First, some background to set the stage.
- Since I am looking at days with zero precipitation, not even a trace, I used data since 1947, since this is entirely within the Weather Bureau/Weather Service era of 24-hour per day observations and there is no missing daily precipitation data.
- The frequency of precipitation varies seasonally, e.g. May in Yakutat averages twice as many days without any precipitation as October, so we need to limit the analysis to this time of year. Therefore I confined the analysis to the early autumn (August through October) season. I'm also assuming there is no trend in dry days streaks (which is the case for the total number of dry days in ASO).
- For statistical analysis, the independence of events is often an important underlying assumption. So while it's easy to generate simple counts of consecutive days without precipitation, it took a bit more work to find the independent streaks. To illustrate this, a simple count revels that there are two streaks of 19 days with zero precipitation during August through October, 1947 to 2018. However, both of these streaks are simply subsets of the 20-day streak from this past September (Sep 2-20 and Sep 3-21). So removing all the streaks that are simply subsets of longer ones, here's what we find for the counts of independent, non-overlapping streaks of specific lengths:
There are a number of ways to potentially answer such questions, but the one I'll provide here involves our old friend, regression. But rather than linear regression (which obviously is not appropriate), I tried mathematical forms that have the potential to represent what we see in the plot above: large and rapid changes as we move from left to right along the x (horizontal) axis. Two commonly used forms for distributions of this shape are exponential and power law. In order to facilitate this analysis I first converted the raw count values into frequencies per year and then plotted the frequency on a log scale, which results in this:
So from this analysis, the 20 dry days in a row at Yakutat this September was likely a once in a lifetime event, at least if you're of mature years. After all, 0.7% annual chance of occurrence means that, assuming no change and no year-to-year correlation, that there is about a 30% that this will happen at least once in the next 50 years.