Home

Context Navigation

source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 2089

Last change on this file since 2089 was 2077, checked in by raasch, 8 years ago
last commit documented
Property svn:keywords set to `Id`
File size: 45.5 KB

Line
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 2077 2016-12-02 13:56:02Z suehring $
27	!
28	! 2076 2016-12-02 13:54:20Z raasch
29	! further openmp bugfix for lookup method
30	!
31	! 2073 2016-11-30 14:34:05Z raasch
32	! openmp bugfix for lookup method
33	!
34	! 2037 2016-10-26 11:15:40Z knoop
35	! Anelastic approximation implemented
36	!
37	! 2011 2016-09-19 17:29:57Z kanani
38	! Flag urban_surface is now defined in module control_parameters.
39	!
40	! 2007 2016-08-24 15:47:17Z kanani
41	! Account for urban surface model in computation of vertical kinematic heatflux
42	!
43	! 2000 2016-08-20 18:09:15Z knoop
44	! Forced header and separation lines into 80 columns
45	!
46	! 1992 2016-08-12 15:14:59Z suehring
47	! Minor bug, declaration of look-up index as INTEGER
48	!
49	! 1960 2016-07-12 16:34:24Z suehring
50	! Treat humidity and passive scalar separately
51	!
52	! 1929 2016-06-09 16:25:25Z suehring
53	! Bugfix: avoid segmentation fault in case one grid point is horizontally
54	! completely surrounded by topography
55	!
56	! 1920 2016-05-30 10:50:15Z suehring
57	! Avoid segmentation fault (see change in 1915) by different initialization of
58	! us instead of adding a very small number in the denominator
59	!
60	! 1915 2016-05-27 11:05:02Z suehring
61	! Bugfix: avoid segmentation fault in case of most_method = 'circular' at first
62	! timestep
63	!
64	! 1850 2016-04-08 13:29:27Z maronga
65	! Module renamed
66	!
67	!
68	! 1822 2016-04-07 07:49:42Z hoffmann
69	! icloud_scheme replaced by microphysics_*
70	!
71	! 1788 2016-03-10 11:01:04Z maronga
72	! Added parameter z0q which replaces z0h in the similarity functions for
73	! humidity.
74	! Syntax layout improved.
75	!
76	! 1757 2016-02-22 15:49:32Z maronga
77	! Minor fixes.
78	!
79	! 1749 2016-02-09 12:19:56Z raasch
80	! further OpenACC adjustments
81	!
82	! 1747 2016-02-08 12:25:53Z raasch
83	! adjustments for OpenACC usage
84	!
85	! 1709 2015-11-04 14:47:01Z maronga
86	! Bugfix: division by zero could occur when calculating rib at low wind speeds
87	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
88	! neutral = .T.
89	!
90	! 1705 2015-11-02 14:28:56Z maronga
91	! Typo removed
92	!
93	! 1697 2015-10-28 17:14:10Z raasch
94	! FORTRAN and OpenMP errors removed
95	!
96	! 1696 2015-10-27 10:03:34Z maronga
97	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
98	! course of the re-writing two additional methods have been implemented. See
99	! updated description.
100	!
101	! 1551 2015-03-03 14:18:16Z maronga
102	! Removed land surface model part. The surface fluxes are now always calculated
103	! within prandtl_fluxes, based on the given surface temperature/humidity (which
104	! is either provided by the land surface model, by large scale forcing data, or
105	! directly prescribed by the user.
106	!
107	! 1496 2014-12-02 17:25:50Z maronga
108	! Adapted for land surface model
109	!
110	! 1494 2014-11-21 17:14:03Z maronga
111	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
112	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
113	! topography for coupled runs (not tested)
114	!
115	! 1361 2014-04-16 15:17:48Z hoffmann
116	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
117	! drop concentration (nrsws) added
118	!
119	! 1340 2014-03-25 19:45:13Z kanani
120	! REAL constants defined as wp-kind
121	!
122	! 1320 2014-03-20 08:40:49Z raasch
123	! ONLY-attribute added to USE-statements,
124	! kind-parameters added to all INTEGER and REAL declaration statements,
125	! kinds are defined in new module kinds,
126	! old module precision_kind is removed,
127	! revision history before 2012 removed,
128	! comment fields (!:) to be used for variable explanations added to
129	! all variable declaration statements
130	!
131	! 1276 2014-01-15 13:40:41Z heinze
132	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
133	!
134	! 1257 2013-11-08 15:18:40Z raasch
135	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
136	!
137	! 1036 2012-10-22 13:43:42Z raasch
138	! code put under GPL (PALM 3.9)
139	!
140	! 1015 2012-09-27 09:23:24Z raasch
141	! OpenACC statements added
142	!
143	! 978 2012-08-09 08:28:32Z fricke
144	! roughness length for scalar quantities z0h added
145	!
146	! Revision 1.1 1998/01/23 10:06:06 raasch
147	! Initial revision
148	!
149	!
150	! Description:
151	! ------------
152	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
153	!> values of the variables at grid point k=1. Three different methods are
154	!> available:
155	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
156	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
157	!> slower
158	!> 3) a method using a lookup table which is fast and accurate. Note, however,
159	!> that this method cannot be used in case of roughness heterogeneity
160	!>
161	!> @todo (re)move large_scale_forcing actions
162	!> @todo check/optimize OpenMP and OpenACC directives
163	!------------------------------------------------------------------------------!
164	MODULE surface_layer_fluxes_mod
165
166	USE arrays_3d, &
167	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
168	s, shf, ss, ssws, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, &
169	z0h, z0q, drho_air_zw, rho_air_zw
170
171	USE cloud_parameters, &
172	ONLY: l_d_cp, pt_d_t
173
174	USE constants, &
175	ONLY: pi
176
177	USE cpulog
178
179	USE control_parameters, &
180	ONLY: cloud_physics, constant_heatflux, constant_scalarflux, &
181	constant_waterflux, coupling_mode, g, humidity, ibc_e_b, &
182	ibc_pt_b, initializing_actions, kappa, &
183	intermediate_timestep_count, &
184	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
185	message_string, microphysics_seifert, most_method, neutral, &
186	passive_scalar, pt_surface, q_surface, run_coupled, &
187	surface_pressure, simulated_time, terminate_run, &
188	urban_surface, &
189	zeta_max, zeta_min
190
191	USE indices, &
192	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
193	nzb_u_inner, nzb_v_inner
194
195	USE kinds
196
197	USE pegrid
198
199	USE land_surface_model_mod, &
200	ONLY: land_surface, skip_time_do_lsm
201
202
203
204	IMPLICIT NONE
205
206	INTEGER(iwp) :: i !< loop index x direction
207	INTEGER(iwp) :: j !< loop index y direction
208	INTEGER(iwp) :: k !< loop index z direction
209	INTEGER(iwp) :: l_bnd = 7500 !< Lookup table index of the last time step
210
211	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
212
213	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
214
215	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
216	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
217	uv_total !< Total velocity at first grid level
218
219	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
220	ol_tab !< Lookup table values of L
221
222	REAL(wp) :: e_s, & !< Saturation water vapor pressure
223	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
224	rib_max, & !< Maximum Richardson number in lookup table
225	rib_min, & !< Minimum Richardson number in lookup table
226	z_mo !< Height of the constant flux layer where MOST is assumed
227
228
229	SAVE
230
231	PRIVATE
232
233	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
234
235	INTERFACE init_surface_layer_fluxes
236	MODULE PROCEDURE init_surface_layer_fluxes
237	END INTERFACE init_surface_layer_fluxes
238
239	INTERFACE surface_layer_fluxes
240	MODULE PROCEDURE surface_layer_fluxes
241	END INTERFACE surface_layer_fluxes
242
243
244	CONTAINS
245
246
247	!------------------------------------------------------------------------------!
248	! Description:
249	! ------------
250	!> Main routine to compute the surface fluxes
251	!------------------------------------------------------------------------------!
252	SUBROUTINE surface_layer_fluxes
253
254	IMPLICIT NONE
255
256	!
257	!-- In case cloud physics is used, it is required to derive potential
258	!-- temperature and specific humidity at first grid level from the fields pt
259	!-- and q
260	IF ( cloud_physics ) THEN
261	CALL calc_pt_q
262	ENDIF
263
264	!
265	!-- First, calculate the new Obukhov length, then new friction velocity,
266	!-- followed by the new scaling parameters (th, q, etc.), and the new
267	!-- surface fluxes if required. The old routine ("circular") requires a
268	!-- different order of calls as the scaling parameters from the previous time
269	!-- steps are used to calculate the Obukhov length
270
271	!
272	!-- Depending on setting of most_method use the "old" routine
273	IF ( most_method == 'circular' ) THEN
274
275	CALL calc_scaling_parameters
276
277	CALL calc_uv_total
278
279	IF ( .NOT. neutral ) THEN
280	CALL calc_ol
281	ENDIF
282
283	CALL calc_us
284
285	CALL calc_surface_fluxes
286
287	!
288	!-- Use either Newton iteration or a lookup table for the bulk Richardson
289	!-- number to calculate the Obukhov length
290	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
291
292	CALL calc_uv_total
293
294	IF ( .NOT. neutral ) THEN
295	CALL calc_ol
296	ENDIF
297
298	CALL calc_us
299
300	CALL calc_scaling_parameters
301
302	CALL calc_surface_fluxes
303
304	ENDIF
305
306	END SUBROUTINE surface_layer_fluxes
307
308
309	!------------------------------------------------------------------------------!
310	! Description:
311	! ------------
312	!> Initializing actions for the surface layer routine. Basically, this involves
313	!> the preparation of a lookup table for the the bulk Richardson number vs
314	!> Obukhov length L when using the lookup table method.
315	!------------------------------------------------------------------------------!
316	SUBROUTINE init_surface_layer_fluxes
317
318	IMPLICIT NONE
319
320	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
321	num_steps_n !< Number of non-stretched zeta steps
322
323	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
324
325	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
326
327	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
328
329
330	REAL(wp) :: zeta_step, & !< Increment of zeta
331	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
332	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
333	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
334	z0_min = 0.0_wp !< Minimum value of z0 to create table
335	!
336	!-- When cloud physics is used, arrays for storing potential temperature and
337	!-- specific humidity at first grid level are required
338	IF ( cloud_physics ) THEN
339	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
340	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
341	ENDIF
342
343	!
344	!-- Allocate field for storing the horizontal velocity
345	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
346
347
348	!
349	!-- In case of runs with neutral statification, set Obukhov length to a
350	!-- large value
351	IF ( neutral ) ol = 1.0E10_wp
352
353	IF ( most_method == 'lookup' ) THEN
354
355	!
356	!-- Check for roughness heterogeneity. In that case terminate run and
357	!-- inform user
358	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
359	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
360	terminate_run_l = .TRUE.
361	ENDIF
362
363	#if defined( __parallel )
364	!
365	!-- Make a logical OR for all processes. Force termiation of model if result
366	!-- is TRUE
367	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
368	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
369	MPI_LOR, comm2d, ierr )
370	#else
371	terminate_run = terminate_run_l
372	#endif
373
374	IF ( terminate_run ) THEN
375	message_string = 'most_method = "lookup" cannot be used in ' // &
376	'combination with a prescribed roughness ' // &
377	'heterogeneity'
378	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
379	ENDIF
380
381	ALLOCATE( zeta_tmp(0:num_steps-1) )
382
383	!
384	!-- Use the lowest possible value for z_mo
385	k = MINVAL(nzb_s_inner)
386	z_mo = zu(k+1) - zw(k)
387
388	!
389	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
390	!-- available steps (num_steps). The calculation is done with negative
391	!-- values of zeta in order to simplify the stretching in the free
392	!-- convection limit for the remaining 10% of steps.
393	zeta_tmp(0) = - zeta_max
394	num_steps_n = ( num_steps * 9 / 10 ) - 1
395	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
396
397	DO l = 1, num_steps_n
398	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
399	ENDDO
400
401	!
402	!-- Calculate stretching factor for the free convection range
403	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
404	regr_old = regr
405	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
406	)**( 10.0_wp / REAL(num_steps) )
407	ENDDO
408
409	!
410	!-- Calculate z/L range from zeta_min to zeta_stretch
411	DO l = num_steps_n+1, num_steps-1
412	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
413	zeta_step = zeta_step * regr
414	ENDDO
415
416	!
417	!-- Save roughness lengths to temporary variables
418	z0h_min = z0h(nys,nxl)
419	z0_min = z0(nys,nxl)
420
421	!
422	!-- Calculate lookup table for the Richardson number versus Obukhov length
423	!-- The Richardson number (rib) is defined depending on the choice of
424	!-- boundary conditions for temperature
425	IF ( ibc_pt_b == 1 ) THEN
426	DO l = 0, num_steps-1
427	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
428	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
429	- psi_m( z_mo / ol_tab(l) ) &
430	+ psi_m( z0_min / ol_tab(l) ) &
431	)**3
432	ENDDO
433	ELSE
434	DO l = 0, num_steps-1
435	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
436	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
437	- psi_h( z_mo / ol_tab(l) ) &
438	+ psi_h( z0h_min / ol_tab(l) ) &
439	) &
440	/ ( LOG( z_mo / z0_min ) &
441	- psi_m( z_mo / ol_tab(l) ) &
442	+ psi_m( z0_min / ol_tab(l) ) &
443	)**2
444	ENDDO
445	ENDIF
446
447	!
448	!-- Determine minimum values of rib in the lookup table. Set upper limit
449	!-- to critical Richardson number (0.25)
450	rib_min = MINVAL(rib_tab)
451	rib_max = 0.25 !MAXVAL(rib_tab)
452
453	DEALLOCATE( zeta_tmp )
454	ENDIF
455
456	END SUBROUTINE init_surface_layer_fluxes
457
458
459	!------------------------------------------------------------------------------!
460	! Description:
461	! ------------
462	!> Compute the absolute value of the horizontal velocity (relative to the
463	!> surface). This is required by all methods
464	!------------------------------------------------------------------------------!
465	SUBROUTINE calc_uv_total
466
467	IMPLICIT NONE
468
469
470	!$OMP PARALLEL DO PRIVATE( k )
471	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
472	DO i = nxl, nxr
473	DO j = nys, nyn
474
475	k = nzb_s_inner(j,i)
476	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
477	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
478	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
479	- v(k,j,i) - v(k,j+1,i) ) )**2 )
480
481	!
482	!-- For too small values of the local wind, MOST does not work. A
483	!-- threshold value is thus set if required
484	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
485
486	ENDDO
487	ENDDO
488
489	!
490	!-- Values of uv_total need to be exchanged at the ghost boundaries
491	!$acc update host( uv_total )
492	CALL exchange_horiz_2d( uv_total )
493	!$acc update device( uv_total )
494
495	END SUBROUTINE calc_uv_total
496
497
498	!------------------------------------------------------------------------------!
499	! Description:
500	! ------------
501	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
502	!------------------------------------------------------------------------------!
503	SUBROUTINE calc_ol
504
505	IMPLICIT NONE
506
507	INTEGER(iwp) :: iter, & !< Newton iteration step
508	l !< look index
509
510	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
511
512	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
513	f_d_ol, & !< Derivative of f
514	ol_l, & !< Lower bound of L for Newton iteration
515	ol_m, & !< Previous value of L for Newton iteration
516	ol_old, & !< Previous time step value of L
517	ol_u !< Upper bound of L for Newton iteration
518
519	IF ( TRIM( most_method ) /= 'circular' ) THEN
520
521	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
522
523	!$OMP PARALLEL DO PRIVATE( k, z_mo )
524	!$acc kernels loop private( j, k, z_mo )
525	DO i = nxl, nxr
526	DO j = nys, nyn
527
528	k = nzb_s_inner(j,i)
529	z_mo = zu(k+1) - zw(k)
530
531	!
532	!-- Evaluate bulk Richardson number (calculation depends on
533	!-- definition based on setting of boundary conditions
534	IF ( ibc_pt_b /= 1 ) THEN
535	IF ( humidity ) THEN
536	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
537	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
538	ELSE
539	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
540	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
541	ENDIF
542	ELSE
543	!
544	!-- When using Neumann boundary conditions, the buoyancy flux
545	!-- is required but cannot be calculated at the surface, as pt
546	!-- and q are not known at the surface. Hence the values at
547	!-- first grid level are used to estimate the buoyancy flux
548	IF ( humidity ) THEN
549	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
550	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
551	* pt(k+1,j,i) * qsws(j,i) ) * drho_air_zw(k) &
552	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
553	+ 1.0E-20_wp)
554	ELSE
555	rib(j,i) = - g * z_mo * shf(j,i) * drho_air_zw(k) &
556	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
557	+ 1.0E-20_wp )
558	ENDIF
559	ENDIF
560
561	ENDDO
562	ENDDO
563	!$acc end data
564
565	ENDIF
566
567	!
568	!-- Calculate the Obukhov length either using a Newton iteration
569	!-- method, via a lookup table, or using the old circular way
570	IF ( TRIM( most_method ) == 'newton' ) THEN
571
572	!$OMP PARALLEL DO PRIVATE( k, z_mo )
573	!# WARNING: does not work on GPU so far because of DO-loop with
574	!# undetermined iterations
575	!!!!!!$acc kernels loop
576	DO i = nxl, nxr
577	DO j = nys, nyn
578
579	k = nzb_s_inner(j,i)
580	z_mo = zu(k+1) - zw(k)
581
582	!
583	!-- Store current value in case the Newton iteration fails
584	ol_old = ol(j,i)
585
586	!
587	!-- Ensure that the bulk Richardson number and the Obukhov
588	!-- lengtH have the same sign
589	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
590	ABS( ol(j,i) ) == ol_max ) THEN
591	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
592	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
593	ENDIF
594	!
595	!-- Iteration to find Obukhov length
596	iter = 0
597	DO
598	iter = iter + 1
599	!
600	!-- In case of divergence, use the value of the previous time step
601	IF ( iter > 1000 ) THEN
602	ol(j,i) = ol_old
603	EXIT
604	ENDIF
605
606	ol_m = ol(j,i)
607	ol_l = ol_m - 0.001_wp * ol_m
608	ol_u = ol_m + 0.001_wp * ol_m
609
610
611	IF ( ibc_pt_b /= 1 ) THEN
612	!
613	!-- Calculate f = Ri - [...]/[...]^2 = 0
614	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
615	- psi_h( z_mo / ol_m ) &
616	+ psi_h( z0h(j,i) / ol_m ) &
617	) &
618	/ ( LOG( z_mo / z0(j,i) ) &
619	- psi_m( z_mo / ol_m ) &
620	+ psi_m( z0(j,i) / ol_m ) &
621	)**2
622
623	!
624	!-- Calculate df/dL
625	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
626	- psi_h( z_mo / ol_u ) &
627	+ psi_h( z0h(j,i) / ol_u ) &
628	) &
629	/ ( LOG( z_mo / z0(j,i) ) &
630	- psi_m( z_mo / ol_u ) &
631	+ psi_m( z0(j,i) / ol_u ) &
632	)**2 &
633	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
634	- psi_h( z_mo / ol_l ) &
635	+ psi_h( z0h(j,i) / ol_l ) &
636	) &
637	/ ( LOG( z_mo / z0(j,i) ) &
638	- psi_m( z_mo / ol_l ) &
639	+ psi_m( z0(j,i) / ol_l ) &
640	)**2 &
641	) / ( ol_u - ol_l )
642	ELSE
643	!
644	!-- Calculate f = Ri - 1 /[...]^3 = 0
645	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
646	- psi_m( z_mo / ol_m ) &
647	+ psi_m( z0(j,i) / ol_m ) &
648	)**3
649
650	!
651	!-- Calculate df/dL
652	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
653	- psi_m( z_mo / ol_u ) &
654	+ psi_m( z0(j,i) / ol_u ) &
655	)**3 &
656	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
657	- psi_m( z_mo / ol_l ) &
658	+ psi_m( z0(j,i) / ol_l ) &
659	)**3 &
660	) / ( ol_u - ol_l )
661	ENDIF
662	!
663	!-- Calculate new L
664	ol(j,i) = ol_m - f / f_d_ol
665
666	!
667	!-- Ensure that the bulk Richardson number and the Obukhov
668	!-- length have the same sign and ensure convergence.
669	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
670
671	!
672	!-- If unrealistic value occurs, set L to the maximum
673	!-- value that is allowed
674	IF ( ABS( ol(j,i) ) > ol_max ) THEN
675	ol(j,i) = ol_max
676	EXIT
677	ENDIF
678	!
679	!-- Check for convergence
680	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
681	EXIT
682	ELSE
683	CYCLE
684	ENDIF
685
686	ENDDO
687
688	ENDDO
689	ENDDO
690
691	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
692
693	!$OMP PARALLEL DO PRIVATE( k, l, z_mo ) FIRSTPRIVATE( l_bnd ) LASTPRIVATE( l_bnd )
694	!# WARNING: does not work on GPU so far because of DO WHILE construct
695	!!!!!!$acc kernels loop
696	DO i = nxl, nxr
697	DO j = nys, nyn
698
699	!
700	!-- If the bulk Richardson number is outside the range of the lookup
701	!-- table, set it to the exceeding threshold value
702	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
703	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
704
705	!
706	!-- Find the correct index bounds for linear interpolation. As the
707	!-- Richardson number will not differ very much from time step to
708	!-- time step , use the index from the last step and search in the
709	!-- correct direction
710	l = l_bnd
711	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
712	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
713	l = l-1
714	ENDDO
715	ELSE
716	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
717	.AND. l < num_steps-1 )
718	l = l+1
719	ENDDO
720	ENDIF
721	l_bnd = l
722
723	!
724	!-- Linear interpolation to find the correct value of z/L
725	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
726	/ ( rib_tab(l) - rib_tab(l-1) ) &
727	* ( rib(j,i) - rib_tab(l-1) ) )
728
729	ENDDO
730	ENDDO
731
732	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
733
734	!$OMP PARALLEL DO PRIVATE( k, z_mo )
735	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
736	DO i = nxl, nxr
737	DO j = nys, nyn
738
739	k = nzb_s_inner(j,i)
740	z_mo = zu(k+1) - zw(k)
741
742	IF ( .NOT. humidity ) THEN
743	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
744	* ts(j,i) + 1E-30_wp )
745	ELSEIF ( cloud_physics ) THEN
746
747	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
748	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
749	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
750	* ql(k+1,j,i) ) + 1E-30_wp )
751	ELSE
752	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
753	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
754	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
755	ENDIF
756	!
757	!-- Limit the value range of the Obukhov length.
758	!-- This is necessary for very small velocities (u,v --> 0), because
759	!-- the absolute value of ol can then become very small, which in
760	!-- consequence would result in very large shear stresses and very
761	!-- small momentum fluxes (both are generally unrealistic).
762	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) < zeta_min ) &
763	ol(j,i) = z_mo / zeta_min
764	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) > zeta_max ) &
765	ol(j,i) = z_mo / zeta_max
766	ENDDO
767	ENDDO
768
769	ENDIF
770
771	!
772	!-- Values of ol at ghost point locations are needed for the evaluation
773	!-- of usws and vsws.
774	!$acc update host( ol )
775	CALL exchange_horiz_2d( ol )
776	!$acc update device( ol )
777
778	END SUBROUTINE calc_ol
779
780	!
781	!-- Calculate friction velocity u*
782	SUBROUTINE calc_us
783
784	IMPLICIT NONE
785
786	!$OMP PARALLEL DO PRIVATE( k, z_mo )
787	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
788	DO i = nxlg, nxrg
789	DO j = nysg, nyng
790
791	k = nzb_s_inner(j,i)+1
792	z_mo = zu(k+1) - zw(k)
793
794	!
795	!-- Compute u* at the scalars' grid points
796	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
797	- psi_m( z_mo / ol(j,i) ) &
798	+ psi_m( z0(j,i) / ol(j,i) ) )
799	ENDDO
800	ENDDO
801
802	END SUBROUTINE calc_us
803
804	!
805	!-- Calculate potential temperature and specific humidity at first grid level
806	SUBROUTINE calc_pt_q
807
808	IMPLICIT NONE
809
810	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
811	DO i = nxlg, nxrg
812	DO j = nysg, nyng
813	k = nzb_s_inner(j,i)+1
814	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
815	qv1(j,i) = q(k,j,i) - ql(k,j,i)
816	ENDDO
817	ENDDO
818
819	END SUBROUTINE calc_pt_q
820
821	!
822	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
823	SUBROUTINE calc_scaling_parameters
824
825	IMPLICIT NONE
826
827	!
828	!-- Data information for accelerators
829	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
830	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
831	!$acc present( vpt, vsws, zu, zw, z0, z0h )
832	!
833	!-- Compute theta*
834	IF ( constant_heatflux ) THEN
835
836	!
837	!-- For a given heat flux in the surface layer:
838	!$OMP PARALLEL DO
839	!$acc kernels loop private( j, k )
840	DO i = nxlg, nxrg
841	DO j = nysg, nyng
842	k = nzb_s_inner(j,i)
843	ts(j,i) = -shf(j,i) * drho_air_zw(k) / ( us(j,i) + 1E-30_wp )
844	!
845	!-- ts must be limited, because otherwise overflow may occur in case
846	!-- of us=0 when computing ol further below
847	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
848	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
849	ENDDO
850	ENDDO
851
852	ELSE
853	!
854	!-- For a given surface temperature:
855	IF ( large_scale_forcing .AND. lsf_surf ) THEN
856	!$OMP PARALLEL DO
857	!$acc kernels loop private( j, k )
858	DO i = nxlg, nxrg
859	DO j = nysg, nyng
860	k = nzb_s_inner(j,i)
861	pt(k,j,i) = pt_surface
862	ENDDO
863	ENDDO
864	ENDIF
865
866	!$OMP PARALLEL DO PRIVATE( k, z_mo )
867	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
868	DO i = nxlg, nxrg
869	DO j = nysg, nyng
870
871	k = nzb_s_inner(j,i)
872	z_mo = zu(k+1) - zw(k)
873
874	IF ( cloud_physics ) THEN
875	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
876	/ ( LOG( z_mo / z0h(j,i) ) &
877	- psi_h( z_mo / ol(j,i) ) &
878	+ psi_h( z0h(j,i) / ol(j,i) ) )
879	ELSE
880	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
881	/ ( LOG( z_mo / z0h(j,i) ) &
882	- psi_h( z_mo / ol(j,i) ) &
883	+ psi_h( z0h(j,i) / ol(j,i) ) )
884	ENDIF
885
886	ENDDO
887	ENDDO
888	ENDIF
889
890	!
891	!-- If required compute q*
892	IF ( humidity ) THEN
893	IF ( constant_waterflux ) THEN
894	!
895	!-- For a given water flux in the surface layer
896	!$OMP PARALLEL DO
897	!$acc kernels loop private( j )
898	DO i = nxlg, nxrg
899	DO j = nysg, nyng
900	k = nzb_s_inner(j,i)
901	qs(j,i) = -qsws(j,i) * drho_air_zw(k) / ( us(j,i) + 1E-30_wp )
902	ENDDO
903	ENDDO
904
905	ELSE
906	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
907	run_coupled )
908
909	IF ( large_scale_forcing .AND. lsf_surf ) THEN
910	!$OMP PARALLEL DO
911	!$acc kernels loop private( j, k )
912	DO i = nxlg, nxrg
913	DO j = nysg, nyng
914	k = nzb_s_inner(j,i)
915	q(k,j,i) = q_surface
916	ENDDO
917	ENDDO
918	ENDIF
919
920	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
921	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
922	DO i = nxlg, nxrg
923	!$acc loop independent
924	DO j = nysg, nyng
925
926	k = nzb_s_inner(j,i)
927	z_mo = zu(k+1) - zw(k)
928
929	!
930	!-- Assume saturation for atmosphere coupled to ocean (but not
931	!-- in case of precursor runs)
932	IF ( coupled_run ) THEN
933	e_s = 6.1_wp * &
934	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
935	- 273.15_wp ) )
936	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
937	ENDIF
938
939	IF ( cloud_physics ) THEN
940	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
941	/ ( LOG( z_mo / z0q(j,i) ) &
942	- psi_h( z_mo / ol(j,i) ) &
943	+ psi_h( z0q(j,i) / ol(j,i) ) )
944
945	ELSE
946	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
947	/ ( LOG( z_mo / z0q(j,i) ) &
948	- psi_h( z_mo / ol(j,i) ) &
949	+ psi_h( z0q(j,i) / ol(j,i) ) )
950	ENDIF
951
952	ENDDO
953	ENDDO
954	ENDIF
955	ENDIF
956
957	!
958	!-- If required compute s*
959	IF ( passive_scalar ) THEN
960	IF ( constant_scalarflux ) THEN
961	!
962	!-- For a given water flux in the surface layer
963	!$OMP PARALLEL DO
964	!$acc kernels loop private( j )
965	DO i = nxlg, nxrg
966	DO j = nysg, nyng
967	ss(j,i) = -ssws(j,i) / ( us(j,i) + 1E-30_wp )
968	ENDDO
969	ENDDO
970	ENDIF
971	ENDIF
972
973
974	!
975	!-- If required compute qr* and nr*
976	IF ( cloud_physics .AND. microphysics_seifert ) &
977	THEN
978
979	!$OMP PARALLEL DO PRIVATE( k, z_mo )
980	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
981	DO i = nxlg, nxrg
982	!$acc loop independent
983	DO j = nysg, nyng
984
985	k = nzb_s_inner(j,i)
986	z_mo = zu(k+1) - zw(k)
987
988	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
989	/ ( LOG( z_mo / z0q(j,i) ) &
990	- psi_h( z_mo / ol(j,i) ) &
991	+ psi_h( z0q(j,i) / ol(j,i) ) )
992
993	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
994	/ ( LOG( z_mo / z0q(j,i) ) &
995	- psi_h( z_mo / ol(j,i) ) &
996	+ psi_h( z0q(j,i) / ol(j,i) ) )
997	ENDDO
998	ENDDO
999
1000	ENDIF
1001	!$acc end data
1002
1003	END SUBROUTINE calc_scaling_parameters
1004
1005
1006
1007	!
1008	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
1009	SUBROUTINE calc_surface_fluxes
1010
1011	IMPLICIT NONE
1012
1013	REAL(wp) :: ol_mid !< Grid-interpolated L
1014
1015	!
1016	!-- Compute u'w' for the total model domain.
1017	!-- First compute the corresponding component of u* and square it.
1018	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
1019	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
1020	DO i = nxl, nxr
1021	DO j = nys, nyn
1022
1023	k = nzb_u_inner(j,i)
1024	z_mo = zu(k+1) - zw(k)
1025	!
1026	!-- Compute bulk Obukhov length for this point
1027	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
1028
1029	IF ( ol_mid == 0.0_wp ) THEN
1030	ol_mid = MIN(ol(j,i-1), ol(j,i))
1031	ENDIF
1032
1033	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
1034	/ ( LOG( z_mo / z0(j,i) ) &
1035	- psi_m( z_mo / ol_mid ) &
1036	+ psi_m( z0(j,i) / ol_mid ) )
1037
1038	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) ) &
1039	* rho_air_zw(k)
1040	ENDDO
1041	ENDDO
1042
1043	!
1044	!-- Compute v'w' for the total model domain.
1045	!-- First compute the corresponding component of u* and square it.
1046	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
1047	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
1048	DO i = nxl, nxr
1049	DO j = nys, nyn
1050
1051	k = nzb_v_inner(j,i)
1052	z_mo = zu(k+1) - zw(k)
1053	!
1054	!-- Compute bulk Obukhov length for this point
1055	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
1056
1057	IF ( ol_mid == 0.0_wp ) THEN
1058	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
1059	ENDIF
1060
1061	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
1062	/ ( LOG( z_mo / z0(j,i) ) &
1063	- psi_m( z_mo / ol_mid ) &
1064	+ psi_m( z0(j,i) / ol_mid ) )
1065
1066	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) ) &
1067	* rho_air_zw(k)
1068
1069	ENDDO
1070	ENDDO
1071
1072	!
1073	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
1074	!$acc update host( usws, vsws )
1075	CALL exchange_horiz_2d( usws )
1076	CALL exchange_horiz_2d( vsws )
1077	!$acc update device( usws, vsws )
1078
1079	!
1080	!-- Compute the vertical kinematic heat flux
1081	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
1082	skip_time_do_lsm .OR. .NOT. land_surface ) .AND. &
1083	.NOT. urban_surface ) THEN
1084	!$OMP PARALLEL DO
1085	!$acc kernels loop independent present( shf, ts, us )
1086	DO i = nxlg, nxrg
1087	!$acc loop independent
1088	DO j = nysg, nyng
1089	k = nzb_s_inner(j,i)
1090	shf(j,i) = -ts(j,i) * us(j,i) * rho_air_zw(k)
1091	ENDDO
1092	ENDDO
1093
1094	ENDIF
1095
1096	!
1097	!-- Compute the vertical water flux
1098	IF ( .NOT. constant_waterflux .AND. humidity .AND. &
1099	( simulated_time <= skip_time_do_lsm &
1100	.OR. .NOT. land_surface ) ) THEN
1101	!$OMP PARALLEL DO
1102	!$acc kernels loop independent present( qs, qsws, us )
1103	DO i = nxlg, nxrg
1104	!$acc loop independent
1105	DO j = nysg, nyng
1106	k = nzb_s_inner(j,i)
1107	qsws(j,i) = -qs(j,i) * us(j,i) * rho_air_zw(k)
1108	ENDDO
1109	ENDDO
1110
1111	ENDIF
1112
1113	!
1114	!-- Compute the vertical scalar flux
1115	IF ( .NOT. constant_scalarflux .AND. passive_scalar .AND. &
1116	( simulated_time <= skip_time_do_lsm &
1117	.OR. .NOT. land_surface ) ) THEN
1118	!$OMP PARALLEL DO
1119	!$acc kernels loop independent present( qs, qsws, us )
1120	DO i = nxlg, nxrg
1121	!$acc loop independent
1122	DO j = nysg, nyng
1123	ssws(j,i) = -ss(j,i) * us(j,i)
1124	ENDDO
1125	ENDDO
1126
1127	ENDIF
1128
1129	!
1130	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
1131	IF ( cloud_physics .AND. microphysics_seifert ) THEN
1132	!$OMP PARALLEL DO
1133	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
1134	DO i = nxlg, nxrg
1135	!$acc loop independent
1136	DO j = nysg, nyng
1137	qrsws(j,i) = -qrs(j,i) * us(j,i)
1138	nrsws(j,i) = -nrs(j,i) * us(j,i)
1139	ENDDO
1140	ENDDO
1141	ENDIF
1142
1143	!
1144	!-- Bottom boundary condition for the TKE
1145	IF ( ibc_e_b == 2 ) THEN
1146	!$OMP PARALLEL DO
1147	!$acc kernels loop independent present( e, nzb_s_inner, us )
1148	DO i = nxlg, nxrg
1149	!$acc loop independent
1150	DO j = nysg, nyng
1151	k = nzb_s_inner(j,i)
1152	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
1153	!
1154	!-- As a test: cm = 0.4
1155	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
1156	e(k,j,i) = e(k+1,j,i)
1157	ENDDO
1158	ENDDO
1159	ENDIF
1160
1161	END SUBROUTINE calc_surface_fluxes
1162
1163
1164	!
1165	!-- Integrated stability function for momentum
1166	FUNCTION psi_m( zeta )
1167
1168	USE kinds
1169
1170	IMPLICIT NONE
1171
1172	REAL(wp) :: psi_m !< Integrated similarity function result
1173	REAL(wp) :: zeta !< Stability parameter z/L
1174	REAL(wp) :: x !< dummy variable
1175
1176	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1177	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1178	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1179	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1180	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1181	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1182
1183
1184	IF ( zeta < 0.0_wp ) THEN
1185	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
1186	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1187	* ( 1.0_wp + x*2 ) 0.125_wp )
1188	ELSE
1189
1190	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1191	- bc_d_d
1192	!
1193	!-- Old version for stable conditions (only valid for z/L < 0.5)
1194	!-- psi_m = - 5.0_wp * zeta
1195
1196	ENDIF
1197
1198	END FUNCTION psi_m
1199
1200
1201	!
1202	!-- Integrated stability function for heat and moisture
1203	FUNCTION psi_h( zeta )
1204
1205	USE kinds
1206
1207	IMPLICIT NONE
1208
1209	REAL(wp) :: psi_h !< Integrated similarity function result
1210	REAL(wp) :: zeta !< Stability parameter z/L
1211	REAL(wp) :: x !< dummy variable
1212
1213	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1214	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1215	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1216	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1217	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1218	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1219
1220
1221	IF ( zeta < 0.0_wp ) THEN
1222	x = SQRT( 1.0_wp - 16.0_wp * zeta )
1223	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1224	ELSE
1225	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1226	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1227	+ 1.0_wp
1228	!
1229	!-- Old version for stable conditions (only valid for z/L < 0.5)
1230	!-- psi_h = - 5.0_wp * zeta
1231	ENDIF
1232
1233	END FUNCTION psi_h
1234
1235	END MODULE surface_layer_fluxes_mod

Note: See TracBrowser for help on using the repository browser.

Download in other formats:

| Impressum | ©Leibniz Universität Hannover |