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1	!> @file surface_layer_fluxes.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.f90 1823 2016-04-07 08:57:52Z hoffmann $
26	!
27	! 1822 2016-04-07 07:49:42Z hoffmann
28	! icloud_scheme replaced by microphysics_*
29	!
30	! 1788 2016-03-10 11:01:04Z maronga
31	! Added parameter z0q which replaces z0h in the similarity functions for
32	! humidity.
33	! Syntax layout improved.
34	!
35	! 1757 2016-02-22 15:49:32Z maronga
36	! Minor fixes.
37	!
38	! 1749 2016-02-09 12:19:56Z raasch
39	! further OpenACC adjustments
40	!
41	! 1747 2016-02-08 12:25:53Z raasch
42	! adjustments for OpenACC usage
43	!
44	! 1709 2015-11-04 14:47:01Z maronga
45	! Bugfix: division by zero could occur when calculating rib at low wind speeds
46	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
47	! neutral = .T.
48	!
49	! 1705 2015-11-02 14:28:56Z maronga
50	! Typo removed
51	!
52	! 1697 2015-10-28 17:14:10Z raasch
53	! FORTRAN and OpenMP errors removed
54	!
55	! 1696 2015-10-27 10:03:34Z maronga
56	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
57	! course of the re-writing two additional methods have been implemented. See
58	! updated description.
59	!
60	! 1551 2015-03-03 14:18:16Z maronga
61	! Removed land surface model part. The surface fluxes are now always calculated
62	! within prandtl_fluxes, based on the given surface temperature/humidity (which
63	! is either provided by the land surface model, by large scale forcing data, or
64	! directly prescribed by the user.
65	!
66	! 1496 2014-12-02 17:25:50Z maronga
67	! Adapted for land surface model
68	!
69	! 1494 2014-11-21 17:14:03Z maronga
70	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
71	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
72	! topography for coupled runs (not tested)
73	!
74	! 1361 2014-04-16 15:17:48Z hoffmann
75	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
76	! drop concentration (nrsws) added
77	!
78	! 1340 2014-03-25 19:45:13Z kanani
79	! REAL constants defined as wp-kind
80	!
81	! 1320 2014-03-20 08:40:49Z raasch
82	! ONLY-attribute added to USE-statements,
83	! kind-parameters added to all INTEGER and REAL declaration statements,
84	! kinds are defined in new module kinds,
85	! old module precision_kind is removed,
86	! revision history before 2012 removed,
87	! comment fields (!:) to be used for variable explanations added to
88	! all variable declaration statements
89	!
90	! 1276 2014-01-15 13:40:41Z heinze
91	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
92	!
93	! 1257 2013-11-08 15:18:40Z raasch
94	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
95	!
96	! 1036 2012-10-22 13:43:42Z raasch
97	! code put under GPL (PALM 3.9)
98	!
99	! 1015 2012-09-27 09:23:24Z raasch
100	! OpenACC statements added
101	!
102	! 978 2012-08-09 08:28:32Z fricke
103	! roughness length for scalar quantities z0h added
104	!
105	! Revision 1.1 1998/01/23 10:06:06 raasch
106	! Initial revision
107	!
108	!
109	! Description:
110	! ------------
111	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
112	!> values of the variables at grid point k=1. Three different methods are
113	!> available:
114	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
115	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
116	!> slower
117	!> 3) a method using a lookup table which is fast and accurate. Note, however,
118	!> that this method cannot be used in case of roughness heterogeneity
119	!>
120	!> @todo (re)move large_scale_forcing actions
121	!> @todo check/optimize OpenMP and OpenACC directives
122	!------------------------------------------------------------------------------!
123	MODULE surface_layer_fluxes_mod
124
125	USE arrays_3d, &
126	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
127	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h, z0q
128
129	USE cloud_parameters, &
130	ONLY: l_d_cp, pt_d_t
131
132	USE constants, &
133	ONLY: pi
134
135	USE cpulog
136
137	USE control_parameters, &
138	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
139	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, &
140	initializing_actions, kappa, intermediate_timestep_count, &
141	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
142	message_string, microphysics_seifert, most_method, neutral, &
143	passive_scalar, pt_surface, q_surface, run_coupled, &
144	surface_pressure, simulated_time, terminate_run, zeta_max, &
145	zeta_min
146
147	USE indices, &
148	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
149	nzb_u_inner, nzb_v_inner
150
151	USE kinds
152
153	USE pegrid
154
155	USE land_surface_model_mod, &
156	ONLY: land_surface, skip_time_do_lsm
157
158	IMPLICIT NONE
159
160	INTEGER(iwp) :: i !< loop index x direction
161	INTEGER(iwp) :: j !< loop index y direction
162	INTEGER(iwp) :: k !< loop index z direction
163
164	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
165
166	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
167
168	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
169	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
170	uv_total !< Total velocity at first grid level
171
172	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
173	ol_tab !< Lookup table values of L
174
175	REAL(wp) :: e_s, & !< Saturation water vapor pressure
176	l_bnd = 7500, & !< Lookup table index of the last time step
177	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
178	rib_max, & !< Maximum Richardson number in lookup table
179	rib_min, & !< Minimum Richardson number in lookup table
180	z_mo !< Height of the constant flux layer where MOST is assumed
181
182
183	SAVE
184
185	PRIVATE
186
187	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
188
189	INTERFACE init_surface_layer_fluxes
190	MODULE PROCEDURE init_surface_layer_fluxes
191	END INTERFACE init_surface_layer_fluxes
192
193	INTERFACE surface_layer_fluxes
194	MODULE PROCEDURE surface_layer_fluxes
195	END INTERFACE surface_layer_fluxes
196
197
198	CONTAINS
199
200
201	!------------------------------------------------------------------------------!
202	! Description:
203	! ------------
204	!> Main routine to compute the surface fluxes
205	!------------------------------------------------------------------------------!
206	SUBROUTINE surface_layer_fluxes
207
208	IMPLICIT NONE
209
210	!
211	!-- In case cloud physics is used, it is required to derive potential
212	!-- temperature and specific humidity at first grid level from the fields pt
213	!-- and q
214	IF ( cloud_physics ) THEN
215	CALL calc_pt_q
216	ENDIF
217
218	!
219	!-- First, calculate the new Obukhov length, then new friction velocity,
220	!-- followed by the new scaling parameters (th, q, etc.), and the new
221	!-- surface fluxes if required. The old routine ("circular") requires a
222	!-- different order of calls as the scaling parameters from the previous time
223	!-- steps are used to calculate the Obukhov length
224
225	!
226	!-- Depending on setting of most_method use the "old" routine
227	IF ( most_method == 'circular' ) THEN
228
229	CALL calc_scaling_parameters
230
231	CALL calc_uv_total
232
233	IF ( .NOT. neutral ) THEN
234	CALL calc_ol
235	ENDIF
236
237	CALL calc_us
238
239	CALL calc_surface_fluxes
240
241	!
242	!-- Use either Newton iteration or a lookup table for the bulk Richardson
243	!-- number to calculate the Obukhov length
244	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
245
246	CALL calc_uv_total
247
248	IF ( .NOT. neutral ) THEN
249	CALL calc_ol
250	ENDIF
251
252	CALL calc_us
253
254	CALL calc_scaling_parameters
255
256	CALL calc_surface_fluxes
257
258	ENDIF
259
260	END SUBROUTINE surface_layer_fluxes
261
262
263	!------------------------------------------------------------------------------!
264	! Description:
265	! ------------
266	!> Initializing actions for the surface layer routine. Basically, this involves
267	!> the preparation of a lookup table for the the bulk Richardson number vs
268	!> Obukhov length L when using the lookup table method.
269	!------------------------------------------------------------------------------!
270	SUBROUTINE init_surface_layer_fluxes
271
272	IMPLICIT NONE
273
274	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
275	num_steps_n !< Number of non-stretched zeta steps
276
277	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
278
279	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
280
281	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
282
283
284	REAL(wp) :: zeta_step, & !< Increment of zeta
285	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
286	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
287	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
288	z0_min = 0.0_wp !< Minimum value of z0 to create table
289	!
290	!-- When cloud physics is used, arrays for storing potential temperature and
291	!-- specific humidity at first grid level are required
292	IF ( cloud_physics ) THEN
293	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
294	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
295	ENDIF
296
297	!
298	!-- Allocate field for storing the horizontal velocity
299	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
300
301
302	!
303	!-- In case of runs with neutral statification, set Obukhov length to a
304	!-- large value
305	IF ( neutral ) ol = 1.0E10_wp
306
307	IF ( most_method == 'lookup' ) THEN
308
309	!
310	!-- Check for roughness heterogeneity. In that case terminate run and
311	!-- inform user
312	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
313	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
314	terminate_run_l = .TRUE.
315	ENDIF
316
317	#if defined( __parallel )
318	!
319	!-- Make a logical OR for all processes. Force termiation of model if result
320	!-- is TRUE
321	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
322	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
323	MPI_LOR, comm2d, ierr )
324	#else
325	terminate_run = terminate_run_l
326	#endif
327
328	IF ( terminate_run ) THEN
329	message_string = 'most_method = "lookup" cannot be used in ' // &
330	'combination with a prescribed roughness ' // &
331	'heterogeneity'
332	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
333	ENDIF
334
335	ALLOCATE( zeta_tmp(0:num_steps-1) )
336
337	!
338	!-- Use the lowest possible value for z_mo
339	k = MINVAL(nzb_s_inner)
340	z_mo = zu(k+1) - zw(k)
341
342	!
343	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
344	!-- available steps (num_steps). The calculation is done with negative
345	!-- values of zeta in order to simplify the stretching in the free
346	!-- convection limit for the remaining 10% of steps.
347	zeta_tmp(0) = - zeta_max
348	num_steps_n = ( num_steps * 9 / 10 ) - 1
349	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
350
351	DO l = 1, num_steps_n
352	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
353	ENDDO
354
355	!
356	!-- Calculate stretching factor for the free convection range
357	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
358	regr_old = regr
359	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
360	)**( 10.0_wp / REAL(num_steps) )
361	ENDDO
362
363	!
364	!-- Calculate z/L range from zeta_min to zeta_stretch
365	DO l = num_steps_n+1, num_steps-1
366	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
367	zeta_step = zeta_step * regr
368	ENDDO
369
370	!
371	!-- Save roughness lengths to temporary variables
372	z0h_min = z0h(nys,nxl)
373	z0_min = z0(nys,nxl)
374
375	!
376	!-- Calculate lookup table for the Richardson number versus Obukhov length
377	!-- The Richardson number (rib) is defined depending on the choice of
378	!-- boundary conditions for temperature
379	IF ( ibc_pt_b == 1 ) THEN
380	DO l = 0, num_steps-1
381	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
382	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
383	- psi_m( z_mo / ol_tab(l) ) &
384	+ psi_m( z0_min / ol_tab(l) ) &
385	)**3
386	ENDDO
387	ELSE
388	DO l = 0, num_steps-1
389	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
390	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
391	- psi_h( z_mo / ol_tab(l) ) &
392	+ psi_h( z0h_min / ol_tab(l) ) &
393	) &
394	/ ( LOG( z_mo / z0_min ) &
395	- psi_m( z_mo / ol_tab(l) ) &
396	+ psi_m( z0_min / ol_tab(l) ) &
397	)**2
398	ENDDO
399	ENDIF
400
401	!
402	!-- Determine minimum values of rib in the lookup table. Set upper limit
403	!-- to critical Richardson number (0.25)
404	rib_min = MINVAL(rib_tab)
405	rib_max = 0.25 !MAXVAL(rib_tab)
406
407	DEALLOCATE( zeta_tmp )
408	ENDIF
409
410	END SUBROUTINE init_surface_layer_fluxes
411
412
413	!------------------------------------------------------------------------------!
414	! Description:
415	! ------------
416	!> Compute the absolute value of the horizontal velocity (relative to the
417	!> surface). This is required by all methods
418	!------------------------------------------------------------------------------!
419	SUBROUTINE calc_uv_total
420
421	IMPLICIT NONE
422
423
424	!$OMP PARALLEL DO PRIVATE( k )
425	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
426	DO i = nxl, nxr
427	DO j = nys, nyn
428
429	k = nzb_s_inner(j,i)
430	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
431	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
432	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
433	- v(k,j,i) - v(k,j+1,i) ) )**2 )
434
435	!
436	!-- For too small values of the local wind, MOST does not work. A
437	!-- threshold value is thus set if required
438	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
439
440	ENDDO
441	ENDDO
442
443	!
444	!-- Values of uv_total need to be exchanged at the ghost boundaries
445	!$acc update host( uv_total )
446	CALL exchange_horiz_2d( uv_total )
447	!$acc update device( uv_total )
448
449	END SUBROUTINE calc_uv_total
450
451
452	!------------------------------------------------------------------------------!
453	! Description:
454	! ------------
455	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
456	!------------------------------------------------------------------------------!
457	SUBROUTINE calc_ol
458
459	IMPLICIT NONE
460
461	INTEGER(iwp) :: iter, & !< Newton iteration step
462	l !< look index
463
464	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
465
466	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
467	f_d_ol, & !< Derivative of f
468	ol_l, & !< Lower bound of L for Newton iteration
469	ol_m, & !< Previous value of L for Newton iteration
470	ol_old, & !< Previous time step value of L
471	ol_u !< Upper bound of L for Newton iteration
472
473	IF ( TRIM( most_method ) /= 'circular' ) THEN
474
475	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
476
477	!$OMP PARALLEL DO PRIVATE( k, z_mo )
478	!$acc kernels loop private( j, k, z_mo )
479	DO i = nxl, nxr
480	DO j = nys, nyn
481
482	k = nzb_s_inner(j,i)
483	z_mo = zu(k+1) - zw(k)
484
485	!
486	!-- Evaluate bulk Richardson number (calculation depends on
487	!-- definition based on setting of boundary conditions
488	IF ( ibc_pt_b /= 1 ) THEN
489	IF ( humidity ) THEN
490	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
491	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
492	ELSE
493	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
494	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
495	ENDIF
496	ELSE
497	!
498	!-- When using Neumann boundary conditions, the buoyancy flux
499	!-- is required but cannot be calculated at the surface, as pt
500	!-- and q are not known at the surface. Hence the values at
501	!-- first grid level are used to estimate the buoyancy flux
502	IF ( humidity ) THEN
503	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
504	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
505	* pt(k+1,j,i) * qsws(j,i) ) &
506	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
507	+ 1.0E-20_wp)
508	ELSE
509	rib(j,i) = - g * z_mo * shf(j,i) &
510	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
511	+ 1.0E-20_wp )
512	ENDIF
513	ENDIF
514
515	ENDDO
516	ENDDO
517	!$acc end data
518
519	ENDIF
520
521	!
522	!-- Calculate the Obukhov length either using a Newton iteration
523	!-- method, via a lookup table, or using the old circular way
524	IF ( TRIM( most_method ) == 'newton' ) THEN
525
526	!$OMP PARALLEL DO PRIVATE( k, z_mo )
527	!# WARNING: does not work on GPU so far because of DO-loop with
528	!# undetermined iterations
529	!!!!!!$acc kernels loop
530	DO i = nxl, nxr
531	DO j = nys, nyn
532
533	k = nzb_s_inner(j,i)
534	z_mo = zu(k+1) - zw(k)
535
536	!
537	!-- Store current value in case the Newton iteration fails
538	ol_old = ol(j,i)
539
540	!
541	!-- Ensure that the bulk Richardson number and the Obukhov
542	!-- lengtH have the same sign
543	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
544	ABS( ol(j,i) ) == ol_max ) THEN
545	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
546	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
547	ENDIF
548	!
549	!-- Iteration to find Obukhov length
550	iter = 0
551	DO
552	iter = iter + 1
553	!
554	!-- In case of divergence, use the value of the previous time step
555	IF ( iter > 1000 ) THEN
556	ol(j,i) = ol_old
557	EXIT
558	ENDIF
559
560	ol_m = ol(j,i)
561	ol_l = ol_m - 0.001_wp * ol_m
562	ol_u = ol_m + 0.001_wp * ol_m
563
564
565	IF ( ibc_pt_b /= 1 ) THEN
566	!
567	!-- Calculate f = Ri - [...]/[...]^2 = 0
568	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
569	- psi_h( z_mo / ol_m ) &
570	+ psi_h( z0h(j,i) / ol_m ) &
571	) &
572	/ ( LOG( z_mo / z0(j,i) ) &
573	- psi_m( z_mo / ol_m ) &
574	+ psi_m( z0(j,i) / ol_m ) &
575	)**2
576
577	!
578	!-- Calculate df/dL
579	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
580	- psi_h( z_mo / ol_u ) &
581	+ psi_h( z0h(j,i) / ol_u ) &
582	) &
583	/ ( LOG( z_mo / z0(j,i) ) &
584	- psi_m( z_mo / ol_u ) &
585	+ psi_m( z0(j,i) / ol_u ) &
586	)**2 &
587	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
588	- psi_h( z_mo / ol_l ) &
589	+ psi_h( z0h(j,i) / ol_l ) &
590	) &
591	/ ( LOG( z_mo / z0(j,i) ) &
592	- psi_m( z_mo / ol_l ) &
593	+ psi_m( z0(j,i) / ol_l ) &
594	)**2 &
595	) / ( ol_u - ol_l )
596	ELSE
597	!
598	!-- Calculate f = Ri - 1 /[...]^3 = 0
599	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
600	- psi_m( z_mo / ol_m ) &
601	+ psi_m( z0(j,i) / ol_m ) &
602	)**3
603
604	!
605	!-- Calculate df/dL
606	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
607	- psi_m( z_mo / ol_u ) &
608	+ psi_m( z0(j,i) / ol_u ) &
609	)**3 &
610	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
611	- psi_m( z_mo / ol_l ) &
612	+ psi_m( z0(j,i) / ol_l ) &
613	)**3 &
614	) / ( ol_u - ol_l )
615	ENDIF
616	!
617	!-- Calculate new L
618	ol(j,i) = ol_m - f / f_d_ol
619
620	!
621	!-- Ensure that the bulk Richardson number and the Obukhov
622	!-- length have the same sign and ensure convergence.
623	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
624
625	!
626	!-- If unrealistic value occurs, set L to the maximum
627	!-- value that is allowed
628	IF ( ABS( ol(j,i) ) > ol_max ) THEN
629	ol(j,i) = ol_max
630	EXIT
631	ENDIF
632	!
633	!-- Check for convergence
634	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
635	EXIT
636	ELSE
637	CYCLE
638	ENDIF
639
640	ENDDO
641
642	ENDDO
643	ENDDO
644
645	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
646
647	!$OMP PARALLEL DO PRIVATE( k, z_mo )
648	!# WARNING: does not work on GPU so far because of DO WHILE construct
649	!!!!!!$acc kernels loop
650	DO i = nxl, nxr
651	DO j = nys, nyn
652
653	!
654	!-- If the bulk Richardson number is outside the range of the lookup
655	!-- table, set it to the exceeding threshold value
656	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
657	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
658
659	!
660	!-- Find the correct index bounds for linear interpolation. As the
661	!-- Richardson number will not differ very much from time step to
662	!-- time step , use the index from the last step and search in the
663	!-- correct direction
664	l = l_bnd
665	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
666	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
667	l = l-1
668	ENDDO
669	ELSE
670	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
671	.AND. l < num_steps-1 )
672	l = l+1
673	ENDDO
674	ENDIF
675	l_bnd = l
676
677	!
678	!-- Linear interpolation to find the correct value of z/L
679	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
680	/ ( rib_tab(l) - rib_tab(l-1) ) &
681	* ( rib(j,i) - rib_tab(l-1) ) )
682
683	ENDDO
684	ENDDO
685
686	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
687
688	!$OMP PARALLEL DO PRIVATE( k, z_mo )
689	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
690	DO i = nxl, nxr
691	DO j = nys, nyn
692
693	k = nzb_s_inner(j,i)
694	z_mo = zu(k+1) - zw(k)
695
696	IF ( .NOT. humidity ) THEN
697	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
698	* ts(j,i) + 1E-30_wp )
699	ELSEIF ( cloud_physics ) THEN
700
701	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
702	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
703	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
704	* ql(k+1,j,i) ) + 1E-30_wp )
705	ELSE
706	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
707	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
708	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
709	ENDIF
710	!
711	!-- Limit the value range of the Obukhov length.
712	!-- This is necessary for very small velocities (u,v --> 0), because
713	!-- the absolute value of ol can then become very small, which in
714	!-- consequence would result in very large shear stresses and very
715	!-- small momentum fluxes (both are generally unrealistic).
716	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
717	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
718
719	ENDDO
720	ENDDO
721
722	ENDIF
723
724	!
725	!-- Values of ol at ghost point locations are needed for the evaluation
726	!-- of usws and vsws.
727	!$acc update host( ol )
728	CALL exchange_horiz_2d( ol )
729	!$acc update device( ol )
730
731	END SUBROUTINE calc_ol
732
733	!
734	!-- Calculate friction velocity u*
735	SUBROUTINE calc_us
736
737	IMPLICIT NONE
738
739	!$OMP PARALLEL DO PRIVATE( k, z_mo )
740	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
741	DO i = nxlg, nxrg
742	DO j = nysg, nyng
743
744	k = nzb_s_inner(j,i)+1
745	z_mo = zu(k+1) - zw(k)
746
747	!
748	!-- Compute u* at the scalars' grid points
749	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
750	- psi_m( z_mo / ol(j,i) ) &
751	+ psi_m( z0(j,i) / ol(j,i) ) )
752	ENDDO
753	ENDDO
754
755	END SUBROUTINE calc_us
756
757	!
758	!-- Calculate potential temperature and specific humidity at first grid level
759	SUBROUTINE calc_pt_q
760
761	IMPLICIT NONE
762
763	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
764	DO i = nxlg, nxrg
765	DO j = nysg, nyng
766	k = nzb_s_inner(j,i)+1
767	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
768	qv1(j,i) = q(k,j,i) - ql(k,j,i)
769	ENDDO
770	ENDDO
771
772	END SUBROUTINE calc_pt_q
773
774	!
775	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
776	SUBROUTINE calc_scaling_parameters
777
778	IMPLICIT NONE
779
780	!
781	!-- Data information for accelerators
782	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
783	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
784	!$acc present( vpt, vsws, zu, zw, z0, z0h )
785	!
786	!-- Compute theta*
787	IF ( constant_heatflux ) THEN
788
789	!
790	!-- For a given heat flux in the surface layer:
791	!$OMP PARALLEL DO
792	!$acc kernels loop private( j )
793	DO i = nxlg, nxrg
794	DO j = nysg, nyng
795	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
796	!
797	!-- ts must be limited, because otherwise overflow may occur in case
798	!-- of us=0 when computing ol further below
799	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
800	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
801	ENDDO
802	ENDDO
803
804	ELSE
805	!
806	!-- For a given surface temperature:
807	IF ( large_scale_forcing .AND. lsf_surf ) THEN
808	!$OMP PARALLEL DO
809	!$acc kernels loop private( j, k )
810	DO i = nxlg, nxrg
811	DO j = nysg, nyng
812	k = nzb_s_inner(j,i)
813	pt(k,j,i) = pt_surface
814	ENDDO
815	ENDDO
816	ENDIF
817
818	!$OMP PARALLEL DO PRIVATE( k, z_mo )
819	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
820	DO i = nxlg, nxrg
821	DO j = nysg, nyng
822
823	k = nzb_s_inner(j,i)
824	z_mo = zu(k+1) - zw(k)
825
826	IF ( cloud_physics ) THEN
827	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
828	/ ( LOG( z_mo / z0h(j,i) ) &
829	- psi_h( z_mo / ol(j,i) ) &
830	+ psi_h( z0h(j,i) / ol(j,i) ) )
831	ELSE
832	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
833	/ ( LOG( z_mo / z0h(j,i) ) &
834	- psi_h( z_mo / ol(j,i) ) &
835	+ psi_h( z0h(j,i) / ol(j,i) ) )
836	ENDIF
837
838	ENDDO
839	ENDDO
840	ENDIF
841
842	!
843	!-- If required compute q*
844	IF ( humidity .OR. passive_scalar ) THEN
845	IF ( constant_waterflux ) THEN
846	!
847	!-- For a given water flux in the surface layer
848	!$OMP PARALLEL DO
849	!$acc kernels loop private( j )
850	DO i = nxlg, nxrg
851	DO j = nysg, nyng
852	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
853	ENDDO
854	ENDDO
855
856	ELSE
857	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
858	run_coupled )
859
860	IF ( large_scale_forcing .AND. lsf_surf ) THEN
861	!$OMP PARALLEL DO
862	!$acc kernels loop private( j, k )
863	DO i = nxlg, nxrg
864	DO j = nysg, nyng
865	k = nzb_s_inner(j,i)
866	q(k,j,i) = q_surface
867	ENDDO
868	ENDDO
869	ENDIF
870
871	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
872	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
873	DO i = nxlg, nxrg
874	!$acc loop independent
875	DO j = nysg, nyng
876
877	k = nzb_s_inner(j,i)
878	z_mo = zu(k+1) - zw(k)
879
880	!
881	!-- Assume saturation for atmosphere coupled to ocean (but not
882	!-- in case of precursor runs)
883	IF ( coupled_run ) THEN
884	e_s = 6.1_wp * &
885	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
886	- 273.15_wp ) )
887	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
888	ENDIF
889
890	IF ( cloud_physics ) THEN
891	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
892	/ ( LOG( z_mo / z0q(j,i) ) &
893	- psi_h( z_mo / ol(j,i) ) &
894	+ psi_h( z0q(j,i) / ol(j,i) ) )
895
896	ELSE
897	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
898	/ ( LOG( z_mo / z0q(j,i) ) &
899	- psi_h( z_mo / ol(j,i) ) &
900	+ psi_h( z0q(j,i) / ol(j,i) ) )
901	ENDIF
902
903	ENDDO
904	ENDDO
905	ENDIF
906	ENDIF
907
908
909	!
910	!-- If required compute qr* and nr*
911	IF ( cloud_physics .AND. microphysics_seifert ) &
912	THEN
913
914	!$OMP PARALLEL DO PRIVATE( k, z_mo )
915	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
916	DO i = nxlg, nxrg
917	!$acc loop independent
918	DO j = nysg, nyng
919
920	k = nzb_s_inner(j,i)
921	z_mo = zu(k+1) - zw(k)
922
923	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
924	/ ( LOG( z_mo / z0q(j,i) ) &
925	- psi_h( z_mo / ol(j,i) ) &
926	+ psi_h( z0q(j,i) / ol(j,i) ) )
927
928	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
929	/ ( LOG( z_mo / z0q(j,i) ) &
930	- psi_h( z_mo / ol(j,i) ) &
931	+ psi_h( z0q(j,i) / ol(j,i) ) )
932	ENDDO
933	ENDDO
934
935	ENDIF
936	!$acc end data
937
938	END SUBROUTINE calc_scaling_parameters
939
940
941
942	!
943	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
944	SUBROUTINE calc_surface_fluxes
945
946	IMPLICIT NONE
947
948	REAL(wp) :: ol_mid !< Grid-interpolated L
949
950	!
951	!-- Compute u'w' for the total model domain.
952	!-- First compute the corresponding component of u* and square it.
953	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
954	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
955	DO i = nxl, nxr
956	DO j = nys, nyn
957
958	k = nzb_u_inner(j,i)
959	z_mo = zu(k+1) - zw(k)
960	!
961	!-- Compute bulk Obukhov length for this point
962	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
963
964	IF ( ol_mid == 0.0_wp ) THEN
965	ol_mid = MIN(ol(j,i-1), ol(j,i))
966	ENDIF
967
968	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
969	/ ( LOG( z_mo / z0(j,i) ) &
970	- psi_m( z_mo / ol_mid ) &
971	+ psi_m( z0(j,i) / ol_mid ) )
972
973	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
974	ENDDO
975	ENDDO
976
977	!
978	!-- Compute v'w' for the total model domain.
979	!-- First compute the corresponding component of u* and square it.
980	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
981	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
982	DO i = nxl, nxr
983	DO j = nys, nyn
984
985	k = nzb_v_inner(j,i)
986	z_mo = zu(k+1) - zw(k)
987	!
988	!-- Compute bulk Obukhov length for this point
989	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
990
991	IF ( ol_mid == 0.0_wp ) THEN
992	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
993	ENDIF
994
995	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
996	/ ( LOG( z_mo / z0(j,i) ) &
997	- psi_m( z_mo / ol_mid ) &
998	+ psi_m( z0(j,i) / ol_mid ) )
999
1000	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
1001
1002	ENDDO
1003	ENDDO
1004
1005	!
1006	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
1007	!$acc update host( usws, vsws )
1008	CALL exchange_horiz_2d( usws )
1009	CALL exchange_horiz_2d( vsws )
1010	!$acc update device( usws, vsws )
1011
1012	!
1013	!-- Compute the vertical kinematic heat flux
1014	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
1015	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
1016	!$OMP PARALLEL DO
1017	!$acc kernels loop independent present( shf, ts, us )
1018	DO i = nxlg, nxrg
1019	!$acc loop independent
1020	DO j = nysg, nyng
1021	shf(j,i) = -ts(j,i) * us(j,i)
1022	ENDDO
1023	ENDDO
1024
1025	ENDIF
1026
1027	!
1028	!-- Compute the vertical water/scalar flux
1029	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. &
1030	passive_scalar ) .AND. ( simulated_time <= skip_time_do_lsm &
1031	.OR. .NOT. land_surface ) ) THEN
1032	!$OMP PARALLEL DO
1033	!$acc kernels loop independent present( qs, qsws, us )
1034	DO i = nxlg, nxrg
1035	!$acc loop independent
1036	DO j = nysg, nyng
1037	qsws(j,i) = -qs(j,i) * us(j,i)
1038	ENDDO
1039	ENDDO
1040
1041	ENDIF
1042
1043	!
1044	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
1045	IF ( cloud_physics .AND. microphysics_seifert ) THEN
1046	!$OMP PARALLEL DO
1047	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
1048	DO i = nxlg, nxrg
1049	!$acc loop independent
1050	DO j = nysg, nyng
1051	qrsws(j,i) = -qrs(j,i) * us(j,i)
1052	nrsws(j,i) = -nrs(j,i) * us(j,i)
1053	ENDDO
1054	ENDDO
1055	ENDIF
1056
1057	!
1058	!-- Bottom boundary condition for the TKE
1059	IF ( ibc_e_b == 2 ) THEN
1060	!$OMP PARALLEL DO
1061	!$acc kernels loop independent present( e, nzb_s_inner, us )
1062	DO i = nxlg, nxrg
1063	!$acc loop independent
1064	DO j = nysg, nyng
1065	k = nzb_s_inner(j,i)
1066	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
1067	!
1068	!-- As a test: cm = 0.4
1069	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
1070	e(k,j,i) = e(k+1,j,i)
1071	ENDDO
1072	ENDDO
1073	ENDIF
1074
1075	END SUBROUTINE calc_surface_fluxes
1076
1077
1078	!
1079	!-- Integrated stability function for momentum
1080	FUNCTION psi_m( zeta )
1081
1082	USE kinds
1083
1084	IMPLICIT NONE
1085
1086	REAL(wp) :: psi_m !< Integrated similarity function result
1087	REAL(wp) :: zeta !< Stability parameter z/L
1088	REAL(wp) :: x !< dummy variable
1089
1090	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1091	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1092	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1093	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1094	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1095	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1096
1097
1098	IF ( zeta < 0.0_wp ) THEN
1099	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
1100	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1101	* ( 1.0_wp + x*2 ) 0.125_wp )
1102	ELSE
1103
1104	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1105	- bc_d_d
1106	!
1107	!-- Old version for stable conditions (only valid for z/L < 0.5)
1108	!-- psi_m = - 5.0_wp * zeta
1109
1110	ENDIF
1111
1112	END FUNCTION psi_m
1113
1114
1115	!
1116	!-- Integrated stability function for heat and moisture
1117	FUNCTION psi_h( zeta )
1118
1119	USE kinds
1120
1121	IMPLICIT NONE
1122
1123	REAL(wp) :: psi_h !< Integrated similarity function result
1124	REAL(wp) :: zeta !< Stability parameter z/L
1125	REAL(wp) :: x !< dummy variable
1126
1127	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1128	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1129	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1130	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1131	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1132	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1133
1134
1135	IF ( zeta < 0.0_wp ) THEN
1136	x = SQRT( 1.0_wp - 16.0_wp * zeta )
1137	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1138	ELSE
1139	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1140	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1141	+ 1.0_wp
1142	!
1143	!-- Old version for stable conditions (only valid for z/L < 0.5)
1144	!-- psi_h = - 5.0_wp * zeta
1145	ENDIF
1146
1147	END FUNCTION psi_h
1148
1149	END MODULE surface_layer_fluxes_mod

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