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source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 2412

Last change on this file since 2412 was 2318, checked in by suehring, 7 years ago
get topograpyhy top index via function call
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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 2318 2017-07-20 17:27:44Z raasch $
27	! Get topography top index via Function call
28	!
29	! 2317 2017-07-20 17:27:19Z suehring
30	! Changed error messages
31	!
32	! 2233 2017-05-30 18:08:54Z suehring
33	!
34	! 2232 2017-05-30 17:47:52Z suehring
35	! Adjustments to new topography concept
36	!
37	! 2213 2017-04-24 15:10:35Z kanani
38	! Bugfix: exchange of ghost points in array pc_heating_rate needed for output
39	! of pcm_heatrate, onetime ghost point exchange of lad_s after initialization.
40	! Formatting and clean-up of subroutine pcm_read_plant_canopy_3d,
41	! minor re-organization of canopy-heating initialization.
42	!
43	! 2209 2017-04-19 09:34:46Z kanani
44	! Added 3d output of leaf area density (pcm_lad) and canopy
45	! heat rate (pcm_heatrate)
46	!
47	! 2024 2016-10-12 16:42:37Z kanani
48	! Added missing lad_s initialization
49	!
50	! 2011 2016-09-19 17:29:57Z kanani
51	! Renamed canopy_heat_flux to pc_heating_rate, since the original meaning/
52	! calculation of the quantity has changed, related to the urban surface model
53	! and similar future applications.
54	!
55	! 2007 2016-08-24 15:47:17Z kanani
56	! Added SUBROUTINE pcm_read_plant_canopy_3d for reading 3d plant canopy data
57	! from file (new case canopy_mode=read_from_file_3d) in the course of
58	! introduction of urban surface model,
59	! introduced variable ext_coef,
60	! resorted SUBROUTINEs to alphabetical order
61	!
62	! 2000 2016-08-20 18:09:15Z knoop
63	! Forced header and separation lines into 80 columns
64	!
65	! 1960 2016-07-12 16:34:24Z suehring
66	! Separate humidity and passive scalar
67	!
68	! 1953 2016-06-21 09:28:42Z suehring
69	! Bugfix, lad_s and lad must be public
70	!
71	! 1826 2016-04-07 12:01:39Z maronga
72	! Further modularization
73	!
74	! 1721 2015-11-16 12:56:48Z raasch
75	! bugfixes: shf is reduced in areas covered with canopy only,
76	! canopy is set on top of topography
77	!
78	! 1682 2015-10-07 23:56:08Z knoop
79	! Code annotations made doxygen readable
80	!
81	! 1484 2014-10-21 10:53:05Z kanani
82	! Changes due to new module structure of the plant canopy model:
83	! module plant_canopy_model_mod now contains a subroutine for the
84	! initialization of the canopy model (pcm_init),
85	! limitation of the canopy drag (previously accounted for by calculation of
86	! a limiting canopy timestep for the determination of the maximum LES timestep
87	! in subroutine timestep) is now realized by the calculation of pre-tendencies
88	! and preliminary velocities in subroutine pcm_tendency,
89	! some redundant MPI communication removed in subroutine pcm_init
90	! (was previously in init_3d_model),
91	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
92	! respective grid is now provided only by lad_s (e.g. in the calculation of
93	! the tendency terms or of cum_lai_hf),
94	! drag_coefficient, lai, leaf_surface_concentration,
95	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
96	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
97	! respectively,
98	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
99	! USE-statements and ONLY-lists modified accordingly
100	!
101	! 1340 2014-03-25 19:45:13Z kanani
102	! REAL constants defined as wp-kind
103	!
104	! 1320 2014-03-20 08:40:49Z raasch
105	! ONLY-attribute added to USE-statements,
106	! kind-parameters added to all INTEGER and REAL declaration statements,
107	! kinds are defined in new module kinds,
108	! old module precision_kind is removed,
109	! revision history before 2012 removed,
110	! comment fields (!:) to be used for variable explanations added to
111	! all variable declaration statements
112	!
113	! 1036 2012-10-22 13:43:42Z raasch
114	! code put under GPL (PALM 3.9)
115	!
116	! 138 2007-11-28 10:03:58Z letzel
117	! Initial revision
118	!
119	! Description:
120	! ------------
121	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
122	!> profile (subroutine pcm_init).
123	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
124	!> due to canopy elements (subroutine pcm_tendency).
125	!------------------------------------------------------------------------------!
126	MODULE plant_canopy_model_mod
127
128	USE arrays_3d, &
129	ONLY: dzu, dzw, e, q, s, tend, u, v, w, zu, zw
130
131	USE indices, &
132	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
133	nz, nzb, nzt
134
135	USE kinds
136
137	USE surface_mod, &
138	ONLY: get_topography_top_index
139
140
141	IMPLICIT NONE
142
143
144	CHARACTER (LEN=20) :: canopy_mode = 'block' !< canopy coverage
145
146	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
147	INTEGER(iwp) :: &
148	lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
149
150	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
151	LOGICAL :: plant_canopy = .FALSE. !< switch for use of canopy model
152
153	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
154	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
155	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
156	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
157	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
158	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
159	REAL(wp) :: ext_coef = 0.6_wp !< extinction coefficient
160	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
161	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
162	REAL(wp) :: &
163	leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
164	REAL(wp) :: &
165	leaf_surface_conc = 0.0_wp !< leaf surface concentration
166	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
167	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
168
169	REAL(wp) :: &
170	lad_vertical_gradient(10) = 0.0_wp !< lad gradient
171	REAL(wp) :: &
172	lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
173
174	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
175	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
176
177	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
178	pc_heating_rate !< plant canopy heating rate
179	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
180	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
181
182
183	SAVE
184
185
186	PRIVATE
187
188	!
189	!-- Public functions
190	PUBLIC pcm_check_data_output, pcm_check_parameters, pcm_data_output_3d, &
191	pcm_define_netcdf_grid, pcm_header, pcm_init, pcm_parin, pcm_tendency
192
193	!
194	!-- Public variables and constants
195	PUBLIC pc_heating_rate, canopy_mode, cthf, dt_plant_canopy, lad, lad_s, &
196	pch_index, plant_canopy
197
198
199	INTERFACE pcm_check_data_output
200	MODULE PROCEDURE pcm_check_data_output
201	END INTERFACE pcm_check_data_output
202
203	INTERFACE pcm_check_parameters
204	MODULE PROCEDURE pcm_check_parameters
205	END INTERFACE pcm_check_parameters
206
207	INTERFACE pcm_data_output_3d
208	MODULE PROCEDURE pcm_data_output_3d
209	END INTERFACE pcm_data_output_3d
210
211	INTERFACE pcm_define_netcdf_grid
212	MODULE PROCEDURE pcm_define_netcdf_grid
213	END INTERFACE pcm_define_netcdf_grid
214
215	INTERFACE pcm_header
216	MODULE PROCEDURE pcm_header
217	END INTERFACE pcm_header
218
219	INTERFACE pcm_init
220	MODULE PROCEDURE pcm_init
221	END INTERFACE pcm_init
222
223	INTERFACE pcm_parin
224	MODULE PROCEDURE pcm_parin
225	END INTERFACE pcm_parin
226
227	INTERFACE pcm_read_plant_canopy_3d
228	MODULE PROCEDURE pcm_read_plant_canopy_3d
229	END INTERFACE pcm_read_plant_canopy_3d
230
231	INTERFACE pcm_tendency
232	MODULE PROCEDURE pcm_tendency
233	MODULE PROCEDURE pcm_tendency_ij
234	END INTERFACE pcm_tendency
235
236
237	CONTAINS
238
239
240	!------------------------------------------------------------------------------!
241	! Description:
242	! ------------
243	!> Check data output for plant canopy model
244	!------------------------------------------------------------------------------!
245	SUBROUTINE pcm_check_data_output( var, unit )
246
247
248	USE control_parameters, &
249	ONLY: data_output, message_string
250
251	IMPLICIT NONE
252
253	CHARACTER (LEN=*) :: unit !<
254	CHARACTER (LEN=*) :: var !<
255
256
257	SELECT CASE ( TRIM( var ) )
258
259	CASE ( 'pcm_heatrate' )
260	unit = 'K s-1'
261
262	CASE ( 'pcm_lad' )
263	unit = 'm2 m-3'
264
265
266	CASE DEFAULT
267	unit = 'illegal'
268
269	END SELECT
270
271
272	END SUBROUTINE pcm_check_data_output
273
274
275	!------------------------------------------------------------------------------!
276	! Description:
277	! ------------
278	!> Check parameters routine for plant canopy model
279	!------------------------------------------------------------------------------!
280	SUBROUTINE pcm_check_parameters
281
282	USE control_parameters, &
283	ONLY: cloud_physics, message_string, microphysics_seifert
284
285
286	IMPLICIT NONE
287
288
289	IF ( canopy_drag_coeff == 0.0_wp ) THEN
290	message_string = 'plant_canopy = .TRUE. requires a non-zero drag '// &
291	'coefficient & given value is canopy_drag_coeff = 0.0'
292	CALL message( 'check_parameters', 'PA0041', 1, 2, 0, 6, 0 )
293	ENDIF
294
295	IF ( ( alpha_lad /= 9999999.9_wp .AND. beta_lad == 9999999.9_wp ) .OR.&
296	beta_lad /= 9999999.9_wp .AND. alpha_lad == 9999999.9_wp ) THEN
297	message_string = 'using the beta function for the construction ' // &
298	'of the leaf area density profile requires ' // &
299	'both alpha_lad and beta_lad to be /= 9999999.9'
300	CALL message( 'check_parameters', 'PA0118', 1, 2, 0, 6, 0 )
301	ENDIF
302
303	IF ( calc_beta_lad_profile .AND. lai_beta == 0.0_wp ) THEN
304	message_string = 'using the beta function for the construction ' // &
305	'of the leaf area density profile requires ' // &
306	'a non-zero lai_beta, but given value is ' // &
307	'lai_beta = 0.0'
308	CALL message( 'check_parameters', 'PA0119', 1, 2, 0, 6, 0 )
309	ENDIF
310
311	IF ( calc_beta_lad_profile .AND. lad_surface /= 0.0_wp ) THEN
312	message_string = 'simultaneous setting of alpha_lad /= 9999999.9 '// &
313	'combined with beta_lad /= 9999999.9 ' // &
314	'and lad_surface /= 0.0 is not possible, ' // &
315	'use either vertical gradients or the beta ' // &
316	'function for the construction of the leaf area '// &
317	'density profile'
318	CALL message( 'check_parameters', 'PA0120', 1, 2, 0, 6, 0 )
319	ENDIF
320
321	IF ( cloud_physics .AND. microphysics_seifert ) THEN
322	message_string = 'plant_canopy = .TRUE. requires cloud_scheme /=' // &
323	' seifert_beheng'
324	CALL message( 'check_parameters', 'PA0360', 1, 2, 0, 6, 0 )
325	ENDIF
326
327
328	END SUBROUTINE pcm_check_parameters
329
330
331	!------------------------------------------------------------------------------!
332	!
333	! Description:
334	! ------------
335	!> Subroutine defining 3D output variables
336	!------------------------------------------------------------------------------!
337	SUBROUTINE pcm_data_output_3d( av, variable, found, local_pf )
338
339	USE control_parameters, &
340	ONLY : nz_do3d
341
342	USE indices
343
344	USE kinds
345
346
347	IMPLICIT NONE
348
349	CHARACTER (LEN=*) :: variable !<
350
351	INTEGER(iwp) :: av !<
352	INTEGER(iwp) :: i !<
353	INTEGER(iwp) :: j !<
354	INTEGER(iwp) :: k !<
355
356	LOGICAL :: found !<
357
358	REAL(sp), DIMENSION(nxlg:nxrg,nysg:nyng,nzb:nz_do3d) :: local_pf !<
359
360
361	found = .TRUE.
362
363
364	SELECT CASE ( TRIM( variable ) )
365
366	CASE ( 'pcm_heatrate' )
367	CALL exchange_horiz( pc_heating_rate, nbgp )
368	IF ( av == 0 ) THEN
369	DO i = nxlg, nxrg
370	DO j = nysg, nyng
371	DO k = nzb_s_inner(j,i), nz_do3d
372	local_pf(i,j,k) = pc_heating_rate(k-nzb_s_inner(j,i),j,i)
373	ENDDO
374	ENDDO
375	ENDDO
376	ENDIF
377
378
379	CASE ( 'pcm_lad' )
380	IF ( av == 0 ) THEN
381	DO i = nxlg, nxrg
382	DO j = nysg, nyng
383	DO k = nzb_s_inner(j,i), nz_do3d
384	local_pf(i,j,k) = lad_s(k-nzb_s_inner(j,i),j,i)
385	ENDDO
386	ENDDO
387	ENDDO
388	ENDIF
389
390
391	CASE DEFAULT
392	found = .FALSE.
393
394	END SELECT
395
396
397	END SUBROUTINE pcm_data_output_3d
398
399	!------------------------------------------------------------------------------!
400	!
401	! Description:
402	! ------------
403	!> Subroutine defining appropriate grid for netcdf variables.
404	!> It is called from subroutine netcdf.
405	!------------------------------------------------------------------------------!
406	SUBROUTINE pcm_define_netcdf_grid( var, found, grid_x, grid_y, grid_z )
407
408	IMPLICIT NONE
409
410	CHARACTER (LEN=*), INTENT(IN) :: var !<
411	LOGICAL, INTENT(OUT) :: found !<
412	CHARACTER (LEN=*), INTENT(OUT) :: grid_x !<
413	CHARACTER (LEN=*), INTENT(OUT) :: grid_y !<
414	CHARACTER (LEN=*), INTENT(OUT) :: grid_z !<
415
416	found = .TRUE.
417
418	!
419	!-- Check for the grid
420	SELECT CASE ( TRIM( var ) )
421
422	CASE ( 'pcm_heatrate', 'pcm_lad' )
423	grid_x = 'x'
424	grid_y = 'y'
425	grid_z = 'zu'
426
427	CASE DEFAULT
428	found = .FALSE.
429	grid_x = 'none'
430	grid_y = 'none'
431	grid_z = 'none'
432	END SELECT
433
434	END SUBROUTINE pcm_define_netcdf_grid
435
436
437	!------------------------------------------------------------------------------!
438	! Description:
439	! ------------
440	!> Header output for plant canopy model
441	!------------------------------------------------------------------------------!
442	SUBROUTINE pcm_header ( io )
443
444	USE control_parameters, &
445	ONLY: dz, passive_scalar
446
447
448	IMPLICIT NONE
449
450	CHARACTER (LEN=10) :: coor_chr !<
451
452	CHARACTER (LEN=86) :: coordinates !<
453	CHARACTER (LEN=86) :: gradients !<
454	CHARACTER (LEN=86) :: leaf_area_density !<
455	CHARACTER (LEN=86) :: slices !<
456
457	INTEGER(iwp) :: i !<
458	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
459	INTEGER(iwp) :: k !<
460
461	REAL(wp) :: canopy_height !< canopy height (in m)
462
463	canopy_height = pch_index * dz
464
465	WRITE ( io, 1 ) canopy_mode, canopy_height, pch_index, &
466	canopy_drag_coeff
467	IF ( passive_scalar ) THEN
468	WRITE ( io, 2 ) leaf_scalar_exch_coeff, &
469	leaf_surface_conc
470	ENDIF
471
472	!
473	!-- Heat flux at the top of vegetation
474	WRITE ( io, 3 ) cthf
475
476	!
477	!-- Leaf area density profile, calculated either from given vertical
478	!-- gradients or from beta probability density function.
479	IF ( .NOT. calc_beta_lad_profile ) THEN
480
481	!-- Building output strings, starting with surface value
482	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
483	gradients = '------'
484	slices = ' 0'
485	coordinates = ' 0.0'
486	i = 1
487	DO WHILE ( i < 11 .AND. lad_vertical_gradient_level_ind(i) &
488	/= -9999 )
489
490	WRITE (coor_chr,'(F7.2)') lad(lad_vertical_gradient_level_ind(i))
491	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
492	TRIM( coor_chr )
493
494	WRITE (coor_chr,'(F7.2)') lad_vertical_gradient(i)
495	gradients = TRIM( gradients ) // ' ' // TRIM( coor_chr )
496
497	WRITE (coor_chr,'(I7)') lad_vertical_gradient_level_ind(i)
498	slices = TRIM( slices ) // ' ' // TRIM( coor_chr )
499
500	WRITE (coor_chr,'(F7.1)') lad_vertical_gradient_level(i)
501	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
502
503	i = i + 1
504	ENDDO
505
506	WRITE ( io, 4 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
507	TRIM( gradients ), TRIM( slices )
508
509	ELSE
510
511	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
512	coordinates = ' 0.0'
513
514	DO k = 1, pch_index
515
516	WRITE (coor_chr,'(F7.2)') lad(k)
517	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
518	TRIM( coor_chr )
519
520	WRITE (coor_chr,'(F7.1)') zu(k)
521	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
522
523	ENDDO
524
525	WRITE ( io, 5 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
526	alpha_lad, beta_lad, lai_beta
527
528	ENDIF
529
530	1 FORMAT (//' Vegetation canopy (drag) model:'/ &
531	' ------------------------------'// &
532	' Canopy mode: ', A / &
533	' Canopy height: ',F6.2,'m (',I4,' grid points)' / &
534	' Leaf drag coefficient: ',F6.2 /)
535	2 FORMAT (/ ' Scalar exchange coefficient: ',F6.2 / &
536	' Scalar concentration at leaf surfaces in kg/m**3: ',F6.2 /)
537	3 FORMAT (' Predefined constant heatflux at the top of the vegetation: ',F6.2, &
538	' K m/s')
539	4 FORMAT (/ ' Characteristic levels of the leaf area density:'// &
540	' Height: ',A,' m'/ &
541	' Leaf area density: ',A,' m2/m3'/ &
542	' Gradient: ',A,' m2/m4'/ &
543	' Gridpoint: ',A)
544	5 FORMAT (//' Characteristic levels of the leaf area density and coefficients:'&
545	// ' Height: ',A,' m'/ &
546	' Leaf area density: ',A,' m2/m3'/ &
547	' Coefficient alpha: ',F6.2 / &
548	' Coefficient beta: ',F6.2 / &
549	' Leaf area index: ',F6.2,' m2/m2' /)
550
551	END SUBROUTINE pcm_header
552
553
554	!------------------------------------------------------------------------------!
555	! Description:
556	! ------------
557	!> Initialization of the plant canopy model
558	!------------------------------------------------------------------------------!
559	SUBROUTINE pcm_init
560
561
562	USE control_parameters, &
563	ONLY: coupling_char, dz, humidity, io_blocks, io_group, &
564	message_string, ocean, passive_scalar, urban_surface
565
566	USE surface_mod, &
567	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
568
569	IMPLICIT NONE
570
571	CHARACTER(10) :: pct
572
573	INTEGER(iwp) :: i !< running index
574	INTEGER(iwp) :: ii !< index
575	INTEGER(iwp) :: j !< running index
576	INTEGER(iwp) :: k !< running index
577	INTEGER(iwp) :: m !< running index
578
579	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
580	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
581	REAL(wp) :: gradient !< gradient for lad-profile construction
582	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
583	REAL(wp) :: pcv(nzb:nzt+1) !<
584
585	!
586	!-- Allocate one-dimensional arrays for the computation of the
587	!-- leaf area density (lad) profile
588	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
589	lad = 0.0_wp
590	pre_lad = 0.0_wp
591
592	!
593	!-- Set flag that indicates that the lad-profile shall be calculated by using
594	!-- a beta probability density function
595	IF ( alpha_lad /= 9999999.9_wp .AND. beta_lad /= 9999999.9_wp ) THEN
596	calc_beta_lad_profile = .TRUE.
597	ENDIF
598
599
600	!
601	!-- Compute the profile of leaf area density used in the plant
602	!-- canopy model. The profile can either be constructed from
603	!-- prescribed vertical gradients of the leaf area density or by
604	!-- using a beta probability density function (see e.g. Markkanen et al.,
605	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
606	IF ( .NOT. calc_beta_lad_profile ) THEN
607
608	!
609	!-- Use vertical gradients for lad-profile construction
610	i = 1
611	gradient = 0.0_wp
612
613	IF ( .NOT. ocean ) THEN
614
615	lad(0) = lad_surface
616	lad_vertical_gradient_level_ind(1) = 0
617
618	DO k = 1, pch_index
619	IF ( i < 11 ) THEN
620	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
621	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
622	gradient = lad_vertical_gradient(i)
623	lad_vertical_gradient_level_ind(i) = k - 1
624	i = i + 1
625	ENDIF
626	ENDIF
627	IF ( gradient /= 0.0_wp ) THEN
628	IF ( k /= 1 ) THEN
629	lad(k) = lad(k-1) + dzu(k) * gradient
630	ELSE
631	lad(k) = lad_surface + dzu(k) * gradient
632	ENDIF
633	ELSE
634	lad(k) = lad(k-1)
635	ENDIF
636	ENDDO
637
638	ENDIF
639
640	!
641	!-- In case of no given leaf area density gradients, choose a vanishing
642	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
643	!-- file.
644	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
645	lad_vertical_gradient_level(1) = 0.0_wp
646	ENDIF
647
648	ELSE
649
650	!
651	!-- Use beta function for lad-profile construction
652	int_bpdf = 0.0_wp
653	canopy_height = pch_index * dz
654
655	DO k = 0, pch_index
656	int_bpdf = int_bpdf + &
657	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
658	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
659	beta_lad-1.0_wp ) ) &
660	* ( ( zw(k+1)-zw(k) ) / canopy_height ) )
661	ENDDO
662
663	!
664	!-- Preliminary lad profile (defined on w-grid)
665	DO k = 0, pch_index
666	pre_lad(k) = lai_beta * &
667	( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) ) &
668	* ( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
669	beta_lad-1.0_wp ) ) / int_bpdf &
670	) / canopy_height
671	ENDDO
672
673	!
674	!-- Final lad profile (defined on scalar-grid level, since most prognostic
675	!-- quantities are defined there, hence, less interpolation is required
676	!-- when calculating the canopy tendencies)
677	lad(0) = pre_lad(0)
678	DO k = 1, pch_index
679	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
680	ENDDO
681
682	ENDIF
683
684	!
685	!-- Allocate 3D-array for the leaf area density (lad_s).
686	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
687
688	!
689	!-- Initialize canopy parameters cdc (canopy drag coefficient),
690	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
691	!-- with the prescribed values
692	cdc = canopy_drag_coeff
693	lsec = leaf_scalar_exch_coeff
694	lsc = leaf_surface_conc
695
696	!
697	!-- Initialization of the canopy coverage in the model domain:
698	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
699	!-- fully covers the domain surface
700	SELECT CASE ( TRIM( canopy_mode ) )
701
702	CASE( 'block' )
703
704	DO i = nxlg, nxrg
705	DO j = nysg, nyng
706	lad_s(:,j,i) = lad(:)
707	ENDDO
708	ENDDO
709
710	CASE ( 'read_from_file_3d' )
711	!
712	!-- Initialize canopy parameters cdc (canopy drag coefficient),
713	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
714	!-- from file which contains complete 3D data (separate vertical profiles for
715	!-- each location).
716	CALL pcm_read_plant_canopy_3d
717
718	CASE DEFAULT
719	!
720	!-- The DEFAULT case is reached either if the parameter
721	!-- canopy mode contains a wrong character string or if the
722	!-- user has coded a special case in the user interface.
723	!-- There, the subroutine user_init_plant_canopy checks
724	!-- which of these two conditions applies.
725	CALL user_init_plant_canopy
726
727	END SELECT
728
729	!
730	!-- Initialization of the canopy heat source distribution due to heating
731	!-- of the canopy layers by incoming solar radiation, in case that a non-zero
732	!-- value is set for the canopy top heat flux (cthf), which equals the
733	!-- available net radiation at canopy top.
734	!-- The heat source distribution is calculated by a decaying exponential
735	!-- function of the downward cumulative leaf area index (cum_lai_hf),
736	!-- assuming that the foliage inside the plant canopy is heated by solar
737	!-- radiation penetrating the canopy layers according to the distribution
738	!-- of net radiation as suggested by Brown & Covey (1966; Agric. Meteorol. 3,
739	!-- 73â96). This approach has been applied e.g. by Shaw & Schumann (1992;
740	!-- Bound.-Layer Meteorol. 61, 47â64).
741	!-- When using the urban surface model (USM), canopy heating (pc_heating_rate)
742	!-- by radiation is calculated in the USM.
743	IF ( cthf /= 0.0_wp .AND. .NOT. urban_surface) THEN
744
745	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
746	pc_heating_rate(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
747	!
748	!-- Piecewise calculation of the cumulative leaf area index by vertical
749	!-- integration of the leaf area density
750	cum_lai_hf(:,:,:) = 0.0_wp
751	DO i = nxlg, nxrg
752	DO j = nysg, nyng
753	DO k = pch_index-1, 0, -1
754	IF ( k == pch_index-1 ) THEN
755	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
756	( 0.5_wp * 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	ELSE
763	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
764	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
765	lad_s(k+1,j,i) ) + &
766	lad_s(k+1,j,i) ) * &
767	( zw(k+1) - zu(k+1) ) ) + &
768	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
769	lad_s(k,j,i) ) + &
770	lad_s(k+1,j,i) ) * &
771	( zu(k+1) - zw(k) ) )
772	ENDIF
773	ENDDO
774	ENDDO
775	ENDDO
776
777	!
778	!-- In areas with canopy the surface value of the canopy heat
779	!-- flux distribution overrides the surface heat flux (shf)
780	!-- Start with default surface type
781	DO m = 1, surf_def_h(0)%ns
782	k = surf_def_h(0)%k(m)
783	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
784	surf_def_h(0)%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
785	ENDDO
786	!
787	!-- Natural surfaces
788	DO m = 1, surf_lsm_h%ns
789	k = surf_lsm_h%k(m)
790	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
791	surf_lsm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
792	ENDDO
793	!
794	!-- Urban surfaces
795	DO m = 1, surf_usm_h%ns
796	k = surf_usm_h%k(m)
797	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
798	surf_usm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
799	ENDDO
800	!
801	!
802	!-- Calculation of the heating rate (K/s) within the different layers of
803	!-- the plant canopy. Calculation is only necessary in areas covered with
804	!-- canopy.
805	!-- Within the different canopy layers the plant-canopy heating
806	!-- rate (pc_heating_rate) is calculated as the vertical
807	!-- divergence of the canopy heat fluxes at the top and bottom
808	!-- of the respective layer
809	DO i = nxlg, nxrg
810	DO j = nysg, nyng
811	DO k = 1, pch_index
812	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) THEN
813	pc_heating_rate(k,j,i) = cthf * &
814	( exp(-ext_coef*cum_lai_hf(k,j,i)) - &
815	exp(-ext_coef*cum_lai_hf(k-1,j,i) ) ) / dzw(k)
816	ENDIF
817	ENDDO
818	ENDDO
819	ENDDO
820
821	ENDIF
822
823
824
825	END SUBROUTINE pcm_init
826
827
828	!------------------------------------------------------------------------------!
829	! Description:
830	! ------------
831	!> Parin for &canopy_par for plant canopy model
832	!------------------------------------------------------------------------------!
833	SUBROUTINE pcm_parin
834
835
836	IMPLICIT NONE
837
838	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
839
840	NAMELIST /canopy_par/ alpha_lad, beta_lad, canopy_drag_coeff, &
841	canopy_mode, cthf, &
842	lad_surface, &
843	lad_vertical_gradient, &
844	lad_vertical_gradient_level, &
845	lai_beta, &
846	leaf_scalar_exch_coeff, &
847	leaf_surface_conc, pch_index
848
849	line = ' '
850
851	!
852	!-- Try to find radiation model package
853	REWIND ( 11 )
854	line = ' '
855	DO WHILE ( INDEX( line, '&canopy_par' ) == 0 )
856	READ ( 11, '(A)', END=10 ) line
857	ENDDO
858	BACKSPACE ( 11 )
859
860	!
861	!-- Read user-defined namelist
862	READ ( 11, canopy_par )
863
864	!
865	!-- Set flag that indicates that the radiation model is switched on
866	plant_canopy = .TRUE.
867
868	10 CONTINUE
869
870
871	END SUBROUTINE pcm_parin
872
873
874
875	!------------------------------------------------------------------------------!
876	! Description:
877	! ------------
878	!
879	!> Loads 3D plant canopy data from file. File format is as follows:
880	!>
881	!> num_levels
882	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
883	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
884	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
885	!> ...
886	!>
887	!> i.e. first line determines number of levels and further lines represent plant
888	!> canopy data, one line per column and variable. In each data line,
889	!> dtype represents variable to be set:
890	!>
891	!> dtype=1: leaf area density (lad_s)
892	!> dtype=2....n: some additional plant canopy input data quantity
893	!>
894	!> Zeros are added automatically above num_levels until top of domain. Any
895	!> non-specified (x,y) columns have zero values as default.
896	!------------------------------------------------------------------------------!
897	SUBROUTINE pcm_read_plant_canopy_3d
898
899	USE control_parameters, &
900	ONLY: message_string, passive_scalar
901
902	USE indices, &
903	ONLY: nbgp
904
905	IMPLICIT NONE
906
907	INTEGER(iwp) :: dtype !< type of input data (1=lad)
908	INTEGER(iwp) :: i, j !< running index
909	INTEGER(iwp) :: nzp !< number of vertical layers of plant canopy
910	INTEGER(iwp) :: nzpltop !<
911	INTEGER(iwp) :: nzpl !<
912
913	REAL(wp), DIMENSION(:), ALLOCATABLE :: col !< vertical column of input data
914
915	!
916	!-- Initialize lad_s array
917	lad_s = 0.0_wp
918
919	!
920	!-- Open and read plant canopy input data
921	OPEN(152, file='PLANT_CANOPY_DATA_3D', access='SEQUENTIAL', &
922	action='READ', status='OLD', form='FORMATTED', err=515)
923	READ(152, *, err=516, end=517) nzp !< read first line = number of vertical layers
924
925	ALLOCATE(col(0:nzp-1))
926
927	DO
928	READ(152, *, err=516, end=517) dtype, i, j, col(:)
929	IF ( i < nxlg .or. i > nxrg .or. j < nysg .or. j > nyng ) CYCLE
930
931	SELECT CASE (dtype)
932	CASE( 1 ) !< leaf area density
933	!
934	!-- This is just the pure canopy layer assumed to be grounded to
935	!-- a flat domain surface. At locations where plant canopy sits
936	!-- on top of any kind of topography, the vertical plant column
937	!-- must be "lifted", which is done in SUBROUTINE pcm_tendency.
938	lad_s(0:nzp-1, j, i) = col(0:nzp-1)
939
940	CASE DEFAULT
941	write(message_string, '(a,i2,a)') &
942	'Unknown record type in file PLANT_CANOPY_DATA_3D: "', dtype, '"'
943	CALL message( 'pcm_read_plant_canopy_3d', 'PA0530', 1, 2, 0, 6, 0 )
944	END SELECT
945	ENDDO
946
947	515 message_string = 'error opening file PLANT_CANOPY_DATA_3D'
948	CALL message( 'pcm_read_plant_canopy_3d', 'PA0531', 1, 2, 0, 6, 0 )
949
950	516 message_string = 'error reading file PLANT_CANOPY_DATA_3D'
951	CALL message( 'pcm_read_plant_canopy_3d', 'PA0532', 1, 2, 0, 6, 0 )
952
953	517 CLOSE(152)
954	DEALLOCATE(col)
955
956	CALL exchange_horiz( lad_s, nbgp )
957
958	END SUBROUTINE pcm_read_plant_canopy_3d
959
960
961
962	!------------------------------------------------------------------------------!
963	! Description:
964	! ------------
965	!> Calculation of the tendency terms, accounting for the effect of the plant
966	!> canopy on momentum and scalar quantities.
967	!>
968	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
969	!> (defined on scalar grid), as initialized in subroutine pcm_init.
970	!> The lad on the w-grid is vertically interpolated from the surrounding
971	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
972	!> k = pch_index. Here, the lad is zero.
973	!>
974	!> The canopy drag must be limited (previously accounted for by calculation of
975	!> a limiting canopy timestep for the determination of the maximum LES timestep
976	!> in subroutine timestep), since it is physically impossible that the canopy
977	!> drag alone can locally change the sign of a velocity component. This
978	!> limitation is realized by calculating preliminary tendencies and velocities.
979	!> It is subsequently checked if the preliminary new velocity has a different
980	!> sign than the current velocity. If so, the tendency is limited in a way that
981	!> the velocity can at maximum be reduced to zero by the canopy drag.
982	!>
983	!>
984	!> Call for all grid points
985	!------------------------------------------------------------------------------!
986	SUBROUTINE pcm_tendency( component )
987
988
989	USE control_parameters, &
990	ONLY: dt_3d, message_string
991
992	USE kinds
993
994	IMPLICIT NONE
995
996	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
997	INTEGER(iwp) :: i !< running index
998	INTEGER(iwp) :: j !< running index
999	INTEGER(iwp) :: k !< running index
1000	INTEGER(iwp) :: k_wall !< vertical index of topography top
1001	INTEGER(iwp) :: kk !< running index for flat lad arrays
1002
1003	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1004	REAL(wp) :: lad_local !< local lad value
1005	REAL(wp) :: pre_tend !< preliminary tendency
1006	REAL(wp) :: pre_u !< preliminary u-value
1007	REAL(wp) :: pre_v !< preliminary v-value
1008	REAL(wp) :: pre_w !< preliminary w-value
1009
1010
1011	ddt_3d = 1.0_wp / dt_3d
1012
1013	!
1014	!-- Compute drag for the three velocity components and the SGS-TKE:
1015	SELECT CASE ( component )
1016
1017	!
1018	!-- u-component
1019	CASE ( 1 )
1020	DO i = nxlu, nxr
1021	DO j = nys, nyn
1022	!
1023	!-- Determine topography-top index on u-grid
1024	k_wall = get_topography_top_index( j, i, 'u' )
1025	DO k = k_wall+1, k_wall+pch_index
1026
1027	kk = k - k_wall !- lad arrays are defined flat
1028	!
1029	!-- In order to create sharp boundaries of the plant canopy,
1030	!-- the lad on the u-grid at index (k,j,i) is equal to
1031	!-- lad_s(k,j,i), rather than being interpolated from the
1032	!-- surrounding lad_s, because this would yield smaller lad
1033	!-- at the canopy boundaries than inside of the canopy.
1034	!-- For the same reason, the lad at the rightmost(i+1)canopy
1035	!-- boundary on the u-grid equals lad_s(k,j,i).
1036	lad_local = lad_s(kk,j,i)
1037	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp )&
1038	THEN
1039	lad_local = lad_s(kk,j,i-1)
1040	ENDIF
1041
1042	pre_tend = 0.0_wp
1043	pre_u = 0.0_wp
1044	!
1045	!-- Calculate preliminary value (pre_tend) of the tendency
1046	pre_tend = - cdc * &
1047	lad_local * &
1048	SQRT( u(k,j,i)**2 + &
1049	( 0.25_wp * ( v(k,j,i-1) + &
1050	v(k,j,i) + &
1051	v(k,j+1,i) + &
1052	v(k,j+1,i-1) ) &
1053	)**2 + &
1054	( 0.25_wp * ( w(k-1,j,i-1) + &
1055	w(k-1,j,i) + &
1056	w(k,j,i-1) + &
1057	w(k,j,i) ) &
1058	)**2 &
1059	) * &
1060	u(k,j,i)
1061
1062	!
1063	!-- Calculate preliminary new velocity, based on pre_tend
1064	pre_u = u(k,j,i) + dt_3d * pre_tend
1065	!
1066	!-- Compare sign of old velocity and new preliminary velocity,
1067	!-- and in case the signs are different, limit the tendency
1068	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1069	pre_tend = - u(k,j,i) * ddt_3d
1070	ELSE
1071	pre_tend = pre_tend
1072	ENDIF
1073	!
1074	!-- Calculate final tendency
1075	tend(k,j,i) = tend(k,j,i) + pre_tend
1076
1077	ENDDO
1078	ENDDO
1079	ENDDO
1080
1081	!
1082	!-- v-component
1083	CASE ( 2 )
1084	DO i = nxl, nxr
1085	DO j = nysv, nyn
1086	!
1087	!-- Determine topography-top index on v-grid
1088	k_wall = get_topography_top_index( j, i, 'v' )
1089
1090	DO k = k_wall+1, k_wall+pch_index
1091
1092	kk = k - k_wall !- lad arrays are defined flat
1093	!
1094	!-- In order to create sharp boundaries of the plant canopy,
1095	!-- the lad on the v-grid at index (k,j,i) is equal to
1096	!-- lad_s(k,j,i), rather than being interpolated from the
1097	!-- surrounding lad_s, because this would yield smaller lad
1098	!-- at the canopy boundaries than inside of the canopy.
1099	!-- For the same reason, the lad at the northmost(j+1) canopy
1100	!-- boundary on the v-grid equals lad_s(k,j,i).
1101	lad_local = lad_s(kk,j,i)
1102	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp )&
1103	THEN
1104	lad_local = lad_s(kk,j-1,i)
1105	ENDIF
1106
1107	pre_tend = 0.0_wp
1108	pre_v = 0.0_wp
1109	!
1110	!-- Calculate preliminary value (pre_tend) of the tendency
1111	pre_tend = - cdc * &
1112	lad_local * &
1113	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1114	u(k,j-1,i+1) + &
1115	u(k,j,i) + &
1116	u(k,j,i+1) ) &
1117	)**2 + &
1118	v(k,j,i)**2 + &
1119	( 0.25_wp * ( w(k-1,j-1,i) + &
1120	w(k-1,j,i) + &
1121	w(k,j-1,i) + &
1122	w(k,j,i) ) &
1123	)**2 &
1124	) * &
1125	v(k,j,i)
1126
1127	!
1128	!-- Calculate preliminary new velocity, based on pre_tend
1129	pre_v = v(k,j,i) + dt_3d * pre_tend
1130	!
1131	!-- Compare sign of old velocity and new preliminary velocity,
1132	!-- and in case the signs are different, limit the tendency
1133	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1134	pre_tend = - v(k,j,i) * ddt_3d
1135	ELSE
1136	pre_tend = pre_tend
1137	ENDIF
1138	!
1139	!-- Calculate final tendency
1140	tend(k,j,i) = tend(k,j,i) + pre_tend
1141
1142	ENDDO
1143	ENDDO
1144	ENDDO
1145
1146	!
1147	!-- w-component
1148	CASE ( 3 )
1149	DO i = nxl, nxr
1150	DO j = nys, nyn
1151	!
1152	!-- Determine topography-top index on w-grid
1153	k_wall = get_topography_top_index( j, i, 'w' )
1154
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 = get_topography_top_index( j, i, 's' )
1206
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 = get_topography_top_index( j, i, 's' )
1223
1224	DO k = k_wall+1, k_wall+pch_index
1225
1226	kk = k - k_wall !- lad arrays are defined flat
1227	tend(k,j,i) = tend(k,j,i) - &
1228	lsec * &
1229	lad_s(kk,j,i) * &
1230	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1231	u(k,j,i+1) ) &
1232	)**2 + &
1233	( 0.5_wp * ( v(k,j,i) + &
1234	v(k,j+1,i) ) &
1235	)**2 + &
1236	( 0.5_wp * ( w(k-1,j,i) + &
1237	w(k,j,i) ) &
1238	)**2 &
1239	) * &
1240	( q(k,j,i) - lsc )
1241	ENDDO
1242	ENDDO
1243	ENDDO
1244
1245	!
1246	!-- sgs-tke
1247	CASE ( 6 )
1248	DO i = nxl, nxr
1249	DO j = nys, nyn
1250	!
1251	!-- Determine topography-top index on scalar-grid
1252	k_wall = get_topography_top_index( j, i, 's' )
1253
1254	DO k = k_wall+1, k_wall+pch_index
1255
1256	kk = k - k_wall !- lad arrays are defined flat
1257	tend(k,j,i) = tend(k,j,i) - &
1258	2.0_wp * cdc * &
1259	lad_s(kk,j,i) * &
1260	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1261	u(k,j,i+1) ) &
1262	)**2 + &
1263	( 0.5_wp * ( v(k,j,i) + &
1264	v(k,j+1,i) ) &
1265	)**2 + &
1266	( 0.5_wp * ( w(k,j,i) + &
1267	w(k+1,j,i) ) &
1268	)**2 &
1269	) * &
1270	e(k,j,i)
1271	ENDDO
1272	ENDDO
1273	ENDDO
1274	!
1275	!-- scalar concentration
1276	CASE ( 7 )
1277	DO i = nxl, nxr
1278	DO j = nys, nyn
1279	!
1280	!-- Determine topography-top index on scalar-grid
1281	k_wall = get_topography_top_index( j, i, 's' )
1282
1283	DO k = k_wall+1, k_wall+pch_index
1284
1285	kk = k - k_wall !- lad arrays are defined flat
1286	tend(k,j,i) = tend(k,j,i) - &
1287	lsec * &
1288	lad_s(kk,j,i) * &
1289	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1290	u(k,j,i+1) ) &
1291	)**2 + &
1292	( 0.5_wp * ( v(k,j,i) + &
1293	v(k,j+1,i) ) &
1294	)**2 + &
1295	( 0.5_wp * ( w(k-1,j,i) + &
1296	w(k,j,i) ) &
1297	)**2 &
1298	) * &
1299	( s(k,j,i) - lsc )
1300	ENDDO
1301	ENDDO
1302	ENDDO
1303
1304
1305
1306	CASE DEFAULT
1307
1308	WRITE( message_string, * ) 'wrong component: ', component
1309	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1310
1311	END SELECT
1312
1313	END SUBROUTINE pcm_tendency
1314
1315
1316	!------------------------------------------------------------------------------!
1317	! Description:
1318	! ------------
1319	!> Calculation of the tendency terms, accounting for the effect of the plant
1320	!> canopy on momentum and scalar quantities.
1321	!>
1322	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
1323	!> (defined on scalar grid), as initialized in subroutine pcm_init.
1324	!> The lad on the w-grid is vertically interpolated from the surrounding
1325	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
1326	!> k = pch_index. Here, the lad is zero.
1327	!>
1328	!> The canopy drag must be limited (previously accounted for by calculation of
1329	!> a limiting canopy timestep for the determination of the maximum LES timestep
1330	!> in subroutine timestep), since it is physically impossible that the canopy
1331	!> drag alone can locally change the sign of a velocity component. This
1332	!> limitation is realized by calculating preliminary tendencies and velocities.
1333	!> It is subsequently checked if the preliminary new velocity has a different
1334	!> sign than the current velocity. If so, the tendency is limited in a way that
1335	!> the velocity can at maximum be reduced to zero by the canopy drag.
1336	!>
1337	!>
1338	!> Call for grid point i,j
1339	!------------------------------------------------------------------------------!
1340	SUBROUTINE pcm_tendency_ij( i, j, component )
1341
1342
1343	USE control_parameters, &
1344	ONLY: dt_3d, message_string
1345
1346	USE kinds
1347
1348	IMPLICIT NONE
1349
1350	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
1351	INTEGER(iwp) :: i !< running index
1352	INTEGER(iwp) :: j !< running index
1353	INTEGER(iwp) :: k !< running index
1354	INTEGER(iwp) :: k_wall !< vertical index of topography top
1355	INTEGER(iwp) :: kk !< running index for flat lad arrays
1356
1357	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1358	REAL(wp) :: lad_local !< local lad value
1359	REAL(wp) :: pre_tend !< preliminary tendency
1360	REAL(wp) :: pre_u !< preliminary u-value
1361	REAL(wp) :: pre_v !< preliminary v-value
1362	REAL(wp) :: pre_w !< preliminary w-value
1363
1364
1365	ddt_3d = 1.0_wp / dt_3d
1366
1367	!
1368	!-- Compute drag for the three velocity components and the SGS-TKE
1369	SELECT CASE ( component )
1370
1371	!
1372	!-- u-component
1373	CASE ( 1 )
1374	!
1375	!-- Determine topography-top index on u-grid
1376	k_wall = get_topography_top_index( j, i, 'u' )
1377
1378	DO k = k_wall+1, k_wall+pch_index
1379
1380	kk = k - k_wall !- lad arrays are defined flat
1381	!
1382	!-- In order to create sharp boundaries of the plant canopy,
1383	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
1384	!-- rather than being interpolated from the surrounding lad_s,
1385	!-- because this would yield smaller lad at the canopy boundaries
1386	!-- than inside of the canopy.
1387	!-- For the same reason, the lad at the rightmost(i+1)canopy
1388	!-- boundary on the u-grid equals lad_s(k,j,i).
1389	lad_local = lad_s(kk,j,i)
1390	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp ) THEN
1391	lad_local = lad_s(kk,j,i-1)
1392	ENDIF
1393
1394	pre_tend = 0.0_wp
1395	pre_u = 0.0_wp
1396	!
1397	!-- Calculate preliminary value (pre_tend) of the tendency
1398	pre_tend = - cdc * &
1399	lad_local * &
1400	SQRT( u(k,j,i)**2 + &
1401	( 0.25_wp * ( v(k,j,i-1) + &
1402	v(k,j,i) + &
1403	v(k,j+1,i) + &
1404	v(k,j+1,i-1) ) &
1405	)**2 + &
1406	( 0.25_wp * ( w(k-1,j,i-1) + &
1407	w(k-1,j,i) + &
1408	w(k,j,i-1) + &
1409	w(k,j,i) ) &
1410	)**2 &
1411	) * &
1412	u(k,j,i)
1413
1414	!
1415	!-- Calculate preliminary new velocity, based on pre_tend
1416	pre_u = u(k,j,i) + dt_3d * pre_tend
1417	!
1418	!-- Compare sign of old velocity and new preliminary velocity,
1419	!-- and in case the signs are different, limit the tendency
1420	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1421	pre_tend = - u(k,j,i) * ddt_3d
1422	ELSE
1423	pre_tend = pre_tend
1424	ENDIF
1425	!
1426	!-- Calculate final tendency
1427	tend(k,j,i) = tend(k,j,i) + pre_tend
1428	ENDDO
1429
1430
1431	!
1432	!-- v-component
1433	CASE ( 2 )
1434	!
1435	!-- Determine topography-top index on v-grid
1436	k_wall = get_topography_top_index( j, i, 'v' )
1437
1438	DO k = k_wall+1, k_wall+pch_index
1439
1440	kk = k - k_wall !- lad arrays are defined flat
1441	!
1442	!-- In order to create sharp boundaries of the plant canopy,
1443	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
1444	!-- rather than being interpolated from the surrounding lad_s,
1445	!-- because this would yield smaller lad at the canopy boundaries
1446	!-- than inside of the canopy.
1447	!-- For the same reason, the lad at the northmost(j+1)canopy
1448	!-- boundary on the v-grid equals lad_s(k,j,i).
1449	lad_local = lad_s(kk,j,i)
1450	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp ) THEN
1451	lad_local = lad_s(kk,j-1,i)
1452	ENDIF
1453
1454	pre_tend = 0.0_wp
1455	pre_v = 0.0_wp
1456	!
1457	!-- Calculate preliminary value (pre_tend) of the tendency
1458	pre_tend = - cdc * &
1459	lad_local * &
1460	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1461	u(k,j-1,i+1) + &
1462	u(k,j,i) + &
1463	u(k,j,i+1) ) &
1464	)**2 + &
1465	v(k,j,i)**2 + &
1466	( 0.25_wp * ( w(k-1,j-1,i) + &
1467	w(k-1,j,i) + &
1468	w(k,j-1,i) + &
1469	w(k,j,i) ) &
1470	)**2 &
1471	) * &
1472	v(k,j,i)
1473
1474	!
1475	!-- Calculate preliminary new velocity, based on pre_tend
1476	pre_v = v(k,j,i) + dt_3d * pre_tend
1477	!
1478	!-- Compare sign of old velocity and new preliminary velocity,
1479	!-- and in case the signs are different, limit the tendency
1480	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1481	pre_tend = - v(k,j,i) * ddt_3d
1482	ELSE
1483	pre_tend = pre_tend
1484	ENDIF
1485	!
1486	!-- Calculate final tendency
1487	tend(k,j,i) = tend(k,j,i) + pre_tend
1488	ENDDO
1489
1490
1491	!
1492	!-- w-component
1493	CASE ( 3 )
1494	!
1495	!-- Determine topography-top index on w-grid
1496	k_wall = get_topography_top_index( j, i, 'w' )
1497
1498	DO k = k_wall+1, k_wall+pch_index-1
1499
1500	kk = k - k_wall !- lad arrays are defined flat
1501
1502	pre_tend = 0.0_wp
1503	pre_w = 0.0_wp
1504	!
1505	!-- Calculate preliminary value (pre_tend) of the tendency
1506	pre_tend = - cdc * &
1507	(0.5_wp * &
1508	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1509	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1510	u(k,j,i+1) + &
1511	u(k+1,j,i) + &
1512	u(k+1,j,i+1) ) &
1513	)**2 + &
1514	( 0.25_wp * ( v(k,j,i) + &
1515	v(k,j+1,i) + &
1516	v(k+1,j,i) + &
1517	v(k+1,j+1,i) ) &
1518	)**2 + &
1519	w(k,j,i)**2 &
1520	) * &
1521	w(k,j,i)
1522	!
1523	!-- Calculate preliminary new velocity, based on pre_tend
1524	pre_w = w(k,j,i) + dt_3d * pre_tend
1525	!
1526	!-- Compare sign of old velocity and new preliminary velocity,
1527	!-- and in case the signs are different, limit the tendency
1528	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1529	pre_tend = - w(k,j,i) * ddt_3d
1530	ELSE
1531	pre_tend = pre_tend
1532	ENDIF
1533	!
1534	!-- Calculate final tendency
1535	tend(k,j,i) = tend(k,j,i) + pre_tend
1536	ENDDO
1537
1538	!
1539	!-- potential temperature
1540	CASE ( 4 )
1541	!
1542	!-- Determine topography-top index on scalar grid
1543	k_wall = get_topography_top_index( j, i, 's' )
1544
1545	DO k = k_wall+1, k_wall+pch_index
1546	kk = k - k_wall !- lad arrays are defined flat
1547	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1548	ENDDO
1549
1550
1551	!
1552	!-- humidity
1553	CASE ( 5 )
1554	!
1555	!-- Determine topography-top index on scalar grid
1556	k_wall = get_topography_top_index( j, i, 's' )
1557
1558	DO k = k_wall+1, k_wall+pch_index
1559
1560	kk = k - k_wall
1561	tend(k,j,i) = tend(k,j,i) - &
1562	lsec * &
1563	lad_s(kk,j,i) * &
1564	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1565	u(k,j,i+1) ) &
1566	)**2 + &
1567	( 0.5_wp * ( v(k,j,i) + &
1568	v(k,j+1,i) ) &
1569	)**2 + &
1570	( 0.5_wp * ( w(k-1,j,i) + &
1571	w(k,j,i) ) &
1572	)**2 &
1573	) * &
1574	( q(k,j,i) - lsc )
1575	ENDDO
1576
1577	!
1578	!-- sgs-tke
1579	CASE ( 6 )
1580	!
1581	!-- Determine topography-top index on scalar grid
1582	k_wall = get_topography_top_index( j, i, 's' )
1583
1584	DO k = k_wall+1, k_wall+pch_index
1585
1586	kk = k - k_wall
1587	tend(k,j,i) = tend(k,j,i) - &
1588	2.0_wp * cdc * &
1589	lad_s(kk,j,i) * &
1590	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1591	u(k,j,i+1) ) &
1592	)**2 + &
1593	( 0.5_wp * ( v(k,j,i) + &
1594	v(k,j+1,i) ) &
1595	)**2 + &
1596	( 0.5_wp * ( w(k,j,i) + &
1597	w(k+1,j,i) ) &
1598	)**2 &
1599	) * &
1600	e(k,j,i)
1601	ENDDO
1602
1603	!
1604	!-- scalar concentration
1605	CASE ( 7 )
1606	!
1607	!-- Determine topography-top index on scalar grid
1608	k_wall = get_topography_top_index( j, i, 's' )
1609
1610	DO k = k_wall+1, k_wall+pch_index
1611
1612	kk = k - k_wall
1613	tend(k,j,i) = tend(k,j,i) - &
1614	lsec * &
1615	lad_s(kk,j,i) * &
1616	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1617	u(k,j,i+1) ) &
1618	)**2 + &
1619	( 0.5_wp * ( v(k,j,i) + &
1620	v(k,j+1,i) ) &
1621	)**2 + &
1622	( 0.5_wp * ( w(k-1,j,i) + &
1623	w(k,j,i) ) &
1624	)**2 &
1625	) * &
1626	( s(k,j,i) - lsc )
1627	ENDDO
1628
1629	CASE DEFAULT
1630
1631	WRITE( message_string, * ) 'wrong component: ', component
1632	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1633
1634	END SELECT
1635
1636	END SUBROUTINE pcm_tendency_ij
1637
1638
1639
1640	END MODULE plant_canopy_model_mod

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