## Properties of Sea Water

### Equation of State

An empriical relationship between pressure, density, temperature, and salinity for sea water, known as the equation of state, is expressed as a more than 20-term polynomial for the various state variables. Some background can be found here. The equation of state for seawater is quite nonlinear and this fact gives reise to some interesting phenomenon such as the thermobaric effect, as explained here and here. It is possible to use the full polynomial expression, but for reasons of computing efficiency, simpler yet accurate polynomial descriptions are sought . An online, java-based equation-of-state calculator is also available here. We will be using the MATLAB-based equation-of-state routines made available by Phil Morgan.

### Computing Exercise

Individual MATLAB routines available from the CSIRO Properties of Sea Water library are avaialable from the table below. The entire libray can be obtained here (zipped). Download the routines and run an example case for each rotuine. You need to create the input for each routine. Along with your input and output results, provide a very brief explanation of what each routine is doing.

 Sea Water Property MATLAB Code Adiabatic temperature gradient SW_ADTG Thermal expansion coefficient (alpha) SW_ALPHA Calculate alpha/beta (a on b) SW_AONB Saline contraction coefficient (beta) SW_BETA Brunt-Vaisala Frequency Squared (N^2) SW_BFRQ Copyright and Licence file SW_COPY Heat Capacity (Cp) of Sea Water SW_CP Density of sea water SW_DENS Density of sea water at atmospheric pressure SW_DENS0 Distance between two lat, lon coordinates SW_DIST Depth from pressure SW_DPTH Coriolis factor "f" SW_F Freezing Point of sea water SW_FP Gravitational acceleration SW_G Geopotential anomaly SW_GPAN Geostrophic velocity SW_GVEL Information on the SEAWATER library SW_INFO Potential Density SW_PDEN Pressure from depth SW_PRES Potential temperature SW_PTMP Salinity of sea water SW_SALS Salinity from cndr, T, P SW_SALT Solubility (saturation) of Ar in seawater SW_SATAr Solubility (saturation) of N2 in seawater SW_SATN2 Solubility (saturation) of O2 in seawater SW_SATO2 Specific volume anomaly SW_SVAN Sound velocity of sea water SW_SVEL Density of standard mean ocean water (pure water) SW_SMOW Temperature from potential temperature SW_TEMP Run test suite on library SW_TEST Version number of SEAWATER library SW_VER

### Acknowledgements

The Properties of Sea Water MATLAB code originates with Phil Morgan and is also available from the SEA-MAT website.