Thursday, April 23, 2015

Temperature Percentiles

A few weeks ago reader Eric suggested that it would be interesting to see a chart of daily temperature percentiles in Fairbanks throughout the year.  I agree, so here it is:

Note that I only used data since 1977, after the PDO shift, because this gives results that are more representative of the modern climate than if we included earlier years.  I did the calculation for each day of the year by using a date window of +/- 10 days, and finally I applied a +/- 3-day smoother to remove the smaller bumps and wiggles.

There are a number of interesting features in the chart, such as the inflection points in the minimum temperature percentiles at the end of April and beginning of October; these are related to the seasonal changes in the likelihood of having snow on the ground.

The sudden drop-off in the 1st percentile in late September appears to be a real feature of the climate, although the precise date of the drop-off on the chart is influenced by the 21-day window technique.  Consider that prior to September 25, sub-20F temperatures were observed in only one year (1992), but within just the next few days (September 25-28) the temperature dropped to 14F or lower in 4 different years (1983, 1992, 1993, 2010).

The slight peak in the 99th percentile in January is also a real feature of the history, although it could be just a statistical fluke.  For example, since 1977, there have been 13 deep winter days (Dec-Feb) with a high temperature of 45F or higher, and 7 of these occurred during January 15-25, in 5 different years (1977, 1981, 1991, 2009, 2014).  Perhaps this is Alaska's equivalent of the lower 48's "January thaw", which (it has been shown) can be explained by random variability.

[Update 5pm AKDT: it occurred to me that I could repeat the calculations for earlier years, 1930-1975, to see if some of the same features were present in the climate of the earlier era.  Here's the chart:

The difference in the lower temperature percentiles between the two periods is striking, with the modern climate being considerably warmer in all seasons of the year except autumn.  Remarkably, the 25th percentile was as low as -38F in mid-January in the earlier years.  It also seems clear that the earlier climate had a wider distribution of temperatures, especially in winter.  As for the September drop-off and the January bump that I mentioned earlier, they do not stand out in the earlier years, so these are either sampling artifacts or they are somehow related to persistent features of the modern climate.]


  1. How does the sliding date window effect how to read the percentiles? For instance, in January there is a 10% chance of being colder than -40. Would that be 10% of 38 years (about once every 4 years)? Or would that be 10% of 38*21 (about once every 80 years)? The stats here aren't do clear. And experience would say once every four years or so.

  2. Eric, Good question but I handled the counts to produce the true daily percentiles, so just read off the probability for any given day. The 1st percentile reflects a 1 percent chance of being exceeded (below) on that day. Conversely, the 99th percentile is exceeded 1 percent of the time on any given day.

    For example, -40 was reached 8 times on Jan 12th, 6 times on the 13th, 4 times on the 14th, and twice on the 15th. If we proceed like this for every day and then take averages over a 21-day window, we get an average of (e.g.) 4.48 times for Jan 5-25, or 11.8 percent of 38 years. Thus -40 is reached 11.8 percent of the time or once every 8.5 years on average.

    It would be easy to produce an equivalent return-period chart, but it would only be a return period for that day of the year; the true return period is always much less because we have all the other days to consider too. So I think that would be too confusing.