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The Geoid and its Use to Compute Ocean Dynamic Topography

By Vinca Rosmorduc

CLS, France

Altimeter significant wave height tracks
The Geoid
Click for larger image and explanation

Gravimetric satellites, including GOCE, have improved our knowledge of the geoid. This lesson explains what is meant by the 'geoid', and how it reflects inhomogeneities in the Earth's mantle as well as sub-marine reliefs (including, for example, the mid-Atlantic Ridge).

The lesson shows the building of a geoid model, and how this is used in oceanography to calculate mean sea surface and mean dynamic topography, which in turn can give information on the speed and direction of the large scale ocean currents.

The electronic book Gravity from Space provides detailed background information on gravity measurements and the ESA gravity mission, GOCE.


The shape of the Earth has been a science subject for a very long time. In the Antiquity, from the 4th century BC, the rotundity was known. Eratosthène (2nd century BC) computed its diameters. Newton defined the relation that is still the basis of gravity computation with the Universal law of gravitation, and he also hypothesized the flattening of the Earth due to its rotation. In the 18th century, expeditions went all around the globe to measure this. Earth became an ellipsoid, no longer a sphere. The data were refined in the 19th and 20th centuries, with instrumental and technical improvements, up to space measurements from the 1960s. Earth is now considered as "potato-shaped", i.e. a bumpy, irregular spheroid.

The irregularities are due to surface processes (mountains, higher density areas in the crust..), but are mostly caused by inhomogeneities in the Earth's mantle.

This is not an idle topic. Improving our knowledge of how gravity affects interaction between processes at the Earth's surface and in its mantle has practical benefits in today's changing world.

An accurate gravity map - the geoid - is also crucial for geodesy applications and for defining a sea surface height reference model with which to accurately survey ocean circulation patterns and sea-level change.

The high-resolution gravity measurements of GOCE will:

In this lesson, we will have a look at a GOCE-derived geoid model. We will look at the different scales of structures, and also at the way such models are made from spherical harmonics (through outputs computed from the GOCE User Toolbox).

We will also show how the geoid is used in oceanography.

Lesson Overview

Aim and objectives

The lesson will show the geoid as computed from GOCE measurements. It will highlight some of the geoid features that match either deep inhomogeneities or reliefs, using filters to bring out specific features.

At the end of the lesson you should be able to:

Lesson content

The lesson is divided into 3 sections:

  1. The geoid large and small scale features
  2. Components of a geoid model: spherical harmonics
  3. Use of the geoid in oceanography: mean dynamic topography

Data and tools for this lesson

Satellite data products grids of geoid heights in the mean tide system and relative to the Topex ellipsoid over the whole Earth at degree/order nnn of spherical harmonics expansion (output of GUT "geoidheight_gf" workflow). Mean sea surface height wrt T/ P reference ellipsoid computed on a 7 years period (1993-1999) (distributed by AVISO Mean sea surface height above geoid computed on a 7 years period (1993-1999). (distributed by AVISO

Bilko tools used in the lesson

Modjet3.pal: colour palette to use with the geoid model data.

palette_s13.pal: colour palette to use with the dynamic topography data.

Downloading the lesson

The lesson downloads contain everything you need to complete the lesson. This includes the data and tools listed above, and three PDF documents:

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