Assessment of the sensitivity and uncertainty of equilibrium river state predictions: A case study on the river Waal

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The natural development of the morphology of rivers in time is important due to the functions rivers fulfil, such as navigability and drinking water supply. Rivers adjust their morphology when there is a change in the river controls, which are mainly the water discharge, sediment discharge and downstream water level. The morphology adjustments continue until a river has reached its equilibrium state (i.e. equilibrium bed slope and equilibrium bed surface sand fraction), which is when all sediment that is supplied upstream of the river can be transported downstream. Even though an assessment of how the river changes towards its equilibrium state is important for the performance of the functions of a river, it is often overlooked. This can for example lead to increased maintenance costs and dangerous situations. A quick method to calculate the equilibrium state of a river can help prevent these negative impacts. The analytical relations by Blom et al. (2017) are a promising method to predict how a river will change, since they give useful and rapid insight in the equilibrium river state. However, the degree of uncertainty of the equilibrium river state as a result of the uncertainty in the input parameters is not yet known. It is recommended to examine this uncertainty before interpreting how a river will change. The aim of this research is therefore to investigate what the range of uncertainty of calculated equilibrium river states is, and to execute a sensitivity analysis to examine which input parameters contribute the most to this uncertainty. The river Waal is chosen as a case study for these analyses. The calculated equilibrium state of the river Waal, including the range of uncertainty, is compared to river state measurements to assess how well an equilibrium state can be identified. A model is created based on the analytical relations, and is used to perform three different analyses; a deterministic analysis that results in a spatially varying equilibrium state without uncertainties, a sensitivity analysis that assesses the influence of each input parameter on the equilibrium state, and an uncertainty analysis that results in a bandwidth of possible equilibrium states. The result of the sensitivity analysis is that the mean gravel content of the total sediment supply and the total sediment supply itself have the largest impact on the uncertainty of the equilibrium state. The result of the uncertainty analysis is that the equilibrium bed slope can be approximately 1.8E-5 smaller or larger than the mean bed slope, with an uncertainty bandwidth of approximately 3.7E-5, and that the equilibrium bed surface sand fraction can be approximately 10% to 20% smaller and 10% to 35% larger than the deterministic bed surface sand fraction, with an uncertainty bandwidth between 20% to 50%, depending on which sediment transport relation has been used. From the comparison between the calculated equilibrium state, including uncertainties, and the measured river state, it follows that the current bed slope is steeper than the equilibrium bed slope, and that the current bed surface sand fraction is either larger than or within the uncertainty bandwidth of the equilibrium bed surface sand fraction. The found milder equilibrium bed slope is as predicted. However, the found equilibrium sand fraction does not match the prediction that the bed surface sand fraction is smaller in the equilibrium state. From the comparison and the results of the uncertainty analysis follows that an equilibrium state cannot yet be identified, because 1) the uncertainty range of the calculated bed surface sand fractions is considered to be too large to predict the equilibrium state of the river Waal, and 2) the equilibrium bed surface sand fraction predictions do not match the expectation. To improve the equilibrium state identification of the river Waal, it is recommended to 1) assess why there is a mismatch between the expected and calculated equilibrium bed surface sand fractions, 2) perform research to reduce the input uncertainty, and 3) validate the equilibrium state predictions.