subroutine AuxVars( xy_Ps,      xyz_Temp, xyr_Temp, xyz_Press,  xyr_Press, xyz_Height, xyr_Height )
    !
    ! 温度の半整数σレベルの補間, 気圧と高度の算出を行います. 
    !
    ! Interpolate temperature on half sigma level, 
    ! and calculate pressure and height. 
    !

    ! モジュール引用 ; USE statements
    !

    ! 座標データ設定
    ! Axes data settings
    !
    use axesset, only: z_Sigma, r_Sigma, z_DelSigma, r_DelSigma
                              ! $ \Delta \sigma $ (半整数). 
                              ! $ \Delta \sigma $ (Half)

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: Grav, GasRDry               ! $ R $ [J kg-1 K-1]. 
                              ! 乾燥大気の気体定数. 
                              ! Gas constant of air

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

    ! 宣言文 ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: xy_Ps       (0:imax-1, 1:jmax)
                              ! $ p_s (t-\Delta t) $ . 地表面気圧. Surface pressure
    real(DP), intent(in):: xyz_Temp    (0:imax-1, 1:jmax, 1:kmax)
                              ! $ T $ .     温度. Temperature
    real(DP), intent(out):: xyr_Temp   (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T} $ . 温度 (半整数レベル). 
                              ! Temperature (half level)
    real(DP), intent(out):: xyz_Press  (0:imax-1, 1:jmax, 1:kmax)
                              ! $ p $ . 気圧 (整数レベル). 
                              ! Air pressure (full level)
    real(DP), intent(out):: xyr_Press  (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . 気圧 (半整数レベル). 
                              ! Air pressure (half level)
    real(DP), intent(out):: xyz_Height (0:imax-1, 1:jmax, 1:kmax)
                              ! 高度 (整数レベル). 
                              ! Height (full level)
    real(DP), intent(out):: xyr_Height (0:imax-1, 1:jmax, 0:kmax)
                              ! 高度 (半整数レベル). 
                              ! Height (half level)


    ! 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
    !

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

    ! 初期化
    ! Initialization
    !
    if ( .not. auxiliary_inited ) call AuxInit

    ! 温度の補間
    ! Interpolate temperature
    !
    do k = 2, kmax
      xyr_Temp(:,:,k-1) =   z_TempInpolM(k) * xyz_Temp(:,:,k-1) + z_TempInpol (k) * xyz_Temp(:,:,k)
    end do

    xyr_Temp(:,:,kmax) = xyz_Temp(:,:,kmax)
    xyr_Temp(:,:,0)    = xyz_Temp(:,:,1)

    ! 気圧の計算
    ! Calculate pressure
    !
    do k = 1, kmax
      xyz_Press(:,:,k) = xy_Ps * z_Sigma(k)
    end do

    do k = 0, kmax
      xyr_Press(:,:,k) = xy_Ps * r_Sigma(k)
    end do

    ! 高度の計算
    ! Calculate height
    !
    xyz_Height(:,:,1) = GasRDry / Grav * xyz_Temp(:,:,1) * ( 1.0_DP - z_Sigma(1) )

    do k = 2, kmax
      xyz_Height(:,:,k) = xyz_Height(:,:,k-1) + GasRDry / Grav * xyr_Temp(:,:,k-1) * r_DelSigma(k-1) / r_Sigma(k-1)
    end do

    xyr_Height = 0.0_DP
    do k = 1, kmax
      xyr_Height(:,:,k) = xyr_Height(:,:,k-1) + GasRDry / Grav * xyz_Temp(:,:,k) * z_DelSigma(k) / z_Sigma(k)
    end do


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

  end subroutine AuxVars

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

    ! モジュール引用 ; USE statements
    !

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

    ! 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

    ! 宣言文 ; Declaration statements
    !
    implicit none

!!$    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

    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

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

    ! 実行文 ; Executable statement
    !

    if ( auxiliary_inited ) return
    call InitCheck

    ! 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 = auxiliary_nml, &  ! (out)
!!$        & iostat = iostat_nml )   ! (out)
!!$      close( unit_nml )
!!$
!!$      call NmlutilMsg( iostat_nml, module_name ) ! (in)
!!$    end if

    !  補間用の係数の計算
    !  Calculate coefficient for interpolation
    !
    allocate( z_TempInpolM(1:kmax) )
    allocate( z_TempInpol(1:kmax) )

    z_TempInpolM = 0.0_DP
    z_TempInpol = 0.0_DP

    do k = 2, kmax
      z_TempInpolM(k) = ( log( r_Sigma( k-1 ) ) - log( z_Sigma( k ) ) ) / ( log( z_Sigma( k-1 ) ) - log( z_Sigma( k ) ) )
      z_TempInpol(k) = ( log( z_Sigma( k-1 ) ) - log( r_Sigma( k-1 ) ) ) / ( log( z_Sigma( k-1 ) ) - log( z_Sigma( k )   ) )
    end  do

    ! 印字 ; Print
    !
    call MessageNotify( 'M', module_name, '----- Initialization Messages -----' )
    call MessageNotify( 'M', module_name, '  z_TempInpolM = %*r', r = real( z_TempInpolM ), n = (/ kmax /) )
    call MessageNotify( 'M', module_name, '  z_TempInpol  = %*r', r = real( z_TempInpol  ), n = (/ kmax /) )
    call MessageNotify( 'M', module_name, '-- version = %c', c1 = trim(version) )

    auxiliary_inited = .true.
  end subroutine AuxInit

  subroutine InitCheck
    !
    ! 依存モジュールの初期化チェック
    !
    ! Check initialization of dependency modules

    ! 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_util_inited

    ! 格子点設定
    ! Grid points settings
    !
    use gridset, only: gridset_inited

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: constants_inited

    ! 座標データ設定
    ! Axes data settings
    !
    use axesset, only: axesset_inited

    ! 実行文 ; Executable statement
    !

    if ( .not. namelist_util_inited ) call MessageNotify( 'E', module_name, '"namelist_util" module is not initialized.' )

    if ( .not. gridset_inited ) call MessageNotify( 'E', module_name, '"gridset" module is not initialized.' )

    if ( .not. constants_inited ) call MessageNotify( 'E', module_name, '"constants" module is not initialized.' )

    if ( .not. axesset_inited ) call MessageNotify( 'E', module_name, '"axesset" module is not initialized.' )

  end subroutine InitCheck