What was done
The authors assembled a number of data sets pertaining to Arctic sea ice extent over the past few decades and compared these observations with predictions of general circulation models of the atmosphere forced by changes in the concentrations of atmospheric CO2 and aerosols.

What was learned
The observed reductions in Arctic sea ice extent over the past few decades were well described by the climate models.  In fact, they were so well described that the authors concluded that "the probability of the observed trends resulting from natural climate variability ... is less than 2 percent for the 1978-98 sea ice trends and less than 0.1 percent for the 1953-98 sea ice trends."  Hence, they concluded further that "this strongly suggests that the observed decrease in Northern Hemispheric sea ice extent is related to anthropogenic global warming."

What it means
Does anyone really believe that the test of the CO2-induced theory of global warming provided by this exercise is more exacting than the purity of ivory soap?  Can anything really be that good?  We think not.

Forget about even trying to link the sea ice variations to carbon dioxide; the authors do not even present any temperature data!  All they offer are model predictions.  What we need to see is what has been the real (not modeled) thermal history of the atmosphere over the Arctic sea ice throughout the period of sea ice extent observations and what has been the real (not modeled) thermal history of the water beneath it.  Until we have such real-world data before us, how can we even begin to think about potential relationships between the real sea ice characteristics of this specific region of the earth and the modeled (it doesn't even sound right, does it?) thermal behavior of the globe?

And look at the caveat that we replaced by the ellipsis in the first quote we lifted from the paper: "assuming that the models' natural variability is similar to that found in nature."  Now that's a great assumption, but it is absolutely false; for it further assumes that the models have incorporated within them all of the various phenomena that can indeed operate to alter earth's climate, which is clearly not true, even for several phenomena we know something about, much less those we have not yet even discovered (yes, there are probably several things about earth's climate system that have still eluded the minds of all of us).

So, if there were ever a conclusion that should be taken with a grain of salt, it is this one: that we can be more than 99.9% sure that the 1953-98 sea ice trend in the Arctic is unnatural and that it consequently likely bears the fingerprint of the climatic consequences of humanity's CO2 emissions.  Believe us, it just ain't so!  (And we're more than 99.9% sure of that.)