subroutine SL09Diffusion( xy_SurfHeight, xyz_Height, xyz_U, xyz_V, xyzf_QMix, xyr_Press, xyr_VirTemp, xyz_DUDt, xyz_DVDt, xyz_DTempDt, xyzf_DQMixDt )
    !
    !
    !

    ! モジュール引用 ; USE statements
    !

    ! 座標データ設定
    ! Axes data settings
    !
    use axesset, only: y_Lat, z_Sigma               ! $ \sigma $ レベル (整数). 
                              ! Full $ \sigma $ level

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

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

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: GasRDry, CpDry    ! $ C_p $ [J kg-1 K-1].
                                  ! 乾燥大気の定圧比熱.
                                  ! Specific heat of air at constant pressure

    ! 鉛直拡散フラックス
    ! Vertical diffusion flux
    !
    use vdiffusion_my, only: VDiffusionExpTendency

    ! 宣言文 ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: xy_SurfHeight(0:imax-1, 1:jmax)
    real(DP), intent(in):: xyz_Height   (0:imax-1, 1:jmax, 1:kmax)
    real(DP), intent(in):: xyz_U    (0:imax-1, 1:jmax, 1:kmax)
                              ! $ u $ . 東西風速. 
                              ! Eastward wind
    real(DP), intent(in):: xyz_V    (0:imax-1, 1:jmax, 1:kmax)
                              ! $ v $ . 南北風速. 
                              ! Northward wind
    real(DP), intent(in):: xyzf_QMix(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
    real(DP), intent(in):: xyr_Press(0:imax-1, 1:jmax, 0:kmax)
                              ! $ p_s $ . 地表面気圧. 
                              ! Surface pressure
    real(DP), intent(in):: xyr_VirTemp  (0:imax-1, 1:jmax, 0:kmax)
    real(DP), intent(out):: xyz_DUDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{u}{t} $ . 東西風速変化. 
                              ! Eastward wind tendency
    real(DP), intent(out):: xyz_DVDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{v}{t} $ . 南北風速変化. 
                              ! Northward wind tendency
    real(DP), intent(out):: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . 温度変化. 
                              ! Temperature tendency
    real(DP), intent(out):: xyzf_DQMixDt (0:imax-1, 1:jmax, 1:kmax, 1:ncmax)

    ! 作業変数
    ! Work variables
    !
    real(DP) :: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 熱フラックス. 
                              ! Heat flux
    real(DP) :: xyrf_QMixFlux (0:imax-1, 1:jmax, 0:kmax, 1:ncmax)

    real(DP) :: xy_SurfQMixTransCoef(0:imax-1, 1:jmax)

!!$    integer:: j               ! 緯度方向に回る DO ループ用作業変数
!!$                              ! Work variables for DO loop in latitude
    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
    ! Initialization
    !
    if ( .not. sl09_diffusion_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 )

    ! 東西風速 $ u $ と南北風速 $ v $ へレイリー摩擦を適用
    ! Apply Rayleigh damping to eastward wind $ u $ and northward wind $ v $
    !
    xyz_DUDt = - xyz_kv * xyz_U
    xyz_DVDt = - xyz_kv * xyz_V


    ! Set heat flux at the lower boundary
    !
    xyr_HeatFlux(:,:,0     ) = LBHeatFlux
    xyr_HeatFlux(:,:,1:kmax) = 0.0_DP

    ! Set moisture flux at the lower boundary
    !
    xyrf_QMixFlux = 0.0_DP
    n = IndexH2OVap
    k = 0
    xy_SurfQMixTransCoef = SurfQMixDiffCoef * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xy_SurfHeight )
    xyrf_QMixFlux(:,:,k,n) = - xy_SurfQMixTransCoef * ( xyzf_QMix(:,:,k+1,n) - SurfQVap )



    ! 時間変化率の計算を行います.
    ! Calculate tendencies.
    !
    call VDiffusionExpTendency( xyr_Press, xyr_HeatFlux  = xyr_HeatFlux, xyrf_QMixFlux = xyrf_QMixFlux, xyz_DTempDt  = xyz_DTempDt, xyzf_DQMixDt = xyzf_DQMixDt )


    ! This is commented out (yot, 2013/05/12) to be consistent with SL09.
    ! Temporarily, xyzf_DQMixDt is overwritten.
!!$    xyzf_DQMixDt = 0.0_DP
!!$    k = 1
!!$    n = IndexH2OVap
!!$    xyzf_DQMixDt(:,:,k,n) = ( SurfQVap - xyzf_QMix(:,:,k,n) ) &
!!$      & / ( 2.0_DP * DelTime )
!!$    xyzf_DQMixDt(:,:,k,n) = ( SurfQVap - xyzf_QMix(:,:,k,n) ) &
!!$      & / ( 2.0_DP * DelTime )


    !
    ! Add heating due to MHD drag dissipation
    !
    xyz_DTempDt = xyz_DTempDt - ( xyz_DUDt * xyz_U + xyz_DVDt * xyz_V ) / CpDry


    ! ヒストリデータ出力
    ! History data output
    !
    call HistoryAutoPut( TimeN, 'DUDtVDiffSL09',    xyz_DUDt    )
    call HistoryAutoPut( TimeN, 'DVDtVDiffSL09',    xyz_DVDt    )
    call HistoryAutoPut( TimeN, 'DTempDtVDiffSL09', xyz_DTempDt )


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

  end subroutine SL09Diffusion

  subroutine SL09DiffusionInit
    !
    ! sl09_diffusion モジュールの初期化を行います. 
    ! NAMELIST#sl09_diffusion_nml の読み込みはこの手続きで行われます. 
    !
    ! "sl09_diffusion" module is initialized. 
    ! "NAMELIST#sl09_diffusion_nml" is loaded in this procedure. 
    !

    ! モジュール引用 ; USE statements
    !

    ! 物理・数学定数設定
    ! Physical and mathematical constants settings
    !
    use constants0, only: PI
                              ! $ \pi $ .
                              ! 円周率.  Circular constant

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: GasRDry, CpDry
                              ! $ C_p $ [J kg-1 K-1]. 
                              ! 乾燥大気の定圧比熱. 
                              ! Specific heat of air at constant pressure

    ! 座標データ設定
    ! Axes data settings
    !
    use axesset, only: y_Lat, z_Sigma               ! $ \sigma $ レベル (整数). 
                              ! Full $ \sigma $ level

    ! 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

    ! 鉛直拡散フラックス
    ! Vertical diffusion flux
    !
    use vdiffusion_my, only: VDiffusionInit


    ! 宣言文 ; Declaration statements
    !
    implicit none

    real(DP), parameter :: day_seconds = 86400.0_DP
                              ! 1 日の秒数. 
                              ! Seconds in day. 
    real(DP):: SigmaB         ! $ \sigma_b $ .
    real(DP):: kf             ! $ k_f $ .

    real(DP):: kfTimeScaleInDay
    real(DP):: FrictionLBLat

    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude
    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:: 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 /sl09_diffusion_nml/ SigmaB, kfTimeScaleInDay, FrictionLBLat, LBHeatFlux, SurfQMixDiffCoef, SurfQVap

          !
          ! デフォルト値については初期化手続 "sl09_diffusion#SL09DiffusionInit" 
          ! のソースコードを参照のこと. 
          !
          ! Refer to source codes in the initialization procedure
          ! "sl09_diffusion#SL09DiffusionInit" for the default values. 
          !

    ! 実行文 ; Executable statement
    !

    if ( sl09_diffusion_inited ) return

    ! デフォルト値の設定
    ! Default values settings
    !
    SigmaB           =  0.8_DP
    kfTimeScaleInDay = 20.0_DP
    FrictionLBLat    = 16.3_DP
    LBHeatFlux       =  5.7_DP
    SurfQMixDiffCoef =  0.0_DP
!!$    SurfQMixDiffCoef = 800.0d2    ! Sugiyama et al. (2009) Nagare Multimedia
    SurfQVap         =  0.0_DP
!!$    SurfQVap         = 7.816d-4   ! Sugiyama et al. (2009) Nagare Multimedia


    ! 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 = sl09_diffusion_nml, iostat = iostat_nml )               ! (out)
      close( unit_nml )

      call NmlutilMsg( iostat_nml, module_name ) ! (in)
!!$      if ( iostat_nml == 0 ) write( STDOUT, nml = held_suarez_1994_nml )
    end if

    ! 係数の設定
    ! Configure coefficients
    !
    kf     = 1.0_DP / ( kfTimeScaleInDay * day_seconds )

    allocate( xyz_kv (0:imax-1, 1:jmax, 1:kmax) )
    do k = 1, kmax
      do j = 1, jmax
        if ( abs( y_Lat(j) ) * 180.0_DP / PI <= FrictionLBLat ) then
          xyz_kv(:,j,k) = 0.0_DP
        else
          xyz_kv(:,j,k) = kf * max( 0.0_DP, ( z_Sigma(k) - SigmaB ) / ( 1.0_DP - SigmaB ) )
        end if
      end do
    end do


    ! 鉛直拡散フラックス (Mellor and Yamada, 1974, レベル 2)
    ! Vertical diffusion flux (Mellor and Yamada, 1974, Level 2)
    !
    call VDiffusionInit


    ! ヒストリデータ出力のためのへの変数登録
    ! Register of variables for history data output
    !
    call HistoryAutoAddVariable( 'DUDtVDiffSL09', (/ 'lon ', 'lat ', 'sig ', 'time' /), 'eastward wind tendency', 'm s-2' )
    call HistoryAutoAddVariable( 'DVDtVDiffSL09', (/ 'lon ', 'lat ', 'sig ', 'time' /), 'northward wind tendency', 'm s-2' )
    call HistoryAutoAddVariable( 'DTempDtVDiffSL09', (/ 'lon ', 'lat ', 'sig ', 'time' /), 'temperature tendency', 'K s-1' )

    ! 印字 ; Print
    !
    call MessageNotify( 'M', module_name, '----- Initialization Messages -----' )
    call MessageNotify( 'M', module_name, 'SigmaB           = %f', d = (/ SigmaB /) )
    call MessageNotify( 'M', module_name, 'kfTimeScaleInDay = %f', d = (/ kfTimeScaleInDay /) )
    call MessageNotify( 'M', module_name, 'FrictionLBLat    = %f', d = (/ FrictionLBLat /) )
    call MessageNotify( 'M', module_name, 'LBHeatFlux       = %f', d = (/ LBHeatFlux /) )
    call MessageNotify( 'M', module_name, 'SurfQMixDiffCoef = %f', d = (/ SurfQMixDiffCoef /) )
    call MessageNotify( 'M', module_name, 'SurfQVap         = %f', d = (/ SurfQVap /) )
    call MessageNotify( 'M', module_name, '-- version = %c', c1 = trim(version) )

    sl09_diffusion_inited = .true.
  end subroutine SL09DiffusionInit