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This corner will help you understand theories and developments of operational oceanography:

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).

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.mathematiquesCaption: 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

The atmostphere is the ocean's motor

Ocean movements are due to the rotation of our planet and to gravitational forces acting between the Earth, the Moon and the Sun (tides), but not only.

This ‘stirring-up’ of the ocean is also due to the action of the atmosphere on the surface of oceans: in particular the effects of the Sun (which heats more at the equator than at the poles), of rain which reduces the salinity of sea water and evaporation which increases salinity. For oceanographers developing ocean models, these phenomena are called atmospheric forcing.

Knowledge of these phenomena is indispensable for modelling the ocean. This is provided by numerical atmosphere models which are those used by meteorologists for weather forecasting.


Copyright: Météo France / Michel Hontarrède

Satellite and in situ measurements

A numerical model is basically a theoretical model. However, while it receives input on the atmospheric conditions on the surface of the ocean, that alone is not enough for simulating the reality of the ocean. To help the model produce more realistic results, it has to be constrained with true measurements. These are provided by Earth observation satellites and oceanography ships.

The ingesting of these measurements in numerical models is known as data assimilation. .

In Mercator systems, there are two types of assimilated data: satellite and in situ (sea measurements).

Satellite data

  • Sea surface height
    This variable, also known as the dynamic height or dynamic topography gives very useful information on currents. It is provided by altimetry satellites. The Mercator systems use altimetry data from 3 satellites: Envisat (European Space Agency), GFO (US Navy), Jason-1 (Nasa/Cnes).
  • Sea surface temperature
    Other satellites measure the temperature at the surface of the sea. These are mainly infrared sensing satellites from NOAA (the American Meteorology department), but also from the European Space Agency (ESA).

In situ data

In situ data is measured at sea, either by oceanographers on oceanography ships or by automatic sensors which transmit their measurements in real time via satellites.


Photo credits: CNES/CNRS INSU

A real-time forecasting system

Les systèmes de prévision Mercator correspondent à un ensemble de logiciels informatiques complexes. Ces logiciels appartiennent à une véritable chaîne de production informatique partant de l’acquisition des données de forçages atmosphériques, des données de mesures satellitaires et in situ, de la “digestion” de ces données dans les modèles de simulation de l’océan, à la sortie et à la distribution des résultats “empaquetés” sous forme de cartes, de bulletins texte ou de fichiers numériques, vers nos utilisateurs.

La spécificité des systèmes Mercator est qu’ils sont opérationnels. C’est-à-dire qu’ils fonctionnent chaque semaine quoiqu’il arrive. En effet, certains de nos utilisateurs (qui sont aussi nos tutelles) ont des missions données par l’état de surveillance de pollution, de sécurité en mer, ou encore de prévision météorologique, pour lesquelles les systèmes Mercator sont utiles, voire indispensables. A la sortie de ces systèmes, on obtient une description de l’océan dans ses trois dimensions en analyse et en prévision. Le principe de la prévision numérique est de partir d’un état initial connu de l’état de l’océan, appelé analyse pour aboutir à une prévision de cet état dans le futur.


L’analyse correspond à l’état de l’océan calculé par le système Mercator s’appuyant sur :

  • Le modèle numérique
  • Les forçages atmosphériques
  • L’assimilation des données mesurées dont on dispose, pendant les 2 semaines précédant la date de l’analyse

La prévision

Elle décrit l’océan dans le futur. Elle s’appuie sur le modèle numérique océanique et sur les forçages prévus par les modèles de prévision numérique du temps. Dans les systèmes Mercator, la prévision est de 2 semaines, à partir de la dernière analyse.