In this paper a modelling approach is presented to predict local scour under time varying flow conditions. The approach is validated using experimental data of unsteady scour at bed sills. The model is based on a number of hypotheses concerning the characteristics of the flow hydrograph, the temporal evolution of the scour and the geometry of the scour hole. A key assumption is that, at any time, the scour depth evolves at the same rate as in an equivalent steady flow. The assumption is supported by existing evidence of geometrical affinity and similarity of scour holes formed under different steady hydraulic conditions. Experimental data are presented that show the scour hole development downstream of bed sills due to flood hydrographs follow a predictable pattern. Numerical simulations are performed with the same input parameters used in the experimental tests but with no post-simulation calibration. Comparison between the experimental and model results indicates good correspondence, especially in the rising limb of the flow hydrograph. This suggests that the underlying assumptions used in the modelling approach are appropriate. In principle, the approach is general and can be applied to a wide range of environments (e.g. bed sills, step-pool systems) in which scouring at rapid bed elevation changes caused by time varying flows occurs, provided appropriate scaling information is available, and the scour response to steady flow conditions can be estimated. Copyright © 2011 John Wiley & Sons, Ltd.