Quantifying parameter uncertainty in predictions of coastal mega-nourishments

Abstract

Continuous sea level rise and growing environmental awareness have led to increasing implementation of nature-based solutions to counter coastal erosion. An example in the Netherlands is the Sand Engine---a mega-scale sand nourishment designed to feed the Dutch coast over a period of 20 years. For such designs to work, a good understanding of the governing natural processes is paramount. The behaviour of the sandy coast, however, is subject to natural variability in future weather and uncertainties in the interactions between sand dynamics and hydrodynamic forcing. To predict the evolution of coastal systems, engineers apply numerical models. Next to uncertainty due to variability in natural forcing, such models introduce a series of model-related uncertainties, which are often not consistently included in predictions. With limited knowledge of the magnitude of these uncertainties, the long-term strategy development and design of projects are impeded. Parameter uncertainty denotes our limited knowledge of the values of free model parameters and is an important source of overall model uncertainty. This study aims to quantify parameter uncertainty in process-based coastal area predictions by analysing uncertainty bounds for morphodynamic predictions of the Sand Engine. The analysis of parameter uncertainty is carried out for a study period of 14 months, from August 2011 (directly after construction of the Sand Engine) until October 2012. Using advanced numerical acceleration techniques, a synthetic dataset of 1024 morphological Delft3D predictions is generated, each with an identical hindcast period but different model parameter settings. First, a sensitivity analysis (elementary effects method) is performed to find the most influential parameters on three morphological indicators: cumulative volume change, shoreline position, and bed level change. Based on the sensitivity analysis, five parameters are selected for an uncertainty analysis. Subsequently, parameter uncertainty is quantified by the Generalised Likelihood Uncertainty Estimation (GLUE). To increase the convergence speed of the samples, quasi-random Sobol sampling is applied. To validate the applied parameter ranges and assess model performance, the predictions are compared to observations. Using GLUE, uncertainty bounds for the morphological indicators and posterior likelihood distributions of the five parameters are derived from the 1024 model runs. Finally, through a simplified uncertainty comparison, the relative influence of parameter uncertainty and wave climate variability is examined. A first key conclusion is that uncertainty in input parameters translates to significant uncertainty in predictions: cumulative erosion volumes for the peninsula show a spread of 1.3 -0.4/+0.7 million m3 after 14 months. Extended to bed level changes in 2D, the uncertainty bounds result in spatial uncertainty maps, which reveal that uncertainty is highest (5--6 $m$ spread) in the northern area of the peninsula, where a sand spit develops. Most uncertainty (90% for volume changes) develops in the first seven months, during which uncertainty growth correlates strongly to periods of high morphological activity (r > 0.95 for volume changes). Further, posterior likelihood distributions of the parameters indicate that, of the five selected parameters based on the sensitivity analysis, only three (f_sus, gamma, and d_50) significantly contribute to parameter induced uncertainty, while the other two (alpha_rol and theta_sd) are considerably less influential. This contrast in results is attributed to a resolution problem in the sensitivity analysis. Optimised parameter sets derived from the posterior likelihood distributions result in similar model skill as the best GLUE simulations (BSS = 0.8), implying that they may be close to the maximum achievable model skill within the examined parameter ranges. Finally, a simplified estimate of the variation due to wave climate variability is in the same order of magnitude as the parameter induced uncertainty bounds, implying that both uncertainty sources form significant contributions to overall prediction uncertainty. The presented results have an impact on two key levels. First, they can be used to communicate and address uncertainty in predictions of coastal change. For example, the spatial uncertainty maps can let stakeholders understand the potential range of outcomes for a certain design. Second, the results, combined with the created dataset, can provide valuable information for future morphodynamic studies. This work contributes to justifying the need for stochastic simulations, which are expected to be increasingly used for many coastal engineering and management purposes in the years to come.