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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1788

Last change on this file since 1788 was 1788, checked in by maronga, 8 years ago
added support for water and paved surfaced in land surface model / minor changes
Property svn:keywords set to `Id`
File size: 42.5 KB

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

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