Assuming the measurements are independent samples from a normal distribution. Which they of course aren't, as measurements of adjacent days are obviously correlated (if they were independent, a 1-in-7000 event could be expected to happen on about 2 days within a 44-year span). Now the question is what the nature of the deviation is.
- How independent are measurements of different years?
- Has there been a systematic change in the distribution mean?
- Has there been a systematic change in the distribution variance?
- Was there a good reason to assume that the temperature distribution would be normally distributed to begin with? (Maybe there are strong non-additive effects.)
In any case, it's clear that assuming the observed temperatures in the 1991-2020 range follow a normal distribution and temperatures outside that date range will follow the same distribution is a bad model of reality.
Yes there are. Scientists compare the measurements from both methods in the time when there's data from both. For example ice cores formed last decade should match direct temperature measurements from last decade. It's the same way the oldest rings from living trees are matched against the newest rings from tree fossils, and radiocarbon dating is checked against all of that.
That does not look very reliable to me, because that implies certain things are only affected by ambient temperature.
Btw, Can you tell me how ancient temperature is measured from ice cores? My lookup only says we can detect atmospheric composition, and not temperatures from the ice cores.
It seems like you're on the trajectory to refuting all historical measurements altogether. In that case, I can't help you. Good luck. I suggest the philosophy of Last Tuesdayism, it may interest you.
> I'm not sure how you can make that claim with only 29 years of data without making some pretty big assumptions about the underlying distribution.
Under what circumstances would 29 years be an insufficient mean to compare to the last few years? Precisely those circumstances in which the climate had changed.
Under any sane statistical model. If we assume that this is a naturally occurring once in century El Nino under an equal probability model we'd expect not to see it before we have 70 years of records.
Within the 1982-2026 span there is an equally negative 3.5 sigmas deviation somewhere (no year labels on the graph). The article doesn't touch on it at all so I have no context as to what it could be. But it definitely suggests 3.5 sigmas is not really 1 in 7000 years.
- How independent are measurements of different years?
- Has there been a systematic change in the distribution mean?
- Has there been a systematic change in the distribution variance?
- Was there a good reason to assume that the temperature distribution would be normally distributed to begin with? (Maybe there are strong non-additive effects.)
In any case, it's clear that assuming the observed temperatures in the 1991-2020 range follow a normal distribution and temperatures outside that date range will follow the same distribution is a bad model of reality.