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source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 1916

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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 1916 2016-05-27 11:09:33Z suehring $
26	!
27	! 1915 2016-05-27 11:05:02Z suehring
28	! Bugfix: avoid segmentation fault in case of most_method = 'circular' at first
29	! timestep
30	!
31	! 1850 2016-04-08 13:29:27Z maronga
32	! Module renamed
33	!
34	!
35	! 1822 2016-04-07 07:49:42Z hoffmann
36	! icloud_scheme replaced by microphysics_*
37	!
38	! 1788 2016-03-10 11:01:04Z maronga
39	! Added parameter z0q which replaces z0h in the similarity functions for
40	! humidity.
41	! Syntax layout improved.
42	!
43	! 1757 2016-02-22 15:49:32Z maronga
44	! Minor fixes.
45	!
46	! 1749 2016-02-09 12:19:56Z raasch
47	! further OpenACC adjustments
48	!
49	! 1747 2016-02-08 12:25:53Z raasch
50	! adjustments for OpenACC usage
51	!
52	! 1709 2015-11-04 14:47:01Z maronga
53	! Bugfix: division by zero could occur when calculating rib at low wind speeds
54	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
55	! neutral = .T.
56	!
57	! 1705 2015-11-02 14:28:56Z maronga
58	! Typo removed
59	!
60	! 1697 2015-10-28 17:14:10Z raasch
61	! FORTRAN and OpenMP errors removed
62	!
63	! 1696 2015-10-27 10:03:34Z maronga
64	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
65	! course of the re-writing two additional methods have been implemented. See
66	! updated description.
67	!
68	! 1551 2015-03-03 14:18:16Z maronga
69	! Removed land surface model part. The surface fluxes are now always calculated
70	! within prandtl_fluxes, based on the given surface temperature/humidity (which
71	! is either provided by the land surface model, by large scale forcing data, or
72	! directly prescribed by the user.
73	!
74	! 1496 2014-12-02 17:25:50Z maronga
75	! Adapted for land surface model
76	!
77	! 1494 2014-11-21 17:14:03Z maronga
78	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
79	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
80	! topography for coupled runs (not tested)
81	!
82	! 1361 2014-04-16 15:17:48Z hoffmann
83	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
84	! drop concentration (nrsws) added
85	!
86	! 1340 2014-03-25 19:45:13Z kanani
87	! REAL constants defined as wp-kind
88	!
89	! 1320 2014-03-20 08:40:49Z raasch
90	! ONLY-attribute added to USE-statements,
91	! kind-parameters added to all INTEGER and REAL declaration statements,
92	! kinds are defined in new module kinds,
93	! old module precision_kind is removed,
94	! revision history before 2012 removed,
95	! comment fields (!:) to be used for variable explanations added to
96	! all variable declaration statements
97	!
98	! 1276 2014-01-15 13:40:41Z heinze
99	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
100	!
101	! 1257 2013-11-08 15:18:40Z raasch
102	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
103	!
104	! 1036 2012-10-22 13:43:42Z raasch
105	! code put under GPL (PALM 3.9)
106	!
107	! 1015 2012-09-27 09:23:24Z raasch
108	! OpenACC statements added
109	!
110	! 978 2012-08-09 08:28:32Z fricke
111	! roughness length for scalar quantities z0h added
112	!
113	! Revision 1.1 1998/01/23 10:06:06 raasch
114	! Initial revision
115	!
116	!
117	! Description:
118	! ------------
119	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
120	!> values of the variables at grid point k=1. Three different methods are
121	!> available:
122	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
123	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
124	!> slower
125	!> 3) a method using a lookup table which is fast and accurate. Note, however,
126	!> that this method cannot be used in case of roughness heterogeneity
127	!>
128	!> @todo (re)move large_scale_forcing actions
129	!> @todo check/optimize OpenMP and OpenACC directives
130	!------------------------------------------------------------------------------!
131	MODULE surface_layer_fluxes_mod
132
133	USE arrays_3d, &
134	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
135	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h, z0q
136
137	USE cloud_parameters, &
138	ONLY: l_d_cp, pt_d_t
139
140	USE constants, &
141	ONLY: pi
142
143	USE cpulog
144
145	USE control_parameters, &
146	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
147	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, &
148	initializing_actions, kappa, intermediate_timestep_count, &
149	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
150	message_string, microphysics_seifert, most_method, neutral, &
151	passive_scalar, pt_surface, q_surface, run_coupled, &
152	surface_pressure, simulated_time, terminate_run, zeta_max, &
153	zeta_min
154
155	USE indices, &
156	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
157	nzb_u_inner, nzb_v_inner
158
159	USE kinds
160
161	USE pegrid
162
163	USE land_surface_model_mod, &
164	ONLY: land_surface, skip_time_do_lsm
165
166	IMPLICIT NONE
167
168	INTEGER(iwp) :: i !< loop index x direction
169	INTEGER(iwp) :: j !< loop index y direction
170	INTEGER(iwp) :: k !< loop index z direction
171
172	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
173
174	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
175
176	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
177	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
178	uv_total !< Total velocity at first grid level
179
180	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
181	ol_tab !< Lookup table values of L
182
183	REAL(wp) :: e_s, & !< Saturation water vapor pressure
184	l_bnd = 7500, & !< Lookup table index of the last time step
185	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
186	rib_max, & !< Maximum Richardson number in lookup table
187	rib_min, & !< Minimum Richardson number in lookup table
188	z_mo !< Height of the constant flux layer where MOST is assumed
189
190
191	SAVE
192
193	PRIVATE
194
195	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
196
197	INTERFACE init_surface_layer_fluxes
198	MODULE PROCEDURE init_surface_layer_fluxes
199	END INTERFACE init_surface_layer_fluxes
200
201	INTERFACE surface_layer_fluxes
202	MODULE PROCEDURE surface_layer_fluxes
203	END INTERFACE surface_layer_fluxes
204
205
206	CONTAINS
207
208
209	!------------------------------------------------------------------------------!
210	! Description:
211	! ------------
212	!> Main routine to compute the surface fluxes
213	!------------------------------------------------------------------------------!
214	SUBROUTINE surface_layer_fluxes
215
216	IMPLICIT NONE
217
218	!
219	!-- In case cloud physics is used, it is required to derive potential
220	!-- temperature and specific humidity at first grid level from the fields pt
221	!-- and q
222	IF ( cloud_physics ) THEN
223	CALL calc_pt_q
224	ENDIF
225
226	!
227	!-- First, calculate the new Obukhov length, then new friction velocity,
228	!-- followed by the new scaling parameters (th, q, etc.), and the new
229	!-- surface fluxes if required. The old routine ("circular") requires a
230	!-- different order of calls as the scaling parameters from the previous time
231	!-- steps are used to calculate the Obukhov length
232
233	!
234	!-- Depending on setting of most_method use the "old" routine
235	IF ( most_method == 'circular' ) THEN
236
237	CALL calc_scaling_parameters
238
239	CALL calc_uv_total
240
241	IF ( .NOT. neutral ) THEN
242	CALL calc_ol
243	ENDIF
244
245	CALL calc_us
246
247	CALL calc_surface_fluxes
248
249	!
250	!-- Use either Newton iteration or a lookup table for the bulk Richardson
251	!-- number to calculate the Obukhov length
252	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
253
254	CALL calc_uv_total
255
256	IF ( .NOT. neutral ) THEN
257	CALL calc_ol
258	ENDIF
259
260	CALL calc_us
261
262	CALL calc_scaling_parameters
263
264	CALL calc_surface_fluxes
265
266	ENDIF
267
268	END SUBROUTINE surface_layer_fluxes
269
270
271	!------------------------------------------------------------------------------!
272	! Description:
273	! ------------
274	!> Initializing actions for the surface layer routine. Basically, this involves
275	!> the preparation of a lookup table for the the bulk Richardson number vs
276	!> Obukhov length L when using the lookup table method.
277	!------------------------------------------------------------------------------!
278	SUBROUTINE init_surface_layer_fluxes
279
280	IMPLICIT NONE
281
282	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
283	num_steps_n !< Number of non-stretched zeta steps
284
285	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
286
287	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
288
289	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
290
291
292	REAL(wp) :: zeta_step, & !< Increment of zeta
293	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
294	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
295	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
296	z0_min = 0.0_wp !< Minimum value of z0 to create table
297	!
298	!-- When cloud physics is used, arrays for storing potential temperature and
299	!-- specific humidity at first grid level are required
300	IF ( cloud_physics ) THEN
301	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
302	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
303	ENDIF
304
305	!
306	!-- Allocate field for storing the horizontal velocity
307	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
308
309
310	!
311	!-- In case of runs with neutral statification, set Obukhov length to a
312	!-- large value
313	IF ( neutral ) ol = 1.0E10_wp
314
315	IF ( most_method == 'lookup' ) THEN
316
317	!
318	!-- Check for roughness heterogeneity. In that case terminate run and
319	!-- inform user
320	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
321	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
322	terminate_run_l = .TRUE.
323	ENDIF
324
325	#if defined( __parallel )
326	!
327	!-- Make a logical OR for all processes. Force termiation of model if result
328	!-- is TRUE
329	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
330	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
331	MPI_LOR, comm2d, ierr )
332	#else
333	terminate_run = terminate_run_l
334	#endif
335
336	IF ( terminate_run ) THEN
337	message_string = 'most_method = "lookup" cannot be used in ' // &
338	'combination with a prescribed roughness ' // &
339	'heterogeneity'
340	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
341	ENDIF
342
343	ALLOCATE( zeta_tmp(0:num_steps-1) )
344
345	!
346	!-- Use the lowest possible value for z_mo
347	k = MINVAL(nzb_s_inner)
348	z_mo = zu(k+1) - zw(k)
349
350	!
351	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
352	!-- available steps (num_steps). The calculation is done with negative
353	!-- values of zeta in order to simplify the stretching in the free
354	!-- convection limit for the remaining 10% of steps.
355	zeta_tmp(0) = - zeta_max
356	num_steps_n = ( num_steps * 9 / 10 ) - 1
357	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
358
359	DO l = 1, num_steps_n
360	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
361	ENDDO
362
363	!
364	!-- Calculate stretching factor for the free convection range
365	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
366	regr_old = regr
367	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
368	)**( 10.0_wp / REAL(num_steps) )
369	ENDDO
370
371	!
372	!-- Calculate z/L range from zeta_min to zeta_stretch
373	DO l = num_steps_n+1, num_steps-1
374	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
375	zeta_step = zeta_step * regr
376	ENDDO
377
378	!
379	!-- Save roughness lengths to temporary variables
380	z0h_min = z0h(nys,nxl)
381	z0_min = z0(nys,nxl)
382
383	!
384	!-- Calculate lookup table for the Richardson number versus Obukhov length
385	!-- The Richardson number (rib) is defined depending on the choice of
386	!-- boundary conditions for temperature
387	IF ( ibc_pt_b == 1 ) THEN
388	DO l = 0, num_steps-1
389	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
390	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
391	- psi_m( z_mo / ol_tab(l) ) &
392	+ psi_m( z0_min / ol_tab(l) ) &
393	)**3
394	ENDDO
395	ELSE
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 / z0h_min ) &
399	- psi_h( z_mo / ol_tab(l) ) &
400	+ psi_h( z0h_min / ol_tab(l) ) &
401	) &
402	/ ( LOG( z_mo / z0_min ) &
403	- psi_m( z_mo / ol_tab(l) ) &
404	+ psi_m( z0_min / ol_tab(l) ) &
405	)**2
406	ENDDO
407	ENDIF
408
409	!
410	!-- Determine minimum values of rib in the lookup table. Set upper limit
411	!-- to critical Richardson number (0.25)
412	rib_min = MINVAL(rib_tab)
413	rib_max = 0.25 !MAXVAL(rib_tab)
414
415	DEALLOCATE( zeta_tmp )
416	ENDIF
417
418	END SUBROUTINE init_surface_layer_fluxes
419
420
421	!------------------------------------------------------------------------------!
422	! Description:
423	! ------------
424	!> Compute the absolute value of the horizontal velocity (relative to the
425	!> surface). This is required by all methods
426	!------------------------------------------------------------------------------!
427	SUBROUTINE calc_uv_total
428
429	IMPLICIT NONE
430
431
432	!$OMP PARALLEL DO PRIVATE( k )
433	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
434	DO i = nxl, nxr
435	DO j = nys, nyn
436
437	k = nzb_s_inner(j,i)
438	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
439	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
440	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
441	- v(k,j,i) - v(k,j+1,i) ) )**2 )
442
443	!
444	!-- For too small values of the local wind, MOST does not work. A
445	!-- threshold value is thus set if required
446	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
447
448	ENDDO
449	ENDDO
450
451	!
452	!-- Values of uv_total need to be exchanged at the ghost boundaries
453	!$acc update host( uv_total )
454	CALL exchange_horiz_2d( uv_total )
455	!$acc update device( uv_total )
456
457	END SUBROUTINE calc_uv_total
458
459
460	!------------------------------------------------------------------------------!
461	! Description:
462	! ------------
463	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
464	!------------------------------------------------------------------------------!
465	SUBROUTINE calc_ol
466
467	IMPLICIT NONE
468
469	INTEGER(iwp) :: iter, & !< Newton iteration step
470	l !< look index
471
472	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
473
474	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
475	f_d_ol, & !< Derivative of f
476	ol_l, & !< Lower bound of L for Newton iteration
477	ol_m, & !< Previous value of L for Newton iteration
478	ol_old, & !< Previous time step value of L
479	ol_u !< Upper bound of L for Newton iteration
480
481	IF ( TRIM( most_method ) /= 'circular' ) THEN
482
483	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
484
485	!$OMP PARALLEL DO PRIVATE( k, z_mo )
486	!$acc kernels loop private( j, k, z_mo )
487	DO i = nxl, nxr
488	DO j = nys, nyn
489
490	k = nzb_s_inner(j,i)
491	z_mo = zu(k+1) - zw(k)
492
493	!
494	!-- Evaluate bulk Richardson number (calculation depends on
495	!-- definition based on setting of boundary conditions
496	IF ( ibc_pt_b /= 1 ) THEN
497	IF ( humidity ) THEN
498	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
499	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
500	ELSE
501	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
502	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
503	ENDIF
504	ELSE
505	!
506	!-- When using Neumann boundary conditions, the buoyancy flux
507	!-- is required but cannot be calculated at the surface, as pt
508	!-- and q are not known at the surface. Hence the values at
509	!-- first grid level are used to estimate the buoyancy flux
510	IF ( humidity ) THEN
511	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
512	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
513	* pt(k+1,j,i) * qsws(j,i) ) &
514	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
515	+ 1.0E-20_wp)
516	ELSE
517	rib(j,i) = - g * z_mo * shf(j,i) &
518	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
519	+ 1.0E-20_wp )
520	ENDIF
521	ENDIF
522
523	ENDDO
524	ENDDO
525	!$acc end data
526
527	ENDIF
528
529	!
530	!-- Calculate the Obukhov length either using a Newton iteration
531	!-- method, via a lookup table, or using the old circular way
532	IF ( TRIM( most_method ) == 'newton' ) THEN
533
534	!$OMP PARALLEL DO PRIVATE( k, z_mo )
535	!# WARNING: does not work on GPU so far because of DO-loop with
536	!# undetermined iterations
537	!!!!!!$acc kernels loop
538	DO i = nxl, nxr
539	DO j = nys, nyn
540
541	k = nzb_s_inner(j,i)
542	z_mo = zu(k+1) - zw(k)
543
544	!
545	!-- Store current value in case the Newton iteration fails
546	ol_old = ol(j,i)
547
548	!
549	!-- Ensure that the bulk Richardson number and the Obukhov
550	!-- lengtH have the same sign
551	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
552	ABS( ol(j,i) ) == ol_max ) THEN
553	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
554	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
555	ENDIF
556	!
557	!-- Iteration to find Obukhov length
558	iter = 0
559	DO
560	iter = iter + 1
561	!
562	!-- In case of divergence, use the value of the previous time step
563	IF ( iter > 1000 ) THEN
564	ol(j,i) = ol_old
565	EXIT
566	ENDIF
567
568	ol_m = ol(j,i)
569	ol_l = ol_m - 0.001_wp * ol_m
570	ol_u = ol_m + 0.001_wp * ol_m
571
572
573	IF ( ibc_pt_b /= 1 ) THEN
574	!
575	!-- Calculate f = Ri - [...]/[...]^2 = 0
576	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
577	- psi_h( z_mo / ol_m ) &
578	+ psi_h( z0h(j,i) / ol_m ) &
579	) &
580	/ ( LOG( z_mo / z0(j,i) ) &
581	- psi_m( z_mo / ol_m ) &
582	+ psi_m( z0(j,i) / ol_m ) &
583	)**2
584
585	!
586	!-- Calculate df/dL
587	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
588	- psi_h( z_mo / ol_u ) &
589	+ psi_h( z0h(j,i) / ol_u ) &
590	) &
591	/ ( LOG( z_mo / z0(j,i) ) &
592	- psi_m( z_mo / ol_u ) &
593	+ psi_m( z0(j,i) / ol_u ) &
594	)**2 &
595	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
596	- psi_h( z_mo / ol_l ) &
597	+ psi_h( z0h(j,i) / ol_l ) &
598	) &
599	/ ( LOG( z_mo / z0(j,i) ) &
600	- psi_m( z_mo / ol_l ) &
601	+ psi_m( z0(j,i) / ol_l ) &
602	)**2 &
603	) / ( ol_u - ol_l )
604	ELSE
605	!
606	!-- Calculate f = Ri - 1 /[...]^3 = 0
607	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
608	- psi_m( z_mo / ol_m ) &
609	+ psi_m( z0(j,i) / ol_m ) &
610	)**3
611
612	!
613	!-- Calculate df/dL
614	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
615	- psi_m( z_mo / ol_u ) &
616	+ psi_m( z0(j,i) / ol_u ) &
617	)**3 &
618	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
619	- psi_m( z_mo / ol_l ) &
620	+ psi_m( z0(j,i) / ol_l ) &
621	)**3 &
622	) / ( ol_u - ol_l )
623	ENDIF
624	!
625	!-- Calculate new L
626	ol(j,i) = ol_m - f / f_d_ol
627
628	!
629	!-- Ensure that the bulk Richardson number and the Obukhov
630	!-- length have the same sign and ensure convergence.
631	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
632
633	!
634	!-- If unrealistic value occurs, set L to the maximum
635	!-- value that is allowed
636	IF ( ABS( ol(j,i) ) > ol_max ) THEN
637	ol(j,i) = ol_max
638	EXIT
639	ENDIF
640	!
641	!-- Check for convergence
642	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
643	EXIT
644	ELSE
645	CYCLE
646	ENDIF
647
648	ENDDO
649
650	ENDDO
651	ENDDO
652
653	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
654
655	!$OMP PARALLEL DO PRIVATE( k, z_mo )
656	!# WARNING: does not work on GPU so far because of DO WHILE construct
657	!!!!!!$acc kernels loop
658	DO i = nxl, nxr
659	DO j = nys, nyn
660
661	!
662	!-- If the bulk Richardson number is outside the range of the lookup
663	!-- table, set it to the exceeding threshold value
664	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
665	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
666
667	!
668	!-- Find the correct index bounds for linear interpolation. As the
669	!-- Richardson number will not differ very much from time step to
670	!-- time step , use the index from the last step and search in the
671	!-- correct direction
672	l = l_bnd
673	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
674	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
675	l = l-1
676	ENDDO
677	ELSE
678	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
679	.AND. l < num_steps-1 )
680	l = l+1
681	ENDDO
682	ENDIF
683	l_bnd = l
684
685	!
686	!-- Linear interpolation to find the correct value of z/L
687	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
688	/ ( rib_tab(l) - rib_tab(l-1) ) &
689	* ( rib(j,i) - rib_tab(l-1) ) )
690
691	ENDDO
692	ENDDO
693
694	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
695
696	!$OMP PARALLEL DO PRIVATE( k, z_mo )
697	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
698	DO i = nxl, nxr
699	DO j = nys, nyn
700
701	k = nzb_s_inner(j,i)
702	z_mo = zu(k+1) - zw(k)
703
704	IF ( .NOT. humidity ) THEN
705	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
706	* ts(j,i) + 1E-30_wp )
707	ELSEIF ( cloud_physics ) THEN
708
709	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
710	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
711	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
712	* ql(k+1,j,i) ) + 1E-30_wp )
713	ELSE
714	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
715	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
716	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
717	ENDIF
718	!
719	!-- Limit the value range of the Obukhov length.
720	!-- This is necessary for very small velocities (u,v --> 0), because
721	!-- the absolute value of ol can then become very small, which in
722	!-- consequence would result in very large shear stresses and very
723	!-- small momentum fluxes (both are generally unrealistic).
724	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
725	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
726
727	ENDDO
728	ENDDO
729
730	ENDIF
731
732	!
733	!-- Values of ol at ghost point locations are needed for the evaluation
734	!-- of usws and vsws.
735	!$acc update host( ol )
736	CALL exchange_horiz_2d( ol )
737	!$acc update device( ol )
738
739	END SUBROUTINE calc_ol
740
741	!
742	!-- Calculate friction velocity u*
743	SUBROUTINE calc_us
744
745	IMPLICIT NONE
746
747	!$OMP PARALLEL DO PRIVATE( k, z_mo )
748	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
749	DO i = nxlg, nxrg
750	DO j = nysg, nyng
751
752	k = nzb_s_inner(j,i)+1
753	z_mo = zu(k+1) - zw(k)
754
755	!
756	!-- Compute u* at the scalars' grid points
757	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
758	- psi_m( z_mo / ol(j,i) ) &
759	+ psi_m( z0(j,i) / ol(j,i) ) )
760	ENDDO
761	ENDDO
762
763	END SUBROUTINE calc_us
764
765	!
766	!-- Calculate potential temperature and specific humidity at first grid level
767	SUBROUTINE calc_pt_q
768
769	IMPLICIT NONE
770
771	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
772	DO i = nxlg, nxrg
773	DO j = nysg, nyng
774	k = nzb_s_inner(j,i)+1
775	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
776	qv1(j,i) = q(k,j,i) - ql(k,j,i)
777	ENDDO
778	ENDDO
779
780	END SUBROUTINE calc_pt_q
781
782	!
783	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
784	SUBROUTINE calc_scaling_parameters
785
786	IMPLICIT NONE
787
788	!
789	!-- Data information for accelerators
790	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
791	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
792	!$acc present( vpt, vsws, zu, zw, z0, z0h )
793	!
794	!-- Compute theta*
795	IF ( constant_heatflux ) THEN
796
797	!
798	!-- For a given heat flux in the surface layer:
799	!$OMP PARALLEL DO
800	!$acc kernels loop private( j )
801	DO i = nxlg, nxrg
802	DO j = nysg, nyng
803	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
804	!
805	!-- ts must be limited, because otherwise overflow may occur in case
806	!-- of us=0 when computing ol further below
807	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
808	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
809	ENDDO
810	ENDDO
811
812	ELSE
813	!
814	!-- For a given surface temperature:
815	IF ( large_scale_forcing .AND. lsf_surf ) THEN
816	!$OMP PARALLEL DO
817	!$acc kernels loop private( j, k )
818	DO i = nxlg, nxrg
819	DO j = nysg, nyng
820	k = nzb_s_inner(j,i)
821	pt(k,j,i) = pt_surface
822	ENDDO
823	ENDDO
824	ENDIF
825
826	!$OMP PARALLEL DO PRIVATE( k, z_mo )
827	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
828	DO i = nxlg, nxrg
829	DO j = nysg, nyng
830
831	k = nzb_s_inner(j,i)
832	z_mo = zu(k+1) - zw(k)
833
834	IF ( cloud_physics ) THEN
835	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
836	/ ( LOG( z_mo / z0h(j,i) ) &
837	- psi_h( z_mo / ol(j,i) ) &
838	+ psi_h( z0h(j,i) / ol(j,i) ) )
839	ELSE
840	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
841	/ ( LOG( z_mo / z0h(j,i) ) &
842	- psi_h( z_mo / ol(j,i) ) &
843	+ psi_h( z0h(j,i) / ol(j,i) ) )
844	ENDIF
845
846	ENDDO
847	ENDDO
848	ENDIF
849
850	!
851	!-- If required compute q*
852	IF ( humidity .OR. passive_scalar ) THEN
853	IF ( constant_waterflux ) THEN
854	!
855	!-- For a given water flux in the surface layer
856	!$OMP PARALLEL DO
857	!$acc kernels loop private( j )
858	DO i = nxlg, nxrg
859	DO j = nysg, nyng
860	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
861	ENDDO
862	ENDDO
863
864	ELSE
865	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
866	run_coupled )
867
868	IF ( large_scale_forcing .AND. lsf_surf ) THEN
869	!$OMP PARALLEL DO
870	!$acc kernels loop private( j, k )
871	DO i = nxlg, nxrg
872	DO j = nysg, nyng
873	k = nzb_s_inner(j,i)
874	q(k,j,i) = q_surface
875	ENDDO
876	ENDDO
877	ENDIF
878
879	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
880	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
881	DO i = nxlg, nxrg
882	!$acc loop independent
883	DO j = nysg, nyng
884
885	k = nzb_s_inner(j,i)
886	z_mo = zu(k+1) - zw(k)
887
888	!
889	!-- Assume saturation for atmosphere coupled to ocean (but not
890	!-- in case of precursor runs)
891	IF ( coupled_run ) THEN
892	e_s = 6.1_wp * &
893	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
894	- 273.15_wp ) )
895	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
896	ENDIF
897
898	IF ( cloud_physics ) THEN
899	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
900	/ ( LOG( z_mo / z0q(j,i) ) &
901	- psi_h( z_mo / ol(j,i) ) &
902	+ psi_h( z0q(j,i) / ol(j,i) ) )
903
904	ELSE
905	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
906	/ ( LOG( z_mo / z0q(j,i) ) &
907	- psi_h( z_mo / ol(j,i) ) &
908	+ psi_h( z0q(j,i) / ol(j,i) ) )
909	ENDIF
910
911	ENDDO
912	ENDDO
913	ENDIF
914	ENDIF
915
916
917	!
918	!-- If required compute qr* and nr*
919	IF ( cloud_physics .AND. microphysics_seifert ) &
920	THEN
921
922	!$OMP PARALLEL DO PRIVATE( k, z_mo )
923	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
924	DO i = nxlg, nxrg
925	!$acc loop independent
926	DO j = nysg, nyng
927
928	k = nzb_s_inner(j,i)
929	z_mo = zu(k+1) - zw(k)
930
931	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
932	/ ( LOG( z_mo / z0q(j,i) ) &
933	- psi_h( z_mo / ol(j,i) ) &
934	+ psi_h( z0q(j,i) / ol(j,i) ) )
935
936	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
937	/ ( LOG( z_mo / z0q(j,i) ) &
938	- psi_h( z_mo / ol(j,i) ) &
939	+ psi_h( z0q(j,i) / ol(j,i) ) )
940	ENDDO
941	ENDDO
942
943	ENDIF
944	!$acc end data
945
946	END SUBROUTINE calc_scaling_parameters
947
948
949
950	!
951	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
952	SUBROUTINE calc_surface_fluxes
953
954	IMPLICIT NONE
955
956	REAL(wp) :: ol_mid !< Grid-interpolated L
957
958	!
959	!-- Compute u'w' for the total model domain.
960	!-- First compute the corresponding component of u* and square it.
961	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
962	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
963	DO i = nxl, nxr
964	DO j = nys, nyn
965
966	k = nzb_u_inner(j,i)
967	z_mo = zu(k+1) - zw(k)
968	!
969	!-- Compute bulk Obukhov length for this point
970	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
971
972	IF ( ol_mid == 0.0_wp ) THEN
973	ol_mid = MIN(ol(j,i-1), ol(j,i))
974	ENDIF
975
976	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
977	/ ( LOG( z_mo / z0(j,i) ) &
978	- psi_m( z_mo / ol_mid ) &
979	+ psi_m( z0(j,i) / ol_mid ) )
980
981	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
982	ENDDO
983	ENDDO
984
985	!
986	!-- Compute v'w' for the total model domain.
987	!-- First compute the corresponding component of u* and square it.
988	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
989	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
990	DO i = nxl, nxr
991	DO j = nys, nyn
992
993	k = nzb_v_inner(j,i)
994	z_mo = zu(k+1) - zw(k)
995	!
996	!-- Compute bulk Obukhov length for this point
997	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
998
999	IF ( ol_mid == 0.0_wp ) THEN
1000	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
1001	ENDIF
1002
1003	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
1004	/ ( LOG( z_mo / z0(j,i) ) &
1005	- psi_m( z_mo / ol_mid ) &
1006	+ psi_m( z0(j,i) / ol_mid ) )
1007
1008	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
1009
1010	ENDDO
1011	ENDDO
1012
1013	!
1014	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
1015	!$acc update host( usws, vsws )
1016	CALL exchange_horiz_2d( usws )
1017	CALL exchange_horiz_2d( vsws )
1018	!$acc update device( usws, vsws )
1019
1020	!
1021	!-- Compute the vertical kinematic heat flux
1022	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
1023	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
1024	!$OMP PARALLEL DO
1025	!$acc kernels loop independent present( shf, ts, us )
1026	DO i = nxlg, nxrg
1027	!$acc loop independent
1028	DO j = nysg, nyng
1029	shf(j,i) = -ts(j,i) * us(j,i)
1030	ENDDO
1031	ENDDO
1032
1033	ENDIF
1034
1035	!
1036	!-- Compute the vertical water/scalar flux
1037	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. &
1038	passive_scalar ) .AND. ( simulated_time <= skip_time_do_lsm &
1039	.OR. .NOT. land_surface ) ) THEN
1040	!$OMP PARALLEL DO
1041	!$acc kernels loop independent present( qs, qsws, us )
1042	DO i = nxlg, nxrg
1043	!$acc loop independent
1044	DO j = nysg, nyng
1045	qsws(j,i) = -qs(j,i) * us(j,i)
1046	ENDDO
1047	ENDDO
1048
1049	ENDIF
1050
1051	!
1052	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
1053	IF ( cloud_physics .AND. microphysics_seifert ) THEN
1054	!$OMP PARALLEL DO
1055	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
1056	DO i = nxlg, nxrg
1057	!$acc loop independent
1058	DO j = nysg, nyng
1059	qrsws(j,i) = -qrs(j,i) * us(j,i)
1060	nrsws(j,i) = -nrs(j,i) * us(j,i)
1061	ENDDO
1062	ENDDO
1063	ENDIF
1064
1065	!
1066	!-- Bottom boundary condition for the TKE
1067	IF ( ibc_e_b == 2 ) THEN
1068	!$OMP PARALLEL DO
1069	!$acc kernels loop independent present( e, nzb_s_inner, us )
1070	DO i = nxlg, nxrg
1071	!$acc loop independent
1072	DO j = nysg, nyng
1073	k = nzb_s_inner(j,i)
1074	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
1075	!
1076	!-- As a test: cm = 0.4
1077	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
1078	e(k,j,i) = e(k+1,j,i)
1079	ENDDO
1080	ENDDO
1081	ENDIF
1082
1083	END SUBROUTINE calc_surface_fluxes
1084
1085
1086	!
1087	!-- Integrated stability function for momentum
1088	FUNCTION psi_m( zeta )
1089
1090	USE kinds
1091
1092	IMPLICIT NONE
1093
1094	REAL(wp) :: psi_m !< Integrated similarity function result
1095	REAL(wp) :: zeta !< Stability parameter z/L
1096	REAL(wp) :: x !< dummy variable
1097
1098	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1099	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1100	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1101	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1102	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1103	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1104
1105
1106	IF ( zeta < 0.0_wp ) THEN
1107	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
1108	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1109	* ( 1.0_wp + x*2 ) 0.125_wp )
1110	ELSE
1111
1112	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1113	- bc_d_d
1114	!
1115	!-- Old version for stable conditions (only valid for z/L < 0.5)
1116	!-- psi_m = - 5.0_wp * zeta
1117
1118	ENDIF
1119
1120	END FUNCTION psi_m
1121
1122
1123	!
1124	!-- Integrated stability function for heat and moisture
1125	FUNCTION psi_h( zeta )
1126
1127	USE kinds
1128
1129	IMPLICIT NONE
1130
1131	REAL(wp) :: psi_h !< Integrated similarity function result
1132	REAL(wp) :: zeta !< Stability parameter z/L
1133	REAL(wp) :: x !< dummy variable
1134
1135	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1136	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1137	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1138	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1139	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1140	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1141
1142
1143	IF ( zeta < 0.0_wp ) THEN
1144	x = SQRT( 1.0_wp - 16.0_wp * zeta )
1145	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1146	ELSE
1147	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1148	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1149	+ 1.0_wp
1150	!
1151	!-- Old version for stable conditions (only valid for z/L < 0.5)
1152	!-- psi_h = - 5.0_wp * zeta
1153	ENDIF
1154
1155	END FUNCTION psi_h
1156
1157	END MODULE surface_layer_fluxes_mod

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