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wall_fluxes.f90 @ 858

Last change on this file since 858 was 667, checked in by suehring, 14 years ago

summary:

Gryschka:

Coupling with different resolution and different numbers of PEs in ocean and atmosphere is available
Exchange of u and v from ocean surface to atmosphere surface
Mirror boundary condition for u and v at the bottom are replaced by dirichlet boundary conditions
Inflow turbulence is now defined by flucuations around spanwise mean
Bugfixes for cyclic_fill and constant_volume_flow

Suehring:

New advection added ( Wicker and Skamarock 5th order ), therefore:
- New module advec_ws.f90
- Modified exchange of ghost boundaries.
- Modified evaluation of turbulent fluxes
- New index bounds nxlg, nxrg, nysg, nyng

advec_ws.f90

Advection scheme for scalars and momentum using the flux formulation of
Wicker and Skamarock 5th order.
Additionally the module contains of a routine using for initialisation and
steering of the statical evaluation. The computation of turbulent fluxes takes
place inside the advection routines.
In case of vector architectures Dirichlet and Radiation boundary conditions are
outstanding and not available. Furthermore simulations within topography are
not possible so far. A further routine local_diss_ij is available and is used
if a control of dissipative fluxes is desired.

check_parameters.f90

Exchange of parameters between ocean and atmosphere via PE0
Check for illegal combination of ws-scheme and timestep scheme.
Check for topography and ws-scheme.
Check for not cyclic boundary conditions in combination with ws-scheme and
loop_optimization = 'vector'.
Check for call_psolver_at_all_substeps and ws-scheme for momentum_advec.

Different processor/grid topology in atmosphere and ocean is now allowed!
Bugfixes in checking for conserve_volume_flow_mode.

exchange_horiz.f90

Dynamic exchange of ghost points with nbgp_local to ensure that no useless
ghost points exchanged in case of multigrid. type_yz(0) and type_xz(0) used for
normal grid, the remaining types used for the several grid levels.
Exchange is done via MPI-Vectors with a dynamic value of ghost points which
depend on the advection scheme. Exchange of left and right PEs is 10% faster
with MPI-Vectors than without.

flow_statistics.f90

When advection is computed with ws-scheme, turbulent fluxes are already
computed in the respective advection routines and buffered in arrays
sums_xxxx_ws_l(). This is due to a consistent treatment of statistics
with the numerics and to avoid unphysical kinks near the surface. So some if-
requests has to be done to dicern between fluxes from ws-scheme other advection
schemes. Furthermore the computation of z_i is only done if the heat flux
exceeds a minimum value. This affects only simulations of a neutral boundary
layer and is due to reasons of computations in the advection scheme.

inflow_turbulence.f90

Using nbgp recycling planes for a better resolution of the turbulent flow near
the inflow.

init_grid.f90

Definition of new array bounds nxlg, nxrg, nysg, nyng on each PE.
Furthermore the allocation of arrays and steering of loops is done with these
parameters. Call of exchange_horiz are modified.
In case of dirichlet bounday condition at the bottom zu(0)=0.0
dzu_mg has to be set explicitly for a equally spaced grid near bottom.
ddzu_pres added to use a equally spaced grid near bottom.

init_pegrid.f90

Moved determination of target_id's from init_coupling
Determination of parameters needed for coupling (coupling_topology, ngp_a, ngp_o)
with different grid/processor-topology in ocean and atmosphere

Adaption of ngp_xy, ngp_y to a dynamic number of ghost points.
The maximum_grid_level changed from 1 to 0. 0 is the normal grid, 1 to
maximum_grid_level the grids for multigrid, in which 0 and 1 are normal grids.
This distinction is due to reasons of data exchange and performance for the
normal grid and grids in poismg.
The definition of MPI-Vectors adapted to a dynamic numer of ghost points.
New MPI-Vectors for data exchange between left and right boundaries added.
This is due to reasons of performance (10% faster).

ATTENTION: nnz_x undefined problem still has to be solved!!!!!!!!
TEST OUTPUT (TO BE REMOVED) logging mpi2 ierr values

parin.f90

Steering parameter dissipation_control added in inipar.

Makefile

Module advec_ws added.

Modules

Removed u_nzb_p1_for_vfc and v_nzb_p1_for_vfc

For coupling with different resolution in ocean and atmophere:
+nx_a, +nx_o, ny_a, +ny_o, ngp_a, ngp_o, +total_2d_o, +total_2d_a,
+coupling_topology

Buffer arrays for the left sided advective fluxes added in arrays_3d.
+flux_s_u, +flux_s_v, +flux_s_w, +diss_s_u, +diss_s_v, +diss_s_w,
+flux_s_pt, +diss_s_pt, +flux_s_e, +diss_s_e, +flux_s_q, +diss_s_q,
+flux_s_sa, +diss_s_sa
3d arrays for dissipation control added. (only necessary for vector arch.)
+var_x, +var_y, +var_z, +gamma_x, +gamma_y, +gamma_z
Default of momentum_advec and scalar_advec changed to 'ws-scheme' .
+exchange_mg added in control_parameters to steer the data exchange.
Parameters +nbgp, +nxlg, +nxrg, +nysg, +nyng added in indices.
flag array +boundary_flags added in indices to steer the degradation of order
of the advective fluxes when non-cyclic boundaries are used.
MPI-datatypes +type_y, +type_y_int and +type_yz for data_exchange added in
pegrid.
+sums_wsus_ws_l, +sums_wsvs_ws_l, +sums_us2_ws_l, +sums_vs2_ws_l,
+sums_ws2_ws_l, +sums_wspts_ws_l, +sums_wssas_ws_l, +sums_wsqs_ws_l
and +weight_substep added in statistics to steer the statistical evaluation
of turbulent fluxes in the advection routines.
LOGICALS +ws_scheme_sca and +ws_scheme_mom added to get a better performance
in prognostic_equations.
LOGICAL +dissipation_control control added to steer numerical dissipation
in ws-scheme.

Changed length of string run_description_header

pres.f90

New allocation of tend when ws-scheme and multigrid is used. This is due to
reasons of perforance of the data_exchange. The same is done with p after
poismg is called.
nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng when no
multigrid is used. Calls of exchange_horiz are modified.

bugfix: After pressure correction no volume flow correction in case of
non-cyclic boundary conditions
(has to be done only before pressure correction)

Call of SOR routine is referenced with ddzu_pres.

prognostic_equations.f90

Calls of the advection routines with WS5 added.
Calls of ws_statistics added to set the statistical arrays to zero after each
time step.

advec_particles.f90

Declaration of de_dx, de_dy, de_dz adapted to additional ghost points.
Furthermore the calls of exchange_horiz were modified.

asselin_filter.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

average_3d_data.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

boundary_conds.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng
Removed mirror boundary conditions for u and v at the bottom in case of
ibc_uv_b == 0. Instead, dirichelt boundary conditions (u=v=0) are set
in init_3d_model

calc_liquid_water_content.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

calc_spectra.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for
allocation of tend.

check_open.f90

Output of total array size was adapted to nbgp.

data_output_2d.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in loops and
allocation of arrays local_2d and total_2d.
Calls of exchange_horiz are modified.

data_output_2d.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in loops and
allocation of arrays. Calls of exchange_horiz are modified.
Skip-value skip_do_avs changed to a dynamic adaption of ghost points.

data_output_mask.f90

Calls of exchange_horiz are modified.

diffusion_e.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_s.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_u.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_v.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusion_w.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusivities.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

diffusivities.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.
Calls of exchange_horiz are modified.

exchange_horiz_2d.f90

Dynamic exchange of ghost points with nbgp, which depends on the advection
scheme. Exchange between left and right PEs is now done with MPI-vectors.

global_min_max.f90

Adapting of the index arrays, because MINLOC assumes lowerbound
at 1 and not at nbgp.

init_3d_model.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in loops and
allocation of arrays. Calls of exchange_horiz are modified.
Call ws_init to initialize arrays needed for statistical evaluation and
optimization when ws-scheme is used.
Initial volume flow is now calculated by using the variable hom_sum.
Therefore the correction of initial volume flow for non-flat topography
removed (removed u_nzb_p1_for_vfc and v_nzb_p1_for_vfc)
Changed surface boundary conditions for u and v in case of ibc_uv_b == 0 from
mirror bc to dirichlet boundary conditions (u=v=0), so that k=nzb is
representative for the height z0

Bugfix: type conversion of '1' to 64bit for the MAX function (ngp_3d_inner)

init_coupling.f90

determination of target_id's moved to init_pegrid

init_pt_anomaly.f90

Call of exchange_horiz are modified.

init_rankine.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.
Calls of exchange_horiz are modified.

init_slope.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

header.f90

Output of advection scheme.

poismg.f90

Calls of exchange_horiz are modified.

prandtl_fluxes.f90

Changed surface boundary conditions for u and v from mirror bc to dirichelt bc,
therefore u(uzb,:,:) and v(nzb,:,:) is now representative for the height z0
nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

production_e.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng

read_3d_binary.f90

+/- 1 replaced with +/- nbgp when swapping and allocating variables.

sor.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.
Call of exchange_horiz are modified.
bug removed in declaration of ddzw(), nz replaced by nzt+1

subsidence.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

sum_up_3d_data.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

surface_coupler.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng in
MPI_SEND() and MPI_RECV.
additional case for nonequivalent processor and grid topopolgy in ocean and
atmosphere added (coupling_topology = 1)

Added exchange of u and v from Ocean to Atmosphere

time_integration.f90

Calls of exchange_horiz are modified.
Adaption to slooping surface.

timestep.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

user_3d_data_averaging.f90, user_data_output_2d.f90, user_data_output_3d.f90,
user_actions.f90, user_init.f90, user_init_plant_canopy.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

user_read_restart_data.f90

Allocation with nbgp.

wall_fluxes.f90

nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.

write_compressed.f90

Array bounds and nx, ny adapted with nbgp.

sor.f90

bug removed in declaration of ddzw(), nz replaced by nzt+1

Property svn:keywords set to Id

File size: 20.8 KB

Rev	Line
[56]	1	MODULE wall_fluxes_mod
[52]	2	!------------------------------------------------------------------------------!
[484]	3	! Current revisions:
[52]	4	! -----------------
[198]	5	!
	6	!
	7	! Former revisions:
	8	! -----------------
	9	! $Id: wall_fluxes.f90 667 2010-12-23 12:06:00Z suehring $
	10	!
	11	! 187 2008-08-06 16:25:09Z letzel
	12	! Bugfix: Modification of the evaluation of the vertical turbulent momentum
	13	! fluxes u'w' and v'w (see prandtl_fluxes), this requires the calculation of
	14	! us_wall (and vel_total, u_i, v_i, ws) also in wall_fluxes_e.
	15	! Bugfix: change definition of us_wall from 1D to 2D
[187]	16	! Bugfix: storage of rifs to rifs_wall in wall_fluxes_e removed
	17	! Change: add 'minus' sign to fluxes produced by subroutine wall_fluxes_e for
[198]	18	! consistency with subroutine wall_fluxes
[187]	19	! Change: Modification of the integrated version of the profile function for
[198]	20	! momentum for unstable stratification
[52]	21	!
	22	! Initial version (2007/03/07)
	23	!
	24	! Description:
	25	! ------------
	26	! Calculates momentum fluxes at vertical walls assuming Monin-Obukhov
	27	! similarity.
	28	! Indices: usvs a=1, vsus b=1, wsvs c1=1, wsus c2=1 (other=0).
[56]	29	! The all-gridpoint version of wall_fluxes_e is not used so far, because
	30	! it gives slightly different results from the ij-version for some unknown
	31	! reason.
[52]	32	!------------------------------------------------------------------------------!
[56]	33	PRIVATE
	34	PUBLIC wall_fluxes, wall_fluxes_e
	35
	36	INTERFACE wall_fluxes
	37	MODULE PROCEDURE wall_fluxes
	38	MODULE PROCEDURE wall_fluxes_ij
	39	END INTERFACE wall_fluxes
	40
	41	INTERFACE wall_fluxes_e
	42	MODULE PROCEDURE wall_fluxes_e
	43	MODULE PROCEDURE wall_fluxes_e_ij
	44	END INTERFACE wall_fluxes_e
	45
	46	CONTAINS
[52]	47
[56]	48	!------------------------------------------------------------------------------!
	49	! Call for all grid points
	50	!------------------------------------------------------------------------------!
[75]	51	SUBROUTINE wall_fluxes( wall_flux, a, b, c1, c2, nzb_uvw_inner, &
[56]	52	nzb_uvw_outer, wall )
[52]	53
[56]	54	USE arrays_3d
	55	USE control_parameters
	56	USE grid_variables
	57	USE indices
	58	USE statistics
[52]	59
[56]	60	IMPLICIT NONE
[52]	61
[75]	62	INTEGER :: i, j, k, wall_index
[52]	63
[667]	64	INTEGER, DIMENSION(nysg:nyng,nxlg:nxrg) :: nzb_uvw_inner, &
[56]	65	nzb_uvw_outer
	66	REAL :: a, b, c1, c2, h1, h2, zp
	67	REAL :: pts, pt_i, rifs, u_i, v_i, us_wall, vel_total, ws, wspts
[52]	68
[667]	69	REAL, DIMENSION(nysg:nyng,nxlg:nxrg) :: wall
[75]	70	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: wall_flux
[52]	71
	72
[56]	73	zp = 0.5 * ( (a+c1) * dy + (b+c2) * dx )
	74	wall_flux = 0.0
	75	wall_index = NINT( a+ 2b + 3c1 + 4*c2 )
	76
[75]	77	DO i = nxl, nxr
	78	DO j = nys, nyn
[56]	79
	80	IF ( wall(j,i) /= 0.0 ) THEN
[52]	81	!
[56]	82	!-- All subsequent variables are computed for the respective
[187]	83	!-- location where the respective flux is defined.
[56]	84	DO k = nzb_uvw_inner(j,i)+1, nzb_uvw_outer(j,i)
[53]	85
[52]	86	!
[56]	87	!-- (1) Compute rifs, u_i, v_i, ws, pt' and w'pt'
	88	rifs = rif_wall(k,j,i,wall_index)
[53]	89
[56]	90	u_i = a * u(k,j,i) + c1 * 0.25 * &
	91	( u(k+1,j,i+1) + u(k+1,j,i) + u(k,j,i+1) + u(k,j,i) )
[53]	92
[56]	93	v_i = b * v(k,j,i) + c2 * 0.25 * &
	94	( v(k+1,j+1,i) + v(k+1,j,i) + v(k,j+1,i) + v(k,j,i) )
[53]	95
[56]	96	ws = ( c1 + c2 ) * w(k,j,i) + 0.25 * ( &
	97	a * ( w(k-1,j,i-1) + w(k-1,j,i) + w(k,j,i-1) + w(k,j,i) ) &
	98	+ b * ( w(k-1,j-1,i) + w(k-1,j,i) + w(k,j-1,i) + w(k,j,i) ) &
	99	)
	100	pt_i = 0.5 * ( pt(k,j,i) + a * pt(k,j,i-1) + &
	101	b * pt(k,j-1,i) + ( c1 + c2 ) * pt(k+1,j,i) )
[53]	102
[56]	103	pts = pt_i - hom(k,1,4,0)
	104	wspts = ws * pts
[53]	105
[52]	106	!
[56]	107	!-- (2) Compute wall-parallel absolute velocity vel_total
	108	vel_total = SQRT( ws*2 + (a+c1) u_i*2 + (b+c2) v_i**2 )
[53]	109
[52]	110	!
[56]	111	!-- (3) Compute wall friction velocity us_wall
	112	IF ( rifs >= 0.0 ) THEN
[53]	113
[52]	114	!
[56]	115	!-- Stable stratification (and neutral)
	116	us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + &
	117	5.0 * rifs * ( zp - z0(j,i) ) / zp &
	118	)
	119	ELSE
[53]	120
[52]	121	!
[56]	122	!-- Unstable stratification
[187]	123	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
	124	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
[53]	125
[187]	126	us_wall = kappa * vel_total / ( &
	127	LOG( zp / z0(j,i) ) - &
	128	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
	129	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
	130	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
	131	)
[56]	132	ENDIF
[53]	133
[52]	134	!
[56]	135	!-- (4) Compute zp/L (corresponds to neutral Richardson flux
	136	!-- number rifs)
	137	rifs = -1.0 * zp * kappa * g * wspts / ( pt_i * &
	138	( us_wall**3 + 1E-30 ) )
[53]	139
[52]	140	!
[56]	141	!-- Limit the value range of the Richardson numbers.
	142	!-- This is necessary for very small velocities (u,w --> 0),
	143	!-- because the absolute value of rif can then become very
	144	!-- large, which in consequence would result in very large
	145	!-- shear stresses and very small momentum fluxes (both are
	146	!-- generally unrealistic).
	147	IF ( rifs < rif_min ) rifs = rif_min
	148	IF ( rifs > rif_max ) rifs = rif_max
[53]	149
[52]	150	!
[56]	151	!-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u')
	152	IF ( rifs >= 0.0 ) THEN
[53]	153
[52]	154	!
[56]	155	!-- Stable stratification (and neutral)
	156	wall_flux(k,j,i) = kappa * &
	157	( au(k,j,i) + bv(k,j,i) + (c1+c2)*w(k,j,i) ) / &
	158	( LOG( zp / z0(j,i) ) + &
	159	5.0 * rifs * ( zp - z0(j,i) ) / zp &
	160	)
	161	ELSE
[53]	162
[52]	163	!
[56]	164	!-- Unstable stratification
[187]	165	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
	166	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
[53]	167
[187]	168	wall_flux(k,j,i) = kappa * &
	169	( au(k,j,i) + bv(k,j,i) + (c1+c2)*w(k,j,i) ) / ( &
	170	LOG( zp / z0(j,i) ) - &
	171	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
	172	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
	173	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
	174	)
[56]	175	ENDIF
[187]	176	wall_flux(k,j,i) = -wall_flux(k,j,i) * us_wall
[56]	177
	178	!
	179	!-- store rifs for next time step
	180	rif_wall(k,j,i,wall_index) = rifs
	181
	182	ENDDO
	183
	184	ENDIF
	185
	186	ENDDO
	187	ENDDO
	188
	189	END SUBROUTINE wall_fluxes
	190
	191
	192
	193	!------------------------------------------------------------------------------!
	194	! Call for all grid point i,j
	195	!------------------------------------------------------------------------------!
	196	SUBROUTINE wall_fluxes_ij( i, j, nzb_w, nzt_w, wall_flux, a, b, c1, c2 )
	197
	198	USE arrays_3d
	199	USE control_parameters
	200	USE grid_variables
	201	USE indices
	202	USE statistics
	203
	204	IMPLICIT NONE
	205
	206	INTEGER :: i, j, k, nzb_w, nzt_w, wall_index
	207	REAL :: a, b, c1, c2, h1, h2, zp
	208
	209	REAL :: pts, pt_i, rifs, u_i, v_i, us_wall, vel_total, ws, wspts
	210
	211	REAL, DIMENSION(nzb:nzt+1) :: wall_flux
	212
	213
	214	zp = 0.5 * ( (a+c1) * dy + (b+c2) * dx )
	215	wall_flux = 0.0
	216	wall_index = NINT( a+ 2b + 3c1 + 4*c2 )
	217
	218	!
	219	!-- All subsequent variables are computed for the respective location where
[187]	220	!-- the respective flux is defined.
[56]	221	DO k = nzb_w, nzt_w
	222
	223	!
	224	!-- (1) Compute rifs, u_i, v_i, ws, pt' and w'pt'
	225	rifs = rif_wall(k,j,i,wall_index)
	226
	227	u_i = a * u(k,j,i) + c1 * 0.25 * &
	228	( u(k+1,j,i+1) + u(k+1,j,i) + u(k,j,i+1) + u(k,j,i) )
	229
	230	v_i = b * v(k,j,i) + c2 * 0.25 * &
	231	( v(k+1,j+1,i) + v(k+1,j,i) + v(k,j+1,i) + v(k,j,i) )
	232
	233	ws = ( c1 + c2 ) * w(k,j,i) + 0.25 * ( &
	234	a * ( w(k-1,j,i-1) + w(k-1,j,i) + w(k,j,i-1) + w(k,j,i) ) &
	235	+ b * ( w(k-1,j-1,i) + w(k-1,j,i) + w(k,j-1,i) + w(k,j,i) ) &
	236	)
	237	pt_i = 0.5 * ( pt(k,j,i) + a * pt(k,j,i-1) + b * pt(k,j-1,i) &
	238	+ ( c1 + c2 ) * pt(k+1,j,i) )
	239
	240	pts = pt_i - hom(k,1,4,0)
	241	wspts = ws * pts
	242
	243	!
	244	!-- (2) Compute wall-parallel absolute velocity vel_total
	245	vel_total = SQRT( ws*2 + ( a+c1 ) u_i*2 + ( b+c2 ) v_i**2 )
	246
	247	!
	248	!-- (3) Compute wall friction velocity us_wall
	249	IF ( rifs >= 0.0 ) THEN
	250
	251	!
	252	!-- Stable stratification (and neutral)
	253	us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + &
	254	5.0 * rifs * ( zp - z0(j,i) ) / zp &
	255	)
	256	ELSE
	257
	258	!
	259	!-- Unstable stratification
[187]	260	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
	261	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
[56]	262
[187]	263	us_wall = kappa * vel_total / ( &
	264	LOG( zp / z0(j,i) ) - &
	265	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
	266	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
	267	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
	268	)
[56]	269	ENDIF
	270
	271	!
	272	!-- (4) Compute zp/L (corresponds to neutral Richardson flux number
	273	!-- rifs)
	274	rifs = -1.0 * zp * kappa * g * wspts / ( pt_i * (us_wall**3 + 1E-30) )
	275
	276	!
	277	!-- Limit the value range of the Richardson numbers.
	278	!-- This is necessary for very small velocities (u,w --> 0), because
	279	!-- the absolute value of rif can then become very large, which in
	280	!-- consequence would result in very large shear stresses and very
	281	!-- small momentum fluxes (both are generally unrealistic).
	282	IF ( rifs < rif_min ) rifs = rif_min
	283	IF ( rifs > rif_max ) rifs = rif_max
	284
	285	!
	286	!-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u')
	287	IF ( rifs >= 0.0 ) THEN
	288
	289	!
	290	!-- Stable stratification (and neutral)
[53]	291	wall_flux(k) = kappa * &
	292	( au(k,j,i) + bv(k,j,i) + (c1+c2)*w(k,j,i) ) / &
[56]	293	( LOG( zp / z0(j,i) ) + &
	294	5.0 * rifs * ( zp - z0(j,i) ) / zp &
[53]	295	)
[52]	296	ELSE
[53]	297
[56]	298	!
	299	!-- Unstable stratification
[187]	300	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
	301	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
[52]	302
[187]	303	wall_flux(k) = kappa * &
	304	( au(k,j,i) + bv(k,j,i) + (c1+c2)*w(k,j,i) ) / ( &
	305	LOG( zp / z0(j,i) ) - &
	306	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
	307	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
	308	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
	309	)
[56]	310	ENDIF
[187]	311	wall_flux(k) = -wall_flux(k) * us_wall
[53]	312
[56]	313	!
	314	!-- store rifs for next time step
	315	rif_wall(k,j,i,wall_index) = rifs
[53]	316
[56]	317	ENDDO
[53]	318
[56]	319	END SUBROUTINE wall_fluxes_ij
[53]	320
[56]	321
	322
[53]	323	!------------------------------------------------------------------------------!
[56]	324	! Call for all grid points
	325	!------------------------------------------------------------------------------!
	326	SUBROUTINE wall_fluxes_e( wall_flux, a, b, c1, c2, wall )
	327
	328	!------------------------------------------------------------------------------!
[53]	329	! Description:
	330	! ------------
	331	! Calculates momentum fluxes at vertical walls for routine production_e
	332	! assuming Monin-Obukhov similarity.
	333	! Indices: usvs a=1, vsus b=1, wsvs c1=1, wsus c2=1 (other=0).
	334	!------------------------------------------------------------------------------!
	335
[56]	336	USE arrays_3d
	337	USE control_parameters
	338	USE grid_variables
	339	USE indices
	340	USE statistics
[53]	341
[56]	342	IMPLICIT NONE
[53]	343
[56]	344	INTEGER :: i, j, k, kk, wall_index
[187]	345	REAL :: a, b, c1, c2, h1, h2, u_i, v_i, us_wall, vel_total, vel_zp, &
	346	ws, zp
[53]	347
[56]	348	REAL :: rifs
[53]	349
[667]	350	REAL, DIMENSION(nysg:nyng,nxlg:nxrg) :: wall
[56]	351	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: wall_flux
[53]	352
	353
[56]	354	zp = 0.5 * ( (a+c1) * dy + (b+c2) * dx )
	355	wall_flux = 0.0
	356	wall_index = NINT( a+ 2b + 3c1 + 4*c2 )
[53]	357
[56]	358	DO i = nxl, nxr
	359	DO j = nys, nyn
	360
	361	IF ( wall(j,i) /= 0.0 ) THEN
[53]	362	!
[187]	363	!-- All subsequent variables are computed for scalar locations.
[56]	364	DO k = nzb_diff_s_inner(j,i)-1, nzb_diff_s_outer(j,i)-2
[53]	365	!
[187]	366	!-- (1) Compute rifs, u_i, v_i, and ws
[56]	367	IF ( k == nzb_diff_s_inner(j,i)-1 ) THEN
	368	kk = nzb_diff_s_inner(j,i)-1
	369	ELSE
	370	kk = k-1
	371	ENDIF
	372	rifs = 0.5 * ( rif_wall(k,j,i,wall_index) + &
	373	a * rif_wall(k,j,i+1,1) + b * rif_wall(k,j+1,i,2) + &
	374	c1 * rif_wall(kk,j,i,3) + c2 * rif_wall(kk,j,i,4) &
	375	)
[53]	376
[187]	377	u_i = 0.5 * ( u(k,j,i) + u(k,j,i+1) )
	378	v_i = 0.5 * ( v(k,j,i) + v(k,j+1,i) )
	379	ws = 0.5 * ( w(k,j,i) + w(k-1,j,i) )
[53]	380	!
[187]	381	!-- (2) Compute wall-parallel absolute velocity vel_total and
	382	!-- interpolate appropriate velocity component vel_zp.
	383	vel_total = SQRT( ws*2 + (a+c1) u_i*2 + (b+c2) v_i**2 )
	384	vel_zp = 0.5 * ( a * u_i + b * v_i + (c1+c2) * ws )
	385	!
	386	!-- (3) Compute wall friction velocity us_wall
	387	IF ( rifs >= 0.0 ) THEN
[53]	388
	389	!
[187]	390	!-- Stable stratification (and neutral)
	391	us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + &
	392	5.0 * rifs * ( zp - z0(j,i) ) / zp &
	393	)
	394	ELSE
	395
	396	!
	397	!-- Unstable stratification
	398	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
	399	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
	400
	401	us_wall = kappa * vel_total / ( &
	402	LOG( zp / z0(j,i) ) - &
	403	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
	404	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
	405	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
	406	)
	407	ENDIF
	408
	409	!
	410	!-- Skip step (4) of wall_fluxes, because here rifs is already
	411	!-- available from (1)
	412	!
[56]	413	!-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u')
[55]	414
[56]	415	IF ( rifs >= 0.0 ) THEN
[53]	416
	417	!
[56]	418	!-- Stable stratification (and neutral)
	419	wall_flux(k,j,i) = kappa * vel_zp / &
	420	( LOG( zp/z0(j,i) ) + 5.0rifs ( zp-z0(j,i) ) / zp )
	421	ELSE
[53]	422
	423	!
[56]	424	!-- Unstable stratification
[187]	425	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
	426	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
[53]	427
[187]	428	wall_flux(k,j,i) = kappa * vel_zp / ( &
	429	LOG( zp / z0(j,i) ) - &
	430	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
	431	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
	432	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
	433	)
[56]	434	ENDIF
[187]	435	wall_flux(k,j,i) = - wall_flux(k,j,i) * us_wall
[56]	436
	437	ENDDO
	438
	439	ENDIF
	440
	441	ENDDO
	442	ENDDO
	443
	444	END SUBROUTINE wall_fluxes_e
	445
	446
	447
	448	!------------------------------------------------------------------------------!
	449	! Call for grid point i,j
	450	!------------------------------------------------------------------------------!
	451	SUBROUTINE wall_fluxes_e_ij( i, j, nzb_w, nzt_w, wall_flux, a, b, c1, c2 )
	452
	453	USE arrays_3d
	454	USE control_parameters
	455	USE grid_variables
	456	USE indices
	457	USE statistics
	458
	459	IMPLICIT NONE
	460
	461	INTEGER :: i, j, k, kk, nzb_w, nzt_w, wall_index
[187]	462	REAL :: a, b, c1, c2, h1, h2, u_i, v_i, us_wall, vel_total, vel_zp, &
	463	ws, zp
[56]	464
	465	REAL :: rifs
	466
	467	REAL, DIMENSION(nzb:nzt+1) :: wall_flux
	468
	469
	470	zp = 0.5 * ( (a+c1) * dy + (b+c2) * dx )
	471	wall_flux = 0.0
	472	wall_index = NINT( a+ 2b + 3c1 + 4*c2 )
	473
	474	!
[187]	475	!-- All subsequent variables are computed for scalar locations.
[56]	476	DO k = nzb_w, nzt_w
	477
	478	!
[187]	479	!-- (1) Compute rifs, u_i, v_i, and ws
[56]	480	IF ( k == nzb_w ) THEN
	481	kk = nzb_w
[53]	482	ELSE
[56]	483	kk = k-1
	484	ENDIF
	485	rifs = 0.5 * ( rif_wall(k,j,i,wall_index) + &
	486	a * rif_wall(k,j,i+1,1) + b * rif_wall(k,j+1,i,2) + &
	487	c1 * rif_wall(kk,j,i,3) + c2 * rif_wall(kk,j,i,4) &
	488	)
	489
[187]	490	u_i = 0.5 * ( u(k,j,i) + u(k,j,i+1) )
	491	v_i = 0.5 * ( v(k,j,i) + v(k,j+1,i) )
	492	ws = 0.5 * ( w(k,j,i) + w(k-1,j,i) )
[56]	493	!
[187]	494	!-- (2) Compute wall-parallel absolute velocity vel_total and
	495	!-- interpolate appropriate velocity component vel_zp.
	496	vel_total = SQRT( ws*2 + (a+c1) u_i*2 + (b+c2) v_i**2 )
	497	vel_zp = 0.5 * ( a * u_i + b * v_i + (c1+c2) * ws )
	498	!
	499	!-- (3) Compute wall friction velocity us_wall
	500	IF ( rifs >= 0.0 ) THEN
[56]	501
	502	!
[187]	503	!-- Stable stratification (and neutral)
	504	us_wall = kappa * vel_total / ( LOG( zp / z0(j,i) ) + &
	505	5.0 * rifs * ( zp - z0(j,i) ) / zp &
	506	)
	507	ELSE
	508
	509	!
	510	!-- Unstable stratification
	511	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
	512	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
	513
	514	us_wall = kappa * vel_total / ( &
	515	LOG( zp / z0(j,i) ) - &
	516	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
	517	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
	518	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
	519	)
	520	ENDIF
	521
	522	!
	523	!-- Skip step (4) of wall_fluxes, because here rifs is already
	524	!-- available from (1)
	525	!
[56]	526	!-- (5) Compute wall_flux (u'v', v'u', w'v', or w'u')
[187]	527	!-- First interpolate the velocity (this is different from
	528	!-- subroutine wall_fluxes because fluxes in subroutine
	529	!-- wall_fluxes_e are defined at scalar locations).
[56]	530	vel_zp = 0.5 * ( a * ( u(k,j,i) + u(k,j,i+1) ) + &
	531	b * ( v(k,j,i) + v(k,j+1,i) ) + &
	532	(c1+c2) * ( w(k,j,i) + w(k-1,j,i) ) &
	533	)
	534
	535	IF ( rifs >= 0.0 ) THEN
	536
	537	!
	538	!-- Stable stratification (and neutral)
	539	wall_flux(k) = kappa * vel_zp / &
	540	( LOG( zp/z0(j,i) ) + 5.0rifs ( zp-z0(j,i) ) / zp )
	541	ELSE
	542
	543	!
	544	!-- Unstable stratification
[187]	545	h1 = SQRT( SQRT( 1.0 - 16.0 * rifs ) )
	546	h2 = SQRT( SQRT( 1.0 - 16.0 * rifs * z0(j,i) / zp ) )
[56]	547
[187]	548	wall_flux(k) = kappa * vel_zp / ( &
	549	LOG( zp / z0(j,i) ) - &
	550	LOG( ( 1.0 + h1 )*2 ( 1.0 + h1**2 ) / ( &
	551	( 1.0 + h2 )*2 ( 1.0 + h2**2 ) ) ) + &
	552	2.0 * ( ATAN( h1 ) - ATAN( h2 ) ) &
	553	)
[53]	554	ENDIF
[187]	555	wall_flux(k) = - wall_flux(k) * us_wall
[53]	556
[56]	557	ENDDO
[53]	558
[56]	559	END SUBROUTINE wall_fluxes_e_ij
	560
	561	END MODULE wall_fluxes_mod

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