diff --git a/src/equation_of_state/MOM_EOS_Wright.F90 b/src/equation_of_state/MOM_EOS_Wright.F90 index 90bb631991..36180d14e8 100644 --- a/src/equation_of_state/MOM_EOS_Wright.F90 +++ b/src/equation_of_state/MOM_EOS_Wright.F90 @@ -3,12 +3,6 @@ module MOM_EOS_Wright ! This file is part of MOM6. See LICENSE.md for the license. -!*********************************************************************** -!* The subroutines in this file implement the equation of state for * -!* sea water using the formulae given by Wright, 1997, J. Atmos. * -!* Ocean. Tech., 14, 735-740. Coded by R. Hallberg, 7/00. * -!*********************************************************************** - use MOM_hor_index, only : hor_index_type implicit none ; private @@ -20,16 +14,10 @@ module MOM_EOS_Wright public calculate_density_second_derivs_wright public int_density_dz_wright, int_spec_vol_dp_wright -! A note on unit descriptions in comments: MOM6 uses units that can be rescaled for dimensional -! consistency testing. These are noted in comments with units like Z, H, L, and T, along with -! their mks counterparts with notation like "a velocity [Z T-1 ~> m s-1]". If the units -! vary with the Boussinesq approximation, the Boussinesq variant is given first. - - !> Compute the in situ density of sea water (in [kg m-3]), or its anomaly with respect to !! a reference density, from salinity in practical salinity units ([PSU]), potential !! temperature (in degrees Celsius [degC]), and pressure [Pa], using the expressions from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the reduced range fit coefficients. interface calculate_density_wright module procedure calculate_density_scalar_wright, calculate_density_array_wright end interface calculate_density_wright @@ -37,23 +25,23 @@ module MOM_EOS_Wright !> 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 in practical salinity units ([PSU]), potential !! temperature (in degrees Celsius [degC]), and pressure [Pa], using the expressions from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the reduced range fit coefficients. interface calculate_spec_vol_wright module procedure calculate_spec_vol_scalar_wright, calculate_spec_vol_array_wright end interface calculate_spec_vol_wright -!> For a given thermodynamic state, return the derivatives of density with temperature and salinity +!> Compute the derivatives of density with temperature and salinity interface calculate_density_derivs_wright module procedure calculate_density_derivs_scalar_wright, calculate_density_derivs_array_wright end interface calculate_density_derivs_wright -!> For a given thermodynamic state, return the second derivatives of density with various combinations +!> Compute the second derivatives of density with various combinations !! of temperature, salinity, and pressure interface calculate_density_second_derivs_wright module procedure calculate_density_second_derivs_scalar_wright, calculate_density_second_derivs_array_wright end interface calculate_density_second_derivs_wright -!>@{ Parameters in the Wright equation of state using the restricted range formula, which is a fit to the UNESCO +!>@{ Parameters in the Wright equation of state using the reduced range formula, which is a fit to the UNESCO ! equation of state for the restricted range: -2 < theta < 30 [degC], 28 < S < 38 [PSU], 0 < p < 5e7 [Pa]. ! Note that a0/a1 ~= 2028 [degC] ; a0/a2 ~= -6343 [PSU] @@ -78,10 +66,11 @@ module MOM_EOS_Wright contains -!> 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]. It uses the expression from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!> Computes the in situ density of sea water for scalar inputs and outputs. +!! +!! Returns the in situ density of sea water (rho in [kg m-3]) from salinity (S [PSU]), +!! potential temperature (T [degC]), and pressure [Pa]. It uses the expression from +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the reduced range fit coefficients. subroutine calculate_density_scalar_wright(T, S, pressure, rho, rho_ref) real, intent(in) :: T !< Potential temperature relative to the surface [degC]. real, intent(in) :: S !< Salinity [PSU]. @@ -89,14 +78,7 @@ subroutine calculate_density_scalar_wright(T, S, pressure, rho, rho_ref) real, intent(out) :: rho !< In situ density [kg m-3]. real, optional, intent(in) :: rho_ref !< A reference density [kg m-3]. -! *====================================================================* -! * 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]. It uses the expression from * -! * Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. * -! * Coded by R. Hallberg, 7/00 * -! *====================================================================* - + ! Local variables real, dimension(1) :: T0 ! A 1-d array with a copy of the potential temperature [degC] real, dimension(1) :: S0 ! A 1-d array with a copy of the salinity [PSU] real, dimension(1) :: pressure0 ! A 1-d array with a copy of the pressure [Pa] @@ -111,10 +93,11 @@ subroutine calculate_density_scalar_wright(T, S, pressure, rho, rho_ref) end subroutine calculate_density_scalar_wright -!> 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]. It uses the expression from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!> Computes the in situ density of sea water for 1-d array inputs and outputs. +!! +!! Returns the in situ density of sea water (rho in [kg m-3]) from salinity (S [PSU]), +!! potential temperature (T [degC]), and pressure [Pa]. It uses the expression from +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the reduced range fit coefficients. subroutine calculate_density_array_wright(T, S, pressure, rho, start, npts, rho_ref) real, dimension(:), intent(in) :: T !< potential temperature relative to the surface [degC]. real, dimension(:), intent(in) :: S !< salinity [PSU]. @@ -124,7 +107,6 @@ subroutine calculate_density_array_wright(T, S, pressure, rho, start, npts, rho_ integer, intent(in) :: npts !< the number of values to calculate. real, optional, intent(in) :: rho_ref !< A reference density [kg m-3]. - ! Original coded by R. Hallberg, 7/00, anomaly coded in 3/18. ! Local variables real :: al0 ! The specific volume at 0 lambda in the Wright EOS [m3 kg-1] real :: p0 ! The pressure offset in the Wright EOS [Pa] @@ -155,10 +137,11 @@ subroutine calculate_density_array_wright(T, S, pressure, rho, start, npts, rho_ end subroutine calculate_density_array_wright -!> 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]. It uses the expression from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!> Computes the Wright in situ specific volume of sea water for scalar inputs and outputs. +!! +!! Returns the in situ specific volume of sea water (specvol in [m3 kg-1]) from salinity (S [PSU]), +!! potential temperature (T [degC]) and pressure [Pa]. It uses the expression from +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the reduced range fit coefficients. !! If spv_ref is present, specvol is an anomaly from spv_ref. subroutine calculate_spec_vol_scalar_wright(T, S, pressure, specvol, spv_ref) real, intent(in) :: T !< potential temperature relative to the surface [degC]. @@ -179,10 +162,11 @@ subroutine calculate_spec_vol_scalar_wright(T, S, pressure, specvol, spv_ref) specvol = spv0(1) end subroutine calculate_spec_vol_scalar_wright -!> 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]. It uses the expression from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!> Computes the Wright in situ specific volume of sea water for 1-d array inputs and outputs. +!! +!! Returns the in situ specific volume of sea water (specvol in [m3 kg-1]) from salinity (S [PSU]), +!! potential temperature (T [degC]) and pressure [Pa]. It uses the expression from +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the reduced range fit coefficients. !! If spv_ref is present, specvol is an anomaly from spv_ref. subroutine calculate_spec_vol_array_wright(T, S, pressure, specvol, start, npts, spv_ref) real, dimension(:), intent(in) :: T !< potential temperature relative to the @@ -213,7 +197,7 @@ subroutine calculate_spec_vol_array_wright(T, S, pressure, specvol, start, npts, enddo end subroutine calculate_spec_vol_array_wright -!> For a given thermodynamic state, return the thermal/haline expansion coefficients +!> Return the thermal/haline expansion coefficients for 1-d array inputs and outputs subroutine calculate_density_derivs_array_wright(T, S, pressure, drho_dT, drho_dS, start, npts) real, intent(in), dimension(:) :: T !< Potential temperature relative to the !! surface [degC]. @@ -250,8 +234,10 @@ subroutine calculate_density_derivs_array_wright(T, S, pressure, drho_dT, drho_d end subroutine calculate_density_derivs_array_wright -!> The scalar version of calculate_density_derivs which promotes scalar inputs to a 1-element array and then -!! demotes the output back to a scalar +!> Return the thermal/haline expansion coefficients for scalar inputs and outputs +!! +!! The scalar version of calculate_density_derivs promotes scalar inputs to 1-element array +!! and then demotes the output back to a scalar subroutine calculate_density_derivs_scalar_wright(T, S, pressure, drho_dT, drho_dS) real, intent(in) :: T !< Potential temperature relative to the surface [degC]. real, intent(in) :: S !< Salinity [PSU]. @@ -277,7 +263,7 @@ subroutine calculate_density_derivs_scalar_wright(T, S, pressure, drho_dT, drho_ end subroutine calculate_density_derivs_scalar_wright -!> Second derivatives of density with respect to temperature, salinity, and pressure +!> Second derivatives of density with respect to temperature, salinity, and pressure for 1-d array inputs and outputs. 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) real, dimension(:), intent(in ) :: T !< Potential temperature referenced to 0 dbar [degC] @@ -337,8 +323,10 @@ subroutine calculate_density_second_derivs_array_wright(T, S, P, drho_ds_ds, drh end subroutine calculate_density_second_derivs_array_wright -!> 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 +!> Second derivatives of density with respect to temperature, salinity, and pressure for scalar inputs. +!! +!! The scalar version of calculate_density_second_derivs promotes scalar inputs to 1-element array +!! and then demotes the output back to a scalar 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) real, intent(in ) :: T !< Potential temperature referenced to 0 dbar @@ -379,8 +367,8 @@ subroutine calculate_density_second_derivs_scalar_wright(T, S, P, drho_ds_ds, dr end subroutine calculate_density_second_derivs_scalar_wright -!> For a given thermodynamic state, return the partial derivatives of specific volume -!! with temperature and salinity +!> Return the partial derivatives of specific volume with temperature and salinity +!! for 1-d array inputs and outputs subroutine calculate_specvol_derivs_wright(T, S, pressure, dSV_dT, dSV_dS, start, npts) real, intent(in), dimension(:) :: T !< Potential temperature relative to the surface [degC]. real, intent(in), dimension(:) :: S !< Salinity [PSU]. @@ -414,11 +402,7 @@ subroutine calculate_specvol_derivs_wright(T, S, pressure, dSV_dT, dSV_dS, start end subroutine calculate_specvol_derivs_wright -!> This subroutine computes the in situ density of sea water (rho in [kg m-3]) -!! and the compressibility (drho/dp = C_sound^-2) (drho_dp [s2 m-2]) from -!! salinity (sal [PSU]), potential temperature (T [degC]), and pressure [Pa]. -!! It uses the expressions from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. -!! Coded by R. Hallberg, 1/01 +!> Computes the compressibility of seawater for 1-d array inputs and outputs subroutine calculate_compress_wright(T, S, pressure, rho, drho_dp, start, npts) real, intent(in), dimension(:) :: T !< Potential temperature relative to the surface [degC]. real, intent(in), dimension(:) :: S !< Salinity [PSU]. @@ -430,7 +414,6 @@ subroutine calculate_compress_wright(T, S, pressure, rho, drho_dp, start, npts) integer, intent(in) :: start !< The starting point in the arrays. integer, intent(in) :: npts !< The number of values to calculate. - ! Coded by R. Hallberg, 1/01 ! Local variables real :: al0 ! The specific volume at 0 lambda in the Wright EOS [m3 kg-1] real :: p0 ! The pressure offset in the Wright EOS [Pa] @@ -449,9 +432,11 @@ subroutine calculate_compress_wright(T, S, pressure, rho, drho_dp, start, npts) enddo end subroutine calculate_compress_wright -!> This subroutine calculates analytical and nearly-analytical integrals of -!! pressure anomalies across layers, which are required for calculating the -!! finite-volume form pressure accelerations in a Boussinesq model. +!> Calculates analytical and nearly-analytical integrals, in geopotential across layers, of pressure +!! anomalies, which are required for calculating the finite-volume form pressure accelerations in a +!! Boussinesq model. There are essentially no free assumptions, apart from the use of Boole's rule +!! rule to do the horizontal integrals, and from a truncation in the series for log(1-eps/1+eps) +!! that assumes that |eps| < 0.34. subroutine int_density_dz_wright(T, S, z_t, z_b, rho_ref, rho_0, G_e, HI, & dpa, intz_dpa, intx_dpa, inty_dpa, bathyT, dz_neglect, & useMassWghtInterp, rho_scale, pres_scale, temp_scale, saln_scale, Z_0p) @@ -707,12 +692,11 @@ subroutine int_density_dz_wright(T, S, z_t, z_b, rho_ref, rho_0, G_e, HI, & end subroutine int_density_dz_wright -!> This subroutine calculates analytical and nearly-analytical integrals in -!! pressure across layers of geopotential anomalies, which are required for -!! calculating the finite-volume form pressure accelerations in a non-Boussinesq -!! model. There are essentially no free assumptions, apart from the use of -!! Boole's rule to do the horizontal integrals, and from a truncation in the -!! series for log(1-eps/1+eps) that assumes that |eps| < 0.34. +!> Calculates analytical and nearly-analytical integrals, in pressure across layers, of geopotential +!! anomalies, which are required for calculating the finite-volume form pressure accelerations in a +!! non-Boussinesq model. There are essentially no free assumptions, apart from the use of Boole's +!! rule to do the horizontal integrals, and from a truncation in the series for log(1-eps/1+eps) +!! that assumes that |eps| < 0.34. subroutine int_spec_vol_dp_wright(T, S, p_t, p_b, spv_ref, HI, dza, & intp_dza, intx_dza, inty_dza, halo_size, bathyP, dP_neglect, & useMassWghtInterp, SV_scale, pres_scale, temp_scale, saln_scale) @@ -947,4 +931,24 @@ subroutine int_spec_vol_dp_wright(T, S, p_t, p_b, spv_ref, HI, dza, & enddo ; enddo ; endif end subroutine int_spec_vol_dp_wright +!> \namespace mom_eos_wright +!! +!! \section section_EOS_Wright Wright equation of state +!! +!! Wright, 1997, provide an approximation for the in situ density as a function of +!! potential temperature, salinity, and pressure. The formula follow the Tumlirz +!! equation of state which are easier to evaluate and make efficient. +!! +!! Two ranges are provided by Wright: a "full" range and "reduced" range. The version in this +!! module uses the reduced range. +!! +!! Originally coded in 2000 by R. Hallberg. +!! Anomaly form coded in 3/18. +!! +!! \subsection section_EOS_Wright_references References +!! +!! Wright, D., 1997: An Equation of State for Use in Ocean Models: Eckart's Formula Revisited. +!! J. Ocean. Atmosph. Tech., 14 (3), 735-740. +!! https://journals.ametsoc.org/doi/abs/10.1175/1520-0426%281997%29014%3C0735%3AAEOSFU%3E2.0.CO%3B2 + end module MOM_EOS_Wright diff --git a/src/equation_of_state/MOM_EOS_Wright_full.F90 b/src/equation_of_state/MOM_EOS_Wright_full.F90 index fec38656c0..72aa38faf3 100644 --- a/src/equation_of_state/MOM_EOS_Wright_full.F90 +++ b/src/equation_of_state/MOM_EOS_Wright_full.F90 @@ -3,12 +3,6 @@ module MOM_EOS_Wright_full ! This file is part of MOM6. See LICENSE.md for the license. -!*********************************************************************** -!* The subroutines in this file implement the equation of state for * -!* sea water using the formulae given by Wright, 1997, J. Atmos. * -!* Ocean. Tech., 14, 735-740. Coded by R. Hallberg, 7/00. * -!*********************************************************************** - use MOM_hor_index, only : hor_index_type implicit none ; private @@ -20,16 +14,10 @@ module MOM_EOS_Wright_full public calculate_density_second_derivs_wright_full public int_density_dz_wright_full, int_spec_vol_dp_wright_full -! A note on unit descriptions in comments: MOM6 uses units that can be rescaled for dimensional -! consistency testing. These are noted in comments with units like Z, H, L, and T, along with -! their mks counterparts with notation like "a velocity [Z T-1 ~> m s-1]". If the units -! vary with the Boussinesq approximation, the Boussinesq variant is given first. - - !> Compute the in situ density of sea water (in [kg m-3]), or its anomaly with respect to !! a reference density, from salinity in practical salinity units ([PSU]), potential !! temperature (in degrees Celsius [degC]), and pressure [Pa], using the expressions from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the full range fit coefficients. interface calculate_density_wright_full module procedure calculate_density_scalar_wright, calculate_density_array_wright end interface calculate_density_wright_full @@ -37,7 +25,7 @@ module MOM_EOS_Wright_full !> 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 in practical salinity units ([PSU]), potential !! temperature (in degrees Celsius [degC]), and pressure [Pa], using the expressions from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the full range fit coefficients. interface calculate_spec_vol_wright_full module procedure calculate_spec_vol_scalar_wright, calculate_spec_vol_array_wright end interface calculate_spec_vol_wright_full @@ -78,10 +66,11 @@ module MOM_EOS_Wright_full contains -!> 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]. It uses the expression from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!> Computes the in situ density of sea water for scalar inputs and outputs. +!! +!! Returns the in situ density of sea water (rho in [kg m-3]) from salinity (S [PSU]), +!! potential temperature (T [degC]), and pressure [Pa]. It uses the expression from +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the full range fit coefficients. subroutine calculate_density_scalar_wright(T, S, pressure, rho, rho_ref) real, intent(in) :: T !< Potential temperature relative to the surface [degC]. real, intent(in) :: S !< Salinity [PSU]. @@ -89,14 +78,7 @@ subroutine calculate_density_scalar_wright(T, S, pressure, rho, rho_ref) real, intent(out) :: rho !< In situ density [kg m-3]. real, optional, intent(in) :: rho_ref !< A reference density [kg m-3]. -! *====================================================================* -! * 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]. It uses the expression from * -! * Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. * -! * Coded by R. Hallberg, 7/00 * -! *====================================================================* - + ! Local variables real, dimension(1) :: T0 ! A 1-d array with a copy of the potential temperature [degC] real, dimension(1) :: S0 ! A 1-d array with a copy of the salinity [PSU] real, dimension(1) :: pressure0 ! A 1-d array with a copy of the pressure [Pa] @@ -111,10 +93,11 @@ subroutine calculate_density_scalar_wright(T, S, pressure, rho, rho_ref) end subroutine calculate_density_scalar_wright -!> 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]. It uses the expression from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!> Computes the in situ density of sea water for 1-d array inputs and outputs. +!! +!! Returns the in situ density of sea water (rho in [kg m-3]) from salinity (S [PSU]), +!! potential temperature (T [degC]), and pressure [Pa]. It uses the expression from +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the full range fit coefficients. subroutine calculate_density_array_wright(T, S, pressure, rho, start, npts, rho_ref) real, dimension(:), intent(in) :: T !< potential temperature relative to the surface [degC]. real, dimension(:), intent(in) :: S !< salinity [PSU]. @@ -124,7 +107,6 @@ subroutine calculate_density_array_wright(T, S, pressure, rho, start, npts, rho_ integer, intent(in) :: npts !< the number of values to calculate. real, optional, intent(in) :: rho_ref !< A reference density [kg m-3]. - ! Original coded by R. Hallberg, 7/00, anomaly coded in 3/18. ! Local variables real :: al0 ! The specific volume at 0 lambda in the Wright EOS [m3 kg-1] real :: p0 ! The pressure offset in the Wright EOS [Pa] @@ -155,10 +137,11 @@ subroutine calculate_density_array_wright(T, S, pressure, rho, start, npts, rho_ end subroutine calculate_density_array_wright -!> 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]. It uses the expression from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!> Computes the Wright in situ specific volume of sea water for scalar inputs and outputs. +!! +!! Returns the in situ specific volume of sea water (specvol in [m3 kg-1]) from salinity (S [PSU]), +!! potential temperature (T [degC]) and pressure [Pa]. It uses the expression from +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the full range fit coefficients. !! If spv_ref is present, specvol is an anomaly from spv_ref. subroutine calculate_spec_vol_scalar_wright(T, S, pressure, specvol, spv_ref) real, intent(in) :: T !< potential temperature relative to the surface [degC]. @@ -179,10 +162,11 @@ subroutine calculate_spec_vol_scalar_wright(T, S, pressure, specvol, spv_ref) specvol = spv0(1) end subroutine calculate_spec_vol_scalar_wright -!> 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]. It uses the expression from -!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. +!> Computes the Wright in situ specific volume of sea water for 1-d array inputs and outputs. +!! +!! Returns the in situ specific volume of sea water (specvol in [m3 kg-1]) from salinity (S [PSU]), +!! potential temperature (T [degC]) and pressure [Pa]. It uses the expression from +!! Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740 with the full range fit coefficients. !! If spv_ref is present, specvol is an anomaly from spv_ref. subroutine calculate_spec_vol_array_wright(T, S, pressure, specvol, start, npts, spv_ref) real, dimension(:), intent(in) :: T !< potential temperature relative to the @@ -213,7 +197,7 @@ subroutine calculate_spec_vol_array_wright(T, S, pressure, specvol, start, npts, enddo end subroutine calculate_spec_vol_array_wright -!> For a given thermodynamic state, return the thermal/haline expansion coefficients +!> Return the thermal/haline expansion coefficients for 1-d array inputs and outputs subroutine calculate_density_derivs_array_wright(T, S, pressure, drho_dT, drho_dS, start, npts) real, intent(in), dimension(:) :: T !< Potential temperature relative to the !! surface [degC]. @@ -250,8 +234,10 @@ subroutine calculate_density_derivs_array_wright(T, S, pressure, drho_dT, drho_d end subroutine calculate_density_derivs_array_wright -!> The scalar version of calculate_density_derivs which promotes scalar inputs to a 1-element array and then -!! demotes the output back to a scalar +!> Return the thermal/haline expansion coefficients for scalar inputs and outputs +!! +!! The scalar version of calculate_density_derivs promotes scalar inputs to 1-element array +!! and then demotes the output back to a scalar subroutine calculate_density_derivs_scalar_wright(T, S, pressure, drho_dT, drho_dS) real, intent(in) :: T !< Potential temperature relative to the surface [degC]. real, intent(in) :: S !< Salinity [PSU]. @@ -277,7 +263,7 @@ subroutine calculate_density_derivs_scalar_wright(T, S, pressure, drho_dT, drho_ end subroutine calculate_density_derivs_scalar_wright -!> Second derivatives of density with respect to temperature, salinity, and pressure +!> Second derivatives of density with respect to temperature, salinity, and pressure for 1-d array inputs and outputs. 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) real, dimension(:), intent(in ) :: T !< Potential temperature referenced to 0 dbar [degC] @@ -337,8 +323,10 @@ subroutine calculate_density_second_derivs_array_wright(T, S, P, drho_ds_ds, drh end subroutine calculate_density_second_derivs_array_wright -!> 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 +!> Second derivatives of density with respect to temperature, salinity, and pressure for scalar inputs. +!! +!! The scalar version of calculate_density_second_derivs promotes scalar inputs to 1-element array +!! and then demotes the output back to a scalar 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) real, intent(in ) :: T !< Potential temperature referenced to 0 dbar @@ -379,8 +367,8 @@ subroutine calculate_density_second_derivs_scalar_wright(T, S, P, drho_ds_ds, dr end subroutine calculate_density_second_derivs_scalar_wright -!> For a given thermodynamic state, return the partial derivatives of specific volume -!! with temperature and salinity +!> Return the partial derivatives of specific volume with temperature and salinity +!! for 1-d array inputs and outputs subroutine calculate_specvol_derivs_wright_full(T, S, pressure, dSV_dT, dSV_dS, start, npts) real, intent(in), dimension(:) :: T !< Potential temperature relative to the surface [degC]. real, intent(in), dimension(:) :: S !< Salinity [PSU]. @@ -414,11 +402,7 @@ subroutine calculate_specvol_derivs_wright_full(T, S, pressure, dSV_dT, dSV_dS, end subroutine calculate_specvol_derivs_wright_full -!> This subroutine computes the in situ density of sea water (rho in [kg m-3]) -!! and the compressibility (drho/dp = C_sound^-2) (drho_dp [s2 m-2]) from -!! salinity (sal [PSU]), potential temperature (T [degC]), and pressure [Pa]. -!! It uses the expressions from Wright, 1997, J. Atmos. Ocean. Tech., 14, 735-740. -!! Coded by R. Hallberg, 1/01 +!> Computes the compressibility of seawater for 1-d array inputs and outputs subroutine calculate_compress_wright_full(T, S, pressure, rho, drho_dp, start, npts) real, intent(in), dimension(:) :: T !< Potential temperature relative to the surface [degC]. real, intent(in), dimension(:) :: S !< Salinity [PSU]. @@ -430,7 +414,6 @@ subroutine calculate_compress_wright_full(T, S, pressure, rho, drho_dp, start, n integer, intent(in) :: start !< The starting point in the arrays. integer, intent(in) :: npts !< The number of values to calculate. - ! Coded by R. Hallberg, 1/01 ! Local variables real :: al0 ! The specific volume at 0 lambda in the Wright EOS [m3 kg-1] real :: p0 ! The pressure offset in the Wright EOS [Pa] @@ -449,9 +432,11 @@ subroutine calculate_compress_wright_full(T, S, pressure, rho, drho_dp, start, n enddo end subroutine calculate_compress_wright_full -!> This subroutine calculates analytical and nearly-analytical integrals of -!! pressure anomalies across layers, which are required for calculating the -!! finite-volume form pressure accelerations in a Boussinesq model. +!> Calculates analytical and nearly-analytical integrals, in geopotential across layers, of pressure +!! anomalies, which are required for calculating the finite-volume form pressure accelerations in a +!! Boussinesq model. There are essentially no free assumptions, apart from the use of Boole's rule +!! rule to do the horizontal integrals, and from a truncation in the series for log(1-eps/1+eps) +!! that assumes that |eps| < 0.34. subroutine int_density_dz_wright_full(T, S, z_t, z_b, rho_ref, rho_0, G_e, HI, & dpa, intz_dpa, intx_dpa, inty_dpa, bathyT, dz_neglect, & useMassWghtInterp, rho_scale, pres_scale, temp_scale, saln_scale, Z_0p) @@ -707,12 +692,11 @@ subroutine int_density_dz_wright_full(T, S, z_t, z_b, rho_ref, rho_0, G_e, HI, & end subroutine int_density_dz_wright_full -!> This subroutine calculates analytical and nearly-analytical integrals in -!! pressure across layers of geopotential anomalies, which are required for -!! calculating the finite-volume form pressure accelerations in a non-Boussinesq -!! model. There are essentially no free assumptions, apart from the use of -!! Boole's rule to do the horizontal integrals, and from a truncation in the -!! series for log(1-eps/1+eps) that assumes that |eps| < 0.34. +!> Calculates analytical and nearly-analytical integrals, in pressure across layers, of geopotential +!! anomalies, which are required for calculating the finite-volume form pressure accelerations in a +!! non-Boussinesq model. There are essentially no free assumptions, apart from the use of Boole's +!! rule to do the horizontal integrals, and from a truncation in the series for log(1-eps/1+eps) +!! that assumes that |eps| < 0.34. subroutine int_spec_vol_dp_wright_full(T, S, p_t, p_b, spv_ref, HI, dza, & intp_dza, intx_dza, inty_dza, halo_size, bathyP, dP_neglect, & useMassWghtInterp, SV_scale, pres_scale, temp_scale, saln_scale) @@ -947,4 +931,24 @@ subroutine int_spec_vol_dp_wright_full(T, S, p_t, p_b, spv_ref, HI, dza, & enddo ; enddo ; endif end subroutine int_spec_vol_dp_wright_full +!> \namespace mom_eos_wright_full +!! +!! \section section_EOS_Wright Wright equation of state +!! +!! Wright, 1997, provide an approximation for the in situ density as a function of +!! potential temperature, salinity, and pressure. The formula follow the Tumlirz +!! equation of state which are easier to evaluate and make efficient. +!! +!! Two ranges are provided by Wright: a "full" range and "reduced" range. The version in this +!! module uses the full range. +!! +!! Originally coded in 2000 by R. Hallberg. +!! Anomaly form coded in 3/18. +!! +!! \subsection section_EOS_Wright_references References +!! +!! Wright, D., 1997: An Equation of State for Use in Ocean Models: Eckart's Formula Revisited. +!! J. Ocean. Atmosph. Tech., 14 (3), 735-740. +!! https://journals.ametsoc.org/doi/abs/10.1175/1520-0426%281997%29014%3C0735%3AAEOSFU%3E2.0.CO%3B2 + end module MOM_EOS_Wright_full