Angstrom exponent

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Angström exponent is the name of the exponent in the formula that describes the dependency of the aerosol optical thickness on wavelength.

Depending on particle size distribution, the spectral dependence of the aerosol optical thickness is given approximately by

$\frac{\tau_\lambda}{\tau_{\lambda_0}}=\left (\frac{\lambda}{\lambda_0}\right )^{-\alpha}$

where $τ λ$ is the optical thickness at wavelength $λ$ , and $\tau_{\lambda_0}$ is the optical thickness at the reference wavelength $λ 0$ . In principle, if the optical thickness at one wavelength and the Angström 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 Angström 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 $\tau_{\lambda_1}\,$ and $\tau_{\lambda_2}\,$ taken at two different wavelengths $\lambda_1\,$ and $\lambda_2\,$ respectively, the Angström exponent is given by

$\alpha = - \frac{\ln \frac{\tau_{\lambda_1}}{\tau_{\lambda_2}}}{\ln \frac{\lambda_1}{\lambda_2}}\,$

The Angström exponent is inversely related to the average size of the particles in the aerosol: the smaller the particles, the larger the exponent. This exponent is now routinely estimated by analyzing radiation measurements acquired on Earth Observation platforms.