Home

Context Navigation

source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 1986

Last change on this file since 1986 was 1961, checked in by suehring, 8 years ago
last commit documented
Property svn:keywords set to `Id`
File size: 44.3 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 terms
6	! of the GNU General Public License as published by the Free Software Foundation,
7	! either version 3 of the License, or (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with
14	! PALM. If not, see <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2016 Leibniz Universitaet Hannover
17	!
18	!--------------------------------------------------------------------------------!
19	! Current revisions:
20	! ------------------
21	!
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: surface_layer_fluxes_mod.f90 1961 2016-07-12 16:37:58Z gronemeier $
26	!
27	! 1960 2016-07-12 16:34:24Z suehring
28	! Treat humidity and passive scalar separately
29	!
30	! 1929 2016-06-09 16:25:25Z suehring
31	! Bugfix: avoid segmentation fault in case one grid point is horizontally
32	! completely surrounded by topography
33	!
34	! 1920 2016-05-30 10:50:15Z suehring
35	! Avoid segmentation fault (see change in 1915) by different initialization of
36	! us instead of adding a very small number in the denominator
37	!
38	! 1915 2016-05-27 11:05:02Z suehring
39	! Bugfix: avoid segmentation fault in case of most_method = 'circular' at first
40	! timestep
41	!
42	! 1850 2016-04-08 13:29:27Z maronga
43	! Module renamed
44	!
45	!
46	! 1822 2016-04-07 07:49:42Z hoffmann
47	! icloud_scheme replaced by microphysics_*
48	!
49	! 1788 2016-03-10 11:01:04Z maronga
50	! Added parameter z0q which replaces z0h in the similarity functions for
51	! humidity.
52	! Syntax layout improved.
53	!
54	! 1757 2016-02-22 15:49:32Z maronga
55	! Minor fixes.
56	!
57	! 1749 2016-02-09 12:19:56Z raasch
58	! further OpenACC adjustments
59	!
60	! 1747 2016-02-08 12:25:53Z raasch
61	! adjustments for OpenACC usage
62	!
63	! 1709 2015-11-04 14:47:01Z maronga
64	! Bugfix: division by zero could occur when calculating rib at low wind speeds
65	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
66	! neutral = .T.
67	!
68	! 1705 2015-11-02 14:28:56Z maronga
69	! Typo removed
70	!
71	! 1697 2015-10-28 17:14:10Z raasch
72	! FORTRAN and OpenMP errors removed
73	!
74	! 1696 2015-10-27 10:03:34Z maronga
75	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
76	! course of the re-writing two additional methods have been implemented. See
77	! updated description.
78	!
79	! 1551 2015-03-03 14:18:16Z maronga
80	! Removed land surface model part. The surface fluxes are now always calculated
81	! within prandtl_fluxes, based on the given surface temperature/humidity (which
82	! is either provided by the land surface model, by large scale forcing data, or
83	! directly prescribed by the user.
84	!
85	! 1496 2014-12-02 17:25:50Z maronga
86	! Adapted for land surface model
87	!
88	! 1494 2014-11-21 17:14:03Z maronga
89	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
90	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
91	! topography for coupled runs (not tested)
92	!
93	! 1361 2014-04-16 15:17:48Z hoffmann
94	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
95	! drop concentration (nrsws) added
96	!
97	! 1340 2014-03-25 19:45:13Z kanani
98	! REAL constants defined as wp-kind
99	!
100	! 1320 2014-03-20 08:40:49Z raasch
101	! ONLY-attribute added to USE-statements,
102	! kind-parameters added to all INTEGER and REAL declaration statements,
103	! kinds are defined in new module kinds,
104	! old module precision_kind is removed,
105	! revision history before 2012 removed,
106	! comment fields (!:) to be used for variable explanations added to
107	! all variable declaration statements
108	!
109	! 1276 2014-01-15 13:40:41Z heinze
110	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
111	!
112	! 1257 2013-11-08 15:18:40Z raasch
113	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
114	!
115	! 1036 2012-10-22 13:43:42Z raasch
116	! code put under GPL (PALM 3.9)
117	!
118	! 1015 2012-09-27 09:23:24Z raasch
119	! OpenACC statements added
120	!
121	! 978 2012-08-09 08:28:32Z fricke
122	! roughness length for scalar quantities z0h added
123	!
124	! Revision 1.1 1998/01/23 10:06:06 raasch
125	! Initial revision
126	!
127	!
128	! Description:
129	! ------------
130	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
131	!> values of the variables at grid point k=1. Three different methods are
132	!> available:
133	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
134	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
135	!> slower
136	!> 3) a method using a lookup table which is fast and accurate. Note, however,
137	!> that this method cannot be used in case of roughness heterogeneity
138	!>
139	!> @todo (re)move large_scale_forcing actions
140	!> @todo check/optimize OpenMP and OpenACC directives
141	!------------------------------------------------------------------------------!
142	MODULE surface_layer_fluxes_mod
143
144	USE arrays_3d, &
145	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
146	s, shf, ss, ssws, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, &
147	z0h, z0q
148
149	USE cloud_parameters, &
150	ONLY: l_d_cp, pt_d_t
151
152	USE constants, &
153	ONLY: pi
154
155	USE cpulog
156
157	USE control_parameters, &
158	ONLY: cloud_physics, constant_heatflux, constant_scalarflux, &
159	constant_waterflux, coupling_mode, g, humidity, ibc_e_b, &
160	ibc_pt_b, initializing_actions, kappa, &
161	intermediate_timestep_count, &
162	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
163	message_string, microphysics_seifert, most_method, neutral, &
164	passive_scalar, pt_surface, q_surface, run_coupled, &
165	surface_pressure, simulated_time, terminate_run, zeta_max, &
166	zeta_min
167
168	USE indices, &
169	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
170	nzb_u_inner, nzb_v_inner
171
172	USE kinds
173
174	USE pegrid
175
176	USE land_surface_model_mod, &
177	ONLY: land_surface, skip_time_do_lsm
178
179	IMPLICIT NONE
180
181	INTEGER(iwp) :: i !< loop index x direction
182	INTEGER(iwp) :: j !< loop index y direction
183	INTEGER(iwp) :: k !< loop index z direction
184
185	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
186
187	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
188
189	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
190	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
191	uv_total !< Total velocity at first grid level
192
193	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
194	ol_tab !< Lookup table values of L
195
196	REAL(wp) :: e_s, & !< Saturation water vapor pressure
197	l_bnd = 7500, & !< Lookup table index of the last time step
198	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
199	rib_max, & !< Maximum Richardson number in lookup table
200	rib_min, & !< Minimum Richardson number in lookup table
201	z_mo !< Height of the constant flux layer where MOST is assumed
202
203
204	SAVE
205
206	PRIVATE
207
208	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
209
210	INTERFACE init_surface_layer_fluxes
211	MODULE PROCEDURE init_surface_layer_fluxes
212	END INTERFACE init_surface_layer_fluxes
213
214	INTERFACE surface_layer_fluxes
215	MODULE PROCEDURE surface_layer_fluxes
216	END INTERFACE surface_layer_fluxes
217
218
219	CONTAINS
220
221
222	!------------------------------------------------------------------------------!
223	! Description:
224	! ------------
225	!> Main routine to compute the surface fluxes
226	!------------------------------------------------------------------------------!
227	SUBROUTINE surface_layer_fluxes
228
229	IMPLICIT NONE
230
231	!
232	!-- In case cloud physics is used, it is required to derive potential
233	!-- temperature and specific humidity at first grid level from the fields pt
234	!-- and q
235	IF ( cloud_physics ) THEN
236	CALL calc_pt_q
237	ENDIF
238
239	!
240	!-- First, calculate the new Obukhov length, then new friction velocity,
241	!-- followed by the new scaling parameters (th, q, etc.), and the new
242	!-- surface fluxes if required. The old routine ("circular") requires a
243	!-- different order of calls as the scaling parameters from the previous time
244	!-- steps are used to calculate the Obukhov length
245
246	!
247	!-- Depending on setting of most_method use the "old" routine
248	IF ( most_method == 'circular' ) THEN
249
250	CALL calc_scaling_parameters
251
252	CALL calc_uv_total
253
254	IF ( .NOT. neutral ) THEN
255	CALL calc_ol
256	ENDIF
257
258	CALL calc_us
259
260	CALL calc_surface_fluxes
261
262	!
263	!-- Use either Newton iteration or a lookup table for the bulk Richardson
264	!-- number to calculate the Obukhov length
265	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
266
267	CALL calc_uv_total
268
269	IF ( .NOT. neutral ) THEN
270	CALL calc_ol
271	ENDIF
272
273	CALL calc_us
274
275	CALL calc_scaling_parameters
276
277	CALL calc_surface_fluxes
278
279	ENDIF
280
281	END SUBROUTINE surface_layer_fluxes
282
283
284	!------------------------------------------------------------------------------!
285	! Description:
286	! ------------
287	!> Initializing actions for the surface layer routine. Basically, this involves
288	!> the preparation of a lookup table for the the bulk Richardson number vs
289	!> Obukhov length L when using the lookup table method.
290	!------------------------------------------------------------------------------!
291	SUBROUTINE init_surface_layer_fluxes
292
293	IMPLICIT NONE
294
295	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
296	num_steps_n !< Number of non-stretched zeta steps
297
298	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
299
300	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
301
302	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
303
304
305	REAL(wp) :: zeta_step, & !< Increment of zeta
306	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
307	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
308	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
309	z0_min = 0.0_wp !< Minimum value of z0 to create table
310	!
311	!-- When cloud physics is used, arrays for storing potential temperature and
312	!-- specific humidity at first grid level are required
313	IF ( cloud_physics ) THEN
314	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
315	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
316	ENDIF
317
318	!
319	!-- Allocate field for storing the horizontal velocity
320	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
321
322
323	!
324	!-- In case of runs with neutral statification, set Obukhov length to a
325	!-- large value
326	IF ( neutral ) ol = 1.0E10_wp
327
328	IF ( most_method == 'lookup' ) THEN
329
330	!
331	!-- Check for roughness heterogeneity. In that case terminate run and
332	!-- inform user
333	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
334	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
335	terminate_run_l = .TRUE.
336	ENDIF
337
338	#if defined( __parallel )
339	!
340	!-- Make a logical OR for all processes. Force termiation of model if result
341	!-- is TRUE
342	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
343	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
344	MPI_LOR, comm2d, ierr )
345	#else
346	terminate_run = terminate_run_l
347	#endif
348
349	IF ( terminate_run ) THEN
350	message_string = 'most_method = "lookup" cannot be used in ' // &
351	'combination with a prescribed roughness ' // &
352	'heterogeneity'
353	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
354	ENDIF
355
356	ALLOCATE( zeta_tmp(0:num_steps-1) )
357
358	!
359	!-- Use the lowest possible value for z_mo
360	k = MINVAL(nzb_s_inner)
361	z_mo = zu(k+1) - zw(k)
362
363	!
364	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
365	!-- available steps (num_steps). The calculation is done with negative
366	!-- values of zeta in order to simplify the stretching in the free
367	!-- convection limit for the remaining 10% of steps.
368	zeta_tmp(0) = - zeta_max
369	num_steps_n = ( num_steps * 9 / 10 ) - 1
370	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
371
372	DO l = 1, num_steps_n
373	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
374	ENDDO
375
376	!
377	!-- Calculate stretching factor for the free convection range
378	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
379	regr_old = regr
380	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
381	)**( 10.0_wp / REAL(num_steps) )
382	ENDDO
383
384	!
385	!-- Calculate z/L range from zeta_min to zeta_stretch
386	DO l = num_steps_n+1, num_steps-1
387	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
388	zeta_step = zeta_step * regr
389	ENDDO
390
391	!
392	!-- Save roughness lengths to temporary variables
393	z0h_min = z0h(nys,nxl)
394	z0_min = z0(nys,nxl)
395
396	!
397	!-- Calculate lookup table for the Richardson number versus Obukhov length
398	!-- The Richardson number (rib) is defined depending on the choice of
399	!-- boundary conditions for temperature
400	IF ( ibc_pt_b == 1 ) THEN
401	DO l = 0, num_steps-1
402	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
403	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
404	- psi_m( z_mo / ol_tab(l) ) &
405	+ psi_m( z0_min / ol_tab(l) ) &
406	)**3
407	ENDDO
408	ELSE
409	DO l = 0, num_steps-1
410	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
411	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
412	- psi_h( z_mo / ol_tab(l) ) &
413	+ psi_h( z0h_min / ol_tab(l) ) &
414	) &
415	/ ( LOG( z_mo / z0_min ) &
416	- psi_m( z_mo / ol_tab(l) ) &
417	+ psi_m( z0_min / ol_tab(l) ) &
418	)**2
419	ENDDO
420	ENDIF
421
422	!
423	!-- Determine minimum values of rib in the lookup table. Set upper limit
424	!-- to critical Richardson number (0.25)
425	rib_min = MINVAL(rib_tab)
426	rib_max = 0.25 !MAXVAL(rib_tab)
427
428	DEALLOCATE( zeta_tmp )
429	ENDIF
430
431	END SUBROUTINE init_surface_layer_fluxes
432
433
434	!------------------------------------------------------------------------------!
435	! Description:
436	! ------------
437	!> Compute the absolute value of the horizontal velocity (relative to the
438	!> surface). This is required by all methods
439	!------------------------------------------------------------------------------!
440	SUBROUTINE calc_uv_total
441
442	IMPLICIT NONE
443
444
445	!$OMP PARALLEL DO PRIVATE( k )
446	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
447	DO i = nxl, nxr
448	DO j = nys, nyn
449
450	k = nzb_s_inner(j,i)
451	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
452	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
453	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
454	- v(k,j,i) - v(k,j+1,i) ) )**2 )
455
456	!
457	!-- For too small values of the local wind, MOST does not work. A
458	!-- threshold value is thus set if required
459	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
460
461	ENDDO
462	ENDDO
463
464	!
465	!-- Values of uv_total need to be exchanged at the ghost boundaries
466	!$acc update host( uv_total )
467	CALL exchange_horiz_2d( uv_total )
468	!$acc update device( uv_total )
469
470	END SUBROUTINE calc_uv_total
471
472
473	!------------------------------------------------------------------------------!
474	! Description:
475	! ------------
476	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
477	!------------------------------------------------------------------------------!
478	SUBROUTINE calc_ol
479
480	IMPLICIT NONE
481
482	INTEGER(iwp) :: iter, & !< Newton iteration step
483	l !< look index
484
485	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
486
487	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
488	f_d_ol, & !< Derivative of f
489	ol_l, & !< Lower bound of L for Newton iteration
490	ol_m, & !< Previous value of L for Newton iteration
491	ol_old, & !< Previous time step value of L
492	ol_u !< Upper bound of L for Newton iteration
493
494	IF ( TRIM( most_method ) /= 'circular' ) THEN
495
496	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
497
498	!$OMP PARALLEL DO PRIVATE( k, z_mo )
499	!$acc kernels loop private( j, k, z_mo )
500	DO i = nxl, nxr
501	DO j = nys, nyn
502
503	k = nzb_s_inner(j,i)
504	z_mo = zu(k+1) - zw(k)
505
506	!
507	!-- Evaluate bulk Richardson number (calculation depends on
508	!-- definition based on setting of boundary conditions
509	IF ( ibc_pt_b /= 1 ) THEN
510	IF ( humidity ) THEN
511	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
512	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
513	ELSE
514	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
515	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
516	ENDIF
517	ELSE
518	!
519	!-- When using Neumann boundary conditions, the buoyancy flux
520	!-- is required but cannot be calculated at the surface, as pt
521	!-- and q are not known at the surface. Hence the values at
522	!-- first grid level are used to estimate the buoyancy flux
523	IF ( humidity ) THEN
524	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
525	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
526	* pt(k+1,j,i) * qsws(j,i) ) &
527	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
528	+ 1.0E-20_wp)
529	ELSE
530	rib(j,i) = - g * z_mo * shf(j,i) &
531	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
532	+ 1.0E-20_wp )
533	ENDIF
534	ENDIF
535
536	ENDDO
537	ENDDO
538	!$acc end data
539
540	ENDIF
541
542	!
543	!-- Calculate the Obukhov length either using a Newton iteration
544	!-- method, via a lookup table, or using the old circular way
545	IF ( TRIM( most_method ) == 'newton' ) THEN
546
547	!$OMP PARALLEL DO PRIVATE( k, z_mo )
548	!# WARNING: does not work on GPU so far because of DO-loop with
549	!# undetermined iterations
550	!!!!!!$acc kernels loop
551	DO i = nxl, nxr
552	DO j = nys, nyn
553
554	k = nzb_s_inner(j,i)
555	z_mo = zu(k+1) - zw(k)
556
557	!
558	!-- Store current value in case the Newton iteration fails
559	ol_old = ol(j,i)
560
561	!
562	!-- Ensure that the bulk Richardson number and the Obukhov
563	!-- lengtH have the same sign
564	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
565	ABS( ol(j,i) ) == ol_max ) THEN
566	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
567	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
568	ENDIF
569	!
570	!-- Iteration to find Obukhov length
571	iter = 0
572	DO
573	iter = iter + 1
574	!
575	!-- In case of divergence, use the value of the previous time step
576	IF ( iter > 1000 ) THEN
577	ol(j,i) = ol_old
578	EXIT
579	ENDIF
580
581	ol_m = ol(j,i)
582	ol_l = ol_m - 0.001_wp * ol_m
583	ol_u = ol_m + 0.001_wp * ol_m
584
585
586	IF ( ibc_pt_b /= 1 ) THEN
587	!
588	!-- Calculate f = Ri - [...]/[...]^2 = 0
589	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
590	- psi_h( z_mo / ol_m ) &
591	+ psi_h( z0h(j,i) / ol_m ) &
592	) &
593	/ ( LOG( z_mo / z0(j,i) ) &
594	- psi_m( z_mo / ol_m ) &
595	+ psi_m( z0(j,i) / ol_m ) &
596	)**2
597
598	!
599	!-- Calculate df/dL
600	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
601	- psi_h( z_mo / ol_u ) &
602	+ psi_h( z0h(j,i) / ol_u ) &
603	) &
604	/ ( LOG( z_mo / z0(j,i) ) &
605	- psi_m( z_mo / ol_u ) &
606	+ psi_m( z0(j,i) / ol_u ) &
607	)**2 &
608	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
609	- psi_h( z_mo / ol_l ) &
610	+ psi_h( z0h(j,i) / ol_l ) &
611	) &
612	/ ( LOG( z_mo / z0(j,i) ) &
613	- psi_m( z_mo / ol_l ) &
614	+ psi_m( z0(j,i) / ol_l ) &
615	)**2 &
616	) / ( ol_u - ol_l )
617	ELSE
618	!
619	!-- Calculate f = Ri - 1 /[...]^3 = 0
620	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
621	- psi_m( z_mo / ol_m ) &
622	+ psi_m( z0(j,i) / ol_m ) &
623	)**3
624
625	!
626	!-- Calculate df/dL
627	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
628	- psi_m( z_mo / ol_u ) &
629	+ psi_m( z0(j,i) / ol_u ) &
630	)**3 &
631	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
632	- psi_m( z_mo / ol_l ) &
633	+ psi_m( z0(j,i) / ol_l ) &
634	)**3 &
635	) / ( ol_u - ol_l )
636	ENDIF
637	!
638	!-- Calculate new L
639	ol(j,i) = ol_m - f / f_d_ol
640
641	!
642	!-- Ensure that the bulk Richardson number and the Obukhov
643	!-- length have the same sign and ensure convergence.
644	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
645
646	!
647	!-- If unrealistic value occurs, set L to the maximum
648	!-- value that is allowed
649	IF ( ABS( ol(j,i) ) > ol_max ) THEN
650	ol(j,i) = ol_max
651	EXIT
652	ENDIF
653	!
654	!-- Check for convergence
655	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
656	EXIT
657	ELSE
658	CYCLE
659	ENDIF
660
661	ENDDO
662
663	ENDDO
664	ENDDO
665
666	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
667
668	!$OMP PARALLEL DO PRIVATE( k, z_mo )
669	!# WARNING: does not work on GPU so far because of DO WHILE construct
670	!!!!!!$acc kernels loop
671	DO i = nxl, nxr
672	DO j = nys, nyn
673
674	!
675	!-- If the bulk Richardson number is outside the range of the lookup
676	!-- table, set it to the exceeding threshold value
677	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
678	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
679
680	!
681	!-- Find the correct index bounds for linear interpolation. As the
682	!-- Richardson number will not differ very much from time step to
683	!-- time step , use the index from the last step and search in the
684	!-- correct direction
685	l = l_bnd
686	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
687	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
688	l = l-1
689	ENDDO
690	ELSE
691	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
692	.AND. l < num_steps-1 )
693	l = l+1
694	ENDDO
695	ENDIF
696	l_bnd = l
697
698	!
699	!-- Linear interpolation to find the correct value of z/L
700	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
701	/ ( rib_tab(l) - rib_tab(l-1) ) &
702	* ( rib(j,i) - rib_tab(l-1) ) )
703
704	ENDDO
705	ENDDO
706
707	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
708
709	!$OMP PARALLEL DO PRIVATE( k, z_mo )
710	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
711	DO i = nxl, nxr
712	DO j = nys, nyn
713
714	k = nzb_s_inner(j,i)
715	z_mo = zu(k+1) - zw(k)
716
717	IF ( .NOT. humidity ) THEN
718	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
719	* ts(j,i) + 1E-30_wp )
720	ELSEIF ( cloud_physics ) THEN
721
722	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
723	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
724	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
725	* ql(k+1,j,i) ) + 1E-30_wp )
726	ELSE
727	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
728	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
729	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
730	ENDIF
731	!
732	!-- Limit the value range of the Obukhov length.
733	!-- This is necessary for very small velocities (u,v --> 0), because
734	!-- the absolute value of ol can then become very small, which in
735	!-- consequence would result in very large shear stresses and very
736	!-- small momentum fluxes (both are generally unrealistic).
737	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) < zeta_min ) &
738	ol(j,i) = z_mo / zeta_min
739	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) > zeta_max ) &
740	ol(j,i) = z_mo / zeta_max
741	ENDDO
742	ENDDO
743
744	ENDIF
745
746	!
747	!-- Values of ol at ghost point locations are needed for the evaluation
748	!-- of usws and vsws.
749	!$acc update host( ol )
750	CALL exchange_horiz_2d( ol )
751	!$acc update device( ol )
752
753	END SUBROUTINE calc_ol
754
755	!
756	!-- Calculate friction velocity u*
757	SUBROUTINE calc_us
758
759	IMPLICIT NONE
760
761	!$OMP PARALLEL DO PRIVATE( k, z_mo )
762	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
763	DO i = nxlg, nxrg
764	DO j = nysg, nyng
765
766	k = nzb_s_inner(j,i)+1
767	z_mo = zu(k+1) - zw(k)
768
769	!
770	!-- Compute u* at the scalars' grid points
771	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
772	- psi_m( z_mo / ol(j,i) ) &
773	+ psi_m( z0(j,i) / ol(j,i) ) )
774	ENDDO
775	ENDDO
776
777	END SUBROUTINE calc_us
778
779	!
780	!-- Calculate potential temperature and specific humidity at first grid level
781	SUBROUTINE calc_pt_q
782
783	IMPLICIT NONE
784
785	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
786	DO i = nxlg, nxrg
787	DO j = nysg, nyng
788	k = nzb_s_inner(j,i)+1
789	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
790	qv1(j,i) = q(k,j,i) - ql(k,j,i)
791	ENDDO
792	ENDDO
793
794	END SUBROUTINE calc_pt_q
795
796	!
797	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
798	SUBROUTINE calc_scaling_parameters
799
800	IMPLICIT NONE
801
802	!
803	!-- Data information for accelerators
804	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
805	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
806	!$acc present( vpt, vsws, zu, zw, z0, z0h )
807	!
808	!-- Compute theta*
809	IF ( constant_heatflux ) THEN
810
811	!
812	!-- For a given heat flux in the surface layer:
813	!$OMP PARALLEL DO
814	!$acc kernels loop private( j )
815	DO i = nxlg, nxrg
816	DO j = nysg, nyng
817	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
818	!
819	!-- ts must be limited, because otherwise overflow may occur in case
820	!-- of us=0 when computing ol further below
821	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
822	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
823	ENDDO
824	ENDDO
825
826	ELSE
827	!
828	!-- For a given surface temperature:
829	IF ( large_scale_forcing .AND. lsf_surf ) THEN
830	!$OMP PARALLEL DO
831	!$acc kernels loop private( j, k )
832	DO i = nxlg, nxrg
833	DO j = nysg, nyng
834	k = nzb_s_inner(j,i)
835	pt(k,j,i) = pt_surface
836	ENDDO
837	ENDDO
838	ENDIF
839
840	!$OMP PARALLEL DO PRIVATE( k, z_mo )
841	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
842	DO i = nxlg, nxrg
843	DO j = nysg, nyng
844
845	k = nzb_s_inner(j,i)
846	z_mo = zu(k+1) - zw(k)
847
848	IF ( cloud_physics ) THEN
849	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
850	/ ( LOG( z_mo / z0h(j,i) ) &
851	- psi_h( z_mo / ol(j,i) ) &
852	+ psi_h( z0h(j,i) / ol(j,i) ) )
853	ELSE
854	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
855	/ ( LOG( z_mo / z0h(j,i) ) &
856	- psi_h( z_mo / ol(j,i) ) &
857	+ psi_h( z0h(j,i) / ol(j,i) ) )
858	ENDIF
859
860	ENDDO
861	ENDDO
862	ENDIF
863
864	!
865	!-- If required compute q*
866	IF ( humidity ) THEN
867	IF ( constant_waterflux ) THEN
868	!
869	!-- For a given water flux in the surface layer
870	!$OMP PARALLEL DO
871	!$acc kernels loop private( j )
872	DO i = nxlg, nxrg
873	DO j = nysg, nyng
874	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
875	ENDDO
876	ENDDO
877
878	ELSE
879	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
880	run_coupled )
881
882	IF ( large_scale_forcing .AND. lsf_surf ) THEN
883	!$OMP PARALLEL DO
884	!$acc kernels loop private( j, k )
885	DO i = nxlg, nxrg
886	DO j = nysg, nyng
887	k = nzb_s_inner(j,i)
888	q(k,j,i) = q_surface
889	ENDDO
890	ENDDO
891	ENDIF
892
893	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
894	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
895	DO i = nxlg, nxrg
896	!$acc loop independent
897	DO j = nysg, nyng
898
899	k = nzb_s_inner(j,i)
900	z_mo = zu(k+1) - zw(k)
901
902	!
903	!-- Assume saturation for atmosphere coupled to ocean (but not
904	!-- in case of precursor runs)
905	IF ( coupled_run ) THEN
906	e_s = 6.1_wp * &
907	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
908	- 273.15_wp ) )
909	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
910	ENDIF
911
912	IF ( cloud_physics ) THEN
913	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
914	/ ( LOG( z_mo / z0q(j,i) ) &
915	- psi_h( z_mo / ol(j,i) ) &
916	+ psi_h( z0q(j,i) / ol(j,i) ) )
917
918	ELSE
919	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
920	/ ( LOG( z_mo / z0q(j,i) ) &
921	- psi_h( z_mo / ol(j,i) ) &
922	+ psi_h( z0q(j,i) / ol(j,i) ) )
923	ENDIF
924
925	ENDDO
926	ENDDO
927	ENDIF
928	ENDIF
929
930	!
931	!-- If required compute s*
932	IF ( passive_scalar ) THEN
933	IF ( constant_scalarflux ) THEN
934	!
935	!-- For a given water flux in the surface layer
936	!$OMP PARALLEL DO
937	!$acc kernels loop private( j )
938	DO i = nxlg, nxrg
939	DO j = nysg, nyng
940	ss(j,i) = -ssws(j,i) / ( us(j,i) + 1E-30_wp )
941	ENDDO
942	ENDDO
943	ENDIF
944	ENDIF
945
946
947	!
948	!-- If required compute qr* and nr*
949	IF ( cloud_physics .AND. microphysics_seifert ) &
950	THEN
951
952	!$OMP PARALLEL DO PRIVATE( k, z_mo )
953	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
954	DO i = nxlg, nxrg
955	!$acc loop independent
956	DO j = nysg, nyng
957
958	k = nzb_s_inner(j,i)
959	z_mo = zu(k+1) - zw(k)
960
961	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
962	/ ( LOG( z_mo / z0q(j,i) ) &
963	- psi_h( z_mo / ol(j,i) ) &
964	+ psi_h( z0q(j,i) / ol(j,i) ) )
965
966	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
967	/ ( LOG( z_mo / z0q(j,i) ) &
968	- psi_h( z_mo / ol(j,i) ) &
969	+ psi_h( z0q(j,i) / ol(j,i) ) )
970	ENDDO
971	ENDDO
972
973	ENDIF
974	!$acc end data
975
976	END SUBROUTINE calc_scaling_parameters
977
978
979
980	!
981	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
982	SUBROUTINE calc_surface_fluxes
983
984	IMPLICIT NONE
985
986	REAL(wp) :: ol_mid !< Grid-interpolated L
987
988	!
989	!-- Compute u'w' for the total model domain.
990	!-- First compute the corresponding component of u* and square it.
991	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
992	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
993	DO i = nxl, nxr
994	DO j = nys, nyn
995
996	k = nzb_u_inner(j,i)
997	z_mo = zu(k+1) - zw(k)
998	!
999	!-- Compute bulk Obukhov length for this point
1000	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
1001
1002	IF ( ol_mid == 0.0_wp ) THEN
1003	ol_mid = MIN(ol(j,i-1), ol(j,i))
1004	ENDIF
1005
1006	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
1007	/ ( LOG( z_mo / z0(j,i) ) &
1008	- psi_m( z_mo / ol_mid ) &
1009	+ psi_m( z0(j,i) / ol_mid ) )
1010
1011	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
1012	ENDDO
1013	ENDDO
1014
1015	!
1016	!-- Compute v'w' for the total model domain.
1017	!-- First compute the corresponding component of u* and square it.
1018	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
1019	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
1020	DO i = nxl, nxr
1021	DO j = nys, nyn
1022
1023	k = nzb_v_inner(j,i)
1024	z_mo = zu(k+1) - zw(k)
1025	!
1026	!-- Compute bulk Obukhov length for this point
1027	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
1028
1029	IF ( ol_mid == 0.0_wp ) THEN
1030	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
1031	ENDIF
1032
1033	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
1034	/ ( LOG( z_mo / z0(j,i) ) &
1035	- psi_m( z_mo / ol_mid ) &
1036	+ psi_m( z0(j,i) / ol_mid ) )
1037
1038	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
1039
1040	ENDDO
1041	ENDDO
1042
1043	!
1044	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
1045	!$acc update host( usws, vsws )
1046	CALL exchange_horiz_2d( usws )
1047	CALL exchange_horiz_2d( vsws )
1048	!$acc update device( usws, vsws )
1049
1050	!
1051	!-- Compute the vertical kinematic heat flux
1052	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
1053	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
1054	!$OMP PARALLEL DO
1055	!$acc kernels loop independent present( shf, ts, us )
1056	DO i = nxlg, nxrg
1057	!$acc loop independent
1058	DO j = nysg, nyng
1059	shf(j,i) = -ts(j,i) * us(j,i)
1060	ENDDO
1061	ENDDO
1062
1063	ENDIF
1064
1065	!
1066	!-- Compute the vertical water flux
1067	IF ( .NOT. constant_waterflux .AND. humidity .AND. &
1068	( simulated_time <= skip_time_do_lsm &
1069	.OR. .NOT. land_surface ) ) THEN
1070	!$OMP PARALLEL DO
1071	!$acc kernels loop independent present( qs, qsws, us )
1072	DO i = nxlg, nxrg
1073	!$acc loop independent
1074	DO j = nysg, nyng
1075	qsws(j,i) = -qs(j,i) * us(j,i)
1076	ENDDO
1077	ENDDO
1078
1079	ENDIF
1080
1081	!
1082	!-- Compute the vertical scalar flux
1083	IF ( .NOT. constant_scalarflux .AND. passive_scalar .AND. &
1084	( simulated_time <= skip_time_do_lsm &
1085	.OR. .NOT. land_surface ) ) THEN
1086	!$OMP PARALLEL DO
1087	!$acc kernels loop independent present( qs, qsws, us )
1088	DO i = nxlg, nxrg
1089	!$acc loop independent
1090	DO j = nysg, nyng
1091	ssws(j,i) = -ss(j,i) * us(j,i)
1092	ENDDO
1093	ENDDO
1094
1095	ENDIF
1096
1097	!
1098	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
1099	IF ( cloud_physics .AND. microphysics_seifert ) THEN
1100	!$OMP PARALLEL DO
1101	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
1102	DO i = nxlg, nxrg
1103	!$acc loop independent
1104	DO j = nysg, nyng
1105	qrsws(j,i) = -qrs(j,i) * us(j,i)
1106	nrsws(j,i) = -nrs(j,i) * us(j,i)
1107	ENDDO
1108	ENDDO
1109	ENDIF
1110
1111	!
1112	!-- Bottom boundary condition for the TKE
1113	IF ( ibc_e_b == 2 ) THEN
1114	!$OMP PARALLEL DO
1115	!$acc kernels loop independent present( e, nzb_s_inner, us )
1116	DO i = nxlg, nxrg
1117	!$acc loop independent
1118	DO j = nysg, nyng
1119	k = nzb_s_inner(j,i)
1120	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
1121	!
1122	!-- As a test: cm = 0.4
1123	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
1124	e(k,j,i) = e(k+1,j,i)
1125	ENDDO
1126	ENDDO
1127	ENDIF
1128
1129	END SUBROUTINE calc_surface_fluxes
1130
1131
1132	!
1133	!-- Integrated stability function for momentum
1134	FUNCTION psi_m( zeta )
1135
1136	USE kinds
1137
1138	IMPLICIT NONE
1139
1140	REAL(wp) :: psi_m !< Integrated similarity function result
1141	REAL(wp) :: zeta !< Stability parameter z/L
1142	REAL(wp) :: x !< dummy variable
1143
1144	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1145	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1146	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1147	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1148	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1149	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1150
1151
1152	IF ( zeta < 0.0_wp ) THEN
1153	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
1154	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1155	* ( 1.0_wp + x*2 ) 0.125_wp )
1156	ELSE
1157
1158	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1159	- bc_d_d
1160	!
1161	!-- Old version for stable conditions (only valid for z/L < 0.5)
1162	!-- psi_m = - 5.0_wp * zeta
1163
1164	ENDIF
1165
1166	END FUNCTION psi_m
1167
1168
1169	!
1170	!-- Integrated stability function for heat and moisture
1171	FUNCTION psi_h( zeta )
1172
1173	USE kinds
1174
1175	IMPLICIT NONE
1176
1177	REAL(wp) :: psi_h !< Integrated similarity function result
1178	REAL(wp) :: zeta !< Stability parameter z/L
1179	REAL(wp) :: x !< dummy variable
1180
1181	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1182	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1183	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1184	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1185	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1186	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1187
1188
1189	IF ( zeta < 0.0_wp ) THEN
1190	x = SQRT( 1.0_wp - 16.0_wp * zeta )
1191	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1192	ELSE
1193	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1194	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1195	+ 1.0_wp
1196	!
1197	!-- Old version for stable conditions (only valid for z/L < 0.5)
1198	!-- psi_h = - 5.0_wp * zeta
1199	ENDIF
1200
1201	END FUNCTION psi_h
1202
1203	END MODULE surface_layer_fluxes_mod

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

Download in other formats:

| Impressum | ©Leibniz Universität Hannover |