Warm streaks in the U.S. temperature record: What are the chances?

A recent observation in NOAA's National Climatic Data Center's monthly assessment of the state of the climate was that contiguous U.S. average monthly temperatures were in the top third of monthly ranked historical temperatures for 13 straight months from June 2011 to June 2012. The chance of such a streak occurring randomly was quoted as (1/3)13, or about one in 1.6 million. The streak continued for three more months before the October 2012 value dropped below the upper tercile. The climate system displays a degree of persistence that increases this probability relative to the assumption of independence. This paper puts forth different statistical techniques that more accurately quantify the probability of this and other such streaks. We consider how much more likely streaks are when an underlying warming trend is accounted for in the record, the chance of streaks occurring anywhere in the record, and the distribution of the record's longest streak.