This paper presents a novel model that predicts how gravel riverbeds may evolve in response to differences in the frequency and severity of flood events. We test our model using a 23-year-long record of river flow and gravel transport from the Swiss Prealps. We find that our model reliably captures yearly patterns in gravel transport in this setting. Our new model is a major advance towards better predictions of river erosion that account for the flood history of a gravel-bed river.