In my last post I suggested that annual dates of river break-up in Alaska may be able to provide quantitative information about long-term temperature changes at this time of year; this is possible because of the high degree of correlation between break-up dates and spring temperatures. The annual date of "green-up" in Fairbanks can function in the same way as a climate marker.
After pondering the topic for a couple more days, it now seems clear that the method I used in the first post (read it here) was far from robust. There's surely no significant difference between a correlation of (say) -0.86 and -0.87, so it's probably not reasonable to pick out the precisely optimal correlation and then claim to have identified a "true" temperature trend. Accordingly, I think it's probably just coincidence that the results for Fairbanks and Nenana lined up so closely.
Not being one to give up, however, I moved on to a different approach by considering what range of temperature trends could be consistent with the observed correlation between temperature and break-up (or green-up) dates. This is something that can be addressed with statistical simulation; so I produced 1000 simulated histories of southeast interior April-May temperatures by generating values based on the observed correlation with break-up date. Each of the simulated histories has approximately the same correlation with break-up date as the actual reported temperature history, but the trends differ widely owing to the random component of the simulations. Note that I'm assuming there are no other long-term changes that have systematically affected the break-up dates one way or the other.
Here are a couple of examples: the top chart shows the break-up dates and a simulated history that happens to have a very low (near zero) temperature trend, and the second chart shows an example with a very high temperature trend.
For both of these examples, the correlation of the simulated temperatures with break-up dates is very close to the correlation observed in reality, so these are outcomes that "could have" happened based on the physical connection between break-up and temperature. However, both of these are unlikely outliers; the chart below shows the full distribution of trends from the 1000 histories, plotted as a cumulative distribution function.
It's nice to see that the 50th percentile of simulated trends lies almost exactly on the reported trend, so we can say that the changes in break-up at Nenana are entirely consistent with the temperature trend reported in the southeast interior climate division. Bear in mind that the simulation process has no knowledge of the actual temperature trend; we have backed it out from the break-up dates.
Here's the same chart derived from green-up dates and April-May temperatures in Fairbanks.
Finally, here's an interesting result based on break-up dates of the Koyukuk River in Bettles.
Here we find that nearly all of the simulated histories have less warming than the reported April-May temperatures from the Bettles observing site; it appears to be 90% likely that Bettles has over-reported the warming trend. In fact, more than 50% of the simulated trends are negative, and when we look at the break-up dates (see chart below) it becomes immediately obvious why this is the case: the linear trend-line for break-up dates shows a very slight increase over this period (although several years are missing near the beginning). The lack of change in break-up date appears to be inconsistent with the reported warming at Bettles; more investigation is required.