Physics of the Greenhouse Effect Pt 2

In the preceding post, on the greenhouse effect, I investigated the role of the greenhouse effect and its play in radiative balance, and how the presence of an atmosphere acts to raise planetary temperatures. The take home points should be that for a planet with no infrared absorbing layer above the surface, the fourth power of the surface temperature always approximates a value determined by the incoming solar radiation. The only way the surface temperatures can exceed this value is if there is an atmosphere which acts to be a blanket to outgoing radiation. A planet can also be heated by internal processes such as radioactive decay or rigorous convections from the mantle, but these are rather negligible on the terrestrial planets. Adding greenhouse gases to an atmosphere whose temperature decreases with height must act to warm the surface by making the net downward emission greater than zero. In this post, I will elaborate on specific greenhouse gases, the runaway greenhouse effect, and an antigreenhouse effect.

Carbon Dioxide makes up just 380 parts per million by volume (ppmv) in our current atmosphere. That is a large jump from 280 ppmv from pre-industrial time, but nonetheless is relatively small number when compared to the other 999,620 molecules that you’d find if you went through a million molecules in the atmosphere. The mixing ratio of a gas is numerically equivalent to the pressure exerted by the gas, denoted for CO2 as pCO₂. CO₂ concentration is then 380 ppmv, or 380 μatm. It is rising by about 2 μatm per year. It would seem counterintuitive that such a small concentration could have a measurable impact on global temperature, but the fact is that most of the atmosphere (N₂, O₂, Argon) does not interact with infrared radiation, and can be ignored in that context. CO₂ also absorbs strongly at areas where Earth is strongly emitting at its temperature. For a list of greenhouse gases, and their concentrations during pre-industrial time and today, see this page
http://cdiac.ornl.gov/pns/current_ghg.html

The effect that a greenhouse gas has on temperature has to do with its concentration, where it absorbs and where the planet emits radiation, as well as the overlap with other gases.

For example, ozone is a greenhouse gas and closes the atmosphere to the transmition of longwave radiation between 9 and 9.7 μm. Because the bandwidth or window at which ozone absorbs radiation is closed, additions of ozone have very little effect on its absorptivity in the atmosphere. CFC’s on the other hand occupy a virtually open window to longwave transmission between 8 and 13 μm, and so their effect is much greater. On a molecule-by-molecule basis, it may be a a thousand times greater than carbon dioxide, but CFC’s are measured in parts per trillion and so overall exerts a rather small effect. Adding gases to places where outgoing radiation freely escapes has more of an impact that enhancing absorption where there is already some. The gases degree of “saturation” is also relevant; it is often remarked that methane is more powerful than CO₂, but this is not due to some intrinsic property of the gas, but precisely because methane exists in lower concentrations and so has yet to fill its primary bands. If methane existed in higher concentrations than CO₂, the reverse would be true: CO₂ would be more powerful on a molecule-by-molecule basis. Adding a gas against lower background concentrations will have more of an effect than adding it against higher background concentrations as the absorption spreads away from the peak. Carbon Dioxide is not yet saturated, but its absorption effects do go up logarithmically rather than linearly for this reason (which is a good thing, as the climate would be overly sensitive to small changes otherwise).

See for example the absorption locations of various gases:

To act as a greenhouse gas the molecule must possess a dipole moment, or some of its vibrational motions must create a temporary dipole moment. This eliminates homonuclear diatomic molecules (O₂, N₂) as being able to interact with the infrared. A dipole moment of a molecule is the product of the charge and the distance between the charge. Gases are not rigid stick figures like in high school chemistry class, but are constantly in motion and are vibrating. The molecules we are discussing in the atmosphere have no net charge (i.e., they are neutral) but they may have localized charges. Consider how water has localized areas of positive (hydrogen) and negative (oxygen), and so individual molecules tend to stick to one another. The diatomic molecule vibrations are very symmetric, and so the center of mass, and of charge, of the system is not displaced during vibration. This is not true when you have three molecules, as the center of charge moves as the molecule vibrates, creating a dipole moment. For carbon dioxide, you can have a symmetric vibration (this acts like the diatomic molecules and so is not infrared active), but you can also have the asymmetric fashion, in which one bond shortens while the other lengthens. There is also the bending mode, and different vibrations correspond to absorption at different wavelengths. As is the well known case for CO₂, infrared radiation at 667 cm^-1 (15.00 μm) excites these vibrations.

Greenhouse molecules are capable of absorbing passing infrared photons; the energy of the photon is converted into an excited vibrational state of the GHG molecule. As I mentioned, the molecules often have more than one vibrational mode that allows them to absorb IR photons of more than one wavelength. Diatomic molecules have a set of energy levels associated with the oscillation caused by pulling the nuclei apart and allowing them to spring back. The infrared light provides a fluctuating electric and magnetic field which alters the molecule’s environment. This displaces the nuclei and electron cloud, and excites vibration or rotation. For a molecule to be a good infrared absorber and emitter, its molecular motions must couple strongly to the electromagnetic field. The two-atom molecules are too tightly bound together to vibrate and thus they do not absorb heat and contribute to the greenhouse effect.

Absorption of energy by a particular gas occurs when the frequency of the electromagnetic radiation is that of the molecular vibrational frequency of the gas in question. Gas molecules collect radiation by their vibrational energy states, forming bands through rotational splitting. The absorption windows are formed by the averaging of a series of narrow bands. If these bands are still partially open, then absorptivity will increase linearly as the gas concentration increases. If the band is saturated, then the gas will begin to enhance absorption at the edges of the band (or band wings).

It is often noted (as I did above) that the diatomic molecules cannot behave as greenhouse gases. However, this does not hold true for many planetary atmosphere cases, such as when the atmosphere is sufficiently dense and collision induced absorption becomes a significant factor. This arises with the collision complex formed by two molecules in the act of colliding; when there are frequent collisions, such as on Titan (Saturn’s largest moon) and on all the giant gas planets, diatomic molecules acquire enough of a dipole moment during the time collisions are taking place such that the electromagnetic field can interact with their transitions. This is a true collisional continuum, and doesn’t come from broadened lines. Because of this pressure-induced opacity, N₂ and H₂ are strong greenhouse gases on Titan, and H₂ on the giant planets. On Titan, collisions between N₂-N₂, CH₄-N₂, and H₂-N₂ are responsible for its greenhouse effect (McCay et al., 1991, Science 253: 1118-1121). This effect plays out big in denser atmospheres, but not a factor on Earth.

Now if radiation had to have exactly the wavelength of the discrete spectral lines there would not be much interaction between the radiation and the molecules because there is such a small probability of the radiation having exactly that wavelength. As it turns out, the motion of the molecules themselves alter this spectrum, and the collisions between molecules in the atmosphere affect absorption as well. Doppler Broadening arises because of the fact that a molecule moving towards a light source will see the frequency shifted to higher values, and a molecule moving away the frequency will be shifted to lower values. When you average over all possible directions of molecular motion, this turns out to be Gaussian (i.e., the normal bell-shaped curve), and so the distribution of the frequencies of the absorbed radiation also is Gaussian. Of more importance to planetary atmosphere is pressure induced broadening. The absorption lines become narrower as pressure goes down, and most of the spectrum is in between lines and so the absorption coefficient changes as a function of atmospheric pressure. This means that the pressure broadening in an atmosphere forces the absorption to spread to a wider range of frequencies/wavelengths.

The antigreenhouse effect

Titan is kept warmer than it would be otherwise by the greenhouse effect of its thick atmosphere, but it is also unique to the solar system in that it has an “antigreenhouse effect.” The greenhouse effect there is more powerful than the antigreenhouse effect, and so the net effect is warming, but the moon would still be over 20 K warmer if you removed the cooling component. The upper atmosphere of Titan carries a “haze layer” of organic compounds which blocks a large part of the incoming radiation, and stops it from warming the surface. Just the opposite of the traditional greenhouse effect in planetary climates, this haze layer is opaque to incoming solar radiation, but transparent to outgoing infrared radiation. This provides comparison to the kind of cooling produced by particles thrown into the stratosphere from volcanic eruptions. The antigreenhouse effect on Titan reduces the surface temperature by 9 K whereas its greenhouse effect increases it by 21 K. The net effect is that the surface temperature (94 K) is 12 K warmer than the effective temperature (82 K) which would be set by just incoming solar radiation and no atmosphere.

When an upper layer that is opaque to shortwave radiation is added, the region of the atmosphere below this layer will become more isothermal. The infrared opacity of the lower atmosphere now loses its strength since the greenhouse effect needs a lapse rate, and the surface becomes colder. Removing the haze layer on Titan would result in more transmission of incoming solar radiation, and enhance the tropospheric greenhouse effect, and so to cause much higher temperatures there. The O₃ in Earth’s stratosphere serves as a very minor antigreenhouse effect, but it only absorbs a tiny fraction of the incident radiation from the sun– in the UV.

Water Vapor feedback

Insofar as water vapor is a powerful greenhouse gas, the tendency for water vapor content to increase with temperature will amplify the warming caused by CO₂. It is often remarked on the internet that water vapor is the most powerful greenhouse gas, and overwhelms carbon dioxide. Somehow, a claim that states that 95% of the greenhouse effect is due to water vapor has made its rounds, but this is clearly erroneous, and is more like 2/3 Water Vapor to 1/3 carbon dioxide (see Kiehl and Trenberth 1997 ). It is however true (see their table 3 for instance) that most infrared absorption is from water vapor, with carbon dioxide in second place. Of the 33 K greenhouse effect, about 10-11 K is due to well-mixed greenhouse gases (ones that do not precipitate out from the atmosphere for the typical range of atmospheric temperatures). This means that if we had no water vapor, but kept the other trace gases constant, the temperatures would be roughly 10-11 K above the baseline 255 K set by Stefan-Boltzmann. The influence of clouds and water vapor closes the gap, so it is quite obvious that it is important (no water vapor = snowball earth), but it is also obvious that the other gases are extremely important, and removing them would generate a similar icehouse. Carbon Dioxide is by far the most important of those trace gases because it absorbs strongly at the peak of Earthlike emission (water vapor absorption is weak here) dominating the 15 micron emission region, and exists in much higher concentrations than the other gases.

Even still, this is a bit misleading. As some may have picked up on, water vapor is generally treated differently than the other trace gases, and sometimes ignored in talking about forcing effects of various agents on global warming. This is because the well-mixed gases have concentrations determined by their addition and removal from the atmosphere. In the case of carbon dioxide, its concentration is regulated by the balance between sources and sinks. Some of the other gases such as Nitrous Oxide or CFC’s may be destroyed chemically. Water Vapor on the other hand, is set by temperature and circulation patterns (which turn out to keep the atmosphere subsaturated). That means that by raising or lowering temperatures, the water vapor influence follows along, with the saturation vapor pressure set by the Clausius-Clapeyron relationship (further discussion on water vapor feedback here, here, and at realclimate. This means two important things: First, the influence of water vapor on the 33 K greenhouse effect is directly tied to the presence of the other gases, as if you removed them and lowered the temperature by 10-11K, you would also lose the water vapor influence and so the global temperatures would close in on the -18 K baseline. In that sense, one can say the water vapor influence depends on carbon dioxide being in the atmosphere. The other point, is that raising temperatures (e.g. by adding CO₂, increasing solar irradiance, etc) will also cause the water vapor content to increase and lead to amplification. This is a positive feedback, and acts to raise climate sensitivity. Water Vapor is not a climate forcing agent, but rather a climate feedback, further pushing the system in the direction that some initial push gave it.

The Runaway Greenhouse

Carbon Dioxide is a necessary component for the explanations of what is going on in many past climates. The Archaean, Cretaceous, and other hothouse periods involved very high CO₂ concentrations, while icehouse climates involve very low CO₂ concentrations. The gas is also shown to force the climate into new states, such as outgassing aiding the snowball earth back to livable conditions, or forcing rapid warming during the Paleocene Eocene Thermal Maximum. CO₂ is also an important player in the coming and going of the glacial cycles over the last million years, mainly serving as a feedback to temperature changes but providing the push necessary for a self sustaining ice age or interglacial period. The gas is also very important on Venus, and without it, the planet would be colder than Earth…but instead, is the hottest planet in the solar system.

At the most intense end of the water vapor feedback, one can get a runaway greenhouse effect. This is an unstable feedback loop that doesn’t end until the entire ocean is evaporated into the atmosphere, and the water breaks down into hydrogen and oxygen from the high energy solar radiation, and the hydrogen escapes to space while the oxygen reacts with rocks. This means that CO₂ cannot turn into limestone and the outgassed CO2 stays in the atmosphere.

Earth and Venus have nearly the same amount of carbon dioxide, but on Earth most of it is locked up into rock and carbon sinks, while on Venus it is in the atmosphere. The CO₂ present in carbonate rocks on Earth is around 60 bars (Kasting and Ackerman 1986; Science 234 (4782): 1383). This is sixty times the current total atmospheric pressure. The very early Earth had a much fainter sun than today (~25-30% reduced solar output), but the Earth was still much hotter, largely due to the fact that CO2 was present at much higher concentrations and we had a denser atmosphere. In fact, a 10 to 20 bar carbon dioxide atmosphere may have existed during the first several hundred million years of the earth’s history which could give it a surface temperature near water’s boiling point.

On Earth, we have an important geophysical modulator of CO₂ concentrations. Too much carbon dioxide causes acid rain that dissolves calcium through the weathering of igneous bedrock. Calcium-rich water can flow into the oceans where it is used by organisms to build calcium carbonate skeletons. When they die, skeletal material settles and accumulates on the ocean floor. Because of plate tectonics, the ocean floor moves outwards from ocean ridges to be consumed by the Earth’s mantle at subduction zones. Calcium Carbonate also moves along, is subducted into the mantle, releases carbon dioxide in magma, and may be released through volcanoes. Without water however, such as on present day Venus, it is impossible for carbon dioxide to dissolve and form acid rain. The carbon dioxide accumulated in the atmosphere over time through planetary degassing, but with no oceans and biomass, there are no carbon sinks and so it stays in the atmosphere. The early atmospheres on Earth and Venus were rather similar, but Venus was just a bit closer to the sun such that the carbon-bearing compounds evaporated rather than remaining in the rocks.

When you increase the concentration of CO₂ you reduce the slope of the line in the below figure. In the same way, the positive water vapor feedback causes the slope of emission vs. T become to be more linear than T⁴ (see below figure). The ability of water vapor to enhance climate sensitivity is shown as the temperature rise from b to b’ becomes much larger than the change from a to a’ (in the dry case) with the same forcing from increased solar irradiance. The OLR curve then flattens out with very high sensitivity. In that sense, the planet’s temperature is not determined purely from Stefan-Boltzmann, but from the OLR with the temperature profile, CO₂, water vapor, etc.

_{Aarnout van Delden}

Here, the figure shows the equilibrium outgoing long wave radiation at the top of the atmosphere with various assumptions on the carbon dioxide concentration and the relative humidity. In this figure, at around 320 W/m² the OLR curve flattens out from very high climate sensitivity, which demonstrates that a limit exists in terms of how much a planet can lose energy. This limit is referred to as the Kombayashi-Ingersoll limit. If the net incoming solar radiation exceeds this limit, then the result will be a runaway greenhouse effect. As it turns out, this limit is influenced by the mass of the atmosphere, and high surface gravity increases the Kombayashi-Ingersoll limit making it harder for a runaway greenhouse to occur. When the temperatures exceed that at which the ocean has become depleted, the OLR can once again rise with temperature as the mass of the atmosphere remains constant, and the planet can then achieve radiative equilibrium but at a temperature greater than the ocean evaporation point.

This is basically what happened on Venus, and the solar radiation was just enough to push Venus into a runaway state. This is not a situation that can occur on Earth today, except for maybe in billions of years when the sun becomes much brighter. Today, the planet is heated nearly entirely by back radiation and is exceedingly hot from its dense atmosphere and high greenhouse concentrations. Although it is closer to the sun now, it receives much less solar radiation at the surface than Earth because of its extremely thick cloud cover (i.e. a very high albedo). Venus’ temperature with no greenhouse would actually be colder than the Earth with no greenhouse because of the very little sunlight (~ 17 W/m² averaged on the surface). The clouds also serve in the greenhouse effect, where sulfuric acid clouds reflect outgoing IR (unlike on Earth where clouds absorb and re-emit) but they can inhibit cooling to space that way. On net though, the clouds are a cooling agent on Venus. There is actually some trace amounts of water vapor on Venus which contributes to the greenhouse effect, but CO2 is the largest contributor. The atmosphere is so opaque in the infrared that less than 1% of the outgoing infrared actually escapes.