Freeze/Thaw Cycles: Appendix

This post is really just house-keeping for our discussion of Edmonton's freeze/thaw cycles, because it turns out that counting freeze/thaw cycles isn't entirely straightforward.

If you want to skip to the final results then please just head over to: Freeze/Thaw Cycles: Part 1.

But if you are wondering about the assumptions which were made (and their inherent inaccuracy) then by all means please keep reading...

The challenge with counting freeze/thaw cycles comes down to Daily data versus Hourly data.


Daily Data


Here we have an example of Daily data, with the Highs & Lows shown for 2 days.

The temperatures flip from below freezing Lows to above freezing Highs, and it is natural to assume things went something like:

• cold night > warm day > cold night > warm day

That would give us 2 thaws and 1 freeze, or 1.5 complete freeze/thaw cycles.

The problem is that for the same data this is also a possibility:

In this case things would have gone:

• cold night > warm day which stayed warm through the next morning > cold day 

This second option is going to be less common than the first, but either of these might have occured. And in this second case we would have only had 1 thaw and 1 freeze, for 1 complete freeze/thaw cycle.

With the Daily data we never know what order the High & Low temperatures actually occurred in, and so there is always uncertainty in exactly how many freeze/thaw cycles there were.

In the first example we are assuming that there was an extra freeze or thaw overnight, so that approach may overcount the total number of freeze/thaw cycles. In the second example we are assuming that there was not a freeze or thaw overnight, and so it may undercount the number of cycles.

We will come back to these in a bit, but for now we are going to move on to:


Hourly Data


Switching over to Hourly data, here we have 24 hours which went through a total of 5.5 freeze/thaw cycles. This is the daily data for January 12, 2010, and it is a good example of the challenges of the Hourly data.

So how do should we count something like this? When people ask "Do we get more freeze/thaw cycles now than we used to?" they really aren't talking about all of these intra-day temperature swings as separate freeze and thaws.


Daily Data versus Hourly Data

Here we have a comparison of different counts:

• The orange line is our upper estimate based on the Daily data (the example with 1.5 cycles from earlier). 
• The green line is our lower Daily estimate (the example with 1 cycle).
• The blue line counts every, single temperature swing from the Hourly data.
• The dotted red line uses the Hourly data, but it filters-out intra-day freeze/thaw cycles by putting a cap on the number of temperature swings each day.

The "Daily - Lower Estimate" is very low, counting about half of the number of freeze/thaw cycles of the other methods. It does not include the overnight temperature swings, and so it is missing a lot of the freeze/thaw cycles.

The "Hourly - All" is almost always the highest, because it is counting all of the intra-day temperatures changes, like the 5.5 cycles on Jaunary 12, 2010. The "Hourly - Adjusted" filters those out, and so it is lower - usually by about 10 cycles each year. Days like that really did have 5.5 freeze/thaw cycles, but counting those intra-day cycles as 1 is probably a better match to how people would have perceived it.

The "Daily - Upper Estimate" is in the same range as the Hourly counts. Typically the difference is less than 10 cycles for an entire year (or about 10%) but for some reason in 2001-2003 the Hourly counts are quite a bit higher, with differences of 20-30.


Summary

For our look at Freeze/Thaw cycles we will be using the "Daily - Upper Estimate". That is mostly for practical reasons, because there is Daily data available back to 1881, while for Hourly data there are only a few decades available.

For both the Daily and Hourly data it is difficult to determine the "exact" number of freeze/thaw cycles that people actually perceive. Theoretically the "Daily - Upper Estimate" method which we will be using may tend to over-count the number of freeze-thaw cycles (1.5 cycles compared to 1 cycle as we saw in the first example), but in practice it is in the same range as the results from the Hourly data.

So using the Daily - Upper Estimate will not be perfect, and there is easily 10% uncertainty in the counts. But it is the best that we've got. And it should work pretty well to discuss the question "Do we get more freeze/thaw cycles now than we used to?"