## Papers on the theory of CO2 absorption properties

Posted by Ari Jokimäki on April 3, 2010

This is a list of papers presenting the theoretical work on the CO2 absorption properties. The list is not complete, and will most likely be updated in the future in order to make it more thorough and more representative.

**UPDATE** (December 23, 2010): Stull *et al.* (1964) added.

Collision-induced absorption by CO_{2} in the far infrared: Analysis of leading-order moments and interpretation of the experiment – Kouzov & Chrysos (2009) *“The diagrammatic theory, developed recently by the authors [Phys. Rev. A 74, 012732 (2006)], is applied to binary collision-induced properties, with emphasis on induced dipole moments. Assuming rototranslational dynamics to be classical and using irreducible spherical tensor formalism, exact analytical formulas are worked out for the two leading order spectral moments of a collision-induced band by two interacting linear molecules. The formulas are applied to the far infrared absorption by CO _{2}-CO_{2}, and permit interpretation of the experiment. This study provides evidence of the adequacy of the electrostatic induction mechanism, provided that hitherto missing vibrational terms of static polarizability are considered.”*

Exact Low-Order Classical Moments in Collision-Induced Bands by Linear Rotors: CO_{2}-CO_{2} – Chrysos *et al.* (2008) *“Exact and general analytic expressions are reported for the integrated intensity and the width of collision-induced absorption (CIA) and collision-induced scattering (CIS) bands by gases of centrosymmetric linear molecules. These expressions provide significant insight and allow assignment of partial second moments to the degrees of freedom of the colliding molecules. The expressions are applied to ambient CO _{2}, whose collisional spectra are reputed to be useful probes for terrestrial and planetary atmospheres. Compelling evidence of the substantial role of hitherto missing polarization and polarizability mechanisms is provided and is in remarkable agreement with experimental observation. Our findings allow the long-overdue simple interpretation of CIA and CIS by CO_{2}-CO_{2} without the need to resort to short-range interactions to offset the discrepancies between theory and experiment.”*

Spectra calculations in central and wing regions of CO_{2} IR bands between 10 and 20 μm. I: model and laboratory measurements – Niro *et al.* (2004) *“In order to analyze the spectra, a theoretical model based on the energy corrected sudden approximation is proposed which accounts for line-mixing effects within the impact approximation. This approach uses the model and associated parameters built previously to model Q branches (JQSRT 1999;61:153) but extends it by now including all P, Q, and R lines. No adjustable parameters are used and fundamental properties of the collisional relaxation operator are verified by using a renormalization procedure. Comparisons between measured and calculated spectra confirm that neglecting line-mixing (Lorentzian model) leads to an overestimation of absorption by up to three orders of magnitude in the far wings. On the other hand, the proposed approach leads to satisfactory results both in regions dominated by contributions of local lines and in the wing: measured spectra are correctly modeled over a range where absorption varies by more than four orders of magnitude. The largest discrepancies, which appear about 150 cm ^{−1} from the ν_{2} center, can be due to finite duration of collisions effects or to uncertainties in the experimental determination of very weak absorption.”*

Semiclassical modeling of infrared pressure-broadened linewidths: A comparative analysis in CO_{2}–Ar at various temperatures – Buldyreva & Chrysos (2001) *“A novel semiclassical approach, which makes use of the exact trajectory implemented within the Robert–Bonamy formalism, is employed for modeling infrared pressure-broadened linewidths. As a prototype, the carbon dioxide molecule perturbed by argon is examined in the temperature range 160–760 K, for which various measurements and computations are available. For a meaningful comparison with previous theoretical works done with both semiclassical and quantum approaches, the ab initio intermolecular potential surface of Parker et al. [J. Chem. Phys. 64, 1668 (1976)] is used. Our values are found to be in agreement with up-to-date experimental data at all temperatures studied.”*

A Study of the Radiative Effects of the 9.4- and 10.4-Micron Bands of Carbon Dioxide – Kratz *et al.* (1991) *“The potential radiative impact of the relatively weak 9.4- and 10.4-μm bands of CO _{2} is investigated. Line-by-line calculations are employed as a standard against which to compare the accuracy of laboratory data, narrow-band models, and broadband models. A comparison of the line-by-line calculations to laboratory data demonstrates that the line-by-line procedure and laboratory data typically yield comparable results; however, there are cases of substantial disagreement between the line-by-line results and the laboratory data. … Clear-sky flux calculations demonstrate that for projected increases of CO_{2} the impact of the 9.4- and 10.4-μm bands is comparable to that attributed to projected increases of tropospheric ozone.”* [Full text]

**Approximate Methods for Finding CO _{2} 15-μm Band Transmission in Planetary Atmospheres – Crisp (1986)**

*“The CO*[Full text]

_{2}15-μm band provides an important source of thermal opacity in the atmospheres of Venus, Earth, and Mars. Efficient and accurate methods for finding the transmission in this band are therefore needed before complete, self-consistent physical models of these atmospheres can be developed. In this paper we describe a hierarchy of such methods. The most versatile and accurate of these is an “exact” line-by-line model (Fels and Schwarzkopf, 1981). Other methods described here employ simplifying assumptions about the structure of the 15-μm band which significantly improve their efficiency. … Physical band models based on the Goody (1952) random model compose the first class of approximate methods. These narrow-band models include a general random model and other more efficient techniques that employ the Malkmus (1967) line-strength distribution. Two simple strategies for including Voigt and Doppler line-shape effects are tested. We show that the accuracy of these models at low pressures is very sensitive to the line-strength distribution as well as the line shape. The second class of approximate methods is represented by an exponential wideband model. This physical band model is much more efficient than those described above, since it can be used to find transmission functions for broad sections of the CO_{2}15-μm band in a single step. When combined with a simple Voigt parameterization, this method produces results almost as accurate as those obtained from the more expensive narrow-band random models. The final class of approximate methods tested here includes the empirical logarithmic wideband models that have been used extensively in climate-modeling studies (Kiehl and Ramanathan, 1983; Pollack et al., 1981). These methods are very efficient, but their range of validity is more limited than that of the other methods tested here. These methods should therefore be used with caution.”The Infrared Transmittance of Carbon Dioxide – Stull *et al.* (1964) *“The infrared transmittance of carbon dioxide has been calculated over a wide range of path lengths, pressures, and temperatures from 500 to 10,000 cm ^{-1}. Values of the transmittance are given at intervals of 2.5 cm^{-1}. In addition, transmittance values are also given which have been averaged over larger intervals. All contributing spectral lines whose relative intensity is greater than 10^{-8} that of the strongest line in any particular band have been included in the calculation. In addition, the contributions from the eight major isotopic species have been included. The calculation of the vibrational energy levels included terms through the third power of the vibrational quantum number and also the effects of Fermi resonance. The final transmittance tables were generated using the quasi-random model of molecular band absorption.”* V. Robert Stull, Philip J. Wyatt, and Gilbert N. Plass, Applied Optics, Vol. 3, Issue 2, pp. 243-254 (1964), doi:10.1364/AO.3.000243.

**The Temperature Effect on the Absorption of 15 Microns Carbon-Dioxide Band – Sasamori (1959)** *“Absorptions of a parallel beam of radiation by the 15 μ carbon-dioxide band were calculated for different temperature conditions of the absorbing gas. With use of the results the temperature effect due to the change of the line intensity in the band was examined. It is shown that for short path lengths the temperature effect is governed mainly by the change of the relatively strong lines in the band and that the changes of the weaker lines in the band become important with increasing path length. In the spectral region distant from band center, because of the rapid change of the line intensity, the effect of the temperature change is as appreciable as the pressure effect.”* [Full text]

The influence of the 15μ carbon-dioxide band on the atmospheric infra-red cooling rate – Plass (1956) *“The upward and downward radiation flux and cooling rate are calculated for the 15μ band of carbon dioxide. Results are obtained for three different carbon-dioxide concentrations from the surface of the earth to 75 km, and for six frequency intervals covering the band. The infra-red absorption measurements of Cloud (1952) are used for calculations, on a high-speed electronic computer, by a method which takes account of the pressure and Doppler broadening, the overlapping of the spectral lines, and the variation of the intensity and half-width of the spectral lines with temperature and pressure. The numerical integration is performed over intervals that are never larger than 1 km and average values over layers are not used. The cooling rate for the present atmospheric carbon-dioxide concentration is greater than 1°C/day from 24 km to 70 km and is greater than 4°C/day from 38 km to 55 km. The sum of the ozone and carbon-dioxide cooling rates is greater than 4°C/day from 33 km to 57 km and agrees reasonably well with the heating due to ozone absorption. The results for different carbon-dioxide concentrations indicate that the average temperature at the surface of the earth would rise by 3.6°C if the carbon-dioxide concentration were doubled and would fall by 3.8°C if the carbon-dioxide concentration were halved, on the assumption that nothing else changed to affect the radiation balance.”*

The Effect of Pressure Broadening of Spectral Lines on Atmospheric Temperature – Gilbert & Plass (1950) A paper that shows one reason why carbon dioxide absorption bands are not saturated. *“Pressure broadening causes lines in infrared absorption bands to have considerably greater half-widths in the lower layers of a planetary atmosphere than in the upper layers. As a result, radiation emitted upward from the wings of lines in the lower atmosphere is not strongly absorbed by the upper layers. Such radiation is thus free to escape to the cosmic cold.”* [For full text, click PDF or GIF links in the abstract page.]

The artificial production of carbon dioxide and its influence on temperature – Callendar (1938) *“By fuel combustion man has added about 150,000 million tons of carbon dioxide to the air during the past half century. The author estimates from the best available data that approximately three quarters of this has remained in the atmosphere. The radiation absorption coefficients of carbon dioxide and water vapour are used to show the effect of carbon dioxide on sky radiation. From this the increase in mean temperature, due to the artificial production of carbon dioxide, is estimated to be at the rate of 0.003°C. per year at the present time. The temperature observations a t zoo meteorological stations are used to show that world temperatures have actually increased at an average rate of 0.005°C. per year during the past half century.”*

**On the Influence of Carbonic Acid in the Air Upon the Temperature of the Ground – Arrhenius (1896)** There’s no abstract, but I’ll just quote one passage on the absorption calculations. *“With the aid of Table III. we may calculate the absorbed fraction of any ray, and then sum up the total absobed heat and determine how great a fraction it is of the total radiation. In this way we find for our example path (air-mass) 1.61. In other words, the total absorbed part of the whole radiation is just as great as if the total radiation traversed the quantities 1.61 of aqueous vapour and of carbonic acid.”* [Full text]

### Closely related

On the significance of the shortwave CO_{2}-absorption in investigations concerning the CO_{2}-theory of climatic change – Gebhart (1967) *“Hitherto absorption of solar radiation has completely been disregarded when investigating how a CO2 increase of the atmosphere modifies the earth’s climate. It can be shown that shortwave and longwave influence of a higher CO2 concentration counteract each other. The temperature change at the earth’s surface is ΔT=+1.2°C when the present concentration is doubled.”*

## Mike said

Terrific list, I’ll be reading my way through these.

Cheers

## Mike said

Also, thanks for the 1896 Arrhenius paper – I’ve been trying to track this down, given it’s importance in the history of science. We may look back at this paper with the same reverence as Einsteins Special/General relativity papers. That the implications where noted over a century ago is worth noting.

## Thomas said

Excellent idea. A long missed resource. It’s so terribly time-consuming to dig out relevant papers if you are not an expert in a particular field.

## Ari Jokimäki said

Well, it would be nice to be an expert. At least this list would have been much easier to do. It was very difficult to find papers for this list and I’m certain there are lot of papers still to be added.

## AGW Observer: papers on “denialism” and de-bunked sceptic research « Watching the Deniers said

[…] of the most relevant papers on climate science organised by topic. Thus, if you want to see the actual science on CO2′s absorption properties, Ari has brought together the most relevant piece of research […]

## Ari Jokimäki said

I added Stull

et al.(1964).