mom_eos_wright_red module reference¶
The equation of state using the Wright 1997 expressions with reduced range of data.
Data Types¶
The EOS_base implementation of the reduced range Wright 1997 equation of state. |
Functions/Subroutines¶
In situ density of sea water using a reduced range fit by Wright, 1997 [kg m-3]. |
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In situ density anomaly of sea water using a reduced range fit by Wright, 1997 [kg m-3]. |
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In situ specific volume of sea water using a reduced range fit by Wright, 1997 [m3 kg-1]. |
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In situ specific volume anomaly of sea water using a reduced range fit by Wright, 1997 [m3 kg-1]. |
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Calculate the partial derivatives of density with potential temperature and salinity using the reduced range equation of state, as fit by Wright, 1997. |
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Second derivatives of density with respect to temperature, salinity, and pressure, using the reduced range equation of state, as fit by Wright, 1997. |
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Calculate the partial derivatives of specific volume with temperature and salinity using the reduced range equation of state, as fit by Wright, 1997. |
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Compute the in situ density of sea water (rho) and the compressibility (drho/dp == C_sound^-2) at the given salinity, potential temperature and pressure using the reduced range equation of state, as fit by Wright, 1997. |
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Calculates analytical and nearly-analytical integrals, in pressure across layers, to determine the layer-average specific volumes. |
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Return the range of temperatures, salinities and pressures for which the reduced-range equation of state from Wright (1997) has been fitted to observations. |
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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. |
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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. |
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Calculate the in-situ density for 1D arraya inputs and outputs. |
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Calculate the in-situ specific volume for 1D array inputs and outputs. |
Detailed Description¶
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.
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
Type Documentation¶
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type
mom_eos_wright_red/
wright_red_eos
¶ The EOS_base implementation of the reduced range Wright 1997 equation of state.
- Type fields:
%
density_elem
[procedure,private] :: Implementation of the in-situ density as an elemental function [kg m-3].%
density_anomaly_elem
[procedure,private] :: Implementation of the in-situ density anomaly as an elemental function [kg m-3].%
spec_vol_elem
[procedure,private] :: Implementation of the in-situ specific volume as an elemental function [m3 kg-1].%
spec_vol_anomaly_elem
[procedure,private] :: Implementation of the in-situ specific volume anomaly as an elemental function [m3 kg-1].%
calculate_density_derivs_elem
[procedure,private] :: Implementation of the calculation of derivatives of density.%
calculate_density_second_derivs_elem
[procedure,private] :: Implementation of the calculation of second derivatives of density.%
calculate_specvol_derivs_elem
[procedure,private] :: Implementation of the calculation of derivatives of specific volume.%
calculate_compress_elem
[procedure,private] :: Implementation of the calculation of compressibility.%
eos_fit_range
[procedure,private] :: Implementation of the range query function.%
calculate_density_array
[procedure,private] :: Local implementation of generic calculate_density_array for efficiency.%
calculate_spec_vol_array
[procedure,private] :: Local implementation of generic calculate_spec_vol_array for efficiency.
Function/Subroutine Documentation¶
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function
mom_eos_wright_red/
density_elem_wright_red
(this, T, S, pressure) [elemental]¶ In situ density of sea water using a reduced range fit by Wright, 1997 [kg m-3].
This is an elemental function that can be applied to any combination of scalar and array inputs.
- Parameters:
this :: [in] This EOS
t :: [in] potential temperature relative to the surface [degC].
s :: [in] salinity [PSU].
pressure :: [in] pressure [Pa].
- Call to:
a0
a1
a2
b0
b1
b2
b3
b4
b5
c0
c1
c2
c3
c4
c5
- Called from:
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function
mom_eos_wright_red/
density_anomaly_elem_wright_red
(this, T, S, pressure, rho_ref) [elemental]¶ In situ density anomaly of sea water using a reduced range fit by Wright, 1997 [kg m-3].
This is an elemental function that can be applied to any combination of scalar and array inputs.
- Parameters:
this :: [in] This EOS
t :: [in] potential temperature relative to the surface [degC].
s :: [in] salinity [PSU].
pressure :: [in] pressure [Pa].
rho_ref :: [in] A reference density [kg m-3].
- Call to:
a0
a1
a2
b0
b1
b2
b3
b4
b5
c0
c1
c2
c3
c4
c5
- Called from:
-
function
mom_eos_wright_red/
spec_vol_elem_wright_red
(this, T, S, pressure) [elemental]¶ In situ specific volume of sea water using a reduced range fit by Wright, 1997 [m3 kg-1].
This is an elemental function that can be applied to any combination of scalar and array inputs.
- Parameters:
this :: [in] This EOS
t :: [in] potential temperature relative to the surface [degC]
s :: [in] salinity [PSU]
pressure :: [in] pressure [Pa]
- Call to:
a0
a1
a2
b0
b1
b2
b3
b4
b5
c0
c1
c2
c3
c4
c5
- Called from:
-
function
mom_eos_wright_red/
spec_vol_anomaly_elem_wright_red
(this, T, S, pressure, spv_ref) [elemental]¶ In situ specific volume anomaly of sea water using a reduced range fit by Wright, 1997 [m3 kg-1].
This is an elemental function that can be applied to any combination of scalar and array inputs.
- Parameters:
this :: [in] This EOS
t :: [in] potential temperature relative to the surface [degC]
s :: [in] salinity [PSU]
pressure :: [in] pressure [Pa]
spv_ref :: [in] A reference specific volume [m3 kg-1]
- Call to:
a0
a1
a2
b0
b1
b2
b3
b4
b5
c0
c1
c2
c3
c4
c5
- Called from:
-
subroutine
mom_eos_wright_red/
calculate_density_derivs_elem_wright_red
(this, T, S, pressure, drho_dT, drho_dS)¶ Calculate the partial derivatives of density with potential temperature and salinity using the reduced range equation of state, as fit by Wright, 1997.
- Parameters:
this :: [in] This EOS
t :: [in] Potential temperature relative to the surface [degC]
s :: [in] Salinity [PSU]
pressure :: [in] Pressure [Pa]
drho_dt :: [out] The partial derivative of density with potential temperature [kg m-3 degC-1]
drho_ds :: [out] The partial derivative of density with salinity, in [kg m-3 PSU-1]
- Call to:
a0
a1
a2
b0
b1
b2
b3
b4
b5
c0
c1
c2
c3
c4
c5
-
subroutine
mom_eos_wright_red/
calculate_density_second_derivs_elem_wright_red
(this, T, S, pressure, 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, using the reduced range equation of state, as fit by Wright, 1997.
- Parameters:
this :: [in] This EOS
t :: [in] Potential temperature referenced to 0 dbar [degC]
s :: [in] Salinity [PSU]
pressure :: [in] Pressure [Pa]
drho_ds_ds :: [inout] Partial derivative of beta with respect to S [kg m-3 PSU-2]
drho_ds_dt :: [inout] Partial derivative of beta with respect to T [kg m-3 PSU-1 degC-1]
drho_dt_dt :: [inout] Partial derivative of alpha with respect to T [kg m-3 degC-2]
drho_ds_dp :: [inout] Partial derivative of beta with respect to pressure [kg m-3 PSU-1 Pa-1] = [s2 m-2 PSU-1]
drho_dt_dp :: [inout] Partial derivative of alpha with respect to pressure [kg m-3 degC-1 Pa-1] = [s2 m-2 degC-1]
- Call to:
a0
a1
a2
b0
b1
b2
b3
b4
b5
c0
c1
c2
c3
c4
c5
-
subroutine
mom_eos_wright_red/
calculate_specvol_derivs_elem_wright_red
(this, T, S, pressure, dSV_dT, dSV_dS)¶ Calculate the partial derivatives of specific volume with temperature and salinity using the reduced range equation of state, as fit by Wright, 1997.
- Parameters:
this :: [in] This EOS
t :: [in] Potential temperature [degC]
s :: [in] Salinity [PSU]
pressure :: [in] Pressure [Pa]
dsv_dt :: [inout] The partial derivative of specific volume with potential temperature [m3 kg-1 degC-1]
dsv_ds :: [inout] The partial derivative of specific volume with salinity [m3 kg-1 PSU-1]
- Call to:
a1
a2
b0
b1
b2
b3
b4
b5
c0
c1
c2
c3
c4
c5
-
subroutine
mom_eos_wright_red/
calculate_compress_elem_wright_red
(this, T, S, pressure, rho, drho_dp)¶ Compute the in situ density of sea water (rho) and the compressibility (drho/dp == C_sound^-2) at the given salinity, potential temperature and pressure using the reduced range equation of state, as fit by Wright, 1997.
- Parameters:
this :: [in] This EOS
t :: [in] Potential temperature relative to the surface [degC]
s :: [in] Salinity [PSU]
pressure :: [in] Pressure [Pa]
rho :: [out] In situ density [kg m-3]
drho_dp :: [out] The partial derivative of density with pressure (also the inverse of the square of sound speed) [s2 m-2].
- Call to:
a0
a1
a2
b0
b1
b2
b3
b4
b5
c0
c1
c2
c3
c4
c5
-
subroutine
mom_eos_wright_red/
avg_spec_vol_wright_red
(T, S, p_t, dp, SpV_avg, start, npts)¶ Calculates analytical and nearly-analytical integrals, in pressure across layers, to determine the layer-average specific volumes. There are essentially no free assumptions, apart from a truncation in the series for log(1-eps/1+eps) that assumes that |eps| < 0.34.
- Parameters:
t :: [in] Potential temperature relative to the surface [degC].
s :: [in] Salinity [PSU].
p_t :: [in] Pressure at the top of the layer [Pa]
dp :: [in] Pressure change in the layer [Pa]
spv_avg :: [inout] The vertical average specific volume in the layer [m3 kg-1]
start :: [in] the starting point in the arrays.
npts :: [in] the number of values to calculate.
- Call to:
a0
a1
a2
b0
b1
b2
b3
b4
b5
c0
c1
c2
c3
c4
c5
-
subroutine
mom_eos_wright_red/
eos_fit_range_wright_red
(this, T_min, T_max, S_min, S_max, p_min, p_max)¶ Return the range of temperatures, salinities and pressures for which the reduced-range equation of state from Wright (1997) has been fitted to observations. Care should be taken when applying this equation of state outside of its fit range.
- Parameters:
this :: [in] This EOS
t_min :: [out] The minimum potential temperature over which this EoS is fitted [degC]
t_max :: [out] The maximum potential temperature over which this EoS is fitted [degC]
s_min :: [out] The minimum practical salinity over which this EoS is fitted [PSU]
s_max :: [out] The maximum practical salinity over which this EoS is fitted [PSU]
p_min :: [out] The minimum pressure over which this EoS is fitted [Pa]
p_max :: [out] The maximum pressure over which this EoS is fitted [Pa]
-
subroutine
mom_eos_wright_red/
int_density_dz_wright_red
(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)¶ 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.
- Parameters:
hi :: [in] The horizontal index type for the arrays.
t :: [in] Potential temperature relative to the surface
s :: [in] Salinity [S ~> PSU].
z_t :: [in] Height at the top of the layer in depth units [Z ~> m].
z_b :: [in] Height at the top of the layer [Z ~> m].
rho_ref :: [in] A mean density [R ~> kg m-3], that is subtracted out to reduce the magnitude of each of the integrals. (The pressure is calculated as p~=-z*rho_0*G_e.)
rho_0 :: [in] Density [R ~> kg m-3], that is used to calculate the pressure (as p~=-z*rho_0*G_e) used in the equation of state.
g_e :: [in] The Earth’s gravitational acceleration [L2 Z-1 T-2 ~> m s-2].
dpa :: [inout] The change in the pressure anomaly across the
intz_dpa :: [inout] The integral through the thickness of the layer
intx_dpa :: [inout] The integral in x of the difference between the
inty_dpa :: [inout] The integral in y of the difference between the
bathyt :: [in] The depth of the bathymetry [Z ~> m].
dz_neglect :: [in] A miniscule thickness change [Z ~> m].
usemasswghtinterp :: [in] If true, uses mass weighting to interpolate T/S for top and bottom integrals.
rho_scale :: [in] A multiplicative factor by which to scale density from kg m-3 to the desired units [R m3 kg-1 ~> 1]
pres_scale :: [in] A multiplicative factor to convert pressure into Pa [Pa T2 R-1 L-2 ~> 1].
temp_scale :: [in] A multiplicative factor by which to scale temperature into degC [degC C-1 ~> 1]
saln_scale :: [in] A multiplicative factor to convert pressure into PSU [PSU S-1 ~> 1].
z_0p :: [in] The height at which the pressure is 0 [Z ~> m]
- Call to:
a0
a1
a2
b0
b1
b2
b3
b4
b5
c0
c1
c2
c3
c4
c5
-
subroutine
mom_eos_wright_red/
int_spec_vol_dp_wright_red
(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)¶ 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.
- Parameters:
hi :: [in] The ocean’s horizontal index type.
t :: [in] Potential temperature relative to the surface
s :: [in] Salinity [S ~> PSU].
p_t :: [in] Pressure at the top of the layer [R L2 T-2 ~> Pa]
p_b :: [in] Pressure at the top of the layer [R L2 T-2 ~> Pa]
spv_ref :: [in] A mean specific volume that is subtracted out to reduce the magnitude of each of the integrals [R-1 ~> m3 kg-1]. The calculation is mathematically identical with different values of spv_ref, but this reduces the effects of roundoff.
dza :: [inout] The change in the geopotential anomaly across
intp_dza :: [inout] The integral in pressure through the layer of
intx_dza :: [inout] The integral in x of the difference between the
inty_dza :: [inout] The integral in y of the difference between the
halo_size :: [in] The width of halo points on which to calculate dza.
bathyp :: [in] The pressure at the bathymetry [R L2 T-2 ~> Pa]
dp_neglect :: [in] A miniscule pressure change with the same units as p_t [R L2 T-2 ~> Pa]
usemasswghtinterp :: [in] If true, uses mass weighting to interpolate T/S for top and bottom integrals.
sv_scale :: [in] A multiplicative factor by which to scale specific volume from m3 kg-1 to the desired units [kg m-3 R-1 ~> 1]
pres_scale :: [in] A multiplicative factor to convert pressure into Pa [Pa T2 R-1 L-2 ~> 1].
temp_scale :: [in] A multiplicative factor by which to scale temperature into degC [degC C-1 ~> 1]
saln_scale :: [in] A multiplicative factor to convert pressure into PSU [PSU S-1 ~> 1].
- Call to:
a0
a1
a2
b0
b1
b2
b3
b4
b5
c0
c1
c2
c3
c4
c5
-
subroutine
mom_eos_wright_red/
calculate_density_array_wright_red
(this, T, S, pressure, rho, start, npts, rho_ref)¶ Calculate the in-situ density for 1D arraya inputs and outputs.
- Parameters:
this :: [in] This EOS
t :: [in] Potential temperature relative to the surface [degC]
s :: [in] Salinity [PSU]
pressure :: [in] Pressure [Pa]
rho :: [out] In situ density [kg m-3]
start :: [in] The starting index for calculations
npts :: [in] The number of values to calculate
rho_ref :: [in] A reference density [kg m-3]
- Call to:
-
subroutine
mom_eos_wright_red/
calculate_spec_vol_array_wright_red
(this, T, S, pressure, specvol, start, npts, spv_ref)¶ Calculate the in-situ specific volume for 1D array inputs and outputs.
- Parameters:
this :: [in] This EOS
t :: [in] Potential temperature relative to the surface [degC]
s :: [in] Salinity [PSU]
pressure :: [in] Pressure [Pa]
specvol :: [out] In situ specific volume [m3 kg-1]
start :: [in] The starting index for calculations
npts :: [in] The number of values to calculate
spv_ref :: [in] A reference specific volume [m3 kg-1]
- Call to: