This is my attempt at contributing to "A Layperson's Introduction" series, here on Tildes. It's why it's here on ~science, rather than ~enviro

Many people have heard about how global warming works. “We are emitting greenhouse gases, and these trap heat, leading to further warming.” So how does this process occur in more detail? What is its physical basis? In this post, I will try to explain the physical basis of these questions in a simple way that is a bit more detailed than what is usually seen.

Electromagnetic Spectrum and Thermal Radiation

The electromagnetic spectrum is a broad spectrum that includes visible light. There are long wavelengths, such as radio waves and infrared light, and short wavelengths, such as ultraviolet light, X-rays, and gamma rays.

Visualization of the electromagnetic spectrum

Thermal radiation is the radiation emitted by the molecules of an object due to thermal movement. It can be in the visible light wavelength, shorter wavelength, or longer wavelength. The length of these wavelengths varies depending on the temperature of the object that is the source of thermal radiation. For example, the thermal radiation emitted by Earth falls into the infrared spectrum, which is at lower energy, because Earth is not as hot as a star. The shift of thermal radiation emitted by colder objects to longer wavelengths is also known as Wien's law.

Energy Budget and Stefan-Boltzmann Law

Our planet Earth has a certain energy budget. In other words, the energy coming to the planet and the energy going out from the planet are specific. The source of the energy coming to the Earth is the Sun, and on average, approximately 340 Watt/m² energy reaches the surface of the planet. In order for this energy to be balanced, the energy radiated from Earth into space must be equal to this amount. This happens in two ways. First, some of the incoming energy is reflected into space by the Earth itself. Both the atmosphere (especially clouds) and the surface make this reflection. The second part can be explained by a physical law called Stefan Boltzmann law. According to this law, each object emits a certain amount of energy as thermal radiation, and the amount of this energy increases with temperature. This increase does not occur linearly, but as the fourth power of temperature. The mathematical expression of the law is given below.

E = σT⁴

In this equation, "E" is the energy, "σ" (sigma) is the Stefan-Boltzmann constant, and "T" is the temperature in Kelvin. However, the law cannot be applied to any object in its current form. The above equation is valid for ideal bodies called "black bodies". In physics, a black body is the name given to an ideal body that absorbs and emits all incoming radiation. However, Earth differs from a black body due to reflection. Therefore, the following equation is more appropriate.

E = εσT⁴

Here, ε (epsilon) means emissivity. Emissivity is the effectiveness of the surface of a material in emitting energy as thermal radiation. For a black body, ε = 1. The Earth's mean ε is less than 1, because it is not a black body. At the same time, emissivity changes depending on which part of the Earth is examined. For example, the emissivity of a vegetated surface and a desert or glacier are different. However, it is more important for us at this point to remember that the mean ε is less than 1.

When we look at the formulae above, we see that, in accordance with the Stefan-Boltzmann law, the Earth emits thermal radiation depending on the temperature, even though it is not a black body. This constitutes the second part of the Earth's energy budget, namely thermal radiation. In summary, Earth receives energy from the Sun and radiates this energy through reflection and thermal radiation.

Radiative Forcing and Greenhouse Effect

The energy budget is very important for our planet. Any change in the budget causes Earth to warm or cool. Natural or human-induced changes that change the balance between incoming and outgoing energy are called radiative forcing. This is the mechanism by which greenhouse gases warm the planet. Some gases in the atmosphere, such as carbon dioxide (CO²) or methane (CH⁴), have physical properties that absorb the thermal radiation emitted by Earth. If you remember, Earth's thermal radiation was in the infrared spectrum. That is, these gases absorb at certain points in the infrared spectrum. As a result of this absorption, the gases emit it again in the form of thermal radiation in all directions. While some of the emitted radiation escapes into space, some of it remains on Earth, causing warming. Since the energy emitted by Earth will increase as it warms up, at a certain point, the incoming and outgoing energy becomes equal again.

CO² emissions, concentration, and radiative forcing

In the image above, in different climate change scenarios, emissions of the greenhouse gas CO²) (left), the corresponding increase in CO² concentration in the atmosphere (middle), and the increasing radiative forcing due to this increase are shown (right). Note that the radiative forcing is shown in Watts/m². It is shown this way because it is calculated based on the change in Earth's energy budget, and Earth's energy budget is shown as Watt/m².

In other words, although the incoming energy is the same, there is a certain decrease in the energy going into space due to the greenhouse effect. This leads to what we call radiative forcing. As a result of radiative forcing, the temperature of Earth increases, and as the temperature increases, the thermal radiation energy emitted by the planet increases. This causes the incoming and outgoing energy to become equal again. As a result, in the long run, radiative forcing (and the greenhouse effect) does not lead to a change in the energy budget. However, it causes solar energy to remain in the atmosphere for a longer period of time, causing a certain amount of warming. This is what we call global warming due to the greenhouse effect.

This process is, of course, more complex than described here. Since the atmosphere has a layered and fluid structure, there are factors that make the job more complicated. For example, while the increase in CO² warms the troposphere (what we call global warming), the lowest layer of the atmosphere, it causes the stratosphere, its upper layer, to cool. Despite these and similar complexities, the physical basis of global warming is still based on the mechanisms described in this post.

Sources

• Schmittner, A. (2018). Introduction to Climate Science. Oregan State University
• van Vuuren, D. P., Edmonds, J., Kainuma, M., Riahi, K., Thomson, A., Hibbard, K., Hurtt, G. C., Kram, T., Krey, V., Lamarque, J.-F., Masui, T., Meinshausen, M., Nakicenovic, N., Smith, S. J., & Rose, S. K. (2011). The Representative Concentration Pathways: An overview. Climatic Change, 109(1-2), 5–31. https://doi.org/10.1007/s10584-011-0148-z
• Wild, M., Folini, D., Schär, C., Loeb, N., Dutton, E.G., König-Langlo, G. (2013). The global energy balance from a surface perspective. Clim Dyn 40, 3107–3134. https://doi.org/10.1007/s00382-012-1569-8
• Zohuri, B., McDaniel, P. (2021). Basic of heat transfer. Introduction to Energy Essentials, 569–578. https://doi.org/10.1016/b978-0-323-90152-9.00017-7

Image Sources

• Image 1: https://science.nasa.gov/ems/01_intro/
• Image 2: van Vuuren et al., 2011