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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1754

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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	! ------------------
[1750]	21	!
[1748]	22	!
[1692]	23	! Former revisions:
	24	! -----------------
	25	! $Id: surface_layer_fluxes.f90 1750 2016-02-09 12:24:00Z maronga $
	26	!
[1750]	27	! 1749 2016-02-09 12:19:56Z raasch
	28	! further OpenACC adjustments
	29	!
[1748]	30	! 1747 2016-02-08 12:25:53Z raasch
	31	! adjustments for OpenACC usage
	32	!
[1710]	33	! 1709 2015-11-04 14:47:01Z maronga
	34	! Bugfix: division by zero could occur when calculating rib at low wind speeds
	35	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
	36	! neutral = .T.
	37	!
[1706]	38	! 1705 2015-11-02 14:28:56Z maronga
	39	! Typo removed
	40	!
[1698]	41	! 1697 2015-10-28 17:14:10Z raasch
	42	! FORTRAN and OpenMP errors removed
	43	!
[1697]	44	! 1696 2015-10-27 10:03:34Z maronga
[1691]	45	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
	46	! course of the re-writing two additional methods have been implemented. See
	47	! updated description.
	48	!
	49	! 1551 2015-03-03 14:18:16Z maronga
	50	! Removed land surface model part. The surface fluxes are now always calculated
	51	! within prandtl_fluxes, based on the given surface temperature/humidity (which
	52	! is either provided by the land surface model, by large scale forcing data, or
	53	! directly prescribed by the user.
	54	!
	55	! 1496 2014-12-02 17:25:50Z maronga
	56	! Adapted for land surface model
	57	!
	58	! 1494 2014-11-21 17:14:03Z maronga
	59	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
	60	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
	61	! topography for coupled runs (not tested)
	62	!
	63	! 1361 2014-04-16 15:17:48Z hoffmann
	64	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
	65	! drop concentration (nrsws) added
	66	!
	67	! 1340 2014-03-25 19:45:13Z kanani
	68	! REAL constants defined as wp-kind
	69	!
	70	! 1320 2014-03-20 08:40:49Z raasch
	71	! ONLY-attribute added to USE-statements,
	72	! kind-parameters added to all INTEGER and REAL declaration statements,
	73	! kinds are defined in new module kinds,
	74	! old module precision_kind is removed,
	75	! revision history before 2012 removed,
	76	! comment fields (!:) to be used for variable explanations added to
	77	! all variable declaration statements
	78	!
	79	! 1276 2014-01-15 13:40:41Z heinze
	80	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
	81	!
	82	! 1257 2013-11-08 15:18:40Z raasch
	83	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
	84	!
	85	! 1036 2012-10-22 13:43:42Z raasch
	86	! code put under GPL (PALM 3.9)
	87	!
	88	! 1015 2012-09-27 09:23:24Z raasch
	89	! OpenACC statements added
	90	!
	91	! 978 2012-08-09 08:28:32Z fricke
	92	! roughness length for scalar quantities z0h added
	93	!
	94	! Revision 1.1 1998/01/23 10:06:06 raasch
	95	! Initial revision
	96	!
	97	!
	98	! Description:
	99	! ------------
	100	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
	101	!> values of the variables at grid point k=1. Three different methods are
	102	!> available:
	103	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
	104	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
	105	!> slower
	106	!> 3) a method using a lookup table which is fast and accurate. Note, however,
	107	!> that this method cannot be used in case of roughness heterogeneity
	108	!>
	109	!> @todo (re)move large_scale_forcing actions
	110	!> @todo check/optimize OpenMP and OpenACC directives
	111	!------------------------------------------------------------------------------!
	112	MODULE surface_layer_fluxes_mod
	113
	114	USE arrays_3d, &
	115	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
	116	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h
	117
	118	USE cloud_parameters, &
	119	ONLY: l_d_cp, pt_d_t
	120
	121	USE constants, &
	122	ONLY: pi
	123
	124	USE cpulog
	125
	126	USE control_parameters, &
	127	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
	128	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, icloud_scheme, &
	129	initializing_actions, kappa, intermediate_timestep_count, &
	130	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
	131	message_string, most_method, neutral, passive_scalar, &
	132	precipitation, pt_surface, q_surface, run_coupled, &
	133	surface_pressure, simulated_time, terminate_run, zeta_max, &
	134	zeta_min
	135
	136	USE indices, &
	137	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
	138	nzb_u_inner, nzb_v_inner
	139
	140	USE kinds
	141
	142	USE pegrid
	143
	144	USE land_surface_model_mod, &
	145	ONLY: land_surface, skip_time_do_lsm
	146
	147	IMPLICIT NONE
	148
	149	INTEGER(iwp) :: i !< loop index x direction
	150	INTEGER(iwp) :: j !< loop index y direction
[1705]	151	INTEGER(iwp) :: k !< loop index z direction
[1691]	152
	153	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
	154
	155	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
	156
	157	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
	158	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
	159	uv_total !< Total velocity at first grid level
	160
	161	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
	162	ol_tab !< Lookup table values of L
	163
	164	REAL(wp) :: e_s, & !< Saturation water vapor pressure
	165	l_bnd = 7500, & !< Lookup table index of the last time step
	166	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
	167	rib_max, & !< Maximum Richardson number in lookup table
	168	rib_min, & !< Minimum Richardson number in lookup table
	169	z_mo !< Height of the constant flux layer where MOST is assumed
	170
	171
	172	SAVE
	173
	174	PRIVATE
	175
[1747]	176	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
[1691]	177
	178	INTERFACE init_surface_layer_fluxes
	179	MODULE PROCEDURE init_surface_layer_fluxes
	180	END INTERFACE init_surface_layer_fluxes
	181
	182	INTERFACE surface_layer_fluxes
	183	MODULE PROCEDURE surface_layer_fluxes
	184	END INTERFACE surface_layer_fluxes
	185
	186
	187	CONTAINS
	188
	189
	190	!------------------------------------------------------------------------------!
	191	! Description:
	192	! ------------
	193	!> Main routine to compute the surface fluxes
	194	!------------------------------------------------------------------------------!
	195	SUBROUTINE surface_layer_fluxes
	196
	197	IMPLICIT NONE
	198
	199	!
	200	!-- In case cloud physics is used, it is required to derive potential
	201	!-- temperature and specific humidity at first grid level from the fields pt
	202	!-- and q
	203	IF ( cloud_physics ) THEN
	204	CALL calc_pt_q
	205	ENDIF
	206
	207	!
	208	!-- First, calculate the new Obukhov length, then new friction velocity,
	209	!-- followed by the new scaling parameters (th, q, etc.), and the new
	210	!-- surface fluxes if required. The old routine ("circular") requires a
	211	!-- different order of calls as the scaling parameters from the previous time
	212	!-- steps are used to calculate the Obukhov length
	213
	214	!
	215	!-- Depending on setting of most_method use the "old" routine
	216	IF ( most_method == 'circular' ) THEN
	217
	218	CALL calc_scaling_parameters
	219
[1709]	220	CALL calc_uv_total
	221
[1691]	222	IF ( .NOT. neutral ) THEN
	223	CALL calc_ol
	224	ENDIF
	225
	226	CALL calc_us
	227
	228	CALL calc_surface_fluxes
	229
	230	!
	231	!-- Use either Newton iteration or a lookup table for the bulk Richardson
	232	!-- number to calculate the Obukhov length
	233	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
	234
[1709]	235	CALL calc_uv_total
	236
[1691]	237	IF ( .NOT. neutral ) THEN
	238	CALL calc_ol
	239	ENDIF
	240
	241	CALL calc_us
	242
	243	CALL calc_scaling_parameters
	244
	245	CALL calc_surface_fluxes
	246
	247	ENDIF
	248
	249	END SUBROUTINE surface_layer_fluxes
	250
	251
	252	!------------------------------------------------------------------------------!
	253	! Description:
	254	! ------------
	255	!> Initializing actions for the surface layer routine. Basically, this involves
	256	!> the preparation of a lookup table for the the bulk Richardson number vs
	257	!> Obukhov length L when using the lookup table method.
	258	!------------------------------------------------------------------------------!
	259	SUBROUTINE init_surface_layer_fluxes
	260
	261	IMPLICIT NONE
	262
	263	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
	264	num_steps_n !< Number of non-stretched zeta steps
	265
	266	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
	267
	268	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
	269
	270	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
	271
	272
	273	REAL(wp) :: zeta_step, & !< Increment of zeta
	274	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
	275	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
	276	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
	277	z0_min = 0.0_wp !< Minimum value of z0 to create table
	278	!
	279	!-- When cloud physics is used, arrays for storing potential temperature and
	280	!-- specific humidity at first grid level are required
	281	IF ( cloud_physics ) THEN
	282	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
	283	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
	284	ENDIF
	285
	286	!
	287	!-- Allocate field for storing the horizontal velocity
	288	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
	289
[1709]	290
	291	!
	292	!-- In case of runs with neutral statification, set Obukhov length to a
	293	!-- large value
	294	IF ( neutral ) ol = 1.0E10_wp
	295
[1691]	296	IF ( most_method == 'lookup' ) THEN
	297
	298	!
	299	!-- Check for roughness heterogeneity. In that case terminate run and
	300	!-- inform user
	301	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
	302	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
	303	terminate_run_l = .TRUE.
	304	ENDIF
	305
	306	#if defined( __parallel )
	307	!
	308	!-- Make a logical OR for all processes. Force termiation of model if result
	309	!-- is TRUE
	310	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	311	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
	312	MPI_LOR, comm2d, ierr )
	313	#else
	314	terminate_run = terminate_run_l
	315	#endif
	316
	317	IF ( terminate_run ) THEN
	318	message_string = 'most_method = "lookup" cannot be used in ' // &
	319	'combination with a prescribed roughness ' // &
	320	'heterogeneity'
	321	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
	322	ENDIF
	323
	324	ALLOCATE( zeta_tmp(0:num_steps-1) )
	325
	326	!
	327	!-- Use the lowest possible value for z_mo
	328	k = MINVAL(nzb_s_inner)
	329	z_mo = zu(k+1) - zw(k)
	330
	331	!
	332	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
	333	!-- available steps (num_steps). The calculation is done with negative
	334	!-- values of zeta in order to simplify the stretching in the free
	335	!-- convection limit for the remaining 10% of steps.
	336	zeta_tmp(0) = - zeta_max
	337	num_steps_n = ( num_steps * 9 / 10 ) - 1
	338	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
	339
	340	DO l = 1, num_steps_n
	341	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	342	ENDDO
	343
	344	!
	345	!-- Calculate stretching factor for the free convection range
	346	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
	347	regr_old = regr
	348	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
	349	)**( 10.0_wp / REAL(num_steps) )
	350	ENDDO
	351
	352	!
	353	!-- Calculate z/L range from zeta_min to zeta_stretch
	354	DO l = num_steps_n+1, num_steps-1
	355	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	356	zeta_step = zeta_step * regr
	357	ENDDO
	358
	359	!
	360	!-- Invert array and switch sign, then calculate Obukhov length and bulk
	361	!-- Richardson number
	362	z0h_min = MINVAL(z0h)
	363	z0_min = MINVAL(z0)
	364
	365	!
	366	!-- Calculate lookup table for the Richardson number versus Obukhov length
	367	!-- The Richardson number (rib) is defined depending on the choice of
	368	!-- boundary conditions for temperature
	369	IF ( ibc_pt_b == 1 ) THEN
	370	DO l = 0, num_steps-1
	371	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	372	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
	373	- psi_m( z_mo / ol_tab(l) ) &
	374	+ psi_m( z0_min / ol_tab(l) ) &
	375	)**3
	376	ENDDO
	377	ELSE
	378	DO l = 0, num_steps-1
	379	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	380	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
	381	- psi_h( z_mo / ol_tab(l) ) &
	382	+ psi_h( z0h_min / ol_tab(l) ) &
	383	) &
	384	/ ( LOG( z_mo / z0_min ) &
	385	- psi_m( z_mo / ol_tab(l) ) &
	386	+ psi_m( z0_min / ol_tab(l) ) &
	387	)**2
	388	ENDDO
	389	ENDIF
	390
	391	!
	392	!-- Determine minimum values of rib in the lookup table. Set upper limit
	393	!-- to critical Richardson number (0.25)
	394	rib_min = MINVAL(rib_tab)
	395	rib_max = 0.25 !MAXVAL(rib_tab)
	396
	397	DEALLOCATE( zeta_tmp )
	398	ENDIF
	399
	400	END SUBROUTINE init_surface_layer_fluxes
	401
	402
	403	!------------------------------------------------------------------------------!
	404	! Description:
	405	! ------------
[1709]	406	!> Compute the absolute value of the horizontal velocity (relative to the
	407	!> surface). This is required by all methods
[1691]	408	!------------------------------------------------------------------------------!
[1709]	409	SUBROUTINE calc_uv_total
[1691]	410
	411	IMPLICIT NONE
	412
	413
[1747]	414	!$OMP PARALLEL DO PRIVATE( k )
	415	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
[1691]	416	DO i = nxl, nxr
	417	DO j = nys, nyn
	418
	419	k = nzb_s_inner(j,i)
	420	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
	421	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
	422	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
	423	- v(k,j,i) - v(k,j+1,i) ) )**2 )
	424
	425	!
	426	!-- For too small values of the local wind, MOST does not work. A
	427	!-- threshold value is thus set if required
	428	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
	429
	430	ENDDO
	431	ENDDO
	432
	433	!
	434	!-- Values of uv_total need to be exchanged at the ghost boundaries
	435	!$acc update host( uv_total )
	436	CALL exchange_horiz_2d( uv_total )
	437	!$acc update device( uv_total )
	438
[1709]	439	END SUBROUTINE calc_uv_total
	440
	441
	442	!------------------------------------------------------------------------------!
	443	! Description:
	444	! ------------
	445	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
	446	!------------------------------------------------------------------------------!
	447	SUBROUTINE calc_ol
	448
	449	IMPLICIT NONE
	450
	451	INTEGER(iwp) :: iter, & !< Newton iteration step
	452	l !< look index
	453
	454	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
	455
	456	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
	457	f_d_ol, & !< Derivative of f
	458	ol_l, & !< Lower bound of L for Newton iteration
	459	ol_m, & !< Previous value of L for Newton iteration
	460	ol_old, & !< Previous time step value of L
	461	ol_u !< Upper bound of L for Newton iteration
	462
[1691]	463	IF ( TRIM( most_method ) /= 'circular' ) THEN
	464
[1747]	465	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
	466
[1691]	467	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1747]	468	!$acc kernels loop private( j, k, z_mo )
[1691]	469	DO i = nxl, nxr
	470	DO j = nys, nyn
	471
	472	k = nzb_s_inner(j,i)
	473	z_mo = zu(k+1) - zw(k)
	474
	475	!
	476	!-- Evaluate bulk Richardson number (calculation depends on
	477	!-- definition based on setting of boundary conditions
	478	IF ( ibc_pt_b /= 1 ) THEN
	479	IF ( humidity ) THEN
	480	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
[1709]	481	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
[1691]	482	ELSE
	483	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
[1709]	484	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
[1691]	485	ENDIF
	486	ELSE
	487	!
	488	!-- When using Neumann boundary conditions, the buoyancy flux
	489	!-- is required but cannot be calculated at the surface, as pt
	490	!-- and q are not known at the surface. Hence the values at
	491	!-- first grid level are used to estimate the buoyancy flux
	492	IF ( humidity ) THEN
	493	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
	494	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
	495	* pt(k+1,j,i) * qsws(j,i) ) &
[1709]	496	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
	497	+ 1.0E-20_wp)
[1691]	498	ELSE
	499	rib(j,i) = - g * z_mo * shf(j,i) &
[1709]	500	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
	501	+ 1.0E-20_wp )
[1691]	502	ENDIF
	503	ENDIF
	504
	505	ENDDO
	506	ENDDO
[1747]	507	!$acc end data
[1691]	508
	509	ENDIF
	510
	511	!
	512	!-- Calculate the Obukhov length either using a Newton iteration
	513	!-- method, via a lookup table, or using the old circular way
	514	IF ( TRIM( most_method ) == 'newton' ) THEN
	515
	516	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	517	!# WARNING: does not work on GPU so far because of DO-loop with
	518	!# undetermined iterations
[1747]	519	!!!!!!$acc kernels loop
[1691]	520	DO i = nxl, nxr
	521	DO j = nys, nyn
	522
	523	k = nzb_s_inner(j,i)
	524	z_mo = zu(k+1) - zw(k)
	525
	526	!
	527	!-- Store current value in case the Newton iteration fails
	528	ol_old = ol(j,i)
	529
	530	!
	531	!-- Ensure that the bulk Richardson number and the Obukhov
	532	!-- lengtH have the same sign
	533	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
	534	ABS( ol(j,i) ) == ol_max ) THEN
	535	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
	536	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
	537	ENDIF
	538	!
	539	!-- Iteration to find Obukhov length
	540	iter = 0
	541	DO
	542	iter = iter + 1
	543	!
	544	!-- In case of divergence, use the value of the previous time step
	545	IF ( iter > 1000 ) THEN
	546	ol(j,i) = ol_old
	547	EXIT
	548	ENDIF
	549
	550	ol_m = ol(j,i)
	551	ol_l = ol_m - 0.001_wp * ol_m
	552	ol_u = ol_m + 0.001_wp * ol_m
	553
	554
	555	IF ( ibc_pt_b /= 1 ) THEN
	556	!
	557	!-- Calculate f = Ri - [...]/[...]^2 = 0
	558	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
	559	- psi_h( z_mo / ol_m ) &
	560	+ psi_h( z0h(j,i) / ol_m ) &
	561	) &
	562	/ ( LOG( z_mo / z0(j,i) ) &
	563	- psi_m( z_mo / ol_m ) &
	564	+ psi_m( z0(j,i) / ol_m ) &
	565	)**2
	566
	567	!
	568	!-- Calculate df/dL
	569	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
	570	- psi_h( z_mo / ol_u ) &
	571	+ psi_h( z0h(j,i) / ol_u ) &
	572	) &
	573	/ ( LOG( z_mo / z0(j,i) ) &
	574	- psi_m( z_mo / ol_u ) &
	575	+ psi_m( z0(j,i) / ol_u ) &
	576	)**2 &
	577	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
	578	- psi_h( z_mo / ol_l ) &
	579	+ psi_h( z0h(j,i) / ol_l ) &
	580	) &
	581	/ ( LOG( z_mo / z0(j,i) ) &
	582	- psi_m( z_mo / ol_l ) &
	583	+ psi_m( z0(j,i) / ol_l ) &
	584	)**2 &
	585	) / ( ol_u - ol_l )
	586	ELSE
	587	!
	588	!-- Calculate f = Ri - 1 /[...]^3 = 0
	589	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
	590	- psi_m( z_mo / ol_m ) &
	591	+ psi_m( z0(j,i) / ol_m ) &
	592	)**3
	593
	594	!
	595	!-- Calculate df/dL
	596	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
	597	- psi_m( z_mo / ol_u ) &
	598	+ psi_m( z0(j,i) / ol_u ) &
	599	)**3 &
	600	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
	601	- psi_m( z_mo / ol_l ) &
	602	+ psi_m( z0(j,i) / ol_l ) &
	603	)**3 &
	604	) / ( ol_u - ol_l )
	605	ENDIF
	606	!
	607	!-- Calculate new L
	608	ol(j,i) = ol_m - f / f_d_ol
	609
	610	!
	611	!-- Ensure that the bulk Richardson number and the Obukhov
	612	!-- length have the same sign and ensure convergence.
	613	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
	614
	615	!
	616	!-- If unrealistic value occurs, set L to the maximum
	617	!-- value that is allowed
	618	IF ( ABS( ol(j,i) ) > ol_max ) THEN
	619	ol(j,i) = ol_max
	620	EXIT
	621	ENDIF
	622	!
	623	!-- Check for convergence
	624	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
	625	EXIT
	626	ELSE
	627	CYCLE
	628	ENDIF
	629
	630	ENDDO
	631
	632	ENDDO
	633	ENDDO
	634
	635	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
	636
	637	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	638	!# WARNING: does not work on GPU so far because of DO WHILE construct
[1747]	639	!!!!!!$acc kernels loop
[1691]	640	DO i = nxl, nxr
	641	DO j = nys, nyn
	642
	643	k = nzb_s_inner(j,i)
	644
	645	!
	646	!-- If the bulk Richardson number is outside the range of the lookup
	647	!-- table, set it to the exceeding threshold value
	648	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
	649	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
	650
	651	!
	652	!-- Find the correct index bounds for linear interpolation. As the
	653	!-- Richardson number will not differ very much from time step to
	654	!-- time step , use the index from the last step and search in the
	655	!-- correct direction
	656	l = l_bnd
	657	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
	658	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
	659	l = l-1
	660	ENDDO
	661	ELSE
	662	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
	663	.AND. l < num_steps-1 )
	664	l = l+1
	665	ENDDO
	666	ENDIF
	667	l_bnd = l
	668
	669	!
	670	!-- Linear interpolation to find the correct value of z/L
	671	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
	672	/ ( rib_tab(l) - rib_tab(l-1) ) &
	673	* ( rib(j,i) - rib_tab(l-1) ) )
	674
	675	ENDDO
	676	ENDDO
	677
	678	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
	679
	680	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1747]	681	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, q, ql, qs, qv1, ts, us, vpt, zu, zw ) private( j, k, z_mo )
[1691]	682	DO i = nxl, nxr
	683	DO j = nys, nyn
	684
	685	k = nzb_s_inner(j,i)
	686	z_mo = zu(k+1) - zw(k)
	687
	688	IF ( .NOT. humidity ) THEN
	689	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	690	* ts(j,i) + 1E-30_wp )
	691	ELSEIF ( cloud_physics ) THEN
	692
	693	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	694	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
	695	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
	696	* ql(k+1,j,i) ) + 1E-30_wp )
	697	ELSE
	698	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	699	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
	700	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
	701	ENDIF
	702	!
	703	!-- Limit the value range of the Obukhov length.
	704	!-- This is necessary for very small velocities (u,v --> 0), because
	705	!-- the absolute value of ol can then become very small, which in
	706	!-- consequence would result in very large shear stresses and very
	707	!-- small momentum fluxes (both are generally unrealistic).
	708	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
	709	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
	710
	711	ENDDO
	712	ENDDO
	713
	714	ENDIF
	715
	716	!
	717	!-- Values of ol at ghost point locations are needed for the evaluation
	718	!-- of usws and vsws.
	719	!$acc update host( ol )
	720	CALL exchange_horiz_2d( ol )
	721	!$acc update device( ol )
	722
	723	END SUBROUTINE calc_ol
	724
	725	!
	726	!-- Calculate friction velocity u*
	727	SUBROUTINE calc_us
	728
	729	IMPLICIT NONE
	730
[1697]	731	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	732	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
[1691]	733	DO i = nxlg, nxrg
	734	DO j = nysg, nyng
	735
	736	k = nzb_s_inner(j,i)+1
	737	z_mo = zu(k+1) - zw(k)
	738
	739	!
	740	!-- Compute u* at the scalars' grid points
	741	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
	742	- psi_m( z_mo / ol(j,i) ) &
	743	+ psi_m( z0(j,i) / ol(j,i) ) )
	744	ENDDO
	745	ENDDO
	746
	747	END SUBROUTINE calc_us
	748
	749	!
	750	!-- Calculate potential temperature and specific humidity at first grid level
	751	SUBROUTINE calc_pt_q
	752
	753	IMPLICIT NONE
	754
[1747]	755	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
[1691]	756	DO i = nxlg, nxrg
	757	DO j = nysg, nyng
	758	k = nzb_s_inner(j,i)+1
	759	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
	760	qv1(j,i) = q(k,j,i) - ql(k,j,i)
	761	ENDDO
	762	ENDDO
	763
	764	END SUBROUTINE calc_pt_q
	765
	766	!
	767	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
	768	SUBROUTINE calc_scaling_parameters
	769
	770	IMPLICIT NONE
	771
	772	!
	773	!-- Data information for accelerators
	774	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
	775	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
	776	!$acc present( vpt, vsws, zu, zw, z0, z0h )
	777	!
	778	!-- Compute theta*
	779	IF ( constant_heatflux ) THEN
	780
	781	!
	782	!-- For a given heat flux in the surface layer:
	783	!$OMP PARALLEL DO
[1747]	784	!$acc kernels loop private( j )
[1691]	785	DO i = nxlg, nxrg
	786	DO j = nysg, nyng
	787	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
	788	!
	789	!-- ts must be limited, because otherwise overflow may occur in case
	790	!-- of us=0 when computing ol further below
	791	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
	792	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
	793	ENDDO
	794	ENDDO
	795
	796	ELSE
	797	!
	798	!-- For a given surface temperature:
	799	IF ( large_scale_forcing .AND. lsf_surf ) THEN
	800	!$OMP PARALLEL DO
[1747]	801	!$acc kernels loop private( j, k )
[1691]	802	DO i = nxlg, nxrg
	803	DO j = nysg, nyng
	804	k = nzb_s_inner(j,i)
	805	pt(k,j,i) = pt_surface
	806	ENDDO
	807	ENDDO
	808	ENDIF
	809
[1697]	810	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	811	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
[1691]	812	DO i = nxlg, nxrg
	813	DO j = nysg, nyng
	814
	815	k = nzb_s_inner(j,i)
	816	z_mo = zu(k+1) - zw(k)
	817
	818	IF ( cloud_physics ) THEN
	819	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
	820	/ ( LOG( z_mo / z0h(j,i) ) &
	821	- psi_h( z_mo / ol(j,i) ) &
	822	+ psi_h( z0h(j,i) / ol(j,i) ) )
	823	ELSE
	824	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
	825	/ ( LOG( z_mo / z0h(j,i) ) &
	826	- psi_h( z_mo / ol(j,i) ) &
	827	+ psi_h( z0h(j,i) / ol(j,i) ) )
	828	ENDIF
	829
	830	ENDDO
	831	ENDDO
	832	ENDIF
	833
	834	!
	835	!-- If required compute q*
	836	IF ( humidity .OR. passive_scalar ) THEN
	837	IF ( constant_waterflux ) THEN
	838	!
	839	!-- For a given water flux in the Prandtl layer:
	840	!$OMP PARALLEL DO
[1747]	841	!$acc kernels loop private( j )
[1691]	842	DO i = nxlg, nxrg
	843	DO j = nysg, nyng
	844	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
	845	ENDDO
	846	ENDDO
	847
	848	ELSE
	849	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
	850	run_coupled )
	851
	852	IF ( large_scale_forcing .AND. lsf_surf ) THEN
	853	!$OMP PARALLEL DO
[1747]	854	!$acc kernels loop private( j, k )
[1691]	855	DO i = nxlg, nxrg
	856	DO j = nysg, nyng
	857	k = nzb_s_inner(j,i)
	858	q(k,j,i) = q_surface
	859	ENDDO
	860	ENDDO
	861	ENDIF
	862
[1697]	863	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
[1749]	864	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0h ) private( e_s, j, k, z_mo )
[1691]	865	DO i = nxlg, nxrg
[1749]	866	!$acc loop independent
[1691]	867	DO j = nysg, nyng
	868
	869	k = nzb_s_inner(j,i)
	870	z_mo = zu(k+1) - zw(k)
	871
	872	!
	873	!-- Assume saturation for atmosphere coupled to ocean (but not
	874	!-- in case of precursor runs)
	875	IF ( coupled_run ) THEN
	876	e_s = 6.1_wp * &
	877	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
	878	- 273.15_wp ) )
	879	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
	880	ENDIF
	881
	882	IF ( cloud_physics ) THEN
	883	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
	884	/ ( LOG( z_mo / z0h(j,i) ) &
	885	- psi_h( z_mo / ol(j,i) ) &
	886	+ psi_h( z0h(j,i) / ol(j,i) ) )
	887
	888	ELSE
	889	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
	890	/ ( LOG( z_mo / z0h(j,i) ) &
	891	- psi_h( z_mo / ol(j,i) ) &
	892	+ psi_h( z0h(j,i) / ol(j,i) ) )
	893	ENDIF
	894
	895	ENDDO
	896	ENDDO
	897	ENDIF
	898	ENDIF
	899
	900
	901	!
	902	!-- If required compute qr* and nr*
	903	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
	904
[1697]	905	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	906	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0h ) private( j, k, z_mo )
[1691]	907	DO i = nxlg, nxrg
[1749]	908	!$acc loop independent
[1691]	909	DO j = nysg, nyng
	910
	911	k = nzb_s_inner(j,i)
	912	z_mo = zu(k+1) - zw(k)
	913
[1749]	914	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
	915	/ ( LOG( z_mo / z0h(j,i) ) &
	916	- psi_h( z_mo / ol(j,i) ) &
	917	+ psi_h( z0h(j,i) / ol(j,i) ) )
[1691]	918
[1749]	919	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
	920	/ ( LOG( z_mo / z0h(j,i) ) &
	921	- psi_h( z_mo / ol(j,i) ) &
	922	+ psi_h( z0h(j,i) / ol(j,i) ) )
[1691]	923	ENDDO
	924	ENDDO
	925
	926	ENDIF
[1747]	927	!$acc end data
[1691]	928
	929	END SUBROUTINE calc_scaling_parameters
	930
	931
	932
	933	!
	934	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
	935	SUBROUTINE calc_surface_fluxes
	936
	937	IMPLICIT NONE
	938
	939	REAL(wp) :: ol_mid !< Grid-interpolated L
	940
	941	!
	942	!-- Compute u'w' for the total model domain.
	943	!-- First compute the corresponding component of u* and square it.
	944	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
[1749]	945	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
[1691]	946	DO i = nxl, nxr
	947	DO j = nys, nyn
	948
	949	k = nzb_u_inner(j,i)
	950	z_mo = zu(k+1) - zw(k)
	951	!
	952	!-- Compute bulk Obukhov length for this point
	953	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
	954
	955	IF ( ol_mid == 0.0_wp ) THEN
	956	ol_mid = MIN(ol(j,i-1), ol(j,i))
	957	ENDIF
	958
	959	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
	960	/ ( LOG( z_mo / z0(j,i) ) &
	961	- psi_m( z_mo / ol_mid ) &
	962	+ psi_m( z0(j,i) / ol_mid ) )
	963
	964	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	965	ENDDO
	966	ENDDO
	967
	968	!
	969	!-- Compute v'w' for the total model domain.
	970	!-- First compute the corresponding component of u* and square it.
	971	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
[1749]	972	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
[1691]	973	DO i = nxl, nxr
	974	DO j = nys, nyn
	975
	976	k = nzb_v_inner(j,i)
	977	z_mo = zu(k+1) - zw(k)
	978	!
	979	!-- Compute bulk Obukhov length for this point
	980	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
	981
	982	IF ( ol_mid == 0.0_wp ) THEN
	983	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
	984	ENDIF
	985
	986	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
	987	/ ( LOG( z_mo / z0(j,i) ) &
	988	- psi_m( z_mo / ol_mid ) &
	989	+ psi_m( z0(j,i) / ol_mid ) )
	990
	991	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	992
	993	ENDDO
	994	ENDDO
	995
	996	!
	997	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
[1749]	998	!$acc update host( usws, vsws )
[1691]	999	CALL exchange_horiz_2d( usws )
	1000	CALL exchange_horiz_2d( vsws )
	1001	!$acc update device( usws, vsws )
	1002
	1003	!
	1004	!-- Compute the vertical kinematic heat flux
	1005	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
	1006	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
	1007	!$OMP PARALLEL DO
[1747]	1008	!$acc kernels loop independent present( shf, ts, us )
[1691]	1009	DO i = nxlg, nxrg
	1010	!$acc loop independent
	1011	DO j = nysg, nyng
	1012	shf(j,i) = -ts(j,i) * us(j,i)
	1013	ENDDO
	1014	ENDDO
	1015
	1016	ENDIF
	1017
	1018	!
	1019	!-- Compute the vertical water/scalar flux
	1020	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. passive_scalar ) &
	1021	.AND. ( simulated_time <= skip_time_do_lsm .OR. .NOT. &
	1022	land_surface ) ) THEN
	1023	!$OMP PARALLEL DO
[1747]	1024	!$acc kernels loop independent present( qs, qsws, us )
[1691]	1025	DO i = nxlg, nxrg
	1026	!$acc loop independent
	1027	DO j = nysg, nyng
	1028	qsws(j,i) = -qs(j,i) * us(j,i)
	1029	ENDDO
	1030	ENDDO
	1031
	1032	ENDIF
	1033
	1034	!
	1035	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
	1036	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
	1037	precipitation ) THEN
	1038	!$OMP PARALLEL DO
[1747]	1039	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
[1691]	1040	DO i = nxlg, nxrg
	1041	!$acc loop independent
	1042	DO j = nysg, nyng
	1043	qrsws(j,i) = -qrs(j,i) * us(j,i)
	1044	nrsws(j,i) = -nrs(j,i) * us(j,i)
	1045	ENDDO
	1046	ENDDO
	1047	ENDIF
	1048
	1049	!
	1050	!-- Bottom boundary condition for the TKE
	1051	IF ( ibc_e_b == 2 ) THEN
	1052	!$OMP PARALLEL DO
[1747]	1053	!$acc kernels loop independent present( e, nzb_s_inner, us )
[1691]	1054	DO i = nxlg, nxrg
	1055	!$acc loop independent
	1056	DO j = nysg, nyng
	1057	e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.1_wp )**2
	1058	!
	1059	!-- As a test: cm = 0.4
	1060	! e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.4_wp )**2
	1061	e(nzb_s_inner(j,i),j,i) = e(nzb_s_inner(j,i)+1,j,i)
	1062	ENDDO
	1063	ENDDO
	1064	ENDIF
	1065
	1066	END SUBROUTINE calc_surface_fluxes
	1067
	1068
	1069	!
	1070	!-- Integrated stability function for momentum
	1071	FUNCTION psi_m( zeta )
	1072
	1073	USE kinds
	1074
	1075	IMPLICIT NONE
	1076
	1077	REAL(wp) :: psi_m !< Integrated similarity function result
	1078	REAL(wp) :: zeta !< Stability parameter z/L
	1079	REAL(wp) :: x !< dummy variable
	1080
	1081	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1082	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1083	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1084	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1085	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1086	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1087
	1088
	1089	IF ( zeta < 0.0_wp ) THEN
	1090	x = SQRT( SQRT(1.0_wp - 16.0_wp * zeta ) )
	1091	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
	1092	* ( 1.0_wp + x*2 ) 0.125_wp )
	1093	ELSE
	1094
	1095	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
	1096	- bc_d_d
	1097	!
	1098	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1099	!-- psi_m = - 5.0_wp * zeta
	1100
	1101	ENDIF
	1102
	1103	END FUNCTION psi_m
	1104
	1105
	1106	!
	1107	!-- Integrated stability function for heat and moisture
	1108	FUNCTION psi_h( zeta )
	1109
	1110	USE kinds
	1111
	1112	IMPLICIT NONE
	1113
	1114	REAL(wp) :: psi_h !< Integrated similarity function result
	1115	REAL(wp) :: zeta !< Stability parameter z/L
	1116	REAL(wp) :: x !< dummy variable
	1117
	1118	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1119	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1120	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1121	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1122	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1123	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1124
	1125
	1126	IF ( zeta < 0.0_wp ) THEN
	1127	x = SQRT(1.0_wp - 16.0_wp * zeta )
	1128	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
	1129	ELSE
	1130	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
	1131	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
	1132	+ 1.0_wp
	1133	!
	1134	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1135	!-- psi_h = - 5.0_wp * zeta
	1136	ENDIF
	1137
	1138	END FUNCTION psi_h
	1139
[1697]	1140	END MODULE surface_layer_fluxes_mod

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