Angstrom exponent and bimodal aerosol size distributions

Power laws have long been used to describe the spectral dependence of aerosol extinction, and the wavelength exponent of the aerosol extinction law is commonly referred to as the Angstrom exponent. The Angstrom exponent is often used as a qualitative indicator of aerosol particle size, with values greater than 2 indicating small particles associated with combustion byproducts, and values less than 1 indicating large particles like sea salt and dust. In this study, we investigate the relationship between the Angstrom exponent and the mode parameters of bimodal aerosol size distributions using Mie theory calculations and Aerosol Robotic Network (AERONET) retrievals. We find that Angstrom exponents based upon seven wavelengths (0.34, 0.38, 0.44, 0.5, 0.67, 0.87, and 1.02 mm) are sensitive to the volume fraction of aerosols with radii less then 0.6 mm but not to the fine mode effective radius. The Angstrom exponent is also known to vary with wavelength, which is commonly referred to as curvature; we show how the spectral curvature can provide additional information about aerosol size distributions for intermediate values of the Angstrom exponent. Curvature also has a significant effect on the conclusions that can be drawn about two-wavelength Angstrom exponents; long wavelengths (0.67, 0.87 mm) are sensitive to fine mode volume fraction of aerosols but not fine mode effective radius, while short wavelengths (0.38, 0.44 mm) are sensitive to the fine mode effective radius but not the fine mode volume fraction.