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source: palm/trunk/SOURCE/surface_layer_fluxes.f90 @ 1709

Last change on this file since 1709 was 1709, checked in by maronga, 8 years ago
several bugfixes related to the new surface layer routine and land-surface-radiation interaction
Property svn:keywords set to `Id`
File size: 41.0 KB

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

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