Thursday, May 4, 2023

April Trend Statistics

In Monday's post I pointed out the rather striking increase in "cold outliers" for April temperature in Fairbanks, as reflected by the rather large difference between the least-squares trend and the median trend.  I suggested it would be interesting to estimate the statistical significance of that difference, so I went ahead and ran the calculation.

Here's how it works: I take the median trend as a reasonable estimate of the "true" (unknown) trend and then repeatedly re-order the years by shuffling the annual departures from that trend.  Here's a completely synthetic example of what the April history "might have been" if random chance had produced the annual departures in a different order:

This example (chosen for this reason) has the opposite behavior to the real world, with fewer cold outliers in recent decades; the median trend (not shown) is less steep than the least-squares trend.  Here's the real world for comparison:


After shuffling the years 5000 times, here's the histogram of the trend-line differences, with the "true" trend difference noted on the far right.

This shows that the observed difference is very unlikely to have occurred by random chance.  To be precise, only 2.8% of realizations have a trend difference as large (either negative or positive) as the observed difference, so we can conclude that the trend difference is statistically significant at better than the 95% level.

In other words, this particular change in April temperature behavior - the tendency to produce more cold outliers in recent decades - appears to be a "real" climate change and is unlikely to be just random chance.

Interestingly, however, if we exclude 2023 from the calculation, then the smaller trend difference is much less significant: nearly 10% of shuffled realizations match the 1930-2022 difference.  So it's only with this year's outcome that the statistically significant signal has emerged.

Again, to restate: this April's cold outcome makes it much more likely that we're looking at a "real" climate change, not a random/chance sequence of events.

Finally, I tested the sensitivity to using the least-squares trend instead of the median trend as the baseline ("true") trend for anchoring the data series, and the results are similar: only 3.4% of realizations exceed the observed trend difference.


  1. FYI, not statistical at all, but I consulted my "dog mushing book" after thinking that running dogs until Apr 25 was a record for me. Turns out I ran dogs until Apr 26 in 1985. So there yah go, history repeats itself!

    1. Yep 1985 was a cold one! You can see it in the chart above (second one, not the randomized one). It was actually the coldest April on record statewide, several degrees colder than 2013.

  2. I caught my first mosquito today, and the small Cottonwood tree next to my deck has emerging buds. I call this the Fairbanks bug and bud index...and it's late. There's still unexposed roofs and huge hidden snow piles left. And freezing temps at night. The winter w/o end.

    1. Winter seems to be making a habit of "hanging around" a long time, and not just in Alaska. Four feet of snow in Michigan the other day.

    2. Be of good faith fellow Fairbanks'ins the Robins of Spring have arrived, Here's a summary:

      The summer breeding grounds of the robin extend as far north as the Brooks Range and as far west as the tip of the Aleutian chain.

      Alaskan children like to keep a lookout for that “first robin” of spring. While some scientists say robin’s spring migration follows the northward creep of 36ºF average temperatures, others believe the availability of food plays a greater role than temperature. Indeed, some Alaskan communities find robins sticking around for the winter foraging for left-over berries. While most robins do migrate south, some also stay, usually during milder winters.