# Improved Estimates of Geocenter Variability from Time-Variable Gravity and Ocean Model Outputs

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## Abstract

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## 1. Introduction

## 2. Data

#### 2.1. Time-Variable Gravity

#### 2.2. Atmospheric Reanalyses and Ocean Models

## 3. Methods

#### 3.1. Eustatic Sea Level from Land Surface Fluxes

#### 3.2. Iterated Solutions

#### 3.3. Spherical Harmonics of Atmospheric and Oceanic Variability

#### 3.4. Time Series Analysis

## 4. Results

#### 4.1. Simulated Geocenter Estimates

#### 4.2. Recovered Geocenter Estimates

#### 4.3. Uncertainty Estimates

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the major geophysical processes contributing to mass variability sensed by time-variable gravity.

**Figure 2.**Flowchart of our processing scheme for estimating geocenter variations from time-variable gravity data and ocean model outputs. Blue nodes denote datasets, red nodes denote calculations, and the green node denotes the final converged solution.

**Figure 3.**Time series of actual and recovered geocenter variations, (

**a**) x, (

**b**) y and (

**c**) z, in mm from synthetic fields of mass variability derived from GLDAS NOAH v2.1 land surface model outputs [53], RACMO2.3 surface mass balance outputs [54,55] and ice sheet mass balance estimates [56]. The gray line is the original degree one time series calculated directly from the synthetic dataset. The orange, purple and green lines are the derived degree one time series using different scenarios to calculate the land-sea fluxes. The orange line uses a static seasonal geocenter from Chen et al. [7], the purple line uses an iterated self-consistent geocenter, and the green line uses an iterated self-consistent geocenter taking into account the effects of self-attraction and loading.

**Figure 4.**Annual amplitudes of (

**a**) actual and (

**b–d**) recovered degree one surface mass variations in mm water equivalent calculated from synthetic fields of mass variability derived from GLDAS NOAH v2.1 land surface model outputs [53], RACMO2.3 surface mass balance outputs [54,55] and ice sheet mass balance estimates [56]. In the recovered solutions, the land-sea exchange is estimated using (

**b**) a static seasonal geocenter from Chen et al. [7], (

**c**) an iterated self-consistent geocenter, and (

**d**) an iterated self-consistent geocenter taking into account the effects of self-attraction and loading.

**Figure 5.**Time series of recovered geocenter variations, (

**a**) x, (

**b**) y and (

**c**) z, in mm calculated using an iterated self-consistent geocenter with self-attraction and loading effects from time-variable gravity fields provided by the Center for Space Research (orange), the German Research Centre for Geosciences (purple) and the Jet Propulsion Laboratory (green). The gray shading denotes the period between the GRACE and GRACE-FO missions.

**Figure 6.**Trends in recovered degree one surface mass variations in mm water equivalent calculated from time-variable gravity fields provided by the Center for Space Research (

**a**–

**c**), the German Research Centre for Geosciences (

**d**–

**f**) and the Jet Propulsion Laboratory (

**g**–

**i**). The land-sea exchange is calculated in the first column (

**a**,

**d**,

**g**) with a static seasonal geocenter from Chen et al. [7], in the second column (

**b**,

**e**,

**h**) with an iterated self-consistent geocenter, and in the third column (

**c**,

**f**,

**i**) with an iterated self-consistent geocenter taking into account the effects of self-attraction and loading.

**Figure 7.**Time series of recovered geocenter variations, (

**a**) x, (

**b**) y and (

**c**) z, in mm calculated using an iterated self-consistent geocenter with self-attraction and loading effects from time-variable gravity fields provided by the Center for Space Research using ocean bottom pressure outputs from ECCO-JPL real-time Kalman-filtered simulations (orange) [36], ECCO Version 4 Release 3 simulations (purple) [38], and Max Planck Institute ocean model (MPIOM) [24].

**Figure 8.**Time series of measured and recovered geocenter variations, (

**a**) x, (

**b**) y and (

**c**) z, in mm from satellite laser ranging (orange and purple) and time-variable gravity fields provided by the Center for Space Research (green). The SLR-derived solutions in orange (CN-CM) are the traditional solutions that center the SLR network [15], and the SLR-derived solutions in purple (CF-CM) include the effects of local site displacements [5]. The solutions derived from GRACE/GRACE-FO in green use an iterated self-consistent geocenter that takes into account the effects of self-attraction and loading.

**Figure 9.**Annual amplitudes of measured and recovered degree one surface mass variations in mm water equivalent calculated from (

**a**–

**c**) time-variable gravity fields provided by the Center for Space Research, and (

**d**) satellite laser ranging (SLR) CF-CM solutions. In the solutions derived from GRACE/GRACE-FO, the land-sea exchange is estimated using (

**a**) a static seasonal geocenter from Chen et al. [7], (

**b**) an iterated self-consistent geocenter, and (

**c**) an iterated self-consistent geocenter taking into account the effects of self-attraction and loading.

**Table 1.**Geocenter motion annual amplitudes, annual phase, and trends for 2002–2017 derived using satellite laser ranging (SLR) and time-variable gravity fields from the Center for Space Research (CSR), the German Research Centre for Geosciences (GFZ) and the Jet Propulsion Laboratory (JPL) corrected for the effects of non-tidal atmospheric and oceanic variation. Errors denote the 95% confidence level.

x | y | z | ||||
---|---|---|---|---|---|---|

Annual Amplitude [mm] | ||||||

CSR | 1.34 ± 0.11 | 1.54 ± 0.12 | 2.25 ± 0.16 | |||

GFZ | 1.38 ± 0.14 | 1.56 ± 0.13 | 2.30 ± 0.16 | |||

JPL | 1.31 ± 0.11 | 1.52 ± 0.12 | 2.20 ± 0.17 | |||

SLR CN-CM | 1.93 ± 0.38 | 1.17 ± 0.38 | 4.25 ± 0.57 | |||

SLR CF-CM | 1.29 ± 0.29 | 1.48 ± 0.23 | 2.97 ± 0.46 | |||

Annual Phase [day] | ||||||

CSR | 356.5 ± 5.0 | 151.9 ± 4.6 | 9.6 ± 4.2 | |||

GFZ | 352.7 ± 5.7 | 150.7 ± 4.9 | 4.5 ± 4.1 | |||

JPL | 355.0 ± 4.8 | 151.4 ± 4.7 | 7.9 ± 4.4 | |||

SLR CN-CM | 5.5 ± 11.7 | 194.7 ± 18.9 | 52.4 ± 7.7 | |||

SLR CF-CM | 347.9 ± 13.3 | 169.6 ± 9.0 | 46.3 ± 9.1 | |||

Trend [mm/yr] | ||||||

CSR | −0.15 ± 0.02 | 0.10 ± 0.02 | −0.62 ± 0.03 | |||

GFZ | −0.19 ± 0.03 | 0.21 ± 0.03 | −0.66 ± 0.03 | |||

JPL | −0.15 ± 0.02 | 0.11 ± 0.03 | −0.63 ± 0.03 |

**Table 2.**Geocenter motion annual amplitudes, annual phase, and trends for 2002–2015 derived using time-variable gravity fields from the Center for Space Research (CSR) using ocean bottom pressure outputs from ECCO-JPL real-time Kalman-filtered simulations (kf080i) [36] and ECCO Version 4 Release 3 simulations (V4r3) [38]. Errors denote the 95% confidence level.

x | y | z | ||||
---|---|---|---|---|---|---|

Annual Amplitude [mm] | ||||||

ECCO-JPL kf080i | 1.46 ± 0.20 | 1.28 ± 0.17 | 1.80 ± 0.31 | |||

ECCO V4r3 | 1.63 ± 0.18 | 1.21 ± 0.16 | 2.31 ± 0.27 | |||

MPIOM | 1.34 ± 0.11 | 1.55 ± 0.13 | 2.24 ± 0.16 | |||

Annual Phase [day] | ||||||

ECCO-JPL kf080i | 307.3 ± 7.9 | 165.5 ± 7.9 | 327.8 ± 9.9 | |||

ECCO V4r3 | 323.0 ± 6.5 | 150.8 ± 7.7 | 326.2 ± 6.9 | |||

MPIOM | 358.3 ± 5.0 | 150.3 ± 4.8 | 9.6 ± 4.3 | |||

Trend [mm/yr] | ||||||

ECCO-JPL kf080i | −0.32 ± 0.04 | 0.16 ± 0.03 | −0.48 ± 0.06 | |||

ECCO V4r3 | −0.10 ± 0.04 | 0.12 ± 0.04 | −0.44 ± 0.06 | |||

MPIOM | −0.12 ± 0.02 | 0.08 ± 0.03 | −0.62 ± 0.03 |

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**MDPI and ACS Style**

Sutterley, T.C.; Velicogna, I.
Improved Estimates of Geocenter Variability from Time-Variable Gravity and Ocean Model Outputs. *Remote Sens.* **2019**, *11*, 2108.
https://doi.org/10.3390/rs11182108

**AMA Style**

Sutterley TC, Velicogna I.
Improved Estimates of Geocenter Variability from Time-Variable Gravity and Ocean Model Outputs. *Remote Sensing*. 2019; 11(18):2108.
https://doi.org/10.3390/rs11182108

**Chicago/Turabian Style**

Sutterley, Tyler C., and Isabella Velicogna.
2019. "Improved Estimates of Geocenter Variability from Time-Variable Gravity and Ocean Model Outputs" *Remote Sensing* 11, no. 18: 2108.
https://doi.org/10.3390/rs11182108