Depending on particle size distribution, the spectral dependence of the aerosol optical thickness is given approximately by
where is the optical thickness at wavelength , and is the optical thickness at the reference wavelength . In principle, if the optical thickness at one wavelength and the Ångström 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 Ångström 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 and taken at two different wavelengths and respectively, the Ångström exponent is given by
The Ångström exponent is inversely related to the average size of the particles in the aerosol: the smaller the particles, the larger the exponent. Thus, Ångström exponent is a useful quantity to assess the particle size of atmospheric aerosols or clouds, and the wavelength dependence of the aerosol/cloud optical properties. For example, cloud droplet, usually with large sizes and thus very smaller Ångström exponent (nearly zero), is spectrally neutral, which means, e.g., the optical depth does not change with wavelength. This exponent is now routinely estimated by analyzing radiation measurements acquired on Earth Observation platforms, such as AErosol RObotic NETwork, or AERONET.
- 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.