source: palm/trunk/SOURCE/init_grid.f90 @ 729

 SUBROUTINE init_grid

!------------------------------------------------------------------------------!
! Current revisions:
! -----------------
! 
!
! Former revisions:
! -----------------
! $Id: init_grid.f90 723 2011-04-11 06:28:19Z heinze $
!
! 722 2011-04-11 06:21:09Z raasch
! Bugfix: bc_lr/ns_cyc replaced by bc_lr/ns, because variables are not yet set
!         here
!
! 709 2011-03-30 09:31:40Z raasch
! formatting adjustments
!
! 707 2011-03-29 11:39:40Z raasch
! bc_lr/ns replaced by bc_lr/ns_cyc
!
! 667 2010-12-23 12:06:00Z suehring/gryschka
! 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.
!
! 555 2010-09-07 07:32:53Z raasch
! Bugfix: default setting of nzb_local for flat topographie
!
! 274 2009-03-26 15:11:21Z heinze
! Output of messages replaced by message handling routine.
! new topography case 'single_street_canyon'
!
! 217 2008-12-09 18:00:48Z letzel
! +topography_grid_convention
!
! 134 2007-11-21 07:28:38Z letzel
! Redefine initial nzb_local as the actual total size of topography (later the 
! extent of topography in nzb_local is reduced by 1dx at the E topography walls 
! and by 1dy at the N topography walls to form the basis for nzb_s_inner); 
! for consistency redefine 'single_building' case.
! Calculation of wall flag arrays
!
! 94 2007-06-01 15:25:22Z raasch
! Grid definition for ocean version
!
! 75 2007-03-22 09:54:05Z raasch
! storage of topography height arrays zu_s_inner and zw_s_inner,
! 2nd+3rd argument removed from exchange horiz
!
! 19 2007-02-23 04:53:48Z raasch
! Setting of nzt_diff
!
! RCS Log replace by Id keyword, revision history cleaned up
!
! Revision 1.17  2006/08/22 14:00:05  raasch
! +dz_max to limit vertical stretching,
! bugfix in index array initialization for line- or point-like topography
! structures
!
! Revision 1.1  1997/08/11 06:17:45  raasch
! Initial revision (Testversion)
!
!
! Description:
! ------------
! Creating grid depending constants
!------------------------------------------------------------------------------!

    USE arrays_3d
    USE control_parameters
    USE grid_variables
    USE indices
    USE pegrid

    IMPLICIT NONE

    INTEGER ::  bh, blx, bly, bxl, bxr, byn, bys, ch, cwx, cwy, cxl, cxr, cyn, &
                cys, gls, i, inc, i_center, j, j_center, k, l, nxl_l, nxr_l, &
                nyn_l, nys_l, nzb_si, nzt_l, vi

    INTEGER, DIMENSION(:), ALLOCATABLE   ::  vertical_influence

    INTEGER, DIMENSION(:,:), ALLOCATABLE ::  corner_nl, corner_nr, corner_sl,  &
                                             corner_sr, wall_l, wall_n, wall_r,&
                                             wall_s, nzb_local, nzb_tmp

    REAL    ::  dx_l, dy_l, dz_stretched

    REAL, DIMENSION(0:ny,0:nx)          ::  topo_height

    REAL, DIMENSION(:,:,:), ALLOCATABLE ::  distance
    
!
!-- Calculation of horizontal array bounds including ghost layers
    nxlg = nxl - nbgp
    nxrg = nxr + nbgp
    nysg = nys - nbgp
    nyng = nyn + nbgp

!
!-- Allocate grid arrays
    ALLOCATE( ddzu(1:nzt+1), ddzw(1:nzt+1), dd2zu(1:nzt), dzu(1:nzt+1), &
              dzw(1:nzt+1), l_grid(1:nzt), zu(nzb:nzt+1), zw(nzb:nzt+1) )

!
!-- Compute height of u-levels from constant grid length and dz stretch factors
    IF ( dz == -1.0 )  THEN
       message_string = 'missing dz'
       CALL message( 'init_grid', 'PA0200', 1, 2, 0, 6, 0 ) 
    ELSEIF ( dz <= 0.0 )  THEN
       WRITE( message_string, * ) 'dz=',dz,' <= 0.0'
       CALL message( 'init_grid', 'PA0201', 1, 2, 0, 6, 0 )
    ENDIF

!
!-- Define the vertical grid levels
    IF ( .NOT. ocean )  THEN
!
!--    Grid for atmosphere with surface at z=0 (k=0, w-grid).
!--    The first u-level above the surface corresponds to the top of the 
!--    Prandtl-layer.

       IF ( ibc_uv_b == 0 .OR. ibc_uv_b == 2 ) THEN
          zu(0) = 0.0
      !    zu(0) = - dz * 0.5
       ELSE
          zu(0) = - dz * 0.5
       ENDIF
       zu(1) =   dz * 0.5

       dz_stretch_level_index = nzt+1
       dz_stretched = dz
       DO  k = 2, nzt+1
          IF ( dz_stretch_level <= zu(k-1)  .AND.  dz_stretched < dz_max )  THEN
             dz_stretched = dz_stretched * dz_stretch_factor
             dz_stretched = MIN( dz_stretched, dz_max )
             IF ( dz_stretch_level_index == nzt+1 ) dz_stretch_level_index = k-1
          ENDIF
          zu(k) = zu(k-1) + dz_stretched
       ENDDO

!
!--    Compute the w-levels. They are always staggered half-way between the 
!--    corresponding u-levels. The top w-level is extrapolated linearly.
       zw(0) = 0.0
       DO  k = 1, nzt
          zw(k) = ( zu(k) + zu(k+1) ) * 0.5
       ENDDO
       zw(nzt+1) = zw(nzt) + 2.0 * ( zu(nzt+1) - zw(nzt) )

    ELSE
!
!--    Grid for ocean with solid surface at z=0 (k=0, w-grid). The free water
!--    surface is at k=nzt (w-grid).
!--    Since the w-level lies always on the surface, the first/last u-level
!--    (staggered!) lies below the bottom surface / above the free surface.
!--    It is used for "mirror" boundary condition.
!--    The first u-level above the bottom surface corresponds to the top of the 
!--    Prandtl-layer.
       zu(nzt+1) =   dz * 0.5
       zu(nzt)   = - dz * 0.5

       dz_stretch_level_index = 0
       dz_stretched = dz
       DO  k = nzt-1, 0, -1
          IF ( dz_stretch_level <= ABS( zu(k+1) )  .AND.  &
               dz_stretched < dz_max )  THEN
             dz_stretched = dz_stretched * dz_stretch_factor
             dz_stretched = MIN( dz_stretched, dz_max )
             IF ( dz_stretch_level_index == 0 ) dz_stretch_level_index = k+1
          ENDIF
          zu(k) = zu(k+1) - dz_stretched
       ENDDO

!
!--    Compute the w-levels. They are always staggered half-way between the 
!--    corresponding u-levels.
!--    The top w-level (nzt+1) is not used but set for consistency, since
!--    w and all scalar variables are defined up tp nzt+1.
       zw(nzt+1) = dz
       zw(nzt)   = 0.0
       DO  k = 0, nzt
          zw(k) = ( zu(k) + zu(k+1) ) * 0.5
       ENDDO

    ENDIF

!
!-- Compute grid lengths.
    DO  k = 1, nzt+1
       dzu(k)  = zu(k) - zu(k-1)
       ddzu(k) = 1.0 / dzu(k)
       dzw(k)  = zw(k) - zw(k-1)
       ddzw(k) = 1.0 / dzw(k)
    ENDDO

    DO  k = 1, nzt
       dd2zu(k) = 1.0 / ( dzu(k) + dzu(k+1) )
    ENDDO
    
!    
!-- The FFT- SOR-pressure solvers assume grid spacings of a staggered grid
!-- everywhere. For the actual grid, the grid spacing at the lowest level
!-- is only dz/2, but should be dz. Therefore, an additional array
!-- containing with appropriate grid information is created for these
!-- solvers.
    IF ( psolver /= 'multigrid' )  THEN
       ALLOCATE( ddzu_pres(1:nzt+1) )
       ddzu_pres = ddzu
       IF( .NOT. ocean )  ddzu_pres(1) = ddzu_pres(2)  ! change for lowest level
    ENDIF   

!
!-- In case of multigrid method, compute grid lengths and grid factors for the
!-- grid levels
    IF ( psolver == 'multigrid' )  THEN

       ALLOCATE( ddx2_mg(maximum_grid_level), ddy2_mg(maximum_grid_level), &
                 dzu_mg(nzb+1:nzt+1,maximum_grid_level),                   &
                 dzw_mg(nzb+1:nzt+1,maximum_grid_level),                   &
                 f1_mg(nzb+1:nzt,maximum_grid_level),                      &
                 f2_mg(nzb+1:nzt,maximum_grid_level),                      &
                 f3_mg(nzb+1:nzt,maximum_grid_level) )

       dzu_mg(:,maximum_grid_level) = dzu
!       
!--    Next line to ensure an equally spaced grid. For ocean runs this is not
!--    necessary, 
!--    because zu(0) does not changed so far. Also this would cause errors 
!--    if a vertical stretching for ocean runs is used.
       IF ( .NOT. ocean ) dzu_mg(1,maximum_grid_level) = dzu(2)

       dzw_mg(:,maximum_grid_level) = dzw
       nzt_l = nzt
       DO  l = maximum_grid_level-1, 1, -1
           dzu_mg(nzb+1,l) = 2.0 * dzu_mg(nzb+1,l+1)
           dzw_mg(nzb+1,l) = 2.0 * dzw_mg(nzb+1,l+1)
           nzt_l = nzt_l / 2
           DO  k = 2, nzt_l+1
              dzu_mg(k,l) = dzu_mg(2*k-2,l+1) + dzu_mg(2*k-1,l+1)
              dzw_mg(k,l) = dzw_mg(2*k-2,l+1) + dzw_mg(2*k-1,l+1)
           ENDDO
       ENDDO

       nzt_l = nzt
       dx_l  = dx
       dy_l  = dy
       DO  l = maximum_grid_level, 1, -1
          ddx2_mg(l) = 1.0 / dx_l**2
          ddy2_mg(l) = 1.0 / dy_l**2
          DO  k = nzb+1, nzt_l
             f2_mg(k,l) = 1.0 / ( dzu_mg(k+1,l) * dzw_mg(k,l) )
             f3_mg(k,l) = 1.0 / ( dzu_mg(k,l)   * dzw_mg(k,l) )
             f1_mg(k,l) = 2.0 * ( ddx2_mg(l) + ddy2_mg(l) ) + &
                          f2_mg(k,l) + f3_mg(k,l)
          ENDDO
          nzt_l = nzt_l / 2
          dx_l  = dx_l * 2.0
          dy_l  = dy_l * 2.0
       ENDDO

    ENDIF

!
!-- Compute the reciprocal values of the horizontal grid lengths.
    ddx = 1.0 / dx
    ddy = 1.0 / dy
    dx2 = dx * dx
    dy2 = dy * dy
    ddx2 = 1.0 / dx2
    ddy2 = 1.0 / dy2

!
!-- Compute the grid-dependent mixing length.
    DO  k = 1, nzt
       l_grid(k)  = ( dx * dy * dzw(k) )**0.33333333333333
    ENDDO

!
!-- Allocate outer and inner index arrays for topography and set
!-- defaults.
!-- nzb_local has to contain additional layers of ghost points for calculating
!-- the flag arrays needed for the multigrid method
    gls = 2**( maximum_grid_level )

    ALLOCATE( corner_nl(nys:nyn,nxl:nxr), corner_nr(nys:nyn,nxl:nxr),       &
              corner_sl(nys:nyn,nxl:nxr), corner_sr(nys:nyn,nxl:nxr),       &
              nzb_local(-gls:ny+gls,-gls:nx+gls),                                   &
              nzb_tmp(-nbgp:ny+nbgp,-nbgp:nx+nbgp),                         &
              wall_l(nys:nyn,nxl:nxr), wall_n(nys:nyn,nxl:nxr),             &
              wall_r(nys:nyn,nxl:nxr), wall_s(nys:nyn,nxl:nxr) )
    ALLOCATE( fwxm(nysg:nyng,nxlg:nxrg), fwxp(nysg:nyng,nxlg:nxrg),         &
              fwym(nysg:nyng,nxlg:nxrg), fwyp(nysg:nyng,nxlg:nxrg),         &
              fxm(nysg:nyng,nxlg:nxrg), fxp(nysg:nyng,nxlg:nxrg),           &
              fym(nysg:nyng,nxlg:nxrg), fyp(nysg:nyng,nxlg:nxrg),           &
              nzb_s_inner(nysg:nyng,nxlg:nxrg),                             &
              nzb_s_outer(nysg:nyng,nxlg:nxrg),                             &
              nzb_u_inner(nysg:nyng,nxlg:nxrg),                             &
              nzb_u_outer(nysg:nyng,nxlg:nxrg),                             &
              nzb_v_inner(nysg:nyng,nxlg:nxrg),                             &
              nzb_v_outer(nysg:nyng,nxlg:nxrg),                             &
              nzb_w_inner(nysg:nyng,nxlg:nxrg),                             &
              nzb_w_outer(nysg:nyng,nxlg:nxrg),                             &
              nzb_diff_s_inner(nysg:nyng,nxlg:nxrg),                        &
              nzb_diff_s_outer(nysg:nyng,nxlg:nxrg),                        &
              nzb_diff_u(nysg:nyng,nxlg:nxrg),                              &
              nzb_diff_v(nysg:nyng,nxlg:nxrg),                              &
              nzb_2d(nysg:nyng,nxlg:nxrg),                                  &
              wall_e_x(nysg:nyng,nxlg:nxrg),                                &
              wall_e_y(nysg:nyng,nxlg:nxrg),                                &
              wall_u(nysg:nyng,nxlg:nxrg),                                  &
              wall_v(nysg:nyng,nxlg:nxrg),                                  &
              wall_w_x(nysg:nyng,nxlg:nxrg),                                &
              wall_w_y(nysg:nyng,nxlg:nxrg) )



    ALLOCATE( l_wall(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )

    nzb_s_inner = nzb;  nzb_s_outer = nzb
    nzb_u_inner = nzb;  nzb_u_outer = nzb
    nzb_v_inner = nzb;  nzb_v_outer = nzb
    nzb_w_inner = nzb;  nzb_w_outer = nzb

!
!-- Define vertical gridpoint from (or to) which on the usual finite difference
!-- form (which does not use surface fluxes) is applied 
    IF ( prandtl_layer  .OR.  use_surface_fluxes )  THEN
       nzb_diff = nzb + 2
    ELSE
       nzb_diff = nzb + 1
    ENDIF
    IF ( use_top_fluxes )  THEN
       nzt_diff = nzt - 1
    ELSE
       nzt_diff = nzt
    ENDIF

    nzb_diff_s_inner = nzb_diff;  nzb_diff_s_outer = nzb_diff
    nzb_diff_u = nzb_diff;  nzb_diff_v = nzb_diff

    wall_e_x = 0.0;  wall_e_y = 0.0;  wall_u = 0.0;  wall_v = 0.0
    wall_w_x = 0.0;  wall_w_y = 0.0
    fwxp = 1.0;  fwxm = 1.0;  fwyp = 1.0;  fwym = 1.0
    fxp  = 1.0;  fxm  = 1.0;  fyp  = 1.0;  fym  = 1.0

!
!-- Initialize near-wall mixing length l_wall only in the vertical direction
!-- for the moment,
!-- multiplication with wall_adjustment_factor near the end of this routine
    l_wall(nzb,:,:)   = l_grid(1)
    DO  k = nzb+1, nzt
       l_wall(k,:,:)  = l_grid(k)
    ENDDO
    l_wall(nzt+1,:,:) = l_grid(nzt)

    ALLOCATE ( vertical_influence(nzb:nzt) )
    DO  k = 1, nzt
       vertical_influence(k) = MIN ( INT( l_grid(k) / &
                     ( wall_adjustment_factor * dzw(k) ) + 0.5 ), nzt - k )
    ENDDO

    DO  k = 1, MAXVAL( nzb_s_inner )
       IF ( l_grid(k) > 1.5 * dx * wall_adjustment_factor .OR.  &
            l_grid(k) > 1.5 * dy * wall_adjustment_factor )  THEN
          WRITE( message_string, * ) 'grid anisotropy exceeds ', &
                                     'threshold given by only local', &
                                     ' &horizontal reduction of near_wall ', &
                                     'mixing length l_wall', &
                                     ' &starting from height level k = ', k, '.'
          CALL message( 'init_grid', 'PA0202', 0, 1, 0, 6, 0 )
          EXIT
       ENDIF
    ENDDO
    vertical_influence(0) = vertical_influence(1)

    DO  i = nxlg, nxrg
       DO  j = nysg, nyng
          DO  k = nzb_s_inner(j,i) + 1, &
                  nzb_s_inner(j,i) + vertical_influence(nzb_s_inner(j,i))
             l_wall(k,j,i) = zu(k) - zw(nzb_s_inner(j,i))
          ENDDO
       ENDDO
    ENDDO

!
!-- Set outer and inner index arrays for non-flat topography.
!-- Here consistency checks concerning domain size and periodicity are
!-- necessary.
!-- Within this SELECT CASE structure only nzb_local is initialized
!-- individually depending on the chosen topography type, all other index 
!-- arrays are initialized further below.
    SELECT CASE ( TRIM( topography ) )

       CASE ( 'flat' )
!
!--       nzb_local is required for the multigrid solver
          nzb_local = 0

       CASE ( 'single_building' )
!
!--       Single rectangular building, by default centered in the middle of the
!--       total domain
          blx = NINT( building_length_x / dx )
          bly = NINT( building_length_y / dy )
          bh  = NINT( building_height / dz )

          IF ( building_wall_left == 9999999.9 )  THEN
             building_wall_left = ( nx + 1 - blx ) / 2 * dx
          ENDIF
          bxl = NINT( building_wall_left / dx )
          bxr = bxl + blx

          IF ( building_wall_south == 9999999.9 )  THEN
             building_wall_south = ( ny + 1 - bly ) / 2 * dy
          ENDIF
          bys = NINT( building_wall_south / dy )
          byn = bys + bly

!
!--       Building size has to meet some requirements
          IF ( ( bxl < 1 ) .OR. ( bxr > nx-1 ) .OR. ( bxr < bxl+3 ) .OR.  &
               ( bys < 1 ) .OR. ( byn > ny-1 ) .OR. ( byn < bys+3 ) )  THEN
             WRITE( message_string, * ) 'inconsistent building parameters:',   &
                                      '& bxl=', bxl, 'bxr=', bxr, 'bys=', bys, &
                                      'byn=', byn, 'nx=', nx, 'ny=', ny
             CALL message( 'init_grid', 'PA0203', 1, 2, 0, 6, 0 )
          ENDIF

!
!--       Define the building.
          nzb_local = 0
          nzb_local(bys:byn,bxl:bxr) = bh

       CASE ( 'single_street_canyon' )
!
!--       Single quasi-2D street canyon of infinite length in x or y direction.
!--       The canyon is centered in the other direction by default.
          IF ( canyon_width_x /= 9999999.9 )  THEN
!
!--          Street canyon in y direction
             cwx = NINT( canyon_width_x / dx )
             IF ( canyon_wall_left == 9999999.9 )  THEN
                canyon_wall_left = ( nx + 1 - cwx ) / 2 * dx
             ENDIF
             cxl = NINT( canyon_wall_left / dx )
             cxr = cxl + cwx

          ELSEIF ( canyon_width_y /= 9999999.9 )  THEN
!
!--          Street canyon in x direction
             cwy = NINT( canyon_width_y / dy )
             IF ( canyon_wall_south == 9999999.9 )  THEN
                canyon_wall_south = ( ny + 1 - cwy ) / 2 * dy
             ENDIF
             cys = NINT( canyon_wall_south / dy )
             cyn = cys + cwy

          ELSE
             
             message_string = 'no street canyon width given'
             CALL message( 'init_grid', 'PA0204', 1, 2, 0, 6, 0 )
  
          ENDIF

          ch             = NINT( canyon_height / dz )
          dp_level_ind_b = ch
!
!--       Street canyon size has to meet some requirements
          IF ( canyon_width_x /= 9999999.9 )  THEN
             IF ( ( cxl < 1 ) .OR. ( cxr > nx-1 ) .OR. ( cwx < 3 ) .OR.  &
               ( ch < 3 ) )  THEN
                WRITE( message_string, * ) 'inconsistent canyon parameters:', &
                                           '&cxl=', cxl, 'cxr=', cxr,         &
                                           'cwx=', cwx,                       &
                                           'ch=', ch, 'nx=', nx, 'ny=', ny
                CALL message( 'init_grid', 'PA0205', 1, 2, 0, 6, 0 ) 
             ENDIF
          ELSEIF ( canyon_width_y /= 9999999.9 )  THEN
             IF ( ( cys < 1 ) .OR. ( cyn > ny-1 ) .OR. ( cwy < 3 ) .OR.  &
               ( ch < 3 ) )  THEN
                WRITE( message_string, * ) 'inconsistent canyon parameters:', &
                                           '&cys=', cys, 'cyn=', cyn,         &
                                           'cwy=', cwy,                       &
                                           'ch=', ch, 'nx=', nx, 'ny=', ny
                CALL message( 'init_grid', 'PA0206', 1, 2, 0, 6, 0 ) 
             ENDIF
          ENDIF
          IF ( canyon_width_x /= 9999999.9 .AND. canyon_width_y /= 9999999.9 ) &
               THEN
             message_string = 'inconsistent canyon parameters:' //     &  
                              '&street canyon can only be oriented' // &
                              '&either in x- or in y-direction'
             CALL message( 'init_grid', 'PA0207', 1, 2, 0, 6, 0 )
          ENDIF

          nzb_local = ch
          IF ( canyon_width_x /= 9999999.9 )  THEN
             nzb_local(:,cxl+1:cxr-1) = 0
          ELSEIF ( canyon_width_y /= 9999999.9 )  THEN
             nzb_local(cys+1:cyn-1,:) = 0
          ENDIF

       CASE ( 'read_from_file' )
!
!--       Arbitrary irregular topography data in PALM format (exactly matching
!--       the grid size and total domain size)
          OPEN( 90, FILE='TOPOGRAPHY_DATA', STATUS='OLD', FORM='FORMATTED',  &
               ERR=10 )
          DO  j = ny, 0, -1
             READ( 90, *, ERR=11, END=11 )  ( topo_height(j,i), i = 0, nx )
          ENDDO
!
!--       Calculate the index height of the topography
          DO  i = 0, nx
             DO  j = 0, ny
                nzb_local(j,i) = NINT( topo_height(j,i) / dz )
             ENDDO
          ENDDO
!
!--       Add cyclic boundaries (additional layers are for calculating flag
!--       arrays needed for the multigrid sover)
          nzb_local(-gls:-1,0:nx)     = nzb_local(ny-gls+1:ny,0:nx)
          nzb_local(ny+1:ny+gls,0:nx) = nzb_local(0:gls-1,0:nx)
          nzb_local(:,-gls:-1)        = nzb_local(:,nx-gls+1:nx)
          nzb_local(:,nx+1:nx+gls)    = nzb_local(:,0:gls-1)


      
          GOTO 12
          
 10       message_string = 'file TOPOGRAPHY_DATA does not exist'
          CALL message( 'init_grid', 'PA0208', 1, 2, 0, 6, 0 )

 11       message_string = 'errors in file TOPOGRAPHY_DATA'
          CALL message( 'init_grid', 'PA0209', 1, 2, 0, 6, 0 )

 12       CLOSE( 90 )

       CASE DEFAULT
!
!--       The DEFAULT case is reached either if the parameter topography
!--       contains a wrong character string or if the user has defined a special
!--       case in the user interface. There, the subroutine user_init_grid 
!--       checks which of these two conditions applies.
          CALL user_init_grid( gls, nzb_local )

    END SELECT

!
!-- Consistency checks and index array initialization are only required for
!-- non-flat topography, also the initialization of topography height arrays
!-- zu_s_inner and zw_w_inner
    IF ( TRIM( topography ) /= 'flat' )  THEN

!
!--    Consistency checks
       IF ( MINVAL( nzb_local ) < 0  .OR.  MAXVAL( nzb_local ) > nz + 1 )  THEN
          WRITE( message_string, * ) 'nzb_local values are outside the',      &
                                'model domain',                               &
                                '&MINVAL( nzb_local ) = ', MINVAL(nzb_local), &
                                '&MAXVAL( nzb_local ) = ', MAXVAL(nzb_local)
          CALL message( 'init_grid', 'PA0210', 1, 2, 0, 6, 0 )
       ENDIF

       IF ( bc_lr == 'cyclic' )  THEN
          IF ( ANY( nzb_local(:,-1) /= nzb_local(:,nx)   )  .OR. &
               ANY( nzb_local(:,0)  /= nzb_local(:,nx+1) ) )  THEN
             message_string = 'nzb_local does not fulfill cyclic' // &
                              ' boundary condition in x-direction'
             CALL message( 'init_grid', 'PA0211', 1, 2, 0, 6, 0 )
          ENDIF
       ENDIF
       IF ( bc_ns == 'cyclic' )  THEN
          IF ( ANY( nzb_local(-1,:) /= nzb_local(ny,:)   )  .OR. &
               ANY( nzb_local(0,:)  /= nzb_local(ny+1,:) ) )  THEN
             message_string = 'nzb_local does not fulfill cyclic' // &
                              ' boundary condition in y-direction'
             CALL message( 'init_grid', 'PA0212', 1, 2, 0, 6, 0 )
          ENDIF
       ENDIF

       IF ( topography_grid_convention == 'cell_edge' )  THEN
! 
!--       The array nzb_local as defined using the 'cell_edge' convention 
!--       describes the actual total size of topography which is defined at the 
!--       cell edges where u=0 on the topography walls in x-direction and v=0 
!--       on the topography walls in y-direction. However, PALM uses individual
!--       arrays nzb_u|v|w|s_inner|outer that are based on nzb_s_inner.
!--       Therefore, the extent of topography in nzb_local is now reduced by 
!--       1dx at the E topography walls and by 1dy at the N topography walls 
!--       to form the basis for nzb_s_inner.
          DO  j = -gls, ny + gls
             DO  i = -gls, nx
                nzb_local(j,i) = MIN( nzb_local(j,i), nzb_local(j,i+1) )
             ENDDO
          ENDDO
!--       apply cyclic boundary conditions in x-direction 
!(ist das erforderlich? Ursache von Seung Bus Fehler?)
          nzb_local(:,nx+1:nx+gls) = nzb_local(:,0:gls-1)
          DO  i = -gls, nx + gls
             DO  j = -gls, ny
                nzb_local(j,i) = MIN( nzb_local(j,i), nzb_local(j+1,i) )
             ENDDO
          ENDDO
!--       apply cyclic boundary conditions in y-direction
!(ist das erforderlich? Ursache von Seung Bus Fehler?)
          nzb_local(ny+1:ny+gls,:) = nzb_local(0:gls-1,:)
       ENDIF

!
!--    Initialize index arrays nzb_s_inner and nzb_w_inner
       nzb_s_inner = nzb_local(nys-1:nyn+1,nxl-1:nxr+1)
       nzb_w_inner = nzb_local(nys-1:nyn+1,nxl-1:nxr+1)

!
!--    Initialize remaining index arrays:
!--    first pre-initialize them with nzb_s_inner...
       nzb_u_inner = nzb_s_inner
       nzb_u_outer = nzb_s_inner
       nzb_v_inner = nzb_s_inner
       nzb_v_outer = nzb_s_inner
       nzb_w_outer = nzb_s_inner
       nzb_s_outer = nzb_s_inner

!
!--    ...then extend pre-initialized arrays in their according directions
!--    based on nzb_local using nzb_tmp as a temporary global index array

!
!--    nzb_s_outer: 
!--    extend nzb_local east-/westwards first, then north-/southwards
       nzb_tmp = nzb_local(-nbgp:ny+nbgp,-nbgp:nx+nbgp)
       DO  j = -1, ny + 1
          DO  i = 0, nx
             nzb_tmp(j,i) = MAX( nzb_local(j,i-1), nzb_local(j,i), &
                                 nzb_local(j,i+1) )
          ENDDO
       ENDDO
       DO  i = nxl, nxr
          DO  j = nys, nyn
             nzb_s_outer(j,i) = MAX( nzb_tmp(j-1,i), nzb_tmp(j,i), &
                                     nzb_tmp(j+1,i) )
          ENDDO
!
!--       non-cyclic boundary conditions (overwritten by call of
!--       exchange_horiz_2d_int below in case of cyclic boundary conditions)
          IF ( nys == 0 )  THEN
             j = -1
             nzb_s_outer(j,i) = MAX( nzb_tmp(j+1,i), nzb_tmp(j,i) )
          ENDIF
          IF ( nys == ny )  THEN
             j = ny + 1
             nzb_s_outer(j,i) = MAX( nzb_tmp(j-1,i), nzb_tmp(j,i) )
          ENDIF
       ENDDO
!
!--    nzb_w_outer: 
!--    identical to nzb_s_outer
       nzb_w_outer = nzb_s_outer

!
!--    nzb_u_inner: 
!--    extend nzb_local rightwards only
       nzb_tmp = nzb_local(-nbgp:ny+nbgp,-nbgp:nx+nbgp)
       DO  j = -1, ny + 1
          DO  i = 0, nx + 1
             nzb_tmp(j,i) = MAX( nzb_local(j,i-1), nzb_local(j,i) )
          ENDDO
       ENDDO
       nzb_u_inner = nzb_tmp(nysg:nyng,nxlg:nxrg)

!
!--    nzb_u_outer: 
!--    extend current nzb_tmp (nzb_u_inner) north-/southwards
       DO  i = nxl, nxr
          DO  j = nys, nyn
             nzb_u_outer(j,i) = MAX( nzb_tmp(j-1,i), nzb_tmp(j,i), &
                                     nzb_tmp(j+1,i) )
          ENDDO
!
!--       non-cyclic boundary conditions (overwritten by call of
!--       exchange_horiz_2d_int below in case of cyclic boundary conditions)
          IF ( nys == 0 )  THEN
             j = -1
             nzb_u_outer(j,i) = MAX( nzb_tmp(j+1,i), nzb_tmp(j,i) )
          ENDIF
          IF ( nys == ny )  THEN
             j = ny + 1
             nzb_u_outer(j,i) = MAX( nzb_tmp(j-1,i), nzb_tmp(j,i) )
          ENDIF
       ENDDO

!
!--    nzb_v_inner:
!--    extend nzb_local northwards only
       nzb_tmp = nzb_local(-nbgp:ny+nbgp,-nbgp:nx+nbgp)
       DO  i = -1, nx + 1
          DO  j = 0, ny + 1
             nzb_tmp(j,i) = MAX( nzb_local(j-1,i), nzb_local(j,i) )
          ENDDO
       ENDDO
       nzb_v_inner = nzb_tmp(nys-nbgp:nyn+nbgp,nxl-nbgp:nxr+nbgp)

!
!--    nzb_v_outer: 
!--    extend current nzb_tmp (nzb_v_inner) right-/leftwards
       DO  j = nys, nyn
          DO  i = nxl, nxr
             nzb_v_outer(j,i) = MAX( nzb_tmp(j,i-1), nzb_tmp(j,i), &
                                     nzb_tmp(j,i+1) )
          ENDDO
!
!--       non-cyclic boundary conditions (overwritten by call of
!--       exchange_horiz_2d_int below in case of cyclic boundary conditions)
          IF ( nxl == 0 )  THEN
             i = -1
             nzb_v_outer(j,i) = MAX( nzb_tmp(j,i+1), nzb_tmp(j,i) )
          ENDIF
          IF ( nxr == nx )  THEN
             i = nx + 1
             nzb_v_outer(j,i) = MAX( nzb_tmp(j,i-1), nzb_tmp(j,i) )
          ENDIF
       ENDDO

!
!--    Exchange of lateral boundary values (parallel computers) and cyclic
!--    boundary conditions, if applicable.
!--    Since nzb_s_inner and nzb_w_inner are derived directly from nzb_local
!--    they do not require exchange and are not included here.
       CALL exchange_horiz_2d_int( nzb_u_inner )
       CALL exchange_horiz_2d_int( nzb_u_outer )
       CALL exchange_horiz_2d_int( nzb_v_inner )
       CALL exchange_horiz_2d_int( nzb_v_outer )
       CALL exchange_horiz_2d_int( nzb_w_outer )
       CALL exchange_horiz_2d_int( nzb_s_outer )

!
!--    Allocate and set the arrays containing the topography height
       IF ( myid == 0 )  THEN

          ALLOCATE( zu_s_inner(0:nx+1,0:ny+1), zw_w_inner(0:nx+1,0:ny+1) )

          DO  i = 0, nx + 1
             DO  j = 0, ny + 1
                zu_s_inner(i,j) = zu(nzb_local(j,i))
                zw_w_inner(i,j) = zw(nzb_local(j,i))
             ENDDO
          ENDDO
          
       ENDIF

    ENDIF

!
!-- Preliminary: to be removed after completion of the topography code!
!-- Set the former default k index arrays nzb_2d
    nzb_2d      = nzb

!
!-- Set the individual index arrays which define the k index from which on
!-- the usual finite difference form (which does not use surface fluxes) is
!-- applied 
    IF ( prandtl_layer  .OR.  use_surface_fluxes )  THEN
       nzb_diff_u         = nzb_u_inner + 2
       nzb_diff_v         = nzb_v_inner + 2
       nzb_diff_s_inner   = nzb_s_inner + 2
       nzb_diff_s_outer   = nzb_s_outer + 2
    ELSE
       nzb_diff_u         = nzb_u_inner + 1
       nzb_diff_v         = nzb_v_inner + 1
       nzb_diff_s_inner   = nzb_s_inner + 1
       nzb_diff_s_outer   = nzb_s_outer + 1
    ENDIF

!
!-- Calculation of wall switches and factors required by diffusion_u/v.f90 and 
!-- for limitation of near-wall mixing length l_wall further below
    corner_nl = 0
    corner_nr = 0
    corner_sl = 0
    corner_sr = 0
    wall_l    = 0
    wall_n    = 0
    wall_r    = 0
    wall_s    = 0

    DO  i = nxl, nxr
       DO  j = nys, nyn
!
!--       u-component
          IF ( nzb_u_outer(j,i) > nzb_u_outer(j+1,i) )  THEN
             wall_u(j,i) = 1.0   ! north wall (location of adjacent fluid)
             fym(j,i)    = 0.0
             fyp(j,i)    = 1.0
          ELSEIF ( nzb_u_outer(j,i) > nzb_u_outer(j-1,i) )  THEN
             wall_u(j,i) = 1.0   ! south wall (location of adjacent fluid)
             fym(j,i)    = 1.0
             fyp(j,i)    = 0.0
          ENDIF
!
!--       v-component
          IF ( nzb_v_outer(j,i) > nzb_v_outer(j,i+1) )  THEN
             wall_v(j,i) = 1.0   ! rigth wall (location of adjacent fluid)
             fxm(j,i)    = 0.0
             fxp(j,i)    = 1.0
          ELSEIF ( nzb_v_outer(j,i) > nzb_v_outer(j,i-1) )  THEN
             wall_v(j,i) = 1.0   ! left wall (location of adjacent fluid)
             fxm(j,i)    = 1.0
             fxp(j,i)    = 0.0
          ENDIF
!
!--       w-component, also used for scalars, separate arrays for shear 
!--       production of tke
          IF ( nzb_w_outer(j,i) > nzb_w_outer(j+1,i) )  THEN
             wall_e_y(j,i) =  1.0   ! north wall (location of adjacent fluid)
             wall_w_y(j,i) =  1.0
             fwym(j,i)     =  0.0
             fwyp(j,i)     =  1.0
          ELSEIF ( nzb_w_outer(j,i) > nzb_w_outer(j-1,i) )  THEN
             wall_e_y(j,i) = -1.0   ! south wall (location of adjacent fluid)
             wall_w_y(j,i) =  1.0
             fwym(j,i)     =  1.0
             fwyp(j,i)     =  0.0
          ENDIF
          IF ( nzb_w_outer(j,i) > nzb_w_outer(j,i+1) )  THEN
             wall_e_x(j,i) =  1.0   ! right wall (location of adjacent fluid)
             wall_w_x(j,i) =  1.0
             fwxm(j,i)     =  0.0
             fwxp(j,i)     =  1.0
          ELSEIF ( nzb_w_outer(j,i) > nzb_w_outer(j,i-1) )  THEN
             wall_e_x(j,i) = -1.0   ! left wall (location of adjacent fluid)
             wall_w_x(j,i) =  1.0
             fwxm(j,i)     =  1.0
             fwxp(j,i)     =  0.0
          ENDIF
!
!--       Wall and corner locations inside buildings for limitation of
!--       near-wall mixing length l_wall
          IF ( nzb_s_inner(j,i) > nzb_s_inner(j+1,i) )  THEN

             wall_n(j,i) = nzb_s_inner(j+1,i) + 1            ! North wall

             IF ( nzb_s_inner(j,i) > nzb_s_inner(j,i-1) )  THEN
                corner_nl(j,i) = MAX( nzb_s_inner(j+1,i),  & ! Northleft corner
                                      nzb_s_inner(j,i-1) ) + 1
             ENDIF

             IF ( nzb_s_inner(j,i) > nzb_s_inner(j,i+1) )  THEN
                corner_nr(j,i) = MAX( nzb_s_inner(j+1,i),  & ! Northright corner
                                      nzb_s_inner(j,i+1) ) + 1
             ENDIF

          ENDIF

          IF ( nzb_s_inner(j,i) > nzb_s_inner(j-1,i) )  THEN

             wall_s(j,i) = nzb_s_inner(j-1,i) + 1            ! South wall
             IF ( nzb_s_inner(j,i) > nzb_s_inner(j,i-1) )  THEN
                corner_sl(j,i) = MAX( nzb_s_inner(j-1,i),  & ! Southleft corner
                                      nzb_s_inner(j,i-1) ) + 1
             ENDIF

             IF ( nzb_s_inner(j,i) > nzb_s_inner(j,i+1) )  THEN
                corner_sr(j,i) = MAX( nzb_s_inner(j-1,i),  & ! Southright corner
                                      nzb_s_inner(j,i+1) ) + 1
             ENDIF

          ENDIF

          IF ( nzb_s_inner(j,i) > nzb_s_inner(j,i-1) )  THEN
             wall_l(j,i) = nzb_s_inner(j,i-1) + 1            ! Left wall
          ENDIF

          IF ( nzb_s_inner(j,i) > nzb_s_inner(j,i+1) )  THEN
             wall_r(j,i) = nzb_s_inner(j,i+1) + 1            ! Right wall
          ENDIF

       ENDDO
    ENDDO

!
!-- Calculate wall flag arrays for the multigrid method
    IF ( psolver == 'multigrid' )  THEN
!
!--    Gridpoint increment of the current level
       inc = 1

       DO  l = maximum_grid_level, 1 , -1

          nxl_l = nxl_mg(l)
          nxr_l = nxr_mg(l)
          nys_l = nys_mg(l)
          nyn_l = nyn_mg(l)
          nzt_l = nzt_mg(l)

!
!--       Assign the flag level to be calculated
          SELECT CASE ( l )
             CASE ( 1 )
                flags => wall_flags_1
             CASE ( 2 )
                flags => wall_flags_2
             CASE ( 3 )
                flags => wall_flags_3
             CASE ( 4 )
                flags => wall_flags_4
             CASE ( 5 )
                flags => wall_flags_5
             CASE ( 6 )
                flags => wall_flags_6
             CASE ( 7 )
                flags => wall_flags_7
             CASE ( 8 )
                flags => wall_flags_8
             CASE ( 9 )
                flags => wall_flags_9
             CASE ( 10 )
                flags => wall_flags_10
          END SELECT

!
!--       Depending on the grid level, set the respective bits in case of
!--       neighbouring walls
!--       Bit 0:  wall to the bottom
!--       Bit 1:  wall to the top (not realized in remaining PALM code so far)
!--       Bit 2:  wall to the south
!--       Bit 3:  wall to the north
!--       Bit 4:  wall to the left
!--       Bit 5:  wall to the right
!--       Bit 6:  inside building

          flags = 0

          DO  i = nxl_l-1, nxr_l+1
             DO  j = nys_l-1, nyn_l+1
                DO  k = nzb, nzt_l+1
                         
!
!--                Inside/outside building (inside building does not need
!--                further tests for walls)
                   IF ( k*inc <= nzb_local(j*inc,i*inc) )  THEN

                      flags(k,j,i) = IBSET( flags(k,j,i), 6 )

                   ELSE
!
!--                   Bottom wall
                      IF ( (k-1)*inc <= nzb_local(j*inc,i*inc) )  THEN
                         flags(k,j,i) = IBSET( flags(k,j,i), 0 )
                      ENDIF
!
!--                   South wall
                      IF ( k*inc <= nzb_local((j-1)*inc,i*inc) )  THEN
                         flags(k,j,i) = IBSET( flags(k,j,i), 2 )
                      ENDIF
!
!--                   North wall
                      IF ( k*inc <= nzb_local((j+1)*inc,i*inc) )  THEN
                         flags(k,j,i) = IBSET( flags(k,j,i), 3 )
                      ENDIF
!
!--                   Left wall
                      IF ( k*inc <= nzb_local(j*inc,(i-1)*inc) )  THEN
                         flags(k,j,i) = IBSET( flags(k,j,i), 4 )
                      ENDIF
!
!--                   Right wall
                      IF ( k*inc <= nzb_local(j*inc,(i+1)*inc) )  THEN
                         flags(k,j,i) = IBSET( flags(k,j,i), 5 )
                      ENDIF

                   ENDIF
                            
                ENDDO
             ENDDO
          ENDDO 

!
!--       Test output of flag arrays
!          i = nxl_l
!          WRITE (9,*)  ' '
!          WRITE (9,*)  '*** mg level ', l, ' ***', mg_switch_to_pe0_level
!          WRITE (9,*)  '    inc=', inc, '  i =', nxl_l
!          WRITE (9,*)  '    nxl_l',nxl_l,' nxr_l=',nxr_l,' nys_l=',nys_l,' nyn_l=',nyn_l
!          DO  k = nzt_l+1, nzb, -1
!             WRITE (9,'(194(1X,I2))')  ( flags(k,j,i), j = nys_l-1, nyn_l+1 )
!          ENDDO

          inc = inc * 2

       ENDDO

    ENDIF

!
!-- In case of topography: limit near-wall mixing length l_wall further:
!-- Go through all points of the subdomain one by one and look for the closest
!-- surface
    IF ( TRIM(topography) /= 'flat' )  THEN
       DO  i = nxl, nxr
          DO  j = nys, nyn

             nzb_si = nzb_s_inner(j,i)
             vi     = vertical_influence(nzb_si)

             IF ( wall_n(j,i) > 0 )  THEN
!
!--             North wall (y distance)
                DO  k = wall_n(j,i), nzb_si
                   l_wall(k,j+1,i) = MIN( l_wall(k,j+1,i), 0.5 * dy )
                ENDDO
!
!--             Above North wall (yz distance)
                DO  k = nzb_si + 1, nzb_si + vi
                   l_wall(k,j+1,i) = MIN( l_wall(k,j+1,i),     &
                                          SQRT( 0.25 * dy**2 + &
                                          ( zu(k) - zw(nzb_si) )**2 ) )
                ENDDO
!
!--             Northleft corner (xy distance)
                IF ( corner_nl(j,i) > 0 )  THEN
                   DO  k = corner_nl(j,i), nzb_si
                      l_wall(k,j+1,i-1) = MIN( l_wall(k,j+1,i-1), &
                                               0.5 * SQRT( dx**2 + dy**2 ) )
                   ENDDO
!
!--                Above Northleft corner (xyz distance)
                   DO  k = nzb_si + 1, nzb_si + vi
                      l_wall(k,j+1,i-1) = MIN( l_wall(k,j+1,i-1),             &
                                               SQRT( 0.25 * (dx**2 + dy**2) + &
                                               ( zu(k) - zw(nzb_si) )**2 ) )
                   ENDDO
                ENDIF
!
!--             Northright corner (xy distance)
                IF ( corner_nr(j,i) > 0 )  THEN
                   DO  k = corner_nr(j,i), nzb_si
                       l_wall(k,j+1,i+1) = MIN( l_wall(k,j+1,i+1), &
                                                0.5 * SQRT( dx**2 + dy**2 ) )
                   ENDDO
!
!--                Above northright corner (xyz distance)
                   DO  k = nzb_si + 1, nzb_si + vi
                      l_wall(k,j+1,i+1) = MIN( l_wall(k,j+1,i+1), &
                                               SQRT( 0.25 * (dx**2 + dy**2) + &
                                               ( zu(k) - zw(nzb_si) )**2 ) )
                   ENDDO
                ENDIF
             ENDIF

             IF ( wall_s(j,i) > 0 )  THEN
!
!--             South wall (y distance)
                DO  k = wall_s(j,i), nzb_si
                   l_wall(k,j-1,i) = MIN( l_wall(k,j-1,i), 0.5 * dy )
                ENDDO
!
!--             Above south wall (yz distance)
                DO  k = nzb_si + 1, &
                        nzb_si + vi
                   l_wall(k,j-1,i) = MIN( l_wall(k,j-1,i),     &
                                          SQRT( 0.25 * dy**2 + &
                                          ( zu(k) - zw(nzb_si) )**2 ) )
                ENDDO
!
!--             Southleft corner (xy distance)
                IF ( corner_sl(j,i) > 0 )  THEN
                   DO  k = corner_sl(j,i), nzb_si
                      l_wall(k,j-1,i-1) = MIN( l_wall(k,j-1,i-1), &
                                               0.5 * SQRT( dx**2 + dy**2 ) )
                   ENDDO
!
!--                Above southleft corner (xyz distance)
                   DO  k = nzb_si + 1, nzb_si + vi
                      l_wall(k,j-1,i-1) = MIN( l_wall(k,j-1,i-1),             &
                                               SQRT( 0.25 * (dx**2 + dy**2) + &
                                               ( zu(k) - zw(nzb_si) )**2 ) )
                   ENDDO
                ENDIF
!
!--             Southright corner (xy distance)
                IF ( corner_sr(j,i) > 0 )  THEN
                   DO  k = corner_sr(j,i), nzb_si
                      l_wall(k,j-1,i+1) = MIN( l_wall(k,j-1,i+1), &
                                               0.5 * SQRT( dx**2 + dy**2 ) )
                   ENDDO
!
!--                Above southright corner (xyz distance)
                   DO  k = nzb_si + 1, nzb_si + vi
                      l_wall(k,j-1,i+1) = MIN( l_wall(k,j-1,i+1),             &
                                               SQRT( 0.25 * (dx**2 + dy**2) + &
                                               ( zu(k) - zw(nzb_si) )**2 ) )
                   ENDDO
                ENDIF

             ENDIF

             IF ( wall_l(j,i) > 0 )  THEN
!
!--             Left wall (x distance)
                DO  k = wall_l(j,i), nzb_si
                   l_wall(k,j,i-1) = MIN( l_wall(k,j,i-1), 0.5 * dx )
                ENDDO
!
!--             Above left wall (xz distance)
                DO  k = nzb_si + 1, nzb_si + vi
                   l_wall(k,j,i-1) = MIN( l_wall(k,j,i-1),     &
                                          SQRT( 0.25 * dx**2 + &
                                          ( zu(k) - zw(nzb_si) )**2 ) )
                ENDDO
             ENDIF

             IF ( wall_r(j,i) > 0 )  THEN
!
!--             Right wall (x distance)
                DO  k = wall_r(j,i), nzb_si
                   l_wall(k,j,i+1) = MIN( l_wall(k,j,i+1), 0.5 * dx )
                ENDDO
!
!--             Above right wall (xz distance)
                DO  k = nzb_si + 1, nzb_si + vi
                   l_wall(k,j,i+1) = MIN( l_wall(k,j,i+1),     &
                                          SQRT( 0.25 * dx**2 + &
                                          ( zu(k) - zw(nzb_si) )**2 ) )
                ENDDO

             ENDIF

          ENDDO
       ENDDO

    ENDIF

!
!-- Multiplication with wall_adjustment_factor
    l_wall = wall_adjustment_factor * l_wall

!
!-- Set lateral boundary conditions for l_wall
    CALL exchange_horiz( l_wall, nbgp )

    DEALLOCATE( corner_nl, corner_nr, corner_sl, corner_sr, nzb_local, &
                nzb_tmp, vertical_influence, wall_l, wall_n, wall_r, wall_s )


 END SUBROUTINE init_grid