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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1747

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

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