subroutine PhyImplEvalRadLFluxA( xyr_RadLFlux, xyz_DTempDt, xy_DSurfTempDt, xyra_DelRadLFlux, xyr_RadLFluxA )
    !
    ! $ t-\Delta t $ における変化率を元に, 
    ! $ t+\Delta t $ の長波フラックス (xyr_RadLFluxA) を算出します. 
    ! 
    ! Evaluate longwave flux at $ t+\Delta t $ (xyr_RadLFluxA) 
    ! from the tendency at $ t-\Delta t $ . 
    !

    ! モジュール引用 ; USE statements
    !

    ! 時刻管理
    ! Time control
    !
    use timeset, only: DelTime, TimesetClockStart, TimesetClockStop

    ! 宣言文 ; Declaration statements
    !
    implicit none
    real(DP), intent(in):: xyr_RadLFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Longwave flux
    real(DP), intent(in):: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . 温度変化. 
                              ! Temperature tendency
    real(DP), intent(in):: xy_DSurfTempDt (0:imax-1, 1:jmax)
                              ! 地表面温度変化率. 
                              ! Surface temperature tendency
    real(DP), intent(in):: xyra_DelRadLFlux (0:imax-1, 1:jmax, 0:kmax,  0:1)
                              ! 長波地表温度変化. 
                              ! Surface temperature tendency with longwave
    real(DP), intent(out):: xyr_RadLFluxA (0:imax-1, 1:jmax, 0:kmax)
                              ! $ t-\Delta t $ における変化率を元に
                              ! 算出された $ t+\Delta t $ における
                              ! 長波フラックス. 
                              !
                              ! Longwave flux at $ t+\Delta t $ 
                              ! calculated from the tendency at 
                              ! $ t-\Delta t $ . 

    ! 作業変数
    ! Work variables
    !
    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. phy_implicit_utils_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! 計算時間計測開始
    ! Start measurement of computation time
    !
    call TimesetClockStart( module_name )


    ! $ t+\Delta t $ の長波フラックス (xyr_RadLFluxA) を算出
    ! Evaluate longwave flux at $ t+\Delta t $ (xyr_RadLFluxA)
    !
    do k = 0, kmax
      xyr_RadLFluxA(:,:,k) = xyr_RadLFlux(:,:,k) + (   xy_DSurfTempDt     * xyra_DelRadLFlux(:,:,k,0) + xyz_DTempDt(:,:,1) * xyra_DelRadLFlux(:,:,k,1) ) * 2. * DelTime
    end do

    ! 計算時間計測一時停止
    ! Pause measurement of computation time
    !
    call TimesetClockStop( module_name )

  end subroutine PhyImplEvalRadLFluxA

  subroutine PhyImplLUDecomp3( jna_LUMtx, JDim, NDim )
    !
    ! 3 重対角行列の LU 分解を行います. 
    !
    ! LU decomposition of triple diagonal matrix.
    !

    ! 宣言文 ; Declaration statements
    !
    implicit none
    integer, intent(in):: JDim
    integer, intent(in):: NDim
    real(DP), intent(inout):: jna_LUMtx(JDim, NDim, -1:1)
                              ! LU 行列. 
                              ! LU matrix

    ! 作業変数
    ! Work variables
    ! 
    integer:: j, n            ! DO ループ用作業変数
                              ! Work variables for DO loop

    ! 実行文 ; Executable statement
    !

    ! LU 分解
    ! LU decomposition
    !
    do j = 1, JDim
      jna_LUMtx(j,1,1) = jna_LUMtx(j,1,1) / jna_LUMtx(j,1,0)
    end do

    do n = 2, NDim-1
      do j = 1, JDim
        jna_LUMtx(j,n,0)  =   jna_LUMtx(j,n,0) - jna_LUMtx(j,n,-1) * jna_LUMtx(j,n-1,1)

        jna_LUMtx(j,n,1)  =   jna_LUMtx(j,n,1) / jna_LUMtx(j,n,0)
      end do
    end do

    do j = 1, JDim
      jna_LUMtx(j,NDim,0) =   jna_LUMtx(j,NDim, 0) - jna_LUMtx(j,NDim,-1) * jna_LUMtx(j,NDim-1,1)
    end do

  end subroutine PhyImplLUDecomp3

  subroutine PhyImplLUSolve3( ijn_Vector, jna_LUMtx, IDim, JDim, NDim )
    !
    ! LU 分解による解の計算 (3重対角行列用) を行います.
    !
    ! Solve with LU decomposition (For triple diagonal matrix). 
    !

    ! 宣言文 ; Declaration statements
    !
    implicit none
    integer, intent(in):: IDim
    integer, intent(in):: JDim
    integer, intent(in):: NDim
    real(DP), intent(in):: jna_LUMtx(JDim, NDim, -1:1)
                              ! LU 行列. 
                              ! LU matrix
    real(DP), intent(inout):: ijn_Vector(IDim, JDim, NDim)
                              ! 右辺ベクトル / 解. 
                              ! Right-hand side vector / solution

    ! 作業変数
    ! Work variables
    ! 
    integer:: i, j, n         ! DO ループ用作業変数
                              ! Work variables for DO loop

    ! 実行文 ; Executable statement
    !

    ! 前進代入
    ! Forward substitution
    !
    do i = 1, IDim
      do j = 1, JDim
        ijn_Vector(i,j,1) = ijn_Vector(i,j,1) / jna_LUMtx(j,1,0)
      end do
    end do

    do n = 2, NDim
      do i = 1, IDim
        do j = 1, JDim
          ijn_Vector(i,j,n) = (   ijn_Vector(i,j,n) - ijn_Vector(i,j,n-1) * jna_LUMtx(j,n,-1) ) / jna_LUMtx(j,n,0)
        end do
      end do
    end do

    ! 後退代入
    ! Backward substitution
    !
    do n = NDim-1, 1, -1
      do i = 1, IDim
        do j = 1, JDim
          ijn_Vector(i,j,n) =   ijn_Vector(i,j,n) - ijn_Vector(i,j,n+1) * jna_LUMtx(j,n,1)
        end do
      end do
    end do

  end subroutine PhyImplLUSolve3

  subroutine PhyImplUtilsInit
    !
    ! phy_implicit_utils モジュールの初期化を行います. 
    ! NAMELIST#phy_implicit_nml の読み込みはこの手続きで行われます. 
    !
    ! "phy_implicit_utils" module is initialized. 
    ! "NAMELIST#phy_implicit_utils_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

    ! 種別型パラメタ
    ! Kind type parameter
    !
    use dc_types, only: STDOUT ! 標準出力の装置番号. Unit number of standard output

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

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

    ! 宣言文 ; Declaration statements
    !
    implicit none

    ! 作業変数
    ! Work variables
    !
!!$    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 /phy_implicit_nml/
!!$          !
!!$          ! デフォルト値については初期化手続 "phy_implicit#PhyImplInit" 
!!$          ! のソースコードを参照のこと. 
!!$          !
!!$          ! Refer to source codes in the initialization procedure
!!$          ! "phy_implicit#PhyImplInit" for the default values. 
!!$          !

    ! 実行文 ; Executable statement
    !

    if ( phy_implicit_utils_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 = phy_implicit_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) )

    phy_implicit_utils_inited = .true.

  end subroutine PhyImplUtilsInit