Desalination designers need to note new salinity equation

Experts attending the 25th assembly of UNESCO’s Intergovernmental Oceanographic Commission (IOC) in Paris on 24 June 2009 recommended that the entire oceanographic community adopt the Thermodynamic Equation of Seawater and the use of Absolute Salinity.

The new equation, which is a more accurate way of measuring salinity anywhere in the ocean, is set to become the next oceanographic standard as of 2010, after becoming an industrial standard last year. Any company interested in providing drinking water for desert cities near the coast, for example, will use the new method of calculation in building seawater desalination plants.

The conductivity method for determining salinity – Practical Salinity Scale – has been used by marine scientists since 1978. UNESCO incorporated the scale into the 1980 equations for calculating the density of seawater.

Rainer Feistel of the Leibniz-Institut für Ostseeforschung in Warnemünde (Germany) found during work in the Baltic sea that the existing equations worked fine for the open ocean but developed inconsistencies in regions that were strongly influenced by river drainage, evaporation, precipitation or extremes in temperature.

The Baltic sea is a prime example of seawater with an unusual composition. It has electrolytes that conduct electricity but they are not the typical sodium chloride. The vast rivers of Poland and Russia drain into the Baltic Sea, bringing with them dissolved calcium carbonate (CaCO3) from the limestone riverbeds. When CaCO3 dissolves, it dissociated into the conductive ions Ca2+ and CO32-. These ions prefer to be bound together but, if they cannot be, they will often bind to other molecules floating in seawater, changing the mass of the molecules and upsetting conductivity measurements.

“As you go to points where there are sensitivities, it’s a real mess,” Feistel says. “There was a missing mathematical component, a ‘Gibbs function’, which physicists had determined for all sorts of various fluids, except apparently seawater.” Named after American mathematician Josiah Willard Gibbs (1839-1903), the ‘Gibb’s function’ defines a fluid in terms of its energy and heat transfer, or thermodynamics.

Feistel’s re-evaluation of the 1980s equations provided seawater with a ‘Gibbs function’. The previous mathematical equations for determining the properties of seawater had not accounted for water’s ability to transfer heat from warmer to cooler currents. Nor did the old equations set a standard for comparing how difficult such a transfer of energy might be, based on the water’s inherent pressure and volume.

The Thermodynamic Equation of Seawater converts all of the old equations into a neat new bundle of computer algorithms ideal for modellers. Unlike the Practical Salinity Scale, which accounts only for ions, the new Absolute Salinity will incorporate non-electrolytes using tables that account for how these additional substances vary region by region. The latitude and longitude at which the seawater samples are taken will play an important role in calculating salinity.

In 2010 for the first time, the algorithm for measuring salinity will incorporate more than dissolved salt into the conductivity conversion. Frank Millero of the Rosenstiel School of Marine and Atmospheric Science at the University of Miami in Florida, USA, who worked on the 1980 equation of seawater, and Feistel have been working with modeller Trevor McDougall of the Centre for Australian Weather & Climate Research in Hobart as part of an international team established in 2005 by the Scientific Committee on Oceanic Research and the International Association for the Physical Sciences of the Ocean.

They are incorporating the location of the conductivity measurements with chemical analysis from those regions into the new Absolute Salinity calculation. The team has also redefined how the properties of seawater are calculated using this new Absolute Salinity method and combining it with the principles behind thermodynamics to form a single new thermodynamic equation for seawater.

For more information, see the complete paper presented at the IOC in June, which can be downloaded as a pdf file.