Thermohaline equation of state for pure water, seawater and brine

ABSTRACT

A thermohaline equation of state (EOS), relating the density of water to its temperature and salinity, is proposed for shallow water hydro-environment applications, at normal atmospheric pressure (101.3 kPa). The seawater is of standard ocean ionic composition. The proposed EOS applies to fresh, brackish, saline, hypersaline and brine water environments, in cold, temperate and hot climates. The density of water is considered nonlinear with temperature, but linear with salinity. This assumption is adequate for practical applications – allowing the transformation of the EOS into a relevant density difference equation – for calculating density differences and buoyancy in models of thermal and thermohaline flows in inland, estuarine, coastal and ocean waters.

Keywords:

• Brine
• density
• desalination
• equation of state
• hypersaline
• seawater
• thermohaline

Acknowledgement

I would like to thank the three anonymous reviewers for their constructive comments and suggestions, which have improved the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Notation

$a_i$	=	coefficient defined in Eq. (1)
$b_i$	=	coefficient defined in Eq. (3)
N	=	number of data points
$S$	=	absolute salinity (g kg−1)
$S_p$	=	practical salinity (ppt or psu)
$S_r$	=	reference salinity (g kg−1)
$T$	=	temperature (°C)
Tf	=	freezing temperature (°C)
Tmd	=	temperature of maximum density (°C)
$T_r$	=	reference temperature (°C)
${\alpha }_i$	=	coefficient defined in Eq. (8)
${\text{β}}_i$	=	coefficient defined in Eq. (9)
$ϵ$	=	per cent error defined in Eq. (5)
$\mathrm{\Delta }$	=	excess value with respect to reference state (–)
$\rho$	=	density (kg m−3)
${\rho }_0$	=	pure water density (kg m−3)
${\rho }_s$	=	surface density (kg m−3)

Additional information

Funding

This work was supported by grants from the Natural Sciences and Engineering Research Council of Canada (NSERC).