# Antarctic Ice Mass Change Products from GRACE/GRACE-FO Using Tailored Sensitivity Kernels

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

#### 2.1. GRACE/GRACE-FO Monthly Solutions

#### 2.2. Synthetic Data Sets

#### 2.3. Regional Mass Change Estimates

#### 2.3.1. Regional Integration Approach

#### 2.3.2. Mascon Approach

#### 2.3.3. Tailored Sensitivity Kernels

- (A)
- mass changes inside the cell are correctly reproduced by the estimate for this cell
- (B)
- mass changes outside the cell have zero effect on the estimate for this cell
- (C)
- the influence of mission errors on the mass change estimate of the cell is zero

#### 2.4. Tailored Sensitivity Kernels for the Antarctic Ice Sheet

#### 2.4.1. General Parametrization

#### 2.4.2. Accounting for Residual Oceanic Mass Changes

#### 2.5. Product Generation and Assessment

#### 2.5.1. Gravimetric Mass Change Products

#### 2.5.2. Noise Level

#### 2.5.3. Signal Leakage

#### 2.5.4. Mass Balance Estimation and Uncertainty Assessment

## 3. Results and Discussion

#### 3.1. Tailored Sensitivity Kernels

#### 3.2. Gravimetric Mass Change Products

#### 3.2.1. Basin Products

#### Mass Change Time Series

#### Noise Level

#### Signal Leakage

#### TSK Selection

#### Mass Balance Estimates

#### Inter-Comparison

#### 3.2.2. Gridded Products

## 4. Conclusions and Outlook

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Tapley, B.; Bettadpur, S.; Ries, J.; Thompson, P.; Watkins, M. GRACE Measurements of Mass Variability in the Earth System. Science
**2004**, 305, 503–505. [Google Scholar] [CrossRef] [PubMed][Green Version] - Tapley, B.; Watkins, M.; Flechtner, F.; Reigber, C.; Bettadpur, S.; Rodell, M.; Sasgen, I.; Famiglietti, J.; Landerer, F.; Chambers, D.; et al. Contributions of GRACE to understanding climate change. Nat. Clim. Chang.
**2019**, 9, 358–369. [Google Scholar] [CrossRef] [PubMed] - Landerer, F.; Flechtner, F.; Save, H.; Webb, F.; Bandikova, T.; Bertiger, W.; Bettadpur, S.; Byun, S.; Dahle, C.; Dobslaw, H.; et al. Extending the global mass change data record: GRACE Follow-On instrument and science data performance. Geophys. Res. Lett.
**2020**, 47, e2020GL088306. [Google Scholar] [CrossRef] - Swenson, S.; Wahr, J. Methods for inferring regional surface-mass anomalies from Gravity Recovery and Climate Experiment (GRACE) measurements of time-variable gravity. J. Geophys. Res.
**2002**, 107, 2193. [Google Scholar] [CrossRef][Green Version] - Baur, O.; Kuhn, M.; Featherstone, W. GRACE-derived ice-mass variations over Greenland by accounting for leakage effects. J. Geophys. Res.
**2009**, 114, B06407. [Google Scholar] [CrossRef][Green Version] - Velicogna, I.; Wahr, J. Greenland mass balance from GRACE. Geophys. Res. Lett.
**2005**, 32, L18505. [Google Scholar] [CrossRef][Green Version] - Horwath, M.; Dietrich, R. Signal and error in mass change inferences from GRACE: The case of Antarctica. Geophys. J. Int.
**2009**, 177, 849–864. [Google Scholar] [CrossRef][Green Version] - Jacob, T.; Wahr, J.; Pfeffer, W.; Swenson, S. Recent contributions of glaciers and ice caps to sea level rise. Nature
**2012**, 482, 514–518. [Google Scholar] [CrossRef] - Wouters, B.; Chambers, D.; Schrama, E. GRACE observes small-scale mass loss in Greenland. Geophys. Res. Lett.
**2008**, 35, L20501. [Google Scholar] [CrossRef][Green Version] - Schrama, E.; Wouters, B.; Rietbroek, R. A mascon approach to assess ice sheet and glacier mass balances and their uncertainties from GRACE data. J. Geophys. Res. Solid Earth
**2014**, 119, 6048–6066. [Google Scholar] [CrossRef] - Forsberg, R.; Sørensen, L.; Simonsen, S. Greenland and Antarctica Ice Sheet Mass Changes and Effects on Global Sea Level. Surv. Geophys.
**2017**, 38, 89–104. [Google Scholar] [CrossRef][Green Version] - Ran, J.; Ditmar, P.; Klees, R.; Farahani, H. Statistically optimal estimation of Greenland Ice Sheet mass variations from GRACE monthly solutions using an improved mascon approach. J. Geod.
**2018**, 92, 299–319. [Google Scholar] [CrossRef] [PubMed][Green Version] - Swenson, S.; Wahr, J. Post-processing removal of correlated errors in GRACE data. Geophys. Res. Lett.
**2006**, 33, L08402. [Google Scholar] [CrossRef] - Kusche, J. Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models. J. Geod.
**2007**, 81, 733–749. [Google Scholar] [CrossRef][Green Version] - Landerer, F.; Swenson, S. Accuracy of scaled GRACE terrestrial water storage estimates. Water Resour. Res.
**2012**, 48. [Google Scholar] [CrossRef] - Vishwakarma, B.; Horwath, M.; Devaraju, B.; Groh, A.; Sneeuw, N. A Data-Driven Approach for Repairing the Hydrological Catchment Signal Damage Due to Filtering of GRACE Products. Water Resour. Res.
**2017**, 53, 9824–9844. [Google Scholar] [CrossRef] - Barletta, V.; Sørensen, L.; Forsberg, R. Scatter of mass changes estimates at basin scale for Greenland and Antarctica. Cryosphere
**2013**, 7, 1411–1432. [Google Scholar] [CrossRef][Green Version] - Groh, A.; Horwath, M.; Horvath, A.; Meister, R.; Sørensen, L.; Barletta, V.; Forsberg, R.; Wouters, B.; Ditmar, P.; Ran, J.; et al. Evaluating GRACE Mass Change Time Series for the Antarctic and Greenland Ice Sheet—Methods and Results. Geosciences
**2019**, 9, 415. [Google Scholar] [CrossRef][Green Version] - Bettadpur, S. UTCSR Level-2 Processing Standards Document for Level-2 Product Release 0006, v5.0; Technical Report; Center for Space Research, The University of Texas at Austin: Austin, TX, USA, 2018. [Google Scholar]
- Save, H. CSR Level-2 Processing Standards Document for Level-2 Product Release 06, v1.1. Technical Report; Center for Space Research, The University of Texas at Austin: Austin, TX, USA, 2019. [Google Scholar]
- Swenson, S.; Chambers, D.; Wahr, J. Estimating geocenter variations from a combination of GRACE and ocean model output. J. Geophys. Res.
**2008**, B113, B08410. [Google Scholar] [CrossRef][Green Version] - 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. [Google Scholar] [CrossRef] - Sun, Y.; Riva, R.; Ditmar, P. Optimizing estimates of annual variations and trends in geocenter motion and J
_{2}from a combination of GRACE data and geophysical models. J. Geophys. Res. Solid Earth**2016**, 121, 8352–8370. [Google Scholar] [CrossRef][Green Version] - Loomis, B.; Rachlin, K.; Luthcke, S. Improved Earth oblateness rate reveals increased ice sheet losses and mass-driven sea level rise. Geophys. Res. Lett.
**2019**, 46, 6910–6917. [Google Scholar] [CrossRef] - Loomis, B.; Rachlin, K.; Wiese, D.; Landerer, F.; Luthcke, S. Replacing GRACE/GRACE-FO C30 with satellite laser ranging: Impacts on Antarctic Ice Sheet mass change. Geophys. Res. Lett.
**2020**. [Google Scholar] [CrossRef] - Landerer, F.; Flechtner, F.; Save, H.; Dahle, C.; Watkins, M. GRACE Follow-on Science Data System Newsletter Report: June/July 2020 (No. 14). 2020. Available online: ftp://isdcftp.gfz-potsdam.de/grace-fo/DOCUMENTS/NEWSLETTER/2020/GRACE-FO_SDS_NL_014_202006.pdf (accessed on 7 March 2021).
- Bruinsma, S.; Lemoine, J.M.; Biancale, R.; Valès, N. CNES/GRGS 10-day gravity field models (release 2) and their evaluation. Adv. Space Res.
**2010**, 45, 587–601. [Google Scholar] [CrossRef] - Ivins, E.; James, T.; Wahr, J.; Schrama, E.; Landerer, F.; Simon, K. Antarctic contribution to sea level rise observed by GRACE with improved GIA correction. J. Geophys. Res. Solid Earth
**2013**, 118, 3126–3141. [Google Scholar] [CrossRef][Green Version] - Farrell, W. Deformation of the Earth by Surface Loads. Rev. Geophys. Space Phys.
**1972**, 10, 761–797. [Google Scholar] [CrossRef] - Ditmar, P. Conversion of time-varying Stokes coefficients into mass anomalies at the Earth’s surface considering the Earth’s oblateness. J. Geod.
**2018**, 92, 1401–1412. [Google Scholar] [CrossRef][Green Version] - Ghobadi-Far, K.; Šprlák, M.; Han, S.C. Determination of ellipsoidal surface mass change from GRACE time-variable gravity data. Geophys. J. Int.
**2019**, 219, 248–259. [Google Scholar] [CrossRef] - Van Wessem, J.; Reijmer, C.; Morlighem, M.; Mouginot, J.; Rignot, E.; Medley, B.; Joughin, I.; Wouters, B.; Depoorter, M.; Bamber, J.; et al. Improved representation of East Antarctic surface mass balance in a regional atmospheric climate model. J. Glaciol.
**2014**, 60, 761–770. [Google Scholar] [CrossRef][Green Version] - Noël, B.; van de Berg, W.; van Meijgaard, E.; Kuipers Munneke, P.; van de Wal, R.; van den Broeke, M. Evaluation of the updated regional climate model RACMO2.3: Summer snowfall impact on the Greenland Ice Sheet. Cryosphere
**2015**, 9, 1831–1844. [Google Scholar] [CrossRef][Green Version] - McMillan, M.; Shepherd, A.; Sundal, A.; Briggs, K.; Muir, A.; Ridout, A.; Hogg, A.; Wingham, D. Increased ice losses from Antarctica detected by CryoSat-2. Geophys. Res. Lett.
**2014**, 41, 3899–3905. [Google Scholar] [CrossRef] - Groh, A.; Ewert, H.; Rosenau, R.; Fagiolini, E.; Gruber, C.; Floricioiu, D.; Abdel Jaber, W.; Linow, S.; Flechtner, F.; Eineder, M.; et al. Mass, volume and velocity of the Antarctic Ice Sheet: Present-day changes and error effects. Surv. Geophys.
**2014**, 35, 1481–1505. [Google Scholar] [CrossRef][Green Version] - Gardner, A.; Moholdt, G.; Wouters, B.; Wolken, G.; Burgess, D.; Sharp, M.; Cogley, J.; Braun, C.; Labine, C. Sharply increased mass loss from glaciers and ice caps in the Canadian Arctic Archipelago. Nature
**2011**, 473, 357–360. [Google Scholar] [CrossRef] [PubMed] - Flechtner, F. AOD1B Product Description Document for Product Releases 01 to 04; Technical Report; Deutsches GeoForschungsZentrum GFZ: Potsdam, Germany, 2007. [Google Scholar]
- Flechtner, F.; Dobslaw, H.; Fagiolini, E. AOD1B Product Description Document for Product Release 05, Rev. 4.3; Technical Report; Deutsches GeoForschungsZentrum GFZ: Potsdam, Germany, 2015. [Google Scholar]
- Döll, P.; Kaspar, F.; Lehner, B. A global hydrological model for deriving water availability indicators: Model tuning and validation. J. Hydrol.
**2003**, 270, 105–134. [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] - Preisendorfer, R. Principal Component Analysis in Meteorology and Oceanography; Elsevier Science Publishers B.V.: Amsterdam, The Netherlands, 1988. [Google Scholar]
- Bergmann, I.; Dobslaw, H. Short-term transport variability of the Antarctic Circumpolar Current from satellite gravity observations. J. Geophys. Res. Ocean.
**2012**, 117, C05044. [Google Scholar] [CrossRef][Green Version] - Zwally, H.; Giovinetto, M.; Beckley, M.; Saba, J. Antarctic and Greenland Drainage Systems. 2012. Available online: http://icesat4.gsfc.nasa.gov/cryo_data/ant_grn_drainage_systems.php (accessed on 7 March 2021).
- Ray, R.; Luthcke, S. Tide model errors and GRACE gravimetry: Towards a more realistic assessment. Geophys. J. Int.
**2006**, 167, 1055–1059. [Google Scholar] [CrossRef][Green Version] - Whitehouse, P.; Bentley, M.; Milne, G.; King, M.; Thomas, I. A new glacial isostatic adjustment model for Antarctica: Calibrated and tested using observations of relative sea-level change and present-day uplift rates. Geophys. J. Int.
**2012**, 190, 1464–1482. [Google Scholar] [CrossRef][Green Version] - Peltier, W.; Argus, D.; Drummond, R. Comment on “An Assessment of the ICE-6G_C (VM5a) Glacial Isostatic Adjustment Model” by Purcell et al. J. Geophys. Res. Solid Earth
**2018**, 123, 2019–2028. [Google Scholar] [CrossRef] - Caron, L.; Ivins, E.; Larour, E.; Adhikari, S.; Nilsson, J.; Blewitt, G. GIA Model Statistics for GRACE Hydrology, Cryosphere, and Ocean Science. Geophys. Res. Lett.
**2018**, 45. [Google Scholar] [CrossRef] - Cheng, M.; Ries, J.; Tapley, B. Geocenter Variations from Analysis of SLR Data. In Reference Frames for Applications in Geosciences; International Association of Geodesy Symposia; Altamimi, Z., Collilieux, X., Eds.; Springer: Berlin/Heidelberg, Germany, 2013; Volume 138, pp. 19–25. [Google Scholar] [CrossRef]
- Rietbroek, R.; Fritsche, M.; Brunnabend, S.E.; Daras, I.; Kusche, J.; Schröter, J.; Flechtner, F.; Dietrich, R. Global surface mass from a new combination of GRACE, modelled OBP and reprocessed GPS data. J. Geodyn.
**2012**, 59–60, 64–71. [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] - Cheng, M.; Tapley, B.; Ries, J. Deceleration in the Earth’s oblateness. J. Geophys. Res. Solid Earth
**2013**, 118, 740–747. [Google Scholar] [CrossRef] - Bloßfeld, M.; Müller, H.; Gerstl, M.; Štefka, V.; Bouman, J.; Göttl, F.; Horwath, M. Second-degree Stokes coefficients from multi-satellite SLR. J. Geod.
**2015**, 89, 857–871. [Google Scholar] [CrossRef] - Cheng, M.; Ries, J. Decadal variation in Earth’s oblateness (J2) from satellite laser ranging data. Geophys. J. Int.
**2017**, 212, 1218–1224. [Google Scholar] [CrossRef] - 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. GFZ Data Services
**2019**. [Google Scholar] [CrossRef] - Lenaerts, J.; van Meijgaard, E.; van den Broeke, M.; Ligtenberg, S.; Horwath, M.; Isaksson, E. Recent snowfall anomalies in Dronning Maud Land, East Antarctica, in a historical and future climate perspective. Geophys. Res. Lett.
**2013**, 40, 2684–2688. [Google Scholar] [CrossRef] - Dahle, C.; Murböck, M.; Flechtner, F.; Dobslaw, H.; Michalak, G.; Neumayer, K.; 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. [Google Scholar] [CrossRef][Green Version] - Pritchard, H.; Arthern, R.; Vaughan, D.; Edwards, L. Extensive dynamic thinning on the margins of the Greenland and Antarctic ice sheets. Nature
**2009**, 461, 971–975. [Google Scholar] [CrossRef] - Martín-Español, A.; King, M.; Zammit-Mangion, A.; Andrews, S.; Moore, P.; Bamber, J. An assessment of forward and inverse GIA solutions for Antarctica. J. Geophys. Res. Solid Earth
**2016**, 121, 6947–6965. [Google Scholar] [CrossRef][Green Version] - Velicogna, I.; Mohajerani, Y.; Landerer, F.; Mouginot, J.; Noel, B.; Rignot, E.; Sutterley, T.; van den Broeke, M.; van Wessem, J.; Wiese, D. Continuity of ice sheet mass loss in Greenland and Antarctica from the GRACE and GRACE Follow-On missions. Geophys. Res. Lett.
**2020**, 47, e2020GL087291. [Google Scholar] [CrossRef][Green Version] - Loomis, B.; Luthcke, S.; Sabaka, T. Regularization and error characterization of GRACE mascons. J. Geod.
**2019**. [Google Scholar] [CrossRef] [PubMed] - Shepherd, A.; Gilbert, L.; Muir, A.; Konrad, H.; McMillan, M.; Slater, T.; Briggs, K.; Sundal, A.; Hogg, A.; Engdahl, M. Trends in Antarctic Ice Sheet Elevation and Mass. Geophys. Res. Lett.
**2019**. [Google Scholar] [CrossRef][Green Version] - The IMBIE Team. Mass balance of the Antarctic Ice Sheet from 1992 to 2017. Nature
**2018**, 558, 219–222. [Google Scholar] [CrossRef] [PubMed][Green Version] - Rignot, E.; Mouginot, J.; Scheuchl, B.; van den Broeke, M.; Van Wessem, J.; Morlighem, M. Four decades of Antarctic Ice Sheet mass balance from 1979–2017. Proc. Natl. Acad. Sci. USA
**2019**, 116, 1095–1103. [Google Scholar] [CrossRef] [PubMed][Green Version] - Baxter, B.; Hubbert, S. Radial Basis Functions for the Sphere. In Recent Progress in Multivariate Approximation; Haussmann, W., Jetter, K., Reimer, M., Eds.; Birkhäuser: Basel, Switzerland, 2001; pp. 33–47. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Residual surface density anomalies with respect to the standard model derived from filtered CSR RL06 monthly solutions (corrected for cumulative surface mass balance anomalies over the Antarctic Ice Sheet): (

**a**) standard deviation and (

**b**) first empirical orthogonal function (EOF) from a principal component analysis of the residuals over the adjacent ocean. The spatial pattern in (

**b**) is scaled by the standard deviation of the corresponding principal component.

**Figure 2.**Different realizations (columns) of tailored sensitivity kernels ${\eta}_{\mathrm{tsk}}$ (unitless) for integrating mass changes of (

**a**–

**c**) the Antarctic Ice Sheet, (

**d**–

**f**) Basin 06, (

**g**–

**i**) Basin 21 and (

**j**–

**l**) a $50\phantom{\rule{0.166667em}{0ex}}\mathrm{km}\times 50\phantom{\rule{0.166667em}{0ex}}\mathrm{km}$ grid cell marked by the red cross. Contour lines (thin) are given at intervals of 0.1 and 0.005 for panels (

**a**–

**i**) and (

**j**–

**l**), respectively. Thick contours lines are shown for multiples of 0.5. Red lines depict the basin outlines. Faint blue dots in panel (

**j**) indicate the locations of additional points from the cluster ICE. Please note the differing color scales for panels (

**a**–

**i**) and (

**j**–

**l**).

**Figure 3.**Mass change time series, i.e., the gravimetric basin product, for (

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

**b**) Basin 06 and (

**c**) Basin 21 derived using different realizations of tailored sensitivity kernels.

**Figure 4.**(

**a**) Root mean square of the noise in gravimetric basin products for individual drainage basins and aggregations. Colored symbols indicate different realizations of tailored sensitivity kernels used to derive the basin products. Grey bars show the ratio between the basin area and the area of the entire AIS (linear scale at the right-hand side ordinate axis). (

**b**) Overview of Antarctic drainage basins and aggregations (grey shades) based on the basin definitions by Zwally et al. [43]. FRIS and RIS indicate the location of the Filchner-Ronne Ice Shelf and the Ross Ice Shelf, respectively.

**Figure 5.**Differences between mass change estimates derived from synthetic data sets (Table 1) and the their corresponding true mass changes for (

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

**b**) Basin 06, (

**c**) Basin 21 derived using different realizations of tailored sensitivity kernels and (

**d**) the root mean square (RMS) over all basins and aggregations (Figure 4b).

**Figure 6.**Components (bars) contributing to the overall uncertainty of the mass balance (numbers) for the final mass change basin products of variant (ICE,FAR,ANTOC,1.0). The overall uncertainty accounts for formal errors from the least-squares adjustment, for uncertainties of the degree $l=1$ addition, related to the ${C}_{20}$ replacement, of the glacial isostatic adjustment (GIA) model correction and for leakage errors. Bars indicate the components’ share of the total variance.

**Figure 7.**Mass change time series from GRACE/GRACE-FO using tailored sensitivity kernels of variant (ICE,FAR,ANTOC,1.0), from satellite altimetry-derived surface elevation changes (SEC, [61]) and from the input–output-method (IOM, [59]) for (

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

**b**) Dronning Maud Land (i.e., Basins 05–08) and (

**c**) Amundsen Sea Sector (i.e., Basins 21–22). Faint lines indicate the corresponding residuals with respect to the linear trend over the period from 2002-04 through 2016-08.

**Figure 8.**(

**a**–

**c**) Linear trends over different periods derived from the gridded mass change product using the standard model. (

**d**) Noise level of each grid cell, assessed as described in Section 2.5.2. All results are based on variant (ICE,FAR,ANTOC,1.0) of the gridded product.

**Table 1.**Synthetic data sets used to assess signal leakage. Dates indicate the epochs selected from perennial model time series.

ID | Acronym | Description |
---|---|---|

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

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

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

08–13 | GIS SMB | Six data sets of modelled spatial variability in Greenland surface mass balance |

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

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

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

16–21 | OCN | 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 | HYD | 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.**Overview of parametrizations, i.e., spatial coverage of the different clusters of points, grid type, grid cell area and assumed signal variance, used to derive tailored sensitivity kernels ${\mathit{\eta}}_{\mathrm{tsk}}$.

Cluster | Coverage | Grid/Cell Area | Signal Variance |
---|---|---|---|

ICE | Grid cells covering the AIS | polar-stereo. ($2.5\times {10}^{3}\phantom{\rule{0.166667em}{0ex}}{\mathrm{km}}^{2}$) | (400 mm w.eq.)${}^{2}$ |

FAR | Far-field grid cells outside the AIS | icosahedron ($1.4\times {10}^{4}\phantom{\rule{0.166667em}{0ex}}{\mathrm{km}}^{2}$) | (33.6 mm w.eq.)${}^{2}$ |

ANTOC | Spatial pattern covering the Antarctic Ocean ($\phi \phantom{\rule{3.33333pt}{0ex}}\le -{60}^{\xb0}$) | icosahedron ($1.4\times {10}^{4}\phantom{\rule{0.166667em}{0ex}}{\mathrm{km}}^{2}$) | Spatially variable, median: (14.7 mm w.eq.)${}^{2}$ |

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**MDPI and ACS Style**

Groh, A.; Horwath, M. Antarctic Ice Mass Change Products from GRACE/GRACE-FO Using Tailored Sensitivity Kernels. *Remote Sens.* **2021**, *13*, 1736.
https://doi.org/10.3390/rs13091736

**AMA Style**

Groh A, Horwath M. Antarctic Ice Mass Change Products from GRACE/GRACE-FO Using Tailored Sensitivity Kernels. *Remote Sensing*. 2021; 13(9):1736.
https://doi.org/10.3390/rs13091736

**Chicago/Turabian Style**

Groh, Andreas, and Martin Horwath. 2021. "Antarctic Ice Mass Change Products from GRACE/GRACE-FO Using Tailored Sensitivity Kernels" *Remote Sensing* 13, no. 9: 1736.
https://doi.org/10.3390/rs13091736