## Record High/Low

For the discussion of math. Duh.

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Goemon
Posts: 442
Joined: Mon Nov 19, 2007 4:57 am UTC

### Record High/Low

We frequently see news noting that today's temperature is a record high (or low). Seems like we see that quite a lot. So I got to wondering... how often should such events occur? For a given location, there are more than 700 record high/low temperatures that might be broken each year - a high and a low temp for each calendar date. As the data has only been kept reliably for a couple of hundred years or so, I suppose it shouldn't be too surprising if there are still record breaking events each year, especially considering the number of locations (e.g. today we have a record high in Boston and a record low in Paris). But what exactly is the expectation?

As a rough estimate... if we were to suppose that the temperature recorded on a given month/day at a specific location every year follows a normal distribution, can we calculate what the odds are that the nth year would be a record high (or low) measurement?
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flownt
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Joined: Sat Feb 09, 2013 5:24 pm UTC

### Re: Record High/Low

Goemon wrote: can we calculate what the odds are that the nth year would be a record high (or low) measurement?

Yes. The probability of finding a current maximum the nth year is 1/n. If we assume all draws are independent and identically distributed, then the probability of a specific one out of n being the maximum is exactly 1/n, independent of the exact distribution (as long as it is continuous).

Irritatingly I only realised this after doing the math but hey, neat answers are neat.

LucasBrown
Posts: 299
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Location: Poway, CA

### Re: Record High/Low

But if the distribution shifts, then the probability of a record is increased in the direction of the shift, with the net result being an increase in the total number of records — for example, the planet is warming up, so we can expect (and in fact we do observe) an excess of record highs and a dearth of record lows.

jestingrabbit
Factoids are just Datas that haven't grown up yet
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### Re: Record High/Low

LucasBrown wrote:But if the distribution shifts, then the probability of a record is increased in the direction of the shift, with the net result being an increase in the total number of records — for example, the planet is warming up, so we can expect (and in fact we do observe) an excess of record highs and a dearth of record lows.

Yeah, this. The difference between the number of highs and lows should be a low multiple of sqrt(n) ie 2sqrt(n) or 3sqrt(n) max, if the distribution that you're drawning them from is static, but we've got warming and cooling occuring in different places, and similar changes with rainfall and an overall increase in storm events, so instead, we've got record highs and lows occurring with greater frequency.

Consider the number of times the global average temp has broken the record in the last 50 years. Even if we had only started collecting records 50 years ago, you'd expect it to have happened about sum(1/i, i=1..50) = 4.499 times, but if you look here

you'll see roughly thrice that in the relevant period. Going for bigger timescales doesn't help, either. The record breaking in recent years is astounding in its intensity and will eclipse the previous 80 odd years of pretty stable temp.
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