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source: palm/trunk/SOURCE/plant_canopy_model.f90 @ 1693

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1	!> @file plant_canopy_model.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 1997-2014 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------!
18	!
19	! Current revisions:
20	! -----------------
21	!
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: plant_canopy_model.f90 1683 2015-10-07 23:57:51Z maronga $
26	!
27	! 1682 2015-10-07 23:56:08Z knoop
28	! Code annotations made doxygen readable
29	!
30	! 1484 2014-10-21 10:53:05Z kanani
31	! Changes due to new module structure of the plant canopy model:
32	! module plant_canopy_model_mod now contains a subroutine for the
33	! initialization of the canopy model (init_plant_canopy),
34	! limitation of the canopy drag (previously accounted for by calculation of
35	! a limiting canopy timestep for the determination of the maximum LES timestep
36	! in subroutine timestep) is now realized by the calculation of pre-tendencies
37	! and preliminary velocities in subroutine plant_canopy_model,
38	! some redundant MPI communication removed in subroutine init_plant_canopy
39	! (was previously in init_3d_model),
40	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
41	! respective grid is now provided only by lad_s (e.g. in the calculation of
42	! the tendency terms or of cum_lai_hf),
43	! drag_coefficient, lai, leaf_surface_concentration,
44	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
45	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
46	! respectively,
47	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
48	! USE-statements and ONLY-lists modified accordingly
49	!
50	! 1340 2014-03-25 19:45:13Z kanani
51	! REAL constants defined as wp-kind
52	!
53	! 1320 2014-03-20 08:40:49Z raasch
54	! ONLY-attribute added to USE-statements,
55	! kind-parameters added to all INTEGER and REAL declaration statements,
56	! kinds are defined in new module kinds,
57	! old module precision_kind is removed,
58	! revision history before 2012 removed,
59	! comment fields (!:) to be used for variable explanations added to
60	! all variable declaration statements
61	!
62	! 1036 2012-10-22 13:43:42Z raasch
63	! code put under GPL (PALM 3.9)
64	!
65	! 138 2007-11-28 10:03:58Z letzel
66	! Initial revision
67	!
68	! Description:
69	! ------------
70	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
71	!> profile (subroutine init_plant_canopy).
72	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
73	!> due to canopy elements (subroutine plant_canopy_model).
74	!------------------------------------------------------------------------------!
75	MODULE plant_canopy_model_mod
76
77	USE arrays_3d, &
78	ONLY: dzu, dzw, e, q, shf, tend, u, v, w, zu, zw
79
80	USE indices, &
81	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
82	nz, nzb, nzb_s_inner, nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt
83
84	USE kinds
85
86
87	IMPLICIT NONE
88
89
90	CHARACTER (LEN=20) :: canopy_mode = 'block' !< canopy coverage
91
92	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
93	INTEGER(iwp) :: &
94	lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
95
96	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
97	LOGICAL :: plant_canopy = .FALSE. !< switch for use of canopy model
98
99	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
100	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
101	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
102	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
103	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
104	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
105	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
106	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
107	REAL(wp) :: &
108	leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
109	REAL(wp) :: &
110	leaf_surface_conc = 0.0_wp !< leaf surface concentration
111	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
112	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
113
114	REAL(wp) :: &
115	lad_vertical_gradient(10) = 0.0_wp !< lad gradient
116	REAL(wp) :: &
117	lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
118
119	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
120	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
121
122	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
123	canopy_heat_flux !< canopy heat flux
124	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
125	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
126
127
128	SAVE
129
130
131	PRIVATE
132	PUBLIC alpha_lad, beta_lad, calc_beta_lad_profile, canopy_drag_coeff, &
133	canopy_mode, cdc, cthf, dt_plant_canopy, init_plant_canopy, lad, &
134	lad_s, lad_surface, lad_vertical_gradient, &
135	lad_vertical_gradient_level, lad_vertical_gradient_level_ind, &
136	lai_beta, leaf_scalar_exch_coeff, leaf_surface_conc, lsc, lsec, &
137	pch_index, plant_canopy, plant_canopy_model
138
139
140	INTERFACE init_plant_canopy
141	MODULE PROCEDURE init_plant_canopy
142	END INTERFACE init_plant_canopy
143
144	INTERFACE plant_canopy_model
145	MODULE PROCEDURE plant_canopy_model
146	MODULE PROCEDURE plant_canopy_model_ij
147	END INTERFACE plant_canopy_model
148
149
150
151
152	CONTAINS
153
154
155	!------------------------------------------------------------------------------!
156	! Description:
157	! ------------
158	!> Initialization of the plant canopy model
159	!------------------------------------------------------------------------------!
160	SUBROUTINE init_plant_canopy
161
162
163	USE control_parameters, &
164	ONLY: dz, ocean, passive_scalar
165
166
167	IMPLICIT NONE
168
169	INTEGER(iwp) :: i !< running index
170	INTEGER(iwp) :: j !< running index
171	INTEGER(iwp) :: k !< running index
172
173	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
174	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
175	REAL(wp) :: gradient !< gradient for lad-profile construction
176	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
177
178	!
179	!-- Allocate one-dimensional arrays for the computation of the
180	!-- leaf area density (lad) profile
181	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
182	lad = 0.0_wp
183	pre_lad = 0.0_wp
184
185	!
186	!-- Compute the profile of leaf area density used in the plant
187	!-- canopy model. The profile can either be constructed from
188	!-- prescribed vertical gradients of the leaf area density or by
189	!-- using a beta probability density function (see e.g. Markkanen et al.,
190	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
191	IF ( .NOT. calc_beta_lad_profile ) THEN
192
193	!
194	!-- Use vertical gradients for lad-profile construction
195	i = 1
196	gradient = 0.0_wp
197
198	IF ( .NOT. ocean ) THEN
199
200	lad(0) = lad_surface
201	lad_vertical_gradient_level_ind(1) = 0
202
203	DO k = 1, pch_index
204	IF ( i < 11 ) THEN
205	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
206	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
207	gradient = lad_vertical_gradient(i)
208	lad_vertical_gradient_level_ind(i) = k - 1
209	i = i + 1
210	ENDIF
211	ENDIF
212	IF ( gradient /= 0.0_wp ) THEN
213	IF ( k /= 1 ) THEN
214	lad(k) = lad(k-1) + dzu(k) * gradient
215	ELSE
216	lad(k) = lad_surface + dzu(k) * gradient
217	ENDIF
218	ELSE
219	lad(k) = lad(k-1)
220	ENDIF
221	ENDDO
222
223	ENDIF
224
225	!
226	!-- In case of no given leaf area density gradients, choose a vanishing
227	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
228	!-- file.
229	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
230	lad_vertical_gradient_level(1) = 0.0_wp
231	ENDIF
232
233	ELSE
234
235	!
236	!-- Use beta function for lad-profile construction
237	int_bpdf = 0.0_wp
238	canopy_height = pch_index * dz
239
240	DO k = nzb, pch_index
241	int_bpdf = int_bpdf + &
242	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
243	( ( 1.0_wp - ( zw(k) / canopy_height ) )*( beta_lad-1.0_wp ) ) &
244	( ( zw(k+1)-zw(k) ) / canopy_height ) )
245	ENDDO
246
247	!
248	!-- Preliminary lad profile (defined on w-grid)
249	DO k = nzb, pch_index
250	pre_lad(k) = lai_beta * &
251	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
252	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( beta_lad-1.0_wp ) ) / &
253	int_bpdf &
254	) / canopy_height
255	ENDDO
256
257	!
258	!-- Final lad profile (defined on scalar-grid level, since most prognostic
259	!-- quantities are defined there, hence, less interpolation is required
260	!-- when calculating the canopy tendencies)
261	lad(0) = pre_lad(0)
262	DO k = nzb+1, pch_index
263	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
264	ENDDO
265
266	ENDIF
267
268	!
269	!-- Allocate 3D-array for the leaf area density (lad_s). In case of a
270	!-- prescribed canopy-top heat flux (cthf), allocate 3D-arrays for
271	!-- the cumulative leaf area index (cum_lai_hf) and the canopy heat flux.
272	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
273
274	IF ( cthf /= 0.0_wp ) THEN
275	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
276	canopy_heat_flux(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
277	ENDIF
278
279	!
280	!-- Initialize canopy parameters cdc (canopy drag coefficient),
281	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
282	!-- with the prescribed values
283	cdc = canopy_drag_coeff
284	lsec = leaf_scalar_exch_coeff
285	lsc = leaf_surface_conc
286
287	!
288	!-- Initialization of the canopy coverage in the model domain:
289	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
290	!-- fully covers the domain surface
291	SELECT CASE ( TRIM( canopy_mode ) )
292
293	CASE( 'block' )
294
295	DO i = nxlg, nxrg
296	DO j = nysg, nyng
297	lad_s(:,j,i) = lad(:)
298	ENDDO
299	ENDDO
300
301	CASE DEFAULT
302
303	!
304	!-- The DEFAULT case is reached either if the parameter
305	!-- canopy mode contains a wrong character string or if the
306	!-- user has coded a special case in the user interface.
307	!-- There, the subroutine user_init_plant_canopy checks
308	!-- which of these two conditions applies.
309	CALL user_init_plant_canopy
310
311	END SELECT
312
313	!
314	!-- Initialization of the canopy heat source distribution
315	IF ( cthf /= 0.0_wp ) THEN
316	!
317	!-- Piecewise calculation of the leaf area index by vertical
318	!-- integration of the leaf area density
319	cum_lai_hf(:,:,:) = 0.0_wp
320	DO i = nxlg, nxrg
321	DO j = nysg, nyng
322	DO k = pch_index-1, 0, -1
323	IF ( k == pch_index-1 ) THEN
324	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
325	( 0.5_wp * lad_s(k+1,j,i) * &
326	( zw(k+1) - zu(k+1) ) ) + &
327	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
328	lad_s(k,j,i) ) + &
329	lad_s(k+1,j,i) ) * &
330	( zu(k+1) - zw(k) ) )
331	ELSE
332	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
333	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
334	lad_s(k+1,j,i) ) + &
335	lad_s(k+1,j,i) ) * &
336	( zw(k+1) - zu(k+1) ) ) + &
337	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
338	lad_s(k,j,i) ) + &
339	lad_s(k+1,j,i) ) * &
340	( zu(k+1) - zw(k) ) )
341	ENDIF
342	ENDDO
343	ENDDO
344	ENDDO
345
346	!
347	!-- Calculation of the upward kinematic vertical heat flux within the
348	!-- canopy
349	DO i = nxlg, nxrg
350	DO j = nysg, nyng
351	DO k = 0, pch_index
352	canopy_heat_flux(k,j,i) = cthf * &
353	exp( -0.6_wp * cum_lai_hf(k,j,i) )
354	ENDDO
355	ENDDO
356	ENDDO
357
358	!
359	!-- The surface heat flux is set to the surface value of the calculated
360	!-- in-canopy heat flux distribution
361	shf(:,:) = canopy_heat_flux(0,:,:)
362
363	ENDIF
364
365
366
367	END SUBROUTINE init_plant_canopy
368
369
370
371	!------------------------------------------------------------------------------!
372	! Description:
373	! ------------
374	!> Calculation of the tendency terms, accounting for the effect of the plant
375	!> canopy on momentum and scalar quantities.
376	!>
377	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
378	!> (defined on scalar grid), as initialized in subroutine init_plant_canopy.
379	!> The lad on the w-grid is vertically interpolated from the surrounding
380	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
381	!> k = pch_index. Here, the lad is zero.
382	!>
383	!> The canopy drag must be limited (previously accounted for by calculation of
384	!> a limiting canopy timestep for the determination of the maximum LES timestep
385	!> in subroutine timestep), since it is physically impossible that the canopy
386	!> drag alone can locally change the sign of a velocity component. This
387	!> limitation is realized by calculating preliminary tendencies and velocities.
388	!> It is subsequently checked if the preliminary new velocity has a different
389	!> sign than the current velocity. If so, the tendency is limited in a way that
390	!> the velocity can at maximum be reduced to zero by the canopy drag.
391	!>
392	!>
393	!> Call for all grid points
394	!------------------------------------------------------------------------------!
395	SUBROUTINE plant_canopy_model( component )
396
397
398	USE control_parameters, &
399	ONLY: dt_3d, message_string
400
401	USE kinds
402
403	IMPLICIT NONE
404
405	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
406	INTEGER(iwp) :: i !< running index
407	INTEGER(iwp) :: j !< running index
408	INTEGER(iwp) :: k !< running index
409
410	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
411	REAL(wp) :: lad_local !< local lad value
412	REAL(wp) :: pre_tend !< preliminary tendency
413	REAL(wp) :: pre_u !< preliminary u-value
414	REAL(wp) :: pre_v !< preliminary v-value
415	REAL(wp) :: pre_w !< preliminary w-value
416
417
418	ddt_3d = 1.0_wp / dt_3d
419
420	!
421	!-- Compute drag for the three velocity components and the SGS-TKE:
422	SELECT CASE ( component )
423
424	!
425	!-- u-component
426	CASE ( 1 )
427	DO i = nxlu, nxr
428	DO j = nys, nyn
429	DO k = nzb_u_inner(j,i)+1, pch_index
430
431	!
432	!-- In order to create sharp boundaries of the plant canopy,
433	!-- the lad on the u-grid at index (k,j,i) is equal to
434	!-- lad_s(k,j,i), rather than being interpolated from the
435	!-- surrounding lad_s, because this would yield smaller lad
436	!-- at the canopy boundaries than inside of the canopy.
437	!-- For the same reason, the lad at the rightmost(i+1)canopy
438	!-- boundary on the u-grid equals lad_s(k,j,i).
439	lad_local = lad_s(k,j,i)
440	IF ( lad_local == 0.0_wp .AND. &
441	lad_s(k,j,i-1) > 0.0_wp ) THEN
442	lad_local = lad_s(k,j,i-1)
443	ENDIF
444
445	pre_tend = 0.0_wp
446	pre_u = 0.0_wp
447	!
448	!-- Calculate preliminary value (pre_tend) of the tendency
449	pre_tend = - cdc * &
450	lad_local * &
451	SQRT( u(k,j,i)**2 + &
452	( 0.25_wp * ( v(k,j,i-1) + &
453	v(k,j,i) + &
454	v(k,j+1,i) + &
455	v(k,j+1,i-1) ) &
456	)**2 + &
457	( 0.25_wp * ( w(k-1,j,i-1) + &
458	w(k-1,j,i) + &
459	w(k,j,i-1) + &
460	w(k,j,i) ) &
461	)**2 &
462	) * &
463	u(k,j,i)
464
465	!
466	!-- Calculate preliminary new velocity, based on pre_tend
467	pre_u = u(k,j,i) + dt_3d * pre_tend
468	!
469	!-- Compare sign of old velocity and new preliminary velocity,
470	!-- and in case the signs are different, limit the tendency
471	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
472	pre_tend = - u(k,j,i) * ddt_3d
473	ELSE
474	pre_tend = pre_tend
475	ENDIF
476	!
477	!-- Calculate final tendency
478	tend(k,j,i) = tend(k,j,i) + pre_tend
479
480	ENDDO
481	ENDDO
482	ENDDO
483
484	!
485	!-- v-component
486	CASE ( 2 )
487	DO i = nxl, nxr
488	DO j = nysv, nyn
489	DO k = nzb_v_inner(j,i)+1, pch_index
490
491	!
492	!-- In order to create sharp boundaries of the plant canopy,
493	!-- the lad on the v-grid at index (k,j,i) is equal to
494	!-- lad_s(k,j,i), rather than being interpolated from the
495	!-- surrounding lad_s, because this would yield smaller lad
496	!-- at the canopy boundaries than inside of the canopy.
497	!-- For the same reason, the lad at the northmost(j+1) canopy
498	!-- boundary on the v-grid equals lad_s(k,j,i).
499	lad_local = lad_s(k,j,i)
500	IF ( lad_local == 0.0_wp .AND. &
501	lad_s(k,j-1,i) > 0.0_wp ) THEN
502	lad_local = lad_s(k,j-1,i)
503	ENDIF
504
505	pre_tend = 0.0_wp
506	pre_v = 0.0_wp
507	!
508	!-- Calculate preliminary value (pre_tend) of the tendency
509	pre_tend = - cdc * &
510	lad_local * &
511	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
512	u(k,j-1,i+1) + &
513	u(k,j,i) + &
514	u(k,j,i+1) ) &
515	)**2 + &
516	v(k,j,i)**2 + &
517	( 0.25_wp * ( w(k-1,j-1,i) + &
518	w(k-1,j,i) + &
519	w(k,j-1,i) + &
520	w(k,j,i) ) &
521	)**2 &
522	) * &
523	v(k,j,i)
524
525	!
526	!-- Calculate preliminary new velocity, based on pre_tend
527	pre_v = v(k,j,i) + dt_3d * pre_tend
528	!
529	!-- Compare sign of old velocity and new preliminary velocity,
530	!-- and in case the signs are different, limit the tendency
531	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
532	pre_tend = - v(k,j,i) * ddt_3d
533	ELSE
534	pre_tend = pre_tend
535	ENDIF
536	!
537	!-- Calculate final tendency
538	tend(k,j,i) = tend(k,j,i) + pre_tend
539
540	ENDDO
541	ENDDO
542	ENDDO
543
544	!
545	!-- w-component
546	CASE ( 3 )
547	DO i = nxl, nxr
548	DO j = nys, nyn
549	DO k = nzb_w_inner(j,i)+1, pch_index-1
550
551	pre_tend = 0.0_wp
552	pre_w = 0.0_wp
553	!
554	!-- Calculate preliminary value (pre_tend) of the tendency
555	pre_tend = - cdc * &
556	(0.5_wp * &
557	( lad_s(k+1,j,i) + lad_s(k,j,i) )) * &
558	SQRT( ( 0.25_wp * ( u(k,j,i) + &
559	u(k,j,i+1) + &
560	u(k+1,j,i) + &
561	u(k+1,j,i+1) ) &
562	)**2 + &
563	( 0.25_wp * ( v(k,j,i) + &
564	v(k,j+1,i) + &
565	v(k+1,j,i) + &
566	v(k+1,j+1,i) ) &
567	)**2 + &
568	w(k,j,i)**2 &
569	) * &
570	w(k,j,i)
571	!
572	!-- Calculate preliminary new velocity, based on pre_tend
573	pre_w = w(k,j,i) + dt_3d * pre_tend
574	!
575	!-- Compare sign of old velocity and new preliminary velocity,
576	!-- and in case the signs are different, limit the tendency
577	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
578	pre_tend = - w(k,j,i) * ddt_3d
579	ELSE
580	pre_tend = pre_tend
581	ENDIF
582	!
583	!-- Calculate final tendency
584	tend(k,j,i) = tend(k,j,i) + pre_tend
585
586	ENDDO
587	ENDDO
588	ENDDO
589
590	!
591	!-- potential temperature
592	CASE ( 4 )
593	DO i = nxl, nxr
594	DO j = nys, nyn
595	DO k = nzb_s_inner(j,i)+1, pch_index
596	tend(k,j,i) = tend(k,j,i) + &
597	( canopy_heat_flux(k,j,i) - &
598	canopy_heat_flux(k-1,j,i) ) / dzw(k)
599	ENDDO
600	ENDDO
601	ENDDO
602
603	!
604	!-- scalar concentration
605	CASE ( 5 )
606	DO i = nxl, nxr
607	DO j = nys, nyn
608	DO k = nzb_s_inner(j,i)+1, pch_index
609	tend(k,j,i) = tend(k,j,i) - &
610	lsec * &
611	lad_s(k,j,i) * &
612	SQRT( ( 0.5_wp * ( u(k,j,i) + &
613	u(k,j,i+1) ) &
614	)**2 + &
615	( 0.5_wp * ( v(k,j,i) + &
616	v(k,j+1,i) ) &
617	)**2 + &
618	( 0.5_wp * ( w(k-1,j,i) + &
619	w(k,j,i) ) &
620	)**2 &
621	) * &
622	( q(k,j,i) - lsc )
623	ENDDO
624	ENDDO
625	ENDDO
626
627	!
628	!-- sgs-tke
629	CASE ( 6 )
630	DO i = nxl, nxr
631	DO j = nys, nyn
632	DO k = nzb_s_inner(j,i)+1, pch_index
633	tend(k,j,i) = tend(k,j,i) - &
634	2.0_wp * cdc * &
635	lad_s(k,j,i) * &
636	SQRT( ( 0.5_wp * ( u(k,j,i) + &
637	u(k,j,i+1) ) &
638	)**2 + &
639	( 0.5_wp * ( v(k,j,i) + &
640	v(k,j+1,i) ) &
641	)**2 + &
642	( 0.5_wp * ( w(k,j,i) + &
643	w(k+1,j,i) ) &
644	)**2 &
645	) * &
646	e(k,j,i)
647	ENDDO
648	ENDDO
649	ENDDO
650
651
652	CASE DEFAULT
653
654	WRITE( message_string, * ) 'wrong component: ', component
655	CALL message( 'plant_canopy_model', 'PA0279', 1, 2, 0, 6, 0 )
656
657	END SELECT
658
659	END SUBROUTINE plant_canopy_model
660
661
662	!------------------------------------------------------------------------------!
663	! Description:
664	! ------------
665	!> Calculation of the tendency terms, accounting for the effect of the plant
666	!> canopy on momentum and scalar quantities.
667	!>
668	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
669	!> (defined on scalar grid), as initialized in subroutine init_plant_canopy.
670	!> The lad on the w-grid is vertically interpolated from the surrounding
671	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
672	!> k = pch_index. Here, the lad is zero.
673	!>
674	!> The canopy drag must be limited (previously accounted for by calculation of
675	!> a limiting canopy timestep for the determination of the maximum LES timestep
676	!> in subroutine timestep), since it is physically impossible that the canopy
677	!> drag alone can locally change the sign of a velocity component. This
678	!> limitation is realized by calculating preliminary tendencies and velocities.
679	!> It is subsequently checked if the preliminary new velocity has a different
680	!> sign than the current velocity. If so, the tendency is limited in a way that
681	!> the velocity can at maximum be reduced to zero by the canopy drag.
682	!>
683	!>
684	!> Call for grid point i,j
685	!------------------------------------------------------------------------------!
686	SUBROUTINE plant_canopy_model_ij( i, j, component )
687
688
689	USE control_parameters, &
690	ONLY: dt_3d, message_string
691
692	USE kinds
693
694	IMPLICIT NONE
695
696	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
697	INTEGER(iwp) :: i !< running index
698	INTEGER(iwp) :: j !< running index
699	INTEGER(iwp) :: k !< running index
700
701	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
702	REAL(wp) :: lad_local !< local lad value
703	REAL(wp) :: pre_tend !< preliminary tendency
704	REAL(wp) :: pre_u !< preliminary u-value
705	REAL(wp) :: pre_v !< preliminary v-value
706	REAL(wp) :: pre_w !< preliminary w-value
707
708
709	ddt_3d = 1.0_wp / dt_3d
710
711	!
712	!-- Compute drag for the three velocity components and the SGS-TKE
713	SELECT CASE ( component )
714
715	!
716	!-- u-component
717	CASE ( 1 )
718	DO k = nzb_u_inner(j,i)+1, pch_index
719
720	!
721	!-- In order to create sharp boundaries of the plant canopy,
722	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
723	!-- rather than being interpolated from the surrounding lad_s,
724	!-- because this would yield smaller lad at the canopy boundaries
725	!-- than inside of the canopy.
726	!-- For the same reason, the lad at the rightmost(i+1)canopy
727	!-- boundary on the u-grid equals lad_s(k,j,i).
728	lad_local = lad_s(k,j,i)
729	IF ( lad_local == 0.0_wp .AND. &
730	lad_s(k,j,i-1) > 0.0_wp ) THEN
731	lad_local = lad_s(k,j,i-1)
732	ENDIF
733
734	pre_tend = 0.0_wp
735	pre_u = 0.0_wp
736	!
737	!-- Calculate preliminary value (pre_tend) of the tendency
738	pre_tend = - cdc * &
739	lad_local * &
740	SQRT( u(k,j,i)**2 + &
741	( 0.25_wp * ( v(k,j,i-1) + &
742	v(k,j,i) + &
743	v(k,j+1,i) + &
744	v(k,j+1,i-1) ) &
745	)**2 + &
746	( 0.25_wp * ( w(k-1,j,i-1) + &
747	w(k-1,j,i) + &
748	w(k,j,i-1) + &
749	w(k,j,i) ) &
750	)**2 &
751	) * &
752	u(k,j,i)
753
754	!
755	!-- Calculate preliminary new velocity, based on pre_tend
756	pre_u = u(k,j,i) + dt_3d * pre_tend
757	!
758	!-- Compare sign of old velocity and new preliminary velocity,
759	!-- and in case the signs are different, limit the tendency
760	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
761	pre_tend = - u(k,j,i) * ddt_3d
762	ELSE
763	pre_tend = pre_tend
764	ENDIF
765	!
766	!-- Calculate final tendency
767	tend(k,j,i) = tend(k,j,i) + pre_tend
768	ENDDO
769
770
771	!
772	!-- v-component
773	CASE ( 2 )
774	DO k = nzb_v_inner(j,i)+1, pch_index
775
776	!
777	!-- In order to create sharp boundaries of the plant canopy,
778	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
779	!-- rather than being interpolated from the surrounding lad_s,
780	!-- because this would yield smaller lad at the canopy boundaries
781	!-- than inside of the canopy.
782	!-- For the same reason, the lad at the northmost(j+1)canopy
783	!-- boundary on the v-grid equals lad_s(k,j,i).
784	lad_local = lad_s(k,j,i)
785	IF ( lad_local == 0.0_wp .AND. &
786	lad_s(k,j-1,i) > 0.0_wp ) THEN
787	lad_local = lad_s(k,j-1,i)
788	ENDIF
789
790	pre_tend = 0.0_wp
791	pre_v = 0.0_wp
792	!
793	!-- Calculate preliminary value (pre_tend) of the tendency
794	pre_tend = - cdc * &
795	lad_local * &
796	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
797	u(k,j-1,i+1) + &
798	u(k,j,i) + &
799	u(k,j,i+1) ) &
800	)**2 + &
801	v(k,j,i)**2 + &
802	( 0.25_wp * ( w(k-1,j-1,i) + &
803	w(k-1,j,i) + &
804	w(k,j-1,i) + &
805	w(k,j,i) ) &
806	)**2 &
807	) * &
808	v(k,j,i)
809
810	!
811	!-- Calculate preliminary new velocity, based on pre_tend
812	pre_v = v(k,j,i) + dt_3d * pre_tend
813	!
814	!-- Compare sign of old velocity and new preliminary velocity,
815	!-- and in case the signs are different, limit the tendency
816	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
817	pre_tend = - v(k,j,i) * ddt_3d
818	ELSE
819	pre_tend = pre_tend
820	ENDIF
821	!
822	!-- Calculate final tendency
823	tend(k,j,i) = tend(k,j,i) + pre_tend
824	ENDDO
825
826
827	!
828	!-- w-component
829	CASE ( 3 )
830	DO k = nzb_w_inner(j,i)+1, pch_index-1
831
832	pre_tend = 0.0_wp
833	pre_w = 0.0_wp
834	!
835	!-- Calculate preliminary value (pre_tend) of the tendency
836	pre_tend = - cdc * &
837	(0.5_wp * &
838	( lad_s(k+1,j,i) + lad_s(k,j,i) )) * &
839	SQRT( ( 0.25_wp * ( u(k,j,i) + &
840	u(k,j,i+1) + &
841	u(k+1,j,i) + &
842	u(k+1,j,i+1) ) &
843	)**2 + &
844	( 0.25_wp * ( v(k,j,i) + &
845	v(k,j+1,i) + &
846	v(k+1,j,i) + &
847	v(k+1,j+1,i) ) &
848	)**2 + &
849	w(k,j,i)**2 &
850	) * &
851	w(k,j,i)
852	!
853	!-- Calculate preliminary new velocity, based on pre_tend
854	pre_w = w(k,j,i) + dt_3d * pre_tend
855	!
856	!-- Compare sign of old velocity and new preliminary velocity,
857	!-- and in case the signs are different, limit the tendency
858	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
859	pre_tend = - w(k,j,i) * ddt_3d
860	ELSE
861	pre_tend = pre_tend
862	ENDIF
863	!
864	!-- Calculate final tendency
865	tend(k,j,i) = tend(k,j,i) + pre_tend
866	ENDDO
867
868	!
869	!-- potential temperature
870	CASE ( 4 )
871	DO k = nzb_s_inner(j,i)+1, pch_index
872	tend(k,j,i) = tend(k,j,i) + &
873	( canopy_heat_flux(k,j,i) - &
874	canopy_heat_flux(k-1,j,i) ) / dzw(k)
875	ENDDO
876
877
878	!
879	!-- scalar concentration
880	CASE ( 5 )
881	DO k = nzb_s_inner(j,i)+1, pch_index
882	tend(k,j,i) = tend(k,j,i) - &
883	lsec * &
884	lad_s(k,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	( q(k,j,i) - lsc )
896	ENDDO
897
898	!
899	!-- sgs-tke
900	CASE ( 6 )
901	DO k = nzb_s_inner(j,i)+1, pch_index
902	tend(k,j,i) = tend(k,j,i) - &
903	2.0_wp * cdc * &
904	lad_s(k,j,i) * &
905	SQRT( ( 0.5_wp * ( u(k,j,i) + &
906	u(k,j,i+1) ) &
907	)**2 + &
908	( 0.5_wp * ( v(k,j,i) + &
909	v(k,j+1,i) ) &
910	)**2 + &
911	( 0.5_wp * ( w(k,j,i) + &
912	w(k+1,j,i) ) &
913	)**2 &
914	) * &
915	e(k,j,i)
916	ENDDO
917
918	CASE DEFAULT
919
920	WRITE( message_string, * ) 'wrong component: ', component
921	CALL message( 'plant_canopy_model', 'PA0279', 1, 2, 0, 6, 0 )
922
923	END SELECT
924
925	END SUBROUTINE plant_canopy_model_ij
926
927	END MODULE plant_canopy_model_mod

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