We report a calculation of the magnitude and direction of the wind force for the self-electromigration of adatoms on heterogeneous metal surfaces. Using layer-KKR and jellium methods we have computed the wind valence of adatoms interacting with adatom islands and voids on the low Miller index surfaces of several simple and noble metals. In the vicinity of an island, we find that the magnitude and direction of the electromigration driving force is significantly different from the force felt by an isolated adatom on a large terrace. Therefore, the usual assumption that driving force in surface electromigration is uniform and isotropic is shown to be inaccurate. Using the results of these calculations as input to kinetic Monte-Carlo simulations, we explore how this inhomogeneity of the wind force is manifest in the driven surface diffusion of adatom islands on a current-carrying metallic substrate.