# ITG-Grace2010

Torsten Mayer-Gürr, Enrico Kurtenbach, Annette Eicker

# Content

The ITG-Grace2010 gravity field model consists of three parts: daily solutions calculated using a Kalman smoother, unconstrained monthly solutions, and a high-resolution long-time mean. The observation period covers GRACE data from 2002-08 to 2009-08.

Daily solutions using Kalman smoothing

Unconstrained monthly solutions

# Daily solutions using Kalman smoothing

In order to recover fast gravity field variations as detailed as possible, it is reasonable to increase the temporal resolution. The goal is the calculation of daily GRACE solutions. This increase in temporal resolution results in less observations per time span and therefore a reduced redundancy in the parameter estimation process. This leads to a decreasing accuracy of the estimated parameters with decreasing time span. It can be assumed, however, that the gravity field does not change arbitrarily from one time step to the next. The information about the temporal correlation patterns can be derived from geophysical models. Utilizing this knowledge, the temporal resolution can be enhanced without losing spatial information within the framework of a Kalman smoother estimation procedure (Kurtenbach et al. 2012).

The following geophysical models were used to derive the temporal correlations: the WaterGAP global hydrology model (WGHM), the atmospheric model ECMWF, and the ocean circulation model OMCT. In order to guarantee that the GRACE solutions are not biased towards the model values themselves but that only the stochastic behavior is exploited, the model output of the years 1976 - 2000 (i.e. outside the GRACE time span) was applied.

For each day of the observation period (2002-08 to 2009-08) a set of spherical harmonic coefficients for degrees n=2...40 was estimated as differences to the static field ITG-Grace2010s. Of course, these sets are not independently estimated, but the gravity model is updated daily by the GRACE observations.

The Kalman smoother delivers daily solutions, even if there are no GRACE data available for a specific day. These days should be handled with care, as they are predictions only and tend towards a mean trend, annual, and semiannual signal. The number of observations for each day can be found in README_dailyObservationCount.txt.

# Unconstrained monthly solutions

For each month of the observation period (2002-08 to 2009-08) a set of spherical harmonic coefficients for degrees n=1...120 was estimated without applying any regularization. In addition to the background models listed in Processing details, the daily Kalman solutions were used as improved de-aliasing product. A monthly mean of the daily solutions was restored afterwards.

The estimated coefficients of degree n=1 (geocenter) are comparably inaccurate and it might be reasonable to set them to zero for further analysis of the gravity field models.

For each solution, the corresponding full variance-covariance matrix is provided for each monthly solution. During the estimation process of the monthly gravity fields 14,640 unknown gravity field parameters were estimated. The covariance matrix is split up into 3 files and only the upper triangle of the matrix is stored. The first file contains the complete covariance information up to degree and order n=60. Users who are only interested in the covariance information of these lower degrees do not need to download the rest of the files. Further information can be found in README_monthly_covariance.txt.

# The static solution ITG-Grace2010s

The ITG-Grace2010s is a long-term mean gravity field model covering the time span 2002-08 to 2009-08 calculated from GRACE data only up to degree and order 180. In addition to the background models listed in Processing details, the daily Kalman solutions were used as improved de-aliasing product. The mean of the AOD1B product and of the daily solutions was restored afterwards. Therefore, ITG-Grace2010s contains the complete gravity field signal including atmosphere and ocean masses. The reference epoch of this mean gravity field model is 1 January 2005.

A full variance-covariance matrix is provided for the static solution. During the estimation process of the monthly gravity fields 32,760 unknown gravity field parameters were estimated. The full variance-covariance matrix has a size of about 8 GB memory. The matrix is split up into smaller files and only the upper triangle of the matrix is stored. Further information is provided in README_static_covariance.txt.

# Processing Details

The ITG-Grace2010 gravity field solutions are calculated with the integral equation approach using short arcs with a maximum length of 60 min (Mayer-Gürr 2006). K-band range rates with a sampling rate of 5 seconds and kinematic Orbits with a sampling rate of 30 seconds were used as observations. The kinematic orbits of the GRACE satellites were processed using the GPS orbits and clock solutions provided by IGS and GFZ.

The following background models were used during the data processing:

Earth rotation: | IERS 2003 |

Moon, sun and planets ephem.: | JPL DE405 |

Earth tide: | IERS 2003 |

Ocean tide: | EOT08a |

Pole tide: | IERS 2003 |

Ocean pole tide: | Deasi 2003 |

Atmosphere and Ocean Dealiasing: | AOD1B RL04 |

Permanent tidal deformation: | included (zero tide) |

The above models were reduced during the analysis process. They are not present in the solutions. (Exception: static solution, see there). The AOD1B product is provided (separately for ocean and atmosphere) as mean values over the specific time spans (daily, monthly) in the download section below.

Additionally, a time variable gravity field was derived from a previous GRACE solution and used as approximation value in the linearization process. This field consists of a static field, a trend, annual, and semiannual variations. This field is restored to the ITG-Grace2010 solutions after the estimation process.

In contrast to most of the other releases, no IERS dot coefficients were applied.

# Download

Format description: ICGEM-Format.pdf |

#### Daily solutions using Kalman smoothing

ITG-Grace2010_Kalman (directory): Daily solutions using Kalman smoothing
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background (directory): Daily mean of background models (AOD1B) (atmosphere (GAA), ocean (GAB), dealiasing (GAC)) | |

README_dailyObservationCount.txt: Number of GRACE observations per day |

Reference for the daily solutions: (Kurtenbach et al. 2012).

#### Unconstrained monthly solutions

ITG-Grace2010 (directory): Unconstrained monthly solutions
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background (directory): Monthly mean of background models (AOD1B) (atmosphere (GAA), ocean (GAB), dealiasing (GAC)) | |

ITG-Grace2010_covariance (directory): Monthly variance-covariance matrix
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Reference: this website "http://www.igg.uni-bonn.de/apmg/index.php?id=itg-grace2010" until further notice.

#### The static solution ITG-Grace2010s

ITG-Grace2010s.gfc: Potential coefficients of the static gravity field model
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ITG-Grace2010s_covariance (directory): Full variance-covariance matrix
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Reference: this website "http://www.igg.uni-bonn.de/apmg/index.php?id=itg-grace2010" until further notice.

# References

[1] Kurtenbach, E., Eicker, A., Mayer-Gürr, T., Holschneider, M., Hayn, M., Fuhrmann, M., & Kusche, J. (2012). Improved daily GRACE gravity field solutions using a Kalman smoother. Journal of Geodynamics, 59, 39-48.. link
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[2] Mayer-Gürr, T. (2006): Gravitationsfeldbestimmung aus der Analyse kurzer Bahnbögen am Beispiel der Satellitenmissionen CHAMP und GRACE, Dissertation, University of Bonn, pdf |