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source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 2065

Last change on this file since 2065 was 2038, checked in by knoop, 8 years ago
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1	!> @file surface_layer_fluxes_mod.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of PALM.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 1997-2016 Leibniz Universitaet Hannover
18	!
19	!------------------------------------------------------------------------------!
20	! Current revisions:
21	! ------------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: surface_layer_fluxes_mod.f90 2038 2016-10-26 11:16:56Z maronga $
27	!
28	! 2037 2016-10-26 11:15:40Z knoop
29	! Anelastic approximation implemented
30	!
31	! 2011 2016-09-19 17:29:57Z kanani
32	! Flag urban_surface is now defined in module control_parameters.
33	!
34	! 2007 2016-08-24 15:47:17Z kanani
35	! Account for urban surface model in computation of vertical kinematic heatflux
36	!
37	! 2000 2016-08-20 18:09:15Z knoop
38	! Forced header and separation lines into 80 columns
39	!
40	! 1992 2016-08-12 15:14:59Z suehring
41	! Minor bug, declaration of look-up index as INTEGER
42	!
43	! 1960 2016-07-12 16:34:24Z suehring
44	! Treat humidity and passive scalar separately
45	!
46	! 1929 2016-06-09 16:25:25Z suehring
47	! Bugfix: avoid segmentation fault in case one grid point is horizontally
48	! completely surrounded by topography
49	!
50	! 1920 2016-05-30 10:50:15Z suehring
51	! Avoid segmentation fault (see change in 1915) by different initialization of
52	! us instead of adding a very small number in the denominator
53	!
54	! 1915 2016-05-27 11:05:02Z suehring
55	! Bugfix: avoid segmentation fault in case of most_method = 'circular' at first
56	! timestep
57	!
58	! 1850 2016-04-08 13:29:27Z maronga
59	! Module renamed
60	!
61	!
62	! 1822 2016-04-07 07:49:42Z hoffmann
63	! icloud_scheme replaced by microphysics_*
64	!
65	! 1788 2016-03-10 11:01:04Z maronga
66	! Added parameter z0q which replaces z0h in the similarity functions for
67	! humidity.
68	! Syntax layout improved.
69	!
70	! 1757 2016-02-22 15:49:32Z maronga
71	! Minor fixes.
72	!
73	! 1749 2016-02-09 12:19:56Z raasch
74	! further OpenACC adjustments
75	!
76	! 1747 2016-02-08 12:25:53Z raasch
77	! adjustments for OpenACC usage
78	!
79	! 1709 2015-11-04 14:47:01Z maronga
80	! Bugfix: division by zero could occur when calculating rib at low wind speeds
81	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
82	! neutral = .T.
83	!
84	! 1705 2015-11-02 14:28:56Z maronga
85	! Typo removed
86	!
87	! 1697 2015-10-28 17:14:10Z raasch
88	! FORTRAN and OpenMP errors removed
89	!
90	! 1696 2015-10-27 10:03:34Z maronga
91	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
92	! course of the re-writing two additional methods have been implemented. See
93	! updated description.
94	!
95	! 1551 2015-03-03 14:18:16Z maronga
96	! Removed land surface model part. The surface fluxes are now always calculated
97	! within prandtl_fluxes, based on the given surface temperature/humidity (which
98	! is either provided by the land surface model, by large scale forcing data, or
99	! directly prescribed by the user.
100	!
101	! 1496 2014-12-02 17:25:50Z maronga
102	! Adapted for land surface model
103	!
104	! 1494 2014-11-21 17:14:03Z maronga
105	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
106	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
107	! topography for coupled runs (not tested)
108	!
109	! 1361 2014-04-16 15:17:48Z hoffmann
110	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
111	! drop concentration (nrsws) added
112	!
113	! 1340 2014-03-25 19:45:13Z kanani
114	! REAL constants defined as wp-kind
115	!
116	! 1320 2014-03-20 08:40:49Z raasch
117	! ONLY-attribute added to USE-statements,
118	! kind-parameters added to all INTEGER and REAL declaration statements,
119	! kinds are defined in new module kinds,
120	! old module precision_kind is removed,
121	! revision history before 2012 removed,
122	! comment fields (!:) to be used for variable explanations added to
123	! all variable declaration statements
124	!
125	! 1276 2014-01-15 13:40:41Z heinze
126	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
127	!
128	! 1257 2013-11-08 15:18:40Z raasch
129	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
130	!
131	! 1036 2012-10-22 13:43:42Z raasch
132	! code put under GPL (PALM 3.9)
133	!
134	! 1015 2012-09-27 09:23:24Z raasch
135	! OpenACC statements added
136	!
137	! 978 2012-08-09 08:28:32Z fricke
138	! roughness length for scalar quantities z0h added
139	!
140	! Revision 1.1 1998/01/23 10:06:06 raasch
141	! Initial revision
142	!
143	!
144	! Description:
145	! ------------
146	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
147	!> values of the variables at grid point k=1. Three different methods are
148	!> available:
149	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
150	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
151	!> slower
152	!> 3) a method using a lookup table which is fast and accurate. Note, however,
153	!> that this method cannot be used in case of roughness heterogeneity
154	!>
155	!> @todo (re)move large_scale_forcing actions
156	!> @todo check/optimize OpenMP and OpenACC directives
157	!------------------------------------------------------------------------------!
158	MODULE surface_layer_fluxes_mod
159
160	USE arrays_3d, &
161	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
162	s, shf, ss, ssws, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, &
163	z0h, z0q, drho_air_zw, rho_air_zw
164
165	USE cloud_parameters, &
166	ONLY: l_d_cp, pt_d_t
167
168	USE constants, &
169	ONLY: pi
170
171	USE cpulog
172
173	USE control_parameters, &
174	ONLY: cloud_physics, constant_heatflux, constant_scalarflux, &
175	constant_waterflux, coupling_mode, g, humidity, ibc_e_b, &
176	ibc_pt_b, initializing_actions, kappa, &
177	intermediate_timestep_count, &
178	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
179	message_string, microphysics_seifert, most_method, neutral, &
180	passive_scalar, pt_surface, q_surface, run_coupled, &
181	surface_pressure, simulated_time, terminate_run, &
182	urban_surface, &
183	zeta_max, zeta_min
184
185	USE indices, &
186	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
187	nzb_u_inner, nzb_v_inner
188
189	USE kinds
190
191	USE pegrid
192
193	USE land_surface_model_mod, &
194	ONLY: land_surface, skip_time_do_lsm
195
196
197
198	IMPLICIT NONE
199
200	INTEGER(iwp) :: i !< loop index x direction
201	INTEGER(iwp) :: j !< loop index y direction
202	INTEGER(iwp) :: k !< loop index z direction
203	INTEGER(iwp) :: l_bnd = 7500 !< Lookup table index of the last time step
204
205	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
206
207	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
208
209	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
210	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
211	uv_total !< Total velocity at first grid level
212
213	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
214	ol_tab !< Lookup table values of L
215
216	REAL(wp) :: e_s, & !< Saturation water vapor pressure
217	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
218	rib_max, & !< Maximum Richardson number in lookup table
219	rib_min, & !< Minimum Richardson number in lookup table
220	z_mo !< Height of the constant flux layer where MOST is assumed
221
222
223	SAVE
224
225	PRIVATE
226
227	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
228
229	INTERFACE init_surface_layer_fluxes
230	MODULE PROCEDURE init_surface_layer_fluxes
231	END INTERFACE init_surface_layer_fluxes
232
233	INTERFACE surface_layer_fluxes
234	MODULE PROCEDURE surface_layer_fluxes
235	END INTERFACE surface_layer_fluxes
236
237
238	CONTAINS
239
240
241	!------------------------------------------------------------------------------!
242	! Description:
243	! ------------
244	!> Main routine to compute the surface fluxes
245	!------------------------------------------------------------------------------!
246	SUBROUTINE surface_layer_fluxes
247
248	IMPLICIT NONE
249
250	!
251	!-- In case cloud physics is used, it is required to derive potential
252	!-- temperature and specific humidity at first grid level from the fields pt
253	!-- and q
254	IF ( cloud_physics ) THEN
255	CALL calc_pt_q
256	ENDIF
257
258	!
259	!-- First, calculate the new Obukhov length, then new friction velocity,
260	!-- followed by the new scaling parameters (th, q, etc.), and the new
261	!-- surface fluxes if required. The old routine ("circular") requires a
262	!-- different order of calls as the scaling parameters from the previous time
263	!-- steps are used to calculate the Obukhov length
264
265	!
266	!-- Depending on setting of most_method use the "old" routine
267	IF ( most_method == 'circular' ) THEN
268
269	CALL calc_scaling_parameters
270
271	CALL calc_uv_total
272
273	IF ( .NOT. neutral ) THEN
274	CALL calc_ol
275	ENDIF
276
277	CALL calc_us
278
279	CALL calc_surface_fluxes
280
281	!
282	!-- Use either Newton iteration or a lookup table for the bulk Richardson
283	!-- number to calculate the Obukhov length
284	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
285
286	CALL calc_uv_total
287
288	IF ( .NOT. neutral ) THEN
289	CALL calc_ol
290	ENDIF
291
292	CALL calc_us
293
294	CALL calc_scaling_parameters
295
296	CALL calc_surface_fluxes
297
298	ENDIF
299
300	END SUBROUTINE surface_layer_fluxes
301
302
303	!------------------------------------------------------------------------------!
304	! Description:
305	! ------------
306	!> Initializing actions for the surface layer routine. Basically, this involves
307	!> the preparation of a lookup table for the the bulk Richardson number vs
308	!> Obukhov length L when using the lookup table method.
309	!------------------------------------------------------------------------------!
310	SUBROUTINE init_surface_layer_fluxes
311
312	IMPLICIT NONE
313
314	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
315	num_steps_n !< Number of non-stretched zeta steps
316
317	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
318
319	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
320
321	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
322
323
324	REAL(wp) :: zeta_step, & !< Increment of zeta
325	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
326	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
327	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
328	z0_min = 0.0_wp !< Minimum value of z0 to create table
329	!
330	!-- When cloud physics is used, arrays for storing potential temperature and
331	!-- specific humidity at first grid level are required
332	IF ( cloud_physics ) THEN
333	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
334	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
335	ENDIF
336
337	!
338	!-- Allocate field for storing the horizontal velocity
339	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
340
341
342	!
343	!-- In case of runs with neutral statification, set Obukhov length to a
344	!-- large value
345	IF ( neutral ) ol = 1.0E10_wp
346
347	IF ( most_method == 'lookup' ) THEN
348
349	!
350	!-- Check for roughness heterogeneity. In that case terminate run and
351	!-- inform user
352	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
353	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
354	terminate_run_l = .TRUE.
355	ENDIF
356
357	#if defined( __parallel )
358	!
359	!-- Make a logical OR for all processes. Force termiation of model if result
360	!-- is TRUE
361	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
362	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
363	MPI_LOR, comm2d, ierr )
364	#else
365	terminate_run = terminate_run_l
366	#endif
367
368	IF ( terminate_run ) THEN
369	message_string = 'most_method = "lookup" cannot be used in ' // &
370	'combination with a prescribed roughness ' // &
371	'heterogeneity'
372	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
373	ENDIF
374
375	ALLOCATE( zeta_tmp(0:num_steps-1) )
376
377	!
378	!-- Use the lowest possible value for z_mo
379	k = MINVAL(nzb_s_inner)
380	z_mo = zu(k+1) - zw(k)
381
382	!
383	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
384	!-- available steps (num_steps). The calculation is done with negative
385	!-- values of zeta in order to simplify the stretching in the free
386	!-- convection limit for the remaining 10% of steps.
387	zeta_tmp(0) = - zeta_max
388	num_steps_n = ( num_steps * 9 / 10 ) - 1
389	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
390
391	DO l = 1, num_steps_n
392	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
393	ENDDO
394
395	!
396	!-- Calculate stretching factor for the free convection range
397	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
398	regr_old = regr
399	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
400	)**( 10.0_wp / REAL(num_steps) )
401	ENDDO
402
403	!
404	!-- Calculate z/L range from zeta_min to zeta_stretch
405	DO l = num_steps_n+1, num_steps-1
406	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
407	zeta_step = zeta_step * regr
408	ENDDO
409
410	!
411	!-- Save roughness lengths to temporary variables
412	z0h_min = z0h(nys,nxl)
413	z0_min = z0(nys,nxl)
414
415	!
416	!-- Calculate lookup table for the Richardson number versus Obukhov length
417	!-- The Richardson number (rib) is defined depending on the choice of
418	!-- boundary conditions for temperature
419	IF ( ibc_pt_b == 1 ) THEN
420	DO l = 0, num_steps-1
421	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
422	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
423	- psi_m( z_mo / ol_tab(l) ) &
424	+ psi_m( z0_min / ol_tab(l) ) &
425	)**3
426	ENDDO
427	ELSE
428	DO l = 0, num_steps-1
429	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
430	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
431	- psi_h( z_mo / ol_tab(l) ) &
432	+ psi_h( z0h_min / ol_tab(l) ) &
433	) &
434	/ ( LOG( z_mo / z0_min ) &
435	- psi_m( z_mo / ol_tab(l) ) &
436	+ psi_m( z0_min / ol_tab(l) ) &
437	)**2
438	ENDDO
439	ENDIF
440
441	!
442	!-- Determine minimum values of rib in the lookup table. Set upper limit
443	!-- to critical Richardson number (0.25)
444	rib_min = MINVAL(rib_tab)
445	rib_max = 0.25 !MAXVAL(rib_tab)
446
447	DEALLOCATE( zeta_tmp )
448	ENDIF
449
450	END SUBROUTINE init_surface_layer_fluxes
451
452
453	!------------------------------------------------------------------------------!
454	! Description:
455	! ------------
456	!> Compute the absolute value of the horizontal velocity (relative to the
457	!> surface). This is required by all methods
458	!------------------------------------------------------------------------------!
459	SUBROUTINE calc_uv_total
460
461	IMPLICIT NONE
462
463
464	!$OMP PARALLEL DO PRIVATE( k )
465	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
466	DO i = nxl, nxr
467	DO j = nys, nyn
468
469	k = nzb_s_inner(j,i)
470	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
471	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
472	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
473	- v(k,j,i) - v(k,j+1,i) ) )**2 )
474
475	!
476	!-- For too small values of the local wind, MOST does not work. A
477	!-- threshold value is thus set if required
478	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
479
480	ENDDO
481	ENDDO
482
483	!
484	!-- Values of uv_total need to be exchanged at the ghost boundaries
485	!$acc update host( uv_total )
486	CALL exchange_horiz_2d( uv_total )
487	!$acc update device( uv_total )
488
489	END SUBROUTINE calc_uv_total
490
491
492	!------------------------------------------------------------------------------!
493	! Description:
494	! ------------
495	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
496	!------------------------------------------------------------------------------!
497	SUBROUTINE calc_ol
498
499	IMPLICIT NONE
500
501	INTEGER(iwp) :: iter, & !< Newton iteration step
502	l !< look index
503
504	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
505
506	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
507	f_d_ol, & !< Derivative of f
508	ol_l, & !< Lower bound of L for Newton iteration
509	ol_m, & !< Previous value of L for Newton iteration
510	ol_old, & !< Previous time step value of L
511	ol_u !< Upper bound of L for Newton iteration
512
513	IF ( TRIM( most_method ) /= 'circular' ) THEN
514
515	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
516
517	!$OMP PARALLEL DO PRIVATE( k, z_mo )
518	!$acc kernels loop private( j, k, z_mo )
519	DO i = nxl, nxr
520	DO j = nys, nyn
521
522	k = nzb_s_inner(j,i)
523	z_mo = zu(k+1) - zw(k)
524
525	!
526	!-- Evaluate bulk Richardson number (calculation depends on
527	!-- definition based on setting of boundary conditions
528	IF ( ibc_pt_b /= 1 ) THEN
529	IF ( humidity ) THEN
530	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
531	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
532	ELSE
533	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
534	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
535	ENDIF
536	ELSE
537	!
538	!-- When using Neumann boundary conditions, the buoyancy flux
539	!-- is required but cannot be calculated at the surface, as pt
540	!-- and q are not known at the surface. Hence the values at
541	!-- first grid level are used to estimate the buoyancy flux
542	IF ( humidity ) THEN
543	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
544	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
545	* pt(k+1,j,i) * qsws(j,i) ) * drho_air_zw(k) &
546	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
547	+ 1.0E-20_wp)
548	ELSE
549	rib(j,i) = - g * z_mo * shf(j,i) * drho_air_zw(k) &
550	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
551	+ 1.0E-20_wp )
552	ENDIF
553	ENDIF
554
555	ENDDO
556	ENDDO
557	!$acc end data
558
559	ENDIF
560
561	!
562	!-- Calculate the Obukhov length either using a Newton iteration
563	!-- method, via a lookup table, or using the old circular way
564	IF ( TRIM( most_method ) == 'newton' ) THEN
565
566	!$OMP PARALLEL DO PRIVATE( k, z_mo )
567	!# WARNING: does not work on GPU so far because of DO-loop with
568	!# undetermined iterations
569	!!!!!!$acc kernels loop
570	DO i = nxl, nxr
571	DO j = nys, nyn
572
573	k = nzb_s_inner(j,i)
574	z_mo = zu(k+1) - zw(k)
575
576	!
577	!-- Store current value in case the Newton iteration fails
578	ol_old = ol(j,i)
579
580	!
581	!-- Ensure that the bulk Richardson number and the Obukhov
582	!-- lengtH have the same sign
583	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
584	ABS( ol(j,i) ) == ol_max ) THEN
585	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
586	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
587	ENDIF
588	!
589	!-- Iteration to find Obukhov length
590	iter = 0
591	DO
592	iter = iter + 1
593	!
594	!-- In case of divergence, use the value of the previous time step
595	IF ( iter > 1000 ) THEN
596	ol(j,i) = ol_old
597	EXIT
598	ENDIF
599
600	ol_m = ol(j,i)
601	ol_l = ol_m - 0.001_wp * ol_m
602	ol_u = ol_m + 0.001_wp * ol_m
603
604
605	IF ( ibc_pt_b /= 1 ) THEN
606	!
607	!-- Calculate f = Ri - [...]/[...]^2 = 0
608	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
609	- psi_h( z_mo / ol_m ) &
610	+ psi_h( z0h(j,i) / ol_m ) &
611	) &
612	/ ( LOG( z_mo / z0(j,i) ) &
613	- psi_m( z_mo / ol_m ) &
614	+ psi_m( z0(j,i) / ol_m ) &
615	)**2
616
617	!
618	!-- Calculate df/dL
619	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
620	- psi_h( z_mo / ol_u ) &
621	+ psi_h( z0h(j,i) / ol_u ) &
622	) &
623	/ ( LOG( z_mo / z0(j,i) ) &
624	- psi_m( z_mo / ol_u ) &
625	+ psi_m( z0(j,i) / ol_u ) &
626	)**2 &
627	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
628	- psi_h( z_mo / ol_l ) &
629	+ psi_h( z0h(j,i) / ol_l ) &
630	) &
631	/ ( LOG( z_mo / z0(j,i) ) &
632	- psi_m( z_mo / ol_l ) &
633	+ psi_m( z0(j,i) / ol_l ) &
634	)**2 &
635	) / ( ol_u - ol_l )
636	ELSE
637	!
638	!-- Calculate f = Ri - 1 /[...]^3 = 0
639	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
640	- psi_m( z_mo / ol_m ) &
641	+ psi_m( z0(j,i) / ol_m ) &
642	)**3
643
644	!
645	!-- Calculate df/dL
646	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
647	- psi_m( z_mo / ol_u ) &
648	+ psi_m( z0(j,i) / ol_u ) &
649	)**3 &
650	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
651	- psi_m( z_mo / ol_l ) &
652	+ psi_m( z0(j,i) / ol_l ) &
653	)**3 &
654	) / ( ol_u - ol_l )
655	ENDIF
656	!
657	!-- Calculate new L
658	ol(j,i) = ol_m - f / f_d_ol
659
660	!
661	!-- Ensure that the bulk Richardson number and the Obukhov
662	!-- length have the same sign and ensure convergence.
663	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
664
665	!
666	!-- If unrealistic value occurs, set L to the maximum
667	!-- value that is allowed
668	IF ( ABS( ol(j,i) ) > ol_max ) THEN
669	ol(j,i) = ol_max
670	EXIT
671	ENDIF
672	!
673	!-- Check for convergence
674	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
675	EXIT
676	ELSE
677	CYCLE
678	ENDIF
679
680	ENDDO
681
682	ENDDO
683	ENDDO
684
685	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
686
687	!$OMP PARALLEL DO PRIVATE( k, z_mo )
688	!# WARNING: does not work on GPU so far because of DO WHILE construct
689	!!!!!!$acc kernels loop
690	DO i = nxl, nxr
691	DO j = nys, nyn
692
693	!
694	!-- If the bulk Richardson number is outside the range of the lookup
695	!-- table, set it to the exceeding threshold value
696	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
697	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
698
699	!
700	!-- Find the correct index bounds for linear interpolation. As the
701	!-- Richardson number will not differ very much from time step to
702	!-- time step , use the index from the last step and search in the
703	!-- correct direction
704	l = l_bnd
705	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
706	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
707	l = l-1
708	ENDDO
709	ELSE
710	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
711	.AND. l < num_steps-1 )
712	l = l+1
713	ENDDO
714	ENDIF
715	l_bnd = l
716
717	!
718	!-- Linear interpolation to find the correct value of z/L
719	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
720	/ ( rib_tab(l) - rib_tab(l-1) ) &
721	* ( rib(j,i) - rib_tab(l-1) ) )
722
723	ENDDO
724	ENDDO
725
726	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
727
728	!$OMP PARALLEL DO PRIVATE( k, z_mo )
729	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
730	DO i = nxl, nxr
731	DO j = nys, nyn
732
733	k = nzb_s_inner(j,i)
734	z_mo = zu(k+1) - zw(k)
735
736	IF ( .NOT. humidity ) THEN
737	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
738	* ts(j,i) + 1E-30_wp )
739	ELSEIF ( cloud_physics ) THEN
740
741	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
742	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
743	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
744	* ql(k+1,j,i) ) + 1E-30_wp )
745	ELSE
746	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
747	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
748	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
749	ENDIF
750	!
751	!-- Limit the value range of the Obukhov length.
752	!-- This is necessary for very small velocities (u,v --> 0), because
753	!-- the absolute value of ol can then become very small, which in
754	!-- consequence would result in very large shear stresses and very
755	!-- small momentum fluxes (both are generally unrealistic).
756	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) < zeta_min ) &
757	ol(j,i) = z_mo / zeta_min
758	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) > zeta_max ) &
759	ol(j,i) = z_mo / zeta_max
760	ENDDO
761	ENDDO
762
763	ENDIF
764
765	!
766	!-- Values of ol at ghost point locations are needed for the evaluation
767	!-- of usws and vsws.
768	!$acc update host( ol )
769	CALL exchange_horiz_2d( ol )
770	!$acc update device( ol )
771
772	END SUBROUTINE calc_ol
773
774	!
775	!-- Calculate friction velocity u*
776	SUBROUTINE calc_us
777
778	IMPLICIT NONE
779
780	!$OMP PARALLEL DO PRIVATE( k, z_mo )
781	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
782	DO i = nxlg, nxrg
783	DO j = nysg, nyng
784
785	k = nzb_s_inner(j,i)+1
786	z_mo = zu(k+1) - zw(k)
787
788	!
789	!-- Compute u* at the scalars' grid points
790	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
791	- psi_m( z_mo / ol(j,i) ) &
792	+ psi_m( z0(j,i) / ol(j,i) ) )
793	ENDDO
794	ENDDO
795
796	END SUBROUTINE calc_us
797
798	!
799	!-- Calculate potential temperature and specific humidity at first grid level
800	SUBROUTINE calc_pt_q
801
802	IMPLICIT NONE
803
804	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
805	DO i = nxlg, nxrg
806	DO j = nysg, nyng
807	k = nzb_s_inner(j,i)+1
808	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
809	qv1(j,i) = q(k,j,i) - ql(k,j,i)
810	ENDDO
811	ENDDO
812
813	END SUBROUTINE calc_pt_q
814
815	!
816	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
817	SUBROUTINE calc_scaling_parameters
818
819	IMPLICIT NONE
820
821	!
822	!-- Data information for accelerators
823	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
824	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
825	!$acc present( vpt, vsws, zu, zw, z0, z0h )
826	!
827	!-- Compute theta*
828	IF ( constant_heatflux ) THEN
829
830	!
831	!-- For a given heat flux in the surface layer:
832	!$OMP PARALLEL DO
833	!$acc kernels loop private( j, k )
834	DO i = nxlg, nxrg
835	DO j = nysg, nyng
836	k = nzb_s_inner(j,i)
837	ts(j,i) = -shf(j,i) * drho_air_zw(k) / ( us(j,i) + 1E-30_wp )
838	!
839	!-- ts must be limited, because otherwise overflow may occur in case
840	!-- of us=0 when computing ol further below
841	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
842	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
843	ENDDO
844	ENDDO
845
846	ELSE
847	!
848	!-- For a given surface temperature:
849	IF ( large_scale_forcing .AND. lsf_surf ) THEN
850	!$OMP PARALLEL DO
851	!$acc kernels loop private( j, k )
852	DO i = nxlg, nxrg
853	DO j = nysg, nyng
854	k = nzb_s_inner(j,i)
855	pt(k,j,i) = pt_surface
856	ENDDO
857	ENDDO
858	ENDIF
859
860	!$OMP PARALLEL DO PRIVATE( k, z_mo )
861	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
862	DO i = nxlg, nxrg
863	DO j = nysg, nyng
864
865	k = nzb_s_inner(j,i)
866	z_mo = zu(k+1) - zw(k)
867
868	IF ( cloud_physics ) THEN
869	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
870	/ ( LOG( z_mo / z0h(j,i) ) &
871	- psi_h( z_mo / ol(j,i) ) &
872	+ psi_h( z0h(j,i) / ol(j,i) ) )
873	ELSE
874	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
875	/ ( LOG( z_mo / z0h(j,i) ) &
876	- psi_h( z_mo / ol(j,i) ) &
877	+ psi_h( z0h(j,i) / ol(j,i) ) )
878	ENDIF
879
880	ENDDO
881	ENDDO
882	ENDIF
883
884	!
885	!-- If required compute q*
886	IF ( humidity ) THEN
887	IF ( constant_waterflux ) THEN
888	!
889	!-- For a given water flux in the surface layer
890	!$OMP PARALLEL DO
891	!$acc kernels loop private( j )
892	DO i = nxlg, nxrg
893	DO j = nysg, nyng
894	k = nzb_s_inner(j,i)
895	qs(j,i) = -qsws(j,i) * drho_air_zw(k) / ( us(j,i) + 1E-30_wp )
896	ENDDO
897	ENDDO
898
899	ELSE
900	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
901	run_coupled )
902
903	IF ( large_scale_forcing .AND. lsf_surf ) THEN
904	!$OMP PARALLEL DO
905	!$acc kernels loop private( j, k )
906	DO i = nxlg, nxrg
907	DO j = nysg, nyng
908	k = nzb_s_inner(j,i)
909	q(k,j,i) = q_surface
910	ENDDO
911	ENDDO
912	ENDIF
913
914	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
915	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
916	DO i = nxlg, nxrg
917	!$acc loop independent
918	DO j = nysg, nyng
919
920	k = nzb_s_inner(j,i)
921	z_mo = zu(k+1) - zw(k)
922
923	!
924	!-- Assume saturation for atmosphere coupled to ocean (but not
925	!-- in case of precursor runs)
926	IF ( coupled_run ) THEN
927	e_s = 6.1_wp * &
928	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
929	- 273.15_wp ) )
930	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
931	ENDIF
932
933	IF ( cloud_physics ) THEN
934	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
935	/ ( LOG( z_mo / z0q(j,i) ) &
936	- psi_h( z_mo / ol(j,i) ) &
937	+ psi_h( z0q(j,i) / ol(j,i) ) )
938
939	ELSE
940	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
941	/ ( LOG( z_mo / z0q(j,i) ) &
942	- psi_h( z_mo / ol(j,i) ) &
943	+ psi_h( z0q(j,i) / ol(j,i) ) )
944	ENDIF
945
946	ENDDO
947	ENDDO
948	ENDIF
949	ENDIF
950
951	!
952	!-- If required compute s*
953	IF ( passive_scalar ) THEN
954	IF ( constant_scalarflux ) THEN
955	!
956	!-- For a given water flux in the surface layer
957	!$OMP PARALLEL DO
958	!$acc kernels loop private( j )
959	DO i = nxlg, nxrg
960	DO j = nysg, nyng
961	ss(j,i) = -ssws(j,i) / ( us(j,i) + 1E-30_wp )
962	ENDDO
963	ENDDO
964	ENDIF
965	ENDIF
966
967
968	!
969	!-- If required compute qr* and nr*
970	IF ( cloud_physics .AND. microphysics_seifert ) &
971	THEN
972
973	!$OMP PARALLEL DO PRIVATE( k, z_mo )
974	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
975	DO i = nxlg, nxrg
976	!$acc loop independent
977	DO j = nysg, nyng
978
979	k = nzb_s_inner(j,i)
980	z_mo = zu(k+1) - zw(k)
981
982	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
983	/ ( LOG( z_mo / z0q(j,i) ) &
984	- psi_h( z_mo / ol(j,i) ) &
985	+ psi_h( z0q(j,i) / ol(j,i) ) )
986
987	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
988	/ ( LOG( z_mo / z0q(j,i) ) &
989	- psi_h( z_mo / ol(j,i) ) &
990	+ psi_h( z0q(j,i) / ol(j,i) ) )
991	ENDDO
992	ENDDO
993
994	ENDIF
995	!$acc end data
996
997	END SUBROUTINE calc_scaling_parameters
998
999
1000
1001	!
1002	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
1003	SUBROUTINE calc_surface_fluxes
1004
1005	IMPLICIT NONE
1006
1007	REAL(wp) :: ol_mid !< Grid-interpolated L
1008
1009	!
1010	!-- Compute u'w' for the total model domain.
1011	!-- First compute the corresponding component of u* and square it.
1012	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
1013	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
1014	DO i = nxl, nxr
1015	DO j = nys, nyn
1016
1017	k = nzb_u_inner(j,i)
1018	z_mo = zu(k+1) - zw(k)
1019	!
1020	!-- Compute bulk Obukhov length for this point
1021	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
1022
1023	IF ( ol_mid == 0.0_wp ) THEN
1024	ol_mid = MIN(ol(j,i-1), ol(j,i))
1025	ENDIF
1026
1027	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
1028	/ ( LOG( z_mo / z0(j,i) ) &
1029	- psi_m( z_mo / ol_mid ) &
1030	+ psi_m( z0(j,i) / ol_mid ) )
1031
1032	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) ) &
1033	* rho_air_zw(k)
1034	ENDDO
1035	ENDDO
1036
1037	!
1038	!-- Compute v'w' for the total model domain.
1039	!-- First compute the corresponding component of u* and square it.
1040	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
1041	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
1042	DO i = nxl, nxr
1043	DO j = nys, nyn
1044
1045	k = nzb_v_inner(j,i)
1046	z_mo = zu(k+1) - zw(k)
1047	!
1048	!-- Compute bulk Obukhov length for this point
1049	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
1050
1051	IF ( ol_mid == 0.0_wp ) THEN
1052	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
1053	ENDIF
1054
1055	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
1056	/ ( LOG( z_mo / z0(j,i) ) &
1057	- psi_m( z_mo / ol_mid ) &
1058	+ psi_m( z0(j,i) / ol_mid ) )
1059
1060	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) ) &
1061	* rho_air_zw(k)
1062
1063	ENDDO
1064	ENDDO
1065
1066	!
1067	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
1068	!$acc update host( usws, vsws )
1069	CALL exchange_horiz_2d( usws )
1070	CALL exchange_horiz_2d( vsws )
1071	!$acc update device( usws, vsws )
1072
1073	!
1074	!-- Compute the vertical kinematic heat flux
1075	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
1076	skip_time_do_lsm .OR. .NOT. land_surface ) .AND. &
1077	.NOT. urban_surface ) THEN
1078	!$OMP PARALLEL DO
1079	!$acc kernels loop independent present( shf, ts, us )
1080	DO i = nxlg, nxrg
1081	!$acc loop independent
1082	DO j = nysg, nyng
1083	k = nzb_s_inner(j,i)
1084	shf(j,i) = -ts(j,i) * us(j,i) * rho_air_zw(k)
1085	ENDDO
1086	ENDDO
1087
1088	ENDIF
1089
1090	!
1091	!-- Compute the vertical water flux
1092	IF ( .NOT. constant_waterflux .AND. humidity .AND. &
1093	( simulated_time <= skip_time_do_lsm &
1094	.OR. .NOT. land_surface ) ) THEN
1095	!$OMP PARALLEL DO
1096	!$acc kernels loop independent present( qs, qsws, us )
1097	DO i = nxlg, nxrg
1098	!$acc loop independent
1099	DO j = nysg, nyng
1100	k = nzb_s_inner(j,i)
1101	qsws(j,i) = -qs(j,i) * us(j,i) * rho_air_zw(k)
1102	ENDDO
1103	ENDDO
1104
1105	ENDIF
1106
1107	!
1108	!-- Compute the vertical scalar flux
1109	IF ( .NOT. constant_scalarflux .AND. passive_scalar .AND. &
1110	( simulated_time <= skip_time_do_lsm &
1111	.OR. .NOT. land_surface ) ) THEN
1112	!$OMP PARALLEL DO
1113	!$acc kernels loop independent present( qs, qsws, us )
1114	DO i = nxlg, nxrg
1115	!$acc loop independent
1116	DO j = nysg, nyng
1117	ssws(j,i) = -ss(j,i) * us(j,i)
1118	ENDDO
1119	ENDDO
1120
1121	ENDIF
1122
1123	!
1124	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
1125	IF ( cloud_physics .AND. microphysics_seifert ) THEN
1126	!$OMP PARALLEL DO
1127	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
1128	DO i = nxlg, nxrg
1129	!$acc loop independent
1130	DO j = nysg, nyng
1131	qrsws(j,i) = -qrs(j,i) * us(j,i)
1132	nrsws(j,i) = -nrs(j,i) * us(j,i)
1133	ENDDO
1134	ENDDO
1135	ENDIF
1136
1137	!
1138	!-- Bottom boundary condition for the TKE
1139	IF ( ibc_e_b == 2 ) THEN
1140	!$OMP PARALLEL DO
1141	!$acc kernels loop independent present( e, nzb_s_inner, us )
1142	DO i = nxlg, nxrg
1143	!$acc loop independent
1144	DO j = nysg, nyng
1145	k = nzb_s_inner(j,i)
1146	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
1147	!
1148	!-- As a test: cm = 0.4
1149	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
1150	e(k,j,i) = e(k+1,j,i)
1151	ENDDO
1152	ENDDO
1153	ENDIF
1154
1155	END SUBROUTINE calc_surface_fluxes
1156
1157
1158	!
1159	!-- Integrated stability function for momentum
1160	FUNCTION psi_m( zeta )
1161
1162	USE kinds
1163
1164	IMPLICIT NONE
1165
1166	REAL(wp) :: psi_m !< Integrated similarity function result
1167	REAL(wp) :: zeta !< Stability parameter z/L
1168	REAL(wp) :: x !< dummy variable
1169
1170	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1171	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1172	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1173	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1174	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1175	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1176
1177
1178	IF ( zeta < 0.0_wp ) THEN
1179	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
1180	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1181	* ( 1.0_wp + x*2 ) 0.125_wp )
1182	ELSE
1183
1184	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1185	- bc_d_d
1186	!
1187	!-- Old version for stable conditions (only valid for z/L < 0.5)
1188	!-- psi_m = - 5.0_wp * zeta
1189
1190	ENDIF
1191
1192	END FUNCTION psi_m
1193
1194
1195	!
1196	!-- Integrated stability function for heat and moisture
1197	FUNCTION psi_h( zeta )
1198
1199	USE kinds
1200
1201	IMPLICIT NONE
1202
1203	REAL(wp) :: psi_h !< Integrated similarity function result
1204	REAL(wp) :: zeta !< Stability parameter z/L
1205	REAL(wp) :: x !< dummy variable
1206
1207	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1208	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1209	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1210	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1211	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1212	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1213
1214
1215	IF ( zeta < 0.0_wp ) THEN
1216	x = SQRT( 1.0_wp - 16.0_wp * zeta )
1217	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1218	ELSE
1219	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1220	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1221	+ 1.0_wp
1222	!
1223	!-- Old version for stable conditions (only valid for z/L < 0.5)
1224	!-- psi_h = - 5.0_wp * zeta
1225	ENDIF
1226
1227	END FUNCTION psi_h
1228
1229	END MODULE surface_layer_fluxes_mod

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