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source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 1947

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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 1930 2016-06-09 16:32:12Z suehring $
26	!
27	! 1929 2016-06-09 16:25:25Z suehring
28	! Bugfix: avoid segmentation fault in case one grid point is horizontally
29	! completely surrounded by topography
30	!
31	! 1920 2016-05-30 10:50:15Z suehring
32	! Avoid segmentation fault (see change in 1915) by different initialization of
33	! us instead of adding a very small number in the denominator
34	!
35	! 1915 2016-05-27 11:05:02Z suehring
36	! Bugfix: avoid segmentation fault in case of most_method = 'circular' at first
37	! timestep
38	!
39	! 1850 2016-04-08 13:29:27Z maronga
40	! Module renamed
41	!
42	!
43	! 1822 2016-04-07 07:49:42Z hoffmann
44	! icloud_scheme replaced by microphysics_*
45	!
46	! 1788 2016-03-10 11:01:04Z maronga
47	! Added parameter z0q which replaces z0h in the similarity functions for
48	! humidity.
49	! Syntax layout improved.
50	!
51	! 1757 2016-02-22 15:49:32Z maronga
52	! Minor fixes.
53	!
54	! 1749 2016-02-09 12:19:56Z raasch
55	! further OpenACC adjustments
56	!
57	! 1747 2016-02-08 12:25:53Z raasch
58	! adjustments for OpenACC usage
59	!
60	! 1709 2015-11-04 14:47:01Z maronga
61	! Bugfix: division by zero could occur when calculating rib at low wind speeds
62	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
63	! neutral = .T.
64	!
65	! 1705 2015-11-02 14:28:56Z maronga
66	! Typo removed
67	!
68	! 1697 2015-10-28 17:14:10Z raasch
69	! FORTRAN and OpenMP errors removed
70	!
71	! 1696 2015-10-27 10:03:34Z maronga
72	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
73	! course of the re-writing two additional methods have been implemented. See
74	! updated description.
75	!
76	! 1551 2015-03-03 14:18:16Z maronga
77	! Removed land surface model part. The surface fluxes are now always calculated
78	! within prandtl_fluxes, based on the given surface temperature/humidity (which
79	! is either provided by the land surface model, by large scale forcing data, or
80	! directly prescribed by the user.
81	!
82	! 1496 2014-12-02 17:25:50Z maronga
83	! Adapted for land surface model
84	!
85	! 1494 2014-11-21 17:14:03Z maronga
86	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
87	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
88	! topography for coupled runs (not tested)
89	!
90	! 1361 2014-04-16 15:17:48Z hoffmann
91	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
92	! drop concentration (nrsws) added
93	!
94	! 1340 2014-03-25 19:45:13Z kanani
95	! REAL constants defined as wp-kind
96	!
97	! 1320 2014-03-20 08:40:49Z raasch
98	! ONLY-attribute added to USE-statements,
99	! kind-parameters added to all INTEGER and REAL declaration statements,
100	! kinds are defined in new module kinds,
101	! old module precision_kind is removed,
102	! revision history before 2012 removed,
103	! comment fields (!:) to be used for variable explanations added to
104	! all variable declaration statements
105	!
106	! 1276 2014-01-15 13:40:41Z heinze
107	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
108	!
109	! 1257 2013-11-08 15:18:40Z raasch
110	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
111	!
112	! 1036 2012-10-22 13:43:42Z raasch
113	! code put under GPL (PALM 3.9)
114	!
115	! 1015 2012-09-27 09:23:24Z raasch
116	! OpenACC statements added
117	!
118	! 978 2012-08-09 08:28:32Z fricke
119	! roughness length for scalar quantities z0h added
120	!
121	! Revision 1.1 1998/01/23 10:06:06 raasch
122	! Initial revision
123	!
124	!
125	! Description:
126	! ------------
127	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
128	!> values of the variables at grid point k=1. Three different methods are
129	!> available:
130	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
131	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
132	!> slower
133	!> 3) a method using a lookup table which is fast and accurate. Note, however,
134	!> that this method cannot be used in case of roughness heterogeneity
135	!>
136	!> @todo (re)move large_scale_forcing actions
137	!> @todo check/optimize OpenMP and OpenACC directives
138	!------------------------------------------------------------------------------!
139	MODULE surface_layer_fluxes_mod
140
141	USE arrays_3d, &
142	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
143	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h, z0q
144
145	USE cloud_parameters, &
146	ONLY: l_d_cp, pt_d_t
147
148	USE constants, &
149	ONLY: pi
150
151	USE cpulog
152
153	USE control_parameters, &
154	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
155	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, &
156	initializing_actions, kappa, intermediate_timestep_count, &
157	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
158	message_string, microphysics_seifert, most_method, neutral, &
159	passive_scalar, pt_surface, q_surface, run_coupled, &
160	surface_pressure, simulated_time, terminate_run, zeta_max, &
161	zeta_min
162
163	USE indices, &
164	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
165	nzb_u_inner, nzb_v_inner
166
167	USE kinds
168
169	USE pegrid
170
171	USE land_surface_model_mod, &
172	ONLY: land_surface, skip_time_do_lsm
173
174	IMPLICIT NONE
175
176	INTEGER(iwp) :: i !< loop index x direction
177	INTEGER(iwp) :: j !< loop index y direction
178	INTEGER(iwp) :: k !< loop index z direction
179
180	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
181
182	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
183
184	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
185	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
186	uv_total !< Total velocity at first grid level
187
188	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
189	ol_tab !< Lookup table values of L
190
191	REAL(wp) :: e_s, & !< Saturation water vapor pressure
192	l_bnd = 7500, & !< Lookup table index of the last time step
193	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
194	rib_max, & !< Maximum Richardson number in lookup table
195	rib_min, & !< Minimum Richardson number in lookup table
196	z_mo !< Height of the constant flux layer where MOST is assumed
197
198
199	SAVE
200
201	PRIVATE
202
203	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
204
205	INTERFACE init_surface_layer_fluxes
206	MODULE PROCEDURE init_surface_layer_fluxes
207	END INTERFACE init_surface_layer_fluxes
208
209	INTERFACE surface_layer_fluxes
210	MODULE PROCEDURE surface_layer_fluxes
211	END INTERFACE surface_layer_fluxes
212
213
214	CONTAINS
215
216
217	!------------------------------------------------------------------------------!
218	! Description:
219	! ------------
220	!> Main routine to compute the surface fluxes
221	!------------------------------------------------------------------------------!
222	SUBROUTINE surface_layer_fluxes
223
224	IMPLICIT NONE
225
226	!
227	!-- In case cloud physics is used, it is required to derive potential
228	!-- temperature and specific humidity at first grid level from the fields pt
229	!-- and q
230	IF ( cloud_physics ) THEN
231	CALL calc_pt_q
232	ENDIF
233
234	!
235	!-- First, calculate the new Obukhov length, then new friction velocity,
236	!-- followed by the new scaling parameters (th, q, etc.), and the new
237	!-- surface fluxes if required. The old routine ("circular") requires a
238	!-- different order of calls as the scaling parameters from the previous time
239	!-- steps are used to calculate the Obukhov length
240
241	!
242	!-- Depending on setting of most_method use the "old" routine
243	IF ( most_method == 'circular' ) THEN
244
245	CALL calc_scaling_parameters
246
247	CALL calc_uv_total
248
249	IF ( .NOT. neutral ) THEN
250	CALL calc_ol
251	ENDIF
252
253	CALL calc_us
254
255	CALL calc_surface_fluxes
256
257	!
258	!-- Use either Newton iteration or a lookup table for the bulk Richardson
259	!-- number to calculate the Obukhov length
260	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
261
262	CALL calc_uv_total
263
264	IF ( .NOT. neutral ) THEN
265	CALL calc_ol
266	ENDIF
267
268	CALL calc_us
269
270	CALL calc_scaling_parameters
271
272	CALL calc_surface_fluxes
273
274	ENDIF
275
276	END SUBROUTINE surface_layer_fluxes
277
278
279	!------------------------------------------------------------------------------!
280	! Description:
281	! ------------
282	!> Initializing actions for the surface layer routine. Basically, this involves
283	!> the preparation of a lookup table for the the bulk Richardson number vs
284	!> Obukhov length L when using the lookup table method.
285	!------------------------------------------------------------------------------!
286	SUBROUTINE init_surface_layer_fluxes
287
288	IMPLICIT NONE
289
290	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
291	num_steps_n !< Number of non-stretched zeta steps
292
293	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
294
295	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
296
297	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
298
299
300	REAL(wp) :: zeta_step, & !< Increment of zeta
301	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
302	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
303	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
304	z0_min = 0.0_wp !< Minimum value of z0 to create table
305	!
306	!-- When cloud physics is used, arrays for storing potential temperature and
307	!-- specific humidity at first grid level are required
308	IF ( cloud_physics ) THEN
309	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
310	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
311	ENDIF
312
313	!
314	!-- Allocate field for storing the horizontal velocity
315	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
316
317
318	!
319	!-- In case of runs with neutral statification, set Obukhov length to a
320	!-- large value
321	IF ( neutral ) ol = 1.0E10_wp
322
323	IF ( most_method == 'lookup' ) THEN
324
325	!
326	!-- Check for roughness heterogeneity. In that case terminate run and
327	!-- inform user
328	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
329	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
330	terminate_run_l = .TRUE.
331	ENDIF
332
333	#if defined( __parallel )
334	!
335	!-- Make a logical OR for all processes. Force termiation of model if result
336	!-- is TRUE
337	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
338	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
339	MPI_LOR, comm2d, ierr )
340	#else
341	terminate_run = terminate_run_l
342	#endif
343
344	IF ( terminate_run ) THEN
345	message_string = 'most_method = "lookup" cannot be used in ' // &
346	'combination with a prescribed roughness ' // &
347	'heterogeneity'
348	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
349	ENDIF
350
351	ALLOCATE( zeta_tmp(0:num_steps-1) )
352
353	!
354	!-- Use the lowest possible value for z_mo
355	k = MINVAL(nzb_s_inner)
356	z_mo = zu(k+1) - zw(k)
357
358	!
359	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
360	!-- available steps (num_steps). The calculation is done with negative
361	!-- values of zeta in order to simplify the stretching in the free
362	!-- convection limit for the remaining 10% of steps.
363	zeta_tmp(0) = - zeta_max
364	num_steps_n = ( num_steps * 9 / 10 ) - 1
365	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
366
367	DO l = 1, num_steps_n
368	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
369	ENDDO
370
371	!
372	!-- Calculate stretching factor for the free convection range
373	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
374	regr_old = regr
375	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
376	)**( 10.0_wp / REAL(num_steps) )
377	ENDDO
378
379	!
380	!-- Calculate z/L range from zeta_min to zeta_stretch
381	DO l = num_steps_n+1, num_steps-1
382	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
383	zeta_step = zeta_step * regr
384	ENDDO
385
386	!
387	!-- Save roughness lengths to temporary variables
388	z0h_min = z0h(nys,nxl)
389	z0_min = z0(nys,nxl)
390
391	!
392	!-- Calculate lookup table for the Richardson number versus Obukhov length
393	!-- The Richardson number (rib) is defined depending on the choice of
394	!-- boundary conditions for temperature
395	IF ( ibc_pt_b == 1 ) THEN
396	DO l = 0, num_steps-1
397	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
398	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
399	- psi_m( z_mo / ol_tab(l) ) &
400	+ psi_m( z0_min / ol_tab(l) ) &
401	)**3
402	ENDDO
403	ELSE
404	DO l = 0, num_steps-1
405	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
406	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
407	- psi_h( z_mo / ol_tab(l) ) &
408	+ psi_h( z0h_min / ol_tab(l) ) &
409	) &
410	/ ( LOG( z_mo / z0_min ) &
411	- psi_m( z_mo / ol_tab(l) ) &
412	+ psi_m( z0_min / ol_tab(l) ) &
413	)**2
414	ENDDO
415	ENDIF
416
417	!
418	!-- Determine minimum values of rib in the lookup table. Set upper limit
419	!-- to critical Richardson number (0.25)
420	rib_min = MINVAL(rib_tab)
421	rib_max = 0.25 !MAXVAL(rib_tab)
422
423	DEALLOCATE( zeta_tmp )
424	ENDIF
425
426	END SUBROUTINE init_surface_layer_fluxes
427
428
429	!------------------------------------------------------------------------------!
430	! Description:
431	! ------------
432	!> Compute the absolute value of the horizontal velocity (relative to the
433	!> surface). This is required by all methods
434	!------------------------------------------------------------------------------!
435	SUBROUTINE calc_uv_total
436
437	IMPLICIT NONE
438
439
440	!$OMP PARALLEL DO PRIVATE( k )
441	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
442	DO i = nxl, nxr
443	DO j = nys, nyn
444
445	k = nzb_s_inner(j,i)
446	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
447	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
448	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
449	- v(k,j,i) - v(k,j+1,i) ) )**2 )
450
451	!
452	!-- For too small values of the local wind, MOST does not work. A
453	!-- threshold value is thus set if required
454	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
455
456	ENDDO
457	ENDDO
458
459	!
460	!-- Values of uv_total need to be exchanged at the ghost boundaries
461	!$acc update host( uv_total )
462	CALL exchange_horiz_2d( uv_total )
463	!$acc update device( uv_total )
464
465	END SUBROUTINE calc_uv_total
466
467
468	!------------------------------------------------------------------------------!
469	! Description:
470	! ------------
471	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
472	!------------------------------------------------------------------------------!
473	SUBROUTINE calc_ol
474
475	IMPLICIT NONE
476
477	INTEGER(iwp) :: iter, & !< Newton iteration step
478	l !< look index
479
480	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
481
482	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
483	f_d_ol, & !< Derivative of f
484	ol_l, & !< Lower bound of L for Newton iteration
485	ol_m, & !< Previous value of L for Newton iteration
486	ol_old, & !< Previous time step value of L
487	ol_u !< Upper bound of L for Newton iteration
488
489	IF ( TRIM( most_method ) /= 'circular' ) THEN
490
491	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
492
493	!$OMP PARALLEL DO PRIVATE( k, z_mo )
494	!$acc kernels loop private( j, k, z_mo )
495	DO i = nxl, nxr
496	DO j = nys, nyn
497
498	k = nzb_s_inner(j,i)
499	z_mo = zu(k+1) - zw(k)
500
501	!
502	!-- Evaluate bulk Richardson number (calculation depends on
503	!-- definition based on setting of boundary conditions
504	IF ( ibc_pt_b /= 1 ) THEN
505	IF ( humidity ) THEN
506	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
507	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
508	ELSE
509	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
510	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
511	ENDIF
512	ELSE
513	!
514	!-- When using Neumann boundary conditions, the buoyancy flux
515	!-- is required but cannot be calculated at the surface, as pt
516	!-- and q are not known at the surface. Hence the values at
517	!-- first grid level are used to estimate the buoyancy flux
518	IF ( humidity ) THEN
519	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
520	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
521	* pt(k+1,j,i) * qsws(j,i) ) &
522	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
523	+ 1.0E-20_wp)
524	ELSE
525	rib(j,i) = - g * z_mo * shf(j,i) &
526	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
527	+ 1.0E-20_wp )
528	ENDIF
529	ENDIF
530
531	ENDDO
532	ENDDO
533	!$acc end data
534
535	ENDIF
536
537	!
538	!-- Calculate the Obukhov length either using a Newton iteration
539	!-- method, via a lookup table, or using the old circular way
540	IF ( TRIM( most_method ) == 'newton' ) THEN
541
542	!$OMP PARALLEL DO PRIVATE( k, z_mo )
543	!# WARNING: does not work on GPU so far because of DO-loop with
544	!# undetermined iterations
545	!!!!!!$acc kernels loop
546	DO i = nxl, nxr
547	DO j = nys, nyn
548
549	k = nzb_s_inner(j,i)
550	z_mo = zu(k+1) - zw(k)
551
552	!
553	!-- Store current value in case the Newton iteration fails
554	ol_old = ol(j,i)
555
556	!
557	!-- Ensure that the bulk Richardson number and the Obukhov
558	!-- lengtH have the same sign
559	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
560	ABS( ol(j,i) ) == ol_max ) THEN
561	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
562	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
563	ENDIF
564	!
565	!-- Iteration to find Obukhov length
566	iter = 0
567	DO
568	iter = iter + 1
569	!
570	!-- In case of divergence, use the value of the previous time step
571	IF ( iter > 1000 ) THEN
572	ol(j,i) = ol_old
573	EXIT
574	ENDIF
575
576	ol_m = ol(j,i)
577	ol_l = ol_m - 0.001_wp * ol_m
578	ol_u = ol_m + 0.001_wp * ol_m
579
580
581	IF ( ibc_pt_b /= 1 ) THEN
582	!
583	!-- Calculate f = Ri - [...]/[...]^2 = 0
584	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
585	- psi_h( z_mo / ol_m ) &
586	+ psi_h( z0h(j,i) / ol_m ) &
587	) &
588	/ ( LOG( z_mo / z0(j,i) ) &
589	- psi_m( z_mo / ol_m ) &
590	+ psi_m( z0(j,i) / ol_m ) &
591	)**2
592
593	!
594	!-- Calculate df/dL
595	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
596	- psi_h( z_mo / ol_u ) &
597	+ psi_h( z0h(j,i) / ol_u ) &
598	) &
599	/ ( LOG( z_mo / z0(j,i) ) &
600	- psi_m( z_mo / ol_u ) &
601	+ psi_m( z0(j,i) / ol_u ) &
602	)**2 &
603	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
604	- psi_h( z_mo / ol_l ) &
605	+ psi_h( z0h(j,i) / ol_l ) &
606	) &
607	/ ( LOG( z_mo / z0(j,i) ) &
608	- psi_m( z_mo / ol_l ) &
609	+ psi_m( z0(j,i) / ol_l ) &
610	)**2 &
611	) / ( ol_u - ol_l )
612	ELSE
613	!
614	!-- Calculate f = Ri - 1 /[...]^3 = 0
615	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
616	- psi_m( z_mo / ol_m ) &
617	+ psi_m( z0(j,i) / ol_m ) &
618	)**3
619
620	!
621	!-- Calculate df/dL
622	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
623	- psi_m( z_mo / ol_u ) &
624	+ psi_m( z0(j,i) / ol_u ) &
625	)**3 &
626	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
627	- psi_m( z_mo / ol_l ) &
628	+ psi_m( z0(j,i) / ol_l ) &
629	)**3 &
630	) / ( ol_u - ol_l )
631	ENDIF
632	!
633	!-- Calculate new L
634	ol(j,i) = ol_m - f / f_d_ol
635
636	!
637	!-- Ensure that the bulk Richardson number and the Obukhov
638	!-- length have the same sign and ensure convergence.
639	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
640
641	!
642	!-- If unrealistic value occurs, set L to the maximum
643	!-- value that is allowed
644	IF ( ABS( ol(j,i) ) > ol_max ) THEN
645	ol(j,i) = ol_max
646	EXIT
647	ENDIF
648	!
649	!-- Check for convergence
650	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
651	EXIT
652	ELSE
653	CYCLE
654	ENDIF
655
656	ENDDO
657
658	ENDDO
659	ENDDO
660
661	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
662
663	!$OMP PARALLEL DO PRIVATE( k, z_mo )
664	!# WARNING: does not work on GPU so far because of DO WHILE construct
665	!!!!!!$acc kernels loop
666	DO i = nxl, nxr
667	DO j = nys, nyn
668
669	!
670	!-- If the bulk Richardson number is outside the range of the lookup
671	!-- table, set it to the exceeding threshold value
672	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
673	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
674
675	!
676	!-- Find the correct index bounds for linear interpolation. As the
677	!-- Richardson number will not differ very much from time step to
678	!-- time step , use the index from the last step and search in the
679	!-- correct direction
680	l = l_bnd
681	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
682	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
683	l = l-1
684	ENDDO
685	ELSE
686	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
687	.AND. l < num_steps-1 )
688	l = l+1
689	ENDDO
690	ENDIF
691	l_bnd = l
692
693	!
694	!-- Linear interpolation to find the correct value of z/L
695	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
696	/ ( rib_tab(l) - rib_tab(l-1) ) &
697	* ( rib(j,i) - rib_tab(l-1) ) )
698
699	ENDDO
700	ENDDO
701
702	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
703
704	!$OMP PARALLEL DO PRIVATE( k, z_mo )
705	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
706	DO i = nxl, nxr
707	DO j = nys, nyn
708
709	k = nzb_s_inner(j,i)
710	z_mo = zu(k+1) - zw(k)
711
712	IF ( .NOT. humidity ) THEN
713	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
714	* ts(j,i) + 1E-30_wp )
715	ELSEIF ( cloud_physics ) THEN
716
717	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
718	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
719	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
720	* ql(k+1,j,i) ) + 1E-30_wp )
721	ELSE
722	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
723	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
724	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
725	ENDIF
726	!
727	!-- Limit the value range of the Obukhov length.
728	!-- This is necessary for very small velocities (u,v --> 0), because
729	!-- the absolute value of ol can then become very small, which in
730	!-- consequence would result in very large shear stresses and very
731	!-- small momentum fluxes (both are generally unrealistic).
732	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) < zeta_min ) &
733	ol(j,i) = z_mo / zeta_min
734	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) > zeta_max ) &
735	ol(j,i) = z_mo / zeta_max
736	ENDDO
737	ENDDO
738
739	ENDIF
740
741	!
742	!-- Values of ol at ghost point locations are needed for the evaluation
743	!-- of usws and vsws.
744	!$acc update host( ol )
745	CALL exchange_horiz_2d( ol )
746	!$acc update device( ol )
747
748	END SUBROUTINE calc_ol
749
750	!
751	!-- Calculate friction velocity u*
752	SUBROUTINE calc_us
753
754	IMPLICIT NONE
755
756	!$OMP PARALLEL DO PRIVATE( k, z_mo )
757	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
758	DO i = nxlg, nxrg
759	DO j = nysg, nyng
760
761	k = nzb_s_inner(j,i)+1
762	z_mo = zu(k+1) - zw(k)
763
764	!
765	!-- Compute u* at the scalars' grid points
766	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
767	- psi_m( z_mo / ol(j,i) ) &
768	+ psi_m( z0(j,i) / ol(j,i) ) )
769	ENDDO
770	ENDDO
771
772	END SUBROUTINE calc_us
773
774	!
775	!-- Calculate potential temperature and specific humidity at first grid level
776	SUBROUTINE calc_pt_q
777
778	IMPLICIT NONE
779
780	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
781	DO i = nxlg, nxrg
782	DO j = nysg, nyng
783	k = nzb_s_inner(j,i)+1
784	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
785	qv1(j,i) = q(k,j,i) - ql(k,j,i)
786	ENDDO
787	ENDDO
788
789	END SUBROUTINE calc_pt_q
790
791	!
792	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
793	SUBROUTINE calc_scaling_parameters
794
795	IMPLICIT NONE
796
797	!
798	!-- Data information for accelerators
799	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
800	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
801	!$acc present( vpt, vsws, zu, zw, z0, z0h )
802	!
803	!-- Compute theta*
804	IF ( constant_heatflux ) THEN
805
806	!
807	!-- For a given heat flux in the surface layer:
808	!$OMP PARALLEL DO
809	!$acc kernels loop private( j )
810	DO i = nxlg, nxrg
811	DO j = nysg, nyng
812	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
813	!
814	!-- ts must be limited, because otherwise overflow may occur in case
815	!-- of us=0 when computing ol further below
816	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
817	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
818	ENDDO
819	ENDDO
820
821	ELSE
822	!
823	!-- For a given surface temperature:
824	IF ( large_scale_forcing .AND. lsf_surf ) THEN
825	!$OMP PARALLEL DO
826	!$acc kernels loop private( j, k )
827	DO i = nxlg, nxrg
828	DO j = nysg, nyng
829	k = nzb_s_inner(j,i)
830	pt(k,j,i) = pt_surface
831	ENDDO
832	ENDDO
833	ENDIF
834
835	!$OMP PARALLEL DO PRIVATE( k, z_mo )
836	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
837	DO i = nxlg, nxrg
838	DO j = nysg, nyng
839
840	k = nzb_s_inner(j,i)
841	z_mo = zu(k+1) - zw(k)
842
843	IF ( cloud_physics ) THEN
844	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
845	/ ( LOG( z_mo / z0h(j,i) ) &
846	- psi_h( z_mo / ol(j,i) ) &
847	+ psi_h( z0h(j,i) / ol(j,i) ) )
848	ELSE
849	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
850	/ ( LOG( z_mo / z0h(j,i) ) &
851	- psi_h( z_mo / ol(j,i) ) &
852	+ psi_h( z0h(j,i) / ol(j,i) ) )
853	ENDIF
854
855	ENDDO
856	ENDDO
857	ENDIF
858
859	!
860	!-- If required compute q*
861	IF ( humidity .OR. passive_scalar ) THEN
862	IF ( constant_waterflux ) THEN
863	!
864	!-- For a given water flux in the surface layer
865	!$OMP PARALLEL DO
866	!$acc kernels loop private( j )
867	DO i = nxlg, nxrg
868	DO j = nysg, nyng
869	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
870	ENDDO
871	ENDDO
872
873	ELSE
874	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
875	run_coupled )
876
877	IF ( large_scale_forcing .AND. lsf_surf ) THEN
878	!$OMP PARALLEL DO
879	!$acc kernels loop private( j, k )
880	DO i = nxlg, nxrg
881	DO j = nysg, nyng
882	k = nzb_s_inner(j,i)
883	q(k,j,i) = q_surface
884	ENDDO
885	ENDDO
886	ENDIF
887
888	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
889	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
890	DO i = nxlg, nxrg
891	!$acc loop independent
892	DO j = nysg, nyng
893
894	k = nzb_s_inner(j,i)
895	z_mo = zu(k+1) - zw(k)
896
897	!
898	!-- Assume saturation for atmosphere coupled to ocean (but not
899	!-- in case of precursor runs)
900	IF ( coupled_run ) THEN
901	e_s = 6.1_wp * &
902	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
903	- 273.15_wp ) )
904	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
905	ENDIF
906
907	IF ( cloud_physics ) THEN
908	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
909	/ ( LOG( z_mo / z0q(j,i) ) &
910	- psi_h( z_mo / ol(j,i) ) &
911	+ psi_h( z0q(j,i) / ol(j,i) ) )
912
913	ELSE
914	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
915	/ ( LOG( z_mo / z0q(j,i) ) &
916	- psi_h( z_mo / ol(j,i) ) &
917	+ psi_h( z0q(j,i) / ol(j,i) ) )
918	ENDIF
919
920	ENDDO
921	ENDDO
922	ENDIF
923	ENDIF
924
925
926	!
927	!-- If required compute qr* and nr*
928	IF ( cloud_physics .AND. microphysics_seifert ) &
929	THEN
930
931	!$OMP PARALLEL DO PRIVATE( k, z_mo )
932	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
933	DO i = nxlg, nxrg
934	!$acc loop independent
935	DO j = nysg, nyng
936
937	k = nzb_s_inner(j,i)
938	z_mo = zu(k+1) - zw(k)
939
940	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
941	/ ( LOG( z_mo / z0q(j,i) ) &
942	- psi_h( z_mo / ol(j,i) ) &
943	+ psi_h( z0q(j,i) / ol(j,i) ) )
944
945	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
946	/ ( LOG( z_mo / z0q(j,i) ) &
947	- psi_h( z_mo / ol(j,i) ) &
948	+ psi_h( z0q(j,i) / ol(j,i) ) )
949	ENDDO
950	ENDDO
951
952	ENDIF
953	!$acc end data
954
955	END SUBROUTINE calc_scaling_parameters
956
957
958
959	!
960	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
961	SUBROUTINE calc_surface_fluxes
962
963	IMPLICIT NONE
964
965	REAL(wp) :: ol_mid !< Grid-interpolated L
966
967	!
968	!-- Compute u'w' for the total model domain.
969	!-- First compute the corresponding component of u* and square it.
970	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
971	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
972	DO i = nxl, nxr
973	DO j = nys, nyn
974
975	k = nzb_u_inner(j,i)
976	z_mo = zu(k+1) - zw(k)
977	!
978	!-- Compute bulk Obukhov length for this point
979	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
980
981	IF ( ol_mid == 0.0_wp ) THEN
982	ol_mid = MIN(ol(j,i-1), ol(j,i))
983	ENDIF
984
985	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
986	/ ( LOG( z_mo / z0(j,i) ) &
987	- psi_m( z_mo / ol_mid ) &
988	+ psi_m( z0(j,i) / ol_mid ) )
989
990	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
991	ENDDO
992	ENDDO
993
994	!
995	!-- Compute v'w' for the total model domain.
996	!-- First compute the corresponding component of u* and square it.
997	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
998	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
999	DO i = nxl, nxr
1000	DO j = nys, nyn
1001
1002	k = nzb_v_inner(j,i)
1003	z_mo = zu(k+1) - zw(k)
1004	!
1005	!-- Compute bulk Obukhov length for this point
1006	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
1007
1008	IF ( ol_mid == 0.0_wp ) THEN
1009	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
1010	ENDIF
1011
1012	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
1013	/ ( LOG( z_mo / z0(j,i) ) &
1014	- psi_m( z_mo / ol_mid ) &
1015	+ psi_m( z0(j,i) / ol_mid ) )
1016
1017	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
1018
1019	ENDDO
1020	ENDDO
1021
1022	!
1023	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
1024	!$acc update host( usws, vsws )
1025	CALL exchange_horiz_2d( usws )
1026	CALL exchange_horiz_2d( vsws )
1027	!$acc update device( usws, vsws )
1028
1029	!
1030	!-- Compute the vertical kinematic heat flux
1031	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
1032	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
1033	!$OMP PARALLEL DO
1034	!$acc kernels loop independent present( shf, ts, us )
1035	DO i = nxlg, nxrg
1036	!$acc loop independent
1037	DO j = nysg, nyng
1038	shf(j,i) = -ts(j,i) * us(j,i)
1039	ENDDO
1040	ENDDO
1041
1042	ENDIF
1043
1044	!
1045	!-- Compute the vertical water/scalar flux
1046	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. &
1047	passive_scalar ) .AND. ( simulated_time <= skip_time_do_lsm &
1048	.OR. .NOT. land_surface ) ) THEN
1049	!$OMP PARALLEL DO
1050	!$acc kernels loop independent present( qs, qsws, us )
1051	DO i = nxlg, nxrg
1052	!$acc loop independent
1053	DO j = nysg, nyng
1054	qsws(j,i) = -qs(j,i) * us(j,i)
1055	ENDDO
1056	ENDDO
1057
1058	ENDIF
1059
1060	!
1061	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
1062	IF ( cloud_physics .AND. microphysics_seifert ) THEN
1063	!$OMP PARALLEL DO
1064	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
1065	DO i = nxlg, nxrg
1066	!$acc loop independent
1067	DO j = nysg, nyng
1068	qrsws(j,i) = -qrs(j,i) * us(j,i)
1069	nrsws(j,i) = -nrs(j,i) * us(j,i)
1070	ENDDO
1071	ENDDO
1072	ENDIF
1073
1074	!
1075	!-- Bottom boundary condition for the TKE
1076	IF ( ibc_e_b == 2 ) THEN
1077	!$OMP PARALLEL DO
1078	!$acc kernels loop independent present( e, nzb_s_inner, us )
1079	DO i = nxlg, nxrg
1080	!$acc loop independent
1081	DO j = nysg, nyng
1082	k = nzb_s_inner(j,i)
1083	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
1084	!
1085	!-- As a test: cm = 0.4
1086	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
1087	e(k,j,i) = e(k+1,j,i)
1088	ENDDO
1089	ENDDO
1090	ENDIF
1091
1092	END SUBROUTINE calc_surface_fluxes
1093
1094
1095	!
1096	!-- Integrated stability function for momentum
1097	FUNCTION psi_m( zeta )
1098
1099	USE kinds
1100
1101	IMPLICIT NONE
1102
1103	REAL(wp) :: psi_m !< Integrated similarity function result
1104	REAL(wp) :: zeta !< Stability parameter z/L
1105	REAL(wp) :: x !< dummy variable
1106
1107	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1108	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1109	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1110	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1111	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1112	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1113
1114
1115	IF ( zeta < 0.0_wp ) THEN
1116	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
1117	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1118	* ( 1.0_wp + x*2 ) 0.125_wp )
1119	ELSE
1120
1121	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1122	- bc_d_d
1123	!
1124	!-- Old version for stable conditions (only valid for z/L < 0.5)
1125	!-- psi_m = - 5.0_wp * zeta
1126
1127	ENDIF
1128
1129	END FUNCTION psi_m
1130
1131
1132	!
1133	!-- Integrated stability function for heat and moisture
1134	FUNCTION psi_h( zeta )
1135
1136	USE kinds
1137
1138	IMPLICIT NONE
1139
1140	REAL(wp) :: psi_h !< Integrated similarity function result
1141	REAL(wp) :: zeta !< Stability parameter z/L
1142	REAL(wp) :: x !< dummy variable
1143
1144	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1145	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1146	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1147	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1148	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1149	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1150
1151
1152	IF ( zeta < 0.0_wp ) THEN
1153	x = SQRT( 1.0_wp - 16.0_wp * zeta )
1154	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1155	ELSE
1156	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1157	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1158	+ 1.0_wp
1159	!
1160	!-- Old version for stable conditions (only valid for z/L < 0.5)
1161	!-- psi_h = - 5.0_wp * zeta
1162	ENDIF
1163
1164	END FUNCTION psi_h
1165
1166	END MODULE surface_layer_fluxes_mod

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