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source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 2229

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1	!> @file plant_canopy_model_mod.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of PALM.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! version.
9	!
10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
13	!
14	! You should have received a copy of the GNU General Public License along with
15	! PALM. If not, see <http://www.gnu.org/licenses/>.
16	!
17	! Copyright 1997-2017 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: plant_canopy_model_mod.f90 2214 2017-04-24 15:11:32Z hellstea $
27	!
28	! 2213 2017-04-24 15:10:35Z kanani
29	! Bugfix: exchange of ghost points in array pc_heating_rate needed for output
30	! of pcm_heatrate, onetime ghost point exchange of lad_s after initialization.
31	! Formatting and clean-up of subroutine pcm_read_plant_canopy_3d,
32	! minor re-organization of canopy-heating initialization.
33	!
34	! 2209 2017-04-19 09:34:46Z kanani
35	! Added 3d output of leaf area density (pcm_lad) and canopy
36	! heat rate (pcm_heatrate)
37	!
38	! 2024 2016-10-12 16:42:37Z kanani
39	! Added missing lad_s initialization
40	!
41	! 2011 2016-09-19 17:29:57Z kanani
42	! Renamed canopy_heat_flux to pc_heating_rate, since the original meaning/
43	! calculation of the quantity has changed, related to the urban surface model
44	! and similar future applications.
45	!
46	! 2007 2016-08-24 15:47:17Z kanani
47	! Added SUBROUTINE pcm_read_plant_canopy_3d for reading 3d plant canopy data
48	! from file (new case canopy_mode=read_from_file_3d) in the course of
49	! introduction of urban surface model,
50	! introduced variable ext_coef,
51	! resorted SUBROUTINEs to alphabetical order
52	!
53	! 2000 2016-08-20 18:09:15Z knoop
54	! Forced header and separation lines into 80 columns
55	!
56	! 1960 2016-07-12 16:34:24Z suehring
57	! Separate humidity and passive scalar
58	!
59	! 1953 2016-06-21 09:28:42Z suehring
60	! Bugfix, lad_s and lad must be public
61	!
62	! 1826 2016-04-07 12:01:39Z maronga
63	! Further modularization
64	!
65	! 1721 2015-11-16 12:56:48Z raasch
66	! bugfixes: shf is reduced in areas covered with canopy only,
67	! canopy is set on top of topography
68	!
69	! 1682 2015-10-07 23:56:08Z knoop
70	! Code annotations made doxygen readable
71	!
72	! 1484 2014-10-21 10:53:05Z kanani
73	! Changes due to new module structure of the plant canopy model:
74	! module plant_canopy_model_mod now contains a subroutine for the
75	! initialization of the canopy model (pcm_init),
76	! limitation of the canopy drag (previously accounted for by calculation of
77	! a limiting canopy timestep for the determination of the maximum LES timestep
78	! in subroutine timestep) is now realized by the calculation of pre-tendencies
79	! and preliminary velocities in subroutine pcm_tendency,
80	! some redundant MPI communication removed in subroutine pcm_init
81	! (was previously in init_3d_model),
82	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
83	! respective grid is now provided only by lad_s (e.g. in the calculation of
84	! the tendency terms or of cum_lai_hf),
85	! drag_coefficient, lai, leaf_surface_concentration,
86	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
87	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
88	! respectively,
89	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
90	! USE-statements and ONLY-lists modified accordingly
91	!
92	! 1340 2014-03-25 19:45:13Z kanani
93	! REAL constants defined as wp-kind
94	!
95	! 1320 2014-03-20 08:40:49Z raasch
96	! ONLY-attribute added to USE-statements,
97	! kind-parameters added to all INTEGER and REAL declaration statements,
98	! kinds are defined in new module kinds,
99	! old module precision_kind is removed,
100	! revision history before 2012 removed,
101	! comment fields (!:) to be used for variable explanations added to
102	! all variable declaration statements
103	!
104	! 1036 2012-10-22 13:43:42Z raasch
105	! code put under GPL (PALM 3.9)
106	!
107	! 138 2007-11-28 10:03:58Z letzel
108	! Initial revision
109	!
110	! Description:
111	! ------------
112	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
113	!> profile (subroutine pcm_init).
114	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
115	!> due to canopy elements (subroutine pcm_tendency).
116	!------------------------------------------------------------------------------!
117	MODULE plant_canopy_model_mod
118
119	USE arrays_3d, &
120	ONLY: dzu, dzw, e, q, s, shf, tend, u, v, w, zu, zw
121
122	USE indices, &
123	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
124	nz, nzb, nzb_s_inner, nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt
125
126	USE kinds
127
128
129	IMPLICIT NONE
130
131
132	CHARACTER (LEN=20) :: canopy_mode = 'block' !< canopy coverage
133
134	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
135	INTEGER(iwp) :: &
136	lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
137
138	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
139	LOGICAL :: plant_canopy = .FALSE. !< switch for use of canopy model
140
141	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
142	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
143	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
144	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
145	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
146	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
147	REAL(wp) :: ext_coef = 0.6_wp !< extinction coefficient
148	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
149	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
150	REAL(wp) :: &
151	leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
152	REAL(wp) :: &
153	leaf_surface_conc = 0.0_wp !< leaf surface concentration
154	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
155	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
156
157	REAL(wp) :: &
158	lad_vertical_gradient(10) = 0.0_wp !< lad gradient
159	REAL(wp) :: &
160	lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
161
162	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
163	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
164
165	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
166	pc_heating_rate !< plant canopy heating rate
167	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
168	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
169
170
171	SAVE
172
173
174	PRIVATE
175
176	!
177	!-- Public functions
178	PUBLIC pcm_check_data_output, pcm_check_parameters, pcm_data_output_3d, &
179	pcm_define_netcdf_grid, pcm_header, pcm_init, pcm_parin, pcm_tendency
180
181	!
182	!-- Public variables and constants
183	PUBLIC pc_heating_rate, canopy_mode, cthf, dt_plant_canopy, lad, lad_s, &
184	pch_index, plant_canopy
185
186
187	INTERFACE pcm_check_data_output
188	MODULE PROCEDURE pcm_check_data_output
189	END INTERFACE pcm_check_data_output
190
191	INTERFACE pcm_check_parameters
192	MODULE PROCEDURE pcm_check_parameters
193	END INTERFACE pcm_check_parameters
194
195	INTERFACE pcm_data_output_3d
196	MODULE PROCEDURE pcm_data_output_3d
197	END INTERFACE pcm_data_output_3d
198
199	INTERFACE pcm_define_netcdf_grid
200	MODULE PROCEDURE pcm_define_netcdf_grid
201	END INTERFACE pcm_define_netcdf_grid
202
203	INTERFACE pcm_header
204	MODULE PROCEDURE pcm_header
205	END INTERFACE pcm_header
206
207	INTERFACE pcm_init
208	MODULE PROCEDURE pcm_init
209	END INTERFACE pcm_init
210
211	INTERFACE pcm_parin
212	MODULE PROCEDURE pcm_parin
213	END INTERFACE pcm_parin
214
215	INTERFACE pcm_read_plant_canopy_3d
216	MODULE PROCEDURE pcm_read_plant_canopy_3d
217	END INTERFACE pcm_read_plant_canopy_3d
218
219	INTERFACE pcm_tendency
220	MODULE PROCEDURE pcm_tendency
221	MODULE PROCEDURE pcm_tendency_ij
222	END INTERFACE pcm_tendency
223
224
225	CONTAINS
226
227
228	!------------------------------------------------------------------------------!
229	! Description:
230	! ------------
231	!> Check data output for plant canopy model
232	!------------------------------------------------------------------------------!
233	SUBROUTINE pcm_check_data_output( var, unit )
234
235
236	USE control_parameters, &
237	ONLY: data_output, message_string
238
239	IMPLICIT NONE
240
241	CHARACTER (LEN=*) :: unit !<
242	CHARACTER (LEN=*) :: var !<
243
244
245	SELECT CASE ( TRIM( var ) )
246
247	CASE ( 'pcm_heatrate' )
248	unit = 'K s-1'
249
250	CASE ( 'pcm_lad' )
251	unit = 'm2 m-3'
252
253
254	CASE DEFAULT
255	unit = 'illegal'
256
257	END SELECT
258
259
260	END SUBROUTINE pcm_check_data_output
261
262
263	!------------------------------------------------------------------------------!
264	! Description:
265	! ------------
266	!> Check parameters routine for plant canopy model
267	!------------------------------------------------------------------------------!
268	SUBROUTINE pcm_check_parameters
269
270	USE control_parameters, &
271	ONLY: cloud_physics, message_string, microphysics_seifert
272
273
274	IMPLICIT NONE
275
276
277	IF ( canopy_drag_coeff == 0.0_wp ) THEN
278	message_string = 'plant_canopy = .TRUE. requires a non-zero drag '// &
279	'coefficient & given value is canopy_drag_coeff = 0.0'
280	CALL message( 'check_parameters', 'PA0041', 1, 2, 0, 6, 0 )
281	ENDIF
282
283	IF ( ( alpha_lad /= 9999999.9_wp .AND. beta_lad == 9999999.9_wp ) .OR.&
284	beta_lad /= 9999999.9_wp .AND. alpha_lad == 9999999.9_wp ) THEN
285	message_string = 'using the beta function for the construction ' // &
286	'of the leaf area density profile requires ' // &
287	'both alpha_lad and beta_lad to be /= 9999999.9'
288	CALL message( 'check_parameters', 'PA0118', 1, 2, 0, 6, 0 )
289	ENDIF
290
291	IF ( calc_beta_lad_profile .AND. lai_beta == 0.0_wp ) THEN
292	message_string = 'using the beta function for the construction ' // &
293	'of the leaf area density profile requires ' // &
294	'a non-zero lai_beta, but given value is ' // &
295	'lai_beta = 0.0'
296	CALL message( 'check_parameters', 'PA0119', 1, 2, 0, 6, 0 )
297	ENDIF
298
299	IF ( calc_beta_lad_profile .AND. lad_surface /= 0.0_wp ) THEN
300	message_string = 'simultaneous setting of alpha_lad /= 9999999.9' // &
301	'and lad_surface /= 0.0 is not possible, ' // &
302	'use either vertical gradients or the beta ' // &
303	'function for the construction of the leaf area '// &
304	'density profile'
305	CALL message( 'check_parameters', 'PA0120', 1, 2, 0, 6, 0 )
306	ENDIF
307
308	IF ( cloud_physics .AND. microphysics_seifert ) THEN
309	message_string = 'plant_canopy = .TRUE. requires cloud_scheme /=' // &
310	' seifert_beheng'
311	CALL message( 'check_parameters', 'PA0360', 1, 2, 0, 6, 0 )
312	ENDIF
313
314
315	END SUBROUTINE pcm_check_parameters
316
317
318	!------------------------------------------------------------------------------!
319	!
320	! Description:
321	! ------------
322	!> Subroutine defining 3D output variables
323	!------------------------------------------------------------------------------!
324	SUBROUTINE pcm_data_output_3d( av, variable, found, local_pf )
325
326	USE control_parameters, &
327	ONLY : nz_do3d
328
329	USE indices
330
331	USE kinds
332
333
334	IMPLICIT NONE
335
336	CHARACTER (LEN=*) :: variable !<
337
338	INTEGER(iwp) :: av !<
339	INTEGER(iwp) :: i !<
340	INTEGER(iwp) :: j !<
341	INTEGER(iwp) :: k !<
342
343	LOGICAL :: found !<
344
345	REAL(sp), DIMENSION(nxlg:nxrg,nysg:nyng,nzb:nz_do3d) :: local_pf !<
346
347
348	found = .TRUE.
349
350
351	SELECT CASE ( TRIM( variable ) )
352
353	CASE ( 'pcm_heatrate' )
354	CALL exchange_horiz( pc_heating_rate, nbgp )
355	IF ( av == 0 ) THEN
356	DO i = nxlg, nxrg
357	DO j = nysg, nyng
358	DO k = nzb_s_inner(j,i), nz_do3d
359	local_pf(i,j,k) = pc_heating_rate(k-nzb_s_inner(j,i),j,i)
360	ENDDO
361	ENDDO
362	ENDDO
363	ENDIF
364
365
366	CASE ( 'pcm_lad' )
367	IF ( av == 0 ) THEN
368	DO i = nxlg, nxrg
369	DO j = nysg, nyng
370	DO k = nzb_s_inner(j,i), nz_do3d
371	local_pf(i,j,k) = lad_s(k-nzb_s_inner(j,i),j,i)
372	ENDDO
373	ENDDO
374	ENDDO
375	ENDIF
376
377
378	CASE DEFAULT
379	found = .FALSE.
380
381	END SELECT
382
383
384	END SUBROUTINE pcm_data_output_3d
385
386	!------------------------------------------------------------------------------!
387	!
388	! Description:
389	! ------------
390	!> Subroutine defining appropriate grid for netcdf variables.
391	!> It is called from subroutine netcdf.
392	!------------------------------------------------------------------------------!
393	SUBROUTINE pcm_define_netcdf_grid( var, found, grid_x, grid_y, grid_z )
394
395	IMPLICIT NONE
396
397	CHARACTER (LEN=*), INTENT(IN) :: var !<
398	LOGICAL, INTENT(OUT) :: found !<
399	CHARACTER (LEN=*), INTENT(OUT) :: grid_x !<
400	CHARACTER (LEN=*), INTENT(OUT) :: grid_y !<
401	CHARACTER (LEN=*), INTENT(OUT) :: grid_z !<
402
403	found = .TRUE.
404
405	!
406	!-- Check for the grid
407	SELECT CASE ( TRIM( var ) )
408
409	CASE ( 'pcm_heatrate', 'pcm_lad' )
410	grid_x = 'x'
411	grid_y = 'y'
412	grid_z = 'zu'
413
414	CASE DEFAULT
415	found = .FALSE.
416	grid_x = 'none'
417	grid_y = 'none'
418	grid_z = 'none'
419	END SELECT
420
421	END SUBROUTINE pcm_define_netcdf_grid
422
423
424	!------------------------------------------------------------------------------!
425	! Description:
426	! ------------
427	!> Header output for plant canopy model
428	!------------------------------------------------------------------------------!
429	SUBROUTINE pcm_header ( io )
430
431	USE control_parameters, &
432	ONLY: dz, passive_scalar
433
434
435	IMPLICIT NONE
436
437	CHARACTER (LEN=10) :: coor_chr !<
438
439	CHARACTER (LEN=86) :: coordinates !<
440	CHARACTER (LEN=86) :: gradients !<
441	CHARACTER (LEN=86) :: leaf_area_density !<
442	CHARACTER (LEN=86) :: slices !<
443
444	INTEGER(iwp) :: i !<
445	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
446	INTEGER(iwp) :: k !<
447
448	REAL(wp) :: canopy_height !< canopy height (in m)
449
450	canopy_height = pch_index * dz
451
452	WRITE ( io, 1 ) canopy_mode, canopy_height, pch_index, &
453	canopy_drag_coeff
454	IF ( passive_scalar ) THEN
455	WRITE ( io, 2 ) leaf_scalar_exch_coeff, &
456	leaf_surface_conc
457	ENDIF
458
459	!
460	!-- Heat flux at the top of vegetation
461	WRITE ( io, 3 ) cthf
462
463	!
464	!-- Leaf area density profile, calculated either from given vertical
465	!-- gradients or from beta probability density function.
466	IF ( .NOT. calc_beta_lad_profile ) THEN
467
468	!-- Building output strings, starting with surface value
469	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
470	gradients = '------'
471	slices = ' 0'
472	coordinates = ' 0.0'
473	i = 1
474	DO WHILE ( i < 11 .AND. lad_vertical_gradient_level_ind(i) &
475	/= -9999 )
476
477	WRITE (coor_chr,'(F7.2)') lad(lad_vertical_gradient_level_ind(i))
478	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
479	TRIM( coor_chr )
480
481	WRITE (coor_chr,'(F7.2)') lad_vertical_gradient(i)
482	gradients = TRIM( gradients ) // ' ' // TRIM( coor_chr )
483
484	WRITE (coor_chr,'(I7)') lad_vertical_gradient_level_ind(i)
485	slices = TRIM( slices ) // ' ' // TRIM( coor_chr )
486
487	WRITE (coor_chr,'(F7.1)') lad_vertical_gradient_level(i)
488	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
489
490	i = i + 1
491	ENDDO
492
493	WRITE ( io, 4 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
494	TRIM( gradients ), TRIM( slices )
495
496	ELSE
497
498	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
499	coordinates = ' 0.0'
500
501	DO k = 1, pch_index
502
503	WRITE (coor_chr,'(F7.2)') lad(k)
504	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
505	TRIM( coor_chr )
506
507	WRITE (coor_chr,'(F7.1)') zu(k)
508	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
509
510	ENDDO
511
512	WRITE ( io, 5 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
513	alpha_lad, beta_lad, lai_beta
514
515	ENDIF
516
517	1 FORMAT (//' Vegetation canopy (drag) model:'/ &
518	' ------------------------------'// &
519	' Canopy mode: ', A / &
520	' Canopy height: ',F6.2,'m (',I4,' grid points)' / &
521	' Leaf drag coefficient: ',F6.2 /)
522	2 FORMAT (/ ' Scalar exchange coefficient: ',F6.2 / &
523	' Scalar concentration at leaf surfaces in kg/m**3: ',F6.2 /)
524	3 FORMAT (' Predefined constant heatflux at the top of the vegetation: ',F6.2, &
525	' K m/s')
526	4 FORMAT (/ ' Characteristic levels of the leaf area density:'// &
527	' Height: ',A,' m'/ &
528	' Leaf area density: ',A,' m2/m3'/ &
529	' Gradient: ',A,' m2/m4'/ &
530	' Gridpoint: ',A)
531	5 FORMAT (//' Characteristic levels of the leaf area density and coefficients:'&
532	// ' Height: ',A,' m'/ &
533	' Leaf area density: ',A,' m2/m3'/ &
534	' Coefficient alpha: ',F6.2 / &
535	' Coefficient beta: ',F6.2 / &
536	' Leaf area index: ',F6.2,' m2/m2' /)
537
538	END SUBROUTINE pcm_header
539
540
541	!------------------------------------------------------------------------------!
542	! Description:
543	! ------------
544	!> Initialization of the plant canopy model
545	!------------------------------------------------------------------------------!
546	SUBROUTINE pcm_init
547
548
549	USE control_parameters, &
550	ONLY: coupling_char, dz, humidity, io_blocks, io_group, &
551	message_string, ocean, passive_scalar
552
553	USE control_parameters, &
554	ONLY: urban_surface
555
556	IMPLICIT NONE
557
558	CHARACTER(10) :: pct
559
560	INTEGER(iwp) :: i !< running index
561	INTEGER(iwp) :: ii !< index
562	INTEGER(iwp) :: j !< running index
563	INTEGER(iwp) :: k !< running index
564
565	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
566	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
567	REAL(wp) :: gradient !< gradient for lad-profile construction
568	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
569	REAL(wp) :: pcv(nzb:nzt+1) !<
570
571	!
572	!-- Allocate one-dimensional arrays for the computation of the
573	!-- leaf area density (lad) profile
574	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
575	lad = 0.0_wp
576	pre_lad = 0.0_wp
577
578	!
579	!-- Set flag that indicates that the lad-profile shall be calculated by using
580	!-- a beta probability density function
581	IF ( alpha_lad /= 9999999.9_wp .AND. beta_lad /= 9999999.9_wp ) THEN
582	calc_beta_lad_profile = .TRUE.
583	ENDIF
584
585
586	!
587	!-- Compute the profile of leaf area density used in the plant
588	!-- canopy model. The profile can either be constructed from
589	!-- prescribed vertical gradients of the leaf area density or by
590	!-- using a beta probability density function (see e.g. Markkanen et al.,
591	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
592	IF ( .NOT. calc_beta_lad_profile ) THEN
593
594	!
595	!-- Use vertical gradients for lad-profile construction
596	i = 1
597	gradient = 0.0_wp
598
599	IF ( .NOT. ocean ) THEN
600
601	lad(0) = lad_surface
602	lad_vertical_gradient_level_ind(1) = 0
603
604	DO k = 1, pch_index
605	IF ( i < 11 ) THEN
606	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
607	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
608	gradient = lad_vertical_gradient(i)
609	lad_vertical_gradient_level_ind(i) = k - 1
610	i = i + 1
611	ENDIF
612	ENDIF
613	IF ( gradient /= 0.0_wp ) THEN
614	IF ( k /= 1 ) THEN
615	lad(k) = lad(k-1) + dzu(k) * gradient
616	ELSE
617	lad(k) = lad_surface + dzu(k) * gradient
618	ENDIF
619	ELSE
620	lad(k) = lad(k-1)
621	ENDIF
622	ENDDO
623
624	ENDIF
625
626	!
627	!-- In case of no given leaf area density gradients, choose a vanishing
628	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
629	!-- file.
630	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
631	lad_vertical_gradient_level(1) = 0.0_wp
632	ENDIF
633
634	ELSE
635
636	!
637	!-- Use beta function for lad-profile construction
638	int_bpdf = 0.0_wp
639	canopy_height = pch_index * dz
640
641	DO k = nzb, pch_index
642	int_bpdf = int_bpdf + &
643	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
644	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
645	beta_lad-1.0_wp ) ) &
646	* ( ( zw(k+1)-zw(k) ) / canopy_height ) )
647	ENDDO
648
649	!
650	!-- Preliminary lad profile (defined on w-grid)
651	DO k = nzb, pch_index
652	pre_lad(k) = lai_beta * &
653	( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) ) &
654	* ( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
655	beta_lad-1.0_wp ) ) / int_bpdf &
656	) / canopy_height
657	ENDDO
658
659	!
660	!-- Final lad profile (defined on scalar-grid level, since most prognostic
661	!-- quantities are defined there, hence, less interpolation is required
662	!-- when calculating the canopy tendencies)
663	lad(0) = pre_lad(0)
664	DO k = nzb+1, pch_index
665	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
666	ENDDO
667
668	ENDIF
669
670	!
671	!-- Allocate 3D-array for the leaf area density (lad_s).
672	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
673
674	!
675	!-- Initialize canopy parameters cdc (canopy drag coefficient),
676	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
677	!-- with the prescribed values
678	cdc = canopy_drag_coeff
679	lsec = leaf_scalar_exch_coeff
680	lsc = leaf_surface_conc
681
682	!
683	!-- Initialization of the canopy coverage in the model domain:
684	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
685	!-- fully covers the domain surface
686	SELECT CASE ( TRIM( canopy_mode ) )
687
688	CASE( 'block' )
689
690	DO i = nxlg, nxrg
691	DO j = nysg, nyng
692	lad_s(:,j,i) = lad(:)
693	ENDDO
694	ENDDO
695
696	CASE ( 'read_from_file_3d' )
697	!
698	!-- Initialize canopy parameters cdc (canopy drag coefficient),
699	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
700	!-- from file which contains complete 3D data (separate vertical profiles for
701	!-- each location).
702	CALL pcm_read_plant_canopy_3d
703
704	CASE DEFAULT
705	!
706	!-- The DEFAULT case is reached either if the parameter
707	!-- canopy mode contains a wrong character string or if the
708	!-- user has coded a special case in the user interface.
709	!-- There, the subroutine user_init_plant_canopy checks
710	!-- which of these two conditions applies.
711	CALL user_init_plant_canopy
712
713	END SELECT
714
715	!
716	!-- Initialization of the canopy heat source distribution due to heating
717	!-- of the canopy layers by incoming solar radiation, in case that a non-zero
718	!-- value is set for the canopy top heat flux (cthf), which equals the
719	!-- available net radiation at canopy top.
720	!-- The heat source distribution is calculated by a decaying exponential
721	!-- function of the downward cumulative leaf area index (cum_lai_hf),
722	!-- assuming that the foliage inside the plant canopy is heated by solar
723	!-- radiation penetrating the canopy layers according to the distribution
724	!-- of net radiation as suggested by Brown & Covey (1966; Agric. Meteorol. 3,
725	!-- 73â96). This approach has been applied e.g. by Shaw & Schumann (1992;
726	!-- Bound.-Layer Meteorol. 61, 47â64).
727	!-- When using the urban surface model (USM), canopy heating (pc_heating_rate)
728	!-- by radiation is calculated in the USM.
729	IF ( cthf /= 0.0_wp .AND. .NOT. urban_surface) THEN
730
731	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
732	pc_heating_rate(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
733	!
734	!-- Piecewise calculation of the cumulative leaf area index by vertical
735	!-- integration of the leaf area density
736	cum_lai_hf(:,:,:) = 0.0_wp
737	DO i = nxlg, nxrg
738	DO j = nysg, nyng
739	DO k = pch_index-1, 0, -1
740	IF ( k == pch_index-1 ) THEN
741	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
742	( 0.5_wp * lad_s(k+1,j,i) * &
743	( zw(k+1) - zu(k+1) ) ) + &
744	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
745	lad_s(k,j,i) ) + &
746	lad_s(k+1,j,i) ) * &
747	( zu(k+1) - zw(k) ) )
748	ELSE
749	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
750	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
751	lad_s(k+1,j,i) ) + &
752	lad_s(k+1,j,i) ) * &
753	( zw(k+1) - zu(k+1) ) ) + &
754	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
755	lad_s(k,j,i) ) + &
756	lad_s(k+1,j,i) ) * &
757	( zu(k+1) - zw(k) ) )
758	ENDIF
759	ENDDO
760	ENDDO
761	ENDDO
762
763	!
764	!-- Calculation of the heating rate (K/s) within the different layers of
765	!-- the plant canopy
766	DO i = nxlg, nxrg
767	DO j = nysg, nyng
768	!
769	!-- Calculation only necessary in areas covered with canopy
770	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) THEN
771	!--
772	!-- In areas with canopy the surface value of the canopy heat
773	!-- flux distribution overrides the surface heat flux (shf)
774	shf(j,i) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
775	!
776	!-- Within the different canopy layers the plant-canopy heating
777	!-- rate (pc_heating_rate) is calculated as the vertical
778	!-- divergence of the canopy heat fluxes at the top and bottom
779	!-- of the respective layer
780	DO k = 1, pch_index
781	pc_heating_rate(k,j,i) = cthf * &
782	( exp(-ext_coef*cum_lai_hf(k,j,i)) - &
783	exp(-ext_coef*cum_lai_hf(k-1,j,i)) ) / dzw(k)
784	ENDDO
785	ENDIF
786	ENDDO
787	ENDDO
788
789	ENDIF
790
791
792
793	END SUBROUTINE pcm_init
794
795
796	!------------------------------------------------------------------------------!
797	! Description:
798	! ------------
799	!> Parin for &canopy_par for plant canopy model
800	!------------------------------------------------------------------------------!
801	SUBROUTINE pcm_parin
802
803
804	IMPLICIT NONE
805
806	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
807
808	NAMELIST /canopy_par/ alpha_lad, beta_lad, canopy_drag_coeff, &
809	canopy_mode, cthf, &
810	lad_surface, &
811	lad_vertical_gradient, &
812	lad_vertical_gradient_level, &
813	lai_beta, &
814	leaf_scalar_exch_coeff, &
815	leaf_surface_conc, pch_index
816
817	line = ' '
818
819	!
820	!-- Try to find radiation model package
821	REWIND ( 11 )
822	line = ' '
823	DO WHILE ( INDEX( line, '&canopy_par' ) == 0 )
824	READ ( 11, '(A)', END=10 ) line
825	ENDDO
826	BACKSPACE ( 11 )
827
828	!
829	!-- Read user-defined namelist
830	READ ( 11, canopy_par )
831
832	!
833	!-- Set flag that indicates that the radiation model is switched on
834	plant_canopy = .TRUE.
835
836	10 CONTINUE
837
838
839	END SUBROUTINE pcm_parin
840
841
842
843	!------------------------------------------------------------------------------!
844	! Description:
845	! ------------
846	!
847	!> Loads 3D plant canopy data from file. File format is as follows:
848	!>
849	!> num_levels
850	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
851	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
852	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
853	!> ...
854	!>
855	!> i.e. first line determines number of levels and further lines represent plant
856	!> canopy data, one line per column and variable. In each data line,
857	!> dtype represents variable to be set:
858	!>
859	!> dtype=1: leaf area density (lad_s)
860	!> dtype=2....n: some additional plant canopy input data quantity
861	!>
862	!> Zeros are added automatically above num_levels until top of domain. Any
863	!> non-specified (x,y) columns have zero values as default.
864	!------------------------------------------------------------------------------!
865	SUBROUTINE pcm_read_plant_canopy_3d
866
867	USE control_parameters, &
868	ONLY: message_string, passive_scalar
869
870	USE indices, &
871	ONLY: nbgp
872
873	IMPLICIT NONE
874
875	INTEGER(iwp) :: dtype !< type of input data (1=lad)
876	INTEGER(iwp) :: i, j !< running index
877	INTEGER(iwp) :: nzp !< number of vertical layers of plant canopy
878	INTEGER(iwp) :: nzpltop !<
879	INTEGER(iwp) :: nzpl !<
880
881	REAL(wp), DIMENSION(:), ALLOCATABLE :: col !< vertical column of input data
882
883	!
884	!-- Initialize lad_s array
885	lad_s = 0.0_wp
886
887	!
888	!-- Open and read plant canopy input data
889	OPEN(152, file='PLANT_CANOPY_DATA_3D', access='SEQUENTIAL', &
890	action='READ', status='OLD', form='FORMATTED', err=515)
891	READ(152, *, err=516, end=517) nzp !< read first line = number of vertical layers
892
893	ALLOCATE(col(0:nzp-1))
894
895	DO
896	READ(152, *, err=516, end=517) dtype, i, j, col(:)
897	IF ( i < nxlg .or. i > nxrg .or. j < nysg .or. j > nyng ) CYCLE
898
899	SELECT CASE (dtype)
900	CASE( 1 ) !< leaf area density
901	!
902	!-- This is just the pure canopy layer assumed to be grounded to
903	!-- a flat domain surface. At locations where plant canopy sits
904	!-- on top of any kind of topography, the vertical plant column
905	!-- must be "lifted", which is done in SUBROUTINE pcm_tendency.
906	lad_s(0:nzp-1, j, i) = col(0:nzp-1)
907
908	CASE DEFAULT
909	write(message_string, '(a,i2,a)') &
910	'Unknown record type in file PLANT_CANOPY_DATA_3D: "', dtype, '"'
911	CALL message( 'pcm_read_plant_canopy_3d', 'PA0530', 1, 2, 0, 6, 0 )
912	END SELECT
913	ENDDO
914
915	515 message_string = 'error opening file PLANT_CANOPY_DATA_3D'
916	CALL message( 'pcm_read_plant_canopy_3d', 'PA0531', 1, 2, 0, 6, 0 )
917
918	516 message_string = 'error reading file PLANT_CANOPY_DATA_3D'
919	CALL message( 'pcm_read_plant_canopy_3d', 'PA0532', 1, 2, 0, 6, 0 )
920
921	517 CLOSE(152)
922	DEALLOCATE(col)
923
924	CALL exchange_horiz( lad_s, nbgp )
925
926	END SUBROUTINE pcm_read_plant_canopy_3d
927
928
929
930	!------------------------------------------------------------------------------!
931	! Description:
932	! ------------
933	!> Calculation of the tendency terms, accounting for the effect of the plant
934	!> canopy on momentum and scalar quantities.
935	!>
936	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
937	!> (defined on scalar grid), as initialized in subroutine pcm_init.
938	!> The lad on the w-grid is vertically interpolated from the surrounding
939	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
940	!> k = pch_index. Here, the lad is zero.
941	!>
942	!> The canopy drag must be limited (previously accounted for by calculation of
943	!> a limiting canopy timestep for the determination of the maximum LES timestep
944	!> in subroutine timestep), since it is physically impossible that the canopy
945	!> drag alone can locally change the sign of a velocity component. This
946	!> limitation is realized by calculating preliminary tendencies and velocities.
947	!> It is subsequently checked if the preliminary new velocity has a different
948	!> sign than the current velocity. If so, the tendency is limited in a way that
949	!> the velocity can at maximum be reduced to zero by the canopy drag.
950	!>
951	!>
952	!> Call for all grid points
953	!------------------------------------------------------------------------------!
954	SUBROUTINE pcm_tendency( component )
955
956
957	USE control_parameters, &
958	ONLY: dt_3d, message_string
959
960	USE kinds
961
962	IMPLICIT NONE
963
964	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
965	INTEGER(iwp) :: i !< running index
966	INTEGER(iwp) :: j !< running index
967	INTEGER(iwp) :: k !< running index
968	INTEGER(iwp) :: kk !< running index for flat lad arrays
969
970	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
971	REAL(wp) :: lad_local !< local lad value
972	REAL(wp) :: pre_tend !< preliminary tendency
973	REAL(wp) :: pre_u !< preliminary u-value
974	REAL(wp) :: pre_v !< preliminary v-value
975	REAL(wp) :: pre_w !< preliminary w-value
976
977
978	ddt_3d = 1.0_wp / dt_3d
979
980	!
981	!-- Compute drag for the three velocity components and the SGS-TKE:
982	SELECT CASE ( component )
983
984	!
985	!-- u-component
986	CASE ( 1 )
987	DO i = nxlu, nxr
988	DO j = nys, nyn
989	DO k = nzb_u_inner(j,i)+1, nzb_u_inner(j,i)+pch_index
990
991	kk = k - nzb_u_inner(j,i) !- lad arrays are defined flat
992	!
993	!-- In order to create sharp boundaries of the plant canopy,
994	!-- the lad on the u-grid at index (k,j,i) is equal to
995	!-- lad_s(k,j,i), rather than being interpolated from the
996	!-- surrounding lad_s, because this would yield smaller lad
997	!-- at the canopy boundaries than inside of the canopy.
998	!-- For the same reason, the lad at the rightmost(i+1)canopy
999	!-- boundary on the u-grid equals lad_s(k,j,i).
1000	lad_local = lad_s(kk,j,i)
1001	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp )&
1002	THEN
1003	lad_local = lad_s(kk,j,i-1)
1004	ENDIF
1005
1006	pre_tend = 0.0_wp
1007	pre_u = 0.0_wp
1008	!
1009	!-- Calculate preliminary value (pre_tend) of the tendency
1010	pre_tend = - cdc * &
1011	lad_local * &
1012	SQRT( u(k,j,i)**2 + &
1013	( 0.25_wp * ( v(k,j,i-1) + &
1014	v(k,j,i) + &
1015	v(k,j+1,i) + &
1016	v(k,j+1,i-1) ) &
1017	)**2 + &
1018	( 0.25_wp * ( w(k-1,j,i-1) + &
1019	w(k-1,j,i) + &
1020	w(k,j,i-1) + &
1021	w(k,j,i) ) &
1022	)**2 &
1023	) * &
1024	u(k,j,i)
1025
1026	!
1027	!-- Calculate preliminary new velocity, based on pre_tend
1028	pre_u = u(k,j,i) + dt_3d * pre_tend
1029	!
1030	!-- Compare sign of old velocity and new preliminary velocity,
1031	!-- and in case the signs are different, limit the tendency
1032	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1033	pre_tend = - u(k,j,i) * ddt_3d
1034	ELSE
1035	pre_tend = pre_tend
1036	ENDIF
1037	!
1038	!-- Calculate final tendency
1039	tend(k,j,i) = tend(k,j,i) + pre_tend
1040
1041	ENDDO
1042	ENDDO
1043	ENDDO
1044
1045	!
1046	!-- v-component
1047	CASE ( 2 )
1048	DO i = nxl, nxr
1049	DO j = nysv, nyn
1050	DO k = nzb_v_inner(j,i)+1, nzb_v_inner(j,i)+pch_index
1051
1052	kk = k - nzb_v_inner(j,i) !- lad arrays are defined flat
1053	!
1054	!-- In order to create sharp boundaries of the plant canopy,
1055	!-- the lad on the v-grid at index (k,j,i) is equal to
1056	!-- lad_s(k,j,i), rather than being interpolated from the
1057	!-- surrounding lad_s, because this would yield smaller lad
1058	!-- at the canopy boundaries than inside of the canopy.
1059	!-- For the same reason, the lad at the northmost(j+1) canopy
1060	!-- boundary on the v-grid equals lad_s(k,j,i).
1061	lad_local = lad_s(kk,j,i)
1062	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp )&
1063	THEN
1064	lad_local = lad_s(kk,j-1,i)
1065	ENDIF
1066
1067	pre_tend = 0.0_wp
1068	pre_v = 0.0_wp
1069	!
1070	!-- Calculate preliminary value (pre_tend) of the tendency
1071	pre_tend = - cdc * &
1072	lad_local * &
1073	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1074	u(k,j-1,i+1) + &
1075	u(k,j,i) + &
1076	u(k,j,i+1) ) &
1077	)**2 + &
1078	v(k,j,i)**2 + &
1079	( 0.25_wp * ( w(k-1,j-1,i) + &
1080	w(k-1,j,i) + &
1081	w(k,j-1,i) + &
1082	w(k,j,i) ) &
1083	)**2 &
1084	) * &
1085	v(k,j,i)
1086
1087	!
1088	!-- Calculate preliminary new velocity, based on pre_tend
1089	pre_v = v(k,j,i) + dt_3d * pre_tend
1090	!
1091	!-- Compare sign of old velocity and new preliminary velocity,
1092	!-- and in case the signs are different, limit the tendency
1093	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1094	pre_tend = - v(k,j,i) * ddt_3d
1095	ELSE
1096	pre_tend = pre_tend
1097	ENDIF
1098	!
1099	!-- Calculate final tendency
1100	tend(k,j,i) = tend(k,j,i) + pre_tend
1101
1102	ENDDO
1103	ENDDO
1104	ENDDO
1105
1106	!
1107	!-- w-component
1108	CASE ( 3 )
1109	DO i = nxl, nxr
1110	DO j = nys, nyn
1111	DO k = nzb_w_inner(j,i)+1, nzb_w_inner(j,i)+pch_index-1
1112
1113	kk = k - nzb_w_inner(j,i) !- lad arrays are defined flat
1114
1115	pre_tend = 0.0_wp
1116	pre_w = 0.0_wp
1117	!
1118	!-- Calculate preliminary value (pre_tend) of the tendency
1119	pre_tend = - cdc * &
1120	(0.5_wp * &
1121	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1122	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1123	u(k,j,i+1) + &
1124	u(k+1,j,i) + &
1125	u(k+1,j,i+1) ) &
1126	)**2 + &
1127	( 0.25_wp * ( v(k,j,i) + &
1128	v(k,j+1,i) + &
1129	v(k+1,j,i) + &
1130	v(k+1,j+1,i) ) &
1131	)**2 + &
1132	w(k,j,i)**2 &
1133	) * &
1134	w(k,j,i)
1135	!
1136	!-- Calculate preliminary new velocity, based on pre_tend
1137	pre_w = w(k,j,i) + dt_3d * pre_tend
1138	!
1139	!-- Compare sign of old velocity and new preliminary velocity,
1140	!-- and in case the signs are different, limit the tendency
1141	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1142	pre_tend = - w(k,j,i) * ddt_3d
1143	ELSE
1144	pre_tend = pre_tend
1145	ENDIF
1146	!
1147	!-- Calculate final tendency
1148	tend(k,j,i) = tend(k,j,i) + pre_tend
1149
1150	ENDDO
1151	ENDDO
1152	ENDDO
1153
1154	!
1155	!-- potential temperature
1156	CASE ( 4 )
1157	DO i = nxl, nxr
1158	DO j = nys, nyn
1159	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1160	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1161	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1162	ENDDO
1163	ENDDO
1164	ENDDO
1165
1166	!
1167	!-- humidity
1168	CASE ( 5 )
1169	DO i = nxl, nxr
1170	DO j = nys, nyn
1171	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1172	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1173	tend(k,j,i) = tend(k,j,i) - &
1174	lsec * &
1175	lad_s(kk,j,i) * &
1176	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1177	u(k,j,i+1) ) &
1178	)**2 + &
1179	( 0.5_wp * ( v(k,j,i) + &
1180	v(k,j+1,i) ) &
1181	)**2 + &
1182	( 0.5_wp * ( w(k-1,j,i) + &
1183	w(k,j,i) ) &
1184	)**2 &
1185	) * &
1186	( q(k,j,i) - lsc )
1187	ENDDO
1188	ENDDO
1189	ENDDO
1190
1191	!
1192	!-- sgs-tke
1193	CASE ( 6 )
1194	DO i = nxl, nxr
1195	DO j = nys, nyn
1196	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1197	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1198	tend(k,j,i) = tend(k,j,i) - &
1199	2.0_wp * cdc * &
1200	lad_s(kk,j,i) * &
1201	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1202	u(k,j,i+1) ) &
1203	)**2 + &
1204	( 0.5_wp * ( v(k,j,i) + &
1205	v(k,j+1,i) ) &
1206	)**2 + &
1207	( 0.5_wp * ( w(k,j,i) + &
1208	w(k+1,j,i) ) &
1209	)**2 &
1210	) * &
1211	e(k,j,i)
1212	ENDDO
1213	ENDDO
1214	ENDDO
1215	!
1216	!-- scalar concentration
1217	CASE ( 7 )
1218	DO i = nxl, nxr
1219	DO j = nys, nyn
1220	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1221	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1222	tend(k,j,i) = tend(k,j,i) - &
1223	lsec * &
1224	lad_s(kk,j,i) * &
1225	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1226	u(k,j,i+1) ) &
1227	)**2 + &
1228	( 0.5_wp * ( v(k,j,i) + &
1229	v(k,j+1,i) ) &
1230	)**2 + &
1231	( 0.5_wp * ( w(k-1,j,i) + &
1232	w(k,j,i) ) &
1233	)**2 &
1234	) * &
1235	( s(k,j,i) - lsc )
1236	ENDDO
1237	ENDDO
1238	ENDDO
1239
1240
1241
1242	CASE DEFAULT
1243
1244	WRITE( message_string, * ) 'wrong component: ', component
1245	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1246
1247	END SELECT
1248
1249	END SUBROUTINE pcm_tendency
1250
1251
1252	!------------------------------------------------------------------------------!
1253	! Description:
1254	! ------------
1255	!> Calculation of the tendency terms, accounting for the effect of the plant
1256	!> canopy on momentum and scalar quantities.
1257	!>
1258	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
1259	!> (defined on scalar grid), as initialized in subroutine pcm_init.
1260	!> The lad on the w-grid is vertically interpolated from the surrounding
1261	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
1262	!> k = pch_index. Here, the lad is zero.
1263	!>
1264	!> The canopy drag must be limited (previously accounted for by calculation of
1265	!> a limiting canopy timestep for the determination of the maximum LES timestep
1266	!> in subroutine timestep), since it is physically impossible that the canopy
1267	!> drag alone can locally change the sign of a velocity component. This
1268	!> limitation is realized by calculating preliminary tendencies and velocities.
1269	!> It is subsequently checked if the preliminary new velocity has a different
1270	!> sign than the current velocity. If so, the tendency is limited in a way that
1271	!> the velocity can at maximum be reduced to zero by the canopy drag.
1272	!>
1273	!>
1274	!> Call for grid point i,j
1275	!------------------------------------------------------------------------------!
1276	SUBROUTINE pcm_tendency_ij( i, j, component )
1277
1278
1279	USE control_parameters, &
1280	ONLY: dt_3d, message_string
1281
1282	USE kinds
1283
1284	IMPLICIT NONE
1285
1286	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
1287	INTEGER(iwp) :: i !< running index
1288	INTEGER(iwp) :: j !< running index
1289	INTEGER(iwp) :: k !< running index
1290	INTEGER(iwp) :: kk !< running index for flat lad arrays
1291
1292	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1293	REAL(wp) :: lad_local !< local lad value
1294	REAL(wp) :: pre_tend !< preliminary tendency
1295	REAL(wp) :: pre_u !< preliminary u-value
1296	REAL(wp) :: pre_v !< preliminary v-value
1297	REAL(wp) :: pre_w !< preliminary w-value
1298
1299
1300	ddt_3d = 1.0_wp / dt_3d
1301
1302	!
1303	!-- Compute drag for the three velocity components and the SGS-TKE
1304	SELECT CASE ( component )
1305
1306	!
1307	!-- u-component
1308	CASE ( 1 )
1309	DO k = nzb_u_inner(j,i)+1, nzb_u_inner(j,i)+pch_index
1310
1311	kk = k - nzb_u_inner(j,i) !- lad arrays are defined flat
1312	!
1313	!-- In order to create sharp boundaries of the plant canopy,
1314	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
1315	!-- rather than being interpolated from the surrounding lad_s,
1316	!-- because this would yield smaller lad at the canopy boundaries
1317	!-- than inside of the canopy.
1318	!-- For the same reason, the lad at the rightmost(i+1)canopy
1319	!-- boundary on the u-grid equals lad_s(k,j,i).
1320	lad_local = lad_s(kk,j,i)
1321	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp ) THEN
1322	lad_local = lad_s(kk,j,i-1)
1323	ENDIF
1324
1325	pre_tend = 0.0_wp
1326	pre_u = 0.0_wp
1327	!
1328	!-- Calculate preliminary value (pre_tend) of the tendency
1329	pre_tend = - cdc * &
1330	lad_local * &
1331	SQRT( u(k,j,i)**2 + &
1332	( 0.25_wp * ( v(k,j,i-1) + &
1333	v(k,j,i) + &
1334	v(k,j+1,i) + &
1335	v(k,j+1,i-1) ) &
1336	)**2 + &
1337	( 0.25_wp * ( w(k-1,j,i-1) + &
1338	w(k-1,j,i) + &
1339	w(k,j,i-1) + &
1340	w(k,j,i) ) &
1341	)**2 &
1342	) * &
1343	u(k,j,i)
1344
1345	!
1346	!-- Calculate preliminary new velocity, based on pre_tend
1347	pre_u = u(k,j,i) + dt_3d * pre_tend
1348	!
1349	!-- Compare sign of old velocity and new preliminary velocity,
1350	!-- and in case the signs are different, limit the tendency
1351	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1352	pre_tend = - u(k,j,i) * ddt_3d
1353	ELSE
1354	pre_tend = pre_tend
1355	ENDIF
1356	!
1357	!-- Calculate final tendency
1358	tend(k,j,i) = tend(k,j,i) + pre_tend
1359	ENDDO
1360
1361
1362	!
1363	!-- v-component
1364	CASE ( 2 )
1365	DO k = nzb_v_inner(j,i)+1, nzb_v_inner(j,i)+pch_index
1366
1367	kk = k - nzb_v_inner(j,i) !- lad arrays are defined flat
1368	!
1369	!-- In order to create sharp boundaries of the plant canopy,
1370	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
1371	!-- rather than being interpolated from the surrounding lad_s,
1372	!-- because this would yield smaller lad at the canopy boundaries
1373	!-- than inside of the canopy.
1374	!-- For the same reason, the lad at the northmost(j+1)canopy
1375	!-- boundary on the v-grid equals lad_s(k,j,i).
1376	lad_local = lad_s(kk,j,i)
1377	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp ) THEN
1378	lad_local = lad_s(kk,j-1,i)
1379	ENDIF
1380
1381	pre_tend = 0.0_wp
1382	pre_v = 0.0_wp
1383	!
1384	!-- Calculate preliminary value (pre_tend) of the tendency
1385	pre_tend = - cdc * &
1386	lad_local * &
1387	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1388	u(k,j-1,i+1) + &
1389	u(k,j,i) + &
1390	u(k,j,i+1) ) &
1391	)**2 + &
1392	v(k,j,i)**2 + &
1393	( 0.25_wp * ( w(k-1,j-1,i) + &
1394	w(k-1,j,i) + &
1395	w(k,j-1,i) + &
1396	w(k,j,i) ) &
1397	)**2 &
1398	) * &
1399	v(k,j,i)
1400
1401	!
1402	!-- Calculate preliminary new velocity, based on pre_tend
1403	pre_v = v(k,j,i) + dt_3d * pre_tend
1404	!
1405	!-- Compare sign of old velocity and new preliminary velocity,
1406	!-- and in case the signs are different, limit the tendency
1407	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1408	pre_tend = - v(k,j,i) * ddt_3d
1409	ELSE
1410	pre_tend = pre_tend
1411	ENDIF
1412	!
1413	!-- Calculate final tendency
1414	tend(k,j,i) = tend(k,j,i) + pre_tend
1415	ENDDO
1416
1417
1418	!
1419	!-- w-component
1420	CASE ( 3 )
1421	DO k = nzb_w_inner(j,i)+1, nzb_w_inner(j,i)+pch_index-1
1422
1423	kk = k - nzb_w_inner(j,i) !- lad arrays are defined flat
1424
1425	pre_tend = 0.0_wp
1426	pre_w = 0.0_wp
1427	!
1428	!-- Calculate preliminary value (pre_tend) of the tendency
1429	pre_tend = - cdc * &
1430	(0.5_wp * &
1431	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1432	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1433	u(k,j,i+1) + &
1434	u(k+1,j,i) + &
1435	u(k+1,j,i+1) ) &
1436	)**2 + &
1437	( 0.25_wp * ( v(k,j,i) + &
1438	v(k,j+1,i) + &
1439	v(k+1,j,i) + &
1440	v(k+1,j+1,i) ) &
1441	)**2 + &
1442	w(k,j,i)**2 &
1443	) * &
1444	w(k,j,i)
1445	!
1446	!-- Calculate preliminary new velocity, based on pre_tend
1447	pre_w = w(k,j,i) + dt_3d * pre_tend
1448	!
1449	!-- Compare sign of old velocity and new preliminary velocity,
1450	!-- and in case the signs are different, limit the tendency
1451	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1452	pre_tend = - w(k,j,i) * ddt_3d
1453	ELSE
1454	pre_tend = pre_tend
1455	ENDIF
1456	!
1457	!-- Calculate final tendency
1458	tend(k,j,i) = tend(k,j,i) + pre_tend
1459	ENDDO
1460
1461	!
1462	!-- potential temperature
1463	CASE ( 4 )
1464	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1465	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1466	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1467	ENDDO
1468
1469
1470	!
1471	!-- humidity
1472	CASE ( 5 )
1473	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1474	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1475	tend(k,j,i) = tend(k,j,i) - &
1476	lsec * &
1477	lad_s(kk,j,i) * &
1478	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1479	u(k,j,i+1) ) &
1480	)**2 + &
1481	( 0.5_wp * ( v(k,j,i) + &
1482	v(k,j+1,i) ) &
1483	)**2 + &
1484	( 0.5_wp * ( w(k-1,j,i) + &
1485	w(k,j,i) ) &
1486	)**2 &
1487	) * &
1488	( q(k,j,i) - lsc )
1489	ENDDO
1490
1491	!
1492	!-- sgs-tke
1493	CASE ( 6 )
1494	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1495	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1496	tend(k,j,i) = tend(k,j,i) - &
1497	2.0_wp * cdc * &
1498	lad_s(kk,j,i) * &
1499	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1500	u(k,j,i+1) ) &
1501	)**2 + &
1502	( 0.5_wp * ( v(k,j,i) + &
1503	v(k,j+1,i) ) &
1504	)**2 + &
1505	( 0.5_wp * ( w(k,j,i) + &
1506	w(k+1,j,i) ) &
1507	)**2 &
1508	) * &
1509	e(k,j,i)
1510	ENDDO
1511
1512	!
1513	!-- scalar concentration
1514	CASE ( 7 )
1515	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1516	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1517	tend(k,j,i) = tend(k,j,i) - &
1518	lsec * &
1519	lad_s(kk,j,i) * &
1520	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1521	u(k,j,i+1) ) &
1522	)**2 + &
1523	( 0.5_wp * ( v(k,j,i) + &
1524	v(k,j+1,i) ) &
1525	)**2 + &
1526	( 0.5_wp * ( w(k-1,j,i) + &
1527	w(k,j,i) ) &
1528	)**2 &
1529	) * &
1530	( s(k,j,i) - lsc )
1531	ENDDO
1532
1533	CASE DEFAULT
1534
1535	WRITE( message_string, * ) 'wrong component: ', component
1536	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1537
1538	END SELECT
1539
1540	END SUBROUTINE pcm_tendency_ij
1541
1542
1543
1544	END MODULE plant_canopy_model_mod

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