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source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 1929

Last change on this file since 1929 was 1929, checked in by suehring, 8 years ago
several bugfixes in particle model and serial mode
Property svn:keywords set to `Id`
File size: 43.1 KB

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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	! Bugfix: avoid segmentation fault in case one grid point is horizontally
22	! completely surrounded by topography
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: surface_layer_fluxes_mod.f90 1929 2016-06-09 16:25:25Z suehring $
27	!
28	! 1920 2016-05-30 10:50:15Z suehring
29	! Avoid segmentation fault (see change in 1915) by different initialization of
30	! us instead of adding a very small number in the denominator
31	!
32	! 1915 2016-05-27 11:05:02Z suehring
33	! Bugfix: avoid segmentation fault in case of most_method = 'circular' at first
34	! timestep
35	!
36	! 1850 2016-04-08 13:29:27Z maronga
37	! Module renamed
38	!
39	!
40	! 1822 2016-04-07 07:49:42Z hoffmann
41	! icloud_scheme replaced by microphysics_*
42	!
43	! 1788 2016-03-10 11:01:04Z maronga
44	! Added parameter z0q which replaces z0h in the similarity functions for
45	! humidity.
46	! Syntax layout improved.
47	!
48	! 1757 2016-02-22 15:49:32Z maronga
49	! Minor fixes.
50	!
51	! 1749 2016-02-09 12:19:56Z raasch
52	! further OpenACC adjustments
53	!
54	! 1747 2016-02-08 12:25:53Z raasch
55	! adjustments for OpenACC usage
56	!
57	! 1709 2015-11-04 14:47:01Z maronga
58	! Bugfix: division by zero could occur when calculating rib at low wind speeds
59	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
60	! neutral = .T.
61	!
62	! 1705 2015-11-02 14:28:56Z maronga
63	! Typo removed
64	!
65	! 1697 2015-10-28 17:14:10Z raasch
66	! FORTRAN and OpenMP errors removed
67	!
68	! 1696 2015-10-27 10:03:34Z maronga
69	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
70	! course of the re-writing two additional methods have been implemented. See
71	! updated description.
72	!
73	! 1551 2015-03-03 14:18:16Z maronga
74	! Removed land surface model part. The surface fluxes are now always calculated
75	! within prandtl_fluxes, based on the given surface temperature/humidity (which
76	! is either provided by the land surface model, by large scale forcing data, or
77	! directly prescribed by the user.
78	!
79	! 1496 2014-12-02 17:25:50Z maronga
80	! Adapted for land surface model
81	!
82	! 1494 2014-11-21 17:14:03Z maronga
83	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
84	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
85	! topography for coupled runs (not tested)
86	!
87	! 1361 2014-04-16 15:17:48Z hoffmann
88	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
89	! drop concentration (nrsws) added
90	!
91	! 1340 2014-03-25 19:45:13Z kanani
92	! REAL constants defined as wp-kind
93	!
94	! 1320 2014-03-20 08:40:49Z raasch
95	! ONLY-attribute added to USE-statements,
96	! kind-parameters added to all INTEGER and REAL declaration statements,
97	! kinds are defined in new module kinds,
98	! old module precision_kind is removed,
99	! revision history before 2012 removed,
100	! comment fields (!:) to be used for variable explanations added to
101	! all variable declaration statements
102	!
103	! 1276 2014-01-15 13:40:41Z heinze
104	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
105	!
106	! 1257 2013-11-08 15:18:40Z raasch
107	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
108	!
109	! 1036 2012-10-22 13:43:42Z raasch
110	! code put under GPL (PALM 3.9)
111	!
112	! 1015 2012-09-27 09:23:24Z raasch
113	! OpenACC statements added
114	!
115	! 978 2012-08-09 08:28:32Z fricke
116	! roughness length for scalar quantities z0h added
117	!
118	! Revision 1.1 1998/01/23 10:06:06 raasch
119	! Initial revision
120	!
121	!
122	! Description:
123	! ------------
124	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
125	!> values of the variables at grid point k=1. Three different methods are
126	!> available:
127	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
128	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
129	!> slower
130	!> 3) a method using a lookup table which is fast and accurate. Note, however,
131	!> that this method cannot be used in case of roughness heterogeneity
132	!>
133	!> @todo (re)move large_scale_forcing actions
134	!> @todo check/optimize OpenMP and OpenACC directives
135	!------------------------------------------------------------------------------!
136	MODULE surface_layer_fluxes_mod
137
138	USE arrays_3d, &
139	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
140	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h, z0q
141
142	USE cloud_parameters, &
143	ONLY: l_d_cp, pt_d_t
144
145	USE constants, &
146	ONLY: pi
147
148	USE cpulog
149
150	USE control_parameters, &
151	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
152	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, &
153	initializing_actions, kappa, intermediate_timestep_count, &
154	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
155	message_string, microphysics_seifert, most_method, neutral, &
156	passive_scalar, pt_surface, q_surface, run_coupled, &
157	surface_pressure, simulated_time, terminate_run, zeta_max, &
158	zeta_min
159
160	USE indices, &
161	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
162	nzb_u_inner, nzb_v_inner
163
164	USE kinds
165
166	USE pegrid
167
168	USE land_surface_model_mod, &
169	ONLY: land_surface, skip_time_do_lsm
170
171	IMPLICIT NONE
172
173	INTEGER(iwp) :: i !< loop index x direction
174	INTEGER(iwp) :: j !< loop index y direction
175	INTEGER(iwp) :: k !< loop index z direction
176
177	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
178
179	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
180
181	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
182	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
183	uv_total !< Total velocity at first grid level
184
185	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
186	ol_tab !< Lookup table values of L
187
188	REAL(wp) :: e_s, & !< Saturation water vapor pressure
189	l_bnd = 7500, & !< Lookup table index of the last time step
190	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
191	rib_max, & !< Maximum Richardson number in lookup table
192	rib_min, & !< Minimum Richardson number in lookup table
193	z_mo !< Height of the constant flux layer where MOST is assumed
194
195
196	SAVE
197
198	PRIVATE
199
200	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
201
202	INTERFACE init_surface_layer_fluxes
203	MODULE PROCEDURE init_surface_layer_fluxes
204	END INTERFACE init_surface_layer_fluxes
205
206	INTERFACE surface_layer_fluxes
207	MODULE PROCEDURE surface_layer_fluxes
208	END INTERFACE surface_layer_fluxes
209
210
211	CONTAINS
212
213
214	!------------------------------------------------------------------------------!
215	! Description:
216	! ------------
217	!> Main routine to compute the surface fluxes
218	!------------------------------------------------------------------------------!
219	SUBROUTINE surface_layer_fluxes
220
221	IMPLICIT NONE
222
223	!
224	!-- In case cloud physics is used, it is required to derive potential
225	!-- temperature and specific humidity at first grid level from the fields pt
226	!-- and q
227	IF ( cloud_physics ) THEN
228	CALL calc_pt_q
229	ENDIF
230
231	!
232	!-- First, calculate the new Obukhov length, then new friction velocity,
233	!-- followed by the new scaling parameters (th, q, etc.), and the new
234	!-- surface fluxes if required. The old routine ("circular") requires a
235	!-- different order of calls as the scaling parameters from the previous time
236	!-- steps are used to calculate the Obukhov length
237
238	!
239	!-- Depending on setting of most_method use the "old" routine
240	IF ( most_method == 'circular' ) THEN
241
242	CALL calc_scaling_parameters
243
244	CALL calc_uv_total
245
246	IF ( .NOT. neutral ) THEN
247	CALL calc_ol
248	ENDIF
249
250	CALL calc_us
251
252	CALL calc_surface_fluxes
253
254	!
255	!-- Use either Newton iteration or a lookup table for the bulk Richardson
256	!-- number to calculate the Obukhov length
257	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
258
259	CALL calc_uv_total
260
261	IF ( .NOT. neutral ) THEN
262	CALL calc_ol
263	ENDIF
264
265	CALL calc_us
266
267	CALL calc_scaling_parameters
268
269	CALL calc_surface_fluxes
270
271	ENDIF
272
273	END SUBROUTINE surface_layer_fluxes
274
275
276	!------------------------------------------------------------------------------!
277	! Description:
278	! ------------
279	!> Initializing actions for the surface layer routine. Basically, this involves
280	!> the preparation of a lookup table for the the bulk Richardson number vs
281	!> Obukhov length L when using the lookup table method.
282	!------------------------------------------------------------------------------!
283	SUBROUTINE init_surface_layer_fluxes
284
285	IMPLICIT NONE
286
287	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
288	num_steps_n !< Number of non-stretched zeta steps
289
290	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
291
292	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
293
294	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
295
296
297	REAL(wp) :: zeta_step, & !< Increment of zeta
298	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
299	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
300	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
301	z0_min = 0.0_wp !< Minimum value of z0 to create table
302	!
303	!-- When cloud physics is used, arrays for storing potential temperature and
304	!-- specific humidity at first grid level are required
305	IF ( cloud_physics ) THEN
306	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
307	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
308	ENDIF
309
310	!
311	!-- Allocate field for storing the horizontal velocity
312	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
313
314
315	!
316	!-- In case of runs with neutral statification, set Obukhov length to a
317	!-- large value
318	IF ( neutral ) ol = 1.0E10_wp
319
320	IF ( most_method == 'lookup' ) THEN
321
322	!
323	!-- Check for roughness heterogeneity. In that case terminate run and
324	!-- inform user
325	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
326	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
327	terminate_run_l = .TRUE.
328	ENDIF
329
330	#if defined( __parallel )
331	!
332	!-- Make a logical OR for all processes. Force termiation of model if result
333	!-- is TRUE
334	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
335	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
336	MPI_LOR, comm2d, ierr )
337	#else
338	terminate_run = terminate_run_l
339	#endif
340
341	IF ( terminate_run ) THEN
342	message_string = 'most_method = "lookup" cannot be used in ' // &
343	'combination with a prescribed roughness ' // &
344	'heterogeneity'
345	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
346	ENDIF
347
348	ALLOCATE( zeta_tmp(0:num_steps-1) )
349
350	!
351	!-- Use the lowest possible value for z_mo
352	k = MINVAL(nzb_s_inner)
353	z_mo = zu(k+1) - zw(k)
354
355	!
356	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
357	!-- available steps (num_steps). The calculation is done with negative
358	!-- values of zeta in order to simplify the stretching in the free
359	!-- convection limit for the remaining 10% of steps.
360	zeta_tmp(0) = - zeta_max
361	num_steps_n = ( num_steps * 9 / 10 ) - 1
362	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
363
364	DO l = 1, num_steps_n
365	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
366	ENDDO
367
368	!
369	!-- Calculate stretching factor for the free convection range
370	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
371	regr_old = regr
372	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
373	)**( 10.0_wp / REAL(num_steps) )
374	ENDDO
375
376	!
377	!-- Calculate z/L range from zeta_min to zeta_stretch
378	DO l = num_steps_n+1, num_steps-1
379	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
380	zeta_step = zeta_step * regr
381	ENDDO
382
383	!
384	!-- Save roughness lengths to temporary variables
385	z0h_min = z0h(nys,nxl)
386	z0_min = z0(nys,nxl)
387
388	!
389	!-- Calculate lookup table for the Richardson number versus Obukhov length
390	!-- The Richardson number (rib) is defined depending on the choice of
391	!-- boundary conditions for temperature
392	IF ( ibc_pt_b == 1 ) THEN
393	DO l = 0, num_steps-1
394	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
395	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
396	- psi_m( z_mo / ol_tab(l) ) &
397	+ psi_m( z0_min / ol_tab(l) ) &
398	)**3
399	ENDDO
400	ELSE
401	DO l = 0, num_steps-1
402	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
403	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
404	- psi_h( z_mo / ol_tab(l) ) &
405	+ psi_h( z0h_min / ol_tab(l) ) &
406	) &
407	/ ( LOG( z_mo / z0_min ) &
408	- psi_m( z_mo / ol_tab(l) ) &
409	+ psi_m( z0_min / ol_tab(l) ) &
410	)**2
411	ENDDO
412	ENDIF
413
414	!
415	!-- Determine minimum values of rib in the lookup table. Set upper limit
416	!-- to critical Richardson number (0.25)
417	rib_min = MINVAL(rib_tab)
418	rib_max = 0.25 !MAXVAL(rib_tab)
419
420	DEALLOCATE( zeta_tmp )
421	ENDIF
422
423	END SUBROUTINE init_surface_layer_fluxes
424
425
426	!------------------------------------------------------------------------------!
427	! Description:
428	! ------------
429	!> Compute the absolute value of the horizontal velocity (relative to the
430	!> surface). This is required by all methods
431	!------------------------------------------------------------------------------!
432	SUBROUTINE calc_uv_total
433
434	IMPLICIT NONE
435
436
437	!$OMP PARALLEL DO PRIVATE( k )
438	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
439	DO i = nxl, nxr
440	DO j = nys, nyn
441
442	k = nzb_s_inner(j,i)
443	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
444	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
445	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
446	- v(k,j,i) - v(k,j+1,i) ) )**2 )
447
448	!
449	!-- For too small values of the local wind, MOST does not work. A
450	!-- threshold value is thus set if required
451	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
452
453	ENDDO
454	ENDDO
455
456	!
457	!-- Values of uv_total need to be exchanged at the ghost boundaries
458	!$acc update host( uv_total )
459	CALL exchange_horiz_2d( uv_total )
460	!$acc update device( uv_total )
461
462	END SUBROUTINE calc_uv_total
463
464
465	!------------------------------------------------------------------------------!
466	! Description:
467	! ------------
468	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
469	!------------------------------------------------------------------------------!
470	SUBROUTINE calc_ol
471
472	IMPLICIT NONE
473
474	INTEGER(iwp) :: iter, & !< Newton iteration step
475	l !< look index
476
477	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
478
479	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
480	f_d_ol, & !< Derivative of f
481	ol_l, & !< Lower bound of L for Newton iteration
482	ol_m, & !< Previous value of L for Newton iteration
483	ol_old, & !< Previous time step value of L
484	ol_u !< Upper bound of L for Newton iteration
485
486	IF ( TRIM( most_method ) /= 'circular' ) THEN
487
488	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
489
490	!$OMP PARALLEL DO PRIVATE( k, z_mo )
491	!$acc kernels loop private( j, k, z_mo )
492	DO i = nxl, nxr
493	DO j = nys, nyn
494
495	k = nzb_s_inner(j,i)
496	z_mo = zu(k+1) - zw(k)
497
498	!
499	!-- Evaluate bulk Richardson number (calculation depends on
500	!-- definition based on setting of boundary conditions
501	IF ( ibc_pt_b /= 1 ) THEN
502	IF ( humidity ) THEN
503	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
504	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
505	ELSE
506	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
507	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
508	ENDIF
509	ELSE
510	!
511	!-- When using Neumann boundary conditions, the buoyancy flux
512	!-- is required but cannot be calculated at the surface, as pt
513	!-- and q are not known at the surface. Hence the values at
514	!-- first grid level are used to estimate the buoyancy flux
515	IF ( humidity ) THEN
516	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
517	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
518	* pt(k+1,j,i) * qsws(j,i) ) &
519	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
520	+ 1.0E-20_wp)
521	ELSE
522	rib(j,i) = - g * z_mo * shf(j,i) &
523	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
524	+ 1.0E-20_wp )
525	ENDIF
526	ENDIF
527
528	ENDDO
529	ENDDO
530	!$acc end data
531
532	ENDIF
533
534	!
535	!-- Calculate the Obukhov length either using a Newton iteration
536	!-- method, via a lookup table, or using the old circular way
537	IF ( TRIM( most_method ) == 'newton' ) THEN
538
539	!$OMP PARALLEL DO PRIVATE( k, z_mo )
540	!# WARNING: does not work on GPU so far because of DO-loop with
541	!# undetermined iterations
542	!!!!!!$acc kernels loop
543	DO i = nxl, nxr
544	DO j = nys, nyn
545
546	k = nzb_s_inner(j,i)
547	z_mo = zu(k+1) - zw(k)
548
549	!
550	!-- Store current value in case the Newton iteration fails
551	ol_old = ol(j,i)
552
553	!
554	!-- Ensure that the bulk Richardson number and the Obukhov
555	!-- lengtH have the same sign
556	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
557	ABS( ol(j,i) ) == ol_max ) THEN
558	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
559	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
560	ENDIF
561	!
562	!-- Iteration to find Obukhov length
563	iter = 0
564	DO
565	iter = iter + 1
566	!
567	!-- In case of divergence, use the value of the previous time step
568	IF ( iter > 1000 ) THEN
569	ol(j,i) = ol_old
570	EXIT
571	ENDIF
572
573	ol_m = ol(j,i)
574	ol_l = ol_m - 0.001_wp * ol_m
575	ol_u = ol_m + 0.001_wp * ol_m
576
577
578	IF ( ibc_pt_b /= 1 ) THEN
579	!
580	!-- Calculate f = Ri - [...]/[...]^2 = 0
581	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
582	- psi_h( z_mo / ol_m ) &
583	+ psi_h( z0h(j,i) / ol_m ) &
584	) &
585	/ ( LOG( z_mo / z0(j,i) ) &
586	- psi_m( z_mo / ol_m ) &
587	+ psi_m( z0(j,i) / ol_m ) &
588	)**2
589
590	!
591	!-- Calculate df/dL
592	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
593	- psi_h( z_mo / ol_u ) &
594	+ psi_h( z0h(j,i) / ol_u ) &
595	) &
596	/ ( LOG( z_mo / z0(j,i) ) &
597	- psi_m( z_mo / ol_u ) &
598	+ psi_m( z0(j,i) / ol_u ) &
599	)**2 &
600	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
601	- psi_h( z_mo / ol_l ) &
602	+ psi_h( z0h(j,i) / ol_l ) &
603	) &
604	/ ( LOG( z_mo / z0(j,i) ) &
605	- psi_m( z_mo / ol_l ) &
606	+ psi_m( z0(j,i) / ol_l ) &
607	)**2 &
608	) / ( ol_u - ol_l )
609	ELSE
610	!
611	!-- Calculate f = Ri - 1 /[...]^3 = 0
612	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
613	- psi_m( z_mo / ol_m ) &
614	+ psi_m( z0(j,i) / ol_m ) &
615	)**3
616
617	!
618	!-- Calculate df/dL
619	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
620	- psi_m( z_mo / ol_u ) &
621	+ psi_m( z0(j,i) / ol_u ) &
622	)**3 &
623	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
624	- psi_m( z_mo / ol_l ) &
625	+ psi_m( z0(j,i) / ol_l ) &
626	)**3 &
627	) / ( ol_u - ol_l )
628	ENDIF
629	!
630	!-- Calculate new L
631	ol(j,i) = ol_m - f / f_d_ol
632
633	!
634	!-- Ensure that the bulk Richardson number and the Obukhov
635	!-- length have the same sign and ensure convergence.
636	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
637
638	!
639	!-- If unrealistic value occurs, set L to the maximum
640	!-- value that is allowed
641	IF ( ABS( ol(j,i) ) > ol_max ) THEN
642	ol(j,i) = ol_max
643	EXIT
644	ENDIF
645	!
646	!-- Check for convergence
647	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
648	EXIT
649	ELSE
650	CYCLE
651	ENDIF
652
653	ENDDO
654
655	ENDDO
656	ENDDO
657
658	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
659
660	!$OMP PARALLEL DO PRIVATE( k, z_mo )
661	!# WARNING: does not work on GPU so far because of DO WHILE construct
662	!!!!!!$acc kernels loop
663	DO i = nxl, nxr
664	DO j = nys, nyn
665
666	!
667	!-- If the bulk Richardson number is outside the range of the lookup
668	!-- table, set it to the exceeding threshold value
669	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
670	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
671
672	!
673	!-- Find the correct index bounds for linear interpolation. As the
674	!-- Richardson number will not differ very much from time step to
675	!-- time step , use the index from the last step and search in the
676	!-- correct direction
677	l = l_bnd
678	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
679	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
680	l = l-1
681	ENDDO
682	ELSE
683	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
684	.AND. l < num_steps-1 )
685	l = l+1
686	ENDDO
687	ENDIF
688	l_bnd = l
689
690	!
691	!-- Linear interpolation to find the correct value of z/L
692	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
693	/ ( rib_tab(l) - rib_tab(l-1) ) &
694	* ( rib(j,i) - rib_tab(l-1) ) )
695
696	ENDDO
697	ENDDO
698
699	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
700
701	!$OMP PARALLEL DO PRIVATE( k, z_mo )
702	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
703	DO i = nxl, nxr
704	DO j = nys, nyn
705
706	k = nzb_s_inner(j,i)
707	z_mo = zu(k+1) - zw(k)
708
709	IF ( .NOT. humidity ) THEN
710	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
711	* ts(j,i) + 1E-30_wp )
712	ELSEIF ( cloud_physics ) THEN
713
714	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
715	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
716	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
717	* ql(k+1,j,i) ) + 1E-30_wp )
718	ELSE
719	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
720	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
721	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
722	ENDIF
723	!
724	!-- Limit the value range of the Obukhov length.
725	!-- This is necessary for very small velocities (u,v --> 0), because
726	!-- the absolute value of ol can then become very small, which in
727	!-- consequence would result in very large shear stresses and very
728	!-- small momentum fluxes (both are generally unrealistic).
729	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) < zeta_min ) &
730	ol(j,i) = z_mo / zeta_min
731	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) > zeta_max ) &
732	ol(j,i) = z_mo / zeta_max
733	ENDDO
734	ENDDO
735
736	ENDIF
737
738	!
739	!-- Values of ol at ghost point locations are needed for the evaluation
740	!-- of usws and vsws.
741	!$acc update host( ol )
742	CALL exchange_horiz_2d( ol )
743	!$acc update device( ol )
744
745	END SUBROUTINE calc_ol
746
747	!
748	!-- Calculate friction velocity u*
749	SUBROUTINE calc_us
750
751	IMPLICIT NONE
752
753	!$OMP PARALLEL DO PRIVATE( k, z_mo )
754	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
755	DO i = nxlg, nxrg
756	DO j = nysg, nyng
757
758	k = nzb_s_inner(j,i)+1
759	z_mo = zu(k+1) - zw(k)
760
761	!
762	!-- Compute u* at the scalars' grid points
763	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
764	- psi_m( z_mo / ol(j,i) ) &
765	+ psi_m( z0(j,i) / ol(j,i) ) )
766	ENDDO
767	ENDDO
768
769	END SUBROUTINE calc_us
770
771	!
772	!-- Calculate potential temperature and specific humidity at first grid level
773	SUBROUTINE calc_pt_q
774
775	IMPLICIT NONE
776
777	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
778	DO i = nxlg, nxrg
779	DO j = nysg, nyng
780	k = nzb_s_inner(j,i)+1
781	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
782	qv1(j,i) = q(k,j,i) - ql(k,j,i)
783	ENDDO
784	ENDDO
785
786	END SUBROUTINE calc_pt_q
787
788	!
789	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
790	SUBROUTINE calc_scaling_parameters
791
792	IMPLICIT NONE
793
794	!
795	!-- Data information for accelerators
796	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
797	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
798	!$acc present( vpt, vsws, zu, zw, z0, z0h )
799	!
800	!-- Compute theta*
801	IF ( constant_heatflux ) THEN
802
803	!
804	!-- For a given heat flux in the surface layer:
805	!$OMP PARALLEL DO
806	!$acc kernels loop private( j )
807	DO i = nxlg, nxrg
808	DO j = nysg, nyng
809	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
810	!
811	!-- ts must be limited, because otherwise overflow may occur in case
812	!-- of us=0 when computing ol further below
813	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
814	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
815	ENDDO
816	ENDDO
817
818	ELSE
819	!
820	!-- For a given surface temperature:
821	IF ( large_scale_forcing .AND. lsf_surf ) THEN
822	!$OMP PARALLEL DO
823	!$acc kernels loop private( j, k )
824	DO i = nxlg, nxrg
825	DO j = nysg, nyng
826	k = nzb_s_inner(j,i)
827	pt(k,j,i) = pt_surface
828	ENDDO
829	ENDDO
830	ENDIF
831
832	!$OMP PARALLEL DO PRIVATE( k, z_mo )
833	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
834	DO i = nxlg, nxrg
835	DO j = nysg, nyng
836
837	k = nzb_s_inner(j,i)
838	z_mo = zu(k+1) - zw(k)
839
840	IF ( cloud_physics ) THEN
841	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
842	/ ( LOG( z_mo / z0h(j,i) ) &
843	- psi_h( z_mo / ol(j,i) ) &
844	+ psi_h( z0h(j,i) / ol(j,i) ) )
845	ELSE
846	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
847	/ ( LOG( z_mo / z0h(j,i) ) &
848	- psi_h( z_mo / ol(j,i) ) &
849	+ psi_h( z0h(j,i) / ol(j,i) ) )
850	ENDIF
851
852	ENDDO
853	ENDDO
854	ENDIF
855
856	!
857	!-- If required compute q*
858	IF ( humidity .OR. passive_scalar ) THEN
859	IF ( constant_waterflux ) THEN
860	!
861	!-- For a given water flux in the surface layer
862	!$OMP PARALLEL DO
863	!$acc kernels loop private( j )
864	DO i = nxlg, nxrg
865	DO j = nysg, nyng
866	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
867	ENDDO
868	ENDDO
869
870	ELSE
871	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
872	run_coupled )
873
874	IF ( large_scale_forcing .AND. lsf_surf ) THEN
875	!$OMP PARALLEL DO
876	!$acc kernels loop private( j, k )
877	DO i = nxlg, nxrg
878	DO j = nysg, nyng
879	k = nzb_s_inner(j,i)
880	q(k,j,i) = q_surface
881	ENDDO
882	ENDDO
883	ENDIF
884
885	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
886	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
887	DO i = nxlg, nxrg
888	!$acc loop independent
889	DO j = nysg, nyng
890
891	k = nzb_s_inner(j,i)
892	z_mo = zu(k+1) - zw(k)
893
894	!
895	!-- Assume saturation for atmosphere coupled to ocean (but not
896	!-- in case of precursor runs)
897	IF ( coupled_run ) THEN
898	e_s = 6.1_wp * &
899	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
900	- 273.15_wp ) )
901	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
902	ENDIF
903
904	IF ( cloud_physics ) THEN
905	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
906	/ ( LOG( z_mo / z0q(j,i) ) &
907	- psi_h( z_mo / ol(j,i) ) &
908	+ psi_h( z0q(j,i) / ol(j,i) ) )
909
910	ELSE
911	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
912	/ ( LOG( z_mo / z0q(j,i) ) &
913	- psi_h( z_mo / ol(j,i) ) &
914	+ psi_h( z0q(j,i) / ol(j,i) ) )
915	ENDIF
916
917	ENDDO
918	ENDDO
919	ENDIF
920	ENDIF
921
922
923	!
924	!-- If required compute qr* and nr*
925	IF ( cloud_physics .AND. microphysics_seifert ) &
926	THEN
927
928	!$OMP PARALLEL DO PRIVATE( k, z_mo )
929	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
930	DO i = nxlg, nxrg
931	!$acc loop independent
932	DO j = nysg, nyng
933
934	k = nzb_s_inner(j,i)
935	z_mo = zu(k+1) - zw(k)
936
937	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
938	/ ( LOG( z_mo / z0q(j,i) ) &
939	- psi_h( z_mo / ol(j,i) ) &
940	+ psi_h( z0q(j,i) / ol(j,i) ) )
941
942	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
943	/ ( LOG( z_mo / z0q(j,i) ) &
944	- psi_h( z_mo / ol(j,i) ) &
945	+ psi_h( z0q(j,i) / ol(j,i) ) )
946	ENDDO
947	ENDDO
948
949	ENDIF
950	!$acc end data
951
952	END SUBROUTINE calc_scaling_parameters
953
954
955
956	!
957	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
958	SUBROUTINE calc_surface_fluxes
959
960	IMPLICIT NONE
961
962	REAL(wp) :: ol_mid !< Grid-interpolated L
963
964	!
965	!-- Compute u'w' for the total model domain.
966	!-- First compute the corresponding component of u* and square it.
967	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
968	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
969	DO i = nxl, nxr
970	DO j = nys, nyn
971
972	k = nzb_u_inner(j,i)
973	z_mo = zu(k+1) - zw(k)
974	!
975	!-- Compute bulk Obukhov length for this point
976	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
977
978	IF ( ol_mid == 0.0_wp ) THEN
979	ol_mid = MIN(ol(j,i-1), ol(j,i))
980	ENDIF
981
982	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
983	/ ( LOG( z_mo / z0(j,i) ) &
984	- psi_m( z_mo / ol_mid ) &
985	+ psi_m( z0(j,i) / ol_mid ) )
986
987	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
988	ENDDO
989	ENDDO
990
991	!
992	!-- Compute v'w' for the total model domain.
993	!-- First compute the corresponding component of u* and square it.
994	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
995	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
996	DO i = nxl, nxr
997	DO j = nys, nyn
998
999	k = nzb_v_inner(j,i)
1000	z_mo = zu(k+1) - zw(k)
1001	!
1002	!-- Compute bulk Obukhov length for this point
1003	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
1004
1005	IF ( ol_mid == 0.0_wp ) THEN
1006	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
1007	ENDIF
1008
1009	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
1010	/ ( LOG( z_mo / z0(j,i) ) &
1011	- psi_m( z_mo / ol_mid ) &
1012	+ psi_m( z0(j,i) / ol_mid ) )
1013
1014	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
1015
1016	ENDDO
1017	ENDDO
1018
1019	!
1020	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
1021	!$acc update host( usws, vsws )
1022	CALL exchange_horiz_2d( usws )
1023	CALL exchange_horiz_2d( vsws )
1024	!$acc update device( usws, vsws )
1025
1026	!
1027	!-- Compute the vertical kinematic heat flux
1028	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
1029	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
1030	!$OMP PARALLEL DO
1031	!$acc kernels loop independent present( shf, ts, us )
1032	DO i = nxlg, nxrg
1033	!$acc loop independent
1034	DO j = nysg, nyng
1035	shf(j,i) = -ts(j,i) * us(j,i)
1036	ENDDO
1037	ENDDO
1038
1039	ENDIF
1040
1041	!
1042	!-- Compute the vertical water/scalar flux
1043	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. &
1044	passive_scalar ) .AND. ( simulated_time <= skip_time_do_lsm &
1045	.OR. .NOT. land_surface ) ) THEN
1046	!$OMP PARALLEL DO
1047	!$acc kernels loop independent present( qs, qsws, us )
1048	DO i = nxlg, nxrg
1049	!$acc loop independent
1050	DO j = nysg, nyng
1051	qsws(j,i) = -qs(j,i) * us(j,i)
1052	ENDDO
1053	ENDDO
1054
1055	ENDIF
1056
1057	!
1058	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
1059	IF ( cloud_physics .AND. microphysics_seifert ) THEN
1060	!$OMP PARALLEL DO
1061	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
1062	DO i = nxlg, nxrg
1063	!$acc loop independent
1064	DO j = nysg, nyng
1065	qrsws(j,i) = -qrs(j,i) * us(j,i)
1066	nrsws(j,i) = -nrs(j,i) * us(j,i)
1067	ENDDO
1068	ENDDO
1069	ENDIF
1070
1071	!
1072	!-- Bottom boundary condition for the TKE
1073	IF ( ibc_e_b == 2 ) THEN
1074	!$OMP PARALLEL DO
1075	!$acc kernels loop independent present( e, nzb_s_inner, us )
1076	DO i = nxlg, nxrg
1077	!$acc loop independent
1078	DO j = nysg, nyng
1079	k = nzb_s_inner(j,i)
1080	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
1081	!
1082	!-- As a test: cm = 0.4
1083	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
1084	e(k,j,i) = e(k+1,j,i)
1085	ENDDO
1086	ENDDO
1087	ENDIF
1088
1089	END SUBROUTINE calc_surface_fluxes
1090
1091
1092	!
1093	!-- Integrated stability function for momentum
1094	FUNCTION psi_m( zeta )
1095
1096	USE kinds
1097
1098	IMPLICIT NONE
1099
1100	REAL(wp) :: psi_m !< Integrated similarity function result
1101	REAL(wp) :: zeta !< Stability parameter z/L
1102	REAL(wp) :: x !< dummy variable
1103
1104	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1105	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1106	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1107	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1108	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1109	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1110
1111
1112	IF ( zeta < 0.0_wp ) THEN
1113	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
1114	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1115	* ( 1.0_wp + x*2 ) 0.125_wp )
1116	ELSE
1117
1118	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1119	- bc_d_d
1120	!
1121	!-- Old version for stable conditions (only valid for z/L < 0.5)
1122	!-- psi_m = - 5.0_wp * zeta
1123
1124	ENDIF
1125
1126	END FUNCTION psi_m
1127
1128
1129	!
1130	!-- Integrated stability function for heat and moisture
1131	FUNCTION psi_h( zeta )
1132
1133	USE kinds
1134
1135	IMPLICIT NONE
1136
1137	REAL(wp) :: psi_h !< Integrated similarity function result
1138	REAL(wp) :: zeta !< Stability parameter z/L
1139	REAL(wp) :: x !< dummy variable
1140
1141	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1142	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1143	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1144	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1145	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1146	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1147
1148
1149	IF ( zeta < 0.0_wp ) THEN
1150	x = SQRT( 1.0_wp - 16.0_wp * zeta )
1151	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1152	ELSE
1153	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1154	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1155	+ 1.0_wp
1156	!
1157	!-- Old version for stable conditions (only valid for z/L < 0.5)
1158	!-- psi_h = - 5.0_wp * zeta
1159	ENDIF
1160
1161	END FUNCTION psi_h
1162
1163	END MODULE surface_layer_fluxes_mod

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