Sunday, August 4, 2013

Unusual Temperatures

As a follow-up to Brian's and Rick's illuminating posts on Friday and Saturday, I thought it would be interesting to examine more closely how "unusual" the "unusual temperatures" of 2013 have been.  Brian showed that, in Fairbanks and Anchorage, temperatures more than 1, 2, or 3 standard deviations from the mean have occurred much more often in 2013 than would be expected based on the normal distribution.  The question is, how often does this occur, or might it be unpredecented in the modern historical record?

The charts below show the number of days each year since 1931 when the daily mean temperature was more than 1, 2, or 3 standard deviations from the preceding 30-year average, for dates between January 1 and August 2.  Note that I compared the temperatures to the preceding 30-year average rather than the 1981-2010 average to help reduce artifacts associated with the long-term warming trend.  For example, temperatures in 1961-1970 are compared to the 1931-1960 mean and standard deviation.  (If we used the modern mean, many of the older temperatures would look artificially cold and would boost the counts in earlier years.)

We can see that 2013 really stands out in the "2 SD or more" category, with this year's count exceeding any previously observed for both Fairbanks and Anchorage.  The number of days at least 1 SD from the mean is very high but not unprecedented, while the 3 SD count is a record in Fairbanks but not Anchorage.

Note that my numbers differ slightly from Brian's for 2013, which is probably because the calculation method was slightly different for the 1981-2010 daily means and standard deviations (a smoothing method is required).

It is interesting that the total 83-year count for the "3 SD or more" category is much higher for Anchorage than Fairbanks (87 versus 39).  If the daily temperature anomalies truly followed a normal distribution, the counts would be around 48.  This suggests that the Jan 1 - Aug 2 Anchorage temperature distribution might have "fat tails" compared to the normal distribution, i.e. a higher chance of high-sigma events.  But strong decadal variability or long-term trends could also be playing a role - more investigation is required.


  1. Richard, there may be a problem with your numbers. For normally distributed data, 68% of values will be with 1 sd, 96% will be with 2 sd, and 99.7% within 3 sd. For a 365 days year, that corresponds to the following expected frequencies (with ANC numbers thrown in):

    Criteria Expected ANC 1920-2012
    Within 1 SD 249.1 265.1
    Between 1 and 2 SD 99.2 88.7
    Between 2 and 3 SD 15.7 10.5
    Over 3 SD 1.0 0.7

  2. Sorry for the formatting issue. Here is what I came up with for the expected distribution of anomalies and the observed distribution of anomalies for Anchorage between 1920 and 2012:

    Criteria --------------> Expected -------> ANC
    Within 1 SD -------------> 249.1 -------> 265.1
    Between 1 and 2 SD -------> 99.2 --------> 88.7
    Between 2 and 3 SD -------> 15.7 --------> 10.5
    Over 3 SD -----------------> 1.0 ---------> 0.7

    It is certainly possible that I have misunderstood how you came up with your numbers. If so, my apologies for adding a layer of confusion.

  3. Brian,

    I agree with the expected frequencies, and these match what I have: for 83 years and 214 days year-to-date, we have 17762 days of data (ignoring leap years), so the expected number beyond 3 SD is 0.0027*17762=48. It is the observed Anchorage numbers that seem different; I'll e-mail you and then we can post the resolution to the issue.

  4. My mistake. I did not notice that the charts display the count of anomalies between 1/1 and 8/2 of each year. I thought they were annual totals - even though it is clearly labeled at the top of each chart.

  5. Can you also do a precipation comparison for the period May 1st-current?
    How dry has Fairbanks really been or are we still within an normal climate variance?

  6. Mike,

    Thanks for the question. I'll work on it and post the results as soon as I have a chance.