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source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 1964

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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 terms
6	! of the GNU General Public License as published by the Free Software Foundation,
7	! either version 3 of the License, or (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with
14	! PALM. If not, see <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2016 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------!
18	!
19	! Current revisions:
20	! -----------------
21	!
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: plant_canopy_model_mod.f90 1961 2016-07-12 16:37:58Z hellstea $
26	!
27	! 1960 2016-07-12 16:34:24Z suehring
28	! Separate humidity and passive scalar
29	!
30	! 1953 2016-06-21 09:28:42Z suehring
31	! Bugfix, lad_s and lad must be public
32	!
33	! 1826 2016-04-07 12:01:39Z maronga
34	! Further modularization
35	!
36	! 1721 2015-11-16 12:56:48Z raasch
37	! bugfixes: shf is reduced in areas covered with canopy only,
38	! canopy is set on top of topography
39	!
40	! 1682 2015-10-07 23:56:08Z knoop
41	! Code annotations made doxygen readable
42	!
43	! 1484 2014-10-21 10:53:05Z kanani
44	! Changes due to new module structure of the plant canopy model:
45	! module plant_canopy_model_mod now contains a subroutine for the
46	! initialization of the canopy model (pcm_init),
47	! limitation of the canopy drag (previously accounted for by calculation of
48	! a limiting canopy timestep for the determination of the maximum LES timestep
49	! in subroutine timestep) is now realized by the calculation of pre-tendencies
50	! and preliminary velocities in subroutine pcm_tendency,
51	! some redundant MPI communication removed in subroutine pcm_init
52	! (was previously in init_3d_model),
53	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
54	! respective grid is now provided only by lad_s (e.g. in the calculation of
55	! the tendency terms or of cum_lai_hf),
56	! drag_coefficient, lai, leaf_surface_concentration,
57	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
58	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
59	! respectively,
60	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
61	! USE-statements and ONLY-lists modified accordingly
62	!
63	! 1340 2014-03-25 19:45:13Z kanani
64	! REAL constants defined as wp-kind
65	!
66	! 1320 2014-03-20 08:40:49Z raasch
67	! ONLY-attribute added to USE-statements,
68	! kind-parameters added to all INTEGER and REAL declaration statements,
69	! kinds are defined in new module kinds,
70	! old module precision_kind is removed,
71	! revision history before 2012 removed,
72	! comment fields (!:) to be used for variable explanations added to
73	! all variable declaration statements
74	!
75	! 1036 2012-10-22 13:43:42Z raasch
76	! code put under GPL (PALM 3.9)
77	!
78	! 138 2007-11-28 10:03:58Z letzel
79	! Initial revision
80	!
81	! Description:
82	! ------------
83	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
84	!> profile (subroutine pcm_init).
85	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
86	!> due to canopy elements (subroutine pcm_tendency).
87	!------------------------------------------------------------------------------!
88	MODULE plant_canopy_model_mod
89
90	USE arrays_3d, &
91	ONLY: dzu, dzw, e, q, s, shf, tend, u, v, w, zu, zw
92
93	USE indices, &
94	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
95	nz, nzb, nzb_s_inner, nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt
96
97	USE kinds
98
99
100	IMPLICIT NONE
101
102
103	CHARACTER (LEN=20) :: canopy_mode = 'block' !< canopy coverage
104
105	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
106	INTEGER(iwp) :: &
107	lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
108
109	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
110	LOGICAL :: plant_canopy = .FALSE. !< switch for use of canopy model
111
112	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
113	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
114	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
115	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
116	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
117	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
118	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
119	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
120	REAL(wp) :: &
121	leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
122	REAL(wp) :: &
123	leaf_surface_conc = 0.0_wp !< leaf surface concentration
124	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
125	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
126
127	REAL(wp) :: &
128	lad_vertical_gradient(10) = 0.0_wp !< lad gradient
129	REAL(wp) :: &
130	lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
131
132	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
133	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
134
135	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
136	canopy_heat_flux !< canopy heat flux
137	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
138	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
139
140
141	SAVE
142
143
144	PRIVATE
145
146	!
147	!-- Public functions
148	PUBLIC pcm_check_parameters, pcm_header, pcm_init, pcm_parin, pcm_tendency
149
150	!
151	!-- Public variables and constants
152	PUBLIC canopy_mode, cthf, dt_plant_canopy, lad, lad_s, plant_canopy
153
154
155	INTERFACE pcm_check_parameters
156	MODULE PROCEDURE pcm_check_parameters
157	END INTERFACE pcm_check_parameters
158
159	INTERFACE pcm_header
160	MODULE PROCEDURE pcm_header
161	END INTERFACE pcm_header
162
163	INTERFACE pcm_init
164	MODULE PROCEDURE pcm_init
165	END INTERFACE pcm_init
166
167	INTERFACE pcm_parin
168	MODULE PROCEDURE pcm_parin
169	END INTERFACE pcm_parin
170
171	INTERFACE pcm_tendency
172	MODULE PROCEDURE pcm_tendency
173	MODULE PROCEDURE pcm_tendency_ij
174	END INTERFACE pcm_tendency
175
176
177	CONTAINS
178
179
180	!------------------------------------------------------------------------------!
181	! Description:
182	! ------------
183	!> Check parameters routine for plant canopy model
184	!------------------------------------------------------------------------------!
185	SUBROUTINE pcm_check_parameters
186
187	USE control_parameters, &
188	ONLY: cloud_physics, message_string, microphysics_seifert
189
190
191	IMPLICIT NONE
192
193
194	IF ( canopy_drag_coeff == 0.0_wp ) THEN
195	message_string = 'plant_canopy = .TRUE. requires a non-zero drag '// &
196	'coefficient & given value is canopy_drag_coeff = 0.0'
197	CALL message( 'check_parameters', 'PA0041', 1, 2, 0, 6, 0 )
198	ENDIF
199
200	IF ( ( alpha_lad /= 9999999.9_wp .AND. beta_lad == 9999999.9_wp ) .OR.&
201	beta_lad /= 9999999.9_wp .AND. alpha_lad == 9999999.9_wp ) THEN
202	message_string = 'using the beta function for the construction ' // &
203	'of the leaf area density profile requires ' // &
204	'both alpha_lad and beta_lad to be /= 9999999.9'
205	CALL message( 'check_parameters', 'PA0118', 1, 2, 0, 6, 0 )
206	ENDIF
207
208	IF ( calc_beta_lad_profile .AND. lai_beta == 0.0_wp ) THEN
209	message_string = 'using the beta function for the construction ' // &
210	'of the leaf area density profile requires ' // &
211	'a non-zero lai_beta, but given value is ' // &
212	'lai_beta = 0.0'
213	CALL message( 'check_parameters', 'PA0119', 1, 2, 0, 6, 0 )
214	ENDIF
215
216	IF ( calc_beta_lad_profile .AND. lad_surface /= 0.0_wp ) THEN
217	message_string = 'simultaneous setting of alpha_lad /= 9999999.9' // &
218	'and lad_surface /= 0.0 is not possible, ' // &
219	'use either vertical gradients or the beta ' // &
220	'function for the construction of the leaf area '// &
221	'density profile'
222	CALL message( 'check_parameters', 'PA0120', 1, 2, 0, 6, 0 )
223	ENDIF
224
225	IF ( cloud_physics .AND. microphysics_seifert ) THEN
226	message_string = 'plant_canopy = .TRUE. requires cloud_scheme /=' // &
227	' seifert_beheng'
228	CALL message( 'check_parameters', 'PA0360', 1, 2, 0, 6, 0 )
229	ENDIF
230
231
232	END SUBROUTINE pcm_check_parameters
233
234
235	!------------------------------------------------------------------------------!
236	! Description:
237	! ------------
238	!> Header output for plant canopy model
239	!------------------------------------------------------------------------------!
240	SUBROUTINE pcm_header ( io )
241
242	USE control_parameters, &
243	ONLY: dz, passive_scalar
244
245
246	IMPLICIT NONE
247
248	CHARACTER (LEN=10) :: coor_chr !<
249
250	CHARACTER (LEN=86) :: coordinates !<
251	CHARACTER (LEN=86) :: gradients !<
252	CHARACTER (LEN=86) :: leaf_area_density !<
253	CHARACTER (LEN=86) :: slices !<
254
255	INTEGER(iwp) :: i !<
256	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
257	INTEGER(iwp) :: k !<
258
259	REAL(wp) :: canopy_height !< canopy height (in m)
260
261	canopy_height = pch_index * dz
262
263	WRITE ( io, 1 ) canopy_mode, canopy_height, pch_index, &
264	canopy_drag_coeff
265	IF ( passive_scalar ) THEN
266	WRITE ( io, 2 ) leaf_scalar_exch_coeff, &
267	leaf_surface_conc
268	ENDIF
269
270	!
271	!-- Heat flux at the top of vegetation
272	WRITE ( io, 3 ) cthf
273
274	!
275	!-- Leaf area density profile, calculated either from given vertical
276	!-- gradients or from beta probability density function.
277	IF ( .NOT. calc_beta_lad_profile ) THEN
278
279	!-- Building output strings, starting with surface value
280	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
281	gradients = '------'
282	slices = ' 0'
283	coordinates = ' 0.0'
284	i = 1
285	DO WHILE ( i < 11 .AND. lad_vertical_gradient_level_ind(i) &
286	/= -9999 )
287
288	WRITE (coor_chr,'(F7.2)') lad(lad_vertical_gradient_level_ind(i))
289	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
290	TRIM( coor_chr )
291
292	WRITE (coor_chr,'(F7.2)') lad_vertical_gradient(i)
293	gradients = TRIM( gradients ) // ' ' // TRIM( coor_chr )
294
295	WRITE (coor_chr,'(I7)') lad_vertical_gradient_level_ind(i)
296	slices = TRIM( slices ) // ' ' // TRIM( coor_chr )
297
298	WRITE (coor_chr,'(F7.1)') lad_vertical_gradient_level(i)
299	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
300
301	i = i + 1
302	ENDDO
303
304	WRITE ( io, 4 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
305	TRIM( gradients ), TRIM( slices )
306
307	ELSE
308
309	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
310	coordinates = ' 0.0'
311
312	DO k = 1, pch_index
313
314	WRITE (coor_chr,'(F7.2)') lad(k)
315	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
316	TRIM( coor_chr )
317
318	WRITE (coor_chr,'(F7.1)') zu(k)
319	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
320
321	ENDDO
322
323	WRITE ( io, 5 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
324	alpha_lad, beta_lad, lai_beta
325
326	ENDIF
327
328	1 FORMAT (//' Vegetation canopy (drag) model:'/ &
329	' ------------------------------'// &
330	' Canopy mode: ', A / &
331	' Canopy height: ',F6.2,'m (',I4,' grid points)' / &
332	' Leaf drag coefficient: ',F6.2 /)
333	2 FORMAT (/ ' Scalar exchange coefficient: ',F6.2 / &
334	' Scalar concentration at leaf surfaces in kg/m**3: ',F6.2 /)
335	3 FORMAT (' Predefined constant heatflux at the top of the vegetation: ',F6.2, &
336	' K m/s')
337	4 FORMAT (/ ' Characteristic levels of the leaf area density:'// &
338	' Height: ',A,' m'/ &
339	' Leaf area density: ',A,' m2/m3'/ &
340	' Gradient: ',A,' m2/m4'/ &
341	' Gridpoint: ',A)
342	5 FORMAT (//' Characteristic levels of the leaf area density and coefficients:'&
343	// ' Height: ',A,' m'/ &
344	' Leaf area density: ',A,' m2/m3'/ &
345	' Coefficient alpha: ',F6.2 / &
346	' Coefficient beta: ',F6.2 / &
347	' Leaf area index: ',F6.2,' m2/m2' /)
348
349	END SUBROUTINE pcm_header
350
351
352	!------------------------------------------------------------------------------!
353	! Description:
354	! ------------
355	!> Initialization of the plant canopy model
356	!------------------------------------------------------------------------------!
357	SUBROUTINE pcm_init
358
359
360	USE control_parameters, &
361	ONLY: dz, ocean, passive_scalar
362
363
364	IMPLICIT NONE
365
366	INTEGER(iwp) :: i !< running index
367	INTEGER(iwp) :: j !< running index
368	INTEGER(iwp) :: k !< running index
369
370	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
371	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
372	REAL(wp) :: gradient !< gradient for lad-profile construction
373	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
374
375	!
376	!-- Allocate one-dimensional arrays for the computation of the
377	!-- leaf area density (lad) profile
378	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
379	lad = 0.0_wp
380	pre_lad = 0.0_wp
381
382	!
383	!-- Set flag that indicates that the lad-profile shall be calculated by using
384	!-- a beta probability density function
385	IF ( alpha_lad /= 9999999.9_wp .AND. beta_lad /= 9999999.9_wp ) THEN
386	calc_beta_lad_profile = .TRUE.
387	ENDIF
388
389
390	!
391	!-- Compute the profile of leaf area density used in the plant
392	!-- canopy model. The profile can either be constructed from
393	!-- prescribed vertical gradients of the leaf area density or by
394	!-- using a beta probability density function (see e.g. Markkanen et al.,
395	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
396	IF ( .NOT. calc_beta_lad_profile ) THEN
397
398	!
399	!-- Use vertical gradients for lad-profile construction
400	i = 1
401	gradient = 0.0_wp
402
403	IF ( .NOT. ocean ) THEN
404
405	lad(0) = lad_surface
406	lad_vertical_gradient_level_ind(1) = 0
407
408	DO k = 1, pch_index
409	IF ( i < 11 ) THEN
410	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
411	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
412	gradient = lad_vertical_gradient(i)
413	lad_vertical_gradient_level_ind(i) = k - 1
414	i = i + 1
415	ENDIF
416	ENDIF
417	IF ( gradient /= 0.0_wp ) THEN
418	IF ( k /= 1 ) THEN
419	lad(k) = lad(k-1) + dzu(k) * gradient
420	ELSE
421	lad(k) = lad_surface + dzu(k) * gradient
422	ENDIF
423	ELSE
424	lad(k) = lad(k-1)
425	ENDIF
426	ENDDO
427
428	ENDIF
429
430	!
431	!-- In case of no given leaf area density gradients, choose a vanishing
432	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
433	!-- file.
434	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
435	lad_vertical_gradient_level(1) = 0.0_wp
436	ENDIF
437
438	ELSE
439
440	!
441	!-- Use beta function for lad-profile construction
442	int_bpdf = 0.0_wp
443	canopy_height = pch_index * dz
444
445	DO k = nzb, pch_index
446	int_bpdf = int_bpdf + &
447	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
448	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
449	beta_lad-1.0_wp ) ) &
450	* ( ( zw(k+1)-zw(k) ) / canopy_height ) )
451	ENDDO
452
453	!
454	!-- Preliminary lad profile (defined on w-grid)
455	DO k = nzb, pch_index
456	pre_lad(k) = lai_beta * &
457	( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) ) &
458	* ( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
459	beta_lad-1.0_wp ) ) / int_bpdf &
460	) / canopy_height
461	ENDDO
462
463	!
464	!-- Final lad profile (defined on scalar-grid level, since most prognostic
465	!-- quantities are defined there, hence, less interpolation is required
466	!-- when calculating the canopy tendencies)
467	lad(0) = pre_lad(0)
468	DO k = nzb+1, pch_index
469	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
470	ENDDO
471
472	ENDIF
473
474	!
475	!-- Allocate 3D-array for the leaf area density (lad_s). In case of a
476	!-- prescribed canopy-top heat flux (cthf), allocate 3D-arrays for
477	!-- the cumulative leaf area index (cum_lai_hf) and the canopy heat flux.
478	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
479
480	IF ( cthf /= 0.0_wp ) THEN
481	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
482	canopy_heat_flux(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
483	ENDIF
484
485	!
486	!-- Initialize canopy parameters cdc (canopy drag coefficient),
487	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
488	!-- with the prescribed values
489	cdc = canopy_drag_coeff
490	lsec = leaf_scalar_exch_coeff
491	lsc = leaf_surface_conc
492
493	!
494	!-- Initialization of the canopy coverage in the model domain:
495	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
496	!-- fully covers the domain surface
497	SELECT CASE ( TRIM( canopy_mode ) )
498
499	CASE( 'block' )
500
501	DO i = nxlg, nxrg
502	DO j = nysg, nyng
503	lad_s(:,j,i) = lad(:)
504	ENDDO
505	ENDDO
506
507	CASE DEFAULT
508
509	!
510	!-- The DEFAULT case is reached either if the parameter
511	!-- canopy mode contains a wrong character string or if the
512	!-- user has coded a special case in the user interface.
513	!-- There, the subroutine user_init_plant_canopy checks
514	!-- which of these two conditions applies.
515	CALL user_init_plant_canopy
516
517	END SELECT
518
519	!
520	!-- Initialization of the canopy heat source distribution
521	IF ( cthf /= 0.0_wp ) THEN
522	!
523	!-- Piecewise calculation of the leaf area index by vertical
524	!-- integration of the leaf area density
525	cum_lai_hf(:,:,:) = 0.0_wp
526	DO i = nxlg, nxrg
527	DO j = nysg, nyng
528	DO k = pch_index-1, 0, -1
529	IF ( k == pch_index-1 ) THEN
530	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
531	( 0.5_wp * lad_s(k+1,j,i) * &
532	( zw(k+1) - zu(k+1) ) ) + &
533	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
534	lad_s(k,j,i) ) + &
535	lad_s(k+1,j,i) ) * &
536	( zu(k+1) - zw(k) ) )
537	ELSE
538	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
539	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
540	lad_s(k+1,j,i) ) + &
541	lad_s(k+1,j,i) ) * &
542	( zw(k+1) - zu(k+1) ) ) + &
543	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
544	lad_s(k,j,i) ) + &
545	lad_s(k+1,j,i) ) * &
546	( zu(k+1) - zw(k) ) )
547	ENDIF
548	ENDDO
549	ENDDO
550	ENDDO
551
552	!
553	!-- Calculation of the upward kinematic vertical heat flux within the
554	!-- canopy
555	DO i = nxlg, nxrg
556	DO j = nysg, nyng
557	DO k = 0, pch_index
558	canopy_heat_flux(k,j,i) = cthf * &
559	exp( -0.6_wp * cum_lai_hf(k,j,i) )
560	ENDDO
561	ENDDO
562	ENDDO
563
564	!
565	!-- In areas covered with canopy, the surface heat flux is set to
566	!-- the surface value of the above calculated in-canopy heat flux
567	!-- distribution
568	DO i = nxlg,nxrg
569	DO j = nysg, nyng
570	IF ( canopy_heat_flux(0,j,i) /= cthf ) THEN
571	shf(j,i) = canopy_heat_flux(0,j,i)
572	ENDIF
573	ENDDO
574	ENDDO
575
576	ENDIF
577
578
579
580	END SUBROUTINE pcm_init
581
582
583
584	!------------------------------------------------------------------------------!
585	! Description:
586	! ------------
587	!> Calculation of the tendency terms, accounting for the effect of the plant
588	!> canopy on momentum and scalar quantities.
589	!>
590	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
591	!> (defined on scalar grid), as initialized in subroutine pcm_init.
592	!> The lad on the w-grid is vertically interpolated from the surrounding
593	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
594	!> k = pch_index. Here, the lad is zero.
595	!>
596	!> The canopy drag must be limited (previously accounted for by calculation of
597	!> a limiting canopy timestep for the determination of the maximum LES timestep
598	!> in subroutine timestep), since it is physically impossible that the canopy
599	!> drag alone can locally change the sign of a velocity component. This
600	!> limitation is realized by calculating preliminary tendencies and velocities.
601	!> It is subsequently checked if the preliminary new velocity has a different
602	!> sign than the current velocity. If so, the tendency is limited in a way that
603	!> the velocity can at maximum be reduced to zero by the canopy drag.
604	!>
605	!>
606	!> Call for all grid points
607	!------------------------------------------------------------------------------!
608	SUBROUTINE pcm_tendency( component )
609
610
611	USE control_parameters, &
612	ONLY: dt_3d, message_string
613
614	USE kinds
615
616	IMPLICIT NONE
617
618	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
619	INTEGER(iwp) :: i !< running index
620	INTEGER(iwp) :: j !< running index
621	INTEGER(iwp) :: k !< running index
622	INTEGER(iwp) :: kk !< running index for flat lad arrays
623
624	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
625	REAL(wp) :: lad_local !< local lad value
626	REAL(wp) :: pre_tend !< preliminary tendency
627	REAL(wp) :: pre_u !< preliminary u-value
628	REAL(wp) :: pre_v !< preliminary v-value
629	REAL(wp) :: pre_w !< preliminary w-value
630
631
632	ddt_3d = 1.0_wp / dt_3d
633
634	!
635	!-- Compute drag for the three velocity components and the SGS-TKE:
636	SELECT CASE ( component )
637
638	!
639	!-- u-component
640	CASE ( 1 )
641	DO i = nxlu, nxr
642	DO j = nys, nyn
643	DO k = nzb_u_inner(j,i)+1, nzb_u_inner(j,i)+pch_index
644
645	kk = k - nzb_u_inner(j,i) !- lad arrays are defined flat
646	!
647	!-- In order to create sharp boundaries of the plant canopy,
648	!-- the lad on the u-grid at index (k,j,i) is equal to
649	!-- lad_s(k,j,i), rather than being interpolated from the
650	!-- surrounding lad_s, because this would yield smaller lad
651	!-- at the canopy boundaries than inside of the canopy.
652	!-- For the same reason, the lad at the rightmost(i+1)canopy
653	!-- boundary on the u-grid equals lad_s(k,j,i).
654	lad_local = lad_s(kk,j,i)
655	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp )&
656	THEN
657	lad_local = lad_s(kk,j,i-1)
658	ENDIF
659
660	pre_tend = 0.0_wp
661	pre_u = 0.0_wp
662	!
663	!-- Calculate preliminary value (pre_tend) of the tendency
664	pre_tend = - cdc * &
665	lad_local * &
666	SQRT( u(k,j,i)**2 + &
667	( 0.25_wp * ( v(k,j,i-1) + &
668	v(k,j,i) + &
669	v(k,j+1,i) + &
670	v(k,j+1,i-1) ) &
671	)**2 + &
672	( 0.25_wp * ( w(k-1,j,i-1) + &
673	w(k-1,j,i) + &
674	w(k,j,i-1) + &
675	w(k,j,i) ) &
676	)**2 &
677	) * &
678	u(k,j,i)
679
680	!
681	!-- Calculate preliminary new velocity, based on pre_tend
682	pre_u = u(k,j,i) + dt_3d * pre_tend
683	!
684	!-- Compare sign of old velocity and new preliminary velocity,
685	!-- and in case the signs are different, limit the tendency
686	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
687	pre_tend = - u(k,j,i) * ddt_3d
688	ELSE
689	pre_tend = pre_tend
690	ENDIF
691	!
692	!-- Calculate final tendency
693	tend(k,j,i) = tend(k,j,i) + pre_tend
694
695	ENDDO
696	ENDDO
697	ENDDO
698
699	!
700	!-- v-component
701	CASE ( 2 )
702	DO i = nxl, nxr
703	DO j = nysv, nyn
704	DO k = nzb_v_inner(j,i)+1, nzb_v_inner(j,i)+pch_index
705
706	kk = k - nzb_v_inner(j,i) !- lad arrays are defined flat
707	!
708	!-- In order to create sharp boundaries of the plant canopy,
709	!-- the lad on the v-grid at index (k,j,i) is equal to
710	!-- lad_s(k,j,i), rather than being interpolated from the
711	!-- surrounding lad_s, because this would yield smaller lad
712	!-- at the canopy boundaries than inside of the canopy.
713	!-- For the same reason, the lad at the northmost(j+1) canopy
714	!-- boundary on the v-grid equals lad_s(k,j,i).
715	lad_local = lad_s(kk,j,i)
716	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp )&
717	THEN
718	lad_local = lad_s(kk,j-1,i)
719	ENDIF
720
721	pre_tend = 0.0_wp
722	pre_v = 0.0_wp
723	!
724	!-- Calculate preliminary value (pre_tend) of the tendency
725	pre_tend = - cdc * &
726	lad_local * &
727	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
728	u(k,j-1,i+1) + &
729	u(k,j,i) + &
730	u(k,j,i+1) ) &
731	)**2 + &
732	v(k,j,i)**2 + &
733	( 0.25_wp * ( w(k-1,j-1,i) + &
734	w(k-1,j,i) + &
735	w(k,j-1,i) + &
736	w(k,j,i) ) &
737	)**2 &
738	) * &
739	v(k,j,i)
740
741	!
742	!-- Calculate preliminary new velocity, based on pre_tend
743	pre_v = v(k,j,i) + dt_3d * pre_tend
744	!
745	!-- Compare sign of old velocity and new preliminary velocity,
746	!-- and in case the signs are different, limit the tendency
747	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
748	pre_tend = - v(k,j,i) * ddt_3d
749	ELSE
750	pre_tend = pre_tend
751	ENDIF
752	!
753	!-- Calculate final tendency
754	tend(k,j,i) = tend(k,j,i) + pre_tend
755
756	ENDDO
757	ENDDO
758	ENDDO
759
760	!
761	!-- w-component
762	CASE ( 3 )
763	DO i = nxl, nxr
764	DO j = nys, nyn
765	DO k = nzb_w_inner(j,i)+1, nzb_w_inner(j,i)+pch_index-1
766
767	kk = k - nzb_w_inner(j,i) !- lad arrays are defined flat
768
769	pre_tend = 0.0_wp
770	pre_w = 0.0_wp
771	!
772	!-- Calculate preliminary value (pre_tend) of the tendency
773	pre_tend = - cdc * &
774	(0.5_wp * &
775	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
776	SQRT( ( 0.25_wp * ( u(k,j,i) + &
777	u(k,j,i+1) + &
778	u(k+1,j,i) + &
779	u(k+1,j,i+1) ) &
780	)**2 + &
781	( 0.25_wp * ( v(k,j,i) + &
782	v(k,j+1,i) + &
783	v(k+1,j,i) + &
784	v(k+1,j+1,i) ) &
785	)**2 + &
786	w(k,j,i)**2 &
787	) * &
788	w(k,j,i)
789	!
790	!-- Calculate preliminary new velocity, based on pre_tend
791	pre_w = w(k,j,i) + dt_3d * pre_tend
792	!
793	!-- Compare sign of old velocity and new preliminary velocity,
794	!-- and in case the signs are different, limit the tendency
795	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
796	pre_tend = - w(k,j,i) * ddt_3d
797	ELSE
798	pre_tend = pre_tend
799	ENDIF
800	!
801	!-- Calculate final tendency
802	tend(k,j,i) = tend(k,j,i) + pre_tend
803
804	ENDDO
805	ENDDO
806	ENDDO
807
808	!
809	!-- potential temperature
810	CASE ( 4 )
811	DO i = nxl, nxr
812	DO j = nys, nyn
813	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
814	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
815	tend(k,j,i) = tend(k,j,i) + &
816	( canopy_heat_flux(kk,j,i) - &
817	canopy_heat_flux(kk-1,j,i) ) / dzw(k)
818	ENDDO
819	ENDDO
820	ENDDO
821
822	!
823	!-- humidity
824	CASE ( 5 )
825	DO i = nxl, nxr
826	DO j = nys, nyn
827	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
828	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
829	tend(k,j,i) = tend(k,j,i) - &
830	lsec * &
831	lad_s(kk,j,i) * &
832	SQRT( ( 0.5_wp * ( u(k,j,i) + &
833	u(k,j,i+1) ) &
834	)**2 + &
835	( 0.5_wp * ( v(k,j,i) + &
836	v(k,j+1,i) ) &
837	)**2 + &
838	( 0.5_wp * ( w(k-1,j,i) + &
839	w(k,j,i) ) &
840	)**2 &
841	) * &
842	( q(k,j,i) - lsc )
843	ENDDO
844	ENDDO
845	ENDDO
846
847	!
848	!-- sgs-tke
849	CASE ( 6 )
850	DO i = nxl, nxr
851	DO j = nys, nyn
852	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
853	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
854	tend(k,j,i) = tend(k,j,i) - &
855	2.0_wp * cdc * &
856	lad_s(kk,j,i) * &
857	SQRT( ( 0.5_wp * ( u(k,j,i) + &
858	u(k,j,i+1) ) &
859	)**2 + &
860	( 0.5_wp * ( v(k,j,i) + &
861	v(k,j+1,i) ) &
862	)**2 + &
863	( 0.5_wp * ( w(k,j,i) + &
864	w(k+1,j,i) ) &
865	)**2 &
866	) * &
867	e(k,j,i)
868	ENDDO
869	ENDDO
870	ENDDO
871	!
872	!-- scalar concentration
873	CASE ( 7 )
874	DO i = nxl, nxr
875	DO j = nys, nyn
876	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
877	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
878	tend(k,j,i) = tend(k,j,i) - &
879	lsec * &
880	lad_s(kk,j,i) * &
881	SQRT( ( 0.5_wp * ( u(k,j,i) + &
882	u(k,j,i+1) ) &
883	)**2 + &
884	( 0.5_wp * ( v(k,j,i) + &
885	v(k,j+1,i) ) &
886	)**2 + &
887	( 0.5_wp * ( w(k-1,j,i) + &
888	w(k,j,i) ) &
889	)**2 &
890	) * &
891	( s(k,j,i) - lsc )
892	ENDDO
893	ENDDO
894	ENDDO
895
896
897
898	CASE DEFAULT
899
900	WRITE( message_string, * ) 'wrong component: ', component
901	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
902
903	END SELECT
904
905	END SUBROUTINE pcm_tendency
906
907
908	!------------------------------------------------------------------------------!
909	! Description:
910	! ------------
911	!> Parin for &canopy_par for plant canopy model
912	!------------------------------------------------------------------------------!
913	SUBROUTINE pcm_parin
914
915
916	IMPLICIT NONE
917
918	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
919
920	NAMELIST /canopy_par/ alpha_lad, beta_lad, canopy_drag_coeff, &
921	canopy_mode, cthf, &
922	lad_surface, &
923	lad_vertical_gradient, &
924	lad_vertical_gradient_level, &
925	lai_beta, &
926	leaf_scalar_exch_coeff, &
927	leaf_surface_conc, pch_index
928
929	line = ' '
930
931	!
932	!-- Try to find radiation model package
933	REWIND ( 11 )
934	line = ' '
935	DO WHILE ( INDEX( line, '&canopy_par' ) == 0 )
936	READ ( 11, '(A)', END=10 ) line
937	ENDDO
938	BACKSPACE ( 11 )
939
940	!
941	!-- Read user-defined namelist
942	READ ( 11, canopy_par )
943
944	!
945	!-- Set flag that indicates that the radiation model is switched on
946	plant_canopy = .TRUE.
947
948	10 CONTINUE
949
950
951	END SUBROUTINE pcm_parin
952
953
954
955	!------------------------------------------------------------------------------!
956	! Description:
957	! ------------
958	!> Calculation of the tendency terms, accounting for the effect of the plant
959	!> canopy on momentum and scalar quantities.
960	!>
961	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
962	!> (defined on scalar grid), as initialized in subroutine pcm_init.
963	!> The lad on the w-grid is vertically interpolated from the surrounding
964	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
965	!> k = pch_index. Here, the lad is zero.
966	!>
967	!> The canopy drag must be limited (previously accounted for by calculation of
968	!> a limiting canopy timestep for the determination of the maximum LES timestep
969	!> in subroutine timestep), since it is physically impossible that the canopy
970	!> drag alone can locally change the sign of a velocity component. This
971	!> limitation is realized by calculating preliminary tendencies and velocities.
972	!> It is subsequently checked if the preliminary new velocity has a different
973	!> sign than the current velocity. If so, the tendency is limited in a way that
974	!> the velocity can at maximum be reduced to zero by the canopy drag.
975	!>
976	!>
977	!> Call for grid point i,j
978	!------------------------------------------------------------------------------!
979	SUBROUTINE pcm_tendency_ij( i, j, component )
980
981
982	USE control_parameters, &
983	ONLY: dt_3d, message_string
984
985	USE kinds
986
987	IMPLICIT NONE
988
989	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
990	INTEGER(iwp) :: i !< running index
991	INTEGER(iwp) :: j !< running index
992	INTEGER(iwp) :: k !< running index
993	INTEGER(iwp) :: kk !< running index for flat lad arrays
994
995	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
996	REAL(wp) :: lad_local !< local lad value
997	REAL(wp) :: pre_tend !< preliminary tendency
998	REAL(wp) :: pre_u !< preliminary u-value
999	REAL(wp) :: pre_v !< preliminary v-value
1000	REAL(wp) :: pre_w !< preliminary w-value
1001
1002
1003	ddt_3d = 1.0_wp / dt_3d
1004
1005	!
1006	!-- Compute drag for the three velocity components and the SGS-TKE
1007	SELECT CASE ( component )
1008
1009	!
1010	!-- u-component
1011	CASE ( 1 )
1012	DO k = nzb_u_inner(j,i)+1, nzb_u_inner(j,i)+pch_index
1013
1014	kk = k - nzb_u_inner(j,i) !- lad arrays are defined flat
1015	!
1016	!-- In order to create sharp boundaries of the plant canopy,
1017	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
1018	!-- rather than being interpolated from the surrounding lad_s,
1019	!-- because this would yield smaller lad at the canopy boundaries
1020	!-- than inside of the canopy.
1021	!-- For the same reason, the lad at the rightmost(i+1)canopy
1022	!-- boundary on the u-grid equals lad_s(k,j,i).
1023	lad_local = lad_s(kk,j,i)
1024	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp ) THEN
1025	lad_local = lad_s(kk,j,i-1)
1026	ENDIF
1027
1028	pre_tend = 0.0_wp
1029	pre_u = 0.0_wp
1030	!
1031	!-- Calculate preliminary value (pre_tend) of the tendency
1032	pre_tend = - cdc * &
1033	lad_local * &
1034	SQRT( u(k,j,i)**2 + &
1035	( 0.25_wp * ( v(k,j,i-1) + &
1036	v(k,j,i) + &
1037	v(k,j+1,i) + &
1038	v(k,j+1,i-1) ) &
1039	)**2 + &
1040	( 0.25_wp * ( w(k-1,j,i-1) + &
1041	w(k-1,j,i) + &
1042	w(k,j,i-1) + &
1043	w(k,j,i) ) &
1044	)**2 &
1045	) * &
1046	u(k,j,i)
1047
1048	!
1049	!-- Calculate preliminary new velocity, based on pre_tend
1050	pre_u = u(k,j,i) + dt_3d * pre_tend
1051	!
1052	!-- Compare sign of old velocity and new preliminary velocity,
1053	!-- and in case the signs are different, limit the tendency
1054	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1055	pre_tend = - u(k,j,i) * ddt_3d
1056	ELSE
1057	pre_tend = pre_tend
1058	ENDIF
1059	!
1060	!-- Calculate final tendency
1061	tend(k,j,i) = tend(k,j,i) + pre_tend
1062	ENDDO
1063
1064
1065	!
1066	!-- v-component
1067	CASE ( 2 )
1068	DO k = nzb_v_inner(j,i)+1, nzb_v_inner(j,i)+pch_index
1069
1070	kk = k - nzb_v_inner(j,i) !- lad arrays are defined flat
1071	!
1072	!-- In order to create sharp boundaries of the plant canopy,
1073	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
1074	!-- rather than being interpolated from the surrounding lad_s,
1075	!-- because this would yield smaller lad at the canopy boundaries
1076	!-- than inside of the canopy.
1077	!-- For the same reason, the lad at the northmost(j+1)canopy
1078	!-- boundary on the v-grid equals lad_s(k,j,i).
1079	lad_local = lad_s(kk,j,i)
1080	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp ) THEN
1081	lad_local = lad_s(kk,j-1,i)
1082	ENDIF
1083
1084	pre_tend = 0.0_wp
1085	pre_v = 0.0_wp
1086	!
1087	!-- Calculate preliminary value (pre_tend) of the tendency
1088	pre_tend = - cdc * &
1089	lad_local * &
1090	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1091	u(k,j-1,i+1) + &
1092	u(k,j,i) + &
1093	u(k,j,i+1) ) &
1094	)**2 + &
1095	v(k,j,i)**2 + &
1096	( 0.25_wp * ( w(k-1,j-1,i) + &
1097	w(k-1,j,i) + &
1098	w(k,j-1,i) + &
1099	w(k,j,i) ) &
1100	)**2 &
1101	) * &
1102	v(k,j,i)
1103
1104	!
1105	!-- Calculate preliminary new velocity, based on pre_tend
1106	pre_v = v(k,j,i) + dt_3d * pre_tend
1107	!
1108	!-- Compare sign of old velocity and new preliminary velocity,
1109	!-- and in case the signs are different, limit the tendency
1110	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1111	pre_tend = - v(k,j,i) * ddt_3d
1112	ELSE
1113	pre_tend = pre_tend
1114	ENDIF
1115	!
1116	!-- Calculate final tendency
1117	tend(k,j,i) = tend(k,j,i) + pre_tend
1118	ENDDO
1119
1120
1121	!
1122	!-- w-component
1123	CASE ( 3 )
1124	DO k = nzb_w_inner(j,i)+1, nzb_w_inner(j,i)+pch_index-1
1125
1126	kk = k - nzb_w_inner(j,i) !- lad arrays are defined flat
1127
1128	pre_tend = 0.0_wp
1129	pre_w = 0.0_wp
1130	!
1131	!-- Calculate preliminary value (pre_tend) of the tendency
1132	pre_tend = - cdc * &
1133	(0.5_wp * &
1134	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1135	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1136	u(k,j,i+1) + &
1137	u(k+1,j,i) + &
1138	u(k+1,j,i+1) ) &
1139	)**2 + &
1140	( 0.25_wp * ( v(k,j,i) + &
1141	v(k,j+1,i) + &
1142	v(k+1,j,i) + &
1143	v(k+1,j+1,i) ) &
1144	)**2 + &
1145	w(k,j,i)**2 &
1146	) * &
1147	w(k,j,i)
1148	!
1149	!-- Calculate preliminary new velocity, based on pre_tend
1150	pre_w = w(k,j,i) + dt_3d * pre_tend
1151	!
1152	!-- Compare sign of old velocity and new preliminary velocity,
1153	!-- and in case the signs are different, limit the tendency
1154	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1155	pre_tend = - w(k,j,i) * ddt_3d
1156	ELSE
1157	pre_tend = pre_tend
1158	ENDIF
1159	!
1160	!-- Calculate final tendency
1161	tend(k,j,i) = tend(k,j,i) + pre_tend
1162	ENDDO
1163
1164	!
1165	!-- potential temperature
1166	CASE ( 4 )
1167	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1168	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1169	tend(k,j,i) = tend(k,j,i) + &
1170	( canopy_heat_flux(kk,j,i) - &
1171	canopy_heat_flux(kk-1,j,i) ) / dzw(k)
1172	ENDDO
1173
1174
1175	!
1176	!-- humidity
1177	CASE ( 5 )
1178	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1179	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1180	tend(k,j,i) = tend(k,j,i) - &
1181	lsec * &
1182	lad_s(kk,j,i) * &
1183	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1184	u(k,j,i+1) ) &
1185	)**2 + &
1186	( 0.5_wp * ( v(k,j,i) + &
1187	v(k,j+1,i) ) &
1188	)**2 + &
1189	( 0.5_wp * ( w(k-1,j,i) + &
1190	w(k,j,i) ) &
1191	)**2 &
1192	) * &
1193	( q(k,j,i) - lsc )
1194	ENDDO
1195
1196	!
1197	!-- sgs-tke
1198	CASE ( 6 )
1199	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1200	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1201	tend(k,j,i) = tend(k,j,i) - &
1202	2.0_wp * cdc * &
1203	lad_s(kk,j,i) * &
1204	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1205	u(k,j,i+1) ) &
1206	)**2 + &
1207	( 0.5_wp * ( v(k,j,i) + &
1208	v(k,j+1,i) ) &
1209	)**2 + &
1210	( 0.5_wp * ( w(k,j,i) + &
1211	w(k+1,j,i) ) &
1212	)**2 &
1213	) * &
1214	e(k,j,i)
1215	ENDDO
1216
1217	!
1218	!-- scalar concentration
1219	CASE ( 7 )
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
1238	CASE DEFAULT
1239
1240	WRITE( message_string, * ) 'wrong component: ', component
1241	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1242
1243	END SELECT
1244
1245	END SUBROUTINE pcm_tendency_ij
1246
1247	END MODULE plant_canopy_model_mod

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