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source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 1928

Last change on this file since 1928 was 1921, checked in by suehring, 8 years ago
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[1850]	1	!> @file surface_layer_fluxes_mod.f90
[1691]	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	!
[1818]	16	! Copyright 1997-2016 Leibniz Universitaet Hannover
[1691]	17	!
	18	!--------------------------------------------------------------------------------!
	19	! Current revisions:
[1747]	20	! ------------------
[1758]	21	!
[1921]	22	!
[1692]	23	! Former revisions:
	24	! -----------------
	25	! $Id: surface_layer_fluxes_mod.f90 1921 2016-05-30 10:52:07Z hellstea $
	26	!
[1921]	27	! 1920 2016-05-30 10:50:15Z suehring
	28	! Avoid segmentation fault (see change in 1915) by different initialization of
	29	! us instead of adding a very small number in the denominator
	30	!
[1916]	31	! 1915 2016-05-27 11:05:02Z suehring
	32	! Bugfix: avoid segmentation fault in case of most_method = 'circular' at first
	33	! timestep
	34	!
[1851]	35	! 1850 2016-04-08 13:29:27Z maronga
	36	! Module renamed
	37	!
	38	!
[1823]	39	! 1822 2016-04-07 07:49:42Z hoffmann
	40	! icloud_scheme replaced by microphysics_*
	41	!
[1789]	42	! 1788 2016-03-10 11:01:04Z maronga
	43	! Added parameter z0q which replaces z0h in the similarity functions for
	44	! humidity.
	45	! Syntax layout improved.
	46	!
[1758]	47	! 1757 2016-02-22 15:49:32Z maronga
	48	! Minor fixes.
	49	!
[1750]	50	! 1749 2016-02-09 12:19:56Z raasch
	51	! further OpenACC adjustments
	52	!
[1748]	53	! 1747 2016-02-08 12:25:53Z raasch
	54	! adjustments for OpenACC usage
	55	!
[1710]	56	! 1709 2015-11-04 14:47:01Z maronga
	57	! Bugfix: division by zero could occur when calculating rib at low wind speeds
	58	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
	59	! neutral = .T.
	60	!
[1706]	61	! 1705 2015-11-02 14:28:56Z maronga
	62	! Typo removed
	63	!
[1698]	64	! 1697 2015-10-28 17:14:10Z raasch
	65	! FORTRAN and OpenMP errors removed
	66	!
[1697]	67	! 1696 2015-10-27 10:03:34Z maronga
[1691]	68	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
	69	! course of the re-writing two additional methods have been implemented. See
	70	! updated description.
	71	!
	72	! 1551 2015-03-03 14:18:16Z maronga
	73	! Removed land surface model part. The surface fluxes are now always calculated
	74	! within prandtl_fluxes, based on the given surface temperature/humidity (which
	75	! is either provided by the land surface model, by large scale forcing data, or
	76	! directly prescribed by the user.
	77	!
	78	! 1496 2014-12-02 17:25:50Z maronga
	79	! Adapted for land surface model
	80	!
	81	! 1494 2014-11-21 17:14:03Z maronga
	82	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
	83	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
	84	! topography for coupled runs (not tested)
	85	!
	86	! 1361 2014-04-16 15:17:48Z hoffmann
	87	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
	88	! drop concentration (nrsws) added
	89	!
	90	! 1340 2014-03-25 19:45:13Z kanani
	91	! REAL constants defined as wp-kind
	92	!
	93	! 1320 2014-03-20 08:40:49Z raasch
	94	! ONLY-attribute added to USE-statements,
	95	! kind-parameters added to all INTEGER and REAL declaration statements,
	96	! kinds are defined in new module kinds,
	97	! old module precision_kind is removed,
	98	! revision history before 2012 removed,
	99	! comment fields (!:) to be used for variable explanations added to
	100	! all variable declaration statements
	101	!
	102	! 1276 2014-01-15 13:40:41Z heinze
	103	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
	104	!
	105	! 1257 2013-11-08 15:18:40Z raasch
	106	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
	107	!
	108	! 1036 2012-10-22 13:43:42Z raasch
	109	! code put under GPL (PALM 3.9)
	110	!
	111	! 1015 2012-09-27 09:23:24Z raasch
	112	! OpenACC statements added
	113	!
	114	! 978 2012-08-09 08:28:32Z fricke
	115	! roughness length for scalar quantities z0h added
	116	!
	117	! Revision 1.1 1998/01/23 10:06:06 raasch
	118	! Initial revision
	119	!
	120	!
	121	! Description:
	122	! ------------
	123	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
	124	!> values of the variables at grid point k=1. Three different methods are
	125	!> available:
	126	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
	127	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
	128	!> slower
	129	!> 3) a method using a lookup table which is fast and accurate. Note, however,
	130	!> that this method cannot be used in case of roughness heterogeneity
	131	!>
	132	!> @todo (re)move large_scale_forcing actions
	133	!> @todo check/optimize OpenMP and OpenACC directives
	134	!------------------------------------------------------------------------------!
	135	MODULE surface_layer_fluxes_mod
	136
	137	USE arrays_3d, &
	138	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
[1788]	139	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h, z0q
[1691]	140
	141	USE cloud_parameters, &
	142	ONLY: l_d_cp, pt_d_t
	143
	144	USE constants, &
	145	ONLY: pi
	146
	147	USE cpulog
	148
	149	USE control_parameters, &
	150	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
[1822]	151	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, &
[1691]	152	initializing_actions, kappa, intermediate_timestep_count, &
	153	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
[1822]	154	message_string, microphysics_seifert, most_method, neutral, &
	155	passive_scalar, pt_surface, q_surface, run_coupled, &
[1691]	156	surface_pressure, simulated_time, terminate_run, zeta_max, &
	157	zeta_min
	158
	159	USE indices, &
	160	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
	161	nzb_u_inner, nzb_v_inner
	162
	163	USE kinds
	164
	165	USE pegrid
	166
	167	USE land_surface_model_mod, &
	168	ONLY: land_surface, skip_time_do_lsm
	169
	170	IMPLICIT NONE
	171
	172	INTEGER(iwp) :: i !< loop index x direction
	173	INTEGER(iwp) :: j !< loop index y direction
[1705]	174	INTEGER(iwp) :: k !< loop index z direction
[1691]	175
	176	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
	177
	178	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
	179
	180	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
	181	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
	182	uv_total !< Total velocity at first grid level
	183
	184	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
	185	ol_tab !< Lookup table values of L
	186
	187	REAL(wp) :: e_s, & !< Saturation water vapor pressure
	188	l_bnd = 7500, & !< Lookup table index of the last time step
	189	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
	190	rib_max, & !< Maximum Richardson number in lookup table
	191	rib_min, & !< Minimum Richardson number in lookup table
	192	z_mo !< Height of the constant flux layer where MOST is assumed
	193
	194
	195	SAVE
	196
	197	PRIVATE
	198
[1747]	199	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
[1691]	200
	201	INTERFACE init_surface_layer_fluxes
	202	MODULE PROCEDURE init_surface_layer_fluxes
	203	END INTERFACE init_surface_layer_fluxes
	204
	205	INTERFACE surface_layer_fluxes
	206	MODULE PROCEDURE surface_layer_fluxes
	207	END INTERFACE surface_layer_fluxes
	208
	209
	210	CONTAINS
	211
	212
	213	!------------------------------------------------------------------------------!
	214	! Description:
	215	! ------------
	216	!> Main routine to compute the surface fluxes
	217	!------------------------------------------------------------------------------!
	218	SUBROUTINE surface_layer_fluxes
	219
	220	IMPLICIT NONE
	221
	222	!
	223	!-- In case cloud physics is used, it is required to derive potential
	224	!-- temperature and specific humidity at first grid level from the fields pt
	225	!-- and q
	226	IF ( cloud_physics ) THEN
	227	CALL calc_pt_q
	228	ENDIF
	229
	230	!
	231	!-- First, calculate the new Obukhov length, then new friction velocity,
	232	!-- followed by the new scaling parameters (th, q, etc.), and the new
	233	!-- surface fluxes if required. The old routine ("circular") requires a
	234	!-- different order of calls as the scaling parameters from the previous time
	235	!-- steps are used to calculate the Obukhov length
	236
	237	!
	238	!-- Depending on setting of most_method use the "old" routine
	239	IF ( most_method == 'circular' ) THEN
	240
	241	CALL calc_scaling_parameters
	242
[1709]	243	CALL calc_uv_total
	244
[1691]	245	IF ( .NOT. neutral ) THEN
	246	CALL calc_ol
	247	ENDIF
	248
	249	CALL calc_us
	250
	251	CALL calc_surface_fluxes
	252
	253	!
	254	!-- Use either Newton iteration or a lookup table for the bulk Richardson
	255	!-- number to calculate the Obukhov length
[1788]	256	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
[1691]	257
[1709]	258	CALL calc_uv_total
	259
[1691]	260	IF ( .NOT. neutral ) THEN
	261	CALL calc_ol
	262	ENDIF
	263
	264	CALL calc_us
	265
	266	CALL calc_scaling_parameters
	267
	268	CALL calc_surface_fluxes
	269
	270	ENDIF
	271
	272	END SUBROUTINE surface_layer_fluxes
	273
	274
	275	!------------------------------------------------------------------------------!
	276	! Description:
	277	! ------------
	278	!> Initializing actions for the surface layer routine. Basically, this involves
	279	!> the preparation of a lookup table for the the bulk Richardson number vs
	280	!> Obukhov length L when using the lookup table method.
	281	!------------------------------------------------------------------------------!
	282	SUBROUTINE init_surface_layer_fluxes
	283
	284	IMPLICIT NONE
	285
	286	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
	287	num_steps_n !< Number of non-stretched zeta steps
	288
	289	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
	290
	291	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
	292
	293	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
	294
	295
	296	REAL(wp) :: zeta_step, & !< Increment of zeta
	297	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
	298	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
	299	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
	300	z0_min = 0.0_wp !< Minimum value of z0 to create table
	301	!
	302	!-- When cloud physics is used, arrays for storing potential temperature and
	303	!-- specific humidity at first grid level are required
	304	IF ( cloud_physics ) THEN
	305	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
	306	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
	307	ENDIF
	308
	309	!
	310	!-- Allocate field for storing the horizontal velocity
	311	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
	312
[1709]	313
	314	!
	315	!-- In case of runs with neutral statification, set Obukhov length to a
	316	!-- large value
	317	IF ( neutral ) ol = 1.0E10_wp
	318
[1691]	319	IF ( most_method == 'lookup' ) THEN
	320
	321	!
	322	!-- Check for roughness heterogeneity. In that case terminate run and
	323	!-- inform user
[1788]	324	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
[1691]	325	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
	326	terminate_run_l = .TRUE.
	327	ENDIF
	328
	329	#if defined( __parallel )
	330	!
	331	!-- Make a logical OR for all processes. Force termiation of model if result
	332	!-- is TRUE
	333	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	334	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
	335	MPI_LOR, comm2d, ierr )
	336	#else
	337	terminate_run = terminate_run_l
	338	#endif
	339
	340	IF ( terminate_run ) THEN
	341	message_string = 'most_method = "lookup" cannot be used in ' // &
	342	'combination with a prescribed roughness ' // &
	343	'heterogeneity'
	344	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
	345	ENDIF
	346
	347	ALLOCATE( zeta_tmp(0:num_steps-1) )
	348
	349	!
	350	!-- Use the lowest possible value for z_mo
	351	k = MINVAL(nzb_s_inner)
	352	z_mo = zu(k+1) - zw(k)
	353
	354	!
	355	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
	356	!-- available steps (num_steps). The calculation is done with negative
	357	!-- values of zeta in order to simplify the stretching in the free
	358	!-- convection limit for the remaining 10% of steps.
	359	zeta_tmp(0) = - zeta_max
	360	num_steps_n = ( num_steps * 9 / 10 ) - 1
	361	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
	362
	363	DO l = 1, num_steps_n
	364	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	365	ENDDO
	366
	367	!
	368	!-- Calculate stretching factor for the free convection range
[1788]	369	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
[1691]	370	regr_old = regr
	371	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
	372	)**( 10.0_wp / REAL(num_steps) )
	373	ENDDO
	374
	375	!
	376	!-- Calculate z/L range from zeta_min to zeta_stretch
	377	DO l = num_steps_n+1, num_steps-1
	378	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	379	zeta_step = zeta_step * regr
	380	ENDDO
	381
	382	!
[1757]	383	!-- Save roughness lengths to temporary variables
	384	z0h_min = z0h(nys,nxl)
	385	z0_min = z0(nys,nxl)
[1691]	386
	387	!
	388	!-- Calculate lookup table for the Richardson number versus Obukhov length
	389	!-- The Richardson number (rib) is defined depending on the choice of
	390	!-- boundary conditions for temperature
	391	IF ( ibc_pt_b == 1 ) THEN
	392	DO l = 0, num_steps-1
	393	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	394	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
	395	- psi_m( z_mo / ol_tab(l) ) &
	396	+ psi_m( z0_min / ol_tab(l) ) &
	397	)**3
	398	ENDDO
	399	ELSE
	400	DO l = 0, num_steps-1
	401	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	402	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
	403	- psi_h( z_mo / ol_tab(l) ) &
	404	+ psi_h( z0h_min / ol_tab(l) ) &
	405	) &
	406	/ ( LOG( z_mo / z0_min ) &
	407	- psi_m( z_mo / ol_tab(l) ) &
	408	+ psi_m( z0_min / ol_tab(l) ) &
	409	)**2
	410	ENDDO
	411	ENDIF
	412
	413	!
	414	!-- Determine minimum values of rib in the lookup table. Set upper limit
	415	!-- to critical Richardson number (0.25)
	416	rib_min = MINVAL(rib_tab)
	417	rib_max = 0.25 !MAXVAL(rib_tab)
	418
	419	DEALLOCATE( zeta_tmp )
	420	ENDIF
	421
	422	END SUBROUTINE init_surface_layer_fluxes
	423
	424
	425	!------------------------------------------------------------------------------!
	426	! Description:
	427	! ------------
[1709]	428	!> Compute the absolute value of the horizontal velocity (relative to the
	429	!> surface). This is required by all methods
[1691]	430	!------------------------------------------------------------------------------!
[1709]	431	SUBROUTINE calc_uv_total
[1691]	432
	433	IMPLICIT NONE
	434
	435
[1747]	436	!$OMP PARALLEL DO PRIVATE( k )
	437	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
[1691]	438	DO i = nxl, nxr
	439	DO j = nys, nyn
	440
	441	k = nzb_s_inner(j,i)
	442	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
	443	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
	444	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
	445	- v(k,j,i) - v(k,j+1,i) ) )**2 )
	446
	447	!
	448	!-- For too small values of the local wind, MOST does not work. A
	449	!-- threshold value is thus set if required
	450	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
	451
	452	ENDDO
	453	ENDDO
	454
	455	!
	456	!-- Values of uv_total need to be exchanged at the ghost boundaries
	457	!$acc update host( uv_total )
	458	CALL exchange_horiz_2d( uv_total )
	459	!$acc update device( uv_total )
	460
[1709]	461	END SUBROUTINE calc_uv_total
	462
	463
	464	!------------------------------------------------------------------------------!
	465	! Description:
	466	! ------------
	467	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
	468	!------------------------------------------------------------------------------!
	469	SUBROUTINE calc_ol
	470
	471	IMPLICIT NONE
	472
	473	INTEGER(iwp) :: iter, & !< Newton iteration step
	474	l !< look index
	475
	476	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
	477
	478	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
	479	f_d_ol, & !< Derivative of f
	480	ol_l, & !< Lower bound of L for Newton iteration
	481	ol_m, & !< Previous value of L for Newton iteration
	482	ol_old, & !< Previous time step value of L
	483	ol_u !< Upper bound of L for Newton iteration
	484
[1691]	485	IF ( TRIM( most_method ) /= 'circular' ) THEN
	486
[1747]	487	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
	488
[1691]	489	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1747]	490	!$acc kernels loop private( j, k, z_mo )
[1691]	491	DO i = nxl, nxr
	492	DO j = nys, nyn
	493
	494	k = nzb_s_inner(j,i)
	495	z_mo = zu(k+1) - zw(k)
	496
	497	!
	498	!-- Evaluate bulk Richardson number (calculation depends on
	499	!-- definition based on setting of boundary conditions
	500	IF ( ibc_pt_b /= 1 ) THEN
	501	IF ( humidity ) THEN
	502	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
[1709]	503	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
[1691]	504	ELSE
	505	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
[1709]	506	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
[1691]	507	ENDIF
	508	ELSE
	509	!
	510	!-- When using Neumann boundary conditions, the buoyancy flux
	511	!-- is required but cannot be calculated at the surface, as pt
	512	!-- and q are not known at the surface. Hence the values at
	513	!-- first grid level are used to estimate the buoyancy flux
	514	IF ( humidity ) THEN
	515	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
	516	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
	517	* pt(k+1,j,i) * qsws(j,i) ) &
[1709]	518	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
	519	+ 1.0E-20_wp)
[1691]	520	ELSE
	521	rib(j,i) = - g * z_mo * shf(j,i) &
[1709]	522	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
	523	+ 1.0E-20_wp )
[1691]	524	ENDIF
	525	ENDIF
	526
	527	ENDDO
	528	ENDDO
[1747]	529	!$acc end data
[1691]	530
	531	ENDIF
	532
	533	!
	534	!-- Calculate the Obukhov length either using a Newton iteration
	535	!-- method, via a lookup table, or using the old circular way
	536	IF ( TRIM( most_method ) == 'newton' ) THEN
	537
	538	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	539	!# WARNING: does not work on GPU so far because of DO-loop with
	540	!# undetermined iterations
[1747]	541	!!!!!!$acc kernels loop
[1691]	542	DO i = nxl, nxr
	543	DO j = nys, nyn
	544
	545	k = nzb_s_inner(j,i)
	546	z_mo = zu(k+1) - zw(k)
	547
	548	!
	549	!-- Store current value in case the Newton iteration fails
	550	ol_old = ol(j,i)
	551
	552	!
	553	!-- Ensure that the bulk Richardson number and the Obukhov
	554	!-- lengtH have the same sign
[1788]	555	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
[1691]	556	ABS( ol(j,i) ) == ol_max ) THEN
	557	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
	558	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
	559	ENDIF
	560	!
	561	!-- Iteration to find Obukhov length
	562	iter = 0
	563	DO
	564	iter = iter + 1
	565	!
	566	!-- In case of divergence, use the value of the previous time step
	567	IF ( iter > 1000 ) THEN
	568	ol(j,i) = ol_old
	569	EXIT
	570	ENDIF
	571
	572	ol_m = ol(j,i)
	573	ol_l = ol_m - 0.001_wp * ol_m
	574	ol_u = ol_m + 0.001_wp * ol_m
	575
	576
	577	IF ( ibc_pt_b /= 1 ) THEN
	578	!
	579	!-- Calculate f = Ri - [...]/[...]^2 = 0
	580	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
	581	- psi_h( z_mo / ol_m ) &
	582	+ psi_h( z0h(j,i) / ol_m ) &
	583	) &
	584	/ ( LOG( z_mo / z0(j,i) ) &
	585	- psi_m( z_mo / ol_m ) &
	586	+ psi_m( z0(j,i) / ol_m ) &
	587	)**2
	588
	589	!
	590	!-- Calculate df/dL
	591	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
	592	- psi_h( z_mo / ol_u ) &
	593	+ psi_h( z0h(j,i) / ol_u ) &
	594	) &
	595	/ ( LOG( z_mo / z0(j,i) ) &
	596	- psi_m( z_mo / ol_u ) &
	597	+ psi_m( z0(j,i) / ol_u ) &
	598	)**2 &
	599	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
	600	- psi_h( z_mo / ol_l ) &
	601	+ psi_h( z0h(j,i) / ol_l ) &
	602	) &
	603	/ ( LOG( z_mo / z0(j,i) ) &
	604	- psi_m( z_mo / ol_l ) &
	605	+ psi_m( z0(j,i) / ol_l ) &
	606	)**2 &
	607	) / ( ol_u - ol_l )
	608	ELSE
	609	!
	610	!-- Calculate f = Ri - 1 /[...]^3 = 0
	611	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
	612	- psi_m( z_mo / ol_m ) &
	613	+ psi_m( z0(j,i) / ol_m ) &
	614	)**3
	615
	616	!
	617	!-- Calculate df/dL
	618	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
	619	- psi_m( z_mo / ol_u ) &
	620	+ psi_m( z0(j,i) / ol_u ) &
	621	)**3 &
	622	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
	623	- psi_m( z_mo / ol_l ) &
	624	+ psi_m( z0(j,i) / ol_l ) &
	625	)**3 &
	626	) / ( ol_u - ol_l )
	627	ENDIF
	628	!
	629	!-- Calculate new L
	630	ol(j,i) = ol_m - f / f_d_ol
	631
	632	!
	633	!-- Ensure that the bulk Richardson number and the Obukhov
	634	!-- length have the same sign and ensure convergence.
	635	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
	636
	637	!
	638	!-- If unrealistic value occurs, set L to the maximum
	639	!-- value that is allowed
	640	IF ( ABS( ol(j,i) ) > ol_max ) THEN
	641	ol(j,i) = ol_max
	642	EXIT
	643	ENDIF
	644	!
	645	!-- Check for convergence
	646	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
	647	EXIT
	648	ELSE
	649	CYCLE
	650	ENDIF
	651
	652	ENDDO
	653
	654	ENDDO
	655	ENDDO
	656
	657	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
	658
	659	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1788]	660	!# WARNING: does not work on GPU so far because of DO WHILE construct
[1747]	661	!!!!!!$acc kernels loop
[1691]	662	DO i = nxl, nxr
	663	DO j = nys, nyn
	664
	665	!
	666	!-- If the bulk Richardson number is outside the range of the lookup
	667	!-- table, set it to the exceeding threshold value
	668	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
	669	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
	670
	671	!
	672	!-- Find the correct index bounds for linear interpolation. As the
	673	!-- Richardson number will not differ very much from time step to
	674	!-- time step , use the index from the last step and search in the
	675	!-- correct direction
	676	l = l_bnd
	677	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
[1788]	678	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
[1691]	679	l = l-1
	680	ENDDO
	681	ELSE
[1788]	682	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
	683	.AND. l < num_steps-1 )
[1691]	684	l = l+1
	685	ENDDO
	686	ENDIF
	687	l_bnd = l
	688
	689	!
	690	!-- Linear interpolation to find the correct value of z/L
[1788]	691	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
	692	/ ( rib_tab(l) - rib_tab(l-1) ) &
[1691]	693	* ( rib(j,i) - rib_tab(l-1) ) )
	694
	695	ENDDO
	696	ENDDO
	697
	698	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
	699
	700	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1747]	701	!$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]	702	DO i = nxl, nxr
	703	DO j = nys, nyn
	704
	705	k = nzb_s_inner(j,i)
	706	z_mo = zu(k+1) - zw(k)
	707
	708	IF ( .NOT. humidity ) THEN
	709	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	710	* ts(j,i) + 1E-30_wp )
	711	ELSEIF ( cloud_physics ) THEN
	712
	713	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	714	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
	715	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
	716	* ql(k+1,j,i) ) + 1E-30_wp )
	717	ELSE
	718	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	719	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
	720	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
	721	ENDIF
	722	!
	723	!-- Limit the value range of the Obukhov length.
	724	!-- This is necessary for very small velocities (u,v --> 0), because
	725	!-- the absolute value of ol can then become very small, which in
	726	!-- consequence would result in very large shear stresses and very
	727	!-- small momentum fluxes (both are generally unrealistic).
[1920]	728	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
	729	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
[1691]	730	ENDDO
	731	ENDDO
	732
	733	ENDIF
	734
	735	!
	736	!-- Values of ol at ghost point locations are needed for the evaluation
	737	!-- of usws and vsws.
	738	!$acc update host( ol )
	739	CALL exchange_horiz_2d( ol )
	740	!$acc update device( ol )
	741
	742	END SUBROUTINE calc_ol
	743
	744	!
	745	!-- Calculate friction velocity u*
	746	SUBROUTINE calc_us
	747
	748	IMPLICIT NONE
	749
[1697]	750	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	751	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
[1691]	752	DO i = nxlg, nxrg
	753	DO j = nysg, nyng
	754
	755	k = nzb_s_inner(j,i)+1
	756	z_mo = zu(k+1) - zw(k)
	757
	758	!
	759	!-- Compute u* at the scalars' grid points
	760	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
	761	- psi_m( z_mo / ol(j,i) ) &
	762	+ psi_m( z0(j,i) / ol(j,i) ) )
	763	ENDDO
	764	ENDDO
	765
	766	END SUBROUTINE calc_us
	767
	768	!
	769	!-- Calculate potential temperature and specific humidity at first grid level
	770	SUBROUTINE calc_pt_q
	771
	772	IMPLICIT NONE
	773
[1747]	774	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
[1691]	775	DO i = nxlg, nxrg
	776	DO j = nysg, nyng
	777	k = nzb_s_inner(j,i)+1
	778	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
	779	qv1(j,i) = q(k,j,i) - ql(k,j,i)
	780	ENDDO
	781	ENDDO
	782
	783	END SUBROUTINE calc_pt_q
	784
	785	!
	786	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
	787	SUBROUTINE calc_scaling_parameters
	788
	789	IMPLICIT NONE
	790
	791	!
	792	!-- Data information for accelerators
	793	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
	794	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
	795	!$acc present( vpt, vsws, zu, zw, z0, z0h )
	796	!
	797	!-- Compute theta*
	798	IF ( constant_heatflux ) THEN
	799
	800	!
	801	!-- For a given heat flux in the surface layer:
	802	!$OMP PARALLEL DO
[1747]	803	!$acc kernels loop private( j )
[1691]	804	DO i = nxlg, nxrg
	805	DO j = nysg, nyng
	806	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
	807	!
	808	!-- ts must be limited, because otherwise overflow may occur in case
	809	!-- of us=0 when computing ol further below
	810	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
	811	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
	812	ENDDO
	813	ENDDO
	814
	815	ELSE
	816	!
	817	!-- For a given surface temperature:
[1788]	818	IF ( large_scale_forcing .AND. lsf_surf ) THEN
[1691]	819	!$OMP PARALLEL DO
[1747]	820	!$acc kernels loop private( j, k )
[1691]	821	DO i = nxlg, nxrg
	822	DO j = nysg, nyng
	823	k = nzb_s_inner(j,i)
	824	pt(k,j,i) = pt_surface
	825	ENDDO
	826	ENDDO
	827	ENDIF
	828
[1697]	829	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	830	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
[1691]	831	DO i = nxlg, nxrg
	832	DO j = nysg, nyng
	833
	834	k = nzb_s_inner(j,i)
	835	z_mo = zu(k+1) - zw(k)
	836
	837	IF ( cloud_physics ) THEN
	838	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
	839	/ ( LOG( z_mo / z0h(j,i) ) &
	840	- psi_h( z_mo / ol(j,i) ) &
	841	+ psi_h( z0h(j,i) / ol(j,i) ) )
	842	ELSE
	843	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
	844	/ ( LOG( z_mo / z0h(j,i) ) &
	845	- psi_h( z_mo / ol(j,i) ) &
	846	+ psi_h( z0h(j,i) / ol(j,i) ) )
	847	ENDIF
	848
	849	ENDDO
	850	ENDDO
	851	ENDIF
	852
	853	!
	854	!-- If required compute q*
	855	IF ( humidity .OR. passive_scalar ) THEN
	856	IF ( constant_waterflux ) THEN
	857	!
[1788]	858	!-- For a given water flux in the surface layer
[1691]	859	!$OMP PARALLEL DO
[1747]	860	!$acc kernels loop private( j )
[1691]	861	DO i = nxlg, nxrg
	862	DO j = nysg, nyng
	863	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
	864	ENDDO
	865	ENDDO
	866
	867	ELSE
[1788]	868	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
[1691]	869	run_coupled )
	870
[1788]	871	IF ( large_scale_forcing .AND. lsf_surf ) THEN
[1691]	872	!$OMP PARALLEL DO
[1747]	873	!$acc kernels loop private( j, k )
[1691]	874	DO i = nxlg, nxrg
	875	DO j = nysg, nyng
	876	k = nzb_s_inner(j,i)
	877	q(k,j,i) = q_surface
	878	ENDDO
	879	ENDDO
	880	ENDIF
	881
[1697]	882	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
[1788]	883	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
[1691]	884	DO i = nxlg, nxrg
[1749]	885	!$acc loop independent
[1691]	886	DO j = nysg, nyng
	887
	888	k = nzb_s_inner(j,i)
	889	z_mo = zu(k+1) - zw(k)
	890
	891	!
	892	!-- Assume saturation for atmosphere coupled to ocean (but not
	893	!-- in case of precursor runs)
	894	IF ( coupled_run ) THEN
	895	e_s = 6.1_wp * &
	896	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
	897	- 273.15_wp ) )
	898	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
	899	ENDIF
	900
	901	IF ( cloud_physics ) THEN
	902	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
[1788]	903	/ ( LOG( z_mo / z0q(j,i) ) &
[1691]	904	- psi_h( z_mo / ol(j,i) ) &
[1788]	905	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	906
	907	ELSE
	908	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
[1788]	909	/ ( LOG( z_mo / z0q(j,i) ) &
[1691]	910	- psi_h( z_mo / ol(j,i) ) &
[1788]	911	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	912	ENDIF
	913
	914	ENDDO
	915	ENDDO
	916	ENDIF
	917	ENDIF
	918
	919
	920	!
	921	!-- If required compute qr* and nr*
[1822]	922	IF ( cloud_physics .AND. microphysics_seifert ) &
[1788]	923	THEN
[1691]	924
[1697]	925	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1788]	926	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
[1691]	927	DO i = nxlg, nxrg
[1749]	928	!$acc loop independent
[1691]	929	DO j = nysg, nyng
	930
	931	k = nzb_s_inner(j,i)
	932	z_mo = zu(k+1) - zw(k)
	933
[1749]	934	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
[1788]	935	/ ( LOG( z_mo / z0q(j,i) ) &
[1749]	936	- psi_h( z_mo / ol(j,i) ) &
[1788]	937	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	938
[1749]	939	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
[1788]	940	/ ( LOG( z_mo / z0q(j,i) ) &
[1749]	941	- psi_h( z_mo / ol(j,i) ) &
[1788]	942	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	943	ENDDO
	944	ENDDO
	945
	946	ENDIF
[1747]	947	!$acc end data
[1691]	948
	949	END SUBROUTINE calc_scaling_parameters
	950
	951
	952
	953	!
	954	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
	955	SUBROUTINE calc_surface_fluxes
	956
	957	IMPLICIT NONE
	958
	959	REAL(wp) :: ol_mid !< Grid-interpolated L
	960
	961	!
	962	!-- Compute u'w' for the total model domain.
	963	!-- First compute the corresponding component of u* and square it.
	964	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
[1749]	965	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
[1691]	966	DO i = nxl, nxr
	967	DO j = nys, nyn
	968
	969	k = nzb_u_inner(j,i)
	970	z_mo = zu(k+1) - zw(k)
	971	!
	972	!-- Compute bulk Obukhov length for this point
	973	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
	974
	975	IF ( ol_mid == 0.0_wp ) THEN
	976	ol_mid = MIN(ol(j,i-1), ol(j,i))
	977	ENDIF
	978
	979	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
	980	/ ( LOG( z_mo / z0(j,i) ) &
	981	- psi_m( z_mo / ol_mid ) &
	982	+ psi_m( z0(j,i) / ol_mid ) )
	983
	984	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	985	ENDDO
	986	ENDDO
	987
	988	!
	989	!-- Compute v'w' for the total model domain.
	990	!-- First compute the corresponding component of u* and square it.
	991	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
[1749]	992	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
[1691]	993	DO i = nxl, nxr
	994	DO j = nys, nyn
	995
	996	k = nzb_v_inner(j,i)
	997	z_mo = zu(k+1) - zw(k)
	998	!
	999	!-- Compute bulk Obukhov length for this point
	1000	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
	1001
	1002	IF ( ol_mid == 0.0_wp ) THEN
	1003	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
	1004	ENDIF
	1005
	1006	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
	1007	/ ( LOG( z_mo / z0(j,i) ) &
	1008	- psi_m( z_mo / ol_mid ) &
	1009	+ psi_m( z0(j,i) / ol_mid ) )
	1010
	1011	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	1012
	1013	ENDDO
	1014	ENDDO
	1015
	1016	!
	1017	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
[1749]	1018	!$acc update host( usws, vsws )
[1691]	1019	CALL exchange_horiz_2d( usws )
	1020	CALL exchange_horiz_2d( vsws )
	1021	!$acc update device( usws, vsws )
	1022
	1023	!
	1024	!-- Compute the vertical kinematic heat flux
[1788]	1025	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
	1026	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
[1691]	1027	!$OMP PARALLEL DO
[1747]	1028	!$acc kernels loop independent present( shf, ts, us )
[1691]	1029	DO i = nxlg, nxrg
	1030	!$acc loop independent
	1031	DO j = nysg, nyng
	1032	shf(j,i) = -ts(j,i) * us(j,i)
	1033	ENDDO
	1034	ENDDO
	1035
	1036	ENDIF
	1037
	1038	!
	1039	!-- Compute the vertical water/scalar flux
[1788]	1040	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. &
	1041	passive_scalar ) .AND. ( simulated_time <= skip_time_do_lsm &
	1042	.OR. .NOT. land_surface ) ) THEN
[1691]	1043	!$OMP PARALLEL DO
[1747]	1044	!$acc kernels loop independent present( qs, qsws, us )
[1691]	1045	DO i = nxlg, nxrg
	1046	!$acc loop independent
	1047	DO j = nysg, nyng
	1048	qsws(j,i) = -qs(j,i) * us(j,i)
	1049	ENDDO
	1050	ENDDO
	1051
	1052	ENDIF
	1053
	1054	!
	1055	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
[1822]	1056	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1691]	1057	!$OMP PARALLEL DO
[1747]	1058	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
[1691]	1059	DO i = nxlg, nxrg
	1060	!$acc loop independent
	1061	DO j = nysg, nyng
	1062	qrsws(j,i) = -qrs(j,i) * us(j,i)
	1063	nrsws(j,i) = -nrs(j,i) * us(j,i)
	1064	ENDDO
	1065	ENDDO
	1066	ENDIF
	1067
	1068	!
	1069	!-- Bottom boundary condition for the TKE
	1070	IF ( ibc_e_b == 2 ) THEN
	1071	!$OMP PARALLEL DO
[1747]	1072	!$acc kernels loop independent present( e, nzb_s_inner, us )
[1691]	1073	DO i = nxlg, nxrg
	1074	!$acc loop independent
	1075	DO j = nysg, nyng
[1757]	1076	k = nzb_s_inner(j,i)
	1077	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
[1691]	1078	!
	1079	!-- As a test: cm = 0.4
[1757]	1080	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
	1081	e(k,j,i) = e(k+1,j,i)
[1691]	1082	ENDDO
	1083	ENDDO
	1084	ENDIF
	1085
	1086	END SUBROUTINE calc_surface_fluxes
	1087
	1088
	1089	!
	1090	!-- Integrated stability function for momentum
	1091	FUNCTION psi_m( zeta )
	1092
	1093	USE kinds
	1094
	1095	IMPLICIT NONE
	1096
	1097	REAL(wp) :: psi_m !< Integrated similarity function result
	1098	REAL(wp) :: zeta !< Stability parameter z/L
	1099	REAL(wp) :: x !< dummy variable
	1100
	1101	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1102	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1103	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1104	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1105	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1106	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1107
	1108
	1109	IF ( zeta < 0.0_wp ) THEN
[1788]	1110	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
[1691]	1111	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
	1112	* ( 1.0_wp + x*2 ) 0.125_wp )
	1113	ELSE
	1114
	1115	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
	1116	- bc_d_d
	1117	!
	1118	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1119	!-- psi_m = - 5.0_wp * zeta
	1120
	1121	ENDIF
	1122
	1123	END FUNCTION psi_m
	1124
	1125
	1126	!
	1127	!-- Integrated stability function for heat and moisture
	1128	FUNCTION psi_h( zeta )
	1129
	1130	USE kinds
	1131
	1132	IMPLICIT NONE
	1133
	1134	REAL(wp) :: psi_h !< Integrated similarity function result
	1135	REAL(wp) :: zeta !< Stability parameter z/L
	1136	REAL(wp) :: x !< dummy variable
	1137
	1138	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1139	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1140	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1141	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1142	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1143	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1144
	1145
	1146	IF ( zeta < 0.0_wp ) THEN
[1788]	1147	x = SQRT( 1.0_wp - 16.0_wp * zeta )
[1691]	1148	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
	1149	ELSE
	1150	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
	1151	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
	1152	+ 1.0_wp
	1153	!
	1154	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1155	!-- psi_h = - 5.0_wp * zeta
	1156	ENDIF
	1157
	1158	END FUNCTION psi_h
	1159
[1697]	1160	END MODULE surface_layer_fluxes_mod

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