What was done
The authors analyzed the history of satellite passive microwave sea ice records that first became available in October of 1978 to derive trends in Arctic sea ice extent and area over the past quarter-century.

What was learned
They discovered a general downward trend in Arctic sea ice "during the passive microwave era" that culminated with record minimums for both sea ice extent and area in 2002.

What it means
The authors correctly report that state-of-the-art climate models predict Arctic sea ice extent and area will decline as the climate warms, noting that "simulations of the past 30 years agree reasonably well with observations in terms of total ice area, lending some confidence to projections of a ~20% reduction in annual mean sea ice extent by the year 2050 [our italics]."

We disagree with the italicized portion of this statement. Although the first part of the quotation may well be correct, a longer view of the temperature history of the Arctic reveals that the warming of the past 30 years, which produced the reduction in sea ice documented in this paper, was preceded by an equally long period of cooling from a level of Arctic warmth that was equally as great as that of today (Polyakov et al., 2002a, 2002b), which was preceded by an even more dramatic warming than that of the past 30 years.

The climate of the Arctic is characterized by multi-decadal fluctuations that provide no support whatsoever for predictions of continued sea ice reductions over the next half-century.  If anything, the temperature record of the past 125 years suggests that just the opposite could well occur.  It's been approximately 65 years since the last peak in Arctic temperature, for example, and if it takes that long for the next peak to occur, it will likely be cooler than it is now in 2050, and it will have been cooler for most of the intervening years.  Hence, projecting forward from the peak warmth of the present, which history suggests will end rather soon, it would be much more logical to expect an increase in the extent and area of Arctic sea ice in 2050 than a decrease.

References
Polyakov, I., Akasofu, S-I., Bhatt, U., Colony, R., Ikeda, M., Makshtas, A., Swingley, C., Walsh, D. and Walsh, J.  2002a.  Trends and variations in Arctic climate system.  EOS, Transactions, American Geophysical Union 83: 547-548.

Polyakov, I.V., Alekseev, G.V., Bekryaev, R.V., Bhatt, U., Colony, R.L., Johnson, M.A., Karklin, V., Makshtas, A.P., Walsh, D. and Yulin, A.V.  2002b.  Observationally based assessment of polar amplification of global warming.  Geophysical Research Letters 29: 10.1029/2001GL011111.