A physically modeled method is presented to obtain accurate turbidity determinations from broadband direct irradiance measurements. The method uses parameterizations of various extinction processes affecting the transfer of shortwave radiation in a cloudless atmosphere. The integration over the shortwave solar spectrum is performed with a more realistic weighting function than is conventionally used. The calculation and properties of the broadband aerosol optical depth are discussed in detail as a function of the aerosol optical characteristics. The method is general, as it can predict any one of the four turbidity coefficients currently used in climatological studies as defined by Ångström, Linke, Unsworth–Monteith, and Schüepp. Formal interrelationships are proposed so that climatological data based on different coefficients can be consistently intercompared without recourse to empirical formulas. The new parameterizations are more detailed than those of the literature, particularly regarding t... Abstract A physically modeled method is presented to obtain accurate turbidity determinations from broadband direct irradiance measurements. The method uses parameterizations of various extinction processes affecting the transfer of shortwave radiation in a cloudless atmosphere. The integration over the shortwave solar spectrum is performed with a more realistic weighting function than is conventionally used. The calculation and properties of the broadband aerosol optical depth are discussed in detail as a function of the aerosol optical characteristics. The method is general, as it can predict any one of the four turbidity coefficients currently used in climatological studies as defined by Ångström, Linke, Unsworth–Monteith, and Schüepp. Formal interrelationships are proposed so that climatological data based on different coefficients can be consistently intercompared without recourse to empirical formulas. The new parameterizations are more detailed than those of the literature, particularly regarding t...