source: palm/trunk/SOURCE/prandtl_fluxes.f90 @ 667

Last change on this file since 667 was 667, checked in by suehring, 13 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: 12.8 KB
Line 
1 SUBROUTINE prandtl_fluxes
2
3!------------------------------------------------------------------------------!
4! Current revisions:
5! -----------------
6!
7! Changed surface boundary conditions for u and v from mirror bc to dirichelt bc,
8! therefore u(uzb,:,:) and v(nzb,:,:) is now representative for the height z0
9!
10! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng
11!
12! Former revisions:
13! -----------------
14! $Id: prandtl_fluxes.f90 667 2010-12-23 12:06:00Z suehring $
15!
16! 315 2009-05-13 10:57:59Z raasch
17! Saturation condition at (sea) surface is not used in precursor runs (only
18! in the following coupled runs)
19! Bugfix: qsws was calculated in case of constant heatflux = .FALSE.
20!
21! 187 2008-08-06 16:25:09Z letzel
22! Bugfix: modification of the calculation of the vertical turbulent momentum
23! fluxes u'w' and v'w'
24! Bugfix: change definition of us_wall from 1D to 2D
25! Change: modification of the integrated version of the profile function for
26! momentum for unstable stratification (does not effect results)
27!
28! 108 2007-08-24 15:10:38Z letzel
29! assume saturation at k=nzb_s_inner(j,i) for atmosphere coupled to ocean
30!
31! 75 2007-03-22 09:54:05Z raasch
32! moisture renamed humidity
33!
34! RCS Log replace by Id keyword, revision history cleaned up
35!
36! Revision 1.19  2006/04/26 12:24:35  raasch
37! +OpenMP directives and optimization (array assignments replaced by DO loops)
38!
39! Revision 1.1  1998/01/23 10:06:06  raasch
40! Initial revision
41!
42!
43! Description:
44! ------------
45! Diagnostic computation of vertical fluxes in the Prandtl layer from the
46! values of the variables at grid point k=1
47!------------------------------------------------------------------------------!
48
49    USE arrays_3d
50    USE control_parameters
51    USE grid_variables
52    USE indices
53
54    IMPLICIT NONE
55
56    INTEGER ::  i, j, k
57    REAL    ::  a, b, e_q, rifm, uv_total, z_p
58
59!
60!-- Compute theta*
61    IF ( constant_heatflux )  THEN
62!
63!--    For a given heat flux in the Prandtl layer:
64!--    for u* use the value from the previous time step
65       !$OMP PARALLEL DO
66       DO  i = nxlg, nxrg
67          DO  j = nysg, nyng
68             ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30 )
69!
70!--          ts must be limited, because otherwise overflow may occur in case of
71!--          us=0 when computing rif further below
72             IF ( ts(j,i) < -1.05E5 )  ts = -1.0E5
73             IF ( ts(j,i) >   1.0E5 )  ts =  1.0E5
74          ENDDO
75       ENDDO
76
77    ELSE
78!
79!--    For a given surface temperature:
80!--    (the Richardson number is still the one from the previous time step)
81       !$OMP PARALLEL DO PRIVATE( a, b, k, z_p )
82       DO  i = nxlg, nxrg
83          DO  j = nysg, nyng
84
85             k   = nzb_s_inner(j,i)
86             z_p = zu(k+1) - zw(k)
87
88             IF ( rif(j,i) >= 0.0 )  THEN
89!
90!--             Stable stratification
91                ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) / (          &
92                                  LOG( z_p / z0(j,i) ) +                   &
93                                  5.0 * rif(j,i) * ( z_p - z0(j,i) ) / z_p &
94                                                                )
95             ELSE
96!
97!--             Unstable stratification
98                a = SQRT( 1.0 - 16.0 * rif(j,i) )
99                b = SQRT( 1.0 - 16.0 * rif(j,i) * z0(j,i) / z_p )
100
101                ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) /  (         &
102                          LOG( z_p / z0(j,i) ) -                           &
103                          2.0 * LOG( ( 1.0 + a ) / ( 1.0 + b ) ) )
104             ENDIF
105
106          ENDDO
107       ENDDO
108    ENDIF
109
110!
111!-- Compute z_p/L (corresponds to the Richardson-flux number)
112    IF ( .NOT. humidity )  THEN
113       !$OMP PARALLEL DO PRIVATE( k, z_p )
114       DO  i = nxlg, nxrg
115          DO  j = nysg, nyng
116             k   = nzb_s_inner(j,i)
117             z_p = zu(k+1) - zw(k)
118             rif(j,i) = z_p * kappa * g * ts(j,i) / &
119                        ( pt(k+1,j,i) * ( us(j,i)**2 + 1E-30 ) )
120!
121!--          Limit the value range of the Richardson numbers.
122!--          This is necessary for very small velocities (u,v --> 0), because
123!--          the absolute value of rif can then become very large, which in
124!--          consequence would result in very large shear stresses and very
125!--          small momentum fluxes (both are generally unrealistic).
126             IF ( rif(j,i) < rif_min )  rif(j,i) = rif_min
127             IF ( rif(j,i) > rif_max )  rif(j,i) = rif_max
128          ENDDO
129       ENDDO
130    ELSE
131       !$OMP PARALLEL DO PRIVATE( k, z_p )
132       DO  i = nxlg, nxrg
133          DO  j = nysg, nyng
134             k   = nzb_s_inner(j,i)
135             z_p = zu(k+1) - zw(k)
136             rif(j,i) = z_p * kappa * g *                            &
137                        ( ts(j,i) + 0.61 * pt(k+1,j,i) * qs(j,i) ) / &
138                        ( vpt(k+1,j,i) * ( us(j,i)**2 + 1E-30 ) )
139!
140!--          Limit the value range of the Richardson numbers.
141!--          This is necessary for very small velocities (u,v --> 0), because
142!--          the absolute value of rif can then become very large, which in
143!--          consequence would result in very large shear stresses and very
144!--          small momentum fluxes (both are generally unrealistic).
145             IF ( rif(j,i) < rif_min )  rif(j,i) = rif_min
146             IF ( rif(j,i) > rif_max )  rif(j,i) = rif_max
147          ENDDO
148       ENDDO       
149    ENDIF
150
151!
152!-- Compute u* at the scalars' grid points
153    !$OMP PARALLEL DO PRIVATE( a, b, k, uv_total, z_p )
154    DO  i = nxl, nxr
155       DO  j = nys, nyn
156
157          k   = nzb_s_inner(j,i)
158          z_p = zu(k+1) - zw(k)
159
160!
161!--       Compute the absolute value of the horizontal velocity
162!--       (relative to the surface)
163          uv_total = SQRT( ( 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1)        &
164                                   - u(k,j,i)   - u(k,j,i+1) ) )**2 + &
165                           ( 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i)        &
166                                   - v(k,j,i)   - v(k,j+1,i) ) )**2 )   
167
168
169          IF ( rif(j,i) >= 0.0 )  THEN
170!
171!--          Stable stratification
172             us(j,i) = kappa * uv_total / (                                &
173                                  LOG( z_p / z0(j,i) ) +                   &
174                                  5.0 * rif(j,i) * ( z_p - z0(j,i) ) / z_p &
175                                          )
176          ELSE
177!
178!--          Unstable stratification
179             a = SQRT( SQRT( 1.0 - 16.0 * rif(j,i) ) )
180             b = SQRT( SQRT( 1.0 - 16.0 * rif(j,i) / z_p * z0(j,i) ) )
181
182             us(j,i) = kappa * uv_total / (                                  &
183                       LOG( z_p / z0(j,i) ) -                                &
184                       LOG( ( 1.0 + a )**2 * ( 1.0 + a**2 ) / (              &
185                            ( 1.0 + b )**2 * ( 1.0 + b**2 )   ) ) +          &
186                            2.0 * ( ATAN( a ) - ATAN( b ) )                  &
187                                           )
188          ENDIF
189       ENDDO
190    ENDDO
191
192!
193!-- Values of us at ghost point locations are needed for the evaluation of usws
194!-- and vsws.
195    CALL exchange_horiz_2d( us )
196!
197!-- Compute u'w' for the total model domain.
198!-- First compute the corresponding component of u* and square it.
199    !$OMP PARALLEL DO PRIVATE( a, b, k, rifm, z_p )
200    DO  i = nxl, nxr
201       DO  j = nys, nyn
202
203          k   = nzb_u_inner(j,i)
204          z_p = zu(k+1) - zw(k)
205
206!
207!--       Compute Richardson-flux number for this point
208          rifm = 0.5 * ( rif(j,i-1) + rif(j,i) )
209          IF ( rifm >= 0.0 )  THEN
210!
211!--          Stable stratification
212             usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) )/ (              &
213                                     LOG( z_p / z0(j,i) ) +               &
214                                     5.0 * rifm * ( z_p - z0(j,i) ) / z_p &
215                                              )
216          ELSE
217!
218!--          Unstable stratification
219             a = SQRT( SQRT( 1.0 - 16.0 * rifm ) )
220             b = SQRT( SQRT( 1.0 - 16.0 * rifm / z_p * z0(j,i) ) )
221
222             usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) / (            &
223                         LOG( z_p / z0(j,i) ) -                           &
224                         LOG( (1.0 + a )**2 * ( 1.0 + a**2 ) / (          &
225                              (1.0 + b )**2 * ( 1.0 + b**2 )   ) ) +      &
226                              2.0 * ( ATAN( a ) - ATAN( b ) )             &
227                                                 )
228          ENDIF
229          usws(j,i) = -usws(j,i) * 0.5 * ( us(j,i-1) + us(j,i) )
230       ENDDO
231    ENDDO
232
233!
234!-- Compute v'w' for the total model domain.
235!-- First compute the corresponding component of u* and square it.
236    !$OMP PARALLEL DO PRIVATE( a, b, k, rifm, z_p )
237    DO  i = nxl, nxr
238       DO  j = nys, nyn
239
240          k   = nzb_v_inner(j,i)
241          z_p = zu(k+1) - zw(k)
242
243!
244!--       Compute Richardson-flux number for this point
245          rifm = 0.5 * ( rif(j-1,i) + rif(j,i) )
246          IF ( rifm >= 0.0 )  THEN
247!
248!--          Stable stratification
249             vsws(j,i) = kappa * ( v(k+1,j,i) -  v(k,j,i) ) / (           &
250                                     LOG( z_p / z0(j,i) ) +               &
251                                     5.0 * rifm * ( z_p - z0(j,i) ) / z_p &
252                                              )
253          ELSE
254!
255!--          Unstable stratification
256             a = SQRT( SQRT( 1.0 - 16.0 * rifm ) )
257             b = SQRT( SQRT( 1.0 - 16.0 * rifm / z_p * z0(j,i) ) )
258
259             vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) / (            &
260                         LOG( z_p / z0(j,i) ) -                           &
261                         LOG( (1.0 + a )**2 * ( 1.0 + a**2 ) / (          &
262                              (1.0 + b )**2 * ( 1.0 + b**2 )   ) ) +      &
263                              2.0 * ( ATAN( a ) - ATAN( b ) )             &
264                                                 )
265          ENDIF
266          vsws(j,i) = -vsws(j,i) * 0.5 * ( us(j-1,i) + us(j,i) )
267       ENDDO
268    ENDDO
269
270!
271!-- If required compute q*
272    IF ( humidity  .OR.  passive_scalar )  THEN
273       IF ( constant_waterflux )  THEN
274!
275!--       For a given water flux in the Prandtl layer:
276          !$OMP PARALLEL DO
277          DO  i = nxlg, nxrg
278             DO  j = nysg, nyng
279                qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30 )
280             ENDDO
281          ENDDO
282         
283       ELSE         
284          !$OMP PARALLEL DO PRIVATE( a, b, k, z_p )
285          DO  i = nxlg, nxrg
286             DO  j = nysg, nyng
287
288                k   = nzb_s_inner(j,i)
289                z_p = zu(k+1) - zw(k)
290
291!
292!--             Assume saturation for atmosphere coupled to ocean (but not
293!--             in case of precursor runs)
294                IF ( coupling_mode == 'atmosphere_to_ocean' .AND. run_coupled )&
295                THEN
296                   e_q = 6.1 * &
297                        EXP( 0.07 * ( MIN(pt(0,j,i),pt(1,j,i)) - 273.15 ) )
298                   q(k,j,i) = 0.622 * e_q / ( surface_pressure - e_q )
299                ENDIF
300                IF ( rif(j,i) >= 0.0 )  THEN
301!
302!--                Stable stratification
303                   qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) / (         &
304                                  LOG( z_p / z0(j,i) ) +                   &
305                                  5.0 * rif(j,i) * ( z_p - z0(j,i) ) / z_p &
306                                                                 )
307                ELSE
308!
309!--                Unstable stratification
310                   a = SQRT( 1.0 - 16.0 * rif(j,i) ) 
311                   b = SQRT( 1.0 - 16.0 * rif(j,i) * z0(j,i) / z_p ) 
312 
313                   qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) /   (   &
314                             LOG( z_p / z0(j,i) ) -                    &
315                              2.0 * LOG( (1.0 + a ) / ( 1.0 + b ) ) )
316                ENDIF
317
318             ENDDO
319          ENDDO
320       ENDIF
321    ENDIF
322
323!
324!-- Exchange the boundaries for the momentum fluxes (only for sake of
325!-- completeness)
326    CALL exchange_horiz_2d( usws )
327    CALL exchange_horiz_2d( vsws )
328    IF ( humidity  .OR.  passive_scalar )  CALL exchange_horiz_2d( qsws )
329
330!
331!-- Compute the vertical kinematic heat flux
332    IF ( .NOT. constant_heatflux )  THEN
333       !$OMP PARALLEL DO
334       DO  i = nxlg, nxrg
335          DO  j = nysg, nyng
336             shf(j,i) = -ts(j,i) * us(j,i)
337          ENDDO
338       ENDDO
339    ENDIF
340
341!
342!-- Compute the vertical water/scalar flux
343    IF ( .NOT. constant_waterflux .AND. ( humidity .OR. passive_scalar ) ) THEN
344       !$OMP PARALLEL DO
345       DO  i = nxlg, nxrg
346          DO  j = nysg, nyng
347             qsws(j,i) = -qs(j,i) * us(j,i)
348          ENDDO
349       ENDDO
350    ENDIF
351
352!
353!-- Bottom boundary condition for the TKE
354    IF ( ibc_e_b == 2 )  THEN
355       !$OMP PARALLEL DO
356       DO  i = nxlg, nxrg
357          DO  j = nysg, nyng
358             e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.1 )**2
359!
360!--          As a test: cm = 0.4
361!            e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.4 )**2
362             e(nzb_s_inner(j,i),j,i)   = e(nzb_s_inner(j,i)+1,j,i)
363          ENDDO
364       ENDDO
365    ENDIF
366
367
368 END SUBROUTINE prandtl_fluxes
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