Bimodal size distribution influences on the variation of Angstrom derivatives in spectral and optical depth space

The variation of the aerosol optical depth and its first and second spectral derivatives (a and alpha') can be largely described in terms of the spectral interaction between the individual optical components of a bimodal size distribution. Simple analytical expressions involving the separate optical components of each mode explain virtually all the features seen in spectra of the aerosol optical depth and its derivatives. Illustrations are given for a variety of measured optical depth spectra; these include comparative simulations of the diurnal behavior of alpha and alpha' spectra as well as the diurnal and general statistical behavior of alpha and alpha' as a function of optical depth (optical depth space). Each mode acts as a fixed basis vector from which much of the behavior in spectral and optical depth space can be generated by varying the extensive (number density dependent) contributions of fine and coarse mode optical depths. Departures from these basis vectors are caused by changes in aerosol type (average size and refractive index) and thus are associated with differing synoptical air masses, source trajectories or humidity conditions. Spectral parameters are very sensitive to interband errors in measured optical depth data. Third-order polynomial fits within the visible-NIR spectral region effectively filter such errors while representing the limit of useful extractable information.