mom_eos_nemo Module Reference

Detailed Description

The equation of state using the expressions of Roquet et al. that are used in NEMO.

Data Types
interface	calculate_density_derivs_nemo
	For a given thermodynamic state, return the derivatives of density with conservative temperature and absolute salinity, the expressions derived for use with NEMO. More...
interface	calculate_density_nemo
	Compute the in situ density of sea water ([kg m-3]), or its anomaly with respect to a reference density, from absolute salinity (g/kg), conservative temperature (in deg C), and pressure [Pa], using the expressions derived for use with NEMO. More...

Functions/Subroutines
subroutine, public	calculate_density_scalar_nemo (T, S, pressure, rho, rho_ref)
	This subroutine computes the in situ density of sea water (rho in [kg m-3]) from absolute salinity (S [g kg-1]), conservative temperature (T [degC]), and pressure [Pa]. It uses the expressions derived for use with NEMO. More...
subroutine, public	calculate_density_array_nemo (T, S, pressure, rho, start, npts, rho_ref)
	This subroutine computes the in situ density of sea water (rho in [kg m-3]) from absolute salinity (S [g kg-1]), conservative temperature (T [degC]), and pressure [Pa]. It uses the expressions derived for use with NEMO. More...
subroutine	calculate_density_derivs_array_nemo (T, S, pressure, drho_dT, drho_dS, start, npts)
	For a given thermodynamic state, calculate the derivatives of density with conservative temperature and absolute salinity, using the expressions derived for use with NEMO. More...
subroutine	calculate_density_derivs_scalar_nemo (T, S, pressure, drho_dt, drho_ds)
	Wrapper to calculate_density_derivs_array for scalar inputs. More...
subroutine, public	calculate_compress_nemo (T, S, pressure, rho, drho_dp, start, npts)
	Compute the in situ density of sea water (rho in [kg m-3]) and the compressibility (drho/dp = C_sound^-2, stored as drho_dp [s2 m-2]) from absolute salinity (sal in g/kg), conservative temperature (T [degC]), and pressure [Pa], using the expressions derived for use with NEMO. More...

Variables
real, parameter	pa2db = 1.e-4
	Conversion factor between Pa and dbar.

Function/Subroutine Documentation

calculate_compress_nemo()

subroutine, public mom_eos_nemo::calculate_compress_nemo	(	real, dimension(:), intent(in)	T,
		real, dimension(:), intent(in)	S,
		real, dimension(:), intent(in)	pressure,
		real, dimension(:), intent(out)	rho,
		real, dimension(:), intent(out)	drho_dp,
		integer, intent(in)	start,
		integer, intent(in)	npts
	)

Compute the in situ density of sea water (rho in [kg m-3]) and the compressibility (drho/dp = C_sound^-2, stored as drho_dp [s2 m-2]) from absolute salinity (sal in g/kg), conservative temperature (T [degC]), and pressure [Pa], using the expressions derived for use with NEMO.

Parameters

[in]	t	Conservative temperature [degC].
[in]	s	Absolute salinity [g/kg].
[in]	pressure	pressure [Pa].
[out]	rho	In situ density [kg m-3].
[out]	drho_dp	The partial derivative of density with pressure (also the inverse of the square of sound speed) [s2 m-2].
[in]	start	The starting point in the arrays.
[in]	npts	The number of values to calculate.

Definition at line 369 of file MOM_EOS_NEMO.F90.

  real,    intent(in),  dimension(:) :: T        !< Conservative temperature [degC].
  real,    intent(in),  dimension(:) :: S        !< Absolute salinity [g/kg].
  real,    intent(in),  dimension(:) :: pressure !< pressure [Pa].
  real,    intent(out), dimension(:) :: rho      !< In situ density [kg m-3].
  real,    intent(out), dimension(:) :: drho_dp  !< The partial derivative of density with pressure
                                                 !! (also the inverse of the square of sound speed)
                                                 !! [s2 m-2].
  integer, intent(in)                :: start    !< The starting point in the arrays.
  integer, intent(in)                :: npts     !< The number of values to calculate.
 
  ! Local variables
  real ::  zs,zt,zp
  integer :: j
 
  call calculate_density_array_nemo(t, s, pressure, rho, start, npts)
  !
  !NOTE: The following calculates the TEOS10 approximation to compressibility
  !      since the corresponding NEMO approximation is not available yet.
  !
  do j=start,start+npts-1
   !Conversions
    zs = s(j) !gsw_sr_from_sp(S(j))       !Convert practical salinity to absolute salinity
    zt = t(j) !gsw_ct_from_pt(S(j),T(j))  !Convert potantial temp to conservative temp
    zp = pressure(j)* pa2db         !Convert pressure from Pascal to decibar
    call gsw_rho_first_derivatives(zs,zt,zp, drho_dp=drho_dp(j))
 enddo

calculate_density_array_nemo()

subroutine, public mom_eos_nemo::calculate_density_array_nemo	(	real, dimension(:), intent(in)	T,
		real, dimension(:), intent(in)	S,
		real, dimension(:), intent(in)	pressure,
		real, dimension(:), intent(out)	rho,
		integer, intent(in)	start,
		integer, intent(in)	npts,
		real, intent(in), optional	rho_ref
	)

This subroutine computes the in situ density of sea water (rho in [kg m-3]) from absolute salinity (S [g kg-1]), conservative temperature (T [degC]), and pressure [Pa]. It uses the expressions derived for use with NEMO.

Parameters

[in]	t	Conservative temperature [degC].
[in]	s	Absolute salinity [g kg-1].
[in]	pressure	pressure [Pa].
[out]	rho	in situ density [kg m-3].
[in]	start	the starting point in the arrays.
[in]	npts	the number of values to calculate.
[in]	rho_ref	A reference density [kg m-3].

Definition at line 206 of file MOM_EOS_NEMO.F90.

  real, dimension(:), intent(in)  :: T        !< Conservative temperature [degC].
  real, dimension(:), intent(in)  :: S        !< Absolute salinity [g kg-1].
  real, dimension(:), intent(in)  :: pressure !< pressure [Pa].
  real, dimension(:), intent(out) :: rho      !< in situ density [kg m-3].
  integer,            intent(in)  :: start    !< the starting point in the arrays.
  integer,            intent(in)  :: npts     !< the number of values to calculate.
  real,     optional, intent(in)  :: rho_ref  !< A reference density [kg m-3].
 
  ! Local variables
  real :: zp, zt, zh, zs, zr0, zn, zn0, zn1, zn2, zn3, zs0
  integer :: j
 
  do j=start,start+npts-1
    !Conversions
    zs = s(j) !gsw_sr_from_sp(S(j))       !Convert practical salinity to absolute salinity
    zt = t(j) !gsw_ct_from_pt(S(j),T(j))  !Convert potential temp to conservative temp
    zp = pressure(j)* pa2db         !Convert pressure from Pascal to decibar
 
    !The following algorithm was provided by Roquet in a private communication.
    !It is not necessarily the algorithm used in NEMO ocean!
    zp  = zp * r1_p0 !pressure
    zt  = zt * r1_t0 !temperature
    zs  = sqrt( abs( zs + rdeltas ) * r1_s0 )   ! square root salinity
 
    zn3 = eos013*zt   &
       &   + eos103*zs+eos003
 
    zn2 = (eos022*zt   &
       &   + eos112*zs+eos012)*zt   &
       &   + (eos202*zs+eos102)*zs+eos002
 
    zn1 = (((eos041*zt   &
       &   + eos131*zs+eos031)*zt   &
       &   + (eos221*zs+eos121)*zs+eos021)*zt   &
       &   + ((eos311*zs+eos211)*zs+eos111)*zs+eos011)*zt   &
       &   + (((eos401*zs+eos301)*zs+eos201)*zs+eos101)*zs+eos001
 
    zn0 = (((((eos060*zt   &
       &   + eos150*zs+eos050)*zt   &
       &   + (eos240*zs+eos140)*zs+eos040)*zt   &
       &   + ((eos330*zs+eos230)*zs+eos130)*zs+eos030)*zt   &
       &   + (((eos420*zs+eos320)*zs+eos220)*zs+eos120)*zs+eos020)*zt   &
       &   + ((((eos510*zs+eos410)*zs+eos310)*zs+eos210)*zs+eos110)*zs+eos010)*zt
 
    zs0 = (((((eos600*zs+eos500)*zs+eos400)*zs+eos300)*zs+eos200)*zs+eos100)*zs + eos000
 
    zr0 = (((((r05 * zp+r04) * zp+r03 ) * zp+r02 ) * zp+r01) * zp+r00) * zp
 
    if (present(rho_ref)) then
      zn  = ( ( zn3 * zp + zn2 ) * zp + zn1 ) * zp + (zn0 + (zs0 - rho_ref))
      rho(j) =  ( zn + zr0 ) ! density
    else
      zn  = ( ( zn3 * zp + zn2 ) * zp + zn1 ) * zp + (zn0 + zs0)
      rho(j) =  ( zn + zr0 ) ! density
    endif
 
 enddo

calculate_density_derivs_array_nemo()

subroutine mom_eos_nemo::calculate_density_derivs_array_nemo ( real, dimension(:), intent(in)  T, real, dimension(:), intent(in)  S, real, dimension(:), intent(in)  pressure, real, dimension(:), intent(out)  drho_dT, real, dimension(:), intent(out)  drho_dS, integer, intent(in)  start, integer, intent(in)  npts  )

private

For a given thermodynamic state, calculate the derivatives of density with conservative temperature and absolute salinity, using the expressions derived for use with NEMO.

Parameters

[in]	t	Conservative temperature [degC].
[in]	s	Absolute salinity [g kg-1].
[in]	pressure	pressure [Pa].
[out]	drho_dt	The partial derivative of density with potential temperature [kg m-3 degC-1].
[out]	drho_ds	The partial derivative of density with salinity, in [kg m-3 ppt-1].
[in]	start	The starting point in the arrays.
[in]	npts	The number of values to calculate.

Definition at line 268 of file MOM_EOS_NEMO.F90.

  real,    intent(in),  dimension(:) :: T        !< Conservative temperature [degC].
  real,    intent(in),  dimension(:) :: S        !< Absolute salinity [g kg-1].
  real,    intent(in),  dimension(:) :: pressure !< pressure [Pa].
  real,    intent(out), dimension(:) :: drho_dT  !< The partial derivative of density with potential
                                                 !! temperature [kg m-3 degC-1].
  real,    intent(out), dimension(:) :: drho_dS  !< The partial derivative of density with salinity,
                                                 !! in [kg m-3 ppt-1].
  integer, intent(in)                :: start    !< The starting point in the arrays.
  integer, intent(in)                :: npts     !< The number of values to calculate.
 
  ! Local variables
  real :: zp,zt , zh , zs , zr0, zn , zn0, zn1, zn2, zn3
  integer :: j
 
  do j=start,start+npts-1
    !Conversions
    zs = s(j) !gsw_sr_from_sp(S(j))       !Convert practical salinity to absolute salinity
    zt = t(j) !gsw_ct_from_pt(S(j),T(j))  !Convert potantial temp to conservative temp
    zp = pressure(j)* pa2db         !Convert pressure from Pascal to decibar
 
    !The following algorithm was provided by Roquet in a private communication.
    !It is not necessarily the algorithm used in NEMO ocean!
    zp  = zp * r1_p0  ! pressure (first converted to decibar)
    zt  = zt * r1_t0                ! temperature
    zs  = sqrt( abs( zs + rdeltas ) * r1_s0 )   ! square root salinity
    !
    ! alpha
    zn3 = alp003
    !
    zn2 = alp012*zt + alp102*zs+alp002
    !
    zn1 = ((alp031*zt   &
       &   + alp121*zs+alp021)*zt   &
       &   + (alp211*zs+alp111)*zs+alp011)*zt   &
       &   + ((alp301*zs+alp201)*zs+alp101)*zs+alp001
       !
    zn0 = ((((alp050*zt   &
       &   + alp140*zs+alp040)*zt   &
       &   + (alp230*zs+alp130)*zs+alp030)*zt   &
       &   + ((alp320*zs+alp220)*zs+alp120)*zs+alp020)*zt   &
       &   + (((alp410*zs+alp310)*zs+alp210)*zs+alp110)*zs+alp010)*zt   &
       &   + ((((alp500*zs+alp400)*zs+alp300)*zs+alp200)*zs+alp100)*zs+alp000
       !
    zn  = ( ( zn3 * zp + zn2 ) * zp + zn1 ) * zp + zn0
    !
    drho_dt(j) = -zn
    !
    ! beta
    !
    zn3 = bet003
    !
    zn2 = bet012*zt + bet102*zs+bet002
    !
    zn1 = ((bet031*zt   &
       &   + bet121*zs+bet021)*zt   &
       &   + (bet211*zs+bet111)*zs+bet011)*zt   &
       &   + ((bet301*zs+bet201)*zs+bet101)*zs+bet001
       !
    zn0 = ((((bet050*zt   &
       &   + bet140*zs+bet040)*zt   &
       &   + (bet230*zs+bet130)*zs+bet030)*zt   &
       &   + ((bet320*zs+bet220)*zs+bet120)*zs+bet020)*zt   &
       &   + (((bet410*zs+bet310)*zs+bet210)*zs+bet110)*zs+bet010)*zt   &
       &   + ((((bet500*zs+bet400)*zs+bet300)*zs+bet200)*zs+bet100)*zs+bet000
       !
    zn  = ( ( zn3 * zp + zn2 ) * zp + zn1 ) * zp + zn0
    !
    drho_ds(j) = zn / zs
  enddo
 

calculate_density_derivs_scalar_nemo()

subroutine mom_eos_nemo::calculate_density_derivs_scalar_nemo ( real, intent(in)  T, real, intent(in)  S, real, intent(in)  pressure, real, intent(out)  drho_dt, real, intent(out)  drho_ds  )

private

Wrapper to calculate_density_derivs_array for scalar inputs.

Parameters

[in]	t	Potential temperature relative to the surface [degC].
[in]	s	Salinity [g kg-1].
[in]	pressure	Pressure [Pa].
[out]	drho_dt	The partial derivative of density with potential temperature [kg m-3 degC-1].
[out]	drho_ds	The partial derivative of density with salinity, in [kg m-3 ppt-1].

Definition at line 342 of file MOM_EOS_NEMO.F90.

  real,    intent(in)  :: T        !< Potential temperature relative to the surface [degC].
  real,    intent(in)  :: S        !< Salinity [g kg-1].
  real,    intent(in)  :: pressure !< Pressure [Pa].
  real,    intent(out) :: drho_dT  !< The partial derivative of density with potential
                                   !! temperature [kg m-3 degC-1].
  real,    intent(out) :: drho_dS  !< The partial derivative of density with salinity,
                                   !! in [kg m-3 ppt-1].
  ! Local variables
  real :: al0, p0, lambda
  integer :: j
  real, dimension(1) :: T0, S0, pressure0
  real, dimension(1) :: drdt0, drds0
 
  t0(1) = t
  s0(1) = s
  pressure0(1) = pressure
 
  call calculate_density_derivs_array_nemo(t0, s0, pressure0, drdt0, drds0, 1, 1)
  drho_dt = drdt0(1)
  drho_ds = drds0(1)

calculate_density_scalar_nemo()

subroutine, public mom_eos_nemo::calculate_density_scalar_nemo	(	real, intent(in)	T,
		real, intent(in)	S,
		real, intent(in)	pressure,
		real, intent(out)	rho,
		real, intent(in), optional	rho_ref
	)

This subroutine computes the in situ density of sea water (rho in [kg m-3]) from absolute salinity (S [g kg-1]), conservative temperature (T [degC]), and pressure [Pa]. It uses the expressions derived for use with NEMO.

Parameters

[in]	t	Conservative temperature [degC].
[in]	s	Absolute salinity [g kg-1].
[in]	pressure	pressure [Pa].
[out]	rho	In situ density [kg m-3].
[in]	rho_ref	A reference density [kg m-3].

Definition at line 181 of file MOM_EOS_NEMO.F90.

  real,           intent(in)  :: T        !< Conservative temperature [degC].
  real,           intent(in)  :: S        !< Absolute salinity [g kg-1].
  real,           intent(in)  :: pressure !< pressure [Pa].
  real,           intent(out) :: rho      !< In situ density [kg m-3].
  real, optional, intent(in)  :: rho_ref  !< A reference density [kg m-3].
 
  real :: al0, p0, lambda
  integer :: j
  real, dimension(1) :: T0, S0, pressure0
  real, dimension(1) :: rho0
 
  t0(1) = t
  s0(1) = s
  pressure0(1) = pressure
 
  call calculate_density_array_nemo(t0, s0, pressure0, rho0, 1, 1, rho_ref)
  rho = rho0(1)