# Evaluating GRACE Mass Change Time Series for the Antarctic and Greenland Ice Sheet—Methods and Results

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## Abstract

**:**

## 1. Introduction

## 2. The Inter-Comparison Exercise

#### 2.1. Overview

#### 2.2. Data Sets

- GRACE monthly gravity field solutions for the period from 2003-01 to 2013-12
- Model predictions to correct GRACE solutions for glacial isostatic adjustment (GIA)
- A series of synthetic data sets to assess the algorithms’ ability to recover the true mass change

#### 2.3. Tasks

- GMB basin product: series of mass changes per basin
- GMB gridded product: series of mass-change grids (entire ice sheets)

#### 2.4. Assessment of Results

- (A)
- Visual inspection of the mass change time series
- (B)
- Comparison with independent data sets (if possible)
- (C)
- Quantification of the temporal changes
- (D)
- Quantification of the noise level
- (E)
- Comparison of the synthetic results and the underlying synthetic truth

## 3. Results

#### 3.1. Submissions

#### 3.2. The Antarctic Ice Sheet

#### 3.2.1. GRACE-Derived Mass Changes per Basin

#### 3.2.2. Synthetic Results per Basin

#### 3.2.3. GRACE-Derived Gridded Mass Changes

#### 3.3. The Greenland Ice Sheet

#### 3.3.1. GRACE-Derived Mass Changes per Basin

#### 3.3.2. Synthetic Results per Basin

#### 3.3.3. GRACE-Derived Gridded Mass Changes

## 4. Discussion and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Drainage basins of the AIS (left) and the GIS (right) based on the basin definitions of Zwally et al. [39]. The inset illustrates basin aggregations for the AIS: Antarctic Peninsula (AP), East Antarctica (EAIS) and West Antarctica (WAIS).

**Figure 2.**Procedure for quantifying the noise level in mass change time series. (

**a**) Original mass change time series of the AIS (black) and the fitted linear, periodic (1 yr, 1/2 yr, 161/365.25 yr) and quadratic model (red). (

**b**) Mass change residuals (black), i.e., original mass change minus fitted model. Red line: Low-pass filtered residuals using a Gaussian average ($\sigma =2.17$ months). (

**c**) High-pass filtered residual, i.e., residuals minus low-pass filtered residuals. The noise assessment is based on the standard deviation of this time series.

**Figure 3.**GRACE-derived mass change time series for (

**a**) the entire Antarctic Ice Sheet (AIS), (

**b**) West Antarctica (WAIS), (

**c**) East Antarctica (EAIS), (

**d**) the Antarctic Peninsula (AP) as well as the drainage basins (

**e**) AIS06 (part of Dronning Maud Land) and (

**f**) AIS21 (part of the Amundsen Sea Sector). Figure 1 gives an overview of all drainage basins. The colour coding indicates the results from different groups (Table 3).

**Figure 4.**Temporal changes in ice mass for all AIS basins and aggregations, derived using a consistent linear, periodic (1 yr, 1/2 yr, 161/365.25 yr) and quadratic model for all time series: (

**a**) linear trend, (

**b**) acceleration, (

**c**) seasonal amplitude, (

**d**) 161-day period, including the formal errors from the least squares adjustment.

**Figure 5.**Noise level, given in terms of the scaled standard deviation of the noise time series, for all AIS basins and aggregations, derived from (

**a**) the mass change time series and (

**b**) the time series of the average surface density change. Grey bars indicate the ratio between the basin areas and the entire AIS area.

**Figure 6.**Differences between mass change estimates derived from different synthetic data sets and the corresponding true mass change for (

**a**) the AIS as well as drainage basins (

**b**) AIS21 and (

**c**) AIS24. True (non-zero) mass changes are indicated by numbers at the top margin (unit: gigatons). (

**d**) RMS of the differences for all drainage basins (AIS01–AIS24, AIS27, AIS28).

**Figure 7.**Linear trends derived from the gridded mass changes, using a consistent linear, periodic (1 yr, 1/2 yr, 161/365.25 yr) and quadratic model, and interpolated to the prescribed regular polar-stereographic grid. Panels (

**a**–

**c**) show results from different groups (Table 3). Grid cells in grey lie outside of the original grid domains.

**Figure 8.**Noise level, given in terms of the scaled standard deviation of the noise time series, estimated from the gridded mass changes. Panels (

**a**–

**c**) show results from different groups (Table 3). Grid cells in grey lie outside of the original grid domains.

**Figure 9.**GRACE-derived mass change time series for (

**a**) the entire Greenland Ice Sheet (GIS) as well as the drainage basins (

**b**) GIS01 (North Greenland), (

**c**) GIS03 (East Greenland) and (

**d**) GIS04 (South-east Greenland). Figure 1 gives an overview of all drainage basins. The colour coding indicates the results from different groups (Table 3).

**Figure 10.**Temporal changes in ice mass for all GIS basins and aggregations, derived using a consistent linear, periodic (1 yr, 1/2 yr, 161/365.25 yr) and quadratic model for all time series: (

**a**) linear trend, (

**b**) acceleration, (

**c**) seasonal amplitude, (

**d**) 161-day period, including the formal errors from the least squares adjustment.

**Figure 11.**Noise level, given in terms of the scaled standard deviation of the noise time series, for all GIS basins and the entire GIS, derived from (

**a**) the mass change time series and (

**b**) the time series of the average surface density change. Grey bars indicate the ratio between the basin areas and the entire GIS area.

**Figure 12.**Differences between mass change estimates derived from different synthetic data sets and the corresponding true mass change for (

**a**) the GIS as well as drainage basins (

**b**) GIS01 and (

**c**) GIS04. True (non-zero) mass changes are indicated by numbers at the top margin (unit: gigatons). (

**d**) RMS of the differences for all drainage basins (GIS01–GIS08).

**Figure 13.**Linear trends derived from the gridded mass changes, using a consistent linear, periodic (1 yr, 1/2 yr, 161/365.25 yr) and quadratic model, and interpolated to the prescribed regular polar-stereographic grid. Panels (

**a**–

**c**) show results from different groups (Table 3). Grid cells in grey lie outside of the original grid domains.

**Figure 14.**Noise level, given in terms of the scaled standard deviation of the noise time series, estimated from the gridded mass changes. Panels (

**a**–

**c**) show results from different groups (Table 3). Grid cells in grey lie outside of the original grid domains.

**Figure 15.**Comparison of GRACE-derived mass change time series for (

**a**) the AIS, (

**b**) the Antarctic Peninsula, (

**c**) East Antarctica and (

**d**) West Antarctica from three participants (faint colours) with a time series based on radar altimetry (RA) and a multi-sensor time series from IMBIE-2 [19].

**Figure 16.**Comparison of GRACE-derived mass change time series for (

**a**) the GIS, (

**b**) AIS, (

**c**) East Antarctica and (

**d**) West Antarctica from the participants (faint colours) with alternative results (bold colours), namely, the updated time series from Schrama et al. [16] and time series extracted from the mascon products provided by CSR, JPL and GSFC. The alternative results are shifted along the y-axis to increase readability.

**Table 1.**Individual synthetic data sets utilised to quantify signal leakage. For data sets extracted from perennial model time series the selected epochs are indicated.

Data Set ID | Description |
---|---|

01–06 | Six data sets of modelled spatial variability in Antarctic surface mass balance (SMB) |

Epochs: 1980-01, 1986-10, 1996-01, 2004-08, 2009-02, 2014-08 | |

07 | Spatial pattern of the mean annual AIS mass change as observed by satellite altimetry |

08–13 | Six data sets of modelled spatial variability in Greenland SMB |

Epochs: 1960-05, 1970-10, 1980-05, 1990-10, 2000-05, 2010-10 | |

14 | Spatial pattern of the mean annual GIS mass change as observed by satellite altimetry |

15 | Spatially uniform mean annual ice mass change over the Canadian Arctic Archipelago |

16–21 | Six data sets simulating residual global oceanic mass variations (e.g., due to errors in the GRACE de-aliasing products) |

Epochs: 2002-09, 2005-03, 2006-09, 2009-03, 2010-09, 2013-03 | |

22–27 | Six data sets of modelled mass changes in global continental hydrology (excluding AIS and GIS) |

Epochs: 2004-03, 2005-09, 2007-01, 2009-01, 2010-12, 2011-10 |

**Table 2.**Spatial coverage of the results contributed by five groups, derived from GRACE data and synthetic input data. Basin-scale products comprise all prescribed basins and the entire ice sheet (Figure 1).

ID | RI1 | RI2 | FM1 | MC1 | MC2/MC3 |
---|---|---|---|---|---|

Results from GRACE data | |||||

Basin mass changes | AIS, GIS | AIS, GIS | AIS, GIS | AIS, GIS | GIS |

Grids | AIS, GIS | AIS, GIS | None | AIS, GIS | None |

Results from synthetic input data | |||||

Basin mass changes | AIS, GIS | None | AIS, GIS | AIS, GIS | None |

Grids | AIS, GIS | None | None | None | None |

**Table 3.**Selected details on the data sets and the processing strategy used by each participating group.

ID | RI1 | RI2 | FM1 | MC1 | MC2/MC3 |
---|---|---|---|---|---|

Software specifications | |||||

Software | Matlab code | C code | Fortran code | Fortran code | Fortran code, Matlab code, UNIX scripts |

Data used | |||||

GRACE data | CSR RL05 [20] | CSR RL05 [20] | CSR RL05 [20] | CSR RL05 [20] | CSR RL05 [20] |

Period | 2003-02– 2013-12 | 2003-01– 2013-12 | 2003-01– 2013-12 | 2003-01– 2013-12 | 2003-01– 2013-12 |

${l}_{\mathrm{max}}$ | 96 (used: 90) | 60 | 60 | 60 | 96 |

Degree 1 | [22] | [22] | [22] | [22] | [22] |

C${}_{2,0}$ | [21] | [21] | [21] | [21] | [21] |

GIA | [23,25] | [23,25] | [23,25] | [23,25] | [23,25] |

Methods applied | |||||

Methods for mass changes per basin | Regional integration with tailored integration kernels [44] | Regional integration [45,46] | Forward modelling [15] | Mascon [17] | Mascon [47,48,49] |

Filtering | Empirical GRACE error variance and covariance model | 300 km Gaussian | 150 km/250 km Gaussian | DDK [8] | None |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Groh, A.; Horwath, M.; Horvath, A.; Meister, R.; Sørensen, L.S.; Barletta, V.R.; Forsberg, R.; Wouters, B.; Ditmar, P.; Ran, J.; Klees, R.; Su, X.; Shang, K.; Guo, J.; Shum, C.K.; Schrama, E.; Shepherd, A. Evaluating GRACE Mass Change Time Series for the Antarctic and Greenland Ice Sheet—Methods and Results. *Geosciences* **2019**, *9*, 415.
https://doi.org/10.3390/geosciences9100415

**AMA Style**

Groh A, Horwath M, Horvath A, Meister R, Sørensen LS, Barletta VR, Forsberg R, Wouters B, Ditmar P, Ran J, Klees R, Su X, Shang K, Guo J, Shum CK, Schrama E, Shepherd A. Evaluating GRACE Mass Change Time Series for the Antarctic and Greenland Ice Sheet—Methods and Results. *Geosciences*. 2019; 9(10):415.
https://doi.org/10.3390/geosciences9100415

**Chicago/Turabian Style**

Groh, Andreas, Martin Horwath, Alexander Horvath, Rakia Meister, Louise Sandberg Sørensen, Valentina R. Barletta, René Forsberg, Bert Wouters, Pavel Ditmar, Jiangjun Ran, Roland Klees, Xiaoli Su, Kun Shang, Junyi Guo, C. K. Shum, Ernst Schrama, and Andrew Shepherd. 2019. "Evaluating GRACE Mass Change Time Series for the Antarctic and Greenland Ice Sheet—Methods and Results" *Geosciences* 9, no. 10: 415.
https://doi.org/10.3390/geosciences9100415