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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1787

Last change on this file since 1787 was 1758, 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:
[1747]	20	! ------------------
[1758]	21	!
	22	!
[1692]	23	! Former revisions:
	24	! -----------------
	25	! $Id: surface_layer_fluxes.f90 1758 2016-02-22 15:53:28Z raasch $
	26	!
[1758]	27	! 1757 2016-02-22 15:49:32Z maronga
	28	! Minor fixes.
	29	!
[1750]	30	! 1749 2016-02-09 12:19:56Z raasch
	31	! further OpenACC adjustments
	32	!
[1748]	33	! 1747 2016-02-08 12:25:53Z raasch
	34	! adjustments for OpenACC usage
	35	!
[1710]	36	! 1709 2015-11-04 14:47:01Z maronga
	37	! Bugfix: division by zero could occur when calculating rib at low wind speeds
	38	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
	39	! neutral = .T.
	40	!
[1706]	41	! 1705 2015-11-02 14:28:56Z maronga
	42	! Typo removed
	43	!
[1698]	44	! 1697 2015-10-28 17:14:10Z raasch
	45	! FORTRAN and OpenMP errors removed
	46	!
[1697]	47	! 1696 2015-10-27 10:03:34Z maronga
[1691]	48	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
	49	! course of the re-writing two additional methods have been implemented. See
	50	! updated description.
	51	!
	52	! 1551 2015-03-03 14:18:16Z maronga
	53	! Removed land surface model part. The surface fluxes are now always calculated
	54	! within prandtl_fluxes, based on the given surface temperature/humidity (which
	55	! is either provided by the land surface model, by large scale forcing data, or
	56	! directly prescribed by the user.
	57	!
	58	! 1496 2014-12-02 17:25:50Z maronga
	59	! Adapted for land surface model
	60	!
	61	! 1494 2014-11-21 17:14:03Z maronga
	62	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
	63	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
	64	! topography for coupled runs (not tested)
	65	!
	66	! 1361 2014-04-16 15:17:48Z hoffmann
	67	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
	68	! drop concentration (nrsws) added
	69	!
	70	! 1340 2014-03-25 19:45:13Z kanani
	71	! REAL constants defined as wp-kind
	72	!
	73	! 1320 2014-03-20 08:40:49Z raasch
	74	! ONLY-attribute added to USE-statements,
	75	! kind-parameters added to all INTEGER and REAL declaration statements,
	76	! kinds are defined in new module kinds,
	77	! old module precision_kind is removed,
	78	! revision history before 2012 removed,
	79	! comment fields (!:) to be used for variable explanations added to
	80	! all variable declaration statements
	81	!
	82	! 1276 2014-01-15 13:40:41Z heinze
	83	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
	84	!
	85	! 1257 2013-11-08 15:18:40Z raasch
	86	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
	87	!
	88	! 1036 2012-10-22 13:43:42Z raasch
	89	! code put under GPL (PALM 3.9)
	90	!
	91	! 1015 2012-09-27 09:23:24Z raasch
	92	! OpenACC statements added
	93	!
	94	! 978 2012-08-09 08:28:32Z fricke
	95	! roughness length for scalar quantities z0h added
	96	!
	97	! Revision 1.1 1998/01/23 10:06:06 raasch
	98	! Initial revision
	99	!
	100	!
	101	! Description:
	102	! ------------
	103	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
	104	!> values of the variables at grid point k=1. Three different methods are
	105	!> available:
	106	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
	107	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
	108	!> slower
	109	!> 3) a method using a lookup table which is fast and accurate. Note, however,
	110	!> that this method cannot be used in case of roughness heterogeneity
	111	!>
	112	!> @todo (re)move large_scale_forcing actions
	113	!> @todo check/optimize OpenMP and OpenACC directives
	114	!------------------------------------------------------------------------------!
	115	MODULE surface_layer_fluxes_mod
	116
	117	USE arrays_3d, &
	118	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
	119	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h
	120
	121	USE cloud_parameters, &
	122	ONLY: l_d_cp, pt_d_t
	123
	124	USE constants, &
	125	ONLY: pi
	126
	127	USE cpulog
	128
	129	USE control_parameters, &
	130	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
	131	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, icloud_scheme, &
	132	initializing_actions, kappa, intermediate_timestep_count, &
	133	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
	134	message_string, most_method, neutral, passive_scalar, &
	135	precipitation, pt_surface, q_surface, run_coupled, &
	136	surface_pressure, simulated_time, terminate_run, zeta_max, &
	137	zeta_min
	138
	139	USE indices, &
	140	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
	141	nzb_u_inner, nzb_v_inner
	142
	143	USE kinds
	144
	145	USE pegrid
	146
	147	USE land_surface_model_mod, &
	148	ONLY: land_surface, skip_time_do_lsm
	149
	150	IMPLICIT NONE
	151
	152	INTEGER(iwp) :: i !< loop index x direction
	153	INTEGER(iwp) :: j !< loop index y direction
[1705]	154	INTEGER(iwp) :: k !< loop index z direction
[1691]	155
	156	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
	157
	158	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
	159
	160	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
	161	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
	162	uv_total !< Total velocity at first grid level
	163
	164	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
	165	ol_tab !< Lookup table values of L
	166
	167	REAL(wp) :: e_s, & !< Saturation water vapor pressure
	168	l_bnd = 7500, & !< Lookup table index of the last time step
	169	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
	170	rib_max, & !< Maximum Richardson number in lookup table
	171	rib_min, & !< Minimum Richardson number in lookup table
	172	z_mo !< Height of the constant flux layer where MOST is assumed
	173
	174
	175	SAVE
	176
	177	PRIVATE
	178
[1747]	179	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
[1691]	180
	181	INTERFACE init_surface_layer_fluxes
	182	MODULE PROCEDURE init_surface_layer_fluxes
	183	END INTERFACE init_surface_layer_fluxes
	184
	185	INTERFACE surface_layer_fluxes
	186	MODULE PROCEDURE surface_layer_fluxes
	187	END INTERFACE surface_layer_fluxes
	188
	189
	190	CONTAINS
	191
	192
	193	!------------------------------------------------------------------------------!
	194	! Description:
	195	! ------------
	196	!> Main routine to compute the surface fluxes
	197	!------------------------------------------------------------------------------!
	198	SUBROUTINE surface_layer_fluxes
	199
	200	IMPLICIT NONE
	201
	202	!
	203	!-- In case cloud physics is used, it is required to derive potential
	204	!-- temperature and specific humidity at first grid level from the fields pt
	205	!-- and q
	206	IF ( cloud_physics ) THEN
	207	CALL calc_pt_q
	208	ENDIF
	209
	210	!
	211	!-- First, calculate the new Obukhov length, then new friction velocity,
	212	!-- followed by the new scaling parameters (th, q, etc.), and the new
	213	!-- surface fluxes if required. The old routine ("circular") requires a
	214	!-- different order of calls as the scaling parameters from the previous time
	215	!-- steps are used to calculate the Obukhov length
	216
	217	!
	218	!-- Depending on setting of most_method use the "old" routine
	219	IF ( most_method == 'circular' ) THEN
	220
	221	CALL calc_scaling_parameters
	222
[1709]	223	CALL calc_uv_total
	224
[1691]	225	IF ( .NOT. neutral ) THEN
	226	CALL calc_ol
	227	ENDIF
	228
	229	CALL calc_us
	230
	231	CALL calc_surface_fluxes
	232
	233	!
	234	!-- Use either Newton iteration or a lookup table for the bulk Richardson
	235	!-- number to calculate the Obukhov length
	236	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
	237
[1709]	238	CALL calc_uv_total
	239
[1691]	240	IF ( .NOT. neutral ) THEN
	241	CALL calc_ol
	242	ENDIF
	243
	244	CALL calc_us
	245
	246	CALL calc_scaling_parameters
	247
	248	CALL calc_surface_fluxes
	249
	250	ENDIF
	251
	252	END SUBROUTINE surface_layer_fluxes
	253
	254
	255	!------------------------------------------------------------------------------!
	256	! Description:
	257	! ------------
	258	!> Initializing actions for the surface layer routine. Basically, this involves
	259	!> the preparation of a lookup table for the the bulk Richardson number vs
	260	!> Obukhov length L when using the lookup table method.
	261	!------------------------------------------------------------------------------!
	262	SUBROUTINE init_surface_layer_fluxes
	263
	264	IMPLICIT NONE
	265
	266	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
	267	num_steps_n !< Number of non-stretched zeta steps
	268
	269	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
	270
	271	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
	272
	273	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
	274
	275
	276	REAL(wp) :: zeta_step, & !< Increment of zeta
	277	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
	278	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
	279	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
	280	z0_min = 0.0_wp !< Minimum value of z0 to create table
	281	!
	282	!-- When cloud physics is used, arrays for storing potential temperature and
	283	!-- specific humidity at first grid level are required
	284	IF ( cloud_physics ) THEN
	285	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
	286	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
	287	ENDIF
	288
	289	!
	290	!-- Allocate field for storing the horizontal velocity
	291	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
	292
[1709]	293
	294	!
	295	!-- In case of runs with neutral statification, set Obukhov length to a
	296	!-- large value
	297	IF ( neutral ) ol = 1.0E10_wp
	298
[1691]	299	IF ( most_method == 'lookup' ) THEN
	300
	301	!
	302	!-- Check for roughness heterogeneity. In that case terminate run and
	303	!-- inform user
	304	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
	305	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
	306	terminate_run_l = .TRUE.
	307	ENDIF
	308
	309	#if defined( __parallel )
	310	!
	311	!-- Make a logical OR for all processes. Force termiation of model if result
	312	!-- is TRUE
	313	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	314	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
	315	MPI_LOR, comm2d, ierr )
	316	#else
	317	terminate_run = terminate_run_l
	318	#endif
	319
	320	IF ( terminate_run ) THEN
	321	message_string = 'most_method = "lookup" cannot be used in ' // &
	322	'combination with a prescribed roughness ' // &
	323	'heterogeneity'
	324	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
	325	ENDIF
	326
	327	ALLOCATE( zeta_tmp(0:num_steps-1) )
	328
	329	!
	330	!-- Use the lowest possible value for z_mo
	331	k = MINVAL(nzb_s_inner)
	332	z_mo = zu(k+1) - zw(k)
	333
	334	!
	335	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
	336	!-- available steps (num_steps). The calculation is done with negative
	337	!-- values of zeta in order to simplify the stretching in the free
	338	!-- convection limit for the remaining 10% of steps.
	339	zeta_tmp(0) = - zeta_max
	340	num_steps_n = ( num_steps * 9 / 10 ) - 1
	341	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
	342
	343	DO l = 1, num_steps_n
	344	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	345	ENDDO
	346
	347	!
	348	!-- Calculate stretching factor for the free convection range
	349	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
	350	regr_old = regr
	351	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
	352	)**( 10.0_wp / REAL(num_steps) )
	353	ENDDO
	354
	355	!
	356	!-- Calculate z/L range from zeta_min to zeta_stretch
	357	DO l = num_steps_n+1, num_steps-1
	358	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	359	zeta_step = zeta_step * regr
	360	ENDDO
	361
	362	!
[1757]	363	!-- Save roughness lengths to temporary variables
	364	z0h_min = z0h(nys,nxl)
	365	z0_min = z0(nys,nxl)
[1691]	366
	367	!
	368	!-- Calculate lookup table for the Richardson number versus Obukhov length
	369	!-- The Richardson number (rib) is defined depending on the choice of
	370	!-- boundary conditions for temperature
	371	IF ( ibc_pt_b == 1 ) THEN
	372	DO l = 0, num_steps-1
	373	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	374	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
	375	- psi_m( z_mo / ol_tab(l) ) &
	376	+ psi_m( z0_min / ol_tab(l) ) &
	377	)**3
	378	ENDDO
	379	ELSE
	380	DO l = 0, num_steps-1
	381	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	382	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
	383	- psi_h( z_mo / ol_tab(l) ) &
	384	+ psi_h( z0h_min / ol_tab(l) ) &
	385	) &
	386	/ ( LOG( z_mo / z0_min ) &
	387	- psi_m( z_mo / ol_tab(l) ) &
	388	+ psi_m( z0_min / ol_tab(l) ) &
	389	)**2
	390	ENDDO
	391	ENDIF
	392
	393	!
	394	!-- Determine minimum values of rib in the lookup table. Set upper limit
	395	!-- to critical Richardson number (0.25)
	396	rib_min = MINVAL(rib_tab)
	397	rib_max = 0.25 !MAXVAL(rib_tab)
	398
	399	DEALLOCATE( zeta_tmp )
	400	ENDIF
	401
	402	END SUBROUTINE init_surface_layer_fluxes
	403
	404
	405	!------------------------------------------------------------------------------!
	406	! Description:
	407	! ------------
[1709]	408	!> Compute the absolute value of the horizontal velocity (relative to the
	409	!> surface). This is required by all methods
[1691]	410	!------------------------------------------------------------------------------!
[1709]	411	SUBROUTINE calc_uv_total
[1691]	412
	413	IMPLICIT NONE
	414
	415
[1747]	416	!$OMP PARALLEL DO PRIVATE( k )
	417	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
[1691]	418	DO i = nxl, nxr
	419	DO j = nys, nyn
	420
	421	k = nzb_s_inner(j,i)
	422	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
	423	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
	424	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
	425	- v(k,j,i) - v(k,j+1,i) ) )**2 )
	426
	427	!
	428	!-- For too small values of the local wind, MOST does not work. A
	429	!-- threshold value is thus set if required
	430	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
	431
	432	ENDDO
	433	ENDDO
	434
	435	!
	436	!-- Values of uv_total need to be exchanged at the ghost boundaries
	437	!$acc update host( uv_total )
	438	CALL exchange_horiz_2d( uv_total )
	439	!$acc update device( uv_total )
	440
[1709]	441	END SUBROUTINE calc_uv_total
	442
	443
	444	!------------------------------------------------------------------------------!
	445	! Description:
	446	! ------------
	447	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
	448	!------------------------------------------------------------------------------!
	449	SUBROUTINE calc_ol
	450
	451	IMPLICIT NONE
	452
	453	INTEGER(iwp) :: iter, & !< Newton iteration step
	454	l !< look index
	455
	456	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
	457
	458	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
	459	f_d_ol, & !< Derivative of f
	460	ol_l, & !< Lower bound of L for Newton iteration
	461	ol_m, & !< Previous value of L for Newton iteration
	462	ol_old, & !< Previous time step value of L
	463	ol_u !< Upper bound of L for Newton iteration
	464
[1691]	465	IF ( TRIM( most_method ) /= 'circular' ) THEN
	466
[1747]	467	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
	468
[1691]	469	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1747]	470	!$acc kernels loop private( j, k, z_mo )
[1691]	471	DO i = nxl, nxr
	472	DO j = nys, nyn
	473
	474	k = nzb_s_inner(j,i)
	475	z_mo = zu(k+1) - zw(k)
	476
	477	!
	478	!-- Evaluate bulk Richardson number (calculation depends on
	479	!-- definition based on setting of boundary conditions
	480	IF ( ibc_pt_b /= 1 ) THEN
	481	IF ( humidity ) THEN
	482	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
[1709]	483	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
[1691]	484	ELSE
	485	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
[1709]	486	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
[1691]	487	ENDIF
	488	ELSE
	489	!
	490	!-- When using Neumann boundary conditions, the buoyancy flux
	491	!-- is required but cannot be calculated at the surface, as pt
	492	!-- and q are not known at the surface. Hence the values at
	493	!-- first grid level are used to estimate the buoyancy flux
	494	IF ( humidity ) THEN
	495	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
	496	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
	497	* pt(k+1,j,i) * qsws(j,i) ) &
[1709]	498	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
	499	+ 1.0E-20_wp)
[1691]	500	ELSE
	501	rib(j,i) = - g * z_mo * shf(j,i) &
[1709]	502	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
	503	+ 1.0E-20_wp )
[1691]	504	ENDIF
	505	ENDIF
	506
	507	ENDDO
	508	ENDDO
[1747]	509	!$acc end data
[1691]	510
	511	ENDIF
	512
	513	!
	514	!-- Calculate the Obukhov length either using a Newton iteration
	515	!-- method, via a lookup table, or using the old circular way
	516	IF ( TRIM( most_method ) == 'newton' ) THEN
	517
	518	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	519	!# WARNING: does not work on GPU so far because of DO-loop with
	520	!# undetermined iterations
[1747]	521	!!!!!!$acc kernels loop
[1691]	522	DO i = nxl, nxr
	523	DO j = nys, nyn
	524
	525	k = nzb_s_inner(j,i)
	526	z_mo = zu(k+1) - zw(k)
	527
	528	!
	529	!-- Store current value in case the Newton iteration fails
	530	ol_old = ol(j,i)
	531
	532	!
	533	!-- Ensure that the bulk Richardson number and the Obukhov
	534	!-- lengtH have the same sign
	535	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
	536	ABS( ol(j,i) ) == ol_max ) THEN
	537	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
	538	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
	539	ENDIF
	540	!
	541	!-- Iteration to find Obukhov length
	542	iter = 0
	543	DO
	544	iter = iter + 1
	545	!
	546	!-- In case of divergence, use the value of the previous time step
	547	IF ( iter > 1000 ) THEN
	548	ol(j,i) = ol_old
	549	EXIT
	550	ENDIF
	551
	552	ol_m = ol(j,i)
	553	ol_l = ol_m - 0.001_wp * ol_m
	554	ol_u = ol_m + 0.001_wp * ol_m
	555
	556
	557	IF ( ibc_pt_b /= 1 ) THEN
	558	!
	559	!-- Calculate f = Ri - [...]/[...]^2 = 0
	560	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
	561	- psi_h( z_mo / ol_m ) &
	562	+ psi_h( z0h(j,i) / ol_m ) &
	563	) &
	564	/ ( LOG( z_mo / z0(j,i) ) &
	565	- psi_m( z_mo / ol_m ) &
	566	+ psi_m( z0(j,i) / ol_m ) &
	567	)**2
	568
	569	!
	570	!-- Calculate df/dL
	571	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
	572	- psi_h( z_mo / ol_u ) &
	573	+ psi_h( z0h(j,i) / ol_u ) &
	574	) &
	575	/ ( LOG( z_mo / z0(j,i) ) &
	576	- psi_m( z_mo / ol_u ) &
	577	+ psi_m( z0(j,i) / ol_u ) &
	578	)**2 &
	579	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
	580	- psi_h( z_mo / ol_l ) &
	581	+ psi_h( z0h(j,i) / ol_l ) &
	582	) &
	583	/ ( LOG( z_mo / z0(j,i) ) &
	584	- psi_m( z_mo / ol_l ) &
	585	+ psi_m( z0(j,i) / ol_l ) &
	586	)**2 &
	587	) / ( ol_u - ol_l )
	588	ELSE
	589	!
	590	!-- Calculate f = Ri - 1 /[...]^3 = 0
	591	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
	592	- psi_m( z_mo / ol_m ) &
	593	+ psi_m( z0(j,i) / ol_m ) &
	594	)**3
	595
	596	!
	597	!-- Calculate df/dL
	598	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
	599	- psi_m( z_mo / ol_u ) &
	600	+ psi_m( z0(j,i) / ol_u ) &
	601	)**3 &
	602	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
	603	- psi_m( z_mo / ol_l ) &
	604	+ psi_m( z0(j,i) / ol_l ) &
	605	)**3 &
	606	) / ( ol_u - ol_l )
	607	ENDIF
	608	!
	609	!-- Calculate new L
	610	ol(j,i) = ol_m - f / f_d_ol
	611
	612	!
	613	!-- Ensure that the bulk Richardson number and the Obukhov
	614	!-- length have the same sign and ensure convergence.
	615	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
	616
	617	!
	618	!-- If unrealistic value occurs, set L to the maximum
	619	!-- value that is allowed
	620	IF ( ABS( ol(j,i) ) > ol_max ) THEN
	621	ol(j,i) = ol_max
	622	EXIT
	623	ENDIF
	624	!
	625	!-- Check for convergence
	626	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
	627	EXIT
	628	ELSE
	629	CYCLE
	630	ENDIF
	631
	632	ENDDO
	633
	634	ENDDO
	635	ENDDO
	636
	637	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
	638
	639	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	640	!# WARNING: does not work on GPU so far because of DO WHILE construct
[1747]	641	!!!!!!$acc kernels loop
[1691]	642	DO i = nxl, nxr
	643	DO j = nys, nyn
	644
	645	!
	646	!-- If the bulk Richardson number is outside the range of the lookup
	647	!-- table, set it to the exceeding threshold value
	648	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
	649	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
	650
	651	!
	652	!-- Find the correct index bounds for linear interpolation. As the
	653	!-- Richardson number will not differ very much from time step to
	654	!-- time step , use the index from the last step and search in the
	655	!-- correct direction
	656	l = l_bnd
	657	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
	658	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
	659	l = l-1
	660	ENDDO
	661	ELSE
	662	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
	663	.AND. l < num_steps-1 )
	664	l = l+1
	665	ENDDO
	666	ENDIF
	667	l_bnd = l
	668
	669	!
	670	!-- Linear interpolation to find the correct value of z/L
	671	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
	672	/ ( rib_tab(l) - rib_tab(l-1) ) &
	673	* ( rib(j,i) - rib_tab(l-1) ) )
	674
	675	ENDDO
	676	ENDDO
	677
	678	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
	679
	680	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1747]	681	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
[1691]	682	DO i = nxl, nxr
	683	DO j = nys, nyn
	684
	685	k = nzb_s_inner(j,i)
	686	z_mo = zu(k+1) - zw(k)
	687
	688	IF ( .NOT. humidity ) THEN
	689	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	690	* ts(j,i) + 1E-30_wp )
	691	ELSEIF ( cloud_physics ) THEN
	692
	693	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	694	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
	695	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
	696	* ql(k+1,j,i) ) + 1E-30_wp )
	697	ELSE
	698	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	699	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
	700	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
	701	ENDIF
	702	!
	703	!-- Limit the value range of the Obukhov length.
	704	!-- This is necessary for very small velocities (u,v --> 0), because
	705	!-- the absolute value of ol can then become very small, which in
	706	!-- consequence would result in very large shear stresses and very
	707	!-- small momentum fluxes (both are generally unrealistic).
	708	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
	709	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
	710
	711	ENDDO
	712	ENDDO
	713
	714	ENDIF
	715
	716	!
	717	!-- Values of ol at ghost point locations are needed for the evaluation
	718	!-- of usws and vsws.
	719	!$acc update host( ol )
	720	CALL exchange_horiz_2d( ol )
	721	!$acc update device( ol )
	722
	723	END SUBROUTINE calc_ol
	724
	725	!
	726	!-- Calculate friction velocity u*
	727	SUBROUTINE calc_us
	728
	729	IMPLICIT NONE
	730
[1697]	731	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	732	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
[1691]	733	DO i = nxlg, nxrg
	734	DO j = nysg, nyng
	735
	736	k = nzb_s_inner(j,i)+1
	737	z_mo = zu(k+1) - zw(k)
	738
	739	!
	740	!-- Compute u* at the scalars' grid points
	741	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
	742	- psi_m( z_mo / ol(j,i) ) &
	743	+ psi_m( z0(j,i) / ol(j,i) ) )
	744	ENDDO
	745	ENDDO
	746
	747	END SUBROUTINE calc_us
	748
	749	!
	750	!-- Calculate potential temperature and specific humidity at first grid level
	751	SUBROUTINE calc_pt_q
	752
	753	IMPLICIT NONE
	754
[1747]	755	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
[1691]	756	DO i = nxlg, nxrg
	757	DO j = nysg, nyng
	758	k = nzb_s_inner(j,i)+1
	759	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
	760	qv1(j,i) = q(k,j,i) - ql(k,j,i)
	761	ENDDO
	762	ENDDO
	763
	764	END SUBROUTINE calc_pt_q
	765
	766	!
	767	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
	768	SUBROUTINE calc_scaling_parameters
	769
	770	IMPLICIT NONE
	771
	772	!
	773	!-- Data information for accelerators
	774	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
	775	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
	776	!$acc present( vpt, vsws, zu, zw, z0, z0h )
	777	!
	778	!-- Compute theta*
	779	IF ( constant_heatflux ) THEN
	780
	781	!
	782	!-- For a given heat flux in the surface layer:
	783	!$OMP PARALLEL DO
[1747]	784	!$acc kernels loop private( j )
[1691]	785	DO i = nxlg, nxrg
	786	DO j = nysg, nyng
	787	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
	788	!
	789	!-- ts must be limited, because otherwise overflow may occur in case
	790	!-- of us=0 when computing ol further below
	791	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
	792	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
	793	ENDDO
	794	ENDDO
	795
	796	ELSE
	797	!
	798	!-- For a given surface temperature:
	799	IF ( large_scale_forcing .AND. lsf_surf ) THEN
	800	!$OMP PARALLEL DO
[1747]	801	!$acc kernels loop private( j, k )
[1691]	802	DO i = nxlg, nxrg
	803	DO j = nysg, nyng
	804	k = nzb_s_inner(j,i)
	805	pt(k,j,i) = pt_surface
	806	ENDDO
	807	ENDDO
	808	ENDIF
	809
[1697]	810	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	811	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
[1691]	812	DO i = nxlg, nxrg
	813	DO j = nysg, nyng
	814
	815	k = nzb_s_inner(j,i)
	816	z_mo = zu(k+1) - zw(k)
	817
	818	IF ( cloud_physics ) THEN
	819	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
	820	/ ( LOG( z_mo / z0h(j,i) ) &
	821	- psi_h( z_mo / ol(j,i) ) &
	822	+ psi_h( z0h(j,i) / ol(j,i) ) )
	823	ELSE
	824	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
	825	/ ( LOG( z_mo / z0h(j,i) ) &
	826	- psi_h( z_mo / ol(j,i) ) &
	827	+ psi_h( z0h(j,i) / ol(j,i) ) )
	828	ENDIF
	829
	830	ENDDO
	831	ENDDO
	832	ENDIF
	833
	834	!
	835	!-- If required compute q*
	836	IF ( humidity .OR. passive_scalar ) THEN
	837	IF ( constant_waterflux ) THEN
	838	!
	839	!-- For a given water flux in the Prandtl layer:
	840	!$OMP PARALLEL DO
[1747]	841	!$acc kernels loop private( j )
[1691]	842	DO i = nxlg, nxrg
	843	DO j = nysg, nyng
	844	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
	845	ENDDO
	846	ENDDO
	847
	848	ELSE
	849	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
	850	run_coupled )
	851
	852	IF ( large_scale_forcing .AND. lsf_surf ) THEN
	853	!$OMP PARALLEL DO
[1747]	854	!$acc kernels loop private( j, k )
[1691]	855	DO i = nxlg, nxrg
	856	DO j = nysg, nyng
	857	k = nzb_s_inner(j,i)
	858	q(k,j,i) = q_surface
	859	ENDDO
	860	ENDDO
	861	ENDIF
	862
[1697]	863	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
[1749]	864	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0h ) private( e_s, j, k, z_mo )
[1691]	865	DO i = nxlg, nxrg
[1749]	866	!$acc loop independent
[1691]	867	DO j = nysg, nyng
	868
	869	k = nzb_s_inner(j,i)
	870	z_mo = zu(k+1) - zw(k)
	871
	872	!
	873	!-- Assume saturation for atmosphere coupled to ocean (but not
	874	!-- in case of precursor runs)
	875	IF ( coupled_run ) THEN
	876	e_s = 6.1_wp * &
	877	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
	878	- 273.15_wp ) )
	879	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
	880	ENDIF
	881
	882	IF ( cloud_physics ) THEN
	883	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
	884	/ ( LOG( z_mo / z0h(j,i) ) &
	885	- psi_h( z_mo / ol(j,i) ) &
	886	+ psi_h( z0h(j,i) / ol(j,i) ) )
	887
	888	ELSE
	889	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
	890	/ ( LOG( z_mo / z0h(j,i) ) &
	891	- psi_h( z_mo / ol(j,i) ) &
	892	+ psi_h( z0h(j,i) / ol(j,i) ) )
	893	ENDIF
	894
	895	ENDDO
	896	ENDDO
	897	ENDIF
	898	ENDIF
	899
	900
	901	!
	902	!-- If required compute qr* and nr*
	903	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
	904
[1697]	905	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	906	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0h ) private( j, k, z_mo )
[1691]	907	DO i = nxlg, nxrg
[1749]	908	!$acc loop independent
[1691]	909	DO j = nysg, nyng
	910
	911	k = nzb_s_inner(j,i)
	912	z_mo = zu(k+1) - zw(k)
	913
[1749]	914	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
	915	/ ( LOG( z_mo / z0h(j,i) ) &
	916	- psi_h( z_mo / ol(j,i) ) &
	917	+ psi_h( z0h(j,i) / ol(j,i) ) )
[1691]	918
[1749]	919	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
	920	/ ( LOG( z_mo / z0h(j,i) ) &
	921	- psi_h( z_mo / ol(j,i) ) &
	922	+ psi_h( z0h(j,i) / ol(j,i) ) )
[1691]	923	ENDDO
	924	ENDDO
	925
	926	ENDIF
[1747]	927	!$acc end data
[1691]	928
	929	END SUBROUTINE calc_scaling_parameters
	930
	931
	932
	933	!
	934	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
	935	SUBROUTINE calc_surface_fluxes
	936
	937	IMPLICIT NONE
	938
	939	REAL(wp) :: ol_mid !< Grid-interpolated L
	940
	941	!
	942	!-- Compute u'w' for the total model domain.
	943	!-- First compute the corresponding component of u* and square it.
	944	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
[1749]	945	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
[1691]	946	DO i = nxl, nxr
	947	DO j = nys, nyn
	948
	949	k = nzb_u_inner(j,i)
	950	z_mo = zu(k+1) - zw(k)
	951	!
	952	!-- Compute bulk Obukhov length for this point
	953	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
	954
	955	IF ( ol_mid == 0.0_wp ) THEN
	956	ol_mid = MIN(ol(j,i-1), ol(j,i))
	957	ENDIF
	958
	959	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
	960	/ ( LOG( z_mo / z0(j,i) ) &
	961	- psi_m( z_mo / ol_mid ) &
	962	+ psi_m( z0(j,i) / ol_mid ) )
	963
	964	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	965	ENDDO
	966	ENDDO
	967
	968	!
	969	!-- Compute v'w' for the total model domain.
	970	!-- First compute the corresponding component of u* and square it.
	971	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
[1749]	972	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
[1691]	973	DO i = nxl, nxr
	974	DO j = nys, nyn
	975
	976	k = nzb_v_inner(j,i)
	977	z_mo = zu(k+1) - zw(k)
	978	!
	979	!-- Compute bulk Obukhov length for this point
	980	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
	981
	982	IF ( ol_mid == 0.0_wp ) THEN
	983	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
	984	ENDIF
	985
	986	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
	987	/ ( LOG( z_mo / z0(j,i) ) &
	988	- psi_m( z_mo / ol_mid ) &
	989	+ psi_m( z0(j,i) / ol_mid ) )
	990
	991	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	992
	993	ENDDO
	994	ENDDO
	995
	996	!
	997	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
[1749]	998	!$acc update host( usws, vsws )
[1691]	999	CALL exchange_horiz_2d( usws )
	1000	CALL exchange_horiz_2d( vsws )
	1001	!$acc update device( usws, vsws )
	1002
	1003	!
	1004	!-- Compute the vertical kinematic heat flux
	1005	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
	1006	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
	1007	!$OMP PARALLEL DO
[1747]	1008	!$acc kernels loop independent present( shf, ts, us )
[1691]	1009	DO i = nxlg, nxrg
	1010	!$acc loop independent
	1011	DO j = nysg, nyng
	1012	shf(j,i) = -ts(j,i) * us(j,i)
	1013	ENDDO
	1014	ENDDO
	1015
	1016	ENDIF
	1017
	1018	!
	1019	!-- Compute the vertical water/scalar flux
	1020	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. passive_scalar ) &
	1021	.AND. ( simulated_time <= skip_time_do_lsm .OR. .NOT. &
	1022	land_surface ) ) THEN
	1023	!$OMP PARALLEL DO
[1747]	1024	!$acc kernels loop independent present( qs, qsws, us )
[1691]	1025	DO i = nxlg, nxrg
	1026	!$acc loop independent
	1027	DO j = nysg, nyng
	1028	qsws(j,i) = -qs(j,i) * us(j,i)
	1029	ENDDO
	1030	ENDDO
	1031
	1032	ENDIF
	1033
	1034	!
	1035	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
	1036	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
	1037	precipitation ) THEN
	1038	!$OMP PARALLEL DO
[1747]	1039	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
[1691]	1040	DO i = nxlg, nxrg
	1041	!$acc loop independent
	1042	DO j = nysg, nyng
	1043	qrsws(j,i) = -qrs(j,i) * us(j,i)
	1044	nrsws(j,i) = -nrs(j,i) * us(j,i)
	1045	ENDDO
	1046	ENDDO
	1047	ENDIF
	1048
	1049	!
	1050	!-- Bottom boundary condition for the TKE
	1051	IF ( ibc_e_b == 2 ) THEN
	1052	!$OMP PARALLEL DO
[1747]	1053	!$acc kernels loop independent present( e, nzb_s_inner, us )
[1691]	1054	DO i = nxlg, nxrg
	1055	!$acc loop independent
	1056	DO j = nysg, nyng
[1757]	1057	k = nzb_s_inner(j,i)
	1058	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
[1691]	1059	!
	1060	!-- As a test: cm = 0.4
[1757]	1061	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
	1062	e(k,j,i) = e(k+1,j,i)
[1691]	1063	ENDDO
	1064	ENDDO
	1065	ENDIF
	1066
	1067	END SUBROUTINE calc_surface_fluxes
	1068
	1069
	1070	!
	1071	!-- Integrated stability function for momentum
	1072	FUNCTION psi_m( zeta )
	1073
	1074	USE kinds
	1075
	1076	IMPLICIT NONE
	1077
	1078	REAL(wp) :: psi_m !< Integrated similarity function result
	1079	REAL(wp) :: zeta !< Stability parameter z/L
	1080	REAL(wp) :: x !< dummy variable
	1081
	1082	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1083	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1084	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1085	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1086	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1087	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1088
	1089
	1090	IF ( zeta < 0.0_wp ) THEN
	1091	x = SQRT( SQRT(1.0_wp - 16.0_wp * zeta ) )
	1092	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
	1093	* ( 1.0_wp + x*2 ) 0.125_wp )
	1094	ELSE
	1095
	1096	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
	1097	- bc_d_d
	1098	!
	1099	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1100	!-- psi_m = - 5.0_wp * zeta
	1101
	1102	ENDIF
	1103
	1104	END FUNCTION psi_m
	1105
	1106
	1107	!
	1108	!-- Integrated stability function for heat and moisture
	1109	FUNCTION psi_h( zeta )
	1110
	1111	USE kinds
	1112
	1113	IMPLICIT NONE
	1114
	1115	REAL(wp) :: psi_h !< Integrated similarity function result
	1116	REAL(wp) :: zeta !< Stability parameter z/L
	1117	REAL(wp) :: x !< dummy variable
	1118
	1119	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1120	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1121	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1122	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1123	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1124	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1125
	1126
	1127	IF ( zeta < 0.0_wp ) THEN
	1128	x = SQRT(1.0_wp - 16.0_wp * zeta )
	1129	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
	1130	ELSE
	1131	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
	1132	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
	1133	+ 1.0_wp
	1134	!
	1135	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1136	!-- psi_h = - 5.0_wp * zeta
	1137	ENDIF
	1138
	1139	END FUNCTION psi_h
	1140
[1697]	1141	END MODULE surface_layer_fluxes_mod

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