Two methods of calculating the effective impedance spectra of acoustically hard, randomly rough, two-dimensional surfaces valid for acoustic wavelengths large compared with the roughness scales have been explored. The first method uses the complex excess attenuation spectrum due to a point source above a rough boundary predicted by a boundary element method (BEM) and solves for effective impedance roots identified by a winding number integral method. The second method is based on an analytical theory in which the contributions from random distributions of surface scatterers are summed to obtain the total scattered field. Effective impedance spectra deduced from measurements of the complex excess attenuation above 2D randomly rough surfaces formed by semicylinders and wedges have been compared to predictions from the two approaches. Although the analytical theory gives relatively poor predictions, BEM-deduced effective impedance spectra agree tolerably well with measured data. Simple polynomials have been found to fit BEM-deduced spectra for surfaces formed by intersecting parabolas corresponding to average roughness heights between 0.25 and 7.5 m and for five incidence angles for each average height. Predicted effects of sea-surface roughness on sonic boom profiles and rise time are comparable to those due to turbulence and molecular relaxation effects.