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

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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1848

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