subroutine max_ovr (nlon_i, nlat_i, numlon_i, nlon_o, nlat_o, numlon_o, &
                    lon_i , lat_i , lon_o   , lat_o , novr_max)

  use shr_kind_mod, only: r8 => shr_kind_r8

! -----------------------------------------------------------------
  implicit none      
! ------------------------ code history ---------------------------
! source file:       max_ovr
! purpose:           determine maximum number of overlapping cells 
!                    input and output grids
! date last revised: March 1997 
! author:            Mariana Vertenstein
! standardized: 
! reviewed:    
! -----------------------------------------------------------------

! ------------------- input variables -----------------------------
  integer, intent(in)  :: nlon_i                 !number of input  longitude points
  integer, intent(in)  :: nlat_i                 !number of input  latitude points
  integer, intent(in)  :: numlon_i(nlat_i)       !number of longitude points for each input grid cell latitude
  integer, intent(in)  :: nlon_o                 !number of output longitude points
  integer, intent(in)  :: nlat_o                 !number of output latitude points
  integer, intent(in)  :: numlon_o(nlat_o)       !number of longitude points for each output grid cell latitude 
  real(r8), intent(in) :: lon_i(nlon_i+1,nlat_i) !input grid cell longitude, western edge
  real(r8), intent(in) :: lat_i(nlat_i+1)        !input grid cell latitude, southern edge
  real(r8), intent(in) :: lon_o(nlon_o+1,nlat_o) !output grid cell longitude, western edge
  real(r8), intent(in) :: lat_o(nlat_o+1)        !output grid cell latitude , southern edge
  integer , intent(out):: novr_max               !maximum number of overlapping input cells
! -----------------------------------------------------------------

! ------------------- local variables -----------------------------
  integer novr                !number of overlapping input cells
  integer io,ii               !output and input grids longitude loop index
  integer jo,ji               !output and input grids latitude  loop index
! -----------------------------------------------------------------


! -----------------------------------------------------------------
! for each output grid cell: find overlapping input grid cell and area of
! input grid cell that overlaps with output grid cell. cells overlap if:
!
! southern edge of input grid < northern edge of output grid AND
! northern edge of input grid > southern edge of output grid
!
! western edge of input grid < eastern edge of output grid AND
! eastern edge of input grid > western edge of output grid
!
!           lon_o(io,jo)       lon_o(io+1,jo)
!
!              |                   |
!              --------------------- lat_o(jo+1)
!              |                   |
!              |                   |
!    xxxxxxxxxxxxxxx lat_i(ji+1)   |
!    x         |   x               |
!    x  input  |   x   output      |
!    x  cell   |   x    cell       |
!    x  ii,ji  |   x   io,jo       |
!    x         |   x               |
!    x         ----x---------------- lat_o(jo  )
!    x             x
!    xxxxxxxxxxxxxxx lat_i(ji  )
!    x             x
! lon_i(ii,ji) lon_i(ii+1,ji)
! -----------------------------------------------------------------

!
! determine maximum number of overlapping cells
! loop through all input grid cells to find overlap with output grid.
! code does not vectorize but is only called during initialization.
!
  novr_max = 0
  do jo = 1, nlat_o
    do io = 1, numlon_o(jo)
      novr = 0
      do ji = 1, nlat_i                            
        if (lat_i(ji  ).lt.lat_o(jo+1) .and. &
            lat_i(ji+1).gt.lat_o(jo  )) then  !lat ok
          do ii = 1, numlon_i(ji)
            if (lon_i(ii  ,ji).lt.lon_o(io+1,jo) .and. &
                lon_i(ii+1,ji).gt.lon_o(io  ,jo)) then !lon okay
              novr = novr + 1    ! increment number of ovrlap cells for io,jo
            end if
          end do
        end if
      end do
      if (novr .gt. novr_max) novr_max = novr
    end do
  end do

  return
end subroutine max_ovr
