How Normal is Average?

A week ago we had a heatwave, and this week we're almost dropping below freezing. It sure seems like temperatures have been bouncing around a lot recently, so today things are going to get extremely nerdy as we look at average temperatures.

Environment Canada data from our record-breaking May 5th, and not-so-record-breaking May 14th

Environment Canada and other meteorologists will often mention seasonal normals, and the question today is: just how "normal" is the average? I've talked about this a few times before, but today we're going to see just how much time we spend at-or-near the average.

(Just for house-keeping purposes, today we''ll be looking at the average temperatures from 1996-2017. A 30-year average is more typically mentioned, but I like 1996 because that was when measurements from the current weather station at Blatchford started. I've talked about the measurement differences between weather stations here.)

2017 so far...

This chart shows the High temperatures for January through May 13, 2017. We can see all of the wild temperature swings that we've gone through, and it highlights how many days were "close" to the average: whether ±1°C away, ±3°C, ±5°C or ±10°C.

The number of days so far this year that were within 1°C of the average is pretty tiny, with only 10 days scattered over the last 4-and-a-half months. ±3°C from the average puts us at one-quarter of the year, and ±5°C moves us to about one-half. Days that are within 10°C of the average captures about three-quarters of the year so far, but we've had several coldsnaps and warmspells which fell outside of that range.

We're only 4-and-a-bit months into 2017 though, so lets take a look back at last year.

2016 Highs

Here we have the High temperatures for 2016, and how many degrees they were away from the recent average.

And the temperatures last year bounced around quite a bit as well. Throughout 2016, 13% of the daytime Highs were within ±1°C of the average, and most of those were right in the middle of summer. For ±3°C it was 37%, for ±5°C it was 56%, and ±10°C was 87%. But to cover 100% of the days - from the May heatwave to the December coldsnap - we have to go all the way to ±18°C.

To dig a little deeper, lets focus on one slide from that animation:

±5°C from Average

Here are the days last year which were ±5°C from the average. 

A range of ±5°C from the average covers 56% of the days from last year. But in the Summer months 84% of days were in that range, while in the Winter it was only 38%. And that's because our range of potential temperatures is much smaller in the Summer than it is during the Winter. A summer day might be anywhere from 10°C up to 35°C, while in winter it could be -30°C to +15°C.

I don't usually talk about Standard Deviation on this blog, but today we'll make an exception because it's really a perfect demonstration of this:

Standard Deviation Throughout the Year

Standard Deviation is a measure of how variable a set of numbers is, and how far they are from the average. In Edmonton, that temperature variation gets much smaller as we move from the Winter into the Summer.

Based on data from 1996-2017, during the winter the standard deviation for our High temperatures is about 9°C. And so about 68% of winter days will fall within ±9°C of the average, and 95% of days will fall within ±18°C.

For the summer though, the standard deviation for Highs drops to about 4°C. And so 68% of the time we'll be within ±4°C from the average, or 95% of the time within ±8°C. For Low temperatures it's even smaller, dropping to about 2.5°C for June through September.

Intuitively this makes a fair bit of sense. If our average temperature in January is around -5°C, then in a typical winter we will certainly bounce up or down 15°C with chinook-days of 10°C or deepfreezes down to -20°C. On the flipside, during July the average is about 23°C, and we've never recorded a single day 15°C above that, at 38°C.

Anyway, that's enough stats.

So far we've looked at the first few months of 2017, and at all of 2016. But how do things compare over the longer term?

Highs for 1996 to April 2017

Here we are looking at each year going back to 1996, and at how much of it was in the range of ±1°C from the average, ±3°C, ±5°C, ±10°C and beyond.

From this chart, you can see roughly how warm or cold a year was based on how high the bar sits. 2015 and 2016 were both warm, so they are up above the 60% mark, meaning they were above average more than 60% of the time. And as we've seen previously, 1996 was one of Edmonton's coldest years since the 1950s, so it drops down below -60%. The more typical years sit balanced somewhere between +50% and -50%.

When we looked at 2016 we saw that 13% of the year was within ±1°C of the average. For all of the years that increases to 14%. And it's pretty consistent, because the lowest year was 2002 at 10%, and then there are 5 years at 16%.

For the ±3°C range it was 37% for 2016, compared to 38% for all these years. 2002 is again the low year at 33%, and for 2007 44% of the year was within 3°C of the average.

Moving on to ±5°C, 2016 was 56% compared to a recent average of 58%, with 2002 at 48% and 2007 at 65%.

And finally, for ±10°C 87% of 2016 was in the range, the average is 88%, 2009 is the low at 83%, and 2012 is the high at 92%.

So even though 2016 was a fairly warm year, the amount of time that it spent near the average temperatures was fairly average. 2017 looks a little different from all of the rest, but that's because right now we only have data from the erratic winter and early-spring, and we're missing the summer months with their tiny temperature ranges to balance things out.

Another way to look at this is as a breakdown of all the days:

Distribution of Highs

With this chart we lose track of the individual years, but we do get to see how things have generally been distributed over the last 2 decades.

This is broken into summer (April-September) and winter (October-March). For the summer Highs the numbers are nicely centered around ±1°C, and they stretch from 16°C below-average to 17°C above. The winter Highs have a much longer tail - stretching from 27°C below-average to 20°C above - and are skewed so that Highs of 4°C or 5°C above the average are actually the most typical.

Now lets take a quick look at the Low Temperatures. We'll just zip through these, since it's the same basic idea.

2017 Lows

So far in 2017 the Lows have also swung around pretty wildly, and the coldsnaps and warmspells are easy to spot in this chart. But when we looked at the Standard Deviations earlier, we saw that Low temperatures are actually a little bit less variable than the Highs, and we see that here too:

For each of these ranges, more Lows are closer to the average than the Highs were. So for the ±1°C days which are basically right on the average, there were twice as many Lows as Highs. And as we move up to ±3°C about 10% more Lows fell in that range than the Highs, and that continues for ±5°C and ±10°C.

In particular, the Lows for April of this year were very close to average, mostly sitting within ±3°C. But everyone will remember April as being a cold month, because the Highs were sitting around 10°C below average for several weeks.

Lows for 1996 to April 2017

Finally for today, this is the breakdown for the Lows going back to 1996.

And similar to what we just saw for 2017, the Lows are a little bit closer to the average than the Highs, which isn't surprising knowing that the standard deviations are lower. The Lows are right on the average about one-fifth of the time, within 3°C half of the time, and within 5°C three-quarters of the time.

Distribution of Lows

Here we have the distributions again, for Lows during the summer (April-September) and winter (October-March).

The summer Lows are centered on ±1°C, and range from 13°C below-average to only 10°C above. That very small range of temperatures matches what we saw with the standard deviations earlier. The winter Lows are more spread out, from 25°C below average to 17°C above.


So how close are our temperatures to the average?

Throughout the year we are within 1°C of the average about 15~20% of the time, which I guess isn't too bad? But that depends a lot on what part of the year it is. In Summer 80% of the days are within ±5°C of the average, but in the Winter that range doubles to ±10°C.

In the middle of winter no one wants to hear a forecast that "tomorrow will be 10°C below normal." But the truth is that it is perfectly normal for about one-fifth of the winter to be 10°C from the the average (sometimes below, but sometimes above).

So while "normal" is a term that weather-people have borrowed from statistics, it's not great. The temperatures are "average" sure, but they're not really something you should expect on a daily basis.

1 comment:

  1. Intersting:

    It's not clear if you are comparing to the current average .e.g. comparing September 2016's highs and lows to September 2016's average temperature or to the last 30 years of average temperature for September.

    The latter would be more interesting to me. How many standard deviations is our present temp for the 30 year average for this time of year.