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Many models have been so far proposed to simulate and understand the long-term evolution of meandering rivers. Nevertheless, some modeling problems still need to be solved, for example, the physical soundness of long-term simulations when width variations are accounted for. The present work proposes the use of statistical tools to capture the spatiotemporal variations of channel width and to embed their effect into a physics-statistics-based model that simulates the river bank evolution. Erosion and deposition processes are assumed to act independently, with a specific shear stress threshold for each of them. In addition, the width evolution is linked with a river-specific probability density function. The analysis of a representative sample of meandering configurations, extracted from Landsat images, indicates that in many cases a generalized extreme value distribution nicely describes the along-channel distribution of cross-section width. For a given river, the parameters of this distribution keep almost constant in time. Significant variations are observed only after cutoff events that shorten the length of the river. The constraint of the river width based on the assumption of a generalized extreme value distribution ensures physically plausible configurations as the river moves throughout the floodplain, adapting continuously its local width. The application of the model to a reach of the Ucayali River appears to reasonably reproduce the planform river morphodynamics and yields realistic values of the cross-section widths.