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source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 3046

Last change on this file since 3046 was 3046, checked in by Giersch, 6 years ago
Remaining error messages revised, comments extended
Property svn:keywords set to `Id`
File size: 75.5 KB

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1	!> @file plant_canopy_model_mod.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
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 1997-2018 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! ------------------
22	! Error messages revised
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: plant_canopy_model_mod.f90 3046 2018-05-29 08:02:15Z Giersch $
27	! Error message revised
28	!
29	! 3022 2018-05-18 11:12:35Z suehring
30	! Bugfix in allocation of transpiration rate
31	!
32	! 3014 2018-05-09 08:42:38Z maronga
33	! Bugfix: nzb_do and nzt_do were not used for 3d data output
34	! Added pc_transpiration_rate
35	!
36	! 2977 2018-04-17 10:27:57Z kanani
37	! Implement changes from branch radiation (r2948-2971) with minor modifications,
38	! plus some formatting.
39	! (moh.hefny):
40	! Add plant canopy type to account for changes in LAD (based on the changes
41	! done by Resler & Pavel) and correct the error message to PALM Standard.
42	!
43	! 2932 2018-03-26 09:39:22Z maronga
44	! renamed canopy_par to plant_canopy_parameters
45	!
46	! 2920 2018-03-22 11:22:01Z kanani
47	! Move usm_lad_rma and prototype_lad to radiation_model (moh.hefny)
48	!
49	! 2892 2018-03-14 15:06:29Z suehring
50	! Bugfix, read separate ASCII LAD files for parent and child model.
51	!
52	! 2770 2018-01-25 15:10:09Z kanani
53	! Correction of parameter check
54	!
55	! 2768 2018-01-24 15:38:29Z kanani
56	! Added check for output quantity pcm_heatrate, some formatting
57	!
58	! 2766 2018-01-22 17:17:47Z kanani
59	! Increased LEN of canopy mode to 30
60	!
61	! 2746 2018-01-15 12:06:04Z suehring
62	! Move flag plant canopy to modules
63	!
64	! 2718 2018-01-02 08:49:38Z maronga
65	! Corrected "Former revisions" section
66	!
67	! 2701 2017-12-15 15:40:50Z suehring
68	! Changes from last commit documented
69	!
70	! 2698 2017-12-14 18:46:24Z suehring
71	! Bugfix in get_topography_top_index
72	!
73	! 2696 2017-12-14 17:12:51Z kanani
74	! Change in file header (GPL part)
75	! Bugfix for vertical loop index pch_index in case of Netcdf input
76	! Introduce 2D index array incorporate canopy top index
77	! Check if canopy on top of topography do not exceed vertical dimension
78	! Add check for canopy_mode in case of Netcdf input.
79	! Enable _FillValue output for 3d quantities
80	! Bugfix in reading of PIDS leaf area density (MS)
81	!
82	! 2669 2017-12-06 16:03:27Z raasch
83	! coupling_char removed
84	!
85	! 2512 2017-10-04 08:26:59Z raasch
86	! upper bounds of 3d output changed from nx+1,ny+1 to nx,ny
87	! no output of ghost layer data
88	!
89	! 2318 2017-07-20 17:27:44Z suehring
90	! Get topography top index via Function call
91	!
92	! 2317 2017-07-20 17:27:19Z suehring
93	! Changed error messages
94	!
95	! 2233 2017-05-30 18:08:54Z suehring
96	!
97	! 2232 2017-05-30 17:47:52Z suehring
98	! Adjustments to new topography concept
99	!
100	! 2213 2017-04-24 15:10:35Z kanani
101	! Bugfix: exchange of ghost points in array pc_heating_rate needed for output
102	! of pcm_heatrate, onetime ghost point exchange of lad_s after initialization.
103	! Formatting and clean-up of subroutine pcm_read_plant_canopy_3d,
104	! minor re-organization of canopy-heating initialization.
105	!
106	! 2209 2017-04-19 09:34:46Z kanani
107	! Added 3d output of leaf area density (pcm_lad) and canopy
108	! heat rate (pcm_heatrate)
109	!
110	! 2024 2016-10-12 16:42:37Z kanani
111	! Added missing lad_s initialization
112	!
113	! 2011 2016-09-19 17:29:57Z kanani
114	! Renamed canopy_heat_flux to pc_heating_rate, since the original meaning/
115	! calculation of the quantity has changed, related to the urban surface model
116	! and similar future applications.
117	!
118	! 2007 2016-08-24 15:47:17Z kanani
119	! Added SUBROUTINE pcm_read_plant_canopy_3d for reading 3d plant canopy data
120	! from file (new case canopy_mode=read_from_file_3d) in the course of
121	! introduction of urban surface model,
122	! introduced variable ext_coef,
123	! resorted SUBROUTINEs to alphabetical order
124	!
125	! 2000 2016-08-20 18:09:15Z knoop
126	! Forced header and separation lines into 80 columns
127	!
128	! 1960 2016-07-12 16:34:24Z suehring
129	! Separate humidity and passive scalar
130	!
131	! 1953 2016-06-21 09:28:42Z suehring
132	! Bugfix, lad_s and lad must be public
133	!
134	! 1826 2016-04-07 12:01:39Z maronga
135	! Further modularization
136	!
137	! 1721 2015-11-16 12:56:48Z raasch
138	! bugfixes: shf is reduced in areas covered with canopy only,
139	! canopy is set on top of topography
140	!
141	! 1682 2015-10-07 23:56:08Z knoop
142	! Code annotations made doxygen readable
143	!
144	! 1484 2014-10-21 10:53:05Z kanani
145	! Changes due to new module structure of the plant canopy model:
146	! module plant_canopy_model_mod now contains a subroutine for the
147	! initialization of the canopy model (pcm_init),
148	! limitation of the canopy drag (previously accounted for by calculation of
149	! a limiting canopy timestep for the determination of the maximum LES timestep
150	! in subroutine timestep) is now realized by the calculation of pre-tendencies
151	! and preliminary velocities in subroutine pcm_tendency,
152	! some redundant MPI communication removed in subroutine pcm_init
153	! (was previously in init_3d_model),
154	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
155	! respective grid is now provided only by lad_s (e.g. in the calculation of
156	! the tendency terms or of cum_lai_hf),
157	! drag_coefficient, lai, leaf_surface_concentration,
158	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
159	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
160	! respectively,
161	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
162	! USE-statements and ONLY-lists modified accordingly
163	!
164	! 1340 2014-03-25 19:45:13Z kanani
165	! REAL constants defined as wp-kind
166	!
167	! 1320 2014-03-20 08:40:49Z raasch
168	! ONLY-attribute added to USE-statements,
169	! kind-parameters added to all INTEGER and REAL declaration statements,
170	! kinds are defined in new module kinds,
171	! old module precision_kind is removed,
172	! revision history before 2012 removed,
173	! comment fields (!:) to be used for variable explanations added to
174	! all variable declaration statements
175	!
176	! 1036 2012-10-22 13:43:42Z raasch
177	! code put under GPL (PALM 3.9)
178	!
179	! 138 2007-11-28 10:03:58Z letzel
180	! Initial revision
181	!
182	! Description:
183	! ------------
184	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
185	!> profile (subroutine pcm_init).
186	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
187	!> due to canopy elements (subroutine pcm_tendency).
188	!------------------------------------------------------------------------------!
189	MODULE plant_canopy_model_mod
190
191	USE arrays_3d, &
192	ONLY: dzu, dzw, e, q, s, tend, u, v, w, zu, zw
193
194	USE indices, &
195	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
196	nz, nzb, nzt
197
198	USE kinds
199
200	USE surface_mod, &
201	ONLY: get_topography_top_index_ji
202
203
204	IMPLICIT NONE
205
206
207	CHARACTER (LEN=30) :: canopy_mode = 'block' !< canopy coverage
208
209	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
210	INTEGER(iwp) :: lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
211
212	INTEGER(iwp), DIMENSION(:,:), ALLOCATABLE :: pch_index_ji !< local plant canopy top
213
214	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
215
216	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
217	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
218	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
219	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
220	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
221	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
222	REAL(wp) :: ext_coef = 0.6_wp !< extinction coefficient
223	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
224	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
225	REAL(wp) :: leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
226	REAL(wp) :: leaf_surface_conc = 0.0_wp !< leaf surface concentration
227	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
228	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
229
230	REAL(wp) :: lad_vertical_gradient(10) = 0.0_wp !< lad gradient
231	REAL(wp) :: lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
232
233	REAL(wp) :: lad_type_coef(0:10) = 1.0_wp !< multiplicative coeficients for particular types
234	!< of plant canopy (e.g. deciduous tree during winter)
235
236	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
237	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
238
239	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
240	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
241	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: pc_heating_rate !< plant canopy heating rate
242	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: pc_transpiration_rate !< plant canopy transpiration rate
243
244	SAVE
245
246
247	PRIVATE
248
249	!
250	!-- Public functions
251	PUBLIC pcm_check_data_output, pcm_check_parameters, pcm_data_output_3d, &
252	pcm_define_netcdf_grid, pcm_header, pcm_init, pcm_parin, pcm_tendency
253
254	!
255	!-- Public variables and constants
256	PUBLIC pc_heating_rate, pc_transpiration_rate, canopy_mode, cthf, dt_plant_canopy, lad, lad_s, &
257	pch_index
258
259
260	INTERFACE pcm_check_data_output
261	MODULE PROCEDURE pcm_check_data_output
262	END INTERFACE pcm_check_data_output
263
264	INTERFACE pcm_check_parameters
265	MODULE PROCEDURE pcm_check_parameters
266	END INTERFACE pcm_check_parameters
267
268	INTERFACE pcm_data_output_3d
269	MODULE PROCEDURE pcm_data_output_3d
270	END INTERFACE pcm_data_output_3d
271
272	INTERFACE pcm_define_netcdf_grid
273	MODULE PROCEDURE pcm_define_netcdf_grid
274	END INTERFACE pcm_define_netcdf_grid
275
276	INTERFACE pcm_header
277	MODULE PROCEDURE pcm_header
278	END INTERFACE pcm_header
279
280	INTERFACE pcm_init
281	MODULE PROCEDURE pcm_init
282	END INTERFACE pcm_init
283
284	INTERFACE pcm_parin
285	MODULE PROCEDURE pcm_parin
286	END INTERFACE pcm_parin
287
288	INTERFACE pcm_read_plant_canopy_3d
289	MODULE PROCEDURE pcm_read_plant_canopy_3d
290	END INTERFACE pcm_read_plant_canopy_3d
291
292	INTERFACE pcm_tendency
293	MODULE PROCEDURE pcm_tendency
294	MODULE PROCEDURE pcm_tendency_ij
295	END INTERFACE pcm_tendency
296
297
298	CONTAINS
299
300
301	!------------------------------------------------------------------------------!
302	! Description:
303	! ------------
304	!> Check data output for plant canopy model
305	!------------------------------------------------------------------------------!
306	SUBROUTINE pcm_check_data_output( var, unit )
307
308
309	USE control_parameters, &
310	ONLY: data_output, message_string, urban_surface
311
312	IMPLICIT NONE
313
314	CHARACTER (LEN=*) :: unit !<
315	CHARACTER (LEN=*) :: var !<
316
317
318	SELECT CASE ( TRIM( var ) )
319
320	CASE ( 'pcm_heatrate' )
321	IF ( cthf == 0.0_wp .AND. .NOT. urban_surface ) THEN
322	message_string = 'output of "' // TRIM( var ) // '" requi' // &
323	'res setting of parameter cthf /= 0.0'
324	CALL message( 'pcm_check_data_output', 'PA1000', 1, 2, 0, 6, 0 )
325	ENDIF
326	unit = 'K s-1'
327
328	CASE ( 'pcm_transpirationrate' )
329	unit = 'kg kg-1 s-1'
330
331	CASE ( 'pcm_lad' )
332	unit = 'm2 m-3'
333
334
335	CASE DEFAULT
336	unit = 'illegal'
337
338	END SELECT
339
340
341	END SUBROUTINE pcm_check_data_output
342
343
344	!------------------------------------------------------------------------------!
345	! Description:
346	! ------------
347	!> Check parameters routine for plant canopy model
348	!------------------------------------------------------------------------------!
349	SUBROUTINE pcm_check_parameters
350
351	USE control_parameters, &
352	ONLY: cloud_physics, coupling_char, message_string, &
353	microphysics_seifert
354
355	USE netcdf_data_input_mod, &
356	ONLY: input_file_static, input_pids_static
357
358
359	IMPLICIT NONE
360
361
362	IF ( canopy_drag_coeff == 0.0_wp ) THEN
363	message_string = 'plant_canopy = .TRUE. requires a non-zero drag '// &
364	'coefficient & given value is canopy_drag_coeff = 0.0'
365	CALL message( 'pcm_check_parameters', 'PA0041', 1, 2, 0, 6, 0 )
366	ENDIF
367
368	IF ( ( alpha_lad /= 9999999.9_wp .AND. beta_lad == 9999999.9_wp ) .OR.&
369	beta_lad /= 9999999.9_wp .AND. alpha_lad == 9999999.9_wp ) THEN
370	message_string = 'using the beta function for the construction ' // &
371	'of the leaf area density profile requires ' // &
372	'both alpha_lad and beta_lad to be /= 9999999.9'
373	CALL message( 'pcm_check_parameters', 'PA0118', 1, 2, 0, 6, 0 )
374	ENDIF
375
376	IF ( calc_beta_lad_profile .AND. lai_beta == 0.0_wp ) THEN
377	message_string = 'using the beta function for the construction ' // &
378	'of the leaf area density profile requires ' // &
379	'a non-zero lai_beta, but given value is ' // &
380	'lai_beta = 0.0'
381	CALL message( 'pcm_check_parameters', 'PA0119', 1, 2, 0, 6, 0 )
382	ENDIF
383
384	IF ( calc_beta_lad_profile .AND. lad_surface /= 0.0_wp ) THEN
385	message_string = 'simultaneous setting of alpha_lad /= 9999999.9 '// &
386	'combined with beta_lad /= 9999999.9 ' // &
387	'and lad_surface /= 0.0 is not possible, ' // &
388	'use either vertical gradients or the beta ' // &
389	'function for the construction of the leaf area '// &
390	'density profile'
391	CALL message( 'pcm_check_parameters', 'PA0120', 1, 2, 0, 6, 0 )
392	ENDIF
393
394	IF ( cloud_physics .AND. microphysics_seifert ) THEN
395	message_string = 'plant_canopy = .TRUE. requires cloud_scheme /=' // &
396	' seifert_beheng'
397	CALL message( 'pcm_check_parameters', 'PA0360', 1, 2, 0, 6, 0 )
398	ENDIF
399	!
400	!-- If dynamic input file is used, canopy need to be read from file
401	IF ( input_pids_static .AND. &
402	TRIM( canopy_mode ) /= 'read_from_file_3d' ) THEN
403	message_string = 'Usage of dynamic input file ' // &
404	TRIM( input_file_static ) // &
405	TRIM( coupling_char ) // ' requires ' // &
406	'canopy_mode = read_from_file_3d'
407	CALL message( 'pcm_check_parameters', 'PA0999', 1, 2, 0, 6, 0 )
408	ENDIF
409
410
411	END SUBROUTINE pcm_check_parameters
412
413
414	!------------------------------------------------------------------------------!
415	!
416	! Description:
417	! ------------
418	!> Subroutine defining 3D output variables
419	!------------------------------------------------------------------------------!
420	SUBROUTINE pcm_data_output_3d( av, variable, found, local_pf, fill_value, &
421	nzb_do, nzt_do )
422
423	USE indices
424
425	USE kinds
426
427
428	IMPLICIT NONE
429
430	CHARACTER (LEN=*) :: variable !<
431
432	INTEGER(iwp) :: av !<
433	INTEGER(iwp) :: i !<
434	INTEGER(iwp) :: j !<
435	INTEGER(iwp) :: k !<
436	INTEGER(iwp) :: k_topo !< topography top index
437	INTEGER(iwp) :: nzb_do !< lower limit of the data output (usually 0)
438	INTEGER(iwp) :: nzt_do !< vertical upper limit of the data output (usually nz_do3d)
439
440	LOGICAL :: found !<
441
442	REAL(wp) :: fill_value
443	REAL(sp), DIMENSION(nxl:nxr,nys:nyn,nzb_do:nzt_do) :: local_pf !<
444
445
446	found = .TRUE.
447
448	local_pf = REAL( fill_value, KIND = 4 )
449
450	SELECT CASE ( TRIM( variable ) )
451
452	CASE ( 'pcm_heatrate' )
453	IF ( av == 0 ) THEN
454	DO i = nxl, nxr
455	DO j = nys, nyn
456	IF ( pch_index_ji(j,i) /= 0 ) THEN
457	k_topo = get_topography_top_index_ji( j, i, 's' )
458	DO k = k_topo, k_topo + pch_index_ji(j,i)
459	local_pf(i,j,k) = pc_heating_rate(k-k_topo,j,i)
460	ENDDO
461	ENDIF
462	ENDDO
463	ENDDO
464	ENDIF
465
466	CASE ( 'pcm_transpirationrate' )
467	IF ( av == 0 ) THEN
468	DO i = nxl, nxr
469	DO j = nys, nyn
470	IF ( pch_index_ji(j,i) /= 0 ) THEN
471	k_topo = get_topography_top_index_ji( j, i, 's' )
472	DO k = k_topo, k_topo + pch_index_ji(j,i)
473	local_pf(i,j,k) = pc_transpiration_rate(k-k_topo,j,i)
474	ENDDO
475	ENDIF
476	ENDDO
477	ENDDO
478	ENDIF
479
480	CASE ( 'pcm_lad' )
481	IF ( av == 0 ) THEN
482	DO i = nxl, nxr
483	DO j = nys, nyn
484	IF ( pch_index_ji(j,i) /= 0 ) THEN
485	k_topo = get_topography_top_index_ji( j, i, 's' )
486	DO k = k_topo, k_topo + pch_index_ji(j,i)
487	local_pf(i,j,k) = lad_s(k-k_topo,j,i)
488	ENDDO
489	ENDIF
490	ENDDO
491	ENDDO
492	ENDIF
493
494
495	CASE DEFAULT
496	found = .FALSE.
497
498	END SELECT
499
500
501	END SUBROUTINE pcm_data_output_3d
502
503	!------------------------------------------------------------------------------!
504	!
505	! Description:
506	! ------------
507	!> Subroutine defining appropriate grid for netcdf variables.
508	!> It is called from subroutine netcdf.
509	!------------------------------------------------------------------------------!
510	SUBROUTINE pcm_define_netcdf_grid( var, found, grid_x, grid_y, grid_z )
511
512	IMPLICIT NONE
513
514	CHARACTER (LEN=*), INTENT(IN) :: var !<
515	LOGICAL, INTENT(OUT) :: found !<
516	CHARACTER (LEN=*), INTENT(OUT) :: grid_x !<
517	CHARACTER (LEN=*), INTENT(OUT) :: grid_y !<
518	CHARACTER (LEN=*), INTENT(OUT) :: grid_z !<
519
520	found = .TRUE.
521
522	!
523	!-- Check for the grid
524	SELECT CASE ( TRIM( var ) )
525
526	CASE ( 'pcm_heatrate', 'pcm_lad', 'pcm_transpirationrate')
527	grid_x = 'x'
528	grid_y = 'y'
529	grid_z = 'zu'
530
531	CASE DEFAULT
532	found = .FALSE.
533	grid_x = 'none'
534	grid_y = 'none'
535	grid_z = 'none'
536	END SELECT
537
538	END SUBROUTINE pcm_define_netcdf_grid
539
540
541	!------------------------------------------------------------------------------!
542	! Description:
543	! ------------
544	!> Header output for plant canopy model
545	!------------------------------------------------------------------------------!
546	SUBROUTINE pcm_header ( io )
547
548	USE control_parameters, &
549	ONLY: dz, passive_scalar
550
551
552	IMPLICIT NONE
553
554	CHARACTER (LEN=10) :: coor_chr !<
555
556	CHARACTER (LEN=86) :: coordinates !<
557	CHARACTER (LEN=86) :: gradients !<
558	CHARACTER (LEN=86) :: leaf_area_density !<
559	CHARACTER (LEN=86) :: slices !<
560
561	INTEGER(iwp) :: i !<
562	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
563	INTEGER(iwp) :: k !<
564
565	REAL(wp) :: canopy_height !< canopy height (in m)
566
567	canopy_height = pch_index * dz
568
569	WRITE ( io, 1 ) canopy_mode, canopy_height, pch_index, &
570	canopy_drag_coeff
571	IF ( passive_scalar ) THEN
572	WRITE ( io, 2 ) leaf_scalar_exch_coeff, &
573	leaf_surface_conc
574	ENDIF
575
576	!
577	!-- Heat flux at the top of vegetation
578	WRITE ( io, 3 ) cthf
579
580	!
581	!-- Leaf area density profile, calculated either from given vertical
582	!-- gradients or from beta probability density function.
583	IF ( .NOT. calc_beta_lad_profile ) THEN
584
585	!-- Building output strings, starting with surface value
586	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
587	gradients = '------'
588	slices = ' 0'
589	coordinates = ' 0.0'
590	i = 1
591	DO WHILE ( i < 11 .AND. lad_vertical_gradient_level_ind(i) &
592	/= -9999 )
593
594	WRITE (coor_chr,'(F7.2)') lad(lad_vertical_gradient_level_ind(i))
595	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
596	TRIM( coor_chr )
597
598	WRITE (coor_chr,'(F7.2)') lad_vertical_gradient(i)
599	gradients = TRIM( gradients ) // ' ' // TRIM( coor_chr )
600
601	WRITE (coor_chr,'(I7)') lad_vertical_gradient_level_ind(i)
602	slices = TRIM( slices ) // ' ' // TRIM( coor_chr )
603
604	WRITE (coor_chr,'(F7.1)') lad_vertical_gradient_level(i)
605	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
606
607	i = i + 1
608	ENDDO
609
610	WRITE ( io, 4 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
611	TRIM( gradients ), TRIM( slices )
612
613	ELSE
614
615	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
616	coordinates = ' 0.0'
617
618	DO k = 1, pch_index
619
620	WRITE (coor_chr,'(F7.2)') lad(k)
621	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
622	TRIM( coor_chr )
623
624	WRITE (coor_chr,'(F7.1)') zu(k)
625	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
626
627	ENDDO
628
629	WRITE ( io, 5 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
630	alpha_lad, beta_lad, lai_beta
631
632	ENDIF
633
634	1 FORMAT (//' Vegetation canopy (drag) model:'/ &
635	' ------------------------------'// &
636	' Canopy mode: ', A / &
637	' Canopy height: ',F6.2,'m (',I4,' grid points)' / &
638	' Leaf drag coefficient: ',F6.2 /)
639	2 FORMAT (/ ' Scalar exchange coefficient: ',F6.2 / &
640	' Scalar concentration at leaf surfaces in kg/m**3: ',F6.2 /)
641	3 FORMAT (' Predefined constant heatflux at the top of the vegetation: ',F6.2, &
642	' K m/s')
643	4 FORMAT (/ ' Characteristic levels of the leaf area density:'// &
644	' Height: ',A,' m'/ &
645	' Leaf area density: ',A,' m2/m3'/ &
646	' Gradient: ',A,' m2/m4'/ &
647	' Gridpoint: ',A)
648	5 FORMAT (//' Characteristic levels of the leaf area density and coefficients:'&
649	// ' Height: ',A,' m'/ &
650	' Leaf area density: ',A,' m2/m3'/ &
651	' Coefficient alpha: ',F6.2 / &
652	' Coefficient beta: ',F6.2 / &
653	' Leaf area index: ',F6.2,' m2/m2' /)
654
655	END SUBROUTINE pcm_header
656
657
658	!------------------------------------------------------------------------------!
659	! Description:
660	! ------------
661	!> Initialization of the plant canopy model
662	!------------------------------------------------------------------------------!
663	SUBROUTINE pcm_init
664
665
666	USE control_parameters, &
667	ONLY: dz, humidity, io_blocks, io_group, message_string, ocean, &
668	passive_scalar, urban_surface
669
670	USE netcdf_data_input_mod, &
671	ONLY: leaf_area_density_f
672
673	USE surface_mod, &
674	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
675
676	IMPLICIT NONE
677
678	CHARACTER(10) :: pct
679
680	INTEGER(iwp) :: i !< running index
681	INTEGER(iwp) :: ii !< index
682	INTEGER(iwp) :: j !< running index
683	INTEGER(iwp) :: k !< running index
684	INTEGER(iwp) :: m !< running index
685
686	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
687	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
688	REAL(wp) :: gradient !< gradient for lad-profile construction
689	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
690	REAL(wp) :: pcv(nzb:nzt+1) !<
691
692	!
693	!-- Allocate one-dimensional arrays for the computation of the
694	!-- leaf area density (lad) profile
695	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
696	lad = 0.0_wp
697	pre_lad = 0.0_wp
698
699	!
700	!-- Set flag that indicates that the lad-profile shall be calculated by using
701	!-- a beta probability density function
702	IF ( alpha_lad /= 9999999.9_wp .AND. beta_lad /= 9999999.9_wp ) THEN
703	calc_beta_lad_profile = .TRUE.
704	ENDIF
705
706
707	!
708	!-- Compute the profile of leaf area density used in the plant
709	!-- canopy model. The profile can either be constructed from
710	!-- prescribed vertical gradients of the leaf area density or by
711	!-- using a beta probability density function (see e.g. Markkanen et al.,
712	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
713	IF ( .NOT. calc_beta_lad_profile ) THEN
714
715	!
716	!-- Use vertical gradients for lad-profile construction
717	i = 1
718	gradient = 0.0_wp
719
720	IF ( .NOT. ocean ) THEN
721
722	lad(0) = lad_surface
723	lad_vertical_gradient_level_ind(1) = 0
724
725	DO k = 1, pch_index
726	IF ( i < 11 ) THEN
727	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
728	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
729	gradient = lad_vertical_gradient(i)
730	lad_vertical_gradient_level_ind(i) = k - 1
731	i = i + 1
732	ENDIF
733	ENDIF
734	IF ( gradient /= 0.0_wp ) THEN
735	IF ( k /= 1 ) THEN
736	lad(k) = lad(k-1) + dzu(k) * gradient
737	ELSE
738	lad(k) = lad_surface + dzu(k) * gradient
739	ENDIF
740	ELSE
741	lad(k) = lad(k-1)
742	ENDIF
743	ENDDO
744
745	ENDIF
746
747	!
748	!-- In case of no given leaf area density gradients, choose a vanishing
749	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
750	!-- file.
751	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
752	lad_vertical_gradient_level(1) = 0.0_wp
753	ENDIF
754
755	ELSE
756
757	!
758	!-- Use beta function for lad-profile construction
759	int_bpdf = 0.0_wp
760	canopy_height = pch_index * dz
761
762	DO k = 0, pch_index
763	int_bpdf = int_bpdf + &
764	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
765	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
766	beta_lad-1.0_wp ) ) &
767	* ( ( zw(k+1)-zw(k) ) / canopy_height ) )
768	ENDDO
769
770	!
771	!-- Preliminary lad profile (defined on w-grid)
772	DO k = 0, pch_index
773	pre_lad(k) = lai_beta * &
774	( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) ) &
775	* ( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
776	beta_lad-1.0_wp ) ) / int_bpdf &
777	) / canopy_height
778	ENDDO
779
780	!
781	!-- Final lad profile (defined on scalar-grid level, since most prognostic
782	!-- quantities are defined there, hence, less interpolation is required
783	!-- when calculating the canopy tendencies)
784	lad(0) = pre_lad(0)
785	DO k = 1, pch_index
786	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
787	ENDDO
788
789	ENDIF
790
791	!
792	!-- Allocate 3D-array for the leaf area density (lad_s).
793	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
794
795	!
796	!-- Initialize canopy parameters cdc (canopy drag coefficient),
797	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
798	!-- with the prescribed values
799	cdc = canopy_drag_coeff
800	lsec = leaf_scalar_exch_coeff
801	lsc = leaf_surface_conc
802
803	!
804	!-- Initialization of the canopy coverage in the model domain:
805	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
806	!-- fully covers the domain surface
807	SELECT CASE ( TRIM( canopy_mode ) )
808
809	CASE( 'block' )
810
811	DO i = nxlg, nxrg
812	DO j = nysg, nyng
813	lad_s(:,j,i) = lad(:)
814	ENDDO
815	ENDDO
816
817	CASE ( 'read_from_file_3d' )
818	!
819	!-- Initialize LAD with data from file. If LAD is given in NetCDF file,
820	!-- use these values, else take LAD profiles from ASCII file.
821	!-- Please note, in NetCDF file LAD is only given up to the maximum
822	!-- canopy top, indicated by leaf_area_density_f%nz.
823	lad_s = 0.0_wp
824	IF ( leaf_area_density_f%from_file ) THEN
825	!
826	!-- Set also pch_index, used to be the upper bound of the vertical
827	!-- loops. Therefore, use the global top of the canopy layer.
828	pch_index = leaf_area_density_f%nz - 1
829
830	DO i = nxl, nxr
831	DO j = nys, nyn
832	DO k = 0, leaf_area_density_f%nz - 1
833	IF ( leaf_area_density_f%var(k,j,i) /= &
834	leaf_area_density_f%fill ) &
835	lad_s(k,j,i) = leaf_area_density_f%var(k,j,i)
836	ENDDO
837	ENDDO
838	ENDDO
839	CALL exchange_horiz( lad_s, nbgp )
840	!
841	! ASCII file
842	!-- Initialize canopy parameters cdc (canopy drag coefficient),
843	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
844	!-- from file which contains complete 3D data (separate vertical profiles for
845	!-- each location).
846	ELSE
847	CALL pcm_read_plant_canopy_3d
848	ENDIF
849
850	CASE DEFAULT
851	!
852	!-- The DEFAULT case is reached either if the parameter
853	!-- canopy mode contains a wrong character string or if the
854	!-- user has coded a special case in the user interface.
855	!-- There, the subroutine user_init_plant_canopy checks
856	!-- which of these two conditions applies.
857	CALL user_init_plant_canopy
858
859	END SELECT
860	!
861	!-- Initialize 2D index array indicating canopy top index.
862	ALLOCATE( pch_index_ji(nysg:nyng,nxlg:nxrg) )
863	pch_index_ji = 0
864
865	DO i = nxl, nxr
866	DO j = nys, nyn
867	DO k = 0, pch_index
868	IF ( lad_s(k,j,i) /= 0 ) pch_index_ji(j,i) = k
869	ENDDO
870	!
871	!-- Check whether topography and local vegetation on top exceed
872	!-- height of the model domain.
873	k = get_topography_top_index_ji( j, i, 's' )
874	IF ( k + pch_index_ji(j,i) >= nzt + 1 ) THEN
875	message_string = 'Local vegetation height on top of ' // &
876	'topography exceeds height of model domain.'
877	CALL message( 'pcm_init', 'PA0999', 2, 2, 0, 6, 0 )
878	ENDIF
879
880	ENDDO
881	ENDDO
882
883	CALL exchange_horiz_2d_int( pch_index_ji, nys, nyn, nxl, nxr, nbgp )
884
885	!
886	!-- Initialization of the canopy heat source distribution due to heating
887	!-- of the canopy layers by incoming solar radiation, in case that a non-zero
888	!-- value is set for the canopy top heat flux (cthf), which equals the
889	!-- available net radiation at canopy top.
890	!-- The heat source distribution is calculated by a decaying exponential
891	!-- function of the downward cumulative leaf area index (cum_lai_hf),
892	!-- assuming that the foliage inside the plant canopy is heated by solar
893	!-- radiation penetrating the canopy layers according to the distribution
894	!-- of net radiation as suggested by Brown & Covey (1966; Agric. Meteorol. 3,
895	!-- 73â96). This approach has been applied e.g. by Shaw & Schumann (1992;
896	!-- Bound.-Layer Meteorol. 61, 47â64).
897	!-- When using the urban surface model (USM), canopy heating (pc_heating_rate)
898	!-- by radiation is calculated in the USM.
899	IF ( cthf /= 0.0_wp .AND. .NOT. urban_surface ) THEN
900
901	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
902	pc_heating_rate(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
903	!
904	!-- Piecewise calculation of the cumulative leaf area index by vertical
905	!-- integration of the leaf area density
906	cum_lai_hf(:,:,:) = 0.0_wp
907	DO i = nxlg, nxrg
908	DO j = nysg, nyng
909	DO k = pch_index_ji(j,i)-1, 0, -1
910	IF ( k == pch_index_ji(j,i)-1 ) THEN
911	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
912	( 0.5_wp * lad_s(k+1,j,i) * &
913	( zw(k+1) - zu(k+1) ) ) + &
914	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
915	lad_s(k,j,i) ) + &
916	lad_s(k+1,j,i) ) * &
917	( zu(k+1) - zw(k) ) )
918	ELSE
919	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
920	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
921	lad_s(k+1,j,i) ) + &
922	lad_s(k+1,j,i) ) * &
923	( zw(k+1) - zu(k+1) ) ) + &
924	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
925	lad_s(k,j,i) ) + &
926	lad_s(k+1,j,i) ) * &
927	( zu(k+1) - zw(k) ) )
928	ENDIF
929	ENDDO
930	ENDDO
931	ENDDO
932
933	!
934	!-- In areas with canopy the surface value of the canopy heat
935	!-- flux distribution overrides the surface heat flux (shf)
936	!-- Start with default surface type
937	DO m = 1, surf_def_h(0)%ns
938	k = surf_def_h(0)%k(m)
939	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
940	surf_def_h(0)%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
941	ENDDO
942	!
943	!-- Natural surfaces
944	DO m = 1, surf_lsm_h%ns
945	k = surf_lsm_h%k(m)
946	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
947	surf_lsm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
948	ENDDO
949	!
950	!-- Urban surfaces
951	DO m = 1, surf_usm_h%ns
952	k = surf_usm_h%k(m)
953	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
954	surf_usm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
955	ENDDO
956	!
957	!
958	!-- Calculation of the heating rate (K/s) within the different layers of
959	!-- the plant canopy. Calculation is only necessary in areas covered with
960	!-- canopy.
961	!-- Within the different canopy layers the plant-canopy heating
962	!-- rate (pc_heating_rate) is calculated as the vertical
963	!-- divergence of the canopy heat fluxes at the top and bottom
964	!-- of the respective layer
965	DO i = nxlg, nxrg
966	DO j = nysg, nyng
967	DO k = 1, pch_index_ji(j,i)
968	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) THEN
969	pc_heating_rate(k,j,i) = cthf * &
970	( exp(-ext_coef*cum_lai_hf(k,j,i)) - &
971	exp(-ext_coef*cum_lai_hf(k-1,j,i) ) ) / dzw(k)
972	ENDIF
973	ENDDO
974	ENDDO
975	ENDDO
976
977	ENDIF
978	!
979	!-- Allocate transpiration rate
980	IF ( humidity ) &
981	ALLOCATE( pc_transpiration_rate(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
982
983
984
985	END SUBROUTINE pcm_init
986
987
988	!------------------------------------------------------------------------------!
989	! Description:
990	! ------------
991	!> Parin for &plant_canopy_parameters for plant canopy model
992	!------------------------------------------------------------------------------!
993	SUBROUTINE pcm_parin
994
995	USE control_parameters, &
996	ONLY: message_string, plant_canopy
997
998	IMPLICIT NONE
999
1000	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
1001
1002	NAMELIST /plant_canopy_parameters/ &
1003	alpha_lad, beta_lad, canopy_drag_coeff, &
1004	canopy_mode, cthf, &
1005	lad_surface, lad_type_coef, &
1006	lad_vertical_gradient, &
1007	lad_vertical_gradient_level, &
1008	lai_beta, &
1009	leaf_scalar_exch_coeff, &
1010	leaf_surface_conc, pch_index
1011
1012	NAMELIST /canopy_par/ alpha_lad, beta_lad, canopy_drag_coeff, &
1013	canopy_mode, cthf, &
1014	lad_surface, lad_type_coef, &
1015	lad_vertical_gradient, &
1016	lad_vertical_gradient_level, &
1017	lai_beta, &
1018	leaf_scalar_exch_coeff, &
1019	leaf_surface_conc, pch_index
1020
1021	line = ' '
1022
1023	!
1024	!-- Try to find radiation model package
1025	REWIND ( 11 )
1026	line = ' '
1027	DO WHILE ( INDEX( line, '&plant_canopy_parameters' ) == 0 )
1028	READ ( 11, '(A)', END=10 ) line
1029	ENDDO
1030	BACKSPACE ( 11 )
1031
1032	!
1033	!-- Read user-defined namelist
1034	READ ( 11, plant_canopy_parameters )
1035
1036	!
1037	!-- Set flag that indicates that the radiation model is switched on
1038	plant_canopy = .TRUE.
1039
1040	GOTO 12
1041	!
1042	!-- Try to find old namelist
1043	10 REWIND ( 11 )
1044	line = ' '
1045	DO WHILE ( INDEX( line, '&canopy_par' ) == 0 )
1046	READ ( 11, '(A)', END=12 ) line
1047	ENDDO
1048	BACKSPACE ( 11 )
1049
1050	!
1051	!-- Read user-defined namelist
1052	READ ( 11, canopy_par )
1053
1054	message_string = 'namelist canopy_par is deprecated and will be ' // &
1055	'removed in near future. Please use namelist ' // &
1056	'plant_canopy_parameters instead'
1057	CALL message( 'pcm_parin', 'PA0487', 0, 1, 0, 6, 0 )
1058
1059	!
1060	!-- Set flag that indicates that the radiation model is switched on
1061	plant_canopy = .TRUE.
1062
1063	12 CONTINUE
1064
1065
1066	END SUBROUTINE pcm_parin
1067
1068
1069
1070	!------------------------------------------------------------------------------!
1071	! Description:
1072	! ------------
1073	!
1074	!> Loads 3D plant canopy data from file. File format is as follows:
1075	!>
1076	!> num_levels
1077	!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
1078	!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
1079	!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
1080	!> ...
1081	!>
1082	!> i.e. first line determines number of levels and further lines represent plant
1083	!> canopy data, one line per column and variable. In each data line,
1084	!> dtype represents variable to be set:
1085	!>
1086	!> dtype=1: leaf area density (lad_s)
1087	!> dtype=2....n: some additional plant canopy input data quantity
1088	!>
1089	!> Zeros are added automatically above num_levels until top of domain. Any
1090	!> non-specified (x,y) columns have zero values as default.
1091	!------------------------------------------------------------------------------!
1092	SUBROUTINE pcm_read_plant_canopy_3d
1093
1094	USE control_parameters, &
1095	ONLY: coupling_char, message_string, passive_scalar
1096
1097	USE indices, &
1098	ONLY: nbgp
1099
1100	IMPLICIT NONE
1101
1102	INTEGER(iwp) :: dtype !< type of input data (1=lad)
1103	INTEGER(iwp) :: pctype !< type of plant canopy (deciduous,non-deciduous,...)
1104	INTEGER(iwp) :: i, j !< running index
1105	INTEGER(iwp) :: nzp !< number of vertical layers of plant canopy
1106	INTEGER(iwp) :: nzpltop !<
1107	INTEGER(iwp) :: nzpl !<
1108
1109	REAL(wp), DIMENSION(:), ALLOCATABLE :: col !< vertical column of input data
1110
1111	!
1112	!-- Initialize lad_s array
1113	lad_s = 0.0_wp
1114
1115	!
1116	!-- Open and read plant canopy input data
1117	OPEN(152, FILE='PLANT_CANOPY_DATA_3D' // TRIM( coupling_char ), &
1118	ACCESS='SEQUENTIAL', ACTION='READ', STATUS='OLD', &
1119	FORM='FORMATTED', ERR=515)
1120	READ(152, *, ERR=516, END=517) nzp !< read first line = number of vertical layers
1121
1122	ALLOCATE( col(0:nzp-1) )
1123
1124	DO
1125	READ(152, *, ERR=516, END=517) dtype, i, j, pctype, col(:)
1126	IF ( i < nxlg .OR. i > nxrg .OR. j < nysg .OR. j > nyng ) CYCLE
1127
1128	SELECT CASE (dtype)
1129	CASE( 1 ) !< leaf area density
1130	!
1131	!-- This is just the pure canopy layer assumed to be grounded to
1132	!-- a flat domain surface. At locations where plant canopy sits
1133	!-- on top of any kind of topography, the vertical plant column
1134	!-- must be "lifted", which is done in SUBROUTINE pcm_tendency.
1135	IF ( pctype < 0 .OR. pctype > 10 ) THEN !< incorrect plant canopy type
1136	WRITE( message_string, * ) 'Incorrect type of plant canopy. ' // &
1137	'Allowed values 0 <= pctype <= 10, ' // &
1138	'but pctype is ', pctype
1139	CALL message( 'pcm_read_plant_canopy_3d', 'PA0349', 1, 2, 0, 6, 0 )
1140	ENDIF
1141	lad_s(0:nzp-1,j,i) = col(0:nzp-1) * lad_type_coef(pctype)
1142
1143	CASE DEFAULT
1144	WRITE(message_string, '(a,i2,a)') &
1145	'Unknown record type in file PLANT_CANOPY_DATA_3D: "', dtype, '"'
1146	CALL message( 'pcm_read_plant_canopy_3d', 'PA0530', 1, 2, 0, 6, 0 )
1147	END SELECT
1148	ENDDO
1149
1150	515 message_string = 'error opening file PLANT_CANOPY_DATA_3D'
1151	CALL message( 'pcm_read_plant_canopy_3d', 'PA0531', 1, 2, 0, 6, 0 )
1152
1153	516 message_string = 'error reading file PLANT_CANOPY_DATA_3D'
1154	CALL message( 'pcm_read_plant_canopy_3d', 'PA0532', 1, 2, 0, 6, 0 )
1155
1156	517 CLOSE(152)
1157	DEALLOCATE( col )
1158
1159	CALL exchange_horiz( lad_s, nbgp )
1160
1161	END SUBROUTINE pcm_read_plant_canopy_3d
1162
1163
1164
1165	!------------------------------------------------------------------------------!
1166	! Description:
1167	! ------------
1168	!> Calculation of the tendency terms, accounting for the effect of the plant
1169	!> canopy on momentum and scalar quantities.
1170	!>
1171	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
1172	!> (defined on scalar grid), as initialized in subroutine pcm_init.
1173	!> The lad on the w-grid is vertically interpolated from the surrounding
1174	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
1175	!> k = pch_index. Here, the lad is zero.
1176	!>
1177	!> The canopy drag must be limited (previously accounted for by calculation of
1178	!> a limiting canopy timestep for the determination of the maximum LES timestep
1179	!> in subroutine timestep), since it is physically impossible that the canopy
1180	!> drag alone can locally change the sign of a velocity component. This
1181	!> limitation is realized by calculating preliminary tendencies and velocities.
1182	!> It is subsequently checked if the preliminary new velocity has a different
1183	!> sign than the current velocity. If so, the tendency is limited in a way that
1184	!> the velocity can at maximum be reduced to zero by the canopy drag.
1185	!>
1186	!>
1187	!> Call for all grid points
1188	!------------------------------------------------------------------------------!
1189	SUBROUTINE pcm_tendency( component )
1190
1191
1192	USE control_parameters, &
1193	ONLY: dt_3d, message_string
1194
1195	USE kinds
1196
1197	IMPLICIT NONE
1198
1199	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
1200	INTEGER(iwp) :: i !< running index
1201	INTEGER(iwp) :: j !< running index
1202	INTEGER(iwp) :: k !< running index
1203	INTEGER(iwp) :: k_wall !< vertical index of topography top
1204	INTEGER(iwp) :: kk !< running index for flat lad arrays
1205
1206	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1207	REAL(wp) :: lad_local !< local lad value
1208	REAL(wp) :: pre_tend !< preliminary tendency
1209	REAL(wp) :: pre_u !< preliminary u-value
1210	REAL(wp) :: pre_v !< preliminary v-value
1211	REAL(wp) :: pre_w !< preliminary w-value
1212
1213
1214	ddt_3d = 1.0_wp / dt_3d
1215
1216	!
1217	!-- Compute drag for the three velocity components and the SGS-TKE:
1218	SELECT CASE ( component )
1219
1220	!
1221	!-- u-component
1222	CASE ( 1 )
1223	DO i = nxlu, nxr
1224	DO j = nys, nyn
1225	!
1226	!-- Determine topography-top index on u-grid
1227	k_wall = get_topography_top_index_ji( j, i, 'u' )
1228	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1229
1230	kk = k - k_wall !- lad arrays are defined flat
1231	!
1232	!-- In order to create sharp boundaries of the plant canopy,
1233	!-- the lad on the u-grid at index (k,j,i) is equal to
1234	!-- lad_s(k,j,i), rather than being interpolated from the
1235	!-- surrounding lad_s, because this would yield smaller lad
1236	!-- at the canopy boundaries than inside of the canopy.
1237	!-- For the same reason, the lad at the rightmost(i+1)canopy
1238	!-- boundary on the u-grid equals lad_s(k,j,i).
1239	lad_local = lad_s(kk,j,i)
1240	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp )&
1241	THEN
1242	lad_local = lad_s(kk,j,i-1)
1243	ENDIF
1244
1245	pre_tend = 0.0_wp
1246	pre_u = 0.0_wp
1247	!
1248	!-- Calculate preliminary value (pre_tend) of the tendency
1249	pre_tend = - cdc * &
1250	lad_local * &
1251	SQRT( u(k,j,i)**2 + &
1252	( 0.25_wp * ( v(k,j,i-1) + &
1253	v(k,j,i) + &
1254	v(k,j+1,i) + &
1255	v(k,j+1,i-1) ) &
1256	)**2 + &
1257	( 0.25_wp * ( w(k-1,j,i-1) + &
1258	w(k-1,j,i) + &
1259	w(k,j,i-1) + &
1260	w(k,j,i) ) &
1261	)**2 &
1262	) * &
1263	u(k,j,i)
1264
1265	!
1266	!-- Calculate preliminary new velocity, based on pre_tend
1267	pre_u = u(k,j,i) + dt_3d * pre_tend
1268	!
1269	!-- Compare sign of old velocity and new preliminary velocity,
1270	!-- and in case the signs are different, limit the tendency
1271	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1272	pre_tend = - u(k,j,i) * ddt_3d
1273	ELSE
1274	pre_tend = pre_tend
1275	ENDIF
1276	!
1277	!-- Calculate final tendency
1278	tend(k,j,i) = tend(k,j,i) + pre_tend
1279
1280	ENDDO
1281	ENDDO
1282	ENDDO
1283
1284	!
1285	!-- v-component
1286	CASE ( 2 )
1287	DO i = nxl, nxr
1288	DO j = nysv, nyn
1289	!
1290	!-- Determine topography-top index on v-grid
1291	k_wall = get_topography_top_index_ji( j, i, 'v' )
1292
1293	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1294
1295	kk = k - k_wall !- lad arrays are defined flat
1296	!
1297	!-- In order to create sharp boundaries of the plant canopy,
1298	!-- the lad on the v-grid at index (k,j,i) is equal to
1299	!-- lad_s(k,j,i), rather than being interpolated from the
1300	!-- surrounding lad_s, because this would yield smaller lad
1301	!-- at the canopy boundaries than inside of the canopy.
1302	!-- For the same reason, the lad at the northmost(j+1) canopy
1303	!-- boundary on the v-grid equals lad_s(k,j,i).
1304	lad_local = lad_s(kk,j,i)
1305	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp )&
1306	THEN
1307	lad_local = lad_s(kk,j-1,i)
1308	ENDIF
1309
1310	pre_tend = 0.0_wp
1311	pre_v = 0.0_wp
1312	!
1313	!-- Calculate preliminary value (pre_tend) of the tendency
1314	pre_tend = - cdc * &
1315	lad_local * &
1316	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1317	u(k,j-1,i+1) + &
1318	u(k,j,i) + &
1319	u(k,j,i+1) ) &
1320	)**2 + &
1321	v(k,j,i)**2 + &
1322	( 0.25_wp * ( w(k-1,j-1,i) + &
1323	w(k-1,j,i) + &
1324	w(k,j-1,i) + &
1325	w(k,j,i) ) &
1326	)**2 &
1327	) * &
1328	v(k,j,i)
1329
1330	!
1331	!-- Calculate preliminary new velocity, based on pre_tend
1332	pre_v = v(k,j,i) + dt_3d * pre_tend
1333	!
1334	!-- Compare sign of old velocity and new preliminary velocity,
1335	!-- and in case the signs are different, limit the tendency
1336	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1337	pre_tend = - v(k,j,i) * ddt_3d
1338	ELSE
1339	pre_tend = pre_tend
1340	ENDIF
1341	!
1342	!-- Calculate final tendency
1343	tend(k,j,i) = tend(k,j,i) + pre_tend
1344
1345	ENDDO
1346	ENDDO
1347	ENDDO
1348
1349	!
1350	!-- w-component
1351	CASE ( 3 )
1352	DO i = nxl, nxr
1353	DO j = nys, nyn
1354	!
1355	!-- Determine topography-top index on w-grid
1356	k_wall = get_topography_top_index_ji( j, i, 'w' )
1357
1358	DO k = k_wall+1, k_wall + pch_index_ji(j,i) - 1
1359
1360	kk = k - k_wall !- lad arrays are defined flat
1361
1362	pre_tend = 0.0_wp
1363	pre_w = 0.0_wp
1364	!
1365	!-- Calculate preliminary value (pre_tend) of the tendency
1366	pre_tend = - cdc * &
1367	(0.5_wp * &
1368	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1369	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1370	u(k,j,i+1) + &
1371	u(k+1,j,i) + &
1372	u(k+1,j,i+1) ) &
1373	)**2 + &
1374	( 0.25_wp * ( v(k,j,i) + &
1375	v(k,j+1,i) + &
1376	v(k+1,j,i) + &
1377	v(k+1,j+1,i) ) &
1378	)**2 + &
1379	w(k,j,i)**2 &
1380	) * &
1381	w(k,j,i)
1382	!
1383	!-- Calculate preliminary new velocity, based on pre_tend
1384	pre_w = w(k,j,i) + dt_3d * pre_tend
1385	!
1386	!-- Compare sign of old velocity and new preliminary velocity,
1387	!-- and in case the signs are different, limit the tendency
1388	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1389	pre_tend = - w(k,j,i) * ddt_3d
1390	ELSE
1391	pre_tend = pre_tend
1392	ENDIF
1393	!
1394	!-- Calculate final tendency
1395	tend(k,j,i) = tend(k,j,i) + pre_tend
1396
1397	ENDDO
1398	ENDDO
1399	ENDDO
1400
1401	!
1402	!-- potential temperature
1403	CASE ( 4 )
1404	DO i = nxl, nxr
1405	DO j = nys, nyn
1406	!
1407	!-- Determine topography-top index on scalar-grid
1408	k_wall = get_topography_top_index_ji( j, i, 's' )
1409
1410	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1411
1412	kk = k - k_wall !- lad arrays are defined flat
1413	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1414	ENDDO
1415	ENDDO
1416	ENDDO
1417
1418	!
1419	!-- humidity
1420	CASE ( 5 )
1421	DO i = nxl, nxr
1422	DO j = nys, nyn
1423	!
1424	!-- Determine topography-top index on scalar-grid
1425	k_wall = get_topography_top_index_ji( j, i, 's' )
1426
1427	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1428
1429	kk = k - k_wall !- lad arrays are defined flat
1430	pc_transpiration_rate(kk,j,i) = - lsec &
1431	* lad_s(kk,j,i) * &
1432	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1433	u(k,j,i+1) ) &
1434	)**2 + &
1435	( 0.5_wp * ( v(k,j,i) + &
1436	v(k,j+1,i) ) &
1437	)**2 + &
1438	( 0.5_wp * ( w(k-1,j,i) + &
1439	w(k,j,i) ) &
1440	)**2 &
1441	) * &
1442	( q(k,j,i) - lsc )
1443
1444	tend(k,j,i) = tend(k,j,i) + pc_transpiration_rate(kk,j,i)
1445	ENDDO
1446	ENDDO
1447	ENDDO
1448
1449	!
1450	!-- sgs-tke
1451	CASE ( 6 )
1452	DO i = nxl, nxr
1453	DO j = nys, nyn
1454	!
1455	!-- Determine topography-top index on scalar-grid
1456	k_wall = get_topography_top_index_ji( j, i, 's' )
1457
1458	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1459
1460	kk = k - k_wall !- lad arrays are defined flat
1461	tend(k,j,i) = tend(k,j,i) - &
1462	2.0_wp * cdc * &
1463	lad_s(kk,j,i) * &
1464	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1465	u(k,j,i+1) ) &
1466	)**2 + &
1467	( 0.5_wp * ( v(k,j,i) + &
1468	v(k,j+1,i) ) &
1469	)**2 + &
1470	( 0.5_wp * ( w(k,j,i) + &
1471	w(k+1,j,i) ) &
1472	)**2 &
1473	) * &
1474	e(k,j,i)
1475	ENDDO
1476	ENDDO
1477	ENDDO
1478	!
1479	!-- scalar concentration
1480	CASE ( 7 )
1481	DO i = nxl, nxr
1482	DO j = nys, nyn
1483	!
1484	!-- Determine topography-top index on scalar-grid
1485	k_wall = get_topography_top_index_ji( j, i, 's' )
1486
1487	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1488
1489	kk = k - k_wall !- lad arrays are defined flat
1490	tend(k,j,i) = tend(k,j,i) - &
1491	lsec * &
1492	lad_s(kk,j,i) * &
1493	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1494	u(k,j,i+1) ) &
1495	)**2 + &
1496	( 0.5_wp * ( v(k,j,i) + &
1497	v(k,j+1,i) ) &
1498	)**2 + &
1499	( 0.5_wp * ( w(k-1,j,i) + &
1500	w(k,j,i) ) &
1501	)**2 &
1502	) * &
1503	( s(k,j,i) - lsc )
1504	ENDDO
1505	ENDDO
1506	ENDDO
1507
1508
1509
1510	CASE DEFAULT
1511
1512	WRITE( message_string, * ) 'wrong component: ', component
1513	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1514
1515	END SELECT
1516
1517	END SUBROUTINE pcm_tendency
1518
1519
1520	!------------------------------------------------------------------------------!
1521	! Description:
1522	! ------------
1523	!> Calculation of the tendency terms, accounting for the effect of the plant
1524	!> canopy on momentum and scalar quantities.
1525	!>
1526	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
1527	!> (defined on scalar grid), as initialized in subroutine pcm_init.
1528	!> The lad on the w-grid is vertically interpolated from the surrounding
1529	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
1530	!> k = pch_index. Here, the lad is zero.
1531	!>
1532	!> The canopy drag must be limited (previously accounted for by calculation of
1533	!> a limiting canopy timestep for the determination of the maximum LES timestep
1534	!> in subroutine timestep), since it is physically impossible that the canopy
1535	!> drag alone can locally change the sign of a velocity component. This
1536	!> limitation is realized by calculating preliminary tendencies and velocities.
1537	!> It is subsequently checked if the preliminary new velocity has a different
1538	!> sign than the current velocity. If so, the tendency is limited in a way that
1539	!> the velocity can at maximum be reduced to zero by the canopy drag.
1540	!>
1541	!>
1542	!> Call for grid point i,j
1543	!------------------------------------------------------------------------------!
1544	SUBROUTINE pcm_tendency_ij( i, j, component )
1545
1546
1547	USE control_parameters, &
1548	ONLY: dt_3d, message_string
1549
1550	USE kinds
1551
1552	IMPLICIT NONE
1553
1554	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
1555	INTEGER(iwp) :: i !< running index
1556	INTEGER(iwp) :: j !< running index
1557	INTEGER(iwp) :: k !< running index
1558	INTEGER(iwp) :: k_wall !< vertical index of topography top
1559	INTEGER(iwp) :: kk !< running index for flat lad arrays
1560
1561	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1562	REAL(wp) :: lad_local !< local lad value
1563	REAL(wp) :: pre_tend !< preliminary tendency
1564	REAL(wp) :: pre_u !< preliminary u-value
1565	REAL(wp) :: pre_v !< preliminary v-value
1566	REAL(wp) :: pre_w !< preliminary w-value
1567
1568
1569	ddt_3d = 1.0_wp / dt_3d
1570	!
1571	!-- Compute drag for the three velocity components and the SGS-TKE
1572	SELECT CASE ( component )
1573
1574	!
1575	!-- u-component
1576	CASE ( 1 )
1577	!
1578	!-- Determine topography-top index on u-grid
1579	k_wall = get_topography_top_index_ji( j, i, 'u' )
1580	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1581
1582	kk = k - k_wall !- lad arrays are defined flat
1583
1584	!
1585	!-- In order to create sharp boundaries of the plant canopy,
1586	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
1587	!-- rather than being interpolated from the surrounding lad_s,
1588	!-- because this would yield smaller lad at the canopy boundaries
1589	!-- than inside of the canopy.
1590	!-- For the same reason, the lad at the rightmost(i+1)canopy
1591	!-- boundary on the u-grid equals lad_s(k,j,i).
1592	lad_local = lad_s(kk,j,i)
1593	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp ) THEN
1594	lad_local = lad_s(kk,j,i-1)
1595	ENDIF
1596
1597	pre_tend = 0.0_wp
1598	pre_u = 0.0_wp
1599	!
1600	!-- Calculate preliminary value (pre_tend) of the tendency
1601	pre_tend = - cdc * &
1602	lad_local * &
1603	SQRT( u(k,j,i)**2 + &
1604	( 0.25_wp * ( v(k,j,i-1) + &
1605	v(k,j,i) + &
1606	v(k,j+1,i) + &
1607	v(k,j+1,i-1) ) &
1608	)**2 + &
1609	( 0.25_wp * ( w(k-1,j,i-1) + &
1610	w(k-1,j,i) + &
1611	w(k,j,i-1) + &
1612	w(k,j,i) ) &
1613	)**2 &
1614	) * &
1615	u(k,j,i)
1616
1617	!
1618	!-- Calculate preliminary new velocity, based on pre_tend
1619	pre_u = u(k,j,i) + dt_3d * pre_tend
1620	!
1621	!-- Compare sign of old velocity and new preliminary velocity,
1622	!-- and in case the signs are different, limit the tendency
1623	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1624	pre_tend = - u(k,j,i) * ddt_3d
1625	ELSE
1626	pre_tend = pre_tend
1627	ENDIF
1628	!
1629	!-- Calculate final tendency
1630	tend(k,j,i) = tend(k,j,i) + pre_tend
1631	ENDDO
1632
1633
1634	!
1635	!-- v-component
1636	CASE ( 2 )
1637	!
1638	!-- Determine topography-top index on v-grid
1639	k_wall = get_topography_top_index_ji( j, i, 'v' )
1640
1641	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1642
1643	kk = k - k_wall !- lad arrays are defined flat
1644	!
1645	!-- In order to create sharp boundaries of the plant canopy,
1646	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
1647	!-- rather than being interpolated from the surrounding lad_s,
1648	!-- because this would yield smaller lad at the canopy boundaries
1649	!-- than inside of the canopy.
1650	!-- For the same reason, the lad at the northmost(j+1)canopy
1651	!-- boundary on the v-grid equals lad_s(k,j,i).
1652	lad_local = lad_s(kk,j,i)
1653	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp ) THEN
1654	lad_local = lad_s(kk,j-1,i)
1655	ENDIF
1656
1657	pre_tend = 0.0_wp
1658	pre_v = 0.0_wp
1659	!
1660	!-- Calculate preliminary value (pre_tend) of the tendency
1661	pre_tend = - cdc * &
1662	lad_local * &
1663	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1664	u(k,j-1,i+1) + &
1665	u(k,j,i) + &
1666	u(k,j,i+1) ) &
1667	)**2 + &
1668	v(k,j,i)**2 + &
1669	( 0.25_wp * ( w(k-1,j-1,i) + &
1670	w(k-1,j,i) + &
1671	w(k,j-1,i) + &
1672	w(k,j,i) ) &
1673	)**2 &
1674	) * &
1675	v(k,j,i)
1676
1677	!
1678	!-- Calculate preliminary new velocity, based on pre_tend
1679	pre_v = v(k,j,i) + dt_3d * pre_tend
1680	!
1681	!-- Compare sign of old velocity and new preliminary velocity,
1682	!-- and in case the signs are different, limit the tendency
1683	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1684	pre_tend = - v(k,j,i) * ddt_3d
1685	ELSE
1686	pre_tend = pre_tend
1687	ENDIF
1688	!
1689	!-- Calculate final tendency
1690	tend(k,j,i) = tend(k,j,i) + pre_tend
1691	ENDDO
1692
1693
1694	!
1695	!-- w-component
1696	CASE ( 3 )
1697	!
1698	!-- Determine topography-top index on w-grid
1699	k_wall = get_topography_top_index_ji( j, i, 'w' )
1700
1701	DO k = k_wall + 1, k_wall + pch_index_ji(j,i) - 1
1702
1703	kk = k - k_wall !- lad arrays are defined flat
1704
1705	pre_tend = 0.0_wp
1706	pre_w = 0.0_wp
1707	!
1708	!-- Calculate preliminary value (pre_tend) of the tendency
1709	pre_tend = - cdc * &
1710	(0.5_wp * &
1711	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1712	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1713	u(k,j,i+1) + &
1714	u(k+1,j,i) + &
1715	u(k+1,j,i+1) ) &
1716	)**2 + &
1717	( 0.25_wp * ( v(k,j,i) + &
1718	v(k,j+1,i) + &
1719	v(k+1,j,i) + &
1720	v(k+1,j+1,i) ) &
1721	)**2 + &
1722	w(k,j,i)**2 &
1723	) * &
1724	w(k,j,i)
1725	!
1726	!-- Calculate preliminary new velocity, based on pre_tend
1727	pre_w = w(k,j,i) + dt_3d * pre_tend
1728	!
1729	!-- Compare sign of old velocity and new preliminary velocity,
1730	!-- and in case the signs are different, limit the tendency
1731	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1732	pre_tend = - w(k,j,i) * ddt_3d
1733	ELSE
1734	pre_tend = pre_tend
1735	ENDIF
1736	!
1737	!-- Calculate final tendency
1738	tend(k,j,i) = tend(k,j,i) + pre_tend
1739	ENDDO
1740
1741	!
1742	!-- potential temperature
1743	CASE ( 4 )
1744	!
1745	!-- Determine topography-top index on scalar grid
1746	k_wall = get_topography_top_index_ji( j, i, 's' )
1747
1748	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1749	kk = k - k_wall !- lad arrays are defined flat
1750	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1751	ENDDO
1752
1753
1754	!
1755	!-- humidity
1756	CASE ( 5 )
1757	!
1758	!-- Determine topography-top index on scalar grid
1759	k_wall = get_topography_top_index_ji( j, i, 's' )
1760
1761	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1762	kk = k - k_wall !- lad arrays are defined flat
1763
1764	pc_transpiration_rate(kk,j,i) = - lsec &
1765	* lad_s(kk,j,i) * &
1766	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1767	u(k,j,i+1) ) &
1768	)**2 + &
1769	( 0.5_wp * ( v(k,j,i) + &
1770	v(k,j+1,i) ) &
1771	)**2 + &
1772	( 0.5_wp * ( w(k-1,j,i) + &
1773	w(k,j,i) ) &
1774	)**2 &
1775	) * &
1776	( q(k,j,i) - lsc )
1777
1778	tend(k,j,i) = tend(k,j,i) + pc_transpiration_rate(kk,j,i)
1779
1780	ENDDO
1781
1782	!
1783	!-- sgs-tke
1784	CASE ( 6 )
1785	!
1786	!-- Determine topography-top index on scalar grid
1787	k_wall = get_topography_top_index_ji( j, i, 's' )
1788
1789	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1790
1791	kk = k - k_wall
1792	tend(k,j,i) = tend(k,j,i) - &
1793	2.0_wp * cdc * &
1794	lad_s(kk,j,i) * &
1795	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1796	u(k,j,i+1) ) &
1797	)**2 + &
1798	( 0.5_wp * ( v(k,j,i) + &
1799	v(k,j+1,i) ) &
1800	)**2 + &
1801	( 0.5_wp * ( w(k,j,i) + &
1802	w(k+1,j,i) ) &
1803	)**2 &
1804	) * &
1805	e(k,j,i)
1806	ENDDO
1807
1808	!
1809	!-- scalar concentration
1810	CASE ( 7 )
1811	!
1812	!-- Determine topography-top index on scalar grid
1813	k_wall = get_topography_top_index_ji( j, i, 's' )
1814
1815	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1816
1817	kk = k - k_wall
1818	tend(k,j,i) = tend(k,j,i) - &
1819	lsec * &
1820	lad_s(kk,j,i) * &
1821	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1822	u(k,j,i+1) ) &
1823	)**2 + &
1824	( 0.5_wp * ( v(k,j,i) + &
1825	v(k,j+1,i) ) &
1826	)**2 + &
1827	( 0.5_wp * ( w(k-1,j,i) + &
1828	w(k,j,i) ) &
1829	)**2 &
1830	) * &
1831	( s(k,j,i) - lsc )
1832	ENDDO
1833
1834	CASE DEFAULT
1835
1836	WRITE( message_string, * ) 'wrong component: ', component
1837	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1838
1839	END SELECT
1840
1841	END SUBROUTINE pcm_tendency_ij
1842
1843
1844
1845	END MODULE plant_canopy_model_mod

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