Lee
Feinman

$CO_2$

$CO_2$'s importance

1. Radiative balance helps us understand earth without carbon dioxide.
2. Porridge is better when its not too hot and not too cold. 'Bear' with me here.
3. Resonance helps us understand carbon dioxide's impact.
4. Black body radiation can show why more $CO_2$ leads to higher temps.

Radiative Balance

This story begins with the coldness of space.

Why is coldness relevant?

Because it's really hard to live in the cold. Imagine Paris, Vienna, and Edinburgh had similar climates to Antarctica. We would be missing out on some pretty good philosophy, right? Culture as we know it would be pretty bland, if existent at all.

Our universe kind-of prefers coldness, so galaxies & their planets need to be pretty nifty in their attempt to stay warm. We generally say cold things have less energy than their hot counterparts. Energy is expressed in movement and light (among other things), and high movement or brightness among matter is correlated to high temperature.

Why is space cold?

If we put a big rock in space and shine light (energy) on it, the rock will get rid of the energy! The inbound energy flux (energy of light on the exposed surface) is always equal to the outbound energy flux. This phenomenon is called radiative balance¹ and it's a really troubling physical principle for anyone interested in living on big rocks in space. Right? Space takes all objects' outbound energy. When something is taking energy from something else, it is cold.

You're saying non-stars emit energy?

Boring, random rocks/objects are not stars, correct. But they do give off energy in the form of light! They abide by the principle of radiative balance.

It's important to remember not all light is visible to us. Earth gives off mainly infrared light (IR is invisible to us).²

Wait, why does the planet maintain a temperature at all?

You know how walking down an empty stairwell compels you, by the overpowering force of immaturity, to pull from the depths of your throat a big "hoooot"? And how if you pull out the "hoooot" note just right, a proper shake buzzes about the air? We call this resonance.³

Earth's outward infrared light happens to have a particularly interesting property: it tickles some molecules' fancies. To be technical, this light causes certain molecules to resonate! This incredible video shows just this.

When light resonates with the vibration of molecules, the molecules move faster... meaning their temperature increases! (Temperature is the average energy of movement.)

Carbon dioxide, water, methane are a few of the molecules that resonate with infrared radiation and absorb it. Without these compounds, Earth would give away energy without warming up. (Earth would be a cold, cold place lacking any good philosophy!)

Why doesn't Earth constantly heat up if the Sun constantly shines?

This is important. The resonating compounds are very good at what they do. More of them $\rightarrow$ more absorbed infrared light $\rightarrow$ higher temperatures.

These compounds are what maintain a temperature of roughly $15\ ^oC/60\ ^oF$ close to Earth's surface. What they don't absorb gets emitted! (Because of radiative balance.)

Goldilocks needed a bowl of porridge with a temperature that was just right. Life as we know it (and good philosophy) also needs Earth stay at a temperature that is just right.

Black body radiation shows $CO_2$ is the most important resonating molecule

Carbon dioxide is:

1. Particularly good at resonating with infrared radiation,
2. in relatively high concentrations in the atmosphere, and
3. resonant with the type of infrared radiation Earth emits most.

Each dashed line in the image below corresponds to an object emitting infrared light. These objects are called black bodies and the profile of the light they emit is characteristic of their temperature.⁴ The area under their curve is unique. Black bodies are ideal objects. This is why their curves look so perfect.

The solid black line represents Earth trying to be a black body. Clearly, it's not doing a great job. The plot shows measurements of infrared light that Earth is emitting from the Sahara Desert. We can see that there are certain "wavelengths" (top axis) of light that we don't see much of. In other words, there are some big dips. (Like at $15 \ \mu m$, $10.5 \ \mu m$, and $8-7.5 \ \mu m$.)

Those dips represent infrared light emitted by Earth that did not reach the measurement device. What happened to it? The resonating molecules (colloquially, greenhouse gasses) absorbed the light before got there!

Why does that matter?

Because of radiative balance! All of that infrared radiation is being absorbed by (and thus heating) the resonating molecules. Because of this, our atmosphere heats up. More resonance $\rightarrow$ higher baseline of Earth's curve in this plot $\rightarrow$ warmer atmosphere.

This visualization hopefully makes clear:

1. If a lot of carbon dioxide is released into the sky, the baseline of this curve will rise;
2. Thus, Earth's temperature will, too — it has to.

¹ Radiative balance of Earth. "The only source of heat on Earth is solar radiation. As any physical body with a temperature above absolute zero, Earth loses heat in the form of infrared radiation proportional to the fourth power of its absolute temperature. The Earth as a planet is in almost perfect thermal steady state and therefore the top of the atmosphere must be in a complete globally-averaged radiative balance." - Heat Transport, Oceanic and Atmospheric
² IR radiation. "That portion of the electromagnetic spectrum that extends from the long wavelength, or red, end of the visible-light range to the microwave range." - Britannica
³ Resonance in chemicals. "When the frequency of an external oscillation or vibration matches an object (or cavity’s) natural frequency, and as a result either causes it to vibrate or increases its amplitude of oscillation." - SCIENCING
⁴ Black body curves. "At thermodynamic equilibrium, the rate at which an object absorbs radiation is the same as the rate at which it emits it. Therefore, a good absorber of radiation (any object that absorbs radiation) is also a good emitter. A perfect absorber absorbs all electromagnetic radiation incident on it; such an object is called a black body." - Physics LibreTexts

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