Global warming: A detailed explanation of the 2021 Physics Nobel Prize for complex stochastic systems

According to the official website of the Nobel Prize, at 17:49 Beijing time on October 5, the 2021 Nobel Prize in Physics was awarded for "pioneering contributions to the understanding of complex systems", of which Syukuro Manabe and Klaus Hasselmann shared half in recognition of their "physical modeling of the Earth's climate, quantification of variability and reliable prediction of global warming, and the other half to Giorgio Parisi in recognition of "discovering the mutual influence of disorder and fluctuations in physical systems from atomic to planetary scales."

Written by | Fanpu

At 11:45 a.m. local time on October 5, 2021 in Sweden (17:45 p.m. Beijing time on October 5), the Nobel Prize in Physics was announced. Half of the award was shared by Japanese-American meteorologist Syukuro Manabe and German oceanographer and climate modeler Klaus Hasselmann in recognition of their "physical modeling of the Earth's climate, quantification of variability, and reliably prediction of global warming"; the other half was awarded to Italian theoretical physicist Giorgio Parisi in recognition of his "discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales."

Parisi was born in 1948 and is a professor at the Department of Physics at the University of Roma I ''La Sapienza''. His research focuses on quantum field theory, statistical mechanics and complex systems. So far, Parisi has won numerous honors, including the 1999 Dirac Prize, the 2002 Fermi Prize, the 2005 Heineman Prize in Mathematical Physics and the 2021 Wolf Prize.

At the Nobel Prize press conference, a reporter asked Parisi whether he expected to win the Nobel Prize. Parisi replied "possibility nonnegligible", which is a very "statistical physics" answer.

Wen Xiaogang, professor at the Massachusetts Institute of Technology and editor-in-chief of Fanpu, said that in physics, Parisi's most famous contribution is the replica method he developed with Mezard and Virasoro. A complex system is often in a random environment. For example, when water flows down a mountain, the terrain is a very complex and random environment. The magnetic moments of magnetic impurities in semiconductors have a random interaction because the distances between the impurities are random. Sometimes, these magnetic moments are arranged into an ordered state due to the interaction, and sometimes they form a disordered state (also called a spin glass state). In order to understand these physical phenomena, we must know how to deal with random interactions. The replica technique is a standard technique for dealing with random interactions. Another technique for dealing with random interactions is to apply somewhat limited supersymmetric techniques (but the supersymmetry here and the supersymmetry in particle physics, although the names are the same, are not the same thing).

The replication technique can be applied to any random interaction. Why the replication technique can produce a correct result is still a mystery to this day. Because the replication technique is a very strange method. It replicates a random system into N copies and then averages the random interactions. But the physical result can only be obtained when N tends to 0. At first glance, this is almost an impossible technique. But interestingly, when the replication technique is used for some strictly solvable models, the results obtained are all correct. Now this technique is widely accepted and applied to a variety of complex random systems, and has become a cornerstone in this field.

The following is the official introduction of the Nobel Prize Committee:

All complex systems are made up of many different parts that interact with each other. Physicists have studied them for centuries, and they can be hard to describe mathematically—they can have a large number of components, or be governed by chance. They can also be chaotic systems, like the weather, where small deviations in initial values ​​can lead to big differences later on. This year's laureates have all contributed to our deepening understanding of such systems and their long-term evolution.

The Earth's climate is one of many examples of a complex system. Manabe and Hasselmann were awarded the Nobel Prize for their pioneering work in developing climate models. Parisi was awarded for his theoretical solutions to a large number of problems in the theory of complex systems.

Manabe demonstrated how increasing atmospheric carbon dioxide concentrations lead to an increase in Earth's surface temperature. In the 1960s, he led the development of physical models of Earth's climate and was the first to explore the interaction between the radiation balance and the vertical transport of air masses. His work laid the foundation for the development of climate models.

About a decade later, Klaus Hasselmann created a model that linked weather and climate together, answering why climate models can be reliable despite the variability and chaos of weather. He also developed methods to identify specific signals and fingerprints left by natural phenomena and human activities in the climate. His methods have been used to prove that the increase in atmospheric temperature is due to human emissions of carbon dioxide.

Around 1980, Giorgio Parisi discovered hidden regularities in disordered complex materials. His discoveries are one of the most important contributions to the theory of complex systems. They make it possible to understand and describe many different, apparently completely random, complex materials and phenomena, not only in physics, but also in other very different fields such as mathematics, biology, neuroscience and machine learning.

The greenhouse effect is essential to life

200 years ago, French physicist Joseph Fourier studied the energy balance between the absorption of solar radiation by the ground and the radiation emitted. He understood the role of the atmosphere in this balance; at the Earth's surface, incoming solar radiation is converted into outgoing radiation - "dark heat" - which is absorbed by the atmosphere, thereby heating it. The protective effect of the atmosphere is now known as the greenhouse effect. The name comes from its resemblance to the glass of a greenhouse, which allows the sun's heating rays to pass through but traps the heat inside. However, the radiation process in the atmosphere is much more complicated.

The task was the same as Fourier's - to study the balance between the shortwave radiation from the sun that hits the Earth and the longwave infrared radiation that is emitted by the Earth. Over the next two centuries, many climate scientists filled in the details. Contemporary climate models are very powerful tools for understanding not only the climate but also human-caused global warming.

These models are based on the laws of physics and developed from models that predict the weather. Weather is described by meteorological quantities such as temperature, precipitation, wind or clouds and is affected by what happens over the ocean and on land. Climate models are based on statistical properties of weather calculations such as mean, standard deviation, highest and lowest measurements etc. They can't tell us what the weather will be like in Stockholm on December 10th next year, but we can learn about the average temperature and rainfall in Stockholm in December.

Establishing the role of carbon dioxide

The greenhouse effect is essential to life on Earth. It controls temperatures because greenhouse gases in the atmosphere — carbon dioxide, methane, water vapor and others — first absorb infrared radiation from the Earth and then release the absorbed energy, warming the surrounding air and the ground below.

Greenhouse gases actually make up only a small part of Earth's dry atmosphere, which is mostly nitrogen and oxygen - they make up 99% by volume. Carbon dioxide makes up just 0.04% by volume. The most powerful greenhouse gas is water vapor, but we can't control the concentration of water vapor in the atmosphere, while we can control the concentration of carbon dioxide.

The amount of water vapor in the atmosphere is highly dependent on temperature, which leads to a feedback mechanism. The more carbon dioxide in the atmosphere, the higher the temperature, and the more water vapor there is in the air, which increases the greenhouse effect and causes temperatures to rise further. If carbon dioxide concentrations fall, some of the water vapor condenses and the temperature drops.

The first important piece of the puzzle about the impact of carbon dioxide came from Swedish researcher and Nobel laureate Svante Arrhenius, whose colleague, meteorologist Nils Ekholm, incidentally, was the first to use the term “greenhouse” in 1901 to describe the atmosphere’s storage and reradiation of heat.

Arrhenius understood the physics of the greenhouse effect at the end of the 19th century - radiation is proportional to the fourth power (T4) of the absolute temperature (T) of the source. The hotter the source, the shorter the wavelength of the rays. The sun has a surface temperature of 6000°C and emits mainly the visible light spectrum. The surface temperature of the earth is only 15°C, and it radiates infrared radiation that we cannot see. If the atmosphere did not absorb this infrared radiation, the surface temperature would be only -18°C.

Arrhenius was actually trying to find out the cause of the recently discovered ice age phenomena. He concluded that if the amount of carbon dioxide in the atmosphere was halved, it would be enough to send the Earth into a new ice age. And vice versa - doubling the amount of carbon dioxide would increase the temperature by 5-6°C, a result that, by some luck, is surprisingly close to current estimates.

Groundbreaking model of carbon dioxide impact

In the 1950s, Japanese atmospheric physicist Tokuro Manabe left war-torn Japan as one of Tokyo's bright young academics to continue his career in the United States. His goal, like Arrhenius's about 70 years earlier, was to understand how increasing carbon dioxide levels led to rising temperatures. While Arrhenius focused on the radiative balance, Manabe led the development of physical models in the 1960s that incorporated vertical transport of air masses due to convection and the latent heat of water vapor.

To make these calculations accessible, he chose to reduce the model to one dimension—a vertical cylinder extending 40 kilometers into the atmosphere. Even so, he spent hundreds of precious computing hours testing the model by varying the concentrations of gases in the atmosphere. Oxygen and nitrogen had a negligible effect on surface temperatures, while the effect of carbon dioxide was significant: when carbon dioxide levels doubled, global temperatures rose by more than 2°C.

Atmospheric heat balance for a given relative humidity distribution. Source: Journal of the atmospheric sciences, Vol. 24, Nr 3, May.

The model confirmed that this warming was indeed due to the increase in carbon dioxide, as it predicted rising temperatures near the ground while the upper atmosphere cooled. If changes in solar radiation were responsible for the warming, the entire atmosphere should have heated up at the same time.

Sixty years ago, computers were hundreds of thousands of times slower than they are today, so the model was relatively simple, but Manabe got the key features right. You have to always simplify, he says. You can't compete with the complexity of nature - there's so much physics involved in every drop of rain that it's impossible to fully calculate everything. Insights from the one-dimensional model led to a three-dimensional climate model, which Manabe published in 1975, another milestone on the road to understanding the secrets of climate.

The weather is chaotic

About a decade after Manabe's results, Klaus Hasselmann succeeded in linking weather and climate by finding a way to account for the rapid and chaotic weather changes that are so cumbersome to calculate. Our planet's weather has huge variations due to the extremely uneven distribution of solar radiation over geography and time. The Earth is round, so fewer solar rays reach high latitudes than reach lower latitudes near the equator. Not only that, but the Earth's axis is tilted, creating seasonal differences in incoming radiation. Differences in density between warm and cold air masses result in huge heat transfers between different latitudes, between ocean and land, and between higher and lower air masses, which drives the weather on our planet.

It is well known that making reliable weather forecasts for the next ten days is a challenge. Two hundred years ago, the famous French scientist Laplace said that if we knew the positions and velocities of all particles in the universe, it would be possible to calculate what has happened and what will happen in our world. In principle, this should be correct, and Newton's laws of motion, which have been in place for three hundred years and also describe the transport of air in the atmosphere, are completely deterministic - they are not determined by chance.

Yet when it comes to the weather, nothing is worse. This is partly because it is impossible to be precise enough in practice - to describe the air temperature, pressure, humidity or wind conditions at every point in the atmosphere. The equations are nonlinear, and small deviations in the initial values ​​can make the weather system evolve in completely different ways. Whether a butterfly flapping its wings in Brazil can cause a tornado in Texas - this phenomenon has been named the butterfly effect. In practice, this means that it is impossible to produce long-term weather forecasts - the weather is chaotic; this discovery was made in the 1960s by Edward Lorenz, an American meteorologist who laid the foundation for today's chaos theory.

Making sense of noisy data

Even though the weather is a classic example of a chaotic system, how can we build reliable climate models for decades or centuries into the future? Around 1980, Klaus Hasselmann demonstrated how chaotically changing weather phenomena can be described as rapidly changing noise, thereby laying a solid scientific foundation for long-term climate forecasts. In addition, he developed a method to determine the human influence on observed global temperatures.

As a young doctor of physics in the 1950s, Hasselmann worked on fluid mechanics in Hamburg, Germany, and then began to develop observational and theoretical models of waves and currents. He then moved to California, where he continued his oceanographic research and met peers such as Charles David Keeling, with whom the Hasselmanns formed a carnival choir. Keeling's legend is that as early as 1958, he began the longest measurement of atmospheric carbon dioxide to date at the Mauna Loa Observatory in Hawaii. Hasselmann didn't know that in his later work, he would often use the Keeling curve, which shows the changes in carbon dioxide levels.

Getting climate models from noisy weather data can be illustrated with a dog walk: the dog is disobedient and runs back and forth, left and right, around your legs. How can you tell from the dog's tracks whether you were walking or standing still? Or whether you were walking fast or slow? The dog's tracks are the weather changes, while your walk is the calculated climate. Is it possible to draw conclusions about long-term trends in the climate using messy and noisy weather data?

Another difficulty is that the fluctuations that affect climate vary greatly over time - they can be fast, like winds or air temperatures, or very slow, like melting ice and warming oceans. For example, a uniform increase of one degree might take a thousand years for the ocean, but only a few weeks for the atmosphere. The decisive trick is to include rapid changes in weather as noise in the calculations and show how this noise affects the climate.

Hasselmann created a stochastic climate model, which means that randomness is built into the model. He was inspired by Einstein's theory of Brownian motion, also known as a random walk. Using this theory, Hasselmann showed that a fast-changing atmosphere actually causes slow changes in the ocean.

Identifying traces of human influence

Once climate change models were completed, Hasselmann developed methods to identify human influences on the climate system. He found that these models, together with observations and theoretical considerations, contained sufficient information about the characteristics of noise and signal. For example, changes in solar radiation, volcanic particles or greenhouse gas levels leave behind unique signals, fingerprints, which can be separated out. This method of identifying fingerprints can also be applied to human influences on the climate system. Hasselmann thus cleared the way for further climate change studies that demonstrated traces of human influence on the climate through a large number of independent observations.

Climate models have become increasingly refined as the complex, interacting processes of climate have been mapped more thoroughly, especially through satellite measurements and weather observations. The models clearly show an acceleration of the greenhouse effect: atmospheric carbon dioxide levels have increased by 40% since the mid-1800s. Earth's atmosphere has not held this much carbon dioxide for hundreds of thousands of years. Correspondingly, temperature measurements show that Earth has warmed by 1°C in the past 150 years.

In the spirit of Alfred Nobel, Manabe and Hasselmann have made the greatest contribution to humanity by providing a solid physical basis for our understanding of the Earth's climate. We can no longer say we don't know - the climate models are unequivocal. Is the Earth warming? Yes. Is it because of the increasing amount of greenhouse gases in the atmosphere? Yes. Can this be explained by natural factors alone? No. Are human emissions responsible for the rising temperatures? Yes.

Standard Methods for Stochastic Systems

Around 1980, Giorgio Parisi presented his discoveries about how random phenomena can be governed by hidden rules. His work is now considered one of the most important contributions to the theory of complex systems.

The modern study of complex systems has its roots in statistical mechanics, which was developed in the second half of the 19th century by Maxwell, Boltzmann, and Gibbs. Gibbs named the field statistical mechanics in 1884. Statistical mechanics arose from the realization that a new method was needed to describe systems consisting of large numbers of particles, such as gases or liquids. Such an approach would have to take into account the random motion of the particles, so the basic idea was to calculate the average effect of the particles rather than studying each particle individually. For example, the temperature in a gas is a measure of the average of the energies of the gas' particles. Statistical mechanics was a huge success because it provided a microscopic explanation for macroscopic properties in gases and liquids, such as temperature and pressure.

The particles in a gas can be thought of as little balls whose speed increases as the temperature increases. When the temperature drops or the pressure increases, the balls condense first into a liquid and then into a solid. This solid is usually a crystal in which the balls are organized in a regular pattern. However, if the change happens quickly, the balls may form an irregular pattern even if the liquid is cooled further or squeezed together. If the experiment is repeated, the balls will take on a new pattern, even though the change happened in exactly the same way. Why are the results different?

Understanding Complexity

These compressed balls are simple models for ordinary glass and granular materials like sand or gravel. The subject of Parisi's original work, however, was a different system - spin glass. This is a special type of metal alloy in which, for example, iron atoms are randomly mixed into a grid of copper atoms. Even if there are just a few iron atoms, they drastically change the material's magnetic properties in a puzzling way. Each iron atom acts like a tiny magnet, or spin, influenced by the other iron atoms in its vicinity. In an ordinary magnet, all the spins point in the same direction, but in spin glass, they are frustrated; some pairs of spins want to point in the same direction, while others point in opposite directions - so how do they find the best orientation?

Parisi writes in the preface to his book on spin glass that studying spin glass is like watching a human tragedy in a Shakespearean play. If you want to be friends with two people at the same time, but they hate each other, it can be frustrating. This is even more true in classic tragedies, where intensely charged friends and enemies meet on stage. How can you keep the tension in the room to a minimum?

Spin glass and its strange properties provide a model for complex systems. In the 1970s, many physicists, including several Nobel Prize winners, searched for a way to describe this mysterious and frustrating spin glass. One approach they used was the replica trick, a mathematical trick that deals with many replicas of a system at the same time. However, the initial calculations turned out to be infeasible from a physics point of view.

In 1979, Parisi made a decisive breakthrough when he showed how to solve the spin glass problem by cleverly using the replica trick. He discovered a hidden structure in these replicas and found a mathematical way to describe it. It took many years for Parisi's solution to be proven mathematically correct. Since then, his method has been applied to many disordered systems and has become a cornerstone of the theory of complex systems.

Spin glasses and granular materials are examples of disordered systems where different components have to arrange themselves in a compromised way that works against each other. The question is what their behavior and consequences are. Parisi is a master at answering these questions for many different materials and phenomena. His fundamental discoveries about the structure of spin glasses were so profound that they have implications not only for physics but also for mathematics, biology, neuroscience, and machine learning, because all of these fields have problems directly related to frustration.

Parisi also studies many other phenomena in which random processes play a decisive role in the formation and development of structures, and addresses questions such as: Why do we have periodic ice ages? Is there a more general mathematical description of chaotic and turbulent systems? Or - how do patterns emerge in the murmuration of thousands of starlings? This question seems far away from spin glasses. However, Parisi says that most of his research is about how simple actions can lead to complex collective behavior, and this applies to both spin glasses and starlings.

Giorgio Parisi (1948-)

Giorgio Parisi was born in Italy in 1948. He received his degree from the University of Rome in 1970. He was a researcher at the Frascati National Laboratory (1971–1981) and a visiting scholar at Columbia University, the Institut des Hautes Études Scientifiques, and the Ecole Normale Supérieure in Paris. He is currently a professor of quantum theory at the Sapienza University of Rome. Parisi is a member of the Italian National Academy of Sciences, a foreign member of the French Academy of Sciences, and a foreign member of the U.S. National Academy of Sciences.

Parisi has won the Boltzmann Prize in 1986 and 1992, the Dirac Prize in 1999, the Enrico Fermi Prize in 2002, the Danny Heinemann Prize in Mathematical Physics in 2005, the Lagrange Prize in 2009, the Max Planck Medal in 2011, the High Energy and Particle Physics Prize in 2015, and the Lars Onsager Prize in 2016.

Syukuro Manabe (1931-)

Syukuro Manabe was born in Ehime Prefecture, Japan in 1931. He obtained his bachelor's, master's and doctoral degrees from the University of Tokyo, Japan from 1953 to 1958. After that, he came to the United States and worked in meteorology research at the U.S. Weather Bureau and the National Oceanic and Atmospheric Administration. From 1997 to 2002, he served as the director of the global warming research project at the Japan Frontier Research Center for Global Change. He is currently a senior researcher at Princeton University.

In the 1960s, Tokuro Manabe developed a numerical model that could reproduce and predict the entire earth's climate on a computer based on the laws of physics. This model clearly demonstrated for the first time the impact of carbon dioxide concentration in the atmosphere on the climate, turned the attention of the international community to global warming, and led to the establishment of the United Nations Intergovernmental Panel on Climate Change (IPCC).

Syukuro Manabe was the first winner of the Blue Planet Award in 1992, the Asahi Prize in 1995, the Volvo Environment Prize in 1997, the Benjamin Franklin Medal in 2015, the BBVA Just Frontier Award in 2016, the Crafoord Prize awarded by the Royal Swedish Academy of Sciences in 2018, and was inducted into the Kyoto Earth Hall of Fame in 2009.

Klaus Hasselmann (1931-)

Klaus Hasselmann was born in Hamburg, Germany in 1931. He studied physics and mathematics at the University of Hamburg, received his Diplom degree in 1955, and received his doctorate in physics from the University of Göttingen and the Max Planck Institute for Fluid Dynamics in 1957. From 1964 to 1975, he worked at the University of Hamburg as a full professor of theoretical geophysics at the Institute of Geophysics. From February 1975 to November 1999, Hasselmann served as the founding director of the Max Planck Institute for Meteorology. Currently, Hasselmann is the vice chairman of the European Climate Forum.

Hasselmann is a leading German oceanographer and climate modeler. He is best known for his work on the Hasselmann model of climate variability, which explains the ubiquitous red noise signal in the climate. In 1996, Hasselmann received the International Lifetime Achievement Award in Oceanography, in 2002 he was awarded the Vilhelm Bjerknes Medal of the European Geophysical Union, in 2007 he received the IMSC Achievement Award from the International Conference on Statistical Climatology, and in 2010 he received the BBVA Foundation Knowledge Frontier Award.