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source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 2026

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

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