## Details

Original language | English |
---|---|

Title of host publication | Lecture Notes in Earth System Sciences |

Place of Publication | Cham |

Publisher | Springer International Publishing AG |

Pages | 97-126 |

Number of pages | 30 |

ISBN (electronic) | 978-3-319-49941-3 |

ISBN (print) | 9783319499406 |

Publication status | Published - 11 Feb 2017 |

## Publication series

Name | Lecture Notes in Earth System Sciences |
---|---|

ISSN (Print) | 2193-8571 |

ISSN (electronic) | 2193-858X |

## Abstract

The Gravity Recovery and Climate Experiment (GRACE) mission is a key instrument to monitor and understand variations in the mass distribution of the Earth. The primary observable is the (biased) range between the two satellites which is a geometric observation. The task is therefore to connect this kind of observation to the physically meaningful gravity field of the Earth or in other words connecting the kinematic observation to a force. Various approaches exist. Here, the focus is on the so-called acceleration approach which conceptually tries to avoid the solution of the variational equations by linking observed range accelerations to the gradient of the gravitational potential. Practically, it requires the observation of range accelerations, the attitude and their changes with matching precision in all three dimensions which are currently not available for GRACE. Three possible solutions are presented: (1) an approximate solution neglecting terms with low precision observations by reducing the basic equation to residual quantities, (2) a stringent solution by considering the term of low precision as unknown and solving it via the variational equations and (3) an alternative description using rotational quantities. Only the second approach yields solutions at the same level of precision as other approaches but offers no conceptual or computational advantage due to the need for solving the variational equations. The first kind of solution results primarily in a mis-modeling of long-wavelength signal but may still serve well for local or regional solutions. The third kind of solution is currently not feasible since the required precision in the attitude information is far from being available. However, it offers interesting insight into the observation system. It allows to describe GRACE as a two-dimensional observation system and explain mathematically the poor East-West sensitivity yielding the striping artifact in today’s GRACE solutions.

## ASJC Scopus subject areas

- Earth and Planetary Sciences(all)
**Computers in Earth Sciences****Earth and Planetary Sciences(all)**

## Cite this

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- Apa
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**The Acceleration Approach.**/ Weigelt, Matthias.

Lecture Notes in Earth System Sciences. Cham: Springer International Publishing AG, 2017. p. 97-126 (Lecture Notes in Earth System Sciences).

Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review

*Lecture Notes in Earth System Sciences.*Lecture Notes in Earth System Sciences, Springer International Publishing AG, Cham, pp. 97-126. https://doi.org/10.1007/978-3-319-49941-3_4

*Lecture Notes in Earth System Sciences*(pp. 97-126). (Lecture Notes in Earth System Sciences). Springer International Publishing AG. https://doi.org/10.1007/978-3-319-49941-3_4

}

TY - CHAP

T1 - The Acceleration Approach

AU - Weigelt, Matthias

PY - 2017/2/11

Y1 - 2017/2/11

N2 - The Gravity Recovery and Climate Experiment (GRACE) mission is a key instrument to monitor and understand variations in the mass distribution of the Earth. The primary observable is the (biased) range between the two satellites which is a geometric observation. The task is therefore to connect this kind of observation to the physically meaningful gravity field of the Earth or in other words connecting the kinematic observation to a force. Various approaches exist. Here, the focus is on the so-called acceleration approach which conceptually tries to avoid the solution of the variational equations by linking observed range accelerations to the gradient of the gravitational potential. Practically, it requires the observation of range accelerations, the attitude and their changes with matching precision in all three dimensions which are currently not available for GRACE. Three possible solutions are presented: (1) an approximate solution neglecting terms with low precision observations by reducing the basic equation to residual quantities, (2) a stringent solution by considering the term of low precision as unknown and solving it via the variational equations and (3) an alternative description using rotational quantities. Only the second approach yields solutions at the same level of precision as other approaches but offers no conceptual or computational advantage due to the need for solving the variational equations. The first kind of solution results primarily in a mis-modeling of long-wavelength signal but may still serve well for local or regional solutions. The third kind of solution is currently not feasible since the required precision in the attitude information is far from being available. However, it offers interesting insight into the observation system. It allows to describe GRACE as a two-dimensional observation system and explain mathematically the poor East-West sensitivity yielding the striping artifact in today’s GRACE solutions.

AB - The Gravity Recovery and Climate Experiment (GRACE) mission is a key instrument to monitor and understand variations in the mass distribution of the Earth. The primary observable is the (biased) range between the two satellites which is a geometric observation. The task is therefore to connect this kind of observation to the physically meaningful gravity field of the Earth or in other words connecting the kinematic observation to a force. Various approaches exist. Here, the focus is on the so-called acceleration approach which conceptually tries to avoid the solution of the variational equations by linking observed range accelerations to the gradient of the gravitational potential. Practically, it requires the observation of range accelerations, the attitude and their changes with matching precision in all three dimensions which are currently not available for GRACE. Three possible solutions are presented: (1) an approximate solution neglecting terms with low precision observations by reducing the basic equation to residual quantities, (2) a stringent solution by considering the term of low precision as unknown and solving it via the variational equations and (3) an alternative description using rotational quantities. Only the second approach yields solutions at the same level of precision as other approaches but offers no conceptual or computational advantage due to the need for solving the variational equations. The first kind of solution results primarily in a mis-modeling of long-wavelength signal but may still serve well for local or regional solutions. The third kind of solution is currently not feasible since the required precision in the attitude information is far from being available. However, it offers interesting insight into the observation system. It allows to describe GRACE as a two-dimensional observation system and explain mathematically the poor East-West sensitivity yielding the striping artifact in today’s GRACE solutions.

UR - http://www.scopus.com/inward/record.url?scp=85031491104&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-49941-3_4

DO - 10.1007/978-3-319-49941-3_4

M3 - Contribution to book/anthology

AN - SCOPUS:85031491104

SN - 9783319499406

T3 - Lecture Notes in Earth System Sciences

SP - 97

EP - 126

BT - Lecture Notes in Earth System Sciences

PB - Springer International Publishing AG

CY - Cham

ER -