1), &
diffm(kdm+1),zm(kdm+1),hm(kdm),dzb(kdm)
!
! --- tridiagonal matrix solution arrays
real tri(kdm,0:1) ! dt/dz/dz factors in trid. matrix
real tcu(kdm), & ! upper coeff for (k-1) on k line of trid.matrix
tcc(kdm), & ! central ... (k ) ..
tcl(kdm), & ! lower ..... (k-1) ..
rhs(kdm) ! right-hand-side terms
!
real presu,froglp
integer k,ka,kmask(idm),nlayer,mixflg
!
froglp=.5*max(2,mixfrq)
!
presu=0.
kmask(1)=0
mixflg=0
do k=1,kk+1
ka=min(k,kk)
if (dpu(i,j,ka,n).lt.tencm.or.k.eq.kk+1) kmask(1)=1
if (presu.lt.depthu(i,j)-tencm.and.kmask(1).eq.0) then
diffm(k+1)=.5*froglp*(vcty(i,j,k+1)+vcty(i-1,j,k+1))
if (diffm(k+1).gt.0.) mixflg=mixflg+1
u1do(k)=u(i,j,k,n)
hm(k)=dpu(i,j,k,n)*qonem
if (k.eq.1) then
zm(k)=-.5*hm(k)
else
zm(k)=zm(k-1)-.5*(hm(k-1)+hm(k))
endif
presu=presu+dpu(i,j,k,n)
nlayer=k
elseif (k.eq.nlayer+1) then
diffm(k)=0.
u1do(k)=u1do(k-1)
zm(k)=zm(k-1)-.5*hm(k-1)
endif
enddo
if (mixflg.le.1) return
!
! --- compute factors for coefficients of tridiagonal matrix elements.
do k=1,nlayer
dzb(k)=zm(k)-zm(k+1)
enddo
!
tri(1,1)=delt1/(hm(1)*dzb(1))
tri(1,0)=0.
do k=2,nlayer
tri(k,1)=delt1/(hm(k)*dzb(k))
tri(k,0)=delt1/(hm(k)*dzb(k-1))
enddo
!
! --- solve the diffusion equation
call tridcof(diffm,tri,nlayer,tcu,tcc,tcl)
do k=1,nlayer
rhs(k)= u1do(k)
enddo
call tridmat(tcu,tcc,tcl,nlayer,hm,rhs,u1do,u1dn,diffm, i,j)
do k=1,nlayer
u(i,j,k,n)=u1dn(k)
enddo
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,106) &
!diag (nstep,i+i0,j+j0,k,hm(k),u1do(k),u1dn(k),k=1,nlayer)
!
return
106 format(23x,' thick u old u new'/(i9,2i5,i3,1x,f10.3,2f8.3))
end
subroutine diapf1vij(m,n, i,j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
! --- KPP-style implicit interior diapycnal mixing
implicit none
!
integer m,n, i,j
!
! -----------------------------------------------------------------
! --- diapycnal mixing, single i,j point, momentum at v grid points
! -----------------------------------------------------------------
!
! --- local 1-d arrays for matrix inversion
real v1do(kdm+1),v1dn(kdm+1), &
diffm(kdm+1),zm(kdm+1),hm(kdm),dzb(kdm)
!
! --- tridiagonal matrix solution arrays
real tri(kdm,0:1) ! dt/dz/dz factors in trid. matrix
real tcu(kdm), & ! upper coeff for (k-1) on k line of trid.matrix
tcc(kdm), & ! central ... (k ) ..
tcl(kdm), & ! lower ..... (k-1) ..
rhs(kdm) ! right-hand-side terms
!
real presv,froglp
integer k,ka,kmask(idm),nlayer,mixflg
!
froglp=.5*max(2,mixfrq)
!
presv=0.
kmask(1)=0
mixflg=0
do k=1,kk+1
ka=min(k,kk)
if (dpv(i,j,ka,n).lt.tencm.or.k.eq.kk+1) kmask(1)=1
if (presv.lt.depthv(i,j)-tencm.and.kmask(1).eq.0) then
diffm(k+1)=.5*froglp*(vcty(i,j,k+1)+vcty(i,j-1,k+1))
if (diffm(k+1).gt.0.) mixflg=mixflg+1
v1do(k)=v(i,j,k,n)
hm(k)=dpv(i,j,k,n)*qonem
if (k.eq.1) then
zm(k)=-.5*hm(k)
else
zm(k)=zm(k-1)-.5*(hm(k-1)+hm(k))
endif
presv=presv+dpv(i,j,k,n)
nlayer=k
elseif (k.eq.nlayer+1) then
diffm(k)=0.
v1do(k)=v1do(k-1)
zm(k)=zm(k-1)-.5*hm(k-1)
endif
enddo
if (mixflg.le.1) return
!
! --- compute factors for coefficients of tridiagonal matrix elements.
!
do k=1,nlayer
dzb(k)=zm(k)-zm(k+1)
enddo
!
tri(1,1)=delt1/(hm(1)*dzb(1))
tri(1,0)=0.
do k=2,nlayer
tri(k,1)=delt1/(hm(k)*dzb(k))
tri(k,0)=delt1/(hm(k)*dzb(k-1))
enddo
!
! --- solve the diffusion equation
call tridcof(diffm,tri,nlayer,tcu,tcc,tcl)
do k=1,nlayer
rhs(k)=v1do(k)
enddo
call tridmat(tcu,tcc,tcl,nlayer,hm,rhs,v1do,v1dn,diffm, i,j)
do k=1,nlayer
v(i,j,k,n)=v1dn(k)
enddo
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,107) &
!diag (nstep,i+i0,j+j0,k,hm(k),v1do(k),v1dn(k),k=1,nlayer)
!
return
107 format(23x,' thick v old v new'/(i9,2i5,i3,1x,f10.3,2f8.3))
end
!
subroutine diapf2(m,n)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
! --- MICOM-style explict interior diapycnal mixing for hybrid coordinates
implicit none
!
integer m,n
!
integer j
!
if (diapyc.eq.0. .or. (mod(nstep ,mixfrq).ne.0 .and. &
mod(nstep+1,mixfrq).ne.0)) return
!diag write (lp,'(i9,3x,a)') nstep,'entering d i a p f l'
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do 31 j=1,jj
call diapf2j(m,n, j)
31 continue
!$OMP END PARALLEL DO
!
call dpudpv(dpu(1-nbdy,1-nbdy,1,n), &
dpv(1-nbdy,1-nbdy,1,n), &
p,depthu,depthv, 0,0)
!
!diag write (lp,'(i9,3x,a)') nstep,'exiting d i a p f l'
return
end
subroutine diapf2j(m,n, j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n, j
!
integer i,k,k1,k2,ka,kmin(idm),kmax(idm),ktr
real flxu(idm,kdm),flxl(idm,kdm),pdot(idm,kdm),flngth(idm,kdm), &
ennsq,alfa,beta,q,qmin,qmax,amount,froglp,delp, &
alfadt1,alfadt2,betads1,betads2,plev, &
trflxu(idm,0:kdm+1,mxtrcr), &
trflxl(idm,0:kdm+1,mxtrcr),cliptr(idm,mxtrcr), &
tflxu(idm,0:kdm+1), tflxl(idm,0:kdm+1),clipt( idm), &
sflxu(idm,0:kdm+1), sflxl(idm,0:kdm+1),clips( idm), &
told(idm,2),sold(idm,2),trold(idm,2,mxtrcr)
! real totem(idm),tosal(idm),tndcyt,tndcys ! col.integrals (diag.use only)
!
real small
parameter (small=1.e-6)
!
# include "stmt_fns.h"
!
! --- -------------------------------
! --- diapycnal mixing, single j-row.
! --- -------------------------------
!
! --- if mixfrq > 1, apply mixing algorithm to both time levels
froglp=max(2,mixfrq)
!
do i=1,ii
if (SEA_P) then
!
! --- t/s conservation diagnostics (optional):
! totem(i)=0.
! tosal(i)=0.
! do k=1,kk
! totem(i)=totem(i)+temp(i,j,k,n)*dp(i,j,k,n)
! tosal(i)=tosal(i)+saln(i,j,k,n)*dp(i,j,k,n)
! enddo
!
do k=1,kk
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
enddo !k
!
sold(i,1)=saln(i,j,kk,n)
told(i,1)=temp(i,j,kk,n)
tflxl(i, 0)=0.
tflxu(i,kk+1)=0.
sflxl(i, 0)=0.
sflxu(i,kk+1)=0.
do ktr= 1,ntracr
trold( i, 1,ktr)=tracer(i,j,kk,n,ktr)
trflxl(i, 0,ktr)=0.
trflxu(i,kk+1,ktr)=0.
enddo !ktr
!
!diag if (i.eq.itest.and.j.eq.jtest) &
!diag write (lp,'(i9,2i5,3x,a/(i36,4f10.3))') nstep,i+i0,j+j0, &
!diag 'before diapf2: thickness salinity temperature density', &
!diag (k,dp(i,j,k,n)*qonem,saln(i,j,k,n), &
!diag temp(i,j,k,n),th3d(i,j,k,n)+thbase,k=1,kk)
!
kmin(i)=kk+1
kmax(i)=1
!
do k=2,kk
!
! --- locate lowest mass-containing layer and upper edge of stratified region
if (p(i,j,k).lt.p(i,j,kk+1)-onemm) then
kmax(i)=k
if (kmin(i).eq.kk+1 .and. &
th3d(i,j,k,n).gt.th3d(i,j,k-1,n)+sigjmp) then
kmin(i)=k
endif
endif
enddo !k
!
!diag if (j.eq.jtest.and.itest.ge.ifp(j,l).and.itest.le.ilp(j,l)) &
!diag write (lp,'(i9,2i5,a,2i5)') &
!diag nstep,itest+i0,j+j0,' kmin,kmax =',kmin(itest),kmax(itest)
!
! --- find buoyancy frequency for each layer
!
do k=2,kk-1
k1=k-1
k2=k+1
!
if (k.gt.kmin(i) .and. k.lt.kmax(i)) then
! --- ennsq = buoy.freq.^2 / g^2
if (locsig) then
alfadt1=dsiglocdt(ahalf*(temp(i,j,k1,n)+ &
temp(i,j,k ,n) ), &
ahalf*(saln(i,j,k1,n)+ &
saln(i,j,k, n) ),p(i,j,k))* &
(temp(i,j,k1,n)- &
temp(i,j,k, n) )
betads1=dsiglocds(ahalf*(temp(i,j,k1,n)+ &
temp(i,j,k ,n) ), &
ahalf*(saln(i,j,k1,n)+ &
saln(i,j,k, n) ),p(i,j,k))* &
(saln(i,j,k1,n)- &
saln(i,j,k, n) )
alfadt2=dsiglocdt(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,k2,n) ), &
ahalf*(saln(i,j,k ,n)+ &
saln(i,j,k2,n) ),p(i,j,k2))* &
(temp(i,j,k, n)- &
temp(i,j,k2,n) )
betads2=dsiglocdt(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,k2,n) ), &
ahalf*(saln(i,j,k ,n)+ &
saln(i,j,k2,n) ),p(i,j,k2))* &
(saln(i,j,k, n)- &
saln(i,j,k2,n) )
ennsq=-min(0.,min(alfadt1+betads1,alfadt2+betads2)) &
/max(p(i,j,k2)-p(i,j,k),onem)
else
ennsq=max(0.,min(th3d(i,j,k2,n)-th3d(i,j,k ,n), &
th3d(i,j,k ,n)-th3d(i,j,k1,n))) &
/max(p(i,j,k2)-p(i,j,k),onem)
endif
! --- store (exch.coeff x buoy.freq.^2 / g x time step) in -flngth-
! --- (dimensions of flngth: length in pressure units)
! -----------------------------------------------------------------------
! --- use the following if exch.coeff. = diapyc / buoyancy frequency
flngth(i,k)=diapyc*sqrt(ennsq) * baclin*froglp * onem
! -----------------------------------------------------------------------
! --- use the following if exch.coeff. = diapyc
!cc flngth(i,k)=diapyc*ennsq*g * baclin*froglp * onem
! -----------------------------------------------------------------------
!
endif
enddo !k
!
! --- find t/s fluxes at the upper and lower interface of each layer
! --- (compute only the part common to t and s fluxes)
!
do k=1,kk
flxu(i,k)=0.
flxl(i,k)=0.
!
if (k.gt.kmin(i) .and. k.lt.kmax(i)) then
!
if (locsig) then
plev=p(i,j,k)+0.5*dp(i,j,k,n)
alfa=-svref*dsiglocdt(temp(i,j,k,n),saln(i,j,k,n),plev)
beta= svref*dsiglocds(temp(i,j,k,n),saln(i,j,k,n),plev)
else
alfa=-svref*dsigdt(temp(i,j,k,n),saln(i,j,k,n))
beta= svref*dsigds(temp(i,j,k,n),saln(i,j,k,n))
endif
!
flxu(i,k)=flngth(i,k)/ &
max(beta*(saln(i,j,k,n)-saln(i,j,k-1,n)) &
-alfa*(temp(i,j,k,n)-temp(i,j,k-1,n)),small)
flxl(i,k)=flngth(i,k)/ &
max(beta*(saln(i,j,k+1,n)-saln(i,j,k,n)) &
-alfa*(temp(i,j,k+1,n)-temp(i,j,k,n)),small)
!
q=min(1.,.5*min(p(i,j,k)-p(i,j,k-1),p(i,j,k+2)-p(i,j,k+1))/ &
max(flxu(i,k),flxl(i,k),epsil))
!
!diag if (q.ne.1.) write (lp,'(i9,2i5,i3,a,1p,2e10.2,0p,2f7.2,f5.2)') &
!diag nstep,i+i0,j+j0,k,' flxu/l,dpu/l,q=',flxu(i,k),flxl(i,k), &
!diag (p(i,j,k)-p(i,j,k-1))*qonem,(p(i,j,k+2)-p(i,j,k+1))*qonem,q
!
flxu(i,k)=flxu(i,k)*q
flxl(i,k)=flxl(i,k)*q
!
endif ! kmin < k < kmax
!
!diag if (i.eq.itest.and.j.eq.jtest.and.k.ge.kmin(i).and.k.le.kmax(i)) &
!diag write (lp,'(i9,2i5,i3,3x,a/22x,f9.3,2f7.3,1p,3e10.3)') &
!diag nstep,i+i0,j+j0,k, &
!diag 'thknss temp saln flngth flxu flxl', &
!diag dp(i,j,k,n)*qonem,temp(i,j,k,n),saln(i,j,k,n),flngth(i,k), &
!diag flxu(i,k)*qonem,flxl(i,k)*qonem
!
enddo !k
!
! --- determine mass flux -pdot- implied by t/s fluxes.
!
do k=1,kk
if (k.gt.kmin(i) .and. k.le.kmax(i)) then
pdot(i,k)=flxu(i,k)-flxl(i,k-1)
else
pdot(i,k)=0.
endif
enddo !k
!
! --- convert flxu,flxl into actual t/s (and tracer) fluxes
!
do k=1,kk
tflxu(i,k)=0.
tflxl(i,k)=0.
sflxu(i,k)=0.
sflxl(i,k)=0.
if (k.gt.kmin(i) .and. k.lt.kmax(i)) then
tflxu(i,k)=flxu(i,k)*temp(i,j,k-1,n)
sflxu(i,k)=flxu(i,k)*saln(i,j,k-1,n)
!
tflxl(i,k)=flxl(i,k)*temp(i,j,k+1,n)
sflxl(i,k)=flxl(i,k)*saln(i,j,k+1,n)
endif
do ktr= 1,ntracr
trflxu(i,k,ktr)=0.
trflxl(i,k,ktr)=0.
if (k.gt.kmin(i) .and. k.lt.kmax(i)) then
trflxu(i,k,ktr)=flxu(i,k)*tracer(i,j,k-1,n,ktr)
trflxl(i,k,ktr)=flxl(i,k)*tracer(i,j,k+1,n,ktr)
endif
enddo !ktr
enddo !k
!
do ktr= 1,ntracr
cliptr(i,ktr)=0.
enddo !ktr
clipt( i)=0.
clips( i)=0.
!
! --- update interface pressure and layer temperature/salinity
do k=kk,1,-1
ka=max(1,k-1)
!
sold(i,2)=sold(i,1)
sold(i,1)=saln(i,j,k,n)
told(i,2)=told(i,1)
told(i,1)=temp(i,j,k,n)
do ktr= 1,ntracr
trold(i,2,ktr)=trold( i,1, ktr)
trold(i,1,ktr)=tracer(i,j,k,n,ktr)
enddo
!
dpo(i,j,k,n)=dp(i,j,k,n)
p(i,j,k)=p(i,j,k)-pdot(i,k)
dp(i,j,k,n)=p(i,j,k+1)-p(i,j,k)
!
if (k.ge.kmin(i) .and. k.le.kmax(i)) then
delp=dp(i,j,k,n)
if (delp.gt.0.) then
amount=temp(i,j,k,n)*dpo(i,j,k,n) &
-(tflxu(i,k+1)-tflxu(i,k)+tflxl(i,k-1)-tflxl(i,k))
q=amount
qmax=max(temp(i,j,ka,n),told(i,1),told(i,2))
qmin=min(temp(i,j,ka,n),told(i,1),told(i,2))
amount=max(qmin*delp,min(amount,qmax*delp))
clipt(i)=clipt(i)+(q-amount)
temp(i,j,k,n)=amount/delp
!
amount=saln(i,j,k,n)*dpo(i,j,k,n) &
-(sflxu(i,k+1)-sflxu(i,k)+sflxl(i,k-1)-sflxl(i,k))
q=amount
qmax=max(saln(i,j,ka,n),sold(i,1),sold(i,2))
qmin=min(saln(i,j,ka,n),sold(i,1),sold(i,2))
amount=max(qmin*delp,min(amount,qmax*delp))
clips(i)=clips(i)+(q-amount)
saln(i,j,k,n)=amount/delp
!
do ktr= 1,ntracr
amount=tracer(i,j,k,n,ktr)*dpo(i,j,k,n) &
-(trflxu(i,k+1,ktr)-trflxu(i,k,ktr)+ &
trflxl(i,k-1,ktr)-trflxl(i,k,ktr))
q=amount
qmax=max(tracer(i,j,ka,n,ktr),trold(i,1,ktr), &
trold(i,2,ktr))
qmin=min(tracer(i,j,ka,n,ktr),trold(i,1,ktr), &
trold(i,2,ktr))
amount=max(qmin*delp,min(amount,qmax*delp))
cliptr(i,ktr)=cliptr(i,ktr)+(q-amount)
tracer(i,j,k,n,ktr)=amount/delp
enddo !ktr
endif
endif
enddo !k
!
clipt(i)=clipt(i)/pbot(i,j) + baclin*froglp*tofset
clips(i)=clips(i)/pbot(i,j) + baclin*froglp*sofset
do ktr= 1,ntracr
cliptr(i,ktr)=cliptr(i,ktr)/pbot(i,j)
enddo !ktr
!
do k=1,kk
!
! --- restore 'clipped' and 'offset' t/s amount to column
temp(i,j,k,n)=temp(i,j,k,n)+clipt(i)
saln(i,j,k,n)=saln(i,j,k,n)+clips(i)
th3d(i,j,k,n)=sig(temp(i,j,k,n),saln(i,j,k,n))-thbase
do ktr= 1,ntracr
tracer(i,j,k,n,ktr)=tracer(i,j,k,n,ktr)+cliptr(i,ktr)
enddo !ktr
!
diaflx(i,j,k)=diaflx(i,j,k)+(dp(i,j,k,n)-dpo(i,j,k,n)) ! diapyc.flx.
! --- make sure p is computed from dp, not the other way around (roundoff!)
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
enddo !k
!
! --- t/s conservation diagnostics (optional):
! tndcyt=-totem(i)
! tndcys=-tosal(i)
! do k=1,kk
! tndcyt=tndcyt+temp(i,j,k,n)*dp(i,j,k,n)
! tndcys=tndcys+saln(i,j,k,n)*dp(i,j,k,n)
! enddo
! if (abs(tndcyt/totem(i)).gt.1.e-11)
! . write (lp,100) i,j,' diapf2 temp.col.intgl.:',totem(i),tndcyt,
! . clipt(i)
! if (abs(tndcys/tosal(i)).gt.1.e-11)
! . write (lp,100)