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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 1818 2016-04-06 15:53:27Z maronga $
26	!
27	! 1788 2016-03-10 11:01:04Z maronga
28	! Added parameter z0q which replaces z0h in the similarity functions for
29	! humidity.
30	! Syntax layout improved.
31	!
32	! 1757 2016-02-22 15:49:32Z maronga
33	! Minor fixes.
34	!
35	! 1749 2016-02-09 12:19:56Z raasch
36	! further OpenACC adjustments
37	!
38	! 1747 2016-02-08 12:25:53Z raasch
39	! adjustments for OpenACC usage
40	!
41	! 1709 2015-11-04 14:47:01Z maronga
42	! Bugfix: division by zero could occur when calculating rib at low wind speeds
43	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
44	! neutral = .T.
45	!
46	! 1705 2015-11-02 14:28:56Z maronga
47	! Typo removed
48	!
49	! 1697 2015-10-28 17:14:10Z raasch
50	! FORTRAN and OpenMP errors removed
51	!
52	! 1696 2015-10-27 10:03:34Z maronga
53	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
54	! course of the re-writing two additional methods have been implemented. See
55	! updated description.
56	!
57	! 1551 2015-03-03 14:18:16Z maronga
58	! Removed land surface model part. The surface fluxes are now always calculated
59	! within prandtl_fluxes, based on the given surface temperature/humidity (which
60	! is either provided by the land surface model, by large scale forcing data, or
61	! directly prescribed by the user.
62	!
63	! 1496 2014-12-02 17:25:50Z maronga
64	! Adapted for land surface model
65	!
66	! 1494 2014-11-21 17:14:03Z maronga
67	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
68	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
69	! topography for coupled runs (not tested)
70	!
71	! 1361 2014-04-16 15:17:48Z hoffmann
72	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
73	! drop concentration (nrsws) added
74	!
75	! 1340 2014-03-25 19:45:13Z kanani
76	! REAL constants defined as wp-kind
77	!
78	! 1320 2014-03-20 08:40:49Z raasch
79	! ONLY-attribute added to USE-statements,
80	! kind-parameters added to all INTEGER and REAL declaration statements,
81	! kinds are defined in new module kinds,
82	! old module precision_kind is removed,
83	! revision history before 2012 removed,
84	! comment fields (!:) to be used for variable explanations added to
85	! all variable declaration statements
86	!
87	! 1276 2014-01-15 13:40:41Z heinze
88	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
89	!
90	! 1257 2013-11-08 15:18:40Z raasch
91	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
92	!
93	! 1036 2012-10-22 13:43:42Z raasch
94	! code put under GPL (PALM 3.9)
95	!
96	! 1015 2012-09-27 09:23:24Z raasch
97	! OpenACC statements added
98	!
99	! 978 2012-08-09 08:28:32Z fricke
100	! roughness length for scalar quantities z0h added
101	!
102	! Revision 1.1 1998/01/23 10:06:06 raasch
103	! Initial revision
104	!
105	!
106	! Description:
107	! ------------
108	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
109	!> values of the variables at grid point k=1. Three different methods are
110	!> available:
111	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
112	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
113	!> slower
114	!> 3) a method using a lookup table which is fast and accurate. Note, however,
115	!> that this method cannot be used in case of roughness heterogeneity
116	!>
117	!> @todo (re)move large_scale_forcing actions
118	!> @todo check/optimize OpenMP and OpenACC directives
119	!------------------------------------------------------------------------------!
120	MODULE surface_layer_fluxes_mod
121
122	USE arrays_3d, &
123	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
124	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h, z0q
125
126	USE cloud_parameters, &
127	ONLY: l_d_cp, pt_d_t
128
129	USE constants, &
130	ONLY: pi
131
132	USE cpulog
133
134	USE control_parameters, &
135	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
136	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, icloud_scheme, &
137	initializing_actions, kappa, intermediate_timestep_count, &
138	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
139	message_string, most_method, neutral, passive_scalar, &
140	precipitation, pt_surface, q_surface, run_coupled, &
141	surface_pressure, simulated_time, terminate_run, zeta_max, &
142	zeta_min
143
144	USE indices, &
145	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
146	nzb_u_inner, nzb_v_inner
147
148	USE kinds
149
150	USE pegrid
151
152	USE land_surface_model_mod, &
153	ONLY: land_surface, skip_time_do_lsm
154
155	IMPLICIT NONE
156
157	INTEGER(iwp) :: i !< loop index x direction
158	INTEGER(iwp) :: j !< loop index y direction
159	INTEGER(iwp) :: k !< loop index z direction
160
161	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
162
163	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
164
165	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
166	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
167	uv_total !< Total velocity at first grid level
168
169	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
170	ol_tab !< Lookup table values of L
171
172	REAL(wp) :: e_s, & !< Saturation water vapor pressure
173	l_bnd = 7500, & !< Lookup table index of the last time step
174	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
175	rib_max, & !< Maximum Richardson number in lookup table
176	rib_min, & !< Minimum Richardson number in lookup table
177	z_mo !< Height of the constant flux layer where MOST is assumed
178
179
180	SAVE
181
182	PRIVATE
183
184	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
185
186	INTERFACE init_surface_layer_fluxes
187	MODULE PROCEDURE init_surface_layer_fluxes
188	END INTERFACE init_surface_layer_fluxes
189
190	INTERFACE surface_layer_fluxes
191	MODULE PROCEDURE surface_layer_fluxes
192	END INTERFACE surface_layer_fluxes
193
194
195	CONTAINS
196
197
198	!------------------------------------------------------------------------------!
199	! Description:
200	! ------------
201	!> Main routine to compute the surface fluxes
202	!------------------------------------------------------------------------------!
203	SUBROUTINE surface_layer_fluxes
204
205	IMPLICIT NONE
206
207	!
208	!-- In case cloud physics is used, it is required to derive potential
209	!-- temperature and specific humidity at first grid level from the fields pt
210	!-- and q
211	IF ( cloud_physics ) THEN
212	CALL calc_pt_q
213	ENDIF
214
215	!
216	!-- First, calculate the new Obukhov length, then new friction velocity,
217	!-- followed by the new scaling parameters (th, q, etc.), and the new
218	!-- surface fluxes if required. The old routine ("circular") requires a
219	!-- different order of calls as the scaling parameters from the previous time
220	!-- steps are used to calculate the Obukhov length
221
222	!
223	!-- Depending on setting of most_method use the "old" routine
224	IF ( most_method == 'circular' ) THEN
225
226	CALL calc_scaling_parameters
227
228	CALL calc_uv_total
229
230	IF ( .NOT. neutral ) THEN
231	CALL calc_ol
232	ENDIF
233
234	CALL calc_us
235
236	CALL calc_surface_fluxes
237
238	!
239	!-- Use either Newton iteration or a lookup table for the bulk Richardson
240	!-- number to calculate the Obukhov length
241	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
242
243	CALL calc_uv_total
244
245	IF ( .NOT. neutral ) THEN
246	CALL calc_ol
247	ENDIF
248
249	CALL calc_us
250
251	CALL calc_scaling_parameters
252
253	CALL calc_surface_fluxes
254
255	ENDIF
256
257	END SUBROUTINE surface_layer_fluxes
258
259
260	!------------------------------------------------------------------------------!
261	! Description:
262	! ------------
263	!> Initializing actions for the surface layer routine. Basically, this involves
264	!> the preparation of a lookup table for the the bulk Richardson number vs
265	!> Obukhov length L when using the lookup table method.
266	!------------------------------------------------------------------------------!
267	SUBROUTINE init_surface_layer_fluxes
268
269	IMPLICIT NONE
270
271	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
272	num_steps_n !< Number of non-stretched zeta steps
273
274	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
275
276	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
277
278	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
279
280
281	REAL(wp) :: zeta_step, & !< Increment of zeta
282	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
283	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
284	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
285	z0_min = 0.0_wp !< Minimum value of z0 to create table
286	!
287	!-- When cloud physics is used, arrays for storing potential temperature and
288	!-- specific humidity at first grid level are required
289	IF ( cloud_physics ) THEN
290	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
291	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
292	ENDIF
293
294	!
295	!-- Allocate field for storing the horizontal velocity
296	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
297
298
299	!
300	!-- In case of runs with neutral statification, set Obukhov length to a
301	!-- large value
302	IF ( neutral ) ol = 1.0E10_wp
303
304	IF ( most_method == 'lookup' ) THEN
305
306	!
307	!-- Check for roughness heterogeneity. In that case terminate run and
308	!-- inform user
309	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
310	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
311	terminate_run_l = .TRUE.
312	ENDIF
313
314	#if defined( __parallel )
315	!
316	!-- Make a logical OR for all processes. Force termiation of model if result
317	!-- is TRUE
318	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
319	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
320	MPI_LOR, comm2d, ierr )
321	#else
322	terminate_run = terminate_run_l
323	#endif
324
325	IF ( terminate_run ) THEN
326	message_string = 'most_method = "lookup" cannot be used in ' // &
327	'combination with a prescribed roughness ' // &
328	'heterogeneity'
329	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
330	ENDIF
331
332	ALLOCATE( zeta_tmp(0:num_steps-1) )
333
334	!
335	!-- Use the lowest possible value for z_mo
336	k = MINVAL(nzb_s_inner)
337	z_mo = zu(k+1) - zw(k)
338
339	!
340	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
341	!-- available steps (num_steps). The calculation is done with negative
342	!-- values of zeta in order to simplify the stretching in the free
343	!-- convection limit for the remaining 10% of steps.
344	zeta_tmp(0) = - zeta_max
345	num_steps_n = ( num_steps * 9 / 10 ) - 1
346	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
347
348	DO l = 1, num_steps_n
349	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
350	ENDDO
351
352	!
353	!-- Calculate stretching factor for the free convection range
354	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
355	regr_old = regr
356	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
357	)**( 10.0_wp / REAL(num_steps) )
358	ENDDO
359
360	!
361	!-- Calculate z/L range from zeta_min to zeta_stretch
362	DO l = num_steps_n+1, num_steps-1
363	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
364	zeta_step = zeta_step * regr
365	ENDDO
366
367	!
368	!-- Save roughness lengths to temporary variables
369	z0h_min = z0h(nys,nxl)
370	z0_min = z0(nys,nxl)
371
372	!
373	!-- Calculate lookup table for the Richardson number versus Obukhov length
374	!-- The Richardson number (rib) is defined depending on the choice of
375	!-- boundary conditions for temperature
376	IF ( ibc_pt_b == 1 ) THEN
377	DO l = 0, num_steps-1
378	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
379	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
380	- psi_m( z_mo / ol_tab(l) ) &
381	+ psi_m( z0_min / ol_tab(l) ) &
382	)**3
383	ENDDO
384	ELSE
385	DO l = 0, num_steps-1
386	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
387	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
388	- psi_h( z_mo / ol_tab(l) ) &
389	+ psi_h( z0h_min / ol_tab(l) ) &
390	) &
391	/ ( LOG( z_mo / z0_min ) &
392	- psi_m( z_mo / ol_tab(l) ) &
393	+ psi_m( z0_min / ol_tab(l) ) &
394	)**2
395	ENDDO
396	ENDIF
397
398	!
399	!-- Determine minimum values of rib in the lookup table. Set upper limit
400	!-- to critical Richardson number (0.25)
401	rib_min = MINVAL(rib_tab)
402	rib_max = 0.25 !MAXVAL(rib_tab)
403
404	DEALLOCATE( zeta_tmp )
405	ENDIF
406
407	END SUBROUTINE init_surface_layer_fluxes
408
409
410	!------------------------------------------------------------------------------!
411	! Description:
412	! ------------
413	!> Compute the absolute value of the horizontal velocity (relative to the
414	!> surface). This is required by all methods
415	!------------------------------------------------------------------------------!
416	SUBROUTINE calc_uv_total
417
418	IMPLICIT NONE
419
420
421	!$OMP PARALLEL DO PRIVATE( k )
422	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
423	DO i = nxl, nxr
424	DO j = nys, nyn
425
426	k = nzb_s_inner(j,i)
427	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
428	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
429	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
430	- v(k,j,i) - v(k,j+1,i) ) )**2 )
431
432	!
433	!-- For too small values of the local wind, MOST does not work. A
434	!-- threshold value is thus set if required
435	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
436
437	ENDDO
438	ENDDO
439
440	!
441	!-- Values of uv_total need to be exchanged at the ghost boundaries
442	!$acc update host( uv_total )
443	CALL exchange_horiz_2d( uv_total )
444	!$acc update device( uv_total )
445
446	END SUBROUTINE calc_uv_total
447
448
449	!------------------------------------------------------------------------------!
450	! Description:
451	! ------------
452	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
453	!------------------------------------------------------------------------------!
454	SUBROUTINE calc_ol
455
456	IMPLICIT NONE
457
458	INTEGER(iwp) :: iter, & !< Newton iteration step
459	l !< look index
460
461	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
462
463	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
464	f_d_ol, & !< Derivative of f
465	ol_l, & !< Lower bound of L for Newton iteration
466	ol_m, & !< Previous value of L for Newton iteration
467	ol_old, & !< Previous time step value of L
468	ol_u !< Upper bound of L for Newton iteration
469
470	IF ( TRIM( most_method ) /= 'circular' ) THEN
471
472	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
473
474	!$OMP PARALLEL DO PRIVATE( k, z_mo )
475	!$acc kernels loop private( j, k, z_mo )
476	DO i = nxl, nxr
477	DO j = nys, nyn
478
479	k = nzb_s_inner(j,i)
480	z_mo = zu(k+1) - zw(k)
481
482	!
483	!-- Evaluate bulk Richardson number (calculation depends on
484	!-- definition based on setting of boundary conditions
485	IF ( ibc_pt_b /= 1 ) THEN
486	IF ( humidity ) THEN
487	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
488	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
489	ELSE
490	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
491	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
492	ENDIF
493	ELSE
494	!
495	!-- When using Neumann boundary conditions, the buoyancy flux
496	!-- is required but cannot be calculated at the surface, as pt
497	!-- and q are not known at the surface. Hence the values at
498	!-- first grid level are used to estimate the buoyancy flux
499	IF ( humidity ) THEN
500	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
501	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
502	* pt(k+1,j,i) * qsws(j,i) ) &
503	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
504	+ 1.0E-20_wp)
505	ELSE
506	rib(j,i) = - g * z_mo * shf(j,i) &
507	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
508	+ 1.0E-20_wp )
509	ENDIF
510	ENDIF
511
512	ENDDO
513	ENDDO
514	!$acc end data
515
516	ENDIF
517
518	!
519	!-- Calculate the Obukhov length either using a Newton iteration
520	!-- method, via a lookup table, or using the old circular way
521	IF ( TRIM( most_method ) == 'newton' ) THEN
522
523	!$OMP PARALLEL DO PRIVATE( k, z_mo )
524	!# WARNING: does not work on GPU so far because of DO-loop with
525	!# undetermined iterations
526	!!!!!!$acc kernels loop
527	DO i = nxl, nxr
528	DO j = nys, nyn
529
530	k = nzb_s_inner(j,i)
531	z_mo = zu(k+1) - zw(k)
532
533	!
534	!-- Store current value in case the Newton iteration fails
535	ol_old = ol(j,i)
536
537	!
538	!-- Ensure that the bulk Richardson number and the Obukhov
539	!-- lengtH have the same sign
540	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
541	ABS( ol(j,i) ) == ol_max ) THEN
542	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
543	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
544	ENDIF
545	!
546	!-- Iteration to find Obukhov length
547	iter = 0
548	DO
549	iter = iter + 1
550	!
551	!-- In case of divergence, use the value of the previous time step
552	IF ( iter > 1000 ) THEN
553	ol(j,i) = ol_old
554	EXIT
555	ENDIF
556
557	ol_m = ol(j,i)
558	ol_l = ol_m - 0.001_wp * ol_m
559	ol_u = ol_m + 0.001_wp * ol_m
560
561
562	IF ( ibc_pt_b /= 1 ) THEN
563	!
564	!-- Calculate f = Ri - [...]/[...]^2 = 0
565	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
566	- psi_h( z_mo / ol_m ) &
567	+ psi_h( z0h(j,i) / ol_m ) &
568	) &
569	/ ( LOG( z_mo / z0(j,i) ) &
570	- psi_m( z_mo / ol_m ) &
571	+ psi_m( z0(j,i) / ol_m ) &
572	)**2
573
574	!
575	!-- Calculate df/dL
576	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
577	- psi_h( z_mo / ol_u ) &
578	+ psi_h( z0h(j,i) / ol_u ) &
579	) &
580	/ ( LOG( z_mo / z0(j,i) ) &
581	- psi_m( z_mo / ol_u ) &
582	+ psi_m( z0(j,i) / ol_u ) &
583	)**2 &
584	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
585	- psi_h( z_mo / ol_l ) &
586	+ psi_h( z0h(j,i) / ol_l ) &
587	) &
588	/ ( LOG( z_mo / z0(j,i) ) &
589	- psi_m( z_mo / ol_l ) &
590	+ psi_m( z0(j,i) / ol_l ) &
591	)**2 &
592	) / ( ol_u - ol_l )
593	ELSE
594	!
595	!-- Calculate f = Ri - 1 /[...]^3 = 0
596	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
597	- psi_m( z_mo / ol_m ) &
598	+ psi_m( z0(j,i) / ol_m ) &
599	)**3
600
601	!
602	!-- Calculate df/dL
603	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
604	- psi_m( z_mo / ol_u ) &
605	+ psi_m( z0(j,i) / ol_u ) &
606	)**3 &
607	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
608	- psi_m( z_mo / ol_l ) &
609	+ psi_m( z0(j,i) / ol_l ) &
610	)**3 &
611	) / ( ol_u - ol_l )
612	ENDIF
613	!
614	!-- Calculate new L
615	ol(j,i) = ol_m - f / f_d_ol
616
617	!
618	!-- Ensure that the bulk Richardson number and the Obukhov
619	!-- length have the same sign and ensure convergence.
620	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
621
622	!
623	!-- If unrealistic value occurs, set L to the maximum
624	!-- value that is allowed
625	IF ( ABS( ol(j,i) ) > ol_max ) THEN
626	ol(j,i) = ol_max
627	EXIT
628	ENDIF
629	!
630	!-- Check for convergence
631	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
632	EXIT
633	ELSE
634	CYCLE
635	ENDIF
636
637	ENDDO
638
639	ENDDO
640	ENDDO
641
642	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
643
644	!$OMP PARALLEL DO PRIVATE( k, z_mo )
645	!# WARNING: does not work on GPU so far because of DO WHILE construct
646	!!!!!!$acc kernels loop
647	DO i = nxl, nxr
648	DO j = nys, nyn
649
650	!
651	!-- If the bulk Richardson number is outside the range of the lookup
652	!-- table, set it to the exceeding threshold value
653	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
654	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
655
656	!
657	!-- Find the correct index bounds for linear interpolation. As the
658	!-- Richardson number will not differ very much from time step to
659	!-- time step , use the index from the last step and search in the
660	!-- correct direction
661	l = l_bnd
662	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
663	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
664	l = l-1
665	ENDDO
666	ELSE
667	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
668	.AND. l < num_steps-1 )
669	l = l+1
670	ENDDO
671	ENDIF
672	l_bnd = l
673
674	!
675	!-- Linear interpolation to find the correct value of z/L
676	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
677	/ ( rib_tab(l) - rib_tab(l-1) ) &
678	* ( rib(j,i) - rib_tab(l-1) ) )
679
680	ENDDO
681	ENDDO
682
683	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
684
685	!$OMP PARALLEL DO PRIVATE( k, z_mo )
686	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
687	DO i = nxl, nxr
688	DO j = nys, nyn
689
690	k = nzb_s_inner(j,i)
691	z_mo = zu(k+1) - zw(k)
692
693	IF ( .NOT. humidity ) THEN
694	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
695	* ts(j,i) + 1E-30_wp )
696	ELSEIF ( cloud_physics ) THEN
697
698	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
699	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
700	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
701	* ql(k+1,j,i) ) + 1E-30_wp )
702	ELSE
703	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
704	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
705	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
706	ENDIF
707	!
708	!-- Limit the value range of the Obukhov length.
709	!-- This is necessary for very small velocities (u,v --> 0), because
710	!-- the absolute value of ol can then become very small, which in
711	!-- consequence would result in very large shear stresses and very
712	!-- small momentum fluxes (both are generally unrealistic).
713	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
714	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
715
716	ENDDO
717	ENDDO
718
719	ENDIF
720
721	!
722	!-- Values of ol at ghost point locations are needed for the evaluation
723	!-- of usws and vsws.
724	!$acc update host( ol )
725	CALL exchange_horiz_2d( ol )
726	!$acc update device( ol )
727
728	END SUBROUTINE calc_ol
729
730	!
731	!-- Calculate friction velocity u*
732	SUBROUTINE calc_us
733
734	IMPLICIT NONE
735
736	!$OMP PARALLEL DO PRIVATE( k, z_mo )
737	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
738	DO i = nxlg, nxrg
739	DO j = nysg, nyng
740
741	k = nzb_s_inner(j,i)+1
742	z_mo = zu(k+1) - zw(k)
743
744	!
745	!-- Compute u* at the scalars' grid points
746	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
747	- psi_m( z_mo / ol(j,i) ) &
748	+ psi_m( z0(j,i) / ol(j,i) ) )
749	ENDDO
750	ENDDO
751
752	END SUBROUTINE calc_us
753
754	!
755	!-- Calculate potential temperature and specific humidity at first grid level
756	SUBROUTINE calc_pt_q
757
758	IMPLICIT NONE
759
760	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
761	DO i = nxlg, nxrg
762	DO j = nysg, nyng
763	k = nzb_s_inner(j,i)+1
764	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
765	qv1(j,i) = q(k,j,i) - ql(k,j,i)
766	ENDDO
767	ENDDO
768
769	END SUBROUTINE calc_pt_q
770
771	!
772	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
773	SUBROUTINE calc_scaling_parameters
774
775	IMPLICIT NONE
776
777	!
778	!-- Data information for accelerators
779	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
780	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
781	!$acc present( vpt, vsws, zu, zw, z0, z0h )
782	!
783	!-- Compute theta*
784	IF ( constant_heatflux ) THEN
785
786	!
787	!-- For a given heat flux in the surface layer:
788	!$OMP PARALLEL DO
789	!$acc kernels loop private( j )
790	DO i = nxlg, nxrg
791	DO j = nysg, nyng
792	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
793	!
794	!-- ts must be limited, because otherwise overflow may occur in case
795	!-- of us=0 when computing ol further below
796	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
797	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
798	ENDDO
799	ENDDO
800
801	ELSE
802	!
803	!-- For a given surface temperature:
804	IF ( large_scale_forcing .AND. lsf_surf ) THEN
805	!$OMP PARALLEL DO
806	!$acc kernels loop private( j, k )
807	DO i = nxlg, nxrg
808	DO j = nysg, nyng
809	k = nzb_s_inner(j,i)
810	pt(k,j,i) = pt_surface
811	ENDDO
812	ENDDO
813	ENDIF
814
815	!$OMP PARALLEL DO PRIVATE( k, z_mo )
816	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
817	DO i = nxlg, nxrg
818	DO j = nysg, nyng
819
820	k = nzb_s_inner(j,i)
821	z_mo = zu(k+1) - zw(k)
822
823	IF ( cloud_physics ) THEN
824	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
825	/ ( LOG( z_mo / z0h(j,i) ) &
826	- psi_h( z_mo / ol(j,i) ) &
827	+ psi_h( z0h(j,i) / ol(j,i) ) )
828	ELSE
829	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
830	/ ( LOG( z_mo / z0h(j,i) ) &
831	- psi_h( z_mo / ol(j,i) ) &
832	+ psi_h( z0h(j,i) / ol(j,i) ) )
833	ENDIF
834
835	ENDDO
836	ENDDO
837	ENDIF
838
839	!
840	!-- If required compute q*
841	IF ( humidity .OR. passive_scalar ) THEN
842	IF ( constant_waterflux ) THEN
843	!
844	!-- For a given water flux in the surface layer
845	!$OMP PARALLEL DO
846	!$acc kernels loop private( j )
847	DO i = nxlg, nxrg
848	DO j = nysg, nyng
849	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
850	ENDDO
851	ENDDO
852
853	ELSE
854	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
855	run_coupled )
856
857	IF ( large_scale_forcing .AND. lsf_surf ) THEN
858	!$OMP PARALLEL DO
859	!$acc kernels loop private( j, k )
860	DO i = nxlg, nxrg
861	DO j = nysg, nyng
862	k = nzb_s_inner(j,i)
863	q(k,j,i) = q_surface
864	ENDDO
865	ENDDO
866	ENDIF
867
868	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
869	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
870	DO i = nxlg, nxrg
871	!$acc loop independent
872	DO j = nysg, nyng
873
874	k = nzb_s_inner(j,i)
875	z_mo = zu(k+1) - zw(k)
876
877	!
878	!-- Assume saturation for atmosphere coupled to ocean (but not
879	!-- in case of precursor runs)
880	IF ( coupled_run ) THEN
881	e_s = 6.1_wp * &
882	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
883	- 273.15_wp ) )
884	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
885	ENDIF
886
887	IF ( cloud_physics ) THEN
888	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
889	/ ( LOG( z_mo / z0q(j,i) ) &
890	- psi_h( z_mo / ol(j,i) ) &
891	+ psi_h( z0q(j,i) / ol(j,i) ) )
892
893	ELSE
894	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
895	/ ( LOG( z_mo / z0q(j,i) ) &
896	- psi_h( z_mo / ol(j,i) ) &
897	+ psi_h( z0q(j,i) / ol(j,i) ) )
898	ENDIF
899
900	ENDDO
901	ENDDO
902	ENDIF
903	ENDIF
904
905
906	!
907	!-- If required compute qr* and nr*
908	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) &
909	THEN
910
911	!$OMP PARALLEL DO PRIVATE( k, z_mo )
912	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
913	DO i = nxlg, nxrg
914	!$acc loop independent
915	DO j = nysg, nyng
916
917	k = nzb_s_inner(j,i)
918	z_mo = zu(k+1) - zw(k)
919
920	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
921	/ ( LOG( z_mo / z0q(j,i) ) &
922	- psi_h( z_mo / ol(j,i) ) &
923	+ psi_h( z0q(j,i) / ol(j,i) ) )
924
925	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
926	/ ( LOG( z_mo / z0q(j,i) ) &
927	- psi_h( z_mo / ol(j,i) ) &
928	+ psi_h( z0q(j,i) / ol(j,i) ) )
929	ENDDO
930	ENDDO
931
932	ENDIF
933	!$acc end data
934
935	END SUBROUTINE calc_scaling_parameters
936
937
938
939	!
940	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
941	SUBROUTINE calc_surface_fluxes
942
943	IMPLICIT NONE
944
945	REAL(wp) :: ol_mid !< Grid-interpolated L
946
947	!
948	!-- Compute u'w' for the total model domain.
949	!-- First compute the corresponding component of u* and square it.
950	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
951	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
952	DO i = nxl, nxr
953	DO j = nys, nyn
954
955	k = nzb_u_inner(j,i)
956	z_mo = zu(k+1) - zw(k)
957	!
958	!-- Compute bulk Obukhov length for this point
959	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
960
961	IF ( ol_mid == 0.0_wp ) THEN
962	ol_mid = MIN(ol(j,i-1), ol(j,i))
963	ENDIF
964
965	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
966	/ ( LOG( z_mo / z0(j,i) ) &
967	- psi_m( z_mo / ol_mid ) &
968	+ psi_m( z0(j,i) / ol_mid ) )
969
970	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
971	ENDDO
972	ENDDO
973
974	!
975	!-- Compute v'w' for the total model domain.
976	!-- First compute the corresponding component of u* and square it.
977	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
978	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
979	DO i = nxl, nxr
980	DO j = nys, nyn
981
982	k = nzb_v_inner(j,i)
983	z_mo = zu(k+1) - zw(k)
984	!
985	!-- Compute bulk Obukhov length for this point
986	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
987
988	IF ( ol_mid == 0.0_wp ) THEN
989	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
990	ENDIF
991
992	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
993	/ ( LOG( z_mo / z0(j,i) ) &
994	- psi_m( z_mo / ol_mid ) &
995	+ psi_m( z0(j,i) / ol_mid ) )
996
997	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
998
999	ENDDO
1000	ENDDO
1001
1002	!
1003	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
1004	!$acc update host( usws, vsws )
1005	CALL exchange_horiz_2d( usws )
1006	CALL exchange_horiz_2d( vsws )
1007	!$acc update device( usws, vsws )
1008
1009	!
1010	!-- Compute the vertical kinematic heat flux
1011	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
1012	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
1013	!$OMP PARALLEL DO
1014	!$acc kernels loop independent present( shf, ts, us )
1015	DO i = nxlg, nxrg
1016	!$acc loop independent
1017	DO j = nysg, nyng
1018	shf(j,i) = -ts(j,i) * us(j,i)
1019	ENDDO
1020	ENDDO
1021
1022	ENDIF
1023
1024	!
1025	!-- Compute the vertical water/scalar flux
1026	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. &
1027	passive_scalar ) .AND. ( simulated_time <= skip_time_do_lsm &
1028	.OR. .NOT. land_surface ) ) THEN
1029	!$OMP PARALLEL DO
1030	!$acc kernels loop independent present( qs, qsws, us )
1031	DO i = nxlg, nxrg
1032	!$acc loop independent
1033	DO j = nysg, nyng
1034	qsws(j,i) = -qs(j,i) * us(j,i)
1035	ENDDO
1036	ENDDO
1037
1038	ENDIF
1039
1040	!
1041	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
1042	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
1043	precipitation ) THEN
1044	!$OMP PARALLEL DO
1045	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
1046	DO i = nxlg, nxrg
1047	!$acc loop independent
1048	DO j = nysg, nyng
1049	qrsws(j,i) = -qrs(j,i) * us(j,i)
1050	nrsws(j,i) = -nrs(j,i) * us(j,i)
1051	ENDDO
1052	ENDDO
1053	ENDIF
1054
1055	!
1056	!-- Bottom boundary condition for the TKE
1057	IF ( ibc_e_b == 2 ) THEN
1058	!$OMP PARALLEL DO
1059	!$acc kernels loop independent present( e, nzb_s_inner, us )
1060	DO i = nxlg, nxrg
1061	!$acc loop independent
1062	DO j = nysg, nyng
1063	k = nzb_s_inner(j,i)
1064	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
1065	!
1066	!-- As a test: cm = 0.4
1067	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
1068	e(k,j,i) = e(k+1,j,i)
1069	ENDDO
1070	ENDDO
1071	ENDIF
1072
1073	END SUBROUTINE calc_surface_fluxes
1074
1075
1076	!
1077	!-- Integrated stability function for momentum
1078	FUNCTION psi_m( zeta )
1079
1080	USE kinds
1081
1082	IMPLICIT NONE
1083
1084	REAL(wp) :: psi_m !< Integrated similarity function result
1085	REAL(wp) :: zeta !< Stability parameter z/L
1086	REAL(wp) :: x !< dummy variable
1087
1088	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1089	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1090	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1091	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1092	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1093	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1094
1095
1096	IF ( zeta < 0.0_wp ) THEN
1097	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
1098	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1099	* ( 1.0_wp + x*2 ) 0.125_wp )
1100	ELSE
1101
1102	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1103	- bc_d_d
1104	!
1105	!-- Old version for stable conditions (only valid for z/L < 0.5)
1106	!-- psi_m = - 5.0_wp * zeta
1107
1108	ENDIF
1109
1110	END FUNCTION psi_m
1111
1112
1113	!
1114	!-- Integrated stability function for heat and moisture
1115	FUNCTION psi_h( zeta )
1116
1117	USE kinds
1118
1119	IMPLICIT NONE
1120
1121	REAL(wp) :: psi_h !< Integrated similarity function result
1122	REAL(wp) :: zeta !< Stability parameter z/L
1123	REAL(wp) :: x !< dummy variable
1124
1125	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1126	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1127	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1128	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1129	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1130	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1131
1132
1133	IF ( zeta < 0.0_wp ) THEN
1134	x = SQRT( 1.0_wp - 16.0_wp * zeta )
1135	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1136	ELSE
1137	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1138	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1139	+ 1.0_wp
1140	!
1141	!-- Old version for stable conditions (only valid for z/L < 0.5)
1142	!-- psi_h = - 5.0_wp * zeta
1143	ENDIF
1144
1145	END FUNCTION psi_h
1146
1147	END MODULE surface_layer_fluxes_mod

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