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source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 1928

Last change on this file since 1928 was 1921, checked in by suehring, 8 years ago
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1	!> @file surface_layer_fluxes_mod.f90
2	!--------------------------------------------------------------------------------!
3	! This file is part of PALM.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the terms
6	! of the GNU General Public License as published by the Free Software Foundation,
7	! either version 3 of the License, or (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with
14	! PALM. If not, see <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2016 Leibniz Universitaet Hannover
17	!
18	!--------------------------------------------------------------------------------!
19	! Current revisions:
20	! ------------------
21	!
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: surface_layer_fluxes_mod.f90 1921 2016-05-30 10:52:07Z hellstea $
26	!
27	! 1920 2016-05-30 10:50:15Z suehring
28	! Avoid segmentation fault (see change in 1915) by different initialization of
29	! us instead of adding a very small number in the denominator
30	!
31	! 1915 2016-05-27 11:05:02Z suehring
32	! Bugfix: avoid segmentation fault in case of most_method = 'circular' at first
33	! timestep
34	!
35	! 1850 2016-04-08 13:29:27Z maronga
36	! Module renamed
37	!
38	!
39	! 1822 2016-04-07 07:49:42Z hoffmann
40	! icloud_scheme replaced by microphysics_*
41	!
42	! 1788 2016-03-10 11:01:04Z maronga
43	! Added parameter z0q which replaces z0h in the similarity functions for
44	! humidity.
45	! Syntax layout improved.
46	!
47	! 1757 2016-02-22 15:49:32Z maronga
48	! Minor fixes.
49	!
50	! 1749 2016-02-09 12:19:56Z raasch
51	! further OpenACC adjustments
52	!
53	! 1747 2016-02-08 12:25:53Z raasch
54	! adjustments for OpenACC usage
55	!
56	! 1709 2015-11-04 14:47:01Z maronga
57	! Bugfix: division by zero could occur when calculating rib at low wind speeds
58	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
59	! neutral = .T.
60	!
61	! 1705 2015-11-02 14:28:56Z maronga
62	! Typo removed
63	!
64	! 1697 2015-10-28 17:14:10Z raasch
65	! FORTRAN and OpenMP errors removed
66	!
67	! 1696 2015-10-27 10:03:34Z maronga
68	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
69	! course of the re-writing two additional methods have been implemented. See
70	! updated description.
71	!
72	! 1551 2015-03-03 14:18:16Z maronga
73	! Removed land surface model part. The surface fluxes are now always calculated
74	! within prandtl_fluxes, based on the given surface temperature/humidity (which
75	! is either provided by the land surface model, by large scale forcing data, or
76	! directly prescribed by the user.
77	!
78	! 1496 2014-12-02 17:25:50Z maronga
79	! Adapted for land surface model
80	!
81	! 1494 2014-11-21 17:14:03Z maronga
82	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
83	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
84	! topography for coupled runs (not tested)
85	!
86	! 1361 2014-04-16 15:17:48Z hoffmann
87	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
88	! drop concentration (nrsws) added
89	!
90	! 1340 2014-03-25 19:45:13Z kanani
91	! REAL constants defined as wp-kind
92	!
93	! 1320 2014-03-20 08:40:49Z raasch
94	! ONLY-attribute added to USE-statements,
95	! kind-parameters added to all INTEGER and REAL declaration statements,
96	! kinds are defined in new module kinds,
97	! old module precision_kind is removed,
98	! revision history before 2012 removed,
99	! comment fields (!:) to be used for variable explanations added to
100	! all variable declaration statements
101	!
102	! 1276 2014-01-15 13:40:41Z heinze
103	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
104	!
105	! 1257 2013-11-08 15:18:40Z raasch
106	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
107	!
108	! 1036 2012-10-22 13:43:42Z raasch
109	! code put under GPL (PALM 3.9)
110	!
111	! 1015 2012-09-27 09:23:24Z raasch
112	! OpenACC statements added
113	!
114	! 978 2012-08-09 08:28:32Z fricke
115	! roughness length for scalar quantities z0h added
116	!
117	! Revision 1.1 1998/01/23 10:06:06 raasch
118	! Initial revision
119	!
120	!
121	! Description:
122	! ------------
123	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
124	!> values of the variables at grid point k=1. Three different methods are
125	!> available:
126	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
127	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
128	!> slower
129	!> 3) a method using a lookup table which is fast and accurate. Note, however,
130	!> that this method cannot be used in case of roughness heterogeneity
131	!>
132	!> @todo (re)move large_scale_forcing actions
133	!> @todo check/optimize OpenMP and OpenACC directives
134	!------------------------------------------------------------------------------!
135	MODULE surface_layer_fluxes_mod
136
137	USE arrays_3d, &
138	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
139	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h, z0q
140
141	USE cloud_parameters, &
142	ONLY: l_d_cp, pt_d_t
143
144	USE constants, &
145	ONLY: pi
146
147	USE cpulog
148
149	USE control_parameters, &
150	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
151	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, &
152	initializing_actions, kappa, intermediate_timestep_count, &
153	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
154	message_string, microphysics_seifert, most_method, neutral, &
155	passive_scalar, pt_surface, q_surface, run_coupled, &
156	surface_pressure, simulated_time, terminate_run, zeta_max, &
157	zeta_min
158
159	USE indices, &
160	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
161	nzb_u_inner, nzb_v_inner
162
163	USE kinds
164
165	USE pegrid
166
167	USE land_surface_model_mod, &
168	ONLY: land_surface, skip_time_do_lsm
169
170	IMPLICIT NONE
171
172	INTEGER(iwp) :: i !< loop index x direction
173	INTEGER(iwp) :: j !< loop index y direction
174	INTEGER(iwp) :: k !< loop index z direction
175
176	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
177
178	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
179
180	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
181	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
182	uv_total !< Total velocity at first grid level
183
184	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
185	ol_tab !< Lookup table values of L
186
187	REAL(wp) :: e_s, & !< Saturation water vapor pressure
188	l_bnd = 7500, & !< Lookup table index of the last time step
189	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
190	rib_max, & !< Maximum Richardson number in lookup table
191	rib_min, & !< Minimum Richardson number in lookup table
192	z_mo !< Height of the constant flux layer where MOST is assumed
193
194
195	SAVE
196
197	PRIVATE
198
199	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
200
201	INTERFACE init_surface_layer_fluxes
202	MODULE PROCEDURE init_surface_layer_fluxes
203	END INTERFACE init_surface_layer_fluxes
204
205	INTERFACE surface_layer_fluxes
206	MODULE PROCEDURE surface_layer_fluxes
207	END INTERFACE surface_layer_fluxes
208
209
210	CONTAINS
211
212
213	!------------------------------------------------------------------------------!
214	! Description:
215	! ------------
216	!> Main routine to compute the surface fluxes
217	!------------------------------------------------------------------------------!
218	SUBROUTINE surface_layer_fluxes
219
220	IMPLICIT NONE
221
222	!
223	!-- In case cloud physics is used, it is required to derive potential
224	!-- temperature and specific humidity at first grid level from the fields pt
225	!-- and q
226	IF ( cloud_physics ) THEN
227	CALL calc_pt_q
228	ENDIF
229
230	!
231	!-- First, calculate the new Obukhov length, then new friction velocity,
232	!-- followed by the new scaling parameters (th, q, etc.), and the new
233	!-- surface fluxes if required. The old routine ("circular") requires a
234	!-- different order of calls as the scaling parameters from the previous time
235	!-- steps are used to calculate the Obukhov length
236
237	!
238	!-- Depending on setting of most_method use the "old" routine
239	IF ( most_method == 'circular' ) THEN
240
241	CALL calc_scaling_parameters
242
243	CALL calc_uv_total
244
245	IF ( .NOT. neutral ) THEN
246	CALL calc_ol
247	ENDIF
248
249	CALL calc_us
250
251	CALL calc_surface_fluxes
252
253	!
254	!-- Use either Newton iteration or a lookup table for the bulk Richardson
255	!-- number to calculate the Obukhov length
256	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
257
258	CALL calc_uv_total
259
260	IF ( .NOT. neutral ) THEN
261	CALL calc_ol
262	ENDIF
263
264	CALL calc_us
265
266	CALL calc_scaling_parameters
267
268	CALL calc_surface_fluxes
269
270	ENDIF
271
272	END SUBROUTINE surface_layer_fluxes
273
274
275	!------------------------------------------------------------------------------!
276	! Description:
277	! ------------
278	!> Initializing actions for the surface layer routine. Basically, this involves
279	!> the preparation of a lookup table for the the bulk Richardson number vs
280	!> Obukhov length L when using the lookup table method.
281	!------------------------------------------------------------------------------!
282	SUBROUTINE init_surface_layer_fluxes
283
284	IMPLICIT NONE
285
286	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
287	num_steps_n !< Number of non-stretched zeta steps
288
289	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
290
291	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
292
293	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
294
295
296	REAL(wp) :: zeta_step, & !< Increment of zeta
297	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
298	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
299	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
300	z0_min = 0.0_wp !< Minimum value of z0 to create table
301	!
302	!-- When cloud physics is used, arrays for storing potential temperature and
303	!-- specific humidity at first grid level are required
304	IF ( cloud_physics ) THEN
305	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
306	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
307	ENDIF
308
309	!
310	!-- Allocate field for storing the horizontal velocity
311	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
312
313
314	!
315	!-- In case of runs with neutral statification, set Obukhov length to a
316	!-- large value
317	IF ( neutral ) ol = 1.0E10_wp
318
319	IF ( most_method == 'lookup' ) THEN
320
321	!
322	!-- Check for roughness heterogeneity. In that case terminate run and
323	!-- inform user
324	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
325	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
326	terminate_run_l = .TRUE.
327	ENDIF
328
329	#if defined( __parallel )
330	!
331	!-- Make a logical OR for all processes. Force termiation of model if result
332	!-- is TRUE
333	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
334	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
335	MPI_LOR, comm2d, ierr )
336	#else
337	terminate_run = terminate_run_l
338	#endif
339
340	IF ( terminate_run ) THEN
341	message_string = 'most_method = "lookup" cannot be used in ' // &
342	'combination with a prescribed roughness ' // &
343	'heterogeneity'
344	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
345	ENDIF
346
347	ALLOCATE( zeta_tmp(0:num_steps-1) )
348
349	!
350	!-- Use the lowest possible value for z_mo
351	k = MINVAL(nzb_s_inner)
352	z_mo = zu(k+1) - zw(k)
353
354	!
355	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
356	!-- available steps (num_steps). The calculation is done with negative
357	!-- values of zeta in order to simplify the stretching in the free
358	!-- convection limit for the remaining 10% of steps.
359	zeta_tmp(0) = - zeta_max
360	num_steps_n = ( num_steps * 9 / 10 ) - 1
361	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
362
363	DO l = 1, num_steps_n
364	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
365	ENDDO
366
367	!
368	!-- Calculate stretching factor for the free convection range
369	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
370	regr_old = regr
371	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
372	)**( 10.0_wp / REAL(num_steps) )
373	ENDDO
374
375	!
376	!-- Calculate z/L range from zeta_min to zeta_stretch
377	DO l = num_steps_n+1, num_steps-1
378	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
379	zeta_step = zeta_step * regr
380	ENDDO
381
382	!
383	!-- Save roughness lengths to temporary variables
384	z0h_min = z0h(nys,nxl)
385	z0_min = z0(nys,nxl)
386
387	!
388	!-- Calculate lookup table for the Richardson number versus Obukhov length
389	!-- The Richardson number (rib) is defined depending on the choice of
390	!-- boundary conditions for temperature
391	IF ( ibc_pt_b == 1 ) THEN
392	DO l = 0, num_steps-1
393	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
394	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
395	- psi_m( z_mo / ol_tab(l) ) &
396	+ psi_m( z0_min / ol_tab(l) ) &
397	)**3
398	ENDDO
399	ELSE
400	DO l = 0, num_steps-1
401	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
402	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
403	- psi_h( z_mo / ol_tab(l) ) &
404	+ psi_h( z0h_min / ol_tab(l) ) &
405	) &
406	/ ( LOG( z_mo / z0_min ) &
407	- psi_m( z_mo / ol_tab(l) ) &
408	+ psi_m( z0_min / ol_tab(l) ) &
409	)**2
410	ENDDO
411	ENDIF
412
413	!
414	!-- Determine minimum values of rib in the lookup table. Set upper limit
415	!-- to critical Richardson number (0.25)
416	rib_min = MINVAL(rib_tab)
417	rib_max = 0.25 !MAXVAL(rib_tab)
418
419	DEALLOCATE( zeta_tmp )
420	ENDIF
421
422	END SUBROUTINE init_surface_layer_fluxes
423
424
425	!------------------------------------------------------------------------------!
426	! Description:
427	! ------------
428	!> Compute the absolute value of the horizontal velocity (relative to the
429	!> surface). This is required by all methods
430	!------------------------------------------------------------------------------!
431	SUBROUTINE calc_uv_total
432
433	IMPLICIT NONE
434
435
436	!$OMP PARALLEL DO PRIVATE( k )
437	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
438	DO i = nxl, nxr
439	DO j = nys, nyn
440
441	k = nzb_s_inner(j,i)
442	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
443	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
444	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
445	- v(k,j,i) - v(k,j+1,i) ) )**2 )
446
447	!
448	!-- For too small values of the local wind, MOST does not work. A
449	!-- threshold value is thus set if required
450	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
451
452	ENDDO
453	ENDDO
454
455	!
456	!-- Values of uv_total need to be exchanged at the ghost boundaries
457	!$acc update host( uv_total )
458	CALL exchange_horiz_2d( uv_total )
459	!$acc update device( uv_total )
460
461	END SUBROUTINE calc_uv_total
462
463
464	!------------------------------------------------------------------------------!
465	! Description:
466	! ------------
467	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
468	!------------------------------------------------------------------------------!
469	SUBROUTINE calc_ol
470
471	IMPLICIT NONE
472
473	INTEGER(iwp) :: iter, & !< Newton iteration step
474	l !< look index
475
476	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
477
478	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
479	f_d_ol, & !< Derivative of f
480	ol_l, & !< Lower bound of L for Newton iteration
481	ol_m, & !< Previous value of L for Newton iteration
482	ol_old, & !< Previous time step value of L
483	ol_u !< Upper bound of L for Newton iteration
484
485	IF ( TRIM( most_method ) /= 'circular' ) THEN
486
487	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
488
489	!$OMP PARALLEL DO PRIVATE( k, z_mo )
490	!$acc kernels loop private( j, k, z_mo )
491	DO i = nxl, nxr
492	DO j = nys, nyn
493
494	k = nzb_s_inner(j,i)
495	z_mo = zu(k+1) - zw(k)
496
497	!
498	!-- Evaluate bulk Richardson number (calculation depends on
499	!-- definition based on setting of boundary conditions
500	IF ( ibc_pt_b /= 1 ) THEN
501	IF ( humidity ) THEN
502	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
503	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
504	ELSE
505	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
506	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
507	ENDIF
508	ELSE
509	!
510	!-- When using Neumann boundary conditions, the buoyancy flux
511	!-- is required but cannot be calculated at the surface, as pt
512	!-- and q are not known at the surface. Hence the values at
513	!-- first grid level are used to estimate the buoyancy flux
514	IF ( humidity ) THEN
515	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
516	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
517	* pt(k+1,j,i) * qsws(j,i) ) &
518	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
519	+ 1.0E-20_wp)
520	ELSE
521	rib(j,i) = - g * z_mo * shf(j,i) &
522	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
523	+ 1.0E-20_wp )
524	ENDIF
525	ENDIF
526
527	ENDDO
528	ENDDO
529	!$acc end data
530
531	ENDIF
532
533	!
534	!-- Calculate the Obukhov length either using a Newton iteration
535	!-- method, via a lookup table, or using the old circular way
536	IF ( TRIM( most_method ) == 'newton' ) THEN
537
538	!$OMP PARALLEL DO PRIVATE( k, z_mo )
539	!# WARNING: does not work on GPU so far because of DO-loop with
540	!# undetermined iterations
541	!!!!!!$acc kernels loop
542	DO i = nxl, nxr
543	DO j = nys, nyn
544
545	k = nzb_s_inner(j,i)
546	z_mo = zu(k+1) - zw(k)
547
548	!
549	!-- Store current value in case the Newton iteration fails
550	ol_old = ol(j,i)
551
552	!
553	!-- Ensure that the bulk Richardson number and the Obukhov
554	!-- lengtH have the same sign
555	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
556	ABS( ol(j,i) ) == ol_max ) THEN
557	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
558	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
559	ENDIF
560	!
561	!-- Iteration to find Obukhov length
562	iter = 0
563	DO
564	iter = iter + 1
565	!
566	!-- In case of divergence, use the value of the previous time step
567	IF ( iter > 1000 ) THEN
568	ol(j,i) = ol_old
569	EXIT
570	ENDIF
571
572	ol_m = ol(j,i)
573	ol_l = ol_m - 0.001_wp * ol_m
574	ol_u = ol_m + 0.001_wp * ol_m
575
576
577	IF ( ibc_pt_b /= 1 ) THEN
578	!
579	!-- Calculate f = Ri - [...]/[...]^2 = 0
580	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
581	- psi_h( z_mo / ol_m ) &
582	+ psi_h( z0h(j,i) / ol_m ) &
583	) &
584	/ ( LOG( z_mo / z0(j,i) ) &
585	- psi_m( z_mo / ol_m ) &
586	+ psi_m( z0(j,i) / ol_m ) &
587	)**2
588
589	!
590	!-- Calculate df/dL
591	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
592	- psi_h( z_mo / ol_u ) &
593	+ psi_h( z0h(j,i) / ol_u ) &
594	) &
595	/ ( LOG( z_mo / z0(j,i) ) &
596	- psi_m( z_mo / ol_u ) &
597	+ psi_m( z0(j,i) / ol_u ) &
598	)**2 &
599	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
600	- psi_h( z_mo / ol_l ) &
601	+ psi_h( z0h(j,i) / ol_l ) &
602	) &
603	/ ( LOG( z_mo / z0(j,i) ) &
604	- psi_m( z_mo / ol_l ) &
605	+ psi_m( z0(j,i) / ol_l ) &
606	)**2 &
607	) / ( ol_u - ol_l )
608	ELSE
609	!
610	!-- Calculate f = Ri - 1 /[...]^3 = 0
611	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
612	- psi_m( z_mo / ol_m ) &
613	+ psi_m( z0(j,i) / ol_m ) &
614	)**3
615
616	!
617	!-- Calculate df/dL
618	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
619	- psi_m( z_mo / ol_u ) &
620	+ psi_m( z0(j,i) / ol_u ) &
621	)**3 &
622	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
623	- psi_m( z_mo / ol_l ) &
624	+ psi_m( z0(j,i) / ol_l ) &
625	)**3 &
626	) / ( ol_u - ol_l )
627	ENDIF
628	!
629	!-- Calculate new L
630	ol(j,i) = ol_m - f / f_d_ol
631
632	!
633	!-- Ensure that the bulk Richardson number and the Obukhov
634	!-- length have the same sign and ensure convergence.
635	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
636
637	!
638	!-- If unrealistic value occurs, set L to the maximum
639	!-- value that is allowed
640	IF ( ABS( ol(j,i) ) > ol_max ) THEN
641	ol(j,i) = ol_max
642	EXIT
643	ENDIF
644	!
645	!-- Check for convergence
646	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
647	EXIT
648	ELSE
649	CYCLE
650	ENDIF
651
652	ENDDO
653
654	ENDDO
655	ENDDO
656
657	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
658
659	!$OMP PARALLEL DO PRIVATE( k, z_mo )
660	!# WARNING: does not work on GPU so far because of DO WHILE construct
661	!!!!!!$acc kernels loop
662	DO i = nxl, nxr
663	DO j = nys, nyn
664
665	!
666	!-- If the bulk Richardson number is outside the range of the lookup
667	!-- table, set it to the exceeding threshold value
668	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
669	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
670
671	!
672	!-- Find the correct index bounds for linear interpolation. As the
673	!-- Richardson number will not differ very much from time step to
674	!-- time step , use the index from the last step and search in the
675	!-- correct direction
676	l = l_bnd
677	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
678	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
679	l = l-1
680	ENDDO
681	ELSE
682	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
683	.AND. l < num_steps-1 )
684	l = l+1
685	ENDDO
686	ENDIF
687	l_bnd = l
688
689	!
690	!-- Linear interpolation to find the correct value of z/L
691	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
692	/ ( rib_tab(l) - rib_tab(l-1) ) &
693	* ( rib(j,i) - rib_tab(l-1) ) )
694
695	ENDDO
696	ENDDO
697
698	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
699
700	!$OMP PARALLEL DO PRIVATE( k, z_mo )
701	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
702	DO i = nxl, nxr
703	DO j = nys, nyn
704
705	k = nzb_s_inner(j,i)
706	z_mo = zu(k+1) - zw(k)
707
708	IF ( .NOT. humidity ) THEN
709	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
710	* ts(j,i) + 1E-30_wp )
711	ELSEIF ( cloud_physics ) THEN
712
713	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
714	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
715	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
716	* ql(k+1,j,i) ) + 1E-30_wp )
717	ELSE
718	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
719	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
720	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
721	ENDIF
722	!
723	!-- Limit the value range of the Obukhov length.
724	!-- This is necessary for very small velocities (u,v --> 0), because
725	!-- the absolute value of ol can then become very small, which in
726	!-- consequence would result in very large shear stresses and very
727	!-- small momentum fluxes (both are generally unrealistic).
728	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
729	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
730	ENDDO
731	ENDDO
732
733	ENDIF
734
735	!
736	!-- Values of ol at ghost point locations are needed for the evaluation
737	!-- of usws and vsws.
738	!$acc update host( ol )
739	CALL exchange_horiz_2d( ol )
740	!$acc update device( ol )
741
742	END SUBROUTINE calc_ol
743
744	!
745	!-- Calculate friction velocity u*
746	SUBROUTINE calc_us
747
748	IMPLICIT NONE
749
750	!$OMP PARALLEL DO PRIVATE( k, z_mo )
751	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
752	DO i = nxlg, nxrg
753	DO j = nysg, nyng
754
755	k = nzb_s_inner(j,i)+1
756	z_mo = zu(k+1) - zw(k)
757
758	!
759	!-- Compute u* at the scalars' grid points
760	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
761	- psi_m( z_mo / ol(j,i) ) &
762	+ psi_m( z0(j,i) / ol(j,i) ) )
763	ENDDO
764	ENDDO
765
766	END SUBROUTINE calc_us
767
768	!
769	!-- Calculate potential temperature and specific humidity at first grid level
770	SUBROUTINE calc_pt_q
771
772	IMPLICIT NONE
773
774	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
775	DO i = nxlg, nxrg
776	DO j = nysg, nyng
777	k = nzb_s_inner(j,i)+1
778	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
779	qv1(j,i) = q(k,j,i) - ql(k,j,i)
780	ENDDO
781	ENDDO
782
783	END SUBROUTINE calc_pt_q
784
785	!
786	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
787	SUBROUTINE calc_scaling_parameters
788
789	IMPLICIT NONE
790
791	!
792	!-- Data information for accelerators
793	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
794	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
795	!$acc present( vpt, vsws, zu, zw, z0, z0h )
796	!
797	!-- Compute theta*
798	IF ( constant_heatflux ) THEN
799
800	!
801	!-- For a given heat flux in the surface layer:
802	!$OMP PARALLEL DO
803	!$acc kernels loop private( j )
804	DO i = nxlg, nxrg
805	DO j = nysg, nyng
806	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
807	!
808	!-- ts must be limited, because otherwise overflow may occur in case
809	!-- of us=0 when computing ol further below
810	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
811	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
812	ENDDO
813	ENDDO
814
815	ELSE
816	!
817	!-- For a given surface temperature:
818	IF ( large_scale_forcing .AND. lsf_surf ) THEN
819	!$OMP PARALLEL DO
820	!$acc kernels loop private( j, k )
821	DO i = nxlg, nxrg
822	DO j = nysg, nyng
823	k = nzb_s_inner(j,i)
824	pt(k,j,i) = pt_surface
825	ENDDO
826	ENDDO
827	ENDIF
828
829	!$OMP PARALLEL DO PRIVATE( k, z_mo )
830	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
831	DO i = nxlg, nxrg
832	DO j = nysg, nyng
833
834	k = nzb_s_inner(j,i)
835	z_mo = zu(k+1) - zw(k)
836
837	IF ( cloud_physics ) THEN
838	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
839	/ ( LOG( z_mo / z0h(j,i) ) &
840	- psi_h( z_mo / ol(j,i) ) &
841	+ psi_h( z0h(j,i) / ol(j,i) ) )
842	ELSE
843	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
844	/ ( LOG( z_mo / z0h(j,i) ) &
845	- psi_h( z_mo / ol(j,i) ) &
846	+ psi_h( z0h(j,i) / ol(j,i) ) )
847	ENDIF
848
849	ENDDO
850	ENDDO
851	ENDIF
852
853	!
854	!-- If required compute q*
855	IF ( humidity .OR. passive_scalar ) THEN
856	IF ( constant_waterflux ) THEN
857	!
858	!-- For a given water flux in the surface layer
859	!$OMP PARALLEL DO
860	!$acc kernels loop private( j )
861	DO i = nxlg, nxrg
862	DO j = nysg, nyng
863	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
864	ENDDO
865	ENDDO
866
867	ELSE
868	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
869	run_coupled )
870
871	IF ( large_scale_forcing .AND. lsf_surf ) THEN
872	!$OMP PARALLEL DO
873	!$acc kernels loop private( j, k )
874	DO i = nxlg, nxrg
875	DO j = nysg, nyng
876	k = nzb_s_inner(j,i)
877	q(k,j,i) = q_surface
878	ENDDO
879	ENDDO
880	ENDIF
881
882	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
883	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
884	DO i = nxlg, nxrg
885	!$acc loop independent
886	DO j = nysg, nyng
887
888	k = nzb_s_inner(j,i)
889	z_mo = zu(k+1) - zw(k)
890
891	!
892	!-- Assume saturation for atmosphere coupled to ocean (but not
893	!-- in case of precursor runs)
894	IF ( coupled_run ) THEN
895	e_s = 6.1_wp * &
896	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
897	- 273.15_wp ) )
898	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
899	ENDIF
900
901	IF ( cloud_physics ) THEN
902	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
903	/ ( LOG( z_mo / z0q(j,i) ) &
904	- psi_h( z_mo / ol(j,i) ) &
905	+ psi_h( z0q(j,i) / ol(j,i) ) )
906
907	ELSE
908	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
909	/ ( LOG( z_mo / z0q(j,i) ) &
910	- psi_h( z_mo / ol(j,i) ) &
911	+ psi_h( z0q(j,i) / ol(j,i) ) )
912	ENDIF
913
914	ENDDO
915	ENDDO
916	ENDIF
917	ENDIF
918
919
920	!
921	!-- If required compute qr* and nr*
922	IF ( cloud_physics .AND. microphysics_seifert ) &
923	THEN
924
925	!$OMP PARALLEL DO PRIVATE( k, z_mo )
926	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
927	DO i = nxlg, nxrg
928	!$acc loop independent
929	DO j = nysg, nyng
930
931	k = nzb_s_inner(j,i)
932	z_mo = zu(k+1) - zw(k)
933
934	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
935	/ ( LOG( z_mo / z0q(j,i) ) &
936	- psi_h( z_mo / ol(j,i) ) &
937	+ psi_h( z0q(j,i) / ol(j,i) ) )
938
939	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
940	/ ( LOG( z_mo / z0q(j,i) ) &
941	- psi_h( z_mo / ol(j,i) ) &
942	+ psi_h( z0q(j,i) / ol(j,i) ) )
943	ENDDO
944	ENDDO
945
946	ENDIF
947	!$acc end data
948
949	END SUBROUTINE calc_scaling_parameters
950
951
952
953	!
954	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
955	SUBROUTINE calc_surface_fluxes
956
957	IMPLICIT NONE
958
959	REAL(wp) :: ol_mid !< Grid-interpolated L
960
961	!
962	!-- Compute u'w' for the total model domain.
963	!-- First compute the corresponding component of u* and square it.
964	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
965	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
966	DO i = nxl, nxr
967	DO j = nys, nyn
968
969	k = nzb_u_inner(j,i)
970	z_mo = zu(k+1) - zw(k)
971	!
972	!-- Compute bulk Obukhov length for this point
973	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
974
975	IF ( ol_mid == 0.0_wp ) THEN
976	ol_mid = MIN(ol(j,i-1), ol(j,i))
977	ENDIF
978
979	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
980	/ ( LOG( z_mo / z0(j,i) ) &
981	- psi_m( z_mo / ol_mid ) &
982	+ psi_m( z0(j,i) / ol_mid ) )
983
984	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
985	ENDDO
986	ENDDO
987
988	!
989	!-- Compute v'w' for the total model domain.
990	!-- First compute the corresponding component of u* and square it.
991	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
992	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
993	DO i = nxl, nxr
994	DO j = nys, nyn
995
996	k = nzb_v_inner(j,i)
997	z_mo = zu(k+1) - zw(k)
998	!
999	!-- Compute bulk Obukhov length for this point
1000	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
1001
1002	IF ( ol_mid == 0.0_wp ) THEN
1003	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
1004	ENDIF
1005
1006	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
1007	/ ( LOG( z_mo / z0(j,i) ) &
1008	- psi_m( z_mo / ol_mid ) &
1009	+ psi_m( z0(j,i) / ol_mid ) )
1010
1011	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
1012
1013	ENDDO
1014	ENDDO
1015
1016	!
1017	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
1018	!$acc update host( usws, vsws )
1019	CALL exchange_horiz_2d( usws )
1020	CALL exchange_horiz_2d( vsws )
1021	!$acc update device( usws, vsws )
1022
1023	!
1024	!-- Compute the vertical kinematic heat flux
1025	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
1026	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
1027	!$OMP PARALLEL DO
1028	!$acc kernels loop independent present( shf, ts, us )
1029	DO i = nxlg, nxrg
1030	!$acc loop independent
1031	DO j = nysg, nyng
1032	shf(j,i) = -ts(j,i) * us(j,i)
1033	ENDDO
1034	ENDDO
1035
1036	ENDIF
1037
1038	!
1039	!-- Compute the vertical water/scalar flux
1040	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. &
1041	passive_scalar ) .AND. ( simulated_time <= skip_time_do_lsm &
1042	.OR. .NOT. land_surface ) ) THEN
1043	!$OMP PARALLEL DO
1044	!$acc kernels loop independent present( qs, qsws, us )
1045	DO i = nxlg, nxrg
1046	!$acc loop independent
1047	DO j = nysg, nyng
1048	qsws(j,i) = -qs(j,i) * us(j,i)
1049	ENDDO
1050	ENDDO
1051
1052	ENDIF
1053
1054	!
1055	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
1056	IF ( cloud_physics .AND. microphysics_seifert ) THEN
1057	!$OMP PARALLEL DO
1058	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
1059	DO i = nxlg, nxrg
1060	!$acc loop independent
1061	DO j = nysg, nyng
1062	qrsws(j,i) = -qrs(j,i) * us(j,i)
1063	nrsws(j,i) = -nrs(j,i) * us(j,i)
1064	ENDDO
1065	ENDDO
1066	ENDIF
1067
1068	!
1069	!-- Bottom boundary condition for the TKE
1070	IF ( ibc_e_b == 2 ) THEN
1071	!$OMP PARALLEL DO
1072	!$acc kernels loop independent present( e, nzb_s_inner, us )
1073	DO i = nxlg, nxrg
1074	!$acc loop independent
1075	DO j = nysg, nyng
1076	k = nzb_s_inner(j,i)
1077	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
1078	!
1079	!-- As a test: cm = 0.4
1080	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
1081	e(k,j,i) = e(k+1,j,i)
1082	ENDDO
1083	ENDDO
1084	ENDIF
1085
1086	END SUBROUTINE calc_surface_fluxes
1087
1088
1089	!
1090	!-- Integrated stability function for momentum
1091	FUNCTION psi_m( zeta )
1092
1093	USE kinds
1094
1095	IMPLICIT NONE
1096
1097	REAL(wp) :: psi_m !< Integrated similarity function result
1098	REAL(wp) :: zeta !< Stability parameter z/L
1099	REAL(wp) :: x !< dummy variable
1100
1101	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1102	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1103	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1104	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1105	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1106	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1107
1108
1109	IF ( zeta < 0.0_wp ) THEN
1110	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
1111	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1112	* ( 1.0_wp + x*2 ) 0.125_wp )
1113	ELSE
1114
1115	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1116	- bc_d_d
1117	!
1118	!-- Old version for stable conditions (only valid for z/L < 0.5)
1119	!-- psi_m = - 5.0_wp * zeta
1120
1121	ENDIF
1122
1123	END FUNCTION psi_m
1124
1125
1126	!
1127	!-- Integrated stability function for heat and moisture
1128	FUNCTION psi_h( zeta )
1129
1130	USE kinds
1131
1132	IMPLICIT NONE
1133
1134	REAL(wp) :: psi_h !< Integrated similarity function result
1135	REAL(wp) :: zeta !< Stability parameter z/L
1136	REAL(wp) :: x !< dummy variable
1137
1138	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1139	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1140	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1141	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1142	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1143	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1144
1145
1146	IF ( zeta < 0.0_wp ) THEN
1147	x = SQRT( 1.0_wp - 16.0_wp * zeta )
1148	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1149	ELSE
1150	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1151	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1152	+ 1.0_wp
1153	!
1154	!-- Old version for stable conditions (only valid for z/L < 0.5)
1155	!-- psi_h = - 5.0_wp * zeta
1156	ENDIF
1157
1158	END FUNCTION psi_h
1159
1160	END MODULE surface_layer_fluxes_mod

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