# Weather and statistics

I overheard the following conversation at the best coffee outlet on campus yesterday:

"Well, winter's nearly over. We're past the shortest day so it's getting warmer. And we've had eleven frosts so far this year, and the record for Hamilton is twelve, so there can only be one more to come." – Anonymous

Where do I begin?

Well, first let's point out that the shortest day does not equal the coldest day. Not by a long shot. In fact, I believe that statistically speaking the coldest week of the year for New Zealand is the last week of July (i.e. now). Why the difference? While it's true that it's the sun that provides the heat input to the earth, and that's at a minimum on the shortest day, there's a lot of thermal inertia on the earth, and particularly on the sea. And there is a lot of sea surrounding New Zealand. Temperatures are slow to change. While the sun remains low in the sky, the sea temperatures are slowly cooling, and that is going to influence the temperature in Hamilton. Conversely, the sea temperature in December is still pretty nippy. It's late summer before the sea temperature hits its maximum. Seasonal temperature variation is more about the cumulative heat put in over an extended period of time, as opposed to the heat input from the sun on a particular day.

And then the second point. I've always found it amusing that Hamiltonians count frosts, and think that  minus 4 Celsius (as it has been a couple of mornings recently) is cold. It is only cold because in New Zealand it is (near enough) compulsory to live in poorly heated, uninsulated, single-glazed detached houses. Europeans find this concept laughable, and, I think, Canadians probably sink their heads in their hands in despair.  Anyway, let's leave that aside. So if there have only ever been twelve frosts in a single winter in Hamilton (I doubt this, but don't have statistics on this at hand), and we've had eleven so far, then does that mean there is only at most one more to come?

Um, no. Probability doesn't work like that.  Our weather systems don't have a memory (not in that sense anyway), and they certainly aren't intelligent enough record the number of frosts a particular place has a year and act accordingly in the weeks ahead. I'd say we would be in for a few more frosts yet. That's simply based on the metservice statistics. Go to http://www.metservice.com/towns-cities/hamilton and look at the historical data tab. You'll see that the mean minimum temperature for August is -2 C, and for September it's 0 C, suggesting there can easily be some more negative temperatures coming for 2014. Enjoy.

I remember several years ago playing a board game with a few friends. We'd had a long run of throws of the dice without seeing a 'six'. One of my friends asked me what the probability was that the next through would be a 'six'.  "One sixth" I answered – "same as for any other throw."  This sparked an intense discussion on whether that was right or not. It is. The dice does not have a memory. It doesn't remember what side it has landed up on in the past. Each throw is equally likely to show 1, 2, 3, 4, 5, or 6.  The probability of a 'six' is one sixth. What was perhaps most interesting is that a friend of mine who was doing a maths degree at the time refused to back me up.

So is winter nearly over? While it's true that today feels rather spring-like, and the days are now noticeably longer than they were a month ago, winter still has plenty of teeth left.