How the Greenhouse Effect Really Works (Patreon)

[This is a transcript with references.]

I thought I understood how carbon dioxide emissions cause global warming. Turned out I got it completely wrong. I was about to sweep my misunderstanding under the carpet. But then I thought, what if I’m not the only one. What if we’re all just pretending to kind of understand something we’re spending trillions of dollars on. Maybe I should talk about it after all.

So how does the greenhouse effect really work? How do we know that global warming is caused by humans? And what predictions have climate models ever made? That’s what we’ll talk about today.

Here’s what I learned in middle school about the greenhouse effect. A literal greenhouse works like this. Glass lets most sunlight through. When the sunlight hits the ground of the greenhouse, or a tomato, or why-are-your-socks-in-the-greenhouse-Dennis, then the sunlight gets absorbed and reemitted at longer wavelengths, in the infrared. We can’t see this infrared light, but we can feel it. It feels warm.

But glass acts like a mirror for light in the infrared. Here is an image of a man with a plastic bag over his hands wearing glasses. On the left you see a normal photo taken with visible light. On the right you see an image taken with infrared light. With the infrared light, you can see through the plastic bag, but you can no longer see through the glasses. So all that glass in a greenhouse traps the infrared radiation and that warms the air. You actually don’t need air in a greenhouse for that to work, except that the air is the thing that you want to warm up. And also, tomatoes don’t grow in vacuum.

That’s how an actual greenhouse work. Now here is how I thought this works for our planet.

Much like glass, the atmosphere of earth is transparent to most of the light that comes from the sun. Some of the light is absorbed in the upper atmosphere, and some is reflected. But most of the light is absorbed by the surface of earth. This heats up the surface, which in return emits light in the infrared.

The infrared light however doesn’t travel through the atmosphere that easily because some molecules in the air absorb it. These are the so-called greenhouse gases of which carbon dioxide is one. More carbon dioxide leads to more absorption of this infrared radiation, which warms the planet. Simple enough!
 
But what if I told you.What if I told you that the infrared light which comes from the surface of the earth is absorbed by greenhouse gases, not way up there in the atmosphere, but after 20 meters or so. Because that’s what happens. Pretty much none of the infrared radiation goes through Earth’s atmosphere already at the current carbon dioxide levels. If the levels increase further, then the distance that the light makes it from the surface decreases a bit more. But so what, it never made it out anyway.

It’s all a hoax. Bring back coal!

Okay, here’s the truth. The greenhouse effect isn’t quite that simple.

So let’s try this again, this time we add some high school physics and see if that makes any more sense.

Sunlight contains many different frequencies, but not in equal amounts. Frequency, as a reminder, is proportional to the energy of the light. So, higher frequency means higher energy. And frequency is inversely proportional to the wavelength of light. A longer wavelength means lower energy.

If one plots the amount of light as a function of its frequency one gets what’s called a “spectrum”. The spectrum of the sun looks roughly like this. It doesn’t change all that much in the visible range, which is why the sun looks pretty much white if you look at it which you shouldn’t because, keep in mind, Isaac Newton did it and we’re still making fun of him today.

But this spectrum isn’t specific to the sun. The spectrum of any object at a constant temperature has a shape like this. The surface of the sun has a temperature of about 5000 degrees Celsius, but the higher the temperature, the more the spectrum shifts to higher frequencies, and the more energy the body emits. And the lower the temperature, the lower the average frequencies, the longer the wavelengths, and the less energy is emitted. It’s called “Planck’s law.” If you know the temperature, then Planck’s law tells you what light is emitted and how much energy is emitted in total.  

If sunlight hits the socks in the greenhouse or the surface of Earth, it’s absorbed and reemitted. And as we just said, the radiation spectrum depends on the temperature. But what’s the temperature of Earth? Well, Earth gets a certain amount of sunlight from the sun and with that a certain amount of energy. The temperature of earth increases until the total energy that’s emitted is the same as what comes in from the sun. When energy-in is the same as the energy-out, the system is in balance, and it doesn’t change any further.

This means one can calculate the temperature of the surface of a planet from the amount of sunlight it receives. If Earth didn’t have an atmosphere, its surface temperature would be -18 degrees Celsius. Good news if you’re selling spiced pumpkin latte. But most of us like it somewhat warmer. Luckily earth does have an atmosphere and that keeps us warm. This works as follows.

Molecules resonate when light of certain frequencies hits them, and then they begin to wiggle. This converts the energy of light into motion of molecules. So the molecules trap the light, basically, and convert it into heat.

But most air molecules don’t wiggle for infrared light. The atmosphere of Earth is more than 99 percent nitrogen, oxygen, and none of them are good infrared wigglers. I mean, we can breathe oxygen, alright, that’s nice. But it does nothing to keep us warm.

Greenhouse gases on the other hand are great infrared wigglers. The infrared light hits them, they wiggle, and those wiggling molecules then bump into other air molecules which distributes the energy in the air. Every once in a while, one of those molecules also emits infrared radiation again, which spreads it throughout the atmosphere. The most relevant greenhouse gases on Earth are water vapor, carbon dioxide, and methane.

To understand how they warm the planet, you need to know one more thing. The earth is round. No, seriously. It’s round. And also seriously, that’s relevant. Because the earth is a sphere it has a gravitational force that drops with an inverse square law. This gravitational force is the reason why the atmosphere doesn’t just float off, so good thing we have it.

But the gravitational force decreases as you go up. And the air pressure balances the gravitational force. This means as you go up, the air pressure decreases. And the density and the temperature decrease with the pressure. This is why you can’t open the windows on an airplane. It’s really not healthy.

If you put a layer of air with greenhouse gas around a planet, then this infrared radiation is absorbed by the air. That heats up the air and that emits some radiation again, and so on. So the infrared radiation slowly spreads through the atmosphere from the surface up.

But if you go to higher and higher altitudes, the air gets thinner. Even if the concentration of a greenhouse gas stays the same, the total amount of greenhouse gas per volume still drops. And eventually there’s so little greenhouse gas that the infrared radiation can escape to outer space.

This means that most of the infrared radiation which leaves our planet doesn’t come from the surface. It comes from an altitude of several kilometres *above the surface. Again, the temperature of the radiation has to balance the energy that comes in from the sun. And since temperature decreased with altitude, this means that the temperature further down, on the surface of the planet, must increase.

This is how the greenhouse effect really works. Greenhouse gases in the atmosphere prevent infrared radiation from the surface from going right into space. Instead, the infrared radiation that goes into space comes from the upper atmosphere. That radiation from the upper atmosphere has to balance the influx of energy from the sun. And since the temperature of the atmosphere decreases with altitude, the surface of the planet has to reach a much higher temperature than without greenhouse gasses. Hey, I got it!

Well, actually, this isn’t how it works either. Or rather, this is how the big planetary greenhouse effect works in general. It’s the reason why our planet has an average surface temperature of 16 degrees Celsius and not minus 18. But it’s not the reason for the enhanced greenhouse effect which currently causes climate change.

Because the temperature of the atmosphere only decreases up to an altitude of about 10 kilometres or so. If you go further up, it remains constant for a bit. And then the temperature actually begins to increase again. That’s because the atmosphere up there absorbs some of the incoming sunlight. This part of the atmosphere where the temperature increases is called the stratosphere. I’ll have more to say about this later, so keep it in mind. Eventually the atmosphere gets so thin that the temperature drops again and fades into that of outer space.

Now remember that the greenhouse effect work because pushing the effective altitude of emission up reduces the temperature of emission, and that brings the system out of balance.

But what if I told you. What if I told you that carbon dioxide at pre-industrial levels already pushes the effective altitude of emission up to the stratosphere. If you further increase the carbon dioxide level after that, the altitude of emission doesn’t change any further because the temperature of the atmosphere doesn’t change. It seems that the warming effect is already saturated at the current level.

So I guess we’re back to “it’s all a hoax”.

Okay, to understand what’s really going on, we have to add one more subtlety. It’s that all those greenhouse gases don’t absorb infrared light equally well at all wavelengths, they absorb light only in certain parts of the infrared spectrum.

The best absorber is water vapor. That’s because the water molecule has a lot of resonances. It’s a really really good infrared wiggler. If we look at earth from above in the infrared and add the absorption from water, then the spectrum changes roughly like this. You can think about this as change as an increase of the effective altitude of emission again, but a slightly different altitude for different wavelengths. For example at shorter wavelengths the light comes on average from an altitude of about 4km. At longer altitude it’s more like 5km. And each of those altitudes have their own effective temperature, which you see on those two sides.

Carbon dioxide now has a much stronger absorption but it’s only in a specific part of the spectrum. This is around a wavelength of about 15 micrometres. The relevance of carbon dioxide for our climate comes from this emission band being pretty much near the peak of the infrared emission. At preindustrial levels, carbon dioxide takes out a big chunk of radiation coming from the surface of earth.

This lower part of the absorption line. That’s the emission curve that belongs to the temperature at the average altitude of emission, about 220 Kelvin or minus 60 degrees Celsius. But here’s the thing. If you increase the carbon dioxide even more, then this ditch can’t get deeper, because the temperature at that altitude doesn’t drop any further.

If you’ve ever had the pleasure of interacting with a climate change denier, this is exhibit A. Look, they’ll say, nothing we do will make any difference. And it’s indeed correct that the bottom of the ditch basically won’t change much. But this isn’t the relevant part.

The relevant part is that carbon dioxide doesn’t just absorb light in this very narrow range. It also absorbs it to both of those sides, and in fact in some other part of the spectrum which I haven’t drawn. If the concentration of carbon dioxide increases further, then the emission of more and more wavelengths in the spectrum moves up to higher altitudes, so they move to lower temperatures. Which in this figure means that the ditch gets wider. So, increasing carbon dioxide levels filters out an increasingly bigger chunk of the wavelength window that we use to cool the planet.

Another way to put it is that when carbon dioxide levels increase, more and more of the infrared radiation is emitted from higher altitudes, where the temperature is lower, which makes the cooling increasingly less efficient. And then the surface of the planet will warm until the energy balance is re-established.

This carbon dioxide ditch doesn’t get wider by a lot. It’s just a tiny bit. But this is the major reason for the enhanced greenhouse effect that we’re seeing right now. Can such a small difference really have so big consequences. Well, if you think about it, global warming *is a small effect in absolute terms. The average temperature of earth is something like 290 Kelvin. We’re talking about a change of a few degrees Kelvin. That’s a percent difference. Not a big change for the planet. But a big change for us, because we’ve made ourselves comfortable on this planet with a different climate.

The full story, you won’t be surprised to hear, is vastly more complicated than this 20 minutes YouTube video suggests. That’s because besides carbon dioxide there’s also methane and water vapor and the temperature in the upper atmosphere isn’t actually constant. But that’s roughly what’s going on.

This tells us another thing. Remember I said that as you up to higher altitudes in the atmosphere, the temperature increases again in a region called the stratosphere. This is because the stratosphere absorbs some of the incoming sunlight, especially in the ultraviolet. The concentration of greenhouse gases up there isn’t high enough anymore to trap the upcoming infrared light. But the concentration of carbon dioxide is still increasing. What does this do to the stratosphere?

Well, these additional greenhouse gas molecules of will still emit infrared light when they wiggle. This means that the stratosphere becomes better at getting rid of energy, which means it cools.

This is called stratospheric cooling and it’s one of the key predictions that climate models have made. It was predicted already in 1967 by Manabe and Wetherald. Wetherald died in 2011. Manabe was one of the recipients of the 2021 Nobel Prize in Physics.

This figure from their 1967 paper shows that when carbon dioxide levels increase, the lower atmosphere should warm, but the stratosphere should cool. This was a super important prediction because if global warming was caused by an increase in solar radiation, rather than by more greenhouse gases, then they should both warm.

And the upper stratosphere has in fact cooled. Here is a summary of the data from some satellites up there. What happened in 1991? That was the eruption of Mount Pinatubo.

So if someone asks you what predictions climate models have ever made a good answer is “stratospheric cooling”. And if someone asks you how we know it’s not a change in solar radiation, a good answer is also “stratospheric cooling.”

I’ve tried to figure out why I misunderstood this for so long, and I think what threw me off is all these arrows for infrared light that go right through the atmosphere. I think it’d be better to draw it like this. The incoming radiation from the sun goes through the atmosphere and hits the surface. It’s converted into infrared radiation and that heats the atmosphere from below.

Somewhere up here, the infrared light escapes for good. If the concentration of carbon dioxide goes up, then the infrared light escapes from somewhat further up where the atmosphere is a little colder. So now the total emitted energy is smaller and the system is out of balance. The earth then has to heat from below until the emission comes into balance again. And the effective altitude of emission can be slightly different for each part of the frequency spectrum.

I believe that those pictures originate from illustrations in climate physics books where the arrows don’t depict the way that the radiation actually goes, but just the total amount of energy that flows through those channels. That is to say, this illustration is all well and fine so long as you don’t think this means that the infrared light actually goes through the atmosphere.

I learned all this from a great book by Raymond Pierrehumbert which I would like to show you but it’s got green on the cover. Can you turn off the chroma key for a moment? Here’s the book. And yeah this is how the sausages are made, just a piece of green cloth pinned to the wall.

Many thanks also to Adam Levy for helping with this video. Adam has his own YouTube channel where he talks about climate stuff. If you’re interested in that, go check it out. Was my explanation of any use? Let me know in the comments.