In 2012 I put together a storify using twitter and weblinks about the Greenland Surface Melt. In that story a bunch of climate scientists and I talked about whether the extreme melt seen in 2012 was a signature of global warming.
An Open Access paper by Sirpa Häkkinen and others Greenland ice sheet melt from MODIS and associated atmospheric variability, published on 10 March 2014, explains how it happened.
It is a clear and well written paper that shows using MODIS (Moderate Resolution Imaging Spectroradiometer) data from satellites that you need two things for a serious surface melt event: atmospheric blocking (which allows warm air from the south to go over Greenland) + warm surface temperatures.
The event in 2012 had both of those conditions whereas 2013 did not. The difference is striking in their Figure 1.
Their data set allows them to go back to 2000 and construct annual time series.
They find all of the features Ruth pointed out (shown in their Figure 4).
"that June-July 2007 had the most blocking days but did not have the largest melt, although 2007 has been identified as a large melt year in a seasonal sense"
The reason it did not have as much surface melt as 2012 is because the air temperatures brought over the ice sheet by the atmospheric blocking "barely reached 1.5 SDs [above the summer average temperature]". (SDs means standard deviations - basically a measure of how variable the temperature is about the mean.)
In 2012 the atmospheric blocking brought in "a long-lasting anomaly of 2–2.5 SDs [above the summer average temperature]". This is a bit bland but 2.5 SD's in this data set corresponds to temperatures ~6°C or greater above the summer average on the surface of Greenland. That is why the melt in 2012 was so large.
Häkkinen et al. (2014) make no comment in the paper about the future, or the impact of anthropogenic climate change on such events over Greenland. Looking at various assessments of the scientific literature (e.g the Arctic Report Card) we may draw our own conclusions about whether to expect more of these melting events.