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source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 2005

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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 1997-2016 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: plant_canopy_model_mod.f90 2001 2016-08-20 18:41:22Z suehring $
27	!
28	! 2000 2016-08-20 18:09:15Z knoop
29	! Forced header and separation lines into 80 columns
30	!
31	! 1960 2016-07-12 16:34:24Z suehring
32	! Separate humidity and passive scalar
33	!
34	! 1953 2016-06-21 09:28:42Z suehring
35	! Bugfix, lad_s and lad must be public
36	!
37	! 1826 2016-04-07 12:01:39Z maronga
38	! Further modularization
39	!
40	! 1721 2015-11-16 12:56:48Z raasch
41	! bugfixes: shf is reduced in areas covered with canopy only,
42	! canopy is set on top of topography
43	!
44	! 1682 2015-10-07 23:56:08Z knoop
45	! Code annotations made doxygen readable
46	!
47	! 1484 2014-10-21 10:53:05Z kanani
48	! Changes due to new module structure of the plant canopy model:
49	! module plant_canopy_model_mod now contains a subroutine for the
50	! initialization of the canopy model (pcm_init),
51	! limitation of the canopy drag (previously accounted for by calculation of
52	! a limiting canopy timestep for the determination of the maximum LES timestep
53	! in subroutine timestep) is now realized by the calculation of pre-tendencies
54	! and preliminary velocities in subroutine pcm_tendency,
55	! some redundant MPI communication removed in subroutine pcm_init
56	! (was previously in init_3d_model),
57	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
58	! respective grid is now provided only by lad_s (e.g. in the calculation of
59	! the tendency terms or of cum_lai_hf),
60	! drag_coefficient, lai, leaf_surface_concentration,
61	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
62	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
63	! respectively,
64	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
65	! USE-statements and ONLY-lists modified accordingly
66	!
67	! 1340 2014-03-25 19:45:13Z kanani
68	! REAL constants defined as wp-kind
69	!
70	! 1320 2014-03-20 08:40:49Z raasch
71	! ONLY-attribute added to USE-statements,
72	! kind-parameters added to all INTEGER and REAL declaration statements,
73	! kinds are defined in new module kinds,
74	! old module precision_kind is removed,
75	! revision history before 2012 removed,
76	! comment fields (!:) to be used for variable explanations added to
77	! all variable declaration statements
78	!
79	! 1036 2012-10-22 13:43:42Z raasch
80	! code put under GPL (PALM 3.9)
81	!
82	! 138 2007-11-28 10:03:58Z letzel
83	! Initial revision
84	!
85	! Description:
86	! ------------
87	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
88	!> profile (subroutine pcm_init).
89	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
90	!> due to canopy elements (subroutine pcm_tendency).
91	!------------------------------------------------------------------------------!
92	MODULE plant_canopy_model_mod
93
94	USE arrays_3d, &
95	ONLY: dzu, dzw, e, q, s, shf, tend, u, v, w, zu, zw
96
97	USE indices, &
98	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
99	nz, nzb, nzb_s_inner, nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt
100
101	USE kinds
102
103
104	IMPLICIT NONE
105
106
107	CHARACTER (LEN=20) :: canopy_mode = 'block' !< canopy coverage
108
109	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
110	INTEGER(iwp) :: &
111	lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
112
113	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
114	LOGICAL :: plant_canopy = .FALSE. !< switch for use of canopy model
115
116	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
117	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
118	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
119	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
120	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
121	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
122	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
123	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
124	REAL(wp) :: &
125	leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
126	REAL(wp) :: &
127	leaf_surface_conc = 0.0_wp !< leaf surface concentration
128	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
129	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
130
131	REAL(wp) :: &
132	lad_vertical_gradient(10) = 0.0_wp !< lad gradient
133	REAL(wp) :: &
134	lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
135
136	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
137	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
138
139	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
140	canopy_heat_flux !< canopy heat flux
141	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
142	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
143
144
145	SAVE
146
147
148	PRIVATE
149
150	!
151	!-- Public functions
152	PUBLIC pcm_check_parameters, pcm_header, pcm_init, pcm_parin, pcm_tendency
153
154	!
155	!-- Public variables and constants
156	PUBLIC canopy_mode, cthf, dt_plant_canopy, lad, lad_s, plant_canopy
157
158
159	INTERFACE pcm_check_parameters
160	MODULE PROCEDURE pcm_check_parameters
161	END INTERFACE pcm_check_parameters
162
163	INTERFACE pcm_header
164	MODULE PROCEDURE pcm_header
165	END INTERFACE pcm_header
166
167	INTERFACE pcm_init
168	MODULE PROCEDURE pcm_init
169	END INTERFACE pcm_init
170
171	INTERFACE pcm_parin
172	MODULE PROCEDURE pcm_parin
173	END INTERFACE pcm_parin
174
175	INTERFACE pcm_tendency
176	MODULE PROCEDURE pcm_tendency
177	MODULE PROCEDURE pcm_tendency_ij
178	END INTERFACE pcm_tendency
179
180
181	CONTAINS
182
183
184	!------------------------------------------------------------------------------!
185	! Description:
186	! ------------
187	!> Check parameters routine for plant canopy model
188	!------------------------------------------------------------------------------!
189	SUBROUTINE pcm_check_parameters
190
191	USE control_parameters, &
192	ONLY: cloud_physics, message_string, microphysics_seifert
193
194
195	IMPLICIT NONE
196
197
198	IF ( canopy_drag_coeff == 0.0_wp ) THEN
199	message_string = 'plant_canopy = .TRUE. requires a non-zero drag '// &
200	'coefficient & given value is canopy_drag_coeff = 0.0'
201	CALL message( 'check_parameters', 'PA0041', 1, 2, 0, 6, 0 )
202	ENDIF
203
204	IF ( ( alpha_lad /= 9999999.9_wp .AND. beta_lad == 9999999.9_wp ) .OR.&
205	beta_lad /= 9999999.9_wp .AND. alpha_lad == 9999999.9_wp ) THEN
206	message_string = 'using the beta function for the construction ' // &
207	'of the leaf area density profile requires ' // &
208	'both alpha_lad and beta_lad to be /= 9999999.9'
209	CALL message( 'check_parameters', 'PA0118', 1, 2, 0, 6, 0 )
210	ENDIF
211
212	IF ( calc_beta_lad_profile .AND. lai_beta == 0.0_wp ) THEN
213	message_string = 'using the beta function for the construction ' // &
214	'of the leaf area density profile requires ' // &
215	'a non-zero lai_beta, but given value is ' // &
216	'lai_beta = 0.0'
217	CALL message( 'check_parameters', 'PA0119', 1, 2, 0, 6, 0 )
218	ENDIF
219
220	IF ( calc_beta_lad_profile .AND. lad_surface /= 0.0_wp ) THEN
221	message_string = 'simultaneous setting of alpha_lad /= 9999999.9' // &
222	'and lad_surface /= 0.0 is not possible, ' // &
223	'use either vertical gradients or the beta ' // &
224	'function for the construction of the leaf area '// &
225	'density profile'
226	CALL message( 'check_parameters', 'PA0120', 1, 2, 0, 6, 0 )
227	ENDIF
228
229	IF ( cloud_physics .AND. microphysics_seifert ) THEN
230	message_string = 'plant_canopy = .TRUE. requires cloud_scheme /=' // &
231	' seifert_beheng'
232	CALL message( 'check_parameters', 'PA0360', 1, 2, 0, 6, 0 )
233	ENDIF
234
235
236	END SUBROUTINE pcm_check_parameters
237
238
239	!------------------------------------------------------------------------------!
240	! Description:
241	! ------------
242	!> Header output for plant canopy model
243	!------------------------------------------------------------------------------!
244	SUBROUTINE pcm_header ( io )
245
246	USE control_parameters, &
247	ONLY: dz, passive_scalar
248
249
250	IMPLICIT NONE
251
252	CHARACTER (LEN=10) :: coor_chr !<
253
254	CHARACTER (LEN=86) :: coordinates !<
255	CHARACTER (LEN=86) :: gradients !<
256	CHARACTER (LEN=86) :: leaf_area_density !<
257	CHARACTER (LEN=86) :: slices !<
258
259	INTEGER(iwp) :: i !<
260	INTEGER(iwp), INTENT(IN) :: io !< Unit of the output file
261	INTEGER(iwp) :: k !<
262
263	REAL(wp) :: canopy_height !< canopy height (in m)
264
265	canopy_height = pch_index * dz
266
267	WRITE ( io, 1 ) canopy_mode, canopy_height, pch_index, &
268	canopy_drag_coeff
269	IF ( passive_scalar ) THEN
270	WRITE ( io, 2 ) leaf_scalar_exch_coeff, &
271	leaf_surface_conc
272	ENDIF
273
274	!
275	!-- Heat flux at the top of vegetation
276	WRITE ( io, 3 ) cthf
277
278	!
279	!-- Leaf area density profile, calculated either from given vertical
280	!-- gradients or from beta probability density function.
281	IF ( .NOT. calc_beta_lad_profile ) THEN
282
283	!-- Building output strings, starting with surface value
284	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
285	gradients = '------'
286	slices = ' 0'
287	coordinates = ' 0.0'
288	i = 1
289	DO WHILE ( i < 11 .AND. lad_vertical_gradient_level_ind(i) &
290	/= -9999 )
291
292	WRITE (coor_chr,'(F7.2)') lad(lad_vertical_gradient_level_ind(i))
293	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
294	TRIM( coor_chr )
295
296	WRITE (coor_chr,'(F7.2)') lad_vertical_gradient(i)
297	gradients = TRIM( gradients ) // ' ' // TRIM( coor_chr )
298
299	WRITE (coor_chr,'(I7)') lad_vertical_gradient_level_ind(i)
300	slices = TRIM( slices ) // ' ' // TRIM( coor_chr )
301
302	WRITE (coor_chr,'(F7.1)') lad_vertical_gradient_level(i)
303	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
304
305	i = i + 1
306	ENDDO
307
308	WRITE ( io, 4 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
309	TRIM( gradients ), TRIM( slices )
310
311	ELSE
312
313	WRITE ( leaf_area_density, '(F7.4)' ) lad_surface
314	coordinates = ' 0.0'
315
316	DO k = 1, pch_index
317
318	WRITE (coor_chr,'(F7.2)') lad(k)
319	leaf_area_density = TRIM( leaf_area_density ) // ' ' // &
320	TRIM( coor_chr )
321
322	WRITE (coor_chr,'(F7.1)') zu(k)
323	coordinates = TRIM( coordinates ) // ' ' // TRIM( coor_chr )
324
325	ENDDO
326
327	WRITE ( io, 5 ) TRIM( coordinates ), TRIM( leaf_area_density ), &
328	alpha_lad, beta_lad, lai_beta
329
330	ENDIF
331
332	1 FORMAT (//' Vegetation canopy (drag) model:'/ &
333	' ------------------------------'// &
334	' Canopy mode: ', A / &
335	' Canopy height: ',F6.2,'m (',I4,' grid points)' / &
336	' Leaf drag coefficient: ',F6.2 /)
337	2 FORMAT (/ ' Scalar exchange coefficient: ',F6.2 / &
338	' Scalar concentration at leaf surfaces in kg/m**3: ',F6.2 /)
339	3 FORMAT (' Predefined constant heatflux at the top of the vegetation: ',F6.2, &
340	' K m/s')
341	4 FORMAT (/ ' Characteristic levels of the leaf area density:'// &
342	' Height: ',A,' m'/ &
343	' Leaf area density: ',A,' m2/m3'/ &
344	' Gradient: ',A,' m2/m4'/ &
345	' Gridpoint: ',A)
346	5 FORMAT (//' Characteristic levels of the leaf area density and coefficients:'&
347	// ' Height: ',A,' m'/ &
348	' Leaf area density: ',A,' m2/m3'/ &
349	' Coefficient alpha: ',F6.2 / &
350	' Coefficient beta: ',F6.2 / &
351	' Leaf area index: ',F6.2,' m2/m2' /)
352
353	END SUBROUTINE pcm_header
354
355
356	!------------------------------------------------------------------------------!
357	! Description:
358	! ------------
359	!> Initialization of the plant canopy model
360	!------------------------------------------------------------------------------!
361	SUBROUTINE pcm_init
362
363
364	USE control_parameters, &
365	ONLY: dz, ocean, passive_scalar
366
367
368	IMPLICIT NONE
369
370	INTEGER(iwp) :: i !< running index
371	INTEGER(iwp) :: j !< running index
372	INTEGER(iwp) :: k !< running index
373
374	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
375	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
376	REAL(wp) :: gradient !< gradient for lad-profile construction
377	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
378
379	!
380	!-- Allocate one-dimensional arrays for the computation of the
381	!-- leaf area density (lad) profile
382	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
383	lad = 0.0_wp
384	pre_lad = 0.0_wp
385
386	!
387	!-- Set flag that indicates that the lad-profile shall be calculated by using
388	!-- a beta probability density function
389	IF ( alpha_lad /= 9999999.9_wp .AND. beta_lad /= 9999999.9_wp ) THEN
390	calc_beta_lad_profile = .TRUE.
391	ENDIF
392
393
394	!
395	!-- Compute the profile of leaf area density used in the plant
396	!-- canopy model. The profile can either be constructed from
397	!-- prescribed vertical gradients of the leaf area density or by
398	!-- using a beta probability density function (see e.g. Markkanen et al.,
399	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
400	IF ( .NOT. calc_beta_lad_profile ) THEN
401
402	!
403	!-- Use vertical gradients for lad-profile construction
404	i = 1
405	gradient = 0.0_wp
406
407	IF ( .NOT. ocean ) THEN
408
409	lad(0) = lad_surface
410	lad_vertical_gradient_level_ind(1) = 0
411
412	DO k = 1, pch_index
413	IF ( i < 11 ) THEN
414	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
415	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
416	gradient = lad_vertical_gradient(i)
417	lad_vertical_gradient_level_ind(i) = k - 1
418	i = i + 1
419	ENDIF
420	ENDIF
421	IF ( gradient /= 0.0_wp ) THEN
422	IF ( k /= 1 ) THEN
423	lad(k) = lad(k-1) + dzu(k) * gradient
424	ELSE
425	lad(k) = lad_surface + dzu(k) * gradient
426	ENDIF
427	ELSE
428	lad(k) = lad(k-1)
429	ENDIF
430	ENDDO
431
432	ENDIF
433
434	!
435	!-- In case of no given leaf area density gradients, choose a vanishing
436	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
437	!-- file.
438	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
439	lad_vertical_gradient_level(1) = 0.0_wp
440	ENDIF
441
442	ELSE
443
444	!
445	!-- Use beta function for lad-profile construction
446	int_bpdf = 0.0_wp
447	canopy_height = pch_index * dz
448
449	DO k = nzb, pch_index
450	int_bpdf = int_bpdf + &
451	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
452	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
453	beta_lad-1.0_wp ) ) &
454	* ( ( zw(k+1)-zw(k) ) / canopy_height ) )
455	ENDDO
456
457	!
458	!-- Preliminary lad profile (defined on w-grid)
459	DO k = nzb, pch_index
460	pre_lad(k) = lai_beta * &
461	( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) ) &
462	* ( ( 1.0_wp - ( zw(k) / canopy_height ) )**( &
463	beta_lad-1.0_wp ) ) / int_bpdf &
464	) / canopy_height
465	ENDDO
466
467	!
468	!-- Final lad profile (defined on scalar-grid level, since most prognostic
469	!-- quantities are defined there, hence, less interpolation is required
470	!-- when calculating the canopy tendencies)
471	lad(0) = pre_lad(0)
472	DO k = nzb+1, pch_index
473	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
474	ENDDO
475
476	ENDIF
477
478	!
479	!-- Allocate 3D-array for the leaf area density (lad_s). In case of a
480	!-- prescribed canopy-top heat flux (cthf), allocate 3D-arrays for
481	!-- the cumulative leaf area index (cum_lai_hf) and the canopy heat flux.
482	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
483
484	IF ( cthf /= 0.0_wp ) THEN
485	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
486	canopy_heat_flux(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
487	ENDIF
488
489	!
490	!-- Initialize canopy parameters cdc (canopy drag coefficient),
491	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
492	!-- with the prescribed values
493	cdc = canopy_drag_coeff
494	lsec = leaf_scalar_exch_coeff
495	lsc = leaf_surface_conc
496
497	!
498	!-- Initialization of the canopy coverage in the model domain:
499	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
500	!-- fully covers the domain surface
501	SELECT CASE ( TRIM( canopy_mode ) )
502
503	CASE( 'block' )
504
505	DO i = nxlg, nxrg
506	DO j = nysg, nyng
507	lad_s(:,j,i) = lad(:)
508	ENDDO
509	ENDDO
510
511	CASE DEFAULT
512
513	!
514	!-- The DEFAULT case is reached either if the parameter
515	!-- canopy mode contains a wrong character string or if the
516	!-- user has coded a special case in the user interface.
517	!-- There, the subroutine user_init_plant_canopy checks
518	!-- which of these two conditions applies.
519	CALL user_init_plant_canopy
520
521	END SELECT
522
523	!
524	!-- Initialization of the canopy heat source distribution
525	IF ( cthf /= 0.0_wp ) THEN
526	!
527	!-- Piecewise calculation of the leaf area index by vertical
528	!-- integration of the leaf area density
529	cum_lai_hf(:,:,:) = 0.0_wp
530	DO i = nxlg, nxrg
531	DO j = nysg, nyng
532	DO k = pch_index-1, 0, -1
533	IF ( k == pch_index-1 ) THEN
534	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
535	( 0.5_wp * lad_s(k+1,j,i) * &
536	( zw(k+1) - zu(k+1) ) ) + &
537	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
538	lad_s(k,j,i) ) + &
539	lad_s(k+1,j,i) ) * &
540	( zu(k+1) - zw(k) ) )
541	ELSE
542	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
543	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
544	lad_s(k+1,j,i) ) + &
545	lad_s(k+1,j,i) ) * &
546	( zw(k+1) - zu(k+1) ) ) + &
547	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
548	lad_s(k,j,i) ) + &
549	lad_s(k+1,j,i) ) * &
550	( zu(k+1) - zw(k) ) )
551	ENDIF
552	ENDDO
553	ENDDO
554	ENDDO
555
556	!
557	!-- Calculation of the upward kinematic vertical heat flux within the
558	!-- canopy
559	DO i = nxlg, nxrg
560	DO j = nysg, nyng
561	DO k = 0, pch_index
562	canopy_heat_flux(k,j,i) = cthf * &
563	exp( -0.6_wp * cum_lai_hf(k,j,i) )
564	ENDDO
565	ENDDO
566	ENDDO
567
568	!
569	!-- In areas covered with canopy, the surface heat flux is set to
570	!-- the surface value of the above calculated in-canopy heat flux
571	!-- distribution
572	DO i = nxlg,nxrg
573	DO j = nysg, nyng
574	IF ( canopy_heat_flux(0,j,i) /= cthf ) THEN
575	shf(j,i) = canopy_heat_flux(0,j,i)
576	ENDIF
577	ENDDO
578	ENDDO
579
580	ENDIF
581
582
583
584	END SUBROUTINE pcm_init
585
586
587
588	!------------------------------------------------------------------------------!
589	! Description:
590	! ------------
591	!> Calculation of the tendency terms, accounting for the effect of the plant
592	!> canopy on momentum and scalar quantities.
593	!>
594	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
595	!> (defined on scalar grid), as initialized in subroutine pcm_init.
596	!> The lad on the w-grid is vertically interpolated from the surrounding
597	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
598	!> k = pch_index. Here, the lad is zero.
599	!>
600	!> The canopy drag must be limited (previously accounted for by calculation of
601	!> a limiting canopy timestep for the determination of the maximum LES timestep
602	!> in subroutine timestep), since it is physically impossible that the canopy
603	!> drag alone can locally change the sign of a velocity component. This
604	!> limitation is realized by calculating preliminary tendencies and velocities.
605	!> It is subsequently checked if the preliminary new velocity has a different
606	!> sign than the current velocity. If so, the tendency is limited in a way that
607	!> the velocity can at maximum be reduced to zero by the canopy drag.
608	!>
609	!>
610	!> Call for all grid points
611	!------------------------------------------------------------------------------!
612	SUBROUTINE pcm_tendency( component )
613
614
615	USE control_parameters, &
616	ONLY: dt_3d, message_string
617
618	USE kinds
619
620	IMPLICIT NONE
621
622	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
623	INTEGER(iwp) :: i !< running index
624	INTEGER(iwp) :: j !< running index
625	INTEGER(iwp) :: k !< running index
626	INTEGER(iwp) :: kk !< running index for flat lad arrays
627
628	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
629	REAL(wp) :: lad_local !< local lad value
630	REAL(wp) :: pre_tend !< preliminary tendency
631	REAL(wp) :: pre_u !< preliminary u-value
632	REAL(wp) :: pre_v !< preliminary v-value
633	REAL(wp) :: pre_w !< preliminary w-value
634
635
636	ddt_3d = 1.0_wp / dt_3d
637
638	!
639	!-- Compute drag for the three velocity components and the SGS-TKE:
640	SELECT CASE ( component )
641
642	!
643	!-- u-component
644	CASE ( 1 )
645	DO i = nxlu, nxr
646	DO j = nys, nyn
647	DO k = nzb_u_inner(j,i)+1, nzb_u_inner(j,i)+pch_index
648
649	kk = k - nzb_u_inner(j,i) !- lad arrays are defined flat
650	!
651	!-- In order to create sharp boundaries of the plant canopy,
652	!-- the lad on the u-grid at index (k,j,i) is equal to
653	!-- lad_s(k,j,i), rather than being interpolated from the
654	!-- surrounding lad_s, because this would yield smaller lad
655	!-- at the canopy boundaries than inside of the canopy.
656	!-- For the same reason, the lad at the rightmost(i+1)canopy
657	!-- boundary on the u-grid equals lad_s(k,j,i).
658	lad_local = lad_s(kk,j,i)
659	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp )&
660	THEN
661	lad_local = lad_s(kk,j,i-1)
662	ENDIF
663
664	pre_tend = 0.0_wp
665	pre_u = 0.0_wp
666	!
667	!-- Calculate preliminary value (pre_tend) of the tendency
668	pre_tend = - cdc * &
669	lad_local * &
670	SQRT( u(k,j,i)**2 + &
671	( 0.25_wp * ( v(k,j,i-1) + &
672	v(k,j,i) + &
673	v(k,j+1,i) + &
674	v(k,j+1,i-1) ) &
675	)**2 + &
676	( 0.25_wp * ( w(k-1,j,i-1) + &
677	w(k-1,j,i) + &
678	w(k,j,i-1) + &
679	w(k,j,i) ) &
680	)**2 &
681	) * &
682	u(k,j,i)
683
684	!
685	!-- Calculate preliminary new velocity, based on pre_tend
686	pre_u = u(k,j,i) + dt_3d * pre_tend
687	!
688	!-- Compare sign of old velocity and new preliminary velocity,
689	!-- and in case the signs are different, limit the tendency
690	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
691	pre_tend = - u(k,j,i) * ddt_3d
692	ELSE
693	pre_tend = pre_tend
694	ENDIF
695	!
696	!-- Calculate final tendency
697	tend(k,j,i) = tend(k,j,i) + pre_tend
698
699	ENDDO
700	ENDDO
701	ENDDO
702
703	!
704	!-- v-component
705	CASE ( 2 )
706	DO i = nxl, nxr
707	DO j = nysv, nyn
708	DO k = nzb_v_inner(j,i)+1, nzb_v_inner(j,i)+pch_index
709
710	kk = k - nzb_v_inner(j,i) !- lad arrays are defined flat
711	!
712	!-- In order to create sharp boundaries of the plant canopy,
713	!-- the lad on the v-grid at index (k,j,i) is equal to
714	!-- lad_s(k,j,i), rather than being interpolated from the
715	!-- surrounding lad_s, because this would yield smaller lad
716	!-- at the canopy boundaries than inside of the canopy.
717	!-- For the same reason, the lad at the northmost(j+1) canopy
718	!-- boundary on the v-grid equals lad_s(k,j,i).
719	lad_local = lad_s(kk,j,i)
720	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp )&
721	THEN
722	lad_local = lad_s(kk,j-1,i)
723	ENDIF
724
725	pre_tend = 0.0_wp
726	pre_v = 0.0_wp
727	!
728	!-- Calculate preliminary value (pre_tend) of the tendency
729	pre_tend = - cdc * &
730	lad_local * &
731	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
732	u(k,j-1,i+1) + &
733	u(k,j,i) + &
734	u(k,j,i+1) ) &
735	)**2 + &
736	v(k,j,i)**2 + &
737	( 0.25_wp * ( w(k-1,j-1,i) + &
738	w(k-1,j,i) + &
739	w(k,j-1,i) + &
740	w(k,j,i) ) &
741	)**2 &
742	) * &
743	v(k,j,i)
744
745	!
746	!-- Calculate preliminary new velocity, based on pre_tend
747	pre_v = v(k,j,i) + dt_3d * pre_tend
748	!
749	!-- Compare sign of old velocity and new preliminary velocity,
750	!-- and in case the signs are different, limit the tendency
751	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
752	pre_tend = - v(k,j,i) * ddt_3d
753	ELSE
754	pre_tend = pre_tend
755	ENDIF
756	!
757	!-- Calculate final tendency
758	tend(k,j,i) = tend(k,j,i) + pre_tend
759
760	ENDDO
761	ENDDO
762	ENDDO
763
764	!
765	!-- w-component
766	CASE ( 3 )
767	DO i = nxl, nxr
768	DO j = nys, nyn
769	DO k = nzb_w_inner(j,i)+1, nzb_w_inner(j,i)+pch_index-1
770
771	kk = k - nzb_w_inner(j,i) !- lad arrays are defined flat
772
773	pre_tend = 0.0_wp
774	pre_w = 0.0_wp
775	!
776	!-- Calculate preliminary value (pre_tend) of the tendency
777	pre_tend = - cdc * &
778	(0.5_wp * &
779	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
780	SQRT( ( 0.25_wp * ( u(k,j,i) + &
781	u(k,j,i+1) + &
782	u(k+1,j,i) + &
783	u(k+1,j,i+1) ) &
784	)**2 + &
785	( 0.25_wp * ( v(k,j,i) + &
786	v(k,j+1,i) + &
787	v(k+1,j,i) + &
788	v(k+1,j+1,i) ) &
789	)**2 + &
790	w(k,j,i)**2 &
791	) * &
792	w(k,j,i)
793	!
794	!-- Calculate preliminary new velocity, based on pre_tend
795	pre_w = w(k,j,i) + dt_3d * pre_tend
796	!
797	!-- Compare sign of old velocity and new preliminary velocity,
798	!-- and in case the signs are different, limit the tendency
799	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
800	pre_tend = - w(k,j,i) * ddt_3d
801	ELSE
802	pre_tend = pre_tend
803	ENDIF
804	!
805	!-- Calculate final tendency
806	tend(k,j,i) = tend(k,j,i) + pre_tend
807
808	ENDDO
809	ENDDO
810	ENDDO
811
812	!
813	!-- potential temperature
814	CASE ( 4 )
815	DO i = nxl, nxr
816	DO j = nys, nyn
817	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
818	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
819	tend(k,j,i) = tend(k,j,i) + &
820	( canopy_heat_flux(kk,j,i) - &
821	canopy_heat_flux(kk-1,j,i) ) / dzw(k)
822	ENDDO
823	ENDDO
824	ENDDO
825
826	!
827	!-- humidity
828	CASE ( 5 )
829	DO i = nxl, nxr
830	DO j = nys, nyn
831	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
832	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
833	tend(k,j,i) = tend(k,j,i) - &
834	lsec * &
835	lad_s(kk,j,i) * &
836	SQRT( ( 0.5_wp * ( u(k,j,i) + &
837	u(k,j,i+1) ) &
838	)**2 + &
839	( 0.5_wp * ( v(k,j,i) + &
840	v(k,j+1,i) ) &
841	)**2 + &
842	( 0.5_wp * ( w(k-1,j,i) + &
843	w(k,j,i) ) &
844	)**2 &
845	) * &
846	( q(k,j,i) - lsc )
847	ENDDO
848	ENDDO
849	ENDDO
850
851	!
852	!-- sgs-tke
853	CASE ( 6 )
854	DO i = nxl, nxr
855	DO j = nys, nyn
856	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
857	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
858	tend(k,j,i) = tend(k,j,i) - &
859	2.0_wp * cdc * &
860	lad_s(kk,j,i) * &
861	SQRT( ( 0.5_wp * ( u(k,j,i) + &
862	u(k,j,i+1) ) &
863	)**2 + &
864	( 0.5_wp * ( v(k,j,i) + &
865	v(k,j+1,i) ) &
866	)**2 + &
867	( 0.5_wp * ( w(k,j,i) + &
868	w(k+1,j,i) ) &
869	)**2 &
870	) * &
871	e(k,j,i)
872	ENDDO
873	ENDDO
874	ENDDO
875	!
876	!-- scalar concentration
877	CASE ( 7 )
878	DO i = nxl, nxr
879	DO j = nys, nyn
880	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
881	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
882	tend(k,j,i) = tend(k,j,i) - &
883	lsec * &
884	lad_s(kk,j,i) * &
885	SQRT( ( 0.5_wp * ( u(k,j,i) + &
886	u(k,j,i+1) ) &
887	)**2 + &
888	( 0.5_wp * ( v(k,j,i) + &
889	v(k,j+1,i) ) &
890	)**2 + &
891	( 0.5_wp * ( w(k-1,j,i) + &
892	w(k,j,i) ) &
893	)**2 &
894	) * &
895	( s(k,j,i) - lsc )
896	ENDDO
897	ENDDO
898	ENDDO
899
900
901
902	CASE DEFAULT
903
904	WRITE( message_string, * ) 'wrong component: ', component
905	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
906
907	END SELECT
908
909	END SUBROUTINE pcm_tendency
910
911
912	!------------------------------------------------------------------------------!
913	! Description:
914	! ------------
915	!> Parin for &canopy_par for plant canopy model
916	!------------------------------------------------------------------------------!
917	SUBROUTINE pcm_parin
918
919
920	IMPLICIT NONE
921
922	CHARACTER (LEN=80) :: line !< dummy string that contains the current line of the parameter file
923
924	NAMELIST /canopy_par/ alpha_lad, beta_lad, canopy_drag_coeff, &
925	canopy_mode, cthf, &
926	lad_surface, &
927	lad_vertical_gradient, &
928	lad_vertical_gradient_level, &
929	lai_beta, &
930	leaf_scalar_exch_coeff, &
931	leaf_surface_conc, pch_index
932
933	line = ' '
934
935	!
936	!-- Try to find radiation model package
937	REWIND ( 11 )
938	line = ' '
939	DO WHILE ( INDEX( line, '&canopy_par' ) == 0 )
940	READ ( 11, '(A)', END=10 ) line
941	ENDDO
942	BACKSPACE ( 11 )
943
944	!
945	!-- Read user-defined namelist
946	READ ( 11, canopy_par )
947
948	!
949	!-- Set flag that indicates that the radiation model is switched on
950	plant_canopy = .TRUE.
951
952	10 CONTINUE
953
954
955	END SUBROUTINE pcm_parin
956
957
958
959	!------------------------------------------------------------------------------!
960	! Description:
961	! ------------
962	!> Calculation of the tendency terms, accounting for the effect of the plant
963	!> canopy on momentum and scalar quantities.
964	!>
965	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
966	!> (defined on scalar grid), as initialized in subroutine pcm_init.
967	!> The lad on the w-grid is vertically interpolated from the surrounding
968	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
969	!> k = pch_index. Here, the lad is zero.
970	!>
971	!> The canopy drag must be limited (previously accounted for by calculation of
972	!> a limiting canopy timestep for the determination of the maximum LES timestep
973	!> in subroutine timestep), since it is physically impossible that the canopy
974	!> drag alone can locally change the sign of a velocity component. This
975	!> limitation is realized by calculating preliminary tendencies and velocities.
976	!> It is subsequently checked if the preliminary new velocity has a different
977	!> sign than the current velocity. If so, the tendency is limited in a way that
978	!> the velocity can at maximum be reduced to zero by the canopy drag.
979	!>
980	!>
981	!> Call for grid point i,j
982	!------------------------------------------------------------------------------!
983	SUBROUTINE pcm_tendency_ij( i, j, component )
984
985
986	USE control_parameters, &
987	ONLY: dt_3d, message_string
988
989	USE kinds
990
991	IMPLICIT NONE
992
993	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
994	INTEGER(iwp) :: i !< running index
995	INTEGER(iwp) :: j !< running index
996	INTEGER(iwp) :: k !< running index
997	INTEGER(iwp) :: kk !< running index for flat lad arrays
998
999	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
1000	REAL(wp) :: lad_local !< local lad value
1001	REAL(wp) :: pre_tend !< preliminary tendency
1002	REAL(wp) :: pre_u !< preliminary u-value
1003	REAL(wp) :: pre_v !< preliminary v-value
1004	REAL(wp) :: pre_w !< preliminary w-value
1005
1006
1007	ddt_3d = 1.0_wp / dt_3d
1008
1009	!
1010	!-- Compute drag for the three velocity components and the SGS-TKE
1011	SELECT CASE ( component )
1012
1013	!
1014	!-- u-component
1015	CASE ( 1 )
1016	DO k = nzb_u_inner(j,i)+1, nzb_u_inner(j,i)+pch_index
1017
1018	kk = k - nzb_u_inner(j,i) !- lad arrays are defined flat
1019	!
1020	!-- In order to create sharp boundaries of the plant canopy,
1021	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
1022	!-- rather than being interpolated from the surrounding lad_s,
1023	!-- because this would yield smaller lad at the canopy boundaries
1024	!-- than inside of the canopy.
1025	!-- For the same reason, the lad at the rightmost(i+1)canopy
1026	!-- boundary on the u-grid equals lad_s(k,j,i).
1027	lad_local = lad_s(kk,j,i)
1028	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp ) THEN
1029	lad_local = lad_s(kk,j,i-1)
1030	ENDIF
1031
1032	pre_tend = 0.0_wp
1033	pre_u = 0.0_wp
1034	!
1035	!-- Calculate preliminary value (pre_tend) of the tendency
1036	pre_tend = - cdc * &
1037	lad_local * &
1038	SQRT( u(k,j,i)**2 + &
1039	( 0.25_wp * ( v(k,j,i-1) + &
1040	v(k,j,i) + &
1041	v(k,j+1,i) + &
1042	v(k,j+1,i-1) ) &
1043	)**2 + &
1044	( 0.25_wp * ( w(k-1,j,i-1) + &
1045	w(k-1,j,i) + &
1046	w(k,j,i-1) + &
1047	w(k,j,i) ) &
1048	)**2 &
1049	) * &
1050	u(k,j,i)
1051
1052	!
1053	!-- Calculate preliminary new velocity, based on pre_tend
1054	pre_u = u(k,j,i) + dt_3d * pre_tend
1055	!
1056	!-- Compare sign of old velocity and new preliminary velocity,
1057	!-- and in case the signs are different, limit the tendency
1058	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
1059	pre_tend = - u(k,j,i) * ddt_3d
1060	ELSE
1061	pre_tend = pre_tend
1062	ENDIF
1063	!
1064	!-- Calculate final tendency
1065	tend(k,j,i) = tend(k,j,i) + pre_tend
1066	ENDDO
1067
1068
1069	!
1070	!-- v-component
1071	CASE ( 2 )
1072	DO k = nzb_v_inner(j,i)+1, nzb_v_inner(j,i)+pch_index
1073
1074	kk = k - nzb_v_inner(j,i) !- lad arrays are defined flat
1075	!
1076	!-- In order to create sharp boundaries of the plant canopy,
1077	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
1078	!-- rather than being interpolated from the surrounding lad_s,
1079	!-- because this would yield smaller lad at the canopy boundaries
1080	!-- than inside of the canopy.
1081	!-- For the same reason, the lad at the northmost(j+1)canopy
1082	!-- boundary on the v-grid equals lad_s(k,j,i).
1083	lad_local = lad_s(kk,j,i)
1084	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp ) THEN
1085	lad_local = lad_s(kk,j-1,i)
1086	ENDIF
1087
1088	pre_tend = 0.0_wp
1089	pre_v = 0.0_wp
1090	!
1091	!-- Calculate preliminary value (pre_tend) of the tendency
1092	pre_tend = - cdc * &
1093	lad_local * &
1094	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
1095	u(k,j-1,i+1) + &
1096	u(k,j,i) + &
1097	u(k,j,i+1) ) &
1098	)**2 + &
1099	v(k,j,i)**2 + &
1100	( 0.25_wp * ( w(k-1,j-1,i) + &
1101	w(k-1,j,i) + &
1102	w(k,j-1,i) + &
1103	w(k,j,i) ) &
1104	)**2 &
1105	) * &
1106	v(k,j,i)
1107
1108	!
1109	!-- Calculate preliminary new velocity, based on pre_tend
1110	pre_v = v(k,j,i) + dt_3d * pre_tend
1111	!
1112	!-- Compare sign of old velocity and new preliminary velocity,
1113	!-- and in case the signs are different, limit the tendency
1114	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
1115	pre_tend = - v(k,j,i) * ddt_3d
1116	ELSE
1117	pre_tend = pre_tend
1118	ENDIF
1119	!
1120	!-- Calculate final tendency
1121	tend(k,j,i) = tend(k,j,i) + pre_tend
1122	ENDDO
1123
1124
1125	!
1126	!-- w-component
1127	CASE ( 3 )
1128	DO k = nzb_w_inner(j,i)+1, nzb_w_inner(j,i)+pch_index-1
1129
1130	kk = k - nzb_w_inner(j,i) !- lad arrays are defined flat
1131
1132	pre_tend = 0.0_wp
1133	pre_w = 0.0_wp
1134	!
1135	!-- Calculate preliminary value (pre_tend) of the tendency
1136	pre_tend = - cdc * &
1137	(0.5_wp * &
1138	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
1139	SQRT( ( 0.25_wp * ( u(k,j,i) + &
1140	u(k,j,i+1) + &
1141	u(k+1,j,i) + &
1142	u(k+1,j,i+1) ) &
1143	)**2 + &
1144	( 0.25_wp * ( v(k,j,i) + &
1145	v(k,j+1,i) + &
1146	v(k+1,j,i) + &
1147	v(k+1,j+1,i) ) &
1148	)**2 + &
1149	w(k,j,i)**2 &
1150	) * &
1151	w(k,j,i)
1152	!
1153	!-- Calculate preliminary new velocity, based on pre_tend
1154	pre_w = w(k,j,i) + dt_3d * pre_tend
1155	!
1156	!-- Compare sign of old velocity and new preliminary velocity,
1157	!-- and in case the signs are different, limit the tendency
1158	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
1159	pre_tend = - w(k,j,i) * ddt_3d
1160	ELSE
1161	pre_tend = pre_tend
1162	ENDIF
1163	!
1164	!-- Calculate final tendency
1165	tend(k,j,i) = tend(k,j,i) + pre_tend
1166	ENDDO
1167
1168	!
1169	!-- potential temperature
1170	CASE ( 4 )
1171	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1172	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1173	tend(k,j,i) = tend(k,j,i) + &
1174	( canopy_heat_flux(kk,j,i) - &
1175	canopy_heat_flux(kk-1,j,i) ) / dzw(k)
1176	ENDDO
1177
1178
1179	!
1180	!-- humidity
1181	CASE ( 5 )
1182	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1183	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1184	tend(k,j,i) = tend(k,j,i) - &
1185	lsec * &
1186	lad_s(kk,j,i) * &
1187	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1188	u(k,j,i+1) ) &
1189	)**2 + &
1190	( 0.5_wp * ( v(k,j,i) + &
1191	v(k,j+1,i) ) &
1192	)**2 + &
1193	( 0.5_wp * ( w(k-1,j,i) + &
1194	w(k,j,i) ) &
1195	)**2 &
1196	) * &
1197	( q(k,j,i) - lsc )
1198	ENDDO
1199
1200	!
1201	!-- sgs-tke
1202	CASE ( 6 )
1203	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1204	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1205	tend(k,j,i) = tend(k,j,i) - &
1206	2.0_wp * cdc * &
1207	lad_s(kk,j,i) * &
1208	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1209	u(k,j,i+1) ) &
1210	)**2 + &
1211	( 0.5_wp * ( v(k,j,i) + &
1212	v(k,j+1,i) ) &
1213	)**2 + &
1214	( 0.5_wp * ( w(k,j,i) + &
1215	w(k+1,j,i) ) &
1216	)**2 &
1217	) * &
1218	e(k,j,i)
1219	ENDDO
1220
1221	!
1222	!-- scalar concentration
1223	CASE ( 7 )
1224	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
1225	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
1226	tend(k,j,i) = tend(k,j,i) - &
1227	lsec * &
1228	lad_s(kk,j,i) * &
1229	SQRT( ( 0.5_wp * ( u(k,j,i) + &
1230	u(k,j,i+1) ) &
1231	)**2 + &
1232	( 0.5_wp * ( v(k,j,i) + &
1233	v(k,j+1,i) ) &
1234	)**2 + &
1235	( 0.5_wp * ( w(k-1,j,i) + &
1236	w(k,j,i) ) &
1237	)**2 &
1238	) * &
1239	( s(k,j,i) - lsc )
1240	ENDDO
1241
1242	CASE DEFAULT
1243
1244	WRITE( message_string, * ) 'wrong component: ', component
1245	CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 )
1246
1247	END SELECT
1248
1249	END SUBROUTINE pcm_tendency_ij
1250
1251	END MODULE plant_canopy_model_mod

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