Joint Session A.1 and A.3 - GRACE Geodesy
(Convener: Frank Flechtner)

Mission Status and Performance of GOCE Gravity Field Models
(Gruber, Floberghagen, Fehringer, Rummel)

Mean background gravity fields for GRACE processing
(Ries, Bettadpur, Richter)

EIGEN-6 - The new combined global gravity field model including GOCE data from the collaboration of GFZ Potsdam and GRGS Toulouse
(Foerste et al.)

Determination of the Earth's mean gravitational field from an optimal combination of the GRACE and GOCE satellites' data
(Farahani, Ditmar, Liu, Klees, Zhao, Guo)

Alternative processing of GRACE gravity field products to overcome present gaps in accelerometer data
Dahle, Biancale, Flechtner)

GRACE K-band ranging data as a tool for the validation of static models of the Earth's gravitational field
(Farahani, Ditmar, Klees, Encarnacao)

Twangs: Charge Redistribution related to Atmospheric Parameters?
(Peterseim, Flury, Schlicht, Apelbaum)

Approximation of Non-Gravitational Acceleration from Co-orbiting Satellite's Accelerometer )
(Kim, Tapley)

Session: A.3 - GRACE & GOCE
Title: Mission Status and Performance of GOCE Gravity Field Models
First Author: Thomas Gruber
Presenter: Thomas Gruber
Co-Authors: R. Floberghagen; M. Fehringer; R. Rummel

Abstract: The GOCE mission is in orbit since spring 2009 and is systematically collecting gravity gradients from space. As of today about 18 months of high quality gravity field data have been observed enabling to estimate the static gravity field of the Earth solely from satellite data with a spatial resolution of about 100 km and an accuracy of a few centimetres globally. Currently GOCE is in its extended mission, which is planned to last until December 2012. The paper gives a short overview about the general mission and ground segment status as well as about the performance of the resulting GOCE gravity field models.

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Session: A.1 - Analysis Techniques
Title: Mean background gravity fields for GRACE processing
First Author: John Ries
Presenter: John Ries
Co-Authors: Srinivas Bettadpur, Thomas Richter

Abstract: An important component of the background model for the monthly GRACE gravity fields is a mean field taken to sufficiently high degree and order. GRACE itself is not able to fully resolve the mean field, so a combination of the GRACE mean field with terrestrial gravity information is required. This combination involves two challenges; realistically calibrating the GRACE mean field errors and weighting the combination of the calibrated GRACE mean field relative to the terrestrial data. The nature of the errors in the GRACE mean fields leads to having to balance the overall accuracy of the mean field against artifacts that can appear in the resulting geoid that may affect, for example, ocean applications.

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A.3 - GRACE & GOCE
Title: EIGEN-6 - The new combined global gravity field model including GOCE data from the collaboration of GFZ Potsdam and GRGS Toulouse
First Author: Foerste Christoph
Presenter: Foerste Christoph
Co-Authors: R. Shako, F. Flechtner, Ch. Dahle, O. Abrikosov, H. Neumayer, F. Barthelmes, R. König, S.L. Bruinsma, J.C. Marty, J.-M. Lemoine, G. Balmino and R. Biancale

Abstract: High-resolution global gravity field models play a fundamental role in geodesy and Earth sciences, ranging from practical purposes, like precise orbit determination, to scientific applications, like investigations of the density structure of the Earth's interior. We report on the latest combined EIGEN-model (EIGEN = European Improved Gravity model of the Earth by New techniques), which is complete to degree and order 1420 and was jointly elaborated by GFZ Potsdam and CNES/GRGS Toulouse. It is the first EIGEN model inferred from a combination of GRACE and GOCE data, enhanced with the DTU10 surface gravity data. Furthermore, EIGEN-6 contains drift parameters as well as annual and semi-annual terms for all spherical harmonic coefficients up to degree/order 50.

The combination of GRACE and GOCE data allows the construction of an accurate satellite-only model to degree and order 240, the gradiometer data of the latter contributing only to degrees upwards of 100. This is achieved through filtering of the GOCE observation equations, which is necessary because of the degraded gradiometer performance outside the measurement bandwidth. Analyses of gradiometer residuals calculated with ITG10S, EIGEN-5C and EGM2008 as background models revealed considerable model errors in current combined gravity field models caused by the inclusion low-quality and/or low resolution surface data in particular over South America, Africa, the Himalayas and New Guinea. Therefore, the combination procedure of satellite and surface data was revisited in order to mitigate this error source. In particular, the surface data normal equations are combined with satellite normal equations at a higher degree than presently applied (for instance at degree 70 in EIGEN-5C).

The comparison of test results (orbit computation, GPS leveling) of this latest EIGEN model with a GOCE-only model, EGM08 and ITG10S demonstrates the gain in accuracy at high degrees, while its performance is identical to a GRACE-only model for the low degrees.

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A.3 - GRACE & GOCE
Title: Determination of the Earth's mean gravitational field from an optimal combination of the GRACE and GOCE satellites' data
First Author: Hassan Hashemi Farahani
Presenter: Hassan Hashemi Farahani
Co-Authors: P. Ditmar; X. Liu; R. Klees; Q. Zhao; J. Guo

Abstract: The objective of the presented study is to obtain a static model of the Earth's global gravitational field on the basis of an optimal combination of the data from the Gravity Recovery and Climate Experiment (GRACE) and the Gravity Field and Steady-Sate Ocean Circulation Explorer (GOCE). The combined model uses (i) kinematic orbits of the GRACE and GOCE satellites; (ii) K-Band Ranging (KBR) data acquired by the GRACE satellites; and (iii) Satellite Gravity Gradiometry (SGG) data measured by the gradiometer on-board the GOCE satellite. The kinematic orbits and inter-satellite ranges are processed according to a variant of the acceleration approach, in which the functional models are respectively based on the average acceleration vectors and the average inter-satellite accelerations (scalar values) derived with a three-point double differentiation scheme. The SGG data comprise the diagonal elements of the gravitational tensor in the satellite reference frame. The involved data sets are reduced to the residual ones by evaluating and subtracting the contribution of background models at a pre-processing stage. The noise power spectral densities of the residual data sets are estimated and then parameterized using an Auto-Regressive Moving-Average (ARMA) process. This allows the dependency of noise on frequency to be taken into account, so that an optimal data combination is secured. The results to be presented are based on approximately four years of the GRACE kinematic orbits (in the time interval 2006-2009), seven years of the GRACE KBR data (in the time interval 2003-2009), and 10 months of the GOCE data (in the time interval September 2009-December 2010). The combined gravitational model is complete up to spherical harmonic degree and order 250 (a Kaula-type regularization has been applied beyond spherical harmonic degree and order 180). The quality of the obtained model has been assessed by comparing it against 1) alternative state-of-the-art static models of the gravitational field, and 2) the GRACE KBR and GOCE SGG data not used in the course of computation of the gravitational field model.

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Session: A.1 - Analysis Techniques
Title: Alternative processing of GRACE gravity field products to overcome present gaps in accelerometer data
First Author: Christoph Dahle
Presenter: Christoph Dahle
Co-Authors: R. Biancale; F. Flechtner

Abstract: After over 9 years in orbit, the GRACE mission still delivers high quality science data without almost any gaps, as the scientific instruments such as K-Band ranging instrument, GPS receivers, accelerometers and star camera assembly are still in good shape. However, the most critical issue regarding the operations of both satellites is the fragile state of the power system which requires a very strict battery management. This has already resulted in a power-off of the accelerometer on GRACE-B around January 2011 and of both accelerometers around June 2011. Further periods with unavailable accelerometers are expected regularly every 5-6 months during the remaining mission life-time. Therefore, the time-series of regular processed (including accelerometer data) monthly gravity field products cannot be provided continuously anymore.

To overcome this problem, two ideas of alternatively processed monthly GRACE gravity field solutions are presented: The first is to artificially generate the missing accelerometer data of one satellite from available accelerometer data of the other satellite. Assuming that both satellites are experiencing the same non-conservative disturbing forces, this simply requires a time-shift and proper modeling of possible satellite maneuvers. Obviously, this approach does not work in periods where both accelerometers are powered off. Therefore, in a second approach standard air drag and solar radiation models and empirical parameters are used instead of accelerometer data.

The presentation gives an overview of both methods and presents results of gravity field solutions in comparison to GFZ's RL04 standard approach.

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Session: A.1 - Analysis Techniques
Title: GRACE K-band ranging data as a tool for the validation of static models of the Earth's gravitational field
First Author: Hassan Hashemi Farahani
Presenter: Hassan Hashemi Farahani
Co-Authors: P. Ditmar; R. Klees; J. Teixeira da Encarnacao

Abstract: We present the results of a study on the validation of static models of the Earth's gravitational field using the data acquired by the K-Band Ranging (KBR) system on-board the Gravity Recovery and Climate Experiment (GRACE). The validation procedure is based on the differences between directly observed and computed inter-satellite ranges. It involves the following basic steps: (i) dynamic orbits of the GRACE satellites are computed using a force model that includes, in particular, the gravitational field model the quality of which is to be assessed; (ii) residual inter-satellite ranges are computed as the difference between the KBR measurements and the inter-satellite ranges derived from the dynamic orbits; (iii) residual inter-satellite accelerations are derived from the residual inter-satellite ranges with a three-point double differentiation scheme; (iv) residual inter-satellite accelerations are subject to a high-pass filtering in order to suppress the low frequency part of the spectrum, where noise is too strong; and (v) the high-pass filtered residual inter-satellite accelerations are used to compute mean values over 1-degree by 1-degree blocks. In order to suppress noise further, while preserving a high sensitivity of the GRACE KBR data to North-South variations of the gravitational field, we optionally stack together a few (5 to 10) adjacent blocks belonging to the same band of latitudes. The obtained quantities allow the quality of different static models of the Earth's gravitational field to be compared up to the highest spectral content of the KBR data, namely up to spherical harmonic degree and order 180 or even higher.

This validation procedure is used to assess the quality of four state-of-the-art models: EGM2008 and three recent models based on the data from the GRACE and GOCE (Gravity Field and Steady-Sate Ocean Circulation Explorer) satellites. Two of these models, GOCO01S and GOCO02S, are publicly available, whereas the third one is a preliminary version of a new model developed at the Delft University of Technology. In order to maximize the independence of the validation, we use primarily the GRACE KBR data within the year 2010, which has not been incorporated in the course of computation of neither of the aforementioned models. The conducted analysis has allowed us, in particular, (i) to quantify the contribution of the GOCE data to the static gravitational field recovery, and (ii) to compare the accuracy of the considered GRACE/GOCE models with each other. We also show that the GOCE data not only lead to significant improvements over areas with a poor coverage with terrestrial gravimetry data (like South America), but may also result in some improvements over well-covered areas with terrestrial gravimetry data (like North America).

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Session: A.1 - Analysis Techniques
Title: Twangs: Charge Redistribution related to Atmospheric Parameters?
First Author: Nadja Peterseim
Presenter: Nadja Peterseim
Co-Authors: J. Flury; A. Schlicht; G. Apelbaum;

Abstract: The Gravity Recovery and Climate Experiment (GRACE) has been launched 9 years ago to determine Earth' gravity field including its temporal variations. Since the beginning of the mission so called twangs can be found in 10 Hz accelerometer data of both GRACE satellites. A twang is the notation for a so far unsufficient explicable phenomena in accelerometer data, usually formed by a sudden spike, consisting of two peaks with a relatively high amplitude, and an oscillating decay.

Abstract In our studies we were able to distinguish between several types of twangs, for which we were able to build models with a high frequency. With these models the concerning type of twang can be found within accelerometer data by cross correlation. Furthermore, using the built models twangs can be on the one hand better characterised as well as they can be helpful for a successful reduction of twangs from accelerometer data. Also, we were able to determine a geographical as well as a temporal distribution of the twangs, and for certain types of twangs now a prediction of occurrence might be possible. We can relate most types of twangs to external forces, whereas we state the hypothesis that they are due to an electrical charge redistribution within the satellite body. In this hypothesis, satellite non-conductive surface planes are charged by the surrounding ionosphere/ thermosphere and this charge is being redistributed in the satellites conductive body as soon as a certain contact voltage threshold is exceeded, leading to a discharge current. This hypothesis was discussed together the manufacturer. Moreover, these investigations could contribute to a better understanding of satellite sensorics as used for gravity field determination from space, especially with regard to upcoming missions.

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Session: A.1 - Analysis Techniques
Title: Approximation of Non-Gravitational Acceleration from Co-orbiting Satellite's Accelerometer
First Author: Jeongrae Kim
Presenter: Jeongrae Kim
Co-Authors: Byron D. Tapley

Abstract: The non-gravitational acceleration acting on the two GRACE satellites are highly correlated with a time difference. When only one accelerometer data is available due to power limitation, another satellite's accelerometer data can be used instead. Two satellite's accelerations are very similar but there are some differences: time difference, passage difference due to Earth rotation, time varying non-gravitational accelerations, thruster firings, accelerometer noise spikes, etc. Due to these reasons, direct use of another satellite's time-shifted accelerometer data is limited. A method is developed to approximate one satellite's non-gravitational by combining another satellite's accelerometer data during certain time period. The performance of the proposed method is evaluated with differential non-gravitational acceleration that is used for the gravity estimation.

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