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. We established under which conditions these simplified models are accurate.

Based on results of linear stability analyses of the St. Venant-Exner equations, we assessed migration celerities and damping of infinitesimal, but long riverbed perturbations. We did this for the full dynamic model, i.e. 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 modelling 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).@en

In July of 2021, large areas in the catchment of the Meuse River in Belgium, the Netherlands and Germany were affected by extreme rainfall and floods. This paper presents the hydraulic and morphological data that were collected during and after the flood. The data were analysed to understand the hydraulic and morphological functioning of the Meuse River in the Netherlands during the flood event. The data showed that measured peak discharges in the upstream part of the Meuse and regional tributaries were the highest ever recorded. However, as the flood had a very short duration, peak attenuation played an important role, resulting in discharges and water levels in downstream reaches that were lower than during previous floods. Furthermore, the implementation of river widening and floodplain lowering measures as part of the Meuse Works programme contributed to a reduction in peak water levels along the Meuse. The analysis also showed that flood forecasts in the upstream part of the Meuse in the Netherlands depended heavily on rainfall forecasts and rainfall-runoff modelling and underestimated the peak water levels up to 36 hours before the flood actually peaked. Further downstream, the lead time increases and forecasts are based on discharge levels that are measured in upstream parts of the catchments. This results in more accurate estimates. The floods have also resulted in unprecedented morphological changes. The armour layer in the riverbed of the ‘Common Meuse’, consisting of very coarse gravel, was mobilised and layers of fine sand quickly eroded. This resulted in multiple scour holes with depths of 3 to 15m, especially in a reach which was hardly or not at all widened in the room for the river programme called Meuse Works. In this reach, the flow velocities were high and even higher than prior to the Meuse Works.@en

Sustainable river management can be supported by models predicting long-term morphological developments. Even for one-dimensional morphological models, run times can be up to several days for simulations over multiple decades. Alternatively, analytical tools yield metrics that allow to estimate migration celerity and damping of sediment waves, which have potential for being used as rapid assessment tools to explore future morphological developments. We evaluate the use of analytical relations based on linear stability analyses of the St. Venant-Exner equations, which apply to sediment waves with spatial scales much larger than the water depth. With a one-dimensional numerical morphological model, we assess the validity range of the analytical approach. The comparison shows that the propagation of small bed perturbations is well-described by the analytical approach. For Froude numbers over 0.3, diffusion becomes important and bed perturbation celerities reduce in time. A spatial-mode linear stability analysis predicts an upper limit for the bed perturbation celerity. For longer and higher bed perturbations, the dimensions relative to the water depth and the backwater-curve length determine whether the analytical approach yields a good approximation. For higher bed wave amplitudes, non-linearity becomes important. For Froude numbers ≤0.3, the celerity of bed waves is increasingly underestimated by the analytical approach. The degree of underestimation is proportional to the ratio of bed wave amplitude to water depth, and the Froude number. For Froude numbers exceeding 0.3, the net impact on the celerity depends on the balance between the decrease due to damping and the increase due to non-linear interaction.@en

Over the course of centuries, river systems have been heavily trained for the purpose of safe discharge of water, sediment and ice, and improves navigation. Traditionally, dikes are used to be reinforced and heightened to protect countries from ever higher flood levels. Other types of solutions than technical engineering solutions, such as measures to increase the flood conveyance capacity (e.g., lowering of groynes and floodplains, setting back dikes) become more popular. These solutions may however increase the river bed dynamics and thus impact negatively navigation, maintenance dredging and flood safety. A variety of numerical models are available to predict the impact of river restoration works on river processes. Often little attention is paid to the assessment of uncertainties. In this paper, we show how we can make uncertainty explicit using a stochastic approach. This approach helps identifying uncertainty sources and assessing their contribution to the overall uncertainty in river processes. The approach gives engineers a better understanding of system behaviour and enables them to intervene with the river system, so as to avoid undesired situations. We illustrate the merits of this stochastic approach for optimising lowland river restoration works in the Rhine in the Netherlands.

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