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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1692

Last change on this file since 1692 was 1692, checked in by maronga, 9 years ago
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[1691]	1	!> @file surface_layer_fluxes.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 1997-2015 Leibniz Universitaet Hannover
	17	!
	18	!--------------------------------------------------------------------------------!
	19	! Current revisions:
	20	! -----------------
[1692]	21	!
	22	!
	23	! Former revisions:
	24	! -----------------
	25	! $Id$
	26	!
	27	!
[1691]	28	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
	29	! course of the re-writing two additional methods have been implemented. See
	30	! updated description.
	31	!
	32	! 1551 2015-03-03 14:18:16Z maronga
	33	! Removed land surface model part. The surface fluxes are now always calculated
	34	! within prandtl_fluxes, based on the given surface temperature/humidity (which
	35	! is either provided by the land surface model, by large scale forcing data, or
	36	! directly prescribed by the user.
	37	!
	38	! 1496 2014-12-02 17:25:50Z maronga
	39	! Adapted for land surface model
	40	!
	41	! 1494 2014-11-21 17:14:03Z maronga
	42	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
	43	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
	44	! topography for coupled runs (not tested)
	45	!
	46	! 1361 2014-04-16 15:17:48Z hoffmann
	47	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
	48	! drop concentration (nrsws) added
	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	! 1276 2014-01-15 13:40:41Z heinze
	63	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
	64	!
	65	! 1257 2013-11-08 15:18:40Z raasch
	66	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
	67	!
	68	! 1036 2012-10-22 13:43:42Z raasch
	69	! code put under GPL (PALM 3.9)
	70	!
	71	! 1015 2012-09-27 09:23:24Z raasch
	72	! OpenACC statements added
	73	!
	74	! 978 2012-08-09 08:28:32Z fricke
	75	! roughness length for scalar quantities z0h added
	76	!
	77	! Revision 1.1 1998/01/23 10:06:06 raasch
	78	! Initial revision
	79	!
	80	!
	81	! Description:
	82	! ------------
	83	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
	84	!> values of the variables at grid point k=1. Three different methods are
	85	!> available:
	86	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
	87	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
	88	!> slower
	89	!> 3) a method using a lookup table which is fast and accurate. Note, however,
	90	!> that this method cannot be used in case of roughness heterogeneity
	91	!>
	92	!> @todo limiting of uv_total might be required is some cases
	93	!> @todo (re)move large_scale_forcing actions
	94	!> @todo check/optimize OpenMP and OpenACC directives
	95	!------------------------------------------------------------------------------!
	96	MODULE surface_layer_fluxes_mod
	97
	98	USE arrays_3d, &
	99	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
	100	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h
	101
	102	USE cloud_parameters, &
	103	ONLY: l_d_cp, pt_d_t
	104
	105	USE constants, &
	106	ONLY: pi
	107
	108	USE cpulog
	109
	110	USE control_parameters, &
	111	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
	112	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, icloud_scheme, &
	113	initializing_actions, kappa, intermediate_timestep_count, &
	114	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
	115	message_string, most_method, neutral, passive_scalar, &
	116	precipitation, pt_surface, q_surface, run_coupled, &
	117	surface_pressure, simulated_time, terminate_run, zeta_max, &
	118	zeta_min
	119
	120	USE indices, &
	121	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
	122	nzb_u_inner, nzb_v_inner
	123
	124	USE kinds
	125
	126	USE pegrid
	127
	128	USE land_surface_model_mod, &
	129	ONLY: land_surface, skip_time_do_lsm
	130
	131	IMPLICIT NONE
	132
	133	INTEGER(iwp) :: i !< loop index x direction
	134	INTEGER(iwp) :: j !< loop index y direction
	135	INTEGER(iwp) :: k !< loop indey z direction
	136
	137	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
	138
	139	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
	140
	141	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
	142	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
	143	uv_total !< Total velocity at first grid level
	144
	145	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
	146	ol_tab !< Lookup table values of L
	147
	148	REAL(wp) :: e_s, & !< Saturation water vapor pressure
	149	l_bnd = 7500, & !< Lookup table index of the last time step
	150	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
	151	rib_max, & !< Maximum Richardson number in lookup table
	152	rib_min, & !< Minimum Richardson number in lookup table
	153	z_mo !< Height of the constant flux layer where MOST is assumed
	154
	155
	156	SAVE
	157
	158	PRIVATE
	159
	160	PUBLIC init_surface_layer_fluxes, surface_layer_fluxes
	161
	162	INTERFACE init_surface_layer_fluxes
	163	MODULE PROCEDURE init_surface_layer_fluxes
	164	END INTERFACE init_surface_layer_fluxes
	165
	166	INTERFACE surface_layer_fluxes
	167	MODULE PROCEDURE surface_layer_fluxes
	168	END INTERFACE surface_layer_fluxes
	169
	170
	171	CONTAINS
	172
	173
	174	!------------------------------------------------------------------------------!
	175	! Description:
	176	! ------------
	177	!> Main routine to compute the surface fluxes
	178	!------------------------------------------------------------------------------!
	179	SUBROUTINE surface_layer_fluxes
	180
	181	IMPLICIT NONE
	182
	183	!
	184	!-- In case cloud physics is used, it is required to derive potential
	185	!-- temperature and specific humidity at first grid level from the fields pt
	186	!-- and q
	187	IF ( cloud_physics ) THEN
	188	CALL calc_pt_q
	189	ENDIF
	190
	191	!
	192	!-- First, calculate the new Obukhov length, then new friction velocity,
	193	!-- followed by the new scaling parameters (th, q, etc.), and the new
	194	!-- surface fluxes if required. The old routine ("circular") requires a
	195	!-- different order of calls as the scaling parameters from the previous time
	196	!-- steps are used to calculate the Obukhov length
	197
	198	!
	199	!-- Depending on setting of most_method use the "old" routine
	200	IF ( most_method == 'circular' ) THEN
	201
	202	CALL calc_scaling_parameters
	203
	204	IF ( .NOT. neutral ) THEN
	205	CALL calc_ol
	206	ENDIF
	207
	208	CALL calc_us
	209
	210	CALL calc_surface_fluxes
	211
	212	!
	213	!-- Use either Newton iteration or a lookup table for the bulk Richardson
	214	!-- number to calculate the Obukhov length
	215	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
	216
	217	IF ( .NOT. neutral ) THEN
	218	CALL calc_ol
	219	ENDIF
	220
	221	CALL calc_us
	222
	223	CALL calc_scaling_parameters
	224
	225	CALL calc_surface_fluxes
	226
	227	ENDIF
	228
	229	END SUBROUTINE surface_layer_fluxes
	230
	231
	232	!------------------------------------------------------------------------------!
	233	! Description:
	234	! ------------
	235	!> Initializing actions for the surface layer routine. Basically, this involves
	236	!> the preparation of a lookup table for the the bulk Richardson number vs
	237	!> Obukhov length L when using the lookup table method.
	238	!------------------------------------------------------------------------------!
	239	SUBROUTINE init_surface_layer_fluxes
	240
	241	IMPLICIT NONE
	242
	243	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
	244	num_steps_n !< Number of non-stretched zeta steps
	245
	246	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
	247
	248	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
	249
	250	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
	251
	252
	253	REAL(wp) :: zeta_step, & !< Increment of zeta
	254	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
	255	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
	256	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
	257	z0_min = 0.0_wp !< Minimum value of z0 to create table
	258	!
	259	!-- When cloud physics is used, arrays for storing potential temperature and
	260	!-- specific humidity at first grid level are required
	261	IF ( cloud_physics ) THEN
	262	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
	263	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
	264	ENDIF
	265
	266	!
	267	!-- Allocate field for storing the horizontal velocity
	268	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
	269
	270	IF ( most_method == 'lookup' ) THEN
	271
	272	!
	273	!-- Check for roughness heterogeneity. In that case terminate run and
	274	!-- inform user
	275	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
	276	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
	277	terminate_run_l = .TRUE.
	278	ENDIF
	279
	280	#if defined( __parallel )
	281	!
	282	!-- Make a logical OR for all processes. Force termiation of model if result
	283	!-- is TRUE
	284	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	285	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
	286	MPI_LOR, comm2d, ierr )
	287	#else
	288	terminate_run = terminate_run_l
	289	#endif
	290
	291	IF ( terminate_run ) THEN
	292	message_string = 'most_method = "lookup" cannot be used in ' // &
	293	'combination with a prescribed roughness ' // &
	294	'heterogeneity'
	295	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
	296	ENDIF
	297
	298	ALLOCATE( zeta_tmp(0:num_steps-1) )
	299
	300	!
	301	!-- Use the lowest possible value for z_mo
	302	k = MINVAL(nzb_s_inner)
	303	z_mo = zu(k+1) - zw(k)
	304
	305	!
	306	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
	307	!-- available steps (num_steps). The calculation is done with negative
	308	!-- values of zeta in order to simplify the stretching in the free
	309	!-- convection limit for the remaining 10% of steps.
	310	zeta_tmp(0) = - zeta_max
	311	num_steps_n = ( num_steps * 9 / 10 ) - 1
	312	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
	313
	314	DO l = 1, num_steps_n
	315	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	316	ENDDO
	317
	318	!
	319	!-- Calculate stretching factor for the free convection range
	320	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
	321	regr_old = regr
	322	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
	323	)**( 10.0_wp / REAL(num_steps) )
	324	ENDDO
	325
	326	!
	327	!-- Calculate z/L range from zeta_min to zeta_stretch
	328	DO l = num_steps_n+1, num_steps-1
	329	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	330	zeta_step = zeta_step * regr
	331	ENDDO
	332
	333	!
	334	!-- Invert array and switch sign, then calculate Obukhov length and bulk
	335	!-- Richardson number
	336	z0h_min = MINVAL(z0h)
	337	z0_min = MINVAL(z0)
	338
	339	!
	340	!-- Calculate lookup table for the Richardson number versus Obukhov length
	341	!-- The Richardson number (rib) is defined depending on the choice of
	342	!-- boundary conditions for temperature
	343	IF ( ibc_pt_b == 1 ) THEN
	344	DO l = 0, num_steps-1
	345	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	346	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
	347	- psi_m( z_mo / ol_tab(l) ) &
	348	+ psi_m( z0_min / ol_tab(l) ) &
	349	)**3
	350	ENDDO
	351	ELSE
	352	DO l = 0, num_steps-1
	353	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	354	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
	355	- psi_h( z_mo / ol_tab(l) ) &
	356	+ psi_h( z0h_min / ol_tab(l) ) &
	357	) &
	358	/ ( LOG( z_mo / z0_min ) &
	359	- psi_m( z_mo / ol_tab(l) ) &
	360	+ psi_m( z0_min / ol_tab(l) ) &
	361	)**2
	362	ENDDO
	363	ENDIF
	364
	365	!
	366	!-- Determine minimum values of rib in the lookup table. Set upper limit
	367	!-- to critical Richardson number (0.25)
	368	rib_min = MINVAL(rib_tab)
	369	rib_max = 0.25 !MAXVAL(rib_tab)
	370
	371	DEALLOCATE( zeta_tmp )
	372	ENDIF
	373
	374	END SUBROUTINE init_surface_layer_fluxes
	375
	376
	377	!------------------------------------------------------------------------------!
	378	! Description:
	379	! ------------
	380	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
	381	!------------------------------------------------------------------------------!
	382	SUBROUTINE calc_ol
	383
	384	IMPLICIT NONE
	385
	386	INTEGER(iwp) :: iter, & !< Newton iteration step
	387	l !< look index
	388
	389	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib
	390
	391	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
	392	f_d_ol, & !< Derivative of f
	393	ol_l, & !< Lower bound of L for Newton iteration
	394	ol_m, & !< Previous value of L for Newton iteration
	395	ol_old, & !< Previous time step value of L
	396	ol_u, & !< Upper bound of L for Newton iteration
	397	rib !< Bulk Richardson number
	398
	399	!
	400	!-- Compute the absolute value of the horizontal velocity (relative to the
	401	!-- surface). This is required by all methods
	402	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	403	!$acc kernels loop
	404	DO i = nxl, nxr
	405	DO j = nys, nyn
	406
	407	k = nzb_s_inner(j,i)
	408
	409	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
	410	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
	411	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
	412	- v(k,j,i) - v(k,j+1,i) ) )**2 )
	413
	414	!
	415	!-- For too small values of the local wind, MOST does not work. A
	416	!-- threshold value is thus set if required
	417	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
	418
	419	ENDDO
	420	ENDDO
	421
	422	!
	423	!-- Values of uv_total need to be exchanged at the ghost boundaries
	424	!$acc update host( uv_total )
	425	CALL exchange_horiz_2d( uv_total )
	426	!$acc update device( uv_total )
	427
	428	IF ( TRIM( most_method ) /= 'circular' ) THEN
	429
	430	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	431	!$acc kernels loop
	432	DO i = nxl, nxr
	433	DO j = nys, nyn
	434
	435	k = nzb_s_inner(j,i)
	436	z_mo = zu(k+1) - zw(k)
	437
	438	!
	439	!-- Evaluate bulk Richardson number (calculation depends on
	440	!-- definition based on setting of boundary conditions
	441	IF ( ibc_pt_b /= 1 ) THEN
	442	IF ( humidity ) THEN
	443	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
	444	/ ( uv_total(j,i)*2 vpt(k+1,j,i) )
	445	ELSE
	446	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
	447	/ ( uv_total(j,i)*2 pt(k+1,j,i) )
	448	ENDIF
	449	ELSE
	450	!
	451	!-- When using Neumann boundary conditions, the buoyancy flux
	452	!-- is required but cannot be calculated at the surface, as pt
	453	!-- and q are not known at the surface. Hence the values at
	454	!-- first grid level are used to estimate the buoyancy flux
	455	IF ( humidity ) THEN
	456	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
	457	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
	458	* pt(k+1,j,i) * qsws(j,i) ) &
	459	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2 )
	460	ELSE
	461	rib(j,i) = - g * z_mo * shf(j,i) &
	462	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 )
	463	ENDIF
	464	ENDIF
	465
	466	ENDDO
	467	ENDDO
	468
	469	ENDIF
	470
	471	!
	472	!-- Calculate the Obukhov length either using a Newton iteration
	473	!-- method, via a lookup table, or using the old circular way
	474	IF ( TRIM( most_method ) == 'newton' ) THEN
	475
	476	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	477	!$acc kernels loop
	478	DO i = nxl, nxr
	479	DO j = nys, nyn
	480
	481	k = nzb_s_inner(j,i)
	482	z_mo = zu(k+1) - zw(k)
	483
	484	!
	485	!-- Store current value in case the Newton iteration fails
	486	ol_old = ol(j,i)
	487
	488	!
	489	!-- Ensure that the bulk Richardson number and the Obukhov
	490	!-- lengtH have the same sign
	491	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
	492	ABS( ol(j,i) ) == ol_max ) THEN
	493	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
	494	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
	495	ENDIF
	496	!
	497	!-- Iteration to find Obukhov length
	498	iter = 0
	499	DO
	500	iter = iter + 1
	501	!
	502	!-- In case of divergence, use the value of the previous time step
	503	IF ( iter > 1000 ) THEN
	504	ol(j,i) = ol_old
	505	EXIT
	506	ENDIF
	507
	508	ol_m = ol(j,i)
	509	ol_l = ol_m - 0.001_wp * ol_m
	510	ol_u = ol_m + 0.001_wp * ol_m
	511
	512
	513	IF ( ibc_pt_b /= 1 ) THEN
	514	!
	515	!-- Calculate f = Ri - [...]/[...]^2 = 0
	516	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
	517	- psi_h( z_mo / ol_m ) &
	518	+ psi_h( z0h(j,i) / ol_m ) &
	519	) &
	520	/ ( LOG( z_mo / z0(j,i) ) &
	521	- psi_m( z_mo / ol_m ) &
	522	+ psi_m( z0(j,i) / ol_m ) &
	523	)**2
	524
	525	!
	526	!-- Calculate df/dL
	527	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
	528	- psi_h( z_mo / ol_u ) &
	529	+ psi_h( z0h(j,i) / ol_u ) &
	530	) &
	531	/ ( LOG( z_mo / z0(j,i) ) &
	532	- psi_m( z_mo / ol_u ) &
	533	+ psi_m( z0(j,i) / ol_u ) &
	534	)**2 &
	535	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
	536	- psi_h( z_mo / ol_l ) &
	537	+ psi_h( z0h(j,i) / ol_l ) &
	538	) &
	539	/ ( LOG( z_mo / z0(j,i) ) &
	540	- psi_m( z_mo / ol_l ) &
	541	+ psi_m( z0(j,i) / ol_l ) &
	542	)**2 &
	543	) / ( ol_u - ol_l )
	544	ELSE
	545	!
	546	!-- Calculate f = Ri - 1 /[...]^3 = 0
	547	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
	548	- psi_m( z_mo / ol_m ) &
	549	+ psi_m( z0(j,i) / ol_m ) &
	550	)**3
	551
	552	!
	553	!-- Calculate df/dL
	554	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
	555	- psi_m( z_mo / ol_u ) &
	556	+ psi_m( z0(j,i) / ol_u ) &
	557	)**3 &
	558	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
	559	- psi_m( z_mo / ol_l ) &
	560	+ psi_m( z0(j,i) / ol_l ) &
	561	)**3 &
	562	) / ( ol_u - ol_l )
	563	ENDIF
	564	!
	565	!-- Calculate new L
	566	ol(j,i) = ol_m - f / f_d_ol
	567
	568	!
	569	!-- Ensure that the bulk Richardson number and the Obukhov
	570	!-- length have the same sign and ensure convergence.
	571	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
	572
	573	!
	574	!-- If unrealistic value occurs, set L to the maximum
	575	!-- value that is allowed
	576	IF ( ABS( ol(j,i) ) > ol_max ) THEN
	577	ol(j,i) = ol_max
	578	EXIT
	579	ENDIF
	580	!
	581	!-- Check for convergence
	582	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
	583	EXIT
	584	ELSE
	585	CYCLE
	586	ENDIF
	587
	588	ENDDO
	589
	590	ENDDO
	591	ENDDO
	592
	593	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
	594
	595	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	596	!$acc kernels loop
	597	DO i = nxl, nxr
	598	DO j = nys, nyn
	599
	600	k = nzb_s_inner(j,i)
	601
	602	!
	603	!-- If the bulk Richardson number is outside the range of the lookup
	604	!-- table, set it to the exceeding threshold value
	605	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
	606	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
	607
	608	!
	609	!-- Find the correct index bounds for linear interpolation. As the
	610	!-- Richardson number will not differ very much from time step to
	611	!-- time step , use the index from the last step and search in the
	612	!-- correct direction
	613	l = l_bnd
	614	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
	615	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
	616	l = l-1
	617	ENDDO
	618	ELSE
	619	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
	620	.AND. l < num_steps-1 )
	621	l = l+1
	622	ENDDO
	623	ENDIF
	624	l_bnd = l
	625
	626	!
	627	!-- Linear interpolation to find the correct value of z/L
	628	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
	629	/ ( rib_tab(l) - rib_tab(l-1) ) &
	630	* ( rib(j,i) - rib_tab(l-1) ) )
	631
	632	ENDDO
	633	ENDDO
	634
	635	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
	636
	637	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	638	!$acc kernels loop
	639	DO i = nxl, nxr
	640	DO j = nys, nyn
	641
	642	k = nzb_s_inner(j,i)
	643	z_mo = zu(k+1) - zw(k)
	644
	645	IF ( .NOT. humidity ) THEN
	646	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	647	* ts(j,i) + 1E-30_wp )
	648	ELSEIF ( cloud_physics ) THEN
	649
	650	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	651	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
	652	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
	653	* ql(k+1,j,i) ) + 1E-30_wp )
	654	ELSE
	655	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	656	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
	657	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
	658	ENDIF
	659	!
	660	!-- Limit the value range of the Obukhov length.
	661	!-- This is necessary for very small velocities (u,v --> 0), because
	662	!-- the absolute value of ol can then become very small, which in
	663	!-- consequence would result in very large shear stresses and very
	664	!-- small momentum fluxes (both are generally unrealistic).
	665	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
	666	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
	667
	668	ENDDO
	669	ENDDO
	670
	671	ENDIF
	672
	673	!
	674	!-- Values of ol at ghost point locations are needed for the evaluation
	675	!-- of usws and vsws.
	676	!$acc update host( ol )
	677	CALL exchange_horiz_2d( ol )
	678	!$acc update device( ol )
	679
	680	END SUBROUTINE calc_ol
	681
	682	!
	683	!-- Calculate friction velocity u*
	684	SUBROUTINE calc_us
	685
	686	IMPLICIT NONE
	687
	688	DO i = nxlg, nxrg
	689	DO j = nysg, nyng
	690
	691	k = nzb_s_inner(j,i)+1
	692	z_mo = zu(k+1) - zw(k)
	693
	694	!
	695	!-- Compute u* at the scalars' grid points
	696	!$OMP PARALLEL DO PRIVATE( a, b, k, uv_total, z_mo )
	697	!$acc kernels loop
	698	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
	699	- psi_m( z_mo / ol(j,i) ) &
	700	+ psi_m( z0(j,i) / ol(j,i) ) )
	701	ENDDO
	702	ENDDO
	703
	704	END SUBROUTINE calc_us
	705
	706	!
	707	!-- Calculate potential temperature and specific humidity at first grid level
	708	SUBROUTINE calc_pt_q
	709
	710	IMPLICIT NONE
	711
	712	DO i = nxlg, nxrg
	713	DO j = nysg, nyng
	714	k = nzb_s_inner(j,i)+1
	715	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
	716	qv1(j,i) = q(k,j,i) - ql(k,j,i)
	717	ENDDO
	718	ENDDO
	719
	720	END SUBROUTINE calc_pt_q
	721
	722	!
	723	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
	724	SUBROUTINE calc_scaling_parameters
	725
	726	IMPLICIT NONE
	727
	728	!
	729	!-- Data information for accelerators
	730	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
	731	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
	732	!$acc present( vpt, vsws, zu, zw, z0, z0h )
	733	!
	734	!-- Compute theta*
	735	IF ( constant_heatflux ) THEN
	736
	737	!
	738	!-- For a given heat flux in the surface layer:
	739	!$OMP PARALLEL DO
	740	!$acc kernels loop
	741	DO i = nxlg, nxrg
	742	DO j = nysg, nyng
	743	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
	744	!
	745	!-- ts must be limited, because otherwise overflow may occur in case
	746	!-- of us=0 when computing ol further below
	747	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
	748	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
	749	ENDDO
	750	ENDDO
	751
	752	ELSE
	753	!
	754	!-- For a given surface temperature:
	755	IF ( large_scale_forcing .AND. lsf_surf ) THEN
	756	!$OMP PARALLEL DO
	757	!$acc kernels loop
	758	DO i = nxlg, nxrg
	759	DO j = nysg, nyng
	760	k = nzb_s_inner(j,i)
	761	pt(k,j,i) = pt_surface
	762	ENDDO
	763	ENDDO
	764	ENDIF
	765
	766	!$OMP PARALLEL DO PRIVATE( a, b, k, z_mo )
	767	!$acc kernels loop
	768	DO i = nxlg, nxrg
	769	DO j = nysg, nyng
	770
	771	k = nzb_s_inner(j,i)
	772	z_mo = zu(k+1) - zw(k)
	773
	774	IF ( cloud_physics ) THEN
	775	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
	776	/ ( LOG( z_mo / z0h(j,i) ) &
	777	- psi_h( z_mo / ol(j,i) ) &
	778	+ psi_h( z0h(j,i) / ol(j,i) ) )
	779	ELSE
	780	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
	781	/ ( LOG( z_mo / z0h(j,i) ) &
	782	- psi_h( z_mo / ol(j,i) ) &
	783	+ psi_h( z0h(j,i) / ol(j,i) ) )
	784	ENDIF
	785
	786	ENDDO
	787	ENDDO
	788	ENDIF
	789
	790	!
	791	!-- If required compute q*
	792	IF ( humidity .OR. passive_scalar ) THEN
	793	IF ( constant_waterflux ) THEN
	794	!
	795	!-- For a given water flux in the Prandtl layer:
	796	!$OMP PARALLEL DO
	797	!$acc kernels loop
	798	DO i = nxlg, nxrg
	799	DO j = nysg, nyng
	800	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
	801	ENDDO
	802	ENDDO
	803
	804	ELSE
	805	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
	806	run_coupled )
	807
	808	IF ( large_scale_forcing .AND. lsf_surf ) THEN
	809	!$OMP PARALLEL DO
	810	!$acc kernels loop
	811	DO i = nxlg, nxrg
	812	DO j = nysg, nyng
	813	k = nzb_s_inner(j,i)
	814	q(k,j,i) = q_surface
	815	ENDDO
	816	ENDDO
	817	ENDIF
	818
	819	!$OMP PARALLEL DO PRIVATE( a, b, k, z_mo )
	820	!$acc kernels loop independent
	821	DO i = nxlg, nxrg
	822	!$acc loop independent
	823	DO j = nysg, nyng
	824
	825	k = nzb_s_inner(j,i)
	826	z_mo = zu(k+1) - zw(k)
	827
	828	!
	829	!-- Assume saturation for atmosphere coupled to ocean (but not
	830	!-- in case of precursor runs)
	831	IF ( coupled_run ) THEN
	832	e_s = 6.1_wp * &
	833	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
	834	- 273.15_wp ) )
	835	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
	836	ENDIF
	837
	838	IF ( cloud_physics ) THEN
	839	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
	840	/ ( LOG( z_mo / z0h(j,i) ) &
	841	- psi_h( z_mo / ol(j,i) ) &
	842	+ psi_h( z0h(j,i) / ol(j,i) ) )
	843
	844	ELSE
	845	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
	846	/ ( LOG( z_mo / z0h(j,i) ) &
	847	- psi_h( z_mo / ol(j,i) ) &
	848	+ psi_h( z0h(j,i) / ol(j,i) ) )
	849	ENDIF
	850
	851	ENDDO
	852	ENDDO
	853	ENDIF
	854	ENDIF
	855
	856
	857	!
	858	!-- If required compute qr* and nr*
	859	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
	860
	861	!$OMP PARALLEL DO PRIVATE( a, b, k, z_mo )
	862	!$acc kernels loop independent
	863	DO i = nxlg, nxrg
	864	!$acc loop independent
	865	DO j = nysg, nyng
	866
	867	k = nzb_s_inner(j,i)
	868	z_mo = zu(k+1) - zw(k)
	869
	870	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
	871	/ ( LOG( z_mo / z0h(j,i) ) &
	872	- psi_h( z_mo / ol(j,i) ) &
	873	+ psi_h( z0h(j,i) / ol(j,i) ) )
	874
	875	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
	876	/ ( LOG( z_mo / z0h(j,i) ) &
	877	- psi_h( z_mo / ol(j,i) ) &
	878	+ psi_h( z0h(j,i) / ol(j,i) ) )
	879	ENDDO
	880	ENDDO
	881
	882	ENDIF
	883
	884	END SUBROUTINE calc_scaling_parameters
	885
	886
	887
	888	!
	889	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
	890	SUBROUTINE calc_surface_fluxes
	891
	892	IMPLICIT NONE
	893
	894	REAL(wp) :: ol_mid !< Grid-interpolated L
	895
	896	!
	897	!-- Compute u'w' for the total model domain.
	898	!-- First compute the corresponding component of u* and square it.
	899	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
	900	!$acc kernels loop
	901	DO i = nxl, nxr
	902	DO j = nys, nyn
	903
	904	k = nzb_u_inner(j,i)
	905	z_mo = zu(k+1) - zw(k)
	906	!
	907	!-- Compute bulk Obukhov length for this point
	908	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
	909
	910	IF ( ol_mid == 0.0_wp ) THEN
	911	ol_mid = MIN(ol(j,i-1), ol(j,i))
	912	ENDIF
	913
	914	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
	915	/ ( LOG( z_mo / z0(j,i) ) &
	916	- psi_m( z_mo / ol_mid ) &
	917	+ psi_m( z0(j,i) / ol_mid ) )
	918
	919	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	920	ENDDO
	921	ENDDO
	922
	923	!
	924	!-- Compute v'w' for the total model domain.
	925	!-- First compute the corresponding component of u* and square it.
	926	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
	927	!$acc kernels loop
	928	DO i = nxl, nxr
	929	DO j = nys, nyn
	930
	931	k = nzb_v_inner(j,i)
	932	z_mo = zu(k+1) - zw(k)
	933	!
	934	!-- Compute bulk Obukhov length for this point
	935	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
	936
	937	IF ( ol_mid == 0.0_wp ) THEN
	938	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
	939	ENDIF
	940
	941	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
	942	/ ( LOG( z_mo / z0(j,i) ) &
	943	- psi_m( z_mo / ol_mid ) &
	944	+ psi_m( z0(j,i) / ol_mid ) )
	945
	946	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	947
	948	ENDDO
	949	ENDDO
	950
	951	!
	952	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
	953	!$acc update host( usws, vsws )
	954	CALL exchange_horiz_2d( usws )
	955	CALL exchange_horiz_2d( vsws )
	956	!$acc update device( usws, vsws )
	957
	958	!
	959	!-- Compute the vertical kinematic heat flux
	960	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
	961	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
	962	!$OMP PARALLEL DO
	963	!$acc kernels loop independent
	964	DO i = nxlg, nxrg
	965	!$acc loop independent
	966	DO j = nysg, nyng
	967	shf(j,i) = -ts(j,i) * us(j,i)
	968	ENDDO
	969	ENDDO
	970
	971	ENDIF
	972
	973	!
	974	!-- Compute the vertical water/scalar flux
	975	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. passive_scalar ) &
	976	.AND. ( simulated_time <= skip_time_do_lsm .OR. .NOT. &
	977	land_surface ) ) THEN
	978	!$OMP PARALLEL DO
	979	!$acc kernels loop independent
	980	DO i = nxlg, nxrg
	981	!$acc loop independent
	982	DO j = nysg, nyng
	983	qsws(j,i) = -qs(j,i) * us(j,i)
	984	ENDDO
	985	ENDDO
	986
	987	ENDIF
	988
	989	!
	990	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
	991	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
	992	precipitation ) THEN
	993	!$OMP PARALLEL DO
	994	!$acc kernels loop independent
	995	DO i = nxlg, nxrg
	996	!$acc loop independent
	997	DO j = nysg, nyng
	998	qrsws(j,i) = -qrs(j,i) * us(j,i)
	999	nrsws(j,i) = -nrs(j,i) * us(j,i)
	1000	ENDDO
	1001	ENDDO
	1002	ENDIF
	1003
	1004	!
	1005	!-- Bottom boundary condition for the TKE
	1006	IF ( ibc_e_b == 2 ) THEN
	1007	!$OMP PARALLEL DO
	1008	!$acc kernels loop independent
	1009	DO i = nxlg, nxrg
	1010	!$acc loop independent
	1011	DO j = nysg, nyng
	1012	e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.1_wp )**2
	1013	!
	1014	!-- As a test: cm = 0.4
	1015	! e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.4_wp )**2
	1016	e(nzb_s_inner(j,i),j,i) = e(nzb_s_inner(j,i)+1,j,i)
	1017	ENDDO
	1018	ENDDO
	1019	ENDIF
	1020	!$acc end data
	1021
	1022	END SUBROUTINE calc_surface_fluxes
	1023
	1024
	1025	!
	1026	!-- Integrated stability function for momentum
	1027	FUNCTION psi_m( zeta )
	1028
	1029	USE kinds
	1030
	1031	IMPLICIT NONE
	1032
	1033	REAL(wp) :: psi_m !< Integrated similarity function result
	1034	REAL(wp) :: zeta !< Stability parameter z/L
	1035	REAL(wp) :: x !< dummy variable
	1036
	1037	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1038	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1039	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1040	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1041	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1042	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1043
	1044
	1045	IF ( zeta < 0.0_wp ) THEN
	1046	x = SQRT( SQRT(1.0_wp - 16.0_wp * zeta ) )
	1047	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
	1048	* ( 1.0_wp + x*2 ) 0.125_wp )
	1049	ELSE
	1050
	1051	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
	1052	- bc_d_d
	1053	!
	1054	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1055	!-- psi_m = - 5.0_wp * zeta
	1056
	1057	ENDIF
	1058
	1059	END FUNCTION psi_m
	1060
	1061
	1062	!
	1063	!-- Integrated stability function for heat and moisture
	1064	FUNCTION psi_h( zeta )
	1065
	1066	USE kinds
	1067
	1068	IMPLICIT NONE
	1069
	1070	REAL(wp) :: psi_h !< Integrated similarity function result
	1071	REAL(wp) :: zeta !< Stability parameter z/L
	1072	REAL(wp) :: x !< dummy variable
	1073
	1074	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1075	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1076	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1077	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1078	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1079	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1080
	1081
	1082	IF ( zeta < 0.0_wp ) THEN
	1083	x = SQRT(1.0_wp - 16.0_wp * zeta )
	1084	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
	1085	ELSE
	1086	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
	1087	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
	1088	+ 1.0_wp
	1089	!
	1090	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1091	!-- psi_h = - 5.0_wp * zeta
	1092	ENDIF
	1093
	1094	END FUNCTION psi_h
	1095
	1096	END MODULE surface_layer_fluxes_mod

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