Spring Warming Trends (continued)

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.

In this case the simulated trends do not line up perfectly with the reported trend, as about 60% of the simulations have more warming than reported by the thermometers.  This is consistent with the simplistic result in my first post, but now we can quantify the probability that the trend is higher than reported.  Based on these results, and if my assumptions are correct, it is about 60% likely that Fairbanks has warmed more than the official climate record indicates (based on a 1974-2016 linear trend line).

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.