# Mass-related excitation of polar motion: an assessment of the new RL06 GRACE gravity field models

**Part of the following topical collections:**

## Abstract

## Keywords

GRACE RL06 gravity field models Polar motion excitation Effective angular momentum functions## Introduction

Mass displacements within the Earth system cause variations of the Earth’s gravity field and its rotation. Thus, temporal variations of the gravity field can be used to study the mass-related excitation of polar motion. By separating the observed integral gravity signal into contributions from different Earth subsystems, also individual mechanisms of polar motion excitation can be studied. Most important are the variations of the degree-2 spherical harmonic potential coefficients \({C}_{21}\) and \({S}_{21}\) as these are directly related to polar motion excitation (Barnes et al. 1983).

Between 2002 and 2017, the satellite gravity mission Gravity Recovery and Climate Experiment (GRACE) observed the time variable gravity field of the Earth. The GRACE science teams at the Center for Space Research (CSR), Austin, the GeoForschungsZentrum (GFZ), Potsdam, and the Jet Propulsion Laboratory (JPL), Pasadena, provide monthly GRACE gravity field solutions. In irregular time intervals release updates were performed: 2003 (RL01), 2005 (RL02 and RL03), 2007 (RL04), 2012 (RL05) and recently in 2018 (RL06). A lot of studies exist in which GRACE RL05 gravity field solutions have been used to estimate the integral as well as individual mass-related effects on Earth rotation (e.g., Adhikari and Ivins 2016; Chen et al. 2013, 2017; Göttl et al. 2015; Malgorzata et al. 2017; Meyrath and van Dam 2016). It was shown that due to the release update from RL04 to RL05 the agreement between GRACE-derived effective angular momentum functions and the mass-related part of the so-called geodetic excitations (Brzeziński 1992) could be slightly improved. The latter can be derived from Earth Orientation Parameter (EOP) time series, such as EOP 14 C04 (Bizouard et al. 2014) of the International Earth Rotation and Reference Systems Service (IERS), reduced by the motion-related effects within the atmosphere (winds) and oceans (currents) based on geophysical model data. Recently, CSR, JPL and GFZ have produced the new RL06 GRACE gravity field solutions applying improved parameters, processing algorithms, data editing and background gravity models. Accordingly, the Institute of Theoretical Geodesy and Satellite Geodesy (ITSG) of the Graz University of Technology provides the new ITSG-Grace2018 monthly and daily gravity field models which also incorporate the new RL06 background gravity models. In particular, the degree-2 potential coefficients \({C}_{21}\) and \({S}_{21}\) are influenced by the change of the mean pole model from cubic to linear. The goal of this study is to analyze the new RL06 GRACE data regarding its consistency with the mass-related part of the geodetic excitation of polar motion (integrally and for individual subsystems), to quantify the improvement of RL06 data with respect to RL05, and to study the differences of the solutions from CSR, JPL, GFZ and ITSG.

The paper is outlined as follows: the next section provides an overview of the GRACE gravity field models [RL05 and RL06 from CSR, JPL and GFZ as well as the GRACE gravity field models ITSG-Grace2016 (incorporating the RL05 background models) and ITSG-Grace2018 (incorporating the RL06 background models)] and the processing steps in order to determine the equatorial effective angular momentum functions for polar motion excitation. Further, we introduce the time series EOP 14 C04 and the steps for the separation of the mass-related part of the geodetic excitation that will be used for the comparison with the GRACE-derived excitation in the third section. There, also maps of equivalent water heights from GRACE RL05 and RL06 data are analyzed with respect to the signal-to-noise ratio and the consistency of the solutions of the processing centers. Finally, the last section provides the conclusions.

## Data and data processing

### GRACE gravity field solutions

^{1}(Watkins and Yuan 2014), JPL RL06 (Yuan 2018), GFZ RL05

^{2}(Dahle et al. 2012) and GFZ RL06 (Dahle et al. 2018). Further, we use the GRACE gravity field solutions from ITSG, namely ITSG-Grace2016 (Mayer-Gürr et al. 2016) and ITSG-Grace2018 (Mayer-Gürr et al. 2018). Beside changes in the processing algorithms and data editing, there are also significant changes in the background models as shown in Table 1. The GRACE gravity field solutions are provided as Level-2 products GSM

^{3}, GAC

^{4}and GAD

^{5}. Figure 1 shows the time series of the potential coefficients \({C}_{21}\) and \({S}_{21}\) of the CSR RL05 and RL06 GSM products. A significant modification of these coefficients was caused in particular by the change of the mean pole model from cubic to linear. The introduction of a new mean pole model was motivated by a significant mismatch between the cubic polygon fitted to a filtered time series of polar motion and the observed polar motion after 2010. Accordingly, the IERS Conventions (Petit and Luzum 2010) have been updated by a new conventional linear mean pole model based on the full extent of the IERS EOP C01 series (1900–2017). The relative standard deviations (RSD) of CSR RL05 and RL06 for \({C}_{21}\) and \({S}_{21}\) are up to 32\(\%\). The RL06 solution is smoother, especially for \({S}_{21}\), and changes of the trend are clearly visible. The new RL06 GRACE Atmosphere and Ocean De-Aliasing Level-1B (AOD1B) product (Dobslaw et al. 2017b) provides, compared to its predecessor in RL05 (Flechtner et al. 2015), an increased temporal and spatial resolution, a clear separation of tidal and non-tidal signals and an improvement of long-term consistency (Dobslaw et al. 2017a). The oceanic component is no longer based on the Ocean Model for Circulation and Tides (OMCT; Dobslaw et al. 2013) but on the Max-Planck-Institute Ocean Model (MPIOM; Jungclaus et al. 2013), while the atmospheric component is still based on atmospheric re-analysis of the European Center for Medium-Range Weather Forecasts (ECMWF). The a posteriori correction models GAE, GAF and GAG of the AOD1B RL05 product (Fagiolini et al. 2015) that account for updates at ECMWF, are no longer necessary for RL06. However, the impact of the changes in the AOD1B product on the coefficients \({C}_{21}\) and \({S}_{21}\) is small (14\(\%\) for \({C}_{21}\) and 8\(\%\) for \({S}_{21}\)).

Background models used within the RL05 and RL06 GRACE gravity field processing

Gravity field model | Mean gravity | Solid Earth tides | Ocean tides | Pole tide | Short-term variations | N body perturbations |
---|---|---|---|---|---|---|

CSR RL05 | GIF48 | IERS 2010 | GOT4.8 | IERS 2010 (cubic) | AOD1B RL05 | DE 405 |

JPL RL05 | GIF48 | IERS 2010 | GOT4.7 | IERS 2010 (cubic) | AOD1B RL05 | DE 421 |

GFZ RL05 | EIGEN-6C | IERS 2010 | EOT11a | Constant mean pole | AOD1B RL05 | DE 421 |

ITSG-Grace2016 | GOCO04s | IERS 2010 | EOT11a | IERS 2010 (cubic) | AOD1B RL05 | DE 421 |

CSR RL06 | GGM05C | IERS 2010 | GOT4.8 | IERS 2010 (linear) | AOD1B RL06 | DE 430 |

JPL RL06 | GGM05C | IERS 2010 | FES2014b | IERS 2010 (linear) | AOD1B RL06 | DE 430 |

GFZ RL06 | EIGEN-6C4 | IERS 2010 | FES2014 | IERS 2010 (linear) | AOD1B RL06 | DE 430 |

ITSG-Grace2018 | ITSG-GraceGoce2017 | IERS 2010 | FES2014b + GRACE | IERS 2010 (linear) | AOD1B RL06 + LSDM | DE 421 |

The coefficients \({C}_{21}\) and \({S}_{21}\) are proportional to the mass-related part of the equatorial effective angular momentum functions \(\chi _1^{{\rm mass}}\) and \(\chi _2^{{\rm mass}}\) that describe the excitation of polar motion (e.g., Barnes et al. 1983; Gross 2007; Wahr 2005). Conversion formulas given by Göttl (2013) are used here. While the integral excitation can be derived directly from the sum of the GSM and GAC products, individual contributions of the continental hydrosphere \(\chi ^{H}\), oceans \(\chi ^{O}\), Antarctica \(\chi ^{A}\) and Greenland \(\chi ^{G}\) are computed from the sum of the GSM and GAD products by applying adequate filter techniques, masks and global spherical harmonic synthesis/analysis. In this study, we use different versions of the anisotropic decorrelation filter DDK (Kusche 2007) in order to demonstrate that the signal-to-noise ratio could be significantly improved due to the release update. The degree-1 Stokes coefficients are replaced by solutions from Swenson et al. (2008) derived from GRACE data and ocean model outputs in order to account for the fact that mass displacements are referenced to a coordinate system attached to the Earth’s crust which moves relative to the Earth’s center-of-mass frame used in the GRACE data processing. Furthermore, as recommended, the inaccurate \({C}_{20}\) coefficient of the GSM product is replaced by an improved external satellite laser ranging (SLR) solution from Cheng et al. (2013) based on GRACE RL05 (GRACE Technical Note 07) or on GRACE RL06 (GRACE Technical Note 11), respectively. In order to identify individual excitations of polar motion, the effect of glacial isostatic adjustment (GIA) must be removed from the GRACE observations. We use the global GIA model IJ05_R2 from Ivins et al. (2013).

### Polar motion

Polar motion values are taken from the time series EOP 14 C04 of the IERS which is based on a combination of space-geodetic observation techniques (Bizouard et al. 2014). The daily pole coordinates *x* and *y* are fully consistent with the International Terrestrial Reference Frame 2014 (ITRF2014), and the mean uncertainties of the pole coordinates are below 40 μas. From this time series, the so-called geodetic excitation of polar motion, i.e., the equatorial effective angular momentum functions \(\chi ^{C04}\), are determined by applying the conversion formulas given by Gross (1992). They represent the combined excitation from the redistribution of masses (mass effect) and their motion (motion effect) within the Earth system. In order to compare the GRACE-derived excitation with the geodetic excitation, the motion-related part needs to be reduced from the latter. This is achieved by using the geophysical model data described below.

### Geophysical models

For the reduction of the motion-related part from the geodetic excitation, we apply geophysical model data describing the effects of wind and ocean currents as provided by the Global Geophysical Fluids Center (GGFC) of the IERS. These data are derived from two consistent atmosphere/ocean model combinations: The atmospheric re-analysis from NCEP (National Centers for Environmental Prediction; Zhou et al. 2006) in combination with the ocean model ECCO (Estimating the Circulation and Climate of the Ocean; ftp://euler.jpl.nasa.gov/sbo/oam_global/ECCO_kf079.chi) (henceforth referred to as NE), and the atmospheric and oceanic effective angular momentum functions computed by the Earth System Modelling group at Deutsches GeoForschungsZentrum (ESMGFZ) based on operational and re-analysis data from the ECMWF and the ocean model MPIOM (henceforth referred to as ESMGFZ; Dobslaw and Dill 2018). Due to the fact that the modeled motion-related effective angular momentum functions suffer from model uncertainties (in particular due to a lack of precise measurements of wind and ocean velocities on global scale), the remaining mass-related part of the geodetic excitation of polar motion \(\chi ^{C04-{\rm NE}}\) and \(\chi ^{\rm C04-ESMGFZ}\) is afflicted with some (unknown) uncertainty. For a comparison with the GRACE-derived oceanic excitation, we will later use the mass-related parts of the two oceanic excitation series from the ocean model ECCO and from ESMGFZ. The latter combines the effective angular momentum functions for the dynamic ocean (OAM) and for the barystatic sea-level (SLAM) to take into account the inflow of terrestrial water into the oceans.

## Results and comparisons

### Mass redistribution within the Earth system

### Polar motion excitation: integral effect

Empirical standard deviations (mas) of the RL05 and RL06 GRACE-based equatorial effective angular momentum functions

\(\chi _1^{{\rm mass}}\) | \(\chi _2^{{\rm mass}}\) | |
---|---|---|

CSR RL05 | 4.4 (10%) | 3.2 (7%) |

JPL RL05 | 5.3 (12%) | 4.2 (9%) |

GFZ RL05 | 7.3 (16%) | 3.5 (7%) |

ITSG-Grace2016 | | |

CSR RL06 | | |

JPL RL06 | 2.6 (7%) | 2.3 (5%) |

GFZ RL06 | 3.9 (11%) | 4.0 (9%) |

ITSG-Grace2018 | 2.2 (6%) | 2.3 (5%) |

RMS differences (mas)/correlation coefficients between the GRACE-based equatorial effective angular momentum functions and the mass-related part of the geodetic excitation of polar motion

\(\chi _1^{{\rm mass}}\) | \(\chi _2^{{\rm mass}}\) | |||
---|---|---|---|---|

C04-NE | C04-ESMGFZ | C04-NE | C04-ESMGFZ | |

CSR RL05 | 7.1/0.76 | 8.4/0.76 | 9.9/0.97 | 9.3/0.96 |

JPL RL05 | 9.6/0.57 | 13.0/0.35 | 11.4/0.93 | 11.6/0.90 |

GFZ RL05 | 7.3/0.75 | 8.7/0.74 | 10.6/0.95 | 10.1/0.94 |

ITSG-Grace2016 | 6.7/0.79 | 8.9/0.71 | 11.1/0.95 | 10.9/0.93 |

CSR RL06 | 6.2/0.82 | 7.3/0.84 | 9.3/0.97 | 8.9/0.96 |

JPL RL06 | 6.9/0.78 | 8.0/0.78 | 10.1/0.97 | 9.7/0.95 |

GFZ RL06 | 7.8/0.71 | 8.2/0.77 | 11.2/0.95 | 11.3/0.92 |

ITSG-Grace2018 | | | | |

### Polar motion excitation: individual effects from subsystems

Empirical standard deviations (mas) of the GRACE-based equatorial effective angular momentum functions for the continental hydrosphere (H), oceans (O), Antarctica (A) and Greenland (G)

\(\chi _2^{H}\) | \(\chi _1^{O}\) | \(\chi _2^{A}\) | \(\chi _2^{G}\) | |
---|---|---|---|---|

CSR RL05 | 1.6 (9%) | 3.5 (13%) | 0.3 (3%) | 0.1 (1%) |

JPL RL05 | 1.9 (10%) | 4.2 (15%) | 0.2 (3%) | 0.1 (1%) |

GFZ RL05 | 2.0 (11%) | 5.9 (21%) | 0.3 (3%) | 0.1 (1%) |

ITSG-Grace2016 | | | | |

CSR RL06 | | | | |

JPL RL06 | 1.2 (6%) | 2.1 (8%) | 0.1 (1%) | 0.1 (1%) |

GFZ RL06 | 2.2 (12%) | 3.2 (12%) | 0.2 (2%) | 0.1 (1%) |

ITSG-Grace2018 | 1.0 (6%) | 1.9 (7%) | 0.1 (1%) | 0.1 (1%) |

RMS differences (mas)/correlation coefficients between the GRACE-based equatorial effective angular momentum functions for the oceanic mass effect and ocean model results

\(\chi _1^{O}\) | \(\chi _2^{O}\) | |||
---|---|---|---|---|

ECCO (OAM) | ESMGFZ (OAM+SLAM) | ECCO (OAM) | ESMGFZ (OAM+SLAM) | |

CSR RL05 | 5.5/0.49 | 4.4/0.72 | 6.0/0.61 | 6.0/0.66 |

JPL RL05 | 8.3/0.35 | 6.8/0.64 | 7.7/0.41 | 6.8/0.60 |

GFZ RL05 | 5.7/0.51 | 4.9/0.69 | 6.8/0.50 | 6.7/0.58 |

ITSG-Grace2016 | 5.3/0.58 | 4.0/0.79 | 6.5/0.54 | 6.1/0.65 |

CSR RL06 | 4.6/0.60 | 3.9/0.76 | 5.7/0.66 | 5.2/0.75 |

JPL RL06 | 5.0/0.57 | 4.4/0.71 | 5.9/0.63 | 5.4/0.74 |

GFZ RL06 | 5.3/0.58 | 4.8/0.69 | 6.2/0.58 | 5.2/0.76 |

ITSG-Grace2018 | | | | |

## Conclusion

With the GRACE Release 06 solution, the estimation of mass redistributions has significantly been improved, and the noise in the GRACE gravity field solutions has been reduced. Furthermore, the consistency of the analyzed GRACE solutions of CSR, JPL, GFZ and ITSG was increased. Concerning polar motion excitation, in particular the change in the potential coefficients \({C}_{21}\) and \({S}_{21}\) (about 32\(\%\) RL05/RL06) due to the change of the mean pole model from cubic to linear plays a great role. On the other hand, the update of the AOD1B product has only a minor influence. The changes in the potential coefficients \({C}_{21}\) and \({S}_{21}\) amount to only 14 and 8\(\%\) respectively. While the integral effect of the mass-related polar motion excitation can be directly derived from the potential coefficients \({C}_{21}\) and \({S}_{21}\) (GSM + GAC), the determination of individual contributions from the Earth’s subsystems is based on the full set of potential coefficients (GSM + GAD) and requires adequate filtering and masking. Due to the improvement of the signal-to-noise ratio in the RL06 gravity field models, the decorrelation filter DDK3 delivers good results (this is not the case for the RL05 gravity field models). Looking at the GRACE-based results for the integral mass-related polar motion excitation, the change due to the update from RL05 to RL06 is about 15\(\%\). The changes of the time series of \({C}_{21}\) and \({S}_{21}\) have a large impact on the oceanic (17\(\%\)) and hydrological excitation (12\(\%\)), but the effect on the contributions from ice loss in Antarctica (4\(\%\)) and Greenland (1\(\%\)) is small. The trend, in particular of the oceanic mass variation, is significantly reduced in RL06, and the agreement of the excitation functions computed from the CSR, JPL, GFZ and ITSG solutions was improved. For the integral polar motion excitation, the empirical standard deviations of the four solutions amount to 3.8 to 7.3 mas for RL05 and only to 2.2 to 3.9 mas for RL06. The largest improvement can be seen for the mass-related polar motion excitation of the ocean (7 percentage points), followed by the continental hydrology (4 percentage points), Antarctica (1 percentage point) and Greenland (0.2 percentage points). A validation with external results is difficult due to the relatively large uncertainties of geophysical models. For the ocean, our results showed that the latest release update led to a generally higher agreement between the excitation functions from GRACE and model data (improvement 4 to 15 percentage points), where the excitation functions from the ITSG-Grace2018 solution and from the ESMGFZ model agree best. The agreement of the GRACE-derived effective angular momentum functions with the mass-related part of the geodetic excitation could be improved by 2 to 7 percentage points due to the release update. The time series of polar motion excitation derived from ITSG-Grace2018 and C04-NE shows the highest agreement.

## Footnotes

- 1.
JPL has reprocessed the RL05 dataset, the new release is officially called RL05.1; here we refer to it as RL05.

- 2.
GFZ’s release is officially called RL05a; here we refer to it as RL05.

- 3.
GSM: Earth gravity field excluding tidal effects and short-term atmospheric and oceanic variations

- 4.
GAC: Non-tidal short-term effects of the atmosphere and oceans.

- 5.
GAD: Ocean bottom pressure.

## Notes

### Authors' contributions

FG planned the research, conducted the data processing and analysis and wrote the majority of the paper. FS contributed significantly to the writing of the manuscript. All authors read and approved the final manuscript.

### Acknowledgements

The GRACE satellite mission was operated and maintained by NASA (National Aeronautics and Space Administration) and DLR (Deutsche Zentrum für Luft- und Raumfahrt). The GRACE gravity field solutions were provided by the GRACE science teams of CSR, JPL and GFZ as well as by the ITSG of the Graz University of Technology. We are grateful to the IERS for providing polar motion observation series and geophysical fluids data. Open access was supported by the TUM Open Access Publishing Funds. We also thank the two reviewers for their suggestions and comments, which greatly improved the manuscript.

### Competing interests

The authors declare that they have no competing interests.

### Availability of data and materials

All GRACE-derived polar motion excitation functions from DGFI-TUM can be provided on request.

### Funding

These studies are performed in the framework of the project CIEROT (Combination of geodetic space observations for estimating cryospheric mass changes and their impact on Earth rotation) funded by the German Research Foundation (DFG) under Grant No. GO 2707/1-1.

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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