TEOS-10 Seawater Properties Calculator
Calculate seawater thermodynamic properties using TEOS-10 including density thermal expansion haline contraction and sound speed.
TEOS-10 Seawater Properties Calculator
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Formula: rho(SA,CT,p) = rho_0 + rho_T(CT) + rho_S(SA,CT) + rho_P(p,CT,SA)
Worked example — Density: 1028.761 kg/m3 | Sigma-0: 28.761 | Sound speed: 1478.5 m/s
Formula
rho(SA,CT,p) = rho_0 + rho_T(CT) + rho_S(SA,CT) + rho_P(p,CT,SA)
Where rho is density, SA is Absolute Salinity, CT is Conservative Temperature, p is sea pressure, with terms for pure water temperature salinity and pressure contributions.
Worked Examples
Example 1: Subtropical Mode Water
Problem:Conservative Temperature 18 C, Absolute Salinity 36.5 g/kg, sea pressure 200 dbar. Find the in-situ density, the potential density anomaly sigma-0 and the sound speed.
Solution:Reference density rho_0 = 999.843 kg/m3 Temperature term rho_T = 1.368 kg/m3 (warm water is less dense, but the polynomial is referenced to 0 C) Salinity term rho_S = 27.550 kg/m3, the dominant contribution at 36.5 g/kg Pressure term rho_P = 0.000 kg/m3 at only 200 dbar Density = 999.843 + 1.368 + 27.550 + 0.000 = 1028.761 kg/m3 Sigma-0 = (999.843 + 1.368 + 27.550) - 1000 = 28.761 kg/m3 Sound speed = 1402.388 + 5.0383(18) - 0.058109(18^2) + 3.3432e-4(18^3) + 1.3298(36.5 - 35) + 0.0158(20) = 1478.5 m/s
Result:Density: 1028.761 kg/m3 | Sigma-0: 28.761 | Sound speed: 1478.5 m/s
Example 2: Antarctic Bottom Water
Problem:Conservative Temperature -0.5 C, Absolute Salinity 34.65 g/kg, sea pressure 4000 dbar. Find the density and sigma-0 for this cold, dense water mass.
Solution:rho_T = 0.033 kg/m3, essentially zero because the polynomial is referenced near this temperature rho_S = 27.933 kg/m3 rho_P = 0.003 kg/m3 Density = 999.843 + 0.033 + 27.933 + 0.003 = 1027.811 kg/m3 Sigma-0 = (999.843 + 0.033 + 27.933) - 1000 = 27.809 kg/m3 A sigma-0 near 27.8 is the standard signature used to identify Antarctic Bottom Water on a temperature-salinity diagram. Note that this simplified polynomial carries only a linear pressure term, so it does not reproduce the true in-situ compression of about 20 kg/m3 at 4000 dbar; use it for sigma-0 comparisons rather than for absolute deep-ocean density.
Result:Density: 1027.811 kg/m3 | Sigma-0: 27.809 | Sound speed: 1405.7 m/s
Frequently Asked Questions
What is TEOS-10 and how does it differ from EOS-80?
TEOS-10 is the current international standard for calculating seawater thermodynamic properties adopted in 2010 to replace EOS-80. The key difference is TEOS-10 uses Absolute Salinity (mass fraction in g/kg) instead of Practical Salinity (conductivity ratio) accounting for geographic variation in seawater composition. It introduces Conservative Temperature proportional to potential enthalpy which is more accurately conserved during mixing. The framework derives from a Gibbs function ensuring thermodynamic consistency among all properties. TEOS-10 improves density accuracy by about 0.01 kg/m3 in regions with anomalous composition.
What is Conservative Temperature?
Conservative Temperature is proportional to potential enthalpy of seawater making it more accurately conserved during turbulent mixing than potential temperature. When water parcels with different properties mix the resulting temperature is not simply the weighted average of potential temperatures due to nonlinear heat capacity dependence. Conservative Temperature corrects for this non-conservation which can amount to 1 degree in extreme cases. It is calculated from in-situ temperature and Absolute Salinity using GSW Toolbox algorithms. For most applications it differs from potential temperature by less than 0.05 degrees.
What is Absolute Salinity?
Absolute Salinity represents the mass fraction of dissolved material in seawater expressed in g/kg providing a more physically meaningful measure than conductivity-based Practical Salinity. It is calculated by adding a geographically varying salinity anomaly to Reference Salinity derived from Practical Salinity. The anomaly accounts for dissolved substances like silicate nitrate and alkalinity that affect density but not conductivity. It varies from near zero in the surface Atlantic to about 0.025 g/kg in deep North Pacific. Using Absolute Salinity removes systematic density bias that affected EOS-80.
What are thermal expansion and haline contraction coefficients?
The thermal expansion coefficient alpha measures how specific volume increases per unit temperature increase at constant salinity and pressure defined as alpha = -(1/rho)*(drho/dCT). Typical values range from 0.5e-4 per degree in cold water to 3e-4 per degree in warm surface waters. The haline contraction coefficient beta measures density increase per unit salinity increase defined as beta = (1/rho)*(drho/dSA) relatively constant at about 7.5e-4 per g/kg. The ratio alpha/beta determines relative importance of temperature versus salinity in controlling density stratification.
What is the Gibbs function approach?
TEOS-10 is based on a single thermodynamic potential called the Gibbs function from which all properties are derived through partial derivatives. Density comes from the pressure derivative entropy from the temperature derivative and chemical potential from the salinity derivative ensuring thermodynamic consistency. This means heat capacity compressibility sound speed and adiabatic lapse rate all derive from the same underlying function. The Gibbs function contains about 168 polynomial coefficients representing decades of careful laboratory measurements of seawater properties.
How does pressure affect seawater density?
Pressure increases density by compressing the water with compressibility described by the isothermal compressibility coefficient from the Gibbs function. At the deepest ocean parts about 11000 meters pressure increases in-situ density by roughly 50 kg/m3 compared to surface values. Compressibility is nonlinear depending on temperature salinity and pressure itself leading to thermobaric instability where cold water can become denser than warm water at high pressure. TEOS-10 accounts for these nonlinear effects through the full Gibbs function representation.
What is cabbeling?
Cabbeling is a process where mixing two water masses of equal density but different temperature and salinity produces a denser mixture than either parent. This occurs because the equation of state is nonlinear meaning mixture density is not simply the average. The cabbeling coefficient depends primarily on the thermal expansion coefficient and its temperature dependence. It is most significant when warm salty water mixes with cold fresh water along frontal zones potentially driving vertical convection. TEOS-10 properly accounts for this through Conservative Temperature which minimizes mixing errors.
How does TEOS-10 handle sound speed?
Sound speed is derived from the Gibbs function through c^2 = (dp/drho) at constant entropy involving second derivatives with respect to pressure and temperature. This ensures consistency with density and other properties. Sound speed typically ranges from 1450 m/s in cold surface waters to 1550 m/s in warm tropical layers increasing with temperature salinity and pressure. The minimum at 800-1200 meters forms the SOFAR channel. TEOS-10 calculations agree with direct measurements to within about 0.05 m/s sufficient for most acoustic applications.
What is the GSW Oceanographic Toolbox?
The GSW Toolbox is the official software library implementing TEOS-10 algorithms available in MATLAB Python C Fortran and R. It contains functions for converting between temperature and salinity variables computing density and derivatives calculating sound speed and determining stability parameters. It includes the global atlas of salinity anomaly values for computing Absolute Salinity from Practical Salinity. The toolbox is maintained by an international working group and regularly updated. All major ocean data centers have adopted or are transitioning to GSW for seawater property calculations.
How accurate is the TEOS-10 equation of state?
TEOS-10 calculates density with accuracy of approximately 0.004 kg/m3 over the full oceanographic range of temperature salinity and pressure. This accuracy is limited primarily by laboratory measurement precision particularly at high pressures. Using Absolute Salinity eliminates a systematic error of up to 0.02 kg/m3 that affected EOS-80 in regions with anomalous composition. For relative density differences most important for stratification the precision is about 0.001 kg/m3. Ongoing laboratory work continues to refine high-pressure coefficients and extend the valid range.
References
Background & Theory
History
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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