AbstractAerosols impact clear-sky surface irradiance ("Equation missing") through the effects of scattering and absorption. Linear or nonlinear relationships between aerosol optical depth (τ_a) and "Equation missing" have been established to describe the aerosol direct radiative effect on "Equation missing" (ADRE). However, considerable uncertainties remain associated with ADRE due to the incorrect estimation of "Equation missing" (τ_a in the absence of aerosols). Based on data from the Aerosol Robotic Network, the effects of τ_a, water vapor content (w) and the cosine of the solar zenith angle (μ) on "Equation missing" are thoroughly considered, leading to an effective parameterization of "Equation missing" as a nonlinear function of these three quantities. The parameterization is proven able to estimate "Equation missing" with a mean bias error of 0.32 W m⁻², which is one order of magnitude smaller than that derived using earlier linear or nonlinear functions. Applications of this new parameterization to estimate τ_a from "Equation missing", or vice versa, show that the root-mean-square errors were 0.08 and 10.0 Wm⁻², respectively. Therefore, this study establishes a straightforward method to derive "Equation missing" from τ_a or estimate τ_a from "Equation missing" measurements if water vapor measurements are available.