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source: palm/trunk/SOURCE/init_1d_model.f90 @ 1350

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1	SUBROUTINE init_1d_model
2
3	!--------------------------------------------------------------------------------!
4	! This file is part of PALM.
5	!
6	! PALM is free software: you can redistribute it and/or modify it under the terms
7	! of the GNU General Public License as published by the Free Software Foundation,
8	! either version 3 of the License, or (at your option) any later 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 1997-2014 Leibniz Universitaet Hannover
18	!--------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: init_1d_model.f90 1347 2014-03-27 13:23:00Z maronga $
27	!
28	! 1346 2014-03-27 13:18:20Z heinze
29	! Bugfix: REAL constants provided with KIND-attribute especially in call of
30	! intrinsic function like MAX, MIN, SIGN
31	!
32	! 1322 2014-03-20 16:38:49Z raasch
33	! REAL functions provided with KIND-attribute
34	!
35	! 1320 2014-03-20 08:40:49Z raasch
36	! ONLY-attribute added to USE-statements,
37	! kind-parameters added to all INTEGER and REAL declaration statements,
38	! kinds are defined in new module kinds,
39	! revision history before 2012 removed,
40	! comment fields (!:) to be used for variable explanations added to
41	! all variable declaration statements
42	!
43	! 1036 2012-10-22 13:43:42Z raasch
44	! code put under GPL (PALM 3.9)
45	!
46	! 1015 2012-09-27 09:23:24Z raasch
47	! adjustment of mixing length to the Prandtl mixing length at first grid point
48	! above ground removed
49	!
50	! 1001 2012-09-13 14:08:46Z raasch
51	! all actions concerning leapfrog scheme removed
52	!
53	! 996 2012-09-07 10:41:47Z raasch
54	! little reformatting
55	!
56	! 978 2012-08-09 08:28:32Z fricke
57	! roughness length for scalar quantities z0h1d added
58	!
59	! Revision 1.1 1998/03/09 16:22:10 raasch
60	! Initial revision
61	!
62	!
63	! Description:
64	! ------------
65	! 1D-model to initialize the 3D-arrays.
66	! The temperature profile is set as steady and a corresponding steady solution
67	! of the wind profile is being computed.
68	! All subroutines required can be found within this file.
69	!------------------------------------------------------------------------------!
70
71	USE arrays_3d, &
72	ONLY: l_grid, ug, u_init, vg, v_init, zu
73
74	USE indices, &
75	ONLY: nzb, nzt
76
77	USE kinds
78
79	USE model_1d, &
80	ONLY: e1d, e1d_p, kh1d, km1d, l1d, l_black, qs1d, rif1d, &
81	simulated_time_1d, te_e, te_em, te_u, te_um, te_v, te_vm, ts1d, &
82	u1d, u1d_p, us1d, usws1d, v1d, v1d_p, vsws1d, z01d, z0h1d
83
84	USE control_parameters, &
85	ONLY: constant_diffusion, f, humidity, kappa, km_constant, &
86	mixing_length_1d, passive_scalar, prandtl_layer, &
87	prandtl_number, roughness_length, simulated_time_chr, &
88	z0h_factor
89
90	IMPLICIT NONE
91
92	CHARACTER (LEN=9) :: time_to_string !:
93
94	INTEGER(iwp) :: k !:
95
96	REAL(wp) :: lambda !:
97
98	!
99	!-- Allocate required 1D-arrays
100	ALLOCATE( e1d(nzb:nzt+1), e1d_p(nzb:nzt+1), &
101	kh1d(nzb:nzt+1), km1d(nzb:nzt+1), &
102	l_black(nzb:nzt+1), l1d(nzb:nzt+1), &
103	rif1d(nzb:nzt+1), te_e(nzb:nzt+1), &
104	te_em(nzb:nzt+1), te_u(nzb:nzt+1), te_um(nzb:nzt+1), &
105	te_v(nzb:nzt+1), te_vm(nzb:nzt+1), u1d(nzb:nzt+1), &
106	u1d_p(nzb:nzt+1), v1d(nzb:nzt+1), &
107	v1d_p(nzb:nzt+1) )
108
109	!
110	!-- Initialize arrays
111	IF ( constant_diffusion ) THEN
112	km1d = km_constant
113	kh1d = km_constant / prandtl_number
114	ELSE
115	e1d = 0.0; e1d_p = 0.0
116	kh1d = 0.0; km1d = 0.0
117	rif1d = 0.0
118	!
119	!-- Compute the mixing length
120	l_black(nzb) = 0.0
121
122	IF ( TRIM( mixing_length_1d ) == 'blackadar' ) THEN
123	!
124	!-- Blackadar mixing length
125	IF ( f /= 0.0 ) THEN
126	lambda = 2.7E-4 * SQRT( ug(nzt+1)2 + vg(nzt+1)2 ) / &
127	ABS( f ) + 1E-10
128	ELSE
129	lambda = 30.0
130	ENDIF
131
132	DO k = nzb+1, nzt+1
133	l_black(k) = kappa * zu(k) / ( 1.0 + kappa * zu(k) / lambda )
134	ENDDO
135
136	ELSEIF ( TRIM( mixing_length_1d ) == 'as_in_3d_model' ) THEN
137	!
138	!-- Use the same mixing length as in 3D model
139	l_black(1:nzt) = l_grid
140	l_black(nzt+1) = l_black(nzt)
141
142	ENDIF
143	ENDIF
144	l1d = l_black
145	u1d = u_init
146	u1d_p = u_init
147	v1d = v_init
148	v1d_p = v_init
149
150	!
151	!-- Set initial horizontal velocities at the lowest grid levels to a very small
152	!-- value in order to avoid too small time steps caused by the diffusion limit
153	!-- in the initial phase of a run (at k=1, dz/2 occurs in the limiting formula!)
154	u1d(0:1) = 0.1
155	u1d_p(0:1) = 0.1
156	v1d(0:1) = 0.1
157	v1d_p(0:1) = 0.1
158
159	!
160	!-- For u, theta and the momentum fluxes plausible values are set
161	IF ( prandtl_layer ) THEN
162	us1d = 0.1 ! without initial friction the flow would not change
163	ELSE
164	e1d(nzb+1) = 1.0
165	km1d(nzb+1) = 1.0
166	us1d = 0.0
167	ENDIF
168	ts1d = 0.0
169	usws1d = 0.0
170	vsws1d = 0.0
171	z01d = roughness_length
172	z0h1d = z0h_factor * z01d
173	IF ( humidity .OR. passive_scalar ) qs1d = 0.0
174
175	!
176	!-- Tendencies must be preset in order to avoid runtime errors within the
177	!-- first Runge-Kutta step
178	te_em = 0.0
179	te_um = 0.0
180	te_vm = 0.0
181
182	!
183	!-- Set start time in hh:mm:ss - format
184	simulated_time_chr = time_to_string( simulated_time_1d )
185
186	!
187	!-- Integrate the 1D-model equations using the leap-frog scheme
188	CALL time_integration_1d
189
190
191	END SUBROUTINE init_1d_model
192
193
194
195	SUBROUTINE time_integration_1d
196
197	!------------------------------------------------------------------------------!
198	! Description:
199	! ------------
200	! Leap-frog time differencing scheme for the 1D-model.
201	!------------------------------------------------------------------------------!
202
203	USE arrays_3d, &
204	ONLY: dd2zu, ddzu, ddzw, l_grid, pt_init, q_init, ug, vg, zu
205
206	USE control_parameters, &
207	ONLY: constant_diffusion, dissipation_1d, humidity, &
208	intermediate_timestep_count, intermediate_timestep_count_max, &
209	f, g, ibc_e_b, kappa, mixing_length_1d, passive_scalar, &
210	prandtl_layer, rif_max, rif_min, simulated_time_chr, &
211	timestep_scheme, tsc
212
213	USE indices, &
214	ONLY: nzb, nzb_diff, nzt
215
216	USE kinds
217
218	USE model_1d, &
219	ONLY: current_timestep_number_1d, damp_level_ind_1d, dt_1d, &
220	dt_pr_1d, dt_run_control_1d, e1d, e1d_p, end_time_1d, &
221	kh1d, km1d, l1d, l_black, qs1d, rif1d, simulated_time_1d, &
222	stop_dt_1d, te_e, te_em, te_u, te_um, te_v, te_vm, time_pr_1d, &
223	ts1d, time_run_control_1d, u1d, u1d_p, us1d, usws1d, v1d, &
224	v1d_p, vsws1d, z01d, z0h1d
225
226	USE pegrid
227
228	IMPLICIT NONE
229
230	CHARACTER (LEN=9) :: time_to_string !:
231
232	INTEGER(iwp) :: k !:
233
234	REAL(wp) :: a !:
235	REAL(wp) :: b !:
236	REAL(wp) :: dissipation !:
237	REAL(wp) :: dpt_dz !:
238	REAL(wp) :: flux !:
239	REAL(wp) :: kmzm !:
240	REAL(wp) :: kmzp !:
241	REAL(wp) :: l_stable !:
242	REAL(wp) :: pt_0 !:
243	REAL(wp) :: uv_total !:
244
245	!
246	!-- Determine the time step at the start of a 1D-simulation and
247	!-- determine and printout quantities used for run control
248	CALL timestep_1d
249	CALL run_control_1d
250
251	!
252	!-- Start of time loop
253	DO WHILE ( simulated_time_1d < end_time_1d .AND. .NOT. stop_dt_1d )
254
255	!
256	!-- Depending on the timestep scheme, carry out one or more intermediate
257	!-- timesteps
258
259	intermediate_timestep_count = 0
260	DO WHILE ( intermediate_timestep_count < &
261	intermediate_timestep_count_max )
262
263	intermediate_timestep_count = intermediate_timestep_count + 1
264
265	CALL timestep_scheme_steering
266
267	!
268	!-- Compute all tendency terms. If a Prandtl-layer is simulated, k starts
269	!-- at nzb+2.
270	DO k = nzb_diff, nzt
271
272	kmzm = 0.5 * ( km1d(k-1) + km1d(k) )
273	kmzp = 0.5 * ( km1d(k) + km1d(k+1) )
274	!
275	!-- u-component
276	te_u(k) = f * ( v1d(k) - vg(k) ) + ( &
277	kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) &
278	- kmzm * ( u1d(k) - u1d(k-1) ) * ddzu(k) &
279	) * ddzw(k)
280	!
281	!-- v-component
282	te_v(k) = -f * ( u1d(k) - ug(k) ) + ( &
283	kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) &
284	- kmzm * ( v1d(k) - v1d(k-1) ) * ddzu(k) &
285	) * ddzw(k)
286	ENDDO
287	IF ( .NOT. constant_diffusion ) THEN
288	DO k = nzb_diff, nzt
289	!
290	!-- TKE
291	kmzm = 0.5 * ( km1d(k-1) + km1d(k) )
292	kmzp = 0.5 * ( km1d(k) + km1d(k+1) )
293	IF ( .NOT. humidity ) THEN
294	pt_0 = pt_init(k)
295	flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k)
296	ELSE
297	pt_0 = pt_init(k) * ( 1.0 + 0.61 * q_init(k) )
298	flux = ( ( pt_init(k+1) - pt_init(k-1) ) + &
299	0.61 * pt_init(k) * ( q_init(k+1) - q_init(k-1) ) &
300	) * dd2zu(k)
301	ENDIF
302
303	IF ( dissipation_1d == 'detering' ) THEN
304	!
305	!-- According to Detering, c_e=0.064
306	dissipation = 0.064 * e1d(k) * SQRT( e1d(k) ) / l1d(k)
307	ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN
308	dissipation = ( 0.19 + 0.74 * l1d(k) / l_grid(k) ) &
309	* e1d(k) * SQRT( e1d(k) ) / l1d(k)
310	ENDIF
311
312	te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2&
313	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2&
314	) &
315	- g / pt_0 * kh1d(k) * flux &
316	+ ( &
317	kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) &
318	- kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) &
319	) * ddzw(k) &
320	- dissipation
321	ENDDO
322	ENDIF
323
324	!
325	!-- Tendency terms at the top of the Prandtl-layer.
326	!-- Finite differences of the momentum fluxes are computed using half the
327	!-- normal grid length (2.0*ddzw(k)) for the sake of enhanced accuracy
328	IF ( prandtl_layer ) THEN
329
330	k = nzb+1
331	kmzm = 0.5 * ( km1d(k-1) + km1d(k) )
332	kmzp = 0.5 * ( km1d(k) + km1d(k+1) )
333	IF ( .NOT. humidity ) THEN
334	pt_0 = pt_init(k)
335	flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k)
336	ELSE
337	pt_0 = pt_init(k) * ( 1.0 + 0.61 * q_init(k) )
338	flux = ( ( pt_init(k+1) - pt_init(k-1) ) + &
339	0.61 * pt_init(k) * ( q_init(k+1) - q_init(k-1) ) &
340	) * dd2zu(k)
341	ENDIF
342
343	IF ( dissipation_1d == 'detering' ) THEN
344	!
345	!-- According to Detering, c_e=0.064
346	dissipation = 0.064 * e1d(k) * SQRT( e1d(k) ) / l1d(k)
347	ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN
348	dissipation = ( 0.19 + 0.74 * l1d(k) / l_grid(k) ) &
349	* e1d(k) * SQRT( e1d(k) ) / l1d(k)
350	ENDIF
351
352	!
353	!-- u-component
354	te_u(k) = f * ( v1d(k) - vg(k) ) + ( &
355	kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) + usws1d &
356	) * 2.0 * ddzw(k)
357	!
358	!-- v-component
359	te_v(k) = -f * ( u1d(k) - ug(k) ) + ( &
360	kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) + vsws1d &
361	) * 2.0 * ddzw(k)
362	!
363	!-- TKE
364	te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
365	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
366	) &
367	- g / pt_0 * kh1d(k) * flux &
368	+ ( &
369	kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) &
370	- kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) &
371	) * ddzw(k) &
372	- dissipation
373	ENDIF
374
375	!
376	!-- Prognostic equations for all 1D variables
377	DO k = nzb+1, nzt
378
379	u1d_p(k) = u1d(k) + dt_1d * ( tsc(2) * te_u(k) + &
380	tsc(3) * te_um(k) )
381	v1d_p(k) = v1d(k) + dt_1d * ( tsc(2) * te_v(k) + &
382	tsc(3) * te_vm(k) )
383
384	ENDDO
385	IF ( .NOT. constant_diffusion ) THEN
386	DO k = nzb+1, nzt
387
388	e1d_p(k) = e1d(k) + dt_1d * ( tsc(2) * te_e(k) + &
389	tsc(3) * te_em(k) )
390
391	ENDDO
392	!
393	!-- Eliminate negative TKE values, which can result from the
394	!-- integration due to numerical inaccuracies. In such cases the TKE
395	!-- value is reduced to 10 percent of its old value.
396	WHERE ( e1d_p < 0.0 ) e1d_p = 0.1 * e1d
397	ENDIF
398
399	!
400	!-- Calculate tendencies for the next Runge-Kutta step
401	IF ( timestep_scheme(1:5) == 'runge' ) THEN
402	IF ( intermediate_timestep_count == 1 ) THEN
403
404	DO k = nzb+1, nzt
405	te_um(k) = te_u(k)
406	te_vm(k) = te_v(k)
407	ENDDO
408
409	IF ( .NOT. constant_diffusion ) THEN
410	DO k = nzb+1, nzt
411	te_em(k) = te_e(k)
412	ENDDO
413	ENDIF
414
415	ELSEIF ( intermediate_timestep_count < &
416	intermediate_timestep_count_max ) THEN
417
418	DO k = nzb+1, nzt
419	te_um(k) = -9.5625 * te_u(k) + 5.3125 * te_um(k)
420	te_vm(k) = -9.5625 * te_v(k) + 5.3125 * te_vm(k)
421	ENDDO
422
423	IF ( .NOT. constant_diffusion ) THEN
424	DO k = nzb+1, nzt
425	te_em(k) = -9.5625 * te_e(k) + 5.3125 * te_em(k)
426	ENDDO
427	ENDIF
428
429	ENDIF
430	ENDIF
431
432
433	!
434	!-- Boundary conditions for the prognostic variables.
435	!-- At the top boundary (nzt+1) u,v and e keep their initial values
436	!-- (ug(nzt+1), vg(nzt+1), 0), at the bottom boundary the mirror
437	!-- boundary condition applies to u and v.
438	!-- The boundary condition for e is set further below ( (u/cm)*2 ).
439	! u1d_p(nzb) = -u1d_p(nzb+1)
440	! v1d_p(nzb) = -v1d_p(nzb+1)
441
442	u1d_p(nzb) = 0.0
443	v1d_p(nzb) = 0.0
444
445	!
446	!-- Swap the time levels in preparation for the next time step.
447	u1d = u1d_p
448	v1d = v1d_p
449	IF ( .NOT. constant_diffusion ) THEN
450	e1d = e1d_p
451	ENDIF
452
453	!
454	!-- Compute diffusion quantities
455	IF ( .NOT. constant_diffusion ) THEN
456
457	!
458	!-- First compute the vertical fluxes in the Prandtl-layer
459	IF ( prandtl_layer ) THEN
460	!
461	!-- Compute theta* using Rif numbers of the previous time step
462	IF ( rif1d(1) >= 0.0 ) THEN
463	!
464	!-- Stable stratification
465	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
466	( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * &
467	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
468	)
469	ELSE
470	!
471	!-- Unstable stratification
472	a = SQRT( 1.0 - 16.0 * rif1d(nzb+1) )
473	b = SQRT( 1.0 - 16.0 * rif1d(nzb+1) / zu(nzb+1) * z0h1d )
474	!
475	!-- In the borderline case the formula for stable stratification
476	!-- must be applied, because otherwise a zero division would
477	!-- occur in the argument of the logarithm.
478	IF ( a == 0.0 .OR. b == 0.0 ) THEN
479	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
480	( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * &
481	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
482	)
483	ELSE
484	ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / &
485	LOG( (a-1.0) / (a+1.0) * (b+1.0) / (b-1.0) )
486	ENDIF
487	ENDIF
488
489	ENDIF ! prandtl_layer
490
491	!
492	!-- Compute the Richardson-flux numbers,
493	!-- first at the top of the Prandtl-layer using u* of the previous
494	!-- time step (+1E-30, if u* = 0), then in the remaining area. There
495	!-- the rif-numbers of the previous time step are used.
496
497	IF ( prandtl_layer ) THEN
498	IF ( .NOT. humidity ) THEN
499	pt_0 = pt_init(nzb+1)
500	flux = ts1d
501	ELSE
502	pt_0 = pt_init(nzb+1) * ( 1.0 + 0.61 * q_init(nzb+1) )
503	flux = ts1d + 0.61 * pt_init(k) * qs1d
504	ENDIF
505	rif1d(nzb+1) = zu(nzb+1) * kappa * g * flux / &
506	( pt_0 * ( us1d**2 + 1E-30 ) )
507	ENDIF
508
509	DO k = nzb_diff, nzt
510	IF ( .NOT. humidity ) THEN
511	pt_0 = pt_init(k)
512	flux = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k)
513	ELSE
514	pt_0 = pt_init(k) * ( 1.0 + 0.61 * q_init(k) )
515	flux = ( ( pt_init(k+1) - pt_init(k-1) ) &
516	+ 0.61 * pt_init(k) * ( q_init(k+1) - q_init(k-1) )&
517	) * dd2zu(k)
518	ENDIF
519	IF ( rif1d(k) >= 0.0 ) THEN
520	rif1d(k) = g / pt_0 * flux / &
521	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
522	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
523	+ 1E-30 &
524	)
525	ELSE
526	rif1d(k) = g / pt_0 * flux / &
527	( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 &
528	+ ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 &
529	+ 1E-30 &
530	) * ( 1.0 - 16.0 * rif1d(k) )**0.25
531	ENDIF
532	ENDDO
533	!
534	!-- Richardson-numbers must remain restricted to a realistic value
535	!-- range. It is exceeded excessively for very small velocities
536	!-- (u,v --> 0).
537	WHERE ( rif1d < rif_min ) rif1d = rif_min
538	WHERE ( rif1d > rif_max ) rif1d = rif_max
539
540	!
541	!-- Compute u* from the absolute velocity value
542	IF ( prandtl_layer ) THEN
543	uv_total = SQRT( u1d(nzb+1)2 + v1d(nzb+1)2 )
544
545	IF ( rif1d(nzb+1) >= 0.0 ) THEN
546	!
547	!-- Stable stratification
548	us1d = kappa * uv_total / ( &
549	LOG( zu(nzb+1) / z01d ) + 5.0 * rif1d(nzb+1) * &
550	( zu(nzb+1) - z01d ) / zu(nzb+1) &
551	)
552	ELSE
553	!
554	!-- Unstable stratification
555	a = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rif1d(nzb+1) ) )
556	b = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rif1d(nzb+1) / zu(nzb+1) &
557	* z01d ) )
558	!
559	!-- In the borderline case the formula for stable stratification
560	!-- must be applied, because otherwise a zero division would
561	!-- occur in the argument of the logarithm.
562	IF ( a == 1.0 .OR. b == 1.0 ) THEN
563	us1d = kappa * uv_total / ( &
564	LOG( zu(nzb+1) / z01d ) + &
565	5.0 * rif1d(nzb+1) * ( zu(nzb+1) - z01d ) / &
566	zu(nzb+1) )
567	ELSE
568	us1d = kappa * uv_total / ( &
569	LOG( (1.0+b) / (1.0-b) * (1.0-a) / (1.0+a) ) +&
570	2.0 * ( ATAN( b ) - ATAN( a ) ) &
571	)
572	ENDIF
573	ENDIF
574
575	!
576	!-- Compute the momentum fluxes for the diffusion terms
577	usws1d = - u1d(nzb+1) / uv_total * us1d**2
578	vsws1d = - v1d(nzb+1) / uv_total * us1d**2
579
580	!
581	!-- Boundary condition for the turbulent kinetic energy at the top
582	!-- of the Prandtl-layer. c_m = 0.4 according to Detering.
583	!-- Additional Neumann condition de/dz = 0 at nzb is set to ensure
584	!-- compatibility with the 3D model.
585	IF ( ibc_e_b == 2 ) THEN
586	e1d(nzb+1) = ( us1d / 0.1 )**2
587	! e1d(nzb+1) = ( us1d / 0.4 )**2 !not used so far, see also
588	!prandtl_fluxes
589	ENDIF
590	e1d(nzb) = e1d(nzb+1)
591
592	IF ( humidity .OR. passive_scalar ) THEN
593	!
594	!-- Compute q*
595	IF ( rif1d(1) >= 0.0 ) THEN
596	!
597	!-- Stable stratification
598	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
599	( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * &
600	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
601	)
602	ELSE
603	!
604	!-- Unstable stratification
605	a = SQRT( 1.0 - 16.0 * rif1d(nzb+1) )
606	b = SQRT( 1.0 - 16.0 * rif1d(nzb+1) / zu(nzb+1) * z0h1d )
607	!
608	!-- In the borderline case the formula for stable stratification
609	!-- must be applied, because otherwise a zero division would
610	!-- occur in the argument of the logarithm.
611	IF ( a == 1.0 .OR. b == 1.0 ) THEN
612	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
613	( LOG( zu(nzb+1) / z0h1d ) + 5.0 * rif1d(nzb+1) * &
614	( zu(nzb+1) - z0h1d ) / zu(nzb+1) &
615	)
616	ELSE
617	qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / &
618	LOG( (a-1.0) / (a+1.0) * (b+1.0) / (b-1.0) )
619	ENDIF
620	ENDIF
621	ELSE
622	qs1d = 0.0
623	ENDIF
624
625	ENDIF ! prandtl_layer
626
627	!
628	!-- Compute the diabatic mixing length
629	IF ( mixing_length_1d == 'blackadar' ) THEN
630	DO k = nzb+1, nzt
631	IF ( rif1d(k) >= 0.0 ) THEN
632	l1d(k) = l_black(k) / ( 1.0 + 5.0 * rif1d(k) )
633	ELSE
634	l1d(k) = l_black(k) * ( 1.0 - 16.0 * rif1d(k) )**0.25
635	ENDIF
636	l1d(k) = l_black(k)
637	ENDDO
638
639	ELSEIF ( mixing_length_1d == 'as_in_3d_model' ) THEN
640	DO k = nzb+1, nzt
641	dpt_dz = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k)
642	IF ( dpt_dz > 0.0 ) THEN
643	l_stable = 0.76 * SQRT( e1d(k) ) / &
644	SQRT( g / pt_init(k) * dpt_dz ) + 1E-5
645	ELSE
646	l_stable = l_grid(k)
647	ENDIF
648	l1d(k) = MIN( l_grid(k), l_stable )
649	ENDDO
650	ENDIF
651
652	!
653	!-- Compute the diffusion coefficients for momentum via the
654	!-- corresponding Prandtl-layer relationship and according to
655	!-- Prandtl-Kolmogorov, respectively. The unstable stratification is
656	!-- computed via the adiabatic mixing length, for the unstability has
657	!-- already been taken account of via the TKE (cf. also Diss.).
658	IF ( prandtl_layer ) THEN
659	IF ( rif1d(nzb+1) >= 0.0 ) THEN
660	km1d(nzb+1) = us1d * kappa * zu(nzb+1) / &
661	( 1.0 + 5.0 * rif1d(nzb+1) )
662	ELSE
663	km1d(nzb+1) = us1d * kappa * zu(nzb+1) * &
664	( 1.0 - 16.0 * rif1d(nzb+1) )**0.25
665	ENDIF
666	ENDIF
667	DO k = nzb_diff, nzt
668	! km1d(k) = 0.4 * SQRT( e1d(k) ) !changed: adjustment to 3D-model
669	km1d(k) = 0.1 * SQRT( e1d(k) )
670	IF ( rif1d(k) >= 0.0 ) THEN
671	km1d(k) = km1d(k) * l1d(k)
672	ELSE
673	km1d(k) = km1d(k) * l_black(k)
674	ENDIF
675	ENDDO
676
677	!
678	!-- Add damping layer
679	DO k = damp_level_ind_1d+1, nzt+1
680	km1d(k) = 1.1 * km1d(k-1)
681	km1d(k) = MIN( km1d(k), 10.0_wp )
682	ENDDO
683
684	!
685	!-- Compute the diffusion coefficient for heat via the relationship
686	!-- kh = phim / phih * km
687	DO k = nzb+1, nzt
688	IF ( rif1d(k) >= 0.0 ) THEN
689	kh1d(k) = km1d(k)
690	ELSE
691	kh1d(k) = km1d(k) * ( 1.0 - 16.0 * rif1d(k) )**0.25
692	ENDIF
693	ENDDO
694
695	ENDIF ! .NOT. constant_diffusion
696
697	ENDDO ! intermediate step loop
698
699	!
700	!-- Increment simulated time and output times
701	current_timestep_number_1d = current_timestep_number_1d + 1
702	simulated_time_1d = simulated_time_1d + dt_1d
703	simulated_time_chr = time_to_string( simulated_time_1d )
704	time_pr_1d = time_pr_1d + dt_1d
705	time_run_control_1d = time_run_control_1d + dt_1d
706
707	!
708	!-- Determine and print out quantities for run control
709	IF ( time_run_control_1d >= dt_run_control_1d ) THEN
710	CALL run_control_1d
711	time_run_control_1d = time_run_control_1d - dt_run_control_1d
712	ENDIF
713
714	!
715	!-- Profile output on file
716	IF ( time_pr_1d >= dt_pr_1d ) THEN
717	CALL print_1d_model
718	time_pr_1d = time_pr_1d - dt_pr_1d
719	ENDIF
720
721	!
722	!-- Determine size of next time step
723	CALL timestep_1d
724
725	ENDDO ! time loop
726
727
728	END SUBROUTINE time_integration_1d
729
730
731	SUBROUTINE run_control_1d
732
733	!------------------------------------------------------------------------------!
734	! Description:
735	! ------------
736	! Compute and print out quantities for run control of the 1D model.
737	!------------------------------------------------------------------------------!
738
739	USE constants, &
740	ONLY: pi
741
742	USE indices, &
743	ONLY: nzb, nzt
744
745	USE kinds
746
747	USE model_1d, &
748	ONLY: current_timestep_number_1d, dt_1d, run_control_header_1d, u1d, &
749	us1d, v1d
750
751	USE pegrid
752
753	USE control_parameters, &
754	ONLY: simulated_time_chr
755
756	IMPLICIT NONE
757
758	INTEGER(iwp) :: k !:
759
760	REAL(wp) :: alpha
761	REAL(wp) :: energy
762	REAL(wp) :: umax
763	REAL(wp) :: uv_total
764	REAL(wp) :: vmax
765
766	!
767	!-- Output
768	IF ( myid == 0 ) THEN
769	!
770	!-- If necessary, write header
771	IF ( .NOT. run_control_header_1d ) THEN
772	CALL check_open( 15 )
773	WRITE ( 15, 100 )
774	run_control_header_1d = .TRUE.
775	ENDIF
776
777	!
778	!-- Compute control quantities
779	!-- grid level nzp is excluded due to mirror boundary condition
780	umax = 0.0; vmax = 0.0; energy = 0.0
781	DO k = nzb+1, nzt+1
782	umax = MAX( ABS( umax ), ABS( u1d(k) ) )
783	vmax = MAX( ABS( vmax ), ABS( v1d(k) ) )
784	energy = energy + 0.5 * ( u1d(k)2 + v1d(k)2 )
785	ENDDO
786	energy = energy / REAL( nzt - nzb + 1, KIND=wp )
787
788	uv_total = SQRT( u1d(nzb+1)2 + v1d(nzb+1)2 )
789	IF ( ABS( v1d(nzb+1) ) .LT. 1.0E-5 ) THEN
790	alpha = ACOS( SIGN( 1.0_wp , u1d(nzb+1) ) )
791	ELSE
792	alpha = ACOS( u1d(nzb+1) / uv_total )
793	IF ( v1d(nzb+1) <= 0.0 ) alpha = 2.0 * pi - alpha
794	ENDIF
795	alpha = alpha / ( 2.0 * pi ) * 360.0
796
797	WRITE ( 15, 101 ) current_timestep_number_1d, simulated_time_chr, &
798	dt_1d, umax, vmax, us1d, alpha, energy
799	!
800	!-- Write buffer contents to disc immediately
801	CALL local_flush( 15 )
802
803	ENDIF
804
805	!
806	!-- formats
807	100 FORMAT (///'1D-Zeitschrittkontrollausgaben:'/ &
808	&'------------------------------'// &
809	&'ITER. HH:MM:SS DT UMAX VMAX U* ALPHA ENERG.'/ &
810	&'-------------------------------------------------------------')
811	101 FORMAT (I5,2X,A9,1X,F6.2,2X,F6.2,1X,F6.2,2X,F5.3,2X,F5.1,2X,F7.2)
812
813
814	END SUBROUTINE run_control_1d
815
816
817
818	SUBROUTINE timestep_1d
819
820	!------------------------------------------------------------------------------!
821	! Description:
822	! ------------
823	! Compute the time step w.r.t. the diffusion criterion
824	!------------------------------------------------------------------------------!
825
826	USE arrays_3d, &
827	ONLY: dzu, zu
828
829	USE indices, &
830	ONLY: nzb, nzt
831
832	USE kinds
833
834	USE model_1d, &
835	ONLY: dt_1d, dt_max_1d, km1d, old_dt_1d, stop_dt_1d
836
837	USE pegrid
838
839	USE control_parameters, &
840	ONLY: message_string
841
842	IMPLICIT NONE
843
844	INTEGER(iwp) :: k !:
845
846	REAL(wp) :: div !:
847	REAL(wp) :: dt_diff !:
848	REAL(wp) :: fac !:
849	REAL(wp) :: value !:
850
851
852	!
853	!-- Compute the currently feasible time step according to the diffusion
854	!-- criterion. At nzb+1 the half grid length is used.
855	fac = 0.35
856	dt_diff = dt_max_1d
857	DO k = nzb+2, nzt
858	value = fac * dzu(k) * dzu(k) / ( km1d(k) + 1E-20 )
859	dt_diff = MIN( value, dt_diff )
860	ENDDO
861	value = fac * zu(nzb+1) * zu(nzb+1) / ( km1d(nzb+1) + 1E-20 )
862	dt_1d = MIN( value, dt_diff )
863
864	!
865	!-- Set flag when the time step becomes too small
866	IF ( dt_1d < ( 0.00001 * dt_max_1d ) ) THEN
867	stop_dt_1d = .TRUE.
868
869	WRITE( message_string, * ) 'timestep has exceeded the lower limit &', &
870	'dt_1d = ',dt_1d,' s simulation stopped!'
871	CALL message( 'timestep_1d', 'PA0192', 1, 2, 0, 6, 0 )
872
873	ENDIF
874
875	!
876	!-- A more or less simple new time step value is obtained taking only the
877	!-- first two significant digits
878	div = 1000.0
879	DO WHILE ( dt_1d < div )
880	div = div / 10.0
881	ENDDO
882	dt_1d = NINT( dt_1d * 100.0 / div ) * div / 100.0
883
884	old_dt_1d = dt_1d
885
886
887	END SUBROUTINE timestep_1d
888
889
890
891	SUBROUTINE print_1d_model
892
893	!------------------------------------------------------------------------------!
894	! Description:
895	! ------------
896	! List output of profiles from the 1D-model
897	!------------------------------------------------------------------------------!
898
899	USE arrays_3d, &
900	ONLY: pt_init, zu
901
902	USE indices, &
903	ONLY: nzb, nzt
904
905	USE kinds
906
907	USE model_1d, &
908	ONLY: e1d, kh1d, km1d, l1d, rif1d, u1d, v1d
909
910	USE pegrid
911
912	USE control_parameters, &
913	ONLY: run_description_header, simulated_time_chr
914
915	IMPLICIT NONE
916
917
918	INTEGER(iwp) :: k !:
919
920
921	IF ( myid == 0 ) THEN
922	!
923	!-- Open list output file for profiles from the 1D-model
924	CALL check_open( 17 )
925
926	!
927	!-- Write Header
928	WRITE ( 17, 100 ) TRIM( run_description_header ), &
929	TRIM( simulated_time_chr )
930	WRITE ( 17, 101 )
931
932	!
933	!-- Write the values
934	WRITE ( 17, 102 )
935	WRITE ( 17, 101 )
936	DO k = nzt+1, nzb, -1
937	WRITE ( 17, 103) k, zu(k), u1d(k), v1d(k), pt_init(k), e1d(k), &
938	rif1d(k), km1d(k), kh1d(k), l1d(k), zu(k), k
939	ENDDO
940	WRITE ( 17, 101 )
941	WRITE ( 17, 102 )
942	WRITE ( 17, 101 )
943
944	!
945	!-- Write buffer contents to disc immediately
946	CALL local_flush( 17 )
947
948	ENDIF
949
950	!
951	!-- Formats
952	100 FORMAT (//1X,A/1X,10('-')/' 1d-model profiles'/ &
953	' Time: ',A)
954	101 FORMAT (1X,79('-'))
955	102 FORMAT (' k zu u v pt e rif Km Kh ', &
956	'l zu k')
957	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, &
958	1X,F5.2,1X,F6.2,1X,F7.1,2X,I4)
959
960
961	END SUBROUTINE print_1d_model

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