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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1749

Last change on this file since 1749 was 1749, checked in by raasch, 8 years ago
further OpenACC adjustments and one bugfix
Property svn:keywords set to `Id`
File size: 42.4 KB

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

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