Riverbeds frequently display a spatial structure where the sediment mixture composing the channel bed has been sorted into discrete patches of similar grain size. Even though patches are a fundamental feature in gravel bed rivers, we have little understanding of how patches form, evolve, and interact. Here we present a two-dimensional morphodynamic model that is used to examine in greater detail the mechanisms responsible for the development of forced bed surface patches and the coevolution of bed morphology and bed surface patchiness. The model computes the depth-averaged channel hydrodynamics, mixed-grain-size sediment transport, and bed evolution by coupling the river morphodynamic model Flow and Sediment Transport with Morphological Evolution of Channels (FaSTMECH) with a transport relation for gravel mixtures and the mixed-grain-size Exner equation using the active layer assumption. To test the model, we use it to simulate a flume experiment in which the bed developed a sequence of alternate bars and temporally and spatially persistent forced patches with a general pattern of coarse bar tops and fine pools. Cross-stream sediment flux causes sediment to be exported off of bars and imported into pools at a rate that balances downstream gradients in the streamwise sediment transport rate, allowing quasi-steady bar-pool topography to persist. The relative importance of lateral gravitational forces on the cross-stream component of sediment transport is a primary control on the amplitude of the bars. Because boundary shear stress declines as flow shoals over the bars, the lateral sediment transport is increasingly size selective and leads to the development of coarse bar tops and fine pools.