# Flow constriction: How the Greenhouse effect warms a planet

Many explanations of the atmospheric Greenhouse effect leave people unclear about how the Greenhouse effect raises the global temperature. I’d like to look at a simple fundamental principle which sheds light on how warming happens.

## Level and flows

How do you raise the level of something?

If we’re talking about water in a reservoir, you might think the answer is pretty simple: to raise the water level, you need to add more water—right?

Yet, what if we’re talking about a situation where water is continuously being added, and continually draining away?

An example of that sort of situation is depicted below.

Figure 1 shows a water reservoir with water flowing in and out. The outlet is designed so that the higher the water level, the greater the rate at which water flows out. If water starts flowing into the reservoir at a steady rate, then the water level will rise until the rate at which water is flowing out equals the rate at which water is flowing in. Once that happens, the water level in the reservoir stabilizes, neither increasing nor decreasing.

What happens if the outflow is subsequently constricted? That’s the situation depicted below.

The outlet of the reservoir in our example has an adjustment mechanism which allows one to constrict the flow, leading to a lower outflow rate for a given water level. Figure 2 shows what happens when that mechanism is adjusted.

1. Initially (top diagram of Figure 2), the system is in equilibrium, with the rate of water flowing out matching the rate of water flowing in.
2. Then the mechanism at the outlet is adjusted to reduce the outflow rate for any given water level. Immediately after the outflow is constricted (middle diagram of Figure 2), the rate of water flowing out is less than the rate of water flowing in. Since there is more water flowing in than is flowing out, the water accumulates inside the reservoir. This accumulation leads to a rising water level.
3. The water level rises until, eventually, the outflow rate once again equals the inflow rate (bottom diagram of Figure 2). The water level stabilizes at this new, higher level. Once again, the water level neither increases nor decreases.

Notice that raising the water level did not involve adding any more water beyond what was already flowing in.

This example illustrates some general principles about water levels. The principles apply in systems where a container can hold a variable amount of water, water is continually flowing in and out, and the outflow rate depends on the water level, with the outflow rate increasing as the water level increases. In these systems:

• The water level naturally adjusts to be the level at which the water inflow and outflow rates are in balance.
• Water level can be raised by either:
• (a)  increasing the rate at which water flows in, or
• (b) constricting the outflow, so that for any given water level, the rate at which water flows out is reduced.

## Temperature and heat flow

We can relate the discussion above to temperature by asking the question: How do you raise the temperature of something?

Temperature is a measure of the level of thermal energy inside something. So, this question is similar to the previous question, “How do you raise the level of something?”

Again, you might think the answer is pretty simple: to raise the temperature, you need to add more thermal energy—right?

Yet, what if we’re talking about a situation where thermal energy is continuously being added, and thermal energy is continually flowing away to someplace cooler?

An example of that sort of situation is depicted below.

Imagine a small cabin being heated by a wood stove during winter. Figure 3 offers a schematic depiction of what happens to thermal energy in that situation:

• Heat from the wood stove flows into the interior of the cabin.
• The interior of the cabin contains a certain amount of thermal energy. Assuming there is a thermometer inside the cabin, that thermometer measures the level of that thermal energy, and reports that level as the “temperature.”
• The level of thermal energy inside the cabin (i.e., the temperature) determines the rate at which heat flows through the walls and into the cold air outside. A higher temperature inside the cabin leads to heat flowing out at a higher rate.
• After a fire is started in the wood stove, heat flows into the cabin and starts to raise the temperature. The temperature rises until the rate at which heat flows out equals the rate at which heat is flowing in. At that point, the temperature inside the cabin stabilizes, neither increasing nor decreasing.

What would happen if we (somehow) quickly added insulation to the walls and ceiling of the cabin? The insulation would constrict the flow of heat out of the cabin. That situation is depicted below.

1. Initially (top diagram of Figure 4), the system is in equilibrium, with the rate of heat flowing out matching the rate of heat flowing in.
2. Then, insulation is added, and this reduces the heat outflow rate for any given interior temperature. Immediately after the heat outflow is constricted (middle diagram of Figure 4), the rate of heat flowing out is less than the rate of heat flowing in. Since there is more heat flowing in than is flowing out, thermal energy accumulates inside the cabin. This accumulation leads to a rising temperature.
3. The temperature rises until, eventually, the heat outflow rate once again equals the heat inflow rate (bottom diagram of Figure 4). The temperature stabilizes at this new, higher level. Once again, the temperature neither increases nor decreases.

Notice that raising the temperature did not involve adding any more thermal energy beyond what was already flowing in.

This example illustrates some general principles about temperatures. The principles apply in systems where heat is continually flowing in and out. In these systems:

• The temperature naturally adjusts towards the temperature at which the heat inflow and outflow rates are in balance.
• Temperature can be raised by either:
• (a) increasing the rate at which heat flows in, or
• (b) constricting the outflow of heat, so that for any given temperature, the rate at which heat flows out is reduced.

Note that option (b) above applies only in situations where heat is flowing in. So:

• If no heat is flowing in, you can’t warm something up just by surrounding it with insulation.
• If an object is being warmed because it’s close to a hot object, even perfect insulation won’t cause the object’s temperature to rise above the temperature of the heat source. (Once the temperatures are equal, there will no longer be any heat flowing in.)

When heat is flowing continually, understanding the principles above is essential to understanding temperatures.

## Temperature of a planet

All planets in our solar system have heat continually flowing in and out. So, the principles about temperature that were outlined in the last section apply to the temperature of a planet.

The situation is depicted schematically below.

• Heat flows into the planet from the hot Sun in the form of absorbed sunlight.
• Heat flows out from the planet to the cold of space in the form of infrared radiation. A higher temperature leads to more infrared radiation being emitted, so that there is a higher rate of radiant heat flow out to space.
• The temperature continually adjusts towards the level that makes the rates of radiant heat flow in and out equal.

What happens if something constricts radiant heat flow outward? This situation is depicted below.

1. Initially (top diagram of Figure 6), the system is in equilibrium, with the rate of radiant heat flowing out matching the rate of radiant heat flowing in.
2. Then, “greenhouse gasses” are added to the atmosphere. This constricts the outflow of radiant heat. In other words, it reduces the heat outflow rate for any given surface temperature. (I’ll go into how greenhouse gasses do this a bit later.) Immediately after the heat outflow is constricted (middle diagram of Figure 6), the rate of radiant heat outflow is less than the rate of radiant heat inflow. Since there is more heat flowing in than is flowing out, thermal energy accumulates in the surface and atmosphere of the planet. This accumulation leads to a rising temperature.
3. The temperature rises, increasing the rate at which infrared radiation is emitted to space. Eventually, the heat outflow rate once again equals the heat inflow rate (bottom diagram of Figure 6). The temperature stabilizes at this new, higher level. Once again, the temperature neither increases nor decreases.

Notice that raising the temperature did not involve adding any more thermal energy beyond what was already flowing in from absorbed sunlight.

So, the way that the Greenhouse effect warms a planet is that it involves Greenhouse gasses constricting the flow of radiant heat to space, allowing thermal energy to accumulate until the temperature rises. It’s analogous to the way that constricting the flow of water from a reservoir can raise the water level.

To complete the explanation, we just need to look at how the radiant heat flow to space is constricted.

## How do Greenhouse gasses constrict radiant heat flow to space?

The only way the Earth as a whole can cool itself is by emitting thermal radiation into space. Other heat transfer mechanisms like convection and conduction require the presence of matter to transfer energy to, and there’s practically no matter in space. So, mechanisms like convection and conduction can move heat around within Earth (i.e., within the surface, oceans, and atmosphere), but aren’t part of energy going into space. The energy that goes into space is all radiative.

All matter which is capable of interacting with electromagnetic (EM) radiation is constantly emitting thermal EM radiation. The warmer matter is, the more thermal radiation is emitted, and the shorter the wavelength of that radiation tends to be:

• Things like a person or a house or the ground or the ocean are at temperatures which cause them to emit thermal radiation in the “longwave” infrared range of wavelengths (wavelengths longer than 4 millions of a meter).
• Hotter things, like a piece of iron in a forge, or the filament in an incandescent light bulb, or the soot particles in a flame, or the surface of the Sun, emit even more thermal radiation at shorter wavelengths. The thermal radiation emitted by these hotter objects can include “shortwave” infrared radiation (with a wavelength shorter than 4 microns), visible light, or ultraviolet light. (The matter at the heart of a thermonuclear explosion can be hot enough that its thermal radiation consists mainly of X-rays.)

So, the surface of the Earth (and everything on that surface) is continually emitting longwave thermal radiation.

Above, I referred to “all matter which is capable of interacting with electromagnetic radiation.” The qualifier is important because the major gasses in air, nitrogen and oxygen, are not capable of significantly interactions with EM radiation (in the longwave part of the spectrum). Those gasses are transparent to longwave radiation, and neither absorb nor emit longwave thermal radiation, for all practical purposes.

There are also materials in the atmosphere that can interact with longwave radiation. I personally call these LongWave-active Atmospheric Materials (LWAMs). [Update: Perhaps it would be friendlier to simply call these “Greenhouse materials.”]

• LWAMs include Greenhouse gasses. The term “Greenhouse gas” means “a gas capable of absorbing and emitting longwave radiation.” The most significant Greenhouse gasses are water vapor and carbon dioxide.
• LWAMs also include the water droplets and ice crystals that make up clouds.

So, how do LWAMs (including Greenhouse gasses) constrict the flow of radiant energy to space?

That question is a little like asking why tinted glass reduces the flow of light to the other side of the glass. When you put something in the way of EM radiation which is capable of absorbing that radiation, then of course you’re going to reduce or constrict the flow of radiation!

That’s a good starting point, for understanding why LWAMs reduce radiant heat flow.

However, to be fair, it’s a bit more complicated than that with LWAMs because, in addition to absorbing thermal radiation, they also emit thermal radiation.

If the atmosphere was transparent to longwave radiation, then all the thermal radiation emitted by the surface would escape to space. That’s the scenario in which there would be the highest possible rate of radiant heat flow to space.

However, Earth’s atmosphere is not transparent to longwave radiation:

• LWAMs absorb around 90% of the thermal radiation emitted by the Earth’s surface.
• LWAMs also emit thermal radiation. Much of the thermal radiation they emit escapes to space. These emissions compensate for a lot of what gets absorbed.
• The net effect is that the rate at which thermal radiation is emitted to space is only about 60% as large as the rate at which thermal radiation is emitted by the surface. (That’s what is empirically observed.)

In other words, for a given surface temperature, the rate of radiant heat flow to space is only 60% of what it would be if there were no LWAMs. The presence of LWAMs constricts radiant heat flow.

That reduction in thermal emissions to space, relative to what is emitted by the surface, is what is referred to as the “Greenhouse effect.”

But, why does it work out that way? If LWAMs emit thermal radiation as well as absorbing it, then why doesn’t it all even out? Why don’t LWAMs emit just as much thermal radiation as they absorb?

LWAMs emit less thermal radiation than does Earth’s surface because they are colder than the surface.

Thermal radiation emissions are determined by temperature.

As matter gets warmer, the rate at which it emits thermal radiation increases rapidly. And, as matter gets cooler, the rate at which it emits thermal radiation decreases rapidly.

If you reduce the temperature of something by merely 12%, that reduces its thermal radiation emissions by 40%.

Since Earth’s thermal emissions that reach space are 40% reduced relative to thermal emissions from the surface, that means that the matter emitting thermal radiation to space is 12% cooler than the surface. For an average surface temperature around 288 Kelvin / 15℃ / 59℉, that would mean that the matter emitting thermal radiation to space is, on average, about 35℃ / 62℉ colder than the surface.

Temperature drops significantly as one goes higher into the atmosphere (at a rate of about 6.5℃/km), so the air at the top of the troposphere (the main and lowest layer of the atmosphere) is around 75℃ / 136℉ colder than the air near the surface.

To find temperatures 35℃ / 62℉ cooler than the surface, you only need to go up to an altitude of around 5 kilometers or 18,000 feet.1The 5 km figure is based on a naive estimate assuming a linear lapse rate. Measurements show that the relevant temperature of 254 K is actually achieved at an average altitude of 7219±2 meters or roughly 24,000 feet.

The presence of LWAMs in the atmosphere creates a situation in which Earth’s thermal radiation to space is, on average, emitted from around the middle of the troposphere instead of simply being emitted from the surface.

Thermal energy is transported into the atmosphere in a variety of ways: by convection, by water evaporating at the surface and then condensing higher up to form clouds, and by radiant heat transfer from the surface to the atmosphere. One consequence of the atmosphere being cold is that any thermal energy which gets transported into the atmosphere (regardless of the heat transport mechanism that carried it there) can’t be emitted as thermal radiation as rapidly as it could have been if that energy was at the surface, where temperatures are higher.

The bottom line is that LWAMs absorb a lot of the thermal radiation from the warm surface, and, being cooler, only replace a portion of what they absorb with their own emissions.

The net effect is that LWAMs constrict the flow of thermal radiation to space, reducing how efficiently Earth can cool itself.

For Earth to balance the rate of radiant heat flow “in” with the rate of radiant heat flow “out”, thermal energy must accumulate until the temperature is high enough that the rate of thermal radiation being emitted to space matches the rate at which heat flows “in” from absorbed sunlight.

That leads to the surface temperature being around 35℃ / 62℉ higher than it would be if the surface could simply radiate directly to space. The surface needs to get that warm so that the the atmosphere above it will be warm enough to emit enough thermal radiation to balance the absorbed sunlight.

That is how the “Greenhouse effect” warms a planet.

• 1
The 5 km figure is based on a naive estimate assuming a linear lapse rate. Measurements show that the relevant temperature of 254 K is actually achieved at an average altitude of 7219±2 meters or roughly 24,000 feet.