Spectrochimica Acta, Vol. 51A, No. 3, pp. 415-417. 1995
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The roles of carbon dioxide and water vapour in warming and cooling the Earth's troposphere
Department of Chemistry, Imperial College London, South Kensington, London SW7 2AY, U.K.
(Received 5 January 1994; in revised form 5 April 1994; accepted 8 April 1994)
The currently perceived mechanism of operation [1-3] of the so-called greenhouse gases, carbon dioxide and water, is dependent upon the atmosphere behaving as an emitter of continuous radiation as would a cavity of the same temperature and upon vibrationally excited carbon dioxide and water molecules being deactivated mainly by the emission of fluorescence radiation at all altitudes. This article maintains that carbon dioxide and gaseous water molecules cannot behave as cavity radiators and presents evidence for vibrational fluorescence of carbon dioxide occurring substantially only at the very low pressures (lower than 0.1 Pa) found in the thermosphere at altitudes above 95 km. Substantial concentrations of water vapour exist only in the troposphere where pressures are too great to allow significant emission of vibrational fluorescence radiation.
The Earth's surface is warmed by the absorption of the fraction of solar radiation which penetrates the atmosphere. The heated Earth warms the atmosphere by a combination of the processes of convection and the emission of terrestrial cavity-type radiation over a broad wavelength range which is dependent upon the surface temperature. The fraction of the emitted radiation within the approximate wavelength range 7.5–14 µm escapes into space unless it is reflected by clouds or absorbed by particulate matter. At sea level the lowest 30 m of the atmosphere usually contain sufficient water vapour and carbon dioxide to absorb totally the remainder of the radiation emitted by the Earth's surface . This initial absorption of terrestrial radiation contributes to the eventual warming of the atmosphere at altitudes up to around 16 km, the upper limit of the troposphere in which the Earth's weather occurs. There is an apparent general acceptance [1-3] that an increase in atmospheric carbon dioxide content will lead to a significant enhancement of the warming of the atmosphere. This conclusion is based upon the assumptions that the atmosphere behaves as a continuous emitter of broad spectrum cavity-type radiation as it re-emits the initially absorbed terrestrial radiation and that vibrational fluorescence of carbon dioxide occurs substantially at all altitudes. A fraction of this re-emitted radiation, that which travels in a direction away from the Earth, either escapes through the 7.5–14 µm window or, if it has wavelengths outside that range, is absorbed and emitted many more times in a reverse cascade process  and contributes to atmospheric cooling. An increase in the atmospheric carbon dioxide level would hinder the reverse cascade process and would possibly cause an enhancement of atmospheric warming. It is claimed [3, 4] that the temperature of the Earth's atmosphere has risen by as much as 0.8°C (0.3%) over the last 100 years. Such an increase is arguably well within the limits of error of such a measurement and, even if it is a real effect, may be due to causes unconnected with variations in the carbon dioxide concentration. During the same time the carbon dioxide content of the atmosphere  has increased significantly by 25%, mainly in the last 25 years.
Computer models of the climate give rise to predictions [3, 4] of significant temperature increases of between 2 and 4.5°C which might result from further increases in the carbon dioxide content of the atmosphere. When carbon dioxide and water molecules absorb terrestrial radiation the populations of their vibrationally excited states are rapidly reduced to their equilibrium values which are governed by the magnitudes of the respective Boltzmann factors at the ambient temperature. The values of the Boltzmann factors for the anti-symmetric stretching vibration of carbon dioxide (2349 cm-1) at 288 K (mean temperature of the atmosphere at sea level ) and 217 K (mean temperature at an altitude  of 16 km) are 8 × 10-6 and 1.7 × 10-7, respectively. The corresponding figures for the bending modes (667 cm-1) are 0.036 and 0.012. The equilibria are established mainly by collisional processes at the pressures which exist in the troposphere (10–100 kPa). The radiative lifetimes of vibrationally excited states of gaseous molecules are not short enough to allow fluorescence emission to compete effectively with collisional deactivation unless the total pressure is sufficiently low . The half-life of the first excited state of the anti-symmetric stretching mode of carbon dioxide  is 10 µs at 1 atm pressure. At sea level the mean free time  before a molecule undergoes a collision is 0.1 ns so that a molecule would participate in 105 collisions during one radiative half-lifetime. At an altitude of 16 km that figure reduces to 104 collisions. At both altitudes radiative return to the ground state is insignificant. The excess of vibrational energy is converted to the kinetic energy of all the atmospheric components as is evident from the warming which occurs. Such an assemblage of gaseous molecules cannot radiate energy over a continuous range of wavelengths as would a cavity with the same temperature. The main components of the warmed atmosphere, N2 and O2, are quantum mechanically forbidden from participating in radiative interactions in the infra-red region. The infra-red spectrum of carbon dioxide, even at 1 atm pressure of the gas, consists of discrete bands . Any exchange of energy between molecules in the troposphere or between the atmosphere and the cooling Earth is almost entirely non-radiative. A major contribution to the cooling of the atmosphere results from the collisional transfer of kinetic energy from the molecules of the heated atmosphere to the cooling Earth's surface as radiation escapes through the 7.5–14 µm window. Rodgers et al.  report that local thermodynamic equilibria, governed by the values of the appropriate Boltzmann factors, between vibrationally excited and ground states of carbon dioxide exist at altitudes below 95 km. This indicates that only in the thermosphere (which begins at around 88 km above the Earth's surface) does significant vibrational fluorescence occur. These figures are in good agreement with those given by Dickenson  who reports that local thermodynamic equilibria for vibrational transitions of carbon dioxide begin to break down in the altitude range from 80 to 93 km. The water content of the atmosphere is restricted to the troposphere, at which pressures the majority of any vibrationally excited states would be collisionally deactivated. Vibrational fluorescence of water molecules cannot be considered as contributing significantly to the cooling of the troposphere.
The implication of this re-interpretation of the roles of carbon dioxide and water in atmospheric warming and cooling is that any increase in the carbon dioxide content of the atmosphere will not affect the average temperature of the troposphere. Measurements of the Earth's temperature made by instruments carried by a network of satellites  since 1978 show that random variations of as much as ±0.5°C occur, some changes of as much as 0.5°C occurring over periods of only two weeks. It would seem inadvisable to attribute variations of this magnitude over the course of a century to the greenhouse effect. A proper scientific conclusion would be that any effects of the 25% increase in atmospheric carbon dioxide on the Earth's average surface temperature cannot be distinguished from the background of natural variability. All the energy that can be absorbed by the atmosphere is being absorbed under present conditions. Any additional carbon dioxide cannot alter the 100% absorption of terrestrial radiation, nor will it interfere with the main mechanism of cooling which is the direct radiative loss of energy from the Earth via the 7.5–14 µm window.
Acknowledgements – The author thanks Professor S. F. Mason, F.R.S., for valuable discussion of the subject matter and Dr K. Shine for his constructive criticism of a previous version of this paper.
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