Statewide Temperature Index

Last week I mentioned the UAF/ACCAP statewide temperature index (developed by Rick Thoman and Brian Brettschneider), which is a useful tool for quickly visualizing the overall ebb and flow of temperature anomalies in Alaska.  Here's the last year or so (click to enlarge):

Two of the more striking anomalies in recent months were the extraordinary warmth of late summer and the April cold spell.

While I'm a big fan of the index that Rick and Brian came up with, I've been tinkering to see if it can be improved still further.  One of the limitations of the existing index is that it assumes a Normal distribution for daily mean temperatures, but we know that the distribution is significantly skewed at certain locations and times of year.  Here's an old post illustrating this:

https://ak-wx.blogspot.com/2014/03/temperature-skewness-maps.html

To account for skewness, I was able to fit a Skew-Normal distribution to the historical temperatures at each of the 25 ASOS locations used in the ACCAP index.  Using these distributions - which vary through the year - the statewide index can then be recalculated from the newly standardized anomalies at the individual locations.

This modification makes a fairly big difference at certain times of the year.  An extreme example is late March 2019, when extremely warm weather occurred at a time of year when skewness is negative for most of the state.  In other words, negative departures from normal tend to be larger than positive departures, and so a large warm anomaly is actually much more unusual than a Normal distribution would imply.  Here's an illustration of the standardized anomalies on March 22 that year, using a Normal distribution (top) and a Skew-Normal distribution (bottom):

The standardized anomalies are much larger in the Skew-Normal framework, and the statewide anomaly jumps from +2.15 to +2.71.  In terms of degree-of-rarity, the Normal distribution estimates a 98.4% percentile for the day, but the Skew-Normal distribution shows 99.7%.  Both are in the upper tail, but accounting for the negative skewness reveals that the warmth was statistically much more extreme.

It works the other way too: a few months later in 2019, extreme heat occurred in early July, but with positive skewness around Alaska's coastal regions, the large warm anomalies were somewhat less significant than a Normal distribution would indicate.  The statewide standardized anomaly drops from +3.16 to +2.88, which although not a large change implies more than a 50% increase in the climatological probability of such an event (0.08% vs 0.20%).

Of course we could find examples on the cold side too.

In addition to the skewness modification, I also adjusted the statewide index calculation to account for the fact that the (weighted) average of the 25 individual (standardized) anomalies has larger variance in winter than in summer.  This is because there is more spatial correlation of temperatures across the state in winter, so the 25 (standardized) temperature measurements are more prone to move up and down together, and the combined average has a relatively high variance.  In contrast, summer temperature anomalies are more prone to cancel each other out across the state in summer, and the statewide average (of standardized anomalies) varies less.  (This is a completely separate issue from the reduced variance of actual temperatures in summer.)

So rather than using a single number to convert the statewide mean into its own standardized index, I used a seasonally varying number, and this varies by nearly 40% between about January 20 and June 20.  The result is that my modified index shows systematically smaller statewide anomalies in winter than the ACCAP method, but larger anomalies in summer.

Here's a comparison of the past year's statewide standardized anomaly from the two methods.  Notice that the revised method shows smaller values in winter, larger values in summer, and significantly less extreme cold in April (because of the negative skewness).

And here's the actual ACCAP index, which shows the statewide value in terms of percentile/frequency rather than standardized anomaly.

The major difference between the anomaly view and the percentile view is that the percentile view doesn't differentiate the magnitude of extreme events, i.e. once you're in the top or bottom 5-10% of events, they all look quite similar in the percentile view.  In contrast, the anomalies clearly delineate the amplitude of extreme events, but on the other hand they don't provide an intuitive measure of frequency: most people don't have a sense of how rare a 2 or 3 standard deviation event is.  Both perspectives are useful.

My next step with this work is to set up an automated process to create daily graphics and perhaps a simple webpage for monitoring purposes.