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Skeptical Swedish climatology

Global warming only visible under a microscope

As noted by Pierre Gosselin (via another blog), a prominent senior climate scientist Lennart Bengtsson whose publication and citation record is rather formidable has said something that you must have heard many times from your humble correspondent:

We Are Creating Great Anxiety Without It Being Justified…there are no indications that the warming is so severe that we need to panic.

‘The warming we have had the last a 100 years is so small that if we didn’t have had meteorologists and climatologists to measure it we wouldn’t have noticed it at all.’

The Earth appears to have cooling properties that exceeds the previous thought ones, and that computer models are inadequate to try to foretell a chaotic object like the climate, where actual observations is the only way to go.
A commenter mentions that this could have been the first time when the Swedish media interviewed an actual achieved climate scientist rather than an activist.

We often argue what the term "global warming" could possibly mean, whether it exists, and whether it's man-made. But there's one key issue – I believe a more important feature for the life of the society than the previous two – that is often overlooked. And it's the fact that the effects of global warming are so extremely weak that we need extremely precise measurements that are simultaneously performed almost everywhere throughout the globe at almost every moment during many decades or a century and we need very sophisticated statistical procedures to process the observations if we want to see an "effect" at all.

And of course, I believe that at the end, we may see an "effect", some 70-30 imbalance between the number of regions that have seen a warming trend and those that have seen a cooling trend over the last century or so. But we have used lots of tools which I will call "the microscope". And if something may be seen through a microscope, it's not the same thing as if it is visible to the naked eyes. Quite on the contrary, if we apparently need this microscope to locate an effect, it means that the effect is almost certainly too tiny to be visible to naked eyes.

Now, my key point is this: If something requires a microscope to be seen, it's almost certainly not an elephant who will crush us underfoot. ;-)

I want to mention an example of how this small effect may be expressed in different words. Alexander Ač referred to a paper that argued that the monthly record temperature readings are about 1.8 times more likely to be topped by the newest figure than they would be without "global warming".

The coefficient of 1.8 seems significant but it's a number that appears in a quantity – the frequency of weather records – that just happens to be immensely sensitive to small additive shifts of the temperature. My goal is now to show that this 1.8 times increase of the rate of monthly weather records is pretty much the same thing as the overall increase of the temperature averaged over many years by less than 1 °C. How do I do it?

The typical temperature record is something like 120 years long, from the late 19th century. That's equivalent to 1,500 months or so. If the monthly figures were independent of each other and random, the probability that the highest one would be the most recent month would be 1/1,500: each month in the set of 1,500 has the same odds given our assumptions (white noise).

So right now, after 120 years of records, the probability of setting a new monthly record at a given place is as likely as \(p=1/1,500\) which is the same probability as the probability that a normally distributed variable exceeds \(\mu+3.4\sigma\) where \(\mu\) is its mean value and \(\sigma\) is the standard deviation. Note that 3 standard deviations are equivalent to a 1 in 370 chance and what we have here is somewhat more extreme than that, 3.4 sigma.
1/(1 - Erf[3.4/Sqrt[2]])
But we were assuming that the monthly readings have no trend – the value of \(\mu\) hasn't changed from the 19th century. What happens if the medium-term average of the monthly temperature readings has been slowly shifting as well? And that's what we could mean by global warming? Well, the numbers change, too. For example, if you want to change the probability 1/1,500 to a probability that is 1.8 times greater, i.e. 1/833, you will obtain a different number of standard deviations, too. It's about 3.24 standard deviations instead of 3.4.
1/(1 - Erf[3.24/Sqrt[2]])
Shifting a Gaussian by a tiny distance has a huge effect on the area beneath the curve in the tails simply because the tails decrease very quickly – faster than a decreasing exponential.

So what you need to make the hot records 1.8 times more likely is a simple thing: the "extreme temperatures" have to be not 3.4 sigmas above the mean but 3.24 sigmas above the mean becomes enough if the increased mean helps you to reach new record high temperatures. In a recent analysis of the Czech temperature record, I told you that the typical standard deviation of the "monthly temperature [anomaly] noise" is about 2 °C. You may see that 3.4 and 3.24 sigmas translate to 6.8 °C and 6.48 °C, respectively. To set a new record temperature anomaly for any month, you need temperatures that are more than 6 Celsius degrees above the mean value. (And yes, you may remember that the maximum temperature anomaly in the Czech temperature record was indeed around 6 °C.)

The two figures - depending on whether or not the mean value \(\mu\) of the distribution has shifted – only differ by 0.32 °C. So if your record is 1,500 months old and you shift the mean value of the temperature by nothing else than 0.32 °C, the temperature anomaly hot records become 1.8 times more frequent. It's that easy. While the number 1.8 suggests that "something" has changed dramatically, you may still see that all this "dramatic change" is due to the 0.32 °C overall temperature change of all the distributions which is unobservable by humans, despite their being rather sensitive. The only change is that the warmest month's temperature anomaly may be 6.48 °C instead of 6.8 °C above the average. Would you really care about the difference if you were not obsessed with tenths of degrees that may be measured by special tools (but not with your skin) and obsessed with "record monthly temperatures"?

Here, my point is that it's very easy to produce "impressive numbers" such as 1.8 as answers to rather natural questions even though it's totally transparent that the underlying change leading to such "impressive numbers" is as unimpressive as a third of a degree of temperature change.

(In the real world, the actual shift of \(\mu\) may be larger than 0.32 °C because the record may be shorter than 1,500 months. Also, you may consider record temperatures for a given month only and not record anomalies in which all 12 months of a year compete against each other. I am sure you can repeat the calculation for your favorite figures and conventions; the qualitative lesson of the exercise is unchanged.)

We should still distinguish bacteria from elephants – you don't need a microscope to see the latter and only the latter may crush your body underfoot.

Incidentally, Prince Charles spoke to an appreciative Low Carbon Prosperity Summit where he labeled all skeptics as "deniers" who have a "corrosive effect" on the public opinion and who can't possibly face their grandchildren.

Fortunately, we have a proof that it's possible to face your grandchildren even if you appreciate global warming skepticism and even if you're a member of a royal family. We don't have to go too far, Charles' father Prince Philip is a good example for us because unlike Charles, he is an experienced grandfather. Duke of Edinburgh has invited David Bellamy to the Buckingham Palace to give the inaugural David Bellamy Lecture.

Bellamy – whom the Telegraph calls the Britain's most famous global warming heretic – was allegedly blacklisted at the BBC when he called global warming "poppycock". Clearly, the queen's husband doesn't have to consider the left-wing media agency's taboos and his son's would-be moralizing rants as his own.

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snail feedback (6) :

reader James Gallagher said...

Prince Charles is a stupid member of a pretty stupid family. He got a B and C at A-level, in History and English - that somehow qualified him to do Anthropology, Archaeology and History at Trinity College, Cambridge. He seems to have struggled with any science based courses and concentrated on history, getting a lower second class degree (~ grade C)

This should have taught him to shut his fucking mouth forever on anything remotely requiring expert knowledge, particularly if it's science related. But no, the knicker sniffing, plant talking eedjit just has to say something that might currently be perceived popular to hopefully promote his appeal as king should QE2 die anytime soon.

reader Shannon said...

Ha :-D !! Royal families always degenerate after a few generations... Charles' IQ isnt a good omen for the younger ones.

reader Honza said...

I just recently read this statement I like: "Every anti-science crank insists science is out to kill us, except
when it comes to global warming, then scientists can be trusted."

reader Mark Luhman said...

Fortunately Charles out breed and at
this point it look like his sons are brighter then him.

reader Alexander Ač said...

Funny, I read peer reviewed paper showing climate deniers are more willing to believe to other conspiracy theories ;-) (h/t Lewandowsky)

reader Luboš Motl said...

Dear Alexander, science has produced the opposite results:

Let me also mention that this "Lewandowsky" asshole has seen its latest "paper" of this kind removed from the journal

and Lewandowsky himself should be physically liquidated because scum like this has no business to oxidize on our blue, not green planet.