Polynomials for efficiently computing the density of seawater
Author glwagner
4 Stars
Updated Last
11 Months Ago
Started In
April 2020


This package provides approximations to the Boussinesq equation of state for seawater expressed as polynomial functions of conservative temperature, absolute salinity, and geopotential height.

Computationally efficient polynomial approximations to the Boussinesq seawater equation of state are crucial components of ocean modeling software.

The Seawater Boussinesq approximation

In the seawater Boussinesq approximation, the density of seawater is expanded around a constant reference value ρᵣ,

ρ = ρᵣ + ρ′(Θ, Sᴬ, Z)

where the anomaly, ρ′, is a function of conservative temperature Θ, absolute salinity Sᴬ, and geopotential height Z. One choice for ρᵣ is the average density at the surface of the world ocean, ρᵣ = 1024.6 kg m⁻³, according to Roquet et al. (2015).

The TEOS-10 standard

The Thermodynamic Equation of SeaWater (TEOS-10) is a Gibbs function formulation of seawater themodynamics.

The error between the polynomials implemented in this package and the TEOS-10 is minimized for current 'climatological' ocean distributions of conservative temperature and absolute salinity. For more information, see

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