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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1817

Last change on this file since 1817 was 1789, checked in by maronga, 9 years ago
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[1691]	1	!> @file surface_layer_fluxes.f90
	2	!--------------------------------------------------------------------------------!
	3	! This file is part of PALM.
	4	!
	5	! PALM is free software: you can redistribute it and/or modify it under the terms
	6	! of the GNU General Public License as published by the Free Software Foundation,
	7	! either version 3 of the License, or (at your option) any later version.
	8	!
	9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	12	!
	13	! You should have received a copy of the GNU General Public License along with
	14	! PALM. If not, see <http://www.gnu.org/licenses/>.
	15	!
	16	! Copyright 1997-2015 Leibniz Universitaet Hannover
	17	!
	18	!--------------------------------------------------------------------------------!
	19	! Current revisions:
[1747]	20	! ------------------
[1758]	21	!
[1789]	22	!
[1692]	23	! Former revisions:
	24	! -----------------
	25	! $Id: surface_layer_fluxes.f90 1789 2016-03-10 11:02:40Z maronga $
	26	!
[1789]	27	! 1788 2016-03-10 11:01:04Z maronga
	28	! Added parameter z0q which replaces z0h in the similarity functions for
	29	! humidity.
	30	! Syntax layout improved.
	31	!
[1758]	32	! 1757 2016-02-22 15:49:32Z maronga
	33	! Minor fixes.
	34	!
[1750]	35	! 1749 2016-02-09 12:19:56Z raasch
	36	! further OpenACC adjustments
	37	!
[1748]	38	! 1747 2016-02-08 12:25:53Z raasch
	39	! adjustments for OpenACC usage
	40	!
[1710]	41	! 1709 2015-11-04 14:47:01Z maronga
	42	! Bugfix: division by zero could occur when calculating rib at low wind speeds
	43	! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for
	44	! neutral = .T.
	45	!
[1706]	46	! 1705 2015-11-02 14:28:56Z maronga
	47	! Typo removed
	48	!
[1698]	49	! 1697 2015-10-28 17:14:10Z raasch
	50	! FORTRAN and OpenMP errors removed
	51	!
[1697]	52	! 1696 2015-10-27 10:03:34Z maronga
[1691]	53	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
	54	! course of the re-writing two additional methods have been implemented. See
	55	! updated description.
	56	!
	57	! 1551 2015-03-03 14:18:16Z maronga
	58	! Removed land surface model part. The surface fluxes are now always calculated
	59	! within prandtl_fluxes, based on the given surface temperature/humidity (which
	60	! is either provided by the land surface model, by large scale forcing data, or
	61	! directly prescribed by the user.
	62	!
	63	! 1496 2014-12-02 17:25:50Z maronga
	64	! Adapted for land surface model
	65	!
	66	! 1494 2014-11-21 17:14:03Z maronga
	67	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
	68	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
	69	! topography for coupled runs (not tested)
	70	!
	71	! 1361 2014-04-16 15:17:48Z hoffmann
	72	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
	73	! drop concentration (nrsws) added
	74	!
	75	! 1340 2014-03-25 19:45:13Z kanani
	76	! REAL constants defined as wp-kind
	77	!
	78	! 1320 2014-03-20 08:40:49Z raasch
	79	! ONLY-attribute added to USE-statements,
	80	! kind-parameters added to all INTEGER and REAL declaration statements,
	81	! kinds are defined in new module kinds,
	82	! old module precision_kind is removed,
	83	! revision history before 2012 removed,
	84	! comment fields (!:) to be used for variable explanations added to
	85	! all variable declaration statements
	86	!
	87	! 1276 2014-01-15 13:40:41Z heinze
	88	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
	89	!
	90	! 1257 2013-11-08 15:18:40Z raasch
	91	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
	92	!
	93	! 1036 2012-10-22 13:43:42Z raasch
	94	! code put under GPL (PALM 3.9)
	95	!
	96	! 1015 2012-09-27 09:23:24Z raasch
	97	! OpenACC statements added
	98	!
	99	! 978 2012-08-09 08:28:32Z fricke
	100	! roughness length for scalar quantities z0h added
	101	!
	102	! Revision 1.1 1998/01/23 10:06:06 raasch
	103	! Initial revision
	104	!
	105	!
	106	! Description:
	107	! ------------
	108	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
	109	!> values of the variables at grid point k=1. Three different methods are
	110	!> available:
	111	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
	112	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
	113	!> slower
	114	!> 3) a method using a lookup table which is fast and accurate. Note, however,
	115	!> that this method cannot be used in case of roughness heterogeneity
	116	!>
	117	!> @todo (re)move large_scale_forcing actions
	118	!> @todo check/optimize OpenMP and OpenACC directives
	119	!------------------------------------------------------------------------------!
	120	MODULE surface_layer_fluxes_mod
	121
	122	USE arrays_3d, &
	123	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
[1788]	124	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h, z0q
[1691]	125
	126	USE cloud_parameters, &
	127	ONLY: l_d_cp, pt_d_t
	128
	129	USE constants, &
	130	ONLY: pi
	131
	132	USE cpulog
	133
	134	USE control_parameters, &
	135	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
	136	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, icloud_scheme, &
	137	initializing_actions, kappa, intermediate_timestep_count, &
	138	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
	139	message_string, most_method, neutral, passive_scalar, &
	140	precipitation, pt_surface, q_surface, run_coupled, &
	141	surface_pressure, simulated_time, terminate_run, zeta_max, &
	142	zeta_min
	143
	144	USE indices, &
	145	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
	146	nzb_u_inner, nzb_v_inner
	147
	148	USE kinds
	149
	150	USE pegrid
	151
	152	USE land_surface_model_mod, &
	153	ONLY: land_surface, skip_time_do_lsm
	154
	155	IMPLICIT NONE
	156
	157	INTEGER(iwp) :: i !< loop index x direction
	158	INTEGER(iwp) :: j !< loop index y direction
[1705]	159	INTEGER(iwp) :: k !< loop index z direction
[1691]	160
	161	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
	162
	163	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
	164
	165	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
	166	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
	167	uv_total !< Total velocity at first grid level
	168
	169	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
	170	ol_tab !< Lookup table values of L
	171
	172	REAL(wp) :: e_s, & !< Saturation water vapor pressure
	173	l_bnd = 7500, & !< Lookup table index of the last time step
	174	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
	175	rib_max, & !< Maximum Richardson number in lookup table
	176	rib_min, & !< Minimum Richardson number in lookup table
	177	z_mo !< Height of the constant flux layer where MOST is assumed
	178
	179
	180	SAVE
	181
	182	PRIVATE
	183
[1747]	184	PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total
[1691]	185
	186	INTERFACE init_surface_layer_fluxes
	187	MODULE PROCEDURE init_surface_layer_fluxes
	188	END INTERFACE init_surface_layer_fluxes
	189
	190	INTERFACE surface_layer_fluxes
	191	MODULE PROCEDURE surface_layer_fluxes
	192	END INTERFACE surface_layer_fluxes
	193
	194
	195	CONTAINS
	196
	197
	198	!------------------------------------------------------------------------------!
	199	! Description:
	200	! ------------
	201	!> Main routine to compute the surface fluxes
	202	!------------------------------------------------------------------------------!
	203	SUBROUTINE surface_layer_fluxes
	204
	205	IMPLICIT NONE
	206
	207	!
	208	!-- In case cloud physics is used, it is required to derive potential
	209	!-- temperature and specific humidity at first grid level from the fields pt
	210	!-- and q
	211	IF ( cloud_physics ) THEN
	212	CALL calc_pt_q
	213	ENDIF
	214
	215	!
	216	!-- First, calculate the new Obukhov length, then new friction velocity,
	217	!-- followed by the new scaling parameters (th, q, etc.), and the new
	218	!-- surface fluxes if required. The old routine ("circular") requires a
	219	!-- different order of calls as the scaling parameters from the previous time
	220	!-- steps are used to calculate the Obukhov length
	221
	222	!
	223	!-- Depending on setting of most_method use the "old" routine
	224	IF ( most_method == 'circular' ) THEN
	225
	226	CALL calc_scaling_parameters
	227
[1709]	228	CALL calc_uv_total
	229
[1691]	230	IF ( .NOT. neutral ) THEN
	231	CALL calc_ol
	232	ENDIF
	233
	234	CALL calc_us
	235
	236	CALL calc_surface_fluxes
	237
	238	!
	239	!-- Use either Newton iteration or a lookup table for the bulk Richardson
	240	!-- number to calculate the Obukhov length
[1788]	241	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
[1691]	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_scaling_parameters
	252
	253	CALL calc_surface_fluxes
	254
	255	ENDIF
	256
	257	END SUBROUTINE surface_layer_fluxes
	258
	259
	260	!------------------------------------------------------------------------------!
	261	! Description:
	262	! ------------
	263	!> Initializing actions for the surface layer routine. Basically, this involves
	264	!> the preparation of a lookup table for the the bulk Richardson number vs
	265	!> Obukhov length L when using the lookup table method.
	266	!------------------------------------------------------------------------------!
	267	SUBROUTINE init_surface_layer_fluxes
	268
	269	IMPLICIT NONE
	270
	271	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
	272	num_steps_n !< Number of non-stretched zeta steps
	273
	274	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
	275
	276	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
	277
	278	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
	279
	280
	281	REAL(wp) :: zeta_step, & !< Increment of zeta
	282	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
	283	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
	284	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
	285	z0_min = 0.0_wp !< Minimum value of z0 to create table
	286	!
	287	!-- When cloud physics is used, arrays for storing potential temperature and
	288	!-- specific humidity at first grid level are required
	289	IF ( cloud_physics ) THEN
	290	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
	291	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
	292	ENDIF
	293
	294	!
	295	!-- Allocate field for storing the horizontal velocity
	296	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
	297
[1709]	298
	299	!
	300	!-- In case of runs with neutral statification, set Obukhov length to a
	301	!-- large value
	302	IF ( neutral ) ol = 1.0E10_wp
	303
[1691]	304	IF ( most_method == 'lookup' ) THEN
	305
	306	!
	307	!-- Check for roughness heterogeneity. In that case terminate run and
	308	!-- inform user
[1788]	309	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
[1691]	310	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
	311	terminate_run_l = .TRUE.
	312	ENDIF
	313
	314	#if defined( __parallel )
	315	!
	316	!-- Make a logical OR for all processes. Force termiation of model if result
	317	!-- is TRUE
	318	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	319	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
	320	MPI_LOR, comm2d, ierr )
	321	#else
	322	terminate_run = terminate_run_l
	323	#endif
	324
	325	IF ( terminate_run ) THEN
	326	message_string = 'most_method = "lookup" cannot be used in ' // &
	327	'combination with a prescribed roughness ' // &
	328	'heterogeneity'
	329	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
	330	ENDIF
	331
	332	ALLOCATE( zeta_tmp(0:num_steps-1) )
	333
	334	!
	335	!-- Use the lowest possible value for z_mo
	336	k = MINVAL(nzb_s_inner)
	337	z_mo = zu(k+1) - zw(k)
	338
	339	!
	340	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
	341	!-- available steps (num_steps). The calculation is done with negative
	342	!-- values of zeta in order to simplify the stretching in the free
	343	!-- convection limit for the remaining 10% of steps.
	344	zeta_tmp(0) = - zeta_max
	345	num_steps_n = ( num_steps * 9 / 10 ) - 1
	346	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
	347
	348	DO l = 1, num_steps_n
	349	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	350	ENDDO
	351
	352	!
	353	!-- Calculate stretching factor for the free convection range
[1788]	354	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
[1691]	355	regr_old = regr
	356	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
	357	)**( 10.0_wp / REAL(num_steps) )
	358	ENDDO
	359
	360	!
	361	!-- Calculate z/L range from zeta_min to zeta_stretch
	362	DO l = num_steps_n+1, num_steps-1
	363	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	364	zeta_step = zeta_step * regr
	365	ENDDO
	366
	367	!
[1757]	368	!-- Save roughness lengths to temporary variables
	369	z0h_min = z0h(nys,nxl)
	370	z0_min = z0(nys,nxl)
[1691]	371
	372	!
	373	!-- Calculate lookup table for the Richardson number versus Obukhov length
	374	!-- The Richardson number (rib) is defined depending on the choice of
	375	!-- boundary conditions for temperature
	376	IF ( ibc_pt_b == 1 ) THEN
	377	DO l = 0, num_steps-1
	378	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	379	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
	380	- psi_m( z_mo / ol_tab(l) ) &
	381	+ psi_m( z0_min / ol_tab(l) ) &
	382	)**3
	383	ENDDO
	384	ELSE
	385	DO l = 0, num_steps-1
	386	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	387	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
	388	- psi_h( z_mo / ol_tab(l) ) &
	389	+ psi_h( z0h_min / ol_tab(l) ) &
	390	) &
	391	/ ( LOG( z_mo / z0_min ) &
	392	- psi_m( z_mo / ol_tab(l) ) &
	393	+ psi_m( z0_min / ol_tab(l) ) &
	394	)**2
	395	ENDDO
	396	ENDIF
	397
	398	!
	399	!-- Determine minimum values of rib in the lookup table. Set upper limit
	400	!-- to critical Richardson number (0.25)
	401	rib_min = MINVAL(rib_tab)
	402	rib_max = 0.25 !MAXVAL(rib_tab)
	403
	404	DEALLOCATE( zeta_tmp )
	405	ENDIF
	406
	407	END SUBROUTINE init_surface_layer_fluxes
	408
	409
	410	!------------------------------------------------------------------------------!
	411	! Description:
	412	! ------------
[1709]	413	!> Compute the absolute value of the horizontal velocity (relative to the
	414	!> surface). This is required by all methods
[1691]	415	!------------------------------------------------------------------------------!
[1709]	416	SUBROUTINE calc_uv_total
[1691]	417
	418	IMPLICIT NONE
	419
	420
[1747]	421	!$OMP PARALLEL DO PRIVATE( k )
	422	!$acc kernels loop present( nzb_s_inner, u, uv_total, v ) private( j, k )
[1691]	423	DO i = nxl, nxr
	424	DO j = nys, nyn
	425
	426	k = nzb_s_inner(j,i)
	427	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
	428	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
	429	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
	430	- v(k,j,i) - v(k,j+1,i) ) )**2 )
	431
	432	!
	433	!-- For too small values of the local wind, MOST does not work. A
	434	!-- threshold value is thus set if required
	435	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
	436
	437	ENDDO
	438	ENDDO
	439
	440	!
	441	!-- Values of uv_total need to be exchanged at the ghost boundaries
	442	!$acc update host( uv_total )
	443	CALL exchange_horiz_2d( uv_total )
	444	!$acc update device( uv_total )
	445
[1709]	446	END SUBROUTINE calc_uv_total
	447
	448
	449	!------------------------------------------------------------------------------!
	450	! Description:
	451	! ------------
	452	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
	453	!------------------------------------------------------------------------------!
	454	SUBROUTINE calc_ol
	455
	456	IMPLICIT NONE
	457
	458	INTEGER(iwp) :: iter, & !< Newton iteration step
	459	l !< look index
	460
	461	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
	462
	463	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
	464	f_d_ol, & !< Derivative of f
	465	ol_l, & !< Lower bound of L for Newton iteration
	466	ol_m, & !< Previous value of L for Newton iteration
	467	ol_old, & !< Previous time step value of L
	468	ol_u !< Upper bound of L for Newton iteration
	469
[1691]	470	IF ( TRIM( most_method ) /= 'circular' ) THEN
	471
[1747]	472	!$acc data present( nzb_s_inner, pt, q, qsws, rib, shf, uv_total, vpt, zu, zw )
	473
[1691]	474	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1747]	475	!$acc kernels loop private( j, k, z_mo )
[1691]	476	DO i = nxl, nxr
	477	DO j = nys, nyn
	478
	479	k = nzb_s_inner(j,i)
	480	z_mo = zu(k+1) - zw(k)
	481
	482	!
	483	!-- Evaluate bulk Richardson number (calculation depends on
	484	!-- definition based on setting of boundary conditions
	485	IF ( ibc_pt_b /= 1 ) THEN
	486	IF ( humidity ) THEN
	487	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
[1709]	488	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
[1691]	489	ELSE
	490	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
[1709]	491	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
[1691]	492	ENDIF
	493	ELSE
	494	!
	495	!-- When using Neumann boundary conditions, the buoyancy flux
	496	!-- is required but cannot be calculated at the surface, as pt
	497	!-- and q are not known at the surface. Hence the values at
	498	!-- first grid level are used to estimate the buoyancy flux
	499	IF ( humidity ) THEN
	500	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
	501	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
	502	* pt(k+1,j,i) * qsws(j,i) ) &
[1709]	503	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
	504	+ 1.0E-20_wp)
[1691]	505	ELSE
	506	rib(j,i) = - g * z_mo * shf(j,i) &
[1709]	507	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
	508	+ 1.0E-20_wp )
[1691]	509	ENDIF
	510	ENDIF
	511
	512	ENDDO
	513	ENDDO
[1747]	514	!$acc end data
[1691]	515
	516	ENDIF
	517
	518	!
	519	!-- Calculate the Obukhov length either using a Newton iteration
	520	!-- method, via a lookup table, or using the old circular way
	521	IF ( TRIM( most_method ) == 'newton' ) THEN
	522
	523	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	524	!# WARNING: does not work on GPU so far because of DO-loop with
	525	!# undetermined iterations
[1747]	526	!!!!!!$acc kernels loop
[1691]	527	DO i = nxl, nxr
	528	DO j = nys, nyn
	529
	530	k = nzb_s_inner(j,i)
	531	z_mo = zu(k+1) - zw(k)
	532
	533	!
	534	!-- Store current value in case the Newton iteration fails
	535	ol_old = ol(j,i)
	536
	537	!
	538	!-- Ensure that the bulk Richardson number and the Obukhov
	539	!-- lengtH have the same sign
[1788]	540	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
[1691]	541	ABS( ol(j,i) ) == ol_max ) THEN
	542	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
	543	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
	544	ENDIF
	545	!
	546	!-- Iteration to find Obukhov length
	547	iter = 0
	548	DO
	549	iter = iter + 1
	550	!
	551	!-- In case of divergence, use the value of the previous time step
	552	IF ( iter > 1000 ) THEN
	553	ol(j,i) = ol_old
	554	EXIT
	555	ENDIF
	556
	557	ol_m = ol(j,i)
	558	ol_l = ol_m - 0.001_wp * ol_m
	559	ol_u = ol_m + 0.001_wp * ol_m
	560
	561
	562	IF ( ibc_pt_b /= 1 ) THEN
	563	!
	564	!-- Calculate f = Ri - [...]/[...]^2 = 0
	565	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
	566	- psi_h( z_mo / ol_m ) &
	567	+ psi_h( z0h(j,i) / ol_m ) &
	568	) &
	569	/ ( LOG( z_mo / z0(j,i) ) &
	570	- psi_m( z_mo / ol_m ) &
	571	+ psi_m( z0(j,i) / ol_m ) &
	572	)**2
	573
	574	!
	575	!-- Calculate df/dL
	576	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
	577	- psi_h( z_mo / ol_u ) &
	578	+ psi_h( z0h(j,i) / ol_u ) &
	579	) &
	580	/ ( LOG( z_mo / z0(j,i) ) &
	581	- psi_m( z_mo / ol_u ) &
	582	+ psi_m( z0(j,i) / ol_u ) &
	583	)**2 &
	584	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
	585	- psi_h( z_mo / ol_l ) &
	586	+ psi_h( z0h(j,i) / ol_l ) &
	587	) &
	588	/ ( LOG( z_mo / z0(j,i) ) &
	589	- psi_m( z_mo / ol_l ) &
	590	+ psi_m( z0(j,i) / ol_l ) &
	591	)**2 &
	592	) / ( ol_u - ol_l )
	593	ELSE
	594	!
	595	!-- Calculate f = Ri - 1 /[...]^3 = 0
	596	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
	597	- psi_m( z_mo / ol_m ) &
	598	+ psi_m( z0(j,i) / ol_m ) &
	599	)**3
	600
	601	!
	602	!-- Calculate df/dL
	603	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
	604	- psi_m( z_mo / ol_u ) &
	605	+ psi_m( z0(j,i) / ol_u ) &
	606	)**3 &
	607	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
	608	- psi_m( z_mo / ol_l ) &
	609	+ psi_m( z0(j,i) / ol_l ) &
	610	)**3 &
	611	) / ( ol_u - ol_l )
	612	ENDIF
	613	!
	614	!-- Calculate new L
	615	ol(j,i) = ol_m - f / f_d_ol
	616
	617	!
	618	!-- Ensure that the bulk Richardson number and the Obukhov
	619	!-- length have the same sign and ensure convergence.
	620	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
	621
	622	!
	623	!-- If unrealistic value occurs, set L to the maximum
	624	!-- value that is allowed
	625	IF ( ABS( ol(j,i) ) > ol_max ) THEN
	626	ol(j,i) = ol_max
	627	EXIT
	628	ENDIF
	629	!
	630	!-- Check for convergence
	631	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
	632	EXIT
	633	ELSE
	634	CYCLE
	635	ENDIF
	636
	637	ENDDO
	638
	639	ENDDO
	640	ENDDO
	641
	642	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
	643
	644	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1788]	645	!# WARNING: does not work on GPU so far because of DO WHILE construct
[1747]	646	!!!!!!$acc kernels loop
[1691]	647	DO i = nxl, nxr
	648	DO j = nys, nyn
	649
	650	!
	651	!-- If the bulk Richardson number is outside the range of the lookup
	652	!-- table, set it to the exceeding threshold value
	653	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
	654	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
	655
	656	!
	657	!-- Find the correct index bounds for linear interpolation. As the
	658	!-- Richardson number will not differ very much from time step to
	659	!-- time step , use the index from the last step and search in the
	660	!-- correct direction
	661	l = l_bnd
	662	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
[1788]	663	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
[1691]	664	l = l-1
	665	ENDDO
	666	ELSE
[1788]	667	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
	668	.AND. l < num_steps-1 )
[1691]	669	l = l+1
	670	ENDDO
	671	ENDIF
	672	l_bnd = l
	673
	674	!
	675	!-- Linear interpolation to find the correct value of z/L
[1788]	676	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
	677	/ ( rib_tab(l) - rib_tab(l-1) ) &
[1691]	678	* ( rib(j,i) - rib_tab(l-1) ) )
	679
	680	ENDDO
	681	ENDDO
	682
	683	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
	684
	685	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1747]	686	!$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]	687	DO i = nxl, nxr
	688	DO j = nys, nyn
	689
	690	k = nzb_s_inner(j,i)
	691	z_mo = zu(k+1) - zw(k)
	692
	693	IF ( .NOT. humidity ) THEN
	694	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	695	* ts(j,i) + 1E-30_wp )
	696	ELSEIF ( cloud_physics ) THEN
	697
	698	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	699	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
	700	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
	701	* ql(k+1,j,i) ) + 1E-30_wp )
	702	ELSE
	703	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	704	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
	705	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
	706	ENDIF
	707	!
	708	!-- Limit the value range of the Obukhov length.
	709	!-- This is necessary for very small velocities (u,v --> 0), because
	710	!-- the absolute value of ol can then become very small, which in
	711	!-- consequence would result in very large shear stresses and very
	712	!-- small momentum fluxes (both are generally unrealistic).
	713	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
	714	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
	715
	716	ENDDO
	717	ENDDO
	718
	719	ENDIF
	720
	721	!
	722	!-- Values of ol at ghost point locations are needed for the evaluation
	723	!-- of usws and vsws.
	724	!$acc update host( ol )
	725	CALL exchange_horiz_2d( ol )
	726	!$acc update device( ol )
	727
	728	END SUBROUTINE calc_ol
	729
	730	!
	731	!-- Calculate friction velocity u*
	732	SUBROUTINE calc_us
	733
	734	IMPLICIT NONE
	735
[1697]	736	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	737	!$acc kernels loop present( nzb_s_inner, ol, us, uv_total, zu, zw, z0 ) private( j, k, z_mo )
[1691]	738	DO i = nxlg, nxrg
	739	DO j = nysg, nyng
	740
	741	k = nzb_s_inner(j,i)+1
	742	z_mo = zu(k+1) - zw(k)
	743
	744	!
	745	!-- Compute u* at the scalars' grid points
	746	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
	747	- psi_m( z_mo / ol(j,i) ) &
	748	+ psi_m( z0(j,i) / ol(j,i) ) )
	749	ENDDO
	750	ENDDO
	751
	752	END SUBROUTINE calc_us
	753
	754	!
	755	!-- Calculate potential temperature and specific humidity at first grid level
	756	SUBROUTINE calc_pt_q
	757
	758	IMPLICIT NONE
	759
[1747]	760	!$acc kernels loop present( nzb_s_inner, pt, pt1, pt_d_t, q, ql, qv1 ) private( j, k )
[1691]	761	DO i = nxlg, nxrg
	762	DO j = nysg, nyng
	763	k = nzb_s_inner(j,i)+1
	764	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
	765	qv1(j,i) = q(k,j,i) - ql(k,j,i)
	766	ENDDO
	767	ENDDO
	768
	769	END SUBROUTINE calc_pt_q
	770
	771	!
	772	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
	773	SUBROUTINE calc_scaling_parameters
	774
	775	IMPLICIT NONE
	776
	777	!
	778	!-- Data information for accelerators
	779	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
	780	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
	781	!$acc present( vpt, vsws, zu, zw, z0, z0h )
	782	!
	783	!-- Compute theta*
	784	IF ( constant_heatflux ) THEN
	785
	786	!
	787	!-- For a given heat flux in the surface layer:
	788	!$OMP PARALLEL DO
[1747]	789	!$acc kernels loop private( j )
[1691]	790	DO i = nxlg, nxrg
	791	DO j = nysg, nyng
	792	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
	793	!
	794	!-- ts must be limited, because otherwise overflow may occur in case
	795	!-- of us=0 when computing ol further below
	796	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
	797	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
	798	ENDDO
	799	ENDDO
	800
	801	ELSE
	802	!
	803	!-- For a given surface temperature:
[1788]	804	IF ( large_scale_forcing .AND. lsf_surf ) THEN
[1691]	805	!$OMP PARALLEL DO
[1747]	806	!$acc kernels loop private( j, k )
[1691]	807	DO i = nxlg, nxrg
	808	DO j = nysg, nyng
	809	k = nzb_s_inner(j,i)
	810	pt(k,j,i) = pt_surface
	811	ENDDO
	812	ENDDO
	813	ENDIF
	814
[1697]	815	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1749]	816	!$acc kernels loop present( nzb_s_inner, ol, pt, pt1, ts, zu, zw, z0h ) private( j, k, z_mo )
[1691]	817	DO i = nxlg, nxrg
	818	DO j = nysg, nyng
	819
	820	k = nzb_s_inner(j,i)
	821	z_mo = zu(k+1) - zw(k)
	822
	823	IF ( cloud_physics ) THEN
	824	ts(j,i) = kappa * ( pt1(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	ELSE
	829	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
	830	/ ( LOG( z_mo / z0h(j,i) ) &
	831	- psi_h( z_mo / ol(j,i) ) &
	832	+ psi_h( z0h(j,i) / ol(j,i) ) )
	833	ENDIF
	834
	835	ENDDO
	836	ENDDO
	837	ENDIF
	838
	839	!
	840	!-- If required compute q*
	841	IF ( humidity .OR. passive_scalar ) THEN
	842	IF ( constant_waterflux ) THEN
	843	!
[1788]	844	!-- For a given water flux in the surface layer
[1691]	845	!$OMP PARALLEL DO
[1747]	846	!$acc kernels loop private( j )
[1691]	847	DO i = nxlg, nxrg
	848	DO j = nysg, nyng
	849	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
	850	ENDDO
	851	ENDDO
	852
	853	ELSE
[1788]	854	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
[1691]	855	run_coupled )
	856
[1788]	857	IF ( large_scale_forcing .AND. lsf_surf ) THEN
[1691]	858	!$OMP PARALLEL DO
[1747]	859	!$acc kernels loop private( j, k )
[1691]	860	DO i = nxlg, nxrg
	861	DO j = nysg, nyng
	862	k = nzb_s_inner(j,i)
	863	q(k,j,i) = q_surface
	864	ENDDO
	865	ENDDO
	866	ENDIF
	867
[1697]	868	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
[1788]	869	!$acc kernels loop independent present( nzb_s_inner, ol, pt, q, qs, qv1, zu, zw, z0q ) private( e_s, j, k, z_mo )
[1691]	870	DO i = nxlg, nxrg
[1749]	871	!$acc loop independent
[1691]	872	DO j = nysg, nyng
	873
	874	k = nzb_s_inner(j,i)
	875	z_mo = zu(k+1) - zw(k)
	876
	877	!
	878	!-- Assume saturation for atmosphere coupled to ocean (but not
	879	!-- in case of precursor runs)
	880	IF ( coupled_run ) THEN
	881	e_s = 6.1_wp * &
	882	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
	883	- 273.15_wp ) )
	884	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
	885	ENDIF
	886
	887	IF ( cloud_physics ) THEN
	888	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
[1788]	889	/ ( LOG( z_mo / z0q(j,i) ) &
[1691]	890	- psi_h( z_mo / ol(j,i) ) &
[1788]	891	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	892
	893	ELSE
	894	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
[1788]	895	/ ( LOG( z_mo / z0q(j,i) ) &
[1691]	896	- psi_h( z_mo / ol(j,i) ) &
[1788]	897	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	898	ENDIF
	899
	900	ENDDO
	901	ENDDO
	902	ENDIF
	903	ENDIF
	904
	905
	906	!
	907	!-- If required compute qr* and nr*
[1788]	908	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) &
	909	THEN
[1691]	910
[1697]	911	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1788]	912	!$acc kernels loop independent present( nr, nrs, nzb_s_inner, ol, qr, qrs, zu, zw, z0q ) private( j, k, z_mo )
[1691]	913	DO i = nxlg, nxrg
[1749]	914	!$acc loop independent
[1691]	915	DO j = nysg, nyng
	916
	917	k = nzb_s_inner(j,i)
	918	z_mo = zu(k+1) - zw(k)
	919
[1749]	920	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
[1788]	921	/ ( LOG( z_mo / z0q(j,i) ) &
[1749]	922	- psi_h( z_mo / ol(j,i) ) &
[1788]	923	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	924
[1749]	925	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
[1788]	926	/ ( LOG( z_mo / z0q(j,i) ) &
[1749]	927	- psi_h( z_mo / ol(j,i) ) &
[1788]	928	+ psi_h( z0q(j,i) / ol(j,i) ) )
[1691]	929	ENDDO
	930	ENDDO
	931
	932	ENDIF
[1747]	933	!$acc end data
[1691]	934
	935	END SUBROUTINE calc_scaling_parameters
	936
	937
	938
	939	!
	940	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
	941	SUBROUTINE calc_surface_fluxes
	942
	943	IMPLICIT NONE
	944
	945	REAL(wp) :: ol_mid !< Grid-interpolated L
	946
	947	!
	948	!-- Compute u'w' for the total model domain.
	949	!-- First compute the corresponding component of u* and square it.
	950	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
[1749]	951	!$acc kernels loop present( nzb_u_inner, ol, u, us, usws, zu, zw, z0 ) private( j, k, z_mo )
[1691]	952	DO i = nxl, nxr
	953	DO j = nys, nyn
	954
	955	k = nzb_u_inner(j,i)
	956	z_mo = zu(k+1) - zw(k)
	957	!
	958	!-- Compute bulk Obukhov length for this point
	959	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
	960
	961	IF ( ol_mid == 0.0_wp ) THEN
	962	ol_mid = MIN(ol(j,i-1), ol(j,i))
	963	ENDIF
	964
	965	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
	966	/ ( LOG( z_mo / z0(j,i) ) &
	967	- psi_m( z_mo / ol_mid ) &
	968	+ psi_m( z0(j,i) / ol_mid ) )
	969
	970	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	971	ENDDO
	972	ENDDO
	973
	974	!
	975	!-- Compute v'w' for the total model domain.
	976	!-- First compute the corresponding component of u* and square it.
	977	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
[1749]	978	!$acc kernels loop present( nzb_v_inner, ol, v, us, vsws, zu, zw, z0 ) private( j, k, ol_mid, z_mo )
[1691]	979	DO i = nxl, nxr
	980	DO j = nys, nyn
	981
	982	k = nzb_v_inner(j,i)
	983	z_mo = zu(k+1) - zw(k)
	984	!
	985	!-- Compute bulk Obukhov length for this point
	986	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
	987
	988	IF ( ol_mid == 0.0_wp ) THEN
	989	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
	990	ENDIF
	991
	992	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
	993	/ ( LOG( z_mo / z0(j,i) ) &
	994	- psi_m( z_mo / ol_mid ) &
	995	+ psi_m( z0(j,i) / ol_mid ) )
	996
	997	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	998
	999	ENDDO
	1000	ENDDO
	1001
	1002	!
	1003	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
[1749]	1004	!$acc update host( usws, vsws )
[1691]	1005	CALL exchange_horiz_2d( usws )
	1006	CALL exchange_horiz_2d( vsws )
	1007	!$acc update device( usws, vsws )
	1008
	1009	!
	1010	!-- Compute the vertical kinematic heat flux
[1788]	1011	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
	1012	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
[1691]	1013	!$OMP PARALLEL DO
[1747]	1014	!$acc kernels loop independent present( shf, ts, us )
[1691]	1015	DO i = nxlg, nxrg
	1016	!$acc loop independent
	1017	DO j = nysg, nyng
	1018	shf(j,i) = -ts(j,i) * us(j,i)
	1019	ENDDO
	1020	ENDDO
	1021
	1022	ENDIF
	1023
	1024	!
	1025	!-- Compute the vertical water/scalar flux
[1788]	1026	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. &
	1027	passive_scalar ) .AND. ( simulated_time <= skip_time_do_lsm &
	1028	.OR. .NOT. land_surface ) ) THEN
[1691]	1029	!$OMP PARALLEL DO
[1747]	1030	!$acc kernels loop independent present( qs, qsws, us )
[1691]	1031	DO i = nxlg, nxrg
	1032	!$acc loop independent
	1033	DO j = nysg, nyng
	1034	qsws(j,i) = -qs(j,i) * us(j,i)
	1035	ENDDO
	1036	ENDDO
	1037
	1038	ENDIF
	1039
	1040	!
	1041	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
	1042	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
	1043	precipitation ) THEN
	1044	!$OMP PARALLEL DO
[1747]	1045	!$acc kernels loop independent present( nrs, nrsws, qrs, qrsws, us )
[1691]	1046	DO i = nxlg, nxrg
	1047	!$acc loop independent
	1048	DO j = nysg, nyng
	1049	qrsws(j,i) = -qrs(j,i) * us(j,i)
	1050	nrsws(j,i) = -nrs(j,i) * us(j,i)
	1051	ENDDO
	1052	ENDDO
	1053	ENDIF
	1054
	1055	!
	1056	!-- Bottom boundary condition for the TKE
	1057	IF ( ibc_e_b == 2 ) THEN
	1058	!$OMP PARALLEL DO
[1747]	1059	!$acc kernels loop independent present( e, nzb_s_inner, us )
[1691]	1060	DO i = nxlg, nxrg
	1061	!$acc loop independent
	1062	DO j = nysg, nyng
[1757]	1063	k = nzb_s_inner(j,i)
	1064	e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2
[1691]	1065	!
	1066	!-- As a test: cm = 0.4
[1757]	1067	! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2
	1068	e(k,j,i) = e(k+1,j,i)
[1691]	1069	ENDDO
	1070	ENDDO
	1071	ENDIF
	1072
	1073	END SUBROUTINE calc_surface_fluxes
	1074
	1075
	1076	!
	1077	!-- Integrated stability function for momentum
	1078	FUNCTION psi_m( zeta )
	1079
	1080	USE kinds
	1081
	1082	IMPLICIT NONE
	1083
	1084	REAL(wp) :: psi_m !< Integrated similarity function result
	1085	REAL(wp) :: zeta !< Stability parameter z/L
	1086	REAL(wp) :: x !< dummy variable
	1087
	1088	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1089	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1090	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1091	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1092	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1093	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1094
	1095
	1096	IF ( zeta < 0.0_wp ) THEN
[1788]	1097	x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) )
[1691]	1098	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
	1099	* ( 1.0_wp + x*2 ) 0.125_wp )
	1100	ELSE
	1101
	1102	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
	1103	- bc_d_d
	1104	!
	1105	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1106	!-- psi_m = - 5.0_wp * zeta
	1107
	1108	ENDIF
	1109
	1110	END FUNCTION psi_m
	1111
	1112
	1113	!
	1114	!-- Integrated stability function for heat and moisture
	1115	FUNCTION psi_h( zeta )
	1116
	1117	USE kinds
	1118
	1119	IMPLICIT NONE
	1120
	1121	REAL(wp) :: psi_h !< Integrated similarity function result
	1122	REAL(wp) :: zeta !< Stability parameter z/L
	1123	REAL(wp) :: x !< dummy variable
	1124
	1125	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1126	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1127	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1128	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1129	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1130	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1131
	1132
	1133	IF ( zeta < 0.0_wp ) THEN
[1788]	1134	x = SQRT( 1.0_wp - 16.0_wp * zeta )
[1691]	1135	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
	1136	ELSE
	1137	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
	1138	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
	1139	+ 1.0_wp
	1140	!
	1141	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1142	!-- psi_h = - 5.0_wp * zeta
	1143	ENDIF
	1144
	1145	END FUNCTION psi_h
	1146
[1697]	1147	END MODULE surface_layer_fluxes_mod

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