What was done
The author reviews a number of studies (122 references) that come to bear upon the question of the stability of the West Antarctic Ice Sheet and its effects on global sea level.

What was learned
The author concludes that "human-induced climate change may play a significant role in controlling the long-term stability of the West Antarctic Ice Sheet and in determining its contribution to sea-level change in the near future."  Other of his statements, however, seem to detract from this conclusion.  He notes, for example, that the Intergovernmental Pannel on Climat Change (IPCC) "estimated a zero Antarctic contribution to sea-level rise over the past century, and projected a small negative (about -1 cm) contribution for the twenty-first century."  Furthermore, with respect to potential anthropogenic modification of the state and behavior of the atmosphere and ocean above and around Antarctica, he acknowledges that "measurements are too sparse to enable the observed changes to be attributed to any such [i.e., human-induced] global warming."  And in the case of sea-ice extent, he admits that there appears to not even be a modification; for he states that "the IPCC assessment is that no trend has yet emerged."

The author concludes his review with four scenarios of the future based upon various assumptions.  One is that the WAIS will experience a sudden collapse that causes a 4-6 m sea-level rise within the coming century.  However, he states that this scenario "may be put aside for the moment, because no convincing model of it has been presented."

A second scenario has the WAIS gradually disintegrating and contributing to a slow sea-level rise over two centuries, followed by a more rapid disintegration over the following 50 to 200 years.  Once again, however, the author notes that "progress on understanding WAIS over the past two decades has enabled us to lower the relative likelihood of [this] scenario."

In another scenario, the WAIS takes 500-700 years to disappear, as it raises sea-level by 60-120 cm per century.  The author assesses the relative likelihood of this scenario to be the highest of all "but with low confidence," as he puts it.

Last of all is what occurs if ice streams slow, as a result of internal ice sheet readjustments, and the discharge of grounded ice decreases, which could well happen even if ice shelves thin and major fast-moving glaciers do not slow: "the Antarctic contribution to sea-level rise turns increasingly negative," i.e., sea level falls.

What it means
In commenting upon the suite of scenarios just described, the author emphatically states that "it is not possible to place high confidence in any specific prediction about the future of WAIS."  Our translation of his assessment: Your guess is as good as mine; and both are only that - guesses.