### Abstract

As the most advanced gravity space mission to date, The Gravity Field and Steady State Ocean Circulation Explorer (GOCE) mapped global variations in the gravity field with remarkable detail and accuracy. Variations are mapped by observing second order derivatives (gradients) of the Earth gravitational potential. The results are Earth geopotential models and the geoid. An important use of GOCE is in oceanography, where an improved understanding of Earth’s gravitational field contributes to an improved description of the ocean circulation.

The GOCE gradients, having a spatially dense data distribution, may potentially provide better predictions of the regional gravity field than those obtained using a spherical harmonic Earth Geopotential Model (EGM). Thus, the success of GOCE is depending on adequate methodologies for extracting the gravity field from its observations as well as on the combination of the gravity field with information from other sources.

The aim of this PhD study is to develop a methodology to improve the use of GOCE gradients and to determine the Earth’s gravity field with better accuracy than by using global models, which have been truncated at a specific harmonic degree and order. The method makes use of all available GOCE gradient data in addition to the global models and aims at improving the determination of Earth’s gravitational field in regional areas. Subsequently, the calculated equipotential surface, known as the geoid, is used together with measurements of sea surface height in a calculation of the Mean Dynamic Topography (MDT). This reflects the geostrophic ocean currents and leads to a better understanding of ocean mass and heat transfer.

In regional geoid recovery from GOCE gradients, two methods are used, one of them being Least-Squares Collocation (LSC). The second method is developed as a part of this study, and it is based on the reduced point mass responses. Such functions are harmonic and may be used to represent the (anomalous) gravity potential globally or locally.

Since the LSC method requires the solution of as many linear equations as the number of data, GOCE gradient data needs to be thinned prior to applying the method. This is not case for the Reduced Point Mass (RPM), where the number of equations we want to solve depends on the number of point masses. The method is tested in a region in the North Atlantic called the Geoid and Ocean Circulation in the North Atlantic (GOCINA) area, i.e. 58.0N to 70.0N latitude, and -30.0W to 10.0E longitude.

The results show that the RPM method and LSC method gives very similar results, i.e. the difference is insignificant when compared to the Earth’s Gravitational Model 2008 (EGM2008) results. However, when all the GOCE gradient data are used with the RPM method, an improvement in the gravitational field determination is achieved.

The enhanced geoid by the RPM method is then used for the improvement of the MDT in the GOCINA region. For the validation of the MDT, comparisons with DTU10 MDT, Maximenko MDT and GOCINA project MDT is made.

The results presented here are based on only 18 months of GOCE data, and they show that GOCE data provides better estimation of the MDT and ocean’s geostrophic circulation in GOCINA region than any previously obtained using only satellite observations. However, it could not be documented in this study whether the regionally enhanced geoid models by the use of GOCE gradients, in addition to the global models, contribute to a further improvement of the determination of the MDT in the GOCINA area.

The GOCE gradients, having a spatially dense data distribution, may potentially provide better predictions of the regional gravity field than those obtained using a spherical harmonic Earth Geopotential Model (EGM). Thus, the success of GOCE is depending on adequate methodologies for extracting the gravity field from its observations as well as on the combination of the gravity field with information from other sources.

The aim of this PhD study is to develop a methodology to improve the use of GOCE gradients and to determine the Earth’s gravity field with better accuracy than by using global models, which have been truncated at a specific harmonic degree and order. The method makes use of all available GOCE gradient data in addition to the global models and aims at improving the determination of Earth’s gravitational field in regional areas. Subsequently, the calculated equipotential surface, known as the geoid, is used together with measurements of sea surface height in a calculation of the Mean Dynamic Topography (MDT). This reflects the geostrophic ocean currents and leads to a better understanding of ocean mass and heat transfer.

In regional geoid recovery from GOCE gradients, two methods are used, one of them being Least-Squares Collocation (LSC). The second method is developed as a part of this study, and it is based on the reduced point mass responses. Such functions are harmonic and may be used to represent the (anomalous) gravity potential globally or locally.

Since the LSC method requires the solution of as many linear equations as the number of data, GOCE gradient data needs to be thinned prior to applying the method. This is not case for the Reduced Point Mass (RPM), where the number of equations we want to solve depends on the number of point masses. The method is tested in a region in the North Atlantic called the Geoid and Ocean Circulation in the North Atlantic (GOCINA) area, i.e. 58.0N to 70.0N latitude, and -30.0W to 10.0E longitude.

The results show that the RPM method and LSC method gives very similar results, i.e. the difference is insignificant when compared to the Earth’s Gravitational Model 2008 (EGM2008) results. However, when all the GOCE gradient data are used with the RPM method, an improvement in the gravitational field determination is achieved.

The enhanced geoid by the RPM method is then used for the improvement of the MDT in the GOCINA region. For the validation of the MDT, comparisons with DTU10 MDT, Maximenko MDT and GOCINA project MDT is made.

The results presented here are based on only 18 months of GOCE data, and they show that GOCE data provides better estimation of the MDT and ocean’s geostrophic circulation in GOCINA region than any previously obtained using only satellite observations. However, it could not be documented in this study whether the regionally enhanced geoid models by the use of GOCE gradients, in addition to the global models, contribute to a further improvement of the determination of the MDT in the GOCINA area.

Original language | English |
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Place of Publication | Kgs. Lyngby |
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Publisher | Technical University of Denmark |

Number of pages | 175 |

Publication status | Published - 2012 |

### Cite this

Herceg, M. (2012).

*GOCE Data for Ocean Modelling*. Kgs. Lyngby: Technical University of Denmark.