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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1730

Last change on this file since 1730 was 1710, checked in by maronga, 9 years ago
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[1691]	1	!> @file surface_layer_fluxes.f90
	2	!--------------------------------------------------------------------------------!
	3	! This file is part of PALM.
	4	!
	5	! PALM is free software: you can redistribute it and/or modify it under the terms
	6	! of the GNU General Public License as published by the Free Software Foundation,
	7	! either version 3 of the License, or (at your option) any later version.
	8	!
	9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	12	!
	13	! You should have received a copy of the GNU General Public License along with
	14	! PALM. If not, see <http://www.gnu.org/licenses/>.
	15	!
	16	! Copyright 1997-2015 Leibniz Universitaet Hannover
	17	!
	18	!--------------------------------------------------------------------------------!
	19	! Current revisions:
	20	! -----------------
[1706]	21	!
[1710]	22	!
[1692]	23	! Former revisions:
	24	! -----------------
	25	! $Id: surface_layer_fluxes.f90 1710 2015-11-04 14:48:36Z gronemeier $
	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
	170	PUBLIC init_surface_layer_fluxes, surface_layer_fluxes
	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
	408	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	409	!$acc kernels loop
	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
	457
[1691]	458	IF ( TRIM( most_method ) /= 'circular' ) THEN
	459
	460	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	461	!$acc kernels loop
	462	DO i = nxl, nxr
	463	DO j = nys, nyn
	464
	465	k = nzb_s_inner(j,i)
	466	z_mo = zu(k+1) - zw(k)
	467
	468	!
	469	!-- Evaluate bulk Richardson number (calculation depends on
	470	!-- definition based on setting of boundary conditions
	471	IF ( ibc_pt_b /= 1 ) THEN
	472	IF ( humidity ) THEN
	473	rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) &
[1709]	474	/ ( uv_total(j,i)*2 vpt(k+1,j,i) + 1.0E-20_wp )
[1691]	475	ELSE
	476	rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) &
[1709]	477	/ ( uv_total(j,i)*2 pt(k+1,j,i) + 1.0E-20_wp )
[1691]	478	ENDIF
	479	ELSE
	480	!
	481	!-- When using Neumann boundary conditions, the buoyancy flux
	482	!-- is required but cannot be calculated at the surface, as pt
	483	!-- and q are not known at the surface. Hence the values at
	484	!-- first grid level are used to estimate the buoyancy flux
	485	IF ( humidity ) THEN
	486	rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp &
	487	* q(k+1,j,i) ) * shf(j,i) + 0.61_wp &
	488	* pt(k+1,j,i) * qsws(j,i) ) &
[1709]	489	/ ( uv_total(j,i)*3 vpt(k+1,j,i) * kappa**2&
	490	+ 1.0E-20_wp)
[1691]	491	ELSE
	492	rib(j,i) = - g * z_mo * shf(j,i) &
[1709]	493	/ ( uv_total(j,i)*3 pt(k+1,j,i) * kappa**2 &
	494	+ 1.0E-20_wp )
[1691]	495	ENDIF
	496	ENDIF
	497
	498	ENDDO
	499	ENDDO
	500
	501	ENDIF
	502
	503	!
	504	!-- Calculate the Obukhov length either using a Newton iteration
	505	!-- method, via a lookup table, or using the old circular way
	506	IF ( TRIM( most_method ) == 'newton' ) THEN
	507
	508	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	509	!$acc kernels loop
	510	DO i = nxl, nxr
	511	DO j = nys, nyn
	512
	513	k = nzb_s_inner(j,i)
	514	z_mo = zu(k+1) - zw(k)
	515
	516	!
	517	!-- Store current value in case the Newton iteration fails
	518	ol_old = ol(j,i)
	519
	520	!
	521	!-- Ensure that the bulk Richardson number and the Obukhov
	522	!-- lengtH have the same sign
	523	IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. &
	524	ABS( ol(j,i) ) == ol_max ) THEN
	525	IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp
	526	IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp
	527	ENDIF
	528	!
	529	!-- Iteration to find Obukhov length
	530	iter = 0
	531	DO
	532	iter = iter + 1
	533	!
	534	!-- In case of divergence, use the value of the previous time step
	535	IF ( iter > 1000 ) THEN
	536	ol(j,i) = ol_old
	537	EXIT
	538	ENDIF
	539
	540	ol_m = ol(j,i)
	541	ol_l = ol_m - 0.001_wp * ol_m
	542	ol_u = ol_m + 0.001_wp * ol_m
	543
	544
	545	IF ( ibc_pt_b /= 1 ) THEN
	546	!
	547	!-- Calculate f = Ri - [...]/[...]^2 = 0
	548	f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )&
	549	- psi_h( z_mo / ol_m ) &
	550	+ psi_h( z0h(j,i) / ol_m ) &
	551	) &
	552	/ ( LOG( z_mo / z0(j,i) ) &
	553	- psi_m( z_mo / ol_m ) &
	554	+ psi_m( z0(j,i) / ol_m ) &
	555	)**2
	556
	557	!
	558	!-- Calculate df/dL
	559	f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) &
	560	- psi_h( z_mo / ol_u ) &
	561	+ psi_h( z0h(j,i) / ol_u ) &
	562	) &
	563	/ ( LOG( z_mo / z0(j,i) ) &
	564	- psi_m( z_mo / ol_u ) &
	565	+ psi_m( z0(j,i) / ol_u ) &
	566	)**2 &
	567	+ ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) &
	568	- psi_h( z_mo / ol_l ) &
	569	+ psi_h( z0h(j,i) / ol_l ) &
	570	) &
	571	/ ( LOG( z_mo / z0(j,i) ) &
	572	- psi_m( z_mo / ol_l ) &
	573	+ psi_m( z0(j,i) / ol_l ) &
	574	)**2 &
	575	) / ( ol_u - ol_l )
	576	ELSE
	577	!
	578	!-- Calculate f = Ri - 1 /[...]^3 = 0
	579	f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )&
	580	- psi_m( z_mo / ol_m ) &
	581	+ psi_m( z0(j,i) / ol_m ) &
	582	)**3
	583
	584	!
	585	!-- Calculate df/dL
	586	f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) &
	587	- psi_m( z_mo / ol_u ) &
	588	+ psi_m( z0(j,i) / ol_u ) &
	589	)**3 &
	590	+ ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) &
	591	- psi_m( z_mo / ol_l ) &
	592	+ psi_m( z0(j,i) / ol_l ) &
	593	)**3 &
	594	) / ( ol_u - ol_l )
	595	ENDIF
	596	!
	597	!-- Calculate new L
	598	ol(j,i) = ol_m - f / f_d_ol
	599
	600	!
	601	!-- Ensure that the bulk Richardson number and the Obukhov
	602	!-- length have the same sign and ensure convergence.
	603	IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp
	604
	605	!
	606	!-- If unrealistic value occurs, set L to the maximum
	607	!-- value that is allowed
	608	IF ( ABS( ol(j,i) ) > ol_max ) THEN
	609	ol(j,i) = ol_max
	610	EXIT
	611	ENDIF
	612	!
	613	!-- Check for convergence
	614	IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN
	615	EXIT
	616	ELSE
	617	CYCLE
	618	ENDIF
	619
	620	ENDDO
	621
	622	ENDDO
	623	ENDDO
	624
	625	ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN
	626
	627	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	628	!$acc kernels loop
	629	DO i = nxl, nxr
	630	DO j = nys, nyn
	631
	632	k = nzb_s_inner(j,i)
	633
	634	!
	635	!-- If the bulk Richardson number is outside the range of the lookup
	636	!-- table, set it to the exceeding threshold value
	637	IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min
	638	IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max
	639
	640	!
	641	!-- Find the correct index bounds for linear interpolation. As the
	642	!-- Richardson number will not differ very much from time step to
	643	!-- time step , use the index from the last step and search in the
	644	!-- correct direction
	645	l = l_bnd
	646	IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN
	647	DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 )
	648	l = l-1
	649	ENDDO
	650	ELSE
	651	DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp &
	652	.AND. l < num_steps-1 )
	653	l = l+1
	654	ENDDO
	655	ENDIF
	656	l_bnd = l
	657
	658	!
	659	!-- Linear interpolation to find the correct value of z/L
	660	ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) &
	661	/ ( rib_tab(l) - rib_tab(l-1) ) &
	662	* ( rib(j,i) - rib_tab(l-1) ) )
	663
	664	ENDDO
	665	ENDDO
	666
	667	ELSEIF ( TRIM( most_method ) == 'circular' ) THEN
	668
	669	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	670	!$acc kernels loop
	671	DO i = nxl, nxr
	672	DO j = nys, nyn
	673
	674	k = nzb_s_inner(j,i)
	675	z_mo = zu(k+1) - zw(k)
	676
	677	IF ( .NOT. humidity ) THEN
	678	ol(j,i) = ( pt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	679	* ts(j,i) + 1E-30_wp )
	680	ELSEIF ( cloud_physics ) THEN
	681
	682	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	683	* ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) &
	684	+ 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) &
	685	* ql(k+1,j,i) ) + 1E-30_wp )
	686	ELSE
	687	ol(j,i) = ( vpt(k+1,j,i) * us(j,i)*2 ) / ( kappa g &
	688	* ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) &
	689	+ 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp )
	690	ENDIF
	691	!
	692	!-- Limit the value range of the Obukhov length.
	693	!-- This is necessary for very small velocities (u,v --> 0), because
	694	!-- the absolute value of ol can then become very small, which in
	695	!-- consequence would result in very large shear stresses and very
	696	!-- small momentum fluxes (both are generally unrealistic).
	697	IF ( ( z_mo / ol(j,i) ) < zeta_min ) ol(j,i) = z_mo / zeta_min
	698	IF ( ( z_mo / ol(j,i) ) > zeta_max ) ol(j,i) = z_mo / zeta_max
	699
	700	ENDDO
	701	ENDDO
	702
	703	ENDIF
	704
	705	!
	706	!-- Values of ol at ghost point locations are needed for the evaluation
	707	!-- of usws and vsws.
	708	!$acc update host( ol )
	709	CALL exchange_horiz_2d( ol )
	710	!$acc update device( ol )
	711
	712	END SUBROUTINE calc_ol
	713
	714	!
	715	!-- Calculate friction velocity u*
	716	SUBROUTINE calc_us
	717
	718	IMPLICIT NONE
	719
[1697]	720	!$OMP PARALLEL DO PRIVATE( k, z_mo )
	721	!$acc kernels loop
[1691]	722	DO i = nxlg, nxrg
	723	DO j = nysg, nyng
	724
	725	k = nzb_s_inner(j,i)+1
	726	z_mo = zu(k+1) - zw(k)
	727
	728	!
	729	!-- Compute u* at the scalars' grid points
	730	us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) &
	731	- psi_m( z_mo / ol(j,i) ) &
	732	+ psi_m( z0(j,i) / ol(j,i) ) )
	733	ENDDO
	734	ENDDO
	735
	736	END SUBROUTINE calc_us
	737
	738	!
	739	!-- Calculate potential temperature and specific humidity at first grid level
	740	SUBROUTINE calc_pt_q
	741
	742	IMPLICIT NONE
	743
	744	DO i = nxlg, nxrg
	745	DO j = nysg, nyng
	746	k = nzb_s_inner(j,i)+1
	747	pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i)
	748	qv1(j,i) = q(k,j,i) - ql(k,j,i)
	749	ENDDO
	750	ENDDO
	751
	752	END SUBROUTINE calc_pt_q
	753
	754	!
	755	!-- Calculate the other MOST scaling parameters theta, q, (qr, nr)
	756	SUBROUTINE calc_scaling_parameters
	757
	758	IMPLICIT NONE
	759
	760	!
	761	!-- Data information for accelerators
	762	!$acc data present( e, nrsws, nzb_u_inner, nzb_v_inner, nzb_s_inner, pt ) &
	763	!$acc present( q, qs, qsws, qrsws, shf, ts, u, us, usws, v ) &
	764	!$acc present( vpt, vsws, zu, zw, z0, z0h )
	765	!
	766	!-- Compute theta*
	767	IF ( constant_heatflux ) THEN
	768
	769	!
	770	!-- For a given heat flux in the surface layer:
	771	!$OMP PARALLEL DO
	772	!$acc kernels loop
	773	DO i = nxlg, nxrg
	774	DO j = nysg, nyng
	775	ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30_wp )
	776	!
	777	!-- ts must be limited, because otherwise overflow may occur in case
	778	!-- of us=0 when computing ol further below
	779	IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp
	780	IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp
	781	ENDDO
	782	ENDDO
	783
	784	ELSE
	785	!
	786	!-- For a given surface temperature:
	787	IF ( large_scale_forcing .AND. lsf_surf ) THEN
	788	!$OMP PARALLEL DO
	789	!$acc kernels loop
	790	DO i = nxlg, nxrg
	791	DO j = nysg, nyng
	792	k = nzb_s_inner(j,i)
	793	pt(k,j,i) = pt_surface
	794	ENDDO
	795	ENDDO
	796	ENDIF
	797
[1697]	798	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1691]	799	!$acc kernels loop
	800	DO i = nxlg, nxrg
	801	DO j = nysg, nyng
	802
	803	k = nzb_s_inner(j,i)
	804	z_mo = zu(k+1) - zw(k)
	805
	806	IF ( cloud_physics ) THEN
	807	ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) &
	808	/ ( LOG( z_mo / z0h(j,i) ) &
	809	- psi_h( z_mo / ol(j,i) ) &
	810	+ psi_h( z0h(j,i) / ol(j,i) ) )
	811	ELSE
	812	ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) &
	813	/ ( LOG( z_mo / z0h(j,i) ) &
	814	- psi_h( z_mo / ol(j,i) ) &
	815	+ psi_h( z0h(j,i) / ol(j,i) ) )
	816	ENDIF
	817
	818	ENDDO
	819	ENDDO
	820	ENDIF
	821
	822	!
	823	!-- If required compute q*
	824	IF ( humidity .OR. passive_scalar ) THEN
	825	IF ( constant_waterflux ) THEN
	826	!
	827	!-- For a given water flux in the Prandtl layer:
	828	!$OMP PARALLEL DO
	829	!$acc kernels loop
	830	DO i = nxlg, nxrg
	831	DO j = nysg, nyng
	832	qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30_wp )
	833	ENDDO
	834	ENDDO
	835
	836	ELSE
	837	coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. &
	838	run_coupled )
	839
	840	IF ( large_scale_forcing .AND. lsf_surf ) THEN
	841	!$OMP PARALLEL DO
	842	!$acc kernels loop
	843	DO i = nxlg, nxrg
	844	DO j = nysg, nyng
	845	k = nzb_s_inner(j,i)
	846	q(k,j,i) = q_surface
	847	ENDDO
	848	ENDDO
	849	ENDIF
	850
[1697]	851	!$OMP PARALLEL DO PRIVATE( e_s, k, z_mo )
[1691]	852	!$acc kernels loop independent
	853	DO i = nxlg, nxrg
	854	!$acc loop independent
	855	DO j = nysg, nyng
	856
	857	k = nzb_s_inner(j,i)
	858	z_mo = zu(k+1) - zw(k)
	859
	860	!
	861	!-- Assume saturation for atmosphere coupled to ocean (but not
	862	!-- in case of precursor runs)
	863	IF ( coupled_run ) THEN
	864	e_s = 6.1_wp * &
	865	EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) &
	866	- 273.15_wp ) )
	867	q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s )
	868	ENDIF
	869
	870	IF ( cloud_physics ) THEN
	871	qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) &
	872	/ ( LOG( z_mo / z0h(j,i) ) &
	873	- psi_h( z_mo / ol(j,i) ) &
	874	+ psi_h( z0h(j,i) / ol(j,i) ) )
	875
	876	ELSE
	877	qs(j,i) = kappa * ( q(k+1,j,i) - q(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	ENDIF
	882
	883	ENDDO
	884	ENDDO
	885	ENDIF
	886	ENDIF
	887
	888
	889	!
	890	!-- If required compute qr* and nr*
	891	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. precipitation ) THEN
	892
[1697]	893	!$OMP PARALLEL DO PRIVATE( k, z_mo )
[1691]	894	!$acc kernels loop independent
	895	DO i = nxlg, nxrg
	896	!$acc loop independent
	897	DO j = nysg, nyng
	898
	899	k = nzb_s_inner(j,i)
	900	z_mo = zu(k+1) - zw(k)
	901
	902	qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) &
	903	/ ( LOG( z_mo / z0h(j,i) ) &
	904	- psi_h( z_mo / ol(j,i) ) &
	905	+ psi_h( z0h(j,i) / ol(j,i) ) )
	906
	907	nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) &
	908	/ ( LOG( z_mo / z0h(j,i) ) &
	909	- psi_h( z_mo / ol(j,i) ) &
	910	+ psi_h( z0h(j,i) / ol(j,i) ) )
	911	ENDDO
	912	ENDDO
	913
	914	ENDIF
	915
	916	END SUBROUTINE calc_scaling_parameters
	917
	918
	919
	920	!
	921	!-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws)
	922	SUBROUTINE calc_surface_fluxes
	923
	924	IMPLICIT NONE
	925
	926	REAL(wp) :: ol_mid !< Grid-interpolated L
	927
	928	!
	929	!-- Compute u'w' for the total model domain.
	930	!-- First compute the corresponding component of u* and square it.
	931	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
	932	!$acc kernels loop
	933	DO i = nxl, nxr
	934	DO j = nys, nyn
	935
	936	k = nzb_u_inner(j,i)
	937	z_mo = zu(k+1) - zw(k)
	938	!
	939	!-- Compute bulk Obukhov length for this point
	940	ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) )
	941
	942	IF ( ol_mid == 0.0_wp ) THEN
	943	ol_mid = MIN(ol(j,i-1), ol(j,i))
	944	ENDIF
	945
	946	usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) &
	947	/ ( LOG( z_mo / z0(j,i) ) &
	948	- psi_m( z_mo / ol_mid ) &
	949	+ psi_m( z0(j,i) / ol_mid ) )
	950
	951	usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	952	ENDDO
	953	ENDDO
	954
	955	!
	956	!-- Compute v'w' for the total model domain.
	957	!-- First compute the corresponding component of u* and square it.
	958	!$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo )
	959	!$acc kernels loop
	960	DO i = nxl, nxr
	961	DO j = nys, nyn
	962
	963	k = nzb_v_inner(j,i)
	964	z_mo = zu(k+1) - zw(k)
	965	!
	966	!-- Compute bulk Obukhov length for this point
	967	ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) )
	968
	969	IF ( ol_mid == 0.0_wp ) THEN
	970	ol_mid = MIN(ol(j-1,i), ol(j-1,i))
	971	ENDIF
	972
	973	vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) &
	974	/ ( LOG( z_mo / z0(j,i) ) &
	975	- psi_m( z_mo / ol_mid ) &
	976	+ psi_m( z0(j,i) / ol_mid ) )
	977
	978	vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) )
	979
	980	ENDDO
	981	ENDDO
	982
	983	!
	984	!-- Exchange the boundaries for the momentum fluxes (is this still required?)
	985	!$acc update host( usws, vsws )
	986	CALL exchange_horiz_2d( usws )
	987	CALL exchange_horiz_2d( vsws )
	988	!$acc update device( usws, vsws )
	989
	990	!
	991	!-- Compute the vertical kinematic heat flux
	992	IF ( .NOT. constant_heatflux .AND. ( simulated_time <= &
	993	skip_time_do_lsm .OR. .NOT. land_surface ) ) THEN
	994	!$OMP PARALLEL DO
	995	!$acc kernels loop independent
	996	DO i = nxlg, nxrg
	997	!$acc loop independent
	998	DO j = nysg, nyng
	999	shf(j,i) = -ts(j,i) * us(j,i)
	1000	ENDDO
	1001	ENDDO
	1002
	1003	ENDIF
	1004
	1005	!
	1006	!-- Compute the vertical water/scalar flux
	1007	IF ( .NOT. constant_waterflux .AND. ( humidity .OR. passive_scalar ) &
	1008	.AND. ( simulated_time <= skip_time_do_lsm .OR. .NOT. &
	1009	land_surface ) ) THEN
	1010	!$OMP PARALLEL DO
	1011	!$acc kernels loop independent
	1012	DO i = nxlg, nxrg
	1013	!$acc loop independent
	1014	DO j = nysg, nyng
	1015	qsws(j,i) = -qs(j,i) * us(j,i)
	1016	ENDDO
	1017	ENDDO
	1018
	1019	ENDIF
	1020
	1021	!
	1022	!-- Compute (turbulent) fluxes of rain water content and rain drop conc.
	1023	IF ( cloud_physics .AND. icloud_scheme == 0 .AND. &
	1024	precipitation ) THEN
	1025	!$OMP PARALLEL DO
	1026	!$acc kernels loop independent
	1027	DO i = nxlg, nxrg
	1028	!$acc loop independent
	1029	DO j = nysg, nyng
	1030	qrsws(j,i) = -qrs(j,i) * us(j,i)
	1031	nrsws(j,i) = -nrs(j,i) * us(j,i)
	1032	ENDDO
	1033	ENDDO
	1034	ENDIF
	1035
	1036	!
	1037	!-- Bottom boundary condition for the TKE
	1038	IF ( ibc_e_b == 2 ) THEN
	1039	!$OMP PARALLEL DO
	1040	!$acc kernels loop independent
	1041	DO i = nxlg, nxrg
	1042	!$acc loop independent
	1043	DO j = nysg, nyng
	1044	e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.1_wp )**2
	1045	!
	1046	!-- As a test: cm = 0.4
	1047	! e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.4_wp )**2
	1048	e(nzb_s_inner(j,i),j,i) = e(nzb_s_inner(j,i)+1,j,i)
	1049	ENDDO
	1050	ENDDO
	1051	ENDIF
	1052	!$acc end data
	1053
	1054	END SUBROUTINE calc_surface_fluxes
	1055
	1056
	1057	!
	1058	!-- Integrated stability function for momentum
	1059	FUNCTION psi_m( zeta )
	1060
	1061	USE kinds
	1062
	1063	IMPLICIT NONE
	1064
	1065	REAL(wp) :: psi_m !< Integrated similarity function result
	1066	REAL(wp) :: zeta !< Stability parameter z/L
	1067	REAL(wp) :: x !< dummy variable
	1068
	1069	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1070	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1071	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1072	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1073	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1074	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1075
	1076
	1077	IF ( zeta < 0.0_wp ) THEN
	1078	x = SQRT( SQRT(1.0_wp - 16.0_wp * zeta ) )
	1079	psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 &
	1080	* ( 1.0_wp + x*2 ) 0.125_wp )
	1081	ELSE
	1082
	1083	psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta &
	1084	- bc_d_d
	1085	!
	1086	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1087	!-- psi_m = - 5.0_wp * zeta
	1088
	1089	ENDIF
	1090
	1091	END FUNCTION psi_m
	1092
	1093
	1094	!
	1095	!-- Integrated stability function for heat and moisture
	1096	FUNCTION psi_h( zeta )
	1097
	1098	USE kinds
	1099
	1100	IMPLICIT NONE
	1101
	1102	REAL(wp) :: psi_h !< Integrated similarity function result
	1103	REAL(wp) :: zeta !< Stability parameter z/L
	1104	REAL(wp) :: x !< dummy variable
	1105
	1106	REAL(wp), PARAMETER :: a = 1.0_wp !< constant
	1107	REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant
	1108	REAL(wp), PARAMETER :: c = 5.0_wp !< constant
	1109	REAL(wp), PARAMETER :: d = 0.35_wp !< constant
	1110	REAL(wp), PARAMETER :: c_d_d = c / d !< constant
	1111	REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant
	1112
	1113
	1114	IF ( zeta < 0.0_wp ) THEN
	1115	x = SQRT(1.0_wp - 16.0_wp * zeta )
	1116	psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp )
	1117	ELSE
	1118	psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp &
	1119	+ 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d &
	1120	+ 1.0_wp
	1121	!
	1122	!-- Old version for stable conditions (only valid for z/L < 0.5)
	1123	!-- psi_h = - 5.0_wp * zeta
	1124	ENDIF
	1125
	1126	END FUNCTION psi_h
	1127
[1697]	1128	END MODULE surface_layer_fluxes_mod

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