## Saturday, August 3, 2013

### Warm Spells and Cold Spells in Fairbanks

I have thought a lot about what constitutes a cold spell or a warm spell over the years. We have all heard countless times something close to, "what a nice stretch of weather we have had" or "it's been really cold for the last two weeks." Based on a cursory review of the literature, there is nothing even approaching a definition of where to put the bounds on a homogeneous grouping of days. So how do we quantify something that is inherently ambiguous. We can all agree that if the temperature is 2 standard deviations above the mean for 15 straight days that that would constitute a warm spell. But what if day 8 (of the 15 days) was cloudy and wet and was 0.1 standard deviations below the mean; leaving 14 of the 15 days 2 standard deviations above the mean. Is the 15-day period a single warm spell with one outlier or is it two distinct warm periods? What I have temporarily proposed is that if 6 out of a group of 7 days are in the upper third (tercile) of the expected temperature range, each of those days is a member of a warm spell. Conversely, if 6 out of a group of 7 days are in the lower third (tercile) of the expected temperature range, each of those days is a member of a cold spell. This is an entirely subjective criteria and I am very interested in suggestions from the readers for an alternative criteria. I discussed this with Rick a few months ago and he chimed in with a few thoughts so he is off the hook (for the time being). The first graphic below shows standard anomalies for Fairbanks during May 2013. The cold spell at the beginning of the month and the warm spell at the end of the month are identified. Make note of the text on the graphic that explains why certain observations are included in the respective groupings. Also, there is usually a transition period between one spell and the next but the example below does not have such a transition period.

The next chart shows the length of cold spells in Fairbanks since 1920 using the methodology described above. The typical length of a cold spell is 13.5 days and has been nearly steady over the last 90 years. However, the time interval between cold spells has not always been steady.

Here is the companion chart for warm spells in Fairbanks. The length of warm spells has increased from 13 days to 14 days over the last 90 years. However, as with cold spells, the interval between warm spells has not been uniform.

The final chart shows the number of days per year that Fairbanks has been in a cold spell (blue), a warm spell (red), and the combined number of days (black dashed).

As stated earlier, I am interested in hearing the thoughts of others on the criteria described in the introductory paragraph.

#### 4 comments:

1. Interesting work, Brian. I like the use of the terciles for the definition. The only minor issue I see with your proposal is that a day could be simultaneously part of a cold spell and a warm spell, if there was a sudden transition. A little counter-intuitive perhaps?

I think the crux of the matter is how many days and what sort of days are needed to break a spell. Say you had 7 very warm days, then 2 slightly above-normal days, then another 4 very warm days. I imagine that most people would view the latter part as a continuation of the warm spell. On the other hand, if the two intervening days were much below-normal, it would change the perception. Three intervening days of near-normal may or may not create the impression that the earlier spell has ended, depending on whether the three days are close to the upper tercile or not.

I wonder if you could use a centered running average of 3 or even 5 days; this allows the relative magnitude of anomalies in nearby days to be taken into account. For example you could use a 5-day centered average and then require 7 or more consecutive days in the upper or lower tercile. It would be interesting to look at some cases and see how this idea plays out.

2. This is really interesting work Brian. I think you would want a method that, per the May example, the start/end of warm/cold spells don't bleed over.

I like Richard's idea of using some kind of running mean: a light (3 or 5 day) binomial smoothing might be worth looking at too as a way to still give some weight to individual day outliers.

3. Thanks guys. I should have mentioned how this all came about. In Alaska, we frequently get "stuck" in patterns for long periods of time. I am looking for measures to quantify how long those patterns are and eventually settled on surface temperatures as a proxy measure. Basically I am trying to develop a climatology of pattern lengths in Alaska.

I will experiment with moving averages and different period lengths as per your suggestions. I might even send you a climograph via e-mail and ask you to identify the beginning and ending of periods to see if the math categorizations can be made to mirror the subjective definitions.

4. I should also add that if any other reader has thoughts on the subject I encourage them to chime in too.