How does greenhouse warming work?

The Earth and the moon are about the same distance from the sun, but their temperature extremes are wildly different. Surface temperatures on the moon range from 250 F on the sunlit side to below -200 F on the night side. Earth is far more hospitable. Why the big difference? The moon has a much longer day (28 Earth days) which gives the illuminated side much longer to bake and the night side much longer to freeze. Also, the Earth's atmospheric air currents and oceanic water currents transport heat from warmer to colder regions, helping to prevent extremes. But there's more to the story.

Luminous beings are we

When you look at people on a sunny day, you are seeing sunlight reflected off of them. But their bodies also give off light. We don't notice this because that light is at infrared wavelengths that the human eye cannot see. This is thermal radiation that all physical objects give off. The hotter the object, the more intense this emitted light; it emits energy at a rate proportional to the fourth power of the temperature measured on the Kelvin scale.

Also, the hotter the object, the shorter the wavelengths in its spectrum. (Shorter wavelengths correspond to more energetic photons, the particles of light.) Below is an illustration. The sun has a surface temperature of 5800 Kelvin, which is about 10,000 degrees on the Fahrenheit scale. Its thermal radiation spectrum peaks in the visible-wavelength region. Human body temperature is 310 Kelvin. Yes, Arnold is hot, but not red hot, just infrared hot.

Thermal radiation spectra of objects at the temperature of the sun and of the human body. The wavelength axis is on a logarithmic scale, and the body temperature spectrum is scaled up 30x so that we can see both spectra on the same graph.

There are cameras that are sensitive to infrared light. The camera software converts the brightness of each point in the scene to an estimated temperature and then displays this temperature as a color.

Midwave IR photo of a person

A moon noon

What determines the temperature of the moon at lunar noon? The surface absorbs energy from the sun at a rate of about 1300 watts per square meter. It will heat up until it emits thermal radiation at the same rate. The temperature will steady at around 250 F when this balance prevails. At nighttime, the moon's surface is receiving light from the stars and sometimes light reflected from the Earth. The thermal radiation from the surface balances this faint illumination at a much lower temperature.

Day and night radiation balance on the moon

Let's do a thought experiment. Suppose the moon were made of a substance that conducts heat perfectly. Any heat absorbed on the sunlit side is instantly spread around to the dark side so that the surface temperature is the same everywhere. What would that temperature be? Answer: the temperature at which the total energy intercepted from the sunlight is the same as the total energy emitted over the surface of the moon. Here's a picture of this balance point:

Radiation balance for a sphere that perfectly conducts heat

The sunrays that are intercepted are those that are within the area of a circle C with the same radius R as the moon. Thermal radiation, on the other hand, is emitted from the surface area of a sphere, which is four times larger than the area of the circle. With all this surface area to emit from, the moon doesn't need to get as hot to achieve balance. The balance point would occur at a surface temperature of about 28 F.

Earth with no greenhouse effect

We can do a similar calculation for Earth. Pretend there's no water vapor, carbon dioxide, or other greenhouse gases. And pretend that the atmosphere neither absorbs nor emits light, but that winds and air currents help to spread heat around. The Earth absorbs less sunlight than the moon because it reflects more, so the balance point is colder, around 0 F.

Energy flow balance with no greenhouse effect

Above is a picture of this balance point. The atmosphere is transparent to both visible and infrared light. F represents the rate of energy flowing down from the sun and being absorbed by the Earth. The Earth's temperature will steady at the point where it emits the same amount of energy flowing up.

The actual average temperature is much warmer than 0 F, close to 59 F, because the greenhouse gases have a warming effect. That's been a good thing. Now we can see how this works.

Greenhouse effect (simplified)

Let's add the greenhouse gases to the atmosphere. The atmosphere is mostly transparent to the sunlight but very absorbing at the Earth's thermal radiation wavelengths. To keep things simple, we'll assume it's completely transparent to sunlight and completely opaque (absorbing) at thermal radiation wavelengths. Think of the atmosphere as a thick slab of stuff, all at the same temperature, hovering above the Earth's surface, able to absorb thermal radiation and give it off from both its top and bottom surfaces.

Energy flow balance with severe greenhouse effect

The temperature of the atmosphere T and of the Earth's surface Te will steady at the point where the downward and upward energy flows are in balance at all three surfaces. Again, F represents the downward energy flow from the sun. To get balance at the top surface of the atmosphere, the thermal radiation from that surface must have an upward energy flow of F. Since the atmosphere is all at the same temperature, its bottom surface must be emitting thermal radiation downward with an energy flow of F. The Earth is receiving a total energy flow of 2F, F from the sun and another F from the atmosphere. To balance this, the Earth must be warm enough to emit thermal radiation with an upward energy flow rate of 2F, double the value for the no-greenhouse case. If we average the solar energy flow over day and night to get a number for F, we find that the balance point occurs at an Earth surface temperature of 86 F. This is severe greenhouse warming.

We're somewhere in the middle!

In fact, the atmosphere is not completely opaque to thermal radiation, so it does not bottle up heat as severely as what I just estimated. We're somewhere in the middle between no greenhouse effect and an extreme greenhouse effect. This means that if we modify the atmosphere, we can move away from the middle. In another post, I present the evidence that we've done just that.