Absorption Coefficients from the Professional Literature

(c) 2014 by Barton Paul Levenson

Introduction

The Beer-Lambert-Bouguer law of radiative transfer is:

I = I₀ exp(k ρ ds)

For a one-dimensional setup (as in a radiative-convective model), you can use F and F₀ for flux density instead of irradiance.

The units for these figures can be very different. In the SI, irradiance is measured in watts of power, per square meter of area, per meter of wavelength, per steradian of solid angle (W m^-2 m^-1 sr^-1). I₀, of course, would be in the same units. k would be in units of square meters per kilogram of absorber, an "extinction cross-section." ρ would be in kilograms per cubic meter, ds in meters. For the 1-D case, F and F₀ would be in watts per square meter (W m^-2).

The product of k, ρ and ds is the optical thickness, τ:

τ = k ρ ds

The units cancel and thus optical thickness is dimensionless. For the 1-D case, as in an RCM, you'd want to multiply the optical thickness by a "diffusion factor," usually taken as ⁵/₃, to correct for the transition from three dimensions to one.

Extinction can be through either of two processes: absorption and scattering, which each have their own k figures:

k_e = k_a + k_s

For the IR, in a thin atmosphere like that of Earth or Mars (but not Venus), scattering is negligible. Thus the coefficients in this catalog are absorption coefficients.

The problem is that not everybody uses the same units. Spectroscopists notoriously prefer "wavenumber" to describe light instead of wavelength or frequency, and like it in cgs units of cm^-1. Absorption coefficients in the professional literature are given in cgs units and in SI units, as molecular cross-sections (σ) in cm², in units of reciprocal pressure times reciprocal length, as "volume" coefficients (β) of reciprocal length alone, etc., etc., etc. In this catalog I just give the original units; translation to the units you prefer is the responsibility of the reader.

Warning: Beer's Law does not apply in all cases. It requires

• a homogeneous medium
• parallel beams of light
• no scattering
• monochromatic light
• independent absorbers, and
• no phase changes

With all these restrictions, you might wonder if it ever applies in the real world. In atmospheric transfer modeling, there are ways around the difficulties; e.g., one uses thin layers of atmosphere to approximate homogeneous media. There are, of course, many radiative transfer schemes that use more sophisticated mathematical models than Beer's Law, but it still has its uses. Without further ado, here's the catalog.

Contents as of 5 December 2014

As of the above date, this catalog references 23 sources for 20 absorbers: 15 gases, 2 aerosol particles, 3 cloud particles. These break down as follows:

Bartko and Hanel 1968

These figures are for very high altitudes on Venus, at perhaps p = 100 Pa, T = 230 K.

Bartko F, Hanel RA 1968. Non-gray equilibrium temperature distributions above the clouds of Venus. ApJ 151, 365-378.

Chou and Lee 1996

These figures are presumably for stratosphere conditions, for the UV and visible range.

Chou M-D, Lee K-T 1996. Parameterizations for the Absorption of Solar Radiation by Water Vapor and Ozone. J. Atm. Sci. 53, 1203-1208.

Essenhigh 2001

These band figures are for sea-level pressure, at 15 °C. Essenhigh is a chemical engineer who argues against the reality of global warming, but there's nothing wrong with his math. "Which seats him in the crazy but not stupid section."

Essenhigh 2001. In Box: Robert Essenhigh Replies. Chemical Innovation 31, 62-64 (Nov. 2001).

Evans 2001

observes that the mass absorption coefficient for CO₂ at 1000 mb pressure and 296 K temperature at a wavenumber of 700.39 cm^-1 is 16.3 m² kg^-1. The wavenumber corresponds to a wavelength of 14.278 μ.

Evans F 2001. Week 2: September 3-7. Beer’s Law and Thermal Radiative Transfer. http://nit.colorado.edu/atoc5560/week2.pdf, accessed 3/5/2007.

Gonima 1972

Gonima L 1972. Validation of a radiation model for estimation of longwave net radiation at the surface. Clim. Res. 2, 55-63.

Griffith et al. 2003

cites methane absorption coefficients, presumably under Titan conditions (pressure 0-1.5 times Earth's sea level, temperatures of 70-140 K) at particular wavelengths.

Griffith CA, Owen T, Geballe TR, Rayner J, Rannou P 2003. Evidence for the Exposure of Water Ice on Titan’s Surface. Science 300, 628-630.

Hanel et al. 1963

Hanel RA, Bandeen WR, Conrath BJ 1963. The Infrared Horizon of the Planet Earth. J. Atmos. Sci. 20, 73-86.

Hanst et al. 1975

These figures for assorted air pollutants are given for single wavenumbers, presumably at sea-level conditions.

Hanst PL, Spiller LL, Watts DM, Spence JW, Miller MF 1975. Infrared Measurement of Fluorocarbons, Carbon Tetrachloride, Carbonyl Sulfide, And Other Atmospheric Trace Gases. J. Air Pollution Control Assn. 25, 1220-1226.

Kondratiev and Niilisk 1960

These figures are for water vapor for 1 atm pressure and 300 K. The pressure exponent used is 0.8.

Kondratiev KY, Niilisk HI 1960. On the question of carbon dioxide heat radiation in the atmosphere. Pure and Appl. Geophys. 46, 216-230.

Larsen et al. 2007

found an SI absorption coefficient of 119 m² kg^-1 for water clouds in the thermal infrared. They also found an assymetry factor g = 0.83 and single-scattering albedo ω = 0.694.

Larsen VE, Kotenberg KE, Wood NB 2007. Derivation and Tests of the GCSS Analytic Longwave Radiation Formula. Mon. Weather Rev. 135, 689-699.

Lubin 1994

found an absorption coefficient in the "mid-infrared" of 65 m² kg^-1 for Antarctic maritime clouds, lower than figures previously used in many climate models.

Lubin D 1994. Infrared Radiative Properties Of the Maritime Antarctic Atmosphere. J. Clim. 7, 121–140.

Lundt and Kinnunen 1976

found an absorption coefficient of 0.145 ± 0.008 m² g^-1 for water vapor at a wavelength of 27.97 μ. They noted that there is negligible absorption from other agents at this wavelength.

Lundt PB, Kinnunen, L 1976. An application of a water vapour laser. J. Physics E: Scientific Instruments 9, 528-529.

McDade 2007

gives the absorption coefficient for ozone (O₃) as 10 m² kg^-1 at a wavenumber of 1110 cm^-1. This corresponds to a wavelength of 9.009 μ.

McDade I 2007. EATS 4230 & ESS 5230, Remote Sensing of the Atmosphere, Assignment #2, Distributed Sunday 18th February 2007 - due Friday 2nd March 2007. http://www.yorku.ca/mcdade/eats4230/ Assignment%202%202007.pdf, accessed 3/05/2007.

Okabe 1978

gives the absorption cross-section of molecular nitrogen (N₂) as σ = 2 x 10^-21 cm² at wavelengths in the far-ultraviolet of 0.116-0.145 μ.

Okabe H 1978. Photochemistry of Small Molecules. NY: Wiley-Interscience.

Phillips 1998

discusses the parameters used in the UK Meteorological Office climate model HadAm1 as of 1993. It listed absorption coefficients, in the thermal infrared, of 130 m² kg^-1 for liquid water clouds and 65 m² kg^-1 for ice clouds. It also noted that effective radii of 7 and 30 μ were used for water and ice clouds, respectively.

Phillips T 1998. United Kingdom Meteorological Office: Model UKMO HadAM1 (2.5x3.75 L19) 1993. http://www-pcmdi.llnl.gov/projects/modeldoc/amip/36ukmo.html, accessed 12/05/2014.

Rinsland et al. 1981

gives absorption coefficients for molecular nitrogen (N₂) at various wavenumbers under stratosphere conditions, presumably about 20,000 Pa pressure, and T = 230 K. The zenith angle as given as 94°, with a "tangent altitude" of 21.8 km. Nitrogen was assumed to have a volume mixing ratio of 0.781.

Rinsland CP, Smith MA, Russell III JM, Park JH, Farmer CB 1981. Stratospheric measurements of continuous absorption near 2400 cm^-1. Appl. Optics 20, 4167-4171.

Roberts et al. 1976

found a wavenumber-dependent absorption coefficient for water vapor, both the molecule and the temporary "dimer" caused by collisions. ν is used here for wavenumber in cm^-1 because I can't find the HTML for the traditional ν-tilde.

k(ν, 296^K) = a + b exp(-β ν)

a = 4.2 cm² g^-1
b = 5588 cm² g^-1
β = 0.00787 cm, and

k(ν, T) = k(ν, 296^K) exp [T₀ (1/T - 1/296)]

where T₀ = 1800 K.

Running through an example, at the wavelength of 10 μ, the wavenumber would be 1000 cm^-1, and k_a would be 6.33 cm² g^-1.

Roberts E, Selby JEA, Biberman IM 1976. Infrared Continuum Absorption by Atmospheric Water Vapor in the 8-12 μm Window. Appl. Opt. 15, 2085-2090.

Tarasova and Fomin 2000

gives visible and near-infrared absorption coefficients for H₂O vapor from a correlated-k approach.

Tarasova TA, Fomin BA 2000. Solar Radiation Absorption due to Water Vapor: Advanced Broadband Parameterizations. J. Appl. Meteorol. 39, 1947-1951.

Varanasi and Nemtchinov 1994

gives molecule cross-sections for the CFC-12 molecule (dichlorodifluoromethane, a chlorofluorocarbon).

Varanasi P, Nemtchinov V 1994. Thermal infrared absorption coefficients of CFC-12 at atmospheric conditions. J. Quant. Spectroscopy Rad. Transfer 51, 679-687.

Verstraete 1986

gives absorption coefficients of smoke as 1500 to 12,000 m² kg^-l, and of dust as 500 to 6000 m² kg^-l, depending on the particle size spectrum. Presumably this is for the visible light range. Geometric means would be 4200 and 1700 for smoke and dust, respectively.

Verstraete MM 1986. NCAR/TN-264 + IA, NCAR TECHNICAL NOTE, A Glossary on the Environmental Impact of a Nuclear War. National Center for Atmospheric Research, Boulder CO, p. 1.

Weissler et al. 1952

gives absorption coefficients for nitrogen in the far-ultraviolet, noting that it appears to obey Beer's Law in these ranges.

Weissler GL, Lee PO, Mohr EI 1952. Absolute Absorption Coefficients of Nitrogen in the Vacuum Ultraviolet. JOSA 42, 84-90.

Werbe-fuentes et al. 2008

measured CO₂ absorption coefficients at peak wavelengths in the near infrared.

Werbe-fuentes J, Moody M, Korol O, Kading T 2008. Carbon dioxide absorption in the near infrared. http://jvarekamp.web.wesleyan.edu/public_htmlA/public_htmlA/CO2/FP-1.pdf, accessed 12/03/2014.

Yamamoto 1953

These figures are for water vapor for 1 atm pressure and 300 K.

Yamamoto G 1953. Radiative equilibrium of Earth's atmosphere (I). The grey case. Sci. Rept. Tohuku Univ., Ser. 5, Geophys. 5, No. 2.