subroutine RadRTENonScat( xyz_IntPF, xy_SurfIntPF, xy_IntDPFDT1, xy_SurfIntDPFDT, xyrr_Trans, xyr_RadLUwFlux, xyr_RadLDwFlux, xyra_DelRadLUwFlux, xyra_DelRadLDwFlux )
    !
    ! 散乱なしの場合の放射伝達方程式の計算
    !
    ! Integrate radiative transfer equation without scattering
    !

    ! モジュール引用 ; USE statements
    !

    ! OpenMP
    !
    !$ use omp_lib


    ! 宣言文 ; Declaration statements
    !

    real(DP), intent(in ) :: xyz_IntPF        (0:imax-1, 1:jmax, 1:kmax)
                              ! Integrated Planck function
    real(DP), intent(in ) :: xy_SurfIntPF     (0:imax-1, 1:jmax)
                              ! Integrated Planck function with surface temperature
    real(DP), intent(in ) :: xy_IntDPFDT1     (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
    real(DP), intent(in ) :: xy_SurfIntDPFDT  (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
                              ! with surface temperature
    real(DP), intent(in ) :: xyrr_Trans   (0:imax-1, 1:jmax, 0:kmax, 0:kmax)
                              ! 透過係数. 
                              ! Transmission coefficient
    real(DP), intent(out) :: xyr_RadLUwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Upward longwave flux
    real(DP), intent(out) :: xyr_RadLDwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Downward longwave flux
    real(DP), intent(out) :: xyra_DelRadLUwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Upward longwave flux derivative
    real(DP), intent(out) :: xyra_DelRadLDwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Downward longwave flux derivative


    ! 作業変数
    ! Work variables
    !
    integer :: js
    integer :: je

    integer :: nthreads
    integer, allocatable :: a_js(:)
    integer, allocatable :: a_je(:)

    integer :: n


    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. rad_rte_nonscat_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    nthreads = 1
    !$ nthreads  = omp_get_max_threads()
!!$    !$ write( 6, * ) "Number of processors : ", omp_get_num_procs()
!!$    !$ write( 6, * ) "Number of threads    : ", nthreads

    allocate( a_js(0:nthreads-1) )
    allocate( a_je(0:nthreads-1) )

    do n = 0, nthreads-1

      if ( n == 0 ) then
        a_js(n) = 1
      else
        a_js(n) = a_je(n-1) + 1
      end if

      a_je(n) = a_js(n  ) + jmax / nthreads - 1
      if ( n + 1 <= mod( jmax, nthreads ) ) then
        a_je(n) = a_je(n) + 1
      end if

    end do

    !$OMP PARALLEL DEFAULT(PRIVATE) &
    !$OMP SHARED( &
    !$OMP         nthreads, a_js, a_je, &
    !$OMP         xyz_IntPF, xy_SurfIntPF, xy_IntDPFDT1, xy_SurfIntDPFDT,  &
    !$OMP         xyrr_Trans, &
    !$OMP         xyr_RadLUwFlux, xyr_RadLDwFlux,                          &
    !$OMP         xyra_DelRadLUwFlux, xyra_DelRadLDwFlux                   &
    !$OMP       )

    !$OMP DO

    do n = 0, nthreads-1

      js = a_js(n)
      je = a_je(n)

      if ( js > je ) cycle

      call RadRTENonScatCore( js, je, xyz_IntPF, xy_SurfIntPF, xy_IntDPFDT1, xy_SurfIntDPFDT, xyrr_Trans, xyr_RadLUwFlux, xyr_RadLDwFlux, xyra_DelRadLUwFlux, xyra_DelRadLDwFlux )

    end do


    !$OMP END DO
    !$OMP END PARALLEL


    deallocate( a_js )
    deallocate( a_je )


  end subroutine RadRTENonScat

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

    ! モジュール引用 ; USE statements
    !

    ! NAMELIST ファイル入力に関するユーティリティ
    ! Utilities for NAMELIST file input
    !
    use namelist_util, only: namelist_filename, NmlutilMsg, NmlutilAryValid

    ! ファイル入出力補助
    ! File I/O support
    !
    use dc_iounit, only: FileOpen

    ! ヒストリデータ出力
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoAddVariable

    ! 文字列操作
    ! Character handling
    !
    use dc_string, only: toChar

    ! ガウス重み, 分点の計算
    ! Calculate Gauss node and Gaussian weight
    !
    use gauss_quad, only : GauLeg

    ! 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 /rad_rte_nonscat_nml/ DiffFact, NumGaussNodeZAInt
          !
          ! デフォルト値については初期化手続 "rad_rte_nonscat#RadRTENonScatInit" 
          ! のソースコードを参照のこと. 
          !
          ! Refer to source codes in the initialization procedure
          ! "rad_rte_nonscat#RadRTENonScatInit" for the default values. 
          !

    ! 実行文 ; Executable statement
    !

    if ( rad_rte_nonscat_inited ) return


    ! デフォルト値の設定
    ! Default values settings
    !
    NumGaussNodeZAInt = 3
    DiffFact          = 1.66_DP


    ! NAMELIST の読み込み
    ! NAMELIST is input
    !
    if ( trim(namelist_filename) /= '' ) then
      call FileOpen( unit_nml, namelist_filename, mode = 'r' ) ! (in)

      rewind( unit_nml )
      read( unit_nml, nml = rad_rte_nonscat_nml, iostat = iostat_nml )             ! (out)
      close( unit_nml )

      call NmlutilMsg( iostat_nml, module_name ) ! (in)
    end if


    if ( NumGaussNodeZAInt > 0 ) then
      allocate( a_CosZA      ( NumGaussNodeZAInt ) )
      allocate( a_GaussWeight( NumGaussNodeZAInt ) )
      call GauLeg( 0.0_DP, 1.0_DP, NumGaussNodeZAInt, a_CosZA, a_GaussWeight )
    end if


    ! 印字 ; Print
    !
    call MessageNotify( 'M', module_name, '----- Initialization Messages -----' )
    call MessageNotify( 'M', module_name, 'NumGaussNodeZAInt = %d', i = (/ NumGaussNodeZAInt /) )
    call MessageNotify( 'M', module_name, 'DiffFact          = %f', d = (/ DiffFact /) )
    call MessageNotify( 'M', module_name, '-- version = %c', c1 = trim(version) )

    rad_rte_nonscat_inited = .true.

  end subroutine RadRTENonScatInit

  subroutine RadRTENonScatMonoSemiAnal( xy_SurfAlbedo, xyr_IntPF, xy_SurfIntPF, xy_IntDPFDT1, xy_SurfIntDPFDT, xyz_OptDep, xyr_RadLUwFlux, xyr_RadLDwFlux, xyra_DelRadLUwFlux, xyra_DelRadLDwFlux )
    !
    ! 散乱なしの場合の放射伝達方程式の計算
    !
    ! Integrate radiative transfer equation without scattering
    !

    ! モジュール引用 ; USE statements
    !


    ! 宣言文 ; Declaration statements
    !

    real(DP), intent(in ) :: xy_SurfAlbedo    (0:imax-1, 1:jmax)
    real(DP), intent(in ) :: xyr_IntPF        (0:imax-1, 1:jmax, 0:kmax)
                              ! Integrated Planck function
    real(DP), intent(in ) :: xy_SurfIntPF     (0:imax-1, 1:jmax)
                              ! Integrated Planck function with surface temperature
    real(DP), intent(in ) :: xy_IntDPFDT1     (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
    real(DP), intent(in ) :: xy_SurfIntDPFDT  (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
                              ! with surface temperature
    real(DP), intent(in ) :: xyz_OptDep   (0:imax-1, 1:jmax, 1:kmax)
                              ! 光学的厚さ. 
                              ! Optical depth
    real(DP), intent(out) :: xyr_RadLUwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Upward longwave flux
    real(DP), intent(out) :: xyr_RadLDwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Downward longwave flux
    real(DP), intent(out) :: xyra_DelRadLUwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Upward longwave flux derivative
    real(DP), intent(out) :: xyra_DelRadLDwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Downward longwave flux derivative


    ! 作業変数
    ! Work variables
    !
    real(DP) :: CosZA
    real(DP) :: GaussWeight

    real(DP) :: xyz_TransEachLayer0(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_TransEachLayer (0:imax-1, 1:jmax, 1:kmax)
                              ! 透過係数. 
                              ! Transmission coefficient
    real(DP) :: xyr_Trans0(0:imax-1, 1:jmax, 0:kmax)
                              ! 
                              ! Transmission coefficient from surface to layer interfaces
    real(DP) :: xyr_Trans1(0:imax-1, 1:jmax, 0:kmax)
                              ! 
                              ! Transmission coefficient from top of the lowest layer to layer interfaces

    real(DP) :: xyz_DPFDOptDep(0:imax-1, 1:jmax, 1:kmax)

    real(DP) :: xyr_UwFlux (0:imax-1, 1:jmax, 0:kmax)
    real(DP) :: xyr_DwFlux (0:imax-1, 1:jmax, 0:kmax)
    real(DP) :: xyra_DelUwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
    real(DP) :: xyra_DelDwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)

    real(DP) :: IntFact

    integer:: i
    integer:: j
    integer:: k               ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction
    integer:: n


    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. rad_rte_nonscat_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if



    ! 放射フラックス計算
    ! Calculate radiation flux
    !

    xyz_TransEachLayer0 = exp( - xyz_OptDep )
    !  This is ad hoc treatment to avoid underflow.
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xyz_TransEachLayer0(i,j,k) < 1.0e-50_DP ) then
            xyz_TransEachLayer0(i,j,k) = 0.0_DP
          end if
        end do
      end do
    end do

    do k = 1, kmax
      xyz_DPFDOptDep(:,:,k) = ( xyr_IntPF(:,:,k-1) - xyr_IntPF(:,:,k) ) / max( xyz_OptDep(:,:,k), 1.0d-100 )
    end do

    if ( NumGaussNodeZAInt > 0 ) then
      ! for case with Gaussian quadrature
      IntFact = 2.0_DP
    else
      ! for two-stream approximation or case with diffusivity factor
      IntFact = 1.0_DP
    end if


    !   Initialization
    !
    xyr_RadLUwFlux     = 0.0_DP
    xyr_RadLDwFlux     = 0.0_DP
    xyra_DelRadLUwFlux = 0.0_DP
    xyra_DelRadLDwFlux = 0.0_DP


    !   Loop for Gaussian quadrature
    !
    loop_gq : do n = 1, max( NumGaussNodeZAInt, 1 )

      ! Preparetion
      !
      if ( NumGaussNodeZAInt > 0 ) then
        CosZA = a_CosZA(n)
      else
        CosZA = 1.0_DP / DiffFact
      end if
      !
      xyz_TransEachLayer = ( xyz_TransEachLayer0 )**(1.0d0/CosZA)
      !
      xyr_Trans0(:,:,0) = 1.0_DP
      do k = 1, kmax
        xyr_Trans0(:,:,k) = xyr_Trans0(:,:,k-1) * xyz_TransEachLayer(:,:,k)
      end do
      xyr_Trans1(:,:,0) = xyz_TransEachLayer(:,:,1)
      xyr_Trans1(:,:,1) = 1.0_DP
      do k = 2, kmax
        xyr_Trans1(:,:,k) = xyr_Trans0(:,:,k-1) * xyz_TransEachLayer(:,:,k)
      end do

      !
      !   Downward flux
      !
      k = kmax
      xyr_DwFlux(:,:,k) = 0.0_DP
      do k = kmax-1, 0, -1
        xyr_DwFlux(:,:,k) = ( xyr_DwFlux(:,:,k+1) - IntFact * xyr_IntPF(:,:,k+1) ) * xyz_TransEachLayer(:,:,k+1) + IntFact * xyr_IntPF(:,:,k) - IntFact * CosZA * xyz_DPFDOptDep(:,:,k+1) * ( 1.0_DP - xyz_TransEachLayer(:,:,k+1) )
      end do
      !
      !   Upward flux
      !
      k = 0
      xyr_UwFlux(:,:,k) = IntFact * xy_SurfIntPF + xy_SurfAlbedo * xyr_DwFlux(:,:,0)
      do k = 1, kmax
        xyr_UwFlux(:,:,k) = ( xyr_UwFlux(:,:,k-1) - IntFact * xyr_IntPF(:,:,k-1) ) * xyz_TransEachLayer(:,:,k) + IntFact * xyr_IntPF(:,:,k) + IntFact * CosZA * xyz_DPFDOptDep(:,:,k) * ( 1.0_DP - xyz_TransEachLayer(:,:,k) )
      end do


      ! 放射フラックスの変化率の計算
      ! Calculate rate of change of radiative flux
      !
      do k = 0, kmax
        xyra_DelUwFlux(:,:,k,0) = IntFact * xy_SurfIntDPFDT * xyr_Trans0(:,:,k)
      end do
      do k = 0, kmax
        xyra_DelDwFlux(:,:,k,0) = 0.0_DP
      end do
      xyra_DelUwFlux(:,:,:,1) = 0.0_DP
      xyra_DelDwFlux(:,:,:,1) = 0.0_DP


      ! Sum over zenith angle
      !
      if ( NumGaussNodeZAInt > 0 ) then
        GaussWeight = a_GaussWeight( n )

        xyr_RadLUwFlux = xyr_RadLUwFlux + xyr_UwFlux * CosZA * GaussWeight
        xyr_RadLDwFlux = xyr_RadLDwFlux + xyr_DwFlux * CosZA * GaussWeight

        xyra_DelRadLUwFlux = xyra_DelRadLUwFlux + xyra_DelUwFlux * CosZA * GaussWeight
        xyra_DelRadLDwFlux = xyra_DelRadLDwFlux + xyra_DelDwFlux * CosZA * GaussWeight
      else
        xyr_RadLUwFlux = xyr_UwFlux
        xyr_RadLDwFlux = xyr_DwFlux

        xyra_DelRadLUwFlux = xyra_DelUwFlux
        xyra_DelRadLDwFlux = xyra_DelDwFlux
      end if

    end do loop_gq


  end subroutine RadRTENonScatMonoSemiAnal

  subroutine RadRTENonScatWrapper( xyz_Temp, xy_SurfTemp, xy_SurfEmis, xyrr_Trans, xyr_RadLUwFlux, xyr_RadLDwFlux, xyra_DelRadLUwFlux, xyra_DelRadLDwFlux, WNs, WNe, NumGaussNode )
    !
    ! 散乱なしの場合の放射伝達方程式の計算
    !
    ! Integrate radiative transfer equation without scattering
    !

    ! モジュール引用 ; USE statements
    !


    ! プランク関数の計算
    ! Calculate Planck function
    !
    use planck_func, only : Integ_PF_GQ_Array3D, Integ_PF_GQ_Array2D, Integ_DPFDT_GQ_Array2D

    ! 宣言文 ; Declaration statements
    !

    real(DP), intent(in ) :: xyz_Temp    (0:imax-1, 1:jmax, 1:kmax)
                              ! $ T $ .     温度. Temperature
    real(DP), intent(in ) :: xy_SurfTemp (0:imax-1, 1:jmax)
                              ! 地表面温度. 
                              ! Surface temperature
    real(DP), intent(in ) :: xy_SurfEmis (0:imax-1, 1:jmax)
                              ! 惑星表面射出率. 
                              ! Surface emissivity
    real(DP), intent(in ) :: xyrr_Trans   (0:imax-1, 1:jmax, 0:kmax, 0:kmax)
                              ! 透過係数. 
                              ! Transmission coefficient
    real(DP), intent(out) :: xyr_RadLUwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Upward longwave flux
    real(DP), intent(out) :: xyr_RadLDwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Downward longwave flux
    real(DP), intent(out) :: xyra_DelRadLUwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Upward longwave flux derivative
    real(DP), intent(out) :: xyra_DelRadLDwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Downward longwave flux derivative
    real(DP), intent(in ), optional :: WNs
    real(DP), intent(in ), optional :: WNe
    integer , intent(in ), optional :: NumGaussNode


    ! 作業変数
    ! Work variables
    !
    real(DP):: xyz_IntPF        (0:imax-1, 1:jmax, 1:kmax)
                              ! Integrated Planck function
    real(DP):: xy_SurfIntPF     (0:imax-1, 1:jmax)
                              ! Integrated Planck function with surface temperature
    real(DP):: xy_IntDPFDT1     (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
    real(DP):: xy_SurfIntDPFDT  (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
                              ! with surface temperature


    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. rad_rte_nonscat_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! Check arguments
    !
    if ( present( WNs ) .or. present( WNe ) .or. present( NumGaussNode ) ) then
      if ( .not. ( present( WNs ) .and. present( WNe ) .and. present( NumGaussNode ) ) ) then
        call MessageNotify( 'E', module_name, 'All of WNs, WNe, and NumGaussNode have to be present.' )
      end if
    end if


    if ( present( WNs ) ) then
      ! Case for non-grey atmosphere
      !

      ! Integrate Planck function and temperature derivative of it
      !
      call Integ_PF_GQ_Array3D( WNs, WNe, NumGaussNode, 0, imax-1, 1, jmax, 1, kmax, xyz_Temp, xyz_IntPF )
      call Integ_PF_GQ_Array2D( WNs, WNe, NumGaussNode, 0, imax-1, 1, jmax, xy_SurfTemp, xy_SurfIntPF )
      call Integ_DPFDT_GQ_Array2D( WNs, WNe, NumGaussNode, 0, imax-1, 1, jmax, xyz_Temp(:,:,1), xy_IntDPFDT1 )
      call Integ_DPFDT_GQ_Array2D( WNs, WNe, NumGaussNode, 0, imax-1, 1, jmax, xy_SurfTemp, xy_SurfIntDPFDT )

      xyz_IntPF       =               PI * xyz_IntPF
      xy_SurfIntPF    = xy_SurfEmis * PI * xy_SurfIntPF
      xy_IntDPFDT1    =               PI * xy_IntDPFDT1
      xy_SurfIntDPFDT = xy_SurfEmis * PI * xy_SurfIntDPFDT

    else

      ! Case for grey atmosphere
      !
      xyz_IntPF       =                        StB * xyz_Temp**4
      xy_SurfIntPF    = xy_SurfEmis          * StB * xy_SurfTemp**4
      xy_IntDPFDT1    =               4.0_DP * StB * xyz_Temp(:,:,1)**3
      xy_SurfIntDPFDT = xy_SurfEmis * 4.0_DP * StB * xy_SurfTemp**3

    end if


    call RadRTENonScat( xyz_IntPF, xy_SurfIntPF, xy_IntDPFDT1, xy_SurfIntDPFDT, xyrr_Trans, xyr_RadLUwFlux, xyr_RadLDwFlux, xyra_DelRadLUwFlux, xyra_DelRadLDwFlux )


  end subroutine RadRTENonScatWrapper

  subroutine RadRTENonScatAnotherForm( xyz_IntPF, xy_SurfIntPF, xy_IntDPFDT1, xy_SurfIntDPFDT, xyrr_Trans, xyr_RadLUwFlux, xyr_RadLDwFlux, xyra_DelRadLUwFlux, xyra_DelRadLDwFlux )
    !
    ! 散乱なしの場合の放射伝達方程式の計算
    !
    ! Integrate radiative transfer equation without scattering
    !

    ! モジュール引用 ; USE statements
    !


    ! 宣言文 ; Declaration statements
    !

    real(DP), intent(in ) :: xyz_IntPF        (0:imax-1, 1:jmax, 1:kmax)
                              ! Integrated Planck function
    real(DP), intent(in ) :: xy_SurfIntPF     (0:imax-1, 1:jmax)
                              ! Integrated Planck function with surface temperature
    real(DP), intent(in ) :: xy_IntDPFDT1     (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
    real(DP), intent(in ) :: xy_SurfIntDPFDT  (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
                              ! with surface temperature
    real(DP), intent(in ) :: xyrr_Trans   (0:imax-1, 1:jmax, 0:kmax, 0:kmax)
                              ! 透過係数. 
                              ! Transmission coefficient
    real(DP), intent(out) :: xyr_RadLUwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Upward longwave flux
    real(DP), intent(out) :: xyr_RadLDwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Downward longwave flux
    real(DP), intent(out) :: xyra_DelRadLUwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Upward longwave flux derivative
    real(DP), intent(out) :: xyra_DelRadLDwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Downward longwave flux derivative


    ! 作業変数
    ! Work variables
    !
    real(DP) :: xyr_IntPF(0:imax-1, 1:jmax, 0:kmax)

    integer:: k, kk           ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction

    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. rad_rte_nonscat_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if



    ! 
    ! Calculate integrated Planck function at layer interface
    !
    xyr_IntPF(:,:,0   ) = xyz_IntPF(:,:,1   )
    do k = 1, kmax-1
      xyr_IntPF(:,:,k) = ( xyz_IntPF(:,:,k) + xyz_IntPF(:,:,k+1) ) / 2.0_DP
    end do
    xyr_IntPF(:,:,kmax) = xyz_IntPF(:,:,kmax)


    ! 放射フラックス計算
    ! Calculate radiation flux
    !

    !   Initialization
    !
    xyr_RadLDwFlux = 0.0_DP
    xyr_RadLUwFlux = 0.0_DP
    !
    !   Downward flux
    !
    do k = kmax, 0, -1

      xyr_RadLDwFlux(:,:,k) = xyr_IntPF(:,:,k   ) - xyr_IntPF(:,:,kmax) * xyrr_Trans(:,:,k,kmax)
      !
      do kk = kmax, k+1, -1
        xyr_RadLDwFlux(:,:,k) = xyr_RadLDwFlux(:,:,k) - ( xyrr_Trans(:,:,k,kk-1) + xyrr_Trans(:,:,k,kk) ) / 2.0_DP * ( xyr_IntPF(:,:,kk-1) - xyr_IntPF(:,:,kk) )
      end do

    end do
    !
    !   Upward flux
    !
    !     Set upward flux
    !
    do k = 0, kmax

      xyr_RadLUwFlux(:,:,k) = ( xy_SurfIntPF - xyr_IntPF(:,:,0) ) * xyrr_Trans(:,:,k,0) + xyr_IntPF(:,:,k)
      !
      do kk = 1, k
        xyr_RadLUwFlux(:,:,k) = xyr_RadLUwFlux(:,:,k) + ( xyrr_Trans(:,:,k,kk-1) + xyrr_Trans(:,:,k,kk) ) / 2.0_DP * ( xyr_IntPF(:,:,kk-1) - xyr_IntPF(:,:,kk) )
      end do

    end do


    ! 放射フラックスの変化率の計算
    ! Calculate rate of change of radiative flux
    !
    do k = 0, kmax
      xyra_DelRadLUwFlux(:,:,k,0) = xy_SurfIntDPFDT * xyrr_Trans(:,:,k,0)
    end do
    k = 0
    xyra_DelRadLUwFlux(:,:,k,1) = 0.0_DP
    k = 1
    xyra_DelRadLUwFlux(:,:,k,1) = xy_IntDPFDT1 * ( - xyrr_Trans(:,:,k,0) + 1.0_DP / 2.0_DP + ( xyrr_Trans(:,:,k,0) + xyrr_Trans(:,:,k,1) ) / 2.0_DP / 2.0_DP )
    do k = 2, kmax
      xyra_DelRadLUwFlux(:,:,k,1) = xy_IntDPFDT1 * ( - xyrr_Trans(:,:,k,0) + ( xyrr_Trans(:,:,k,0) + xyrr_Trans(:,:,k,1) ) / 2.0_DP / 2.0_DP + ( xyrr_Trans(:,:,k,1) + xyrr_Trans(:,:,k,2) ) / 2.0_DP / 2.0_DP )
    end do
    do k = 0, kmax
      xyra_DelRadLDwFlux(:,:,k,0) = 0.0_DP
    end do
    if ( kmax <= 1 ) then
      k = 0
      xyra_DelRadLDwFlux(:,:,k,1) = + xy_IntDPFDT1 * (   1.0_DP - xyrr_Trans(:,:,k,k+1) )
      k = 1
      xyra_DelRadLDwFlux(:,:,k,1) = 0.0_DP
    else
      k = 0
      xyra_DelRadLDwFlux(:,:,k,1) = + xy_IntDPFDT1 * (   1.0_DP - ( xyrr_Trans(:,:,k,k  ) + xyrr_Trans(:,:,k,k+1) ) / 2.0_DP / 2.0_DP - ( xyrr_Trans(:,:,k,k+1) + xyrr_Trans(:,:,k,k+2) ) / 2.0_DP / 2.0_DP )
      k = 1
      xyra_DelRadLDwFlux(:,:,k,1) = + xy_IntDPFDT1 * (   1.0_DP / 2.0_DP - ( xyrr_Trans(:,:,k,k  ) + xyrr_Trans(:,:,k,k+1) ) / 2.0_DP / 2.0_DP )
    end if
    do k = 2, kmax
      xyra_DelRadLDwFlux(:,:,k,1) = 0.0_DP
    end do


  end subroutine RadRTENonScatAnotherForm

  subroutine RadRTENonScatCore( js, je, xyz_IntPF, xy_SurfIntPF, xy_IntDPFDT1, xy_SurfIntDPFDT, xyrr_Trans, xyr_RadLUwFlux, xyr_RadLDwFlux, xyra_DelRadLUwFlux, xyra_DelRadLDwFlux )
    !
    ! 散乱なしの場合の放射伝達方程式の計算
    !
    ! Integrate radiative transfer equation without scattering
    !

    ! モジュール引用 ; USE statements
    !


    ! 宣言文 ; Declaration statements
    !

    integer , intent(in ) :: js
    integer , intent(in ) :: je
    real(DP), intent(in ) :: xyz_IntPF        (0:imax-1, 1:jmax, 1:kmax)
                              ! Integrated Planck function
    real(DP), intent(in ) :: xy_SurfIntPF     (0:imax-1, 1:jmax)
                              ! Integrated Planck function with surface temperature
    real(DP), intent(in ) :: xy_IntDPFDT1     (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
    real(DP), intent(in ) :: xy_SurfIntDPFDT  (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
                              ! with surface temperature
    real(DP), intent(in ) :: xyrr_Trans   (0:imax-1, 1:jmax, 0:kmax, 0:kmax)
                              ! 透過係数. 
                              ! Transmission coefficient
    real(DP), intent(out) :: xyr_RadLUwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Upward longwave flux
    real(DP), intent(out) :: xyr_RadLDwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Downward longwave flux
    real(DP), intent(out) :: xyra_DelRadLUwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Upward longwave flux derivative
    real(DP), intent(out) :: xyra_DelRadLDwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Downward longwave flux derivative


    ! 作業変数
    ! Work variables
    !
    integer:: j
    integer:: k, kk           ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction

    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. rad_rte_nonscat_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if



    ! 放射フラックス計算
    ! Calculate radiation flux
    !

    !   Initialization
    !
    do k = 0, kmax
      do j = js, je
        xyr_RadLDwFlux(:,j,k) = 0.0_DP
        xyr_RadLUwFlux(:,j,k) = 0.0_DP
      end do
    end do
    !
    !   Downward flux
    !
    do k = kmax, 0, -1

      do kk = kmax, k+1, -1
        do j = js, je
          xyr_RadLDwFlux(:,j,k) = xyr_RadLDwFlux(:,j,k) + xyz_IntPF(:,j,kk) * ( xyrr_Trans(:,j,k,kk-1) - xyrr_Trans(:,j,k,kk) )
        end do
      end do

    end do
    !
    !   Upward flux
    !
    !     Set upward flux
    !
    do k = 0, kmax
      do j = js, je

        xyr_RadLUwFlux(:,j,k) = xy_SurfIntPF(:,j) * xyrr_Trans(:,j,k,0)

        do kk = 1, k
          xyr_RadLUwFlux(:,j,k) = xyr_RadLUwFlux(:,j,k) - xyz_IntPF(:,j,kk) * ( xyrr_Trans(:,j,k,kk-1) - xyrr_Trans(:,j,k,kk) )
        end do

      end do
    end do


    ! 放射フラックスの変化率の計算
    ! Calculate rate of change of radiative flux
    !
    do k = 0, kmax
      do j = js, je
        xyra_DelRadLUwFlux(:,j,k,0) = xy_SurfIntDPFDT(:,j) * xyrr_Trans(:,j,k,0)
      end do
    end do
    k = 0
    do j = js, je
      xyra_DelRadLUwFlux(:,j,k,1) = 0.0_DP
    end do
    do k = 1, kmax
      do j = js, je
        xyra_DelRadLUwFlux(:,j,k,1) = - xy_IntDPFDT1(:,j) * ( xyrr_Trans(:,j,k,0) - xyrr_Trans(:,j,k,1) )
      end do
    end do
    do k = 0, kmax
      do j = js, je
        xyra_DelRadLDwFlux(:,j,k,0) = 0.0_DP
      end do
    end do
    k = 0
    do j = js, je
      xyra_DelRadLDwFlux(:,j,k,1) = + xy_IntDPFDT1(:,j) * ( xyrr_Trans(:,j,k,0) - xyrr_Trans(:,j,k,1) )
    end do
    do k = 1, kmax
      do j = js, je
        xyra_DelRadLDwFlux(:,j,k,1) = 0.0_DP
      end do
    end do


  end subroutine RadRTENonScatCore

  subroutine RadRTENonScatMonoWithDiffFact( DiffFact, xyz_IntPF, xy_SurfIntPF, xy_IntDPFDT1, xy_SurfIntDPFDT, xyz_OptDep, xyr_RadLUwFlux, xyr_RadLDwFlux, xyra_DelRadLUwFlux, xyra_DelRadLDwFlux )
    !
    ! 散乱なしの場合の放射伝達方程式の計算
    !
    ! Integrate radiative transfer equation without scattering
    !

    ! モジュール引用 ; USE statements
    !


    ! 宣言文 ; Declaration statements
    !

    real(DP), intent(in ) :: DiffFact
                              ! Diffusivity factor
    real(DP), intent(in ) :: xyz_IntPF        (0:imax-1, 1:jmax, 1:kmax)
                              ! Integrated Planck function
    real(DP), intent(in ) :: xy_SurfIntPF     (0:imax-1, 1:jmax)
                              ! Integrated Planck function with surface temperature
    real(DP), intent(in ) :: xy_IntDPFDT1     (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
    real(DP), intent(in ) :: xy_SurfIntDPFDT  (0:imax-1, 1:jmax)
                              ! Integrated temperature derivative of Planck function
                              ! with surface temperature
    real(DP), intent(in ) :: xyz_OptDep   (0:imax-1, 1:jmax, 1:kmax)
                              ! 光学的厚さ. 
                              ! Optical depth
    real(DP), intent(out) :: xyr_RadLUwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Upward longwave flux
    real(DP), intent(out) :: xyr_RadLDwFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Downward longwave flux
    real(DP), intent(out) :: xyra_DelRadLUwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Upward longwave flux derivative
    real(DP), intent(out) :: xyra_DelRadLDwFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Downward longwave flux derivative


    ! 作業変数
    ! Work variables
    !
    real(DP) :: xyz_TransEachLayer(0:imax-1, 1:jmax, 1:kmax)
                              ! 透過係数. 
                              ! Transmission coefficient
    real(DP) :: xyr_Trans0(0:imax-1, 1:jmax, 0:kmax)
                              ! 
                              ! Transmission coefficient from surface to layer interfaces
    real(DP) :: xyr_Trans1(0:imax-1, 1:jmax, 0:kmax)
                              ! 
                              ! Transmission coefficient from top of the lowest layer to layer interfaces

    integer:: k               ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction

    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. rad_rte_nonscat_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if



    ! 放射フラックス計算
    ! Calculate radiation flux
    !

    xyz_TransEachLayer = exp( - DiffFact * xyz_OptDep )
    !
    xyr_Trans0(:,:,0) = 1.0_DP
    do k = 1, kmax
      xyr_Trans0(:,:,k) = xyr_Trans0(:,:,k-1) * xyz_TransEachLayer(:,:,k)
    end do
    xyr_Trans1(:,:,0) = xyz_TransEachLayer(:,:,1)
    xyr_Trans1(:,:,1) = 1.0_DP
    do k = 2, kmax
      xyr_Trans1(:,:,k) = xyr_Trans0(:,:,k-1) * xyz_TransEachLayer(:,:,k)
    end do

    !   Initialization
    !
    xyr_RadLDwFlux = 0.0_DP
    xyr_RadLUwFlux = 0.0_DP
    !
    !   Downward flux
    !
    k = kmax
    xyr_RadLDwFlux(:,:,k) = 0.0_DP
    do k = kmax-1, 0, -1
      xyr_RadLDwFlux(:,:,k) = xyr_RadLDwFlux(:,:,k+1) * xyz_TransEachLayer(:,:,k+1) + xyz_IntPF(:,:,k+1) * ( 1.0_DP - xyz_TransEachLayer(:,:,k+1) )
    end do
    !
    !   Upward flux
    !
    k = 0
    xyr_RadLUwFlux(:,:,k) = xy_SurfIntPF
    do k = 1, kmax
      xyr_RadLUwFlux(:,:,k) = xyr_RadLUwFlux(:,:,k-1) * xyz_TransEachLayer(:,:,k) - xyz_IntPF(:,:,k) * ( xyz_TransEachLayer(:,:,k) - 1.0_DP )
    end do


    ! 放射フラックスの変化率の計算
    ! Calculate rate of change of radiative flux
    !
    do k = 0, kmax
      xyra_DelRadLUwFlux(:,:,k,0) = xy_SurfIntDPFDT * xyr_Trans0(:,:,k)
    end do
    k = 0
    xyra_DelRadLUwFlux(:,:,k,1) = 0.0_DP
    do k = 1, kmax
      xyra_DelRadLUwFlux(:,:,k,1) = - xy_IntDPFDT1 * ( xyr_Trans0(:,:,k) - xyr_Trans1(:,:,k) )
    end do
    do k = 0, kmax
      xyra_DelRadLDwFlux(:,:,k,0) = 0.0_DP
    end do
    k = 0
    xyra_DelRadLDwFlux(:,:,k,1) = + xy_IntDPFDT1 * ( xyr_Trans0(:,:,k) - xyr_Trans1(:,:,k) )
    do k = 1, kmax
      xyra_DelRadLDwFlux(:,:,k,1) = 0.0_DP
    end do


  end subroutine RadRTENonScatMonoWithDiffFact