The equivalent wavelength (lambda (E)), which the aerosol optical depth (AO
D)is equal to broadband AOD (BAOD), can change in a wide range from 0.619 m
um to 1.575 mum in the usual aerosol conditions. By using the least squares
technique and some empirical corrections, a parameterized relationship of
lambda (E) with BAOD. Angstrom wavelength exponent (alpha), solar zenith an
gle (0(0)) and H2O amount is developed. Using this relationship, and based
on the strong sensitivity of BAOD on theta (0) when theta (0) > 70(-). the
broadband extinction method to derive the spectral AOD and alpha is further
proposed. As shown in comparative simulations to retrieve AOD by the prese
nt, Molineaux ct al. and Gueymard methods, the present method has the best
accuracy in most simulations using Junge, MODTRAN, log-normal and Deirmendj
ian aerosol models. A key question of the pyrheliometer method to determine
wavelength-dependent AODs is the effect of uncertainty in the aerosol size
distribution. It is found that the AOD solution around lambda (E) is less
sensitive to the uncertainty. The wavelength exponent alpha is derived usin
g an assumption of the stable atmospheric turbidity. If the pyrheliometer d
ata From 0(0) = 85 to 70 are used and the change of the turbidity is +/- 10
%, the error of solution alpha is usually within +/-0.31. If the variation
of the turbidity is random, the mean value of a lot of the measurements of
alpha would be very reasonable.