Seawater Equation of State Teos 10 Calculator
Compute seawater equation state teos 10 using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
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 18C Absolute Salinity 36.5 g/kg at 200 dbar.
Solution: rho_T = 1.394, rho_S = 27.247\nDensity = 999.843 + 1.394 + 27.247 = 1025.79 kg/m3\nSigma-0 = 25.79
Result: Density: 1025.79 kg/m3 | Sigma-0: 25.79 | Sound: 1523 m/s
Example 2: Antarctic Bottom Water
Problem: CT = -0.5C SA = 34.65 g/kg pressure 4000 dbar.
Solution: Surface density = 999.84 + 0.030 + 27.73 = 1027.60 kg/m3\nSigma-0 = 27.60\nalpha small at cold temperatures
Result: Pot. Density: 1027.60 kg/m3 | Sigma-0: 27.60
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.
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.
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.
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.
Is Seawater Equation of State Teos 10 Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.
How accurate are the results from Seawater Equation of State Teos 10 Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.