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This the first and only in-depth talk about one of the three winners of 2021 Nobel Prize in Physics, Klaus Hasselmann, and his original and obscure work, called "Stochastic Climax Model".

#inferentialstatistics #stochastic #correlation #correlationcoefficient #coupling #climatechange #agw #computersimulation #chaos #fluctuation #fouriertransform #nobelprize

Based on Hasselmann’s biography, he was trained and worked as an oceaNographer in the 60s and the early 70s. He also wrote quantum-field-like papers on ocean wave scattering with the Feynman diagrams.

According to the Nobel Prize Committee,“He has provided the relationship between weather and climate; developed the fingerprinting methods to assess the human impact on earth’s climate.” Sounds very important.

To my surprise, as I have found, his fingerprinting method is not based on physics, but inferential statistics, such as the Central Limit Theorem, and Confidence Interval, that are taught in high school. How did he do that?

10.Well, before I answer this question, let’s talk about Fourier again. It is known that any time-dependent variations, which form time-series, can be mathematically transformed into the so-called power spectral density, PSD, or power spectrum. This transformation was introduced by Fourier, who also speculated the atmosphere could keep the surface warm.

11.In this diagram, time series and their frequency spectra of several musical instruments are shown. In this way, the colors of sound can be easily identified. Hence, one can call such frequency spectra as the fingerprints, similar to how DNA base-pair sequences for characterizing genes.

12.Not only did Hasselmann know this spectral analysis quite well, but also he had a crazy idea, namely, he wanted to use the Fourier transformation to prove the global warming is man-made, or anthroponetic, without using physics!

13.In 1976, as Chairman Mao was dying, Hassemann published his idea that slow climate change can be treated as a cumulative response to continuous random excitation by short-time-scale weather disturbance, just as the Brownian motion. Do you know the Brownian motion?

14.In 1905, Einstein first derived a formula, based on molecular motion, for random movements of tiny pollen particles suspended in a fluid, first observed by a botanist Brown in 1827.

15.The random walks of the particles can either described by stochastic trajectories, or deterministic evolution of probability density function. In this 3D diagram I generated based on Einstein’s formula, you can see how the probability distribution changes with time.

16.Notice that the observable Brownian motion is caused by random molecular collisions, but the causality between climate and weather proposed by Hasselmann is merely hypothetical, namely, CO2 can make the surface warmer by radiative forcing, or the gaslight as one viewer called it. Where did he get this hypothesis? You may wonder as I did in 2021 after I heard the news.

17.Remember? As I mentioned, Hasselmann had studied ocean waves for many years before he became a climate activist. As early as 1962, he reported that certain “resonant coupling” between random ocean waves could make a non-linear energy transfer, which are visible in the Fourier transformed spectrum.

18.I think that was why he came up with the assumption that two distinct peaks exist in the Fourier transformed spectra of the time series of stochastic weather changes: the high-frequency noises associated with weather, and the low-frequency signal associated with climate.

19.Contrary to Hasselmann’s assumption, however, almost everyone in this research field knows the Fourier transformed power distributions from both the instrumental data and that inferred from ice cores from time scale from days to 1 million years are continuous, as shown in this figure. Let’s see how this Nobel physics laureate responded cunningly.