Angstrom exponent

Short description: Mathematical parameter

The Angstrom exponent[1][2] or Ångström exponent[3][4] or absorption Ångström exponent is a parameter that describes how the optical thickness of an aerosol typically depends on the wavelength of the light.

## Contents

* 1 Definition
* 2 Significance
* 3 Determining the exponent
* 4 See also
* 5 References
* 6 External links

## Definition

In 1929, the Swedish physicist Anders K. Ångström found that the optical thickness of an aerosol depends on the wavelength of light according to the power law

τλτλ0=(λλ0)−α

where τλ is the optical thickness at wavelength λ, and τλ0 is the optical thickness at the reference wavelength λ0.[5][4] The parameter α is the Angstrom exponent of the aerosol.

## Significance

The Angstrom exponent is inversely related to the average size of the particles in the aerosol: the smaller the particles, the larger the exponent. For example, cloud droplets are usually large, and thus clouds have very small Angstrom exponent (nearly zero), and the optical depth does not change with wavelength. That is why clouds appear to be white or grey.

This relation can be used to estimate the particle size of an aerosol by measuring its optical depth at different wavelengths.

## Determining the exponent

In principle, if the optical thickness at one wavelength and the Angstrom exponent are known, the optical thickness can be computed at a different wavelength. In practice, measurements are made of the optical thickness of an aerosol layer at two different wavelengths, and the Angstrom exponent is estimated from these measurements using this formula. The aerosol optical thickness can then be derived at all other wavelengths, within the range of validity of this formula.

For measurements of optical thickness τλ1 and τλ2 taken at two different wavelengths λ1 and λ2 respectively, the Angstrom exponent is given by

α=−log⁡τλ1τλ2log⁡λ1λ2

The Angstrom exponent is now routinely estimated by analyzing radiation measurements acquired on Earth Observation platforms, such as AErosol RObotic NETwork, or AERONET.

## See also

* Langley extrapolation

## References

1. ↑ Gregory L. Schuster, Oleg Dubovik and Brent N. Holben (2006): "Angstrom exponent and bimodal aerosol size distributions". Journal of Geophysical Research: Atmospheres, volume 111, issue D7, article D07207, pages 1-14. doi:10.1029/2005JD006328
2. ↑ Itaru Sano (2004): "Optical thickness and Angstrom exponent of aerosols over the land and ocean from space-borne polarimetric data". Advances in Space Research, volume 34, issue 4, pages 833-837. doi:10.1016/j.asr.2003.06.039
3. ↑ D. A. Lack1 and J. M. Langridge (2013): "On the attribution of black and brown carbon light absorption using the Ångström exponent". Atmospheric Chemistry and Physics, volume 13, issue 20, pages 10535-10543. doi:10.5194/acp-13-10535-2013
4. ↑ 4.0 4.1 Ji Li, Chao Liu, Yan Yin, and K. Raghavendra Kumar (2016): "Numerical investigation on the Ångström exponent of black carbon aerosol". Journal of Geophysical Research: Atmospheres, volume 121, issue 7, pages 3506-3518. doi:10.1002/2015JD024718
5. ↑ Anders Ångström (1929): "On the Atmospheric Transmission of Sun Radiation and on Dust in the Air". Geografiska Annaler, volume 11, issue 2, pages 156–166. doi:10.1080/20014422.1929.11880498

* IPCC Third Assessment Report, has extensive coverage of aerosol-climate interactions.
* Kuo-nan Liou (2002) An Introduction to Atmospheric Radiation, International Geophysics Series, No. 84, Academic Press, 583 p, ISBN 0-12-451451-0.

## External links

* Angstrom coefficient page at NASA GSFC.
* AERONET: an international network of sunphotometers measuring aerosol properties.
* Spatial distributions of the Angstrom coefficient as derived from MISR.

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