The greenhouse effect part 5: Differences between model and reality

2022 September 12
  1. Part 1: What is the greenhouse effect? An accessible, scientific introduction
  2. Appendix A: What is the atmosphere?
  3. Appendix B: Ozone
  4. Part 2: Physics of light and temperature
  5. Part 3: Temperature of the Earth without an atmosphere
  6. Part 4: A model of the greenhouse effect
  7. Part 5: Differences between model and reality

We have considered several simple examples of atmospheric models where we were able to exactly calculate the temperature that the surface of the Earth would have to maintain the system in equilibrium. While the greenhouse effect acts in the real world to raise the temperature of the Earth in just the same way as it acts in the model, there are many additional complications to the real climate system that our simple examples do not represent. With the aid of detailed observations of the atmosphere it is possible to build sophisticated computer simulations of the climate; but our simple model is sufficient to understand the basic principles underlying the greenhouse effect.

In part 4 we introduced a “single layer” model, that is, we assumed that the atmosphere was a single uniform temperature. The real atmosphere has temperatures that wildly vary with height, and the greenhouse gases in the atmosphere are only sensitive to specific wavelengths of infrared light, with different gases located in different concentrations in different parts of the atmosphere.

We briefly discuss the structure of the atmosphere; a more detailed explanation can be found in appendix A. The lowest layer of the atmosphere, called the troposphere, is the bottom 10 to 15 km of the atmosphere and contains about 80% of its mass. The troposphere is well-mixed because it is heated from below1This fact is how real-world greenhouses work, which is totally unrelated to the greenhouse effect. A greenhouse prevents the air near the ground from rising and mixing with the air above, causing hot air to be trapped near the surface. It has nothing to do with blocking infrared radiation, as can be demonstrated by placing a small vents in the roof and sides of a greenhouse, which causes it to cool to ambient temperatures.. While infrared radiation is one way that energy goes upwards in the troposphere, another major component is hot air rising. Above the troposphere is the stratosphere, which is well stratified into distinct layers because it is heated from above by the ozone layer.

The main greenhouse gases located in the Earth’s atmosphere are water vapor, carbon dioxide, methane, and ozone, listed in decreasing order of their contribution to the greenhouse effect. Ozone is mostly located in the ozone layer in the stratosphere. While ozone only has a small greenhouse effect, it plays a very important role in Earth’s climate and ecosystem because it absorbs ultraviolet radiation.

Methane is a very efficient greenhouse gas compared to carbon dioxide, but it is present at a much lower concentration. Most methane released into the atmosphere decays to carbon dioxide within about 10 years. Levels of atmospheric methane today are approximately 3 times the natural amount, with the main sources being natural gas mining and livestock.

Carbon dioxide is a very stable gas that is only removed in significant amounts through photosynthesis and diffusion into the surface of the ocean. When excess carbon dioxide is added to the atmosphere, most of it remains for hundreds of years, and some remains for tens of thousands of years. Because of its stability, carbon dioxide is well-mixed through all layers of the atmosphere and plays a key role in the greenhouse effect.

Today carbon dioxide is about 410 ppm as of 2018 415 ppm (as of 2022) in the Earth’s atmosphere, of which about 135 ppm is from artificial sources. Natural levels of carbon dioxide vary from 180 ppm to 280 ppm on a timescale of about 100 000 years2Before the industrial revolution, the natural level of carbon dioxide was already at roughly 280 ppm, at the high end of the natural cycle.. The main artificial source of carbon dioxide is fossil fuel burning.

Water is the most important gas in the atmosphere and has a direct effect on almost every aspect of the climate. While water is chemically unreactive in atmospheric conditions, it readily condenses from vapor into liquid or solid, making clouds, and sometimes precipitating out. Because of this, almost all water vapor is located in the warm air nearest the surface, with very little found at higher altitudes. Since water is mostly confined near the surface it does not have as large a greenhouse effect as it would if it were evenly mixed throughout the atmosphere.

Furthermore, water rapidly enters or leaves the atmosphere in response to changes in weather conditions, with warmer conditions typically increasing the amount of water. This gives other greenhouse gases a compounding effect: any warming caused by the addition of carbon dioxide to the atmosphere results in an increase in water concentration, causing further warming. In extreme cases this could cause a “runaway” greenhouse effect, as is thought to have happened to Venus. Finally, water forms clouds when it condenses, which have complicated and hard to understand effects on the climate, and are capable of either warming or cooling the Earth depending on what altitude they are.

These gases are capable of absorbing different wavelengths of infrared light, as seen below. The attenuation of light due to a gas is what fraction of light would be absorbed by the gas – that is, how opaque it is, or the opposite of how transparent it is. For example, a photon with a wavelength of 13 microns emitted by the surface of the Earth going directly upwards has about a 50% chance of being absorbed by a water molecule, assuming it is not scattered or absorbed by any other gas. At 15 microns we see that both water and carbon dioxide are capable of absorbing almost all light emitted by the surface of the Earth, whereas around 11 microns, called the infrared atmospheric window, most light emitted by the surface of the Earth passes to space without being absorbed by the atmosphere.

Although the atmosphere absorbs almost all emissions from the surface of the Earth at specific wavelengths, that does not mean that light of that wavelength is not emitted to space. Recall that in the single-layer model, even when the atmosphere was totally opaque to infrared radiation, infrared radiation still reached space because the atmosphere itself was emitting it. Therefore, at wavelengths like 7 microns and 15 microns where the atmosphere is very effective at absorbing the Earth’s radiation, almost all light at those wavelengths that reaches space was emitted by the atmosphere. Because the atmosphere is colder than the surface of the Earth, the atmosphere is less effective at emitting heat to space. In particular, this gives us another perspective for understanding the Earth’s effective temperature: the effective temperature measures the temperature of the part of the atmosphere that is emitting infrared radiation directly to space3Or more specifically, the average of the temperatures of the various parts of the Earth and atmosphere, weighted according to what proportion of the emissions to space come from that part..

Another way to describe this situation is that instead of the surface of the Earth radiating energy directly to space, instead energy flows from the surface to/through the atmosphere in the form of infrared radiation, and then from the atmosphere to space. The atmosphere itself has many layers, with the lower layers warming the upper layers. The surface of the Earth must be warmer than the atmosphere, as otherwise energy would not flow from the surface to the atmosphere; and likewise each layer of the atmosphere must be warmer than the layers above it so that energy will flow from the lower layers to the upper layers4Although note that this simplified explanation ignores the ozone layer, where temperatures actually increase with height. Ozone absorbs ultraviolet radiation, which comes only from the Sun, and not from the Earth, so this causes the reverse behavior of temperature increasing with height.. The more layers there are, the hotter the surface of the Earth needs to be to push the same amount of heat outwards. Since the surface continues to receive the same amount of energy from the Sun no matter how many layers of greenhouse gases are added, if not enough heat is being expelled from the surface, then the surface will simply heat up until there is.

The total effects of the greenhouse gases in the Earth’s atmosphere can be seen in the following figure. The figure presents typical infrared emissions from the Earth when the surface of the Earth is 294.2 K (21 C, 70 F) and there are no clouds. The blue line illustrates the emissions of a perfect blackbody the same size and shape of the Earth at 294.2 K. In the absence of the atmosphere, the Earth’s emissions would be very close to the blue line; note that the emissions are closest to the blue line in the infrared atmospheric window around 8 to 12 microns. However, in the presence of the atmosphere, certain regions of the Earth’s emission spectrum are dominated by emissions from the atmosphere, which is cooler than the surface of the Earth. The green and red lines show blackbody spectra of other temperatures; for example, this allows us to estimate that the emissions near 15 microns, which are caused by carbon dioxide, come from a layer of the atmosphere with a temperature near 225 K (-48 C, -55 F).

Observe the close relationship between the attenuation of the four gases, particularly water and carbon dioxide, and the features of the Earth’s infrared spectrum. The wavelengths that are strongly attenuated by the gases are those that have much lower emissions to space. Particularly, notice that at wavelengths where water strongly attenuates, the spectrum has a temperature of about 255 K, and at wavelengths where carbon dioxide strongly attenuates, the spectrum has a temperature of about 225 K. This suggests that the highest levels of the atmosphere with high concentrations of water typically have a temperature of around 255 K, whereas the highest levels of the atmosphere with sufficient carbon dioxide typically have a temperature of around 225 K.

Since water is typically only found in the lowest parts of the atmosphere (see appendix A), whereas carbon dioxide is uniformly found throughout, in the region near 15 microns where both water and carbon dioxide strongly attenuate, it is carbon dioxide that determines the temperature of the emissions to space. (The small spike right at 15 microns is due to carbon dioxide found in the upper stratosphere.)

What happens if carbon dioxide is increased?

The previous figure of the Earth’s spectrum was made using a radiative transfer model, which uses the same ideas presented in part 4 but with much greater sophistication. Given the temperature of the surface and a description of the temperature and chemical composition of each level of the atmosphere, the radiative transfer model highly accurately computes the emission and absorption of radiation at every level, taking into account the different properties of each chemical at every wavelength5Our model of part 4 only considered two wavelengths of light, shortwave and longwave. However the radiative transfer model, LBLRTM, simulated 15 million different wavelengths, which was smoothed to about 1000 wavelengths in the figure – without this smoothing the graph would have been so spiky as to be totally unreadable. Numerous other details we ignored in our simple model were properly simulated by LBLRTM. The atmospheric composition used is the US Atmospheric Standard of 1976, which defined a carbon dioxide concentration of 314 ppm, far below the current value of 415 ppm as of 2022..

So, what happens if the amount of carbon dioxide is increased in the atmosphere? As we saw in the previous sections, adding carbon dioxide should increase the temperature of the Earth; but with the use of a highly accurate radiative transfer model, it seems that it should be easy to give a quantitative and exact answer. Indeed, if we re-run the radiative transfer model with the same surface temperature but a higher concentration of carbon dioxide, we find that the “holes” in the emission spectrum corresponding to attenuation from carbon dioxide become slightly deeper and wider, so that less infrared emissions reach space, and a higher surface temperature is needed to maintain the same infrared emissions.

While this gives a first decent estimate of the increase in temperature due to an increase in carbon dioxide, it assumes that the temperature and composition of the atmosphere is unchanged by the addition of carbon dioxide. However, as the surface temperature rises, the temperature of the lowest layers of the atmosphere also rises. Since warmer air holds much more water, this increases the amount of atmospheric water, which is the most potent greenhouse gas.

This process by which any warming causes an increase in atmospheric water, thereby causing further warming, is called the water vapor feedback process. This makes the climate more sensitive to changes in temperature – any perturbation is amplified. Fortunately, this amplification is self-limiting, and does not compound upon itself endlessly6It is thought that Venus entered in a water vapor feedback process that was not self-limiting, and just grew forever in a runaway greenhouse effect until its oceans boiled away entirely. It is also expected that Earth will eventually enter a similar runaway greenhouse effect in about one billion years, and that artificial climate change will not be able to trigger this early..

It is the existence of climate change feedbacks like the water vapor feedback that makes it very challenging to accurately predict how much the temperature will rise when carbon dioxide is added to the atmosphere. Water vapor feedback is an example of a linear feedback process where every time a bit of carbon dioxide is added, the amount of water vapor goes up a bit in response. Much more difficult are nonlinear feedback processes, particularly so-called “tipping points” which have no observable effect on the climate until a critical threshold is reached, at which point there is a very large feedback effect.

Many of these nonlinear feedback processes are poorly understood and difficult to predict, or sometimes not even known if they exist or not. One widely speculated process regards the release of methane clathrates, which are vast reserves of methane trapped in ice buried under the ocean floor, particularly in the arctic. Estimates of the size of these reserves vary widely, but are typically on the order of thousands of gigatons of carbon. If this methane were to be released to the atmosphere by the melting of the ice, it would cause a large and rapid rise in temperature. Some scientists believe that a process like this was responsible for certain sudden climate changes in the past7Specifically the Permian-Triassic extinction event of 252 million years ago and the Paleocene-Eocene Thermal Maximum of 55 million years ago., and measurements have found an increase in methane releases in the arctic, but the role of methane clathrates in climate change is still unknown.

A nonlinear feedback process which scientists have more understanding of is the ice-albedo feedback, a process by which rising temperatures causes ice to melt, which lowers the albedo of the Earth (as ice is very reflective), which then warms the planet further. This is particularly important in the arctic, where highly-reflective ice covers sea, which has very low reflectivity. A simplified perspective of the arctic ice-albedo feedback is the idea that the arctic supports two stable states: a high ice state, where cold global temperatures allow a large ice cap, whose high albedo encourages cold temperatures; or a low ice state, where warm global temperatures cause a small ice cap, so that the low albedo of dark ocean waters encourages warm temperatures. It is speculated that intermediate ice levels are unstable, which explains why the Earth has sharply transitioned between glacial periods (popularly called “ice ages”, although that term has a different technical meaning) and interglacial periods instead of smoothly varying. Again, the extent to which this will play a role in the climate response to an increase in carbon dioxide is hard to predict.


  1. This fact is how real-world greenhouses work, which is totally unrelated to the greenhouse effect. A greenhouse prevents the air near the ground from rising and mixing with the air above, causing hot air to be trapped near the surface. It has nothing to do with blocking infrared radiation, as can be demonstrated by placing a small vents in the roof and sides of a greenhouse, which causes it to cool to ambient temperatures.↩︎

  2. Before the industrial revolution, the natural level of carbon dioxide was already at roughly 280 ppm, at the high end of the natural cycle.↩︎

  3. Or more specifically, the average of the temperatures of the various parts of the Earth and atmosphere, weighted according to what proportion of the emissions to space come from that part.↩︎

  4. Although note that this simplified explanation ignores the ozone layer, where temperatures actually increase with height. Ozone absorbs ultraviolet radiation, which comes only from the Sun, and not from the Earth, so this causes the reverse behavior of temperature increasing with height.↩︎

  5. Our model of part 4 only considered two wavelengths of light, shortwave and longwave. However the radiative transfer model, LBLRTM, simulated 15 million different wavelengths, which was smoothed to about 1000 wavelengths in the figure – without this smoothing the graph would have been so spiky as to be totally unreadable. Numerous other details we ignored in our simple model were properly simulated by LBLRTM. The atmospheric composition used is the US Atmospheric Standard of 1976, which defined a carbon dioxide concentration of 314 ppm, far below the current value of 415 ppm as of 2022.↩︎

  6. It is thought that Venus entered in a water vapor feedback process that was not self-limiting, and just grew forever in a runaway greenhouse effect until its oceans boiled away entirely. It is also expected that Earth will eventually enter a similar runaway greenhouse effect in about one billion years, and that artificial climate change will not be able to trigger this early.↩︎

  7. Specifically the Permian-Triassic extinction event of 252 million years ago and the Paleocene-Eocene Thermal Maximum of 55 million years ago.↩︎

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