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Physicists Roger Cohen, William Happer, and Richard Lindzen wrote a calm and sensible text about weather extremes in the Wall Street Journal:



They mention that the optimum CO2 concentration is probably significantly higher than the present one and enumerate some climate skeptics who are not conservative, among related sociological things.But the bulk of the article is dedicated to clarifications of the fact that there's no unusual trend in the weather extremes. Tornadoes, droughts, hurricanes, and wildfires are discussed as the most important examples of the fact that these largely unpredictable events are doing what they have always been doing. They randomly appear and disappear.Despite the fact that these topics have been discussed for years and one could say decades, I think that most people – and maybe even most people who have science degrees – remain remarkably ignorant about the basic logic of all these things, especially the statistical properties of weather events. In particular, people don't distinguish "red noise" (or similar "pink noise") from the "white noise" (or quantities well approximated by it).The global mean temperature has been changing during the glaciation cycles; the maximum and the minimum differ by nearly 10 °C which is significant. A cool world or a warm world persists for thousands of years. Smaller but qualitatively similar changes may be seen at shorter timescales such as several centuries (compare the medieval warm period and the little ice age). There are numerous drivers that influence the temperatures and allow them to remain "elevated" or "depressed". So it is surely incorrect to say that the annual global mean temperatures for each year are independent from those in the previous year or two. That would be needed for us to say that they behave as the "white noise".Still, the white noise is the only "type of random data" that most people are familiar with. The white noise would look like this:At every "moment", whatever its tiny length is, the quantity is distributed according to some fixed distribution and it is independent from the value at any previous moment. For that reason, the "jump" of the quantity from one moment to another is almost always infinite. In other words, the huge frequencies are heavily represented in the Fourier decomposition of the white noise.We could say that tornadoes, hurricanes, wildfires, and other things are more or less described by the white noise. Every year is different, the previous year is forgotten and the "qualitative" weather events and natural catastrophes arrive randomly according to this most widely understood type of a random distribution. Each year, you throw dice and the number you get (reparameterized by a fixed function) gives you an estimate how many natural catastrophes of a certain type you get during the year.Everything we know indicates that extreme weather events that depend on dramatic changes of temperature, pressure, or humidity as a function of space or time are nicely described as the white noise. That's why we don't observe any trend in those graphs. The graphs are highly variable but each year, the previous year (or two) are forgotten. It's always more sensible to build your expectation upon the ensemble of many (or thousands of) previous years, regardless of the fact that most of them are very far.The climate alarmists often say that the number of extreme events such as tornadoes and hurricanes increases and they like to pretend that such claims are scientifically justified and that such claims are a part of the "greenhouse effect science" package. But these propositions are complete lies that are unfortunately often bought by a large fraction of the public. Once you look at extreme things driven by rapid change or large gradients such as tornadoes, there exists no empirical reason to think that anything is changing about them; and there exists no theoretical explanation why it should be happening. According to everything that science may say, such changes are simply not happening. Tornadoes are as random and as frequent as they were decades or centuries ago.On the other hand, the temperature is more accurately modeled by the "red noise" or at least some kind of "pink noise" which is something in between the red noise and the white noise. While the "white noise" is a collection of random numbers that are independent from the previous ones, "red noise" is what you get by integrating (or partial summing of) the "white noise". In other words, "red noise" is the graph of a random walk. To emphasize the relationship between the two, let me also say that the derivative of the red noise is the white noise.Graphs of red noise. Good enough model for temperatures or prices of stocks.Each new year or new moment or new datapoint isn't independent from the previous one. Instead, it stands on the "shoulders" of the previous one and adds a random deviation away from it. Consequently, as you can see on the picture above, the graphs of red noise are much more continuous than the graphs of white noise we started with. In other words, the Fourier decomposition of the red noise suppresses the contribution from the very high-frequency oscillations and it adds strong low-frequency wiggles.(If the graphs depict pressure as a function of time, you will hear a lower-pitch noisy sound than in the case of the white noise. If the graphs depict the electromagnetic field, the resulting noisy "light" will look redder because the lower-frequency red light will be overrepresented relatively to the white noise which is considered "color neutral" here; that's why it's called "red noise".)These low-frequency wiggles inevitably look like "trends" over arbitrarily long timeframes.Another concept in physics that is almost synonymous with "red noise" or "random walk" is the Brownian motion. Albert Einstein's 1905 paper – and an independent Polish mountaineer Marian Smoluchowski's 1906 paper – derived some basic mathematical patterns about the Brownian motion. The typical distance \(s(t)\) that the particle moves after time \(t\) goes like\[\overline{s(t)} \sim C\cdot \sqrt{t}.\] So it increases with \(t\) but it increases less quickly than the direct proportionality would predict. The graph of \(s(t)\) may be drawn and you may calculate the apparent trend between \(t=0\) and \(t=t\):\[\overline {|v(t)|} = \frac{s(t)}{t} \sim \frac{C}{\sqrt{t}}.\] You see that the "apparent velocity" or "apparent rate" goes to zero as you increase the period of time over which you look at the quantity. But it goes to zero very slowly. You need to increase the timescale 9 times for the apparent rate to decrease 3 times.The global mean temperature is at least morally closer to the red noise, much like the prices of stocks. The price of a stock is pretty random and if you look at its evolution over a few years, it's often twice as high at one moment than another moment. But it's very unlikely for the stock to jump 100 percent or drop 50 percent overnight. Instead, it's the change of the price from the previous day to the new day that is random so to see large enough changes, you usually have to wait for a longer time. (That wasn't the case of the white noise.)For this reason, it's totally normal for the temperature in a year (or few years) after a warm year to be comparably warm, too. The year 1998 was warm and due to the basic properties of the red noise or pink noise, it's very unlikely for nearby years to among the coolest ones. That's simply prohibited by the continuity of the temperature graph. And the temperature graph is continuous (although not smooth) because the Earth has a finite heat capacity and an infinitely abrupt change of the temperature would require an infinite amount of energy.That's why all the comments of the type "most of the years in the last decade are among the top 10 warmest years" are not surprising at all. That's exactly what the natural theory of the noisy graphs – even without any human or other "special" influences – predicts. It predicts such a clustering of warm years simply because the temperature is a continuous function of time; the noise apparent in the temperature graphs is closer to the red noise than the white noise.Being excited about this clustering is exactly as silly as saying "Look, 4 out of the history's 5 best days for the Apple stock price occurred in April 2012 (the only exception is yesterday, isn't it a stunning proof of something?". No, it's not shocking at all. There simply had to be a maximum near $640 and the moments near the maximum are likely to have similarly high values. (I am not claiming that the Apple stock won't get above $632 in the future; I am not claimiing that it will, either. Instead, we just talk about the known history.)On the other hand, there are many other quantities that depend on time and that have no reason to be continuous – e.g. the number of tornadoes in the year Y – and those things don't have to remember and don't remember the previous year or two. So you will find no trends in them.Things related to the drought are somewhere in between. The precipitation itself is more or less "white noise" (especially above the ocean) because whether it rains today is mostly independent on whether it was raining a month or a year ago. However, the soil and other entities on the surface of the globe have some inertia. They store water or they may run out of water (and this also influences the evaporation rate and precipitation) and if they do so, chances are that such conditions will continue for the following year or two or three, too. This inertia means that the dry years will tend to be clumped more than what you would expect from the white noise, i.e. from the complete independence. But the inertia diminishes if you look at timescales longer than a decade. If there are some unlucky coincidences that create drought in some region, chances are high that in 10 years, the situation returns to the "normal" (calculable from recent centuries, for example). That was the case of the Dust Bowl in the 1930s.The actual things that have changed are things such as the global mean temperature that are expected to change and "oscillate around the new values" because their behavior is closer to the red noise (random walk), much like the behavior of the stock prices or the position of a particle undergoing the Brownian motion. But the global mean temperature – which may only be calculated with the desired accuracy if you have accurate thermometers everywhere and at all times and you're extremely careful about the statistical procedures used to compute the average – has only changed by something like 0.7 °C per century, something a human would probably not be able to detect at all even if the surrounding temperature was stable (the real one has additional oscillations by dozens of degrees at all time so the human detection of the underlying "global trend" is completely impossible).If one focuses on the precise values of the temperature, it is totally inevitable – a trivial consequence of the red noise – that he gets some "apparent trends". That's what the red noise always does. But the actual temperature changes coming from this stuff are tiny and they affect neither humans nor tornadoes. All things such as tornadoes depend on properties of the climate system that are not changing. And if they're changing, the changes are negligible.You know, one could naturally expect that there is some residual dependence. For example, the number of tornadoes could be proportional to a power of the absolute temperature, \(T^k\). I am talking about the absolute temperature because it is the more natural quantity describing temperature in physics (for example, the volume of the ideal gas at fixed pressure is proportional to the absolute temperature).Now, the global mean temperature has changed from 288 kelvins to 288.7 kelvins in a century (or some numbers of this kind, no one knows because there is not even any precise universal definition of the "global mean temperature"). That's a change by 0.25 percent. Consequently, \(T^k\) has changed by \(k\) times 0.25 percent per century. Unless \(k\) is much greater than one, and it would be unnatural if it were much greater (so it is unlikely), we see that change in the predicted number of tornadoes per year will be smaller than one percent or so (relatively to the average predicted for the year 1912). That's obviously undetectable even if such an effect existed. And by the way, if it existed, it's likely that a warmer world will lead to smaller, and not greater, amount of similar activity because this activity depends on temperature gradients and they're predicted to decrease, and not increase, in a warming world (because the equator-to-pole temperature difference drops as the poles are claimed to be warming faster).There's an immense layer of irrationality underlying the whole climate panic. Every rational person knows that a 0.7 °C increase of some carefully-averaged temperature is undetectable by humans and irrelevant for all other phenomena that matter. It's just a tiny change of the temperature. Nature routinely deals with much larger and harsher changes every day – larger changes per day than the centennial change someone claims to be dangerous. For the same reason, things like tornadoes and hurricanes have no good reason to behave as anything else than the "white noise", so there won't be any trend and there isn't any statistically significant trend in any of these quantities. So it's trivial to see that given the estimates for the rates that we have measured, there can't exist absolutely any reason for concern when it comes to the climate change.Saying that people talking about a dangerous climate change are good scientists is preposterous beyond imagination. They're dimwits incapable of understanding (or unwilling to understand) basic concepts of mathematics, statistics, and natural sciences.And that's the memo.