Maps are shown below for the four climatological "seasons" of December-February, March-May, June-August, and September-November. These don't correspond particularly well to meteorological times of transition in Alaska, but they are conventional categories for dividing up the data. Recall that positive skewness indicates a long upper tail, so that large warm anomalies are more common than large cold anomalies; and conversely, when there is negative skewness, large cold anomalies are more common. Qualitatively, the warmer/red colors on the maps show regions and seasons that are more often "very warm" (relative to the mean), whereas colder/blue colors on the maps indicate locations that are more often "very cold" (relative to the mean).

Interesting features of the maps include the general lack of significant skewness in the central Interior, except in spring, the pronounced skewness in many places in spring, and the strong positive skewness in far southern Alaska in summer. Each of these features describes characteristics of the climate that go beyond the traditional "seasonal norms" and even "seasonal variability/variance", but are nevertheless important and perceptible aspects of the local environment.

[Update March 16:] The chart below shows the summer temperature distribution for Kodiak, where the skewness is strongly positive. In the period 1981-2010, the daily mean temperature in June through August was never more than 10 °F below the mean, but daily anomalies of +15 °F or more occurred on a number of occasions. It seems that the favored setup for the warm anomalies involves high pressure to the west, thus bringing warm air from the mainland to the north - and sometimes the air is very warm. In winter the large-anomaly air from the mainland would be cold, and so the distribution is negatively skewed.

I've been trying to wrap my head around what this measure if skewness means and it's significance. If a red area means that extreme warm days are more likely than extreme cold days, what does that say about our interpertation of the mean? Here in Fairbanks, the mean daily temp on the first of the year is around -10ºF. But despite the potential for -40 or -50, the map above suggests that we are more likely to have 30 or 40 above temps. So is -10 a valid mean or should we look at the median of (guessing) -8? Perhaps this is all inconsequential for Fairbanks. But the extreme red on Kodiak or at Wainwright should make a difference.

ReplyDeleteAnd what would cause the red in Kodiak? Kodiak has a small variance compared to the Interior. So any extremes would be more pronounced. A summer emphasis on heat would be due to what? Persistant high pressure?

Would any higher moments in the temp distribution mean anything?

Eric, I think you are highlighting the difference between the mean and what is "normal" for the location. When the distribution is skewed, the two are not at all the same. In general, median is a much better measure of normal than mean - especially for non-Gaussian variables like precipitation, but also for temperature it turns out.

ReplyDeleteFairbanks actually has little skewness in winter despite a few significantly negative values on the map in the same area. So the mean temperature adequately represents normal.

I updated the post with a histogram for Kodiak and a brief comment.

One could certainly look at higher moments; the fourth moment is the kurtosis and measures the relative importance of tails versus shoulders of the distribution in causing dispersion. It could be quite an important climatological descriptor.

So is the "normal" usually given in temp forecasts the mean or median? I've always assumed it was the mean.

DeleteHow has skewness changed in the last 30+ years? How much of the reported warming in Alaska is due to extreme events causing skewness and thus changing the mean more than the median?

Eric,

DeleteThe "normal" for temperature is always (as far as I'm aware) given as the mean, under the assumption of normality or non-skewness. What we've shown is that this is a poor assumption in some places and seasons.

I would have to dig into the historical data to begin to address your second question. My guess is that the spatial and seasonal patterns of skewness have remained generally similar over time, because they depend on physics of the regional environment, but there will be some important changes due to the PDO phase, etc. Rick has written about this in the past, and gave a talk at AMS last month:

http://weather.arsc.edu/Events/LAWS08/Presentations/Thoman.pdf

https://ams.confex.com/ams/94Annual/videogateway.cgi/id/26571?recordingid=26571