URL: http://www.mercator-ocean.fr/html/science/piste_verte/initiation1_en.html

ScienceBeginner's trailInitiation to operational ocean forecasting

Mathematics for describing the ocean

The heart of an ocean forecasting system is a mathematical model describing the ocean in three dimensions (horizontally and vertically) as well as its evolution over time (temporal dimension or fourth dimension).

A model is a mathematical description of physical phenomena. For the ocean, as for the atmosphere, the mathematical model describes the movement of fluids (water, air) on the surface of the Earth, as well as transporting of heat (temperature) and matter (salt) associated with the fluid movements. This results in equations which describe the current, the temperature and the salinity at any place in the modelled zone and as a function of time.

To resolve these complex equations, scientists 'cut the ocean up' into thousands of small boxes called model cells (see figure opposite). Each small cell represented on the surface of the ocean is conceived as being on top of a stack of small boxes pilled up on top of each other, from the bottom of the sea up to its surface. For instance, the global ocean model used at Mercator has 46 million small boxes (1 million for the horizontal plane and 46 for the vertical plane).

The 'breakdown' of the ocean in the Mercator global ocean model, seen from the North Pole. Ocean variables of temperature, salinity, horizontal velocity and sea surface height are calculated in each of the cells. The different colours represent the variable size (in km) of the cells

In order for numerical ocean forecasting to be as realistic as possible, models need certain indispensable data: atmospheric conditions at the surface of the sea and measurements made by Earth observation satellites but also measurements taken from inside the ocean. The latter are called in situ measurements.

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