Accuracy Assessment of Numerical Morphological Models Based on Reduced Saint‐Venant Equations.

Sustainable river management often requires long‐term morphological simulations. As the future is unknown, uncertainty needs to be accounted for, which may require probabilistic simulations covering a large parameter domain. Even for one‐dimensional models, simulation times can be long. One of the acceleration strategies is simplification of models by neglecting terms in the governing hydrodynamic equations. Examples are the quasi‐steady model and the diffusive wave model, both widely used by scientists and practitioners. Here, we establish under which conditions these simplified models are accurate. Based on results of linear stability analyses of the St. Venant‐Exner equations, we assess migration celerities and damping of infinitesimal, but long riverbed perturbations. We did this for the full dynamic model, that is, no terms neglected, as well as for the simplified models. The accuracy of the simplified models was obtained from comparison between the characteristics of the riverbed perturbations for simplified models and the full dynamic model. We executed a spatial‐mode and a temporal‐mode linear analysis and compared the results with numerical modeling results for the full dynamic and simplified models, for very small and large bed waves. The numerical results match best with the temporal‐mode linear analysis. We show that the quasi‐steady model is highly accurate for Froude numbers up to 0.7, probably even for long river reaches with large flood wave damping. Although the diffusive wave model accurately predicts flood wave migration and damping, key morphological metrics deviate more than 5% (10%) from the full dynamic model when Froude numbers exceed 0.2 (0.3). Plain Language Summary: Human interference in rivers impact the transport of sediment in these rivers and cause aggradation and erosion of the riverbed. This may cause problems for navigation, flood safety, groundwater levels, nature, agriculture and stability of infrastructure in and along the river. The changes in the riverbed are called morphological changes, which develop slowly and may continue for hundreds or even thousands of years. For future plans in river basins, it is important to know what the impact of these plans may be on the riverbed development in the future. Numerical models are widely used for this. For simulations of long river reaches and predictive horizons of decades or more, run times of these models can be very long. Shorter run times are possible with simplified models. However, it has remained unclear whether these simplified numerical models provide reliable projections of the future riverbed development. This research provides a method to assess under which conditions of flow and sediment load in the river simplified numerical models can be applied. We prove that a widely used quasi‐steady modeling approach yields accurate morphological predictions for a wide range of lowland rivers. Key Points: Morphodynamic metrics of quasi‐steady models deviate less than 1% from full‐dynamic models for Froude numbers up to 0.7Bed wave migration and damping based on the diffusive wave approach are 10% accurate only for Froude numbers of 0.3 or lowerTemporal‐mode linear analysis predicts the accuracy of simplified hydrodynamics in 1D numerical morphological river models [ABSTRACT FROM AUTHOR]