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source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 1960

Last change on this file since 1960 was 1960, checked in by suehring, 8 years ago
Separate balance equations for humidity and passive_scalar
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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	! Separate humidity and passive scalar
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: plant_canopy_model_mod.f90 1960 2016-07-12 16:34:24Z suehring $
26	!
27	! 1953 2016-06-21 09:28:42Z suehring
28	! Bugfix, lad_s and lad must be public
29	!
30	! 1826 2016-04-07 12:01:39Z maronga
31	! Further modularization
32	!
33	! 1721 2015-11-16 12:56:48Z raasch
34	! bugfixes: shf is reduced in areas covered with canopy only,
35	! canopy is set on top of topography
36	!
37	! 1682 2015-10-07 23:56:08Z knoop
38	! Code annotations made doxygen readable
39	!
40	! 1484 2014-10-21 10:53:05Z kanani
41	! Changes due to new module structure of the plant canopy model:
42	! module plant_canopy_model_mod now contains a subroutine for the
43	! initialization of the canopy model (pcm_init),
44	! limitation of the canopy drag (previously accounted for by calculation of
45	! a limiting canopy timestep for the determination of the maximum LES timestep
46	! in subroutine timestep) is now realized by the calculation of pre-tendencies
47	! and preliminary velocities in subroutine pcm_tendency,
48	! some redundant MPI communication removed in subroutine pcm_init
49	! (was previously in init_3d_model),
50	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
51	! respective grid is now provided only by lad_s (e.g. in the calculation of
52	! the tendency terms or of cum_lai_hf),
53	! drag_coefficient, lai, leaf_surface_concentration,
54	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
55	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
56	! respectively,
57	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
58	! USE-statements and ONLY-lists modified accordingly
59	!
60	! 1340 2014-03-25 19:45:13Z kanani
61	! REAL constants defined as wp-kind
62	!
63	! 1320 2014-03-20 08:40:49Z raasch
64	! ONLY-attribute added to USE-statements,
65	! kind-parameters added to all INTEGER and REAL declaration statements,
66	! kinds are defined in new module kinds,
67	! old module precision_kind is removed,
68	! revision history before 2012 removed,
69	! comment fields (!:) to be used for variable explanations added to
70	! all variable declaration statements
71	!
72	! 1036 2012-10-22 13:43:42Z raasch
73	! code put under GPL (PALM 3.9)
74	!
75	! 138 2007-11-28 10:03:58Z letzel
76	! Initial revision
77	!
78	! Description:
79	! ------------
80	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
81	!> profile (subroutine pcm_init).
82	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
83	!> due to canopy elements (subroutine pcm_tendency).
84	!------------------------------------------------------------------------------!
85	MODULE plant_canopy_model_mod
86
87	USE arrays_3d, &
88	ONLY: dzu, dzw, e, q, s, shf, tend, u, v, w, zu, zw
89
90	USE indices, &
91	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
92	nz, nzb, nzb_s_inner, nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt
93
94	USE kinds
95
96
97	IMPLICIT NONE
98
99
100	CHARACTER (LEN=20) :: canopy_mode = 'block' !< canopy coverage
101
102	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
103	INTEGER(iwp) :: &
104	lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
105
106	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
107	LOGICAL :: plant_canopy = .FALSE. !< switch for use of canopy model
108
109	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
110	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
111	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
112	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
113	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
114	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
115	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
116	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
117	REAL(wp) :: &
118	leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
119	REAL(wp) :: &
120	leaf_surface_conc = 0.0_wp !< leaf surface concentration
121	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
122	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
123
124	REAL(wp) :: &
125	lad_vertical_gradient(10) = 0.0_wp !< lad gradient
126	REAL(wp) :: &
127	lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
128
129	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
130	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
131
132	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
133	canopy_heat_flux !< canopy heat flux
134	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
135	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
136
137
138	SAVE
139
140
141	PRIVATE
142
143	!
144	!-- Public functions
145	PUBLIC pcm_check_parameters, pcm_header, pcm_init, pcm_parin, pcm_tendency
146
147	!
148	!-- Public variables and constants
149	PUBLIC canopy_mode, cthf, dt_plant_canopy, lad, lad_s, plant_canopy
150
151
152	INTERFACE pcm_check_parameters
153	MODULE PROCEDURE pcm_check_parameters
154	END INTERFACE pcm_check_parameters
155
156	INTERFACE pcm_header
157	MODULE PROCEDURE pcm_header
158	END INTERFACE pcm_header
159
160	INTERFACE pcm_init
161	MODULE PROCEDURE pcm_init
162	END INTERFACE pcm_init
163
164	INTERFACE pcm_parin
165	MODULE PROCEDURE pcm_parin
166	END INTERFACE pcm_parin
167
168	INTERFACE pcm_tendency
169	MODULE PROCEDURE pcm_tendency
170	MODULE PROCEDURE pcm_tendency_ij
171	END INTERFACE pcm_tendency
172
173
174	CONTAINS
175
176
177	!------------------------------------------------------------------------------!
178	! Description:
179	! ------------
180	!> Check parameters routine for plant canopy model
181	!------------------------------------------------------------------------------!
182	SUBROUTINE pcm_check_parameters
183
184	USE control_parameters, &
185	ONLY: cloud_physics, message_string, microphysics_seifert
186
187
188	IMPLICIT NONE
189
190
191	IF ( canopy_drag_coeff == 0.0_wp ) THEN
192	message_string = 'plant_canopy = .TRUE. requires a non-zero drag '// &
193	'coefficient & given value is canopy_drag_coeff = 0.0'
194	CALL message( 'check_parameters', 'PA0041', 1, 2, 0, 6, 0 )
195	ENDIF
196
197	IF ( ( alpha_lad /= 9999999.9_wp .AND. beta_lad == 9999999.9_wp ) .OR.&
198	beta_lad /= 9999999.9_wp .AND. alpha_lad == 9999999.9_wp ) THEN
199	message_string = 'using the beta function for the construction ' // &
200	'of the leaf area density profile requires ' // &
201	'both alpha_lad and beta_lad to be /= 9999999.9'
202	CALL message( 'check_parameters', 'PA0118', 1, 2, 0, 6, 0 )
203	ENDIF
204
205	IF ( calc_beta_lad_profile .AND. lai_beta == 0.0_wp ) THEN
206	message_string = 'using the beta function for the construction ' // &
207	'of the leaf area density profile requires ' // &
208	'a non-zero lai_beta, but given value is ' // &
209	'lai_beta = 0.0'
210	CALL message( 'check_parameters', 'PA0119', 1, 2, 0, 6, 0 )
211	ENDIF
212
213	IF ( calc_beta_lad_profile .AND. lad_surface /= 0.0_wp ) THEN
214	message_string = 'simultaneous setting of alpha_lad /= 9999999.9' // &
215	'and lad_surface /= 0.0 is not possible, ' // &
216	'use either vertical gradients or the beta ' // &
217	'function for the construction of the leaf area '// &
218	'density profile'
219	CALL message( 'check_parameters', 'PA0120', 1, 2, 0, 6, 0 )
220	ENDIF
221
222	IF ( cloud_physics .AND. microphysics_seifert ) THEN
223	message_string = 'plant_canopy = .TRUE. requires cloud_scheme /=' // &
224	' seifert_beheng'
225	CALL message( 'check_parameters', 'PA0360', 1, 2, 0, 6, 0 )
226	ENDIF
227
228
229	END SUBROUTINE pcm_check_parameters
230
231
232	!------------------------------------------------------------------------------!
233	! Description:
234	! ------------
235	!> Header output for plant canopy model
236	!------------------------------------------------------------------------------!
237	SUBROUTINE pcm_header ( io )
238
239	USE control_parameters, &
240	ONLY: dz, passive_scalar
241
242
243	IMPLICIT NONE
244
245	CHARACTER (LEN=10) :: coor_chr !<
246
247	CHARACTER (LEN=86) :: coordinates !<
248	CHARACTER (LEN=86) :: gradients !<
249	CHARACTER (LEN=86) :: leaf_area_density !<
250	CHARACTER (LEN=86) :: slices !<
251
252	INTEGER(iwp) :: i !<
253	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
254	INTEGER(iwp) :: k !<
255
256	REAL(wp) :: canopy_height !< canopy height (in m)
257
258	canopy_height = pch_index * dz
259
260	WRITE ( io, 1 ) canopy_mode, canopy_height, pch_index, &
261	canopy_drag_coeff
262	IF ( passive_scalar ) THEN
263	WRITE ( io, 2 ) leaf_scalar_exch_coeff, &
264	leaf_surface_conc
265	ENDIF
266
267	!
268	!-- Heat flux at the top of vegetation
269	WRITE ( io, 3 ) cthf
270
271	!
272	!-- Leaf area density profile, calculated either from given vertical
273	!-- gradients or from beta probability density function.
274	IF ( .NOT. calc_beta_lad_profile ) THEN
275
276	!-- Building output strings, starting with surface value
277	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
278	gradients = '------'
279	slices = ' 0'
280	coordinates = ' 0.0'
281	i = 1
282	DO WHILE ( i < 11 .AND. lad_vertical_gradient_level_ind(i) &
283	/= -9999 )
284
285	WRITE (coor_chr,'(F7.2)') lad(lad_vertical_gradient_level_ind(i))
286	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
287	TRIM( coor_chr )
288
289	WRITE (coor_chr,'(F7.2)') lad_vertical_gradient(i)
290	gradients = TRIM( gradients ) // ' ' // TRIM( coor_chr )
291
292	WRITE (coor_chr,'(I7)') lad_vertical_gradient_level_ind(i)
293	slices = TRIM( slices ) // ' ' // TRIM( coor_chr )
294
295	WRITE (coor_chr,'(F7.1)') lad_vertical_gradient_level(i)
296	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
297
298	i = i + 1
299	ENDDO
300
301	WRITE ( io, 4 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
302	TRIM( gradients ), TRIM( slices )
303
304	ELSE
305
306	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
307	coordinates = ' 0.0'
308
309	DO k = 1, pch_index
310
311	WRITE (coor_chr,'(F7.2)') lad(k)
312	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
313	TRIM( coor_chr )
314
315	WRITE (coor_chr,'(F7.1)') zu(k)
316	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
317
318	ENDDO
319
320	WRITE ( io, 5 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
321	alpha_lad, beta_lad, lai_beta
322
323	ENDIF
324
325	1 FORMAT (//' Vegetation canopy (drag) model:'/ &
326	' ------------------------------'// &
327	' Canopy mode: ', A / &
328	' Canopy height: ',F6.2,'m (',I4,' grid points)' / &
329	' Leaf drag coefficient: ',F6.2 /)
330	2 FORMAT (/ ' Scalar exchange coefficient: ',F6.2 / &
331	' Scalar concentration at leaf surfaces in kg/m**3: ',F6.2 /)
332	3 FORMAT (' Predefined constant heatflux at the top of the vegetation: ',F6.2, &
333	' K m/s')
334	4 FORMAT (/ ' Characteristic levels of the leaf area density:'// &
335	' Height: ',A,' m'/ &
336	' Leaf area density: ',A,' m2/m3'/ &
337	' Gradient: ',A,' m2/m4'/ &
338	' Gridpoint: ',A)
339	5 FORMAT (//' Characteristic levels of the leaf area density and coefficients:'&
340	// ' Height: ',A,' m'/ &
341	' Leaf area density: ',A,' m2/m3'/ &
342	' Coefficient alpha: ',F6.2 / &
343	' Coefficient beta: ',F6.2 / &
344	' Leaf area index: ',F6.2,' m2/m2' /)
345
346	END SUBROUTINE pcm_header
347
348
349	!------------------------------------------------------------------------------!
350	! Description:
351	! ------------
352	!> Initialization of the plant canopy model
353	!------------------------------------------------------------------------------!
354	SUBROUTINE pcm_init
355
356
357	USE control_parameters, &
358	ONLY: dz, ocean, passive_scalar
359
360
361	IMPLICIT NONE
362
363	INTEGER(iwp) :: i !< running index
364	INTEGER(iwp) :: j !< running index
365	INTEGER(iwp) :: k !< running index
366
367	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
368	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
369	REAL(wp) :: gradient !< gradient for lad-profile construction
370	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
371
372	!
373	!-- Allocate one-dimensional arrays for the computation of the
374	!-- leaf area density (lad) profile
375	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
376	lad = 0.0_wp
377	pre_lad = 0.0_wp
378
379	!
380	!-- Set flag that indicates that the lad-profile shall be calculated by using
381	!-- a beta probability density function
382	IF ( alpha_lad /= 9999999.9_wp .AND. beta_lad /= 9999999.9_wp ) THEN
383	calc_beta_lad_profile = .TRUE.
384	ENDIF
385
386
387	!
388	!-- Compute the profile of leaf area density used in the plant
389	!-- canopy model. The profile can either be constructed from
390	!-- prescribed vertical gradients of the leaf area density or by
391	!-- using a beta probability density function (see e.g. Markkanen et al.,
392	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
393	IF ( .NOT. calc_beta_lad_profile ) THEN
394
395	!
396	!-- Use vertical gradients for lad-profile construction
397	i = 1
398	gradient = 0.0_wp
399
400	IF ( .NOT. ocean ) THEN
401
402	lad(0) = lad_surface
403	lad_vertical_gradient_level_ind(1) = 0
404
405	DO k = 1, pch_index
406	IF ( i < 11 ) THEN
407	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
408	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
409	gradient = lad_vertical_gradient(i)
410	lad_vertical_gradient_level_ind(i) = k - 1
411	i = i + 1
412	ENDIF
413	ENDIF
414	IF ( gradient /= 0.0_wp ) THEN
415	IF ( k /= 1 ) THEN
416	lad(k) = lad(k-1) + dzu(k) * gradient
417	ELSE
418	lad(k) = lad_surface + dzu(k) * gradient
419	ENDIF
420	ELSE
421	lad(k) = lad(k-1)
422	ENDIF
423	ENDDO
424
425	ENDIF
426
427	!
428	!-- In case of no given leaf area density gradients, choose a vanishing
429	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
430	!-- file.
431	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
432	lad_vertical_gradient_level(1) = 0.0_wp
433	ENDIF
434
435	ELSE
436
437	!
438	!-- Use beta function for lad-profile construction
439	int_bpdf = 0.0_wp
440	canopy_height = pch_index * dz
441
442	DO k = nzb, pch_index
443	int_bpdf = int_bpdf + &
444	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
445	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
446	beta_lad-1.0_wp ) ) &
447	* ( ( zw(k+1)-zw(k) ) / canopy_height ) )
448	ENDDO
449
450	!
451	!-- Preliminary lad profile (defined on w-grid)
452	DO k = nzb, pch_index
453	pre_lad(k) = lai_beta * &
454	( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) ) &
455	* ( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
456	beta_lad-1.0_wp ) ) / int_bpdf &
457	) / canopy_height
458	ENDDO
459
460	!
461	!-- Final lad profile (defined on scalar-grid level, since most prognostic
462	!-- quantities are defined there, hence, less interpolation is required
463	!-- when calculating the canopy tendencies)
464	lad(0) = pre_lad(0)
465	DO k = nzb+1, pch_index
466	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
467	ENDDO
468
469	ENDIF
470
471	!
472	!-- Allocate 3D-array for the leaf area density (lad_s). In case of a
473	!-- prescribed canopy-top heat flux (cthf), allocate 3D-arrays for
474	!-- the cumulative leaf area index (cum_lai_hf) and the canopy heat flux.
475	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
476
477	IF ( cthf /= 0.0_wp ) THEN
478	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
479	canopy_heat_flux(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
480	ENDIF
481
482	!
483	!-- Initialize canopy parameters cdc (canopy drag coefficient),
484	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
485	!-- with the prescribed values
486	cdc = canopy_drag_coeff
487	lsec = leaf_scalar_exch_coeff
488	lsc = leaf_surface_conc
489
490	!
491	!-- Initialization of the canopy coverage in the model domain:
492	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
493	!-- fully covers the domain surface
494	SELECT CASE ( TRIM( canopy_mode ) )
495
496	CASE( 'block' )
497
498	DO i = nxlg, nxrg
499	DO j = nysg, nyng
500	lad_s(:,j,i) = lad(:)
501	ENDDO
502	ENDDO
503
504	CASE DEFAULT
505
506	!
507	!-- The DEFAULT case is reached either if the parameter
508	!-- canopy mode contains a wrong character string or if the
509	!-- user has coded a special case in the user interface.
510	!-- There, the subroutine user_init_plant_canopy checks
511	!-- which of these two conditions applies.
512	CALL user_init_plant_canopy
513
514	END SELECT
515
516	!
517	!-- Initialization of the canopy heat source distribution
518	IF ( cthf /= 0.0_wp ) THEN
519	!
520	!-- Piecewise calculation of the leaf area index by vertical
521	!-- integration of the leaf area density
522	cum_lai_hf(:,:,:) = 0.0_wp
523	DO i = nxlg, nxrg
524	DO j = nysg, nyng
525	DO k = pch_index-1, 0, -1
526	IF ( k == pch_index-1 ) THEN
527	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
528	( 0.5_wp * lad_s(k+1,j,i) * &
529	( zw(k+1) - zu(k+1) ) ) + &
530	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
531	lad_s(k,j,i) ) + &
532	lad_s(k+1,j,i) ) * &
533	( zu(k+1) - zw(k) ) )
534	ELSE
535	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
536	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
537	lad_s(k+1,j,i) ) + &
538	lad_s(k+1,j,i) ) * &
539	( zw(k+1) - zu(k+1) ) ) + &
540	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
541	lad_s(k,j,i) ) + &
542	lad_s(k+1,j,i) ) * &
543	( zu(k+1) - zw(k) ) )
544	ENDIF
545	ENDDO
546	ENDDO
547	ENDDO
548
549	!
550	!-- Calculation of the upward kinematic vertical heat flux within the
551	!-- canopy
552	DO i = nxlg, nxrg
553	DO j = nysg, nyng
554	DO k = 0, pch_index
555	canopy_heat_flux(k,j,i) = cthf * &
556	exp( -0.6_wp * cum_lai_hf(k,j,i) )
557	ENDDO
558	ENDDO
559	ENDDO
560
561	!
562	!-- In areas covered with canopy, the surface heat flux is set to
563	!-- the surface value of the above calculated in-canopy heat flux
564	!-- distribution
565	DO i = nxlg,nxrg
566	DO j = nysg, nyng
567	IF ( canopy_heat_flux(0,j,i) /= cthf ) THEN
568	shf(j,i) = canopy_heat_flux(0,j,i)
569	ENDIF
570	ENDDO
571	ENDDO
572
573	ENDIF
574
575
576
577	END SUBROUTINE pcm_init
578
579
580
581	!------------------------------------------------------------------------------!
582	! Description:
583	! ------------
584	!> Calculation of the tendency terms, accounting for the effect of the plant
585	!> canopy on momentum and scalar quantities.
586	!>
587	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
588	!> (defined on scalar grid), as initialized in subroutine pcm_init.
589	!> The lad on the w-grid is vertically interpolated from the surrounding
590	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
591	!> k = pch_index. Here, the lad is zero.
592	!>
593	!> The canopy drag must be limited (previously accounted for by calculation of
594	!> a limiting canopy timestep for the determination of the maximum LES timestep
595	!> in subroutine timestep), since it is physically impossible that the canopy
596	!> drag alone can locally change the sign of a velocity component. This
597	!> limitation is realized by calculating preliminary tendencies and velocities.
598	!> It is subsequently checked if the preliminary new velocity has a different
599	!> sign than the current velocity. If so, the tendency is limited in a way that
600	!> the velocity can at maximum be reduced to zero by the canopy drag.
601	!>
602	!>
603	!> Call for all grid points
604	!------------------------------------------------------------------------------!
605	SUBROUTINE pcm_tendency( component )
606
607
608	USE control_parameters, &
609	ONLY: dt_3d, message_string
610
611	USE kinds
612
613	IMPLICIT NONE
614
615	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
616	INTEGER(iwp) :: i !< running index
617	INTEGER(iwp) :: j !< running index
618	INTEGER(iwp) :: k !< running index
619	INTEGER(iwp) :: kk !< running index for flat lad arrays
620
621	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
622	REAL(wp) :: lad_local !< local lad value
623	REAL(wp) :: pre_tend !< preliminary tendency
624	REAL(wp) :: pre_u !< preliminary u-value
625	REAL(wp) :: pre_v !< preliminary v-value
626	REAL(wp) :: pre_w !< preliminary w-value
627
628
629	ddt_3d = 1.0_wp / dt_3d
630
631	!
632	!-- Compute drag for the three velocity components and the SGS-TKE:
633	SELECT CASE ( component )
634
635	!
636	!-- u-component
637	CASE ( 1 )
638	DO i = nxlu, nxr
639	DO j = nys, nyn
640	DO k = nzb_u_inner(j,i)+1, nzb_u_inner(j,i)+pch_index
641
642	kk = k - nzb_u_inner(j,i) !- lad arrays are defined flat
643	!
644	!-- In order to create sharp boundaries of the plant canopy,
645	!-- the lad on the u-grid at index (k,j,i) is equal to
646	!-- lad_s(k,j,i), rather than being interpolated from the
647	!-- surrounding lad_s, because this would yield smaller lad
648	!-- at the canopy boundaries than inside of the canopy.
649	!-- For the same reason, the lad at the rightmost(i+1)canopy
650	!-- boundary on the u-grid equals lad_s(k,j,i).
651	lad_local = lad_s(kk,j,i)
652	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp )&
653	THEN
654	lad_local = lad_s(kk,j,i-1)
655	ENDIF
656
657	pre_tend = 0.0_wp
658	pre_u = 0.0_wp
659	!
660	!-- Calculate preliminary value (pre_tend) of the tendency
661	pre_tend = - cdc * &
662	lad_local * &
663	SQRT( u(k,j,i)**2 + &
664	( 0.25_wp * ( v(k,j,i-1) + &
665	v(k,j,i) + &
666	v(k,j+1,i) + &
667	v(k,j+1,i-1) ) &
668	)**2 + &
669	( 0.25_wp * ( w(k-1,j,i-1) + &
670	w(k-1,j,i) + &
671	w(k,j,i-1) + &
672	w(k,j,i) ) &
673	)**2 &
674	) * &
675	u(k,j,i)
676
677	!
678	!-- Calculate preliminary new velocity, based on pre_tend
679	pre_u = u(k,j,i) + dt_3d * pre_tend
680	!
681	!-- Compare sign of old velocity and new preliminary velocity,
682	!-- and in case the signs are different, limit the tendency
683	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
684	pre_tend = - u(k,j,i) * ddt_3d
685	ELSE
686	pre_tend = pre_tend
687	ENDIF
688	!
689	!-- Calculate final tendency
690	tend(k,j,i) = tend(k,j,i) + pre_tend
691
692	ENDDO
693	ENDDO
694	ENDDO
695
696	!
697	!-- v-component
698	CASE ( 2 )
699	DO i = nxl, nxr
700	DO j = nysv, nyn
701	DO k = nzb_v_inner(j,i)+1, nzb_v_inner(j,i)+pch_index
702
703	kk = k - nzb_v_inner(j,i) !- lad arrays are defined flat
704	!
705	!-- In order to create sharp boundaries of the plant canopy,
706	!-- the lad on the v-grid at index (k,j,i) is equal to
707	!-- lad_s(k,j,i), rather than being interpolated from the
708	!-- surrounding lad_s, because this would yield smaller lad
709	!-- at the canopy boundaries than inside of the canopy.
710	!-- For the same reason, the lad at the northmost(j+1) canopy
711	!-- boundary on the v-grid equals lad_s(k,j,i).
712	lad_local = lad_s(kk,j,i)
713	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp )&
714	THEN
715	lad_local = lad_s(kk,j-1,i)
716	ENDIF
717
718	pre_tend = 0.0_wp
719	pre_v = 0.0_wp
720	!
721	!-- Calculate preliminary value (pre_tend) of the tendency
722	pre_tend = - cdc * &
723	lad_local * &
724	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
725	u(k,j-1,i+1) + &
726	u(k,j,i) + &
727	u(k,j,i+1) ) &
728	)**2 + &
729	v(k,j,i)**2 + &
730	( 0.25_wp * ( w(k-1,j-1,i) + &
731	w(k-1,j,i) + &
732	w(k,j-1,i) + &
733	w(k,j,i) ) &
734	)**2 &
735	) * &
736	v(k,j,i)
737
738	!
739	!-- Calculate preliminary new velocity, based on pre_tend
740	pre_v = v(k,j,i) + dt_3d * pre_tend
741	!
742	!-- Compare sign of old velocity and new preliminary velocity,
743	!-- and in case the signs are different, limit the tendency
744	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
745	pre_tend = - v(k,j,i) * ddt_3d
746	ELSE
747	pre_tend = pre_tend
748	ENDIF
749	!
750	!-- Calculate final tendency
751	tend(k,j,i) = tend(k,j,i) + pre_tend
752
753	ENDDO
754	ENDDO
755	ENDDO
756
757	!
758	!-- w-component
759	CASE ( 3 )
760	DO i = nxl, nxr
761	DO j = nys, nyn
762	DO k = nzb_w_inner(j,i)+1, nzb_w_inner(j,i)+pch_index-1
763
764	kk = k - nzb_w_inner(j,i) !- lad arrays are defined flat
765
766	pre_tend = 0.0_wp
767	pre_w = 0.0_wp
768	!
769	!-- Calculate preliminary value (pre_tend) of the tendency
770	pre_tend = - cdc * &
771	(0.5_wp * &
772	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
773	SQRT( ( 0.25_wp * ( u(k,j,i) + &
774	u(k,j,i+1) + &
775	u(k+1,j,i) + &
776	u(k+1,j,i+1) ) &
777	)**2 + &
778	( 0.25_wp * ( v(k,j,i) + &
779	v(k,j+1,i) + &
780	v(k+1,j,i) + &
781	v(k+1,j+1,i) ) &
782	)**2 + &
783	w(k,j,i)**2 &
784	) * &
785	w(k,j,i)
786	!
787	!-- Calculate preliminary new velocity, based on pre_tend
788	pre_w = w(k,j,i) + dt_3d * pre_tend
789	!
790	!-- Compare sign of old velocity and new preliminary velocity,
791	!-- and in case the signs are different, limit the tendency
792	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
793	pre_tend = - w(k,j,i) * ddt_3d
794	ELSE
795	pre_tend = pre_tend
796	ENDIF
797	!
798	!-- Calculate final tendency
799	tend(k,j,i) = tend(k,j,i) + pre_tend
800
801	ENDDO
802	ENDDO
803	ENDDO
804
805	!
806	!-- potential temperature
807	CASE ( 4 )
808	DO i = nxl, nxr
809	DO j = nys, nyn
810	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
811	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
812	tend(k,j,i) = tend(k,j,i) + &
813	( canopy_heat_flux(kk,j,i) - &
814	canopy_heat_flux(kk-1,j,i) ) / dzw(k)
815	ENDDO
816	ENDDO
817	ENDDO
818
819	!
820	!-- humidity
821	CASE ( 5 )
822	DO i = nxl, nxr
823	DO j = nys, nyn
824	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
825	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
826	tend(k,j,i) = tend(k,j,i) - &
827	lsec * &
828	lad_s(kk,j,i) * &
829	SQRT( ( 0.5_wp * ( u(k,j,i) + &
830	u(k,j,i+1) ) &
831	)**2 + &
832	( 0.5_wp * ( v(k,j,i) + &
833	v(k,j+1,i) ) &
834	)**2 + &
835	( 0.5_wp * ( w(k-1,j,i) + &
836	w(k,j,i) ) &
837	)**2 &
838	) * &
839	( q(k,j,i) - lsc )
840	ENDDO
841	ENDDO
842	ENDDO
843
844	!
845	!-- sgs-tke
846	CASE ( 6 )
847	DO i = nxl, nxr
848	DO j = nys, nyn
849	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
850	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
851	tend(k,j,i) = tend(k,j,i) - &
852	2.0_wp * cdc * &
853	lad_s(kk,j,i) * &
854	SQRT( ( 0.5_wp * ( u(k,j,i) + &
855	u(k,j,i+1) ) &
856	)**2 + &
857	( 0.5_wp * ( v(k,j,i) + &
858	v(k,j+1,i) ) &
859	)**2 + &
860	( 0.5_wp * ( w(k,j,i) + &
861	w(k+1,j,i) ) &
862	)**2 &
863	) * &
864	e(k,j,i)
865	ENDDO
866	ENDDO
867	ENDDO
868	!
869	!-- scalar concentration
870	CASE ( 7 )
871	DO i = nxl, nxr
872	DO j = nys, nyn
873	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
874	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
875	tend(k,j,i) = tend(k,j,i) - &
876	lsec * &
877	lad_s(kk,j,i) * &
878	SQRT( ( 0.5_wp * ( u(k,j,i) + &
879	u(k,j,i+1) ) &
880	)**2 + &
881	( 0.5_wp * ( v(k,j,i) + &
882	v(k,j+1,i) ) &
883	)**2 + &
884	( 0.5_wp * ( w(k-1,j,i) + &
885	w(k,j,i) ) &
886	)**2 &
887	) * &
888	( s(k,j,i) - lsc )
889	ENDDO
890	ENDDO
891	ENDDO
892
893
894
895	CASE DEFAULT
896
897	WRITE( message_string, * ) 'wrong component: ', component
898	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
899
900	END SELECT
901
902	END SUBROUTINE pcm_tendency
903
904
905	!------------------------------------------------------------------------------!
906	! Description:
907	! ------------
908	!> Parin for &canopy_par for plant canopy model
909	!------------------------------------------------------------------------------!
910	SUBROUTINE pcm_parin
911
912
913	IMPLICIT NONE
914
915	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
916
917	NAMELIST /canopy_par/ alpha_lad, beta_lad, canopy_drag_coeff, &
918	canopy_mode, cthf, &
919	lad_surface, &
920	lad_vertical_gradient, &
921	lad_vertical_gradient_level, &
922	lai_beta, &
923	leaf_scalar_exch_coeff, &
924	leaf_surface_conc, pch_index
925
926	line = ' '
927
928	!
929	!-- Try to find radiation model package
930	REWIND ( 11 )
931	line = ' '
932	DO WHILE ( INDEX( line, '&canopy_par' ) == 0 )
933	READ ( 11, '(A)', END=10 ) line
934	ENDDO
935	BACKSPACE ( 11 )
936
937	!
938	!-- Read user-defined namelist
939	READ ( 11, canopy_par )
940
941	!
942	!-- Set flag that indicates that the radiation model is switched on
943	plant_canopy = .TRUE.
944
945	10 CONTINUE
946
947
948	END SUBROUTINE pcm_parin
949
950
951
952	!------------------------------------------------------------------------------!
953	! Description:
954	! ------------
955	!> Calculation of the tendency terms, accounting for the effect of the plant
956	!> canopy on momentum and scalar quantities.
957	!>
958	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
959	!> (defined on scalar grid), as initialized in subroutine pcm_init.
960	!> The lad on the w-grid is vertically interpolated from the surrounding
961	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
962	!> k = pch_index. Here, the lad is zero.
963	!>
964	!> The canopy drag must be limited (previously accounted for by calculation of
965	!> a limiting canopy timestep for the determination of the maximum LES timestep
966	!> in subroutine timestep), since it is physically impossible that the canopy
967	!> drag alone can locally change the sign of a velocity component. This
968	!> limitation is realized by calculating preliminary tendencies and velocities.
969	!> It is subsequently checked if the preliminary new velocity has a different
970	!> sign than the current velocity. If so, the tendency is limited in a way that
971	!> the velocity can at maximum be reduced to zero by the canopy drag.
972	!>
973	!>
974	!> Call for grid point i,j
975	!------------------------------------------------------------------------------!
976	SUBROUTINE pcm_tendency_ij( i, j, component )
977
978
979	USE control_parameters, &
980	ONLY: dt_3d, message_string
981
982	USE kinds
983
984	IMPLICIT NONE
985
986	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
987	INTEGER(iwp) :: i !< running index
988	INTEGER(iwp) :: j !< running index
989	INTEGER(iwp) :: k !< running index
990	INTEGER(iwp) :: kk !< running index for flat lad arrays
991
992	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
993	REAL(wp) :: lad_local !< local lad value
994	REAL(wp) :: pre_tend !< preliminary tendency
995	REAL(wp) :: pre_u !< preliminary u-value
996	REAL(wp) :: pre_v !< preliminary v-value
997	REAL(wp) :: pre_w !< preliminary w-value
998
999
1000	ddt_3d = 1.0_wp / dt_3d
1001
1002	!
1003	!-- Compute drag for the three velocity components and the SGS-TKE
1004	SELECT CASE ( component )
1005
1006	!
1007	!-- u-component
1008	CASE ( 1 )
1009	DO k = nzb_u_inner(j,i)+1, nzb_u_inner(j,i)+pch_index
1010
1011	kk = k - nzb_u_inner(j,i) !- lad arrays are defined flat
1012	!
1013	!-- In order to create sharp boundaries of the plant canopy,
1014	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
1015	!-- rather than being interpolated from the surrounding lad_s,
1016	!-- because this would yield smaller lad at the canopy boundaries
1017	!-- than inside of the canopy.
1018	!-- For the same reason, the lad at the rightmost(i+1)canopy
1019	!-- boundary on the u-grid equals lad_s(k,j,i).
1020	lad_local = lad_s(kk,j,i)
1021	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp ) THEN
1022	lad_local = lad_s(kk,j,i-1)
1023	ENDIF
1024
1025	pre_tend = 0.0_wp
1026	pre_u = 0.0_wp
1027	!
1028	!-- Calculate preliminary value (pre_tend) of the tendency
1029	pre_tend = - cdc * &
1030	lad_local * &
1031	SQRT( u(k,j,i)**2 + &
1032	( 0.25_wp * ( v(k,j,i-1) + &
1033	v(k,j,i) + &
1034	v(k,j+1,i) + &
1035	v(k,j+1,i-1) ) &
1036	)**2 + &
1037	( 0.25_wp * ( w(k-1,j,i-1) + &
1038	w(k-1,j,i) + &
1039	w(k,j,i-1) + &
1040	w(k,j,i) ) &
1041	)**2 &
1042	) * &
1043	u(k,j,i)
1044
1045	!
1046	!-- Calculate preliminary new velocity, based on pre_tend
1047	pre_u = u(k,j,i) + dt_3d * pre_tend
1048	!
1049	!-- Compare sign of old velocity and new preliminary velocity,
1050	!-- and in case the signs are different, limit the tendency
1051	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1052	pre_tend = - u(k,j,i) * ddt_3d
1053	ELSE
1054	pre_tend = pre_tend
1055	ENDIF
1056	!
1057	!-- Calculate final tendency
1058	tend(k,j,i) = tend(k,j,i) + pre_tend
1059	ENDDO
1060
1061
1062	!
1063	!-- v-component
1064	CASE ( 2 )
1065	DO k = nzb_v_inner(j,i)+1, nzb_v_inner(j,i)+pch_index
1066
1067	kk = k - nzb_v_inner(j,i) !- lad arrays are defined flat
1068	!
1069	!-- In order to create sharp boundaries of the plant canopy,
1070	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
1071	!-- rather than being interpolated from the surrounding lad_s,
1072	!-- because this would yield smaller lad at the canopy boundaries
1073	!-- than inside of the canopy.
1074	!-- For the same reason, the lad at the northmost(j+1)canopy
1075	!-- boundary on the v-grid equals lad_s(k,j,i).
1076	lad_local = lad_s(kk,j,i)
1077	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp ) THEN
1078	lad_local = lad_s(kk,j-1,i)
1079	ENDIF
1080
1081	pre_tend = 0.0_wp
1082	pre_v = 0.0_wp
1083	!
1084	!-- Calculate preliminary value (pre_tend) of the tendency
1085	pre_tend = - cdc * &
1086	lad_local * &
1087	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1088	u(k,j-1,i+1) + &
1089	u(k,j,i) + &
1090	u(k,j,i+1) ) &
1091	)**2 + &
1092	v(k,j,i)**2 + &
1093	( 0.25_wp * ( w(k-1,j-1,i) + &
1094	w(k-1,j,i) + &
1095	w(k,j-1,i) + &
1096	w(k,j,i) ) &
1097	)**2 &
1098	) * &
1099	v(k,j,i)
1100
1101	!
1102	!-- Calculate preliminary new velocity, based on pre_tend
1103	pre_v = v(k,j,i) + dt_3d * pre_tend
1104	!
1105	!-- Compare sign of old velocity and new preliminary velocity,
1106	!-- and in case the signs are different, limit the tendency
1107	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1108	pre_tend = - v(k,j,i) * ddt_3d
1109	ELSE
1110	pre_tend = pre_tend
1111	ENDIF
1112	!
1113	!-- Calculate final tendency
1114	tend(k,j,i) = tend(k,j,i) + pre_tend
1115	ENDDO
1116
1117
1118	!
1119	!-- w-component
1120	CASE ( 3 )
1121	DO k = nzb_w_inner(j,i)+1, nzb_w_inner(j,i)+pch_index-1
1122
1123	kk = k - nzb_w_inner(j,i) !- lad arrays are defined flat
1124
1125	pre_tend = 0.0_wp
1126	pre_w = 0.0_wp
1127	!
1128	!-- Calculate preliminary value (pre_tend) of the tendency
1129	pre_tend = - cdc * &
1130	(0.5_wp * &
1131	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1132	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1133	u(k,j,i+1) + &
1134	u(k+1,j,i) + &
1135	u(k+1,j,i+1) ) &
1136	)**2 + &
1137	( 0.25_wp * ( v(k,j,i) + &
1138	v(k,j+1,i) + &
1139	v(k+1,j,i) + &
1140	v(k+1,j+1,i) ) &
1141	)**2 + &
1142	w(k,j,i)**2 &
1143	) * &
1144	w(k,j,i)
1145	!
1146	!-- Calculate preliminary new velocity, based on pre_tend
1147	pre_w = w(k,j,i) + dt_3d * pre_tend
1148	!
1149	!-- Compare sign of old velocity and new preliminary velocity,
1150	!-- and in case the signs are different, limit the tendency
1151	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1152	pre_tend = - w(k,j,i) * ddt_3d
1153	ELSE
1154	pre_tend = pre_tend
1155	ENDIF
1156	!
1157	!-- Calculate final tendency
1158	tend(k,j,i) = tend(k,j,i) + pre_tend
1159	ENDDO
1160
1161	!
1162	!-- potential temperature
1163	CASE ( 4 )
1164	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1165	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1166	tend(k,j,i) = tend(k,j,i) + &
1167	( canopy_heat_flux(kk,j,i) - &
1168	canopy_heat_flux(kk-1,j,i) ) / dzw(k)
1169	ENDDO
1170
1171
1172	!
1173	!-- humidity
1174	CASE ( 5 )
1175	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1176	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1177	tend(k,j,i) = tend(k,j,i) - &
1178	lsec * &
1179	lad_s(kk,j,i) * &
1180	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1181	u(k,j,i+1) ) &
1182	)**2 + &
1183	( 0.5_wp * ( v(k,j,i) + &
1184	v(k,j+1,i) ) &
1185	)**2 + &
1186	( 0.5_wp * ( w(k-1,j,i) + &
1187	w(k,j,i) ) &
1188	)**2 &
1189	) * &
1190	( q(k,j,i) - lsc )
1191	ENDDO
1192
1193	!
1194	!-- sgs-tke
1195	CASE ( 6 )
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
1214	!
1215	!-- scalar concentration
1216	CASE ( 7 )
1217	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1218	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1219	tend(k,j,i) = tend(k,j,i) - &
1220	lsec * &
1221	lad_s(kk,j,i) * &
1222	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1223	u(k,j,i+1) ) &
1224	)**2 + &
1225	( 0.5_wp * ( v(k,j,i) + &
1226	v(k,j+1,i) ) &
1227	)**2 + &
1228	( 0.5_wp * ( w(k-1,j,i) + &
1229	w(k,j,i) ) &
1230	)**2 &
1231	) * &
1232	( s(k,j,i) - lsc )
1233	ENDDO
1234
1235	CASE DEFAULT
1236
1237	WRITE( message_string, * ) 'wrong component: ', component
1238	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1239
1240	END SELECT
1241
1242	END SUBROUTINE pcm_tendency_ij
1243
1244	END MODULE plant_canopy_model_mod

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