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source: palm/trunk/SOURCE/init_1d_model.f90 @ 1703

Last change on this file since 1703 was 1698, checked in by raasch, 9 years ago
last commit documented example_cbl_rc updated
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[1682]	1	!> @file init_1d_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	!
[1691]	16	! Copyright 1997-2015 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[254]	19	! Current revisions:
[1]	20	! -----------------
[1347]	21	!
[1698]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: init_1d_model.f90 1698 2015-10-28 17:26:17Z raasch $
	26	!
[1698]	27	! 1697 2015-10-28 17:14:10Z raasch
	28	! small E- and F-FORMAT changes to avoid informative compiler messages about
	29	! insufficient field width
	30	!
[1692]	31	! 1691 2015-10-26 16:17:44Z maronga
	32	! Renamed prandtl_layer to constant_flux_layer. rif is replaced by ol and zeta.
	33	!
[1683]	34	! 1682 2015-10-07 23:56:08Z knoop
	35	! Code annotations made doxygen readable
	36	!
[1354]	37	! 1353 2014-04-08 15:21:23Z heinze
	38	! REAL constants provided with KIND-attribute
	39	!
[1347]	40	! 1346 2014-03-27 13:18:20Z heinze
	41	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	42	! intrinsic function like MAX, MIN, SIGN
	43	!
[1323]	44	! 1322 2014-03-20 16:38:49Z raasch
	45	! REAL functions provided with KIND-attribute
	46	!
[1321]	47	! 1320 2014-03-20 08:40:49Z raasch
[1320]	48	! ONLY-attribute added to USE-statements,
	49	! kind-parameters added to all INTEGER and REAL declaration statements,
	50	! kinds are defined in new module kinds,
	51	! revision history before 2012 removed,
	52	! comment fields (!:) to be used for variable explanations added to
	53	! all variable declaration statements
[1321]	54	!
[1037]	55	! 1036 2012-10-22 13:43:42Z raasch
	56	! code put under GPL (PALM 3.9)
	57	!
[1017]	58	! 1015 2012-09-27 09:23:24Z raasch
	59	! adjustment of mixing length to the Prandtl mixing length at first grid point
	60	! above ground removed
	61	!
[1002]	62	! 1001 2012-09-13 14:08:46Z raasch
	63	! all actions concerning leapfrog scheme removed
	64	!
[997]	65	! 996 2012-09-07 10:41:47Z raasch
	66	! little reformatting
	67	!
[979]	68	! 978 2012-08-09 08:28:32Z fricke
	69	! roughness length for scalar quantities z0h1d added
	70	!
[1]	71	! Revision 1.1 1998/03/09 16:22:10 raasch
	72	! Initial revision
	73	!
	74	!
	75	! Description:
	76	! ------------
[1682]	77	!> 1D-model to initialize the 3D-arrays.
	78	!> The temperature profile is set as steady and a corresponding steady solution
	79	!> of the wind profile is being computed.
	80	!> All subroutines required can be found within this file.
[1691]	81	!>
	82	!> @todo harmonize code with new surface_layer_fluxes module
[1]	83	!------------------------------------------------------------------------------!
[1682]	84	SUBROUTINE init_1d_model
	85
[1]	86
[1320]	87	USE arrays_3d, &
	88	ONLY: l_grid, ug, u_init, vg, v_init, zu
	89
	90	USE indices, &
	91	ONLY: nzb, nzt
	92
	93	USE kinds
	94
	95	USE model_1d, &
	96	ONLY: e1d, e1d_p, kh1d, km1d, l1d, l_black, qs1d, rif1d, &
	97	simulated_time_1d, te_e, te_em, te_u, te_um, te_v, te_vm, ts1d, &
	98	u1d, u1d_p, us1d, usws1d, v1d, v1d_p, vsws1d, z01d, z0h1d
	99
	100	USE control_parameters, &
[1691]	101	ONLY: constant_diffusion, constant_flux_layer, f, humidity, kappa, &
	102	km_constant, mixing_length_1d, passive_scalar, prandtl_number, &
	103	roughness_length, simulated_time_chr, z0h_factor
[1]	104
	105	IMPLICIT NONE
	106
[1682]	107	CHARACTER (LEN=9) :: time_to_string !<
[1320]	108
[1682]	109	INTEGER(iwp) :: k !<
[1320]	110
[1682]	111	REAL(wp) :: lambda !<
[1]	112
	113	!
	114	!-- Allocate required 1D-arrays
[1320]	115	ALLOCATE( e1d(nzb:nzt+1), e1d_p(nzb:nzt+1), &
	116	kh1d(nzb:nzt+1), km1d(nzb:nzt+1), &
	117	l_black(nzb:nzt+1), l1d(nzb:nzt+1), &
	118	rif1d(nzb:nzt+1), te_e(nzb:nzt+1), &
	119	te_em(nzb:nzt+1), te_u(nzb:nzt+1), te_um(nzb:nzt+1), &
	120	te_v(nzb:nzt+1), te_vm(nzb:nzt+1), u1d(nzb:nzt+1), &
	121	u1d_p(nzb:nzt+1), v1d(nzb:nzt+1), &
[1001]	122	v1d_p(nzb:nzt+1) )
[1]	123
	124	!
	125	!-- Initialize arrays
	126	IF ( constant_diffusion ) THEN
[1001]	127	km1d = km_constant
	128	kh1d = km_constant / prandtl_number
[1]	129	ELSE
[1353]	130	e1d = 0.0_wp; e1d_p = 0.0_wp
	131	kh1d = 0.0_wp; km1d = 0.0_wp
	132	rif1d = 0.0_wp
[1]	133	!
	134	!-- Compute the mixing length
[1353]	135	l_black(nzb) = 0.0_wp
[1]	136
	137	IF ( TRIM( mixing_length_1d ) == 'blackadar' ) THEN
	138	!
	139	!-- Blackadar mixing length
[1353]	140	IF ( f /= 0.0_wp ) THEN
	141	lambda = 2.7E-4_wp * SQRT( ug(nzt+1)2 + vg(nzt+1)2 ) / &
	142	ABS( f ) + 1E-10_wp
[1]	143	ELSE
[1353]	144	lambda = 30.0_wp
[1]	145	ENDIF
	146
	147	DO k = nzb+1, nzt+1
[1353]	148	l_black(k) = kappa * zu(k) / ( 1.0_wp + kappa * zu(k) / lambda )
[1]	149	ENDDO
	150
	151	ELSEIF ( TRIM( mixing_length_1d ) == 'as_in_3d_model' ) THEN
	152	!
	153	!-- Use the same mixing length as in 3D model
	154	l_black(1:nzt) = l_grid
	155	l_black(nzt+1) = l_black(nzt)
	156
	157	ENDIF
	158	ENDIF
	159	l1d = l_black
	160	u1d = u_init
	161	u1d_p = u_init
	162	v1d = v_init
	163	v1d_p = v_init
	164
	165	!
	166	!-- Set initial horizontal velocities at the lowest grid levels to a very small
	167	!-- value in order to avoid too small time steps caused by the diffusion limit
	168	!-- in the initial phase of a run (at k=1, dz/2 occurs in the limiting formula!)
[1353]	169	u1d(0:1) = 0.1_wp
	170	u1d_p(0:1) = 0.1_wp
	171	v1d(0:1) = 0.1_wp
	172	v1d_p(0:1) = 0.1_wp
[1]	173
	174	!
	175	!-- For u, theta and the momentum fluxes plausible values are set
[1691]	176	IF ( constant_flux_layer ) THEN
[1353]	177	us1d = 0.1_wp ! without initial friction the flow would not change
[1]	178	ELSE
[1353]	179	e1d(nzb+1) = 1.0_wp
	180	km1d(nzb+1) = 1.0_wp
	181	us1d = 0.0_wp
[1]	182	ENDIF
[1353]	183	ts1d = 0.0_wp
	184	usws1d = 0.0_wp
	185	vsws1d = 0.0_wp
[996]	186	z01d = roughness_length
[978]	187	z0h1d = z0h_factor * z01d
[1353]	188	IF ( humidity .OR. passive_scalar ) qs1d = 0.0_wp
[1]	189
	190	!
[46]	191	!-- Tendencies must be preset in order to avoid runtime errors within the
	192	!-- first Runge-Kutta step
[1353]	193	te_em = 0.0_wp
	194	te_um = 0.0_wp
	195	te_vm = 0.0_wp
[46]	196
	197	!
[1]	198	!-- Set start time in hh:mm:ss - format
	199	simulated_time_chr = time_to_string( simulated_time_1d )
	200
	201	!
	202	!-- Integrate the 1D-model equations using the leap-frog scheme
	203	CALL time_integration_1d
	204
	205
	206	END SUBROUTINE init_1d_model
	207
	208
	209
	210	!------------------------------------------------------------------------------!
	211	! Description:
	212	! ------------
[1682]	213	!> Leap-frog time differencing scheme for the 1D-model.
[1]	214	!------------------------------------------------------------------------------!
[1682]	215
	216	SUBROUTINE time_integration_1d
[1]	217
[1682]	218
[1320]	219	USE arrays_3d, &
	220	ONLY: dd2zu, ddzu, ddzw, l_grid, pt_init, q_init, ug, vg, zu
	221
	222	USE control_parameters, &
[1691]	223	ONLY: constant_diffusion, constant_flux_layer, dissipation_1d, &
	224	humidity, intermediate_timestep_count, &
	225	intermediate_timestep_count_max, f, g, ibc_e_b, kappa, &
	226	mixing_length_1d, passive_scalar, &
	227	simulated_time_chr, timestep_scheme, tsc, zeta_max, zeta_min
[1320]	228
	229	USE indices, &
	230	ONLY: nzb, nzb_diff, nzt
	231
	232	USE kinds
	233
	234	USE model_1d, &
	235	ONLY: current_timestep_number_1d, damp_level_ind_1d, dt_1d, &
	236	dt_pr_1d, dt_run_control_1d, e1d, e1d_p, end_time_1d, &
	237	kh1d, km1d, l1d, l_black, qs1d, rif1d, simulated_time_1d, &
	238	stop_dt_1d, te_e, te_em, te_u, te_um, te_v, te_vm, time_pr_1d, &
	239	ts1d, time_run_control_1d, u1d, u1d_p, us1d, usws1d, v1d, &
	240	v1d_p, vsws1d, z01d, z0h1d
	241
[1]	242	USE pegrid
	243
	244	IMPLICIT NONE
	245
[1682]	246	CHARACTER (LEN=9) :: time_to_string !<
[1320]	247
[1682]	248	INTEGER(iwp) :: k !<
[1320]	249
[1682]	250	REAL(wp) :: a !<
	251	REAL(wp) :: b !<
	252	REAL(wp) :: dissipation !<
	253	REAL(wp) :: dpt_dz !<
	254	REAL(wp) :: flux !<
	255	REAL(wp) :: kmzm !<
	256	REAL(wp) :: kmzp !<
	257	REAL(wp) :: l_stable !<
	258	REAL(wp) :: pt_0 !<
	259	REAL(wp) :: uv_total !<
[1]	260
	261	!
	262	!-- Determine the time step at the start of a 1D-simulation and
	263	!-- determine and printout quantities used for run control
	264	CALL timestep_1d
	265	CALL run_control_1d
	266
	267	!
	268	!-- Start of time loop
	269	DO WHILE ( simulated_time_1d < end_time_1d .AND. .NOT. stop_dt_1d )
	270
	271	!
	272	!-- Depending on the timestep scheme, carry out one or more intermediate
	273	!-- timesteps
	274
	275	intermediate_timestep_count = 0
	276	DO WHILE ( intermediate_timestep_count < &
	277	intermediate_timestep_count_max )
	278
	279	intermediate_timestep_count = intermediate_timestep_count + 1
	280
	281	CALL timestep_scheme_steering
	282
	283	!
	284	!-- Compute all tendency terms. If a Prandtl-layer is simulated, k starts
	285	!-- at nzb+2.
	286	DO k = nzb_diff, nzt
	287
[1353]	288	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	289	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[1]	290	!
	291	!-- u-component
	292	te_u(k) = f * ( v1d(k) - vg(k) ) + ( &
[1001]	293	kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) &
	294	- kmzm * ( u1d(k) - u1d(k-1) ) * ddzu(k) &
	295	) * ddzw(k)
[1]	296	!
	297	!-- v-component
[1001]	298	te_v(k) = -f * ( u1d(k) - ug(k) ) + ( &
	299	kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) &
	300	- kmzm * ( v1d(k) - v1d(k-1) ) * ddzu(k) &
	301	) * ddzw(k)
[1]	302	ENDDO
	303	IF ( .NOT. constant_diffusion ) THEN
	304	DO k = nzb_diff, nzt
	305	!
	306	!-- TKE
[1353]	307	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	308	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[75]	309	IF ( .NOT. humidity ) THEN
[1]	310	pt_0 = pt_init(k)
	311	flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k)
	312	ELSE
[1353]	313	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
	314	flux = ( ( pt_init(k+1) - pt_init(k-1) ) + &
	315	0.61_wp * pt_init(k) * &
	316	( q_init(k+1) - q_init(k-1) ) ) * dd2zu(k)
[1]	317	ENDIF
	318
	319	IF ( dissipation_1d == 'detering' ) THEN
	320	!
	321	!-- According to Detering, c_e=0.064
[1353]	322	dissipation = 0.064_wp * e1d(k) * SQRT( e1d(k) ) / l1d(k)
[1]	323	ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN
[1353]	324	dissipation = ( 0.19_wp + 0.74_wp * l1d(k) / l_grid(k) ) &
[1001]	325	* e1d(k) * SQRT( e1d(k) ) / l1d(k)
[1]	326	ENDIF
	327
	328	te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2&
	329	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2&
	330	) &
	331	- g / pt_0 * kh1d(k) * flux &
	332	+ ( &
[1001]	333	kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) &
	334	- kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) &
[1]	335	) * ddzw(k) &
[1001]	336	- dissipation
[1]	337	ENDDO
	338	ENDIF
	339
	340	!
	341	!-- Tendency terms at the top of the Prandtl-layer.
	342	!-- Finite differences of the momentum fluxes are computed using half the
	343	!-- normal grid length (2.0*ddzw(k)) for the sake of enhanced accuracy
[1691]	344	IF ( constant_flux_layer ) THEN
[1]	345
	346	k = nzb+1
[1353]	347	kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) )
	348	kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) )
[75]	349	IF ( .NOT. humidity ) THEN
[1]	350	pt_0 = pt_init(k)
	351	flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k)
	352	ELSE
[1353]	353	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
	354	flux = ( ( pt_init(k+1) - pt_init(k-1) ) + &
	355	0.61_wp * pt_init(k) * ( q_init(k+1) - q_init(k-1) ) &
[1]	356	) * dd2zu(k)
	357	ENDIF
	358
	359	IF ( dissipation_1d == 'detering' ) THEN
	360	!
	361	!-- According to Detering, c_e=0.064
[1353]	362	dissipation = 0.064_wp * e1d(k) * SQRT( e1d(k) ) / l1d(k)
[1]	363	ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN
[1353]	364	dissipation = ( 0.19_wp + 0.74_wp * l1d(k) / l_grid(k) ) &
[1001]	365	* e1d(k) * SQRT( e1d(k) ) / l1d(k)
[1]	366	ENDIF
	367
	368	!
	369	!-- u-component
[1001]	370	te_u(k) = f * ( v1d(k) - vg(k) ) + ( &
	371	kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) + usws1d &
[1353]	372	) * 2.0_wp * ddzw(k)
[1]	373	!
	374	!-- v-component
[1001]	375	te_v(k) = -f * ( u1d(k) - ug(k) ) + ( &
	376	kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) + vsws1d &
[1353]	377	) * 2.0_wp * ddzw(k)
[1]	378	!
	379	!-- TKE
	380	te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
	381	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
	382	) &
	383	- g / pt_0 * kh1d(k) * flux &
	384	+ ( &
[1001]	385	kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) &
	386	- kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) &
[1]	387	) * ddzw(k) &
[1001]	388	- dissipation
[1]	389	ENDIF
	390
	391	!
	392	!-- Prognostic equations for all 1D variables
	393	DO k = nzb+1, nzt
	394
[1001]	395	u1d_p(k) = u1d(k) + dt_1d * ( tsc(2) * te_u(k) + &
	396	tsc(3) * te_um(k) )
	397	v1d_p(k) = v1d(k) + dt_1d * ( tsc(2) * te_v(k) + &
	398	tsc(3) * te_vm(k) )
[1]	399
	400	ENDDO
	401	IF ( .NOT. constant_diffusion ) THEN
	402	DO k = nzb+1, nzt
	403
[1001]	404	e1d_p(k) = e1d(k) + dt_1d * ( tsc(2) * te_e(k) + &
	405	tsc(3) * te_em(k) )
[1]	406
	407	ENDDO
	408	!
	409	!-- Eliminate negative TKE values, which can result from the
	410	!-- integration due to numerical inaccuracies. In such cases the TKE
	411	!-- value is reduced to 10 percent of its old value.
[1353]	412	WHERE ( e1d_p < 0.0_wp ) e1d_p = 0.1_wp * e1d
[1]	413	ENDIF
	414
	415	!
	416	!-- Calculate tendencies for the next Runge-Kutta step
	417	IF ( timestep_scheme(1:5) == 'runge' ) THEN
	418	IF ( intermediate_timestep_count == 1 ) THEN
	419
	420	DO k = nzb+1, nzt
	421	te_um(k) = te_u(k)
	422	te_vm(k) = te_v(k)
	423	ENDDO
	424
	425	IF ( .NOT. constant_diffusion ) THEN
	426	DO k = nzb+1, nzt
	427	te_em(k) = te_e(k)
	428	ENDDO
	429	ENDIF
	430
	431	ELSEIF ( intermediate_timestep_count < &
	432	intermediate_timestep_count_max ) THEN
	433
	434	DO k = nzb+1, nzt
[1353]	435	te_um(k) = -9.5625_wp * te_u(k) + 5.3125_wp * te_um(k)
	436	te_vm(k) = -9.5625_wp * te_v(k) + 5.3125_wp * te_vm(k)
[1]	437	ENDDO
	438
	439	IF ( .NOT. constant_diffusion ) THEN
	440	DO k = nzb+1, nzt
[1353]	441	te_em(k) = -9.5625_wp * te_e(k) + 5.3125_wp * te_em(k)
[1]	442	ENDDO
	443	ENDIF
	444
	445	ENDIF
	446	ENDIF
	447
	448
	449	!
	450	!-- Boundary conditions for the prognostic variables.
	451	!-- At the top boundary (nzt+1) u,v and e keep their initial values
	452	!-- (ug(nzt+1), vg(nzt+1), 0), at the bottom boundary the mirror
	453	!-- boundary condition applies to u and v.
	454	!-- The boundary condition for e is set further below ( (u/cm)*2 ).
[667]	455	! u1d_p(nzb) = -u1d_p(nzb+1)
	456	! v1d_p(nzb) = -v1d_p(nzb+1)
[1]	457
[1353]	458	u1d_p(nzb) = 0.0_wp
	459	v1d_p(nzb) = 0.0_wp
[667]	460
[1]	461	!
	462	!-- Swap the time levels in preparation for the next time step.
	463	u1d = u1d_p
	464	v1d = v1d_p
	465	IF ( .NOT. constant_diffusion ) THEN
	466	e1d = e1d_p
	467	ENDIF
	468
	469	!
	470	!-- Compute diffusion quantities
	471	IF ( .NOT. constant_diffusion ) THEN
	472
	473	!
	474	!-- First compute the vertical fluxes in the Prandtl-layer
[1691]	475	IF ( constant_flux_layer ) THEN
[1]	476	!
	477	!-- Compute theta* using Rif numbers of the previous time step
[1353]	478	IF ( rif1d(1) >= 0.0_wp ) THEN
[1]	479	!
	480	!-- Stable stratification
[1353]	481	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
	482	( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * &
	483	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
[1]	484	)
	485	ELSE
	486	!
	487	!-- Unstable stratification
[1353]	488	a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) )
	489	b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	490	zu(nzb+1) * z0h1d )
[1]	491	!
	492	!-- In the borderline case the formula for stable stratification
	493	!-- must be applied, because otherwise a zero division would
	494	!-- occur in the argument of the logarithm.
[1353]	495	IF ( a == 0.0_wp .OR. b == 0.0_wp ) THEN
[996]	496	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
[1353]	497	( LOG( zu(nzb+1) / z0h1d ) + &
	498	5.0_wp * rif1d(nzb+1) * &
	499	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
[1]	500	)
	501	ELSE
[1353]	502	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
	503	LOG( (a-1.0_wp) / (a+1.0_wp) * &
	504	(b+1.0_wp) / (b-1.0_wp) )
[1]	505	ENDIF
	506	ENDIF
	507
[1691]	508	ENDIF ! constant_flux_layer
[1]	509
	510	!
	511	!-- Compute the Richardson-flux numbers,
	512	!-- first at the top of the Prandtl-layer using u* of the previous
	513	!-- time step (+1E-30, if u* = 0), then in the remaining area. There
	514	!-- the rif-numbers of the previous time step are used.
	515
[1691]	516	IF ( constant_flux_layer ) THEN
[75]	517	IF ( .NOT. humidity ) THEN
[1]	518	pt_0 = pt_init(nzb+1)
	519	flux = ts1d
	520	ELSE
[1353]	521	pt_0 = pt_init(nzb+1) * ( 1.0_wp + 0.61_wp * q_init(nzb+1) )
	522	flux = ts1d + 0.61_wp * pt_init(k) * qs1d
[1]	523	ENDIF
	524	rif1d(nzb+1) = zu(nzb+1) * kappa * g * flux / &
[1353]	525	( pt_0 * ( us1d**2 + 1E-30_wp ) )
[1]	526	ENDIF
	527
	528	DO k = nzb_diff, nzt
[75]	529	IF ( .NOT. humidity ) THEN
[1]	530	pt_0 = pt_init(k)
	531	flux = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k)
	532	ELSE
[1353]	533	pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) )
[1]	534	flux = ( ( pt_init(k+1) - pt_init(k-1) ) &
[1353]	535	+ 0.61_wp * pt_init(k) &
	536	* ( q_init(k+1) - q_init(k-1) ) &
[1]	537	) * dd2zu(k)
	538	ENDIF
[1353]	539	IF ( rif1d(k) >= 0.0_wp ) THEN
	540	rif1d(k) = g / pt_0 * flux / &
	541	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
	542	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
	543	+ 1E-30_wp &
[1]	544	)
	545	ELSE
[1353]	546	rif1d(k) = g / pt_0 * flux / &
	547	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
	548	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
	549	+ 1E-30_wp &
	550	) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp
[1]	551	ENDIF
	552	ENDDO
	553	!
	554	!-- Richardson-numbers must remain restricted to a realistic value
	555	!-- range. It is exceeded excessively for very small velocities
	556	!-- (u,v --> 0).
[1691]	557	WHERE ( rif1d < zeta_min ) rif1d = zeta_min
	558	WHERE ( rif1d > zeta_max ) rif1d = zeta_max
[1]	559
	560	!
	561	!-- Compute u* from the absolute velocity value
[1691]	562	IF ( constant_flux_layer ) THEN
[1]	563	uv_total = SQRT( u1d(nzb+1)2 + v1d(nzb+1)2 )
	564
[1353]	565	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
[1]	566	!
	567	!-- Stable stratification
	568	us1d = kappa * uv_total / ( &
[1353]	569	LOG( zu(nzb+1) / z01d ) + 5.0_wp * rif1d(nzb+1) * &
[1]	570	( zu(nzb+1) - z01d ) / zu(nzb+1) &
	571	)
	572	ELSE
	573	!
	574	!-- Unstable stratification
[1353]	575	a = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) )
	576	b = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	577	zu(nzb+1) * z01d ) )
[1]	578	!
	579	!-- In the borderline case the formula for stable stratification
	580	!-- must be applied, because otherwise a zero division would
	581	!-- occur in the argument of the logarithm.
[1353]	582	IF ( a == 1.0_wp .OR. b == 1.0_wp ) THEN
	583	us1d = kappa * uv_total / ( &
	584	LOG( zu(nzb+1) / z01d ) + &
	585	5.0_wp * rif1d(nzb+1) * ( zu(nzb+1) - z01d ) / &
[1]	586	zu(nzb+1) )
	587	ELSE
	588	us1d = kappa * uv_total / ( &
[1353]	589	LOG( (1.0_wp+b) / (1.0_wp-b) * (1.0_wp-a) / &
	590	(1.0_wp+a) ) + &
	591	2.0_wp * ( ATAN( b ) - ATAN( a ) ) &
[1]	592	)
	593	ENDIF
	594	ENDIF
	595
	596	!
	597	!-- Compute the momentum fluxes for the diffusion terms
	598	usws1d = - u1d(nzb+1) / uv_total * us1d**2
	599	vsws1d = - v1d(nzb+1) / uv_total * us1d**2
	600
	601	!
	602	!-- Boundary condition for the turbulent kinetic energy at the top
	603	!-- of the Prandtl-layer. c_m = 0.4 according to Detering.
	604	!-- Additional Neumann condition de/dz = 0 at nzb is set to ensure
	605	!-- compatibility with the 3D model.
	606	IF ( ibc_e_b == 2 ) THEN
[1353]	607	e1d(nzb+1) = ( us1d / 0.1_wp )**2
	608	! e1d(nzb+1) = ( us1d / 0.4_wp )**2 !not used so far, see also
	609	!prandtl_fluxes
[1]	610	ENDIF
	611	e1d(nzb) = e1d(nzb+1)
	612
[75]	613	IF ( humidity .OR. passive_scalar ) THEN
[1]	614	!
	615	!-- Compute q*
[1353]	616	IF ( rif1d(1) >= 0.0_wp ) THEN
[1]	617	!
	618	!-- Stable stratification
[1353]	619	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
	620	( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * &
	621	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
[1]	622	)
	623	ELSE
	624	!
	625	!-- Unstable stratification
[1353]	626	a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) )
	627	b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / &
	628	zu(nzb+1) * z0h1d )
[1]	629	!
	630	!-- In the borderline case the formula for stable stratification
	631	!-- must be applied, because otherwise a zero division would
	632	!-- occur in the argument of the logarithm.
[1353]	633	IF ( a == 1.0_wp .OR. b == 1.0_wp ) THEN
[996]	634	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
[1353]	635	( LOG( zu(nzb+1) / z0h1d ) + &
	636	5.0_wp * rif1d(nzb+1) * &
	637	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
[1]	638	)
	639	ELSE
[1353]	640	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
	641	LOG( (a-1.0_wp) / (a+1.0_wp) * &
	642	(b+1.0_wp) / (b-1.0_wp) )
[1]	643	ENDIF
	644	ENDIF
	645	ELSE
[1353]	646	qs1d = 0.0_wp
[1]	647	ENDIF
	648
[1691]	649	ENDIF ! constant_flux_layer
[1]	650
	651	!
	652	!-- Compute the diabatic mixing length
	653	IF ( mixing_length_1d == 'blackadar' ) THEN
	654	DO k = nzb+1, nzt
[1353]	655	IF ( rif1d(k) >= 0.0_wp ) THEN
	656	l1d(k) = l_black(k) / ( 1.0_wp + 5.0_wp * rif1d(k) )
[1]	657	ELSE
[1353]	658	l1d(k) = l_black(k) * &
	659	( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp
[1]	660	ENDIF
	661	l1d(k) = l_black(k)
	662	ENDDO
	663
	664	ELSEIF ( mixing_length_1d == 'as_in_3d_model' ) THEN
	665	DO k = nzb+1, nzt
	666	dpt_dz = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k)
[1353]	667	IF ( dpt_dz > 0.0_wp ) THEN
	668	l_stable = 0.76_wp * SQRT( e1d(k) ) / &
	669	SQRT( g / pt_init(k) * dpt_dz ) + 1E-5_wp
[1]	670	ELSE
	671	l_stable = l_grid(k)
	672	ENDIF
	673	l1d(k) = MIN( l_grid(k), l_stable )
	674	ENDDO
	675	ENDIF
	676
	677	!
	678	!-- Compute the diffusion coefficients for momentum via the
	679	!-- corresponding Prandtl-layer relationship and according to
	680	!-- Prandtl-Kolmogorov, respectively. The unstable stratification is
	681	!-- computed via the adiabatic mixing length, for the unstability has
	682	!-- already been taken account of via the TKE (cf. also Diss.).
[1691]	683	IF ( constant_flux_layer ) THEN
[1353]	684	IF ( rif1d(nzb+1) >= 0.0_wp ) THEN
	685	km1d(nzb+1) = us1d * kappa * zu(nzb+1) / &
	686	( 1.0_wp + 5.0_wp * rif1d(nzb+1) )
[1]	687	ELSE
[1353]	688	km1d(nzb+1) = us1d * kappa * zu(nzb+1) * &
	689	( 1.0_wp - 16.0_wp * rif1d(nzb+1) )**0.25_wp
[1]	690	ENDIF
	691	ENDIF
	692	DO k = nzb_diff, nzt
	693	! km1d(k) = 0.4 * SQRT( e1d(k) ) !changed: adjustment to 3D-model
[1353]	694	km1d(k) = 0.1_wp * SQRT( e1d(k) )
	695	IF ( rif1d(k) >= 0.0_wp ) THEN
[1]	696	km1d(k) = km1d(k) * l1d(k)
	697	ELSE
	698	km1d(k) = km1d(k) * l_black(k)
	699	ENDIF
	700	ENDDO
	701
	702	!
	703	!-- Add damping layer
	704	DO k = damp_level_ind_1d+1, nzt+1
[1353]	705	km1d(k) = 1.1_wp * km1d(k-1)
[1346]	706	km1d(k) = MIN( km1d(k), 10.0_wp )
[1]	707	ENDDO
	708
	709	!
	710	!-- Compute the diffusion coefficient for heat via the relationship
	711	!-- kh = phim / phih * km
	712	DO k = nzb+1, nzt
[1353]	713	IF ( rif1d(k) >= 0.0_wp ) THEN
[1]	714	kh1d(k) = km1d(k)
	715	ELSE
[1353]	716	kh1d(k) = km1d(k) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp
[1]	717	ENDIF
	718	ENDDO
	719
	720	ENDIF ! .NOT. constant_diffusion
	721
	722	ENDDO ! intermediate step loop
	723
	724	!
	725	!-- Increment simulated time and output times
	726	current_timestep_number_1d = current_timestep_number_1d + 1
	727	simulated_time_1d = simulated_time_1d + dt_1d
	728	simulated_time_chr = time_to_string( simulated_time_1d )
	729	time_pr_1d = time_pr_1d + dt_1d
	730	time_run_control_1d = time_run_control_1d + dt_1d
	731
	732	!
	733	!-- Determine and print out quantities for run control
	734	IF ( time_run_control_1d >= dt_run_control_1d ) THEN
	735	CALL run_control_1d
	736	time_run_control_1d = time_run_control_1d - dt_run_control_1d
	737	ENDIF
	738
	739	!
	740	!-- Profile output on file
	741	IF ( time_pr_1d >= dt_pr_1d ) THEN
	742	CALL print_1d_model
	743	time_pr_1d = time_pr_1d - dt_pr_1d
	744	ENDIF
	745
	746	!
	747	!-- Determine size of next time step
	748	CALL timestep_1d
	749
	750	ENDDO ! time loop
	751
	752
	753	END SUBROUTINE time_integration_1d
	754
	755
	756	!------------------------------------------------------------------------------!
	757	! Description:
	758	! ------------
[1682]	759	!> Compute and print out quantities for run control of the 1D model.
[1]	760	!------------------------------------------------------------------------------!
[1682]	761
	762	SUBROUTINE run_control_1d
[1]	763
[1682]	764
[1320]	765	USE constants, &
	766	ONLY: pi
	767
	768	USE indices, &
	769	ONLY: nzb, nzt
	770
	771	USE kinds
	772
	773	USE model_1d, &
	774	ONLY: current_timestep_number_1d, dt_1d, run_control_header_1d, u1d, &
	775	us1d, v1d
	776
[1]	777	USE pegrid
[1320]	778
	779	USE control_parameters, &
	780	ONLY: simulated_time_chr
[1]	781
	782	IMPLICIT NONE
	783
[1682]	784	INTEGER(iwp) :: k !<
[1320]	785
	786	REAL(wp) :: alpha
	787	REAL(wp) :: energy
	788	REAL(wp) :: umax
	789	REAL(wp) :: uv_total
	790	REAL(wp) :: vmax
[1]	791
	792	!
	793	!-- Output
	794	IF ( myid == 0 ) THEN
	795	!
	796	!-- If necessary, write header
	797	IF ( .NOT. run_control_header_1d ) THEN
[184]	798	CALL check_open( 15 )
[1]	799	WRITE ( 15, 100 )
	800	run_control_header_1d = .TRUE.
	801	ENDIF
	802
	803	!
	804	!-- Compute control quantities
	805	!-- grid level nzp is excluded due to mirror boundary condition
[1353]	806	umax = 0.0_wp; vmax = 0.0_wp; energy = 0.0_wp
[1]	807	DO k = nzb+1, nzt+1
	808	umax = MAX( ABS( umax ), ABS( u1d(k) ) )
	809	vmax = MAX( ABS( vmax ), ABS( v1d(k) ) )
[1353]	810	energy = energy + 0.5_wp * ( u1d(k)2 + v1d(k)2 )
[1]	811	ENDDO
[1322]	812	energy = energy / REAL( nzt - nzb + 1, KIND=wp )
[1]	813
	814	uv_total = SQRT( u1d(nzb+1)2 + v1d(nzb+1)2 )
[1691]	815	IF ( ABS( v1d(nzb+1) ) < 1.0E-5_wp ) THEN
[1346]	816	alpha = ACOS( SIGN( 1.0_wp , u1d(nzb+1) ) )
[1]	817	ELSE
	818	alpha = ACOS( u1d(nzb+1) / uv_total )
[1353]	819	IF ( v1d(nzb+1) <= 0.0_wp ) alpha = 2.0_wp * pi - alpha
[1]	820	ENDIF
[1353]	821	alpha = alpha / ( 2.0_wp * pi ) * 360.0_wp
[1]	822
	823	WRITE ( 15, 101 ) current_timestep_number_1d, simulated_time_chr, &
	824	dt_1d, umax, vmax, us1d, alpha, energy
	825	!
	826	!-- Write buffer contents to disc immediately
[82]	827	CALL local_flush( 15 )
[1]	828
	829	ENDIF
	830
	831	!
	832	!-- formats
	833	100 FORMAT (///'1D-Zeitschrittkontrollausgaben:'/ &
	834	&'------------------------------'// &
	835	&'ITER. HH:MM:SS DT UMAX VMAX U* ALPHA ENERG.'/ &
	836	&'-------------------------------------------------------------')
[1697]	837	101 FORMAT (I5,2X,A9,1X,F6.2,2X,F6.2,1X,F6.2,1X,F6.3,2X,F5.1,2X,F7.2)
[1]	838
	839
	840	END SUBROUTINE run_control_1d
	841
	842
	843
	844	!------------------------------------------------------------------------------!
	845	! Description:
	846	! ------------
[1682]	847	!> Compute the time step w.r.t. the diffusion criterion
[1]	848	!------------------------------------------------------------------------------!
[1682]	849
	850	SUBROUTINE timestep_1d
[1]	851
[1682]	852
[1320]	853	USE arrays_3d, &
	854	ONLY: dzu, zu
	855
	856	USE indices, &
	857	ONLY: nzb, nzt
	858
	859	USE kinds
	860
	861	USE model_1d, &
	862	ONLY: dt_1d, dt_max_1d, km1d, old_dt_1d, stop_dt_1d
	863
[1]	864	USE pegrid
[1320]	865
	866	USE control_parameters, &
	867	ONLY: message_string
[1]	868
	869	IMPLICIT NONE
	870
[1682]	871	INTEGER(iwp) :: k !<
[1320]	872
[1682]	873	REAL(wp) :: div !<
	874	REAL(wp) :: dt_diff !<
	875	REAL(wp) :: fac !<
	876	REAL(wp) :: value !<
[1]	877
	878
	879	!
	880	!-- Compute the currently feasible time step according to the diffusion
	881	!-- criterion. At nzb+1 the half grid length is used.
[1353]	882	fac = 0.35_wp
[1]	883	dt_diff = dt_max_1d
	884	DO k = nzb+2, nzt
[1353]	885	value = fac * dzu(k) * dzu(k) / ( km1d(k) + 1E-20_wp )
[1]	886	dt_diff = MIN( value, dt_diff )
	887	ENDDO
[1353]	888	value = fac * zu(nzb+1) * zu(nzb+1) / ( km1d(nzb+1) + 1E-20_wp )
[1]	889	dt_1d = MIN( value, dt_diff )
	890
	891	!
	892	!-- Set flag when the time step becomes too small
[1353]	893	IF ( dt_1d < ( 0.00001_wp * dt_max_1d ) ) THEN
[1]	894	stop_dt_1d = .TRUE.
[254]	895
	896	WRITE( message_string, * ) 'timestep has exceeded the lower limit &', &
	897	'dt_1d = ',dt_1d,' s simulation stopped!'
	898	CALL message( 'timestep_1d', 'PA0192', 1, 2, 0, 6, 0 )
	899
[1]	900	ENDIF
	901
	902	!
[1001]	903	!-- A more or less simple new time step value is obtained taking only the
	904	!-- first two significant digits
[1353]	905	div = 1000.0_wp
[1001]	906	DO WHILE ( dt_1d < div )
[1353]	907	div = div / 10.0_wp
[1001]	908	ENDDO
[1353]	909	dt_1d = NINT( dt_1d * 100.0_wp / div ) * div / 100.0_wp
[1]	910
[1001]	911	old_dt_1d = dt_1d
[1]	912
	913
	914	END SUBROUTINE timestep_1d
	915
	916
	917
	918	!------------------------------------------------------------------------------!
	919	! Description:
	920	! ------------
[1682]	921	!> List output of profiles from the 1D-model
[1]	922	!------------------------------------------------------------------------------!
[1682]	923
	924	SUBROUTINE print_1d_model
[1]	925
[1682]	926
[1320]	927	USE arrays_3d, &
	928	ONLY: pt_init, zu
	929
	930	USE indices, &
	931	ONLY: nzb, nzt
	932
	933	USE kinds
	934
	935	USE model_1d, &
	936	ONLY: e1d, kh1d, km1d, l1d, rif1d, u1d, v1d
	937
[1]	938	USE pegrid
[1320]	939
	940	USE control_parameters, &
	941	ONLY: run_description_header, simulated_time_chr
[1]	942
	943	IMPLICIT NONE
	944
	945
[1682]	946	INTEGER(iwp) :: k !<
[1]	947
	948
	949	IF ( myid == 0 ) THEN
	950	!
	951	!-- Open list output file for profiles from the 1D-model
	952	CALL check_open( 17 )
	953
	954	!
	955	!-- Write Header
	956	WRITE ( 17, 100 ) TRIM( run_description_header ), &
	957	TRIM( simulated_time_chr )
	958	WRITE ( 17, 101 )
	959
	960	!
	961	!-- Write the values
	962	WRITE ( 17, 102 )
	963	WRITE ( 17, 101 )
	964	DO k = nzt+1, nzb, -1
	965	WRITE ( 17, 103) k, zu(k), u1d(k), v1d(k), pt_init(k), e1d(k), &
	966	rif1d(k), km1d(k), kh1d(k), l1d(k), zu(k), k
	967	ENDDO
	968	WRITE ( 17, 101 )
	969	WRITE ( 17, 102 )
	970	WRITE ( 17, 101 )
	971
	972	!
	973	!-- Write buffer contents to disc immediately
[82]	974	CALL local_flush( 17 )
[1]	975
	976	ENDIF
	977
	978	!
	979	!-- Formats
	980	100 FORMAT (//1X,A/1X,10('-')/' 1d-model profiles'/ &
	981	' Time: ',A)
	982	101 FORMAT (1X,79('-'))
	983	102 FORMAT (' k zu u v pt e rif Km Kh ', &
	984	'l zu k')
	985	103 FORMAT (1X,I4,1X,F7.1,1X,F6.2,1X,F6.2,1X,F6.2,1X,F6.2,1X,F5.2,1X,F5.2, &
	986	1X,F5.2,1X,F6.2,1X,F7.1,2X,I4)
	987
	988
	989	END SUBROUTINE print_1d_model

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