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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1703

Last change on this file since 1703 was 1698, checked in by raasch, 9 years ago
last commit documented example_cbl_rc updated
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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:
	20	! -----------------
[1692]	21	!
[1698]	22	!
[1692]	23	! Former revisions:
	24	! -----------------
	25	! $Id: surface_layer_fluxes.f90 1698 2015-10-28 17:26:17Z raasch $
	26	!
[1698]	27	! 1697 2015-10-28 17:14:10Z raasch
	28	! FORTRAN and OpenMP errors removed
	29	!
[1697]	30	! 1696 2015-10-27 10:03:34Z maronga
[1691]	31	! Modularized and completely re-written version of prandtl_fluxes.f90. In the
	32	! course of the re-writing two additional methods have been implemented. See
	33	! updated description.
	34	!
	35	! 1551 2015-03-03 14:18:16Z maronga
	36	! Removed land surface model part. The surface fluxes are now always calculated
	37	! within prandtl_fluxes, based on the given surface temperature/humidity (which
	38	! is either provided by the land surface model, by large scale forcing data, or
	39	! directly prescribed by the user.
	40	!
	41	! 1496 2014-12-02 17:25:50Z maronga
	42	! Adapted for land surface model
	43	!
	44	! 1494 2014-11-21 17:14:03Z maronga
	45	! Bugfixes: qs is now calculated before calculation of Rif. calculation of
	46	! buoyancy flux in Rif corrected (added missing humidity term), allow use of
	47	! topography for coupled runs (not tested)
	48	!
	49	! 1361 2014-04-16 15:17:48Z hoffmann
	50	! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain
	51	! drop concentration (nrsws) added
	52	!
	53	! 1340 2014-03-25 19:45:13Z kanani
	54	! REAL constants defined as wp-kind
	55	!
	56	! 1320 2014-03-20 08:40:49Z raasch
	57	! ONLY-attribute added to USE-statements,
	58	! kind-parameters added to all INTEGER and REAL declaration statements,
	59	! kinds are defined in new module kinds,
	60	! old module precision_kind is removed,
	61	! revision history before 2012 removed,
	62	! comment fields (!:) to be used for variable explanations added to
	63	! all variable declaration statements
	64	!
	65	! 1276 2014-01-15 13:40:41Z heinze
	66	! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars
	67	!
	68	! 1257 2013-11-08 15:18:40Z raasch
	69	! openACC "kernels do" replaced by "kernels loop", "loop independent" added
	70	!
	71	! 1036 2012-10-22 13:43:42Z raasch
	72	! code put under GPL (PALM 3.9)
	73	!
	74	! 1015 2012-09-27 09:23:24Z raasch
	75	! OpenACC statements added
	76	!
	77	! 978 2012-08-09 08:28:32Z fricke
	78	! roughness length for scalar quantities z0h added
	79	!
	80	! Revision 1.1 1998/01/23 10:06:06 raasch
	81	! Initial revision
	82	!
	83	!
	84	! Description:
	85	! ------------
	86	!> Diagnostic computation of vertical fluxes in the constant flux layer from the
	87	!> values of the variables at grid point k=1. Three different methods are
	88	!> available:
	89	!> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate
	90	!> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but
	91	!> slower
	92	!> 3) a method using a lookup table which is fast and accurate. Note, however,
	93	!> that this method cannot be used in case of roughness heterogeneity
	94	!>
[1697]	95	!> @todo limiting of uv_total might be required in some cases
[1691]	96	!> @todo (re)move large_scale_forcing actions
	97	!> @todo check/optimize OpenMP and OpenACC directives
	98	!------------------------------------------------------------------------------!
	99	MODULE surface_layer_fluxes_mod
	100
	101	USE arrays_3d, &
	102	ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, &
	103	shf, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, z0h
	104
	105	USE cloud_parameters, &
	106	ONLY: l_d_cp, pt_d_t
	107
	108	USE constants, &
	109	ONLY: pi
	110
	111	USE cpulog
	112
	113	USE control_parameters, &
	114	ONLY: cloud_physics, constant_heatflux, constant_waterflux, &
	115	coupling_mode, g, humidity, ibc_e_b, ibc_pt_b, icloud_scheme, &
	116	initializing_actions, kappa, intermediate_timestep_count, &
	117	intermediate_timestep_count_max, large_scale_forcing, lsf_surf, &
	118	message_string, most_method, neutral, passive_scalar, &
	119	precipitation, pt_surface, q_surface, run_coupled, &
	120	surface_pressure, simulated_time, terminate_run, zeta_max, &
	121	zeta_min
	122
	123	USE indices, &
	124	ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, &
	125	nzb_u_inner, nzb_v_inner
	126
	127	USE kinds
	128
	129	USE pegrid
	130
	131	USE land_surface_model_mod, &
	132	ONLY: land_surface, skip_time_do_lsm
	133
	134	IMPLICIT NONE
	135
	136	INTEGER(iwp) :: i !< loop index x direction
	137	INTEGER(iwp) :: j !< loop index y direction
	138	INTEGER(iwp) :: k !< loop indey z direction
	139
	140	INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table
	141
	142	LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs
	143
	144	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.)
	145	qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.)
	146	uv_total !< Total velocity at first grid level
	147
	148	REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number
	149	ol_tab !< Lookup table values of L
	150
	151	REAL(wp) :: e_s, & !< Saturation water vapor pressure
	152	l_bnd = 7500, & !< Lookup table index of the last time step
	153	ol_max = 1.0E6_wp, & !< Maximum Obukhov length
	154	rib_max, & !< Maximum Richardson number in lookup table
	155	rib_min, & !< Minimum Richardson number in lookup table
	156	z_mo !< Height of the constant flux layer where MOST is assumed
	157
	158
	159	SAVE
	160
	161	PRIVATE
	162
	163	PUBLIC init_surface_layer_fluxes, surface_layer_fluxes
	164
	165	INTERFACE init_surface_layer_fluxes
	166	MODULE PROCEDURE init_surface_layer_fluxes
	167	END INTERFACE init_surface_layer_fluxes
	168
	169	INTERFACE surface_layer_fluxes
	170	MODULE PROCEDURE surface_layer_fluxes
	171	END INTERFACE surface_layer_fluxes
	172
	173
	174	CONTAINS
	175
	176
	177	!------------------------------------------------------------------------------!
	178	! Description:
	179	! ------------
	180	!> Main routine to compute the surface fluxes
	181	!------------------------------------------------------------------------------!
	182	SUBROUTINE surface_layer_fluxes
	183
	184	IMPLICIT NONE
	185
	186	!
	187	!-- In case cloud physics is used, it is required to derive potential
	188	!-- temperature and specific humidity at first grid level from the fields pt
	189	!-- and q
	190	IF ( cloud_physics ) THEN
	191	CALL calc_pt_q
	192	ENDIF
	193
	194	!
	195	!-- First, calculate the new Obukhov length, then new friction velocity,
	196	!-- followed by the new scaling parameters (th, q, etc.), and the new
	197	!-- surface fluxes if required. The old routine ("circular") requires a
	198	!-- different order of calls as the scaling parameters from the previous time
	199	!-- steps are used to calculate the Obukhov length
	200
	201	!
	202	!-- Depending on setting of most_method use the "old" routine
	203	IF ( most_method == 'circular' ) THEN
	204
	205	CALL calc_scaling_parameters
	206
	207	IF ( .NOT. neutral ) THEN
	208	CALL calc_ol
	209	ENDIF
	210
	211	CALL calc_us
	212
	213	CALL calc_surface_fluxes
	214
	215	!
	216	!-- Use either Newton iteration or a lookup table for the bulk Richardson
	217	!-- number to calculate the Obukhov length
	218	ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN
	219
	220	IF ( .NOT. neutral ) THEN
	221	CALL calc_ol
	222	ENDIF
	223
	224	CALL calc_us
	225
	226	CALL calc_scaling_parameters
	227
	228	CALL calc_surface_fluxes
	229
	230	ENDIF
	231
	232	END SUBROUTINE surface_layer_fluxes
	233
	234
	235	!------------------------------------------------------------------------------!
	236	! Description:
	237	! ------------
	238	!> Initializing actions for the surface layer routine. Basically, this involves
	239	!> the preparation of a lookup table for the the bulk Richardson number vs
	240	!> Obukhov length L when using the lookup table method.
	241	!------------------------------------------------------------------------------!
	242	SUBROUTINE init_surface_layer_fluxes
	243
	244	IMPLICIT NONE
	245
	246	INTEGER(iwp) :: l, & !< Index for loop to create lookup table
	247	num_steps_n !< Number of non-stretched zeta steps
	248
	249	LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global)
	250
	251	REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit
	252
	253	REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp
	254
	255
	256	REAL(wp) :: zeta_step, & !< Increment of zeta
	257	regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit
	258	regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step
	259	z0h_min = 0.0_wp, & !< Minimum value of z0h to create table
	260	z0_min = 0.0_wp !< Minimum value of z0 to create table
	261	!
	262	!-- When cloud physics is used, arrays for storing potential temperature and
	263	!-- specific humidity at first grid level are required
	264	IF ( cloud_physics ) THEN
	265	ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) )
	266	ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) )
	267	ENDIF
	268
	269	!
	270	!-- Allocate field for storing the horizontal velocity
	271	ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) )
	272
	273	IF ( most_method == 'lookup' ) THEN
	274
	275	!
	276	!-- Check for roughness heterogeneity. In that case terminate run and
	277	!-- inform user
	278	IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. &
	279	MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN
	280	terminate_run_l = .TRUE.
	281	ENDIF
	282
	283	#if defined( __parallel )
	284	!
	285	!-- Make a logical OR for all processes. Force termiation of model if result
	286	!-- is TRUE
	287	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	288	CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, &
	289	MPI_LOR, comm2d, ierr )
	290	#else
	291	terminate_run = terminate_run_l
	292	#endif
	293
	294	IF ( terminate_run ) THEN
	295	message_string = 'most_method = "lookup" cannot be used in ' // &
	296	'combination with a prescribed roughness ' // &
	297	'heterogeneity'
	298	CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 )
	299	ENDIF
	300
	301	ALLOCATE( zeta_tmp(0:num_steps-1) )
	302
	303	!
	304	!-- Use the lowest possible value for z_mo
	305	k = MINVAL(nzb_s_inner)
	306	z_mo = zu(k+1) - zw(k)
	307
	308	!
	309	!-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the
	310	!-- available steps (num_steps). The calculation is done with negative
	311	!-- values of zeta in order to simplify the stretching in the free
	312	!-- convection limit for the remaining 10% of steps.
	313	zeta_tmp(0) = - zeta_max
	314	num_steps_n = ( num_steps * 9 / 10 ) - 1
	315	zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n)
	316
	317	DO l = 1, num_steps_n
	318	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	319	ENDDO
	320
	321	!
	322	!-- Calculate stretching factor for the free convection range
	323	DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp )
	324	regr_old = regr
	325	regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) &
	326	)**( 10.0_wp / REAL(num_steps) )
	327	ENDDO
	328
	329	!
	330	!-- Calculate z/L range from zeta_min to zeta_stretch
	331	DO l = num_steps_n+1, num_steps-1
	332	zeta_tmp(l) = zeta_tmp(l-1) + zeta_step
	333	zeta_step = zeta_step * regr
	334	ENDDO
	335
	336	!
	337	!-- Invert array and switch sign, then calculate Obukhov length and bulk
	338	!-- Richardson number
	339	z0h_min = MINVAL(z0h)
	340	z0_min = MINVAL(z0)
	341
	342	!
	343	!-- Calculate lookup table for the Richardson number versus Obukhov length
	344	!-- The Richardson number (rib) is defined depending on the choice of
	345	!-- boundary conditions for temperature
	346	IF ( ibc_pt_b == 1 ) THEN
	347	DO l = 0, num_steps-1
	348	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	349	rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) &
	350	- psi_m( z_mo / ol_tab(l) ) &
	351	+ psi_m( z0_min / ol_tab(l) ) &
	352	)**3
	353	ENDDO
	354	ELSE
	355	DO l = 0, num_steps-1
	356	ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l)
	357	rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) &
	358	- psi_h( z_mo / ol_tab(l) ) &
	359	+ psi_h( z0h_min / ol_tab(l) ) &
	360	) &
	361	/ ( LOG( z_mo / z0_min ) &
	362	- psi_m( z_mo / ol_tab(l) ) &
	363	+ psi_m( z0_min / ol_tab(l) ) &
	364	)**2
	365	ENDDO
	366	ENDIF
	367
	368	!
	369	!-- Determine minimum values of rib in the lookup table. Set upper limit
	370	!-- to critical Richardson number (0.25)
	371	rib_min = MINVAL(rib_tab)
	372	rib_max = 0.25 !MAXVAL(rib_tab)
	373
	374	DEALLOCATE( zeta_tmp )
	375	ENDIF
	376
	377	END SUBROUTINE init_surface_layer_fluxes
	378
	379
	380	!------------------------------------------------------------------------------!
	381	! Description:
	382	! ------------
	383	!> Calculate the Obukhov length (L) and Richardson flux number (z/L)
	384	!------------------------------------------------------------------------------!
	385	SUBROUTINE calc_ol
	386
	387	IMPLICIT NONE
	388
	389	INTEGER(iwp) :: iter, & !< Newton iteration step
	390	l !< look index
	391
[1697]	392	REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number
[1691]	393
	394	REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0
	395	f_d_ol, & !< Derivative of f
	396	ol_l, & !< Lower bound of L for Newton iteration
	397	ol_m, & !< Previous value of L for Newton iteration
	398	ol_old, & !< Previous time step value of L
[1697]	399	ol_u !< Upper bound of L for Newton iteration
[1691]	400
	401	!
	402	!-- Compute the absolute value of the horizontal velocity (relative to the
	403	!-- surface). This is required by all methods
	404	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	405	!$acc kernels loop
	406	DO i = nxl, nxr
	407	DO j = nys, nyn
	408
	409	k = nzb_s_inner(j,i)
	410
	411	uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) &
	412	- u(k,j,i) - u(k,j,i+1) ) )**2 + &
	413	( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) &
	414	- v(k,j,i) - v(k,j+1,i) ) )**2 )
	415
	416	!
	417	!-- For too small values of the local wind, MOST does not work. A
	418	!-- threshold value is thus set if required
	419	! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i))
	420
	421	ENDDO
	422	ENDDO
	423
	424	!
	425	!-- Values of uv_total need to be exchanged at the ghost boundaries
	426	!$acc update host( uv_total )
	427	CALL exchange_horiz_2d( uv_total )
	428	!$acc update device( uv_total )
	429
	430	IF ( TRIM( most_method ) /= 'circular' ) THEN
	431
	432	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	433	!$acc kernels loop
	434	DO i = nxl, nxr
	435	DO j = nys, nyn
	436
	437	k = nzb_s_inner(j,i)
	438	z_mo = zu(k+1) - zw(k)
	439
	440	!
	441	!-- Evaluate bulk Richardson number (calculation depends on
	442	!-- definition based on setting of boundary conditions
	443	IF ( ibc_pt_b /= 1 ) THEN
	444	IF ( humidity ) THEN
	445	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
	446	/ ( uv_total(j,i)*2 vpt(k+1,j,i) )
	447	ELSE
	448	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
	449	/ ( uv_total(j,i)*2 pt(k+1,j,i) )
	450	ENDIF
	451	ELSE
	452	!
	453	!-- When using Neumann boundary conditions, the buoyancy flux
	454	!-- is required but cannot be calculated at the surface, as pt
	455	!-- and q are not known at the surface. Hence the values at
	456	!-- first grid level are used to estimate the buoyancy flux
	457	IF ( humidity ) THEN
	458	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
	459	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
	460	* pt(k+1,j,i) * qsws(j,i) ) &
	461	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2 )
	462	ELSE
	463	rib(j,i) = - g * z_mo * shf(j,i) &
	464	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 )
	465	ENDIF
	466	ENDIF
	467
	468	ENDDO
	469	ENDDO
	470
	471	ENDIF
	472
	473	!
	474	!-- Calculate the Obukhov length either using a Newton iteration
	475	!-- method, via a lookup table, or using the old circular way
	476	IF ( TRIM( most_method ) == 'newton' ) THEN
	477
	478	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	479	!$acc kernels loop
	480	DO i = nxl, nxr
	481	DO j = nys, nyn
	482
	483	k = nzb_s_inner(j,i)
	484	z_mo = zu(k+1) - zw(k)
	485
	486	!
	487	!-- Store current value in case the Newton iteration fails
	488	ol_old = ol(j,i)
	489
	490	!
	491	!-- Ensure that the bulk Richardson number and the Obukhov
	492	!-- lengtH have the same sign
	493	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
	494	ABS( ol(j,i) ) == ol_max ) THEN
	495	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
	496	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
	497	ENDIF
	498	!
	499	!-- Iteration to find Obukhov length
	500	iter = 0
	501	DO
	502	iter = iter + 1
	503	!
	504	!-- In case of divergence, use the value of the previous time step
	505	IF ( iter > 1000 ) THEN
	506	ol(j,i) = ol_old
	507	EXIT
	508	ENDIF
	509
	510	ol_m = ol(j,i)
	511	ol_l = ol_m - 0.001_wp * ol_m
	512	ol_u = ol_m + 0.001_wp * ol_m
	513
	514
	515	IF ( ibc_pt_b /= 1 ) THEN
	516	!
	517	!-- Calculate f = Ri - [...]/[...]^2 = 0
	518	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
	519	- psi_h( z_mo / ol_m ) &
	520	+ psi_h( z0h(j,i) / ol_m ) &
	521	) &
	522	/ ( LOG( z_mo / z0(j,i) ) &
	523	- psi_m( z_mo / ol_m ) &
	524	+ psi_m( z0(j,i) / ol_m ) &
	525	)**2
	526
	527	!
	528	!-- Calculate df/dL
	529	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
	530	- psi_h( z_mo / ol_u ) &
	531	+ psi_h( z0h(j,i) / ol_u ) &
	532	) &
	533	/ ( LOG( z_mo / z0(j,i) ) &
	534	- psi_m( z_mo / ol_u ) &
	535	+ psi_m( z0(j,i) / ol_u ) &
	536	)**2 &
	537	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
	538	- psi_h( z_mo / ol_l ) &
	539	+ psi_h( z0h(j,i) / ol_l ) &
	540	) &
	541	/ ( LOG( z_mo / z0(j,i) ) &
	542	- psi_m( z_mo / ol_l ) &
	543	+ psi_m( z0(j,i) / ol_l ) &
	544	)**2 &
	545	) / ( ol_u - ol_l )
	546	ELSE
	547	!
	548	!-- Calculate f = Ri - 1 /[...]^3 = 0
	549	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
	550	- psi_m( z_mo / ol_m ) &
	551	+ psi_m( z0(j,i) / ol_m ) &
	552	)**3
	553
	554	!
	555	!-- Calculate df/dL
	556	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
	557	- psi_m( z_mo / ol_u ) &
	558	+ psi_m( z0(j,i) / ol_u ) &
	559	)**3 &
	560	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
	561	- psi_m( z_mo / ol_l ) &
	562	+ psi_m( z0(j,i) / ol_l ) &
	563	)**3 &
	564	) / ( ol_u - ol_l )
	565	ENDIF
	566	!
	567	!-- Calculate new L
	568	ol(j,i) = ol_m - f / f_d_ol
	569
	570	!
	571	!-- Ensure that the bulk Richardson number and the Obukhov
	572	!-- length have the same sign and ensure convergence.
	573	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
	574
	575	!
	576	!-- If unrealistic value occurs, set L to the maximum
	577	!-- value that is allowed
	578	IF ( ABS( ol(j,i) ) > ol_max ) THEN
	579	ol(j,i) = ol_max
	580	EXIT
	581	ENDIF
	582	!
	583	!-- Check for convergence
	584	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
	585	EXIT
	586	ELSE
	587	CYCLE
	588	ENDIF
	589
	590	ENDDO
	591
	592	ENDDO
	593	ENDDO
	594
	595	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
	596
	597	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	598	!$acc kernels loop
	599	DO i = nxl, nxr
	600	DO j = nys, nyn
	601
	602	k = nzb_s_inner(j,i)
	603
	604	!
	605	!-- If the bulk Richardson number is outside the range of the lookup
	606	!-- table, set it to the exceeding threshold value
	607	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
	608	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
	609
	610	!
	611	!-- Find the correct index bounds for linear interpolation. As the
	612	!-- Richardson number will not differ very much from time step to
	613	!-- time step , use the index from the last step and search in the
	614	!-- correct direction
	615	l = l_bnd
	616	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
	617	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
	618	l = l-1
	619	ENDDO
	620	ELSE
	621	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
	622	.AND. l < num_steps-1 )
	623	l = l+1
	624	ENDDO
	625	ENDIF
	626	l_bnd = l
	627
	628	!
	629	!-- Linear interpolation to find the correct value of z/L
	630	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
	631	/ ( rib_tab(l) - rib_tab(l-1) ) &
	632	* ( rib(j,i) - rib_tab(l-1) ) )
	633
	634	ENDDO
	635	ENDDO
	636
	637	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
	638
	639	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	640	!$acc kernels loop
	641	DO i = nxl, nxr
	642	DO j = nys, nyn
	643
	644	k = nzb_s_inner(j,i)
	645	z_mo = zu(k+1) - zw(k)
	646
	647	IF ( .NOT. humidity ) THEN
	648	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	649	* ts(j,i) + 1E-30_wp )
	650	ELSEIF ( cloud_physics ) THEN
	651
	652	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	653	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
	654	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
	655	* ql(k+1,j,i) ) + 1E-30_wp )
	656	ELSE
	657	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	658	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
	659	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
	660	ENDIF
	661	!
	662	!-- Limit the value range of the Obukhov length.
	663	!-- This is necessary for very small velocities (u,v --> 0), because
	664	!-- the absolute value of ol can then become very small, which in
	665	!-- consequence would result in very large shear stresses and very
	666	!-- small momentum fluxes (both are generally unrealistic).
	667	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
	668	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
	669
	670	ENDDO
	671	ENDDO
	672
	673	ENDIF
	674
	675	!
	676	!-- Values of ol at ghost point locations are needed for the evaluation
	677	!-- of usws and vsws.
	678	!$acc update host( ol )
	679	CALL exchange_horiz_2d( ol )
	680	!$acc update device( ol )
	681
	682	END SUBROUTINE calc_ol
	683
	684	!
	685	!-- Calculate friction velocity u*
	686	SUBROUTINE calc_us
	687
	688	IMPLICIT NONE
	689
[1697]	690	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	691	!$acc kernels loop
[1691]	692	DO i = nxlg, nxrg
	693	DO j = nysg, nyng
	694
	695	k = nzb_s_inner(j,i)+1
	696	z_mo = zu(k+1) - zw(k)
	697
	698	!
	699	!-- Compute u* at the scalars' grid points
	700	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
	701	- psi_m( z_mo / ol(j,i) ) &
	702	+ psi_m( z0(j,i) / ol(j,i) ) )
	703	ENDDO
	704	ENDDO
	705
	706	END SUBROUTINE calc_us
	707
	708	!
	709	!-- Calculate potential temperature and specific humidity at first grid level
	710	SUBROUTINE calc_pt_q
	711
	712	IMPLICIT NONE
	713
	714	DO i = nxlg, nxrg
	715	DO j = nysg, nyng
	716	k = nzb_s_inner(j,i)+1
	717	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
	718	qv1(j,i) = q(k,j,i) - ql(k,j,i)
	719	ENDDO
	720	ENDDO
	721
	722	END SUBROUTINE calc_pt_q
	723
	724	!
	725	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
	726	SUBROUTINE calc_scaling_parameters
	727
	728	IMPLICIT NONE
	729
	730	!
	731	!-- Data information for accelerators
	732	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
	733	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
	734	!$acc present( vpt, vsws, zu, zw, z0, z0h )
	735	!
	736	!-- Compute theta*
	737	IF ( constant_heatflux ) THEN
	738
	739	!
	740	!-- For a given heat flux in the surface layer:
	741	!$OMP PARALLEL DO
	742	!$acc kernels loop
	743	DO i = nxlg, nxrg
	744	DO j = nysg, nyng
	745	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
	746	!
	747	!-- ts must be limited, because otherwise overflow may occur in case
	748	!-- of us=0 when computing ol further below
	749	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
	750	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
	751	ENDDO
	752	ENDDO
	753
	754	ELSE
	755	!
	756	!-- For a given surface temperature:
	757	IF ( large_scale_forcing .AND. lsf_surf ) THEN
	758	!$OMP PARALLEL DO
	759	!$acc kernels loop
	760	DO i = nxlg, nxrg
	761	DO j = nysg, nyng
	762	k = nzb_s_inner(j,i)
	763	pt(k,j,i) = pt_surface
	764	ENDDO
	765	ENDDO
	766	ENDIF
	767
[1697]	768	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1691]	769	!$acc kernels loop
	770	DO i = nxlg, nxrg
	771	DO j = nysg, nyng
	772
	773	k = nzb_s_inner(j,i)
	774	z_mo = zu(k+1) - zw(k)
	775
	776	IF ( cloud_physics ) THEN
	777	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
	778	/ ( LOG( z_mo / z0h(j,i) ) &
	779	- psi_h( z_mo / ol(j,i) ) &
	780	+ psi_h( z0h(j,i) / ol(j,i) ) )
	781	ELSE
	782	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
	783	/ ( LOG( z_mo / z0h(j,i) ) &
	784	- psi_h( z_mo / ol(j,i) ) &
	785	+ psi_h( z0h(j,i) / ol(j,i) ) )
	786	ENDIF
	787
	788	ENDDO
	789	ENDDO
	790	ENDIF
	791
	792	!
	793	!-- If required compute q*
	794	IF ( humidity .OR. passive_scalar ) THEN
	795	IF ( constant_waterflux ) THEN
	796	!
	797	!-- For a given water flux in the Prandtl layer:
	798	!$OMP PARALLEL DO
	799	!$acc kernels loop
	800	DO i = nxlg, nxrg
	801	DO j = nysg, nyng
	802	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
	803	ENDDO
	804	ENDDO
	805
	806	ELSE
	807	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
	808	run_coupled )
	809
	810	IF ( large_scale_forcing .AND. lsf_surf ) THEN
	811	!$OMP PARALLEL DO
	812	!$acc kernels loop
	813	DO i = nxlg, nxrg
	814	DO j = nysg, nyng
	815	k = nzb_s_inner(j,i)
	816	q(k,j,i) = q_surface
	817	ENDDO
	818	ENDDO
	819	ENDIF
	820
[1697]	821	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
[1691]	822	!$acc kernels loop independent
	823	DO i = nxlg, nxrg
	824	!$acc loop independent
	825	DO j = nysg, nyng
	826
	827	k = nzb_s_inner(j,i)
	828	z_mo = zu(k+1) - zw(k)
	829
	830	!
	831	!-- Assume saturation for atmosphere coupled to ocean (but not
	832	!-- in case of precursor runs)
	833	IF ( coupled_run ) THEN
	834	e_s = 6.1_wp * &
	835	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
	836	- 273.15_wp ) )
	837	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
	838	ENDIF
	839
	840	IF ( cloud_physics ) THEN
	841	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
	842	/ ( LOG( z_mo / z0h(j,i) ) &
	843	- psi_h( z_mo / ol(j,i) ) &
	844	+ psi_h( z0h(j,i) / ol(j,i) ) )
	845
	846	ELSE
	847	qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) &
	848	/ ( LOG( z_mo / z0h(j,i) ) &
	849	- psi_h( z_mo / ol(j,i) ) &
	850	+ psi_h( z0h(j,i) / ol(j,i) ) )
	851	ENDIF
	852
	853	ENDDO
	854	ENDDO
	855	ENDIF
	856	ENDIF
	857
	858
	859	!
	860	!-- If required compute qr* and nr*
	861	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
	862
[1697]	863	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1691]	864	!$acc kernels loop independent
	865	DO i = nxlg, nxrg
	866	!$acc loop independent
	867	DO j = nysg, nyng
	868
	869	k = nzb_s_inner(j,i)
	870	z_mo = zu(k+1) - zw(k)
	871
	872	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
	873	/ ( LOG( z_mo / z0h(j,i) ) &
	874	- psi_h( z_mo / ol(j,i) ) &
	875	+ psi_h( z0h(j,i) / ol(j,i) ) )
	876
	877	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
	878	/ ( LOG( z_mo / z0h(j,i) ) &
	879	- psi_h( z_mo / ol(j,i) ) &
	880	+ psi_h( z0h(j,i) / ol(j,i) ) )
	881	ENDDO
	882	ENDDO
	883
	884	ENDIF
	885
	886	END SUBROUTINE calc_scaling_parameters
	887
	888
	889
	890	!
	891	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
	892	SUBROUTINE calc_surface_fluxes
	893
	894	IMPLICIT NONE
	895
	896	REAL(wp) :: ol_mid !< Grid-interpolated L
	897
	898	!
	899	!-- Compute u'w' for the total model domain.
	900	!-- First compute the corresponding component of u* and square it.
	901	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
	902	!$acc kernels loop
	903	DO i = nxl, nxr
	904	DO j = nys, nyn
	905
	906	k = nzb_u_inner(j,i)
	907	z_mo = zu(k+1) - zw(k)
	908	!
	909	!-- Compute bulk Obukhov length for this point
	910	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
	911
	912	IF ( ol_mid == 0.0_wp ) THEN
	913	ol_mid = MIN(ol(j,i-1), ol(j,i))
	914	ENDIF
	915
	916	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
	917	/ ( LOG( z_mo / z0(j,i) ) &
	918	- psi_m( z_mo / ol_mid ) &
	919	+ psi_m( z0(j,i) / ol_mid ) )
	920
	921	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	922	ENDDO
	923	ENDDO
	924
	925	!
	926	!-- Compute v'w' for the total model domain.
	927	!-- First compute the corresponding component of u* and square it.
	928	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
	929	!$acc kernels loop
	930	DO i = nxl, nxr
	931	DO j = nys, nyn
	932
	933	k = nzb_v_inner(j,i)
	934	z_mo = zu(k+1) - zw(k)
	935	!
	936	!-- Compute bulk Obukhov length for this point
	937	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
	938
	939	IF ( ol_mid == 0.0_wp ) THEN
	940	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
	941	ENDIF
	942
	943	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
	944	/ ( LOG( z_mo / z0(j,i) ) &
	945	- psi_m( z_mo / ol_mid ) &
	946	+ psi_m( z0(j,i) / ol_mid ) )
	947
	948	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	949
	950	ENDDO
	951	ENDDO
	952
	953	!
	954	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
	955	!$acc update host( usws, vsws )
	956	CALL exchange_horiz_2d( usws )
	957	CALL exchange_horiz_2d( vsws )
	958	!$acc update device( usws, vsws )
	959
	960	!
	961	!-- Compute the vertical kinematic heat flux
	962	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
	963	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
	964	!$OMP PARALLEL DO
	965	!$acc kernels loop independent
	966	DO i = nxlg, nxrg
	967	!$acc loop independent
	968	DO j = nysg, nyng
	969	shf(j,i) = -ts(j,i) * us(j,i)
	970	ENDDO
	971	ENDDO
	972
	973	ENDIF
	974
	975	!
	976	!-- Compute the vertical water/scalar flux
	977	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. passive_scalar ) &
	978	.AND. ( simulated_time <= skip_time_do_lsm .OR. .NOT. &
	979	land_surface ) ) THEN
	980	!$OMP PARALLEL DO
	981	!$acc kernels loop independent
	982	DO i = nxlg, nxrg
	983	!$acc loop independent
	984	DO j = nysg, nyng
	985	qsws(j,i) = -qs(j,i) * us(j,i)
	986	ENDDO
	987	ENDDO
	988
	989	ENDIF
	990
	991	!
	992	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
	993	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
	994	precipitation ) THEN
	995	!$OMP PARALLEL DO
	996	!$acc kernels loop independent
	997	DO i = nxlg, nxrg
	998	!$acc loop independent
	999	DO j = nysg, nyng
	1000	qrsws(j,i) = -qrs(j,i) * us(j,i)
	1001	nrsws(j,i) = -nrs(j,i) * us(j,i)
	1002	ENDDO
	1003	ENDDO
	1004	ENDIF
	1005
	1006	!
	1007	!-- Bottom boundary condition for the TKE
	1008	IF ( ibc_e_b == 2 ) THEN
	1009	!$OMP PARALLEL DO
	1010	!$acc kernels loop independent
	1011	DO i = nxlg, nxrg
	1012	!$acc loop independent
	1013	DO j = nysg, nyng
	1014	e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.1_wp )**2
	1015	!
	1016	!-- As a test: cm = 0.4
	1017	! e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.4_wp )**2
	1018	e(nzb_s_inner(j,i),j,i) = e(nzb_s_inner(j,i)+1,j,i)
	1019	ENDDO
	1020	ENDDO
	1021	ENDIF
	1022	!$acc end data
	1023
	1024	END SUBROUTINE calc_surface_fluxes
	1025
	1026
	1027	!
	1028	!-- Integrated stability function for momentum
	1029	FUNCTION psi_m( zeta )
	1030
	1031	USE kinds
	1032
	1033	IMPLICIT NONE
	1034
	1035	REAL(wp) :: psi_m !< Integrated similarity function result
	1036	REAL(wp) :: zeta !< Stability parameter z/L
	1037	REAL(wp) :: x !< dummy variable
	1038
	1039	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1040	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1041	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1042	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1043	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1044	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1045
	1046
	1047	IF ( zeta < 0.0_wp ) THEN
	1048	x = SQRT( SQRT(1.0_wp - 16.0_wp * zeta ) )
	1049	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
	1050	* ( 1.0_wp + x*2 ) 0.125_wp )
	1051	ELSE
	1052
	1053	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
	1054	- bc_d_d
	1055	!
	1056	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1057	!-- psi_m = - 5.0_wp * zeta
	1058
	1059	ENDIF
	1060
	1061	END FUNCTION psi_m
	1062
	1063
	1064	!
	1065	!-- Integrated stability function for heat and moisture
	1066	FUNCTION psi_h( zeta )
	1067
	1068	USE kinds
	1069
	1070	IMPLICIT NONE
	1071
	1072	REAL(wp) :: psi_h !< Integrated similarity function result
	1073	REAL(wp) :: zeta !< Stability parameter z/L
	1074	REAL(wp) :: x !< dummy variable
	1075
	1076	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1077	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1078	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1079	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1080	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1081	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1082
	1083
	1084	IF ( zeta < 0.0_wp ) THEN
	1085	x = SQRT(1.0_wp - 16.0_wp * zeta )
	1086	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
	1087	ELSE
	1088	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
	1089	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
	1090	+ 1.0_wp
	1091	!
	1092	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1093	!-- psi_h = - 5.0_wp * zeta
	1094	ENDIF
	1095
	1096	END FUNCTION psi_h
	1097
[1697]	1098	END MODULE surface_layer_fluxes_mod

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