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source: palm/trunk/SOURCE/surface_layer_fluxes_mod.f90 @ 1936

Last change on this file since 1936 was 1930, 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	! ------------------
[1930]	21	!
[1758]	22	!
[1692]	23	! Former revisions:
	24	! -----------------
	25	! $Id: surface_layer_fluxes_mod.f90 1930 2016-06-09 16:32:12Z suehring $
	26	!
[1930]	27	! 1929 2016-06-09 16:25:25Z suehring
	28	! Bugfix: avoid segmentation fault in case one grid point is horizontally
	29	! completely surrounded by topography
	30	!
[1921]	31	! 1920 2016-05-30 10:50:15Z suehring
	32	! Avoid segmentation fault (see change in 1915) by different initialization of
	33	! us instead of adding a very small number in the denominator
	34	!
[1916]	35	! 1915 2016-05-27 11:05:02Z suehring
	36	! Bugfix: avoid segmentation fault in case of most_method = 'circular' at first
	37	! timestep
	38	!
[1851]	39	! 1850 2016-04-08 13:29:27Z maronga
	40	! Module renamed
	41	!
	42	!
[1823]	43	! 1822 2016-04-07 07:49:42Z hoffmann
	44	! icloud_scheme replaced by microphysics_*
	45	!
[1789]	46	! 1788 2016-03-10 11:01:04Z maronga
	47	! Added parameter z0q which replaces z0h in the similarity functions for
	48	! humidity.
	49	! Syntax layout improved.
	50	!
[1758]	51	! 1757 2016-02-22 15:49:32Z maronga
	52	! Minor fixes.
	53	!
[1750]	54	! 1749 2016-02-09 12:19:56Z raasch
	55	! further OpenACC adjustments
	56	!
[1748]	57	! 1747 2016-02-08 12:25:53Z raasch
	58	! adjustments for OpenACC usage
	59	!
[1710]	60	! 1709 2015-11-04 14:47:01Z maronga
	61	! Bugfix: division by zero could occur when calculating rib at low wind speeds
	62	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
	63	! neutral = .T.
	64	!
[1706]	65	! 1705 2015-11-02 14:28:56Z maronga
	66	! Typo removed
	67	!
[1698]	68	! 1697 2015-10-28 17:14:10Z raasch
	69	! FORTRAN and OpenMP errors removed
	70	!
[1697]	71	! 1696 2015-10-27 10:03:34Z maronga
[1691]	72	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
	73	! course of the re-writing two additional methods have been implemented. See
	74	! updated description.
	75	!
	76	! 1551 2015-03-03 14:18:16Z maronga
	77	! Removed land surface model part. The surface fluxes are now always calculated
	78	! within prandtl_fluxes, based on the given surface temperature/humidity (which
	79	! is either provided by the land surface model, by large scale forcing data, or
	80	! directly prescribed by the user.
	81	!
	82	! 1496 2014-12-02 17:25:50Z maronga
	83	! Adapted for land surface model
	84	!
	85	! 1494 2014-11-21 17:14:03Z maronga
	86	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
	87	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
	88	! topography for coupled runs (not tested)
	89	!
	90	! 1361 2014-04-16 15:17:48Z hoffmann
	91	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
	92	! drop concentration (nrsws) added
	93	!
	94	! 1340 2014-03-25 19:45:13Z kanani
	95	! REAL constants defined as wp-kind
	96	!
	97	! 1320 2014-03-20 08:40:49Z raasch
	98	! ONLY-attribute added to USE-statements,
	99	! kind-parameters added to all INTEGER and REAL declaration statements,
	100	! kinds are defined in new module kinds,
	101	! old module precision_kind is removed,
	102	! revision history before 2012 removed,
	103	! comment fields (!:) to be used for variable explanations added to
	104	! all variable declaration statements
	105	!
	106	! 1276 2014-01-15 13:40:41Z heinze
	107	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
	108	!
	109	! 1257 2013-11-08 15:18:40Z raasch
	110	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
	111	!
	112	! 1036 2012-10-22 13:43:42Z raasch
	113	! code put under GPL (PALM 3.9)
	114	!
	115	! 1015 2012-09-27 09:23:24Z raasch
	116	! OpenACC statements added
	117	!
	118	! 978 2012-08-09 08:28:32Z fricke
	119	! roughness length for scalar quantities z0h added
	120	!
	121	! Revision 1.1 1998/01/23 10:06:06 raasch
	122	! Initial revision
	123	!
	124	!
	125	! Description:
	126	! ------------
	127	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
	128	!> values of the variables at grid point k=1. Three different methods are
	129	!> available:
	130	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
	131	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
	132	!> slower
	133	!> 3) a method using a lookup table which is fast and accurate. Note, however,
	134	!> that this method cannot be used in case of roughness heterogeneity
	135	!>
	136	!> @todo (re)move large_scale_forcing actions
	137	!> @todo check/optimize OpenMP and OpenACC directives
	138	!------------------------------------------------------------------------------!
	139	MODULE surface_layer_fluxes_mod
	140
	141	USE arrays_3d, &
	142	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
[1788]	143	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h, z0q
[1691]	144
	145	USE cloud_parameters, &
	146	ONLY: l_d_cp, pt_d_t
	147
	148	USE constants, &
	149	ONLY: pi
	150
	151	USE cpulog
	152
	153	USE control_parameters, &
	154	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
[1822]	155	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, &
[1691]	156	initializing_actions, kappa, intermediate_timestep_count, &
	157	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
[1822]	158	message_string, microphysics_seifert, most_method, neutral, &
	159	passive_scalar, pt_surface, q_surface, run_coupled, &
[1691]	160	surface_pressure, simulated_time, terminate_run, zeta_max, &
	161	zeta_min
	162
	163	USE indices, &
	164	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
	165	nzb_u_inner, nzb_v_inner
	166
	167	USE kinds
	168
	169	USE pegrid
	170
	171	USE land_surface_model_mod, &
	172	ONLY: land_surface, skip_time_do_lsm
	173
	174	IMPLICIT NONE
	175
	176	INTEGER(iwp) :: i !< loop index x direction
	177	INTEGER(iwp) :: j !< loop index y direction
[1705]	178	INTEGER(iwp) :: k !< loop index z direction
[1691]	179
	180	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
	181
	182	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
	183
	184	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
	185	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
	186	uv_total !< Total velocity at first grid level
	187
	188	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
	189	ol_tab !< Lookup table values of L
	190
	191	REAL(wp) :: e_s, & !< Saturation water vapor pressure
	192	l_bnd = 7500, & !< Lookup table index of the last time step
	193	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
	194	rib_max, & !< Maximum Richardson number in lookup table
	195	rib_min, & !< Minimum Richardson number in lookup table
	196	z_mo !< Height of the constant flux layer where MOST is assumed
	197
	198
	199	SAVE
	200
	201	PRIVATE
	202
[1747]	203	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
[1691]	204
	205	INTERFACE init_surface_layer_fluxes
	206	MODULE PROCEDURE init_surface_layer_fluxes
	207	END INTERFACE init_surface_layer_fluxes
	208
	209	INTERFACE surface_layer_fluxes
	210	MODULE PROCEDURE surface_layer_fluxes
	211	END INTERFACE surface_layer_fluxes
	212
	213
	214	CONTAINS
	215
	216
	217	!------------------------------------------------------------------------------!
	218	! Description:
	219	! ------------
	220	!> Main routine to compute the surface fluxes
	221	!------------------------------------------------------------------------------!
	222	SUBROUTINE surface_layer_fluxes
	223
	224	IMPLICIT NONE
	225
	226	!
	227	!-- In case cloud physics is used, it is required to derive potential
	228	!-- temperature and specific humidity at first grid level from the fields pt
	229	!-- and q
	230	IF ( cloud_physics ) THEN
	231	CALL calc_pt_q
	232	ENDIF
	233
	234	!
	235	!-- First, calculate the new Obukhov length, then new friction velocity,
	236	!-- followed by the new scaling parameters (th, q, etc.), and the new
	237	!-- surface fluxes if required. The old routine ("circular") requires a
	238	!-- different order of calls as the scaling parameters from the previous time
	239	!-- steps are used to calculate the Obukhov length
	240
	241	!
	242	!-- Depending on setting of most_method use the "old" routine
	243	IF ( most_method == 'circular' ) THEN
	244
	245	CALL calc_scaling_parameters
	246
[1709]	247	CALL calc_uv_total
	248
[1691]	249	IF ( .NOT. neutral ) THEN
	250	CALL calc_ol
	251	ENDIF
	252
	253	CALL calc_us
	254
	255	CALL calc_surface_fluxes
	256
	257	!
	258	!-- Use either Newton iteration or a lookup table for the bulk Richardson
	259	!-- number to calculate the Obukhov length
[1788]	260	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
[1691]	261
[1709]	262	CALL calc_uv_total
	263
[1691]	264	IF ( .NOT. neutral ) THEN
	265	CALL calc_ol
	266	ENDIF
	267
	268	CALL calc_us
	269
	270	CALL calc_scaling_parameters
	271
	272	CALL calc_surface_fluxes
	273
	274	ENDIF
	275
	276	END SUBROUTINE surface_layer_fluxes
	277
	278
	279	!------------------------------------------------------------------------------!
	280	! Description:
	281	! ------------
	282	!> Initializing actions for the surface layer routine. Basically, this involves
	283	!> the preparation of a lookup table for the the bulk Richardson number vs
	284	!> Obukhov length L when using the lookup table method.
	285	!------------------------------------------------------------------------------!
	286	SUBROUTINE init_surface_layer_fluxes
	287
	288	IMPLICIT NONE
	289
	290	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
	291	num_steps_n !< Number of non-stretched zeta steps
	292
	293	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
	294
	295	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
	296
	297	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
	298
	299
	300	REAL(wp) :: zeta_step, & !< Increment of zeta
	301	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
	302	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
	303	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
	304	z0_min = 0.0_wp !< Minimum value of z0 to create table
	305	!
	306	!-- When cloud physics is used, arrays for storing potential temperature and
	307	!-- specific humidity at first grid level are required
	308	IF ( cloud_physics ) THEN
	309	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
	310	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
	311	ENDIF
	312
	313	!
	314	!-- Allocate field for storing the horizontal velocity
	315	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
	316
[1709]	317
	318	!
	319	!-- In case of runs with neutral statification, set Obukhov length to a
	320	!-- large value
	321	IF ( neutral ) ol = 1.0E10_wp
	322
[1691]	323	IF ( most_method == 'lookup' ) THEN
	324
	325	!
	326	!-- Check for roughness heterogeneity. In that case terminate run and
	327	!-- inform user
[1788]	328	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
[1691]	329	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
	330	terminate_run_l = .TRUE.
	331	ENDIF
	332
	333	#if defined( __parallel )
	334	!
	335	!-- Make a logical OR for all processes. Force termiation of model if result
	336	!-- is TRUE
	337	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	338	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
	339	MPI_LOR, comm2d, ierr )
	340	#else
	341	terminate_run = terminate_run_l
	342	#endif
	343
	344	IF ( terminate_run ) THEN
	345	message_string = 'most_method = "lookup" cannot be used in ' // &
	346	'combination with a prescribed roughness ' // &
	347	'heterogeneity'
	348	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
	349	ENDIF
	350
	351	ALLOCATE( zeta_tmp(0:num_steps-1) )
	352
	353	!
	354	!-- Use the lowest possible value for z_mo
	355	k = MINVAL(nzb_s_inner)
	356	z_mo = zu(k+1) - zw(k)
	357
	358	!
	359	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
	360	!-- available steps (num_steps). The calculation is done with negative
	361	!-- values of zeta in order to simplify the stretching in the free
	362	!-- convection limit for the remaining 10% of steps.
	363	zeta_tmp(0) = - zeta_max
	364	num_steps_n = ( num_steps * 9 / 10 ) - 1
	365	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
	366
	367	DO l = 1, num_steps_n
	368	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	369	ENDDO
	370
	371	!
	372	!-- Calculate stretching factor for the free convection range
[1788]	373	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
[1691]	374	regr_old = regr
	375	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
	376	)**( 10.0_wp / REAL(num_steps) )
	377	ENDDO
	378
	379	!
	380	!-- Calculate z/L range from zeta_min to zeta_stretch
	381	DO l = num_steps_n+1, num_steps-1
	382	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	383	zeta_step = zeta_step * regr
	384	ENDDO
	385
	386	!
[1757]	387	!-- Save roughness lengths to temporary variables
	388	z0h_min = z0h(nys,nxl)
	389	z0_min = z0(nys,nxl)
[1691]	390
	391	!
	392	!-- Calculate lookup table for the Richardson number versus Obukhov length
	393	!-- The Richardson number (rib) is defined depending on the choice of
	394	!-- boundary conditions for temperature
	395	IF ( ibc_pt_b == 1 ) THEN
	396	DO l = 0, num_steps-1
	397	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	398	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
	399	- psi_m( z_mo / ol_tab(l) ) &
	400	+ psi_m( z0_min / ol_tab(l) ) &
	401	)**3
	402	ENDDO
	403	ELSE
	404	DO l = 0, num_steps-1
	405	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	406	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
	407	- psi_h( z_mo / ol_tab(l) ) &
	408	+ psi_h( z0h_min / ol_tab(l) ) &
	409	) &
	410	/ ( LOG( z_mo / z0_min ) &
	411	- psi_m( z_mo / ol_tab(l) ) &
	412	+ psi_m( z0_min / ol_tab(l) ) &
	413	)**2
	414	ENDDO
	415	ENDIF
	416
	417	!
	418	!-- Determine minimum values of rib in the lookup table. Set upper limit
	419	!-- to critical Richardson number (0.25)
	420	rib_min = MINVAL(rib_tab)
	421	rib_max = 0.25 !MAXVAL(rib_tab)
	422
	423	DEALLOCATE( zeta_tmp )
	424	ENDIF
	425
	426	END SUBROUTINE init_surface_layer_fluxes
	427
	428
	429	!------------------------------------------------------------------------------!
	430	! Description:
	431	! ------------
[1709]	432	!> Compute the absolute value of the horizontal velocity (relative to the
	433	!> surface). This is required by all methods
[1691]	434	!------------------------------------------------------------------------------!
[1709]	435	SUBROUTINE calc_uv_total
[1691]	436
	437	IMPLICIT NONE
	438
	439
[1747]	440	!$OMP PARALLEL DO PRIVATE( k )
	441	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
[1691]	442	DO i = nxl, nxr
	443	DO j = nys, nyn
	444
	445	k = nzb_s_inner(j,i)
	446	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
	447	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
	448	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
	449	- v(k,j,i) - v(k,j+1,i) ) )**2 )
	450
	451	!
	452	!-- For too small values of the local wind, MOST does not work. A
	453	!-- threshold value is thus set if required
	454	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
	455
	456	ENDDO
	457	ENDDO
	458
	459	!
	460	!-- Values of uv_total need to be exchanged at the ghost boundaries
	461	!$acc update host( uv_total )
	462	CALL exchange_horiz_2d( uv_total )
	463	!$acc update device( uv_total )
	464
[1709]	465	END SUBROUTINE calc_uv_total
	466
	467
	468	!------------------------------------------------------------------------------!
	469	! Description:
	470	! ------------
	471	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
	472	!------------------------------------------------------------------------------!
	473	SUBROUTINE calc_ol
	474
	475	IMPLICIT NONE
	476
	477	INTEGER(iwp) :: iter, & !< Newton iteration step
	478	l !< look index
	479
	480	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
	481
	482	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
	483	f_d_ol, & !< Derivative of f
	484	ol_l, & !< Lower bound of L for Newton iteration
	485	ol_m, & !< Previous value of L for Newton iteration
	486	ol_old, & !< Previous time step value of L
	487	ol_u !< Upper bound of L for Newton iteration
	488
[1691]	489	IF ( TRIM( most_method ) /= 'circular' ) THEN
	490
[1747]	491	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
	492
[1691]	493	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1747]	494	!$acc kernels loop private( j, k, z_mo )
[1691]	495	DO i = nxl, nxr
	496	DO j = nys, nyn
	497
	498	k = nzb_s_inner(j,i)
	499	z_mo = zu(k+1) - zw(k)
	500
	501	!
	502	!-- Evaluate bulk Richardson number (calculation depends on
	503	!-- definition based on setting of boundary conditions
	504	IF ( ibc_pt_b /= 1 ) THEN
	505	IF ( humidity ) THEN
	506	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
[1709]	507	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
[1691]	508	ELSE
	509	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
[1709]	510	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
[1691]	511	ENDIF
	512	ELSE
	513	!
	514	!-- When using Neumann boundary conditions, the buoyancy flux
	515	!-- is required but cannot be calculated at the surface, as pt
	516	!-- and q are not known at the surface. Hence the values at
	517	!-- first grid level are used to estimate the buoyancy flux
	518	IF ( humidity ) THEN
	519	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
	520	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
	521	* pt(k+1,j,i) * qsws(j,i) ) &
[1709]	522	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
	523	+ 1.0E-20_wp)
[1691]	524	ELSE
	525	rib(j,i) = - g * z_mo * shf(j,i) &
[1709]	526	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
	527	+ 1.0E-20_wp )
[1691]	528	ENDIF
	529	ENDIF
	530
	531	ENDDO
	532	ENDDO
[1747]	533	!$acc end data
[1691]	534
	535	ENDIF
	536
	537	!
	538	!-- Calculate the Obukhov length either using a Newton iteration
	539	!-- method, via a lookup table, or using the old circular way
	540	IF ( TRIM( most_method ) == 'newton' ) THEN
	541
	542	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	543	!# WARNING: does not work on GPU so far because of DO-loop with
	544	!# undetermined iterations
[1747]	545	!!!!!!$acc kernels loop
[1691]	546	DO i = nxl, nxr
	547	DO j = nys, nyn
	548
	549	k = nzb_s_inner(j,i)
	550	z_mo = zu(k+1) - zw(k)
	551
	552	!
	553	!-- Store current value in case the Newton iteration fails
	554	ol_old = ol(j,i)
	555
	556	!
	557	!-- Ensure that the bulk Richardson number and the Obukhov
	558	!-- lengtH have the same sign
[1788]	559	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
[1691]	560	ABS( ol(j,i) ) == ol_max ) THEN
	561	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
	562	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
	563	ENDIF
	564	!
	565	!-- Iteration to find Obukhov length
	566	iter = 0
	567	DO
	568	iter = iter + 1
	569	!
	570	!-- In case of divergence, use the value of the previous time step
	571	IF ( iter > 1000 ) THEN
	572	ol(j,i) = ol_old
	573	EXIT
	574	ENDIF
	575
	576	ol_m = ol(j,i)
	577	ol_l = ol_m - 0.001_wp * ol_m
	578	ol_u = ol_m + 0.001_wp * ol_m
	579
	580
	581	IF ( ibc_pt_b /= 1 ) THEN
	582	!
	583	!-- Calculate f = Ri - [...]/[...]^2 = 0
	584	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
	585	- psi_h( z_mo / ol_m ) &
	586	+ psi_h( z0h(j,i) / ol_m ) &
	587	) &
	588	/ ( LOG( z_mo / z0(j,i) ) &
	589	- psi_m( z_mo / ol_m ) &
	590	+ psi_m( z0(j,i) / ol_m ) &
	591	)**2
	592
	593	!
	594	!-- Calculate df/dL
	595	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
	596	- psi_h( z_mo / ol_u ) &
	597	+ psi_h( z0h(j,i) / ol_u ) &
	598	) &
	599	/ ( LOG( z_mo / z0(j,i) ) &
	600	- psi_m( z_mo / ol_u ) &
	601	+ psi_m( z0(j,i) / ol_u ) &
	602	)**2 &
	603	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
	604	- psi_h( z_mo / ol_l ) &
	605	+ psi_h( z0h(j,i) / ol_l ) &
	606	) &
	607	/ ( LOG( z_mo / z0(j,i) ) &
	608	- psi_m( z_mo / ol_l ) &
	609	+ psi_m( z0(j,i) / ol_l ) &
	610	)**2 &
	611	) / ( ol_u - ol_l )
	612	ELSE
	613	!
	614	!-- Calculate f = Ri - 1 /[...]^3 = 0
	615	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
	616	- psi_m( z_mo / ol_m ) &
	617	+ psi_m( z0(j,i) / ol_m ) &
	618	)**3
	619
	620	!
	621	!-- Calculate df/dL
	622	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
	623	- psi_m( z_mo / ol_u ) &
	624	+ psi_m( z0(j,i) / ol_u ) &
	625	)**3 &
	626	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
	627	- psi_m( z_mo / ol_l ) &
	628	+ psi_m( z0(j,i) / ol_l ) &
	629	)**3 &
	630	) / ( ol_u - ol_l )
	631	ENDIF
	632	!
	633	!-- Calculate new L
	634	ol(j,i) = ol_m - f / f_d_ol
	635
	636	!
	637	!-- Ensure that the bulk Richardson number and the Obukhov
	638	!-- length have the same sign and ensure convergence.
	639	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
	640
	641	!
	642	!-- If unrealistic value occurs, set L to the maximum
	643	!-- value that is allowed
	644	IF ( ABS( ol(j,i) ) > ol_max ) THEN
	645	ol(j,i) = ol_max
	646	EXIT
	647	ENDIF
	648	!
	649	!-- Check for convergence
	650	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
	651	EXIT
	652	ELSE
	653	CYCLE
	654	ENDIF
	655
	656	ENDDO
	657
	658	ENDDO
	659	ENDDO
	660
	661	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
	662
	663	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1788]	664	!# WARNING: does not work on GPU so far because of DO WHILE construct
[1747]	665	!!!!!!$acc kernels loop
[1691]	666	DO i = nxl, nxr
	667	DO j = nys, nyn
	668
	669	!
	670	!-- If the bulk Richardson number is outside the range of the lookup
	671	!-- table, set it to the exceeding threshold value
	672	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
	673	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
	674
	675	!
	676	!-- Find the correct index bounds for linear interpolation. As the
	677	!-- Richardson number will not differ very much from time step to
	678	!-- time step , use the index from the last step and search in the
	679	!-- correct direction
	680	l = l_bnd
	681	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
[1788]	682	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
[1691]	683	l = l-1
	684	ENDDO
	685	ELSE
[1788]	686	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
	687	.AND. l < num_steps-1 )
[1691]	688	l = l+1
	689	ENDDO
	690	ENDIF
	691	l_bnd = l
	692
	693	!
	694	!-- Linear interpolation to find the correct value of z/L
[1788]	695	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
	696	/ ( rib_tab(l) - rib_tab(l-1) ) &
[1691]	697	* ( rib(j,i) - rib_tab(l-1) ) )
	698
	699	ENDDO
	700	ENDDO
	701
	702	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
	703
	704	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1747]	705	!$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]	706	DO i = nxl, nxr
	707	DO j = nys, nyn
	708
	709	k = nzb_s_inner(j,i)
	710	z_mo = zu(k+1) - zw(k)
	711
	712	IF ( .NOT. humidity ) THEN
	713	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	714	* ts(j,i) + 1E-30_wp )
	715	ELSEIF ( cloud_physics ) THEN
	716
	717	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	718	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
	719	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
	720	* ql(k+1,j,i) ) + 1E-30_wp )
	721	ELSE
	722	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	723	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
	724	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
	725	ENDIF
	726	!
	727	!-- Limit the value range of the Obukhov length.
	728	!-- This is necessary for very small velocities (u,v --> 0), because
	729	!-- the absolute value of ol can then become very small, which in
	730	!-- consequence would result in very large shear stresses and very
	731	!-- small momentum fluxes (both are generally unrealistic).
[1929]	732	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) < zeta_min ) &
	733	ol(j,i) = z_mo / zeta_min
	734	IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) > zeta_max ) &
	735	ol(j,i) = z_mo / zeta_max
[1691]	736	ENDDO
	737	ENDDO
	738
	739	ENDIF
	740
	741	!
	742	!-- Values of ol at ghost point locations are needed for the evaluation
	743	!-- of usws and vsws.
	744	!$acc update host( ol )
	745	CALL exchange_horiz_2d( ol )
	746	!$acc update device( ol )
	747
	748	END SUBROUTINE calc_ol
	749
	750	!
	751	!-- Calculate friction velocity u*
	752	SUBROUTINE calc_us
	753
	754	IMPLICIT NONE
	755
[1697]	756	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	757	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
[1691]	758	DO i = nxlg, nxrg
	759	DO j = nysg, nyng
	760
	761	k = nzb_s_inner(j,i)+1
	762	z_mo = zu(k+1) - zw(k)
	763
	764	!
	765	!-- Compute u* at the scalars' grid points
	766	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
	767	- psi_m( z_mo / ol(j,i) ) &
	768	+ psi_m( z0(j,i) / ol(j,i) ) )
	769	ENDDO
	770	ENDDO
	771
	772	END SUBROUTINE calc_us
	773
	774	!
	775	!-- Calculate potential temperature and specific humidity at first grid level
	776	SUBROUTINE calc_pt_q
	777
	778	IMPLICIT NONE
	779
[1747]	780	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
[1691]	781	DO i = nxlg, nxrg
	782	DO j = nysg, nyng
	783	k = nzb_s_inner(j,i)+1
	784	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
	785	qv1(j,i) = q(k,j,i) - ql(k,j,i)
	786	ENDDO
	787	ENDDO
	788
	789	END SUBROUTINE calc_pt_q
	790
	791	!
	792	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
	793	SUBROUTINE calc_scaling_parameters
	794
	795	IMPLICIT NONE
	796
	797	!
	798	!-- Data information for accelerators
	799	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
	800	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
	801	!$acc present( vpt, vsws, zu, zw, z0, z0h )
	802	!
	803	!-- Compute theta*
	804	IF ( constant_heatflux ) THEN
	805
	806	!
	807	!-- For a given heat flux in the surface layer:
	808	!$OMP PARALLEL DO
[1747]	809	!$acc kernels loop private( j )
[1691]	810	DO i = nxlg, nxrg
	811	DO j = nysg, nyng
	812	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
	813	!
	814	!-- ts must be limited, because otherwise overflow may occur in case
	815	!-- of us=0 when computing ol further below
	816	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
	817	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
	818	ENDDO
	819	ENDDO
	820
	821	ELSE
	822	!
	823	!-- For a given surface temperature:
[1788]	824	IF ( large_scale_forcing .AND. lsf_surf ) THEN
[1691]	825	!$OMP PARALLEL DO
[1747]	826	!$acc kernels loop private( j, k )
[1691]	827	DO i = nxlg, nxrg
	828	DO j = nysg, nyng
	829	k = nzb_s_inner(j,i)
	830	pt(k,j,i) = pt_surface
	831	ENDDO
	832	ENDDO
	833	ENDIF
	834
[1697]	835	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	836	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
[1691]	837	DO i = nxlg, nxrg
	838	DO j = nysg, nyng
	839
	840	k = nzb_s_inner(j,i)
	841	z_mo = zu(k+1) - zw(k)
	842
	843	IF ( cloud_physics ) THEN
	844	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
	845	/ ( LOG( z_mo / z0h(j,i) ) &
	846	- psi_h( z_mo / ol(j,i) ) &
	847	+ psi_h( z0h(j,i) / ol(j,i) ) )
	848	ELSE
	849	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
	850	/ ( LOG( z_mo / z0h(j,i) ) &
	851	- psi_h( z_mo / ol(j,i) ) &
	852	+ psi_h( z0h(j,i) / ol(j,i) ) )
	853	ENDIF
	854
	855	ENDDO
	856	ENDDO
	857	ENDIF
	858
	859	!
	860	!-- If required compute q*
	861	IF ( humidity .OR. passive_scalar ) THEN
	862	IF ( constant_waterflux ) THEN
	863	!
[1788]	864	!-- For a given water flux in the surface layer
[1691]	865	!$OMP PARALLEL DO
[1747]	866	!$acc kernels loop private( j )
[1691]	867	DO i = nxlg, nxrg
	868	DO j = nysg, nyng
	869	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
	870	ENDDO
	871	ENDDO
	872
	873	ELSE
[1788]	874	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
[1691]	875	run_coupled )
	876
[1788]	877	IF ( large_scale_forcing .AND. lsf_surf ) THEN
[1691]	878	!$OMP PARALLEL DO
[1747]	879	!$acc kernels loop private( j, k )
[1691]	880	DO i = nxlg, nxrg
	881	DO j = nysg, nyng
	882	k = nzb_s_inner(j,i)
	883	q(k,j,i) = q_surface
	884	ENDDO
	885	ENDDO
	886	ENDIF
	887
[1697]	888	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
[1788]	889	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
[1691]	890	DO i = nxlg, nxrg
[1749]	891	!$acc loop independent
[1691]	892	DO j = nysg, nyng
	893
	894	k = nzb_s_inner(j,i)
	895	z_mo = zu(k+1) - zw(k)
	896
	897	!
	898	!-- Assume saturation for atmosphere coupled to ocean (but not
	899	!-- in case of precursor runs)
	900	IF ( coupled_run ) THEN
	901	e_s = 6.1_wp * &
	902	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
	903	- 273.15_wp ) )
	904	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
	905	ENDIF
	906
	907	IF ( cloud_physics ) THEN
	908	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
[1788]	909	/ ( LOG( z_mo / z0q(j,i) ) &
[1691]	910	- psi_h( z_mo / ol(j,i) ) &
[1788]	911	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	912
	913	ELSE
	914	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
[1788]	915	/ ( LOG( z_mo / z0q(j,i) ) &
[1691]	916	- psi_h( z_mo / ol(j,i) ) &
[1788]	917	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	918	ENDIF
	919
	920	ENDDO
	921	ENDDO
	922	ENDIF
	923	ENDIF
	924
	925
	926	!
	927	!-- If required compute qr* and nr*
[1822]	928	IF ( cloud_physics .AND. microphysics_seifert ) &
[1788]	929	THEN
[1691]	930
[1697]	931	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1788]	932	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
[1691]	933	DO i = nxlg, nxrg
[1749]	934	!$acc loop independent
[1691]	935	DO j = nysg, nyng
	936
	937	k = nzb_s_inner(j,i)
	938	z_mo = zu(k+1) - zw(k)
	939
[1749]	940	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
[1788]	941	/ ( LOG( z_mo / z0q(j,i) ) &
[1749]	942	- psi_h( z_mo / ol(j,i) ) &
[1788]	943	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	944
[1749]	945	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
[1788]	946	/ ( LOG( z_mo / z0q(j,i) ) &
[1749]	947	- psi_h( z_mo / ol(j,i) ) &
[1788]	948	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	949	ENDDO
	950	ENDDO
	951
	952	ENDIF
[1747]	953	!$acc end data
[1691]	954
	955	END SUBROUTINE calc_scaling_parameters
	956
	957
	958
	959	!
	960	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
	961	SUBROUTINE calc_surface_fluxes
	962
	963	IMPLICIT NONE
	964
	965	REAL(wp) :: ol_mid !< Grid-interpolated L
	966
	967	!
	968	!-- Compute u'w' for the total model domain.
	969	!-- First compute the corresponding component of u* and square it.
	970	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
[1749]	971	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
[1691]	972	DO i = nxl, nxr
	973	DO j = nys, nyn
	974
	975	k = nzb_u_inner(j,i)
	976	z_mo = zu(k+1) - zw(k)
	977	!
	978	!-- Compute bulk Obukhov length for this point
	979	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
	980
	981	IF ( ol_mid == 0.0_wp ) THEN
	982	ol_mid = MIN(ol(j,i-1), ol(j,i))
	983	ENDIF
	984
	985	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
	986	/ ( LOG( z_mo / z0(j,i) ) &
	987	- psi_m( z_mo / ol_mid ) &
	988	+ psi_m( z0(j,i) / ol_mid ) )
	989
	990	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	991	ENDDO
	992	ENDDO
	993
	994	!
	995	!-- Compute v'w' for the total model domain.
	996	!-- First compute the corresponding component of u* and square it.
	997	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
[1749]	998	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
[1691]	999	DO i = nxl, nxr
	1000	DO j = nys, nyn
	1001
	1002	k = nzb_v_inner(j,i)
	1003	z_mo = zu(k+1) - zw(k)
	1004	!
	1005	!-- Compute bulk Obukhov length for this point
	1006	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
	1007
	1008	IF ( ol_mid == 0.0_wp ) THEN
	1009	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
	1010	ENDIF
	1011
	1012	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
	1013	/ ( LOG( z_mo / z0(j,i) ) &
	1014	- psi_m( z_mo / ol_mid ) &
	1015	+ psi_m( z0(j,i) / ol_mid ) )
	1016
	1017	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	1018
	1019	ENDDO
	1020	ENDDO
	1021
	1022	!
	1023	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
[1749]	1024	!$acc update host( usws, vsws )
[1691]	1025	CALL exchange_horiz_2d( usws )
	1026	CALL exchange_horiz_2d( vsws )
	1027	!$acc update device( usws, vsws )
	1028
	1029	!
	1030	!-- Compute the vertical kinematic heat flux
[1788]	1031	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
	1032	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
[1691]	1033	!$OMP PARALLEL DO
[1747]	1034	!$acc kernels loop independent present( shf, ts, us )
[1691]	1035	DO i = nxlg, nxrg
	1036	!$acc loop independent
	1037	DO j = nysg, nyng
	1038	shf(j,i) = -ts(j,i) * us(j,i)
	1039	ENDDO
	1040	ENDDO
	1041
	1042	ENDIF
	1043
	1044	!
	1045	!-- Compute the vertical water/scalar flux
[1788]	1046	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. &
	1047	passive_scalar ) .AND. ( simulated_time <= skip_time_do_lsm &
	1048	.OR. .NOT. land_surface ) ) THEN
[1691]	1049	!$OMP PARALLEL DO
[1747]	1050	!$acc kernels loop independent present( qs, qsws, us )
[1691]	1051	DO i = nxlg, nxrg
	1052	!$acc loop independent
	1053	DO j = nysg, nyng
	1054	qsws(j,i) = -qs(j,i) * us(j,i)
	1055	ENDDO
	1056	ENDDO
	1057
	1058	ENDIF
	1059
	1060	!
	1061	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
[1822]	1062	IF ( cloud_physics .AND. microphysics_seifert ) THEN
[1691]	1063	!$OMP PARALLEL DO
[1747]	1064	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
[1691]	1065	DO i = nxlg, nxrg
	1066	!$acc loop independent
	1067	DO j = nysg, nyng
	1068	qrsws(j,i) = -qrs(j,i) * us(j,i)
	1069	nrsws(j,i) = -nrs(j,i) * us(j,i)
	1070	ENDDO
	1071	ENDDO
	1072	ENDIF
	1073
	1074	!
	1075	!-- Bottom boundary condition for the TKE
	1076	IF ( ibc_e_b == 2 ) THEN
	1077	!$OMP PARALLEL DO
[1747]	1078	!$acc kernels loop independent present( e, nzb_s_inner, us )
[1691]	1079	DO i = nxlg, nxrg
	1080	!$acc loop independent
	1081	DO j = nysg, nyng
[1757]	1082	k = nzb_s_inner(j,i)
	1083	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
[1691]	1084	!
	1085	!-- As a test: cm = 0.4
[1757]	1086	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
	1087	e(k,j,i) = e(k+1,j,i)
[1691]	1088	ENDDO
	1089	ENDDO
	1090	ENDIF
	1091
	1092	END SUBROUTINE calc_surface_fluxes
	1093
	1094
	1095	!
	1096	!-- Integrated stability function for momentum
	1097	FUNCTION psi_m( zeta )
	1098
	1099	USE kinds
	1100
	1101	IMPLICIT NONE
	1102
	1103	REAL(wp) :: psi_m !< Integrated similarity function result
	1104	REAL(wp) :: zeta !< Stability parameter z/L
	1105	REAL(wp) :: x !< dummy variable
	1106
	1107	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1108	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1109	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1110	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1111	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1112	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1113
	1114
	1115	IF ( zeta < 0.0_wp ) THEN
[1788]	1116	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
[1691]	1117	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
	1118	* ( 1.0_wp + x*2 ) 0.125_wp )
	1119	ELSE
	1120
	1121	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
	1122	- bc_d_d
	1123	!
	1124	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1125	!-- psi_m = - 5.0_wp * zeta
	1126
	1127	ENDIF
	1128
	1129	END FUNCTION psi_m
	1130
	1131
	1132	!
	1133	!-- Integrated stability function for heat and moisture
	1134	FUNCTION psi_h( zeta )
	1135
	1136	USE kinds
	1137
	1138	IMPLICIT NONE
	1139
	1140	REAL(wp) :: psi_h !< Integrated similarity function result
	1141	REAL(wp) :: zeta !< Stability parameter z/L
	1142	REAL(wp) :: x !< dummy variable
	1143
	1144	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1145	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1146	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1147	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1148	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1149	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1150
	1151
	1152	IF ( zeta < 0.0_wp ) THEN
[1788]	1153	x = SQRT( 1.0_wp - 16.0_wp * zeta )
[1691]	1154	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
	1155	ELSE
	1156	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
	1157	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
	1158	+ 1.0_wp
	1159	!
	1160	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1161	!-- psi_h = - 5.0_wp * zeta
	1162	ENDIF
	1163
	1164	END FUNCTION psi_h
	1165
[1697]	1166	END MODULE surface_layer_fluxes_mod

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