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The infrared atmospheric window is the overall dynamic property of the earth's atmosphere, taken as a whole at each place and occasion of interest, that lets some infrared radiation from the cloud tops and land-sea surface pass directly to space without intermediate absorption and re-emission, and thus without heating the atmosphere. It cannot be defined simply as a part or set of parts of the electromagnetic spectrum, because the spectral composition of window radiation varies greatly with varying local environmental conditions, such as water vapour content and land-sea surface temperature, and because few or no parts of the spectrum are simply not absorbed at all, and because some of the diffuse radiation is passing nearly vertically upwards and some is passing nearly horizontally. A large gap in the absorption spectrum of water vapor, the main greenhouse gas, is most important in the dynamics of the window. Other gases, especially carbon dioxide and ozone, partly block transmission.
One should take care to distinguish between the atmospheric window and the spectral window. An atmospheric window is a dynamic property of the atmosphere, while the spectral window is a static characteristic of the electromagnetic radiative absorption spectra of many greenhouse gases, including water vapour. The atmospheric window tells what actually happens in the atmosphere, while the spectral window tells of one of the several abstract factors that potentially contribute to the actual concrete happenings in the atmosphere.
It is also important to distinguish between the terms window radiation and radiation of window wavelength (window wavelength radiation). Window radiation is radiation that actually passes through the atmospheric window. Non-window radiation is radiation that actually does not pass through the atmospheric window. Window wavelength radiation is radiation that, judging only from its wavelength, potentially might or might not, but is likely to pass through the atmospheric window. Non-window wavelength radiation is radiation that, judging only from its wavelength, is unlikely to pass through the atmospheric window. The difference between window radiation and window wavelength radiation is that window radiation is an actual component of the radiation, determined by the full dynamics of the atmosphere, taking in all determining factors, while window wavelength radiation is merely theoretically potential, defined only by one factor, the wavelength.
The importance of the infrared atmospheric window in the atmospheric energy balance was discovered by George Simpson in 1928, based on G. Hettner's 1918 laboratory studies of the gap in the absorption spectrum of water vapor. In those days, computers were not available, and Simpson notes that he used approximations; he writes: "There is no hope of getting an exact solution; but by making suitable simplifying assumptions . . . ."  Nowadays, accurate line-by-line computations are possible, and careful studies of the infrared atmospheric window have been published.
The infrared atmospheric window is a path from the land-sea surface of the earth to space. It separates two radiative components, window and non-window radiation, that are not of the kind that have kinetics suitable for description by the Beer-Lambert law. The window radiation and the non-window radiation from the land-sea surface are not defined in the terms that are necessary for the application of the Beer-Lambert Law. It would therefore be a logical and conceptual error to try to apply the Beer-Lambert Law either to window or non-window radiation considered separately.
The reason for this is that the window and non-window radiation have already been conditioned by the Beer-Lambert Law and the law cannot validly be re-applied to its own products. Logically, the Beer-Lambert Law applies to radiation of which the origin is known but the destination is unknown. Such is not the case for window and non-window radiation. Logically, it is part of the definition of window radiation that its destination is known, namely that it is destined to go to space, and likewise, by definition the destination of non-window radiation is known to be entire absorption by the atmosphere. Thus it makes sense to state the precise spectral distribution and spatial, especially altitudinal, distribution of locations of absorption of non-window radiation in the atmosphere. But none of those locations can be beyond the atmosphere; by definition, non-window radiation has zero probability of escaping absorption by the atmosphere; all of the locations of absorption are within the atmosphere. Radiation that can be described by the Beer-Lambert Law can partly escape absorption by the medium of interest; the law tells just how much that part is. This is a deep conceptual point that distinguishes the kinetic description of window and non-window radiation from the kinetic description of the kind of radiation that is covered by the Beer-Lambert Law.
Non-window radiation is by definition absorbed by the atmosphere, and its energy is thereby transduced into kinetic energy of atmospheric molecules. That kinetic energy is then transferred according to the usual dynamics of atmospheric energy transfer.
These kinetic principles for window and non-window radiation arise in the light of the definition of the atmospheric window as a dynamic property of the whole atmosphere, logically distinct from the electromagnetic spectral window.
The infrared absorptions of the principal natural greenhouse gases are mostly in two ranges. At wavelengths longer than 14 µm (micrometres), gases such as CO2 and CH4 (along with less abundant hydrocarbons) absorb due to the presence of relatively long C-H and carbonyl bonds, as well as water (H2O) vapor absorbing in rotation modes. The bonds of H2O and NH3 absorb at wavelengths shorter than 8 µm. Except for the bonds in O3, no bonds between carbon, hydrogen, oxygen and nitrogen atoms absorb in the interval between about 8 and 14 µm, though there is weaker continuum absorption in that interval.
Over the Atlas Mountains, interferometrically recorded spectra of outgoing longwave radiation show emission that has arisen from the land surface at a temperature of about 320 K and passed through the atmospheric window, and non-window emission that has arisen mainly from the troposphere at temperatures about 260 K.
Over the Ivory Coast, interferometrically recorded spectra of outgoing longwave radiation show emission that has arisen from the cloud tops at a temperature of about 265 K and passed through the atmospheric window, and non-window emission that has arisen mainly from the troposphere at temperatures about 240 K.
This means that, at the scarcely absorbed continuum of wavelengths (8 to 14 µm), the radiation emitted, by the earth's surface into a dry atmosphere, and by the cloud tops, mostly passes unabsorbed through the atmosphere, and is emitted directly to space; there is also partial window transmission in far infrared spectral lines between about 16 and 28 µm. Clouds are excellent emitters of infrared radiation. Window radiation from cloud tops arises at altitudes where the air temperature is low, but as seen from those altitudes, the water vapor content of the air above is much lower than that of the air at the land-sea surface. Moreover, the water vapour continuum absorptivity, molecule for molecule, decreases with pressure decrease. Thus water vapour above the clouds, besides being less concentrated, is also less absorptive than water vapour at lower altitudes. Consequently, the effective window as seen from the cloud-top altitudes is more open, with the result that the cloud tops are effectively strong sources of window radiation; that is to say, in effect the clouds obstruct the window only to a small degree (see another opinion about this, proposed by Ahrens (2009) on page 43).
Without the infrared atmospheric window, the Earth would become much too warm to support life, and possibly so warm that it would lose its water as Venus did early in solar system history. Thus, the existence of an atmospheric window is critical to Earth remaining a habitable planet.
In recent decades, the existence of the infrared atmospheric window has become threatened by the development of highly unreactive gases containing bonds between fluorine and either carbon or sulfur. The "stretching frequencies" of bonds between fluorine and other light nonmetals are such that strong absorption in the atmospheric window will always be characteristic of compounds containing such bonds. This absorption is strengthened because these bonds are highly polar due to the extreme electronegativity of the fluorine atom. Bonds to other halogens also absorb in the atmospheric window, though much less strongly.
Moreover, the unreactive nature of such compounds that makes them so valuable for many industrial purposes means that they are not removable in the natural circulation of the Earth's atmosphere. It is estimated, for instance, that perfluorocarbons (CF4, C2F6, C3F8) can stay in the atmosphere for over fifty thousand years, a figure which may be an underestimate given the absence of natural sources of these gases.
This means that such compounds have an enormous global warming potential. One kilogram of sulfur hexafluoride will, for example, cause as much warming as 23 tonnes of carbon dioxide over 100 years. Perfluorocarbons are similar in this respect, and even carbon tetrachloride (CCl4) has a global warming potential of 1800 compared to carbon dioxide.
Efforts to find substitutes for these compounds are still going on and remain highly problematic.