4 ms·

So I'll take one of the statements to ask a question. > This was the highest for November in the 1880–2015 record, surpassing the previous record set in 2013 b

by tertius 11y ago

So I'll take one of the statements to ask a question. > This was the highest for November in the 1880–2015 record, surpassing the previous record set in 2013 by 0.27°F (0.15°C) So the NOAA claims that this November was 0.15C higher than the previous record high. What does this mean in a larger climate context? Probability theory tells me that a single number like this is meaningless, but other than that I don't know how to interpret this except that it is information that was published with no specific agenda other than reporting it.

imglorp 11y ago
It seems the number of records set per year in either direction is a useful signal to climatologists. More records than prior years indicates a trend.
eCa 11y ago
> Probability theory tells me that a single number like this is meaningless That is true. But when considering that the ten warmest years since 1880 all have occurred since 1998[1] it is no longer a single number. I'm guessing after 2015 that the eleven warmest years will have occurred after 1998. [1] http://climate.nasa.gov/blog/2224 http://climate.nasa.gov/blog/2224
mrow84 11y ago
I'm not sure that the single number is entirely meaningless, because you would expect reversion to the mean in the absence of a trend, so if you computed the likelihood function then I guess it would be weighted toward there being a positive trend, if only slightly. I think :-/.
- paulmd 11y ago
  The null hypothesis (no warming) would posit independent events with equal probability (the chance of an above-average and below-average year are equivalent). So in that case you're basically asking the question "given that I've flipped a fair coin and gotten heads 9 times in a row, what is the probability of heads on the 10th flip?" It's deceptive because you want to say 0.5^10, but the answer is actually 50% (because it's one throw of a fair coin). The 0.5^10 is the chance of 10 heads in a row occurring, but you can't disregard the prior (you have already thrown 9 heads). Reversion to the mean is a trend, it says nothing about any individual event in a series. In the event that it's not warming, the chance of a warm year is just as likely as a cool year. Now, as a trend, the evidence is highly suggestive of global warming being the case. When you have a sufficient sample of throws with a huge number of heads, the chance of the coin being biased* increases. * Note: you cannot actually bias a flipped coin. But you can bias a die, or a spun coin: https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf
  - nonbel 11y ago
    >"The null hypothesis would posit independent events with equal probability (the chance of an above-average and below-average year are equivalent)." Why should that be the null hypothesis? Is that a theory someone subscribes to? That would be a theory of no trends and no auto-correlation in temperature. I doubt you will find someone espousing such a theory, so why should we make something no one believes a null hypothesis? If you can find someone claiming that, I am interested in the reasoning.
  - mrow84 11y ago
    I think the difference in this case is that we are looking at a point that exceeds the current series maximum. If we had a single value from a series without a trend, we would expect it to fall below the maximum value observed so far (perhaps after sampling at least 2 points - I will think about that later), and so I reckon that the likelihood of a positive trend will be higher than for a zero or negative trend because of that fact. I may try and actually work it out to see if what I'm saying is correct, but one thing I can tell you that likelihood of me not doing so is greater ;-).
    - paulmd 11y ago
      Yes, looking at the sample minimum/maximum does change the probabilities. You're looking for Extreme Value Theory. https://en.wikipedia.org/wiki/Extreme_value_theory https://en.wikipedia.org/wiki/Extreme_value_theory I kept it simple (above or below average should be equal probability if your average is really average) to try and avoid that. I have no idea what kind of distributions weather follows, and as the other guy noted weather is not fully independent either. But it works for a simple explanation. :) It's been a long time since my stat courses and I don't remember this stuff all that well. Maybe there is something that expresses it better. Either way the fact that we're suddenly having a big run of Nth Warmest Year events is pretty suggestive that something is going on. But you do have to look at it as a trend, particular years aren't all that meaningful.
DougWebb 11y ago
Two things strike me about that quote. First, the range starts in 1880, which is just about the end of the Little Ice Age.[1] So yeah, pretty much every year since then is likely to be warmer than the last one. For a fairer comparison, you'd have to go back to 1100 or so to the Medieval Warm Period. We're still warmer today than back then, but not by as much. The second thing that struck me was the same thing that struck you: a single number is meaningless. If the fluctuations were completely random, you'd still always have a 'highest' one, but it wouldn't mean anything. And since we're trending upwards anyway (still coming out of that cool period, which only ended 100 or so years ago) you'd expect new highs to occur fairly often and fairly recently. I don't think this particular record says much; at most it fits with the fairly obvious warming trend we're in. If it was the coldest November since 1880, that'd be news because it would be a really odd occurrence. [1] https://en.wikipedia.org/wiki/Little_Ice_Age https://en.wikipedia.org/wiki/Little_Ice_Age

by tertius 11y ago

imglorp 11y ago

It seems the number of records set per year in either direction is a useful signal to climatologists. More records than prior years indicates a trend.

eCa 11y ago

> Probability theory tells me that a single number like this is meaningless That is true. But when considering that the ten warmest years since 1880 all have occurred since 1998[1] it is no longer a single number. I'm guessing after 2015 that the eleven warmest years will have occurred after 1998. [1] http://climate.nasa.gov/blog/2224 http://climate.nasa.gov/blog/2224

mrow84 11y ago

I'm not sure that the single number is entirely meaningless, because you would expect reversion to the mean in the absence of a trend, so if you computed the likelihood function then I guess it would be weighted toward there being a positive trend, if only slightly. I think :-/.

paulmd 11y ago
The null hypothesis (no warming) would posit independent events with equal probability (the chance of an above-average and below-average year are equivalent). So in that case you're basically asking the question "given that I've flipped a fair coin and gotten heads 9 times in a row, what is the probability of heads on the 10th flip?" It's deceptive because you want to say 0.5^10, but the answer is actually 50% (because it's one throw of a fair coin). The 0.5^10 is the chance of 10 heads in a row occurring, but you can't disregard the prior (you have already thrown 9 heads). Reversion to the mean is a trend, it says nothing about any individual event in a series. In the event that it's not warming, the chance of a warm year is just as likely as a cool year. Now, as a trend, the evidence is highly suggestive of global warming being the case. When you have a sufficient sample of throws with a huge number of heads, the chance of the coin being biased* increases. * Note: you cannot actually bias a flipped coin. But you can bias a die, or a spun coin: https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf https://www.stat.berkeley.edu/~nolan/Papers/dice.pdf
- nonbel 11y ago
  >"The null hypothesis would posit independent events with equal probability (the chance of an above-average and below-average year are equivalent)." Why should that be the null hypothesis? Is that a theory someone subscribes to? That would be a theory of no trends and no auto-correlation in temperature. I doubt you will find someone espousing such a theory, so why should we make something no one believes a null hypothesis? If you can find someone claiming that, I am interested in the reasoning.
- mrow84 11y ago
  I think the difference in this case is that we are looking at a point that exceeds the current series maximum. If we had a single value from a series without a trend, we would expect it to fall below the maximum value observed so far (perhaps after sampling at least 2 points - I will think about that later), and so I reckon that the likelihood of a positive trend will be higher than for a zero or negative trend because of that fact. I may try and actually work it out to see if what I'm saying is correct, but one thing I can tell you that likelihood of me not doing so is greater ;-).
  - paulmd 11y ago
    Yes, looking at the sample minimum/maximum does change the probabilities. You're looking for Extreme Value Theory. https://en.wikipedia.org/wiki/Extreme_value_theory https://en.wikipedia.org/wiki/Extreme_value_theory I kept it simple (above or below average should be equal probability if your average is really average) to try and avoid that. I have no idea what kind of distributions weather follows, and as the other guy noted weather is not fully independent either. But it works for a simple explanation. :) It's been a long time since my stat courses and I don't remember this stuff all that well. Maybe there is something that expresses it better. Either way the fact that we're suddenly having a big run of Nth Warmest Year events is pretty suggestive that something is going on. But you do have to look at it as a trend, particular years aren't all that meaningful.

DougWebb 11y ago

Two things strike me about that quote. First, the range starts in 1880, which is just about the end of the Little Ice Age.[1] So yeah, pretty much every year since then is likely to be warmer than the last one. For a fairer comparison, you'd have to go back to 1100 or so to the Medieval Warm Period. We're still warmer today than back then, but not by as much. The second thing that struck me was the same thing that struck you: a single number is meaningless. If the fluctuations were completely random, you'd still always have a 'highest' one, but it wouldn't mean anything. And since we're trending upwards anyway (still coming out of that cool period, which only ended 100 or so years ago) you'd expect new highs to occur fairly often and fairly recently. I don't think this particular record says much; at most it fits with the fairly obvious warming trend we're in. If it was the coldest November since 1880, that'd be news because it would be a really odd occurrence. [1] https://en.wikipedia.org/wiki/Little_Ice_Age https://en.wikipedia.org/wiki/Little_Ice_Age