MOM_TFreeze.F90

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!> Freezing point expressions
module mom_tfreeze
 
! This file is part of MOM6. See LICENSE.md for the license.
 
!********+*********+*********+*********+*********+*********+*********+**
!*  The subroutines in this file determine the potential temperature   *
!* at which sea-water freezes.                                         *
!********+*********+*********+*********+*********+*********+*********+**
use gsw_mod_toolbox, only : gsw_ct_freezing_exact
 
implicit none ; private
 
public calculate_tfreeze_linear, calculate_tfreeze_millero, calculate_tfreeze_teos10
 
!> Compute the freezing point potential temperature [degC] from salinity [ppt] and
!! pressure [Pa] using a simple linear expression, with coefficients passed in as arguments.
interface calculate_tfreeze_linear
  module procedure calculate_tfreeze_linear_scalar, calculate_tfreeze_linear_array
end interface calculate_tfreeze_linear
 
!> Compute the freezing point potential temperature [degC] from salinity [PSU] and
!! pressure [Pa] using the expression from Millero (1978) (and in appendix A of Gill 1982),
!! but with the of the pressure dependence changed from 7.53e-8 to 7.75e-8 to make this an
!! expression for potential temperature (not in situ temperature), using a
!! value that is correct at the freezing point at 35 PSU and 5e6 Pa (500 dbar).
interface calculate_tfreeze_millero
  module procedure calculate_tfreeze_millero_scalar, calculate_tfreeze_millero_array
end interface calculate_tfreeze_millero
 
!> Compute the freezing point conservative temperature [degC] from absolute salinity [g/kg]
!! and pressure [Pa] using the TEOS10 package.
interface calculate_tfreeze_teos10
  module procedure calculate_tfreeze_teos10_scalar, calculate_tfreeze_teos10_array
end interface calculate_tfreeze_teos10
 
contains
 
!>  This subroutine computes the freezing point potential temperature
!!  [degC] from salinity [ppt], and pressure [Pa] using a simple
!!  linear expression, with coefficients passed in as arguments.
subroutine calculate_tfreeze_linear_scalar(S, pres, T_Fr, TFr_S0_P0, &
                                           dTFr_dS, dTFr_dp)
  real,  intent(in)  :: S         !< salinity [ppt].
  real,  intent(in)  :: pres      !< pressure [Pa].
  real,  intent(out) :: T_Fr      !< Freezing point potential temperature [degC].
  real,  intent(in)  :: TFr_S0_P0 !< The freezing point at S=0, p=0 [degC].
  real,  intent(in)  :: dTFr_dS   !< The derivative of freezing point with salinity,
                                  !! [degC ppt-1].
  real,  intent(in)  :: dTFr_dp   !< The derivative of freezing point with pressure,
                                  !! [degC Pa-1].
 
  t_fr = (tfr_s0_p0 + dtfr_ds*s) + dtfr_dp*pres
 
end subroutine calculate_tfreeze_linear_scalar
 
!>  This subroutine computes an array of freezing point potential temperatures
!!  [degC] from salinity [ppt], and pressure [Pa] using a simple
!!  linear expression, with coefficients passed in as arguments.
subroutine calculate_tfreeze_linear_array(S, pres, T_Fr, start, npts, &
                                          TFr_S0_P0, dTFr_dS, dTFr_dp)
  real,  dimension(:), intent(in)  :: S         !< salinity [ppt].
  real,  dimension(:), intent(in)  :: pres      !< pressure [Pa].
  real,  dimension(:), intent(out) :: T_Fr      !< Freezing point potential temperature [degC].
  integer,             intent(in)  :: start     !< the starting point in the arrays.
  integer,             intent(in)  :: npts      !< the number of values to calculate.
  real,                intent(in)  :: TFr_S0_P0 !< The freezing point at S=0, p=0, [degC].
  real,                intent(in)  :: dTFr_dS   !< The derivative of freezing point with salinity,
                                                !! [degC PSU-1].
  real,                intent(in)  :: dTFr_dp   !< The derivative of freezing point with pressure,
                                                !! [degC Pa-1].
  integer :: j
 
  do j=start,start+npts-1
    t_fr(j) = (tfr_s0_p0 + dtfr_ds*s(j)) + dtfr_dp*pres(j)
  enddo
 
end subroutine calculate_tfreeze_linear_array
 
!> This subroutine computes the freezing point potential temperature
!! [degC] from salinity [ppt], and pressure [Pa] using the expression
!! from Millero (1978) (and in appendix A of Gill 1982), but with the of the
!! pressure dependence changed from 7.53e-8 to 7.75e-8 to make this an
!! expression for potential temperature (not in situ temperature), using a
!! value that is correct at the freezing point at 35 PSU and 5e6 Pa (500 dbar).
subroutine calculate_tfreeze_millero_scalar(S, pres, T_Fr)
  real,    intent(in)  :: S    !< Salinity in PSU.
  real,    intent(in)  :: pres !< Pressure [Pa].
  real,    intent(out) :: T_Fr !< Freezing point potential temperature [degC].
 
  ! Local variables
  real, parameter :: cS1 = -0.0575, cs3_2 = 1.710523e-3, cs2 = -2.154996e-4
  real, parameter :: dTFr_dp = -7.75e-8
 
  t_fr = s*(cs1 + (cs3_2 * sqrt(max(s,0.0)) + cs2 * s)) + dtfr_dp*pres
 
end subroutine calculate_tfreeze_millero_scalar
 
!> This subroutine computes the freezing point potential temperature
!! [degC] from salinity [ppt], and pressure [Pa] using the expression
!! from Millero (1978) (and in appendix A of Gill 1982), but with the of the
!! pressure dependence changed from 7.53e-8 to 7.75e-8 to make this an
!! expression for potential temperature (not in situ temperature), using a
!! value that is correct at the freezing point at 35 PSU and 5e6 Pa (500 dbar).
subroutine calculate_tfreeze_millero_array(S, pres, T_Fr, start, npts)
  real,  dimension(:), intent(in)  :: S     !< Salinity [PSU].
  real,  dimension(:), intent(in)  :: pres  !< Pressure [Pa].
  real,  dimension(:), intent(out) :: T_Fr  !< Freezing point potential temperature [degC].
  integer,             intent(in)  :: start !< The starting point in the arrays.
  integer,             intent(in)  :: npts  !< The number of values to calculate.
 
  ! Local variables
  real, parameter :: cS1 = -0.0575, cs3_2 = 1.710523e-3, cs2 = -2.154996e-4
  real, parameter :: dTFr_dp = -7.75e-8
  integer :: j
 
  do j=start,start+npts-1
    t_fr(j) = s(j)*(cs1 + (cs3_2 * sqrt(max(s(j),0.0)) + cs2 * s(j))) + &
              dtfr_dp*pres(j)
  enddo
 
end subroutine calculate_tfreeze_millero_array
 
!> This subroutine computes the freezing point conservative temperature
!! [degC] from absolute salinity [g/kg], and pressure [Pa] using the
!! TEOS10 package.
subroutine calculate_tfreeze_teos10_scalar(S, pres, T_Fr)
  real,    intent(in)  :: S    !< Absolute salinity [g/kg].
  real,    intent(in)  :: pres !< Pressure [Pa].
  real,    intent(out) :: T_Fr !< Freezing point conservative temperature [degC].
 
  ! Local variables
  real, dimension(1) :: S0, pres0
  real, dimension(1) :: tfr0
 
  s0(1) = s
  pres0(1) = pres
 
  call calculate_tfreeze_teos10_array(s0, pres0, tfr0, 1, 1)
  t_fr = tfr0(1)
 
end subroutine calculate_tfreeze_teos10_scalar
 
!> This subroutine computes the freezing point conservative temperature
!! [degC] from absolute salinity [g/kg], and pressure [Pa] using the
!! TEOS10 package.
subroutine calculate_tfreeze_teos10_array(S, pres, T_Fr, start, npts)
  real, dimension(:), intent(in)  :: S     !< absolute salinity [g/kg].
  real, dimension(:), intent(in)  :: pres  !< pressure [Pa].
  real, dimension(:), intent(out) :: T_Fr  !< Freezing point conservative temperature [degC].
  integer,            intent(in)  :: start !< the starting point in the arrays.
  integer,            intent(in)  :: npts  !< the number of values to calculate.
 
  ! Local variables
  real, parameter :: Pa2db  = 1.e-4  ! The conversion factor from Pa to dbar.
  real :: zs,zp
  integer :: j
  ! Assume sea-water contains no dissolved air.
  real, parameter :: saturation_fraction = 0.0
 
  do j=start,start+npts-1
    !Conversions
    zs = s(j)
    zp = pres(j)* pa2db         !Convert pressure from Pascal to decibar
 
    if (s(j) < -1.0e-10) cycle !Can we assume safely that this is a missing value?
    t_fr(j) = gsw_ct_freezing_exact(zs,zp,saturation_fraction)
 enddo
 
end subroutine calculate_tfreeze_teos10_array
 
end module mom_tfreeze