Uncertainty in the direct radiative forcing by anthropogenic sulfate aerosols is analyzed for four different aerosol model structures with 13 uncertain parameters using a second-order probabilistic collocation method. The resulting probability density functions agree well with those determined here by a computationally much more expensive 10,000-point Monte Carlo method. The structural difference, measured by the range of the mean responses in models with different approximations, is -0.28 to -1.3 W m-2, and the parametric uncertainty, induced by the uncertainties in the model parameters, is -0.1 to -4.2 W m-2, both with 95% confidence. This implies that refining uncertain input parameters may be more important than improving models in order to minimize the overall uncertainty in the direct radiative forcing by anthropogenic sulfate aerosols in these four models. The variance analysis indicates that the parametric uncertainty comes mainly from sulfate yield, sulfate lifetime, and ambient relative humidity. Variance contributions from aerosol size parameters are much smaller, and this finding agrees with the sensitivity analysis by Boucher and Anderson <1995>. Note that the conclusions reached here are dependent on the chosen model structures and parameter distributions. This study presents a computationally efficient framework for assessing uncertainty in aerosol radiative forcing which could be used to address an even wider range of structures and parameters in the future.¿ 1997 American Geophysical Union