function IntLonLat_xy( xy_Data )
    !
    ! 2 次元緯度経度格子点データの全領域積分(1 層用). 
    !
    ! 実際には格子点データ各点毎に x_Lon_Weight, y_Lat_Weight を掛けた
    ! 総和を計算している. 
    !
    ! Global integration of 2-dimensional (latitude and longitude)
    ! grid data.
    !
    ! Practically, the sum total of grid data is calculated
    ! by multiplying in each grid "x_Lon_Weight" and "y_Lat_Weight".
    !

    real(DP), intent(in) :: xy_Data (0:imax-1, 1:jmax)
    real(DP)             :: IntLonLat_xy

    ! 実行文 ; Executable statement
    !

    IntLonLat_xy = IntLat_y( y_IntLon_xy( xy_Data ) )

  end function IntLonLat_xy

  function a_IntLonLat_xya( xya_Data )
    !
    ! 2 次元緯度経度格子点データの全領域積分(1 層用). 
    !
    ! 実際には格子点データ各点毎に x_Lon_Weight, y_Lat_Weight を掛けた
    ! 総和を計算している. 
    !
    ! Global integration of 2-dimensional (latitude and longitude)
    ! grid data.
    !
    ! Practically, the sum total of grid data is calculated
    ! by multiplying in each grid "x_Lon_Weight" and "y_Lat_Weight".
    !

    real(DP), intent(in) :: xya_Data       (:,:,:)
    real(DP)             :: a_IntLonLat_xya(size(xya_Data,3))


    ! 実行文 ; Executable statement
    !


    a_IntLonLat_xya = a_IntLat_ya( ya_IntLon_xya( xya_Data ) )


  end function a_IntLonLat_xya

  subroutine IntAvrOprInit
    !
    ! intavr_operate モジュールの初期化を行います. 
    ! NAMELIST#intavr_operate_nml の読み込みはこの手続きで行われます. 
    !
    ! "intavr_operate" module is initialized. 
    ! "NAMELIST#intavr_operate_nml" is loaded in this procedure. 
    !

    ! モジュール引用 ; USE statements
    !

    ! 宣言文 ; Declaration statements
    !

!!$    integer:: unit_nml        ! NAMELIST ファイルオープン用装置番号. 
!!$                              ! Unit number for NAMELIST file open
!!$    integer:: iostat_nml      ! NAMELIST 読み込み時の IOSTAT. 
!!$                              ! IOSTAT of NAMELIST read

    ! NAMELIST 変数群
    ! NAMELIST group name
    !
!!$    namelist /intavr_operate_nml/
          !
          ! デフォルト値については初期化手続 "intavr_operate#IntAvrOprInit" 
          ! のソースコードを参照のこと. 
          !
          ! Refer to source codes in the initialization procedure
          ! "intavr_operate#IntAvrOprInit" for the default values. 
          !

    ! 実行文 ; Executable statement
    !

    if ( intavr_operate_inited ) return


    ! デフォルト値の設定
    ! Default values settings
    !

!!$    ! NAMELIST の読み込み
!!$    ! NAMELIST is input
!!$    !
!!$    if ( trim(namelist_filename) /= '' ) then
!!$      call FileOpen( unit_nml, &          ! (out)
!!$        & namelist_filename, mode = 'r' ) ! (in)
!!$
!!$      rewind( unit_nml )
!!$      read( unit_nml, &           ! (in)
!!$        & nml = intavr_operate_nml, &  ! (out)
!!$        & iostat = iostat_nml )   ! (out)
!!$      close( unit_nml )
!!$
!!$      call NmlutilMsg( iostat_nml, module_name ) ! (in)
!!$    end if

    ! 印字 ; Print
    !
    call MessageNotify( 'M', module_name, '----- Initialization Messages -----' )
    call MessageNotify( 'M', module_name, '-- version = %c', c1 = trim(version) )
    intavr_operate_inited = .true.
  end subroutine IntAvrOprInit

  function IntLat_y( y_Data )
    !
    ! 1 次元緯度格子点データの緯度方向積分(1 層用). 
    !
    ! 実際には格子点データ各点毎に y_Lat_Weight を掛けた
    ! 総和を計算している. 
    !
    ! Meridonal integration of 1-dimensional (latitude)
    ! grid data.
    !
    ! Practically, the sum total of grid data is calculated
    ! by multiplying in each grid "y_Lat_Weight".
    !
    real(DP), intent(in) :: y_Data (1:jmax)
    real(DP)             :: IntLat_y

    ! 作業変数
    ! Work variables
    !

    ! 実行文 ; Executable statement
    !
    IntLat_y = sum( y_Data * y_Lat_Weight )

  end function IntLat_y

  function IntLat_y( y_Data )
    !
    ! 1 次元緯度経度格子点データの全領域平均(1 層用). 
    !
    ! Global mean of 2-dimensional (latitude and longitude)
    ! grid data.
    !

    ! MPI
    !
    use mpi_wrapper, only: nprocs, myrank, MPIWrapperISend, MPIWrapperIRecv, MPIWrapperWait

    ! 格子点数・最大波数設定
    ! Number of grid points and maximum truncated wavenumber settings
    !
    use gridset, only: a_jmax, jmax_max

    real(DP), intent(in) :: y_Data (1:jmax)
    real(DP)             :: IntLat_y


    ! Local variable
    !
    real(DP), allocatable :: a_SendBuf (:)
    real(DP), allocatable :: aa_RecvBuf(:,:)
    integer , allocatable :: a_iReqSend(:)
    integer , allocatable :: a_iReqRecv(:)

    integer               :: j
    integer               :: n


    ! 実行文 ; Executable statement
    !


    allocate( a_SendBuf (1:jmax_max) )
    allocate( aa_RecvBuf(1:jmax_max,0:nprocs-1) )
    allocate( a_iReqSend(0:nprocs-1) )
    allocate( a_iReqRecv(0:nprocs-1) )

    do j = 1, jmax
      a_SendBuf(j) = y_Data(j) * y_Lat_Weight(j)
    end do
    do j = jmax+1, jmax_max
      a_SendBuf(j) = -1.0d0
    end do

    do n = 0, nprocs-1
      if ( n == myrank ) then
        aa_RecvBuf(:,n) = a_SendBuf
      else
        call MPIWrapperISend( n, jmax_max, a_SendBuf      , a_iReqSend(n) )
        call MPIWrapperIRecv( n, jmax_max, aa_RecvBuf(:,n), a_iReqRecv(n) )
      end if
    end do
    do n = 0, nprocs-1
      if ( n == myrank ) cycle
      call MPIWrapperWait( a_iReqSend(n) )
      call MPIWrapperWait( a_iReqRecv(n) )
    end do


    IntLat_y = 0.0d0
    do n = nprocs-1, 0, -1
      do j = 1, a_jmax(n) / 2
        IntLat_y = IntLat_y + aa_RecvBuf(j,n)
      end do
    end do
    do n = 0, nprocs-1
      do j = a_jmax(n) / 2 + 1, a_jmax(n)
        IntLat_y = IntLat_y + aa_RecvBuf(j,n)
      end do
    end do


    deallocate( a_SendBuf  )
    deallocate( aa_RecvBuf )
    deallocate( a_iReqSend )
    deallocate( a_iReqRecv )


  end function IntLat_y

  function a_IntLat_ya( ya_Data )
    !
    ! 1 次元緯度格子点データの緯度方向積分(1 層用). 
    !
    ! 実際には格子点データ各点毎に y_Lat_Weight を掛けた
    ! 総和を計算している. 
    !
    ! Meridonal integration of 1-dimensional (latitude)
    ! grid data.
    !
    ! Practically, the sum total of grid data is calculated
    ! by multiplying in each grid "y_Lat_Weight".
    !
    real(DP), intent(in) :: ya_Data    (:,:)
    real(DP)             :: a_IntLat_ya(size(ya_Data,2))

    ! 作業変数
    ! Work variables
    !
    integer :: lmax
    integer :: l


    ! 実行文 ; Executable statement
    !
    lmax = size(ya_Data,2)

    do l = 1, lmax
      a_IntLat_ya(l) = sum( ya_Data(:,l) * y_Lat_Weight )
    end do


  end function a_IntLat_ya

  function a_IntLat_ya( ya_Data )
    !
    ! 1 次元緯度経度格子点データの全領域平均(1 層用). 
    !
    ! Global mean of 2-dimensional (latitude and longitude)
    ! grid data.
    !

    ! MPI
    !
    use mpi_wrapper, only: nprocs, myrank, MPIWrapperISend, MPIWrapperIRecv, MPIWrapperWait

    ! 格子点数・最大波数設定
    ! Number of grid points and maximum truncated wavenumber settings
    !
    use gridset, only: a_jmax, jmax_max

    real(DP), intent(in) :: ya_Data (:,:)
    real(DP)             :: a_IntLat_ya(size(ya_Data,2))


    ! Local variable
    !
    integer               :: lmax
    real(DP), allocatable :: aa_SendBuf (:,:)
    real(DP), allocatable :: aaa_RecvBuf(:,:,:)
    integer , allocatable :: a_iReqSend (:)
    integer , allocatable :: a_iReqRecv (:)

    integer               :: j
    integer               :: l
    integer               :: n


    ! 実行文 ; Executable statement
    !
    lmax = size(ya_Data,2)


    allocate( aa_SendBuf (1:jmax_max, 1:lmax) )
    allocate( aaa_RecvBuf(1:jmax_max, 1:lmax, 0:nprocs-1) )
    allocate( a_iReqSend(0:nprocs-1) )
    allocate( a_iReqRecv(0:nprocs-1) )

    do l = 1, lmax
      do j = 1, jmax
        aa_SendBuf(j,l) = ya_Data(j,l) * y_Lat_Weight(j)
      end do
      do j = jmax+1, jmax_max
        aa_SendBuf(j,l) = -1.0d0
      end do
    end do

    do n = 0, nprocs-1
      if ( n == myrank ) then
        aaa_RecvBuf(:,:,n) = aa_SendBuf
      else
        call MPIWrapperISend( n, jmax_max, lmax, aa_SendBuf        , a_iReqSend(n) )
        call MPIWrapperIRecv( n, jmax_max, lmax, aaa_RecvBuf(:,:,n), a_iReqRecv(n) )
      end if
    end do
    do n = 0, nprocs-1
      if ( n == myrank ) cycle
      call MPIWrapperWait( a_iReqSend(n) )
      call MPIWrapperWait( a_iReqRecv(n) )
    end do


    a_IntLat_ya = 0.0d0
    do n = nprocs-1, 0, -1
      do l = 1, lmax
        do j = 1, a_jmax(n) / 2
          a_IntLat_ya(l) = a_IntLat_ya(l) + aaa_RecvBuf(j,l,n)
        end do
      end do
    end do
    do n = 0, nprocs-1
      do l = 1, lmax
        do j = a_jmax(n) / 2 + 1, a_jmax(n)
          a_IntLat_ya(l) = a_IntLat_ya(l) + aaa_RecvBuf(j,l,n)
        end do
      end do
    end do


    deallocate( aa_SendBuf  )
    deallocate( aaa_RecvBuf )
    deallocate( a_iReqSend  )
    deallocate( a_iReqRecv  )


  end function a_IntLat_ya

  function y_IntLon_xy( xy_Data )
    !
    ! 2 次元緯度経度格子点データの経度方向積分(1 層用). 
    !
    ! 実際には格子点データ各点毎に x_Lon_Weight を掛けた
    ! 総和を計算している. 
    !
    ! Zonal integration of 2-dimensional (latitude and longitude)
    ! grid data.
    !
    ! Practically, the sum total of grid data is calculated
    ! by multiplying in each grid "x_Lon_Weight".
    !

    real(DP), intent(in) :: xy_Data (0:imax-1, 1:jmax)
    real(DP)             :: y_IntLon_xy (1:jmax)

    ! 作業変数
    ! Work variables
    !
    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitudinal direction
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitudinal direction

    ! 実行文 ; Executable statement
    !

    y_IntLon_xy = 0.0_DP
    do j = 1, jmax
      do i = 0, imax - 1
        y_IntLon_xy(j) = y_IntLon_xy(j) + xy_Data (i,j) * x_Lon_Weight(i)
      end do
    end do

  end function y_IntLon_xy

  function ya_IntLon_xya( xya_Data )
    !
    ! 2 次元緯度経度格子点データの経度方向積分(1 層用). 
    !
    ! 実際には格子点データ各点毎に x_Lon_Weight を掛けた
    ! 総和を計算している. 
    !
    ! Zonal integration of 2-dimensional (latitude and longitude)
    ! grid data.
    !
    ! Practically, the sum total of grid data is calculated
    ! by multiplying in each grid "x_Lon_Weight".
    !

    real(DP), intent(in) :: xya_Data     (:,:,:)
    real(DP)             :: ya_IntLon_xya(size(xya_Data,2), size(xya_Data,3))

    ! 作業変数
    ! Work variables
    !
    integer:: lmax
    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitudinal direction
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitudinal direction
    integer:: l


    ! 実行文 ; Executable statement
    !
    lmax = size( xya_Data, 3 )

    ya_IntLon_xya = 0.0_DP
    do l = 1, lmax
      do j = 1, jmax
        do i = 0, imax - 1
!!$          ya_IntLon_xya(j,l) = ya_IntLon_xya(j,l) + xya_Data(i,j,l) * x_Lon_Weight(i)
          ya_IntLon_xya(j,l) = ya_IntLon_xya(j,l) + xya_Data(i+1,j,l) * x_Lon_Weight(i)
        end do
      end do
    end do


  end function ya_IntLon_xya