Application of a fast stochastic storm surge model on estimating the high water level frequency in the Lower Rhine Delta

Abstract

In the Lower Rhine Delta of the Netherlands, the high water level is driven by a joint impact of the downstream storm surge and the upstream fluvial discharge, and affected by the operation of existing man-made structures. In scenario-based risk assessment, a large number of stochastic scenarios of storm surges are required for estimating the high water level frequency. In this article, a fast computing stochastic storm surge model is applied to the gauge station of Hook of Holland in the west of the Netherlands. A fixed number of tides are considered in this model based on the information of historical storm surge events. Based on this model, a large number of stochastic storm surge scenarios are derived and forced into a one-dimensional hydrodynamic model of the Netherlands, resulting in peak water levels in Rotterdam, the most vulnerable city in the delta. These peak water levels are statistically analyzed and converted to the high water level frequency curve in Rotterdam. The high water level frequency curve in Rotterdam tends to a much lower design water level compared to the official design water level that is used to design the dikes and structures for protection of the city. Moreover, there is a significant difference in the high water level frequency curves due to the fact that the stochastic storm surge model considers different numbers of tides. This highlights the critical impact of the storm surge duration on the high water level frequency in the Lower Rhine Delta.

Appendix

• 1. The peak height of the storm surge P₁₀ fits the generalized Pareto distribution:

  $$f(h_{{{\text{P}}_{10} }} ) = \frac{1}{\sigma }\left( {1 + \xi \frac{{h_{{{\text{P}}_{10} }} - \mu }}{\sigma }} \right)^{{ - \left( {\frac{1}{\xi } + 1} \right)}}$$

  where the shape parameter ξ is 0.0143; the scale parameter σ is 0.2390 m; the location parameter u is 2.15 m.

• 2. The marginal distribution of high Rhine discharge Q _r fits the generalized Pareto distribution:

  $$f(Q_{\text{r}} ) = \frac{1}{\sigma }\left( {1 + \xi \frac{{Q_{\text{r}} - \mu }}{\sigma }} \right)^{{\left( { - \frac{1}{\xi }} \right) - 1}}$$

  where ξ is the shape parameter; σ is the scale parameter; u is the location parameter; and the parameters’ values are −0.0667, 1,629.7 and 6,000 m³/s, respectively.

• 3. The marginal distribution of the associated Meuse discharge Q _m fits the Log-normal distribution:

  $$f(Q_{{\text{m}}} ) = \frac{1}{{\sigma \cdot Q_{{\text{m}}} \cdot \sqrt {2\pi } }}e^{{ - \frac{{(\ln Q_{{\text{m}}} - \mu )}}{{2\cdot\sigma ^{2} }}}}$$

  where μ is the mean value 6.8667; σ is the stand deviation value, 0.3752.

• 4. The joint cumulative probability distribution of high Rhine discharge and high Meuse discharge fits a Gumbel Copula function:

  $$F_{{Q_{{{\text{r}},}} Q_{\text{m}} }} (Q_{\text{r,}} Q_{\text{m}} ) = C_{\alpha } (u,v) = \exp \{ - [( - \ln u)^{\alpha } ] + ( - \ln v)^{\alpha } ]^{{\frac{1}{\alpha }}} \}$$
  $$u = F_{\text{r}} (Q_{\text{r}} ) \,$$
  $$v = F_{\text{m}} (Q_{\text{m}} )$$
  $$\alpha = \frac{1}{1 - \tau }$$

  where the relationship between the Gumbel copula parameter α and Kendall’s tau τ is also shown. α is estimated as 1.7158; F _r is the marginal cumulative distribution of high Rhine discharge; F _m is the marginal cumulative distribution of the associated Meuse discharge.