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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1788

Last change on this file since 1788 was 1788, checked in by maronga, 9 years ago
added support for water and paved surfaced in land surface model / minor changes
Property svn:keywords set to `Id`
File size: 42.5 KB

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

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