mom_eos_wright::calculate_density_second_derivs_wright Interface Reference

Detailed Description

For a given thermodynamic state, return the second derivatives of density with various combinations of temperature, salinity, and pressure.

Definition at line 50 of file MOM_EOS_Wright.F90.

Private functions
subroutine	calculate_density_second_derivs_scalar_wright (T, S, P, drho_ds_ds, drho_ds_dt, drho_dt_dt, drho_ds_dp, drho_dt_dp)
	Second derivatives of density with respect to temperature, salinity, and pressure for scalar inputs. Inputs promoted to 1-element array and output demoted to scalar. More...
subroutine	calculate_density_second_derivs_array_wright (T, S, P, drho_ds_ds, drho_ds_dt, drho_dt_dt, drho_ds_dp, drho_dt_dp, start, npts)
	Second derivatives of density with respect to temperature, salinity, and pressure. More...

Functions and subroutines

calculate_density_second_derivs_array_wright()

subroutine mom_eos_wright::calculate_density_second_derivs_wright::calculate_density_second_derivs_array_wright ( real, dimension(:), intent(in)  T, real, dimension(:), intent(in)  S, real, dimension(:), intent(in)  P, real, dimension(:), intent(out)  drho_ds_ds, real, dimension(:), intent(out)  drho_ds_dt, real, dimension(:), intent(out)  drho_dt_dt, real, dimension(:), intent(out)  drho_ds_dp, real, dimension(:), intent(out)  drho_dt_dp, integer, intent(in)  start, integer, intent(in)  npts  )

private

Second derivatives of density with respect to temperature, salinity, and pressure.

Parameters

[in]	t	Potential temperature referenced to 0 dbar [degC]
[in]	s	Salinity [PSU]
[in]	p	Pressure [Pa]
[out]	drho_ds_ds	Partial derivative of beta with respect to S [kg m-3 PSU-2]
[out]	drho_ds_dt	Partial derivative of beta with respcct to T [kg m-3 PSU-1 degC-1]
[out]	drho_dt_dt	Partial derivative of alpha with respect to T [kg m-3 degC-2]
[out]	drho_ds_dp	Partial derivative of beta with respect to pressure [kg m-3 PSU-1 Pa-1]
[out]	drho_dt_dp	Partial derivative of alpha with respect to pressure [kg m-3 degC-1 Pa-1]
[in]	start	Starting index in T,S,P
[in]	npts	Number of points to loop over

Definition at line 259 of file MOM_EOS_Wright.F90.

  real, dimension(:), intent(in   ) :: T !< Potential temperature referenced to 0 dbar [degC]
  real, dimension(:), intent(in   ) :: S !< Salinity [PSU]
  real, dimension(:), intent(in   ) :: P !< Pressure [Pa]
  real, dimension(:), intent(  out) :: drho_ds_ds !< Partial derivative of beta with respect
                                                  !! to S [kg m-3 PSU-2]
  real, dimension(:), intent(  out) :: drho_ds_dt !< Partial derivative of beta with respcct
                                                  !! to T [kg m-3 PSU-1 degC-1]
  real, dimension(:), intent(  out) :: drho_dt_dt !< Partial derivative of alpha with respect
                                                  !! to T [kg m-3 degC-2]
  real, dimension(:), intent(  out) :: drho_ds_dp !< Partial derivative of beta with respect
                                                  !! to pressure [kg m-3 PSU-1 Pa-1]
  real, dimension(:), intent(  out) :: drho_dt_dp !< Partial derivative of alpha with respect
                                                  !! to pressure [kg m-3 degC-1 Pa-1]
  integer,            intent(in   ) :: start !< Starting index in T,S,P
  integer,            intent(in   ) :: npts  !< Number of points to loop over
 
  ! Local variables
  real :: z0, z1, z2, z3, z4, z5, z6 ,z7, z8, z9, z10, z11, z2_2, z2_3
  integer :: j
  ! Based on the above expression with common terms factored, there probably exists a more numerically stable
  ! and/or efficient expression
 
  do j = start,start+npts-1
    z0 = t(j)*(b1 + b5*s(j) + t(j)*(b2 + b3*t(j)))
    z1 = (b0 + p(j) + b4*s(j) + z0)
    z3 = (b1 + b5*s(j) + t(j)*(2.*b2 + 2.*b3*t(j)))
    z4 = (c0 + c4*s(j) + t(j)*(c1 + c5*s(j) + t(j)*(c2 + c3*t(j))))
    z5 = (b1 + b5*s(j) + t(j)*(b2 + b3*t(j)) + t(j)*(b2 + 2.*b3*t(j)))
    z6 = c1 + c5*s(j) + t(j)*(c2 + c3*t(j)) + t(j)*(c2 + 2.*c3*t(j))
    z7 = (c4 + c5*t(j) + a2*z1)
    z8 = (c1 + c5*s(j) + t(j)*(2.*c2 + 3.*c3*t(j)) + a1*z1)
    z9 = (a0 + a2*s(j) + a1*t(j))
    z10 = (b4 + b5*t(j))
    z11 = (z10*z4 - z1*z7)
    z2 = (c0 + c4*s(j) + t(j)*(c1 + c5*s(j) + t(j)*(c2 + c3*t(j))) + z9*z1)
    z2_2 = z2*z2
    z2_3 = z2_2*z2
 
    drho_ds_ds(j) = (z10*(c4 + c5*t(j)) - a2*z10*z1 - z10*z7)/z2_2 - (2.*(c4 + c5*t(j) + z9*z10 + a2*z1)*z11)/z2_3
    drho_ds_dt(j) = (z10*z6 - z1*(c5 + a2*z5) + b5*z4 - z5*z7)/z2_2 - (2.*(z6 + z9*z5 + a1*z1)*z11)/z2_3
    drho_dt_dt(j) = (z3*z6 - z1*(2.*c2 + 6.*c3*t(j) + a1*z5) + (2.*b2 + 4.*b3*t(j))*z4 - z5*z8)/z2_2 - &
                    (2.*(z6 + z9*z5 + a1*z1)*(z3*z4 - z1*z8))/z2_3
    drho_ds_dp(j) = (-c4 - c5*t(j) - 2.*a2*z1)/z2_2 - (2.*z9*z11)/z2_3
    drho_dt_dp(j) = (-c1 - c5*s(j) - t(j)*(2.*c2 + 3.*c3*t(j)) - 2.*a1*z1)/z2_2 - (2.*z9*(z3*z4 - z1*z8))/z2_3
  enddo
 

calculate_density_second_derivs_scalar_wright()

subroutine mom_eos_wright::calculate_density_second_derivs_wright::calculate_density_second_derivs_scalar_wright ( real, intent(in)  T, real, intent(in)  S, real, intent(in)  P, real, intent(out)  drho_ds_ds, real, intent(out)  drho_ds_dt, real, intent(out)  drho_dt_dt, real, intent(out)  drho_ds_dp, real, intent(out)  drho_dt_dp  )

private

Second derivatives of density with respect to temperature, salinity, and pressure for scalar inputs. Inputs promoted to 1-element array and output demoted to scalar.

Parameters

[in]	t	Potential temperature referenced to 0 dbar
[in]	s	Salinity [PSU]
[in]	p	pressure [Pa]
[out]	drho_ds_ds	Partial derivative of beta with respect to S [kg m-3 PSU-2]
[out]	drho_ds_dt	Partial derivative of beta with respcct to T [kg m-3 PSU-1 degC-1]
[out]	drho_dt_dt	Partial derivative of alpha with respect to T [kg m-3 degC-2]
[out]	drho_ds_dp	Partial derivative of beta with respect to pressure [kg m-3 PSU-1 Pa-1]
[out]	drho_dt_dp	Partial derivative of alpha with respect to pressure [kg m-3 degC-1 Pa-1]

Definition at line 311 of file MOM_EOS_Wright.F90.

  real, intent(in   ) :: T          !< Potential temperature referenced to 0 dbar
  real, intent(in   ) :: S          !< Salinity [PSU]
  real, intent(in   ) :: P          !< pressure [Pa]
  real, intent(  out) :: drho_ds_ds !< Partial derivative of beta with respect
                                    !! to S [kg m-3 PSU-2]
  real, intent(  out) :: drho_ds_dt !< Partial derivative of beta with respcct
                                    !! to T [kg m-3 PSU-1 degC-1]
  real, intent(  out) :: drho_dt_dt !< Partial derivative of alpha with respect
                                    !! to T [kg m-3 degC-2]
  real, intent(  out) :: drho_ds_dp !< Partial derivative of beta with respect
                                    !! to pressure [kg m-3 PSU-1 Pa-1]
  real, intent(  out) :: drho_dt_dp !< Partial derivative of alpha with respect
                                    !! to pressure [kg m-3 degC-1 Pa-1]
  ! Local variables
  real, dimension(1) :: T0, S0, P0
  real, dimension(1) :: drdsds, drdsdt, drdtdt, drdsdp, drdtdp
 
  t0(1) = t
  s0(1) = s
  p0(1) = p
  call calculate_density_second_derivs_array_wright(t0, s0, p0, drdsds, drdsdt, drdtdt, drdsdp, drdtdp, 1, 1)
  drho_ds_ds = drdsds(1)
  drho_ds_dt = drdsdt(1)
  drho_dt_dt = drdtdt(1)
  drho_ds_dp = drdsdp(1)
  drho_dt_dp = drdtdp(1)
 

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The documentation for this interface was generated from the following file:

• /glade/work/altuntas/cesm.sandboxes/cesm2_2_alpha_X_mom/components/mom/MOM6/src/equation_of_state/MOM_EOS_Wright.F90