A new method for parametric uncertainty analysis of numerical geophysical models is presented. It approximates model response surfaces, which are functions of model input parameters, using orthogonal polynomials, whose weighting functions are the probabilistic density functions (PDFs) of the input uncertain parameters. This approach has been applied to the uncertainty analysis of an analytical model of the direct radiative forcing by anthropogenic sulfate aerosols which has nine uncertain parameters. This method is shown to generate PDFs of the radiative forcing which are very similar to the exact analytical PDF. Compared with the Monte Carlo method for this problem, the new method is a factor of 25 to 60 times faster, depending on the error tolerance, and exhibits an exponential decrease of error with increasing order of the approximation.¿ 1997 American Geophysical Union