## Saturday, May 22, 2021

### Sleeping Beauty wakes to a cold April

In 2021, Czechia experienced the coldest April since 1997. Around April 20th, the ranking was expected to be even more extreme but the end of the month just wasn't extreme enough. Surprisingly enough, the precipitation was well below the normal (60% of normal at "most" places) but the middle of May – when the rain in a few days was enough for 2 months – overcompensated that (see some dramatic scenes from Úslava, normally the smallest of the 4 rivers of Pilsen).

In the past, Sleeping Beauty (pictured in her Neuschwanstein am Disneyland des Plagiarism) was discussed on this blog as a key character to explain an elementary misunderstanding of the probabilistic calculus – that seems impossibly hard even for some theoretical physics PhDs.

Why don't we ask her to help us convey the point that the noise wins when it comes to almost all the questions that we (and she) may face? Will you help us, Sleeping Beauty? Jawohl!

Fine. On this page of the Czech Hydrometeorological Institute, you may find the actual temperatures; normal temperatures; and the differences (anomalies) for every month in 1961-2021, both in Czechia as a whole and in the 14 regions of the country. The anomalies may be expressed either relatively to the 1961-1990 period (of 30 years), or the 1991-2020 period.

Good. The average Czech temperature in April 2021 was +5.4 °C which was 1.9 °C colder than the average April in 1961-1990; or 2.5 °C colder than the average April in 1991-2020 (the difference between the anomalies, 0.6 °C, is roughly the land-based global warming trend accumulated over 30 years, about 2 °C per century). The deviations that are this extreme are rather rare but not too rare. Thankfully, someone else has analyzed the hitparade of temperatures interestingly enough, namely a page at IndustrialEcology.CZ which took the analysis from the Association of Heating Plants.

Here is an interesting table from that page, one with the top ten coldest (left) and top ten warmest (right) Aprils from the 61 years 1961-2021.

You see that April 2021 was the sixth coldest month between these 61 candidate Aprils, and the only one in this top ten list after 1997 (and 1997 was the third coldest among 61). You see a bias – the warmest Aprils tend to be the rather recent ones; while the coldest Aprils tend to be those from a long time ago. But the latter rule has been violated by a counterexample: April 2021 was very cold not just relatively to the recent Aprils but to most Aprils between 1961-1990, too.

If you care, you may construct a model for an April temperature which has the mean +8.5 °C but you add some trend-like correction comparable to 0.02 °C per year (times the year-1991, including the sign); and plus something like the normal distribution with the standard deviation of 1.8 °C (but note that there is an asymmetry; the temperature variations are much smaller when the temperatures are closer to the freezing point – which means the "coldest Aprils", in this case). You see that a part of the deviation from the mean April temperature is trend-like, due to global warming of a sort (whose cause won't be discussed at all); and a part is random, represented by some normally distributed white noise (you may analyze the data and decide whether there is evidence for some non-Gaussianity on top of that). Which of these two deviations is more important for some questions?

It's time to ask our friend Ms Sleeping Beauty for some help. As you can study in the scientific literature, she was cursed by an evil fairy to sleep for 100 years. The evil fairy did this nasty act in 1861, if you need to know. And Ms Sleeping Beauty may only be woken up by a handsome prince. But those weren't easily accessible in Czechoslovakia of 1961 so her sleeping could have been extended by 0-60 years.

OK, a handsome prince finally licked her on April 1st of some year (it is as great a day to be kissed as May 1st). And Ms Sleeping Beauty happily lived her first month outside the 19th century. And it was a cold April. She has carefully measured the temperature and found the average temperature for that April. On April 30th, probably because she was considered a witch, she was cursed to sleep again – but now she was promised to wake up on May 22nd, 2021 (today!), regardless of the availability of handsome princes on the market.

Because she is with us now, we know that the April she experienced was among the top 10 coldest Aprils among the 61 Aprils, 1961-2021. We may ask her:
Do you think that when you were woken up for a month last time, it was in the older 1/2 of the possible years, i.e. in 1961-1991?
If the global warming trend were totally decisive and the trend would be unimportant, her answer would be "of course, I am 100% certain that one of the coldest Aprils had to be in the early part of the 1961-2021 interval because the global warming real". ;-) But because she is rather intelligent, not a Gr@tin, she realizes that the certainty is far from 100%. She offers us a quantitative answer expressed in terms of probabilities. But there are many precise choices for "probability of what". She allows us to choose the question and we ask her:
If I tell you that your secret April was a top 10-of-61 coldest April from the period, what is your subjective probability that you assign to the proposition that "you have lived through an April in the older one-half, 1961-1991"?
As we have discussed, this probability isn't 100%. Can she calculate or estimate the probability? You bet. For a "calculation", it would be better to consider the full model for the April temperatures (8.5 °C plus the global warming trend plus the Gaussian white noise). But at the end, I may use a data-driven approach because the model probably agrees with the real world data and they are not extremely atypical.

Well, the data-driven estimate is straightforward. Among the 10 coldest Aprils in 1961-2021, there are exactly two Aprils, 1997 and 2021, which took place in the second half of the period, i.e. in 1991-2021. (Yes, I repeatedly include 1991 into both, let's imagine that April 1991 is divided into the first and second half of the 61-year-long interval.) As you can see, our smart enough Ms Sleeping Beauty will tell us
I feel 80% confident that I was woken in April of a year between 1961 and 1991 (first half of that month).
And you know, my point is that 80% is extremely far from the certainty. Using a conversion between $$z$$-scores and $$p$$-values, 80% corresponds to some 1.3 sigma. It's no proof (5 sigma). It's not even strong evidence (3 sigma). It is just a slight bias favoring the colder 30-year-long period. Even though she has measured a whole country for a whole month and she saw a rather extreme temperature, her global-warming-free neutral estimate (50-50 for the first and second half of 1961-2021) was only skewed to 80-20, a slight bias favoring the cooler temperatures in the past.

And the answer won't be too different if she happens to live in a top 10-of-61 warmest April. Out of the 10 warmest Aprils, 1 was before 1991 (1966 was 9th warmest among 61; also note 1993, the 10th warmest month, was pretty close to the middle year 1991). So at most, similar questions may end up with the 90-10 odds. The lesson is similar as the geographic one in the TRF articles saying things like
HadCRUT3: 30% of stations recorded a cooling trend in their whole history.
You know, an important global warming would be seen everywhere, globally (but in each weather station separately). However, the percentage of the stations that have seen a warming trend or a cooling trend in their whole history is just 70-to-30 which is closer to 50-to-50 than to 100-to-0! So the global warming hasn't been "global" in the strong sense, i.e. something that has occurred at each point separately. Instead, the global warming only exists in the very weak sense, namely that if you compute the averages for all places so that the geographic part of the noise gets averaged out, then you get a single function of time that has had a nonzero trend – what a surprise. But the slope is still very small relatively to the noise. It follows that if you study the temperatures locally, you just can't be any certain that the temperature trend is "towards warmer temperatures".

Similarly here, Ms Sleeping Beauty allows us to see that the global warming "doesn't occur in every year". You may only start to see the trend clearly if you average many years because in individual years, it is perfectly possible to see temperatures that contradict the naive predictions from the "global warming trend and nothing else".

These odds, 70-to-30 or 80-to-20 or at most 90-to-10 are the answers to almost all the practical questions that someone will actually face. Imagine that someone pays for a new ski lift but the question is whether there will be enough snow (and skiers) during a season in the future. Ski lifts are more economically sensitive to small, global-warming-like changes of the temperature but even they are not sensitive enough. Even without snow guns, the probability of a good, snowy season decreases just by dozens of percent in 50 years, not "hugely".

I just picked the snow because in 2000, The Independent posted the notorious text Snowfalls now are just a thing of the past. We find ourselves in a world 21 years later which is a long enough time and every sane person can see how criminally stupid – or a hardcore intentional lie – this article has been. Of course we've seen a lot of snow (especially in Czechia in the 2020-2021 season) and we will see snow in most coming years, too.

It seems to me that it should be obvious to everyone, including (and especially) the ordinary people, that even if a 1-2 °C per century global warming trend exists, it is basically zero for almost all practical purposes. One degree and even two degrees are just a tiny change if you need to wait for a century. Let me remind you that, as the tables reproduced above taught us, April 2018 was 12.7 °C in Czechia and April 2021 was 5.4 °C. Let me subtract these two numbers for you. This April was just a whopping 7.3 °C colder than the same month just three years ago! Changes by very many degrees occur from one year to another year, and from one day to the following day, and when some trend lines apparently add 1-2 °C per century, it is guaranteed to be comparable to the residues of the noise, unless you measure and record the temperatures really carefully and average out both the intermittent and geographic noise (which you basically can't do without a professional experimental infrastructure).

When it comes to the normal life, the global warming trend is effectively zero – it is indistinguishable from noise and the noise (also known as the random weather) dominates. It is completely insane to sell the aforementioned hypothetical underlying trend as a serious problem for everybody; or even to waste trillions of money for this self-evident non-problem.