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source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 3025

Last change on this file since 3025 was 3022, checked in by suehring, 7 years ago
Revise recent bugfix in nested runs at left and south boundary; bugfix in advection of u in case of OpenMP parallelization; bugfix in plant transpiration
Property svn:keywords set to `Id`
File size: 75.4 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	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: plant_canopy_model_mod.f90 3022 2018-05-18 11:12:35Z raasch $
27	! Bugfix in allocation of transpiration rate
28	!
29	! 3014 2018-05-09 08:42:38Z maronga
30	! Bugfix: nzb_do and nzt_do were not used for 3d data output
31	! Added pc_transpiration_rate
32	!
33	! 2977 2018-04-17 10:27:57Z kanani
34	! Implement changes from branch radiation (r2948-2971) with minor modifications,
35	! plus some formatting.
36	! (moh.hefny):
37	! Add plant canopy type to account for changes in LAD (based on the changes
38	! done by Resler & Pavel) and correct the error message to PALM Standard.
39	!
40	! 2932 2018-03-26 09:39:22Z maronga
41	! renamed canopy_par to plant_canopy_parameters
42	!
43	! 2920 2018-03-22 11:22:01Z kanani
44	! Move usm_lad_rma and prototype_lad to radiation_model (moh.hefny)
45	!
46	! 2892 2018-03-14 15:06:29Z suehring
47	! Bugfix, read separate ASCII LAD files for parent and child model.
48	!
49	! 2770 2018-01-25 15:10:09Z kanani
50	! Correction of parameter check
51	!
52	! 2768 2018-01-24 15:38:29Z kanani
53	! Added check for output quantity pcm_heatrate, some formatting
54	!
55	! 2766 2018-01-22 17:17:47Z kanani
56	! Increased LEN of canopy mode to 30
57	!
58	! 2746 2018-01-15 12:06:04Z suehring
59	! Move flag plant canopy to modules
60	!
61	! 2718 2018-01-02 08:49:38Z maronga
62	! Corrected "Former revisions" section
63	!
64	! 2701 2017-12-15 15:40:50Z suehring
65	! Changes from last commit documented
66	!
67	! 2698 2017-12-14 18:46:24Z suehring
68	! Bugfix in get_topography_top_index
69	!
70	! 2696 2017-12-14 17:12:51Z kanani
71	! Change in file header (GPL part)
72	! Bugfix for vertical loop index pch_index in case of Netcdf input
73	! Introduce 2D index array incorporate canopy top index
74	! Check if canopy on top of topography do not exceed vertical dimension
75	! Add check for canopy_mode in case of Netcdf input.
76	! Enable _FillValue output for 3d quantities
77	! Bugfix in reading of PIDS leaf area density (MS)
78	!
79	! 2669 2017-12-06 16:03:27Z raasch
80	! coupling_char removed
81	!
82	! 2512 2017-10-04 08:26:59Z raasch
83	! upper bounds of 3d output changed from nx+1,ny+1 to nx,ny
84	! no output of ghost layer data
85	!
86	! 2318 2017-07-20 17:27:44Z suehring
87	! Get topography top index via Function call
88	!
89	! 2317 2017-07-20 17:27:19Z suehring
90	! Changed error messages
91	!
92	! 2233 2017-05-30 18:08:54Z suehring
93	!
94	! 2232 2017-05-30 17:47:52Z suehring
95	! Adjustments to new topography concept
96	!
97	! 2213 2017-04-24 15:10:35Z kanani
98	! Bugfix: exchange of ghost points in array pc_heating_rate needed for output
99	! of pcm_heatrate, onetime ghost point exchange of lad_s after initialization.
100	! Formatting and clean-up of subroutine pcm_read_plant_canopy_3d,
101	! minor re-organization of canopy-heating initialization.
102	!
103	! 2209 2017-04-19 09:34:46Z kanani
104	! Added 3d output of leaf area density (pcm_lad) and canopy
105	! heat rate (pcm_heatrate)
106	!
107	! 2024 2016-10-12 16:42:37Z kanani
108	! Added missing lad_s initialization
109	!
110	! 2011 2016-09-19 17:29:57Z kanani
111	! Renamed canopy_heat_flux to pc_heating_rate, since the original meaning/
112	! calculation of the quantity has changed, related to the urban surface model
113	! and similar future applications.
114	!
115	! 2007 2016-08-24 15:47:17Z kanani
116	! Added SUBROUTINE pcm_read_plant_canopy_3d for reading 3d plant canopy data
117	! from file (new case canopy_mode=read_from_file_3d) in the course of
118	! introduction of urban surface model,
119	! introduced variable ext_coef,
120	! resorted SUBROUTINEs to alphabetical order
121	!
122	! 2000 2016-08-20 18:09:15Z knoop
123	! Forced header and separation lines into 80 columns
124	!
125	! 1960 2016-07-12 16:34:24Z suehring
126	! Separate humidity and passive scalar
127	!
128	! 1953 2016-06-21 09:28:42Z suehring
129	! Bugfix, lad_s and lad must be public
130	!
131	! 1826 2016-04-07 12:01:39Z maronga
132	! Further modularization
133	!
134	! 1721 2015-11-16 12:56:48Z raasch
135	! bugfixes: shf is reduced in areas covered with canopy only,
136	! canopy is set on top of topography
137	!
138	! 1682 2015-10-07 23:56:08Z knoop
139	! Code annotations made doxygen readable
140	!
141	! 1484 2014-10-21 10:53:05Z kanani
142	! Changes due to new module structure of the plant canopy model:
143	! module plant_canopy_model_mod now contains a subroutine for the
144	! initialization of the canopy model (pcm_init),
145	! limitation of the canopy drag (previously accounted for by calculation of
146	! a limiting canopy timestep for the determination of the maximum LES timestep
147	! in subroutine timestep) is now realized by the calculation of pre-tendencies
148	! and preliminary velocities in subroutine pcm_tendency,
149	! some redundant MPI communication removed in subroutine pcm_init
150	! (was previously in init_3d_model),
151	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
152	! respective grid is now provided only by lad_s (e.g. in the calculation of
153	! the tendency terms or of cum_lai_hf),
154	! drag_coefficient, lai, leaf_surface_concentration,
155	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
156	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
157	! respectively,
158	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
159	! USE-statements and ONLY-lists modified accordingly
160	!
161	! 1340 2014-03-25 19:45:13Z kanani
162	! REAL constants defined as wp-kind
163	!
164	! 1320 2014-03-20 08:40:49Z raasch
165	! ONLY-attribute added to USE-statements,
166	! kind-parameters added to all INTEGER and REAL declaration statements,
167	! kinds are defined in new module kinds,
168	! old module precision_kind is removed,
169	! revision history before 2012 removed,
170	! comment fields (!:) to be used for variable explanations added to
171	! all variable declaration statements
172	!
173	! 1036 2012-10-22 13:43:42Z raasch
174	! code put under GPL (PALM 3.9)
175	!
176	! 138 2007-11-28 10:03:58Z letzel
177	! Initial revision
178	!
179	! Description:
180	! ------------
181	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
182	!> profile (subroutine pcm_init).
183	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
184	!> due to canopy elements (subroutine pcm_tendency).
185	!------------------------------------------------------------------------------!
186	MODULE plant_canopy_model_mod
187
188	USE arrays_3d, &
189	ONLY: dzu, dzw, e, q, s, tend, u, v, w, zu, zw
190
191	USE indices, &
192	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
193	nz, nzb, nzt
194
195	USE kinds
196
197	USE surface_mod, &
198	ONLY: get_topography_top_index_ji
199
200
201	IMPLICIT NONE
202
203
204	CHARACTER (LEN=30) :: canopy_mode = 'block' !< canopy coverage
205
206	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
207	INTEGER(iwp) :: lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
208
209	INTEGER(iwp), DIMENSION(:,:), ALLOCATABLE :: pch_index_ji !< local plant canopy top
210
211	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
212
213	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
214	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
215	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
216	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
217	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
218	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
219	REAL(wp) :: ext_coef = 0.6_wp !< extinction coefficient
220	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
221	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
222	REAL(wp) :: leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
223	REAL(wp) :: leaf_surface_conc = 0.0_wp !< leaf surface concentration
224	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
225	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
226
227	REAL(wp) :: lad_vertical_gradient(10) = 0.0_wp !< lad gradient
228	REAL(wp) :: lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
229
230	REAL(wp) :: lad_type_coef(0:10) = 1.0_wp !< multiplicative coeficients for particular types
231	!< of plant canopy (e.g. deciduous tree during winter)
232
233	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
234	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
235
236	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
237	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
238	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: pc_heating_rate !< plant canopy heating rate
239	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: pc_transpiration_rate !< plant canopy transpiration rate
240
241	SAVE
242
243
244	PRIVATE
245
246	!
247	!-- Public functions
248	PUBLIC pcm_check_data_output, pcm_check_parameters, pcm_data_output_3d, &
249	pcm_define_netcdf_grid, pcm_header, pcm_init, pcm_parin, pcm_tendency
250
251	!
252	!-- Public variables and constants
253	PUBLIC pc_heating_rate, pc_transpiration_rate, canopy_mode, cthf, dt_plant_canopy, lad, lad_s, &
254	pch_index
255
256
257	INTERFACE pcm_check_data_output
258	MODULE PROCEDURE pcm_check_data_output
259	END INTERFACE pcm_check_data_output
260
261	INTERFACE pcm_check_parameters
262	MODULE PROCEDURE pcm_check_parameters
263	END INTERFACE pcm_check_parameters
264
265	INTERFACE pcm_data_output_3d
266	MODULE PROCEDURE pcm_data_output_3d
267	END INTERFACE pcm_data_output_3d
268
269	INTERFACE pcm_define_netcdf_grid
270	MODULE PROCEDURE pcm_define_netcdf_grid
271	END INTERFACE pcm_define_netcdf_grid
272
273	INTERFACE pcm_header
274	MODULE PROCEDURE pcm_header
275	END INTERFACE pcm_header
276
277	INTERFACE pcm_init
278	MODULE PROCEDURE pcm_init
279	END INTERFACE pcm_init
280
281	INTERFACE pcm_parin
282	MODULE PROCEDURE pcm_parin
283	END INTERFACE pcm_parin
284
285	INTERFACE pcm_read_plant_canopy_3d
286	MODULE PROCEDURE pcm_read_plant_canopy_3d
287	END INTERFACE pcm_read_plant_canopy_3d
288
289	INTERFACE pcm_tendency
290	MODULE PROCEDURE pcm_tendency
291	MODULE PROCEDURE pcm_tendency_ij
292	END INTERFACE pcm_tendency
293
294
295	CONTAINS
296
297
298	!------------------------------------------------------------------------------!
299	! Description:
300	! ------------
301	!> Check data output for plant canopy model
302	!------------------------------------------------------------------------------!
303	SUBROUTINE pcm_check_data_output( var, unit )
304
305
306	USE control_parameters, &
307	ONLY: data_output, message_string, urban_surface
308
309	IMPLICIT NONE
310
311	CHARACTER (LEN=*) :: unit !<
312	CHARACTER (LEN=*) :: var !<
313
314
315	SELECT CASE ( TRIM( var ) )
316
317	CASE ( 'pcm_heatrate' )
318	IF ( cthf == 0.0_wp .AND. .NOT. urban_surface ) THEN
319	message_string = 'output of "' // TRIM( var ) // '" requi' // &
320	'res setting of parameter cthf /= 0.0'
321	CALL message( 'pcm_check_data_output', 'PA1000', 1, 2, 0, 6, 0 )
322	ENDIF
323	unit = 'K s-1'
324
325	CASE ( 'pcm_transpirationrate' )
326	unit = 'kg kg-1 s-1'
327
328	CASE ( 'pcm_lad' )
329	unit = 'm2 m-3'
330
331
332	CASE DEFAULT
333	unit = 'illegal'
334
335	END SELECT
336
337
338	END SUBROUTINE pcm_check_data_output
339
340
341	!------------------------------------------------------------------------------!
342	! Description:
343	! ------------
344	!> Check parameters routine for plant canopy model
345	!------------------------------------------------------------------------------!
346	SUBROUTINE pcm_check_parameters
347
348	USE control_parameters, &
349	ONLY: cloud_physics, coupling_char, message_string, &
350	microphysics_seifert
351
352	USE netcdf_data_input_mod, &
353	ONLY: input_file_static, input_pids_static
354
355
356	IMPLICIT NONE
357
358
359	IF ( canopy_drag_coeff == 0.0_wp ) THEN
360	message_string = 'plant_canopy = .TRUE. requires a non-zero drag '// &
361	'coefficient & given value is canopy_drag_coeff = 0.0'
362	CALL message( 'pcm_check_parameters', 'PA0041', 1, 2, 0, 6, 0 )
363	ENDIF
364
365	IF ( ( alpha_lad /= 9999999.9_wp .AND. beta_lad == 9999999.9_wp ) .OR.&
366	beta_lad /= 9999999.9_wp .AND. alpha_lad == 9999999.9_wp ) THEN
367	message_string = 'using the beta function for the construction ' // &
368	'of the leaf area density profile requires ' // &
369	'both alpha_lad and beta_lad to be /= 9999999.9'
370	CALL message( 'pcm_check_parameters', 'PA0118', 1, 2, 0, 6, 0 )
371	ENDIF
372
373	IF ( calc_beta_lad_profile .AND. lai_beta == 0.0_wp ) THEN
374	message_string = 'using the beta function for the construction ' // &
375	'of the leaf area density profile requires ' // &
376	'a non-zero lai_beta, but given value is ' // &
377	'lai_beta = 0.0'
378	CALL message( 'pcm_check_parameters', 'PA0119', 1, 2, 0, 6, 0 )
379	ENDIF
380
381	IF ( calc_beta_lad_profile .AND. lad_surface /= 0.0_wp ) THEN
382	message_string = 'simultaneous setting of alpha_lad /= 9999999.9 '// &
383	'combined with beta_lad /= 9999999.9 ' // &
384	'and lad_surface /= 0.0 is not possible, ' // &
385	'use either vertical gradients or the beta ' // &
386	'function for the construction of the leaf area '// &
387	'density profile'
388	CALL message( 'pcm_check_parameters', 'PA0120', 1, 2, 0, 6, 0 )
389	ENDIF
390
391	IF ( cloud_physics .AND. microphysics_seifert ) THEN
392	message_string = 'plant_canopy = .TRUE. requires cloud_scheme /=' // &
393	' seifert_beheng'
394	CALL message( 'pcm_check_parameters', 'PA0360', 1, 2, 0, 6, 0 )
395	ENDIF
396	!
397	!-- If dynamic input file is used, canopy need to be read from file
398	IF ( input_pids_static .AND. &
399	TRIM( canopy_mode ) /= 'read_from_file_3d' ) THEN
400	message_string = 'Usage of dynamic input file ' // &
401	TRIM( input_file_static ) // &
402	TRIM( coupling_char ) // ' requires ' // &
403	'canopy_mode = read_from_file_3d'
404	CALL message( 'pcm_check_parameters', 'PA0999', 1, 2, 0, 6, 0 )
405	ENDIF
406
407
408	END SUBROUTINE pcm_check_parameters
409
410
411	!------------------------------------------------------------------------------!
412	!
413	! Description:
414	! ------------
415	!> Subroutine defining 3D output variables
416	!------------------------------------------------------------------------------!
417	SUBROUTINE pcm_data_output_3d( av, variable, found, local_pf, fill_value, &
418	nzb_do, nzt_do )
419
420	USE indices
421
422	USE kinds
423
424
425	IMPLICIT NONE
426
427	CHARACTER (LEN=*) :: variable !<
428
429	INTEGER(iwp) :: av !<
430	INTEGER(iwp) :: i !<
431	INTEGER(iwp) :: j !<
432	INTEGER(iwp) :: k !<
433	INTEGER(iwp) :: k_topo !< topography top index
434	INTEGER(iwp) :: nzb_do !< lower limit of the data output (usually 0)
435	INTEGER(iwp) :: nzt_do !< vertical upper limit of the data output (usually nz_do3d)
436
437	LOGICAL :: found !<
438
439	REAL(wp) :: fill_value
440	REAL(sp), DIMENSION(nxl:nxr,nys:nyn,nzb_do:nzt_do) :: local_pf !<
441
442
443	found = .TRUE.
444
445	local_pf = REAL( fill_value, KIND = 4 )
446
447	SELECT CASE ( TRIM( variable ) )
448
449	CASE ( 'pcm_heatrate' )
450	IF ( av == 0 ) THEN
451	DO i = nxl, nxr
452	DO j = nys, nyn
453	IF ( pch_index_ji(j,i) /= 0 ) THEN
454	k_topo = get_topography_top_index_ji( j, i, 's' )
455	DO k = k_topo, k_topo + pch_index_ji(j,i)
456	local_pf(i,j,k) = pc_heating_rate(k-k_topo,j,i)
457	ENDDO
458	ENDIF
459	ENDDO
460	ENDDO
461	ENDIF
462
463	CASE ( 'pcm_transpirationrate' )
464	IF ( av == 0 ) THEN
465	DO i = nxl, nxr
466	DO j = nys, nyn
467	IF ( pch_index_ji(j,i) /= 0 ) THEN
468	k_topo = get_topography_top_index_ji( j, i, 's' )
469	DO k = k_topo, k_topo + pch_index_ji(j,i)
470	local_pf(i,j,k) = pc_transpiration_rate(k-k_topo,j,i)
471	ENDDO
472	ENDIF
473	ENDDO
474	ENDDO
475	ENDIF
476
477	CASE ( 'pcm_lad' )
478	IF ( av == 0 ) THEN
479	DO i = nxl, nxr
480	DO j = nys, nyn
481	IF ( pch_index_ji(j,i) /= 0 ) THEN
482	k_topo = get_topography_top_index_ji( j, i, 's' )
483	DO k = k_topo, k_topo + pch_index_ji(j,i)
484	local_pf(i,j,k) = lad_s(k-k_topo,j,i)
485	ENDDO
486	ENDIF
487	ENDDO
488	ENDDO
489	ENDIF
490
491
492	CASE DEFAULT
493	found = .FALSE.
494
495	END SELECT
496
497
498	END SUBROUTINE pcm_data_output_3d
499
500	!------------------------------------------------------------------------------!
501	!
502	! Description:
503	! ------------
504	!> Subroutine defining appropriate grid for netcdf variables.
505	!> It is called from subroutine netcdf.
506	!------------------------------------------------------------------------------!
507	SUBROUTINE pcm_define_netcdf_grid( var, found, grid_x, grid_y, grid_z )
508
509	IMPLICIT NONE
510
511	CHARACTER (LEN=*), INTENT(IN) :: var !<
512	LOGICAL, INTENT(OUT) :: found !<
513	CHARACTER (LEN=*), INTENT(OUT) :: grid_x !<
514	CHARACTER (LEN=*), INTENT(OUT) :: grid_y !<
515	CHARACTER (LEN=*), INTENT(OUT) :: grid_z !<
516
517	found = .TRUE.
518
519	!
520	!-- Check for the grid
521	SELECT CASE ( TRIM( var ) )
522
523	CASE ( 'pcm_heatrate', 'pcm_lad', 'pcm_transpirationrate')
524	grid_x = 'x'
525	grid_y = 'y'
526	grid_z = 'zu'
527
528	CASE DEFAULT
529	found = .FALSE.
530	grid_x = 'none'
531	grid_y = 'none'
532	grid_z = 'none'
533	END SELECT
534
535	END SUBROUTINE pcm_define_netcdf_grid
536
537
538	!------------------------------------------------------------------------------!
539	! Description:
540	! ------------
541	!> Header output for plant canopy model
542	!------------------------------------------------------------------------------!
543	SUBROUTINE pcm_header ( io )
544
545	USE control_parameters, &
546	ONLY: dz, passive_scalar
547
548
549	IMPLICIT NONE
550
551	CHARACTER (LEN=10) :: coor_chr !<
552
553	CHARACTER (LEN=86) :: coordinates !<
554	CHARACTER (LEN=86) :: gradients !<
555	CHARACTER (LEN=86) :: leaf_area_density !<
556	CHARACTER (LEN=86) :: slices !<
557
558	INTEGER(iwp) :: i !<
559	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
560	INTEGER(iwp) :: k !<
561
562	REAL(wp) :: canopy_height !< canopy height (in m)
563
564	canopy_height = pch_index * dz
565
566	WRITE ( io, 1 ) canopy_mode, canopy_height, pch_index, &
567	canopy_drag_coeff
568	IF ( passive_scalar ) THEN
569	WRITE ( io, 2 ) leaf_scalar_exch_coeff, &
570	leaf_surface_conc
571	ENDIF
572
573	!
574	!-- Heat flux at the top of vegetation
575	WRITE ( io, 3 ) cthf
576
577	!
578	!-- Leaf area density profile, calculated either from given vertical
579	!-- gradients or from beta probability density function.
580	IF ( .NOT. calc_beta_lad_profile ) THEN
581
582	!-- Building output strings, starting with surface value
583	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
584	gradients = '------'
585	slices = ' 0'
586	coordinates = ' 0.0'
587	i = 1
588	DO WHILE ( i < 11 .AND. lad_vertical_gradient_level_ind(i) &
589	/= -9999 )
590
591	WRITE (coor_chr,'(F7.2)') lad(lad_vertical_gradient_level_ind(i))
592	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
593	TRIM( coor_chr )
594
595	WRITE (coor_chr,'(F7.2)') lad_vertical_gradient(i)
596	gradients = TRIM( gradients ) // ' ' // TRIM( coor_chr )
597
598	WRITE (coor_chr,'(I7)') lad_vertical_gradient_level_ind(i)
599	slices = TRIM( slices ) // ' ' // TRIM( coor_chr )
600
601	WRITE (coor_chr,'(F7.1)') lad_vertical_gradient_level(i)
602	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
603
604	i = i + 1
605	ENDDO
606
607	WRITE ( io, 4 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
608	TRIM( gradients ), TRIM( slices )
609
610	ELSE
611
612	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
613	coordinates = ' 0.0'
614
615	DO k = 1, pch_index
616
617	WRITE (coor_chr,'(F7.2)') lad(k)
618	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
619	TRIM( coor_chr )
620
621	WRITE (coor_chr,'(F7.1)') zu(k)
622	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
623
624	ENDDO
625
626	WRITE ( io, 5 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
627	alpha_lad, beta_lad, lai_beta
628
629	ENDIF
630
631	1 FORMAT (//' Vegetation canopy (drag) model:'/ &
632	' ------------------------------'// &
633	' Canopy mode: ', A / &
634	' Canopy height: ',F6.2,'m (',I4,' grid points)' / &
635	' Leaf drag coefficient: ',F6.2 /)
636	2 FORMAT (/ ' Scalar exchange coefficient: ',F6.2 / &
637	' Scalar concentration at leaf surfaces in kg/m**3: ',F6.2 /)
638	3 FORMAT (' Predefined constant heatflux at the top of the vegetation: ',F6.2, &
639	' K m/s')
640	4 FORMAT (/ ' Characteristic levels of the leaf area density:'// &
641	' Height: ',A,' m'/ &
642	' Leaf area density: ',A,' m2/m3'/ &
643	' Gradient: ',A,' m2/m4'/ &
644	' Gridpoint: ',A)
645	5 FORMAT (//' Characteristic levels of the leaf area density and coefficients:'&
646	// ' Height: ',A,' m'/ &
647	' Leaf area density: ',A,' m2/m3'/ &
648	' Coefficient alpha: ',F6.2 / &
649	' Coefficient beta: ',F6.2 / &
650	' Leaf area index: ',F6.2,' m2/m2' /)
651
652	END SUBROUTINE pcm_header
653
654
655	!------------------------------------------------------------------------------!
656	! Description:
657	! ------------
658	!> Initialization of the plant canopy model
659	!------------------------------------------------------------------------------!
660	SUBROUTINE pcm_init
661
662
663	USE control_parameters, &
664	ONLY: dz, humidity, io_blocks, io_group, message_string, ocean, &
665	passive_scalar, urban_surface
666
667	USE netcdf_data_input_mod, &
668	ONLY: leaf_area_density_f
669
670	USE surface_mod, &
671	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
672
673	IMPLICIT NONE
674
675	CHARACTER(10) :: pct
676
677	INTEGER(iwp) :: i !< running index
678	INTEGER(iwp) :: ii !< index
679	INTEGER(iwp) :: j !< running index
680	INTEGER(iwp) :: k !< running index
681	INTEGER(iwp) :: m !< running index
682
683	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
684	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
685	REAL(wp) :: gradient !< gradient for lad-profile construction
686	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
687	REAL(wp) :: pcv(nzb:nzt+1) !<
688
689	!
690	!-- Allocate one-dimensional arrays for the computation of the
691	!-- leaf area density (lad) profile
692	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
693	lad = 0.0_wp
694	pre_lad = 0.0_wp
695
696	!
697	!-- Set flag that indicates that the lad-profile shall be calculated by using
698	!-- a beta probability density function
699	IF ( alpha_lad /= 9999999.9_wp .AND. beta_lad /= 9999999.9_wp ) THEN
700	calc_beta_lad_profile = .TRUE.
701	ENDIF
702
703
704	!
705	!-- Compute the profile of leaf area density used in the plant
706	!-- canopy model. The profile can either be constructed from
707	!-- prescribed vertical gradients of the leaf area density or by
708	!-- using a beta probability density function (see e.g. Markkanen et al.,
709	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
710	IF ( .NOT. calc_beta_lad_profile ) THEN
711
712	!
713	!-- Use vertical gradients for lad-profile construction
714	i = 1
715	gradient = 0.0_wp
716
717	IF ( .NOT. ocean ) THEN
718
719	lad(0) = lad_surface
720	lad_vertical_gradient_level_ind(1) = 0
721
722	DO k = 1, pch_index
723	IF ( i < 11 ) THEN
724	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
725	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
726	gradient = lad_vertical_gradient(i)
727	lad_vertical_gradient_level_ind(i) = k - 1
728	i = i + 1
729	ENDIF
730	ENDIF
731	IF ( gradient /= 0.0_wp ) THEN
732	IF ( k /= 1 ) THEN
733	lad(k) = lad(k-1) + dzu(k) * gradient
734	ELSE
735	lad(k) = lad_surface + dzu(k) * gradient
736	ENDIF
737	ELSE
738	lad(k) = lad(k-1)
739	ENDIF
740	ENDDO
741
742	ENDIF
743
744	!
745	!-- In case of no given leaf area density gradients, choose a vanishing
746	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
747	!-- file.
748	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
749	lad_vertical_gradient_level(1) = 0.0_wp
750	ENDIF
751
752	ELSE
753
754	!
755	!-- Use beta function for lad-profile construction
756	int_bpdf = 0.0_wp
757	canopy_height = pch_index * dz
758
759	DO k = 0, pch_index
760	int_bpdf = int_bpdf + &
761	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
762	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
763	beta_lad-1.0_wp ) ) &
764	* ( ( zw(k+1)-zw(k) ) / canopy_height ) )
765	ENDDO
766
767	!
768	!-- Preliminary lad profile (defined on w-grid)
769	DO k = 0, pch_index
770	pre_lad(k) = lai_beta * &
771	( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) ) &
772	* ( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
773	beta_lad-1.0_wp ) ) / int_bpdf &
774	) / canopy_height
775	ENDDO
776
777	!
778	!-- Final lad profile (defined on scalar-grid level, since most prognostic
779	!-- quantities are defined there, hence, less interpolation is required
780	!-- when calculating the canopy tendencies)
781	lad(0) = pre_lad(0)
782	DO k = 1, pch_index
783	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
784	ENDDO
785
786	ENDIF
787
788	!
789	!-- Allocate 3D-array for the leaf area density (lad_s).
790	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
791
792	!
793	!-- Initialize canopy parameters cdc (canopy drag coefficient),
794	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
795	!-- with the prescribed values
796	cdc = canopy_drag_coeff
797	lsec = leaf_scalar_exch_coeff
798	lsc = leaf_surface_conc
799
800	!
801	!-- Initialization of the canopy coverage in the model domain:
802	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
803	!-- fully covers the domain surface
804	SELECT CASE ( TRIM( canopy_mode ) )
805
806	CASE( 'block' )
807
808	DO i = nxlg, nxrg
809	DO j = nysg, nyng
810	lad_s(:,j,i) = lad(:)
811	ENDDO
812	ENDDO
813
814	CASE ( 'read_from_file_3d' )
815	!
816	!-- Initialize LAD with data from file. If LAD is given in NetCDF file,
817	!-- use these values, else take LAD profiles from ASCII file.
818	!-- Please note, in NetCDF file LAD is only given up to the maximum
819	!-- canopy top, indicated by leaf_area_density_f%nz.
820	lad_s = 0.0_wp
821	IF ( leaf_area_density_f%from_file ) THEN
822	!
823	!-- Set also pch_index, used to be the upper bound of the vertical
824	!-- loops. Therefore, use the global top of the canopy layer.
825	pch_index = leaf_area_density_f%nz - 1
826
827	DO i = nxl, nxr
828	DO j = nys, nyn
829	DO k = 0, leaf_area_density_f%nz - 1
830	IF ( leaf_area_density_f%var(k,j,i) /= &
831	leaf_area_density_f%fill ) &
832	lad_s(k,j,i) = leaf_area_density_f%var(k,j,i)
833	ENDDO
834	ENDDO
835	ENDDO
836	CALL exchange_horiz( lad_s, nbgp )
837	!
838	! ASCII file
839	!-- Initialize canopy parameters cdc (canopy drag coefficient),
840	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
841	!-- from file which contains complete 3D data (separate vertical profiles for
842	!-- each location).
843	ELSE
844	CALL pcm_read_plant_canopy_3d
845	ENDIF
846
847	CASE DEFAULT
848	!
849	!-- The DEFAULT case is reached either if the parameter
850	!-- canopy mode contains a wrong character string or if the
851	!-- user has coded a special case in the user interface.
852	!-- There, the subroutine user_init_plant_canopy checks
853	!-- which of these two conditions applies.
854	CALL user_init_plant_canopy
855
856	END SELECT
857	!
858	!-- Initialize 2D index array indicating canopy top index.
859	ALLOCATE( pch_index_ji(nysg:nyng,nxlg:nxrg) )
860	pch_index_ji = 0
861
862	DO i = nxl, nxr
863	DO j = nys, nyn
864	DO k = 0, pch_index
865	IF ( lad_s(k,j,i) /= 0 ) pch_index_ji(j,i) = k
866	ENDDO
867	!
868	!-- Check whether topography and local vegetation on top exceed
869	!-- height of the model domain.
870	k = get_topography_top_index_ji( j, i, 's' )
871	IF ( k + pch_index_ji(j,i) >= nzt + 1 ) THEN
872	message_string = 'Local vegetation height on top of ' // &
873	'topography exceeds height of model domain.'
874	CALL message( 'pcm_init', 'PA0999', 2, 2, 0, 6, 0 )
875	ENDIF
876
877	ENDDO
878	ENDDO
879
880	CALL exchange_horiz_2d_int( pch_index_ji, nys, nyn, nxl, nxr, nbgp )
881
882	!
883	!-- Initialization of the canopy heat source distribution due to heating
884	!-- of the canopy layers by incoming solar radiation, in case that a non-zero
885	!-- value is set for the canopy top heat flux (cthf), which equals the
886	!-- available net radiation at canopy top.
887	!-- The heat source distribution is calculated by a decaying exponential
888	!-- function of the downward cumulative leaf area index (cum_lai_hf),
889	!-- assuming that the foliage inside the plant canopy is heated by solar
890	!-- radiation penetrating the canopy layers according to the distribution
891	!-- of net radiation as suggested by Brown & Covey (1966; Agric. Meteorol. 3,
892	!-- 73â96). This approach has been applied e.g. by Shaw & Schumann (1992;
893	!-- Bound.-Layer Meteorol. 61, 47â64).
894	!-- When using the urban surface model (USM), canopy heating (pc_heating_rate)
895	!-- by radiation is calculated in the USM.
896	IF ( cthf /= 0.0_wp .AND. .NOT. urban_surface ) THEN
897
898	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
899	pc_heating_rate(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
900	!
901	!-- Piecewise calculation of the cumulative leaf area index by vertical
902	!-- integration of the leaf area density
903	cum_lai_hf(:,:,:) = 0.0_wp
904	DO i = nxlg, nxrg
905	DO j = nysg, nyng
906	DO k = pch_index_ji(j,i)-1, 0, -1
907	IF ( k == pch_index_ji(j,i)-1 ) THEN
908	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
909	( 0.5_wp * lad_s(k+1,j,i) * &
910	( zw(k+1) - zu(k+1) ) ) + &
911	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
912	lad_s(k,j,i) ) + &
913	lad_s(k+1,j,i) ) * &
914	( zu(k+1) - zw(k) ) )
915	ELSE
916	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
917	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
918	lad_s(k+1,j,i) ) + &
919	lad_s(k+1,j,i) ) * &
920	( zw(k+1) - zu(k+1) ) ) + &
921	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
922	lad_s(k,j,i) ) + &
923	lad_s(k+1,j,i) ) * &
924	( zu(k+1) - zw(k) ) )
925	ENDIF
926	ENDDO
927	ENDDO
928	ENDDO
929
930	!
931	!-- In areas with canopy the surface value of the canopy heat
932	!-- flux distribution overrides the surface heat flux (shf)
933	!-- Start with default surface type
934	DO m = 1, surf_def_h(0)%ns
935	k = surf_def_h(0)%k(m)
936	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
937	surf_def_h(0)%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
938	ENDDO
939	!
940	!-- Natural surfaces
941	DO m = 1, surf_lsm_h%ns
942	k = surf_lsm_h%k(m)
943	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
944	surf_lsm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
945	ENDDO
946	!
947	!-- Urban surfaces
948	DO m = 1, surf_usm_h%ns
949	k = surf_usm_h%k(m)
950	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
951	surf_usm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
952	ENDDO
953	!
954	!
955	!-- Calculation of the heating rate (K/s) within the different layers of
956	!-- the plant canopy. Calculation is only necessary in areas covered with
957	!-- canopy.
958	!-- Within the different canopy layers the plant-canopy heating
959	!-- rate (pc_heating_rate) is calculated as the vertical
960	!-- divergence of the canopy heat fluxes at the top and bottom
961	!-- of the respective layer
962	DO i = nxlg, nxrg
963	DO j = nysg, nyng
964	DO k = 1, pch_index_ji(j,i)
965	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) THEN
966	pc_heating_rate(k,j,i) = cthf * &
967	( exp(-ext_coef*cum_lai_hf(k,j,i)) - &
968	exp(-ext_coef*cum_lai_hf(k-1,j,i) ) ) / dzw(k)
969	ENDIF
970	ENDDO
971	ENDDO
972	ENDDO
973
974	ENDIF
975	!
976	!-- Allocate transpiration rate
977	IF ( humidity ) &
978	ALLOCATE( pc_transpiration_rate(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
979
980
981
982	END SUBROUTINE pcm_init
983
984
985	!------------------------------------------------------------------------------!
986	! Description:
987	! ------------
988	!> Parin for &plant_canopy_parameters for plant canopy model
989	!------------------------------------------------------------------------------!
990	SUBROUTINE pcm_parin
991
992	USE control_parameters, &
993	ONLY: message_string, plant_canopy
994
995	IMPLICIT NONE
996
997	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
998
999	NAMELIST /plant_canopy_parameters/ &
1000	alpha_lad, beta_lad, canopy_drag_coeff, &
1001	canopy_mode, cthf, &
1002	lad_surface, lad_type_coef, &
1003	lad_vertical_gradient, &
1004	lad_vertical_gradient_level, &
1005	lai_beta, &
1006	leaf_scalar_exch_coeff, &
1007	leaf_surface_conc, pch_index
1008
1009	NAMELIST /canopy_par/ alpha_lad, beta_lad, canopy_drag_coeff, &
1010	canopy_mode, cthf, &
1011	lad_surface, lad_type_coef, &
1012	lad_vertical_gradient, &
1013	lad_vertical_gradient_level, &
1014	lai_beta, &
1015	leaf_scalar_exch_coeff, &
1016	leaf_surface_conc, pch_index
1017
1018	line = ' '
1019
1020	!
1021	!-- Try to find radiation model package
1022	REWIND ( 11 )
1023	line = ' '
1024	DO WHILE ( INDEX( line, '&plant_canopy_parameters' ) == 0 )
1025	READ ( 11, '(A)', END=10 ) line
1026	ENDDO
1027	BACKSPACE ( 11 )
1028
1029	!
1030	!-- Read user-defined namelist
1031	READ ( 11, plant_canopy_parameters )
1032
1033	!
1034	!-- Set flag that indicates that the radiation model is switched on
1035	plant_canopy = .TRUE.
1036
1037	GOTO 12
1038	!
1039	!-- Try to find old namelist
1040	10 REWIND ( 11 )
1041	line = ' '
1042	DO WHILE ( INDEX( line, '&canopy_par' ) == 0 )
1043	READ ( 11, '(A)', END=12 ) line
1044	ENDDO
1045	BACKSPACE ( 11 )
1046
1047	!
1048	!-- Read user-defined namelist
1049	READ ( 11, canopy_par )
1050
1051	message_string = 'namelist canopy_par is deprecated and will be ' // &
1052	'removed in near future. Please &use namelist ' // &
1053	'plant_canopy_parameters instead'
1054	CALL message( 'pcm_parin', 'PA0487', 0, 1, 0, 6, 0 )
1055
1056	!
1057	!-- Set flag that indicates that the radiation model is switched on
1058	plant_canopy = .TRUE.
1059
1060	12 CONTINUE
1061
1062
1063	END SUBROUTINE pcm_parin
1064
1065
1066
1067	!------------------------------------------------------------------------------!
1068	! Description:
1069	! ------------
1070	!
1071	!> Loads 3D plant canopy data from file. File format is as follows:
1072	!>
1073	!> num_levels
1074	!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
1075	!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
1076	!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
1077	!> ...
1078	!>
1079	!> i.e. first line determines number of levels and further lines represent plant
1080	!> canopy data, one line per column and variable. In each data line,
1081	!> dtype represents variable to be set:
1082	!>
1083	!> dtype=1: leaf area density (lad_s)
1084	!> dtype=2....n: some additional plant canopy input data quantity
1085	!>
1086	!> Zeros are added automatically above num_levels until top of domain. Any
1087	!> non-specified (x,y) columns have zero values as default.
1088	!------------------------------------------------------------------------------!
1089	SUBROUTINE pcm_read_plant_canopy_3d
1090
1091	USE control_parameters, &
1092	ONLY: coupling_char, message_string, passive_scalar
1093
1094	USE indices, &
1095	ONLY: nbgp
1096
1097	IMPLICIT NONE
1098
1099	INTEGER(iwp) :: dtype !< type of input data (1=lad)
1100	INTEGER(iwp) :: pctype !< type of plant canopy (deciduous,non-deciduous,...)
1101	INTEGER(iwp) :: i, j !< running index
1102	INTEGER(iwp) :: nzp !< number of vertical layers of plant canopy
1103	INTEGER(iwp) :: nzpltop !<
1104	INTEGER(iwp) :: nzpl !<
1105
1106	REAL(wp), DIMENSION(:), ALLOCATABLE :: col !< vertical column of input data
1107
1108	!
1109	!-- Initialize lad_s array
1110	lad_s = 0.0_wp
1111
1112	!
1113	!-- Open and read plant canopy input data
1114	OPEN(152, FILE='PLANT_CANOPY_DATA_3D' // TRIM( coupling_char ), &
1115	ACCESS='SEQUENTIAL', ACTION='READ', STATUS='OLD', &
1116	FORM='FORMATTED', ERR=515)
1117	READ(152, *, ERR=516, END=517) nzp !< read first line = number of vertical layers
1118
1119	ALLOCATE( col(0:nzp-1) )
1120
1121	DO
1122	READ(152, *, ERR=516, END=517) dtype, i, j, pctype, col(:)
1123	IF ( i < nxlg .OR. i > nxrg .OR. j < nysg .OR. j > nyng ) CYCLE
1124
1125	SELECT CASE (dtype)
1126	CASE( 1 ) !< leaf area density
1127	!
1128	!-- This is just the pure canopy layer assumed to be grounded to
1129	!-- a flat domain surface. At locations where plant canopy sits
1130	!-- on top of any kind of topography, the vertical plant column
1131	!-- must be "lifted", which is done in SUBROUTINE pcm_tendency.
1132	IF ( pctype < 0 .OR. pctype > 10 ) THEN !< incorrect plant canopy type
1133	WRITE( message_string, * ) 'Incorrect type of plant canopy. ' // &
1134	'Allowed values 0 <= pctype <= 10, ' // &
1135	'but pctype is ', pctype
1136	CALL message( 'pcm_read_plant_canopy_3d', 'PA0349', 1, 2, 0, 6, 0 )
1137	ENDIF
1138	lad_s(0:nzp-1,j,i) = col(0:nzp-1) * lad_type_coef(pctype)
1139
1140	CASE DEFAULT
1141	WRITE(message_string, '(a,i2,a)') &
1142	'Unknown record type in file PLANT_CANOPY_DATA_3D: "', dtype, '"'
1143	CALL message( 'pcm_read_plant_canopy_3d', 'PA0530', 1, 2, 0, 6, 0 )
1144	END SELECT
1145	ENDDO
1146
1147	515 message_string = 'error opening file PLANT_CANOPY_DATA_3D'
1148	CALL message( 'pcm_read_plant_canopy_3d', 'PA0531', 1, 2, 0, 6, 0 )
1149
1150	516 message_string = 'error reading file PLANT_CANOPY_DATA_3D'
1151	CALL message( 'pcm_read_plant_canopy_3d', 'PA0532', 1, 2, 0, 6, 0 )
1152
1153	517 CLOSE(152)
1154	DEALLOCATE( col )
1155
1156	CALL exchange_horiz( lad_s, nbgp )
1157
1158	END SUBROUTINE pcm_read_plant_canopy_3d
1159
1160
1161
1162	!------------------------------------------------------------------------------!
1163	! Description:
1164	! ------------
1165	!> Calculation of the tendency terms, accounting for the effect of the plant
1166	!> canopy on momentum and scalar quantities.
1167	!>
1168	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
1169	!> (defined on scalar grid), as initialized in subroutine pcm_init.
1170	!> The lad on the w-grid is vertically interpolated from the surrounding
1171	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
1172	!> k = pch_index. Here, the lad is zero.
1173	!>
1174	!> The canopy drag must be limited (previously accounted for by calculation of
1175	!> a limiting canopy timestep for the determination of the maximum LES timestep
1176	!> in subroutine timestep), since it is physically impossible that the canopy
1177	!> drag alone can locally change the sign of a velocity component. This
1178	!> limitation is realized by calculating preliminary tendencies and velocities.
1179	!> It is subsequently checked if the preliminary new velocity has a different
1180	!> sign than the current velocity. If so, the tendency is limited in a way that
1181	!> the velocity can at maximum be reduced to zero by the canopy drag.
1182	!>
1183	!>
1184	!> Call for all grid points
1185	!------------------------------------------------------------------------------!
1186	SUBROUTINE pcm_tendency( component )
1187
1188
1189	USE control_parameters, &
1190	ONLY: dt_3d, message_string
1191
1192	USE kinds
1193
1194	IMPLICIT NONE
1195
1196	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
1197	INTEGER(iwp) :: i !< running index
1198	INTEGER(iwp) :: j !< running index
1199	INTEGER(iwp) :: k !< running index
1200	INTEGER(iwp) :: k_wall !< vertical index of topography top
1201	INTEGER(iwp) :: kk !< running index for flat lad arrays
1202
1203	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1204	REAL(wp) :: lad_local !< local lad value
1205	REAL(wp) :: pre_tend !< preliminary tendency
1206	REAL(wp) :: pre_u !< preliminary u-value
1207	REAL(wp) :: pre_v !< preliminary v-value
1208	REAL(wp) :: pre_w !< preliminary w-value
1209
1210
1211	ddt_3d = 1.0_wp / dt_3d
1212
1213	!
1214	!-- Compute drag for the three velocity components and the SGS-TKE:
1215	SELECT CASE ( component )
1216
1217	!
1218	!-- u-component
1219	CASE ( 1 )
1220	DO i = nxlu, nxr
1221	DO j = nys, nyn
1222	!
1223	!-- Determine topography-top index on u-grid
1224	k_wall = get_topography_top_index_ji( j, i, 'u' )
1225	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1226
1227	kk = k - k_wall !- lad arrays are defined flat
1228	!
1229	!-- In order to create sharp boundaries of the plant canopy,
1230	!-- the lad on the u-grid at index (k,j,i) is equal to
1231	!-- lad_s(k,j,i), rather than being interpolated from the
1232	!-- surrounding lad_s, because this would yield smaller lad
1233	!-- at the canopy boundaries than inside of the canopy.
1234	!-- For the same reason, the lad at the rightmost(i+1)canopy
1235	!-- boundary on the u-grid equals lad_s(k,j,i).
1236	lad_local = lad_s(kk,j,i)
1237	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp )&
1238	THEN
1239	lad_local = lad_s(kk,j,i-1)
1240	ENDIF
1241
1242	pre_tend = 0.0_wp
1243	pre_u = 0.0_wp
1244	!
1245	!-- Calculate preliminary value (pre_tend) of the tendency
1246	pre_tend = - cdc * &
1247	lad_local * &
1248	SQRT( u(k,j,i)**2 + &
1249	( 0.25_wp * ( v(k,j,i-1) + &
1250	v(k,j,i) + &
1251	v(k,j+1,i) + &
1252	v(k,j+1,i-1) ) &
1253	)**2 + &
1254	( 0.25_wp * ( w(k-1,j,i-1) + &
1255	w(k-1,j,i) + &
1256	w(k,j,i-1) + &
1257	w(k,j,i) ) &
1258	)**2 &
1259	) * &
1260	u(k,j,i)
1261
1262	!
1263	!-- Calculate preliminary new velocity, based on pre_tend
1264	pre_u = u(k,j,i) + dt_3d * pre_tend
1265	!
1266	!-- Compare sign of old velocity and new preliminary velocity,
1267	!-- and in case the signs are different, limit the tendency
1268	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1269	pre_tend = - u(k,j,i) * ddt_3d
1270	ELSE
1271	pre_tend = pre_tend
1272	ENDIF
1273	!
1274	!-- Calculate final tendency
1275	tend(k,j,i) = tend(k,j,i) + pre_tend
1276
1277	ENDDO
1278	ENDDO
1279	ENDDO
1280
1281	!
1282	!-- v-component
1283	CASE ( 2 )
1284	DO i = nxl, nxr
1285	DO j = nysv, nyn
1286	!
1287	!-- Determine topography-top index on v-grid
1288	k_wall = get_topography_top_index_ji( j, i, 'v' )
1289
1290	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1291
1292	kk = k - k_wall !- lad arrays are defined flat
1293	!
1294	!-- In order to create sharp boundaries of the plant canopy,
1295	!-- the lad on the v-grid at index (k,j,i) is equal to
1296	!-- lad_s(k,j,i), rather than being interpolated from the
1297	!-- surrounding lad_s, because this would yield smaller lad
1298	!-- at the canopy boundaries than inside of the canopy.
1299	!-- For the same reason, the lad at the northmost(j+1) canopy
1300	!-- boundary on the v-grid equals lad_s(k,j,i).
1301	lad_local = lad_s(kk,j,i)
1302	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp )&
1303	THEN
1304	lad_local = lad_s(kk,j-1,i)
1305	ENDIF
1306
1307	pre_tend = 0.0_wp
1308	pre_v = 0.0_wp
1309	!
1310	!-- Calculate preliminary value (pre_tend) of the tendency
1311	pre_tend = - cdc * &
1312	lad_local * &
1313	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1314	u(k,j-1,i+1) + &
1315	u(k,j,i) + &
1316	u(k,j,i+1) ) &
1317	)**2 + &
1318	v(k,j,i)**2 + &
1319	( 0.25_wp * ( w(k-1,j-1,i) + &
1320	w(k-1,j,i) + &
1321	w(k,j-1,i) + &
1322	w(k,j,i) ) &
1323	)**2 &
1324	) * &
1325	v(k,j,i)
1326
1327	!
1328	!-- Calculate preliminary new velocity, based on pre_tend
1329	pre_v = v(k,j,i) + dt_3d * pre_tend
1330	!
1331	!-- Compare sign of old velocity and new preliminary velocity,
1332	!-- and in case the signs are different, limit the tendency
1333	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1334	pre_tend = - v(k,j,i) * ddt_3d
1335	ELSE
1336	pre_tend = pre_tend
1337	ENDIF
1338	!
1339	!-- Calculate final tendency
1340	tend(k,j,i) = tend(k,j,i) + pre_tend
1341
1342	ENDDO
1343	ENDDO
1344	ENDDO
1345
1346	!
1347	!-- w-component
1348	CASE ( 3 )
1349	DO i = nxl, nxr
1350	DO j = nys, nyn
1351	!
1352	!-- Determine topography-top index on w-grid
1353	k_wall = get_topography_top_index_ji( j, i, 'w' )
1354
1355	DO k = k_wall+1, k_wall + pch_index_ji(j,i) - 1
1356
1357	kk = k - k_wall !- lad arrays are defined flat
1358
1359	pre_tend = 0.0_wp
1360	pre_w = 0.0_wp
1361	!
1362	!-- Calculate preliminary value (pre_tend) of the tendency
1363	pre_tend = - cdc * &
1364	(0.5_wp * &
1365	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1366	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1367	u(k,j,i+1) + &
1368	u(k+1,j,i) + &
1369	u(k+1,j,i+1) ) &
1370	)**2 + &
1371	( 0.25_wp * ( v(k,j,i) + &
1372	v(k,j+1,i) + &
1373	v(k+1,j,i) + &
1374	v(k+1,j+1,i) ) &
1375	)**2 + &
1376	w(k,j,i)**2 &
1377	) * &
1378	w(k,j,i)
1379	!
1380	!-- Calculate preliminary new velocity, based on pre_tend
1381	pre_w = w(k,j,i) + dt_3d * pre_tend
1382	!
1383	!-- Compare sign of old velocity and new preliminary velocity,
1384	!-- and in case the signs are different, limit the tendency
1385	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1386	pre_tend = - w(k,j,i) * ddt_3d
1387	ELSE
1388	pre_tend = pre_tend
1389	ENDIF
1390	!
1391	!-- Calculate final tendency
1392	tend(k,j,i) = tend(k,j,i) + pre_tend
1393
1394	ENDDO
1395	ENDDO
1396	ENDDO
1397
1398	!
1399	!-- potential temperature
1400	CASE ( 4 )
1401	DO i = nxl, nxr
1402	DO j = nys, nyn
1403	!
1404	!-- Determine topography-top index on scalar-grid
1405	k_wall = get_topography_top_index_ji( j, i, 's' )
1406
1407	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1408
1409	kk = k - k_wall !- lad arrays are defined flat
1410	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1411	ENDDO
1412	ENDDO
1413	ENDDO
1414
1415	!
1416	!-- humidity
1417	CASE ( 5 )
1418	DO i = nxl, nxr
1419	DO j = nys, nyn
1420	!
1421	!-- Determine topography-top index on scalar-grid
1422	k_wall = get_topography_top_index_ji( j, i, 's' )
1423
1424	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1425
1426	kk = k - k_wall !- lad arrays are defined flat
1427	pc_transpiration_rate(kk,j,i) = - lsec &
1428	* lad_s(kk,j,i) * &
1429	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1430	u(k,j,i+1) ) &
1431	)**2 + &
1432	( 0.5_wp * ( v(k,j,i) + &
1433	v(k,j+1,i) ) &
1434	)**2 + &
1435	( 0.5_wp * ( w(k-1,j,i) + &
1436	w(k,j,i) ) &
1437	)**2 &
1438	) * &
1439	( q(k,j,i) - lsc )
1440
1441	tend(k,j,i) = tend(k,j,i) + pc_transpiration_rate(kk,j,i)
1442	ENDDO
1443	ENDDO
1444	ENDDO
1445
1446	!
1447	!-- sgs-tke
1448	CASE ( 6 )
1449	DO i = nxl, nxr
1450	DO j = nys, nyn
1451	!
1452	!-- Determine topography-top index on scalar-grid
1453	k_wall = get_topography_top_index_ji( j, i, 's' )
1454
1455	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1456
1457	kk = k - k_wall !- lad arrays are defined flat
1458	tend(k,j,i) = tend(k,j,i) - &
1459	2.0_wp * cdc * &
1460	lad_s(kk,j,i) * &
1461	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1462	u(k,j,i+1) ) &
1463	)**2 + &
1464	( 0.5_wp * ( v(k,j,i) + &
1465	v(k,j+1,i) ) &
1466	)**2 + &
1467	( 0.5_wp * ( w(k,j,i) + &
1468	w(k+1,j,i) ) &
1469	)**2 &
1470	) * &
1471	e(k,j,i)
1472	ENDDO
1473	ENDDO
1474	ENDDO
1475	!
1476	!-- scalar concentration
1477	CASE ( 7 )
1478	DO i = nxl, nxr
1479	DO j = nys, nyn
1480	!
1481	!-- Determine topography-top index on scalar-grid
1482	k_wall = get_topography_top_index_ji( j, i, 's' )
1483
1484	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1485
1486	kk = k - k_wall !- lad arrays are defined flat
1487	tend(k,j,i) = tend(k,j,i) - &
1488	lsec * &
1489	lad_s(kk,j,i) * &
1490	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1491	u(k,j,i+1) ) &
1492	)**2 + &
1493	( 0.5_wp * ( v(k,j,i) + &
1494	v(k,j+1,i) ) &
1495	)**2 + &
1496	( 0.5_wp * ( w(k-1,j,i) + &
1497	w(k,j,i) ) &
1498	)**2 &
1499	) * &
1500	( s(k,j,i) - lsc )
1501	ENDDO
1502	ENDDO
1503	ENDDO
1504
1505
1506
1507	CASE DEFAULT
1508
1509	WRITE( message_string, * ) 'wrong component: ', component
1510	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1511
1512	END SELECT
1513
1514	END SUBROUTINE pcm_tendency
1515
1516
1517	!------------------------------------------------------------------------------!
1518	! Description:
1519	! ------------
1520	!> Calculation of the tendency terms, accounting for the effect of the plant
1521	!> canopy on momentum and scalar quantities.
1522	!>
1523	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
1524	!> (defined on scalar grid), as initialized in subroutine pcm_init.
1525	!> The lad on the w-grid is vertically interpolated from the surrounding
1526	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
1527	!> k = pch_index. Here, the lad is zero.
1528	!>
1529	!> The canopy drag must be limited (previously accounted for by calculation of
1530	!> a limiting canopy timestep for the determination of the maximum LES timestep
1531	!> in subroutine timestep), since it is physically impossible that the canopy
1532	!> drag alone can locally change the sign of a velocity component. This
1533	!> limitation is realized by calculating preliminary tendencies and velocities.
1534	!> It is subsequently checked if the preliminary new velocity has a different
1535	!> sign than the current velocity. If so, the tendency is limited in a way that
1536	!> the velocity can at maximum be reduced to zero by the canopy drag.
1537	!>
1538	!>
1539	!> Call for grid point i,j
1540	!------------------------------------------------------------------------------!
1541	SUBROUTINE pcm_tendency_ij( i, j, component )
1542
1543
1544	USE control_parameters, &
1545	ONLY: dt_3d, message_string
1546
1547	USE kinds
1548
1549	IMPLICIT NONE
1550
1551	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
1552	INTEGER(iwp) :: i !< running index
1553	INTEGER(iwp) :: j !< running index
1554	INTEGER(iwp) :: k !< running index
1555	INTEGER(iwp) :: k_wall !< vertical index of topography top
1556	INTEGER(iwp) :: kk !< running index for flat lad arrays
1557
1558	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1559	REAL(wp) :: lad_local !< local lad value
1560	REAL(wp) :: pre_tend !< preliminary tendency
1561	REAL(wp) :: pre_u !< preliminary u-value
1562	REAL(wp) :: pre_v !< preliminary v-value
1563	REAL(wp) :: pre_w !< preliminary w-value
1564
1565
1566	ddt_3d = 1.0_wp / dt_3d
1567	!
1568	!-- Compute drag for the three velocity components and the SGS-TKE
1569	SELECT CASE ( component )
1570
1571	!
1572	!-- u-component
1573	CASE ( 1 )
1574	!
1575	!-- Determine topography-top index on u-grid
1576	k_wall = get_topography_top_index_ji( j, i, 'u' )
1577	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1578
1579	kk = k - k_wall !- lad arrays are defined flat
1580
1581	!
1582	!-- In order to create sharp boundaries of the plant canopy,
1583	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
1584	!-- rather than being interpolated from the surrounding lad_s,
1585	!-- because this would yield smaller lad at the canopy boundaries
1586	!-- than inside of the canopy.
1587	!-- For the same reason, the lad at the rightmost(i+1)canopy
1588	!-- boundary on the u-grid equals lad_s(k,j,i).
1589	lad_local = lad_s(kk,j,i)
1590	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp ) THEN
1591	lad_local = lad_s(kk,j,i-1)
1592	ENDIF
1593
1594	pre_tend = 0.0_wp
1595	pre_u = 0.0_wp
1596	!
1597	!-- Calculate preliminary value (pre_tend) of the tendency
1598	pre_tend = - cdc * &
1599	lad_local * &
1600	SQRT( u(k,j,i)**2 + &
1601	( 0.25_wp * ( v(k,j,i-1) + &
1602	v(k,j,i) + &
1603	v(k,j+1,i) + &
1604	v(k,j+1,i-1) ) &
1605	)**2 + &
1606	( 0.25_wp * ( w(k-1,j,i-1) + &
1607	w(k-1,j,i) + &
1608	w(k,j,i-1) + &
1609	w(k,j,i) ) &
1610	)**2 &
1611	) * &
1612	u(k,j,i)
1613
1614	!
1615	!-- Calculate preliminary new velocity, based on pre_tend
1616	pre_u = u(k,j,i) + dt_3d * pre_tend
1617	!
1618	!-- Compare sign of old velocity and new preliminary velocity,
1619	!-- and in case the signs are different, limit the tendency
1620	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1621	pre_tend = - u(k,j,i) * ddt_3d
1622	ELSE
1623	pre_tend = pre_tend
1624	ENDIF
1625	!
1626	!-- Calculate final tendency
1627	tend(k,j,i) = tend(k,j,i) + pre_tend
1628	ENDDO
1629
1630
1631	!
1632	!-- v-component
1633	CASE ( 2 )
1634	!
1635	!-- Determine topography-top index on v-grid
1636	k_wall = get_topography_top_index_ji( j, i, 'v' )
1637
1638	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1639
1640	kk = k - k_wall !- lad arrays are defined flat
1641	!
1642	!-- In order to create sharp boundaries of the plant canopy,
1643	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
1644	!-- rather than being interpolated from the surrounding lad_s,
1645	!-- because this would yield smaller lad at the canopy boundaries
1646	!-- than inside of the canopy.
1647	!-- For the same reason, the lad at the northmost(j+1)canopy
1648	!-- boundary on the v-grid equals lad_s(k,j,i).
1649	lad_local = lad_s(kk,j,i)
1650	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp ) THEN
1651	lad_local = lad_s(kk,j-1,i)
1652	ENDIF
1653
1654	pre_tend = 0.0_wp
1655	pre_v = 0.0_wp
1656	!
1657	!-- Calculate preliminary value (pre_tend) of the tendency
1658	pre_tend = - cdc * &
1659	lad_local * &
1660	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1661	u(k,j-1,i+1) + &
1662	u(k,j,i) + &
1663	u(k,j,i+1) ) &
1664	)**2 + &
1665	v(k,j,i)**2 + &
1666	( 0.25_wp * ( w(k-1,j-1,i) + &
1667	w(k-1,j,i) + &
1668	w(k,j-1,i) + &
1669	w(k,j,i) ) &
1670	)**2 &
1671	) * &
1672	v(k,j,i)
1673
1674	!
1675	!-- Calculate preliminary new velocity, based on pre_tend
1676	pre_v = v(k,j,i) + dt_3d * pre_tend
1677	!
1678	!-- Compare sign of old velocity and new preliminary velocity,
1679	!-- and in case the signs are different, limit the tendency
1680	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1681	pre_tend = - v(k,j,i) * ddt_3d
1682	ELSE
1683	pre_tend = pre_tend
1684	ENDIF
1685	!
1686	!-- Calculate final tendency
1687	tend(k,j,i) = tend(k,j,i) + pre_tend
1688	ENDDO
1689
1690
1691	!
1692	!-- w-component
1693	CASE ( 3 )
1694	!
1695	!-- Determine topography-top index on w-grid
1696	k_wall = get_topography_top_index_ji( j, i, 'w' )
1697
1698	DO k = k_wall + 1, k_wall + pch_index_ji(j,i) - 1
1699
1700	kk = k - k_wall !- lad arrays are defined flat
1701
1702	pre_tend = 0.0_wp
1703	pre_w = 0.0_wp
1704	!
1705	!-- Calculate preliminary value (pre_tend) of the tendency
1706	pre_tend = - cdc * &
1707	(0.5_wp * &
1708	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1709	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1710	u(k,j,i+1) + &
1711	u(k+1,j,i) + &
1712	u(k+1,j,i+1) ) &
1713	)**2 + &
1714	( 0.25_wp * ( v(k,j,i) + &
1715	v(k,j+1,i) + &
1716	v(k+1,j,i) + &
1717	v(k+1,j+1,i) ) &
1718	)**2 + &
1719	w(k,j,i)**2 &
1720	) * &
1721	w(k,j,i)
1722	!
1723	!-- Calculate preliminary new velocity, based on pre_tend
1724	pre_w = w(k,j,i) + dt_3d * pre_tend
1725	!
1726	!-- Compare sign of old velocity and new preliminary velocity,
1727	!-- and in case the signs are different, limit the tendency
1728	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1729	pre_tend = - w(k,j,i) * ddt_3d
1730	ELSE
1731	pre_tend = pre_tend
1732	ENDIF
1733	!
1734	!-- Calculate final tendency
1735	tend(k,j,i) = tend(k,j,i) + pre_tend
1736	ENDDO
1737
1738	!
1739	!-- potential temperature
1740	CASE ( 4 )
1741	!
1742	!-- Determine topography-top index on scalar grid
1743	k_wall = get_topography_top_index_ji( j, i, 's' )
1744
1745	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1746	kk = k - k_wall !- lad arrays are defined flat
1747	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1748	ENDDO
1749
1750
1751	!
1752	!-- humidity
1753	CASE ( 5 )
1754	!
1755	!-- Determine topography-top index on scalar grid
1756	k_wall = get_topography_top_index_ji( j, i, 's' )
1757
1758	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1759	kk = k - k_wall !- lad arrays are defined flat
1760
1761	pc_transpiration_rate(kk,j,i) = - lsec &
1762	* lad_s(kk,j,i) * &
1763	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1764	u(k,j,i+1) ) &
1765	)**2 + &
1766	( 0.5_wp * ( v(k,j,i) + &
1767	v(k,j+1,i) ) &
1768	)**2 + &
1769	( 0.5_wp * ( w(k-1,j,i) + &
1770	w(k,j,i) ) &
1771	)**2 &
1772	) * &
1773	( q(k,j,i) - lsc )
1774
1775	tend(k,j,i) = tend(k,j,i) + pc_transpiration_rate(kk,j,i)
1776
1777	ENDDO
1778
1779	!
1780	!-- sgs-tke
1781	CASE ( 6 )
1782	!
1783	!-- Determine topography-top index on scalar grid
1784	k_wall = get_topography_top_index_ji( j, i, 's' )
1785
1786	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1787
1788	kk = k - k_wall
1789	tend(k,j,i) = tend(k,j,i) - &
1790	2.0_wp * cdc * &
1791	lad_s(kk,j,i) * &
1792	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1793	u(k,j,i+1) ) &
1794	)**2 + &
1795	( 0.5_wp * ( v(k,j,i) + &
1796	v(k,j+1,i) ) &
1797	)**2 + &
1798	( 0.5_wp * ( w(k,j,i) + &
1799	w(k+1,j,i) ) &
1800	)**2 &
1801	) * &
1802	e(k,j,i)
1803	ENDDO
1804
1805	!
1806	!-- scalar concentration
1807	CASE ( 7 )
1808	!
1809	!-- Determine topography-top index on scalar grid
1810	k_wall = get_topography_top_index_ji( j, i, 's' )
1811
1812	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1813
1814	kk = k - k_wall
1815	tend(k,j,i) = tend(k,j,i) - &
1816	lsec * &
1817	lad_s(kk,j,i) * &
1818	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1819	u(k,j,i+1) ) &
1820	)**2 + &
1821	( 0.5_wp * ( v(k,j,i) + &
1822	v(k,j+1,i) ) &
1823	)**2 + &
1824	( 0.5_wp * ( w(k-1,j,i) + &
1825	w(k,j,i) ) &
1826	)**2 &
1827	) * &
1828	( s(k,j,i) - lsc )
1829	ENDDO
1830
1831	CASE DEFAULT
1832
1833	WRITE( message_string, * ) 'wrong component: ', component
1834	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1835
1836	END SELECT
1837
1838	END SUBROUTINE pcm_tendency_ij
1839
1840
1841
1842	END MODULE plant_canopy_model_mod

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