The Arctic: Alaska, Canadian Archipelago, and Greenland
Below are the results continued from our recent paper Harig and Simons [2016], Geophys. Res. Let., 2016. http://dx.doi.org/10.1002/2016GL067759. As of the most recent update January 2016 here, these results use the Release level 5 UTCSR (http://www.csr.utexas.edu/grace/) data solutions from January 2003 up to and including February 2015.

In the latest trend estimate from our paper Antarctica as a whole has lost -92 Gigatons per year since the beginning of 2003 (Fig 1, panel e). We also estimate mass changes for smaller regions within Antarctica (panels a-d), the most dramatic of these being West Antarctica which has lost -121 Gigatons per year of ice mass and has been strongly accelerating.
Total Trend
Figure 1: Map of the total ice mass change [mass corrected using the GIA model by Paulson et al., 2007] for the regions (black dashed lines) around a) Greenland and b) Gulf of Alaska. Coastlines are shown in light grey. Glaciated regions, as determined from the Randolph Glacier Inventory (RGI) version 3.2, are outlined in dark grey. For more technical details please see the Methods/Code webpage.
Below we show several of the Slepian basis functions we use for our analysis. These functions are bandlimited up to degree L=60 and are localized to the dashed regions. When the regions are small compared to the bandwidth there will be only a few functions that fit into each region. In the regions below the Shannon number, or the number of functions which are well localized, is only N=3 or 4 functions.
Total Map
Figure 2: Slepian eigenfunctions that are optimally concentrated within regions (grouped by row) outlining a) Ellesmere Island, b) Baffin Island, c) Gulf of Alaska North, and d) Gulf of Alaska South. Dashed lines indicate the regions of concentration. Functions are bandlimited to L=60 and are scaled to unit magnitude. The parameter alpha denotes which eigenfunction is shown. The parameter lambda is the corresponding eigenvalue for each function, indicating the amount of concentration. Magnitude values whose absolute values are smaller than 0.01 are left white. For more technical details please see the Methods/Code webpage.
In Fig. 3 we shows the mass trends for two regions in the Gulf of Alaska. In the Northern region, mass loss has been steady over the past 13 years with very little acceleration. The Southern region in contrast has had little mass loss or acceleration over this period. Both regions show large seasonal cycles which are 3-4 times larger per square meter than in areas of the Canadian Archipelago or Greenland.
Yearly Maps
Figure 3: Ice mass changes [mass corrected using the GIA model by Paulson et al., 2007] in gigatons (Gt) for a) North and b) South regions of the Gulf of Alaska. The regions covered by each localization are shaded in red in the top right inset. The black lines are monthly GRACE observations with two sigma error bars determined from our analysis. The solid blue lines are the best-fit estimates including a quadratic curve and the periodic annual and semi-annual terms. For each year in the analysis two numbers indicate the maximum (top) and minimum (bottom) difference between the observations and the fitted curves. For more technical details please see the Methods/Code webpage.
The mass trends for Greenland and the Canadian Archipelago, seen in Figure 4, show the strong mass loss observed during the GRACE epoch in these regions. This figure also shows how the mass change in 2013 diverged from the long term trend of the prior ten years. This departure can be seen more clearly when we remove the long term trend and acceleration, and show, as in Figure 5, the remaining seasonal components of the data and fit. This is a good reminder that the GRACE measurement period is not yet long enough to fully capture the ice mass variability of the Greenland ice sheet.
Yearly Maps
Figure 4: Ice mass changes [mass corrected using the GIA model by Paulson et al., 2007] in gigatons (Gt) for regions of a) Ellesmere Island, b) Baffin Island, and c) Greenland. The regions covered by each localization are shaded red in the top right inset. The black lines are monthly GRACE observations with two sigma grey error bars determined from our analysis. The solid blue lines are the best-fit estimates including a quadratic curve and the periodic annual and semi-annual terms. Estimates are fit using data prior to June 2013 (left of vertical grey lines), and then extrapolated forward through 2014 (right of vertical grey lines) to show the departure of recent data from the long-term trends. For more technical details please see the Methods/Code webpage.
Yearly Maps
Figure 5: Ice mass changes found after removing the long-term trend and accelerations from the curves shows in Fig. 4, leaving only the annual and semiannual components (blue lines) fitted from the data (black lines). The regions covered by each localization for a) Ellesmere, b) Baffin, and c) Greenland are shaded red in the insert. As in Fig. 4, estimates are fit using data prior to June 2013 (left of vertical grey lines), and then extrapolated forward through 2014 (right of vertical grey lines) to show the departure of recent data from the long-term trends. The grey bands around the blue lines represent the two sigma confidence intervals for the prediction of new data points. Yearly numbers indicate the maximum (top) and minimum (bottom) difference between the observations and the fitted curves. For more technical details please see the Methods/Code webpage.
References (see also Publications)
Harig, Christopher and Frederik J. Simons. Ice mass loss in Greenland, the Gulf of Alaska, and the Canadian Archipelago: Seasonal cycles and decadal trends. Geophys. Res. Let., 2016. http://dx.doi.org/10.1002/2016GL067759