Detailed Description

The equation of state using the Jackett and McDougall fits to the UNESCO EOS.

Data Types
interface	calculate_density_unesco
	Compute the in situ density of sea water (in [kg m-3]), or its anomaly with respect to a reference density, from salinity [PSU], potential temperature [degC], and pressure [Pa], using the UNESCO (1981) equation of state. More...

interface	calculate_spec_vol_unesco
	Compute the in situ specific volume of sea water (in [m3 kg-1]), or an anomaly with respect to a reference specific volume, from salinity [PSU], potential temperature [degC], and pressure [Pa], using the UNESCO (1981) equation of state. More...

real, parameter	r00 = 999.842594
	Parameters in the UNESCO equation of state. More...

real, parameter	r10 = 6.793952e-2
	Parameters in the UNESCO equation of state. More...

real, parameter	r20 = -9.095290e-3
	Parameters in the UNESCO equation of state. More...

real, parameter	r30 = 1.001685e-4
	Parameters in the UNESCO equation of state. More...

real, parameter	r40 = -1.120083e-6
	Parameters in the UNESCO equation of state. More...

real, parameter	r50 = 6.536332e-9
	Parameters in the UNESCO equation of state. More...

real, parameter	r01 = 0.824493
	Parameters in the UNESCO equation of state. More...

real, parameter	r11 = -4.0899e-3
	Parameters in the UNESCO equation of state. More...

real, parameter	r21 = 7.6438e-5
	Parameters in the UNESCO equation of state. More...

real, parameter	r31 = -8.2467e-7
	Parameters in the UNESCO equation of state. More...

real, parameter	r41 = 5.3875e-9
	Parameters in the UNESCO equation of state. More...

real, parameter	r032 = -5.72466e-3
	Parameters in the UNESCO equation of state. More...

real, parameter	r132 = 1.0227e-4
	Parameters in the UNESCO equation of state. More...

real, parameter	r232 = -1.6546e-6
	Parameters in the UNESCO equation of state. More...

real, parameter	r02 = 4.8314e-4
	Parameters in the UNESCO equation of state. More...

real, parameter	s00 = 1.965933e4
	Parameters in the UNESCO equation of state. More...

real, parameter	s10 = 1.444304e2
	Parameters in the UNESCO equation of state. More...

real, parameter	s20 = -1.706103
	Parameters in the UNESCO equation of state. More...

real, parameter	s30 = 9.648704e-3
	Parameters in the UNESCO equation of state. More...

real, parameter	s40 = -4.190253e-5
	Parameters in the UNESCO equation of state. More...

real, parameter	s01 = 52.84855
	Parameters in the UNESCO equation of state. More...

real, parameter	s11 = -3.101089e-1
	Parameters in the UNESCO equation of state. More...

real, parameter	s21 = 6.283263e-3
	Parameters in the UNESCO equation of state. More...

real, parameter	s31 = -5.084188e-5
	Parameters in the UNESCO equation of state. More...

real, parameter	s032 = 3.886640e-1
	Parameters in the UNESCO equation of state. More...

real, parameter	s132 = 9.085835e-3
	Parameters in the UNESCO equation of state. More...

real, parameter	s232 = -4.619924e-4
	Parameters in the UNESCO equation of state. More...

real, parameter	sp00 = 3.186519
	Parameters in the UNESCO equation of state. More...

real, parameter	sp10 = 2.212276e-2
	Parameters in the UNESCO equation of state. More...

real, parameter	sp20 = -2.984642e-4
	Parameters in the UNESCO equation of state. More...

real, parameter	sp30 = 1.956415e-6
	Parameters in the UNESCO equation of state. More...

real, parameter	sp01 = 6.704388e-3
	Parameters in the UNESCO equation of state. More...

real, parameter	sp11 = -1.847318e-4
	Parameters in the UNESCO equation of state. More...

real, parameter	sp21 = 2.059331e-7
	Parameters in the UNESCO equation of state. More...

real, parameter	sp032 = 1.480266e-4
	Parameters in the UNESCO equation of state. More...

real, parameter	sp000 = 2.102898e-4
	Parameters in the UNESCO equation of state. More...

real, parameter	sp010 = -1.202016e-5
	Parameters in the UNESCO equation of state. More...

real, parameter	sp020 = 1.394680e-7
	Parameters in the UNESCO equation of state. More...

real, parameter	sp001 = -2.040237e-6
	Parameters in the UNESCO equation of state. More...

real, parameter	sp011 = 6.128773e-8
	Parameters in the UNESCO equation of state. More...

real, parameter	sp021 = 6.207323e-10
	Parameters in the UNESCO equation of state. More...

subroutine, public	calculate_density_scalar_unesco (T, S, pressure, rho, rho_ref)
	This subroutine computes the in situ density of sea water (rho in [kg m-3]) from salinity (S [PSU]), potential temperature (T [degC]), and pressure [Pa], using the UNESCO (1981) equation of state. More...

subroutine, public	calculate_density_array_unesco (T, S, pressure, rho, start, npts, rho_ref)
	This subroutine computes the in situ density of sea water (rho in [kg m-3]) from salinity (S [PSU]), potential temperature (T [degC]), and pressure [Pa], using the UNESCO (1981) equation of state. More...

subroutine	calculate_spec_vol_scalar_unesco (T, S, pressure, specvol, spv_ref)
	This subroutine computes the in situ specific volume of sea water (specvol in [m3 kg-1]) from salinity (S [PSU]), potential temperature (T [degC]) and pressure [Pa], using the UNESCO (1981) equation of state. If spv_ref is present, specvol is an anomaly from spv_ref. More...

subroutine	calculate_spec_vol_array_unesco (T, S, pressure, specvol, start, npts, spv_ref)
	This subroutine computes the in situ specific volume of sea water (specvol in [m3 kg-1]) from salinity (S [PSU]), potential temperature (T [degC]) and pressure [Pa], using the UNESCO (1981) equation of state. If spv_ref is present, specvol is an anomaly from spv_ref. More...

subroutine, public	calculate_density_derivs_unesco (T, S, pressure, drho_dT, drho_dS, start, npts)
	This subroutine calculates the partial derivatives of density with potential temperature and salinity. More...

subroutine, public	calculate_compress_unesco (T, S, pressure, rho, drho_dp, start, npts)
	This subroutine computes the in situ density of sea water (rho) and the compressibility (drho/dp == C_sound^-2) at the given salinity, potential temperature, and pressure. More...

Function/Subroutine Documentation

◆ calculate_compress_unesco()

subroutine, public mom_eos_unesco::calculate_compress_unesco	(	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
	)

This subroutine computes the in situ density of sea water (rho) and the compressibility (drho/dp == C_sound^-2) at the given salinity, potential temperature, and pressure.

Parameters

[in]	t	Potential temperature relative to the surface [degC].
[in]	s	Salinity [PSU].
[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 284 of file MOM_EOS_UNESCO.F90.

   real,    intent(in),  dimension(:) :: T        !< Potential temperature relative to the surface
                                                  !! [degC].
   real,    intent(in),  dimension(:) :: S        !< Salinity [PSU].
   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 :: t_local, t2, t3, t4, t5  ! Temperature to the 1st - 5th power [degC^n].
   real :: s_local, s32, s2         ! Salinity to the 1st, 3/2, & 2nd power [PSU^n].
   real :: p1, p2          ! Pressure to the 1st & 2nd power [bar] and [bar2].
   real :: rho0            ! Density at 1 bar pressure [kg m-3].
   real :: ks              ! The secant bulk modulus [bar].
   real :: ks_0, ks_1, ks_2
   real :: dks_dp       ! The derivative of the secant bulk modulus
                        ! with pressure, nondimensional.
   integer :: j
  
   do j=start,start+npts-1
     if (s(j) < -1.0e-10) then !Can we assume safely that this is a missing value?
       rho(j) = 1000.0 ; drho_dp(j) = 0.0
       cycle
     endif
  
     p1 = pressure(j)*1.0e-5; p2 = p1*p1
     t_local = t(j); t2 = t_local*t_local; t3 = t_local*t2; t4 = t2*t2; t5 = t3*t2
     s_local = s(j); s2 = s_local*s_local; s32 = s_local*sqrt(s_local)
  
 !  Compute rho(s,theta,p=0) - (same as rho(s,t_insitu,p=0) ).
  
     rho0 = r00 + r10*t_local + r20*t2 + r30*t3 + r40*t4 + r50*t5 + &
            s_local*(r01 + r11*t_local + r21*t2 + r31*t3 + r41*t4) + &
            s32*(r032 + r132*t_local + r232*t2) + r02*s2
  
 !  Compute rho(s,theta,p), first calculating the secant bulk modulus.
     ks_0 = s00 + s10*t_local + s20*t2 + s30*t3 + s40*t4 + &
            s_local*(s01 + s11*t_local + s21*t2 + s31*t3) + s32*(s032 + s132*t_local + s232*t2)
     ks_1 = sp00 + sp10*t_local + sp20*t2 + sp30*t3 + &
            s_local*(sp01 + sp11*t_local + sp21*t2) + sp032*s32
     ks_2 = sp000 + sp010*t_local + sp020*t2 + s_local*(sp001 + sp011*t_local + sp021*t2)
  
     ks = ks_0 + p1*ks_1 + p2*ks_2
     dks_dp = ks_1 + 2.0*p1*ks_2
  
     rho(j) = rho0*ks / (ks - p1)
 ! The factor of 1.0e-5 is because pressure here is in bars, not Pa.
     drho_dp(j) = 1.0e-5 * (rho(j) / (ks - p1)) * (1.0 - dks_dp*p1/ks)
   enddo

References r00, r01, r02, r032, r10, r11, r132, r20, r21, r232, r30, r31, r40, r41, r50, s00, s01, s032, s10, s11, s132, s20, s21, s232, s30, s31, s40, sp00, sp000, sp001, sp01, sp010, sp011, sp020, sp021, sp032, sp10, sp11, sp20, sp21, and sp30.

Referenced by mom_eos::calculate_compress_array().

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◆ calculate_density_array_unesco()

subroutine, public mom_eos_unesco::calculate_density_array_unesco	(	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 salinity (S [PSU]), potential temperature (T [degC]), and pressure [Pa], using the UNESCO (1981) equation of state.

Parameters

[in]	t	potential temperature relative to the surface [degC].
[in]	s	salinity [PSU].
[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 83 of file MOM_EOS_UNESCO.F90.

   real, dimension(:), intent(in)  :: T        !< potential temperature relative to the surface [degC].
   real, dimension(:), intent(in)  :: S        !< salinity [PSU].
   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 :: t_local, t2, t3, t4, t5  ! Temperature to the 1st - 5th power [degC^n].
   real :: s_local, s32, s2         ! Salinity to the 1st, 3/2, & 2nd power [PSU^n].
   real :: p1, p2      ! Pressure (in bars) to the 1st and 2nd power [bar] and [bar2].
   real :: rho0        ! Density at 1 bar pressure [kg m-3].
   real :: sig0        ! The anomaly of rho0 from R00 [kg m-3].
   real :: ks          ! The secant bulk modulus [bar].
   integer :: j
  
   do j=start,start+npts-1
     if (s(j) < -1.0e-10) then !Can we assume safely that this is a missing value?
       rho(j) = 1000.0
       cycle
     endif
  
     p1 = pressure(j)*1.0e-5; p2 = p1*p1
     t_local = t(j); t2 = t_local*t_local; t3 = t_local*t2; t4 = t2*t2; t5 = t3*t2
     s_local = s(j); s2 = s_local*s_local; s32 = s_local*sqrt(s_local)
  
 !  Compute rho(s,theta,p=0) - (same as rho(s,t_insitu,p=0) ).
  
     sig0 = r10*t_local + r20*t2 + r30*t3 + r40*t4 + r50*t5 + &
            s_local*(r01 + r11*t_local + r21*t2 + r31*t3 + r41*t4) + &
            s32*(r032 + r132*t_local + r232*t2) + r02*s2
     rho0 = r00 + sig0
  
 !  Compute rho(s,theta,p), first calculating the secant bulk modulus.
  
     ks = s00 + s10*t_local + s20*t2 + s30*t3 + s40*t4 + s_local*(s01 + s11*t_local + s21*t2 + s31*t3) + &
          s32*(s032 + s132*t_local + s232*t2) + &
          p1*(sp00 + sp10*t_local + sp20*t2 + sp30*t3 + &
              s_local*(sp01 + sp11*t_local + sp21*t2) + sp032*s32) + &
          p2*(sp000 + sp010*t_local + sp020*t2 + s_local*(sp001 + sp011*t_local + sp021*t2))
  
     if (present(rho_ref)) then
       rho(j) = ((r00 - rho_ref)*ks + (sig0*ks + p1*rho_ref)) / (ks - p1)
     else
       rho(j) = rho0*ks / (ks - p1)
     endif
   enddo

References r00, r01, r02, r032, r10, r11, r132, r20, r21, r232, r30, r31, r40, r41, r50, s00, s01, s032, s10, s11, s132, s20, s21, s232, s30, s31, s40, sp00, sp000, sp001, sp01, sp010, sp011, sp020, sp021, sp032, sp10, sp11, sp20, sp21, and sp30.

Referenced by calculate_density_scalar_unesco().

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◆ calculate_density_derivs_unesco()

subroutine, public mom_eos_unesco::calculate_density_derivs_unesco	(	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
	)

This subroutine calculates the partial derivatives of density with potential temperature and salinity.

Parameters

[in]	t	Potential temperature relative to the surface [degC].
[in]	s	Salinity [PSU].
[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 PSU-1].
[in]	start	The starting point in the arrays.
[in]	npts	The number of values to calculate.

Definition at line 213 of file MOM_EOS_UNESCO.F90.

   real,    intent(in),  dimension(:) :: T        !< Potential temperature relative to the surface
                                                  !! [degC].
   real,    intent(in),  dimension(:) :: S        !< Salinity [PSU].
   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 PSU-1].
   integer, intent(in)                :: start    !< The starting point in the arrays.
   integer, intent(in)                :: npts     !< The number of values to calculate.
  
   ! Local variables
   real :: t_local, t2, t3, t4, t5  ! Temperature to the 1st - 5th power [degC^n].
   real :: s12, s_local, s32, s2    ! Salinity to the 1/2 - 2nd powers [PSU^n].
   real :: p1, p2          ! Pressure to the 1st & 2nd power [bar] and [bar2].
   real :: rho0            ! Density at 1 bar pressure [kg m-3].
   real :: ks              ! The secant bulk modulus [bar].
   real :: drho0_dT        ! Derivative of rho0 with T [kg m-3 degC-1].
   real :: drho0_dS        ! Derivative of rho0 with S [kg m-3 PSU-1].
   real :: dks_dT          ! Derivative of ks with T [bar degC-1].
   real :: dks_dS          ! Derivative of ks with S [bar psu-1].
   real :: denom           ! 1.0 / (ks - p1) [bar-1].
   integer :: j
  
   do j=start,start+npts-1
     if (s(j) < -1.0e-10) then !Can we assume safely that this is a missing value?
       drho_dt(j) = 0.0 ; drho_ds(j) = 0.0
       cycle
     endif
  
     p1 = pressure(j)*1.0e-5; p2 = p1*p1
     t_local = t(j); t2 = t_local*t_local; t3 = t_local*t2; t4 = t2*t2; t5 = t3*t2
     s_local = s(j); s2 = s_local*s_local; s12 = sqrt(s_local); s32 = s_local*s12
  
 !       compute rho(s,theta,p=0) - (same as rho(s,t_insitu,p=0) )
  
     rho0 = r00 + r10*t_local + r20*t2 + r30*t3 + r40*t4 + r50*t5 + &
            s_local*(r01 + r11*t_local + r21*t2 + r31*t3 + r41*t4) + &
            s32*(r032 + r132*t_local + r232*t2) + r02*s2
     drho0_dt = r10 + 2.0*r20*t_local + 3.0*r30*t2 + 4.0*r40*t3 + 5.0*r50*t4 + &
                s_local*(r11 + 2.0*r21*t_local + 3.0*r31*t2 + 4.0*r41*t3) + &
                s32*(r132 + 2.0*r232*t_local)
     drho0_ds = (r01 + r11*t_local + r21*t2 + r31*t3 + r41*t4) + &
                1.5*s12*(r032 + r132*t_local + r232*t2) + 2.0*r02*s_local
  
 !       compute rho(s,theta,p)
  
     ks = s00 + s10*t_local + s20*t2 + s30*t3 + s40*t4 + s_local*(s01 + s11*t_local + s21*t2 + s31*t3) + &
          s32*(s032 + s132*t_local + s232*t2) + &
          p1*(sp00 + sp10*t_local + sp20*t2 + sp30*t3 + &
              s_local*(sp01 + sp11*t_local + sp21*t2) + sp032*s32) + &
          p2*(sp000 + sp010*t_local + sp020*t2 + s_local*(sp001 + sp011*t_local + sp021*t2))
     dks_dt = s10 + 2.0*s20*t_local + 3.0*s30*t2 + 4.0*s40*t3 + &
              s_local*(s11 + 2.0*s21*t_local + 3.0*s31*t2) + s32*(s132 + 2.0*s232*t_local) + &
              p1*(sp10 + 2.0*sp20*t_local + 3.0*sp30*t2 + s_local*(sp11 + 2.0*sp21*t_local)) + &
              p2*(sp010 + 2.0*sp020*t_local + s_local*(sp011 + 2.0*sp021*t_local))
     dks_ds = (s01 + s11*t_local + s21*t2 + s31*t3) + 1.5*s12*(s032 + s132*t_local + s232*t2) + &
              p1*(sp01 + sp11*t_local + sp21*t2 + 1.5*sp032*s12) + &
              p2*(sp001 + sp011*t_local + sp021*t2)
  
     denom = 1.0 / (ks - p1)
     drho_dt(j) = denom*(ks*drho0_dt - rho0*p1*denom*dks_dt)
     drho_ds(j) = denom*(ks*drho0_ds - rho0*p1*denom*dks_ds)
   enddo
  

References r00, r01, r02, r032, r10, r11, r132, r20, r21, r232, r30, r31, r40, r41, r50, s00, s01, s032, s10, s11, s132, s20, s21, s232, s30, s31, s40, sp00, sp000, sp001, sp01, sp010, sp011, sp020, sp021, sp032, sp10, sp11, sp20, sp21, and sp30.

◆ calculate_density_scalar_unesco()

subroutine, public mom_eos_unesco::calculate_density_scalar_unesco	(	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 salinity (S [PSU]), potential temperature (T [degC]), and pressure [Pa], using the UNESCO (1981) equation of state.

Parameters

[in]	t	Potential temperature relative to the surface [degC].
[in]	s	Salinity [PSU].
[in]	pressure	pressure [Pa].
[out]	rho	In situ density [kg m-3].
[in]	rho_ref	A reference density [kg m-3].

Definition at line 60 of file MOM_EOS_UNESCO.F90.

   real,           intent(in)  :: T        !< Potential temperature relative to the surface [degC].
   real,           intent(in)  :: S        !< Salinity [PSU].
   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].
  
   ! Local variables
   real, dimension(1) :: T0, S0, pressure0
   real, dimension(1) :: rho0
  
   t0(1) = t
   s0(1) = s
   pressure0(1) = pressure
  
   call calculate_density_array_unesco(t0, s0, pressure0, rho0, 1, 1, rho_ref)
   rho = rho0(1)
  

References calculate_density_array_unesco().

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◆ calculate_spec_vol_array_unesco()

subroutine mom_eos_unesco::calculate_spec_vol_array_unesco	(	real, dimension(:), intent(in)	T,
		real, dimension(:), intent(in)	S,
		real, dimension(:), intent(in)	pressure,
		real, dimension(:), intent(out)	specvol,
		integer, intent(in)	start,
		integer, intent(in)	npts,
		real, intent(in), optional	spv_ref
	)

private

This subroutine computes the in situ specific volume of sea water (specvol in [m3 kg-1]) from salinity (S [PSU]), potential temperature (T [degC]) and pressure [Pa], using the UNESCO (1981) equation of state. If spv_ref is present, specvol is an anomaly from spv_ref.

Parameters

[in]	t	potential temperature relative to the surface [degC].
[in]	s	salinity [PSU].
[in]	pressure	pressure [Pa].
[out]	specvol	in situ specific volume [m3 kg-1].
[in]	start	the starting point in the arrays.
[in]	npts	the number of values to calculate.
[in]	spv_ref	A reference specific volume [m3 kg-1].

Definition at line 159 of file MOM_EOS_UNESCO.F90.

   real, dimension(:), intent(in)  :: T        !< potential temperature relative to the surface
                                               !! [degC].
   real, dimension(:), intent(in)  :: S        !< salinity [PSU].
   real, dimension(:), intent(in)  :: pressure !< pressure [Pa].
   real, dimension(:), intent(out) :: specvol  !< in situ specific volume [m3 kg-1].
   integer,            intent(in)  :: start    !< the starting point in the arrays.
   integer,            intent(in)  :: npts     !< the number of values to calculate.
   real,     optional, intent(in)  :: spv_ref  !< A reference specific volume [m3 kg-1].
  
   ! Local variables
   real :: t_local, t2, t3, t4, t5  ! Temperature to the 1st - 5th power [degC^n].
   real :: s_local, s32, s2         ! Salinity to the 1st, 3/2, & 2nd power [PSU^n].
   real :: p1, p2       ! Pressure (in bars) to the 1st and 2nd power [bar] and [bar2].
   real :: rho0         ! Density at 1 bar pressure [kg m-3].
   real :: ks           ! The secant bulk modulus [bar].
   integer :: j
  
   do j=start,start+npts-1
     if (s(j) < -1.0e-10) then !Can we assume safely that this is a missing value?
       specvol(j) = 0.001
       if (present(spv_ref)) specvol(j) = 0.001 - spv_ref
       cycle
     endif
  
     p1 = pressure(j)*1.0e-5; p2 = p1*p1
     t_local = t(j); t2 = t_local*t_local; t3 = t_local*t2; t4 = t2*t2; t5 = t3*t2
     s_local = s(j); s2 = s_local*s_local; s32 = s_local*sqrt(s_local)
  
 !  Compute rho(s,theta,p=0) - (same as rho(s,t_insitu,p=0) ).
  
     rho0 = r00 + r10*t_local + r20*t2 + r30*t3 + r40*t4 + r50*t5 + &
            s_local*(r01 + r11*t_local + r21*t2 + r31*t3 + r41*t4) + &
            s32*(r032 + r132*t_local + r232*t2) + r02*s2
  
 !  Compute rho(s,theta,p), first calculating the secant bulk modulus.
  
     ks = s00 + s10*t_local + s20*t2 + s30*t3 + s40*t4 + s_local*(s01 + s11*t_local + s21*t2 + s31*t3) + &
          s32*(s032 + s132*t_local + s232*t2) + &
          p1*(sp00 + sp10*t_local + sp20*t2 + sp30*t3 + &
              s_local*(sp01 + sp11*t_local + sp21*t2) + sp032*s32) + &
          p2*(sp000 + sp010*t_local + sp020*t2 + s_local*(sp001 + sp011*t_local + sp021*t2))
  
     if (present(spv_ref)) then
       specvol(j) = (ks*(1.0 - (rho0*spv_ref)) - p1) / (rho0*ks)
     else
       specvol(j) = (ks - p1) / (rho0*ks)
     endif
   enddo

References r00, r01, r02, r032, r10, r11, r132, r20, r21, r232, r30, r31, r40, r41, r50, s00, s01, s032, s10, s11, s132, s20, s21, s232, s30, s31, s40, sp00, sp000, sp001, sp01, sp010, sp011, sp020, sp021, sp032, sp10, sp11, sp20, sp21, and sp30.

Referenced by calculate_spec_vol_scalar_unesco().

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◆ calculate_spec_vol_scalar_unesco()

subroutine mom_eos_unesco::calculate_spec_vol_scalar_unesco	(	real, intent(in)	T,
		real, intent(in)	S,
		real, intent(in)	pressure,
		real, intent(out)	specvol,
		real, intent(in), optional	spv_ref
	)

private

This subroutine computes the in situ specific volume of sea water (specvol in [m3 kg-1]) from salinity (S [PSU]), potential temperature (T [degC]) and pressure [Pa], using the UNESCO (1981) equation of state. If spv_ref is present, specvol is an anomaly from spv_ref.

Parameters

[in]	t	potential temperature relative to the surface [degC].
[in]	s	salinity [PSU].
[in]	pressure	pressure [Pa].
[out]	specvol	in situ specific volume [m3 kg-1].
[in]	spv_ref	A reference specific volume [m3 kg-1].

Definition at line 138 of file MOM_EOS_UNESCO.F90.

   real,           intent(in)  :: T        !< potential temperature relative to the surface
                                           !! [degC].
   real,           intent(in)  :: S        !< salinity [PSU].
   real,           intent(in)  :: pressure !< pressure [Pa].
   real,           intent(out) :: specvol  !< in situ specific volume [m3 kg-1].
   real, optional, intent(in)  :: spv_ref  !< A reference specific volume [m3 kg-1].
  
   ! Local variables
   real, dimension(1) :: T0, S0, pressure0, spv0
  
   t0(1) = t ; s0(1) = s ; pressure0(1) = pressure
  
   call calculate_spec_vol_array_unesco(t0, s0, pressure0, spv0, 1, 1, spv_ref)
   specvol = spv0(1)

References calculate_spec_vol_array_unesco().

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Variable Documentation

◆ r00

real, parameter mom_eos_unesco::r00 = 999.842594

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

 real, parameter ::  R00 = 999.842594, r10 = 6.793952e-2, r20 = -9.095290e-3, &
   r30 = 1.001685e-4, r40 = -1.120083e-6, r50 = 6.536332e-9, r01 = 0.824493, &
   r11 = -4.0899e-3, r21 = 7.6438e-5, r31 = -8.2467e-7, r41 = 5.3875e-9, &
   r032 = -5.72466e-3, r132 = 1.0227e-4, r232 = -1.6546e-6, r02 = 4.8314e-4

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r01

real, parameter mom_eos_unesco::r01 = 0.824493

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r02

real, parameter mom_eos_unesco::r02 = 4.8314e-4

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r032

real, parameter mom_eos_unesco::r032 = -5.72466e-3

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r10

real, parameter mom_eos_unesco::r10 = 6.793952e-2

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r11

real, parameter mom_eos_unesco::r11 = -4.0899e-3

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r132

real, parameter mom_eos_unesco::r132 = 1.0227e-4

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r20

real, parameter mom_eos_unesco::r20 = -9.095290e-3

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r21

real, parameter mom_eos_unesco::r21 = 7.6438e-5

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r232

real, parameter mom_eos_unesco::r232 = -1.6546e-6

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r30

real, parameter mom_eos_unesco::r30 = 1.001685e-4

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r31

real, parameter mom_eos_unesco::r31 = -8.2467e-7

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r40

real, parameter mom_eos_unesco::r40 = -1.120083e-6

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r41

real, parameter mom_eos_unesco::r41 = 5.3875e-9

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ r50

real, parameter mom_eos_unesco::r50 = 6.536332e-9

private

Parameters in the UNESCO equation of state.

Definition at line 36 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s00

real, parameter mom_eos_unesco::s00 = 1.965933e4

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

 real, parameter ::  S00 = 1.965933e4, s10 = 1.444304e2, s20 = -1.706103, &
   s30 = 9.648704e-3, s40 = -4.190253e-5, s01 = 52.84855, s11 = -3.101089e-1, &
   s21 = 6.283263e-3, s31 = -5.084188e-5, s032 = 3.886640e-1, s132 = 9.085835e-3, &
   s232 = -4.619924e-4, sp00 = 3.186519, sp10 = 2.212276e-2, sp20 = -2.984642e-4, &
   sp30 = 1.956415e-6, sp01 = 6.704388e-3, sp11 = -1.847318e-4, sp21 = 2.059331e-7, &
   sp032 = 1.480266e-4, sp000 = 2.102898e-4, sp010 = -1.202016e-5, sp020 = 1.394680e-7, &
   sp001 = -2.040237e-6, sp011 = 6.128773e-8, sp021 = 6.207323e-10

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s01

real, parameter mom_eos_unesco::s01 = 52.84855

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s032

real, parameter mom_eos_unesco::s032 = 3.886640e-1

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s10

real, parameter mom_eos_unesco::s10 = 1.444304e2

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s11

real, parameter mom_eos_unesco::s11 = -3.101089e-1

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s132

real, parameter mom_eos_unesco::s132 = 9.085835e-3

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s20

real, parameter mom_eos_unesco::s20 = -1.706103

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s21

real, parameter mom_eos_unesco::s21 = 6.283263e-3

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s232

real, parameter mom_eos_unesco::s232 = -4.619924e-4

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s30

real, parameter mom_eos_unesco::s30 = 9.648704e-3

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s31

real, parameter mom_eos_unesco::s31 = -5.084188e-5

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ s40

real, parameter mom_eos_unesco::s40 = -4.190253e-5

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp00

real, parameter mom_eos_unesco::sp00 = 3.186519

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp000

real, parameter mom_eos_unesco::sp000 = 2.102898e-4

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp001

real, parameter mom_eos_unesco::sp001 = -2.040237e-6

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp01

real, parameter mom_eos_unesco::sp01 = 6.704388e-3

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp010

real, parameter mom_eos_unesco::sp010 = -1.202016e-5

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp011

real, parameter mom_eos_unesco::sp011 = 6.128773e-8

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp020

real, parameter mom_eos_unesco::sp020 = 1.394680e-7

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp021

real, parameter mom_eos_unesco::sp021 = 6.207323e-10

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp032

real, parameter mom_eos_unesco::sp032 = 1.480266e-4

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp10

real, parameter mom_eos_unesco::sp10 = 2.212276e-2

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp11

real, parameter mom_eos_unesco::sp11 = -1.847318e-4

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp20

real, parameter mom_eos_unesco::sp20 = -2.984642e-4

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp21

real, parameter mom_eos_unesco::sp21 = 2.059331e-7

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

◆ sp30

real, parameter mom_eos_unesco::sp30 = 1.956415e-6

private

Parameters in the UNESCO equation of state.

Definition at line 45 of file MOM_EOS_UNESCO.F90.

Referenced by calculate_compress_unesco(), calculate_density_array_unesco(), calculate_density_derivs_unesco(), and calculate_spec_vol_array_unesco().

Detailed Description

Data Types

Function/Subroutine Documentation

◆ calculate_compress_unesco()

◆ calculate_density_array_unesco()

◆ calculate_density_derivs_unesco()

◆ calculate_density_scalar_unesco()

◆ calculate_spec_vol_array_unesco()

◆ calculate_spec_vol_scalar_unesco()

Variable Documentation

◆ r00

◆ r01

◆ r02

◆ r032

◆ r10

◆ r11

◆ r132

◆ r20

◆ r21

◆ r232

◆ r30

◆ r31

◆ r40

◆ r41

◆ r50

◆ s00

◆ s01

◆ s032

◆ s10

◆ s11

◆ s132

◆ s20

◆ s21

◆ s232

◆ s30

◆ s31

◆ s40

◆ sp00

◆ sp000

◆ sp001

◆ sp01

◆ sp010

◆ sp011

◆ sp020

◆ sp021

◆ sp032

◆ sp10

◆ sp11

◆ sp20

◆ sp21

◆ sp30