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source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 2241

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1	!> @file plant_canopy_model_mod.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of PALM.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 1997-2017 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: plant_canopy_model_mod.f90 2233 2017-05-30 18:08:54Z hellstea $
27	!
28	! 2232 2017-05-30 17:47:52Z suehring
29	! Adjustments to new topography concept
30	!
31	! 2213 2017-04-24 15:10:35Z kanani
32	! Bugfix: exchange of ghost points in array pc_heating_rate needed for output
33	! of pcm_heatrate, onetime ghost point exchange of lad_s after initialization.
34	! Formatting and clean-up of subroutine pcm_read_plant_canopy_3d,
35	! minor re-organization of canopy-heating initialization.
36	!
37	! 2209 2017-04-19 09:34:46Z kanani
38	! Added 3d output of leaf area density (pcm_lad) and canopy
39	! heat rate (pcm_heatrate)
40	!
41	! 2024 2016-10-12 16:42:37Z kanani
42	! Added missing lad_s initialization
43	!
44	! 2011 2016-09-19 17:29:57Z kanani
45	! Renamed canopy_heat_flux to pc_heating_rate, since the original meaning/
46	! calculation of the quantity has changed, related to the urban surface model
47	! and similar future applications.
48	!
49	! 2007 2016-08-24 15:47:17Z kanani
50	! Added SUBROUTINE pcm_read_plant_canopy_3d for reading 3d plant canopy data
51	! from file (new case canopy_mode=read_from_file_3d) in the course of
52	! introduction of urban surface model,
53	! introduced variable ext_coef,
54	! resorted SUBROUTINEs to alphabetical order
55	!
56	! 2000 2016-08-20 18:09:15Z knoop
57	! Forced header and separation lines into 80 columns
58	!
59	! 1960 2016-07-12 16:34:24Z suehring
60	! Separate humidity and passive scalar
61	!
62	! 1953 2016-06-21 09:28:42Z suehring
63	! Bugfix, lad_s and lad must be public
64	!
65	! 1826 2016-04-07 12:01:39Z maronga
66	! Further modularization
67	!
68	! 1721 2015-11-16 12:56:48Z raasch
69	! bugfixes: shf is reduced in areas covered with canopy only,
70	! canopy is set on top of topography
71	!
72	! 1682 2015-10-07 23:56:08Z knoop
73	! Code annotations made doxygen readable
74	!
75	! 1484 2014-10-21 10:53:05Z kanani
76	! Changes due to new module structure of the plant canopy model:
77	! module plant_canopy_model_mod now contains a subroutine for the
78	! initialization of the canopy model (pcm_init),
79	! limitation of the canopy drag (previously accounted for by calculation of
80	! a limiting canopy timestep for the determination of the maximum LES timestep
81	! in subroutine timestep) is now realized by the calculation of pre-tendencies
82	! and preliminary velocities in subroutine pcm_tendency,
83	! some redundant MPI communication removed in subroutine pcm_init
84	! (was previously in init_3d_model),
85	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
86	! respective grid is now provided only by lad_s (e.g. in the calculation of
87	! the tendency terms or of cum_lai_hf),
88	! drag_coefficient, lai, leaf_surface_concentration,
89	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
90	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
91	! respectively,
92	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
93	! USE-statements and ONLY-lists modified accordingly
94	!
95	! 1340 2014-03-25 19:45:13Z kanani
96	! REAL constants defined as wp-kind
97	!
98	! 1320 2014-03-20 08:40:49Z raasch
99	! ONLY-attribute added to USE-statements,
100	! kind-parameters added to all INTEGER and REAL declaration statements,
101	! kinds are defined in new module kinds,
102	! old module precision_kind is removed,
103	! revision history before 2012 removed,
104	! comment fields (!:) to be used for variable explanations added to
105	! all variable declaration statements
106	!
107	! 1036 2012-10-22 13:43:42Z raasch
108	! code put under GPL (PALM 3.9)
109	!
110	! 138 2007-11-28 10:03:58Z letzel
111	! Initial revision
112	!
113	! Description:
114	! ------------
115	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
116	!> profile (subroutine pcm_init).
117	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
118	!> due to canopy elements (subroutine pcm_tendency).
119	!------------------------------------------------------------------------------!
120	MODULE plant_canopy_model_mod
121
122	USE arrays_3d, &
123	ONLY: dzu, dzw, e, q, s, tend, u, v, w, zu, zw
124
125	USE indices, &
126	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
127	nz, nzb, nzb_max, nzt, wall_flags_0
128
129	USE kinds
130
131
132	IMPLICIT NONE
133
134
135	CHARACTER (LEN=20) :: canopy_mode = 'block' !< canopy coverage
136
137	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
138	INTEGER(iwp) :: &
139	lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
140
141	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
142	LOGICAL :: plant_canopy = .FALSE. !< switch for use of canopy model
143
144	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
145	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
146	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
147	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
148	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
149	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
150	REAL(wp) :: ext_coef = 0.6_wp !< extinction coefficient
151	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
152	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
153	REAL(wp) :: &
154	leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
155	REAL(wp) :: &
156	leaf_surface_conc = 0.0_wp !< leaf surface concentration
157	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
158	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
159
160	REAL(wp) :: &
161	lad_vertical_gradient(10) = 0.0_wp !< lad gradient
162	REAL(wp) :: &
163	lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
164
165	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
166	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
167
168	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
169	pc_heating_rate !< plant canopy heating rate
170	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
171	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
172
173
174	SAVE
175
176
177	PRIVATE
178
179	!
180	!-- Public functions
181	PUBLIC pcm_check_data_output, pcm_check_parameters, pcm_data_output_3d, &
182	pcm_define_netcdf_grid, pcm_header, pcm_init, pcm_parin, pcm_tendency
183
184	!
185	!-- Public variables and constants
186	PUBLIC pc_heating_rate, canopy_mode, cthf, dt_plant_canopy, lad, lad_s, &
187	pch_index, plant_canopy
188
189
190	INTERFACE pcm_check_data_output
191	MODULE PROCEDURE pcm_check_data_output
192	END INTERFACE pcm_check_data_output
193
194	INTERFACE pcm_check_parameters
195	MODULE PROCEDURE pcm_check_parameters
196	END INTERFACE pcm_check_parameters
197
198	INTERFACE pcm_data_output_3d
199	MODULE PROCEDURE pcm_data_output_3d
200	END INTERFACE pcm_data_output_3d
201
202	INTERFACE pcm_define_netcdf_grid
203	MODULE PROCEDURE pcm_define_netcdf_grid
204	END INTERFACE pcm_define_netcdf_grid
205
206	INTERFACE pcm_header
207	MODULE PROCEDURE pcm_header
208	END INTERFACE pcm_header
209
210	INTERFACE pcm_init
211	MODULE PROCEDURE pcm_init
212	END INTERFACE pcm_init
213
214	INTERFACE pcm_parin
215	MODULE PROCEDURE pcm_parin
216	END INTERFACE pcm_parin
217
218	INTERFACE pcm_read_plant_canopy_3d
219	MODULE PROCEDURE pcm_read_plant_canopy_3d
220	END INTERFACE pcm_read_plant_canopy_3d
221
222	INTERFACE pcm_tendency
223	MODULE PROCEDURE pcm_tendency
224	MODULE PROCEDURE pcm_tendency_ij
225	END INTERFACE pcm_tendency
226
227
228	CONTAINS
229
230
231	!------------------------------------------------------------------------------!
232	! Description:
233	! ------------
234	!> Check data output for plant canopy model
235	!------------------------------------------------------------------------------!
236	SUBROUTINE pcm_check_data_output( var, unit )
237
238
239	USE control_parameters, &
240	ONLY: data_output, message_string
241
242	IMPLICIT NONE
243
244	CHARACTER (LEN=*) :: unit !<
245	CHARACTER (LEN=*) :: var !<
246
247
248	SELECT CASE ( TRIM( var ) )
249
250	CASE ( 'pcm_heatrate' )
251	unit = 'K s-1'
252
253	CASE ( 'pcm_lad' )
254	unit = 'm2 m-3'
255
256
257	CASE DEFAULT
258	unit = 'illegal'
259
260	END SELECT
261
262
263	END SUBROUTINE pcm_check_data_output
264
265
266	!------------------------------------------------------------------------------!
267	! Description:
268	! ------------
269	!> Check parameters routine for plant canopy model
270	!------------------------------------------------------------------------------!
271	SUBROUTINE pcm_check_parameters
272
273	USE control_parameters, &
274	ONLY: cloud_physics, message_string, microphysics_seifert
275
276
277	IMPLICIT NONE
278
279
280	IF ( canopy_drag_coeff == 0.0_wp ) THEN
281	message_string = 'plant_canopy = .TRUE. requires a non-zero drag '// &
282	'coefficient & given value is canopy_drag_coeff = 0.0'
283	CALL message( 'check_parameters', 'PA0041', 1, 2, 0, 6, 0 )
284	ENDIF
285
286	IF ( ( alpha_lad /= 9999999.9_wp .AND. beta_lad == 9999999.9_wp ) .OR.&
287	beta_lad /= 9999999.9_wp .AND. alpha_lad == 9999999.9_wp ) THEN
288	message_string = 'using the beta function for the construction ' // &
289	'of the leaf area density profile requires ' // &
290	'both alpha_lad and beta_lad to be /= 9999999.9'
291	CALL message( 'check_parameters', 'PA0118', 1, 2, 0, 6, 0 )
292	ENDIF
293
294	IF ( calc_beta_lad_profile .AND. lai_beta == 0.0_wp ) THEN
295	message_string = 'using the beta function for the construction ' // &
296	'of the leaf area density profile requires ' // &
297	'a non-zero lai_beta, but given value is ' // &
298	'lai_beta = 0.0'
299	CALL message( 'check_parameters', 'PA0119', 1, 2, 0, 6, 0 )
300	ENDIF
301
302	IF ( calc_beta_lad_profile .AND. lad_surface /= 0.0_wp ) THEN
303	message_string = 'simultaneous setting of alpha_lad /= 9999999.9' // &
304	'and lad_surface /= 0.0 is not possible, ' // &
305	'use either vertical gradients or the beta ' // &
306	'function for the construction of the leaf area '// &
307	'density profile'
308	CALL message( 'check_parameters', 'PA0120', 1, 2, 0, 6, 0 )
309	ENDIF
310
311	IF ( cloud_physics .AND. microphysics_seifert ) THEN
312	message_string = 'plant_canopy = .TRUE. requires cloud_scheme /=' // &
313	' seifert_beheng'
314	CALL message( 'check_parameters', 'PA0360', 1, 2, 0, 6, 0 )
315	ENDIF
316
317
318	END SUBROUTINE pcm_check_parameters
319
320
321	!------------------------------------------------------------------------------!
322	!
323	! Description:
324	! ------------
325	!> Subroutine defining 3D output variables
326	!------------------------------------------------------------------------------!
327	SUBROUTINE pcm_data_output_3d( av, variable, found, local_pf )
328
329	USE control_parameters, &
330	ONLY : nz_do3d
331
332	USE indices
333
334	USE kinds
335
336
337	IMPLICIT NONE
338
339	CHARACTER (LEN=*) :: variable !<
340
341	INTEGER(iwp) :: av !<
342	INTEGER(iwp) :: i !<
343	INTEGER(iwp) :: j !<
344	INTEGER(iwp) :: k !<
345
346	LOGICAL :: found !<
347
348	REAL(sp), DIMENSION(nxlg:nxrg,nysg:nyng,nzb:nz_do3d) :: local_pf !<
349
350
351	found = .TRUE.
352
353
354	SELECT CASE ( TRIM( variable ) )
355
356	CASE ( 'pcm_heatrate' )
357	CALL exchange_horiz( pc_heating_rate, nbgp )
358	IF ( av == 0 ) THEN
359	DO i = nxlg, nxrg
360	DO j = nysg, nyng
361	DO k = nzb_s_inner(j,i), nz_do3d
362	local_pf(i,j,k) = pc_heating_rate(k-nzb_s_inner(j,i),j,i)
363	ENDDO
364	ENDDO
365	ENDDO
366	ENDIF
367
368
369	CASE ( 'pcm_lad' )
370	IF ( av == 0 ) THEN
371	DO i = nxlg, nxrg
372	DO j = nysg, nyng
373	DO k = nzb_s_inner(j,i), nz_do3d
374	local_pf(i,j,k) = lad_s(k-nzb_s_inner(j,i),j,i)
375	ENDDO
376	ENDDO
377	ENDDO
378	ENDIF
379
380
381	CASE DEFAULT
382	found = .FALSE.
383
384	END SELECT
385
386
387	END SUBROUTINE pcm_data_output_3d
388
389	!------------------------------------------------------------------------------!
390	!
391	! Description:
392	! ------------
393	!> Subroutine defining appropriate grid for netcdf variables.
394	!> It is called from subroutine netcdf.
395	!------------------------------------------------------------------------------!
396	SUBROUTINE pcm_define_netcdf_grid( var, found, grid_x, grid_y, grid_z )
397
398	IMPLICIT NONE
399
400	CHARACTER (LEN=*), INTENT(IN) :: var !<
401	LOGICAL, INTENT(OUT) :: found !<
402	CHARACTER (LEN=*), INTENT(OUT) :: grid_x !<
403	CHARACTER (LEN=*), INTENT(OUT) :: grid_y !<
404	CHARACTER (LEN=*), INTENT(OUT) :: grid_z !<
405
406	found = .TRUE.
407
408	!
409	!-- Check for the grid
410	SELECT CASE ( TRIM( var ) )
411
412	CASE ( 'pcm_heatrate', 'pcm_lad' )
413	grid_x = 'x'
414	grid_y = 'y'
415	grid_z = 'zu'
416
417	CASE DEFAULT
418	found = .FALSE.
419	grid_x = 'none'
420	grid_y = 'none'
421	grid_z = 'none'
422	END SELECT
423
424	END SUBROUTINE pcm_define_netcdf_grid
425
426
427	!------------------------------------------------------------------------------!
428	! Description:
429	! ------------
430	!> Header output for plant canopy model
431	!------------------------------------------------------------------------------!
432	SUBROUTINE pcm_header ( io )
433
434	USE control_parameters, &
435	ONLY: dz, passive_scalar
436
437
438	IMPLICIT NONE
439
440	CHARACTER (LEN=10) :: coor_chr !<
441
442	CHARACTER (LEN=86) :: coordinates !<
443	CHARACTER (LEN=86) :: gradients !<
444	CHARACTER (LEN=86) :: leaf_area_density !<
445	CHARACTER (LEN=86) :: slices !<
446
447	INTEGER(iwp) :: i !<
448	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
449	INTEGER(iwp) :: k !<
450
451	REAL(wp) :: canopy_height !< canopy height (in m)
452
453	canopy_height = pch_index * dz
454
455	WRITE ( io, 1 ) canopy_mode, canopy_height, pch_index, &
456	canopy_drag_coeff
457	IF ( passive_scalar ) THEN
458	WRITE ( io, 2 ) leaf_scalar_exch_coeff, &
459	leaf_surface_conc
460	ENDIF
461
462	!
463	!-- Heat flux at the top of vegetation
464	WRITE ( io, 3 ) cthf
465
466	!
467	!-- Leaf area density profile, calculated either from given vertical
468	!-- gradients or from beta probability density function.
469	IF ( .NOT. calc_beta_lad_profile ) THEN
470
471	!-- Building output strings, starting with surface value
472	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
473	gradients = '------'
474	slices = ' 0'
475	coordinates = ' 0.0'
476	i = 1
477	DO WHILE ( i < 11 .AND. lad_vertical_gradient_level_ind(i) &
478	/= -9999 )
479
480	WRITE (coor_chr,'(F7.2)') lad(lad_vertical_gradient_level_ind(i))
481	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
482	TRIM( coor_chr )
483
484	WRITE (coor_chr,'(F7.2)') lad_vertical_gradient(i)
485	gradients = TRIM( gradients ) // ' ' // TRIM( coor_chr )
486
487	WRITE (coor_chr,'(I7)') lad_vertical_gradient_level_ind(i)
488	slices = TRIM( slices ) // ' ' // TRIM( coor_chr )
489
490	WRITE (coor_chr,'(F7.1)') lad_vertical_gradient_level(i)
491	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
492
493	i = i + 1
494	ENDDO
495
496	WRITE ( io, 4 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
497	TRIM( gradients ), TRIM( slices )
498
499	ELSE
500
501	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
502	coordinates = ' 0.0'
503
504	DO k = 1, pch_index
505
506	WRITE (coor_chr,'(F7.2)') lad(k)
507	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
508	TRIM( coor_chr )
509
510	WRITE (coor_chr,'(F7.1)') zu(k)
511	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
512
513	ENDDO
514
515	WRITE ( io, 5 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
516	alpha_lad, beta_lad, lai_beta
517
518	ENDIF
519
520	1 FORMAT (//' Vegetation canopy (drag) model:'/ &
521	' ------------------------------'// &
522	' Canopy mode: ', A / &
523	' Canopy height: ',F6.2,'m (',I4,' grid points)' / &
524	' Leaf drag coefficient: ',F6.2 /)
525	2 FORMAT (/ ' Scalar exchange coefficient: ',F6.2 / &
526	' Scalar concentration at leaf surfaces in kg/m**3: ',F6.2 /)
527	3 FORMAT (' Predefined constant heatflux at the top of the vegetation: ',F6.2, &
528	' K m/s')
529	4 FORMAT (/ ' Characteristic levels of the leaf area density:'// &
530	' Height: ',A,' m'/ &
531	' Leaf area density: ',A,' m2/m3'/ &
532	' Gradient: ',A,' m2/m4'/ &
533	' Gridpoint: ',A)
534	5 FORMAT (//' Characteristic levels of the leaf area density and coefficients:'&
535	// ' Height: ',A,' m'/ &
536	' Leaf area density: ',A,' m2/m3'/ &
537	' Coefficient alpha: ',F6.2 / &
538	' Coefficient beta: ',F6.2 / &
539	' Leaf area index: ',F6.2,' m2/m2' /)
540
541	END SUBROUTINE pcm_header
542
543
544	!------------------------------------------------------------------------------!
545	! Description:
546	! ------------
547	!> Initialization of the plant canopy model
548	!------------------------------------------------------------------------------!
549	SUBROUTINE pcm_init
550
551
552	USE control_parameters, &
553	ONLY: coupling_char, dz, humidity, io_blocks, io_group, &
554	message_string, ocean, passive_scalar, urban_surface
555
556	USE surface_mod, &
557	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
558
559	IMPLICIT NONE
560
561	CHARACTER(10) :: pct
562
563	INTEGER(iwp) :: i !< running index
564	INTEGER(iwp) :: ii !< index
565	INTEGER(iwp) :: j !< running index
566	INTEGER(iwp) :: k !< running index
567	INTEGER(iwp) :: m !< running index
568
569	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
570	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
571	REAL(wp) :: gradient !< gradient for lad-profile construction
572	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
573	REAL(wp) :: pcv(nzb:nzt+1) !<
574
575	!
576	!-- Allocate one-dimensional arrays for the computation of the
577	!-- leaf area density (lad) profile
578	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
579	lad = 0.0_wp
580	pre_lad = 0.0_wp
581
582	!
583	!-- Set flag that indicates that the lad-profile shall be calculated by using
584	!-- a beta probability density function
585	IF ( alpha_lad /= 9999999.9_wp .AND. beta_lad /= 9999999.9_wp ) THEN
586	calc_beta_lad_profile = .TRUE.
587	ENDIF
588
589
590	!
591	!-- Compute the profile of leaf area density used in the plant
592	!-- canopy model. The profile can either be constructed from
593	!-- prescribed vertical gradients of the leaf area density or by
594	!-- using a beta probability density function (see e.g. Markkanen et al.,
595	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
596	IF ( .NOT. calc_beta_lad_profile ) THEN
597
598	!
599	!-- Use vertical gradients for lad-profile construction
600	i = 1
601	gradient = 0.0_wp
602
603	IF ( .NOT. ocean ) THEN
604
605	lad(0) = lad_surface
606	lad_vertical_gradient_level_ind(1) = 0
607
608	DO k = 1, pch_index
609	IF ( i < 11 ) THEN
610	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
611	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
612	gradient = lad_vertical_gradient(i)
613	lad_vertical_gradient_level_ind(i) = k - 1
614	i = i + 1
615	ENDIF
616	ENDIF
617	IF ( gradient /= 0.0_wp ) THEN
618	IF ( k /= 1 ) THEN
619	lad(k) = lad(k-1) + dzu(k) * gradient
620	ELSE
621	lad(k) = lad_surface + dzu(k) * gradient
622	ENDIF
623	ELSE
624	lad(k) = lad(k-1)
625	ENDIF
626	ENDDO
627
628	ENDIF
629
630	!
631	!-- In case of no given leaf area density gradients, choose a vanishing
632	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
633	!-- file.
634	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
635	lad_vertical_gradient_level(1) = 0.0_wp
636	ENDIF
637
638	ELSE
639
640	!
641	!-- Use beta function for lad-profile construction
642	int_bpdf = 0.0_wp
643	canopy_height = pch_index * dz
644
645	DO k = 0, pch_index
646	int_bpdf = int_bpdf + &
647	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
648	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
649	beta_lad-1.0_wp ) ) &
650	* ( ( zw(k+1)-zw(k) ) / canopy_height ) )
651	ENDDO
652
653	!
654	!-- Preliminary lad profile (defined on w-grid)
655	DO k = 0, pch_index
656	pre_lad(k) = lai_beta * &
657	( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) ) &
658	* ( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
659	beta_lad-1.0_wp ) ) / int_bpdf &
660	) / canopy_height
661	ENDDO
662
663	!
664	!-- Final lad profile (defined on scalar-grid level, since most prognostic
665	!-- quantities are defined there, hence, less interpolation is required
666	!-- when calculating the canopy tendencies)
667	lad(0) = pre_lad(0)
668	DO k = 1, pch_index
669	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
670	ENDDO
671
672	ENDIF
673
674	!
675	!-- Allocate 3D-array for the leaf area density (lad_s).
676	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
677
678	!
679	!-- Initialize canopy parameters cdc (canopy drag coefficient),
680	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
681	!-- with the prescribed values
682	cdc = canopy_drag_coeff
683	lsec = leaf_scalar_exch_coeff
684	lsc = leaf_surface_conc
685
686	!
687	!-- Initialization of the canopy coverage in the model domain:
688	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
689	!-- fully covers the domain surface
690	SELECT CASE ( TRIM( canopy_mode ) )
691
692	CASE( 'block' )
693
694	DO i = nxlg, nxrg
695	DO j = nysg, nyng
696	lad_s(:,j,i) = lad(:)
697	ENDDO
698	ENDDO
699
700	CASE ( 'read_from_file_3d' )
701	!
702	!-- Initialize canopy parameters cdc (canopy drag coefficient),
703	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
704	!-- from file which contains complete 3D data (separate vertical profiles for
705	!-- each location).
706	CALL pcm_read_plant_canopy_3d
707
708	CASE DEFAULT
709	!
710	!-- The DEFAULT case is reached either if the parameter
711	!-- canopy mode contains a wrong character string or if the
712	!-- user has coded a special case in the user interface.
713	!-- There, the subroutine user_init_plant_canopy checks
714	!-- which of these two conditions applies.
715	CALL user_init_plant_canopy
716
717	END SELECT
718
719	!
720	!-- Initialization of the canopy heat source distribution due to heating
721	!-- of the canopy layers by incoming solar radiation, in case that a non-zero
722	!-- value is set for the canopy top heat flux (cthf), which equals the
723	!-- available net radiation at canopy top.
724	!-- The heat source distribution is calculated by a decaying exponential
725	!-- function of the downward cumulative leaf area index (cum_lai_hf),
726	!-- assuming that the foliage inside the plant canopy is heated by solar
727	!-- radiation penetrating the canopy layers according to the distribution
728	!-- of net radiation as suggested by Brown & Covey (1966; Agric. Meteorol. 3,
729	!-- 73â96). This approach has been applied e.g. by Shaw & Schumann (1992;
730	!-- Bound.-Layer Meteorol. 61, 47â64).
731	!-- When using the urban surface model (USM), canopy heating (pc_heating_rate)
732	!-- by radiation is calculated in the USM.
733	IF ( cthf /= 0.0_wp .AND. .NOT. urban_surface) THEN
734
735	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
736	pc_heating_rate(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
737	!
738	!-- Piecewise calculation of the cumulative leaf area index by vertical
739	!-- integration of the leaf area density
740	cum_lai_hf(:,:,:) = 0.0_wp
741	DO i = nxlg, nxrg
742	DO j = nysg, nyng
743	DO k = pch_index-1, 0, -1
744	IF ( k == pch_index-1 ) THEN
745	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
746	( 0.5_wp * lad_s(k+1,j,i) * &
747	( zw(k+1) - zu(k+1) ) ) + &
748	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
749	lad_s(k,j,i) ) + &
750	lad_s(k+1,j,i) ) * &
751	( zu(k+1) - zw(k) ) )
752	ELSE
753	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
754	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
755	lad_s(k+1,j,i) ) + &
756	lad_s(k+1,j,i) ) * &
757	( zw(k+1) - zu(k+1) ) ) + &
758	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
759	lad_s(k,j,i) ) + &
760	lad_s(k+1,j,i) ) * &
761	( zu(k+1) - zw(k) ) )
762	ENDIF
763	ENDDO
764	ENDDO
765	ENDDO
766
767	!
768	!-- In areas with canopy the surface value of the canopy heat
769	!-- flux distribution overrides the surface heat flux (shf)
770	!-- Start with default surface type
771	DO m = 1, surf_def_h(0)%ns
772	k = surf_def_h(0)%k(m)
773	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
774	surf_def_h(0)%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
775	ENDDO
776	!
777	!-- Natural surfaces
778	DO m = 1, surf_lsm_h%ns
779	k = surf_lsm_h%k(m)
780	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
781	surf_lsm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
782	ENDDO
783	!
784	!-- Urban surfaces
785	DO m = 1, surf_usm_h%ns
786	k = surf_usm_h%k(m)
787	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
788	surf_usm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
789	ENDDO
790	!
791	!
792	!-- Calculation of the heating rate (K/s) within the different layers of
793	!-- the plant canopy. Calculation is only necessary in areas covered with
794	!-- canopy.
795	!-- Within the different canopy layers the plant-canopy heating
796	!-- rate (pc_heating_rate) is calculated as the vertical
797	!-- divergence of the canopy heat fluxes at the top and bottom
798	!-- of the respective layer
799	DO i = nxlg, nxrg
800	DO j = nysg, nyng
801	DO k = 1, pch_index
802	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) THEN
803	pc_heating_rate(k,j,i) = cthf * &
804	( exp(-ext_coef*cum_lai_hf(k,j,i)) - &
805	exp(-ext_coef*cum_lai_hf(k-1,j,i) ) ) / dzw(k)
806	ENDIF
807	ENDDO
808	ENDDO
809	ENDDO
810
811	ENDIF
812
813
814
815	END SUBROUTINE pcm_init
816
817
818	!------------------------------------------------------------------------------!
819	! Description:
820	! ------------
821	!> Parin for &canopy_par for plant canopy model
822	!------------------------------------------------------------------------------!
823	SUBROUTINE pcm_parin
824
825
826	IMPLICIT NONE
827
828	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
829
830	NAMELIST /canopy_par/ alpha_lad, beta_lad, canopy_drag_coeff, &
831	canopy_mode, cthf, &
832	lad_surface, &
833	lad_vertical_gradient, &
834	lad_vertical_gradient_level, &
835	lai_beta, &
836	leaf_scalar_exch_coeff, &
837	leaf_surface_conc, pch_index
838
839	line = ' '
840
841	!
842	!-- Try to find radiation model package
843	REWIND ( 11 )
844	line = ' '
845	DO WHILE ( INDEX( line, '&canopy_par' ) == 0 )
846	READ ( 11, '(A)', END=10 ) line
847	ENDDO
848	BACKSPACE ( 11 )
849
850	!
851	!-- Read user-defined namelist
852	READ ( 11, canopy_par )
853
854	!
855	!-- Set flag that indicates that the radiation model is switched on
856	plant_canopy = .TRUE.
857
858	10 CONTINUE
859
860
861	END SUBROUTINE pcm_parin
862
863
864
865	!------------------------------------------------------------------------------!
866	! Description:
867	! ------------
868	!
869	!> Loads 3D plant canopy data from file. File format is as follows:
870	!>
871	!> num_levels
872	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
873	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
874	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
875	!> ...
876	!>
877	!> i.e. first line determines number of levels and further lines represent plant
878	!> canopy data, one line per column and variable. In each data line,
879	!> dtype represents variable to be set:
880	!>
881	!> dtype=1: leaf area density (lad_s)
882	!> dtype=2....n: some additional plant canopy input data quantity
883	!>
884	!> Zeros are added automatically above num_levels until top of domain. Any
885	!> non-specified (x,y) columns have zero values as default.
886	!------------------------------------------------------------------------------!
887	SUBROUTINE pcm_read_plant_canopy_3d
888
889	USE control_parameters, &
890	ONLY: message_string, passive_scalar
891
892	USE indices, &
893	ONLY: nbgp
894
895	IMPLICIT NONE
896
897	INTEGER(iwp) :: dtype !< type of input data (1=lad)
898	INTEGER(iwp) :: i, j !< running index
899	INTEGER(iwp) :: nzp !< number of vertical layers of plant canopy
900	INTEGER(iwp) :: nzpltop !<
901	INTEGER(iwp) :: nzpl !<
902
903	REAL(wp), DIMENSION(:), ALLOCATABLE :: col !< vertical column of input data
904
905	!
906	!-- Initialize lad_s array
907	lad_s = 0.0_wp
908
909	!
910	!-- Open and read plant canopy input data
911	OPEN(152, file='PLANT_CANOPY_DATA_3D', access='SEQUENTIAL', &
912	action='READ', status='OLD', form='FORMATTED', err=515)
913	READ(152, *, err=516, end=517) nzp !< read first line = number of vertical layers
914
915	ALLOCATE(col(0:nzp-1))
916
917	DO
918	READ(152, *, err=516, end=517) dtype, i, j, col(:)
919	IF ( i < nxlg .or. i > nxrg .or. j < nysg .or. j > nyng ) CYCLE
920
921	SELECT CASE (dtype)
922	CASE( 1 ) !< leaf area density
923	!
924	!-- This is just the pure canopy layer assumed to be grounded to
925	!-- a flat domain surface. At locations where plant canopy sits
926	!-- on top of any kind of topography, the vertical plant column
927	!-- must be "lifted", which is done in SUBROUTINE pcm_tendency.
928	lad_s(0:nzp-1, j, i) = col(0:nzp-1)
929
930	CASE DEFAULT
931	write(message_string, '(a,i2,a)') &
932	'Unknown record type in file PLANT_CANOPY_DATA_3D: "', dtype, '"'
933	CALL message( 'pcm_read_plant_canopy_3d', 'PA0530', 1, 2, 0, 6, 0 )
934	END SELECT
935	ENDDO
936
937	515 message_string = 'error opening file PLANT_CANOPY_DATA_3D'
938	CALL message( 'pcm_read_plant_canopy_3d', 'PA0531', 1, 2, 0, 6, 0 )
939
940	516 message_string = 'error reading file PLANT_CANOPY_DATA_3D'
941	CALL message( 'pcm_read_plant_canopy_3d', 'PA0532', 1, 2, 0, 6, 0 )
942
943	517 CLOSE(152)
944	DEALLOCATE(col)
945
946	CALL exchange_horiz( lad_s, nbgp )
947
948	END SUBROUTINE pcm_read_plant_canopy_3d
949
950
951
952	!------------------------------------------------------------------------------!
953	! Description:
954	! ------------
955	!> Calculation of the tendency terms, accounting for the effect of the plant
956	!> canopy on momentum and scalar quantities.
957	!>
958	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
959	!> (defined on scalar grid), as initialized in subroutine pcm_init.
960	!> The lad on the w-grid is vertically interpolated from the surrounding
961	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
962	!> k = pch_index. Here, the lad is zero.
963	!>
964	!> The canopy drag must be limited (previously accounted for by calculation of
965	!> a limiting canopy timestep for the determination of the maximum LES timestep
966	!> in subroutine timestep), since it is physically impossible that the canopy
967	!> drag alone can locally change the sign of a velocity component. This
968	!> limitation is realized by calculating preliminary tendencies and velocities.
969	!> It is subsequently checked if the preliminary new velocity has a different
970	!> sign than the current velocity. If so, the tendency is limited in a way that
971	!> the velocity can at maximum be reduced to zero by the canopy drag.
972	!>
973	!>
974	!> Call for all grid points
975	!------------------------------------------------------------------------------!
976	SUBROUTINE pcm_tendency( component )
977
978
979	USE control_parameters, &
980	ONLY: dt_3d, message_string
981
982	USE kinds
983
984	IMPLICIT NONE
985
986	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
987	INTEGER(iwp) :: i !< running index
988	INTEGER(iwp) :: j !< running index
989	INTEGER(iwp) :: k !< running index
990	INTEGER(iwp) :: k_wall !< vertical index of topography top
991	INTEGER(iwp) :: kk !< running index for flat lad arrays
992
993	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
994	REAL(wp) :: lad_local !< local lad value
995	REAL(wp) :: pre_tend !< preliminary tendency
996	REAL(wp) :: pre_u !< preliminary u-value
997	REAL(wp) :: pre_v !< preliminary v-value
998	REAL(wp) :: pre_w !< preliminary w-value
999
1000
1001	ddt_3d = 1.0_wp / dt_3d
1002
1003	!
1004	!-- Compute drag for the three velocity components and the SGS-TKE:
1005	SELECT CASE ( component )
1006
1007	!
1008	!-- u-component
1009	CASE ( 1 )
1010	DO i = nxlu, nxr
1011	DO j = nys, nyn
1012	!
1013	!-- Determine topography-top index on u-grid
1014	k_wall = MAXLOC( &
1015	MERGE( 1, 0, &
1016	BTEST( wall_flags_0(nzb:nzb_max,j,i), 14 ) &
1017	), DIM = 1 &
1018	) - 1
1019	DO k = k_wall+1, k_wall+pch_index
1020
1021	kk = k - k_wall !- lad arrays are defined flat
1022	!
1023	!-- In order to create sharp boundaries of the plant canopy,
1024	!-- the lad on the u-grid at index (k,j,i) is equal to
1025	!-- lad_s(k,j,i), rather than being interpolated from the
1026	!-- surrounding lad_s, because this would yield smaller lad
1027	!-- at the canopy boundaries than inside of the canopy.
1028	!-- For the same reason, the lad at the rightmost(i+1)canopy
1029	!-- boundary on the u-grid equals lad_s(k,j,i).
1030	lad_local = lad_s(kk,j,i)
1031	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp )&
1032	THEN
1033	lad_local = lad_s(kk,j,i-1)
1034	ENDIF
1035
1036	pre_tend = 0.0_wp
1037	pre_u = 0.0_wp
1038	!
1039	!-- Calculate preliminary value (pre_tend) of the tendency
1040	pre_tend = - cdc * &
1041	lad_local * &
1042	SQRT( u(k,j,i)**2 + &
1043	( 0.25_wp * ( v(k,j,i-1) + &
1044	v(k,j,i) + &
1045	v(k,j+1,i) + &
1046	v(k,j+1,i-1) ) &
1047	)**2 + &
1048	( 0.25_wp * ( w(k-1,j,i-1) + &
1049	w(k-1,j,i) + &
1050	w(k,j,i-1) + &
1051	w(k,j,i) ) &
1052	)**2 &
1053	) * &
1054	u(k,j,i)
1055
1056	!
1057	!-- Calculate preliminary new velocity, based on pre_tend
1058	pre_u = u(k,j,i) + dt_3d * pre_tend
1059	!
1060	!-- Compare sign of old velocity and new preliminary velocity,
1061	!-- and in case the signs are different, limit the tendency
1062	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1063	pre_tend = - u(k,j,i) * ddt_3d
1064	ELSE
1065	pre_tend = pre_tend
1066	ENDIF
1067	!
1068	!-- Calculate final tendency
1069	tend(k,j,i) = tend(k,j,i) + pre_tend
1070
1071	ENDDO
1072	ENDDO
1073	ENDDO
1074
1075	!
1076	!-- v-component
1077	CASE ( 2 )
1078	DO i = nxl, nxr
1079	DO j = nysv, nyn
1080	!
1081	!-- Determine topography-top index on v-grid
1082	k_wall = MAXLOC( &
1083	MERGE( 1, 0, &
1084	BTEST( wall_flags_0(nzb:nzb_max,j,i), 16 ) &
1085	), DIM = 1 &
1086	) - 1
1087	DO k = k_wall+1, k_wall+pch_index
1088
1089	kk = k - k_wall !- lad arrays are defined flat
1090	!
1091	!-- In order to create sharp boundaries of the plant canopy,
1092	!-- the lad on the v-grid at index (k,j,i) is equal to
1093	!-- lad_s(k,j,i), rather than being interpolated from the
1094	!-- surrounding lad_s, because this would yield smaller lad
1095	!-- at the canopy boundaries than inside of the canopy.
1096	!-- For the same reason, the lad at the northmost(j+1) canopy
1097	!-- boundary on the v-grid equals lad_s(k,j,i).
1098	lad_local = lad_s(kk,j,i)
1099	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp )&
1100	THEN
1101	lad_local = lad_s(kk,j-1,i)
1102	ENDIF
1103
1104	pre_tend = 0.0_wp
1105	pre_v = 0.0_wp
1106	!
1107	!-- Calculate preliminary value (pre_tend) of the tendency
1108	pre_tend = - cdc * &
1109	lad_local * &
1110	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1111	u(k,j-1,i+1) + &
1112	u(k,j,i) + &
1113	u(k,j,i+1) ) &
1114	)**2 + &
1115	v(k,j,i)**2 + &
1116	( 0.25_wp * ( w(k-1,j-1,i) + &
1117	w(k-1,j,i) + &
1118	w(k,j-1,i) + &
1119	w(k,j,i) ) &
1120	)**2 &
1121	) * &
1122	v(k,j,i)
1123
1124	!
1125	!-- Calculate preliminary new velocity, based on pre_tend
1126	pre_v = v(k,j,i) + dt_3d * pre_tend
1127	!
1128	!-- Compare sign of old velocity and new preliminary velocity,
1129	!-- and in case the signs are different, limit the tendency
1130	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1131	pre_tend = - v(k,j,i) * ddt_3d
1132	ELSE
1133	pre_tend = pre_tend
1134	ENDIF
1135	!
1136	!-- Calculate final tendency
1137	tend(k,j,i) = tend(k,j,i) + pre_tend
1138
1139	ENDDO
1140	ENDDO
1141	ENDDO
1142
1143	!
1144	!-- w-component
1145	CASE ( 3 )
1146	DO i = nxl, nxr
1147	DO j = nys, nyn
1148	!
1149	!-- Determine topography-top index on w-grid
1150	k_wall = MAXLOC( &
1151	MERGE( 1, 0, &
1152	BTEST( wall_flags_0(nzb:nzb_max,j,i), 18 ) &
1153	), DIM = 1 &
1154	) - 1
1155	DO k = k_wall+1, k_wall+pch_index-1
1156
1157	kk = k - k_wall !- lad arrays are defined flat
1158
1159	pre_tend = 0.0_wp
1160	pre_w = 0.0_wp
1161	!
1162	!-- Calculate preliminary value (pre_tend) of the tendency
1163	pre_tend = - cdc * &
1164	(0.5_wp * &
1165	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1166	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1167	u(k,j,i+1) + &
1168	u(k+1,j,i) + &
1169	u(k+1,j,i+1) ) &
1170	)**2 + &
1171	( 0.25_wp * ( v(k,j,i) + &
1172	v(k,j+1,i) + &
1173	v(k+1,j,i) + &
1174	v(k+1,j+1,i) ) &
1175	)**2 + &
1176	w(k,j,i)**2 &
1177	) * &
1178	w(k,j,i)
1179	!
1180	!-- Calculate preliminary new velocity, based on pre_tend
1181	pre_w = w(k,j,i) + dt_3d * pre_tend
1182	!
1183	!-- Compare sign of old velocity and new preliminary velocity,
1184	!-- and in case the signs are different, limit the tendency
1185	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1186	pre_tend = - w(k,j,i) * ddt_3d
1187	ELSE
1188	pre_tend = pre_tend
1189	ENDIF
1190	!
1191	!-- Calculate final tendency
1192	tend(k,j,i) = tend(k,j,i) + pre_tend
1193
1194	ENDDO
1195	ENDDO
1196	ENDDO
1197
1198	!
1199	!-- potential temperature
1200	CASE ( 4 )
1201	DO i = nxl, nxr
1202	DO j = nys, nyn
1203	!
1204	!-- Determine topography-top index on scalar-grid
1205	k_wall = MAXLOC( &
1206	MERGE( 1, 0, &
1207	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1208	), DIM = 1 &
1209	) - 1
1210	DO k = k_wall+1, k_wall+pch_index
1211
1212	kk = k - k_wall !- lad arrays are defined flat
1213	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1214	ENDDO
1215	ENDDO
1216	ENDDO
1217
1218	!
1219	!-- humidity
1220	CASE ( 5 )
1221	DO i = nxl, nxr
1222	DO j = nys, nyn
1223	!
1224	!-- Determine topography-top index on scalar-grid
1225	k_wall = MAXLOC( &
1226	MERGE( 1, 0, &
1227	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1228	), DIM = 1 &
1229	) - 1
1230	DO k = k_wall+1, k_wall+pch_index
1231
1232	kk = k - k_wall !- lad arrays are defined flat
1233	tend(k,j,i) = tend(k,j,i) - &
1234	lsec * &
1235	lad_s(kk,j,i) * &
1236	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1237	u(k,j,i+1) ) &
1238	)**2 + &
1239	( 0.5_wp * ( v(k,j,i) + &
1240	v(k,j+1,i) ) &
1241	)**2 + &
1242	( 0.5_wp * ( w(k-1,j,i) + &
1243	w(k,j,i) ) &
1244	)**2 &
1245	) * &
1246	( q(k,j,i) - lsc )
1247	ENDDO
1248	ENDDO
1249	ENDDO
1250
1251	!
1252	!-- sgs-tke
1253	CASE ( 6 )
1254	DO i = nxl, nxr
1255	DO j = nys, nyn
1256	!
1257	!-- Determine topography-top index on scalar-grid
1258	k_wall = MAXLOC( &
1259	MERGE( 1, 0, &
1260	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1261	), DIM = 1 &
1262	) - 1
1263	DO k = k_wall+1, k_wall+pch_index
1264
1265	kk = k - k_wall !- lad arrays are defined flat
1266	tend(k,j,i) = tend(k,j,i) - &
1267	2.0_wp * cdc * &
1268	lad_s(kk,j,i) * &
1269	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1270	u(k,j,i+1) ) &
1271	)**2 + &
1272	( 0.5_wp * ( v(k,j,i) + &
1273	v(k,j+1,i) ) &
1274	)**2 + &
1275	( 0.5_wp * ( w(k,j,i) + &
1276	w(k+1,j,i) ) &
1277	)**2 &
1278	) * &
1279	e(k,j,i)
1280	ENDDO
1281	ENDDO
1282	ENDDO
1283	!
1284	!-- scalar concentration
1285	CASE ( 7 )
1286	DO i = nxl, nxr
1287	DO j = nys, nyn
1288	!
1289	!-- Determine topography-top index on scalar-grid
1290	k_wall = MAXLOC( &
1291	MERGE( 1, 0, &
1292	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1293	), DIM = 1 &
1294	) - 1
1295	DO k = k_wall+1, k_wall+pch_index
1296
1297	kk = k - k_wall !- lad arrays are defined flat
1298	tend(k,j,i) = tend(k,j,i) - &
1299	lsec * &
1300	lad_s(kk,j,i) * &
1301	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1302	u(k,j,i+1) ) &
1303	)**2 + &
1304	( 0.5_wp * ( v(k,j,i) + &
1305	v(k,j+1,i) ) &
1306	)**2 + &
1307	( 0.5_wp * ( w(k-1,j,i) + &
1308	w(k,j,i) ) &
1309	)**2 &
1310	) * &
1311	( s(k,j,i) - lsc )
1312	ENDDO
1313	ENDDO
1314	ENDDO
1315
1316
1317
1318	CASE DEFAULT
1319
1320	WRITE( message_string, * ) 'wrong component: ', component
1321	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1322
1323	END SELECT
1324
1325	END SUBROUTINE pcm_tendency
1326
1327
1328	!------------------------------------------------------------------------------!
1329	! Description:
1330	! ------------
1331	!> Calculation of the tendency terms, accounting for the effect of the plant
1332	!> canopy on momentum and scalar quantities.
1333	!>
1334	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
1335	!> (defined on scalar grid), as initialized in subroutine pcm_init.
1336	!> The lad on the w-grid is vertically interpolated from the surrounding
1337	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
1338	!> k = pch_index. Here, the lad is zero.
1339	!>
1340	!> The canopy drag must be limited (previously accounted for by calculation of
1341	!> a limiting canopy timestep for the determination of the maximum LES timestep
1342	!> in subroutine timestep), since it is physically impossible that the canopy
1343	!> drag alone can locally change the sign of a velocity component. This
1344	!> limitation is realized by calculating preliminary tendencies and velocities.
1345	!> It is subsequently checked if the preliminary new velocity has a different
1346	!> sign than the current velocity. If so, the tendency is limited in a way that
1347	!> the velocity can at maximum be reduced to zero by the canopy drag.
1348	!>
1349	!>
1350	!> Call for grid point i,j
1351	!------------------------------------------------------------------------------!
1352	SUBROUTINE pcm_tendency_ij( i, j, component )
1353
1354
1355	USE control_parameters, &
1356	ONLY: dt_3d, message_string
1357
1358	USE kinds
1359
1360	IMPLICIT NONE
1361
1362	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
1363	INTEGER(iwp) :: i !< running index
1364	INTEGER(iwp) :: j !< running index
1365	INTEGER(iwp) :: k !< running index
1366	INTEGER(iwp) :: k_wall !< vertical index of topography top
1367	INTEGER(iwp) :: kk !< running index for flat lad arrays
1368
1369	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1370	REAL(wp) :: lad_local !< local lad value
1371	REAL(wp) :: pre_tend !< preliminary tendency
1372	REAL(wp) :: pre_u !< preliminary u-value
1373	REAL(wp) :: pre_v !< preliminary v-value
1374	REAL(wp) :: pre_w !< preliminary w-value
1375
1376
1377	ddt_3d = 1.0_wp / dt_3d
1378
1379	!
1380	!-- Compute drag for the three velocity components and the SGS-TKE
1381	SELECT CASE ( component )
1382
1383	!
1384	!-- u-component
1385	CASE ( 1 )
1386	!
1387	!-- Determine topography-top index on u-grid
1388	k_wall = MAXLOC( &
1389	MERGE( 1, 0, &
1390	BTEST( wall_flags_0(nzb:nzb_max,j,i), 14 ) &
1391	), DIM = 1 &
1392	) - 1
1393	DO k = k_wall+1, k_wall+pch_index
1394
1395	kk = k - k_wall !- lad arrays are defined flat
1396	!
1397	!-- In order to create sharp boundaries of the plant canopy,
1398	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
1399	!-- rather than being interpolated from the surrounding lad_s,
1400	!-- because this would yield smaller lad at the canopy boundaries
1401	!-- than inside of the canopy.
1402	!-- For the same reason, the lad at the rightmost(i+1)canopy
1403	!-- boundary on the u-grid equals lad_s(k,j,i).
1404	lad_local = lad_s(kk,j,i)
1405	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp ) THEN
1406	lad_local = lad_s(kk,j,i-1)
1407	ENDIF
1408
1409	pre_tend = 0.0_wp
1410	pre_u = 0.0_wp
1411	!
1412	!-- Calculate preliminary value (pre_tend) of the tendency
1413	pre_tend = - cdc * &
1414	lad_local * &
1415	SQRT( u(k,j,i)**2 + &
1416	( 0.25_wp * ( v(k,j,i-1) + &
1417	v(k,j,i) + &
1418	v(k,j+1,i) + &
1419	v(k,j+1,i-1) ) &
1420	)**2 + &
1421	( 0.25_wp * ( w(k-1,j,i-1) + &
1422	w(k-1,j,i) + &
1423	w(k,j,i-1) + &
1424	w(k,j,i) ) &
1425	)**2 &
1426	) * &
1427	u(k,j,i)
1428
1429	!
1430	!-- Calculate preliminary new velocity, based on pre_tend
1431	pre_u = u(k,j,i) + dt_3d * pre_tend
1432	!
1433	!-- Compare sign of old velocity and new preliminary velocity,
1434	!-- and in case the signs are different, limit the tendency
1435	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1436	pre_tend = - u(k,j,i) * ddt_3d
1437	ELSE
1438	pre_tend = pre_tend
1439	ENDIF
1440	!
1441	!-- Calculate final tendency
1442	tend(k,j,i) = tend(k,j,i) + pre_tend
1443	ENDDO
1444
1445
1446	!
1447	!-- v-component
1448	CASE ( 2 )
1449	!
1450	!-- Determine topography-top index on v-grid
1451	k_wall = MAXLOC( &
1452	MERGE( 1, 0, &
1453	BTEST( wall_flags_0(nzb:nzb_max,j,i), 16 ) &
1454	), DIM = 1 &
1455	) - 1
1456	DO k = k_wall+1, k_wall+pch_index
1457
1458	kk = k - k_wall !- lad arrays are defined flat
1459	!
1460	!-- In order to create sharp boundaries of the plant canopy,
1461	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
1462	!-- rather than being interpolated from the surrounding lad_s,
1463	!-- because this would yield smaller lad at the canopy boundaries
1464	!-- than inside of the canopy.
1465	!-- For the same reason, the lad at the northmost(j+1)canopy
1466	!-- boundary on the v-grid equals lad_s(k,j,i).
1467	lad_local = lad_s(kk,j,i)
1468	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp ) THEN
1469	lad_local = lad_s(kk,j-1,i)
1470	ENDIF
1471
1472	pre_tend = 0.0_wp
1473	pre_v = 0.0_wp
1474	!
1475	!-- Calculate preliminary value (pre_tend) of the tendency
1476	pre_tend = - cdc * &
1477	lad_local * &
1478	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1479	u(k,j-1,i+1) + &
1480	u(k,j,i) + &
1481	u(k,j,i+1) ) &
1482	)**2 + &
1483	v(k,j,i)**2 + &
1484	( 0.25_wp * ( w(k-1,j-1,i) + &
1485	w(k-1,j,i) + &
1486	w(k,j-1,i) + &
1487	w(k,j,i) ) &
1488	)**2 &
1489	) * &
1490	v(k,j,i)
1491
1492	!
1493	!-- Calculate preliminary new velocity, based on pre_tend
1494	pre_v = v(k,j,i) + dt_3d * pre_tend
1495	!
1496	!-- Compare sign of old velocity and new preliminary velocity,
1497	!-- and in case the signs are different, limit the tendency
1498	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1499	pre_tend = - v(k,j,i) * ddt_3d
1500	ELSE
1501	pre_tend = pre_tend
1502	ENDIF
1503	!
1504	!-- Calculate final tendency
1505	tend(k,j,i) = tend(k,j,i) + pre_tend
1506	ENDDO
1507
1508
1509	!
1510	!-- w-component
1511	CASE ( 3 )
1512	!
1513	!-- Determine topography-top index on w-grid
1514	k_wall = MAXLOC( &
1515	MERGE( 1, 0, &
1516	BTEST( wall_flags_0(nzb:nzb_max,j,i), 18 ) &
1517	), DIM = 1 &
1518	) - 1
1519	DO k = k_wall+1, k_wall+pch_index-1
1520
1521	kk = k - k_wall !- lad arrays are defined flat
1522
1523	pre_tend = 0.0_wp
1524	pre_w = 0.0_wp
1525	!
1526	!-- Calculate preliminary value (pre_tend) of the tendency
1527	pre_tend = - cdc * &
1528	(0.5_wp * &
1529	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1530	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1531	u(k,j,i+1) + &
1532	u(k+1,j,i) + &
1533	u(k+1,j,i+1) ) &
1534	)**2 + &
1535	( 0.25_wp * ( v(k,j,i) + &
1536	v(k,j+1,i) + &
1537	v(k+1,j,i) + &
1538	v(k+1,j+1,i) ) &
1539	)**2 + &
1540	w(k,j,i)**2 &
1541	) * &
1542	w(k,j,i)
1543	!
1544	!-- Calculate preliminary new velocity, based on pre_tend
1545	pre_w = w(k,j,i) + dt_3d * pre_tend
1546	!
1547	!-- Compare sign of old velocity and new preliminary velocity,
1548	!-- and in case the signs are different, limit the tendency
1549	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1550	pre_tend = - w(k,j,i) * ddt_3d
1551	ELSE
1552	pre_tend = pre_tend
1553	ENDIF
1554	!
1555	!-- Calculate final tendency
1556	tend(k,j,i) = tend(k,j,i) + pre_tend
1557	ENDDO
1558
1559	!
1560	!-- potential temperature
1561	CASE ( 4 )
1562	!
1563	!-- Determine topography-top index on scalar grid
1564	k_wall = MAXLOC( &
1565	MERGE( 1, 0, &
1566	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1567	), DIM = 1 &
1568	) - 1
1569	DO k = k_wall+1, k_wall+pch_index
1570	kk = k - k_wall !- lad arrays are defined flat
1571	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1572	ENDDO
1573
1574
1575	!
1576	!-- humidity
1577	CASE ( 5 )
1578	!
1579	!-- Determine topography-top index on scalar grid
1580	k_wall = MAXLOC( &
1581	MERGE( 1, 0, &
1582	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1583	), DIM = 1 &
1584	) - 1
1585	DO k = k_wall+1, k_wall+pch_index
1586
1587	kk = k - k_wall
1588	tend(k,j,i) = tend(k,j,i) - &
1589	lsec * &
1590	lad_s(kk,j,i) * &
1591	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1592	u(k,j,i+1) ) &
1593	)**2 + &
1594	( 0.5_wp * ( v(k,j,i) + &
1595	v(k,j+1,i) ) &
1596	)**2 + &
1597	( 0.5_wp * ( w(k-1,j,i) + &
1598	w(k,j,i) ) &
1599	)**2 &
1600	) * &
1601	( q(k,j,i) - lsc )
1602	ENDDO
1603
1604	!
1605	!-- sgs-tke
1606	CASE ( 6 )
1607	!
1608	!-- Determine topography-top index on scalar grid
1609	k_wall = MAXLOC( &
1610	MERGE( 1, 0, &
1611	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1612	), DIM = 1 &
1613	) - 1
1614	DO k = k_wall+1, k_wall+pch_index
1615
1616	kk = k - k_wall
1617	tend(k,j,i) = tend(k,j,i) - &
1618	2.0_wp * cdc * &
1619	lad_s(kk,j,i) * &
1620	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1621	u(k,j,i+1) ) &
1622	)**2 + &
1623	( 0.5_wp * ( v(k,j,i) + &
1624	v(k,j+1,i) ) &
1625	)**2 + &
1626	( 0.5_wp * ( w(k,j,i) + &
1627	w(k+1,j,i) ) &
1628	)**2 &
1629	) * &
1630	e(k,j,i)
1631	ENDDO
1632
1633	!
1634	!-- scalar concentration
1635	CASE ( 7 )
1636	!
1637	!-- Determine topography-top index on scalar grid
1638	k_wall = MAXLOC( &
1639	MERGE( 1, 0, &
1640	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1641	), DIM = 1 &
1642	) - 1
1643	DO k = k_wall+1, k_wall+pch_index
1644
1645	kk = k - k_wall
1646	tend(k,j,i) = tend(k,j,i) - &
1647	lsec * &
1648	lad_s(kk,j,i) * &
1649	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1650	u(k,j,i+1) ) &
1651	)**2 + &
1652	( 0.5_wp * ( v(k,j,i) + &
1653	v(k,j+1,i) ) &
1654	)**2 + &
1655	( 0.5_wp * ( w(k-1,j,i) + &
1656	w(k,j,i) ) &
1657	)**2 &
1658	) * &
1659	( s(k,j,i) - lsc )
1660	ENDDO
1661
1662	CASE DEFAULT
1663
1664	WRITE( message_string, * ) 'wrong component: ', component
1665	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1666
1667	END SELECT
1668
1669	END SUBROUTINE pcm_tendency_ij
1670
1671
1672
1673	END MODULE plant_canopy_model_mod

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