There is a strong scientific consensus that greenhouse effect due to carbon dioxide is a main driver of climate change. Following is an illustrative model meant for a pedagogical purpose, showing the main physical determinants of the effect. Under this understanding, global warming is determined by a simple energy budget: In the long run, Earth emits radiation in the same amount as it receives from the sun. However, the amount emitted depends both on Earth's temperature and on its albedo: The more reflective the Earth in a certain wavelength, the less radiation it would both receive and emit in this wavelength; the warmer the Earth, the more radiation it emits. Thus changes in the albedo may have an effect on Earth's temperature, and the effect can be calculated by assuming a new steady state would be arrived at. In most of the electromagnetic spectrum, atmospheric carbon dioxide either blocks the radiation emitted from the ground almost completely, or is almost transparent, so that increasing the amount of carbon dioxide in the atmosphere, e.g. doubling the amount, will have negligible effects. However, in some narrow parts of the spectrum this is not so; doubling the amount of atmospheric carbon dioxide will make Earth's atmosphere relatively opaque to in these wavelengths, which would result in Earth emitting light in these wavelengths from the upper layers of the atmosphere, rather from lower layers or from the ground. Since the upper layers are colder, the amount emitted would be lower, leading to warming of Earth until the reduction in emission is compensated by the rise in temperature. Furthermore, such warming may cause a feedback mechanism due to other changes in Earth's albedo, e.g. due to ice melting.
Structure of the atmosphere Most of the air—including ~88% of the CO2—is located in the lower part of the atmosphere known as troposphere. The troposphere is thicker in the equator and thinner at the poles, but the global mean of its thickness is around 11 km. Inside the troposphere, the temperature drops approximately linearly at a rate of 6.5 Celsius degrees per km, from a global mean of 288 Kelvin (15 Celsius) on the ground to 220 K (-53 Celsius). At higher altitudes, up to 20 km, the temperature is approximately constant; this layer is called the tropopause. The troposphere and tropopause together consist of ~99% of the atmospheric CO2. Inside the troposphere, the CO2 drops with altitude approximately exponentially, with a typical length of 6.3 km; this means that the density at height y is approximately proportional to exp(-y/6.3 km), and it goes down to 37% at 6.3 km, and to 17% at 11 km. Higher through the tropopause, density continues dropping exponentially, albeit faster, with a typical length of 4.2 km.
Effect of carbon dioxide on the Earth's energy budget Earth constantly absorbs energy from sunlight and emits thermal radiation as infrared light. In the long run, Earth radiates the same amount of energy per second as it absorbs, because the amount of thermal radiation emitted depends upon temperature: If Earth absorbs more energy per second than it radiates, Earth heats up and the thermal radiation will increase, until balance is restored; if Earth absorbs less energy than it radiates, it cools down and the thermal radiation will decrease, again until balance is restored. Atmospheric CO2 absorbs some of the energy radiated by the ground, but it emits itself thermal radiation: For example, in some wavelengths the atmosphere is totally opaque due to absorption by CO2; at these wavelengths, looking at Earth from outer space one would not see the ground, but the atmospheric CO2, and hence its thermal radiation—rather than the ground's thermal radiation. Had the atmosphere been at the same temperature as the ground, this would not change Earth's energy budget; but since the radiation is emitted from atmosphere layers that are cooler than the ground, less radiation is emitted. As CO2 content of the atmosphere increases due to human activity, this process intensifies, and the total radiation emitted by Earth diminishes; therefore, Earth heats up until the balance is restored.
Radiation absorption by carbon dioxide
CO2 absorbs the ground's thermal radiation mainly at wavelengths between 13 and 17 micron. At this wavelength range, it is almost solely responsible for the attenuation of radiation from the ground. The amount of ground radiation that is transmitted through the atmosphere in each wavelength is related to the optical depth of the atmosphere at this wavelength, OD, by:
T = e − O D {\displaystyle T=e^{-OD}}
The optical depth itself is given by Beer–Lambert law:
O D ( y ) = σ ∫ y ∞ n ( y ′ ) d y ′ {\displaystyle OD(y)=\sigma \int _{y}^{\infty }n(y^{\prime })dy^{\prime }}
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