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source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 2232

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

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