Peak Climatological Cooling

First, an update on temperatures: the first 0°F observations this season occurred today at the usual cold spot of Chicken and also at the Chalkyitsik RAWS.  Remarkably, the latter site had measured +1°F each of the 3 previous nights.  Circle Hot Springs has been to 3°F and the Salcha RAWS made it to 4°F today.  There was a bit of ice running on the Yukon River at Dawson, Yukon Territory, today, where the temperature has been struggling to get above freezing in recent days, even under clear skies.

We're approaching the date on the calendar when climatological normal temperatures drop most rapidly in interior Alaska; this occurs around October 24 in Fairbanks, at which point daily normal mean temperatures are dropping more than 6°F per week.  Based on published normals, the station with the most rapid drop is Woodsmoke (7°F per week), as noted in this post from 3 years ago:

http://ak-wx.blogspot.com/2013/10/peak-cooling.html

The very rapid cooling at this time of year means it is quite likely that any given week will be cooler than the previous week in Fairbanks.  But how likely is quite likely?  I got to wondering about this, because of course any given day is only slightly more likely to be cooler than the last, but a full month is certain to be cooler than the last at this time of year.  How do these probabilities vary with calendar date and with the length of the averaging period?  The chart below answers this question, which I've been curious about for some time.

It's interesting to see that the rate of cooling in mid-October is so great that any given day is more than 60% likely to be cooler than the previous day, and any given week is 80% likely to be cooler than the last.  It's still possible, though unusual, for consecutive 2-week periods to defy the seasonal trend, but by the time we get to 20-day periods this is virtually impossible - so for example, the last 20 days of October are nearly certain to be cooler than the 20 days prior.

Looking at calendar months, it's interesting to note that August has never been warmer than July in Fairbanks (although it's bound to happen one of these years), September has never been warmer than August (although remarkably in 1969 it came close), and of course October and November have never been warmer than the preceding months respectively.  On the other side of the year, April, May, and June have always been warmer than the calendar months immediately prior.

An unrelated but surprising detail on the chart is that the series for consecutive single days (black line) doesn't drop below zero until early August: so even in late July, each day is more than 50% likely to be warmer than the previous day.  This is inconsistent with the 1981-2010 normals, which show the climatological peak of daily mean temperature on July 3 in Fairbanks.  More surprising still is that the other series don't show the same thing, so for example 10 day periods ending in late July are considerably more likely to be cooler than the one before.  I suspect the anomaly for single days has to do with some skewness in the temperature distribution, but a bit more investigation would be needed to clarify this.