subroutine CloudUtilsCalcOverlapCloudTrans( xyz_TransCloudOneLayer, xyz_CloudCover, xyrr_OverlappedCloudTrans )

    ! USE statements
    !

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

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

!!$    use sort, only : SortQuick

    real(DP), intent(in ) :: xyz_TransCloudOneLayer   (0:imax-1, 1:jmax, 1:kmax)
    real(DP), intent(in ) :: xyz_CloudCover           (0:imax-1, 1:jmax, 1:kmax)
    real(DP), intent(out) :: xyrr_OverlappedCloudTrans(0:imax-1, 1:jmax, 0:kmax, 0:kmax)


    real(DP) :: xyz_EffCloudCover           (0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_CloudCoverSorted        (0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_EffCloudCoverSorted     (0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_TransCloudOneLayerSorted(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: CloudCoverSortedCur
    real(DP) :: EffCloudCoverSortedCur
    real(DP) :: TransCloudOneLayerSortedCur
    integer  :: KInsPos
    integer  :: i
    integer  :: j
    integer  :: k
    integer  :: kk
    integer  :: kkk



    ! 実行文 ; Executable statement
    !

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


    ! Cloud optical depth
    !

    select case ( IDCloudOverlapType )
    case ( IDCloudOverlapTypeRandom )

      xyz_EffCloudCover = xyz_CloudCover * ( 1.0_DP - xyz_TransCloudOneLayer )

      do k = 0, kmax
        kk = k
        xyrr_OverlappedCloudTrans(:,:,k,kk) = 1.0_DP
        do kk = k+1, kmax
          xyrr_OverlappedCloudTrans(:,:,k,kk) = xyrr_OverlappedCloudTrans(:,:,k,kk-1) * ( 1.0_DP - xyz_EffCloudCover(:,:,kk) )
        end do
      end do

      do k = 0, kmax
        do kk = 0, k-1
          xyrr_OverlappedCloudTrans(:,:,k,kk) = xyrr_OverlappedCloudTrans(:,:,kk,k)
        end do
      end do

    case ( IDCloudOverlapTypeMaxOverlap )

      ! see Chou et al. (2001)

      xyz_EffCloudCover = xyz_CloudCover * ( 1.0_DP - xyz_TransCloudOneLayer )


      ! Original method (computationally expensive, probably)
      !
!!$        do k = 0, kmax
!!$          kk = k
!!$          xyrr_OverlappedCloudTrans(:,:,k,kk) = 1.0_DP
!!$          do kk = k+1, kmax
!!$
!!$            xyz_CloudCoverSorted         = xyz_CloudCover
!!$            xyz_EffCloudCoverSorted      = xyz_EffCloudCover
!!$            xyz_TransCloudOneLayerSorted = xyz_TransCloudOneLayer
!!$
!!$            call SortQuick( imax, jmax, kk-k,             &
!!$              & xyz_CloudCoverSorted        (:,:,k+1:kk), &
!!$              & xyz_EffCloudCoverSorted     (:,:,k+1:kk), &
!!$              & xyz_TransCloudOneLayerSorted(:,:,k+1:kk)  &
!!$              & )
!!$
!!$            xyrr_OverlappedCloudTrans(:,:,k,kk) = 0.0_DP
!!$            do kkk = k+1, kk
!!$              xyrr_OverlappedCloudTrans(:,:,k,kk) =         &
!!$                & xyz_EffCloudCoverSorted(:,:,kkk)          &
!!$                & + xyrr_OverlappedCloudTrans(:,:,k,kk)     &
!!$                &   * xyz_TransCloudOneLayerSorted(:,:,kkk)
!!$            end do
!!$            xyrr_OverlappedCloudTrans(:,:,k,kk) = &
!!$              & 1.0_DP - xyrr_OverlappedCloudTrans(:,:,k,kk)
!!$
!!$          end do
!!$        end do


      ! Economical method (probably)
      !
      do k = 0, kmax

!!$          do kkk = 1, kmax
!!$              xyz_CloudCoverSorted(:,:,kkk) = real( kmax-kkk ) / real(kmax)
!!$!              xyz_CloudCoverSorted(:,:,kkk) = abs( 0.55d0 - real( kmax-kkk ) / real(kmax) )
!!$          end do
!!$          ! debug output
!!$          if ( k == 0 ) then
!!$            kk = kmax
!!$            do kkk = k+1, kk
!!$              write( 6, * ) kkk, xyz_CloudCoverSorted(0,jmax/2+1,kkk)
!!$            end do
!!$          end if

        xyz_CloudCoverSorted         = xyz_CloudCover
        xyz_EffCloudCoverSorted      = xyz_EffCloudCover
        xyz_TransCloudOneLayerSorted = xyz_TransCloudOneLayer

        kk = k
        xyrr_OverlappedCloudTrans(:,:,k,kk) = 1.0_DP
        do kk = k+1, kmax


          do j = 1, jmax
            do i = 0, imax-1

              ! xyz_CloudCoverSorted(i,j,kk) is inserved in an appropriate position.
              !
              KInsPos = kk
              loop : do kkk = k+1, kk-1

                if ( xyz_CloudCoverSorted(i,j,kk) < xyz_CloudCoverSorted(i,j,kkk) ) then
                  KInsPos = kkk
                  exit loop
                end if

              end do loop

              ! values are saved
              CloudCoverSortedCur         = xyz_CloudCoverSorted        (i,j,kk)
              EffCloudCoverSortedCur      = xyz_EffCloudCoverSorted     (i,j,kk)
              TransCloudOneLayerSortedCur = xyz_TransCloudOneLayerSorted(i,j,kk)

              ! values are shifted upward to empty an array at insert position
              do kkk = kk, KInsPos+1, -1
                xyz_CloudCoverSorted        (i,j,kkk) = xyz_CloudCoverSorted        (i,j,kkk-1)
                xyz_EffCloudCoverSorted     (i,j,kkk) = xyz_EffCloudCoverSorted     (i,j,kkk-1)
                xyz_TransCloudOneLayerSorted(i,j,kkk) = xyz_TransCloudOneLayerSorted(i,j,kkk-1)
              end do
              kkk = KInsPos
              xyz_CloudCoverSorted        (i,j,kkk) = CloudCoverSortedCur
              xyz_EffCloudCoverSorted     (i,j,kkk) = EffCloudCoverSortedCur
              xyz_TransCloudOneLayerSorted(i,j,kkk) = TransCloudOneLayerSortedCur

            end do
          end do


!!$            xyz_CloudCoverSorted         = xyz_CloudCover
!!$            do kkk = 1, kmax
!!$              xyz_CloudCoverSorted(:,:,kkk) = real( kmax-kkk ) / real(kmax)
!!$            end do
!!$            xyz_EffCloudCoverSorted      = xyz_EffCloudCover
!!$            xyz_TransCloudOneLayerSorted = xyz_TransCloudOneLayer
!!$
!!$            call SortQuick( imax, jmax, kk-k,             &
!!$              & xyz_CloudCoverSorted        (:,:,k+1:kk), &
!!$              & xyz_EffCloudCoverSorted     (:,:,k+1:kk), &
!!$              & xyz_TransCloudOneLayerSorted(:,:,k+1:kk)  &
!!$              & )


!!$            ! debug output
!!$            if ( ( k == 0 ) .and. ( kk == kmax-2 ) ) then
!!$              do kkk = k+1, kk
!!$                write( 6, * ) kkk, xyz_CloudCoverSorted(0,jmax/2+1,kkk)
!!$              end do
!!$              write( 6, * ) '-----'
!!$            end if


          xyrr_OverlappedCloudTrans(:,:,k,kk) = 0.0_DP
          do kkk = k+1, kk
            xyrr_OverlappedCloudTrans(:,:,k,kk) = xyz_EffCloudCoverSorted(:,:,kkk) + xyrr_OverlappedCloudTrans(:,:,k,kk) * xyz_TransCloudOneLayerSorted(:,:,kkk)
          end do
          xyrr_OverlappedCloudTrans(:,:,k,kk) = 1.0_DP - xyrr_OverlappedCloudTrans(:,:,k,kk)

        end do
      end do



      do k = 0, kmax
        do kk = 0, k-1
          xyrr_OverlappedCloudTrans(:,:,k,kk) = xyrr_OverlappedCloudTrans(:,:,kk,k)
        end do
      end do


    end select

    ! Output effective cloud cover
    !
!!$    call HistoryAutoPut( TimeN, 'EffCloudCover', &
!!$      & 1.0_DP - xyrr_OverlappedCloudTrans(:,:,0,kmax) )


  end subroutine CloudUtilsCalcOverlapCloudTrans

  subroutine CloudUtilsCalcPRCPKeyLLTemp( xyz_Temp, xy_PRCP, xy_SurfRainFlux, xy_SurfSnowFlux )


    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: TempCondWater


    real(DP), intent(in ) :: xyz_Temp       ( 0:imax-1, 1:jmax, 1:kmax )
    real(DP), intent(in ) :: xy_PRCP        ( 0:imax-1, 1:jmax )
    real(DP), intent(out) :: xy_SurfRainFlux( 0:imax-1, 1:jmax )
    real(DP), intent(out) :: xy_SurfSnowFlux( 0:imax-1, 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 longitude
    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


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


    if ( FlagSnow ) then

      do j = 1, jmax
        do i = 0, imax-1
          if ( xyz_Temp(i,j,1) > TempCondWater ) then
            xy_SurfRainFlux(i,j) = xy_PRCP(i,j)
            xy_SurfSnowFlux(i,j) = 0.0_DP
          else
            xy_SurfRainFlux(i,j) = 0.0_DP
            xy_SurfSnowFlux(i,j) = xy_PRCP(i,j)
          end if
        end do
      end do

    else

      xy_SurfRainFlux = xy_PRCP
      xy_SurfSnowFlux = 0.0_DP

    end if


  end subroutine CloudUtilsCalcPRCPKeyLLTemp

  subroutine CloudUtilsCalcPRCPKeyLLTemp3D( xyr_Press, xyz_Temp, xyz_DQH2OLiqDt, xy_SurfRainFlux, xy_SurfSnowFlux )

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: Grav
                              ! $ g $ [m s-2].
                              ! 重力加速度.
                              ! Gravitational acceleration

    real(DP), intent(in ) :: xyr_Press       ( 0:imax-1, 1:jmax, 0:kmax )
    real(DP), intent(in ) :: xyz_Temp        ( 0:imax-1, 1:jmax, 1:kmax )
    real(DP), intent(in ) :: xyz_DQH2OLiqDt  ( 0:imax-1, 1:jmax, 1:kmax )
    real(DP), intent(out) :: xy_SurfRainFlux ( 0:imax-1, 1:jmax )
    real(DP), intent(out) :: xy_SurfSnowFlux ( 0:imax-1, 1:jmax )


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

    integer  :: k


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



    xy_PRCP = 0.0d0
    do k = kmax, 1, -1
      xy_PRCP = xy_PRCP + xyz_DQH2OLiqDt(:,:,k) * ( xyr_Press(:,:,k-1) - xyr_Press(:,:,k) ) / Grav
    end do


    call CloudUtilsCalcPRCPKeyLLTemp( xyz_Temp, xy_PRCP, xy_SurfRainFlux, xy_SurfSnowFlux )


  end subroutine CloudUtilsCalcPRCPKeyLLTemp3D

  subroutine CloudUtilsInit( ArgFlagSnow )

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

    ! 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

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


    ! 宣言文 ; Declaration statements
    !

    logical, intent(in) :: ArgFlagSnow


    character(STRING) :: CloudWatIceFracType
    character(STRING) :: CloudOverlapType

    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 /cloud_utils_nml/ CloudWatIceFracType, CloudOverlapType, TempWatLim, TempIceLim
          !
          ! デフォルト値については初期化手続 "cloud_utils#CloudUtilsInit"
          ! のソースコードを参照のこと.
          !
          ! Refer to source codes in the initialization procedure
          ! "cloud_utils#CloudUtilsInit" for the default values.
          !

    ! 実行文 ; Executable statement
    !

    if ( cloud_utils_inited ) return


    FlagSnow = ArgFlagSnow


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

    CloudWatIceFracType = "Lin"
    CloudOverlapType    = "Random"
!!$    CloudOverlapType    = "MaxOverlap"

!!$    TempWatLim          = 273.15_DP
!!$    TempIceLim          = 273.15_DP - 40.0_DP
    TempWatLim          = 0.0_DP
    TempIceLim          = 0.0_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 = cloud_utils_nml, iostat = iostat_nml )             ! (out)
      close( unit_nml )

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


    select case ( CloudOverlapType )
    case ( 'Random' )
      IDCloudOverlapType = IDCloudOverlapTypeRandom
    case ( 'MaxOverlap' )
      IDCloudOverlapType = IDCloudOverlapTypeMaxOverlap
    case default
      call MessageNotify( 'E', module_name, 'CloudOverlapType=<%c> is not supported.', c1 = trim(CloudOverlapType) )
    end select


    select case ( CloudWatIceFracType )
    case ( 'WatOnly' )
      IDCloudWatIceFracType = IDCloudWatIceFracTypeWatOnly
    case ( 'IceOnly' )
      IDCloudWatIceFracType = IDCloudWatIceFracTypeIceOnly
    case ( 'Lin' )
      IDCloudWatIceFracType = IDCloudWatIceFracTypeLin
      if ( TempWatLim < TempIceLim ) then
        call MessageNotify( 'E', module_name, 'TempWatLim must be greater than or equal to TempIceLim.' )
      end if
    case default
      call MessageNotify( 'E', module_name, 'CloudWatIceFracType=<%c> is not supported.', c1 = trim(CloudWatIceFracType) )
    end select


    ! Initialization of modules used in this module
    !


    ! 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( 'EffCloudCover', &
!!$      & (/ 'lon ', 'lat ', 'time' /), &
!!$      & 'effective cloud cover', '1' )



    ! 印字 ; Print
    !
    call MessageNotify( 'M', module_name, '----- Initialization Messages -----' )
    call MessageNotify( 'M', module_name, 'CloudOverlapType    = %c', c1 = trim(CloudOverlapType) )
    call MessageNotify( 'M', module_name, 'CloudWatIceFracType = %c', c1 = trim(CloudWatIceFracType) )
    call MessageNotify( 'M', module_name, 'TempWatLim          = %f', d = (/ TempWatLim /) )
    call MessageNotify( 'M', module_name, 'TempIceLim          = %f', d = (/ TempIceLim /) )
    call MessageNotify( 'M', module_name, '-- version = %c', c1 = trim(version) )


    cloud_utils_inited = .true.

  end subroutine CloudUtilsInit

  subroutine CloudUtilsLocalizeCloud( xyz_CloudCover, xyz_DelCloudOptDep )

    ! USE statements
    !

    real(DP), intent(in   ) :: xyz_CloudCover    (0:imax-1, 1:jmax, 1:kmax)
    real(DP), intent(inout) :: xyz_DelCloudOptDep(0:imax-1, 1:jmax, 1:kmax)


    ! 実行文 ; Executable statement
    !

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


    ! Cloud optical depth is scaled by considering cloud cover less than 1. 

    xyz_DelCloudOptDep = xyz_DelCloudOptDep / max( xyz_CloudCover, 1.0d-3 )


  end subroutine CloudUtilsLocalizeCloud

  subroutine CloudUtilsSmearCloudOptDep( xyz_CloudCover, xyz_DelCloudOptDep )

    ! USE statements
    !

    real(DP), intent(in   ) :: xyz_CloudCover    (0:imax-1, 1:jmax, 1:kmax)
    real(DP), intent(inout) :: xyz_DelCloudOptDep(0:imax-1, 1:jmax, 1:kmax)


    ! 実行文 ; Executable statement
    !

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


    ! Cloud optical depth is scaled by the way of Kiehl et al. (1994).

    xyz_DelCloudOptDep = xyz_DelCloudOptDep * xyz_CloudCover**1.5_DP


  end subroutine CloudUtilsSmearCloudOptDep

  subroutine CloudUtilsWatFraction0D( Temp, WatFrac )

    ! USE statements
    !

    real(DP), intent(in ) :: Temp
    real(DP), intent(out) :: WatFrac


    real(DP) :: xyz_Temp   (1,1,1)
    real(DP) :: xyz_WatFrac(1,1,1)

    ! 実行文 ; Executable statement
    !

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


    xyz_Temp = Temp
    call CloudUtilsWatFraction3D( xyz_Temp, xyz_WatFrac )
    WatFrac = xyz_WatFrac(1,1,1)


  end subroutine CloudUtilsWatFraction0D

  subroutine CloudUtilsWatFraction3D( xyz_Temp, xyz_WatFrac )

    ! USE statements
    !

!!$    real(DP), intent(in ) :: xyz_Temp   (0:imax-1, 1:jmax, 1:kmax)
!!$    real(DP), intent(out) :: xyz_WatFrac(0:imax-1, 1:jmax, 1:kmax)
    real(DP), intent(in ) :: xyz_Temp   (:,:,:)
    real(DP), intent(out) :: xyz_WatFrac(:,:,:)


    ! 実行文 ; Executable statement
    !

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


    if ( FlagSnow ) then

      select case ( IDCloudWatIceFracType )
      case ( IDCloudWatIceFracTypeWatOnly  )
        xyz_WatFrac = 1.0_DP
      case ( IDCloudWatIceFracTypeIceOnly  )
        xyz_WatFrac = 0.0_DP
      case ( IDCloudWatIceFracTypeLin      )
        if ( TempWatLim == TempIceLim ) then
          xyz_WatFrac = ( sign( 1.0_DP, xyz_Temp - TempWatLim ) + 1.0d0 ) / 2.0_DP
        else
          xyz_WatFrac = ( 1.0_DP - 0.0_DP ) / ( TempWatLim - TempIceLim ) * ( xyz_Temp - TempIceLim )
          xyz_WatFrac = min( xyz_WatFrac, 1.0_DP )
          xyz_WatFrac = max( xyz_WatFrac, 0.0_DP )
        end if
      end select

    else

      xyz_WatFrac = 1.0_DP

    end if


  end subroutine CloudUtilsWatFraction3D