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source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 1876

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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 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 1851 2016-04-08 13:32:50Z raasch $
26	!
27	! 1850 2016-04-08 13:29:27Z maronga
28	! Module renamed
29	!
30	!
31	! 1822 2016-04-07 07:49:42Z hoffmann
32	! icloud_scheme replaced by microphysics_*
33	!
34	! 1788 2016-03-10 11:01:04Z maronga
35	! Added parameter z0q which replaces z0h in the similarity functions for
36	! humidity.
37	! Syntax layout improved.
38	!
39	! 1757 2016-02-22 15:49:32Z maronga
40	! Minor fixes.
41	!
42	! 1749 2016-02-09 12:19:56Z raasch
43	! further OpenACC adjustments
44	!
45	! 1747 2016-02-08 12:25:53Z raasch
46	! adjustments for OpenACC usage
47	!
48	! 1709 2015-11-04 14:47:01Z maronga
49	! Bugfix: division by zero could occur when calculating rib at low wind speeds
50	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
51	! neutral = .T.
52	!
53	! 1705 2015-11-02 14:28:56Z maronga
54	! Typo removed
55	!
56	! 1697 2015-10-28 17:14:10Z raasch
57	! FORTRAN and OpenMP errors removed
58	!
59	! 1696 2015-10-27 10:03:34Z maronga
60	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
61	! course of the re-writing two additional methods have been implemented. See
62	! updated description.
63	!
64	! 1551 2015-03-03 14:18:16Z maronga
65	! Removed land surface model part. The surface fluxes are now always calculated
66	! within prandtl_fluxes, based on the given surface temperature/humidity (which
67	! is either provided by the land surface model, by large scale forcing data, or
68	! directly prescribed by the user.
69	!
70	! 1496 2014-12-02 17:25:50Z maronga
71	! Adapted for land surface model
72	!
73	! 1494 2014-11-21 17:14:03Z maronga
74	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
75	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
76	! topography for coupled runs (not tested)
77	!
78	! 1361 2014-04-16 15:17:48Z hoffmann
79	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
80	! drop concentration (nrsws) added
81	!
82	! 1340 2014-03-25 19:45:13Z kanani
83	! REAL constants defined as wp-kind
84	!
85	! 1320 2014-03-20 08:40:49Z raasch
86	! ONLY-attribute added to USE-statements,
87	! kind-parameters added to all INTEGER and REAL declaration statements,
88	! kinds are defined in new module kinds,
89	! old module precision_kind is removed,
90	! revision history before 2012 removed,
91	! comment fields (!:) to be used for variable explanations added to
92	! all variable declaration statements
93	!
94	! 1276 2014-01-15 13:40:41Z heinze
95	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
96	!
97	! 1257 2013-11-08 15:18:40Z raasch
98	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
99	!
100	! 1036 2012-10-22 13:43:42Z raasch
101	! code put under GPL (PALM 3.9)
102	!
103	! 1015 2012-09-27 09:23:24Z raasch
104	! OpenACC statements added
105	!
106	! 978 2012-08-09 08:28:32Z fricke
107	! roughness length for scalar quantities z0h added
108	!
109	! Revision 1.1 1998/01/23 10:06:06 raasch
110	! Initial revision
111	!
112	!
113	! Description:
114	! ------------
115	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
116	!> values of the variables at grid point k=1. Three different methods are
117	!> available:
118	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
119	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
120	!> slower
121	!> 3) a method using a lookup table which is fast and accurate. Note, however,
122	!> that this method cannot be used in case of roughness heterogeneity
123	!>
124	!> @todo (re)move large_scale_forcing actions
125	!> @todo check/optimize OpenMP and OpenACC directives
126	!------------------------------------------------------------------------------!
127	MODULE surface_layer_fluxes_mod
128
129	USE arrays_3d, &
130	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
131	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h, z0q
132
133	USE cloud_parameters, &
134	ONLY: l_d_cp, pt_d_t
135
136	USE constants, &
137	ONLY: pi
138
139	USE cpulog
140
141	USE control_parameters, &
142	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
143	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, &
144	initializing_actions, kappa, intermediate_timestep_count, &
145	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
146	message_string, microphysics_seifert, most_method, neutral, &
147	passive_scalar, pt_surface, q_surface, run_coupled, &
148	surface_pressure, simulated_time, terminate_run, zeta_max, &
149	zeta_min
150
151	USE indices, &
152	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
153	nzb_u_inner, nzb_v_inner
154
155	USE kinds
156
157	USE pegrid
158
159	USE land_surface_model_mod, &
160	ONLY: land_surface, skip_time_do_lsm
161
162	IMPLICIT NONE
163
164	INTEGER(iwp) :: i !< loop index x direction
165	INTEGER(iwp) :: j !< loop index y direction
166	INTEGER(iwp) :: k !< loop index z direction
167
168	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
169
170	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
171
172	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
173	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
174	uv_total !< Total velocity at first grid level
175
176	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
177	ol_tab !< Lookup table values of L
178
179	REAL(wp) :: e_s, & !< Saturation water vapor pressure
180	l_bnd = 7500, & !< Lookup table index of the last time step
181	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
182	rib_max, & !< Maximum Richardson number in lookup table
183	rib_min, & !< Minimum Richardson number in lookup table
184	z_mo !< Height of the constant flux layer where MOST is assumed
185
186
187	SAVE
188
189	PRIVATE
190
191	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
192
193	INTERFACE init_surface_layer_fluxes
194	MODULE PROCEDURE init_surface_layer_fluxes
195	END INTERFACE init_surface_layer_fluxes
196
197	INTERFACE surface_layer_fluxes
198	MODULE PROCEDURE surface_layer_fluxes
199	END INTERFACE surface_layer_fluxes
200
201
202	CONTAINS
203
204
205	!------------------------------------------------------------------------------!
206	! Description:
207	! ------------
208	!> Main routine to compute the surface fluxes
209	!------------------------------------------------------------------------------!
210	SUBROUTINE surface_layer_fluxes
211
212	IMPLICIT NONE
213
214	!
215	!-- In case cloud physics is used, it is required to derive potential
216	!-- temperature and specific humidity at first grid level from the fields pt
217	!-- and q
218	IF ( cloud_physics ) THEN
219	CALL calc_pt_q
220	ENDIF
221
222	!
223	!-- First, calculate the new Obukhov length, then new friction velocity,
224	!-- followed by the new scaling parameters (th, q, etc.), and the new
225	!-- surface fluxes if required. The old routine ("circular") requires a
226	!-- different order of calls as the scaling parameters from the previous time
227	!-- steps are used to calculate the Obukhov length
228
229	!
230	!-- Depending on setting of most_method use the "old" routine
231	IF ( most_method == 'circular' ) THEN
232
233	CALL calc_scaling_parameters
234
235	CALL calc_uv_total
236
237	IF ( .NOT. neutral ) THEN
238	CALL calc_ol
239	ENDIF
240
241	CALL calc_us
242
243	CALL calc_surface_fluxes
244
245	!
246	!-- Use either Newton iteration or a lookup table for the bulk Richardson
247	!-- number to calculate the Obukhov length
248	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
249
250	CALL calc_uv_total
251
252	IF ( .NOT. neutral ) THEN
253	CALL calc_ol
254	ENDIF
255
256	CALL calc_us
257
258	CALL calc_scaling_parameters
259
260	CALL calc_surface_fluxes
261
262	ENDIF
263
264	END SUBROUTINE surface_layer_fluxes
265
266
267	!------------------------------------------------------------------------------!
268	! Description:
269	! ------------
270	!> Initializing actions for the surface layer routine. Basically, this involves
271	!> the preparation of a lookup table for the the bulk Richardson number vs
272	!> Obukhov length L when using the lookup table method.
273	!------------------------------------------------------------------------------!
274	SUBROUTINE init_surface_layer_fluxes
275
276	IMPLICIT NONE
277
278	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
279	num_steps_n !< Number of non-stretched zeta steps
280
281	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
282
283	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
284
285	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
286
287
288	REAL(wp) :: zeta_step, & !< Increment of zeta
289	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
290	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
291	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
292	z0_min = 0.0_wp !< Minimum value of z0 to create table
293	!
294	!-- When cloud physics is used, arrays for storing potential temperature and
295	!-- specific humidity at first grid level are required
296	IF ( cloud_physics ) THEN
297	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
298	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
299	ENDIF
300
301	!
302	!-- Allocate field for storing the horizontal velocity
303	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
304
305
306	!
307	!-- In case of runs with neutral statification, set Obukhov length to a
308	!-- large value
309	IF ( neutral ) ol = 1.0E10_wp
310
311	IF ( most_method == 'lookup' ) THEN
312
313	!
314	!-- Check for roughness heterogeneity. In that case terminate run and
315	!-- inform user
316	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
317	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
318	terminate_run_l = .TRUE.
319	ENDIF
320
321	#if defined( __parallel )
322	!
323	!-- Make a logical OR for all processes. Force termiation of model if result
324	!-- is TRUE
325	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
326	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
327	MPI_LOR, comm2d, ierr )
328	#else
329	terminate_run = terminate_run_l
330	#endif
331
332	IF ( terminate_run ) THEN
333	message_string = 'most_method = "lookup" cannot be used in ' // &
334	'combination with a prescribed roughness ' // &
335	'heterogeneity'
336	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
337	ENDIF
338
339	ALLOCATE( zeta_tmp(0:num_steps-1) )
340
341	!
342	!-- Use the lowest possible value for z_mo
343	k = MINVAL(nzb_s_inner)
344	z_mo = zu(k+1) - zw(k)
345
346	!
347	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
348	!-- available steps (num_steps). The calculation is done with negative
349	!-- values of zeta in order to simplify the stretching in the free
350	!-- convection limit for the remaining 10% of steps.
351	zeta_tmp(0) = - zeta_max
352	num_steps_n = ( num_steps * 9 / 10 ) - 1
353	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
354
355	DO l = 1, num_steps_n
356	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
357	ENDDO
358
359	!
360	!-- Calculate stretching factor for the free convection range
361	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
362	regr_old = regr
363	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
364	)**( 10.0_wp / REAL(num_steps) )
365	ENDDO
366
367	!
368	!-- Calculate z/L range from zeta_min to zeta_stretch
369	DO l = num_steps_n+1, num_steps-1
370	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
371	zeta_step = zeta_step * regr
372	ENDDO
373
374	!
375	!-- Save roughness lengths to temporary variables
376	z0h_min = z0h(nys,nxl)
377	z0_min = z0(nys,nxl)
378
379	!
380	!-- Calculate lookup table for the Richardson number versus Obukhov length
381	!-- The Richardson number (rib) is defined depending on the choice of
382	!-- boundary conditions for temperature
383	IF ( ibc_pt_b == 1 ) THEN
384	DO l = 0, num_steps-1
385	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
386	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
387	- psi_m( z_mo / ol_tab(l) ) &
388	+ psi_m( z0_min / ol_tab(l) ) &
389	)**3
390	ENDDO
391	ELSE
392	DO l = 0, num_steps-1
393	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
394	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
395	- psi_h( z_mo / ol_tab(l) ) &
396	+ psi_h( z0h_min / ol_tab(l) ) &
397	) &
398	/ ( LOG( z_mo / z0_min ) &
399	- psi_m( z_mo / ol_tab(l) ) &
400	+ psi_m( z0_min / ol_tab(l) ) &
401	)**2
402	ENDDO
403	ENDIF
404
405	!
406	!-- Determine minimum values of rib in the lookup table. Set upper limit
407	!-- to critical Richardson number (0.25)
408	rib_min = MINVAL(rib_tab)
409	rib_max = 0.25 !MAXVAL(rib_tab)
410
411	DEALLOCATE( zeta_tmp )
412	ENDIF
413
414	END SUBROUTINE init_surface_layer_fluxes
415
416
417	!------------------------------------------------------------------------------!
418	! Description:
419	! ------------
420	!> Compute the absolute value of the horizontal velocity (relative to the
421	!> surface). This is required by all methods
422	!------------------------------------------------------------------------------!
423	SUBROUTINE calc_uv_total
424
425	IMPLICIT NONE
426
427
428	!$OMP PARALLEL DO PRIVATE( k )
429	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
430	DO i = nxl, nxr
431	DO j = nys, nyn
432
433	k = nzb_s_inner(j,i)
434	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
435	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
436	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
437	- v(k,j,i) - v(k,j+1,i) ) )**2 )
438
439	!
440	!-- For too small values of the local wind, MOST does not work. A
441	!-- threshold value is thus set if required
442	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
443
444	ENDDO
445	ENDDO
446
447	!
448	!-- Values of uv_total need to be exchanged at the ghost boundaries
449	!$acc update host( uv_total )
450	CALL exchange_horiz_2d( uv_total )
451	!$acc update device( uv_total )
452
453	END SUBROUTINE calc_uv_total
454
455
456	!------------------------------------------------------------------------------!
457	! Description:
458	! ------------
459	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
460	!------------------------------------------------------------------------------!
461	SUBROUTINE calc_ol
462
463	IMPLICIT NONE
464
465	INTEGER(iwp) :: iter, & !< Newton iteration step
466	l !< look index
467
468	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
469
470	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
471	f_d_ol, & !< Derivative of f
472	ol_l, & !< Lower bound of L for Newton iteration
473	ol_m, & !< Previous value of L for Newton iteration
474	ol_old, & !< Previous time step value of L
475	ol_u !< Upper bound of L for Newton iteration
476
477	IF ( TRIM( most_method ) /= 'circular' ) THEN
478
479	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
480
481	!$OMP PARALLEL DO PRIVATE( k, z_mo )
482	!$acc kernels loop private( j, k, z_mo )
483	DO i = nxl, nxr
484	DO j = nys, nyn
485
486	k = nzb_s_inner(j,i)
487	z_mo = zu(k+1) - zw(k)
488
489	!
490	!-- Evaluate bulk Richardson number (calculation depends on
491	!-- definition based on setting of boundary conditions
492	IF ( ibc_pt_b /= 1 ) THEN
493	IF ( humidity ) THEN
494	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
495	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
496	ELSE
497	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
498	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
499	ENDIF
500	ELSE
501	!
502	!-- When using Neumann boundary conditions, the buoyancy flux
503	!-- is required but cannot be calculated at the surface, as pt
504	!-- and q are not known at the surface. Hence the values at
505	!-- first grid level are used to estimate the buoyancy flux
506	IF ( humidity ) THEN
507	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
508	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
509	* pt(k+1,j,i) * qsws(j,i) ) &
510	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
511	+ 1.0E-20_wp)
512	ELSE
513	rib(j,i) = - g * z_mo * shf(j,i) &
514	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
515	+ 1.0E-20_wp )
516	ENDIF
517	ENDIF
518
519	ENDDO
520	ENDDO
521	!$acc end data
522
523	ENDIF
524
525	!
526	!-- Calculate the Obukhov length either using a Newton iteration
527	!-- method, via a lookup table, or using the old circular way
528	IF ( TRIM( most_method ) == 'newton' ) THEN
529
530	!$OMP PARALLEL DO PRIVATE( k, z_mo )
531	!# WARNING: does not work on GPU so far because of DO-loop with
532	!# undetermined iterations
533	!!!!!!$acc kernels loop
534	DO i = nxl, nxr
535	DO j = nys, nyn
536
537	k = nzb_s_inner(j,i)
538	z_mo = zu(k+1) - zw(k)
539
540	!
541	!-- Store current value in case the Newton iteration fails
542	ol_old = ol(j,i)
543
544	!
545	!-- Ensure that the bulk Richardson number and the Obukhov
546	!-- lengtH have the same sign
547	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
548	ABS( ol(j,i) ) == ol_max ) THEN
549	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
550	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
551	ENDIF
552	!
553	!-- Iteration to find Obukhov length
554	iter = 0
555	DO
556	iter = iter + 1
557	!
558	!-- In case of divergence, use the value of the previous time step
559	IF ( iter > 1000 ) THEN
560	ol(j,i) = ol_old
561	EXIT
562	ENDIF
563
564	ol_m = ol(j,i)
565	ol_l = ol_m - 0.001_wp * ol_m
566	ol_u = ol_m + 0.001_wp * ol_m
567
568
569	IF ( ibc_pt_b /= 1 ) THEN
570	!
571	!-- Calculate f = Ri - [...]/[...]^2 = 0
572	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
573	- psi_h( z_mo / ol_m ) &
574	+ psi_h( z0h(j,i) / ol_m ) &
575	) &
576	/ ( LOG( z_mo / z0(j,i) ) &
577	- psi_m( z_mo / ol_m ) &
578	+ psi_m( z0(j,i) / ol_m ) &
579	)**2
580
581	!
582	!-- Calculate df/dL
583	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
584	- psi_h( z_mo / ol_u ) &
585	+ psi_h( z0h(j,i) / ol_u ) &
586	) &
587	/ ( LOG( z_mo / z0(j,i) ) &
588	- psi_m( z_mo / ol_u ) &
589	+ psi_m( z0(j,i) / ol_u ) &
590	)**2 &
591	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
592	- psi_h( z_mo / ol_l ) &
593	+ psi_h( z0h(j,i) / ol_l ) &
594	) &
595	/ ( LOG( z_mo / z0(j,i) ) &
596	- psi_m( z_mo / ol_l ) &
597	+ psi_m( z0(j,i) / ol_l ) &
598	)**2 &
599	) / ( ol_u - ol_l )
600	ELSE
601	!
602	!-- Calculate f = Ri - 1 /[...]^3 = 0
603	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
604	- psi_m( z_mo / ol_m ) &
605	+ psi_m( z0(j,i) / ol_m ) &
606	)**3
607
608	!
609	!-- Calculate df/dL
610	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
611	- psi_m( z_mo / ol_u ) &
612	+ psi_m( z0(j,i) / ol_u ) &
613	)**3 &
614	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
615	- psi_m( z_mo / ol_l ) &
616	+ psi_m( z0(j,i) / ol_l ) &
617	)**3 &
618	) / ( ol_u - ol_l )
619	ENDIF
620	!
621	!-- Calculate new L
622	ol(j,i) = ol_m - f / f_d_ol
623
624	!
625	!-- Ensure that the bulk Richardson number and the Obukhov
626	!-- length have the same sign and ensure convergence.
627	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
628
629	!
630	!-- If unrealistic value occurs, set L to the maximum
631	!-- value that is allowed
632	IF ( ABS( ol(j,i) ) > ol_max ) THEN
633	ol(j,i) = ol_max
634	EXIT
635	ENDIF
636	!
637	!-- Check for convergence
638	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
639	EXIT
640	ELSE
641	CYCLE
642	ENDIF
643
644	ENDDO
645
646	ENDDO
647	ENDDO
648
649	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
650
651	!$OMP PARALLEL DO PRIVATE( k, z_mo )
652	!# WARNING: does not work on GPU so far because of DO WHILE construct
653	!!!!!!$acc kernels loop
654	DO i = nxl, nxr
655	DO j = nys, nyn
656
657	!
658	!-- If the bulk Richardson number is outside the range of the lookup
659	!-- table, set it to the exceeding threshold value
660	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
661	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
662
663	!
664	!-- Find the correct index bounds for linear interpolation. As the
665	!-- Richardson number will not differ very much from time step to
666	!-- time step , use the index from the last step and search in the
667	!-- correct direction
668	l = l_bnd
669	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
670	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
671	l = l-1
672	ENDDO
673	ELSE
674	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
675	.AND. l < num_steps-1 )
676	l = l+1
677	ENDDO
678	ENDIF
679	l_bnd = l
680
681	!
682	!-- Linear interpolation to find the correct value of z/L
683	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
684	/ ( rib_tab(l) - rib_tab(l-1) ) &
685	* ( rib(j,i) - rib_tab(l-1) ) )
686
687	ENDDO
688	ENDDO
689
690	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
691
692	!$OMP PARALLEL DO PRIVATE( k, z_mo )
693	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
694	DO i = nxl, nxr
695	DO j = nys, nyn
696
697	k = nzb_s_inner(j,i)
698	z_mo = zu(k+1) - zw(k)
699
700	IF ( .NOT. humidity ) THEN
701	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
702	* ts(j,i) + 1E-30_wp )
703	ELSEIF ( cloud_physics ) THEN
704
705	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
706	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
707	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
708	* ql(k+1,j,i) ) + 1E-30_wp )
709	ELSE
710	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
711	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
712	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
713	ENDIF
714	!
715	!-- Limit the value range of the Obukhov length.
716	!-- This is necessary for very small velocities (u,v --> 0), because
717	!-- the absolute value of ol can then become very small, which in
718	!-- consequence would result in very large shear stresses and very
719	!-- small momentum fluxes (both are generally unrealistic).
720	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
721	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
722
723	ENDDO
724	ENDDO
725
726	ENDIF
727
728	!
729	!-- Values of ol at ghost point locations are needed for the evaluation
730	!-- of usws and vsws.
731	!$acc update host( ol )
732	CALL exchange_horiz_2d( ol )
733	!$acc update device( ol )
734
735	END SUBROUTINE calc_ol
736
737	!
738	!-- Calculate friction velocity u*
739	SUBROUTINE calc_us
740
741	IMPLICIT NONE
742
743	!$OMP PARALLEL DO PRIVATE( k, z_mo )
744	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
745	DO i = nxlg, nxrg
746	DO j = nysg, nyng
747
748	k = nzb_s_inner(j,i)+1
749	z_mo = zu(k+1) - zw(k)
750
751	!
752	!-- Compute u* at the scalars' grid points
753	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
754	- psi_m( z_mo / ol(j,i) ) &
755	+ psi_m( z0(j,i) / ol(j,i) ) )
756	ENDDO
757	ENDDO
758
759	END SUBROUTINE calc_us
760
761	!
762	!-- Calculate potential temperature and specific humidity at first grid level
763	SUBROUTINE calc_pt_q
764
765	IMPLICIT NONE
766
767	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
768	DO i = nxlg, nxrg
769	DO j = nysg, nyng
770	k = nzb_s_inner(j,i)+1
771	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
772	qv1(j,i) = q(k,j,i) - ql(k,j,i)
773	ENDDO
774	ENDDO
775
776	END SUBROUTINE calc_pt_q
777
778	!
779	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
780	SUBROUTINE calc_scaling_parameters
781
782	IMPLICIT NONE
783
784	!
785	!-- Data information for accelerators
786	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
787	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
788	!$acc present( vpt, vsws, zu, zw, z0, z0h )
789	!
790	!-- Compute theta*
791	IF ( constant_heatflux ) THEN
792
793	!
794	!-- For a given heat flux in the surface layer:
795	!$OMP PARALLEL DO
796	!$acc kernels loop private( j )
797	DO i = nxlg, nxrg
798	DO j = nysg, nyng
799	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
800	!
801	!-- ts must be limited, because otherwise overflow may occur in case
802	!-- of us=0 when computing ol further below
803	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
804	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
805	ENDDO
806	ENDDO
807
808	ELSE
809	!
810	!-- For a given surface temperature:
811	IF ( large_scale_forcing .AND. lsf_surf ) THEN
812	!$OMP PARALLEL DO
813	!$acc kernels loop private( j, k )
814	DO i = nxlg, nxrg
815	DO j = nysg, nyng
816	k = nzb_s_inner(j,i)
817	pt(k,j,i) = pt_surface
818	ENDDO
819	ENDDO
820	ENDIF
821
822	!$OMP PARALLEL DO PRIVATE( k, z_mo )
823	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
824	DO i = nxlg, nxrg
825	DO j = nysg, nyng
826
827	k = nzb_s_inner(j,i)
828	z_mo = zu(k+1) - zw(k)
829
830	IF ( cloud_physics ) THEN
831	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
832	/ ( LOG( z_mo / z0h(j,i) ) &
833	- psi_h( z_mo / ol(j,i) ) &
834	+ psi_h( z0h(j,i) / ol(j,i) ) )
835	ELSE
836	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
837	/ ( LOG( z_mo / z0h(j,i) ) &
838	- psi_h( z_mo / ol(j,i) ) &
839	+ psi_h( z0h(j,i) / ol(j,i) ) )
840	ENDIF
841
842	ENDDO
843	ENDDO
844	ENDIF
845
846	!
847	!-- If required compute q*
848	IF ( humidity .OR. passive_scalar ) THEN
849	IF ( constant_waterflux ) THEN
850	!
851	!-- For a given water flux in the surface layer
852	!$OMP PARALLEL DO
853	!$acc kernels loop private( j )
854	DO i = nxlg, nxrg
855	DO j = nysg, nyng
856	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
857	ENDDO
858	ENDDO
859
860	ELSE
861	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
862	run_coupled )
863
864	IF ( large_scale_forcing .AND. lsf_surf ) THEN
865	!$OMP PARALLEL DO
866	!$acc kernels loop private( j, k )
867	DO i = nxlg, nxrg
868	DO j = nysg, nyng
869	k = nzb_s_inner(j,i)
870	q(k,j,i) = q_surface
871	ENDDO
872	ENDDO
873	ENDIF
874
875	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
876	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
877	DO i = nxlg, nxrg
878	!$acc loop independent
879	DO j = nysg, nyng
880
881	k = nzb_s_inner(j,i)
882	z_mo = zu(k+1) - zw(k)
883
884	!
885	!-- Assume saturation for atmosphere coupled to ocean (but not
886	!-- in case of precursor runs)
887	IF ( coupled_run ) THEN
888	e_s = 6.1_wp * &
889	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
890	- 273.15_wp ) )
891	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
892	ENDIF
893
894	IF ( cloud_physics ) THEN
895	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
896	/ ( LOG( z_mo / z0q(j,i) ) &
897	- psi_h( z_mo / ol(j,i) ) &
898	+ psi_h( z0q(j,i) / ol(j,i) ) )
899
900	ELSE
901	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
902	/ ( LOG( z_mo / z0q(j,i) ) &
903	- psi_h( z_mo / ol(j,i) ) &
904	+ psi_h( z0q(j,i) / ol(j,i) ) )
905	ENDIF
906
907	ENDDO
908	ENDDO
909	ENDIF
910	ENDIF
911
912
913	!
914	!-- If required compute qr* and nr*
915	IF ( cloud_physics .AND. microphysics_seifert ) &
916	THEN
917
918	!$OMP PARALLEL DO PRIVATE( k, z_mo )
919	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
920	DO i = nxlg, nxrg
921	!$acc loop independent
922	DO j = nysg, nyng
923
924	k = nzb_s_inner(j,i)
925	z_mo = zu(k+1) - zw(k)
926
927	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
928	/ ( LOG( z_mo / z0q(j,i) ) &
929	- psi_h( z_mo / ol(j,i) ) &
930	+ psi_h( z0q(j,i) / ol(j,i) ) )
931
932	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
933	/ ( LOG( z_mo / z0q(j,i) ) &
934	- psi_h( z_mo / ol(j,i) ) &
935	+ psi_h( z0q(j,i) / ol(j,i) ) )
936	ENDDO
937	ENDDO
938
939	ENDIF
940	!$acc end data
941
942	END SUBROUTINE calc_scaling_parameters
943
944
945
946	!
947	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
948	SUBROUTINE calc_surface_fluxes
949
950	IMPLICIT NONE
951
952	REAL(wp) :: ol_mid !< Grid-interpolated L
953
954	!
955	!-- Compute u'w' for the total model domain.
956	!-- First compute the corresponding component of u* and square it.
957	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
958	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
959	DO i = nxl, nxr
960	DO j = nys, nyn
961
962	k = nzb_u_inner(j,i)
963	z_mo = zu(k+1) - zw(k)
964	!
965	!-- Compute bulk Obukhov length for this point
966	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
967
968	IF ( ol_mid == 0.0_wp ) THEN
969	ol_mid = MIN(ol(j,i-1), ol(j,i))
970	ENDIF
971
972	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
973	/ ( LOG( z_mo / z0(j,i) ) &
974	- psi_m( z_mo / ol_mid ) &
975	+ psi_m( z0(j,i) / ol_mid ) )
976
977	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
978	ENDDO
979	ENDDO
980
981	!
982	!-- Compute v'w' for the total model domain.
983	!-- First compute the corresponding component of u* and square it.
984	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
985	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
986	DO i = nxl, nxr
987	DO j = nys, nyn
988
989	k = nzb_v_inner(j,i)
990	z_mo = zu(k+1) - zw(k)
991	!
992	!-- Compute bulk Obukhov length for this point
993	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
994
995	IF ( ol_mid == 0.0_wp ) THEN
996	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
997	ENDIF
998
999	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
1000	/ ( LOG( z_mo / z0(j,i) ) &
1001	- psi_m( z_mo / ol_mid ) &
1002	+ psi_m( z0(j,i) / ol_mid ) )
1003
1004	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
1005
1006	ENDDO
1007	ENDDO
1008
1009	!
1010	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
1011	!$acc update host( usws, vsws )
1012	CALL exchange_horiz_2d( usws )
1013	CALL exchange_horiz_2d( vsws )
1014	!$acc update device( usws, vsws )
1015
1016	!
1017	!-- Compute the vertical kinematic heat flux
1018	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
1019	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
1020	!$OMP PARALLEL DO
1021	!$acc kernels loop independent present( shf, ts, us )
1022	DO i = nxlg, nxrg
1023	!$acc loop independent
1024	DO j = nysg, nyng
1025	shf(j,i) = -ts(j,i) * us(j,i)
1026	ENDDO
1027	ENDDO
1028
1029	ENDIF
1030
1031	!
1032	!-- Compute the vertical water/scalar flux
1033	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. &
1034	passive_scalar ) .AND. ( simulated_time <= skip_time_do_lsm &
1035	.OR. .NOT. land_surface ) ) THEN
1036	!$OMP PARALLEL DO
1037	!$acc kernels loop independent present( qs, qsws, us )
1038	DO i = nxlg, nxrg
1039	!$acc loop independent
1040	DO j = nysg, nyng
1041	qsws(j,i) = -qs(j,i) * us(j,i)
1042	ENDDO
1043	ENDDO
1044
1045	ENDIF
1046
1047	!
1048	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
1049	IF ( cloud_physics .AND. microphysics_seifert ) THEN
1050	!$OMP PARALLEL DO
1051	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
1052	DO i = nxlg, nxrg
1053	!$acc loop independent
1054	DO j = nysg, nyng
1055	qrsws(j,i) = -qrs(j,i) * us(j,i)
1056	nrsws(j,i) = -nrs(j,i) * us(j,i)
1057	ENDDO
1058	ENDDO
1059	ENDIF
1060
1061	!
1062	!-- Bottom boundary condition for the TKE
1063	IF ( ibc_e_b == 2 ) THEN
1064	!$OMP PARALLEL DO
1065	!$acc kernels loop independent present( e, nzb_s_inner, us )
1066	DO i = nxlg, nxrg
1067	!$acc loop independent
1068	DO j = nysg, nyng
1069	k = nzb_s_inner(j,i)
1070	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
1071	!
1072	!-- As a test: cm = 0.4
1073	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
1074	e(k,j,i) = e(k+1,j,i)
1075	ENDDO
1076	ENDDO
1077	ENDIF
1078
1079	END SUBROUTINE calc_surface_fluxes
1080
1081
1082	!
1083	!-- Integrated stability function for momentum
1084	FUNCTION psi_m( zeta )
1085
1086	USE kinds
1087
1088	IMPLICIT NONE
1089
1090	REAL(wp) :: psi_m !< Integrated similarity function result
1091	REAL(wp) :: zeta !< Stability parameter z/L
1092	REAL(wp) :: x !< dummy variable
1093
1094	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1095	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1096	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1097	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1098	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1099	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1100
1101
1102	IF ( zeta < 0.0_wp ) THEN
1103	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
1104	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1105	* ( 1.0_wp + x*2 ) 0.125_wp )
1106	ELSE
1107
1108	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1109	- bc_d_d
1110	!
1111	!-- Old version for stable conditions (only valid for z/L < 0.5)
1112	!-- psi_m = - 5.0_wp * zeta
1113
1114	ENDIF
1115
1116	END FUNCTION psi_m
1117
1118
1119	!
1120	!-- Integrated stability function for heat and moisture
1121	FUNCTION psi_h( zeta )
1122
1123	USE kinds
1124
1125	IMPLICIT NONE
1126
1127	REAL(wp) :: psi_h !< Integrated similarity function result
1128	REAL(wp) :: zeta !< Stability parameter z/L
1129	REAL(wp) :: x !< dummy variable
1130
1131	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1132	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1133	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1134	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1135	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1136	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1137
1138
1139	IF ( zeta < 0.0_wp ) THEN
1140	x = SQRT( 1.0_wp - 16.0_wp * zeta )
1141	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1142	ELSE
1143	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1144	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1145	+ 1.0_wp
1146	!
1147	!-- Old version for stable conditions (only valid for z/L < 0.5)
1148	!-- psi_h = - 5.0_wp * zeta
1149	ENDIF
1150
1151	END FUNCTION psi_h
1152
1153	END MODULE surface_layer_fluxes_mod

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