The inclusion of model uncertainty : preliminary examination on how model uncertainties affect frequency lines for water levels

The transition towards a new risk approach for the Dutch national safety assessment of primary flood defences has been taken as an opportunity to improve the dealings with uncertainties. The probabilistic models for the new safety assessment (WBI2017) not only deal with the natural variability, but also with so-called epistemological uncertainties. One class of epistemological uncertainties is the model uncertainty in the hydrodynamic models used. According to WBI2017 the model uncertainty related to water levels is included by considering the water level as an additional stochastic variable. The quantification of the water level uncertainty depends on the dominant hydraulic processes in each water system and is chosen to be independent of the return period. However, water level frequency lines derived including model uncertainty sometimes conflict with the physics. The main objective of this thesis is to analyse how model uncertainties affect the water level frequency lines in different fresh water systems in the Netherlands and to provide insights into different methods to deal with model uncertainties for the Dutch national safety assessments. A comparative analysis is carried out to assess the performance of Hydra-NL w.r.t. observations and to analyse if physical processes that play an important role in each fresh water system are represented correctly after the inclusion of model uncertainty with the WBI2017 method. This study shows that the estimated exceedance probability of actual water levels in the tidal river area and lake area are often overestimated by the Hydra-model even without model uncertainty. When model uncertainties are included the overestimations become even larger. Furthermore, the inclusion of model uncertainty sometimes gives an incorrect representation of the underlying physical processes. The effect of the model uncertainty gets larger when the water level frequency line becomes flatter. This is e.g. the case at locations where the water levels are influenced by the closure of the Europoortkering and upstream of the flood channel near Veessen-Wapenveld. It can be argued that water level uncertainties are likely to decrease in these situations, because a reservoir is more predictable than a flowing river and the operation of the flood channel results in an enlarged conveyance that is less sensitive than an average river profile. The hypothesis that the inclusion of model uncertainty according to WBI2017 results in an incorrect representation of the underlying physical processes is further analysed for several case studies in the upper river area and the lake area. According to WBI2017 the peak discharge at Lobith is the only stochastic variable in the upper river area apart from the model uncertainty. The most important sources of model uncertainty in the hydrodynamic model used are the calibration approach, hydraulic roughness and physical processes or morphological changes under extreme conditions. In this study a simplified physical model is set up based on normal flow equations and backwater equations. This model is able to transpose discharge to corresponding water levels for different hydrodynamic systems. Varying river schematisations and two river interventions (flood channel and retention area) are modelled to compare the WBI2017 method with a more physics-based approach. In this physics-based approach the hydraulic roughness of the main channel and/or floodplains is incorporated as additional stochastic variable for the derivation of water level frequency lines. Rivers have a dynamic behaviour where the geometry of the river varies for every branch and even within the branch. It is shown that the water level uncertainty becomes smaller for wide rivers where the water level frequency line becomes flatter. The cases where river interventions are present the water level uncertainty is bounded, because of the environment/geometry that influences the water levels. According to the physics-based method the water level uncertainties are location and discharge dependent, which are both not integrated in the WBI2017 method. The physics-based approach shows potential possibilities to include model uncertainty that represents the physical processes in a better manner. For the lake area the focus is on locations where high water levels are predominantly determined by the wind that is causing a set-up on the lake. Wind transformation, modelling of the drag coefficient and schematisation of the wind fields are for wind-dominated locations the most important model uncertainties in the hydrodynamic model used in the lake area. In this study, a simplified physical model is used that simulates an one-dimensional closed basin in which the wind causes shear stresses at the water surface that result in a water level gradient. By considering an empirical parameter of the "capped Wu" formula as additional stochastic variable the uncertainty of the drag coefficient is modelled for the physics-based method. The quantification is performed pragmatically by matching the 95 % confidence bounds of the water level for the physics-based method and the WBI2017 method. The decimate heights along a lake gets larger for locations that are further away from the center of gravity of the water surface, where the wind set-up is the largest. The physics-based method demonstrates that the water level uncertainty is larger for higher decimate heights and vice versa. It can be concluded that it is not valid to choose one uniform standard deviation of the water level for all wind-dominated locations, as it is done for WBI2017. Including the model uncertainty according to the physics-based method shows potential possibilities to address this problem. The physical models used provided rapid insights into system behaviour, but the findings should be verified by using more sophisticated hydrodynamic models in which the water dynamics are represented in more detail. It is recommended to include the model uncertainty by considering a model parameter in the hydrodynamic model for the upper river area and lake area as additional stochastic variable in the Hydra-models, to model uncertainty in the water level. For the upper river area the hydraulic roughness seems the best candidate and because of computational restrictions the main channel and floodplain roughness could be considered fully dependent. For wind-dominated locations in the lake area it is recommended to use an empirical parameter of the "capped Wu" formula as additional stochastic variable. In other water systems it becomes more complex, because several equally important sources of uncertainty are present. Still, the most important model uncertainty sources could considered stochastically, but computational effort would become the limiting factor.