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.

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 |

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