Class saturate_nha1992
In: saturate/saturate_nha1992.f90

Nakajima et al. (1992) を用いた飽和比湿の算出

Evaluate saturation specific humidity with Nakajima et al. (1992)

Note that Japanese and English are described in parallel.

Nakajima et al. (1992) で用いられた飽和蒸気圧 $ p^{*} $ に関する以下の式 を用い, 飽和比湿および飽和比湿の温度微分の値を算出します.

Saturation specific humidity and temperature derivative of it are calculated with a folloing formula for saturation watar vapor pressure $ p^{*} $ in Nakajima et al. (1992).

\[ 

   p^{*} (T) = p_0^{*} \exp \left( - \frac{l}{RT} \right).

\]

ここで, $ T $ は温度, $ R $ は普遍気体定数です. $ R $ および潜熱 $ l $ , 水蒸気飽和曲線の定数 $ p_0^{*} $ は以下のように与えられます.

where $ T $ is temperature, $ R $ is the gas constant. $ R $ and latent heat $ l $ , constant for the water vapor saturation curve $ p_0^{*} $ are as follows.

  • $ R = 8.314 $ [J mol-1 K-1]
  • $ l = 43655 $ [J mol-1]
  • $ p_0^{*} = 1.4 times 10^{11} $ [Pa]

飽和水蒸気圧から飽和比湿 $ q^{*} $ を求める際には, 以下の式を用います.

Saturation specific humidity $ q^{*} $ is calculated from saturation watar vapor pressure as follows.

\[ 

   q^{*} (T, p) = \varepsilon \frac{p^{*} (T)}{p}

\]

ここで $ varepsilon $ は凝結成分と大気の分子量比, $ p $ は気圧です.

where $ varepsilon $ is molecular weight ratio of water vapor to air, $ p $ is air pressure.

従って, 飽和比湿, 飽和比湿の温度変化を求める式は以下のように なります.

Therefore, saturation specific humidity and temperature derivative of it are calculated as follows.

\[ 

   q^{*} (T, p) = \varepsilon \frac{p_0^{*}}{p} \exp \left( - \frac{l}{RT} \right), \] \[
   \DP{q^{*} (T, p)}{T} = \varepsilon \frac{p_0^{*}}{p} \frac{l}{RT^2} \exp \left( - \frac{l}{RT} \right)
   = q^{*} \frac{l}{RT^2}

\]

References

  • Nakajima, S., Hayashi, Y.-Y., Abe, Y., 1992: A study on the "runaway greenhouse effect" with a one dimensional radiative convective equilibrium model. J. Atmos. Sci., 49, 2256--2266.

Procedures List

CalcQVapSat :飽和比湿の計算
CalcDQVapSatDTemp :飽和比湿の温度微分の計算
———— :————
CalcQVapSat :Calculate saturation specific humidity
CalcDQVapSatDTemp :Calculate temperature derivative of saturation specific humidity

Methods

LatHeat   P0   SaturateInit   module_name   saturate_nha1992_inited   version   xy_CalcDQVapSatDTemp   xy_CalcQVapSat   xyz_CalcDQVapSatDTemp   xyz_CalcQVapSat  

Included Modules

dc_types dc_message constants0 constants namelist_util dc_iounit dc_string gtool_historyauto

Public Instance methods

SaturateInit( )
Subroutine :

saturate_nha1992 モジュールの初期化を行います.

"saturate_nha1992" module is initialized.

[Source]

  subroutine SaturateInit
    !
    ! saturate_nha1992 モジュールの初期化を行います. 
    !
    !
    ! "saturate_nha1992" module is initialized. 
    !

    ! 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

    ! 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

!!$    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 /saturate_nha1992_nml/ 
          !
          ! デフォルト値については初期化手続 "saturate_nha1992#SaturateInit" 
          ! のソースコードを参照のこと. 
          !
          ! Refer to source codes in the initialization procedure
          ! "saturate_nha1992#SaturateInit" for the default values. 
          !

    ! 実行文 ; Executable statement
    !

    if ( saturate_nha1992_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 = saturate_nha1992_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) )

    saturate_nha1992_inited = .true.

  end subroutine SaturateInit
saturate_nha1992_inited
Variable :
saturate_nha1992_inited = .false. :logical, save, public
: 初期設定フラグ. Initialization flag
xy_CalcDQVapSatDTemp( xy_Temp, xy_QVapSat ) result(xy_DQVapSatDTemp)
Function :
xy_DQVapSatDTemp(size(xy_Temp,1), size(xy_Temp,2)) :real(DP)
: $ DP{q^{*}}{T} $ . 飽和比湿の温度微分. Temperature derivative of saturation specific humidity.
xy_Temp(:,:) :real(DP), intent(in)
: $ T $ . 温度. Temperature
xy_QVapSat(:,:) :real(DP), intent(in)
: $ q^{*} $ . 飽和比湿. Saturation specific humidity

温度 Temp と飽和比湿 QVapSat を用い, 飽和比湿の温度微分 DQVapSatDTemp を求めます.

Calculate temperature derivative of saturation specific humidity DQVapSatDTemp using temperature Temp and saturation specific humidity QVapSat.

[Source]

  function xy_CalcDQVapSatDTemp( xy_Temp, xy_QVapSat ) result( xy_DQVapSatDTemp )
    !
    ! 温度 *Temp* と飽和比湿 *QVapSat* を用い, 
    ! 飽和比湿の温度微分 *DQVapSatDTemp* を求めます. 
    !
    ! Calculate temperature derivative of saturation specific humidity 
    ! *DQVapSatDTemp* using
    ! temperature *Temp* and saturation specific humidity *QVapSat*. 
    !

    ! モジュール引用 ; USE statements
    !

    ! 宣言文 ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: xy_Temp   (:,:)
                              ! $ T $ . 温度. Temperature
    real(DP), intent(in):: xy_QVapSat(:,:)
                              ! $ q^{*} $ . 飽和比湿. Saturation specific humidity
    real(DP):: xy_DQVapSatDTemp(size(xy_Temp,1), size(xy_Temp,2))
                              ! $ \DP{q^{*}}{T} $ . 飽和比湿の温度微分. 
                              ! Temperature derivative of saturation specific humidity. 

    ! 作業変数
    ! Work variables
    !
    real(DP):: xyz_Temp         (size(xy_Temp,1), size(xy_Temp,2), 1:1)
                              ! $ T $ . 温度. Temperature
    real(DP):: xyz_QVapSat      (size(xy_Temp,1), size(xy_Temp,2), 1:1)
                              ! $ q^{*} $ . 飽和比湿. Saturation specific humidity
    real(DP):: xyz_DQVapSatDTemp(size(xy_Temp,1), size(xy_Temp,2), 1:1)
                              ! $ \DP{q^{*}}{T} $ . 飽和比湿の温度微分. 
                              ! Temperature derivative of saturation specific humidity. 

    if ( .not. saturate_nha1992_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if

    xyz_Temp   (:,:,1) = xy_Temp
    xyz_QVapSat(:,:,1) = xy_QVapSat

    xyz_DQVapSatDTemp = xyz_CalcDQVapSatDTemp( xyz_Temp, xyz_QVapSat )

    xy_DQVapSatDTemp = xyz_DQVapSatDTemp(:,:,1)


  end function xy_CalcDQVapSatDTemp
xy_CalcQVapSat( xy_Temp, xy_Press ) result(xy_QVapSat)
Function :
xy_QVapSat(size(xy_Temp,1), size(xy_Temp,2)) :real(DP)
: $ q^{*} $ . 飽和比湿. Saturation specific humidity
xy_Temp(:,:) :real(DP), intent(in)
: $ T $ . 温度. Temperature
xy_Press(:,:) :real(DP), intent(in)
: $ p $ . 気圧. Air pressure

温度 Temp と気圧 Press を用い, 飽和比湿 QVapSat を求めます.

Calculate saturation specific humidity QVapSat using temperature Temp and air pressure Press.

[Source]

  function xy_CalcQVapSat( xy_Temp, xy_Press ) result( xy_QVapSat )
    !
    ! 温度 *Temp* と気圧 *Press* を用い, 
    ! 飽和比湿 *QVapSat* を求めます. 
    !
    ! Calculate saturation specific humidity *QVapSat* using
    ! temperature *Temp* and air pressure *Press*. 
    !

    ! モジュール引用 ; USE statements
    !

    ! 宣言文 ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: xy_Temp (:,:)
                              ! $ T $ . 温度. Temperature
    real(DP), intent(in):: xy_Press(:,:)
                              ! $ p $ . 気圧. Air pressure
    real(DP):: xy_QVapSat(size(xy_Temp,1), size(xy_Temp,2))
                              ! $ q^{*} $ . 飽和比湿. Saturation specific humidity

    ! 作業変数
    ! Work variables
    !
    real(DP):: xyz_Temp   (size(xy_Temp,1), size(xy_Temp,2), 1:1)
                              ! $ T $ . 温度. Temperature
    real(DP):: xyz_Press  (size(xy_Temp,1), size(xy_Temp,2), 1:1)
                              ! $ p $ . 気圧. Air pressure
    real(DP):: xyz_QVapSat(size(xy_Temp,1), size(xy_Temp,2), 1:1)
                              ! $ q^{*} $ . 飽和比湿. Saturation specific humidity

    ! 実行文 ; Executable statement
    !

    if ( .not. saturate_nha1992_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if

    ! 飽和比湿の計算
    ! Calculate saturation specific humidity
    !
    xyz_Temp (:,:,1) = xy_Temp
    xyz_Press(:,:,1) = xy_Press

    xyz_QVapSat = xyz_CalcQVapSat( xyz_Temp, xyz_Press )

    xy_QVapSat = xyz_QVapSat(:,:,1)


  end function xy_CalcQVapSat
xyz_CalcDQVapSatDTemp( xyz_Temp, xyz_QVapSat ) result(xyz_DQVapSatDTemp)
Function :
xyz_DQVapSatDTemp(size(xyz_Temp,1), size(xyz_Temp,2), size(xyz_Temp,3)) :real(DP)
: $ DP{q^{*}}{T} $ . 飽和比湿の温度微分. Temperature derivative of saturation specific humidity.
xyz_Temp(:,:,:) :real(DP), intent(in)
: $ T $ . 温度. Temperature
xyz_QVapSat(:,:,:) :real(DP), intent(in)
: $ q^{*} $ . 飽和比湿. Saturation specific humidity

温度 Temp と飽和比湿 QVapSat を用い, 飽和比湿の温度微分 DQVapSatDTemp を求めます.

Calculate temperature derivative of saturation specific humidity DQVapSatDTemp using temperature Temp and saturation specific humidity QVapSat.

[Source]

  function xyz_CalcDQVapSatDTemp( xyz_Temp, xyz_QVapSat ) result( xyz_DQVapSatDTemp )
    !
    ! 温度 *Temp* と飽和比湿 *QVapSat* を用い, 
    ! 飽和比湿の温度微分 *DQVapSatDTemp* を求めます. 
    !
    ! Calculate temperature derivative of saturation specific humidity 
    ! *DQVapSatDTemp* using
    ! temperature *Temp* and saturation specific humidity *QVapSat*. 
    !

    ! 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: GasRUniv              ! $ R^{*} $ [J K-1 mol-1].
                              ! 普遍気体定数.  Universal gas constant

    ! 宣言文 ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: xyz_Temp   (:,:,:)
                              ! $ T $ . 温度. Temperature
    real(DP), intent(in):: xyz_QVapSat(:,:,:)
                              ! $ q^{*} $ . 飽和比湿. Saturation specific humidity
    real(DP):: xyz_DQVapSatDTemp(size(xyz_Temp,1), size(xyz_Temp,2), size(xyz_Temp,3))
                              ! $ \DP{q^{*}}{T} $ . 飽和比湿の温度微分. 
                              ! Temperature derivative of saturation specific humidity. 

    ! 作業変数
    ! Work variables
    !

    ! 実行文 ; Executable statement
    !

    if ( .not. saturate_nha1992_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if

    ! 飽和比湿の温度微分の計算
    ! Calculate temperature derivative of saturation specific humidity
    !
    xyz_DQVapSatDTemp = xyz_QVapSat * LatHeat / ( GasRUniv * xyz_Temp**2 )


  end function xyz_CalcDQVapSatDTemp
xyz_CalcQVapSat( xyz_Temp, xyz_Press ) result(xyz_QVapSat)
Function :
xyz_QVapSat(size(xyz_Temp,1), size(xyz_Temp,2), size(xyz_Temp,3)) :real(DP)
: $ q^{*} $ . 飽和比湿. Saturation specific humidity
xyz_Temp(:,:,:) :real(DP), intent(in)
: $ T $ . 温度. Temperature
xyz_Press(:,:,:) :real(DP), intent(in)
: $ p $ . 気圧. Air pressure

温度 Temp と気圧 Press を用い, 飽和比湿 QVapSat を求めます.

Calculate saturation specific humidity QVapSat using temperature Temp and air pressure Press.

[Source]

  function xyz_CalcQVapSat( xyz_Temp, xyz_Press ) result( xyz_QVapSat )
    !
    ! 温度 *Temp* と気圧 *Press* を用い, 
    ! 飽和比湿 *QVapSat* を求めます. 
    !
    ! Calculate saturation specific humidity *QVapSat* using
    ! temperature *Temp* and air pressure *Press*. 
    !

    ! 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: GasRUniv              ! $ R^{*} $ [J K-1 mol-1].
                              ! 普遍気体定数.  Universal gas constant

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: EpsV                  ! $ \epsilon_v $ . 
                              ! 水蒸気分子量比. 
                              ! Molecular weight of water vapor

    ! 宣言文 ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: xyz_Temp (:,:,:)
                              ! $ T $ . 温度. Temperature
    real(DP), intent(in):: xyz_Press(:,:,:)
                              ! $ p $ . 気圧. Air pressure
    real(DP):: xyz_QVapSat(size(xyz_Temp,1), size(xyz_Temp,2), size(xyz_Temp,3))
                              ! $ q^{*} $ . 飽和比湿. Saturation specific humidity

    ! 作業変数
    ! Work variables
    !

    ! 実行文 ; Executable statement
    !

    if ( .not. saturate_nha1992_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if

    ! 飽和比湿の計算
    ! Calculate saturation specific humidity
    !
    xyz_QVapSat = EpsV * ( P0 / xyz_Press ) * exp ( - LatHeat / ( GasRUniv * xyz_Temp ) )


  end function xyz_CalcQVapSat

Private Instance methods

LatHeat
Constant :
LatHeat = 43655_DP :real(DP), parameter
: $ l $ [J mol-1]. 水の凝結の潜熱. Latent heat of condensation of water vapor
P0
Constant :
P0 = 1.4e+11_DP :real(DP), parameter
: $ p_0^{*} $ [Pa]. 水蒸気飽和曲線の定数. constant for water vapor saturation curve
module_name
Constant :
module_name = ‘saturate_nha1992‘ :character(*), parameter
: モジュールの名称. Module name
version
Constant :
version = ’$Name: dcpam5-20140204-5 $’ // ’$Id: saturate_nha1992.f90,v 1.7 2014-02-04 10:21:01 yot Exp $’ :character(*), parameter
: モジュールのバージョン Module version