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source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 2284

Last change on this file since 2284 was 2274, checked in by Giersch, 8 years ago
Changed error messages
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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 2274 2017-06-09 13:27:48Z witha $
27	! Changed error messages
28	!
29	! 2233 2017-05-30 18:08:54Z suehring
30	!
31	! 2232 2017-05-30 17:47:52Z suehring
32	! Adjustments to new topography concept
33	!
34	! 2213 2017-04-24 15:10:35Z kanani
35	! Bugfix: exchange of ghost points in array pc_heating_rate needed for output
36	! of pcm_heatrate, onetime ghost point exchange of lad_s after initialization.
37	! Formatting and clean-up of subroutine pcm_read_plant_canopy_3d,
38	! minor re-organization of canopy-heating initialization.
39	!
40	! 2209 2017-04-19 09:34:46Z kanani
41	! Added 3d output of leaf area density (pcm_lad) and canopy
42	! heat rate (pcm_heatrate)
43	!
44	! 2024 2016-10-12 16:42:37Z kanani
45	! Added missing lad_s initialization
46	!
47	! 2011 2016-09-19 17:29:57Z kanani
48	! Renamed canopy_heat_flux to pc_heating_rate, since the original meaning/
49	! calculation of the quantity has changed, related to the urban surface model
50	! and similar future applications.
51	!
52	! 2007 2016-08-24 15:47:17Z kanani
53	! Added SUBROUTINE pcm_read_plant_canopy_3d for reading 3d plant canopy data
54	! from file (new case canopy_mode=read_from_file_3d) in the course of
55	! introduction of urban surface model,
56	! introduced variable ext_coef,
57	! resorted SUBROUTINEs to alphabetical order
58	!
59	! 2000 2016-08-20 18:09:15Z knoop
60	! Forced header and separation lines into 80 columns
61	!
62	! 1960 2016-07-12 16:34:24Z suehring
63	! Separate humidity and passive scalar
64	!
65	! 1953 2016-06-21 09:28:42Z suehring
66	! Bugfix, lad_s and lad must be public
67	!
68	! 1826 2016-04-07 12:01:39Z maronga
69	! Further modularization
70	!
71	! 1721 2015-11-16 12:56:48Z raasch
72	! bugfixes: shf is reduced in areas covered with canopy only,
73	! canopy is set on top of topography
74	!
75	! 1682 2015-10-07 23:56:08Z knoop
76	! Code annotations made doxygen readable
77	!
78	! 1484 2014-10-21 10:53:05Z kanani
79	! Changes due to new module structure of the plant canopy model:
80	! module plant_canopy_model_mod now contains a subroutine for the
81	! initialization of the canopy model (pcm_init),
82	! limitation of the canopy drag (previously accounted for by calculation of
83	! a limiting canopy timestep for the determination of the maximum LES timestep
84	! in subroutine timestep) is now realized by the calculation of pre-tendencies
85	! and preliminary velocities in subroutine pcm_tendency,
86	! some redundant MPI communication removed in subroutine pcm_init
87	! (was previously in init_3d_model),
88	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
89	! respective grid is now provided only by lad_s (e.g. in the calculation of
90	! the tendency terms or of cum_lai_hf),
91	! drag_coefficient, lai, leaf_surface_concentration,
92	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
93	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
94	! respectively,
95	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
96	! USE-statements and ONLY-lists modified accordingly
97	!
98	! 1340 2014-03-25 19:45:13Z kanani
99	! REAL constants defined as wp-kind
100	!
101	! 1320 2014-03-20 08:40:49Z raasch
102	! ONLY-attribute added to USE-statements,
103	! kind-parameters added to all INTEGER and REAL declaration statements,
104	! kinds are defined in new module kinds,
105	! old module precision_kind is removed,
106	! revision history before 2012 removed,
107	! comment fields (!:) to be used for variable explanations added to
108	! all variable declaration statements
109	!
110	! 1036 2012-10-22 13:43:42Z raasch
111	! code put under GPL (PALM 3.9)
112	!
113	! 138 2007-11-28 10:03:58Z letzel
114	! Initial revision
115	!
116	! Description:
117	! ------------
118	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
119	!> profile (subroutine pcm_init).
120	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
121	!> due to canopy elements (subroutine pcm_tendency).
122	!------------------------------------------------------------------------------!
123	MODULE plant_canopy_model_mod
124
125	USE arrays_3d, &
126	ONLY: dzu, dzw, e, q, s, tend, u, v, w, zu, zw
127
128	USE indices, &
129	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
130	nz, nzb, nzb_max, nzt, wall_flags_0
131
132	USE kinds
133
134
135	IMPLICIT NONE
136
137
138	CHARACTER (LEN=20) :: canopy_mode = 'block' !< canopy coverage
139
140	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
141	INTEGER(iwp) :: &
142	lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
143
144	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
145	LOGICAL :: plant_canopy = .FALSE. !< switch for use of canopy model
146
147	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
148	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
149	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
150	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
151	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
152	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
153	REAL(wp) :: ext_coef = 0.6_wp !< extinction coefficient
154	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
155	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
156	REAL(wp) :: &
157	leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
158	REAL(wp) :: &
159	leaf_surface_conc = 0.0_wp !< leaf surface concentration
160	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
161	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
162
163	REAL(wp) :: &
164	lad_vertical_gradient(10) = 0.0_wp !< lad gradient
165	REAL(wp) :: &
166	lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
167
168	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
169	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
170
171	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
172	pc_heating_rate !< plant canopy heating rate
173	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
174	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
175
176
177	SAVE
178
179
180	PRIVATE
181
182	!
183	!-- Public functions
184	PUBLIC pcm_check_data_output, pcm_check_parameters, pcm_data_output_3d, &
185	pcm_define_netcdf_grid, pcm_header, pcm_init, pcm_parin, pcm_tendency
186
187	!
188	!-- Public variables and constants
189	PUBLIC pc_heating_rate, canopy_mode, cthf, dt_plant_canopy, lad, lad_s, &
190	pch_index, plant_canopy
191
192
193	INTERFACE pcm_check_data_output
194	MODULE PROCEDURE pcm_check_data_output
195	END INTERFACE pcm_check_data_output
196
197	INTERFACE pcm_check_parameters
198	MODULE PROCEDURE pcm_check_parameters
199	END INTERFACE pcm_check_parameters
200
201	INTERFACE pcm_data_output_3d
202	MODULE PROCEDURE pcm_data_output_3d
203	END INTERFACE pcm_data_output_3d
204
205	INTERFACE pcm_define_netcdf_grid
206	MODULE PROCEDURE pcm_define_netcdf_grid
207	END INTERFACE pcm_define_netcdf_grid
208
209	INTERFACE pcm_header
210	MODULE PROCEDURE pcm_header
211	END INTERFACE pcm_header
212
213	INTERFACE pcm_init
214	MODULE PROCEDURE pcm_init
215	END INTERFACE pcm_init
216
217	INTERFACE pcm_parin
218	MODULE PROCEDURE pcm_parin
219	END INTERFACE pcm_parin
220
221	INTERFACE pcm_read_plant_canopy_3d
222	MODULE PROCEDURE pcm_read_plant_canopy_3d
223	END INTERFACE pcm_read_plant_canopy_3d
224
225	INTERFACE pcm_tendency
226	MODULE PROCEDURE pcm_tendency
227	MODULE PROCEDURE pcm_tendency_ij
228	END INTERFACE pcm_tendency
229
230
231	CONTAINS
232
233
234	!------------------------------------------------------------------------------!
235	! Description:
236	! ------------
237	!> Check data output for plant canopy model
238	!------------------------------------------------------------------------------!
239	SUBROUTINE pcm_check_data_output( var, unit )
240
241
242	USE control_parameters, &
243	ONLY: data_output, message_string
244
245	IMPLICIT NONE
246
247	CHARACTER (LEN=*) :: unit !<
248	CHARACTER (LEN=*) :: var !<
249
250
251	SELECT CASE ( TRIM( var ) )
252
253	CASE ( 'pcm_heatrate' )
254	unit = 'K s-1'
255
256	CASE ( 'pcm_lad' )
257	unit = 'm2 m-3'
258
259
260	CASE DEFAULT
261	unit = 'illegal'
262
263	END SELECT
264
265
266	END SUBROUTINE pcm_check_data_output
267
268
269	!------------------------------------------------------------------------------!
270	! Description:
271	! ------------
272	!> Check parameters routine for plant canopy model
273	!------------------------------------------------------------------------------!
274	SUBROUTINE pcm_check_parameters
275
276	USE control_parameters, &
277	ONLY: cloud_physics, message_string, microphysics_seifert
278
279
280	IMPLICIT NONE
281
282
283	IF ( canopy_drag_coeff == 0.0_wp ) THEN
284	message_string = 'plant_canopy = .TRUE. requires a non-zero drag '// &
285	'coefficient & given value is canopy_drag_coeff = 0.0'
286	CALL message( 'check_parameters', 'PA0041', 1, 2, 0, 6, 0 )
287	ENDIF
288
289	IF ( ( alpha_lad /= 9999999.9_wp .AND. beta_lad == 9999999.9_wp ) .OR.&
290	beta_lad /= 9999999.9_wp .AND. alpha_lad == 9999999.9_wp ) THEN
291	message_string = 'using the beta function for the construction ' // &
292	'of the leaf area density profile requires ' // &
293	'both alpha_lad and beta_lad to be /= 9999999.9'
294	CALL message( 'check_parameters', 'PA0118', 1, 2, 0, 6, 0 )
295	ENDIF
296
297	IF ( calc_beta_lad_profile .AND. lai_beta == 0.0_wp ) THEN
298	message_string = 'using the beta function for the construction ' // &
299	'of the leaf area density profile requires ' // &
300	'a non-zero lai_beta, but given value is ' // &
301	'lai_beta = 0.0'
302	CALL message( 'check_parameters', 'PA0119', 1, 2, 0, 6, 0 )
303	ENDIF
304
305	IF ( calc_beta_lad_profile .AND. lad_surface /= 0.0_wp ) THEN
306	message_string = 'simultaneous setting of alpha_lad /= 9999999.9 '// &
307	'combined with beta_lad /= 9999999.9 ' // &
308	'and lad_surface /= 0.0 is not possible, ' // &
309	'use either vertical gradients or the beta ' // &
310	'function for the construction of the leaf area '// &
311	'density profile'
312	CALL message( 'check_parameters', 'PA0120', 1, 2, 0, 6, 0 )
313	ENDIF
314
315	IF ( cloud_physics .AND. microphysics_seifert ) THEN
316	message_string = 'plant_canopy = .TRUE. requires cloud_scheme /=' // &
317	' seifert_beheng'
318	CALL message( 'check_parameters', 'PA0360', 1, 2, 0, 6, 0 )
319	ENDIF
320
321
322	END SUBROUTINE pcm_check_parameters
323
324
325	!------------------------------------------------------------------------------!
326	!
327	! Description:
328	! ------------
329	!> Subroutine defining 3D output variables
330	!------------------------------------------------------------------------------!
331	SUBROUTINE pcm_data_output_3d( av, variable, found, local_pf )
332
333	USE control_parameters, &
334	ONLY : nz_do3d
335
336	USE indices
337
338	USE kinds
339
340
341	IMPLICIT NONE
342
343	CHARACTER (LEN=*) :: variable !<
344
345	INTEGER(iwp) :: av !<
346	INTEGER(iwp) :: i !<
347	INTEGER(iwp) :: j !<
348	INTEGER(iwp) :: k !<
349
350	LOGICAL :: found !<
351
352	REAL(sp), DIMENSION(nxlg:nxrg,nysg:nyng,nzb:nz_do3d) :: local_pf !<
353
354
355	found = .TRUE.
356
357
358	SELECT CASE ( TRIM( variable ) )
359
360	CASE ( 'pcm_heatrate' )
361	CALL exchange_horiz( pc_heating_rate, nbgp )
362	IF ( av == 0 ) THEN
363	DO i = nxlg, nxrg
364	DO j = nysg, nyng
365	DO k = nzb_s_inner(j,i), nz_do3d
366	local_pf(i,j,k) = pc_heating_rate(k-nzb_s_inner(j,i),j,i)
367	ENDDO
368	ENDDO
369	ENDDO
370	ENDIF
371
372
373	CASE ( 'pcm_lad' )
374	IF ( av == 0 ) THEN
375	DO i = nxlg, nxrg
376	DO j = nysg, nyng
377	DO k = nzb_s_inner(j,i), nz_do3d
378	local_pf(i,j,k) = lad_s(k-nzb_s_inner(j,i),j,i)
379	ENDDO
380	ENDDO
381	ENDDO
382	ENDIF
383
384
385	CASE DEFAULT
386	found = .FALSE.
387
388	END SELECT
389
390
391	END SUBROUTINE pcm_data_output_3d
392
393	!------------------------------------------------------------------------------!
394	!
395	! Description:
396	! ------------
397	!> Subroutine defining appropriate grid for netcdf variables.
398	!> It is called from subroutine netcdf.
399	!------------------------------------------------------------------------------!
400	SUBROUTINE pcm_define_netcdf_grid( var, found, grid_x, grid_y, grid_z )
401
402	IMPLICIT NONE
403
404	CHARACTER (LEN=*), INTENT(IN) :: var !<
405	LOGICAL, INTENT(OUT) :: found !<
406	CHARACTER (LEN=*), INTENT(OUT) :: grid_x !<
407	CHARACTER (LEN=*), INTENT(OUT) :: grid_y !<
408	CHARACTER (LEN=*), INTENT(OUT) :: grid_z !<
409
410	found = .TRUE.
411
412	!
413	!-- Check for the grid
414	SELECT CASE ( TRIM( var ) )
415
416	CASE ( 'pcm_heatrate', 'pcm_lad' )
417	grid_x = 'x'
418	grid_y = 'y'
419	grid_z = 'zu'
420
421	CASE DEFAULT
422	found = .FALSE.
423	grid_x = 'none'
424	grid_y = 'none'
425	grid_z = 'none'
426	END SELECT
427
428	END SUBROUTINE pcm_define_netcdf_grid
429
430
431	!------------------------------------------------------------------------------!
432	! Description:
433	! ------------
434	!> Header output for plant canopy model
435	!------------------------------------------------------------------------------!
436	SUBROUTINE pcm_header ( io )
437
438	USE control_parameters, &
439	ONLY: dz, passive_scalar
440
441
442	IMPLICIT NONE
443
444	CHARACTER (LEN=10) :: coor_chr !<
445
446	CHARACTER (LEN=86) :: coordinates !<
447	CHARACTER (LEN=86) :: gradients !<
448	CHARACTER (LEN=86) :: leaf_area_density !<
449	CHARACTER (LEN=86) :: slices !<
450
451	INTEGER(iwp) :: i !<
452	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
453	INTEGER(iwp) :: k !<
454
455	REAL(wp) :: canopy_height !< canopy height (in m)
456
457	canopy_height = pch_index * dz
458
459	WRITE ( io, 1 ) canopy_mode, canopy_height, pch_index, &
460	canopy_drag_coeff
461	IF ( passive_scalar ) THEN
462	WRITE ( io, 2 ) leaf_scalar_exch_coeff, &
463	leaf_surface_conc
464	ENDIF
465
466	!
467	!-- Heat flux at the top of vegetation
468	WRITE ( io, 3 ) cthf
469
470	!
471	!-- Leaf area density profile, calculated either from given vertical
472	!-- gradients or from beta probability density function.
473	IF ( .NOT. calc_beta_lad_profile ) THEN
474
475	!-- Building output strings, starting with surface value
476	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
477	gradients = '------'
478	slices = ' 0'
479	coordinates = ' 0.0'
480	i = 1
481	DO WHILE ( i < 11 .AND. lad_vertical_gradient_level_ind(i) &
482	/= -9999 )
483
484	WRITE (coor_chr,'(F7.2)') lad(lad_vertical_gradient_level_ind(i))
485	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
486	TRIM( coor_chr )
487
488	WRITE (coor_chr,'(F7.2)') lad_vertical_gradient(i)
489	gradients = TRIM( gradients ) // ' ' // TRIM( coor_chr )
490
491	WRITE (coor_chr,'(I7)') lad_vertical_gradient_level_ind(i)
492	slices = TRIM( slices ) // ' ' // TRIM( coor_chr )
493
494	WRITE (coor_chr,'(F7.1)') lad_vertical_gradient_level(i)
495	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
496
497	i = i + 1
498	ENDDO
499
500	WRITE ( io, 4 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
501	TRIM( gradients ), TRIM( slices )
502
503	ELSE
504
505	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
506	coordinates = ' 0.0'
507
508	DO k = 1, pch_index
509
510	WRITE (coor_chr,'(F7.2)') lad(k)
511	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
512	TRIM( coor_chr )
513
514	WRITE (coor_chr,'(F7.1)') zu(k)
515	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
516
517	ENDDO
518
519	WRITE ( io, 5 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
520	alpha_lad, beta_lad, lai_beta
521
522	ENDIF
523
524	1 FORMAT (//' Vegetation canopy (drag) model:'/ &
525	' ------------------------------'// &
526	' Canopy mode: ', A / &
527	' Canopy height: ',F6.2,'m (',I4,' grid points)' / &
528	' Leaf drag coefficient: ',F6.2 /)
529	2 FORMAT (/ ' Scalar exchange coefficient: ',F6.2 / &
530	' Scalar concentration at leaf surfaces in kg/m**3: ',F6.2 /)
531	3 FORMAT (' Predefined constant heatflux at the top of the vegetation: ',F6.2, &
532	' K m/s')
533	4 FORMAT (/ ' Characteristic levels of the leaf area density:'// &
534	' Height: ',A,' m'/ &
535	' Leaf area density: ',A,' m2/m3'/ &
536	' Gradient: ',A,' m2/m4'/ &
537	' Gridpoint: ',A)
538	5 FORMAT (//' Characteristic levels of the leaf area density and coefficients:'&
539	// ' Height: ',A,' m'/ &
540	' Leaf area density: ',A,' m2/m3'/ &
541	' Coefficient alpha: ',F6.2 / &
542	' Coefficient beta: ',F6.2 / &
543	' Leaf area index: ',F6.2,' m2/m2' /)
544
545	END SUBROUTINE pcm_header
546
547
548	!------------------------------------------------------------------------------!
549	! Description:
550	! ------------
551	!> Initialization of the plant canopy model
552	!------------------------------------------------------------------------------!
553	SUBROUTINE pcm_init
554
555
556	USE control_parameters, &
557	ONLY: coupling_char, dz, humidity, io_blocks, io_group, &
558	message_string, ocean, passive_scalar, urban_surface
559
560	USE surface_mod, &
561	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
562
563	IMPLICIT NONE
564
565	CHARACTER(10) :: pct
566
567	INTEGER(iwp) :: i !< running index
568	INTEGER(iwp) :: ii !< index
569	INTEGER(iwp) :: j !< running index
570	INTEGER(iwp) :: k !< running index
571	INTEGER(iwp) :: m !< running index
572
573	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
574	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
575	REAL(wp) :: gradient !< gradient for lad-profile construction
576	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
577	REAL(wp) :: pcv(nzb:nzt+1) !<
578
579	!
580	!-- Allocate one-dimensional arrays for the computation of the
581	!-- leaf area density (lad) profile
582	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
583	lad = 0.0_wp
584	pre_lad = 0.0_wp
585
586	!
587	!-- Set flag that indicates that the lad-profile shall be calculated by using
588	!-- a beta probability density function
589	IF ( alpha_lad /= 9999999.9_wp .AND. beta_lad /= 9999999.9_wp ) THEN
590	calc_beta_lad_profile = .TRUE.
591	ENDIF
592
593
594	!
595	!-- Compute the profile of leaf area density used in the plant
596	!-- canopy model. The profile can either be constructed from
597	!-- prescribed vertical gradients of the leaf area density or by
598	!-- using a beta probability density function (see e.g. Markkanen et al.,
599	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
600	IF ( .NOT. calc_beta_lad_profile ) THEN
601
602	!
603	!-- Use vertical gradients for lad-profile construction
604	i = 1
605	gradient = 0.0_wp
606
607	IF ( .NOT. ocean ) THEN
608
609	lad(0) = lad_surface
610	lad_vertical_gradient_level_ind(1) = 0
611
612	DO k = 1, pch_index
613	IF ( i < 11 ) THEN
614	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
615	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
616	gradient = lad_vertical_gradient(i)
617	lad_vertical_gradient_level_ind(i) = k - 1
618	i = i + 1
619	ENDIF
620	ENDIF
621	IF ( gradient /= 0.0_wp ) THEN
622	IF ( k /= 1 ) THEN
623	lad(k) = lad(k-1) + dzu(k) * gradient
624	ELSE
625	lad(k) = lad_surface + dzu(k) * gradient
626	ENDIF
627	ELSE
628	lad(k) = lad(k-1)
629	ENDIF
630	ENDDO
631
632	ENDIF
633
634	!
635	!-- In case of no given leaf area density gradients, choose a vanishing
636	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
637	!-- file.
638	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
639	lad_vertical_gradient_level(1) = 0.0_wp
640	ENDIF
641
642	ELSE
643
644	!
645	!-- Use beta function for lad-profile construction
646	int_bpdf = 0.0_wp
647	canopy_height = pch_index * dz
648
649	DO k = 0, pch_index
650	int_bpdf = int_bpdf + &
651	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
652	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
653	beta_lad-1.0_wp ) ) &
654	* ( ( zw(k+1)-zw(k) ) / canopy_height ) )
655	ENDDO
656
657	!
658	!-- Preliminary lad profile (defined on w-grid)
659	DO k = 0, pch_index
660	pre_lad(k) = lai_beta * &
661	( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) ) &
662	* ( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
663	beta_lad-1.0_wp ) ) / int_bpdf &
664	) / canopy_height
665	ENDDO
666
667	!
668	!-- Final lad profile (defined on scalar-grid level, since most prognostic
669	!-- quantities are defined there, hence, less interpolation is required
670	!-- when calculating the canopy tendencies)
671	lad(0) = pre_lad(0)
672	DO k = 1, pch_index
673	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
674	ENDDO
675
676	ENDIF
677
678	!
679	!-- Allocate 3D-array for the leaf area density (lad_s).
680	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
681
682	!
683	!-- Initialize canopy parameters cdc (canopy drag coefficient),
684	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
685	!-- with the prescribed values
686	cdc = canopy_drag_coeff
687	lsec = leaf_scalar_exch_coeff
688	lsc = leaf_surface_conc
689
690	!
691	!-- Initialization of the canopy coverage in the model domain:
692	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
693	!-- fully covers the domain surface
694	SELECT CASE ( TRIM( canopy_mode ) )
695
696	CASE( 'block' )
697
698	DO i = nxlg, nxrg
699	DO j = nysg, nyng
700	lad_s(:,j,i) = lad(:)
701	ENDDO
702	ENDDO
703
704	CASE ( 'read_from_file_3d' )
705	!
706	!-- Initialize canopy parameters cdc (canopy drag coefficient),
707	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
708	!-- from file which contains complete 3D data (separate vertical profiles for
709	!-- each location).
710	CALL pcm_read_plant_canopy_3d
711
712	CASE DEFAULT
713	!
714	!-- The DEFAULT case is reached either if the parameter
715	!-- canopy mode contains a wrong character string or if the
716	!-- user has coded a special case in the user interface.
717	!-- There, the subroutine user_init_plant_canopy checks
718	!-- which of these two conditions applies.
719	CALL user_init_plant_canopy
720
721	END SELECT
722
723	!
724	!-- Initialization of the canopy heat source distribution due to heating
725	!-- of the canopy layers by incoming solar radiation, in case that a non-zero
726	!-- value is set for the canopy top heat flux (cthf), which equals the
727	!-- available net radiation at canopy top.
728	!-- The heat source distribution is calculated by a decaying exponential
729	!-- function of the downward cumulative leaf area index (cum_lai_hf),
730	!-- assuming that the foliage inside the plant canopy is heated by solar
731	!-- radiation penetrating the canopy layers according to the distribution
732	!-- of net radiation as suggested by Brown & Covey (1966; Agric. Meteorol. 3,
733	!-- 73â96). This approach has been applied e.g. by Shaw & Schumann (1992;
734	!-- Bound.-Layer Meteorol. 61, 47â64).
735	!-- When using the urban surface model (USM), canopy heating (pc_heating_rate)
736	!-- by radiation is calculated in the USM.
737	IF ( cthf /= 0.0_wp .AND. .NOT. urban_surface) THEN
738
739	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
740	pc_heating_rate(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
741	!
742	!-- Piecewise calculation of the cumulative leaf area index by vertical
743	!-- integration of the leaf area density
744	cum_lai_hf(:,:,:) = 0.0_wp
745	DO i = nxlg, nxrg
746	DO j = nysg, nyng
747	DO k = pch_index-1, 0, -1
748	IF ( k == pch_index-1 ) THEN
749	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
750	( 0.5_wp * lad_s(k+1,j,i) * &
751	( zw(k+1) - zu(k+1) ) ) + &
752	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
753	lad_s(k,j,i) ) + &
754	lad_s(k+1,j,i) ) * &
755	( zu(k+1) - zw(k) ) )
756	ELSE
757	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
758	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
759	lad_s(k+1,j,i) ) + &
760	lad_s(k+1,j,i) ) * &
761	( zw(k+1) - zu(k+1) ) ) + &
762	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
763	lad_s(k,j,i) ) + &
764	lad_s(k+1,j,i) ) * &
765	( zu(k+1) - zw(k) ) )
766	ENDIF
767	ENDDO
768	ENDDO
769	ENDDO
770
771	!
772	!-- In areas with canopy the surface value of the canopy heat
773	!-- flux distribution overrides the surface heat flux (shf)
774	!-- Start with default surface type
775	DO m = 1, surf_def_h(0)%ns
776	k = surf_def_h(0)%k(m)
777	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
778	surf_def_h(0)%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
779	ENDDO
780	!
781	!-- Natural surfaces
782	DO m = 1, surf_lsm_h%ns
783	k = surf_lsm_h%k(m)
784	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
785	surf_lsm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
786	ENDDO
787	!
788	!-- Urban surfaces
789	DO m = 1, surf_usm_h%ns
790	k = surf_usm_h%k(m)
791	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) &
792	surf_usm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
793	ENDDO
794	!
795	!
796	!-- Calculation of the heating rate (K/s) within the different layers of
797	!-- the plant canopy. Calculation is only necessary in areas covered with
798	!-- canopy.
799	!-- Within the different canopy layers the plant-canopy heating
800	!-- rate (pc_heating_rate) is calculated as the vertical
801	!-- divergence of the canopy heat fluxes at the top and bottom
802	!-- of the respective layer
803	DO i = nxlg, nxrg
804	DO j = nysg, nyng
805	DO k = 1, pch_index
806	IF ( cum_lai_hf(0,j,i) /= 0.0_wp ) THEN
807	pc_heating_rate(k,j,i) = cthf * &
808	( exp(-ext_coef*cum_lai_hf(k,j,i)) - &
809	exp(-ext_coef*cum_lai_hf(k-1,j,i) ) ) / dzw(k)
810	ENDIF
811	ENDDO
812	ENDDO
813	ENDDO
814
815	ENDIF
816
817
818
819	END SUBROUTINE pcm_init
820
821
822	!------------------------------------------------------------------------------!
823	! Description:
824	! ------------
825	!> Parin for &canopy_par for plant canopy model
826	!------------------------------------------------------------------------------!
827	SUBROUTINE pcm_parin
828
829
830	IMPLICIT NONE
831
832	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
833
834	NAMELIST /canopy_par/ alpha_lad, beta_lad, canopy_drag_coeff, &
835	canopy_mode, cthf, &
836	lad_surface, &
837	lad_vertical_gradient, &
838	lad_vertical_gradient_level, &
839	lai_beta, &
840	leaf_scalar_exch_coeff, &
841	leaf_surface_conc, pch_index
842
843	line = ' '
844
845	!
846	!-- Try to find radiation model package
847	REWIND ( 11 )
848	line = ' '
849	DO WHILE ( INDEX( line, '&canopy_par' ) == 0 )
850	READ ( 11, '(A)', END=10 ) line
851	ENDDO
852	BACKSPACE ( 11 )
853
854	!
855	!-- Read user-defined namelist
856	READ ( 11, canopy_par )
857
858	!
859	!-- Set flag that indicates that the radiation model is switched on
860	plant_canopy = .TRUE.
861
862	10 CONTINUE
863
864
865	END SUBROUTINE pcm_parin
866
867
868
869	!------------------------------------------------------------------------------!
870	! Description:
871	! ------------
872	!
873	!> Loads 3D plant canopy data from file. File format is as follows:
874	!>
875	!> num_levels
876	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
877	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
878	!> dtype,x,y,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
879	!> ...
880	!>
881	!> i.e. first line determines number of levels and further lines represent plant
882	!> canopy data, one line per column and variable. In each data line,
883	!> dtype represents variable to be set:
884	!>
885	!> dtype=1: leaf area density (lad_s)
886	!> dtype=2....n: some additional plant canopy input data quantity
887	!>
888	!> Zeros are added automatically above num_levels until top of domain. Any
889	!> non-specified (x,y) columns have zero values as default.
890	!------------------------------------------------------------------------------!
891	SUBROUTINE pcm_read_plant_canopy_3d
892
893	USE control_parameters, &
894	ONLY: message_string, passive_scalar
895
896	USE indices, &
897	ONLY: nbgp
898
899	IMPLICIT NONE
900
901	INTEGER(iwp) :: dtype !< type of input data (1=lad)
902	INTEGER(iwp) :: i, j !< running index
903	INTEGER(iwp) :: nzp !< number of vertical layers of plant canopy
904	INTEGER(iwp) :: nzpltop !<
905	INTEGER(iwp) :: nzpl !<
906
907	REAL(wp), DIMENSION(:), ALLOCATABLE :: col !< vertical column of input data
908
909	!
910	!-- Initialize lad_s array
911	lad_s = 0.0_wp
912
913	!
914	!-- Open and read plant canopy input data
915	OPEN(152, file='PLANT_CANOPY_DATA_3D', access='SEQUENTIAL', &
916	action='READ', status='OLD', form='FORMATTED', err=515)
917	READ(152, *, err=516, end=517) nzp !< read first line = number of vertical layers
918
919	ALLOCATE(col(0:nzp-1))
920
921	DO
922	READ(152, *, err=516, end=517) dtype, i, j, col(:)
923	IF ( i < nxlg .or. i > nxrg .or. j < nysg .or. j > nyng ) CYCLE
924
925	SELECT CASE (dtype)
926	CASE( 1 ) !< leaf area density
927	!
928	!-- This is just the pure canopy layer assumed to be grounded to
929	!-- a flat domain surface. At locations where plant canopy sits
930	!-- on top of any kind of topography, the vertical plant column
931	!-- must be "lifted", which is done in SUBROUTINE pcm_tendency.
932	lad_s(0:nzp-1, j, i) = col(0:nzp-1)
933
934	CASE DEFAULT
935	write(message_string, '(a,i2,a)') &
936	'Unknown record type in file PLANT_CANOPY_DATA_3D: "', dtype, '"'
937	CALL message( 'pcm_read_plant_canopy_3d', 'PA0530', 1, 2, 0, 6, 0 )
938	END SELECT
939	ENDDO
940
941	515 message_string = 'error opening file PLANT_CANOPY_DATA_3D'
942	CALL message( 'pcm_read_plant_canopy_3d', 'PA0531', 1, 2, 0, 6, 0 )
943
944	516 message_string = 'error reading file PLANT_CANOPY_DATA_3D'
945	CALL message( 'pcm_read_plant_canopy_3d', 'PA0532', 1, 2, 0, 6, 0 )
946
947	517 CLOSE(152)
948	DEALLOCATE(col)
949
950	CALL exchange_horiz( lad_s, nbgp )
951
952	END SUBROUTINE pcm_read_plant_canopy_3d
953
954
955
956	!------------------------------------------------------------------------------!
957	! Description:
958	! ------------
959	!> Calculation of the tendency terms, accounting for the effect of the plant
960	!> canopy on momentum and scalar quantities.
961	!>
962	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
963	!> (defined on scalar grid), as initialized in subroutine pcm_init.
964	!> The lad on the w-grid is vertically interpolated from the surrounding
965	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
966	!> k = pch_index. Here, the lad is zero.
967	!>
968	!> The canopy drag must be limited (previously accounted for by calculation of
969	!> a limiting canopy timestep for the determination of the maximum LES timestep
970	!> in subroutine timestep), since it is physically impossible that the canopy
971	!> drag alone can locally change the sign of a velocity component. This
972	!> limitation is realized by calculating preliminary tendencies and velocities.
973	!> It is subsequently checked if the preliminary new velocity has a different
974	!> sign than the current velocity. If so, the tendency is limited in a way that
975	!> the velocity can at maximum be reduced to zero by the canopy drag.
976	!>
977	!>
978	!> Call for all grid points
979	!------------------------------------------------------------------------------!
980	SUBROUTINE pcm_tendency( component )
981
982
983	USE control_parameters, &
984	ONLY: dt_3d, message_string
985
986	USE kinds
987
988	IMPLICIT NONE
989
990	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
991	INTEGER(iwp) :: i !< running index
992	INTEGER(iwp) :: j !< running index
993	INTEGER(iwp) :: k !< running index
994	INTEGER(iwp) :: k_wall !< vertical index of topography top
995	INTEGER(iwp) :: kk !< running index for flat lad arrays
996
997	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
998	REAL(wp) :: lad_local !< local lad value
999	REAL(wp) :: pre_tend !< preliminary tendency
1000	REAL(wp) :: pre_u !< preliminary u-value
1001	REAL(wp) :: pre_v !< preliminary v-value
1002	REAL(wp) :: pre_w !< preliminary w-value
1003
1004
1005	ddt_3d = 1.0_wp / dt_3d
1006
1007	!
1008	!-- Compute drag for the three velocity components and the SGS-TKE:
1009	SELECT CASE ( component )
1010
1011	!
1012	!-- u-component
1013	CASE ( 1 )
1014	DO i = nxlu, nxr
1015	DO j = nys, nyn
1016	!
1017	!-- Determine topography-top index on u-grid
1018	k_wall = MAXLOC( &
1019	MERGE( 1, 0, &
1020	BTEST( wall_flags_0(nzb:nzb_max,j,i), 14 ) &
1021	), DIM = 1 &
1022	) - 1
1023	DO k = k_wall+1, k_wall+pch_index
1024
1025	kk = k - k_wall !- lad arrays are defined flat
1026	!
1027	!-- In order to create sharp boundaries of the plant canopy,
1028	!-- the lad on the u-grid at index (k,j,i) is equal to
1029	!-- lad_s(k,j,i), rather than being interpolated from the
1030	!-- surrounding lad_s, because this would yield smaller lad
1031	!-- at the canopy boundaries than inside of the canopy.
1032	!-- For the same reason, the lad at the rightmost(i+1)canopy
1033	!-- boundary on the u-grid equals lad_s(k,j,i).
1034	lad_local = lad_s(kk,j,i)
1035	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp )&
1036	THEN
1037	lad_local = lad_s(kk,j,i-1)
1038	ENDIF
1039
1040	pre_tend = 0.0_wp
1041	pre_u = 0.0_wp
1042	!
1043	!-- Calculate preliminary value (pre_tend) of the tendency
1044	pre_tend = - cdc * &
1045	lad_local * &
1046	SQRT( u(k,j,i)**2 + &
1047	( 0.25_wp * ( v(k,j,i-1) + &
1048	v(k,j,i) + &
1049	v(k,j+1,i) + &
1050	v(k,j+1,i-1) ) &
1051	)**2 + &
1052	( 0.25_wp * ( w(k-1,j,i-1) + &
1053	w(k-1,j,i) + &
1054	w(k,j,i-1) + &
1055	w(k,j,i) ) &
1056	)**2 &
1057	) * &
1058	u(k,j,i)
1059
1060	!
1061	!-- Calculate preliminary new velocity, based on pre_tend
1062	pre_u = u(k,j,i) + dt_3d * pre_tend
1063	!
1064	!-- Compare sign of old velocity and new preliminary velocity,
1065	!-- and in case the signs are different, limit the tendency
1066	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1067	pre_tend = - u(k,j,i) * ddt_3d
1068	ELSE
1069	pre_tend = pre_tend
1070	ENDIF
1071	!
1072	!-- Calculate final tendency
1073	tend(k,j,i) = tend(k,j,i) + pre_tend
1074
1075	ENDDO
1076	ENDDO
1077	ENDDO
1078
1079	!
1080	!-- v-component
1081	CASE ( 2 )
1082	DO i = nxl, nxr
1083	DO j = nysv, nyn
1084	!
1085	!-- Determine topography-top index on v-grid
1086	k_wall = MAXLOC( &
1087	MERGE( 1, 0, &
1088	BTEST( wall_flags_0(nzb:nzb_max,j,i), 16 ) &
1089	), DIM = 1 &
1090	) - 1
1091	DO k = k_wall+1, k_wall+pch_index
1092
1093	kk = k - k_wall !- lad arrays are defined flat
1094	!
1095	!-- In order to create sharp boundaries of the plant canopy,
1096	!-- the lad on the v-grid at index (k,j,i) is equal to
1097	!-- lad_s(k,j,i), rather than being interpolated from the
1098	!-- surrounding lad_s, because this would yield smaller lad
1099	!-- at the canopy boundaries than inside of the canopy.
1100	!-- For the same reason, the lad at the northmost(j+1) canopy
1101	!-- boundary on the v-grid equals lad_s(k,j,i).
1102	lad_local = lad_s(kk,j,i)
1103	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp )&
1104	THEN
1105	lad_local = lad_s(kk,j-1,i)
1106	ENDIF
1107
1108	pre_tend = 0.0_wp
1109	pre_v = 0.0_wp
1110	!
1111	!-- Calculate preliminary value (pre_tend) of the tendency
1112	pre_tend = - cdc * &
1113	lad_local * &
1114	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1115	u(k,j-1,i+1) + &
1116	u(k,j,i) + &
1117	u(k,j,i+1) ) &
1118	)**2 + &
1119	v(k,j,i)**2 + &
1120	( 0.25_wp * ( w(k-1,j-1,i) + &
1121	w(k-1,j,i) + &
1122	w(k,j-1,i) + &
1123	w(k,j,i) ) &
1124	)**2 &
1125	) * &
1126	v(k,j,i)
1127
1128	!
1129	!-- Calculate preliminary new velocity, based on pre_tend
1130	pre_v = v(k,j,i) + dt_3d * pre_tend
1131	!
1132	!-- Compare sign of old velocity and new preliminary velocity,
1133	!-- and in case the signs are different, limit the tendency
1134	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1135	pre_tend = - v(k,j,i) * ddt_3d
1136	ELSE
1137	pre_tend = pre_tend
1138	ENDIF
1139	!
1140	!-- Calculate final tendency
1141	tend(k,j,i) = tend(k,j,i) + pre_tend
1142
1143	ENDDO
1144	ENDDO
1145	ENDDO
1146
1147	!
1148	!-- w-component
1149	CASE ( 3 )
1150	DO i = nxl, nxr
1151	DO j = nys, nyn
1152	!
1153	!-- Determine topography-top index on w-grid
1154	k_wall = MAXLOC( &
1155	MERGE( 1, 0, &
1156	BTEST( wall_flags_0(nzb:nzb_max,j,i), 18 ) &
1157	), DIM = 1 &
1158	) - 1
1159	DO k = k_wall+1, k_wall+pch_index-1
1160
1161	kk = k - k_wall !- lad arrays are defined flat
1162
1163	pre_tend = 0.0_wp
1164	pre_w = 0.0_wp
1165	!
1166	!-- Calculate preliminary value (pre_tend) of the tendency
1167	pre_tend = - cdc * &
1168	(0.5_wp * &
1169	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1170	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1171	u(k,j,i+1) + &
1172	u(k+1,j,i) + &
1173	u(k+1,j,i+1) ) &
1174	)**2 + &
1175	( 0.25_wp * ( v(k,j,i) + &
1176	v(k,j+1,i) + &
1177	v(k+1,j,i) + &
1178	v(k+1,j+1,i) ) &
1179	)**2 + &
1180	w(k,j,i)**2 &
1181	) * &
1182	w(k,j,i)
1183	!
1184	!-- Calculate preliminary new velocity, based on pre_tend
1185	pre_w = w(k,j,i) + dt_3d * pre_tend
1186	!
1187	!-- Compare sign of old velocity and new preliminary velocity,
1188	!-- and in case the signs are different, limit the tendency
1189	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1190	pre_tend = - w(k,j,i) * ddt_3d
1191	ELSE
1192	pre_tend = pre_tend
1193	ENDIF
1194	!
1195	!-- Calculate final tendency
1196	tend(k,j,i) = tend(k,j,i) + pre_tend
1197
1198	ENDDO
1199	ENDDO
1200	ENDDO
1201
1202	!
1203	!-- potential temperature
1204	CASE ( 4 )
1205	DO i = nxl, nxr
1206	DO j = nys, nyn
1207	!
1208	!-- Determine topography-top index on scalar-grid
1209	k_wall = MAXLOC( &
1210	MERGE( 1, 0, &
1211	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1212	), DIM = 1 &
1213	) - 1
1214	DO k = k_wall+1, k_wall+pch_index
1215
1216	kk = k - k_wall !- lad arrays are defined flat
1217	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1218	ENDDO
1219	ENDDO
1220	ENDDO
1221
1222	!
1223	!-- humidity
1224	CASE ( 5 )
1225	DO i = nxl, nxr
1226	DO j = nys, nyn
1227	!
1228	!-- Determine topography-top index on scalar-grid
1229	k_wall = MAXLOC( &
1230	MERGE( 1, 0, &
1231	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1232	), DIM = 1 &
1233	) - 1
1234	DO k = k_wall+1, k_wall+pch_index
1235
1236	kk = k - k_wall !- lad arrays are defined flat
1237	tend(k,j,i) = tend(k,j,i) - &
1238	lsec * &
1239	lad_s(kk,j,i) * &
1240	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1241	u(k,j,i+1) ) &
1242	)**2 + &
1243	( 0.5_wp * ( v(k,j,i) + &
1244	v(k,j+1,i) ) &
1245	)**2 + &
1246	( 0.5_wp * ( w(k-1,j,i) + &
1247	w(k,j,i) ) &
1248	)**2 &
1249	) * &
1250	( q(k,j,i) - lsc )
1251	ENDDO
1252	ENDDO
1253	ENDDO
1254
1255	!
1256	!-- sgs-tke
1257	CASE ( 6 )
1258	DO i = nxl, nxr
1259	DO j = nys, nyn
1260	!
1261	!-- Determine topography-top index on scalar-grid
1262	k_wall = MAXLOC( &
1263	MERGE( 1, 0, &
1264	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1265	), DIM = 1 &
1266	) - 1
1267	DO k = k_wall+1, k_wall+pch_index
1268
1269	kk = k - k_wall !- lad arrays are defined flat
1270	tend(k,j,i) = tend(k,j,i) - &
1271	2.0_wp * cdc * &
1272	lad_s(kk,j,i) * &
1273	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1274	u(k,j,i+1) ) &
1275	)**2 + &
1276	( 0.5_wp * ( v(k,j,i) + &
1277	v(k,j+1,i) ) &
1278	)**2 + &
1279	( 0.5_wp * ( w(k,j,i) + &
1280	w(k+1,j,i) ) &
1281	)**2 &
1282	) * &
1283	e(k,j,i)
1284	ENDDO
1285	ENDDO
1286	ENDDO
1287	!
1288	!-- scalar concentration
1289	CASE ( 7 )
1290	DO i = nxl, nxr
1291	DO j = nys, nyn
1292	!
1293	!-- Determine topography-top index on scalar-grid
1294	k_wall = MAXLOC( &
1295	MERGE( 1, 0, &
1296	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1297	), DIM = 1 &
1298	) - 1
1299	DO k = k_wall+1, k_wall+pch_index
1300
1301	kk = k - k_wall !- lad arrays are defined flat
1302	tend(k,j,i) = tend(k,j,i) - &
1303	lsec * &
1304	lad_s(kk,j,i) * &
1305	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1306	u(k,j,i+1) ) &
1307	)**2 + &
1308	( 0.5_wp * ( v(k,j,i) + &
1309	v(k,j+1,i) ) &
1310	)**2 + &
1311	( 0.5_wp * ( w(k-1,j,i) + &
1312	w(k,j,i) ) &
1313	)**2 &
1314	) * &
1315	( s(k,j,i) - lsc )
1316	ENDDO
1317	ENDDO
1318	ENDDO
1319
1320
1321
1322	CASE DEFAULT
1323
1324	WRITE( message_string, * ) 'wrong component: ', component
1325	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1326
1327	END SELECT
1328
1329	END SUBROUTINE pcm_tendency
1330
1331
1332	!------------------------------------------------------------------------------!
1333	! Description:
1334	! ------------
1335	!> Calculation of the tendency terms, accounting for the effect of the plant
1336	!> canopy on momentum and scalar quantities.
1337	!>
1338	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
1339	!> (defined on scalar grid), as initialized in subroutine pcm_init.
1340	!> The lad on the w-grid is vertically interpolated from the surrounding
1341	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
1342	!> k = pch_index. Here, the lad is zero.
1343	!>
1344	!> The canopy drag must be limited (previously accounted for by calculation of
1345	!> a limiting canopy timestep for the determination of the maximum LES timestep
1346	!> in subroutine timestep), since it is physically impossible that the canopy
1347	!> drag alone can locally change the sign of a velocity component. This
1348	!> limitation is realized by calculating preliminary tendencies and velocities.
1349	!> It is subsequently checked if the preliminary new velocity has a different
1350	!> sign than the current velocity. If so, the tendency is limited in a way that
1351	!> the velocity can at maximum be reduced to zero by the canopy drag.
1352	!>
1353	!>
1354	!> Call for grid point i,j
1355	!------------------------------------------------------------------------------!
1356	SUBROUTINE pcm_tendency_ij( i, j, component )
1357
1358
1359	USE control_parameters, &
1360	ONLY: dt_3d, message_string
1361
1362	USE kinds
1363
1364	IMPLICIT NONE
1365
1366	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
1367	INTEGER(iwp) :: i !< running index
1368	INTEGER(iwp) :: j !< running index
1369	INTEGER(iwp) :: k !< running index
1370	INTEGER(iwp) :: k_wall !< vertical index of topography top
1371	INTEGER(iwp) :: kk !< running index for flat lad arrays
1372
1373	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1374	REAL(wp) :: lad_local !< local lad value
1375	REAL(wp) :: pre_tend !< preliminary tendency
1376	REAL(wp) :: pre_u !< preliminary u-value
1377	REAL(wp) :: pre_v !< preliminary v-value
1378	REAL(wp) :: pre_w !< preliminary w-value
1379
1380
1381	ddt_3d = 1.0_wp / dt_3d
1382
1383	!
1384	!-- Compute drag for the three velocity components and the SGS-TKE
1385	SELECT CASE ( component )
1386
1387	!
1388	!-- u-component
1389	CASE ( 1 )
1390	!
1391	!-- Determine topography-top index on u-grid
1392	k_wall = MAXLOC( &
1393	MERGE( 1, 0, &
1394	BTEST( wall_flags_0(nzb:nzb_max,j,i), 14 ) &
1395	), DIM = 1 &
1396	) - 1
1397	DO k = k_wall+1, k_wall+pch_index
1398
1399	kk = k - k_wall !- lad arrays are defined flat
1400	!
1401	!-- In order to create sharp boundaries of the plant canopy,
1402	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
1403	!-- rather than being interpolated from the surrounding lad_s,
1404	!-- because this would yield smaller lad at the canopy boundaries
1405	!-- than inside of the canopy.
1406	!-- For the same reason, the lad at the rightmost(i+1)canopy
1407	!-- boundary on the u-grid equals lad_s(k,j,i).
1408	lad_local = lad_s(kk,j,i)
1409	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp ) THEN
1410	lad_local = lad_s(kk,j,i-1)
1411	ENDIF
1412
1413	pre_tend = 0.0_wp
1414	pre_u = 0.0_wp
1415	!
1416	!-- Calculate preliminary value (pre_tend) of the tendency
1417	pre_tend = - cdc * &
1418	lad_local * &
1419	SQRT( u(k,j,i)**2 + &
1420	( 0.25_wp * ( v(k,j,i-1) + &
1421	v(k,j,i) + &
1422	v(k,j+1,i) + &
1423	v(k,j+1,i-1) ) &
1424	)**2 + &
1425	( 0.25_wp * ( w(k-1,j,i-1) + &
1426	w(k-1,j,i) + &
1427	w(k,j,i-1) + &
1428	w(k,j,i) ) &
1429	)**2 &
1430	) * &
1431	u(k,j,i)
1432
1433	!
1434	!-- Calculate preliminary new velocity, based on pre_tend
1435	pre_u = u(k,j,i) + dt_3d * pre_tend
1436	!
1437	!-- Compare sign of old velocity and new preliminary velocity,
1438	!-- and in case the signs are different, limit the tendency
1439	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1440	pre_tend = - u(k,j,i) * ddt_3d
1441	ELSE
1442	pre_tend = pre_tend
1443	ENDIF
1444	!
1445	!-- Calculate final tendency
1446	tend(k,j,i) = tend(k,j,i) + pre_tend
1447	ENDDO
1448
1449
1450	!
1451	!-- v-component
1452	CASE ( 2 )
1453	!
1454	!-- Determine topography-top index on v-grid
1455	k_wall = MAXLOC( &
1456	MERGE( 1, 0, &
1457	BTEST( wall_flags_0(nzb:nzb_max,j,i), 16 ) &
1458	), DIM = 1 &
1459	) - 1
1460	DO k = k_wall+1, k_wall+pch_index
1461
1462	kk = k - k_wall !- lad arrays are defined flat
1463	!
1464	!-- In order to create sharp boundaries of the plant canopy,
1465	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
1466	!-- rather than being interpolated from the surrounding lad_s,
1467	!-- because this would yield smaller lad at the canopy boundaries
1468	!-- than inside of the canopy.
1469	!-- For the same reason, the lad at the northmost(j+1)canopy
1470	!-- boundary on the v-grid equals lad_s(k,j,i).
1471	lad_local = lad_s(kk,j,i)
1472	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp ) THEN
1473	lad_local = lad_s(kk,j-1,i)
1474	ENDIF
1475
1476	pre_tend = 0.0_wp
1477	pre_v = 0.0_wp
1478	!
1479	!-- Calculate preliminary value (pre_tend) of the tendency
1480	pre_tend = - cdc * &
1481	lad_local * &
1482	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1483	u(k,j-1,i+1) + &
1484	u(k,j,i) + &
1485	u(k,j,i+1) ) &
1486	)**2 + &
1487	v(k,j,i)**2 + &
1488	( 0.25_wp * ( w(k-1,j-1,i) + &
1489	w(k-1,j,i) + &
1490	w(k,j-1,i) + &
1491	w(k,j,i) ) &
1492	)**2 &
1493	) * &
1494	v(k,j,i)
1495
1496	!
1497	!-- Calculate preliminary new velocity, based on pre_tend
1498	pre_v = v(k,j,i) + dt_3d * pre_tend
1499	!
1500	!-- Compare sign of old velocity and new preliminary velocity,
1501	!-- and in case the signs are different, limit the tendency
1502	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1503	pre_tend = - v(k,j,i) * ddt_3d
1504	ELSE
1505	pre_tend = pre_tend
1506	ENDIF
1507	!
1508	!-- Calculate final tendency
1509	tend(k,j,i) = tend(k,j,i) + pre_tend
1510	ENDDO
1511
1512
1513	!
1514	!-- w-component
1515	CASE ( 3 )
1516	!
1517	!-- Determine topography-top index on w-grid
1518	k_wall = MAXLOC( &
1519	MERGE( 1, 0, &
1520	BTEST( wall_flags_0(nzb:nzb_max,j,i), 18 ) &
1521	), DIM = 1 &
1522	) - 1
1523	DO k = k_wall+1, k_wall+pch_index-1
1524
1525	kk = k - k_wall !- lad arrays are defined flat
1526
1527	pre_tend = 0.0_wp
1528	pre_w = 0.0_wp
1529	!
1530	!-- Calculate preliminary value (pre_tend) of the tendency
1531	pre_tend = - cdc * &
1532	(0.5_wp * &
1533	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1534	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1535	u(k,j,i+1) + &
1536	u(k+1,j,i) + &
1537	u(k+1,j,i+1) ) &
1538	)**2 + &
1539	( 0.25_wp * ( v(k,j,i) + &
1540	v(k,j+1,i) + &
1541	v(k+1,j,i) + &
1542	v(k+1,j+1,i) ) &
1543	)**2 + &
1544	w(k,j,i)**2 &
1545	) * &
1546	w(k,j,i)
1547	!
1548	!-- Calculate preliminary new velocity, based on pre_tend
1549	pre_w = w(k,j,i) + dt_3d * pre_tend
1550	!
1551	!-- Compare sign of old velocity and new preliminary velocity,
1552	!-- and in case the signs are different, limit the tendency
1553	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1554	pre_tend = - w(k,j,i) * ddt_3d
1555	ELSE
1556	pre_tend = pre_tend
1557	ENDIF
1558	!
1559	!-- Calculate final tendency
1560	tend(k,j,i) = tend(k,j,i) + pre_tend
1561	ENDDO
1562
1563	!
1564	!-- potential temperature
1565	CASE ( 4 )
1566	!
1567	!-- Determine topography-top index on scalar grid
1568	k_wall = MAXLOC( &
1569	MERGE( 1, 0, &
1570	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1571	), DIM = 1 &
1572	) - 1
1573	DO k = k_wall+1, k_wall+pch_index
1574	kk = k - k_wall !- lad arrays are defined flat
1575	tend(k,j,i) = tend(k,j,i) + pc_heating_rate(kk,j,i)
1576	ENDDO
1577
1578
1579	!
1580	!-- humidity
1581	CASE ( 5 )
1582	!
1583	!-- Determine topography-top index on scalar grid
1584	k_wall = MAXLOC( &
1585	MERGE( 1, 0, &
1586	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1587	), DIM = 1 &
1588	) - 1
1589	DO k = k_wall+1, k_wall+pch_index
1590
1591	kk = k - k_wall
1592	tend(k,j,i) = tend(k,j,i) - &
1593	lsec * &
1594	lad_s(kk,j,i) * &
1595	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1596	u(k,j,i+1) ) &
1597	)**2 + &
1598	( 0.5_wp * ( v(k,j,i) + &
1599	v(k,j+1,i) ) &
1600	)**2 + &
1601	( 0.5_wp * ( w(k-1,j,i) + &
1602	w(k,j,i) ) &
1603	)**2 &
1604	) * &
1605	( q(k,j,i) - lsc )
1606	ENDDO
1607
1608	!
1609	!-- sgs-tke
1610	CASE ( 6 )
1611	!
1612	!-- Determine topography-top index on scalar grid
1613	k_wall = MAXLOC( &
1614	MERGE( 1, 0, &
1615	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1616	), DIM = 1 &
1617	) - 1
1618	DO k = k_wall+1, k_wall+pch_index
1619
1620	kk = k - k_wall
1621	tend(k,j,i) = tend(k,j,i) - &
1622	2.0_wp * cdc * &
1623	lad_s(kk,j,i) * &
1624	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1625	u(k,j,i+1) ) &
1626	)**2 + &
1627	( 0.5_wp * ( v(k,j,i) + &
1628	v(k,j+1,i) ) &
1629	)**2 + &
1630	( 0.5_wp * ( w(k,j,i) + &
1631	w(k+1,j,i) ) &
1632	)**2 &
1633	) * &
1634	e(k,j,i)
1635	ENDDO
1636
1637	!
1638	!-- scalar concentration
1639	CASE ( 7 )
1640	!
1641	!-- Determine topography-top index on scalar grid
1642	k_wall = MAXLOC( &
1643	MERGE( 1, 0, &
1644	BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) &
1645	), DIM = 1 &
1646	) - 1
1647	DO k = k_wall+1, k_wall+pch_index
1648
1649	kk = k - k_wall
1650	tend(k,j,i) = tend(k,j,i) - &
1651	lsec * &
1652	lad_s(kk,j,i) * &
1653	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1654	u(k,j,i+1) ) &
1655	)**2 + &
1656	( 0.5_wp * ( v(k,j,i) + &
1657	v(k,j+1,i) ) &
1658	)**2 + &
1659	( 0.5_wp * ( w(k-1,j,i) + &
1660	w(k,j,i) ) &
1661	)**2 &
1662	) * &
1663	( s(k,j,i) - lsc )
1664	ENDDO
1665
1666	CASE DEFAULT
1667
1668	WRITE( message_string, * ) 'wrong component: ', component
1669	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1670
1671	END SELECT
1672
1673	END SUBROUTINE pcm_tendency_ij
1674
1675
1676
1677	END MODULE plant_canopy_model_mod

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