Tetens (1930) を用いた飽和比湿の算出

Evaluate saturation specific humidity with Tetens (1930)

Note that Japanese and English are described in parallel.

Tetens (1930) より, 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 Tetens (1930).

   q^{*} (T, p)
     = 611 \varepsilon
       \frac{ \exp \left( \frac{l}{R_v}
                          \left( \frac{1}{273} - \frac{1}{T} \right)
                   \right) } { p } \] \[
   \DP{q^{*} (T, p)}{T}
     = 611 \varepsilon \frac{l}{R_v T^2}
       \frac{ \exp \left( \frac{l}{R_v}
                          \left( \frac{1}{273} - \frac{1}{T} \right)
                   \right) } { p }
     = \frac{q^{*} l}{R_v T^2}

ここで, $ T $ は温度, $ p $ は気圧, $ R_v $ は凝結成分の気体定数, $ varepsilon $ は凝結成分と大気の分子量比, $ l $ は凝結成分の潜熱です.

References

Tetens, O., 1930: Uder einige meteorologische Begriffe. Zeitschrift fur Geophysik, 6, 297--309.

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

Es0 InitCheck SaturateInit module_name saturate_t1930_inited version xy_CalcDQVapSatDTemp xy_CalcQVapSat xyz_CalcDQVapSatDTemp xyz_CalcQVapSat

Included Modules

dc_types dc_message constants namelist_util dc_iounit dc_string gtool_historyauto gridset

Public Instance methods

saturate_t1930_inited

Variable :

saturate_t1930_inited = .false. :

logical, save, public

:	初期設定フラグ. Initialization flag

xy_CalcDQVapSatDTemp( is, ie, js, je, xy_Temp, xy_QVapSat ) result(xy_DQVapSatDTemp)

Function :

xy_DQVapSatDTemp(is:ie, js:je) :

real(DP)

:	$ DP{q^{*}}{T} $ . 飽和比湿の温度微分. Temperature derivative of saturation specific humidity.

is : integer , intent(in)

ie : integer , intent(in)

js : integer , intent(in)

je : integer , intent(in)

xy_Temp(is:ie, js:je) :

real(DP), intent(in)

:	$ T $ . 温度. Temperature

xy_QVapSat(is:ie, js:je) :

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( is, ie, js, je, 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

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


    ! 実行文 ; Executable statement
    !

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

    xyz_DQVapSatDTemp = xyz_CalcDQVapSatDTemp( is, ie, js, je, 1, 1, xyz_Temp, xyz_QVapSat )

    xy_DQVapSatDTemp = xyz_DQVapSatDTemp(:,:,1)


  end function xy_CalcDQVapSatDTemp

xy_CalcQVapSat( is, ie, js, je, xy_Temp, xy_Press ) result(xy_QVapSat)

Function :

xy_QVapSat(is:ie, js:je) :

real(DP)

:	$ q^{*} $ . 飽和比湿. Saturation specific humidity

is : integer , intent(in)

ie : integer , intent(in)

js : integer , intent(in)

je : integer , intent(in)

xy_Temp(is:ie, js:je) :

real(DP), intent(in)

:	$ T $ . 温度. Temperature

xy_Press(is:ie, js:je) :

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( is, ie, js, je, 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

    integer , intent(in):: is
    integer , intent(in):: ie
    integer , intent(in):: js
    integer , intent(in):: je
    real(DP), intent(in):: xy_Temp (is:ie, js:je)
                              ! $ T $ . 温度. Temperature
    real(DP), intent(in):: xy_Press(is:ie, js:je)
                              ! $ p $ . 気圧. Air pressure

    real(DP):: xy_QVapSat(is:ie, js:je)
                              ! $ q^{*} $ . 飽和比湿. Saturation specific humidity

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


    xyz_Temp (:,:,1) = xy_Temp
    xyz_Press(:,:,1) = xy_Press

    xyz_QVapSat = xyz_CalcQVapSat( is, ie, js, je, 1, 1, xyz_Temp, xyz_Press )

    xy_QVapSat = xyz_QVapSat(:,:,1)


  end function xy_CalcQVapSat

xyz_CalcDQVapSatDTemp( is, ie, js, je, ks, ke, xyz_Temp, xyz_QVapSat ) result(xyz_DQVapSatDTemp)

Function :

xyz_DQVapSatDTemp(is:ie, js:je, ks:ke) :

real(DP)

:	$ DP{q^{*}}{T} $ . 飽和比湿の温度微分. Temperature derivative of saturation specific humidity.

is : integer , intent(in)

ie : integer , intent(in)

js : integer , intent(in)

je : integer , intent(in)

ks : integer , intent(in)

ke : integer , intent(in)

xyz_Temp(is:ie, js:je, ks:ke) :

real(DP), intent(in)

:	$ T $ . 温度. Temperature

xyz_QVapSat(is:ie, js:je, ks:ke) :

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( is, ie, js, je, ks, ke, 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
    !

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

    ! 宣言文 ; Declaration statements
    !
    implicit none

    integer , intent(in):: is
    integer , intent(in):: ie
    integer , intent(in):: js
    integer , intent(in):: je
    integer , intent(in):: ks
    integer , intent(in):: ke
    real(DP), intent(in):: xyz_Temp   (is:ie, js:je, ks:ke)
                              ! $ T $ . 温度. Temperature
    real(DP), intent(in):: xyz_QVapSat(is:ie, js:je, ks:ke)
                              ! $ q^{*} $ . 飽和比湿. Saturation specific humidity
    real(DP):: xyz_DQVapSatDTemp(is:ie, js:je, ks:ke)
                              ! $ \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
    !
    xyz_DQVapSatDTemp = LatentHeat * xyz_QVapSat / ( GasRWet * xyz_Temp**2 )


  end function xyz_CalcDQVapSatDTemp

xyz_CalcQVapSat( is, ie, js, je, ks, ke, xyz_Temp, xyz_Press ) result(xyz_QVapSat)

Function :

xyz_QVapSat(is:ie, js:je, ks:ke) :

real(DP)

:	$ q^{*} $ . 飽和比湿. Saturation specific humidity

is : integer , intent(in)

ie : integer , intent(in)

js : integer , intent(in)

je : integer , intent(in)

ks : integer , intent(in)

ke : integer , intent(in)

xyz_Temp(is:ie, js:je, ks:ke) :

real(DP), intent(in)

:	$ T $ . 温度. Temperature

xyz_Press(is:ie, js:je, ks:ke) :

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( is, ie, js, je, ks, ke, 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
    !

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

    ! 宣言文 ; Declaration statements
    !
    implicit none

    integer , intent(in):: is
    integer , intent(in):: ie
    integer , intent(in):: js
    integer , intent(in):: je
    integer , intent(in):: ks
    integer , intent(in):: ke
    real(DP), intent(in):: xyz_Temp (is:ie, js:je, ks:ke)
                              ! $ T $ . 温度. Temperature
    real(DP), intent(in):: xyz_Press(is:ie, js:je, ks:ke)
                              ! $ p $ . 気圧. Air pressure

    real(DP):: xyz_QVapSat(is:ie, js:je, ks:ke)
                              ! $ q^{*} $ . 飽和比湿. Saturation specific humidity

    ! 作業変数
    ! Work variables
    !

    ! 実行文 ; Executable statement
    !

    xyz_QVapSat = EpsV * Es0 * exp( LatentHeat / GasRWet * ( 1./273. - 1./xyz_Temp ) ) / xyz_Press


  end function xyz_CalcQVapSat

Private Instance methods

Es0

Constant :

Es0 = 611.0_DP :

real(DP), parameter

:	0 ℃の飽和蒸気圧 [Pa]. Saturation water vapor pressure at 0 deg C [Pa]

InitCheck( )

Subroutine :

依存モジュールの初期化チェック

Check initialization of dependency modules

[Source]

  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
    !

    ! 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

    ! 実行文 ; Executable statement
    !

    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.' )

  end subroutine InitCheck

SaturateInit( )

Subroutine :

saturate_t1930 モジュールの初期化を行います.

"saturate_t1930" module is initialized.

[Source]

  subroutine SaturateInit
    !
    ! saturate_t1930 モジュールの初期化を行います. 
    !
    !
    ! "saturate_t1930" 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_t1930_nml/ 
          !
          ! デフォルト値については初期化手続 "saturate_t1930#SaturateInit" 
          ! のソースコードを参照のこと. 
          !
          ! Refer to source codes in the initialization procedure
          ! "saturate_t1930#SaturateInit" for the default values. 
          !

    ! 実行文 ; Executable statement
    !

    if ( saturate_t1930_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 = saturate_t1930_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_t1930_inited = .true.
  end subroutine SaturateInit

module_name

Constant :

module_name = ‘saturate_t1930‘ :

character(*), parameter

:	モジュールの名称. Module name

version

Constant :

version = ’$Name: dcpam5-20110221-4 $’ // ’$Id: saturate_t1930.f90,v 1.1 2010-09-12 02:07:27 yot Exp $’ :

character(*), parameter

:	モジュールのバージョン Module version