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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1703

Last change on this file since 1703 was 1698, checked in by raasch, 9 years ago
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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 1997-2015 Leibniz Universitaet Hannover
17	!
18	!--------------------------------------------------------------------------------!
19	! Current revisions:
20	! -----------------
21	!
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: surface_layer_fluxes.f90 1698 2015-10-28 17:26:17Z raasch $
26	!
27	! 1697 2015-10-28 17:14:10Z raasch
28	! FORTRAN and OpenMP errors removed
29	!
30	! 1696 2015-10-27 10:03:34Z maronga
31	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
32	! course of the re-writing two additional methods have been implemented. See
33	! updated description.
34	!
35	! 1551 2015-03-03 14:18:16Z maronga
36	! Removed land surface model part. The surface fluxes are now always calculated
37	! within prandtl_fluxes, based on the given surface temperature/humidity (which
38	! is either provided by the land surface model, by large scale forcing data, or
39	! directly prescribed by the user.
40	!
41	! 1496 2014-12-02 17:25:50Z maronga
42	! Adapted for land surface model
43	!
44	! 1494 2014-11-21 17:14:03Z maronga
45	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
46	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
47	! topography for coupled runs (not tested)
48	!
49	! 1361 2014-04-16 15:17:48Z hoffmann
50	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
51	! drop concentration (nrsws) added
52	!
53	! 1340 2014-03-25 19:45:13Z kanani
54	! REAL constants defined as wp-kind
55	!
56	! 1320 2014-03-20 08:40:49Z raasch
57	! ONLY-attribute added to USE-statements,
58	! kind-parameters added to all INTEGER and REAL declaration statements,
59	! kinds are defined in new module kinds,
60	! old module precision_kind is removed,
61	! revision history before 2012 removed,
62	! comment fields (!:) to be used for variable explanations added to
63	! all variable declaration statements
64	!
65	! 1276 2014-01-15 13:40:41Z heinze
66	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
67	!
68	! 1257 2013-11-08 15:18:40Z raasch
69	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
70	!
71	! 1036 2012-10-22 13:43:42Z raasch
72	! code put under GPL (PALM 3.9)
73	!
74	! 1015 2012-09-27 09:23:24Z raasch
75	! OpenACC statements added
76	!
77	! 978 2012-08-09 08:28:32Z fricke
78	! roughness length for scalar quantities z0h added
79	!
80	! Revision 1.1 1998/01/23 10:06:06 raasch
81	! Initial revision
82	!
83	!
84	! Description:
85	! ------------
86	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
87	!> values of the variables at grid point k=1. Three different methods are
88	!> available:
89	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
90	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
91	!> slower
92	!> 3) a method using a lookup table which is fast and accurate. Note, however,
93	!> that this method cannot be used in case of roughness heterogeneity
94	!>
95	!> @todo limiting of uv_total might be required in some cases
96	!> @todo (re)move large_scale_forcing actions
97	!> @todo check/optimize OpenMP and OpenACC directives
98	!------------------------------------------------------------------------------!
99	MODULE surface_layer_fluxes_mod
100
101	USE arrays_3d, &
102	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
103	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h
104
105	USE cloud_parameters, &
106	ONLY: l_d_cp, pt_d_t
107
108	USE constants, &
109	ONLY: pi
110
111	USE cpulog
112
113	USE control_parameters, &
114	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
115	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, icloud_scheme, &
116	initializing_actions, kappa, intermediate_timestep_count, &
117	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
118	message_string, most_method, neutral, passive_scalar, &
119	precipitation, pt_surface, q_surface, run_coupled, &
120	surface_pressure, simulated_time, terminate_run, zeta_max, &
121	zeta_min
122
123	USE indices, &
124	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
125	nzb_u_inner, nzb_v_inner
126
127	USE kinds
128
129	USE pegrid
130
131	USE land_surface_model_mod, &
132	ONLY: land_surface, skip_time_do_lsm
133
134	IMPLICIT NONE
135
136	INTEGER(iwp) :: i !< loop index x direction
137	INTEGER(iwp) :: j !< loop index y direction
138	INTEGER(iwp) :: k !< loop indey z direction
139
140	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
141
142	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
143
144	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
145	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
146	uv_total !< Total velocity at first grid level
147
148	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
149	ol_tab !< Lookup table values of L
150
151	REAL(wp) :: e_s, & !< Saturation water vapor pressure
152	l_bnd = 7500, & !< Lookup table index of the last time step
153	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
154	rib_max, & !< Maximum Richardson number in lookup table
155	rib_min, & !< Minimum Richardson number in lookup table
156	z_mo !< Height of the constant flux layer where MOST is assumed
157
158
159	SAVE
160
161	PRIVATE
162
163	PUBLIC init_surface_layer_fluxes, surface_layer_fluxes
164
165	INTERFACE init_surface_layer_fluxes
166	MODULE PROCEDURE init_surface_layer_fluxes
167	END INTERFACE init_surface_layer_fluxes
168
169	INTERFACE surface_layer_fluxes
170	MODULE PROCEDURE surface_layer_fluxes
171	END INTERFACE surface_layer_fluxes
172
173
174	CONTAINS
175
176
177	!------------------------------------------------------------------------------!
178	! Description:
179	! ------------
180	!> Main routine to compute the surface fluxes
181	!------------------------------------------------------------------------------!
182	SUBROUTINE surface_layer_fluxes
183
184	IMPLICIT NONE
185
186	!
187	!-- In case cloud physics is used, it is required to derive potential
188	!-- temperature and specific humidity at first grid level from the fields pt
189	!-- and q
190	IF ( cloud_physics ) THEN
191	CALL calc_pt_q
192	ENDIF
193
194	!
195	!-- First, calculate the new Obukhov length, then new friction velocity,
196	!-- followed by the new scaling parameters (th, q, etc.), and the new
197	!-- surface fluxes if required. The old routine ("circular") requires a
198	!-- different order of calls as the scaling parameters from the previous time
199	!-- steps are used to calculate the Obukhov length
200
201	!
202	!-- Depending on setting of most_method use the "old" routine
203	IF ( most_method == 'circular' ) THEN
204
205	CALL calc_scaling_parameters
206
207	IF ( .NOT. neutral ) THEN
208	CALL calc_ol
209	ENDIF
210
211	CALL calc_us
212
213	CALL calc_surface_fluxes
214
215	!
216	!-- Use either Newton iteration or a lookup table for the bulk Richardson
217	!-- number to calculate the Obukhov length
218	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
219
220	IF ( .NOT. neutral ) THEN
221	CALL calc_ol
222	ENDIF
223
224	CALL calc_us
225
226	CALL calc_scaling_parameters
227
228	CALL calc_surface_fluxes
229
230	ENDIF
231
232	END SUBROUTINE surface_layer_fluxes
233
234
235	!------------------------------------------------------------------------------!
236	! Description:
237	! ------------
238	!> Initializing actions for the surface layer routine. Basically, this involves
239	!> the preparation of a lookup table for the the bulk Richardson number vs
240	!> Obukhov length L when using the lookup table method.
241	!------------------------------------------------------------------------------!
242	SUBROUTINE init_surface_layer_fluxes
243
244	IMPLICIT NONE
245
246	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
247	num_steps_n !< Number of non-stretched zeta steps
248
249	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
250
251	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
252
253	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
254
255
256	REAL(wp) :: zeta_step, & !< Increment of zeta
257	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
258	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
259	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
260	z0_min = 0.0_wp !< Minimum value of z0 to create table
261	!
262	!-- When cloud physics is used, arrays for storing potential temperature and
263	!-- specific humidity at first grid level are required
264	IF ( cloud_physics ) THEN
265	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
266	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
267	ENDIF
268
269	!
270	!-- Allocate field for storing the horizontal velocity
271	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
272
273	IF ( most_method == 'lookup' ) THEN
274
275	!
276	!-- Check for roughness heterogeneity. In that case terminate run and
277	!-- inform user
278	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
279	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
280	terminate_run_l = .TRUE.
281	ENDIF
282
283	#if defined( __parallel )
284	!
285	!-- Make a logical OR for all processes. Force termiation of model if result
286	!-- is TRUE
287	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
288	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
289	MPI_LOR, comm2d, ierr )
290	#else
291	terminate_run = terminate_run_l
292	#endif
293
294	IF ( terminate_run ) THEN
295	message_string = 'most_method = "lookup" cannot be used in ' // &
296	'combination with a prescribed roughness ' // &
297	'heterogeneity'
298	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
299	ENDIF
300
301	ALLOCATE( zeta_tmp(0:num_steps-1) )
302
303	!
304	!-- Use the lowest possible value for z_mo
305	k = MINVAL(nzb_s_inner)
306	z_mo = zu(k+1) - zw(k)
307
308	!
309	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
310	!-- available steps (num_steps). The calculation is done with negative
311	!-- values of zeta in order to simplify the stretching in the free
312	!-- convection limit for the remaining 10% of steps.
313	zeta_tmp(0) = - zeta_max
314	num_steps_n = ( num_steps * 9 / 10 ) - 1
315	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
316
317	DO l = 1, num_steps_n
318	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
319	ENDDO
320
321	!
322	!-- Calculate stretching factor for the free convection range
323	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
324	regr_old = regr
325	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
326	)**( 10.0_wp / REAL(num_steps) )
327	ENDDO
328
329	!
330	!-- Calculate z/L range from zeta_min to zeta_stretch
331	DO l = num_steps_n+1, num_steps-1
332	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
333	zeta_step = zeta_step * regr
334	ENDDO
335
336	!
337	!-- Invert array and switch sign, then calculate Obukhov length and bulk
338	!-- Richardson number
339	z0h_min = MINVAL(z0h)
340	z0_min = MINVAL(z0)
341
342	!
343	!-- Calculate lookup table for the Richardson number versus Obukhov length
344	!-- The Richardson number (rib) is defined depending on the choice of
345	!-- boundary conditions for temperature
346	IF ( ibc_pt_b == 1 ) THEN
347	DO l = 0, num_steps-1
348	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
349	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
350	- psi_m( z_mo / ol_tab(l) ) &
351	+ psi_m( z0_min / ol_tab(l) ) &
352	)**3
353	ENDDO
354	ELSE
355	DO l = 0, num_steps-1
356	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
357	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
358	- psi_h( z_mo / ol_tab(l) ) &
359	+ psi_h( z0h_min / ol_tab(l) ) &
360	) &
361	/ ( LOG( z_mo / z0_min ) &
362	- psi_m( z_mo / ol_tab(l) ) &
363	+ psi_m( z0_min / ol_tab(l) ) &
364	)**2
365	ENDDO
366	ENDIF
367
368	!
369	!-- Determine minimum values of rib in the lookup table. Set upper limit
370	!-- to critical Richardson number (0.25)
371	rib_min = MINVAL(rib_tab)
372	rib_max = 0.25 !MAXVAL(rib_tab)
373
374	DEALLOCATE( zeta_tmp )
375	ENDIF
376
377	END SUBROUTINE init_surface_layer_fluxes
378
379
380	!------------------------------------------------------------------------------!
381	! Description:
382	! ------------
383	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
384	!------------------------------------------------------------------------------!
385	SUBROUTINE calc_ol
386
387	IMPLICIT NONE
388
389	INTEGER(iwp) :: iter, & !< Newton iteration step
390	l !< look index
391
392	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
393
394	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
395	f_d_ol, & !< Derivative of f
396	ol_l, & !< Lower bound of L for Newton iteration
397	ol_m, & !< Previous value of L for Newton iteration
398	ol_old, & !< Previous time step value of L
399	ol_u !< Upper bound of L for Newton iteration
400
401	!
402	!-- Compute the absolute value of the horizontal velocity (relative to the
403	!-- surface). This is required by all methods
404	!$OMP PARALLEL DO PRIVATE( k, z_mo )
405	!$acc kernels loop
406	DO i = nxl, nxr
407	DO j = nys, nyn
408
409	k = nzb_s_inner(j,i)
410
411	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
412	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
413	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
414	- v(k,j,i) - v(k,j+1,i) ) )**2 )
415
416	!
417	!-- For too small values of the local wind, MOST does not work. A
418	!-- threshold value is thus set if required
419	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
420
421	ENDDO
422	ENDDO
423
424	!
425	!-- Values of uv_total need to be exchanged at the ghost boundaries
426	!$acc update host( uv_total )
427	CALL exchange_horiz_2d( uv_total )
428	!$acc update device( uv_total )
429
430	IF ( TRIM( most_method ) /= 'circular' ) THEN
431
432	!$OMP PARALLEL DO PRIVATE( k, z_mo )
433	!$acc kernels loop
434	DO i = nxl, nxr
435	DO j = nys, nyn
436
437	k = nzb_s_inner(j,i)
438	z_mo = zu(k+1) - zw(k)
439
440	!
441	!-- Evaluate bulk Richardson number (calculation depends on
442	!-- definition based on setting of boundary conditions
443	IF ( ibc_pt_b /= 1 ) THEN
444	IF ( humidity ) THEN
445	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
446	/ ( uv_total(j,i)*2 vpt(k+1,j,i) )
447	ELSE
448	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
449	/ ( uv_total(j,i)*2 pt(k+1,j,i) )
450	ENDIF
451	ELSE
452	!
453	!-- When using Neumann boundary conditions, the buoyancy flux
454	!-- is required but cannot be calculated at the surface, as pt
455	!-- and q are not known at the surface. Hence the values at
456	!-- first grid level are used to estimate the buoyancy flux
457	IF ( humidity ) THEN
458	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
459	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
460	* pt(k+1,j,i) * qsws(j,i) ) &
461	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2 )
462	ELSE
463	rib(j,i) = - g * z_mo * shf(j,i) &
464	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 )
465	ENDIF
466	ENDIF
467
468	ENDDO
469	ENDDO
470
471	ENDIF
472
473	!
474	!-- Calculate the Obukhov length either using a Newton iteration
475	!-- method, via a lookup table, or using the old circular way
476	IF ( TRIM( most_method ) == 'newton' ) THEN
477
478	!$OMP PARALLEL DO PRIVATE( k, z_mo )
479	!$acc kernels loop
480	DO i = nxl, nxr
481	DO j = nys, nyn
482
483	k = nzb_s_inner(j,i)
484	z_mo = zu(k+1) - zw(k)
485
486	!
487	!-- Store current value in case the Newton iteration fails
488	ol_old = ol(j,i)
489
490	!
491	!-- Ensure that the bulk Richardson number and the Obukhov
492	!-- lengtH have the same sign
493	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
494	ABS( ol(j,i) ) == ol_max ) THEN
495	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
496	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
497	ENDIF
498	!
499	!-- Iteration to find Obukhov length
500	iter = 0
501	DO
502	iter = iter + 1
503	!
504	!-- In case of divergence, use the value of the previous time step
505	IF ( iter > 1000 ) THEN
506	ol(j,i) = ol_old
507	EXIT
508	ENDIF
509
510	ol_m = ol(j,i)
511	ol_l = ol_m - 0.001_wp * ol_m
512	ol_u = ol_m + 0.001_wp * ol_m
513
514
515	IF ( ibc_pt_b /= 1 ) THEN
516	!
517	!-- Calculate f = Ri - [...]/[...]^2 = 0
518	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
519	- psi_h( z_mo / ol_m ) &
520	+ psi_h( z0h(j,i) / ol_m ) &
521	) &
522	/ ( LOG( z_mo / z0(j,i) ) &
523	- psi_m( z_mo / ol_m ) &
524	+ psi_m( z0(j,i) / ol_m ) &
525	)**2
526
527	!
528	!-- Calculate df/dL
529	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
530	- psi_h( z_mo / ol_u ) &
531	+ psi_h( z0h(j,i) / ol_u ) &
532	) &
533	/ ( LOG( z_mo / z0(j,i) ) &
534	- psi_m( z_mo / ol_u ) &
535	+ psi_m( z0(j,i) / ol_u ) &
536	)**2 &
537	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
538	- psi_h( z_mo / ol_l ) &
539	+ psi_h( z0h(j,i) / ol_l ) &
540	) &
541	/ ( LOG( z_mo / z0(j,i) ) &
542	- psi_m( z_mo / ol_l ) &
543	+ psi_m( z0(j,i) / ol_l ) &
544	)**2 &
545	) / ( ol_u - ol_l )
546	ELSE
547	!
548	!-- Calculate f = Ri - 1 /[...]^3 = 0
549	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
550	- psi_m( z_mo / ol_m ) &
551	+ psi_m( z0(j,i) / ol_m ) &
552	)**3
553
554	!
555	!-- Calculate df/dL
556	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
557	- psi_m( z_mo / ol_u ) &
558	+ psi_m( z0(j,i) / ol_u ) &
559	)**3 &
560	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
561	- psi_m( z_mo / ol_l ) &
562	+ psi_m( z0(j,i) / ol_l ) &
563	)**3 &
564	) / ( ol_u - ol_l )
565	ENDIF
566	!
567	!-- Calculate new L
568	ol(j,i) = ol_m - f / f_d_ol
569
570	!
571	!-- Ensure that the bulk Richardson number and the Obukhov
572	!-- length have the same sign and ensure convergence.
573	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
574
575	!
576	!-- If unrealistic value occurs, set L to the maximum
577	!-- value that is allowed
578	IF ( ABS( ol(j,i) ) > ol_max ) THEN
579	ol(j,i) = ol_max
580	EXIT
581	ENDIF
582	!
583	!-- Check for convergence
584	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
585	EXIT
586	ELSE
587	CYCLE
588	ENDIF
589
590	ENDDO
591
592	ENDDO
593	ENDDO
594
595	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
596
597	!$OMP PARALLEL DO PRIVATE( k, z_mo )
598	!$acc kernels loop
599	DO i = nxl, nxr
600	DO j = nys, nyn
601
602	k = nzb_s_inner(j,i)
603
604	!
605	!-- If the bulk Richardson number is outside the range of the lookup
606	!-- table, set it to the exceeding threshold value
607	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
608	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
609
610	!
611	!-- Find the correct index bounds for linear interpolation. As the
612	!-- Richardson number will not differ very much from time step to
613	!-- time step , use the index from the last step and search in the
614	!-- correct direction
615	l = l_bnd
616	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
617	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
618	l = l-1
619	ENDDO
620	ELSE
621	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
622	.AND. l < num_steps-1 )
623	l = l+1
624	ENDDO
625	ENDIF
626	l_bnd = l
627
628	!
629	!-- Linear interpolation to find the correct value of z/L
630	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
631	/ ( rib_tab(l) - rib_tab(l-1) ) &
632	* ( rib(j,i) - rib_tab(l-1) ) )
633
634	ENDDO
635	ENDDO
636
637	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
638
639	!$OMP PARALLEL DO PRIVATE( k, z_mo )
640	!$acc kernels loop
641	DO i = nxl, nxr
642	DO j = nys, nyn
643
644	k = nzb_s_inner(j,i)
645	z_mo = zu(k+1) - zw(k)
646
647	IF ( .NOT. humidity ) THEN
648	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
649	* ts(j,i) + 1E-30_wp )
650	ELSEIF ( cloud_physics ) THEN
651
652	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
653	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
654	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
655	* ql(k+1,j,i) ) + 1E-30_wp )
656	ELSE
657	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
658	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
659	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
660	ENDIF
661	!
662	!-- Limit the value range of the Obukhov length.
663	!-- This is necessary for very small velocities (u,v --> 0), because
664	!-- the absolute value of ol can then become very small, which in
665	!-- consequence would result in very large shear stresses and very
666	!-- small momentum fluxes (both are generally unrealistic).
667	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
668	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
669
670	ENDDO
671	ENDDO
672
673	ENDIF
674
675	!
676	!-- Values of ol at ghost point locations are needed for the evaluation
677	!-- of usws and vsws.
678	!$acc update host( ol )
679	CALL exchange_horiz_2d( ol )
680	!$acc update device( ol )
681
682	END SUBROUTINE calc_ol
683
684	!
685	!-- Calculate friction velocity u*
686	SUBROUTINE calc_us
687
688	IMPLICIT NONE
689
690	!$OMP PARALLEL DO PRIVATE( k, z_mo )
691	!$acc kernels loop
692	DO i = nxlg, nxrg
693	DO j = nysg, nyng
694
695	k = nzb_s_inner(j,i)+1
696	z_mo = zu(k+1) - zw(k)
697
698	!
699	!-- Compute u* at the scalars' grid points
700	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
701	- psi_m( z_mo / ol(j,i) ) &
702	+ psi_m( z0(j,i) / ol(j,i) ) )
703	ENDDO
704	ENDDO
705
706	END SUBROUTINE calc_us
707
708	!
709	!-- Calculate potential temperature and specific humidity at first grid level
710	SUBROUTINE calc_pt_q
711
712	IMPLICIT NONE
713
714	DO i = nxlg, nxrg
715	DO j = nysg, nyng
716	k = nzb_s_inner(j,i)+1
717	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
718	qv1(j,i) = q(k,j,i) - ql(k,j,i)
719	ENDDO
720	ENDDO
721
722	END SUBROUTINE calc_pt_q
723
724	!
725	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
726	SUBROUTINE calc_scaling_parameters
727
728	IMPLICIT NONE
729
730	!
731	!-- Data information for accelerators
732	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
733	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
734	!$acc present( vpt, vsws, zu, zw, z0, z0h )
735	!
736	!-- Compute theta*
737	IF ( constant_heatflux ) THEN
738
739	!
740	!-- For a given heat flux in the surface layer:
741	!$OMP PARALLEL DO
742	!$acc kernels loop
743	DO i = nxlg, nxrg
744	DO j = nysg, nyng
745	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
746	!
747	!-- ts must be limited, because otherwise overflow may occur in case
748	!-- of us=0 when computing ol further below
749	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
750	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
751	ENDDO
752	ENDDO
753
754	ELSE
755	!
756	!-- For a given surface temperature:
757	IF ( large_scale_forcing .AND. lsf_surf ) THEN
758	!$OMP PARALLEL DO
759	!$acc kernels loop
760	DO i = nxlg, nxrg
761	DO j = nysg, nyng
762	k = nzb_s_inner(j,i)
763	pt(k,j,i) = pt_surface
764	ENDDO
765	ENDDO
766	ENDIF
767
768	!$OMP PARALLEL DO PRIVATE( k, z_mo )
769	!$acc kernels loop
770	DO i = nxlg, nxrg
771	DO j = nysg, nyng
772
773	k = nzb_s_inner(j,i)
774	z_mo = zu(k+1) - zw(k)
775
776	IF ( cloud_physics ) THEN
777	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
778	/ ( LOG( z_mo / z0h(j,i) ) &
779	- psi_h( z_mo / ol(j,i) ) &
780	+ psi_h( z0h(j,i) / ol(j,i) ) )
781	ELSE
782	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
783	/ ( LOG( z_mo / z0h(j,i) ) &
784	- psi_h( z_mo / ol(j,i) ) &
785	+ psi_h( z0h(j,i) / ol(j,i) ) )
786	ENDIF
787
788	ENDDO
789	ENDDO
790	ENDIF
791
792	!
793	!-- If required compute q*
794	IF ( humidity .OR. passive_scalar ) THEN
795	IF ( constant_waterflux ) THEN
796	!
797	!-- For a given water flux in the Prandtl layer:
798	!$OMP PARALLEL DO
799	!$acc kernels loop
800	DO i = nxlg, nxrg
801	DO j = nysg, nyng
802	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
803	ENDDO
804	ENDDO
805
806	ELSE
807	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
808	run_coupled )
809
810	IF ( large_scale_forcing .AND. lsf_surf ) THEN
811	!$OMP PARALLEL DO
812	!$acc kernels loop
813	DO i = nxlg, nxrg
814	DO j = nysg, nyng
815	k = nzb_s_inner(j,i)
816	q(k,j,i) = q_surface
817	ENDDO
818	ENDDO
819	ENDIF
820
821	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
822	!$acc kernels loop independent
823	DO i = nxlg, nxrg
824	!$acc loop independent
825	DO j = nysg, nyng
826
827	k = nzb_s_inner(j,i)
828	z_mo = zu(k+1) - zw(k)
829
830	!
831	!-- Assume saturation for atmosphere coupled to ocean (but not
832	!-- in case of precursor runs)
833	IF ( coupled_run ) THEN
834	e_s = 6.1_wp * &
835	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
836	- 273.15_wp ) )
837	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
838	ENDIF
839
840	IF ( cloud_physics ) THEN
841	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
842	/ ( LOG( z_mo / z0h(j,i) ) &
843	- psi_h( z_mo / ol(j,i) ) &
844	+ psi_h( z0h(j,i) / ol(j,i) ) )
845
846	ELSE
847	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
848	/ ( LOG( z_mo / z0h(j,i) ) &
849	- psi_h( z_mo / ol(j,i) ) &
850	+ psi_h( z0h(j,i) / ol(j,i) ) )
851	ENDIF
852
853	ENDDO
854	ENDDO
855	ENDIF
856	ENDIF
857
858
859	!
860	!-- If required compute qr* and nr*
861	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
862
863	!$OMP PARALLEL DO PRIVATE( k, z_mo )
864	!$acc kernels loop independent
865	DO i = nxlg, nxrg
866	!$acc loop independent
867	DO j = nysg, nyng
868
869	k = nzb_s_inner(j,i)
870	z_mo = zu(k+1) - zw(k)
871
872	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
873	/ ( LOG( z_mo / z0h(j,i) ) &
874	- psi_h( z_mo / ol(j,i) ) &
875	+ psi_h( z0h(j,i) / ol(j,i) ) )
876
877	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
878	/ ( LOG( z_mo / z0h(j,i) ) &
879	- psi_h( z_mo / ol(j,i) ) &
880	+ psi_h( z0h(j,i) / ol(j,i) ) )
881	ENDDO
882	ENDDO
883
884	ENDIF
885
886	END SUBROUTINE calc_scaling_parameters
887
888
889
890	!
891	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
892	SUBROUTINE calc_surface_fluxes
893
894	IMPLICIT NONE
895
896	REAL(wp) :: ol_mid !< Grid-interpolated L
897
898	!
899	!-- Compute u'w' for the total model domain.
900	!-- First compute the corresponding component of u* and square it.
901	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
902	!$acc kernels loop
903	DO i = nxl, nxr
904	DO j = nys, nyn
905
906	k = nzb_u_inner(j,i)
907	z_mo = zu(k+1) - zw(k)
908	!
909	!-- Compute bulk Obukhov length for this point
910	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
911
912	IF ( ol_mid == 0.0_wp ) THEN
913	ol_mid = MIN(ol(j,i-1), ol(j,i))
914	ENDIF
915
916	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
917	/ ( LOG( z_mo / z0(j,i) ) &
918	- psi_m( z_mo / ol_mid ) &
919	+ psi_m( z0(j,i) / ol_mid ) )
920
921	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
922	ENDDO
923	ENDDO
924
925	!
926	!-- Compute v'w' for the total model domain.
927	!-- First compute the corresponding component of u* and square it.
928	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
929	!$acc kernels loop
930	DO i = nxl, nxr
931	DO j = nys, nyn
932
933	k = nzb_v_inner(j,i)
934	z_mo = zu(k+1) - zw(k)
935	!
936	!-- Compute bulk Obukhov length for this point
937	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
938
939	IF ( ol_mid == 0.0_wp ) THEN
940	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
941	ENDIF
942
943	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
944	/ ( LOG( z_mo / z0(j,i) ) &
945	- psi_m( z_mo / ol_mid ) &
946	+ psi_m( z0(j,i) / ol_mid ) )
947
948	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
949
950	ENDDO
951	ENDDO
952
953	!
954	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
955	!$acc update host( usws, vsws )
956	CALL exchange_horiz_2d( usws )
957	CALL exchange_horiz_2d( vsws )
958	!$acc update device( usws, vsws )
959
960	!
961	!-- Compute the vertical kinematic heat flux
962	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
963	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
964	!$OMP PARALLEL DO
965	!$acc kernels loop independent
966	DO i = nxlg, nxrg
967	!$acc loop independent
968	DO j = nysg, nyng
969	shf(j,i) = -ts(j,i) * us(j,i)
970	ENDDO
971	ENDDO
972
973	ENDIF
974
975	!
976	!-- Compute the vertical water/scalar flux
977	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. passive_scalar ) &
978	.AND. ( simulated_time <= skip_time_do_lsm .OR. .NOT. &
979	land_surface ) ) THEN
980	!$OMP PARALLEL DO
981	!$acc kernels loop independent
982	DO i = nxlg, nxrg
983	!$acc loop independent
984	DO j = nysg, nyng
985	qsws(j,i) = -qs(j,i) * us(j,i)
986	ENDDO
987	ENDDO
988
989	ENDIF
990
991	!
992	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
993	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
994	precipitation ) THEN
995	!$OMP PARALLEL DO
996	!$acc kernels loop independent
997	DO i = nxlg, nxrg
998	!$acc loop independent
999	DO j = nysg, nyng
1000	qrsws(j,i) = -qrs(j,i) * us(j,i)
1001	nrsws(j,i) = -nrs(j,i) * us(j,i)
1002	ENDDO
1003	ENDDO
1004	ENDIF
1005
1006	!
1007	!-- Bottom boundary condition for the TKE
1008	IF ( ibc_e_b == 2 ) THEN
1009	!$OMP PARALLEL DO
1010	!$acc kernels loop independent
1011	DO i = nxlg, nxrg
1012	!$acc loop independent
1013	DO j = nysg, nyng
1014	e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.1_wp )**2
1015	!
1016	!-- As a test: cm = 0.4
1017	! e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.4_wp )**2
1018	e(nzb_s_inner(j,i),j,i) = e(nzb_s_inner(j,i)+1,j,i)
1019	ENDDO
1020	ENDDO
1021	ENDIF
1022	!$acc end data
1023
1024	END SUBROUTINE calc_surface_fluxes
1025
1026
1027	!
1028	!-- Integrated stability function for momentum
1029	FUNCTION psi_m( zeta )
1030
1031	USE kinds
1032
1033	IMPLICIT NONE
1034
1035	REAL(wp) :: psi_m !< Integrated similarity function result
1036	REAL(wp) :: zeta !< Stability parameter z/L
1037	REAL(wp) :: x !< dummy variable
1038
1039	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1040	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1041	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1042	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1043	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1044	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1045
1046
1047	IF ( zeta < 0.0_wp ) THEN
1048	x = SQRT( SQRT(1.0_wp - 16.0_wp * zeta ) )
1049	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
1050	* ( 1.0_wp + x*2 ) 0.125_wp )
1051	ELSE
1052
1053	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
1054	- bc_d_d
1055	!
1056	!-- Old version for stable conditions (only valid for z/L < 0.5)
1057	!-- psi_m = - 5.0_wp * zeta
1058
1059	ENDIF
1060
1061	END FUNCTION psi_m
1062
1063
1064	!
1065	!-- Integrated stability function for heat and moisture
1066	FUNCTION psi_h( zeta )
1067
1068	USE kinds
1069
1070	IMPLICIT NONE
1071
1072	REAL(wp) :: psi_h !< Integrated similarity function result
1073	REAL(wp) :: zeta !< Stability parameter z/L
1074	REAL(wp) :: x !< dummy variable
1075
1076	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
1077	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
1078	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
1079	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
1080	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
1081	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
1082
1083
1084	IF ( zeta < 0.0_wp ) THEN
1085	x = SQRT(1.0_wp - 16.0_wp * zeta )
1086	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
1087	ELSE
1088	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
1089	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
1090	+ 1.0_wp
1091	!
1092	!-- Old version for stable conditions (only valid for z/L < 0.5)
1093	!-- psi_h = - 5.0_wp * zeta
1094	ENDIF
1095
1096	END FUNCTION psi_h
1097
1098	END MODULE surface_layer_fluxes_mod

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