Saturday, March 14, 2015

Frequency of Extremes

I've spent some time recently working with the NCEP/NCAR reanalysis data to assess patterns of upper-level temperature and pressure extremes over the Northern Hemisphere, and the changing distribution of these extremes over time.  I won't dive into the details of this investigation now, but I did want to put up one figure that I thought was interesting - see below.

The map shows the long-term average of the frequency of +/- 2 standard deviation anomalies in the daily mean 850mb temperature.  The anomalies are calculated with respect to a baseline climatology that includes a long-term trend, so that patterns of extremes do not simply reflect overall warming.

The interesting result is that southern Alaska, western Canada, and the northern Gulf of Alaska see the highest frequency of 2 SD extremes of anywhere in the northern extratropics.  If the distribution of daily anomalies were perfectly Gaussian, then the frequency would be 0.0455, so the 850mb climate over southern Alaska has more frequent extreme temperature events than would be expected.  Most of the northern extratropics have slightly less frequent extremes than expected.

Looking at the distribution by season, it is mainly the winter and spring that contribute to the excess of extremes in the Gulf of Alaska.  The map below shows the mean frequency for December through February.

In contrast to the peak frequency near Kodiak Island, the lowest annual frequency of 2 SD extremes is over the North Atlantic, and the two distributions can be compared as follows:

Category (SD)57.5°N 155°W50°N 35°WExpected Gaussian
-3SD or lower0.00380.00010.0013
-3SD to -2SD0.02260.01350.0214
-2SD to -1SD0.11410.16080.1359
-1SD to +1SD0.72330.64140.6827
+1SD to +2SD0.10690.17010.1359
+2SD to +3SD0.02560.01420.0214
3SD or higher0.00370.00000.0013

The chart below shows how the frequencies in three categories have changed over time near the peak in the Gulf of Alaska.  Relatively high frequencies - higher than expected based on a Gaussian distribution - were observed prior to the PDO shift in 1976, but the frequency of extremes has been generally lower since then.


  1. Interesting idea, Richard!

    How long has Kodiak had weather records? How much of the red is based on actual input and how much is the model estimating? I would like to know how reasonable such a extreme deviation from the norm is.

    Also, could you put together a simple line chart for the deviation data table? That will make it easier to see the distribution become wider for Kodiak versus the North Atlantic.

    The extreme Alaskan deviations might track an occasional change in the Aleutian Low and subsequent storm track. This would lead to overall changes in temperature and precipitation in Alaska.

    I'm a little surprised that deviations are lower after the 1976 PDO change. Other analysis on this blog has suggested that overall deviations have increased over the years. And if the deviations of Kodiak have decreased for 1, 2, and 3 SD, where in the distribution has it increased? The overall area of the distribution must remain the same through time, right?

    1. Eric, I'm glad to hear that I'm not the only one who finds it interesting.

      Kodiak has had balloon observations since at least 1948, but I only used the data from 1958 as that is when the number of global radiosondes increased dramatically (with the International Geophysical Year). The reanalysis should follow the radiosonde data quite closely at the observation points, but this could be checked. I'll do a follow-up when time permits.

      If the frequency in the tails has decreased over time, then the frequency near the normal has increased, i.e. -1 to +1 SD. I calculated one standard deviation from the entire history (for each day of the year), so the fraction in each category can change over time. I too find it surprising to see no evidence of increased extremes in recent years. More on that to follow.

  2. Examining the associated pressure extremes would be interesting. There's quite some current interest in studying the trends of the teleconnections associated with the PNA and NAO.



  3. Kodiak's climate is influenced by nearby water temperatures more than Interior Alaska. The strength of the + and - phases of the PNA is associated with similar strengths of the Aleutian Low. Their values and anomalies in relation to Kodiak's T850 observations may be worth investigating. Also, don't discount Solar SSN impacts on Earth's climate.

    Fisheries Climate is where the $ and research is focused in these brief examples versus overall NA climate:

    Gary the fish squeezer (who spent two years observing Kodiak's climate and never returned)