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source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 2106

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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 1997-2017 Leibniz Universitaet Hannover
18	!
19	!------------------------------------------------------------------------------!
20	! Current revisions:
21	! ------------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: surface_layer_fluxes_mod.f90 2101 2017-01-05 16:42:31Z suehring $
27	!
28	! 2091 2016-12-21 16:38:18Z suehring
29	! Bugfix in calculation of vsws ( incorrect linear interpolation of us )
30	!
31	! 2076 2016-12-02 13:54:20Z raasch
32	! further openmp bugfix for lookup method
33	!
34	! 2073 2016-11-30 14:34:05Z raasch
35	! openmp bugfix for lookup method
36	!
37	! 2037 2016-10-26 11:15:40Z knoop
38	! Anelastic approximation implemented
39	!
40	! 2011 2016-09-19 17:29:57Z kanani
41	! Flag urban_surface is now defined in module control_parameters.
42	!
43	! 2007 2016-08-24 15:47:17Z kanani
44	! Account for urban surface model in computation of vertical kinematic heatflux
45	!
46	! 2000 2016-08-20 18:09:15Z knoop
47	! Forced header and separation lines into 80 columns
48	!
49	! 1992 2016-08-12 15:14:59Z suehring
50	! Minor bug, declaration of look-up index as INTEGER
51	!
52	! 1960 2016-07-12 16:34:24Z suehring
53	! Treat humidity and passive scalar separately
54	!
55	! 1929 2016-06-09 16:25:25Z suehring
56	! Bugfix: avoid segmentation fault in case one grid point is horizontally
57	! completely surrounded by topography
58	!
59	! 1920 2016-05-30 10:50:15Z suehring
60	! Avoid segmentation fault (see change in 1915) by different initialization of
61	! us instead of adding a very small number in the denominator
62	!
63	! 1915 2016-05-27 11:05:02Z suehring
64	! Bugfix: avoid segmentation fault in case of most_method = 'circular' at first
65	! timestep
66	!
67	! 1850 2016-04-08 13:29:27Z maronga
68	! Module renamed
69	!
70	!
71	! 1822 2016-04-07 07:49:42Z hoffmann
72	! icloud_scheme replaced by microphysics_*
73	!
74	! 1788 2016-03-10 11:01:04Z maronga
75	! Added parameter z0q which replaces z0h in the similarity functions for
76	! humidity.
77	! Syntax layout improved.
78	!
79	! 1757 2016-02-22 15:49:32Z maronga
80	! Minor fixes.
81	!
82	! 1749 2016-02-09 12:19:56Z raasch
83	! further OpenACC adjustments
84	!
85	! 1747 2016-02-08 12:25:53Z raasch
86	! adjustments for OpenACC usage
87	!
88	! 1709 2015-11-04 14:47:01Z maronga
89	! Bugfix: division by zero could occur when calculating rib at low wind speeds
90	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
91	! neutral = .T.
92	!
93	! 1705 2015-11-02 14:28:56Z maronga
94	! Typo removed
95	!
96	! 1697 2015-10-28 17:14:10Z raasch
97	! FORTRAN and OpenMP errors removed
98	!
99	! 1696 2015-10-27 10:03:34Z maronga
100	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
101	! course of the re-writing two additional methods have been implemented. See
102	! updated description.
103	!
104	! 1551 2015-03-03 14:18:16Z maronga
105	! Removed land surface model part. The surface fluxes are now always calculated
106	! within prandtl_fluxes, based on the given surface temperature/humidity (which
107	! is either provided by the land surface model, by large scale forcing data, or
108	! directly prescribed by the user.
109	!
110	! 1496 2014-12-02 17:25:50Z maronga
111	! Adapted for land surface model
112	!
113	! 1494 2014-11-21 17:14:03Z maronga
114	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
115	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
116	! topography for coupled runs (not tested)
117	!
118	! 1361 2014-04-16 15:17:48Z hoffmann
119	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
120	! drop concentration (nrsws) added
121	!
122	! 1340 2014-03-25 19:45:13Z kanani
123	! REAL constants defined as wp-kind
124	!
125	! 1320 2014-03-20 08:40:49Z raasch
126	! ONLY-attribute added to USE-statements,
127	! kind-parameters added to all INTEGER and REAL declaration statements,
128	! kinds are defined in new module kinds,
129	! old module precision_kind is removed,
130	! revision history before 2012 removed,
131	! comment fields (!:) to be used for variable explanations added to
132	! all variable declaration statements
133	!
134	! 1276 2014-01-15 13:40:41Z heinze
135	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
136	!
137	! 1257 2013-11-08 15:18:40Z raasch
138	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
139	!
140	! 1036 2012-10-22 13:43:42Z raasch
141	! code put under GPL (PALM 3.9)
142	!
143	! 1015 2012-09-27 09:23:24Z raasch
144	! OpenACC statements added
145	!
146	! 978 2012-08-09 08:28:32Z fricke
147	! roughness length for scalar quantities z0h added
148	!
149	! Revision 1.1 1998/01/23 10:06:06 raasch
150	! Initial revision
151	!
152	!
153	! Description:
154	! ------------
155	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
156	!> values of the variables at grid point k=1. Three different methods are
157	!> available:
158	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
159	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
160	!> slower
161	!> 3) a method using a lookup table which is fast and accurate. Note, however,
162	!> that this method cannot be used in case of roughness heterogeneity
163	!>
164	!> @todo (re)move large_scale_forcing actions
165	!> @todo check/optimize OpenMP and OpenACC directives
166	!------------------------------------------------------------------------------!
167	MODULE surface_layer_fluxes_mod
168
169	USE arrays_3d, &
170	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
171	s, shf, ss, ssws, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, &
172	z0h, z0q, drho_air_zw, rho_air_zw
173
174	USE cloud_parameters, &
175	ONLY: l_d_cp, pt_d_t
176
177	USE constants, &
178	ONLY: pi
179
180	USE cpulog
181
182	USE control_parameters, &
183	ONLY: cloud_physics, constant_heatflux, constant_scalarflux, &
184	constant_waterflux, coupling_mode, g, humidity, ibc_e_b, &
185	ibc_pt_b, initializing_actions, kappa, &
186	intermediate_timestep_count, &
187	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
188	message_string, microphysics_seifert, most_method, neutral, &
189	passive_scalar, pt_surface, q_surface, run_coupled, &
190	surface_pressure, simulated_time, terminate_run, &
191	urban_surface, &
192	zeta_max, zeta_min
193
194	USE indices, &
195	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
196	nzb_u_inner, nzb_v_inner
197
198	USE kinds
199
200	USE pegrid
201
202	USE land_surface_model_mod, &
203	ONLY: land_surface, skip_time_do_lsm
204
205
206
207	IMPLICIT NONE
208
209	INTEGER(iwp) :: i !< loop index x direction
210	INTEGER(iwp) :: j !< loop index y direction
211	INTEGER(iwp) :: k !< loop index z direction
212	INTEGER(iwp) :: l_bnd = 7500 !< Lookup table index of the last time step
213
214	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
215
216	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
217
218	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
219	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
220	uv_total !< Total velocity at first grid level
221
222	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
223	ol_tab !< Lookup table values of L
224
225	REAL(wp) :: e_s, & !< Saturation water vapor pressure
226	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
227	rib_max, & !< Maximum Richardson number in lookup table
228	rib_min, & !< Minimum Richardson number in lookup table
229	z_mo !< Height of the constant flux layer where MOST is assumed
230
231
232	SAVE
233
234	PRIVATE
235
236	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
237
238	INTERFACE init_surface_layer_fluxes
239	MODULE PROCEDURE init_surface_layer_fluxes
240	END INTERFACE init_surface_layer_fluxes
241
242	INTERFACE surface_layer_fluxes
243	MODULE PROCEDURE surface_layer_fluxes
244	END INTERFACE surface_layer_fluxes
245
246
247	CONTAINS
248
249
250	!------------------------------------------------------------------------------!
251	! Description:
252	! ------------
253	!> Main routine to compute the surface fluxes
254	!------------------------------------------------------------------------------!
255	SUBROUTINE surface_layer_fluxes
256
257	IMPLICIT NONE
258
259	!
260	!-- In case cloud physics is used, it is required to derive potential
261	!-- temperature and specific humidity at first grid level from the fields pt
262	!-- and q
263	IF ( cloud_physics ) THEN
264	CALL calc_pt_q
265	ENDIF
266
267	!
268	!-- First, calculate the new Obukhov length, then new friction velocity,
269	!-- followed by the new scaling parameters (th, q, etc.), and the new
270	!-- surface fluxes if required. The old routine ("circular") requires a
271	!-- different order of calls as the scaling parameters from the previous time
272	!-- steps are used to calculate the Obukhov length
273
274	!
275	!-- Depending on setting of most_method use the "old" routine
276	IF ( most_method == 'circular' ) THEN
277
278	CALL calc_scaling_parameters
279
280	CALL calc_uv_total
281
282	IF ( .NOT. neutral ) THEN
283	CALL calc_ol
284	ENDIF
285
286	CALL calc_us
287
288	CALL calc_surface_fluxes
289
290	!
291	!-- Use either Newton iteration or a lookup table for the bulk Richardson
292	!-- number to calculate the Obukhov length
293	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
294
295	CALL calc_uv_total
296
297	IF ( .NOT. neutral ) THEN
298	CALL calc_ol
299	ENDIF
300
301	CALL calc_us
302
303	CALL calc_scaling_parameters
304
305	CALL calc_surface_fluxes
306
307	ENDIF
308
309	END SUBROUTINE surface_layer_fluxes
310
311
312	!------------------------------------------------------------------------------!
313	! Description:
314	! ------------
315	!> Initializing actions for the surface layer routine. Basically, this involves
316	!> the preparation of a lookup table for the the bulk Richardson number vs
317	!> Obukhov length L when using the lookup table method.
318	!------------------------------------------------------------------------------!
319	SUBROUTINE init_surface_layer_fluxes
320
321	IMPLICIT NONE
322
323	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
324	num_steps_n !< Number of non-stretched zeta steps
325
326	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
327
328	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
329
330	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
331
332
333	REAL(wp) :: zeta_step, & !< Increment of zeta
334	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
335	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
336	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
337	z0_min = 0.0_wp !< Minimum value of z0 to create table
338	!
339	!-- When cloud physics is used, arrays for storing potential temperature and
340	!-- specific humidity at first grid level are required
341	IF ( cloud_physics ) THEN
342	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
343	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
344	ENDIF
345
346	!
347	!-- Allocate field for storing the horizontal velocity
348	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
349
350
351	!
352	!-- In case of runs with neutral statification, set Obukhov length to a
353	!-- large value
354	IF ( neutral ) ol = 1.0E10_wp
355
356	IF ( most_method == 'lookup' ) THEN
357
358	!
359	!-- Check for roughness heterogeneity. In that case terminate run and
360	!-- inform user
361	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
362	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
363	terminate_run_l = .TRUE.
364	ENDIF
365
366	#if defined( __parallel )
367	!
368	!-- Make a logical OR for all processes. Force termiation of model if result
369	!-- is TRUE
370	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
371	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
372	MPI_LOR, comm2d, ierr )
373	#else
374	terminate_run = terminate_run_l
375	#endif
376
377	IF ( terminate_run ) THEN
378	message_string = 'most_method = "lookup" cannot be used in ' // &
379	'combination with a prescribed roughness ' // &
380	'heterogeneity'
381	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
382	ENDIF
383
384	ALLOCATE( zeta_tmp(0:num_steps-1) )
385
386	!
387	!-- Use the lowest possible value for z_mo
388	k = MINVAL(nzb_s_inner)
389	z_mo = zu(k+1) - zw(k)
390
391	!
392	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
393	!-- available steps (num_steps). The calculation is done with negative
394	!-- values of zeta in order to simplify the stretching in the free
395	!-- convection limit for the remaining 10% of steps.
396	zeta_tmp(0) = - zeta_max
397	num_steps_n = ( num_steps * 9 / 10 ) - 1
398	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
399
400	DO l = 1, num_steps_n
401	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
402	ENDDO
403
404	!
405	!-- Calculate stretching factor for the free convection range
406	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
407	regr_old = regr
408	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
409	)**( 10.0_wp / REAL(num_steps) )
410	ENDDO
411
412	!
413	!-- Calculate z/L range from zeta_min to zeta_stretch
414	DO l = num_steps_n+1, num_steps-1
415	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
416	zeta_step = zeta_step * regr
417	ENDDO
418
419	!
420	!-- Save roughness lengths to temporary variables
421	z0h_min = z0h(nys,nxl)
422	z0_min = z0(nys,nxl)
423
424	!
425	!-- Calculate lookup table for the Richardson number versus Obukhov length
426	!-- The Richardson number (rib) is defined depending on the choice of
427	!-- boundary conditions for temperature
428	IF ( ibc_pt_b == 1 ) THEN
429	DO l = 0, num_steps-1
430	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
431	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
432	- psi_m( z_mo / ol_tab(l) ) &
433	+ psi_m( z0_min / ol_tab(l) ) &
434	)**3
435	ENDDO
436	ELSE
437	DO l = 0, num_steps-1
438	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
439	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
440	- psi_h( z_mo / ol_tab(l) ) &
441	+ psi_h( z0h_min / ol_tab(l) ) &
442	) &
443	/ ( LOG( z_mo / z0_min ) &
444	- psi_m( z_mo / ol_tab(l) ) &
445	+ psi_m( z0_min / ol_tab(l) ) &
446	)**2
447	ENDDO
448	ENDIF
449
450	!
451	!-- Determine minimum values of rib in the lookup table. Set upper limit
452	!-- to critical Richardson number (0.25)
453	rib_min = MINVAL(rib_tab)
454	rib_max = 0.25 !MAXVAL(rib_tab)
455
456	DEALLOCATE( zeta_tmp )
457	ENDIF
458
459	END SUBROUTINE init_surface_layer_fluxes
460
461
462	!------------------------------------------------------------------------------!
463	! Description:
464	! ------------
465	!> Compute the absolute value of the horizontal velocity (relative to the
466	!> surface). This is required by all methods
467	!------------------------------------------------------------------------------!
468	SUBROUTINE calc_uv_total
469
470	IMPLICIT NONE
471
472
473	!$OMP PARALLEL DO PRIVATE( k )
474	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
475	DO i = nxl, nxr
476	DO j = nys, nyn
477
478	k = nzb_s_inner(j,i)
479	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
480	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
481	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
482	- v(k,j,i) - v(k,j+1,i) ) )**2 )
483
484	!
485	!-- For too small values of the local wind, MOST does not work. A
486	!-- threshold value is thus set if required
487	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
488
489	ENDDO
490	ENDDO
491
492	!
493	!-- Values of uv_total need to be exchanged at the ghost boundaries
494	!$acc update host( uv_total )
495	CALL exchange_horiz_2d( uv_total )
496	!$acc update device( uv_total )
497
498	END SUBROUTINE calc_uv_total
499
500
501	!------------------------------------------------------------------------------!
502	! Description:
503	! ------------
504	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
505	!------------------------------------------------------------------------------!
506	SUBROUTINE calc_ol
507
508	IMPLICIT NONE
509
510	INTEGER(iwp) :: iter, & !< Newton iteration step
511	l !< look index
512
513	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
514
515	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
516	f_d_ol, & !< Derivative of f
517	ol_l, & !< Lower bound of L for Newton iteration
518	ol_m, & !< Previous value of L for Newton iteration
519	ol_old, & !< Previous time step value of L
520	ol_u !< Upper bound of L for Newton iteration
521
522	IF ( TRIM( most_method ) /= 'circular' ) THEN
523
524	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
525
526	!$OMP PARALLEL DO PRIVATE( k, z_mo )
527	!$acc kernels loop private( j, k, z_mo )
528	DO i = nxl, nxr
529	DO j = nys, nyn
530
531	k = nzb_s_inner(j,i)
532	z_mo = zu(k+1) - zw(k)
533
534	!
535	!-- Evaluate bulk Richardson number (calculation depends on
536	!-- definition based on setting of boundary conditions
537	IF ( ibc_pt_b /= 1 ) THEN
538	IF ( humidity ) THEN
539	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
540	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
541	ELSE
542	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
543	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
544	ENDIF
545	ELSE
546	!
547	!-- When using Neumann boundary conditions, the buoyancy flux
548	!-- is required but cannot be calculated at the surface, as pt
549	!-- and q are not known at the surface. Hence the values at
550	!-- first grid level are used to estimate the buoyancy flux
551	IF ( humidity ) THEN
552	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
553	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
554	* pt(k+1,j,i) * qsws(j,i) ) * drho_air_zw(k) &
555	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
556	+ 1.0E-20_wp)
557	ELSE
558	rib(j,i) = - g * z_mo * shf(j,i) * drho_air_zw(k) &
559	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
560	+ 1.0E-20_wp )
561	ENDIF
562	ENDIF
563
564	ENDDO
565	ENDDO
566	!$acc end data
567
568	ENDIF
569
570	!
571	!-- Calculate the Obukhov length either using a Newton iteration
572	!-- method, via a lookup table, or using the old circular way
573	IF ( TRIM( most_method ) == 'newton' ) THEN
574
575	!$OMP PARALLEL DO PRIVATE( k, z_mo )
576	!# WARNING: does not work on GPU so far because of DO-loop with
577	!# undetermined iterations
578	!!!!!!$acc kernels loop
579	DO i = nxl, nxr
580	DO j = nys, nyn
581
582	k = nzb_s_inner(j,i)
583	z_mo = zu(k+1) - zw(k)
584
585	!
586	!-- Store current value in case the Newton iteration fails
587	ol_old = ol(j,i)
588
589	!
590	!-- Ensure that the bulk Richardson number and the Obukhov
591	!-- lengtH have the same sign
592	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
593	ABS( ol(j,i) ) == ol_max ) THEN
594	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
595	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
596	ENDIF
597	!
598	!-- Iteration to find Obukhov length
599	iter = 0
600	DO
601	iter = iter + 1
602	!
603	!-- In case of divergence, use the value of the previous time step
604	IF ( iter > 1000 ) THEN
605	ol(j,i) = ol_old
606	EXIT
607	ENDIF
608
609	ol_m = ol(j,i)
610	ol_l = ol_m - 0.001_wp * ol_m
611	ol_u = ol_m + 0.001_wp * ol_m
612
613
614	IF ( ibc_pt_b /= 1 ) THEN
615	!
616	!-- Calculate f = Ri - [...]/[...]^2 = 0
617	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
618	- psi_h( z_mo / ol_m ) &
619	+ psi_h( z0h(j,i) / ol_m ) &
620	) &
621	/ ( LOG( z_mo / z0(j,i) ) &
622	- psi_m( z_mo / ol_m ) &
623	+ psi_m( z0(j,i) / ol_m ) &
624	)**2
625
626	!
627	!-- Calculate df/dL
628	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
629	- psi_h( z_mo / ol_u ) &
630	+ psi_h( z0h(j,i) / ol_u ) &
631	) &
632	/ ( LOG( z_mo / z0(j,i) ) &
633	- psi_m( z_mo / ol_u ) &
634	+ psi_m( z0(j,i) / ol_u ) &
635	)**2 &
636	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
637	- psi_h( z_mo / ol_l ) &
638	+ psi_h( z0h(j,i) / ol_l ) &
639	) &
640	/ ( LOG( z_mo / z0(j,i) ) &
641	- psi_m( z_mo / ol_l ) &
642	+ psi_m( z0(j,i) / ol_l ) &
643	)**2 &
644	) / ( ol_u - ol_l )
645	ELSE
646	!
647	!-- Calculate f = Ri - 1 /[...]^3 = 0
648	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
649	- psi_m( z_mo / ol_m ) &
650	+ psi_m( z0(j,i) / ol_m ) &
651	)**3
652
653	!
654	!-- Calculate df/dL
655	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
656	- psi_m( z_mo / ol_u ) &
657	+ psi_m( z0(j,i) / ol_u ) &
658	)**3 &
659	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
660	- psi_m( z_mo / ol_l ) &
661	+ psi_m( z0(j,i) / ol_l ) &
662	)**3 &
663	) / ( ol_u - ol_l )
664	ENDIF
665	!
666	!-- Calculate new L
667	ol(j,i) = ol_m - f / f_d_ol
668
669	!
670	!-- Ensure that the bulk Richardson number and the Obukhov
671	!-- length have the same sign and ensure convergence.
672	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
673
674	!
675	!-- If unrealistic value occurs, set L to the maximum
676	!-- value that is allowed
677	IF ( ABS( ol(j,i) ) > ol_max ) THEN
678	ol(j,i) = ol_max
679	EXIT
680	ENDIF
681	!
682	!-- Check for convergence
683	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
684	EXIT
685	ELSE
686	CYCLE
687	ENDIF
688
689	ENDDO
690
691	ENDDO
692	ENDDO
693
694	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
695
696	!$OMP PARALLEL DO PRIVATE( k, l, z_mo ) FIRSTPRIVATE( l_bnd ) LASTPRIVATE( l_bnd )
697	!# WARNING: does not work on GPU so far because of DO WHILE construct
698	!!!!!!$acc kernels loop
699	DO i = nxl, nxr
700	DO j = nys, nyn
701
702	!
703	!-- If the bulk Richardson number is outside the range of the lookup
704	!-- table, set it to the exceeding threshold value
705	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
706	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
707
708	!
709	!-- Find the correct index bounds for linear interpolation. As the
710	!-- Richardson number will not differ very much from time step to
711	!-- time step , use the index from the last step and search in the
712	!-- correct direction
713	l = l_bnd
714	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
715	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
716	l = l-1
717	ENDDO
718	ELSE
719	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
720	.AND. l < num_steps-1 )
721	l = l+1
722	ENDDO
723	ENDIF
724	l_bnd = l
725
726	!
727	!-- Linear interpolation to find the correct value of z/L
728	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
729	/ ( rib_tab(l) - rib_tab(l-1) ) &
730	* ( rib(j,i) - rib_tab(l-1) ) )
731
732	ENDDO
733	ENDDO
734
735	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
736
737	!$OMP PARALLEL DO PRIVATE( k, z_mo )
738	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
739	DO i = nxl, nxr
740	DO j = nys, nyn
741
742	k = nzb_s_inner(j,i)
743	z_mo = zu(k+1) - zw(k)
744
745	IF ( .NOT. humidity ) THEN
746	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
747	* ts(j,i) + 1E-30_wp )
748	ELSEIF ( cloud_physics ) THEN
749
750	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
751	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
752	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
753	* ql(k+1,j,i) ) + 1E-30_wp )
754	ELSE
755	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
756	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
757	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
758	ENDIF
759	!
760	!-- Limit the value range of the Obukhov length.
761	!-- This is necessary for very small velocities (u,v --> 0), because
762	!-- the absolute value of ol can then become very small, which in
763	!-- consequence would result in very large shear stresses and very
764	!-- small momentum fluxes (both are generally unrealistic).
765	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) < zeta_min ) &
766	ol(j,i) = z_mo / zeta_min
767	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) > zeta_max ) &
768	ol(j,i) = z_mo / zeta_max
769	ENDDO
770	ENDDO
771
772	ENDIF
773
774	!
775	!-- Values of ol at ghost point locations are needed for the evaluation
776	!-- of usws and vsws.
777	!$acc update host( ol )
778	CALL exchange_horiz_2d( ol )
779	!$acc update device( ol )
780
781	END SUBROUTINE calc_ol
782
783	!
784	!-- Calculate friction velocity u*
785	SUBROUTINE calc_us
786
787	IMPLICIT NONE
788
789	!$OMP PARALLEL DO PRIVATE( k, z_mo )
790	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
791	DO i = nxlg, nxrg
792	DO j = nysg, nyng
793
794	k = nzb_s_inner(j,i)+1
795	z_mo = zu(k+1) - zw(k)
796
797	!
798	!-- Compute u* at the scalars' grid points
799	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
800	- psi_m( z_mo / ol(j,i) ) &
801	+ psi_m( z0(j,i) / ol(j,i) ) )
802	ENDDO
803	ENDDO
804
805	END SUBROUTINE calc_us
806
807	!
808	!-- Calculate potential temperature and specific humidity at first grid level
809	SUBROUTINE calc_pt_q
810
811	IMPLICIT NONE
812
813	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
814	DO i = nxlg, nxrg
815	DO j = nysg, nyng
816	k = nzb_s_inner(j,i)+1
817	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
818	qv1(j,i) = q(k,j,i) - ql(k,j,i)
819	ENDDO
820	ENDDO
821
822	END SUBROUTINE calc_pt_q
823
824	!
825	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
826	SUBROUTINE calc_scaling_parameters
827
828	IMPLICIT NONE
829
830	!
831	!-- Data information for accelerators
832	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
833	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
834	!$acc present( vpt, vsws, zu, zw, z0, z0h )
835	!
836	!-- Compute theta*
837	IF ( constant_heatflux ) THEN
838
839	!
840	!-- For a given heat flux in the surface layer:
841	!$OMP PARALLEL DO
842	!$acc kernels loop private( j, k )
843	DO i = nxlg, nxrg
844	DO j = nysg, nyng
845	k = nzb_s_inner(j,i)
846	ts(j,i) = -shf(j,i) * drho_air_zw(k) / ( us(j,i) + 1E-30_wp )
847	!
848	!-- ts must be limited, because otherwise overflow may occur in case
849	!-- of us=0 when computing ol further below
850	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
851	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
852	ENDDO
853	ENDDO
854
855	ELSE
856	!
857	!-- For a given surface temperature:
858	IF ( large_scale_forcing .AND. lsf_surf ) THEN
859	!$OMP PARALLEL DO
860	!$acc kernels loop private( j, k )
861	DO i = nxlg, nxrg
862	DO j = nysg, nyng
863	k = nzb_s_inner(j,i)
864	pt(k,j,i) = pt_surface
865	ENDDO
866	ENDDO
867	ENDIF
868
869	!$OMP PARALLEL DO PRIVATE( k, z_mo )
870	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
871	DO i = nxlg, nxrg
872	DO j = nysg, nyng
873
874	k = nzb_s_inner(j,i)
875	z_mo = zu(k+1) - zw(k)
876
877	IF ( cloud_physics ) THEN
878	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
879	/ ( LOG( z_mo / z0h(j,i) ) &
880	- psi_h( z_mo / ol(j,i) ) &
881	+ psi_h( z0h(j,i) / ol(j,i) ) )
882	ELSE
883	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
884	/ ( LOG( z_mo / z0h(j,i) ) &
885	- psi_h( z_mo / ol(j,i) ) &
886	+ psi_h( z0h(j,i) / ol(j,i) ) )
887	ENDIF
888
889	ENDDO
890	ENDDO
891	ENDIF
892
893	!
894	!-- If required compute q*
895	IF ( humidity ) THEN
896	IF ( constant_waterflux ) THEN
897	!
898	!-- For a given water flux in the surface layer
899	!$OMP PARALLEL DO
900	!$acc kernels loop private( j )
901	DO i = nxlg, nxrg
902	DO j = nysg, nyng
903	k = nzb_s_inner(j,i)
904	qs(j,i) = -qsws(j,i) * drho_air_zw(k) / ( us(j,i) + 1E-30_wp )
905	ENDDO
906	ENDDO
907
908	ELSE
909	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
910	run_coupled )
911
912	IF ( large_scale_forcing .AND. lsf_surf ) THEN
913	!$OMP PARALLEL DO
914	!$acc kernels loop private( j, k )
915	DO i = nxlg, nxrg
916	DO j = nysg, nyng
917	k = nzb_s_inner(j,i)
918	q(k,j,i) = q_surface
919	ENDDO
920	ENDDO
921	ENDIF
922
923	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
924	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
925	DO i = nxlg, nxrg
926	!$acc loop independent
927	DO j = nysg, nyng
928
929	k = nzb_s_inner(j,i)
930	z_mo = zu(k+1) - zw(k)
931
932	!
933	!-- Assume saturation for atmosphere coupled to ocean (but not
934	!-- in case of precursor runs)
935	IF ( coupled_run ) THEN
936	e_s = 6.1_wp * &
937	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
938	- 273.15_wp ) )
939	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
940	ENDIF
941
942	IF ( cloud_physics ) THEN
943	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
944	/ ( LOG( z_mo / z0q(j,i) ) &
945	- psi_h( z_mo / ol(j,i) ) &
946	+ psi_h( z0q(j,i) / ol(j,i) ) )
947
948	ELSE
949	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
950	/ ( LOG( z_mo / z0q(j,i) ) &
951	- psi_h( z_mo / ol(j,i) ) &
952	+ psi_h( z0q(j,i) / ol(j,i) ) )
953	ENDIF
954
955	ENDDO
956	ENDDO
957	ENDIF
958	ENDIF
959
960	!
961	!-- If required compute s*
962	IF ( passive_scalar ) THEN
963	IF ( constant_scalarflux ) THEN
964	!
965	!-- For a given water flux in the surface layer
966	!$OMP PARALLEL DO
967	!$acc kernels loop private( j )
968	DO i = nxlg, nxrg
969	DO j = nysg, nyng
970	ss(j,i) = -ssws(j,i) / ( us(j,i) + 1E-30_wp )
971	ENDDO
972	ENDDO
973	ENDIF
974	ENDIF
975
976
977	!
978	!-- If required compute qr* and nr*
979	IF ( cloud_physics .AND. microphysics_seifert ) &
980	THEN
981
982	!$OMP PARALLEL DO PRIVATE( k, z_mo )
983	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
984	DO i = nxlg, nxrg
985	!$acc loop independent
986	DO j = nysg, nyng
987
988	k = nzb_s_inner(j,i)
989	z_mo = zu(k+1) - zw(k)
990
991	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
992	/ ( LOG( z_mo / z0q(j,i) ) &
993	- psi_h( z_mo / ol(j,i) ) &
994	+ psi_h( z0q(j,i) / ol(j,i) ) )
995
996	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
997	/ ( LOG( z_mo / z0q(j,i) ) &
998	- psi_h( z_mo / ol(j,i) ) &
999	+ psi_h( z0q(j,i) / ol(j,i) ) )
1000	ENDDO
1001	ENDDO
1002
1003	ENDIF
1004	!$acc end data
1005
1006	END SUBROUTINE calc_scaling_parameters
1007
1008
1009
1010	!
1011	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
1012	SUBROUTINE calc_surface_fluxes
1013
1014	IMPLICIT NONE
1015
1016	REAL(wp) :: ol_mid !< Grid-interpolated L
1017
1018	!
1019	!-- Compute u'w' for the total model domain.
1020	!-- First compute the corresponding component of u* and square it.
1021	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
1022	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
1023	DO i = nxl, nxr
1024	DO j = nys, nyn
1025
1026	k = nzb_u_inner(j,i)
1027	z_mo = zu(k+1) - zw(k)
1028	!
1029	!-- Compute bulk Obukhov length for this point
1030	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
1031
1032	IF ( ol_mid == 0.0_wp ) THEN
1033	ol_mid = MIN(ol(j,i-1), ol(j,i))
1034	ENDIF
1035
1036	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
1037	/ ( LOG( z_mo / z0(j,i) ) &
1038	- psi_m( z_mo / ol_mid ) &
1039	+ psi_m( z0(j,i) / ol_mid ) )
1040
1041	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) ) &
1042	* rho_air_zw(k)
1043	ENDDO
1044	ENDDO
1045
1046	!
1047	!-- Compute v'w' for the total model domain.
1048	!-- First compute the corresponding component of u* and square it.
1049	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
1050	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
1051	DO i = nxl, nxr
1052	DO j = nys, nyn
1053
1054	k = nzb_v_inner(j,i)
1055	z_mo = zu(k+1) - zw(k)
1056	!
1057	!-- Compute bulk Obukhov length for this point
1058	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
1059
1060	IF ( ol_mid == 0.0_wp ) THEN
1061	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
1062	ENDIF
1063
1064	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
1065	/ ( LOG( z_mo / z0(j,i) ) &
1066	- psi_m( z_mo / ol_mid ) &
1067	+ psi_m( z0(j,i) / ol_mid ) )
1068
1069	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j-1,i) + us(j,i) ) &
1070	* rho_air_zw(k)
1071
1072	ENDDO
1073	ENDDO
1074
1075	!
1076	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
1077	!$acc update host( usws, vsws )
1078	CALL exchange_horiz_2d( usws )
1079	CALL exchange_horiz_2d( vsws )
1080	!$acc update device( usws, vsws )
1081
1082	!
1083	!-- Compute the vertical kinematic heat flux
1084	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
1085	skip_time_do_lsm .OR. .NOT. land_surface ) .AND. &
1086	.NOT. urban_surface ) THEN
1087	!$OMP PARALLEL DO
1088	!$acc kernels loop independent present( shf, ts, us )
1089	DO i = nxlg, nxrg
1090	!$acc loop independent
1091	DO j = nysg, nyng
1092	k = nzb_s_inner(j,i)
1093	shf(j,i) = -ts(j,i) * us(j,i) * rho_air_zw(k)
1094	ENDDO
1095	ENDDO
1096
1097	ENDIF
1098
1099	!
1100	!-- Compute the vertical water flux
1101	IF ( .NOT. constant_waterflux .AND. humidity .AND. &
1102	( simulated_time <= skip_time_do_lsm &
1103	.OR. .NOT. land_surface ) ) THEN
1104	!$OMP PARALLEL DO
1105	!$acc kernels loop independent present( qs, qsws, us )
1106	DO i = nxlg, nxrg
1107	!$acc loop independent
1108	DO j = nysg, nyng
1109	k = nzb_s_inner(j,i)
1110	qsws(j,i) = -qs(j,i) * us(j,i) * rho_air_zw(k)
1111	ENDDO
1112	ENDDO
1113
1114	ENDIF
1115
1116	!
1117	!-- Compute the vertical scalar flux
1118	IF ( .NOT. constant_scalarflux .AND. passive_scalar .AND. &
1119	( simulated_time <= skip_time_do_lsm &
1120	.OR. .NOT. land_surface ) ) THEN
1121	!$OMP PARALLEL DO
1122	!$acc kernels loop independent present( qs, qsws, us )
1123	DO i = nxlg, nxrg
1124	!$acc loop independent
1125	DO j = nysg, nyng
1126	ssws(j,i) = -ss(j,i) * us(j,i)
1127	ENDDO
1128	ENDDO
1129
1130	ENDIF
1131
1132	!
1133	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
1134	IF ( cloud_physics .AND. microphysics_seifert ) THEN
1135	!$OMP PARALLEL DO
1136	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
1137	DO i = nxlg, nxrg
1138	!$acc loop independent
1139	DO j = nysg, nyng
1140	qrsws(j,i) = -qrs(j,i) * us(j,i)
1141	nrsws(j,i) = -nrs(j,i) * us(j,i)
1142	ENDDO
1143	ENDDO
1144	ENDIF
1145
1146	!
1147	!-- Bottom boundary condition for the TKE
1148	IF ( ibc_e_b == 2 ) THEN
1149	!$OMP PARALLEL DO
1150	!$acc kernels loop independent present( e, nzb_s_inner, us )
1151	DO i = nxlg, nxrg
1152	!$acc loop independent
1153	DO j = nysg, nyng
1154	k = nzb_s_inner(j,i)
1155	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
1156	!
1157	!-- As a test: cm = 0.4
1158	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
1159	e(k,j,i) = e(k+1,j,i)
1160	ENDDO
1161	ENDDO
1162	ENDIF
1163
1164	END SUBROUTINE calc_surface_fluxes
1165
1166
1167	!
1168	!-- Integrated stability function for momentum
1169	FUNCTION psi_m( zeta )
1170
1171	USE kinds
1172
1173	IMPLICIT NONE
1174
1175	REAL(wp) :: psi_m !< Integrated similarity function result
1176	REAL(wp) :: zeta !< Stability parameter z/L
1177	REAL(wp) :: x !< dummy variable
1178
1179	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1180	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1181	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1182	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1183	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1184	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1185
1186
1187	IF ( zeta < 0.0_wp ) THEN
1188	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
1189	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1190	* ( 1.0_wp + x*2 ) 0.125_wp )
1191	ELSE
1192
1193	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1194	- bc_d_d
1195	!
1196	!-- Old version for stable conditions (only valid for z/L < 0.5)
1197	!-- psi_m = - 5.0_wp * zeta
1198
1199	ENDIF
1200
1201	END FUNCTION psi_m
1202
1203
1204	!
1205	!-- Integrated stability function for heat and moisture
1206	FUNCTION psi_h( zeta )
1207
1208	USE kinds
1209
1210	IMPLICIT NONE
1211
1212	REAL(wp) :: psi_h !< Integrated similarity function result
1213	REAL(wp) :: zeta !< Stability parameter z/L
1214	REAL(wp) :: x !< dummy variable
1215
1216	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1217	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1218	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1219	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1220	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1221	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1222
1223
1224	IF ( zeta < 0.0_wp ) THEN
1225	x = SQRT( 1.0_wp - 16.0_wp * zeta )
1226	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1227	ELSE
1228	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1229	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1230	+ 1.0_wp
1231	!
1232	!-- Old version for stable conditions (only valid for z/L < 0.5)
1233	!-- psi_h = - 5.0_wp * zeta
1234	ENDIF
1235
1236	END FUNCTION psi_h
1237
1238	END MODULE surface_layer_fluxes_mod

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