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source: palm/trunk/SOURCE/plant_canopy_model.f90 @ 1730

Last change on this file since 1730 was 1722, checked in by raasch, 9 years ago
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[1682]	1	!> @file plant_canopy_model.f90
[1036]	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	!
[1310]	16	! Copyright 1997-2014 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[257]	19	! Current revisions:
[138]	20	! -----------------
[1485]	21	!
[1722]	22	!
[1485]	23	! Former revisions:
	24	! -----------------
	25	! $Id: plant_canopy_model.f90 1722 2015-11-16 13:06:09Z gronemeier $
	26	!
[1722]	27	! 1721 2015-11-16 12:56:48Z raasch
	28	! bugfixes: shf is reduced in areas covered with canopy only,
	29	! canopy is set on top of topography
	30	!
[1683]	31	! 1682 2015-10-07 23:56:08Z knoop
	32	! Code annotations made doxygen readable
	33	!
[1485]	34	! 1484 2014-10-21 10:53:05Z kanani
[1484]	35	! Changes due to new module structure of the plant canopy model:
	36	! module plant_canopy_model_mod now contains a subroutine for the
	37	! initialization of the canopy model (init_plant_canopy),
	38	! limitation of the canopy drag (previously accounted for by calculation of
	39	! a limiting canopy timestep for the determination of the maximum LES timestep
	40	! in subroutine timestep) is now realized by the calculation of pre-tendencies
	41	! and preliminary velocities in subroutine plant_canopy_model,
	42	! some redundant MPI communication removed in subroutine init_plant_canopy
	43	! (was previously in init_3d_model),
	44	! unnecessary 3d-arrays lad_u, lad_v, lad_w removed - lad information on the
	45	! respective grid is now provided only by lad_s (e.g. in the calculation of
	46	! the tendency terms or of cum_lai_hf),
	47	! drag_coefficient, lai, leaf_surface_concentration,
	48	! scalar_exchange_coefficient, sec and sls renamed to canopy_drag_coeff,
	49	! cum_lai_hf, leaf_surface_conc, leaf_scalar_exch_coeff, lsec and lsc,
	50	! respectively,
	51	! unnecessary 3d-arrays cdc, lsc and lsec now defined as single-value constants,
	52	! USE-statements and ONLY-lists modified accordingly
[1341]	53	!
	54	! 1340 2014-03-25 19:45:13Z kanani
	55	! REAL constants defined as wp-kind
	56	!
[1321]	57	! 1320 2014-03-20 08:40:49Z raasch
[1320]	58	! ONLY-attribute added to USE-statements,
	59	! kind-parameters added to all INTEGER and REAL declaration statements,
	60	! kinds are defined in new module kinds,
	61	! old module precision_kind is removed,
	62	! revision history before 2012 removed,
	63	! comment fields (!:) to be used for variable explanations added to
	64	! all variable declaration statements
[153]	65	!
[1037]	66	! 1036 2012-10-22 13:43:42Z raasch
	67	! code put under GPL (PALM 3.9)
	68	!
[139]	69	! 138 2007-11-28 10:03:58Z letzel
	70	! Initial revision
	71	!
[138]	72	! Description:
	73	! ------------
[1682]	74	!> 1) Initialization of the canopy model, e.g. construction of leaf area density
	75	!> profile (subroutine init_plant_canopy).
	76	!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration
	77	!> due to canopy elements (subroutine plant_canopy_model).
[138]	78	!------------------------------------------------------------------------------!
[1682]	79	MODULE plant_canopy_model_mod
	80
[1484]	81	USE arrays_3d, &
	82	ONLY: dzu, dzw, e, q, shf, tend, u, v, w, zu, zw
[138]	83
[1484]	84	USE indices, &
	85	ONLY: nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv, &
	86	nz, nzb, nzb_s_inner, nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt
	87
	88	USE kinds
	89
	90
	91	IMPLICIT NONE
	92
	93
[1682]	94	CHARACTER (LEN=20) :: canopy_mode = 'block' !< canopy coverage
[1484]	95
[1682]	96	INTEGER(iwp) :: pch_index = 0 !< plant canopy height/top index
[1484]	97	INTEGER(iwp) :: &
[1682]	98	lad_vertical_gradient_level_ind(10) = -9999 !< lad-profile levels (index)
[1484]	99
[1682]	100	LOGICAL :: calc_beta_lad_profile = .FALSE. !< switch for calc. of lad from beta func.
	101	LOGICAL :: plant_canopy = .FALSE. !< switch for use of canopy model
[1484]	102
[1682]	103	REAL(wp) :: alpha_lad = 9999999.9_wp !< coefficient for lad calculation
	104	REAL(wp) :: beta_lad = 9999999.9_wp !< coefficient for lad calculation
	105	REAL(wp) :: canopy_drag_coeff = 0.0_wp !< canopy drag coefficient (parameter)
	106	REAL(wp) :: cdc = 0.0_wp !< canopy drag coeff. (abbreviation used in equations)
	107	REAL(wp) :: cthf = 0.0_wp !< canopy top heat flux
	108	REAL(wp) :: dt_plant_canopy = 0.0_wp !< timestep account. for canopy drag
	109	REAL(wp) :: lad_surface = 0.0_wp !< lad surface value
	110	REAL(wp) :: lai_beta = 0.0_wp !< leaf area index (lai) for lad calc.
[1484]	111	REAL(wp) :: &
[1682]	112	leaf_scalar_exch_coeff = 0.0_wp !< canopy scalar exchange coeff.
[1484]	113	REAL(wp) :: &
[1682]	114	leaf_surface_conc = 0.0_wp !< leaf surface concentration
	115	REAL(wp) :: lsec = 0.0_wp !< leaf scalar exchange coeff.
	116	REAL(wp) :: lsc = 0.0_wp !< leaf surface concentration
[1484]	117
	118	REAL(wp) :: &
[1682]	119	lad_vertical_gradient(10) = 0.0_wp !< lad gradient
[1484]	120	REAL(wp) :: &
[1682]	121	lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)
[1484]	122
[1682]	123	REAL(wp), DIMENSION(:), ALLOCATABLE :: lad !< leaf area density
	124	REAL(wp), DIMENSION(:), ALLOCATABLE :: pre_lad !< preliminary lad
[1484]	125
	126	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: &
[1682]	127	canopy_heat_flux !< canopy heat flux
	128	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: cum_lai_hf !< cumulative lai for heatflux calc.
	129	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: lad_s !< lad on scalar-grid
[1484]	130
	131
	132	SAVE
	133
	134
[138]	135	PRIVATE
[1484]	136	PUBLIC alpha_lad, beta_lad, calc_beta_lad_profile, canopy_drag_coeff, &
	137	canopy_mode, cdc, cthf, dt_plant_canopy, init_plant_canopy, lad, &
	138	lad_s, lad_surface, lad_vertical_gradient, &
	139	lad_vertical_gradient_level, lad_vertical_gradient_level_ind, &
	140	lai_beta, leaf_scalar_exch_coeff, leaf_surface_conc, lsc, lsec, &
	141	pch_index, plant_canopy, plant_canopy_model
[138]	142
[1484]	143
	144	INTERFACE init_plant_canopy
	145	MODULE PROCEDURE init_plant_canopy
	146	END INTERFACE init_plant_canopy
	147
[138]	148	INTERFACE plant_canopy_model
	149	MODULE PROCEDURE plant_canopy_model
	150	MODULE PROCEDURE plant_canopy_model_ij
	151	END INTERFACE plant_canopy_model
	152
[1484]	153
	154
	155
[138]	156	CONTAINS
	157
	158
	159	!------------------------------------------------------------------------------!
[1484]	160	! Description:
	161	! ------------
[1682]	162	!> Initialization of the plant canopy model
[138]	163	!------------------------------------------------------------------------------!
[1484]	164	SUBROUTINE init_plant_canopy
	165
	166
	167	USE control_parameters, &
	168	ONLY: dz, ocean, passive_scalar
	169
	170
	171	IMPLICIT NONE
	172
[1682]	173	INTEGER(iwp) :: i !< running index
	174	INTEGER(iwp) :: j !< running index
	175	INTEGER(iwp) :: k !< running index
[1484]	176
[1682]	177	REAL(wp) :: int_bpdf !< vertical integral for lad-profile construction
	178	REAL(wp) :: dzh !< vertical grid spacing in units of canopy height
	179	REAL(wp) :: gradient !< gradient for lad-profile construction
	180	REAL(wp) :: canopy_height !< canopy height for lad-profile construction
[1484]	181
	182	!
	183	!-- Allocate one-dimensional arrays for the computation of the
	184	!-- leaf area density (lad) profile
	185	ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
	186	lad = 0.0_wp
	187	pre_lad = 0.0_wp
	188
	189	!
	190	!-- Compute the profile of leaf area density used in the plant
	191	!-- canopy model. The profile can either be constructed from
	192	!-- prescribed vertical gradients of the leaf area density or by
	193	!-- using a beta probability density function (see e.g. Markkanen et al.,
	194	!-- 2003: Boundary-Layer Meteorology, 106, 437-459)
	195	IF ( .NOT. calc_beta_lad_profile ) THEN
	196
	197	!
	198	!-- Use vertical gradients for lad-profile construction
	199	i = 1
	200	gradient = 0.0_wp
	201
	202	IF ( .NOT. ocean ) THEN
	203
	204	lad(0) = lad_surface
	205	lad_vertical_gradient_level_ind(1) = 0
	206
	207	DO k = 1, pch_index
	208	IF ( i < 11 ) THEN
	209	IF ( lad_vertical_gradient_level(i) < zu(k) .AND. &
	210	lad_vertical_gradient_level(i) >= 0.0_wp ) THEN
	211	gradient = lad_vertical_gradient(i)
	212	lad_vertical_gradient_level_ind(i) = k - 1
	213	i = i + 1
	214	ENDIF
	215	ENDIF
	216	IF ( gradient /= 0.0_wp ) THEN
	217	IF ( k /= 1 ) THEN
	218	lad(k) = lad(k-1) + dzu(k) * gradient
	219	ELSE
	220	lad(k) = lad_surface + dzu(k) * gradient
	221	ENDIF
	222	ELSE
	223	lad(k) = lad(k-1)
	224	ENDIF
	225	ENDDO
	226
	227	ENDIF
	228
	229	!
	230	!-- In case of no given leaf area density gradients, choose a vanishing
	231	!-- gradient. This information is used for the HEADER and the RUN_CONTROL
	232	!-- file.
	233	IF ( lad_vertical_gradient_level(1) == -9999999.9_wp ) THEN
	234	lad_vertical_gradient_level(1) = 0.0_wp
	235	ENDIF
	236
	237	ELSE
	238
	239	!
	240	!-- Use beta function for lad-profile construction
	241	int_bpdf = 0.0_wp
	242	canopy_height = pch_index * dz
	243
	244	DO k = nzb, pch_index
	245	int_bpdf = int_bpdf + &
	246	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
	247	( ( 1.0_wp - ( zw(k) / canopy_height ) )*( beta_lad-1.0_wp ) ) &
	248	( ( zw(k+1)-zw(k) ) / canopy_height ) )
	249	ENDDO
	250
	251	!
	252	!-- Preliminary lad profile (defined on w-grid)
	253	DO k = nzb, pch_index
	254	pre_lad(k) = lai_beta * &
	255	( ( ( zw(k) / canopy_height )*( alpha_lad-1.0_wp ) ) &
	256	( ( 1.0_wp - ( zw(k) / canopy_height ) )**( beta_lad-1.0_wp ) ) / &
	257	int_bpdf &
	258	) / canopy_height
	259	ENDDO
	260
	261	!
	262	!-- Final lad profile (defined on scalar-grid level, since most prognostic
	263	!-- quantities are defined there, hence, less interpolation is required
	264	!-- when calculating the canopy tendencies)
	265	lad(0) = pre_lad(0)
	266	DO k = nzb+1, pch_index
	267	lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
	268	ENDDO
	269
	270	ENDIF
	271
	272	!
	273	!-- Allocate 3D-array for the leaf area density (lad_s). In case of a
	274	!-- prescribed canopy-top heat flux (cthf), allocate 3D-arrays for
	275	!-- the cumulative leaf area index (cum_lai_hf) and the canopy heat flux.
	276	ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
	277
	278	IF ( cthf /= 0.0_wp ) THEN
	279	ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
	280	canopy_heat_flux(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
	281	ENDIF
	282
	283	!
	284	!-- Initialize canopy parameters cdc (canopy drag coefficient),
	285	!-- lsec (leaf scalar exchange coefficient), lsc (leaf surface concentration)
	286	!-- with the prescribed values
	287	cdc = canopy_drag_coeff
	288	lsec = leaf_scalar_exch_coeff
	289	lsc = leaf_surface_conc
	290
	291	!
	292	!-- Initialization of the canopy coverage in the model domain:
	293	!-- Setting the parameter canopy_mode = 'block' initializes a canopy, which
	294	!-- fully covers the domain surface
	295	SELECT CASE ( TRIM( canopy_mode ) )
	296
	297	CASE( 'block' )
	298
	299	DO i = nxlg, nxrg
	300	DO j = nysg, nyng
	301	lad_s(:,j,i) = lad(:)
	302	ENDDO
	303	ENDDO
	304
	305	CASE DEFAULT
	306
	307	!
	308	!-- The DEFAULT case is reached either if the parameter
	309	!-- canopy mode contains a wrong character string or if the
	310	!-- user has coded a special case in the user interface.
	311	!-- There, the subroutine user_init_plant_canopy checks
	312	!-- which of these two conditions applies.
	313	CALL user_init_plant_canopy
	314
	315	END SELECT
	316
	317	!
	318	!-- Initialization of the canopy heat source distribution
	319	IF ( cthf /= 0.0_wp ) THEN
	320	!
	321	!-- Piecewise calculation of the leaf area index by vertical
	322	!-- integration of the leaf area density
	323	cum_lai_hf(:,:,:) = 0.0_wp
	324	DO i = nxlg, nxrg
	325	DO j = nysg, nyng
	326	DO k = pch_index-1, 0, -1
	327	IF ( k == pch_index-1 ) THEN
	328	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
	329	( 0.5_wp * lad_s(k+1,j,i) * &
	330	( zw(k+1) - zu(k+1) ) ) + &
	331	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
	332	lad_s(k,j,i) ) + &
	333	lad_s(k+1,j,i) ) * &
	334	( zu(k+1) - zw(k) ) )
	335	ELSE
	336	cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) + &
	337	( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) + &
	338	lad_s(k+1,j,i) ) + &
	339	lad_s(k+1,j,i) ) * &
	340	( zw(k+1) - zu(k+1) ) ) + &
	341	( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) + &
	342	lad_s(k,j,i) ) + &
	343	lad_s(k+1,j,i) ) * &
	344	( zu(k+1) - zw(k) ) )
	345	ENDIF
	346	ENDDO
	347	ENDDO
	348	ENDDO
	349
	350	!
	351	!-- Calculation of the upward kinematic vertical heat flux within the
	352	!-- canopy
	353	DO i = nxlg, nxrg
	354	DO j = nysg, nyng
	355	DO k = 0, pch_index
	356	canopy_heat_flux(k,j,i) = cthf * &
	357	exp( -0.6_wp * cum_lai_hf(k,j,i) )
	358	ENDDO
	359	ENDDO
	360	ENDDO
	361
	362	!
[1721]	363	!-- In areas covered with canopy, the surface heat flux is set to
	364	!-- the surface value of the above calculated in-canopy heat flux
	365	!-- distribution
	366	DO i = nxlg,nxrg
	367	DO j = nysg, nyng
	368	IF ( canopy_heat_flux(0,j,i) /= cthf ) THEN
	369	shf(j,i) = canopy_heat_flux(0,j,i)
	370	ENDIF
	371	ENDDO
	372	ENDDO
[1484]	373
	374	ENDIF
	375
	376
	377
	378	END SUBROUTINE init_plant_canopy
	379
	380
	381
	382	!------------------------------------------------------------------------------!
	383	! Description:
	384	! ------------
[1682]	385	!> Calculation of the tendency terms, accounting for the effect of the plant
	386	!> canopy on momentum and scalar quantities.
	387	!>
	388	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
	389	!> (defined on scalar grid), as initialized in subroutine init_plant_canopy.
	390	!> The lad on the w-grid is vertically interpolated from the surrounding
	391	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
	392	!> k = pch_index. Here, the lad is zero.
	393	!>
	394	!> The canopy drag must be limited (previously accounted for by calculation of
	395	!> a limiting canopy timestep for the determination of the maximum LES timestep
	396	!> in subroutine timestep), since it is physically impossible that the canopy
	397	!> drag alone can locally change the sign of a velocity component. This
	398	!> limitation is realized by calculating preliminary tendencies and velocities.
	399	!> It is subsequently checked if the preliminary new velocity has a different
	400	!> sign than the current velocity. If so, the tendency is limited in a way that
	401	!> the velocity can at maximum be reduced to zero by the canopy drag.
	402	!>
	403	!>
	404	!> Call for all grid points
[1484]	405	!------------------------------------------------------------------------------!
[138]	406	SUBROUTINE plant_canopy_model( component )
	407
	408
[1320]	409	USE control_parameters, &
[1484]	410	ONLY: dt_3d, message_string
[1320]	411
	412	USE kinds
	413
[138]	414	IMPLICIT NONE
	415
[1682]	416	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
	417	INTEGER(iwp) :: i !< running index
	418	INTEGER(iwp) :: j !< running index
	419	INTEGER(iwp) :: k !< running index
[1721]	420	INTEGER(iwp) :: kk !< running index for flat lad arrays
[1484]	421
[1682]	422	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
	423	REAL(wp) :: lad_local !< local lad value
	424	REAL(wp) :: pre_tend !< preliminary tendency
	425	REAL(wp) :: pre_u !< preliminary u-value
	426	REAL(wp) :: pre_v !< preliminary v-value
	427	REAL(wp) :: pre_w !< preliminary w-value
[1484]	428
	429
	430	ddt_3d = 1.0_wp / dt_3d
[138]	431
	432	!
[1484]	433	!-- Compute drag for the three velocity components and the SGS-TKE:
[138]	434	SELECT CASE ( component )
	435
	436	!
	437	!-- u-component
	438	CASE ( 1 )
	439	DO i = nxlu, nxr
	440	DO j = nys, nyn
[1721]	441	DO k = nzb_u_inner(j,i)+1, nzb_u_inner(j,i)+pch_index
[1484]	442
[1721]	443	kk = k - nzb_u_inner(j,i) !- lad arrays are defined flat
[1484]	444	!
	445	!-- In order to create sharp boundaries of the plant canopy,
	446	!-- the lad on the u-grid at index (k,j,i) is equal to
	447	!-- lad_s(k,j,i), rather than being interpolated from the
	448	!-- surrounding lad_s, because this would yield smaller lad
	449	!-- at the canopy boundaries than inside of the canopy.
	450	!-- For the same reason, the lad at the rightmost(i+1)canopy
	451	!-- boundary on the u-grid equals lad_s(k,j,i).
[1721]	452	lad_local = lad_s(kk,j,i)
	453	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp )&
	454	THEN
	455	lad_local = lad_s(kk,j,i-1)
[1484]	456	ENDIF
	457
	458	pre_tend = 0.0_wp
	459	pre_u = 0.0_wp
	460	!
	461	!-- Calculate preliminary value (pre_tend) of the tendency
	462	pre_tend = - cdc * &
	463	lad_local * &
	464	SQRT( u(k,j,i)**2 + &
	465	( 0.25_wp * ( v(k,j,i-1) + &
	466	v(k,j,i) + &
	467	v(k,j+1,i) + &
	468	v(k,j+1,i-1) ) &
	469	)**2 + &
	470	( 0.25_wp * ( w(k-1,j,i-1) + &
	471	w(k-1,j,i) + &
	472	w(k,j,i-1) + &
	473	w(k,j,i) ) &
	474	)**2 &
	475	) * &
	476	u(k,j,i)
	477
	478	!
	479	!-- Calculate preliminary new velocity, based on pre_tend
	480	pre_u = u(k,j,i) + dt_3d * pre_tend
	481	!
	482	!-- Compare sign of old velocity and new preliminary velocity,
	483	!-- and in case the signs are different, limit the tendency
	484	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
	485	pre_tend = - u(k,j,i) * ddt_3d
	486	ELSE
	487	pre_tend = pre_tend
	488	ENDIF
	489	!
	490	!-- Calculate final tendency
	491	tend(k,j,i) = tend(k,j,i) + pre_tend
	492
[138]	493	ENDDO
	494	ENDDO
	495	ENDDO
	496
	497	!
	498	!-- v-component
	499	CASE ( 2 )
	500	DO i = nxl, nxr
	501	DO j = nysv, nyn
[1721]	502	DO k = nzb_v_inner(j,i)+1, nzb_v_inner(j,i)+pch_index
[1484]	503
[1721]	504	kk = k - nzb_v_inner(j,i) !- lad arrays are defined flat
[1484]	505	!
	506	!-- In order to create sharp boundaries of the plant canopy,
	507	!-- the lad on the v-grid at index (k,j,i) is equal to
	508	!-- lad_s(k,j,i), rather than being interpolated from the
	509	!-- surrounding lad_s, because this would yield smaller lad
	510	!-- at the canopy boundaries than inside of the canopy.
	511	!-- For the same reason, the lad at the northmost(j+1) canopy
	512	!-- boundary on the v-grid equals lad_s(k,j,i).
[1721]	513	lad_local = lad_s(kk,j,i)
	514	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp )&
	515	THEN
	516	lad_local = lad_s(kk,j-1,i)
[1484]	517	ENDIF
	518
	519	pre_tend = 0.0_wp
	520	pre_v = 0.0_wp
	521	!
	522	!-- Calculate preliminary value (pre_tend) of the tendency
	523	pre_tend = - cdc * &
	524	lad_local * &
	525	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
	526	u(k,j-1,i+1) + &
	527	u(k,j,i) + &
	528	u(k,j,i+1) ) &
	529	)**2 + &
	530	v(k,j,i)**2 + &
	531	( 0.25_wp * ( w(k-1,j-1,i) + &
	532	w(k-1,j,i) + &
	533	w(k,j-1,i) + &
	534	w(k,j,i) ) &
	535	)**2 &
	536	) * &
	537	v(k,j,i)
	538
	539	!
	540	!-- Calculate preliminary new velocity, based on pre_tend
	541	pre_v = v(k,j,i) + dt_3d * pre_tend
	542	!
	543	!-- Compare sign of old velocity and new preliminary velocity,
	544	!-- and in case the signs are different, limit the tendency
	545	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
	546	pre_tend = - v(k,j,i) * ddt_3d
	547	ELSE
	548	pre_tend = pre_tend
	549	ENDIF
	550	!
	551	!-- Calculate final tendency
	552	tend(k,j,i) = tend(k,j,i) + pre_tend
	553
[138]	554	ENDDO
	555	ENDDO
	556	ENDDO
	557
	558	!
	559	!-- w-component
	560	CASE ( 3 )
	561	DO i = nxl, nxr
	562	DO j = nys, nyn
[1721]	563	DO k = nzb_w_inner(j,i)+1, nzb_w_inner(j,i)+pch_index-1
[1484]	564
[1721]	565	kk = k - nzb_w_inner(j,i) !- lad arrays are defined flat
	566
[1484]	567	pre_tend = 0.0_wp
	568	pre_w = 0.0_wp
	569	!
	570	!-- Calculate preliminary value (pre_tend) of the tendency
	571	pre_tend = - cdc * &
	572	(0.5_wp * &
[1721]	573	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
[1484]	574	SQRT( ( 0.25_wp * ( u(k,j,i) + &
	575	u(k,j,i+1) + &
	576	u(k+1,j,i) + &
	577	u(k+1,j,i+1) ) &
	578	)**2 + &
	579	( 0.25_wp * ( v(k,j,i) + &
	580	v(k,j+1,i) + &
	581	v(k+1,j,i) + &
	582	v(k+1,j+1,i) ) &
	583	)**2 + &
	584	w(k,j,i)**2 &
	585	) * &
	586	w(k,j,i)
	587	!
	588	!-- Calculate preliminary new velocity, based on pre_tend
	589	pre_w = w(k,j,i) + dt_3d * pre_tend
	590	!
	591	!-- Compare sign of old velocity and new preliminary velocity,
	592	!-- and in case the signs are different, limit the tendency
	593	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
	594	pre_tend = - w(k,j,i) * ddt_3d
	595	ELSE
	596	pre_tend = pre_tend
	597	ENDIF
	598	!
	599	!-- Calculate final tendency
	600	tend(k,j,i) = tend(k,j,i) + pre_tend
	601
[138]	602	ENDDO
	603	ENDDO
	604	ENDDO
	605
	606	!
[153]	607	!-- potential temperature
[138]	608	CASE ( 4 )
	609	DO i = nxl, nxr
	610	DO j = nys, nyn
[1721]	611	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
	612	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
[1484]	613	tend(k,j,i) = tend(k,j,i) + &
[1721]	614	( canopy_heat_flux(kk,j,i) - &
	615	canopy_heat_flux(kk-1,j,i) ) / dzw(k)
[153]	616	ENDDO
	617	ENDDO
	618	ENDDO
	619
	620	!
	621	!-- scalar concentration
	622	CASE ( 5 )
	623	DO i = nxl, nxr
	624	DO j = nys, nyn
[1721]	625	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
	626	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
[1484]	627	tend(k,j,i) = tend(k,j,i) - &
	628	lsec * &
[1721]	629	lad_s(kk,j,i) * &
[1484]	630	SQRT( ( 0.5_wp * ( u(k,j,i) + &
	631	u(k,j,i+1) ) &
	632	)**2 + &
	633	( 0.5_wp * ( v(k,j,i) + &
	634	v(k,j+1,i) ) &
	635	)**2 + &
	636	( 0.5_wp * ( w(k-1,j,i) + &
	637	w(k,j,i) ) &
	638	)**2 &
	639	) * &
	640	( q(k,j,i) - lsc )
[153]	641	ENDDO
	642	ENDDO
	643	ENDDO
	644
	645	!
	646	!-- sgs-tke
	647	CASE ( 6 )
	648	DO i = nxl, nxr
	649	DO j = nys, nyn
[1721]	650	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
	651	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
[1484]	652	tend(k,j,i) = tend(k,j,i) - &
	653	2.0_wp * cdc * &
[1721]	654	lad_s(kk,j,i) * &
[1484]	655	SQRT( ( 0.5_wp * ( u(k,j,i) + &
	656	u(k,j,i+1) ) &
	657	)**2 + &
	658	( 0.5_wp * ( v(k,j,i) + &
	659	v(k,j+1,i) ) &
	660	)**2 + &
	661	( 0.5_wp * ( w(k,j,i) + &
	662	w(k+1,j,i) ) &
	663	)**2 &
	664	) * &
	665	e(k,j,i)
[138]	666	ENDDO
	667	ENDDO
	668	ENDDO
[1484]	669
	670
[138]	671	CASE DEFAULT
	672
[257]	673	WRITE( message_string, * ) 'wrong component: ', component
	674	CALL message( 'plant_canopy_model', 'PA0279', 1, 2, 0, 6, 0 )
[138]	675
	676	END SELECT
	677
	678	END SUBROUTINE plant_canopy_model
	679
	680
	681	!------------------------------------------------------------------------------!
[1484]	682	! Description:
	683	! ------------
[1682]	684	!> Calculation of the tendency terms, accounting for the effect of the plant
	685	!> canopy on momentum and scalar quantities.
	686	!>
	687	!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0
	688	!> (defined on scalar grid), as initialized in subroutine init_plant_canopy.
	689	!> The lad on the w-grid is vertically interpolated from the surrounding
	690	!> lad_s. The upper boundary of the canopy is defined on the w-grid at
	691	!> k = pch_index. Here, the lad is zero.
	692	!>
	693	!> The canopy drag must be limited (previously accounted for by calculation of
	694	!> a limiting canopy timestep for the determination of the maximum LES timestep
	695	!> in subroutine timestep), since it is physically impossible that the canopy
	696	!> drag alone can locally change the sign of a velocity component. This
	697	!> limitation is realized by calculating preliminary tendencies and velocities.
	698	!> It is subsequently checked if the preliminary new velocity has a different
	699	!> sign than the current velocity. If so, the tendency is limited in a way that
	700	!> the velocity can at maximum be reduced to zero by the canopy drag.
	701	!>
	702	!>
	703	!> Call for grid point i,j
[138]	704	!------------------------------------------------------------------------------!
	705	SUBROUTINE plant_canopy_model_ij( i, j, component )
	706
	707
[1320]	708	USE control_parameters, &
[1484]	709	ONLY: dt_3d, message_string
[1320]	710
	711	USE kinds
	712
[138]	713	IMPLICIT NONE
	714
[1682]	715	INTEGER(iwp) :: component !< prognostic variable (u,v,w,pt,q,e)
	716	INTEGER(iwp) :: i !< running index
	717	INTEGER(iwp) :: j !< running index
	718	INTEGER(iwp) :: k !< running index
[1721]	719	INTEGER(iwp) :: kk !< running index for flat lad arrays
[138]	720
[1682]	721	REAL(wp) :: ddt_3d !< inverse of the LES timestep (dt_3d)
	722	REAL(wp) :: lad_local !< local lad value
	723	REAL(wp) :: pre_tend !< preliminary tendency
	724	REAL(wp) :: pre_u !< preliminary u-value
	725	REAL(wp) :: pre_v !< preliminary v-value
	726	REAL(wp) :: pre_w !< preliminary w-value
[1484]	727
	728
	729	ddt_3d = 1.0_wp / dt_3d
	730
[138]	731	!
[1484]	732	!-- Compute drag for the three velocity components and the SGS-TKE
[142]	733	SELECT CASE ( component )
[138]	734
	735	!
[142]	736	!-- u-component
[1484]	737	CASE ( 1 )
[1721]	738	DO k = nzb_u_inner(j,i)+1, nzb_u_inner(j,i)+pch_index
[138]	739
[1721]	740	kk = k - nzb_u_inner(j,i) !- lad arrays are defined flat
[138]	741	!
[1484]	742	!-- In order to create sharp boundaries of the plant canopy,
	743	!-- the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
	744	!-- rather than being interpolated from the surrounding lad_s,
	745	!-- because this would yield smaller lad at the canopy boundaries
	746	!-- than inside of the canopy.
	747	!-- For the same reason, the lad at the rightmost(i+1)canopy
	748	!-- boundary on the u-grid equals lad_s(k,j,i).
[1721]	749	lad_local = lad_s(kk,j,i)
	750	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp ) THEN
	751	lad_local = lad_s(kk,j,i-1)
[1484]	752	ENDIF
	753
	754	pre_tend = 0.0_wp
	755	pre_u = 0.0_wp
	756	!
	757	!-- Calculate preliminary value (pre_tend) of the tendency
	758	pre_tend = - cdc * &
	759	lad_local * &
	760	SQRT( u(k,j,i)**2 + &
	761	( 0.25_wp * ( v(k,j,i-1) + &
	762	v(k,j,i) + &
	763	v(k,j+1,i) + &
	764	v(k,j+1,i-1) ) &
	765	)**2 + &
	766	( 0.25_wp * ( w(k-1,j,i-1) + &
	767	w(k-1,j,i) + &
	768	w(k,j,i-1) + &
	769	w(k,j,i) ) &
	770	)**2 &
	771	) * &
	772	u(k,j,i)
	773
	774	!
	775	!-- Calculate preliminary new velocity, based on pre_tend
	776	pre_u = u(k,j,i) + dt_3d * pre_tend
	777	!
	778	!-- Compare sign of old velocity and new preliminary velocity,
	779	!-- and in case the signs are different, limit the tendency
	780	IF ( SIGN(pre_u,u(k,j,i)) /= pre_u ) THEN
	781	pre_tend = - u(k,j,i) * ddt_3d
	782	ELSE
	783	pre_tend = pre_tend
	784	ENDIF
	785	!
	786	!-- Calculate final tendency
	787	tend(k,j,i) = tend(k,j,i) + pre_tend
	788	ENDDO
	789
	790
	791	!
[142]	792	!-- v-component
[1484]	793	CASE ( 2 )
[1721]	794	DO k = nzb_v_inner(j,i)+1, nzb_v_inner(j,i)+pch_index
[138]	795
[1721]	796	kk = k - nzb_v_inner(j,i) !- lad arrays are defined flat
[138]	797	!
[1484]	798	!-- In order to create sharp boundaries of the plant canopy,
	799	!-- the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
	800	!-- rather than being interpolated from the surrounding lad_s,
	801	!-- because this would yield smaller lad at the canopy boundaries
	802	!-- than inside of the canopy.
	803	!-- For the same reason, the lad at the northmost(j+1)canopy
	804	!-- boundary on the v-grid equals lad_s(k,j,i).
[1721]	805	lad_local = lad_s(kk,j,i)
	806	IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp ) THEN
	807	lad_local = lad_s(kk,j-1,i)
[1484]	808	ENDIF
	809
	810	pre_tend = 0.0_wp
	811	pre_v = 0.0_wp
	812	!
	813	!-- Calculate preliminary value (pre_tend) of the tendency
	814	pre_tend = - cdc * &
	815	lad_local * &
	816	SQRT( ( 0.25_wp * ( u(k,j-1,i) + &
	817	u(k,j-1,i+1) + &
	818	u(k,j,i) + &
	819	u(k,j,i+1) ) &
	820	)**2 + &
	821	v(k,j,i)**2 + &
	822	( 0.25_wp * ( w(k-1,j-1,i) + &
	823	w(k-1,j,i) + &
	824	w(k,j-1,i) + &
	825	w(k,j,i) ) &
	826	)**2 &
	827	) * &
	828	v(k,j,i)
	829
	830	!
	831	!-- Calculate preliminary new velocity, based on pre_tend
	832	pre_v = v(k,j,i) + dt_3d * pre_tend
	833	!
	834	!-- Compare sign of old velocity and new preliminary velocity,
	835	!-- and in case the signs are different, limit the tendency
	836	IF ( SIGN(pre_v,v(k,j,i)) /= pre_v ) THEN
	837	pre_tend = - v(k,j,i) * ddt_3d
	838	ELSE
	839	pre_tend = pre_tend
	840	ENDIF
	841	!
	842	!-- Calculate final tendency
	843	tend(k,j,i) = tend(k,j,i) + pre_tend
	844	ENDDO
	845
	846
	847	!
[142]	848	!-- w-component
[1484]	849	CASE ( 3 )
[1721]	850	DO k = nzb_w_inner(j,i)+1, nzb_w_inner(j,i)+pch_index-1
[138]	851
[1721]	852	kk = k - nzb_w_inner(j,i) !- lad arrays are defined flat
	853
[1484]	854	pre_tend = 0.0_wp
	855	pre_w = 0.0_wp
[138]	856	!
[1484]	857	!-- Calculate preliminary value (pre_tend) of the tendency
	858	pre_tend = - cdc * &
	859	(0.5_wp * &
[1721]	860	( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) * &
[1484]	861	SQRT( ( 0.25_wp * ( u(k,j,i) + &
	862	u(k,j,i+1) + &
	863	u(k+1,j,i) + &
	864	u(k+1,j,i+1) ) &
	865	)**2 + &
	866	( 0.25_wp * ( v(k,j,i) + &
	867	v(k,j+1,i) + &
	868	v(k+1,j,i) + &
	869	v(k+1,j+1,i) ) &
	870	)**2 + &
	871	w(k,j,i)**2 &
	872	) * &
	873	w(k,j,i)
	874	!
	875	!-- Calculate preliminary new velocity, based on pre_tend
	876	pre_w = w(k,j,i) + dt_3d * pre_tend
	877	!
	878	!-- Compare sign of old velocity and new preliminary velocity,
	879	!-- and in case the signs are different, limit the tendency
	880	IF ( SIGN(pre_w,w(k,j,i)) /= pre_w ) THEN
	881	pre_tend = - w(k,j,i) * ddt_3d
	882	ELSE
	883	pre_tend = pre_tend
	884	ENDIF
	885	!
	886	!-- Calculate final tendency
	887	tend(k,j,i) = tend(k,j,i) + pre_tend
	888	ENDDO
	889
	890	!
[153]	891	!-- potential temperature
	892	CASE ( 4 )
[1721]	893	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
	894	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
[1484]	895	tend(k,j,i) = tend(k,j,i) + &
[1721]	896	( canopy_heat_flux(kk,j,i) - &
	897	canopy_heat_flux(kk-1,j,i) ) / dzw(k)
[153]	898	ENDDO
	899
	900
	901	!
	902	!-- scalar concentration
	903	CASE ( 5 )
[1721]	904	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
	905	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
[1484]	906	tend(k,j,i) = tend(k,j,i) - &
	907	lsec * &
[1721]	908	lad_s(kk,j,i) * &
[1484]	909	SQRT( ( 0.5_wp * ( u(k,j,i) + &
	910	u(k,j,i+1) ) &
	911	)**2 + &
	912	( 0.5_wp * ( v(k,j,i) + &
	913	v(k,j+1,i) ) &
	914	)**2 + &
	915	( 0.5_wp * ( w(k-1,j,i) + &
	916	w(k,j,i) ) &
	917	)**2 &
	918	) * &
	919	( q(k,j,i) - lsc )
[153]	920	ENDDO
	921
	922	!
[142]	923	!-- sgs-tke
[1484]	924	CASE ( 6 )
[1721]	925	DO k = nzb_s_inner(j,i)+1, nzb_s_inner(j,i)+pch_index
	926	kk = k - nzb_s_inner(j,i) !- lad arrays are defined flat
[1484]	927	tend(k,j,i) = tend(k,j,i) - &
	928	2.0_wp * cdc * &
[1721]	929	lad_s(kk,j,i) * &
[1484]	930	SQRT( ( 0.5_wp * ( u(k,j,i) + &
	931	u(k,j,i+1) ) &
	932	)**2 + &
	933	( 0.5_wp * ( v(k,j,i) + &
	934	v(k,j+1,i) ) &
	935	)**2 + &
	936	( 0.5_wp * ( w(k,j,i) + &
	937	w(k+1,j,i) ) &
	938	)**2 &
	939	) * &
	940	e(k,j,i)
	941	ENDDO
[138]	942
[142]	943	CASE DEFAULT
[138]	944
[257]	945	WRITE( message_string, * ) 'wrong component: ', component
	946	CALL message( 'plant_canopy_model', 'PA0279', 1, 2, 0, 6, 0 )
[138]	947
[142]	948	END SELECT
[138]	949
	950	END SUBROUTINE plant_canopy_model_ij
	951
	952	END MODULE plant_canopy_model_mod

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