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The thing with these "all time high records" is they have an intrinsic trend to the upside. Consider the following thought experiment: Draw a continuous random

The thing with these "all time high records" is they have an intrinsic trend to the upside. Consider the following thought experiment: Draw a continuous random number between 0 and 100 and compare it with the previous result. If the new number is higher than before, keep it as the new record value. Draw a time evolution of all the record numbers and you will see a straight line going up. But this is not a statistical trend. So, while I am not saying there is no climate change, the evidence they provide is questionable.

robotresearcher 5y ago
What's the distribution over time of the new records? Is it what you'd expect from a random process?
tasty_freeze 5y ago
Here is the counter evidence: count the number of record high days and the number of record low days. For the past few decades, and increasingly so, the number of high days far outpaces the number of record low days, something your example doesn't exhibit.
- georgeplusplus 5y ago
  I would then say your counter evidence could be flawed if the period you chose was not sufficiently long enough. If your decades period is biased towards record high then the original evidence stands.
  - alpaca128 5y ago
    The temperature change in the last 100 years was larger than in the 5000 years before that. You can cherry-pick time periods however you like, you won't find another with such a drastic change in such a short timeframe.
    - georgeplusplus 5y ago
      The OP is about the flaw of using record highs or lows to show a rising/falling trend. Not temperature changes in general. You can indeed cherry pick decades long periods of both cooling and warming which would show a biased in the last 100 years. In the 80s, scientists thought there was Global Cooling. There was also an Ice age that shows temperatures were indeed cooler. At least understand what is being discussed before you make a response and downvote.
thenoblesunfish 5y ago
"Straight" is not correct - it implies that that the maximum increases linearly with time. The maximum will clearly asymptote at 100, and since it's an increasing function of time, the rate of increase must slow with time.
jfim 5y ago
If that was the case, the number of record lows and record highs would be roughly equal, assuming no shift in distribution. However, according to this paper (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2009GL040736 https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/200...), it's not the case, with record highs outnumbering record lows. > Since January 1, 2009 (also compiled to the end of September, 2009), there had been 11,711 record highs and 7,449 record lows, with a ratio of just less than two to one. We can also check whether that ratio is consistent with a random process that has an even probability of giving record lows and record highs: > binom.test(c(7449,11711), p=0.5) Exact binomial test data: c(7449, 11711) number of successes = 7449, number of trials = 19160, p-value < 2.2e-16 alternative hypothesis: true probability of success is not equal to 0.5 As such, the data indicates that there is a shift in distribution.
- blix 5y ago
  > 11,711 record highs and 7,449 record lows, with a ratio of just less than two to one. If 1.57 is "just less than 2", I am just less than 8 ft tall. I am a staunch believer in the dangers of climate change, but it's easy to see why people are skeptical of arguments like this. The evidence is compelling enough that it doesn't need to be massaged into more.
  - jfim 5y ago
    It makes more sense in the context of the paper. The previous sentence ends with > [...] since January 1, 2000, there had been 291,237 record high maximum daily temperatures set, and 142,420 record low minimum daily temperatures, or a ratio of roughly two to one. It seems like "just" shouldn't be in that sentence though.
- G3rn0ti 5y ago
  Thanks, this is a well written and accessible article! To other commenters: Of course, there wouldn’t be a straight line but rather the curve would flatten out the longer the random sampling would take place. This is due to the fact that it gets increasingly unlikely that a random „temperature“ would be higher than any drawn before. As the paper explains the ratio between the number of maxima and the number of minima decays in a 1/n law if there is no underlying temperature trend and approach 1:1. What is observed is that the ratio between maximum and minimum temperatures indeed approached this limit until the 1970s but since then increased to almost 2:1 — at least for the US. Simulations suggest the number to increase up to 100:1 by the end of the 21st century. However, this would not so much be due to ever increasing extreme high temperatures but due to a decreasing number of extreme temperature lows.
tgv 5y ago
Record values occurring more often certainly is a statistical trend, even if the average stays the same. It's a change in distribution, just like a rising average is a change in distribution. Or is that not what you were referring too?
boudin 5y ago
Weather is not a random number pick. And your proof is wrong it's not if the number is higher than the previous one, but higher than all the previous ones. This means that you should have a curve getting flat, or potentially no curve at all if your first draw is 100.
sgt101 5y ago
>Draw a time evolution of all the record numbers and you will see a straight line going up. Ok, to understand this as evidence what you actually need to do is to repeat this process after you have got to ~0.99 many times, this will give you a way to understand the expectation of the evolution of this process, then you will see a curve with an initial rise that flattens as you approach 0.99 - you will have many trials at that level before you can have a expectation of getting to 0.991 So getting to a record level - if the bias of instrumentation is understood - is a surprising and significant thing; it's not something that we should expect. It's an event that can be interpreted as either a rare and surprising coincidence or an significant piece of evidence of a change. As a bayesian it makes me update my priors towards a stronger belief in climate change - but I had strong priors for that already.

robotresearcher 5y ago

What's the distribution over time of the new records? Is it what you'd expect from a random process?

tasty_freeze 5y ago

Here is the counter evidence: count the number of record high days and the number of record low days. For the past few decades, and increasingly so, the number of high days far outpaces the number of record low days, something your example doesn't exhibit.

georgeplusplus 5y ago
I would then say your counter evidence could be flawed if the period you chose was not sufficiently long enough. If your decades period is biased towards record high then the original evidence stands.
- alpaca128 5y ago
  The temperature change in the last 100 years was larger than in the 5000 years before that. You can cherry-pick time periods however you like, you won't find another with such a drastic change in such a short timeframe.
  - georgeplusplus 5y ago
    The OP is about the flaw of using record highs or lows to show a rising/falling trend. Not temperature changes in general. You can indeed cherry pick decades long periods of both cooling and warming which would show a biased in the last 100 years. In the 80s, scientists thought there was Global Cooling. There was also an Ice age that shows temperatures were indeed cooler. At least understand what is being discussed before you make a response and downvote.

thenoblesunfish 5y ago

"Straight" is not correct - it implies that that the maximum increases linearly with time. The maximum will clearly asymptote at 100, and since it's an increasing function of time, the rate of increase must slow with time.

jfim 5y ago

If that was the case, the number of record lows and record highs would be roughly equal, assuming no shift in distribution. However, according to this paper (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2009GL040736 https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/200...), it's not the case, with record highs outnumbering record lows. > Since January 1, 2009 (also compiled to the end of September, 2009), there had been 11,711 record highs and 7,449 record lows, with a ratio of just less than two to one. We can also check whether that ratio is consistent with a random process that has an even probability of giving record lows and record highs: > binom.test(c(7449,11711), p=0.5) Exact binomial test data: c(7449, 11711) number of successes = 7449, number of trials = 19160, p-value < 2.2e-16 alternative hypothesis: true probability of success is not equal to 0.5 As such, the data indicates that there is a shift in distribution.

blix 5y ago
> 11,711 record highs and 7,449 record lows, with a ratio of just less than two to one. If 1.57 is "just less than 2", I am just less than 8 ft tall. I am a staunch believer in the dangers of climate change, but it's easy to see why people are skeptical of arguments like this. The evidence is compelling enough that it doesn't need to be massaged into more.
- jfim 5y ago
  It makes more sense in the context of the paper. The previous sentence ends with > [...] since January 1, 2000, there had been 291,237 record high maximum daily temperatures set, and 142,420 record low minimum daily temperatures, or a ratio of roughly two to one. It seems like "just" shouldn't be in that sentence though.
G3rn0ti 5y ago
Thanks, this is a well written and accessible article! To other commenters: Of course, there wouldn’t be a straight line but rather the curve would flatten out the longer the random sampling would take place. This is due to the fact that it gets increasingly unlikely that a random „temperature“ would be higher than any drawn before. As the paper explains the ratio between the number of maxima and the number of minima decays in a 1/n law if there is no underlying temperature trend and approach 1:1. What is observed is that the ratio between maximum and minimum temperatures indeed approached this limit until the 1970s but since then increased to almost 2:1 — at least for the US. Simulations suggest the number to increase up to 100:1 by the end of the 21st century. However, this would not so much be due to ever increasing extreme high temperatures but due to a decreasing number of extreme temperature lows.

tgv 5y ago

Record values occurring more often certainly is a statistical trend, even if the average stays the same. It's a change in distribution, just like a rising average is a change in distribution. Or is that not what you were referring too?

boudin 5y ago

Weather is not a random number pick. And your proof is wrong it's not if the number is higher than the previous one, but higher than all the previous ones. This means that you should have a curve getting flat, or potentially no curve at all if your first draw is 100.

sgt101 5y ago

>Draw a time evolution of all the record numbers and you will see a straight line going up. Ok, to understand this as evidence what you actually need to do is to repeat this process after you have got to ~0.99 many times, this will give you a way to understand the expectation of the evolution of this process, then you will see a curve with an initial rise that flattens as you approach 0.99 - you will have many trials at that level before you can have a expectation of getting to 0.991 So getting to a record level - if the bias of instrumentation is understood - is a surprising and significant thing; it's not something that we should expect. It's an event that can be interpreted as either a rare and surprising coincidence or an significant piece of evidence of a change. As a bayesian it makes me update my priors towards a stronger belief in climate change - but I had strong priors for that already.