Class saturate_nha1992 In: saturate/saturate_nha1992.f90

# 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]

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.

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

### Included Modules

dc_types dc_message constants0 constants namelist_util dc_iounit dc_string gtool_historyauto

### Public Instance methods

 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
!

! 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
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

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

[Source]

  function xyz_CalcDQVapSatDTempOnLiq( 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_CalcDQVapSatDTempOnLiq

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

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

[Source]

  function xyz_CalcDQVapSatDTempOnSol( 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
!

! 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_CalcDQVapSatDTempOnLiq( xyz_Temp, xyz_QVapSat )

end function xyz_CalcDQVapSatDTempOnSol

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

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

[Source]

  function xyz_CalcQVapSatOnLiq( 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_CalcQVapSatOnLiq

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

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

[Source]

  function xyz_CalcQVapSatOnSol( 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
!

! 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 = xyz_CalcQVapSatOnLiq( xyz_Temp, xyz_Press )

end function xyz_CalcQVapSatOnSol


### 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 = ’$Name:$’ // ’$Id: saturate_nha1992.f90,v 1.9 2015/01/29 12:07:16 yot Exp$’ :character(*), parameter
 : モジュールのバージョン Module version