The influence of statistical uncertainty in the hydraulic boundary conditions on the probabilistically computed highwater level frequency curve in the Rhine Delta

The hydrodynamic characteristics of a delta or estuary are mainly governed by discharges of rivers and water level at the sea (or lake) boundaries. A joint probability approach is widely applied to quantify the high water level frequency in deltas. In the approach the relevant hydrodynamic loading variables, namely the astronomical tides, the wind induced storm surge and the river flows, are jointly investigated. The joint probability distribution is used to generate a large number of scenarios of boundary conditions which can drive a deterministic model to derive the water levels at locations of interest. The resulting water levels as well as their associated joint probabilities can be inverted to the high water level frequency curve. However, in the joint probability distribution, marginal distributions may contain large statistical uncertainties due to their relevant parameters being estimated from a limited length of data. In the case of the Rhine Delta, a nonparametric bootstrap method is applied to quantify the statistical uncertainties in three critical marginal distributions: wind induced storm surge peak level, wind induced storm surge duration and River Rhine discharge. The uncertainties are incorporated into the marginal distributions with a Monte Carlo integration method. Further the uncertainty-incorporated marginal distributions are used for the high water level frequency assessment. Compared to previous studies, water levels for given return periods are much higher. The uncertainty differs in each marginal distribution and its impact on the high water level frequency curve also varies.