What was done
With respect to the ongoing quest to determine the nature and magnitude of long-term climate change, which typically focuses on detecting presumed anthropogenic-induced global warming, the authors note that "any putative trend of increasingly negative mass balance [of glaciers or ice sheets] has to be detected against the background of year-to-year variations."  In view of this requirement, they explore the relationship between long-term mass balance and interannual variability in the totality of earth's glaciers for which such data exist.

What was learned
The authors begin by noting there are over 200 glaciers for which mass balance data exist for at least one year.  When the length-of-record criterion is increased to five years, this number drops to 115; and if both winter and summer mass balances are required, the number drops to 79.  Furthermore, if ten years of record is used as a cutoff point, only 42 glaciers qualify; and more stringent requirements result in much lower numbers.  At the extreme record length of 50 years is the Storglaciaren of northern Sweden, which exhibited a negative mass balance of little trend for the first 15 years of record but which then began to trend upward, actually becoming positive over about the last decade.

Working with various sets of these glaciers, the authors develop relationships that allow them to calculate how long a period of mass balance measurements would be required to determine whether or not the Greenland ice sheet was in a state of flux or equilibrium.  They conclude that "the ice sheet can thicken or thin by several meters over 20-30 years without giving statistically significant evidence of non-zero balance under present climate."

What it means
In the words of the authors, "one of the most important problems for mass-balance glaciology, after more than 50 years of hard work, is the sad fact that many glacierized regions of the world remain unsampled, or only poorly sampled," suggesting that we really know very little about the true state of balance of most of the world's glaciers.  As for the Greenland ice sheet, they conclude that it might "have to be monitored over many decades to detect unambiguous evidence of either thinning, due to increased melting, or thickening, due to increased accumulation."

The moral of the story?  Don't hold your breath waiting for a definitive answer about the state of the Greenland ice sheet.  And without a definitive answer, don't jump to conclusions; you'll only be speculating.  In the case of the glacier with the longest mass balance on record, however, we need not speculate.  It is clear there has been a significant upward trend in its mass balance state over the past 30-40 years and that it has been in a mass accumulation state for at least the past decade.