An efficient novel algorithm is introduced for ground wave propagation problems. First, ground wave propagation characteristics for a vertically polarized short electric dipole over a smooth spherical earth are reviewed, reducing the vector electromagnetic problem for the three-dimensional spherical geometry to an equivalent two-dimensional rectilinear scalar potential problem which is solved by spectral analysis and synthesis. Alternative evaluations of the spectral integral yield ray optical and normal mode solutions, which are conventionally referred to as the Norton and Wait formulations, respectively. Combining these formulations in an efficient manner yields a hybrid algorithm which is constructed so as to account adaptively for the characteristics of ground wave propagation in interference, intermediate and diffraction regions (including mixed paths) for various source and/or receiver heights. Numerical comparisons are made with reference results obtained via the parabolic equation (PE) method, in parametric ranges where PE is reliable; this permits assessment of the effectiveness of the hybrid approach. (C) 1998 John Wiley & Sons, Ltd.