# The GFZ GRACE RL06 Monthly Gravity Field Time Series: Processing Details and Quality Assessment

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## Abstract

**:**

## 1. Introduction

## 2. GRACE Level-2 Gravity Field Processing at GFZ

#### 2.1. GPS Constellation

#### 2.2. GRACE Observations

- K-band range-rate (KRR) observations (KBR1B product) as primary observations to retrieve monthly gravity field estimates.
- GPS code and carrier phase observations (GPS1B product) used for precise orbit determination of the GRACE satellites. Please note that inside GFZ’s EPOS software, zero-difference ionosphere-free (L3) linear combinations of the measurements are generated and processed.
- Linear accelerations (ACC1B product) to model non-conservative forces acting on the GRACE satellites. Please note that these onboard accelerometer (ACC) observations are not treated as classical observations in a least-squares sense, but only as part of the right-hand side force model.
- Star camera observations (SCA1B product) describing the GRACE satellites’ attitude, required for the rotation from the satellite reference frame (SRF) to the inertial frame.

#### 2.3. Background Models

#### 2.4. Processing Strategy

#### 2.5. Parametrization

#### 2.6. Orbit Quality

## 3. Results

#### 3.1. Formal and Empirical Errors

#### 3.2. Degree Amplitudes

#### 3.3. RMS of Residuals in the Spatial Domain

#### 3.4. Low Degree Harmonics

## 4. External Validation

#### 4.1. OBP Validation

#### 4.2. GOCE Orbit Tests

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Rodell, M.; Famiglietti, J.S.; Wiese, D.N.; Reager, J.T.; Beaudoing, H.K.; Landerer, F.W.; Lo, M.H. Emerging trends in global freshwater availability. Nature
**2018**, 557, 651–659. [Google Scholar] [CrossRef] [PubMed] - Kusche, J.; Eicker, A.; Forootan, E.; Springer, A.; Longuevergne, L. Mapping probabilities of extreme continental water storage changes from space gravimetry. Geophys. Res. Lett.
**2016**, 43, 8026–8034. [Google Scholar] [CrossRef] [Green Version] - Sasgen, I.; Konrad, H.; Ivins, E.R.; Van den Broeke, M.R.; Bamber, J.L.; Martinec, Z.; Klemann, V. Antarctic ice-mass balance 2003 to 2012: Regional reanalysis of GRACE satellite gravimetry measurements with improved estimate of glacial-isostatic adjustment based on GPS uplift rates. Cryosphere
**2013**, 7, 1499–1512. [Google Scholar] [CrossRef] - Wouters, B.; Gardner, A.S.; Moholdt, G. Global Glacier Mass Loss During the GRACE Satellite Mission (2002–2016). Front. Earth Sci.
**2019**, 7, 96. [Google Scholar] [CrossRef] - Reager, J.T.; Gardner, A.S.; Famiglietti, J.S.; Wiese, D.N.; Eicker, A.; Lo, M.H. A decade of sea level rise slowed by climate-driven hydrology. Science
**2016**, 351, 699–703. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Rietbroek, R.; Brunnabend, S.E.; Kusche, J.; Schröter, J.; Dahle, C. Revisiting the contemporary sea-level budget on global and regional scales. Proc. Natl. Acad. Sci. USA
**2016**, 113, 1504–1509. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Poropat, L.; Dobslaw, H.; Zhang, L.; Macrander, A.; Boebel, O.; Thomas, M. Time variations in ocean bottom pressure from a few hours to many years: In situ data, numerical models, and GRACE satellite gravimetry. J. Geophys. Res. Ocean
**2018**, 123, 5612–5623. [Google Scholar] [CrossRef] - Landerer, F.W.; Wiese, D.N.; Bentel, K.; Boening, C.; Watkins, M.M. North Atlantic meridional overturning circulation variations from GRACE ocean bottom pressure anomalies. Geophys. Res. Lett.
**2015**, 42, 8114–8121. [Google Scholar] [CrossRef] - Tapley, B.D.; Watkins, M.M.; Flechtner, F.; Reigber, C.; Bettadpur, S.; Rodell, M.; Sasgen, I.; Famiglietti, J.S.; Landerer, F.W.; Chambers, D.P.; et al. Contributions of GRACE to understanding climate change. Nat. Clim. Chang.
**2019**, 9, 358–369. [Google Scholar] [CrossRef] - Bettadpur, S. UTCSR Level-2 Processing Standards Document (For Level-2 Product Release 0006) (Rev. 5.0, April 18, 2018). GRACE Publication 327–742. 2018. Available online: ftp://isdcftp.gfz-potsdam.de/grace/DOCUMENTS/Level-2/ (accessed on 10 September 2019).
- Yuan, D.N. JPL Level-2 Processing Standards Document For Level-2 Product Release 06 (Rev. 6.0, June 1, 2018). GRACE Publication 327–744. 2018. Available online: ftp://isdcftp.gfz-potsdam.de/grace/DOCUMENTS/Level-2/ (accessed on 10 September 2019).
- Dahle, C.; Flechtner, F.; Murböck, M.; Michalak, G.; Neumayer, K.; Abrykosov, O.; Reinhold, A.; König, R. GRACE 327-743 (Gravity Recovery and Climate Experiment): GFZ Level-2 Processing Standards Document for Level-2 Product Release 06 (Rev. 1.0, October 26, 2018); Scientific Technical Report STR - Data, 18/04; GFZ German Research Centre for Geosciences: Potsdam, Germany, 2018. [Google Scholar] [CrossRef]
- Kornfeld, R.P.; Arnold, B.W.; Gross, M.A.; Dahya, N.T.; Klipstein, W.M.; Gath, P.F.; Bettadpur, S. GRACE-FO: The Gravity Recovery and Climate Experiment Follow-On Mission. J. Spacecr. Rocket.
**2019**, 56, 931–951. [Google Scholar] [CrossRef] - Kvas, A.; Behzadpour, S.; Ellmer, M.; Klinger, B.; Strasser, S.; Zehentner, N.; Mayer-Gürr, T. ITSG-Grace2018: Overview and Evaluation of a New GRACE-Only Gravity Field Time Series. J. Geophys. Res. Solid Earth
**2019**, 124. [Google Scholar] [CrossRef] - Lemoine, J.M.; Bourgogne, S.; Biancale, R.; Bruinsma, S. RL04 monthly gravity field solutions from CNES/GRGS. In Proceedings of the the GRACE/GRACE-FO Science Team Meeting, Potsdam, Germany, 9–11 October 2018. [Google Scholar]
- Meyer, U.; Jäggi, A.; Jean, Y.; Beutler, G. AIUB-RL02: An improved time-series of monthly gravity fields from GRACE data. Geophys. J. Int.
**2016**, 205, 1196–1207. [Google Scholar] [CrossRef] - Chen, Q.; Shen, Y.; Chen, W.; Francis, O.; Zhang, X.; Chen, Q.; Li, W.; Chen, T. An optimized short-arc approach: Methodology and application to develop refined time series of Tongji-Grace2018 GRACE monthly solutions. J. Geophys. Res. Solid Earth
**2019**, 124, 6010–6038. [Google Scholar] [CrossRef] - Dahle, C.; Flechtner, F.; König, R.; Michalak, G.; Neumayer, K.; Gruber, C.; König, D. GFZ RL05: An Improved Time-Series of Monthly GRACE Gravity Field Solutions. In Observation of the System Earth from Space - CHAMP, GRACE, GOCE and Future Missions. Advanced Technologies in Earth Sciences; Flechtner, F., Sneeuw, N., Schuh, W., Eds.; Springer: Berlin/Heidelberg, Germany, 2014; pp. 29–39. ISBN 978-3-642-32134-4. [Google Scholar] [CrossRef]
- Reigber, C. Gravity field recovery from satellite tracking data. In Theory of Satellite Geodesy and Gravity Field Determination; Lecture Notes in Earth Sciences; Sanso, F., Rummel, R., Eds.; Springer: Berlin/Heidelberg, Germany, 1989; Volume 25, pp. 197–234. ISBN 3-540-51528-3. [Google Scholar]
- König, D. A Terrestrial Reference Frame realised on the observation level using a GPS-LEO satellite constellation. J. Geod.
**2018**, 92, 1299–1312. [Google Scholar] [CrossRef] - Case, K.; Kruizinga, G.; Wu, S. GRACE Level 1B Data Product User Handbook (Rev. 1.3). JPL Publication D-22027.
**2010**. Available online: ftp://isdcftp.gfz-potsdam.de/grace/DOCUMENTS/Level-1/ (accessed on 10 September 2019). - GRACE. GRACE Level 1B JPL Release 3.0; Data Publication; PO.DAAC: CA, USA, 2018. [Google Scholar] [CrossRef]
- Bandikova, T.; McCullough, C.; Kruizinga, G.L.; Save, H.; Christophe, B. GRACE accelerometer data transplant. Adv. Space Res.
**2019**, 64, 623–644. [Google Scholar] [CrossRef] [Green Version] - Flechtner, F.; Neumayer, K.H.; Dahle, C.; Dobslaw, H.; Fagiolini, E.; Raimondo, J.C.; Güntner, A. What Can be Expected from the GRACE-FO Laser Ranging Interferometer for Earth Science Applications? Surv. Geophys.
**2016**, 37, 453–470. [Google Scholar] [CrossRef] - Förste, C.; Bruinsma, S.; Shako, R.; Marty, J.C.; Flechtner, F.; Abrykosov, O.; Dahle, C.; Lemoine, J.M.; Neumayer, K.H.; Biancale, R.; et al. EIGEN-6—A New Combined Global Gravity Field Model Including GOCE Data from the Collaboration of GFZ-Potsdam and GRGS-Toulouse; Geophysical Research Abstracts Vol. 13, EGU2011-3242-2; EGU General Assembly: Vienna, Austria, 2011. [Google Scholar]
- Förste, C.; Bruinsma, S.; Abrykosov, O.; Lemoine, J.M.; Marty, J.C.; Flechtner, F.; Balmino, G.; Barthelmes, F.; Biancale, R. EIGEN-6C4 The Latest Combined Global Gravity Field Model Including GOCE Data Up to Degree and Order 2190 of GFZ Potsdam and GRGS Toulouse; Data Publication; GFZ Data Services: Potsdam, Germany, 2014. [Google Scholar] [CrossRef]
- Savcenko, R.; Bosch, W. EOT11a—Empirical Ocean Tide Model from Multi-Mission Satellite Altimetry; Report No. 89; Deutsches Geodätisches Forschungsinstitut: München, Germany, 2012. [Google Scholar]
- Carrere, L.; Lyard, F.; Cancet, M.; Guillot, A.; Picot, N. FES2014, a new tidal model—Validation results and perspectives for improvements. In Proceedings of the ESA Living Planet Symposium 2016, Prague, Czech Republic, 9–13 May 2016. [Google Scholar]
- Biancale, R.; Bode, A. Mean Annual and Seasonal Atmospheric Tide Models Based on 3-hourly and 6-hourly ECMWF Surface Pressure Data; Scientific Technical Report STR, 06/01; GFZ German Research Centre for Geosciences: Potsdam, Germany, 2006. [Google Scholar] [CrossRef]
- Dobslaw, H.; Flechtner, F.; Bergmann-Wolf, I.; Dahle, C.; Dill, R.; Esselborn, S.; Sasgen, I.; Thomas, M. Simulating high-frequency atmosphere-ocean mass variability for de-aliasing of satellite gravity observations: AOD1B RL05. J. Geophys. Res. Ocean
**2013**, 118, 3704–3711. [Google Scholar] [CrossRef] - Dobslaw, H.; Bergmann-Wolf, I.; Dill, R.; Poropat, L.; Thomas, M.; Dahle, C.; Esselborn, S.; König, R.; Flechtner, F. A new high-resolution model of non-tidal atmosphere and ocean mass variability for de-aliasing of satellite gravity observations: AOD1B RL06. Geophys. J. Int.
**2017**, 211, 263–269. [Google Scholar] [CrossRef] [Green Version] - Desai, S.D. Observing the pole tide with satellite altimetry. J. Geophys. Res.
**2002**, 107, 3186. [Google Scholar] [CrossRef] - Petit, G.; Luzum, B. IERS Conventions (2010); IERS Technical Note No. 36; Verlag des Bundesamts für Kartographie und Geodäsie: Frankfurt am Main, Germany, 2010; p. 179. ISBN 3-89888-989-6. [Google Scholar]
- Ray, R.D.; Loomis, B.D.; Luthcke, S.B.; Rachlin, K.E. Tests of ocean-tide models by analysis of satellite-to-satellite range measurements: An update. Geophys. J. Int.
**2019**, 217, 1174–1178. [Google Scholar] [CrossRef] - Schmidt, R. Zur Bestimmung des cm-Geoids und Dessen Zeitlicher Variationen mit GRACE. Scientific Technical Report STR, 07/04. Ph.D. Thesis, GFZ German Research Centre for Geosciences, Potsdam, Germany, 2007. [Google Scholar] [CrossRef]
- Klinger, B.; Mayer-Gürr, T. The role of accelerometer data calibration within GRACE gravity field recovery: Results from ITSG-Grace2016. Adv. Space Res.
**2016**, 58, 1597–1609. [Google Scholar] [CrossRef] [Green Version] - Arnold, D.; Montenbruck, O.; Hackel, S.; Sosnica, K. Satellite laser ranging to low Earth orbiters: Orbit and network validation. J. Geod.
**2018**. [Google Scholar] [CrossRef] - Montenbruck, O.; Garcia-Fernandez, M.; Yoon, Y.; Schön, S.; Jäggi, A. Antenna phase center calibration for precise positioning of LEO satellites. GPS Solut.
**2009**, 13, 23. [Google Scholar] [CrossRef] - Kusche, J.; Schmidt, R.; Petrovic, S.; Rietbroek, R. Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model. J. Geod.
**2009**, 83, 903–913. [Google Scholar] [CrossRef] [Green Version] - Cheng, M.K.; Ries, J.C. The unexpected signal in GRACE estimates of C20. J. Geod.
**2017**, 91, 897–914. [Google Scholar] [CrossRef] - Cheng, M.K.; Ries, J.C. Monthly estimates of C20 from 5 SLR Satellites Based on GRACE RL06 Models. GRACE Technical Note TN-11. Available online: ftp://isdcftp.gfz-potsdam.de/grace/DOCUMENTS/TECHNICAL_NOTES/TN-11_C20_SLR_RL06.txt (accessed on 10 September 2019).
- König, R.; Schreiner, P.; Dahle, C. Monthly Estimates of C(2,0) Generated by GFZ from SLR Satellites Based on GFZ GRACE/GRACE-FO RL06 Background Models. V. 1.0; Data Publication; GFZ Data Services: Potsdam, Germany, 2019. [Google Scholar] [CrossRef]
- Wahr, J.; Nerem, R.S.; Bettadpur, S.V. The pole tide and its effect on GRACE time-variable gravity measurements: Implications for estimates of surface mass variations. J. Geophys. Res.: Solid Earth
**2015**, 120, 4597–4615. [Google Scholar] [CrossRef] - Macrander, A.; Böning, C.; Boebel, O.; Schröter, J. Validation of GRACE Gravity Fields by In-Situ Data of Ocean Bottom Pressure. In System Earth via Geodetic-Geophysical Space Techniques. Advanced Technologies in Earth Sciences; Flechtner, F., Gruber, T., Güntner, A., Mandea, M., Rothacher, M., Schöne, T., Wickert, J., Eds.; Springer: Berlin/Heidelberg, Germany, 2010; pp. 169–185. ISBN 978-3-642-10227-1. [Google Scholar] [CrossRef]
- A, G.; Wahr, J.; Zhong, S. Computations of the viscoelastic response of a 3-D compressible Earth to surface loading: An application to glacial isostatic adjustment in Antarctica and Canada. Geophys. J. Int.
**2013**, 192, 557–572. [Google Scholar] [CrossRef] - Kvas, A.; Mayer-Gürr, T.; Krauss, S.; Brockmann, J.M.; Schubert, T.; Schuh, W.D.; Pail, R.; Gruber, T.; Jäggi, A.; Meyer, U. The Satellite-Only Gravity Field Model GOCO06s; Data Publication; GFZ Data Services: Potsdam, Germany, 2019. [Google Scholar] [CrossRef]
- Bergmann-Wolf, I.; Zhang, L.; Dobslaw, H. Global eustatic sea-level variations for the approximation of geocenter motion from GRACE. J. Geod. Sci.
**2014**, 4, 37–48. [Google Scholar] [CrossRef] - Dobslaw, H.; Dill, R.; Dahle, C. GRACE Geopotential GAD Coefficients GFZ RL06. V. 6.0; Data Publication; GFZ Data Services: Potsdam, Germany, 2018. [Google Scholar] [CrossRef]
- Böning, C.; Timmermann, R.; Macrander, A.; Schröter, J. A pattern-filtering method for the determination of ocean bottom pressure anomalies from GRACE solutions. Geophys. Res. Lett.
**2008**, 35, L18611. [Google Scholar] [CrossRef] - Drinkwater, M.; Haagmans, R.; Muzi, D.; Popescu, A.; Floberghagen, R.; Kern, M.; Fehringer, M. The GOCE gravity mission: ESA’s first core explorer. In Proceedings of the 3rd International GOCE User Workshop, Frascati, Italy, 6–9 November 2006; ESA SP-627. pp. 1–3, ISBN 92-9092-938-3. [Google Scholar]
- Bock, H.; Jäggi, A.; Beutler, G.; Meyer, U. GOCE: Precise orbit determination for the entire mission. J. Geod.
**2014**, 88, 1047–1060. [Google Scholar] [CrossRef] - Gruber, T.; Visser, P.N.A.M.; Ackermann, C.; Hosse, M. Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons. J. Geod.
**2011**, 85, 845–860. [Google Scholar] [CrossRef] - Visser, P.N.A.M.; van den Ijssel, J. Calibration and validation of individual GOCE accelerometers by precise orbit determination. J. Geod.
**2016**, 90, 1–13. [Google Scholar] [CrossRef] - Pail, R.; Bruinsma, S.; Migliaccio, F.; Förste, C.; Goiginger, H.; Schuh, W.D.; Höck, E.; Reguzzoni, M.; Brockmann, J.M.; Abrikosov, O.; et al. First GOCE gravity field models derived by three different approaches. J. Geod.
**2011**, 85, 819. [Google Scholar] [CrossRef] - Förste, C.; Abrykosov, O.; Bruinsma, S.; Dahle, C.; König, R.; Lemoine, J.M. ESA’s Release 6 GOCE Gravity Field Model by Means of the Direct Approach Based on Improved Filtering of the Reprocessed Gradients of the Entire Mission; Data Publication; GFZ Data Services: Potsdam, Germany, 2019. [Google Scholar] [CrossRef]
- Göttl, F.; Schmidt, M.; Seitz, F. Mass-related excitation of polar motion: An assessment of the new RL06 GRACE gravity field models. Earth Planets Space
**2018**, 70, 195. [Google Scholar] [CrossRef] - Adhikari, S.; Ivins, E.R.; Frederikse, T.; Landerer, F.W.; Caron, L. Sea-level fingerprints emergent from GRACE mission data. Earth Syst. Sci. Data
**2019**, 11, 629–646. [Google Scholar] [CrossRef] [Green Version] - Dahle, C.; Flechtner, F.; Murböck, M.; Michalak, G.; Neumayer, K.; Abrykosov, O.; Reinhold, A.; König, R. GRACE-FO D-103919 (Gravity Recovery and Climate Experiment Follow-On): GFZ Level-2 Processing Standards Document for Level-2 Product Release 06 (Rev. 1.0, June 3, 2019); Scientific Technical Report STR - Data, 19/09; GFZ German Research Centre for Geosciences: Potsdam, Germany, 2019. [Google Scholar] [CrossRef]

**Figure 1.**Code residual variation maps of GRACE-A (

**top**) and GRACE-B (

**bottom**) for June 2014 (

**left**) and August 2014 (

**right**). Radio occultation measurements on GRACE-A were activated in June 2014 and deactivated in August 2014 and vice versa on GRACE-B, after a satellite swap in July 2014.

**Figure 2.**Mean and standard deviation per year of GRACE-A (blue) and -B (red) SLR residuals during the different GRACE processing steps for all available stations and a subset of high-quality stations.

**Figure 3.**(

**a**–

**d**) SH spectra of empirical error RMS for RL05a (

**a**) and RL06 (

**b**); and of formal error RMS for RL05a (

**c**) and RL06 (

**d**); (

**e**) Ratio of SH spectra of empirical error RMS “RL05a/RL06”; (

**f**) SH degree amplitudes of the ratio of empirical error RMS “RL05a/RL06” (blue), and the ratios “empirical/formal error RMS” for RL05a (red), and RL06 (green).

**Figure 4.**Degree amplitudes relative to a climatology model for GFZ RL05a (

**left**) and GFZ RL06 (

**right**); thin lines represent monthly solutions (without “GRACE single ACC” solutions and those regularized in RL05a), and bold lines represent the median curves (the same curves are shown in both plots) for RL05a (red), RL06 (96 × 96, green), RL06 (60 × 60, blue), and the “GRACE single ACC” months only for RL05a (black) and RL06 (96 × 96, grey).

**Figure 5.**RMS of the time series of residuals (cm EWH) relative to a climatology model (without months regularized in RL05a) for GFZ RL05a (left) and GFZ RL06 (right); the following different cases are shown: period from 2002/04 through 2016/08, DDK5 filtered (

**a**) and DDK3 filtered (

**b**); and “GRACE single ACC” period, DDK3 filtered (

**c**).

**Figure 6.**wRMS over the oceans (cm EWH) of DDK5 filtered residuals relative to a climatology model for the complete GFZ RL05a (red), GFZ RL06 (96 × 96, green), and GFZ RL06 (60 × 60, blue) time series.

**Figure 7.**Time series of SH coefficients C

_{20}(

**a**); C

_{21}(

**b**); and S

_{21}(

**c**); each plot shows values of GFZ RL05a (red), GFZ RL06 (96 × 96, green), and GFZ RL06 (60 × 60, blue); for C

_{20}, the SLR-based time series König et al. [42] is shown additionally (black).

**Figure 8.**(

**a**) Relative explained variances ${\sigma}_{r}^{2}$ at in situ OBP stations for GFZ RL06; (

**b**) Correlation coefficients between in situ OBP and GRACE OBP for GFZ RL06; (

**c**) Difference of relative explained variances for GFZ RL06 and GFZ RL05a; (

**d**) Difference of correlation coefficients for GFZ RL06 and GFZ RL05a. For (

**c**) and (

**d**), red colors indicate improvements of GFZ RL06 over GFZ RL05a; stationswith relative explained variances or correlation coefficients < 0 for both RL06 and RL05a are marked with white crosses.

**Figure 9.**Gravity field anomalies in terms of cm EWH (DDK3 filtered) for the month 2003/08 for all GFZ GRACE releases so far: RL01 (

**top left**), RL02 (

**top middle**), RL03 (

**top right**), RL04 (

**bottom left**), RL05a (

**bottom middle**), and RL06 (

**bottom right**).

Background Model | GFZ RL05a | GFZ RL06 |
---|---|---|

Static a priori gravity field | EIGEN-6C [25] (up to d/o 200) | EIGEN-6C4 [26] (up to d/o 200) |

Time-variable a priori gravity field | Trend, annual and semi-annual | GFZ RL05a (DDK1 smoothed, |

coefficients of EIGEN-6C | up to d/o 50), only used | |

(up to d/o 50) | during data editing | |

Ocean tides | EOT11a [27] | FES2014 [28] |

Atmospheric tides | Biancale & Bode [29] | same as RL05a |

Non-tidal atmospheric and | AOD1B RL05 [30] | AOD1B RL06 [31] |

oceanic mass variations | ||

Ocean pole tide | Desai [32] | same as RL05a |

Solid Earth and pole tides | IERS2010 [33] | same as RL05a |

3rd body ephemerides | JPL DE421 | JPL DE430 |

GFZ RL05a | GFZ RL06 | ||
---|---|---|---|

GPS data editing | |||

Remarks | GRACE-A & -B jointly processed | GRACE-A & -B independently processed | |

Time-variable a priori | yes | yes | |

gravity field | |||

Observation weights | ${\sigma}_{GPSphase}$ | 0.7 cm | 0.3 cm |

${\sigma}_{GPScode}$ | 70.0 cm | 40.0 cm | |

${\sigma}_{KRR}$ | 50 $\mathsf{\mu}$m/s | no KRR observations | |

KRR data editing | |||

Remarks | further GPS data editing | no further GPS | |

still possible | data editing | ||

automated editing based | no automated editing, instead | ||

on 8-sigma elimination | visual inspection of residuals | ||

Time-variable a priori | yes | yes | |

gravity field | |||

Observation weights | ${\sigma}_{GPSphase}$ | 0.7 cm | 0.3 cm |

${\sigma}_{GPScode}$ | 70.0 cm | 40.0 cm | |

${\sigma}_{KRR}$ | 0.1 $\mathsf{\mu}$m/s | 0.3 $\mathsf{\mu}$m/s | |

Generation of a priori orbits / generation of arc-wise NEQs | |||

Time-variable a priori | yes | no | |

gravity field | |||

Observation weights | ${\sigma}_{GPSphase}$ | 0.7 cm | arc-wise based on residuals scaled by empirical factor of 7 |

${\sigma}_{GPScode}$ | 70.0 cm | ||

${\sigma}_{KRR}$ | 0.1 $\mathsf{\mu}$m/s | arc-wise based on residuals |

**Table 3.**Number and properties of GFZ RL05a and RL06 orbit and instrument parameters (numbers are per arc representative for the nominal arc length of 24 h).

GFZ RL05a | GFZ RL06 | |||
---|---|---|---|---|

GPS editing step | subsequent steps | GPS editing step | subsequent steps | |

Orbital elements | 6/6 (GRACE-A/GRACE-B) | |||

Empirical accel. | 20/20 | none | 64/64 | |

Details | cos/sin coefficients of 1/rev periodical model | |||

every 4.8 h in TN | - | 1/rev in TN | ||

no constraint | - | constraint: $\sigma $ = 1E-8 m/s${}^{2}$ | ||

K-band param. | none | 48 | none | |

Details | - | range-rate bias & | - | |

drift every 90 min; | ||||

cos/sin coeff. of range | ||||

bias every 180 min | ||||

ACC param. | 75/75 ${}^{\left(1\right)}$ | 18/18 ${}^{\left(3\right)}$ | ||

54/54 ${}^{\left(2\right)}$ | 18/18 ${}^{\left(4\right)}$ | 24/24 ${}^{\left(4\right)}$ | ||

Details | 1-hourly biases in RTN; | 3 biases per arc in RT; 9 in N | ||

scale factors fixed to 1 ${}^{\left(1\right)}$ | 1 scale factor per arc in RTN | |||

3-hourly biases in RTN; | 6 off-diagonal elements | |||

3-hourly scale factors in RTN${}^{\left(2\right)}$ | of scale factor matrix; | |||

constraint: $\sigma $ = 1E-3 ${}^{\left(4\right)}$ |

**Table 4.**RMS of orbit fits [cm] for the time-variable GFZ RL05a and RL06 gravity field models and (only for reference) for the static model GO_CONS_GCF_2_DIR_R6. RMS values are based on 3D residuals and represent mean values of the 30 individual arcs within a particular month.

Gravity Field Model | Month | |||
---|---|---|---|---|

2009/11 | 2009/12 | 2010/10 | 2010/11 | |

GFZ RL05a | 8.39 | 9.14 | 7.53 | 7.40 |

GFZ RL06 | 7.39 | 6.84 | 6.24 | 6.21 |

GO_CONS_GCF_2_DIR_R6 | 3.56 | 3.37 | 3.82 | 3.76 |

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**MDPI and ACS Style**

Dahle, C.; Murböck, M.; Flechtner, F.; Dobslaw, H.; Michalak, G.; Neumayer, K.H.; Abrykosov, O.; Reinhold, A.; König, R.; Sulzbach, R.;
et al. The GFZ GRACE RL06 Monthly Gravity Field Time Series: Processing Details and Quality Assessment. *Remote Sens.* **2019**, *11*, 2116.
https://doi.org/10.3390/rs11182116

**AMA Style**

Dahle C, Murböck M, Flechtner F, Dobslaw H, Michalak G, Neumayer KH, Abrykosov O, Reinhold A, König R, Sulzbach R,
et al. The GFZ GRACE RL06 Monthly Gravity Field Time Series: Processing Details and Quality Assessment. *Remote Sensing*. 2019; 11(18):2116.
https://doi.org/10.3390/rs11182116

**Chicago/Turabian Style**

Dahle, Christoph, Michael Murböck, Frank Flechtner, Henryk Dobslaw, Grzegorz Michalak, Karl Hans Neumayer, Oleh Abrykosov, Anton Reinhold, Rolf König, Roman Sulzbach,
and et al. 2019. "The GFZ GRACE RL06 Monthly Gravity Field Time Series: Processing Details and Quality Assessment" *Remote Sensing* 11, no. 18: 2116.
https://doi.org/10.3390/rs11182116