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source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 3014

Last change on this file since 3014 was 3014, checked in by maronga, 6 years ago
series of bugfixes
Property svn:keywords set to `Id`
File size: 75.2 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 3014 2018-05-09 08:42:38Z maronga $
27	! Bugfix: nzb_do and nzt_do were not used for 3d data output
28	! Added pc_transpiration_rate
29	!
30	! 2977 2018-04-17 10:27:57Z kanani
31	! Implement changes from branch radiation (r2948-2971) with minor modifications,
32	! plus some formatting.
33	! (moh.hefny):
34	! Add plant canopy type to account for changes in LAD (based on the changes
35	! done by Resler & Pavel) and correct the error message to PALM Standard.
36	!
37	! 2932 2018-03-26 09:39:22Z maronga
38	! renamed canopy_par to plant_canopy_parameters
39	!
40	! 2920 2018-03-22 11:22:01Z kanani
41	! Move usm_lad_rma and prototype_lad to radiation_model (moh.hefny)
42	!
43	! 2892 2018-03-14 15:06:29Z suehring
44	! Bugfix, read separate ASCII LAD files for parent and child model.
45	!
46	! 2770 2018-01-25 15:10:09Z kanani
47	! Correction of parameter check
48	!
49	! 2768 2018-01-24 15:38:29Z kanani
50	! Added check for output quantity pcm_heatrate, some formatting
51	!
52	! 2766 2018-01-22 17:17:47Z kanani
53	! Increased LEN of canopy mode to 30
54	!
55	! 2746 2018-01-15 12:06:04Z suehring
56	! Move flag plant canopy to modules
57	!
58	! 2718 2018-01-02 08:49:38Z maronga
59	! Corrected "Former revisions" section
60	!
61	! 2701 2017-12-15 15:40:50Z suehring
62	! Changes from last commit documented
63	!
64	! 2698 2017-12-14 18:46:24Z suehring
65	! Bugfix in get_topography_top_index
66	!
67	! 2696 2017-12-14 17:12:51Z kanani
68	! Change in file header (GPL part)
69	! Bugfix for vertical loop index pch_index in case of Netcdf input
70	! Introduce 2D index array incorporate canopy top index
71	! Check if canopy on top of topography do not exceed vertical dimension
72	! Add check for canopy_mode in case of Netcdf input.
73	! Enable _FillValue output for 3d quantities
74	! Bugfix in reading of PIDS leaf area density (MS)
75	!
76	! 2669 2017-12-06 16:03:27Z raasch
77	! coupling_char removed
78	!
79	! 2512 2017-10-04 08:26:59Z raasch
80	! upper bounds of 3d output changed from nx+1,ny+1 to nx,ny
81	! no output of ghost layer data
82	!
83	! 2318 2017-07-20 17:27:44Z suehring
84	! Get topography top index via Function call
85	!
86	! 2317 2017-07-20 17:27:19Z suehring
87	! Changed error messages
88	!
89	! 2233 2017-05-30 18:08:54Z suehring
90	!
91	! 2232 2017-05-30 17:47:52Z suehring
92	! Adjustments to new topography concept
93	!
94	! 2213 2017-04-24 15:10:35Z kanani
95	! Bugfix: exchange of ghost points in array pc_heating_rate needed for output
96	! of pcm_heatrate, onetime ghost point exchange of lad_s after initialization.
97	! Formatting and clean-up of subroutine pcm_read_plant_canopy_3d,
98	! minor re-organization of canopy-heating initialization.
99	!
100	! 2209 2017-04-19 09:34:46Z kanani
101	! Added 3d output of leaf area density (pcm_lad) and canopy
102	! heat rate (pcm_heatrate)
103	!
104	! 2024 2016-10-12 16:42:37Z kanani
105	! Added missing lad_s initialization
106	!
107	! 2011 2016-09-19 17:29:57Z kanani
108	! Renamed canopy_heat_flux to pc_heating_rate, since the original meaning/
109	! calculation of the quantity has changed, related to the urban surface model
110	! and similar future applications.
111	!
112	! 2007 2016-08-24 15:47:17Z kanani
113	! Added SUBROUTINE pcm_read_plant_canopy_3d for reading 3d plant canopy data
114	! from file (new case canopy_mode=read_from_file_3d) in the course of
115	! introduction of urban surface model,
116	! introduced variable ext_coef,
117	! resorted SUBROUTINEs to alphabetical order
118	!
119	! 2000 2016-08-20 18:09:15Z knoop
120	! Forced header and separation lines into 80 columns
121	!
122	! 1960 2016-07-12 16:34:24Z suehring
123	! Separate humidity and passive scalar
124	!
125	! 1953 2016-06-21 09:28:42Z suehring
126	! Bugfix, lad_s and lad must be public
127	!
128	! 1826 2016-04-07 12:01:39Z maronga
129	! Further modularization
130	!
131	! 1721 2015-11-16 12:56:48Z raasch
132	! bugfixes: shf is reduced in areas covered with canopy only,
133	! canopy is set on top of topography
134	!
135	! 1682 2015-10-07 23:56:08Z knoop
136	! Code annotations made doxygen readable
137	!
138	! 1484 2014-10-21 10:53:05Z kanani
139	! Changes due to new module structure of the plant canopy model:
140	! module plant_canopy_model_mod now contains a subroutine for the
141	! initialization of the canopy model (pcm_init),
142	! limitation of the canopy drag (previously accounted for by calculation of
143	! a limiting canopy timestep for the determination of the maximum LES timestep
144	! in subroutine timestep) is now realized by the calculation of pre-tendencies
145	! and preliminary velocities in subroutine pcm_tendency,
146	! some redundant MPI communication removed in subroutine pcm_init
147	! (was previously in init_3d_model),
148	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
149	! respective grid is now provided only by lad_s (e.g. in the calculation of
150	! the tendency terms or of cum_lai_hf),
151	! drag_coefficient, lai, leaf_surface_concentration,
152	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
153	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
154	! respectively,
155	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
156	! USE-statements and ONLY-lists modified accordingly
157	!
158	! 1340 2014-03-25 19:45:13Z kanani
159	! REAL constants defined as wp-kind
160	!
161	! 1320 2014-03-20 08:40:49Z raasch
162	! ONLY-attribute added to USE-statements,
163	! kind-parameters added to all INTEGER and REAL declaration statements,
164	! kinds are defined in new module kinds,
165	! old module precision_kind is removed,
166	! revision history before 2012 removed,
167	! comment fields (!:) to be used for variable explanations added to
168	! all variable declaration statements
169	!
170	! 1036 2012-10-22 13:43:42Z raasch
171	! code put under GPL (PALM 3.9)
172	!
173	! 138 2007-11-28 10:03:58Z letzel
174	! Initial revision
175	!
176	! Description:
177	! ------------
178	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
179	!> profile (subroutine pcm_init).
180	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
181	!> due to canopy elements (subroutine pcm_tendency).
182	!------------------------------------------------------------------------------!
183	MODULE plant_canopy_model_mod
184
185	USE arrays_3d, &
186	ONLY: dzu, dzw, e, q, s, tend, u, v, w, zu, zw
187
188	USE indices, &
189	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
190	nz, nzb, nzt
191
192	USE kinds
193
194	USE surface_mod, &
195	ONLY: get_topography_top_index_ji
196
197
198	IMPLICIT NONE
199
200
201	CHARACTER (LEN=30) :: canopy_mode = 'block' !< canopy coverage
202
203	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
204	INTEGER(iwp) :: lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
205
206	INTEGER(iwp), DIMENSION(:,:), ALLOCATABLE :: pch_index_ji !< local plant canopy top
207
208	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
209
210	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
211	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
212	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
213	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
214	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
215	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
216	REAL(wp) :: ext_coef = 0.6_wp !< extinction coefficient
217	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
218	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
219	REAL(wp) :: leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
220	REAL(wp) :: leaf_surface_conc = 0.0_wp !< leaf surface concentration
221	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
222	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
223
224	REAL(wp) :: lad_vertical_gradient(10) = 0.0_wp !< lad gradient
225	REAL(wp) :: lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
226
227	REAL(wp) :: lad_type_coef(0:10) = 1.0_wp !< multiplicative coeficients for particular types
228	!< of plant canopy (e.g. deciduous tree during winter)
229
230	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
231	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
232
233	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
234	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
235	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: pc_heating_rate !< plant canopy heating rate
236	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: pc_transpiration_rate !< plant canopy transpiration rate
237
238	SAVE
239
240
241	PRIVATE
242
243	!
244	!-- Public functions
245	PUBLIC pcm_check_data_output, pcm_check_parameters, pcm_data_output_3d, &
246	pcm_define_netcdf_grid, pcm_header, pcm_init, pcm_parin, pcm_tendency
247
248	!
249	!-- Public variables and constants
250	PUBLIC pc_heating_rate, pc_transpiration_rate, canopy_mode, cthf, dt_plant_canopy, lad, lad_s, &
251	pch_index
252
253
254	INTERFACE pcm_check_data_output
255	MODULE PROCEDURE pcm_check_data_output
256	END INTERFACE pcm_check_data_output
257
258	INTERFACE pcm_check_parameters
259	MODULE PROCEDURE pcm_check_parameters
260	END INTERFACE pcm_check_parameters
261
262	INTERFACE pcm_data_output_3d
263	MODULE PROCEDURE pcm_data_output_3d
264	END INTERFACE pcm_data_output_3d
265
266	INTERFACE pcm_define_netcdf_grid
267	MODULE PROCEDURE pcm_define_netcdf_grid
268	END INTERFACE pcm_define_netcdf_grid
269
270	INTERFACE pcm_header
271	MODULE PROCEDURE pcm_header
272	END INTERFACE pcm_header
273
274	INTERFACE pcm_init
275	MODULE PROCEDURE pcm_init
276	END INTERFACE pcm_init
277
278	INTERFACE pcm_parin
279	MODULE PROCEDURE pcm_parin
280	END INTERFACE pcm_parin
281
282	INTERFACE pcm_read_plant_canopy_3d
283	MODULE PROCEDURE pcm_read_plant_canopy_3d
284	END INTERFACE pcm_read_plant_canopy_3d
285
286	INTERFACE pcm_tendency
287	MODULE PROCEDURE pcm_tendency
288	MODULE PROCEDURE pcm_tendency_ij
289	END INTERFACE pcm_tendency
290
291
292	CONTAINS
293
294
295	!------------------------------------------------------------------------------!
296	! Description:
297	! ------------
298	!> Check data output for plant canopy model
299	!------------------------------------------------------------------------------!
300	SUBROUTINE pcm_check_data_output( var, unit )
301
302
303	USE control_parameters, &
304	ONLY: data_output, message_string, urban_surface
305
306	IMPLICIT NONE
307
308	CHARACTER (LEN=*) :: unit !<
309	CHARACTER (LEN=*) :: var !<
310
311
312	SELECT CASE ( TRIM( var ) )
313
314	CASE ( 'pcm_heatrate' )
315	IF ( cthf == 0.0_wp .AND. .NOT. urban_surface ) THEN
316	message_string = 'output of "' // TRIM( var ) // '" requi' // &
317	'res setting of parameter cthf /= 0.0'
318	CALL message( 'pcm_check_data_output', 'PA1000', 1, 2, 0, 6, 0 )
319	ENDIF
320	unit = 'K s-1'
321
322	CASE ( 'pcm_transpirationrate' )
323	unit = 'kg kg-1 s-1'
324
325	CASE ( 'pcm_lad' )
326	unit = 'm2 m-3'
327
328
329	CASE DEFAULT
330	unit = 'illegal'
331
332	END SELECT
333
334
335	END SUBROUTINE pcm_check_data_output
336
337
338	!------------------------------------------------------------------------------!
339	! Description:
340	! ------------
341	!> Check parameters routine for plant canopy model
342	!------------------------------------------------------------------------------!
343	SUBROUTINE pcm_check_parameters
344
345	USE control_parameters, &
346	ONLY: cloud_physics, coupling_char, message_string, &
347	microphysics_seifert
348
349	USE netcdf_data_input_mod, &
350	ONLY: input_file_static, input_pids_static
351
352
353	IMPLICIT NONE
354
355
356	IF ( canopy_drag_coeff == 0.0_wp ) THEN
357	message_string = 'plant_canopy = .TRUE. requires a non-zero drag '// &
358	'coefficient & given value is canopy_drag_coeff = 0.0'
359	CALL message( 'pcm_check_parameters', 'PA0041', 1, 2, 0, 6, 0 )
360	ENDIF
361
362	IF ( ( alpha_lad /= 9999999.9_wp .AND. beta_lad == 9999999.9_wp ) .OR.&
363	beta_lad /= 9999999.9_wp .AND. alpha_lad == 9999999.9_wp ) THEN
364	message_string = 'using the beta function for the construction ' // &
365	'of the leaf area density profile requires ' // &
366	'both alpha_lad and beta_lad to be /= 9999999.9'
367	CALL message( 'pcm_check_parameters', 'PA0118', 1, 2, 0, 6, 0 )
368	ENDIF
369
370	IF ( calc_beta_lad_profile .AND. lai_beta == 0.0_wp ) THEN
371	message_string = 'using the beta function for the construction ' // &
372	'of the leaf area density profile requires ' // &
373	'a non-zero lai_beta, but given value is ' // &
374	'lai_beta = 0.0'
375	CALL message( 'pcm_check_parameters', 'PA0119', 1, 2, 0, 6, 0 )
376	ENDIF
377
378	IF ( calc_beta_lad_profile .AND. lad_surface /= 0.0_wp ) THEN
379	message_string = 'simultaneous setting of alpha_lad /= 9999999.9 '// &
380	'combined with beta_lad /= 9999999.9 ' // &
381	'and lad_surface /= 0.0 is not possible, ' // &
382	'use either vertical gradients or the beta ' // &
383	'function for the construction of the leaf area '// &
384	'density profile'
385	CALL message( 'pcm_check_parameters', 'PA0120', 1, 2, 0, 6, 0 )
386	ENDIF
387
388	IF ( cloud_physics .AND. microphysics_seifert ) THEN
389	message_string = 'plant_canopy = .TRUE. requires cloud_scheme /=' // &
390	' seifert_beheng'
391	CALL message( 'pcm_check_parameters', 'PA0360', 1, 2, 0, 6, 0 )
392	ENDIF
393	!
394	!-- If dynamic input file is used, canopy need to be read from file
395	IF ( input_pids_static .AND. &
396	TRIM( canopy_mode ) /= 'read_from_file_3d' ) THEN
397	message_string = 'Usage of dynamic input file ' // &
398	TRIM( input_file_static ) // &
399	TRIM( coupling_char ) // ' requires ' // &
400	'canopy_mode = read_from_file_3d'
401	CALL message( 'pcm_check_parameters', 'PA0999', 1, 2, 0, 6, 0 )
402	ENDIF
403
404
405	END SUBROUTINE pcm_check_parameters
406
407
408	!------------------------------------------------------------------------------!
409	!
410	! Description:
411	! ------------
412	!> Subroutine defining 3D output variables
413	!------------------------------------------------------------------------------!
414	SUBROUTINE pcm_data_output_3d( av, variable, found, local_pf, fill_value, &
415	nzb_do, nzt_do )
416
417	USE indices
418
419	USE kinds
420
421
422	IMPLICIT NONE
423
424	CHARACTER (LEN=*) :: variable !<
425
426	INTEGER(iwp) :: av !<
427	INTEGER(iwp) :: i !<
428	INTEGER(iwp) :: j !<
429	INTEGER(iwp) :: k !<
430	INTEGER(iwp) :: k_topo !< topography top index
431	INTEGER(iwp) :: nzb_do !< lower limit of the data output (usually 0)
432	INTEGER(iwp) :: nzt_do !< vertical upper limit of the data output (usually nz_do3d)
433
434	LOGICAL :: found !<
435
436	REAL(wp) :: fill_value
437	REAL(sp), DIMENSION(nxl:nxr,nys:nyn,nzb_do:nzt_do) :: local_pf !<
438
439
440	found = .TRUE.
441
442	local_pf = REAL( fill_value, KIND = 4 )
443
444	SELECT CASE ( TRIM( variable ) )
445
446	CASE ( 'pcm_heatrate' )
447	IF ( av == 0 ) THEN
448	DO i = nxl, nxr
449	DO j = nys, nyn
450	IF ( pch_index_ji(j,i) /= 0 ) THEN
451	k_topo = get_topography_top_index_ji( j, i, 's' )
452	DO k = k_topo, k_topo + pch_index_ji(j,i)
453	local_pf(i,j,k) = pc_heating_rate(k-k_topo,j,i)
454	ENDDO
455	ENDIF
456	ENDDO
457	ENDDO
458	ENDIF
459
460	CASE ( 'pcm_transpirationrate' )
461	IF ( av == 0 ) THEN
462	DO i = nxl, nxr
463	DO j = nys, nyn
464	IF ( pch_index_ji(j,i) /= 0 ) THEN
465	k_topo = get_topography_top_index_ji( j, i, 's' )
466	DO k = k_topo, k_topo + pch_index_ji(j,i)
467	local_pf(i,j,k) = pc_transpiration_rate(k-k_topo,j,i)
468	ENDDO
469	ENDIF
470	ENDDO
471	ENDDO
472	ENDIF
473
474	CASE ( 'pcm_lad' )
475	IF ( av == 0 ) THEN
476	DO i = nxl, nxr
477	DO j = nys, nyn
478	IF ( pch_index_ji(j,i) /= 0 ) THEN
479	k_topo = get_topography_top_index_ji( j, i, 's' )
480	DO k = k_topo, k_topo + pch_index_ji(j,i)
481	local_pf(i,j,k) = lad_s(k-k_topo,j,i)
482	ENDDO
483	ENDIF
484	ENDDO
485	ENDDO
486	ENDIF
487
488
489	CASE DEFAULT
490	found = .FALSE.
491
492	END SELECT
493
494
495	END SUBROUTINE pcm_data_output_3d
496
497	!------------------------------------------------------------------------------!
498	!
499	! Description:
500	! ------------
501	!> Subroutine defining appropriate grid for netcdf variables.
502	!> It is called from subroutine netcdf.
503	!------------------------------------------------------------------------------!
504	SUBROUTINE pcm_define_netcdf_grid( var, found, grid_x, grid_y, grid_z )
505
506	IMPLICIT NONE
507
508	CHARACTER (LEN=*), INTENT(IN) :: var !<
509	LOGICAL, INTENT(OUT) :: found !<
510	CHARACTER (LEN=*), INTENT(OUT) :: grid_x !<
511	CHARACTER (LEN=*), INTENT(OUT) :: grid_y !<
512	CHARACTER (LEN=*), INTENT(OUT) :: grid_z !<
513
514	found = .TRUE.
515
516	!
517	!-- Check for the grid
518	SELECT CASE ( TRIM( var ) )
519
520	CASE ( 'pcm_heatrate', 'pcm_lad', 'pcm_transpirationrate')
521	grid_x = 'x'
522	grid_y = 'y'
523	grid_z = 'zu'
524
525	CASE DEFAULT
526	found = .FALSE.
527	grid_x = 'none'
528	grid_y = 'none'
529	grid_z = 'none'
530	END SELECT
531
532	END SUBROUTINE pcm_define_netcdf_grid
533
534
535	!------------------------------------------------------------------------------!
536	! Description:
537	! ------------
538	!> Header output for plant canopy model
539	!------------------------------------------------------------------------------!
540	SUBROUTINE pcm_header ( io )
541
542	USE control_parameters, &
543	ONLY: dz, passive_scalar
544
545
546	IMPLICIT NONE
547
548	CHARACTER (LEN=10) :: coor_chr !<
549
550	CHARACTER (LEN=86) :: coordinates !<
551	CHARACTER (LEN=86) :: gradients !<
552	CHARACTER (LEN=86) :: leaf_area_density !<
553	CHARACTER (LEN=86) :: slices !<
554
555	INTEGER(iwp) :: i !<
556	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
557	INTEGER(iwp) :: k !<
558
559	REAL(wp) :: canopy_height !< canopy height (in m)
560
561	canopy_height = pch_index * dz
562
563	WRITE ( io, 1 ) canopy_mode, canopy_height, pch_index, &
564	canopy_drag_coeff
565	IF ( passive_scalar ) THEN
566	WRITE ( io, 2 ) leaf_scalar_exch_coeff, &
567	leaf_surface_conc
568	ENDIF
569
570	!
571	!-- Heat flux at the top of vegetation
572	WRITE ( io, 3 ) cthf
573
574	!
575	!-- Leaf area density profile, calculated either from given vertical
576	!-- gradients or from beta probability density function.
577	IF ( .NOT. calc_beta_lad_profile ) THEN
578
579	!-- Building output strings, starting with surface value
580	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
581	gradients = '------'
582	slices = ' 0'
583	coordinates = ' 0.0'
584	i = 1
585	DO WHILE ( i < 11 .AND. lad_vertical_gradient_level_ind(i) &
586	/= -9999 )
587
588	WRITE (coor_chr,'(F7.2)') lad(lad_vertical_gradient_level_ind(i))
589	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
590	TRIM( coor_chr )
591
592	WRITE (coor_chr,'(F7.2)') lad_vertical_gradient(i)
593	gradients = TRIM( gradients ) // ' ' // TRIM( coor_chr )
594
595	WRITE (coor_chr,'(I7)') lad_vertical_gradient_level_ind(i)
596	slices = TRIM( slices ) // ' ' // TRIM( coor_chr )
597
598	WRITE (coor_chr,'(F7.1)') lad_vertical_gradient_level(i)
599	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
600
601	i = i + 1
602	ENDDO
603
604	WRITE ( io, 4 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
605	TRIM( gradients ), TRIM( slices )
606
607	ELSE
608
609	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
610	coordinates = ' 0.0'
611
612	DO k = 1, pch_index
613
614	WRITE (coor_chr,'(F7.2)') lad(k)
615	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
616	TRIM( coor_chr )
617
618	WRITE (coor_chr,'(F7.1)') zu(k)
619	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
620
621	ENDDO
622
623	WRITE ( io, 5 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
624	alpha_lad, beta_lad, lai_beta
625
626	ENDIF
627
628	1 FORMAT (//' Vegetation canopy (drag) model:'/ &
629	' ------------------------------'// &
630	' Canopy mode: ', A / &
631	' Canopy height: ',F6.2,'m (',I4,' grid points)' / &
632	' Leaf drag coefficient: ',F6.2 /)
633	2 FORMAT (/ ' Scalar exchange coefficient: ',F6.2 / &
634	' Scalar concentration at leaf surfaces in kg/m**3: ',F6.2 /)
635	3 FORMAT (' Predefined constant heatflux at the top of the vegetation: ',F6.2, &
636	' K m/s')
637	4 FORMAT (/ ' Characteristic levels of the leaf area density:'// &
638	' Height: ',A,' m'/ &
639	' Leaf area density: ',A,' m2/m3'/ &
640	' Gradient: ',A,' m2/m4'/ &
641	' Gridpoint: ',A)
642	5 FORMAT (//' Characteristic levels of the leaf area density and coefficients:'&
643	// ' Height: ',A,' m'/ &
644	' Leaf area density: ',A,' m2/m3'/ &
645	' Coefficient alpha: ',F6.2 / &
646	' Coefficient beta: ',F6.2 / &
647	' Leaf area index: ',F6.2,' m2/m2' /)
648
649	END SUBROUTINE pcm_header
650
651
652	!------------------------------------------------------------------------------!
653	! Description:
654	! ------------
655	!> Initialization of the plant canopy model
656	!------------------------------------------------------------------------------!
657	SUBROUTINE pcm_init
658
659
660	USE control_parameters, &
661	ONLY: dz, humidity, io_blocks, io_group, message_string, ocean, &
662	passive_scalar, urban_surface
663
664	USE netcdf_data_input_mod, &
665	ONLY: leaf_area_density_f
666
667	USE surface_mod, &
668	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
669
670	IMPLICIT NONE
671
672	CHARACTER(10) :: pct
673
674	INTEGER(iwp) :: i !< running index
675	INTEGER(iwp) :: ii !< index
676	INTEGER(iwp) :: j !< running index
677	INTEGER(iwp) :: k !< running index
678	INTEGER(iwp) :: m !< running index
679
680	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
681	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
682	REAL(wp) :: gradient !< gradient for lad-profile construction
683	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
684	REAL(wp) :: pcv(nzb:nzt+1) !<
685
686	!
687	!-- Allocate one-dimensional arrays for the computation of the
688	!-- leaf area density (lad) profile
689	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
690	lad = 0.0_wp
691	pre_lad = 0.0_wp
692
693	!
694	!-- Set flag that indicates that the lad-profile shall be calculated by using
695	!-- a beta probability density function
696	IF ( alpha_lad /= 9999999.9_wp .AND. beta_lad /= 9999999.9_wp ) THEN
697	calc_beta_lad_profile = .TRUE.
698	ENDIF
699
700
701	!
702	!-- Compute the profile of leaf area density used in the plant
703	!-- canopy model. The profile can either be constructed from
704	!-- prescribed vertical gradients of the leaf area density or by
705	!-- using a beta probability density function (see e.g. Markkanen et al.,
706	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
707	IF ( .NOT. calc_beta_lad_profile ) THEN
708
709	!
710	!-- Use vertical gradients for lad-profile construction
711	i = 1
712	gradient = 0.0_wp
713
714	IF ( .NOT. ocean ) THEN
715
716	lad(0) = lad_surface
717	lad_vertical_gradient_level_ind(1) = 0
718
719	DO k = 1, pch_index
720	IF ( i < 11 ) THEN
721	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
722	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
723	gradient = lad_vertical_gradient(i)
724	lad_vertical_gradient_level_ind(i) = k - 1
725	i = i + 1
726	ENDIF
727	ENDIF
728	IF ( gradient /= 0.0_wp ) THEN
729	IF ( k /= 1 ) THEN
730	lad(k) = lad(k-1) + dzu(k) * gradient
731	ELSE
732	lad(k) = lad_surface + dzu(k) * gradient
733	ENDIF
734	ELSE
735	lad(k) = lad(k-1)
736	ENDIF
737	ENDDO
738
739	ENDIF
740
741	!
742	!-- In case of no given leaf area density gradients, choose a vanishing
743	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
744	!-- file.
745	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
746	lad_vertical_gradient_level(1) = 0.0_wp
747	ENDIF
748
749	ELSE
750
751	!
752	!-- Use beta function for lad-profile construction
753	int_bpdf = 0.0_wp
754	canopy_height = pch_index * dz
755
756	DO k = 0, pch_index
757	int_bpdf = int_bpdf + &
758	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
759	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
760	beta_lad-1.0_wp ) ) &
761	* ( ( zw(k+1)-zw(k) ) / canopy_height ) )
762	ENDDO
763
764	!
765	!-- Preliminary lad profile (defined on w-grid)
766	DO k = 0, pch_index
767	pre_lad(k) = lai_beta * &
768	( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) ) &
769	* ( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
770	beta_lad-1.0_wp ) ) / int_bpdf &
771	) / canopy_height
772	ENDDO
773
774	!
775	!-- Final lad profile (defined on scalar-grid level, since most prognostic
776	!-- quantities are defined there, hence, less interpolation is required
777	!-- when calculating the canopy tendencies)
778	lad(0) = pre_lad(0)
779	DO k = 1, pch_index
780	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
781	ENDDO
782
783	ENDIF
784
785	!
786	!-- Allocate 3D-array for the leaf area density (lad_s).
787	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
788
789	!
790	!-- Initialize canopy parameters cdc (canopy drag coefficient),
791	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
792	!-- with the prescribed values
793	cdc = canopy_drag_coeff
794	lsec = leaf_scalar_exch_coeff
795	lsc = leaf_surface_conc
796
797	!
798	!-- Initialization of the canopy coverage in the model domain:
799	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
800	!-- fully covers the domain surface
801	SELECT CASE ( TRIM( canopy_mode ) )
802
803	CASE( 'block' )
804
805	DO i = nxlg, nxrg
806	DO j = nysg, nyng
807	lad_s(:,j,i) = lad(:)
808	ENDDO
809	ENDDO
810
811	CASE ( 'read_from_file_3d' )
812	!
813	!-- Initialize LAD with data from file. If LAD is given in NetCDF file,
814	!-- use these values, else take LAD profiles from ASCII file.
815	!-- Please note, in NetCDF file LAD is only given up to the maximum
816	!-- canopy top, indicated by leaf_area_density_f%nz.
817	lad_s = 0.0_wp
818	IF ( leaf_area_density_f%from_file ) THEN
819	!
820	!-- Set also pch_index, used to be the upper bound of the vertical
821	!-- loops. Therefore, use the global top of the canopy layer.
822	pch_index = leaf_area_density_f%nz - 1
823
824	DO i = nxl, nxr
825	DO j = nys, nyn
826	DO k = 0, leaf_area_density_f%nz - 1
827	IF ( leaf_area_density_f%var(k,j,i) /= &
828	leaf_area_density_f%fill ) &
829	lad_s(k,j,i) = leaf_area_density_f%var(k,j,i)
830	ENDDO
831	ENDDO
832	ENDDO
833	CALL exchange_horiz( lad_s, nbgp )
834	!
835	! ASCII file
836	!-- Initialize canopy parameters cdc (canopy drag coefficient),
837	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
838	!-- from file which contains complete 3D data (separate vertical profiles for
839	!-- each location).
840	ELSE
841	CALL pcm_read_plant_canopy_3d
842	ENDIF
843
844	CASE DEFAULT
845	!
846	!-- The DEFAULT case is reached either if the parameter
847	!-- canopy mode contains a wrong character string or if the
848	!-- user has coded a special case in the user interface.
849	!-- There, the subroutine user_init_plant_canopy checks
850	!-- which of these two conditions applies.
851	CALL user_init_plant_canopy
852
853	END SELECT
854	!
855	!-- Initialize 2D index array indicating canopy top index.
856	ALLOCATE( pch_index_ji(nysg:nyng,nxlg:nxrg) )
857	pch_index_ji = 0
858
859	DO i = nxl, nxr
860	DO j = nys, nyn
861	DO k = 0, pch_index
862	IF ( lad_s(k,j,i) /= 0 ) pch_index_ji(j,i) = k
863	ENDDO
864	!
865	!-- Check whether topography and local vegetation on top exceed
866	!-- height of the model domain.
867	k = get_topography_top_index_ji( j, i, 's' )
868	IF ( k + pch_index_ji(j,i) >= nzt + 1 ) THEN
869	message_string = 'Local vegetation height on top of ' // &
870	'topography exceeds height of model domain.'
871	CALL message( 'pcm_init', 'PA0999', 2, 2, 0, 6, 0 )
872	ENDIF
873
874	ENDDO
875	ENDDO
876
877	CALL exchange_horiz_2d_int( pch_index_ji, nys, nyn, nxl, nxr, nbgp )
878
879	!
880	!-- Initialization of the canopy heat source distribution due to heating
881	!-- of the canopy layers by incoming solar radiation, in case that a non-zero
882	!-- value is set for the canopy top heat flux (cthf), which equals the
883	!-- available net radiation at canopy top.
884	!-- The heat source distribution is calculated by a decaying exponential
885	!-- function of the downward cumulative leaf area index (cum_lai_hf),
886	!-- assuming that the foliage inside the plant canopy is heated by solar
887	!-- radiation penetrating the canopy layers according to the distribution
888	!-- of net radiation as suggested by Brown & Covey (1966; Agric. Meteorol. 3,
889	!-- 73â96). This approach has been applied e.g. by Shaw & Schumann (1992;
890	!-- Bound.-Layer Meteorol. 61, 47â64).
891	!-- When using the urban surface model (USM), canopy heating (pc_heating_rate)
892	!-- by radiation is calculated in the USM.
893	IF ( cthf /= 0.0_wp .AND. .NOT. urban_surface ) THEN
894
895	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
896	pc_heating_rate(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
897	pc_transpiration_rate(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
898	!
899	!-- Piecewise calculation of the cumulative leaf area index by vertical
900	!-- integration of the leaf area density
901	cum_lai_hf(:,:,:) = 0.0_wp
902	DO i = nxlg, nxrg
903	DO j = nysg, nyng
904	DO k = pch_index_ji(j,i)-1, 0, -1
905	IF ( k == pch_index_ji(j,i)-1 ) THEN
906	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
907	( 0.5_wp * lad_s(k+1,j,i) * &
908	( zw(k+1) - zu(k+1) ) ) + &
909	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
910	lad_s(k,j,i) ) + &
911	lad_s(k+1,j,i) ) * &
912	( zu(k+1) - zw(k) ) )
913	ELSE
914	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
915	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
916	lad_s(k+1,j,i) ) + &
917	lad_s(k+1,j,i) ) * &
918	( zw(k+1) - zu(k+1) ) ) + &
919	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
920	lad_s(k,j,i) ) + &
921	lad_s(k+1,j,i) ) * &
922	( zu(k+1) - zw(k) ) )
923	ENDIF
924	ENDDO
925	ENDDO
926	ENDDO
927
928	!
929	!-- In areas with canopy the surface value of the canopy heat
930	!-- flux distribution overrides the surface heat flux (shf)
931	!-- Start with default surface type
932	DO m = 1, surf_def_h(0)%ns
933	k = surf_def_h(0)%k(m)
934	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
935	surf_def_h(0)%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
936	ENDDO
937	!
938	!-- Natural surfaces
939	DO m = 1, surf_lsm_h%ns
940	k = surf_lsm_h%k(m)
941	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
942	surf_lsm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
943	ENDDO
944	!
945	!-- Urban surfaces
946	DO m = 1, surf_usm_h%ns
947	k = surf_usm_h%k(m)
948	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
949	surf_usm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
950	ENDDO
951	!
952	!
953	!-- Calculation of the heating rate (K/s) within the different layers of
954	!-- the plant canopy. Calculation is only necessary in areas covered with
955	!-- canopy.
956	!-- Within the different canopy layers the plant-canopy heating
957	!-- rate (pc_heating_rate) is calculated as the vertical
958	!-- divergence of the canopy heat fluxes at the top and bottom
959	!-- of the respective layer
960	DO i = nxlg, nxrg
961	DO j = nysg, nyng
962	DO k = 1, pch_index_ji(j,i)
963	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) THEN
964	pc_heating_rate(k,j,i) = cthf * &
965	( exp(-ext_coef*cum_lai_hf(k,j,i)) - &
966	exp(-ext_coef*cum_lai_hf(k-1,j,i) ) ) / dzw(k)
967	ENDIF
968	ENDDO
969	ENDDO
970	ENDDO
971
972	ENDIF
973
974
975
976	END SUBROUTINE pcm_init
977
978
979	!------------------------------------------------------------------------------!
980	! Description:
981	! ------------
982	!> Parin for &plant_canopy_parameters for plant canopy model
983	!------------------------------------------------------------------------------!
984	SUBROUTINE pcm_parin
985
986	USE control_parameters, &
987	ONLY: message_string, plant_canopy
988
989	IMPLICIT NONE
990
991	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
992
993	NAMELIST /plant_canopy_parameters/ &
994	alpha_lad, beta_lad, canopy_drag_coeff, &
995	canopy_mode, cthf, &
996	lad_surface, lad_type_coef, &
997	lad_vertical_gradient, &
998	lad_vertical_gradient_level, &
999	lai_beta, &
1000	leaf_scalar_exch_coeff, &
1001	leaf_surface_conc, pch_index
1002
1003	NAMELIST /canopy_par/ 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	line = ' '
1013
1014	!
1015	!-- Try to find radiation model package
1016	REWIND ( 11 )
1017	line = ' '
1018	DO WHILE ( INDEX( line, '&plant_canopy_parameters' ) == 0 )
1019	READ ( 11, '(A)', END=10 ) line
1020	ENDDO
1021	BACKSPACE ( 11 )
1022
1023	!
1024	!-- Read user-defined namelist
1025	READ ( 11, plant_canopy_parameters )
1026
1027	!
1028	!-- Set flag that indicates that the radiation model is switched on
1029	plant_canopy = .TRUE.
1030
1031	GOTO 12
1032	!
1033	!-- Try to find old namelist
1034	10 REWIND ( 11 )
1035	line = ' '
1036	DO WHILE ( INDEX( line, '&canopy_par' ) == 0 )
1037	READ ( 11, '(A)', END=12 ) line
1038	ENDDO
1039	BACKSPACE ( 11 )
1040
1041	!
1042	!-- Read user-defined namelist
1043	READ ( 11, canopy_par )
1044
1045	message_string = 'namelist canopy_par is deprecated and will be ' // &
1046	'removed in near future. Please &use namelist ' // &
1047	'plant_canopy_parameters instead'
1048	CALL message( 'pcm_parin', 'PA0487', 0, 1, 0, 6, 0 )
1049
1050	!
1051	!-- Set flag that indicates that the radiation model is switched on
1052	plant_canopy = .TRUE.
1053
1054	12 CONTINUE
1055
1056
1057	END SUBROUTINE pcm_parin
1058
1059
1060
1061	!------------------------------------------------------------------------------!
1062	! Description:
1063	! ------------
1064	!
1065	!> Loads 3D plant canopy data from file. File format is as follows:
1066	!>
1067	!> num_levels
1068	!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
1069	!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
1070	!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
1071	!> ...
1072	!>
1073	!> i.e. first line determines number of levels and further lines represent plant
1074	!> canopy data, one line per column and variable. In each data line,
1075	!> dtype represents variable to be set:
1076	!>
1077	!> dtype=1: leaf area density (lad_s)
1078	!> dtype=2....n: some additional plant canopy input data quantity
1079	!>
1080	!> Zeros are added automatically above num_levels until top of domain. Any
1081	!> non-specified (x,y) columns have zero values as default.
1082	!------------------------------------------------------------------------------!
1083	SUBROUTINE pcm_read_plant_canopy_3d
1084
1085	USE control_parameters, &
1086	ONLY: coupling_char, message_string, passive_scalar
1087
1088	USE indices, &
1089	ONLY: nbgp
1090
1091	IMPLICIT NONE
1092
1093	INTEGER(iwp) :: dtype !< type of input data (1=lad)
1094	INTEGER(iwp) :: pctype !< type of plant canopy (deciduous,non-deciduous,...)
1095	INTEGER(iwp) :: i, j !< running index
1096	INTEGER(iwp) :: nzp !< number of vertical layers of plant canopy
1097	INTEGER(iwp) :: nzpltop !<
1098	INTEGER(iwp) :: nzpl !<
1099
1100	REAL(wp), DIMENSION(:), ALLOCATABLE :: col !< vertical column of input data
1101
1102	!
1103	!-- Initialize lad_s array
1104	lad_s = 0.0_wp
1105
1106	!
1107	!-- Open and read plant canopy input data
1108	OPEN(152, FILE='PLANT_CANOPY_DATA_3D' // TRIM( coupling_char ), &
1109	ACCESS='SEQUENTIAL', ACTION='READ', STATUS='OLD', &
1110	FORM='FORMATTED', ERR=515)
1111	READ(152, *, ERR=516, END=517) nzp !< read first line = number of vertical layers
1112
1113	ALLOCATE( col(0:nzp-1) )
1114
1115	DO
1116	READ(152, *, ERR=516, END=517) dtype, i, j, pctype, col(:)
1117	IF ( i < nxlg .OR. i > nxrg .OR. j < nysg .OR. j > nyng ) CYCLE
1118
1119	SELECT CASE (dtype)
1120	CASE( 1 ) !< leaf area density
1121	!
1122	!-- This is just the pure canopy layer assumed to be grounded to
1123	!-- a flat domain surface. At locations where plant canopy sits
1124	!-- on top of any kind of topography, the vertical plant column
1125	!-- must be "lifted", which is done in SUBROUTINE pcm_tendency.
1126	IF ( pctype < 0 .OR. pctype > 10 ) THEN !< incorrect plant canopy type
1127	WRITE( message_string, * ) 'Incorrect type of plant canopy. ' // &
1128	'Allowed values 0 <= pctype <= 10, ' // &
1129	'but pctype is ', pctype
1130	CALL message( 'pcm_read_plant_canopy_3d', 'PA0349', 1, 2, 0, 6, 0 )
1131	ENDIF
1132	lad_s(0:nzp-1,j,i) = col(0:nzp-1) * lad_type_coef(pctype)
1133
1134	CASE DEFAULT
1135	WRITE(message_string, '(a,i2,a)') &
1136	'Unknown record type in file PLANT_CANOPY_DATA_3D: "', dtype, '"'
1137	CALL message( 'pcm_read_plant_canopy_3d', 'PA0530', 1, 2, 0, 6, 0 )
1138	END SELECT
1139	ENDDO
1140
1141	515 message_string = 'error opening file PLANT_CANOPY_DATA_3D'
1142	CALL message( 'pcm_read_plant_canopy_3d', 'PA0531', 1, 2, 0, 6, 0 )
1143
1144	516 message_string = 'error reading file PLANT_CANOPY_DATA_3D'
1145	CALL message( 'pcm_read_plant_canopy_3d', 'PA0532', 1, 2, 0, 6, 0 )
1146
1147	517 CLOSE(152)
1148	DEALLOCATE( col )
1149
1150	CALL exchange_horiz( lad_s, nbgp )
1151
1152	END SUBROUTINE pcm_read_plant_canopy_3d
1153
1154
1155
1156	!------------------------------------------------------------------------------!
1157	! Description:
1158	! ------------
1159	!> Calculation of the tendency terms, accounting for the effect of the plant
1160	!> canopy on momentum and scalar quantities.
1161	!>
1162	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
1163	!> (defined on scalar grid), as initialized in subroutine pcm_init.
1164	!> The lad on the w-grid is vertically interpolated from the surrounding
1165	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
1166	!> k = pch_index. Here, the lad is zero.
1167	!>
1168	!> The canopy drag must be limited (previously accounted for by calculation of
1169	!> a limiting canopy timestep for the determination of the maximum LES timestep
1170	!> in subroutine timestep), since it is physically impossible that the canopy
1171	!> drag alone can locally change the sign of a velocity component. This
1172	!> limitation is realized by calculating preliminary tendencies and velocities.
1173	!> It is subsequently checked if the preliminary new velocity has a different
1174	!> sign than the current velocity. If so, the tendency is limited in a way that
1175	!> the velocity can at maximum be reduced to zero by the canopy drag.
1176	!>
1177	!>
1178	!> Call for all grid points
1179	!------------------------------------------------------------------------------!
1180	SUBROUTINE pcm_tendency( component )
1181
1182
1183	USE control_parameters, &
1184	ONLY: dt_3d, message_string
1185
1186	USE kinds
1187
1188	IMPLICIT NONE
1189
1190	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
1191	INTEGER(iwp) :: i !< running index
1192	INTEGER(iwp) :: j !< running index
1193	INTEGER(iwp) :: k !< running index
1194	INTEGER(iwp) :: k_wall !< vertical index of topography top
1195	INTEGER(iwp) :: kk !< running index for flat lad arrays
1196
1197	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1198	REAL(wp) :: lad_local !< local lad value
1199	REAL(wp) :: pre_tend !< preliminary tendency
1200	REAL(wp) :: pre_u !< preliminary u-value
1201	REAL(wp) :: pre_v !< preliminary v-value
1202	REAL(wp) :: pre_w !< preliminary w-value
1203
1204
1205	ddt_3d = 1.0_wp / dt_3d
1206
1207	!
1208	!-- Compute drag for the three velocity components and the SGS-TKE:
1209	SELECT CASE ( component )
1210
1211	!
1212	!-- u-component
1213	CASE ( 1 )
1214	DO i = nxlu, nxr
1215	DO j = nys, nyn
1216	!
1217	!-- Determine topography-top index on u-grid
1218	k_wall = get_topography_top_index_ji( j, i, 'u' )
1219	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1220
1221	kk = k - k_wall !- lad arrays are defined flat
1222	!
1223	!-- In order to create sharp boundaries of the plant canopy,
1224	!-- the lad on the u-grid at index (k,j,i) is equal to
1225	!-- lad_s(k,j,i), rather than being interpolated from the
1226	!-- surrounding lad_s, because this would yield smaller lad
1227	!-- at the canopy boundaries than inside of the canopy.
1228	!-- For the same reason, the lad at the rightmost(i+1)canopy
1229	!-- boundary on the u-grid equals lad_s(k,j,i).
1230	lad_local = lad_s(kk,j,i)
1231	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp )&
1232	THEN
1233	lad_local = lad_s(kk,j,i-1)
1234	ENDIF
1235
1236	pre_tend = 0.0_wp
1237	pre_u = 0.0_wp
1238	!
1239	!-- Calculate preliminary value (pre_tend) of the tendency
1240	pre_tend = - cdc * &
1241	lad_local * &
1242	SQRT( u(k,j,i)**2 + &
1243	( 0.25_wp * ( v(k,j,i-1) + &
1244	v(k,j,i) + &
1245	v(k,j+1,i) + &
1246	v(k,j+1,i-1) ) &
1247	)**2 + &
1248	( 0.25_wp * ( w(k-1,j,i-1) + &
1249	w(k-1,j,i) + &
1250	w(k,j,i-1) + &
1251	w(k,j,i) ) &
1252	)**2 &
1253	) * &
1254	u(k,j,i)
1255
1256	!
1257	!-- Calculate preliminary new velocity, based on pre_tend
1258	pre_u = u(k,j,i) + dt_3d * pre_tend
1259	!
1260	!-- Compare sign of old velocity and new preliminary velocity,
1261	!-- and in case the signs are different, limit the tendency
1262	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1263	pre_tend = - u(k,j,i) * ddt_3d
1264	ELSE
1265	pre_tend = pre_tend
1266	ENDIF
1267	!
1268	!-- Calculate final tendency
1269	tend(k,j,i) = tend(k,j,i) + pre_tend
1270
1271	ENDDO
1272	ENDDO
1273	ENDDO
1274
1275	!
1276	!-- v-component
1277	CASE ( 2 )
1278	DO i = nxl, nxr
1279	DO j = nysv, nyn
1280	!
1281	!-- Determine topography-top index on v-grid
1282	k_wall = get_topography_top_index_ji( j, i, 'v' )
1283
1284	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1285
1286	kk = k - k_wall !- lad arrays are defined flat
1287	!
1288	!-- In order to create sharp boundaries of the plant canopy,
1289	!-- the lad on the v-grid at index (k,j,i) is equal to
1290	!-- lad_s(k,j,i), rather than being interpolated from the
1291	!-- surrounding lad_s, because this would yield smaller lad
1292	!-- at the canopy boundaries than inside of the canopy.
1293	!-- For the same reason, the lad at the northmost(j+1) canopy
1294	!-- boundary on the v-grid equals lad_s(k,j,i).
1295	lad_local = lad_s(kk,j,i)
1296	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp )&
1297	THEN
1298	lad_local = lad_s(kk,j-1,i)
1299	ENDIF
1300
1301	pre_tend = 0.0_wp
1302	pre_v = 0.0_wp
1303	!
1304	!-- Calculate preliminary value (pre_tend) of the tendency
1305	pre_tend = - cdc * &
1306	lad_local * &
1307	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1308	u(k,j-1,i+1) + &
1309	u(k,j,i) + &
1310	u(k,j,i+1) ) &
1311	)**2 + &
1312	v(k,j,i)**2 + &
1313	( 0.25_wp * ( w(k-1,j-1,i) + &
1314	w(k-1,j,i) + &
1315	w(k,j-1,i) + &
1316	w(k,j,i) ) &
1317	)**2 &
1318	) * &
1319	v(k,j,i)
1320
1321	!
1322	!-- Calculate preliminary new velocity, based on pre_tend
1323	pre_v = v(k,j,i) + dt_3d * pre_tend
1324	!
1325	!-- Compare sign of old velocity and new preliminary velocity,
1326	!-- and in case the signs are different, limit the tendency
1327	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1328	pre_tend = - v(k,j,i) * ddt_3d
1329	ELSE
1330	pre_tend = pre_tend
1331	ENDIF
1332	!
1333	!-- Calculate final tendency
1334	tend(k,j,i) = tend(k,j,i) + pre_tend
1335
1336	ENDDO
1337	ENDDO
1338	ENDDO
1339
1340	!
1341	!-- w-component
1342	CASE ( 3 )
1343	DO i = nxl, nxr
1344	DO j = nys, nyn
1345	!
1346	!-- Determine topography-top index on w-grid
1347	k_wall = get_topography_top_index_ji( j, i, 'w' )
1348
1349	DO k = k_wall+1, k_wall + pch_index_ji(j,i) - 1
1350
1351	kk = k - k_wall !- lad arrays are defined flat
1352
1353	pre_tend = 0.0_wp
1354	pre_w = 0.0_wp
1355	!
1356	!-- Calculate preliminary value (pre_tend) of the tendency
1357	pre_tend = - cdc * &
1358	(0.5_wp * &
1359	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1360	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1361	u(k,j,i+1) + &
1362	u(k+1,j,i) + &
1363	u(k+1,j,i+1) ) &
1364	)**2 + &
1365	( 0.25_wp * ( v(k,j,i) + &
1366	v(k,j+1,i) + &
1367	v(k+1,j,i) + &
1368	v(k+1,j+1,i) ) &
1369	)**2 + &
1370	w(k,j,i)**2 &
1371	) * &
1372	w(k,j,i)
1373	!
1374	!-- Calculate preliminary new velocity, based on pre_tend
1375	pre_w = w(k,j,i) + dt_3d * pre_tend
1376	!
1377	!-- Compare sign of old velocity and new preliminary velocity,
1378	!-- and in case the signs are different, limit the tendency
1379	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1380	pre_tend = - w(k,j,i) * ddt_3d
1381	ELSE
1382	pre_tend = pre_tend
1383	ENDIF
1384	!
1385	!-- Calculate final tendency
1386	tend(k,j,i) = tend(k,j,i) + pre_tend
1387
1388	ENDDO
1389	ENDDO
1390	ENDDO
1391
1392	!
1393	!-- potential temperature
1394	CASE ( 4 )
1395	DO i = nxl, nxr
1396	DO j = nys, nyn
1397	!
1398	!-- Determine topography-top index on scalar-grid
1399	k_wall = get_topography_top_index_ji( j, i, 's' )
1400
1401	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1402
1403	kk = k - k_wall !- lad arrays are defined flat
1404	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1405	ENDDO
1406	ENDDO
1407	ENDDO
1408
1409	!
1410	!-- humidity
1411	CASE ( 5 )
1412	DO i = nxl, nxr
1413	DO j = nys, nyn
1414	!
1415	!-- Determine topography-top index on scalar-grid
1416	k_wall = get_topography_top_index_ji( j, i, 's' )
1417
1418	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1419
1420	kk = k - k_wall !- lad arrays are defined flat
1421	pc_transpiration_rate(kk,j,i) = - lsec &
1422	* lad_s(kk,j,i) * &
1423	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1424	u(k,j,i+1) ) &
1425	)**2 + &
1426	( 0.5_wp * ( v(k,j,i) + &
1427	v(k,j+1,i) ) &
1428	)**2 + &
1429	( 0.5_wp * ( w(k-1,j,i) + &
1430	w(k,j,i) ) &
1431	)**2 &
1432	) * &
1433	( q(k,j,i) - lsc )
1434
1435	tend(k,j,i) = tend(k,j,i) + pc_transpiration_rate(kk,j,i)
1436	ENDDO
1437	ENDDO
1438	ENDDO
1439
1440	!
1441	!-- sgs-tke
1442	CASE ( 6 )
1443	DO i = nxl, nxr
1444	DO j = nys, nyn
1445	!
1446	!-- Determine topography-top index on scalar-grid
1447	k_wall = get_topography_top_index_ji( j, i, 's' )
1448
1449	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1450
1451	kk = k - k_wall !- lad arrays are defined flat
1452	tend(k,j,i) = tend(k,j,i) - &
1453	2.0_wp * cdc * &
1454	lad_s(kk,j,i) * &
1455	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1456	u(k,j,i+1) ) &
1457	)**2 + &
1458	( 0.5_wp * ( v(k,j,i) + &
1459	v(k,j+1,i) ) &
1460	)**2 + &
1461	( 0.5_wp * ( w(k,j,i) + &
1462	w(k+1,j,i) ) &
1463	)**2 &
1464	) * &
1465	e(k,j,i)
1466	ENDDO
1467	ENDDO
1468	ENDDO
1469	!
1470	!-- scalar concentration
1471	CASE ( 7 )
1472	DO i = nxl, nxr
1473	DO j = nys, nyn
1474	!
1475	!-- Determine topography-top index on scalar-grid
1476	k_wall = get_topography_top_index_ji( j, i, 's' )
1477
1478	DO k = k_wall+1, k_wall + pch_index_ji(j,i)
1479
1480	kk = k - k_wall !- lad arrays are defined flat
1481	tend(k,j,i) = tend(k,j,i) - &
1482	lsec * &
1483	lad_s(kk,j,i) * &
1484	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1485	u(k,j,i+1) ) &
1486	)**2 + &
1487	( 0.5_wp * ( v(k,j,i) + &
1488	v(k,j+1,i) ) &
1489	)**2 + &
1490	( 0.5_wp * ( w(k-1,j,i) + &
1491	w(k,j,i) ) &
1492	)**2 &
1493	) * &
1494	( s(k,j,i) - lsc )
1495	ENDDO
1496	ENDDO
1497	ENDDO
1498
1499
1500
1501	CASE DEFAULT
1502
1503	WRITE( message_string, * ) 'wrong component: ', component
1504	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1505
1506	END SELECT
1507
1508	END SUBROUTINE pcm_tendency
1509
1510
1511	!------------------------------------------------------------------------------!
1512	! Description:
1513	! ------------
1514	!> Calculation of the tendency terms, accounting for the effect of the plant
1515	!> canopy on momentum and scalar quantities.
1516	!>
1517	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
1518	!> (defined on scalar grid), as initialized in subroutine pcm_init.
1519	!> The lad on the w-grid is vertically interpolated from the surrounding
1520	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
1521	!> k = pch_index. Here, the lad is zero.
1522	!>
1523	!> The canopy drag must be limited (previously accounted for by calculation of
1524	!> a limiting canopy timestep for the determination of the maximum LES timestep
1525	!> in subroutine timestep), since it is physically impossible that the canopy
1526	!> drag alone can locally change the sign of a velocity component. This
1527	!> limitation is realized by calculating preliminary tendencies and velocities.
1528	!> It is subsequently checked if the preliminary new velocity has a different
1529	!> sign than the current velocity. If so, the tendency is limited in a way that
1530	!> the velocity can at maximum be reduced to zero by the canopy drag.
1531	!>
1532	!>
1533	!> Call for grid point i,j
1534	!------------------------------------------------------------------------------!
1535	SUBROUTINE pcm_tendency_ij( i, j, component )
1536
1537
1538	USE control_parameters, &
1539	ONLY: dt_3d, message_string
1540
1541	USE kinds
1542
1543	IMPLICIT NONE
1544
1545	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
1546	INTEGER(iwp) :: i !< running index
1547	INTEGER(iwp) :: j !< running index
1548	INTEGER(iwp) :: k !< running index
1549	INTEGER(iwp) :: k_wall !< vertical index of topography top
1550	INTEGER(iwp) :: kk !< running index for flat lad arrays
1551
1552	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1553	REAL(wp) :: lad_local !< local lad value
1554	REAL(wp) :: pre_tend !< preliminary tendency
1555	REAL(wp) :: pre_u !< preliminary u-value
1556	REAL(wp) :: pre_v !< preliminary v-value
1557	REAL(wp) :: pre_w !< preliminary w-value
1558
1559
1560	ddt_3d = 1.0_wp / dt_3d
1561	!
1562	!-- Compute drag for the three velocity components and the SGS-TKE
1563	SELECT CASE ( component )
1564
1565	!
1566	!-- u-component
1567	CASE ( 1 )
1568	!
1569	!-- Determine topography-top index on u-grid
1570	k_wall = get_topography_top_index_ji( j, i, 'u' )
1571	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1572
1573	kk = k - k_wall !- lad arrays are defined flat
1574
1575	!
1576	!-- In order to create sharp boundaries of the plant canopy,
1577	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
1578	!-- rather than being interpolated from the surrounding lad_s,
1579	!-- because this would yield smaller lad at the canopy boundaries
1580	!-- than inside of the canopy.
1581	!-- For the same reason, the lad at the rightmost(i+1)canopy
1582	!-- boundary on the u-grid equals lad_s(k,j,i).
1583	lad_local = lad_s(kk,j,i)
1584	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp ) THEN
1585	lad_local = lad_s(kk,j,i-1)
1586	ENDIF
1587
1588	pre_tend = 0.0_wp
1589	pre_u = 0.0_wp
1590	!
1591	!-- Calculate preliminary value (pre_tend) of the tendency
1592	pre_tend = - cdc * &
1593	lad_local * &
1594	SQRT( u(k,j,i)**2 + &
1595	( 0.25_wp * ( v(k,j,i-1) + &
1596	v(k,j,i) + &
1597	v(k,j+1,i) + &
1598	v(k,j+1,i-1) ) &
1599	)**2 + &
1600	( 0.25_wp * ( w(k-1,j,i-1) + &
1601	w(k-1,j,i) + &
1602	w(k,j,i-1) + &
1603	w(k,j,i) ) &
1604	)**2 &
1605	) * &
1606	u(k,j,i)
1607
1608	!
1609	!-- Calculate preliminary new velocity, based on pre_tend
1610	pre_u = u(k,j,i) + dt_3d * pre_tend
1611	!
1612	!-- Compare sign of old velocity and new preliminary velocity,
1613	!-- and in case the signs are different, limit the tendency
1614	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1615	pre_tend = - u(k,j,i) * ddt_3d
1616	ELSE
1617	pre_tend = pre_tend
1618	ENDIF
1619	!
1620	!-- Calculate final tendency
1621	tend(k,j,i) = tend(k,j,i) + pre_tend
1622	ENDDO
1623
1624
1625	!
1626	!-- v-component
1627	CASE ( 2 )
1628	!
1629	!-- Determine topography-top index on v-grid
1630	k_wall = get_topography_top_index_ji( j, i, 'v' )
1631
1632	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1633
1634	kk = k - k_wall !- lad arrays are defined flat
1635	!
1636	!-- In order to create sharp boundaries of the plant canopy,
1637	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
1638	!-- rather than being interpolated from the surrounding lad_s,
1639	!-- because this would yield smaller lad at the canopy boundaries
1640	!-- than inside of the canopy.
1641	!-- For the same reason, the lad at the northmost(j+1)canopy
1642	!-- boundary on the v-grid equals lad_s(k,j,i).
1643	lad_local = lad_s(kk,j,i)
1644	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp ) THEN
1645	lad_local = lad_s(kk,j-1,i)
1646	ENDIF
1647
1648	pre_tend = 0.0_wp
1649	pre_v = 0.0_wp
1650	!
1651	!-- Calculate preliminary value (pre_tend) of the tendency
1652	pre_tend = - cdc * &
1653	lad_local * &
1654	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1655	u(k,j-1,i+1) + &
1656	u(k,j,i) + &
1657	u(k,j,i+1) ) &
1658	)**2 + &
1659	v(k,j,i)**2 + &
1660	( 0.25_wp * ( w(k-1,j-1,i) + &
1661	w(k-1,j,i) + &
1662	w(k,j-1,i) + &
1663	w(k,j,i) ) &
1664	)**2 &
1665	) * &
1666	v(k,j,i)
1667
1668	!
1669	!-- Calculate preliminary new velocity, based on pre_tend
1670	pre_v = v(k,j,i) + dt_3d * pre_tend
1671	!
1672	!-- Compare sign of old velocity and new preliminary velocity,
1673	!-- and in case the signs are different, limit the tendency
1674	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1675	pre_tend = - v(k,j,i) * ddt_3d
1676	ELSE
1677	pre_tend = pre_tend
1678	ENDIF
1679	!
1680	!-- Calculate final tendency
1681	tend(k,j,i) = tend(k,j,i) + pre_tend
1682	ENDDO
1683
1684
1685	!
1686	!-- w-component
1687	CASE ( 3 )
1688	!
1689	!-- Determine topography-top index on w-grid
1690	k_wall = get_topography_top_index_ji( j, i, 'w' )
1691
1692	DO k = k_wall + 1, k_wall + pch_index_ji(j,i) - 1
1693
1694	kk = k - k_wall !- lad arrays are defined flat
1695
1696	pre_tend = 0.0_wp
1697	pre_w = 0.0_wp
1698	!
1699	!-- Calculate preliminary value (pre_tend) of the tendency
1700	pre_tend = - cdc * &
1701	(0.5_wp * &
1702	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1703	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1704	u(k,j,i+1) + &
1705	u(k+1,j,i) + &
1706	u(k+1,j,i+1) ) &
1707	)**2 + &
1708	( 0.25_wp * ( v(k,j,i) + &
1709	v(k,j+1,i) + &
1710	v(k+1,j,i) + &
1711	v(k+1,j+1,i) ) &
1712	)**2 + &
1713	w(k,j,i)**2 &
1714	) * &
1715	w(k,j,i)
1716	!
1717	!-- Calculate preliminary new velocity, based on pre_tend
1718	pre_w = w(k,j,i) + dt_3d * pre_tend
1719	!
1720	!-- Compare sign of old velocity and new preliminary velocity,
1721	!-- and in case the signs are different, limit the tendency
1722	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1723	pre_tend = - w(k,j,i) * ddt_3d
1724	ELSE
1725	pre_tend = pre_tend
1726	ENDIF
1727	!
1728	!-- Calculate final tendency
1729	tend(k,j,i) = tend(k,j,i) + pre_tend
1730	ENDDO
1731
1732	!
1733	!-- potential temperature
1734	CASE ( 4 )
1735	!
1736	!-- Determine topography-top index on scalar grid
1737	k_wall = get_topography_top_index_ji( j, i, 's' )
1738
1739	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1740	kk = k - k_wall !- lad arrays are defined flat
1741	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1742	ENDDO
1743
1744
1745	!
1746	!-- humidity
1747	CASE ( 5 )
1748	!
1749	!-- Determine topography-top index on scalar grid
1750	k_wall = get_topography_top_index_ji( j, i, 's' )
1751
1752	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1753	kk = k - k_wall !- lad arrays are defined flat
1754
1755	pc_transpiration_rate(kk,j,i) = - lsec &
1756	* lad_s(kk,j,i) * &
1757	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1758	u(k,j,i+1) ) &
1759	)**2 + &
1760	( 0.5_wp * ( v(k,j,i) + &
1761	v(k,j+1,i) ) &
1762	)**2 + &
1763	( 0.5_wp * ( w(k-1,j,i) + &
1764	w(k,j,i) ) &
1765	)**2 &
1766	) * &
1767	( q(k,j,i) - lsc )
1768
1769	tend(k,j,i) = tend(k,j,i) + pc_transpiration_rate(kk,j,i)
1770
1771	ENDDO
1772
1773	!
1774	!-- sgs-tke
1775	CASE ( 6 )
1776	!
1777	!-- Determine topography-top index on scalar grid
1778	k_wall = get_topography_top_index_ji( j, i, 's' )
1779
1780	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1781
1782	kk = k - k_wall
1783	tend(k,j,i) = tend(k,j,i) - &
1784	2.0_wp * cdc * &
1785	lad_s(kk,j,i) * &
1786	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1787	u(k,j,i+1) ) &
1788	)**2 + &
1789	( 0.5_wp * ( v(k,j,i) + &
1790	v(k,j+1,i) ) &
1791	)**2 + &
1792	( 0.5_wp * ( w(k,j,i) + &
1793	w(k+1,j,i) ) &
1794	)**2 &
1795	) * &
1796	e(k,j,i)
1797	ENDDO
1798
1799	!
1800	!-- scalar concentration
1801	CASE ( 7 )
1802	!
1803	!-- Determine topography-top index on scalar grid
1804	k_wall = get_topography_top_index_ji( j, i, 's' )
1805
1806	DO k = k_wall + 1, k_wall + pch_index_ji(j,i)
1807
1808	kk = k - k_wall
1809	tend(k,j,i) = tend(k,j,i) - &
1810	lsec * &
1811	lad_s(kk,j,i) * &
1812	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1813	u(k,j,i+1) ) &
1814	)**2 + &
1815	( 0.5_wp * ( v(k,j,i) + &
1816	v(k,j+1,i) ) &
1817	)**2 + &
1818	( 0.5_wp * ( w(k-1,j,i) + &
1819	w(k,j,i) ) &
1820	)**2 &
1821	) * &
1822	( s(k,j,i) - lsc )
1823	ENDDO
1824
1825	CASE DEFAULT
1826
1827	WRITE( message_string, * ) 'wrong component: ', component
1828	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1829
1830	END SELECT
1831
1832	END SUBROUTINE pcm_tendency_ij
1833
1834
1835
1836	END MODULE plant_canopy_model_mod

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