SUBROUTINE init_slope

!--------------------------------------------------------------------------------!
! This file is part of PALM.
!
! PALM is free software: you can redistribute it and/or modify it under the terms
! of the GNU General Public License as published by the Free Software Foundation,
! either version 3 of the License, or (at your option) any later version.
!
! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
! A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License along with
! PALM. If not, see <http://www.gnu.org/licenses/>.
!
! Copyright 1997-2012  Leibniz University Hannover
!--------------------------------------------------------------------------------!
!
! Current revisions:
! -----------------
!
! Former revisions:
! -----------------
! $Id: init_slope.f90 1037 2012-10-22 14:10:22Z gryschka $
!
! 1036 2012-10-22 13:43:42Z raasch
! code put under GPL (PALM 3.9)
!
! 667 2010-12-23 12:06:00Z suehring/gryschka
! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng.
!
! 622 2010-12-10 08:08:13Z raasch
! optional barriers included in order to speed up collective operations
!
! Feb. 2007
! RCS Log replace by Id keyword, revision history cleaned up
!
! Revision 1.5  2006/02/23 12:35:34  raasch
! nanz_2dh renamed ngp_2dh
!
! Revision 1.1  2000/04/27 07:06:24  raasch
! Initial revision
!
!
! Description:
! ------------
! Initialization of the temperature field and other variables used in case
! of a sloping surface.
! Remember: when a sloping surface is used, only one constant temperature
!           gradient is allowed!
!------------------------------------------------------------------------------!

    USE arrays_3d
    USE constants
    USE grid_variables
    USE indices
    USE pegrid
    USE control_parameters

    IMPLICIT NONE

    INTEGER ::  i, j, k
    REAL    ::  alpha, height, pt_value, radius
    REAL, DIMENSION(:), ALLOCATABLE ::  pt_init_local

!
!-- Calculate reference temperature field needed for computing buoyancy
    ALLOCATE( pt_slope_ref(nzb:nzt+1,nxlg:nxrg) )

    DO  i = nxlg, nxrg
       DO  k = nzb, nzt+1

!
!--       Compute height of grid-point relative to lower left corner of
!--       the total domain.
!--       First compute the distance between the actual grid point and the
!--       lower left corner as well as the angle between the line connecting
!--       these points and the bottom of the model.
          IF ( k /= nzb )  THEN
             radius = SQRT( ( i * dx )**2 + zu(k)**2 )
             height = zu(k)
          ELSE
             radius = SQRT( ( i * dx )**2 )
             height = 0.0
          ENDIF
          IF ( radius /= 0.0 )  THEN
             alpha = ASIN( height / radius )
          ELSE
             alpha = 0.0
          ENDIF
!
!--       Compute temperatures in the rotated coordinate system
          alpha    = alpha + alpha_surface / 180.0 * pi
          pt_value = pt_surface + radius * SIN( alpha ) * &
                                  pt_vertical_gradient(1) / 100.0
          pt_slope_ref(k,i) = pt_value
       ENDDO                
    ENDDO

!
!-- Temperature difference between left and right boundary of the total domain,
!-- used for the cyclic boundary in x-direction
    pt_slope_offset = (nx+1) * dx * sin_alpha_surface * &
                      pt_vertical_gradient(1) / 100.0


!
!-- Following action must only be executed for initial runs
    IF ( TRIM( initializing_actions ) /= 'read_restart_data' )  THEN
!
!--    Set initial temperature equal to the reference temperature field
       DO  j = nysg, nyng
          pt(:,j,:) = pt_slope_ref
       ENDDO

!
!--    Recompute the mean initial temperature profile (mean along x-direction of
!--    the rotated coordinate system)
       ALLOCATE( pt_init_local(nzb:nzt+1) )
       pt_init_local = 0.0
       DO  i = nxl, nxr
          DO  j =  nys, nyn
             DO  k = nzb, nzt+1
                pt_init_local(k) = pt_init_local(k) + pt(k,j,i)
             ENDDO
          ENDDO
       ENDDO

#if defined( __parallel )
       IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
       CALL MPI_ALLREDUCE( pt_init_local, pt_init, nzt+2-nzb, MPI_REAL, &
                            MPI_SUM, comm2d, ierr )
#else
       pt_init = pt_init_local
#endif

       pt_init = pt_init / ngp_2dh(0)
       DEALLOCATE( pt_init_local )

    ENDIF

 END SUBROUTINE init_slope