Knowing where and how mass currently changes in polar ice sheets is of great importance (Oppenheimer, 1998, Mitrovica et al., 2011 and Stocker et al., 2013). Observations indicate that the Antarctic Ice Sheet is very sensitive to climate change (Raymo and Mitrovica, 2012, Bromwich et al., 2013, Cook et al., 2013 and Kopp et al., 2013), and knowledge of individual glaciers and ice streams is important to understand the process. Ultimately, the continental ice sheet response to global change is the sum of the behaviors within individual drainage basins, which are subject to the combined effects of surface mass balance, calving and basal melting, and influenced by their geographic location and topography. The contemporary record of ice sheet mass balance has solidified significantly partly owing to the data gathered since 2002 by GRACE, the Gravity Recovery and Climate Experiment (Chen et al., 2006 and Chen et al., 2009; Velicogna and Wahr, 2006). The continent-wide, decadally averaged mass balances of Antarctica, estimated by a variety of techniques, all show that Antarctica is losing mass (Shepherd et al., 2012 and Hanna et al., 2013) at an accelerated rate (Luthcke et al., 2013 and Williams et al., 2014).

While the large-scale spatial and long-term temporal signal trends during the 1990s and 2000s have been well determined, we focus here on the smaller scales recoverable by satellite gravity, and quantify their uncertainty. In Antarctica, improvements in modeling the ongoing glacio-isostatic adjustment from the Last Glacial Maximum deglaciation (for an accessible review, see King, 2013) have increased the precision of gravimetric mass balance estimates. As a result, the detailed pattern of mass change has been the focus of recent GRACE studies (Sasgen et al., 2010 and Sasgen et al., 2013; Harig and Simons, 2012, Horwath et al., 2012, King et al., 2012, Lee et al., 2012, Luthcke et al., 2013, Velicogna and Wahr, 2013 and Bouman et al., 2014). To inform our estimates of sea level change for the coming century it is imperative that we continue to build and improve the detailed record of changes in ice mass (Overpeck et al., 2006; Little et al., 2013a and Little et al., 2013b). In this paper we show when and where Antarctica has been losing mass over the last decade, using a method of spherical Slepian functions.

As GRACE processing of intersatellite range-rates (Rowlands et al., 2005, Luthcke et al., 2006 and Bettadpur and the CSR Level-2 Team, 2012) and global statistical estimation techniques (Schmidt et al., 2006, Han et al., 2008, Baur et al., 2009 and Rowlands et al., 2010) have improved in recent years, the opportunity for contemporary gravimetric studies is to produce a better-resolved ice mass history and to understand its error structure at the same time. Knowledge of ice mass balance at a fine level of spatial detail is ultimately required to enable comparisons of gravity-based estimates with other data sets and models that discretely sample the surface. Data sets and models from point estimates (e.g., laser and radar altimetric observations, GPS time series, or surface mass balance studies) show that Antarctica's mass flux is highly spatially variable (Rignot et al., 2008a, Lenaerts et al., 2012 and Pritchard et al., 2012). Fast-moving glaciers along the Amundsen Sea coast contribute the greatest amount of mass loss (Rignot, 2008, Rignot et al., 2011 and Pritchard et al., 2009), while areas of the Antarctic Peninsula (Rignot et al., 2004) and Wilkes Land (Rignot et al., 2008a) are estimated to have experienced more modest losses. These high-resolution non-gravimetric observations are substantiated by our own new gravity-based results, which are aggregate, not point-based, measurements. The subtle differences between our regional solutions and those of other authors suggest that refining analysis approaches, increasing spatial resolution, and noise mitigation will all remain important research topics in the near future.

Rather than building a consensus model from different data types, each mismatched in their footprint and individual sensitivities to ice mass changes, here we use a uniquely sensitive Slepian-function based gravimetric processing method to localize global GRACE data to several Antarctic regions that display distinct geographic variability, and subsequently focus on the map changes over time within each region. In the main body of this paper we focus our attention on results obtained for the regions of greatest mass change in West Antarctica, and discuss ice mass loss trends in the Peninsula and Dronning Maud Land. Additional details are examined in the Supplementary Material.Knowing where and how mass currently changes in polar ice sheets is of great importance (Oppenheimer, 1998, Mitrovica et al., 2011 and Stocker et al., 2013). Observations indicate that the Antarctic Ice Sheet is very sensitive to climate change (Raymo and Mitrovica, 2012, Bromwich et al., 2013, Cook et al., 2013 and Kopp et al., 2013), and knowledge of individual glaciers and ice streams is important to understand the process. Ultimately, the continental ice sheet response to global change is the sum of the behaviors within individual drainage basins, which are subject to the combined effects of surface mass balance, calving and basal melting, and influenced by their geographic location and topography. The contemporary record of ice sheet mass balance has solidified significantly partly owing to the data gathered since 2002 by GRACE, the Gravity Recovery and Climate Experiment (Chen et al., 2006 and Chen et al., 2009; Velicogna and Wahr, 2006). The continent-wide, decadally averaged mass balances of Antarctica, estimated by a variety of techniques, all show that Antarctica is losing mass (Shepherd et al., 2012 and Hanna et al., 2013) at an accelerated rate (Luthcke et al., 2013 and Williams et al., 2014).

While the large-scale spatial and long-term temporal signal trends during the 1990s and 2000s have been well determined, we focus here on the smaller scales recoverable by satellite gravity, and quantify their uncertainty. In Antarctica, improvements in modeling the ongoing glacio-isostatic adjustment from the Last Glacial Maximum deglaciation (for an accessible review, see King, 2013) have increased the precision of gravimetric mass balance estimates. As a result, the detailed pattern of mass change has been the focus of recent GRACE studies (Sasgen et al., 2010 and Sasgen et al., 2013; Harig and Simons, 2012, Horwath et al., 2012, King et al., 2012, Lee et al., 2012, Luthcke et al., 2013, Velicogna and Wahr, 2013 and Bouman et al., 2014). To inform our estimates of sea level change for the coming century it is imperative that we continue to build and improve the detailed record of changes in ice mass (Overpeck et al., 2006; Little et al., 2013a and Little et al., 2013b). In this paper we show when and where Antarctica has been losing mass over the last decade, using a method of spherical Slepian functions.

As GRACE processing of intersatellite range-rates (Rowlands et al., 2005, Luthcke et al., 2006 and Bettadpur and the CSR Level-2 Team, 2012) and global statistical estimation techniques (Schmidt et al., 2006, Han et al., 2008, Baur et al., 2009 and Rowlands et al., 2010) have improved in recent years, the opportunity for contemporary gravimetric studies is to produce a better-resolved ice mass history and to understand its error structure at the same time. Knowledge of ice mass balance at a fine level of spatial detail is ultimately required to enable comparisons of gravity-based estimates with other data sets and models that discretely sample the surface. Data sets and models from point estimates (e.g., laser and radar altimetric observations, GPS time series, or surface mass balance studies) show that Antarctica's mass flux is highly spatially variable (Rignot et al., 2008a, Lenaerts et al., 2012 and Pritchard et al., 2012). Fast-moving glaciers along the Amundsen Sea coast contribute the greatest amount of mass loss (Rignot, 2008, Rignot et al., 2011 and Pritchard et al., 2009), while areas of the Antarctic Peninsula (Rignot et al., 2004) and Wilkes Land (Rignot et al., 2008a) are estimated to have experienced more modest losses. These high-resolution non-gravimetric observations are substantiated by our own new gravity-based results, which are aggregate, not point-based, measurements. The subtle differences between our regional solutions and those of other authors suggest that refining analysis approaches, increasing spatial resolution, and noise mitigation will all remain important research topics in the near future.

Rather than building a consensus model from different data types, each mismatched in their footprint and individual sensitivities to ice mass changes, here we use a uniquely sensitive Slepian-function based gravimetric processing method to localize global GRACE data to several Antarctic regions that display distinct geographic variability, and subsequently focus on the map changes over time within each region. In the main body of this paper we focus our attention on results obtained for the regions of greatest mass change in West Antarctica, and discuss ice mass loss trends in the Peninsula and Dronning Maud Land. Additional details are examined in the Supplementary Material.