Nobel Prize in Physics: Climate and its Understanding
D. Indumathi, The Institute of Mathematical Sciences, Chennai

The Nobel Prize in Physics in 2021 was awarded "for groundbreaking contributions to our understanding of complex systems". Let us try and understand what this means. The rather complicated statement of the Nobel Committee is:
"This year’s Nobel Prize in Physics is awarded with one half jointly to Syukuro Manabe, Klaus Hasselmann and the other half to Giorgio Parisi. They have laid the foundation of our knowledge of the Earth’s climate and how humanity influences it, as well as revolutionized the theory of disordered materials and random processes."
The phrases we need to understand are, "complex systems" "climate and how humanity influences it", "disordered materials" and random processes". Let us look at them one by one.

Complex systems
As the name suggests, all complex systems consist of many different interacting parts. They have been studied by physicists for a couple of centuries, and can be difficult to describe mathematically. For instance, Earth's climate is an example of a complex system.
One of the key properties of such systems is called chaos. The english dictionary meaning of "chaos" is "complete disorder and confusion". However, scientists still try and make sense of such disorder. For instance, many of you must have been following the recent heavy rainfall patterns and their predictions. You could see that it is very difficult to accurately predict the weather, although we have so many instruments and measurements to help us.
In physics, the word "chaos" has a very specific meaning. Very often, the reason for this disorder is the lack of accuracy with which we know the initial conditions. For instance, we roughly know the position and velocity (and other parameters such as pressure, etc) of a moving cyclone. But we stll cannot accurately tell where exactly it will hit and how severe its impact will be. The theory of chaos states that in fact, in truly "chaotic systems", it will be impossible to know some factors to the accuracy required. Hence even if there is a very very small change in some property of the system (like its pressure or velocity), it may end up behaving very differently from expectation. How, then, can we reliably predict the behaviour of such systems?
Chaos theory tells us that there are still patterns and repetitions in the behaviour of such systems so that there is still predictive value. After all, we can see patterns such as the onset of the South West or North East monsoons, although we may not be able to predict exactly how much rain there will be over Chennai today. All the scientists who have been awarded this year's Nobel Prize in Physics have contributed to our understanding of scuch complex systems.

The greenhouse effect
Two hundred years ago, French physicist Joseph Fourier studied the energy balance between the Sun’s radiation towards the ground and the radiation from the ground. He found that the Earth's atmosphere played an important role in this balance. Sunlight consists mostly of visible light, although it has invisible ultraviolet (UV) and infrared (IR) components as well. 
A part (about a quarter) of the incoming sunlight is reflected back to space by the atmosphere and clouds, while another part is absorbed by the gases and clouds in our atmosphere. About half the remaining energy is absorbed by Earth's surface.
We know that hot bodies radiate (you must have felt the heat coming off from your hot glass of milk). The Earth's surface then radiates back this absorbed energy, but in the form of heat (thermal energy). This heat is absorbed by Earth's atmosphere and hence the layer of atmosphere/air just above the surface gets warm. This heat slowly disperses through the entire atmosphere which becomes hot and therefore also begins to radiate! Now, the atmosphere radiates in all directions (like all hot things do). The part of the heat that is radiated downwards is re-absorbed by the Earth which therefore becomes warmer.
BOX
The greenhouse effect is the process by which radiation from a planet's atmosphere warms the planet's surface to a temperature above what it would be without this atmosphere.
END OF BOX
In summary, because of the action of Earth's atmosphere in trapping heat, the Earth's surface is warmer than it would have been if it did not have an atmosphere. For instance, instead of the average 15 degrees that it currently is, it would have been cold, at -18 degrees, much below freezing, and not convenient for living things.
Fourier understood that the atmosphere therefore plays a role in protecting the temperature of the Earth. The effect is due to the gases and aerosols (see box) in the atmosphere which play an important role in this so-called "greenhouse effect". 

BOX Greenhouse gases and aerosols
There are four major greenhouse gases. While water vapour is the largest contributor, at 36–70%, while carbon dioxide (9–26%), methane (4–9%) and ozone (3–7%) account for the rest. Note that the gases which are prevalent in large amounts in the atmosphere such as nitrogen (78%), oxygen (21%), and argon (0.9%), are not greenhouse gases.
Water vapour is not much affected by human activity. In fact, the average time of a water molecule in the atmosphere is only about nine days, compared to years or centuries for other greenhouse gases such as methane or carbon-dioxide. Hence, when talking about climate change, carbon-dioxide is most often mentioned. However, warm air can hold more water vapour than cold air and so the presence of this extra water in warm air, makes the air even hotter since water vapour is a greenhouse gas.
Recently the role of aerosols has also been studied. They are tiny particles suspended in the air, both natural and man-made, such as sea-salt, mineral dust, ash, soot, sulphates, nitrates, and black carbon. They remain in the air for around 10 days, and act as a nucleus for water droplets to form around them. This increases clouds, which shield us from sunlight, thus cooling the Earth. So there is a delicate balance between greenhouse gases and aerosols in the air: greenhouse gases warm the surface; aerosols cool the surface.
END OF BOX

Human activity and climate change
Industrialisation that happened around 250 years ago has caused increased human activity (electricity, cars, and other utilities that use petrol, coal, etc) that has increased the amount of greenhouse gases in the atmosphere. The main emissions are carbon-dioxide (from burning fuel and methane (from agriculture). For instance, the amount of carbon-dioxide in the air has increased by almost 50% compared to the pre-industrial era. This has upset the balance and caused climate change. Hence the Nobel laureates have worked in an area that will help to understand climate change. The question is, how is carbon dioxide emission related to global warming and climate change?
Carbon dioxide and its role in the atmospheric temperature The Swedish scientist, Svante Arrhenius, first understood the physics of the greenhouse effect more than 100 years ago.
It had just been discovered that the Earth had gone through a series of ice ages, and Arrhenius was trying to find out the cause. He realised that if the amount of carbon dioxide in the atmosphere halved, this would cause a new ice age. And if the carbon dioxide doubled, the temperature of the atmosphere would increase by 5–6°C. This is because of the protective nature of this greenhouse gas that traps heat in the atmosphere.
Over the years, these theories have been improved but the understanding is basically the same: human activity causes emission of greenhouse gases, which drive global warming and climate change.
Now that we have understood the role of carbon dioxide in climate change, let us see what each of the Nobel laureates has found.
Syukuro Manabe showed in the 1960s that if there is more carbon dioxide in the atmosphere, then the surface of the Earth gets warmer. He wrote down one of the first models of the Earth's climate by considering the atmosphere as a one dimensional column and considering the flow of air across it. He and his colleague R.T. Wetherald calculated that there is 2.3 degrees C warming per doubling of atmospheric CO2.
The model confirmed that this heating really was due to the increase in carbon dioxide, because it predicted rising temperatures closer to the ground while the upper atmosphere got colder. If the increase in temperature was instead due to changed in the amount of sunlight, the entire atmosphere should have been heating at the same time. Today's more complicated climate models are based on this work.

Climate versus weather
It may or may not rain tomorrow. That is a weather prediction. It is valid over a short time. Climate, on the other hand, is a long-term pattern. It is in a sense, the average over the daily weather at any place. In order to determine whether humans are causing climate change, it is important to factor out variable weather (short-term) conditions and look at long term effects. How is this possible?
This question was answered about ten years later, by Klaus Hasselmann. He created a model that links together weather and climate, thus answering the question of why climate models can be reliable despite weather being changeable and chaotic. It was a very technical approach, which took into account the complexity of climate.
This complexity is expressed often as the possibility of whether a butterfly flapping its wings in Brazil could cause a tornado in Texas, and is called the butterfly effect. This is because the equations governing the evolution of the system are non-linear: small changes in the initial values cause the system to change very differently, and this is called chaotic behaviour.

Making sense of noisy data
How can we produce reliable climate models that are valid for hundreds of years although we cannot predict the weather 10 days ahead?! In 1980, Klaus Hasselmann showed that chaotically changing weather is like rapidly changing noise on your radio: the song (or long-term climate) that is actually playing can still be heard and understood. More importantly, it can be extracted and processed by removing the noise. Hasselmann created a stochastic climate model, which is difficult to explain. But this model showed that the rapidly changing atmosphere can actually cause slow variations in the ocean.

Determining human impact
Hasselmann also developed methods for identifying specific signals, which he called fingerprints. These are activities that leave imprints in the climate and can be both natural and due to human activities.
It soon became clear that Hasselmann had discovered a way to detect the signal of global warming due to human activity like burning fossil fuels. Satellite-borne microwave sounders began to monitor atmospheric temperature. Data was slowly collected that would be used by the Hasselmann model to provide global patterns for change. 
Modern climate models show that the amount of carbon dioxide in the atmosphere has increased by 40 per cent. Earth’s atmosphere has not contained this much carbon dioxide for hundreds of thousands of years. Accordingly, temperature measurements show that the world has heated by 1°C over the past 150 years.

BOX Humans and climate change
Syukuro Manabe and Klaus Hasselmann have contributed to the greatest benefit for humankind, in the spirit of Alfred Nobel, by providing a solid physical foundation for our knowledge of Earth’s climate. We can no longer say that we did not know – the climate models are unequivocal. Is Earth heating up? Yes. Is the cause the increased amounts of greenhouse gases in the atmosphere? Yes. Can this be explained solely by natural factors? No. Are humanity’s emissions the reason for the increasing temperature? Yes.
END OF BOX

Methods for disordered systems
The Nobel committee has awarded half the Physics prize to Giorgio Parisi of Italy “for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales”. This is a very complicated area of research.
Around 1980, Parisi discovered hidden patterns in complex materials which were not ordered. For example, you may know that crystals like common salt (Sodium chloride or NaCl) are placed in regular arrangements on a lattice. Disordered systems do not show such periodic arrangements.
One such example is that of spin glasses. You know that each iron atom behaves like a small magnet, or spin, which is affected by the other iron atoms close to it. In an ordinary magnet, all the spins point in the same direction, so we say they are magnetised. In a spin glass they are frustrated; some spin pairs want to point in the same direction and others in the opposite direction – so how do they find an optimal orientation?
His solution to this and similar problems are among the most important contributions to the theory of complex systems. His insight made it possible to understand very different materials in physics. It also led to understanding in various fields such as mathematics, biology, neuroscience and machine learning.
Parisi has also studied many other phenomena in which random processes play a decisive role. The fundamental questions are, how structures are created and how they develop? For instance, Why do we have periodically recurring ice ages? Is there a more general mathematical description of chaos and turbulent systems?
Parisi says that most of his research has dealt with how simple behaviours give rise to complex collective behaviour. This is also the case with Earth's atmosphere models and understanding climate change.
Adapted from the popular information on the Nobel Prize pages