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The Rhine River Delta is crucial to the Dutch economy. The Maeslant barrier was built in 1997 to protect the Rhine estuary, with the city and port of Rotterdam, from storm surges. This research takes a simple approach to quantify the influence of the Maeslant storm surge barrier on design water levels behind the barrier. The dikes in the area are supposed to be able to withstand these levels. Equal Level Curves approach is used to calculate the Rotterdam water levels by using Rhine discharges and sea water levels as input. Their joint probability function generates the occurrence frequency of a certain combination that will lead to a certain high water level in Rotterdam. The results show that the flood frequency in Rotterdam is reduced effectively with the controlled barrier in current and in future scenarios influenced by climate change. In addition, an investigation of the sensitivity of the operational parameters suggests that there is a negligible influence on the high water level frequency when the decision closing water level for the barrier is set higher due to the benefits of navigation (but not exceeding the design safety level 4 m MSL).

A delta is a landform that is formed at the mouth of a river where that river flows into an ocean, sea or other water body. Its size ranges from tens to several hundreds of kilometers. Due to the special location regarding trade activities, many deltas become economic centers with a highly dense population. However, they are also vulnerable to flooding, and floods are one of the most dangerous hazards of a delta area. To mitigate the effects of flooding, many manmade structures have been constructed in low-lying delta areas all over the world.

A storm surge barrier is a structure that prevents a storm surge or spring tide from propagating into a river, channel or lake behind the barrier. It is usually a part of a larger flood protection system, which consists of floodwalls, levees and other constructions. In England, the Thames barrier was established at the mouth of Thames River. In the USA, a series of storm surge barriers are under discussion as a possible way to deal with the increasing risks of storm surges in New York City [

The Maeslant storm surge barrier is located in the mouth of the New Waterway in the Rhine Delta. If flooded, the inundation damage in the delta would be enormous. For example, the 1953 sea flooding caused more than 1,800 casualties, and over 150,000 hectares of land flooded, about 9,000 buildings were demolished and 38,000 buildings damaged, 67 breaches occurred and hundreds of kilometers of dikes were heavily damaged. The total economic loss was estimated at 680–900 million Euros [

The city of Rotterdam is commonly taken as the reference point in the flood frequency analysis because of its important economic role. Van Dantzig [

In the assessment, annual maximum North Sea levels and their corresponding Rhine flows are selected. Although a peaks over threshold (POT) assessment would have been better as it could offer more extreme North Sea level events, considering a 100 year long annual maximum (AM) assessment avoids possible inhomogeneities in the data. The combination of extreme Rhine flow and its corresponding sea level is excluded, as the water level at Rotterdam is mostly influenced by the North Sea level. This assumption will be illustrated later. Because of lack of data, the possibility of the occurrence of simultaneously extreme North Sea level and Rhine flow is hard to estimate. Van der Made [

The joint probability method will be used to assess the frequency of the transitional water level. Here, with the help of the simplified hydraulic functions—Equal Level Curves [

Climate change will influence North Sea level and Rhine flow in the Rhine Delta. In 2006, the Royal Dutch Meteorological Institute (KNMI) worked out two scenarios of sea level rise for the Dutch coast, which resulted in the mean sea level rising from 0.15 up to 0.35 m by 2050 and from 0.35 up to 0.85 m by 2100 [^{3}/s over the 21st century. Obviously, future mean sea level rise combined with higher winter Rhine flow will increase the probability of extreme water level events in the delta. The adaption to future increasing flood probabilities including the operation of the Maeslant Barrier will be studied in this article.

The goal of this research is to compare the flood frequency with and without the controlled barrier in order to assess the influence of the barrier operations on flood risk reduction. The paper is organized as follows: First a description of the delta area will be presented, followed by the outline of the applied methodology. Next, ‘Equal Level Curves’ is illustrated, followed by the flood frequency analysis. Next, the parameters of the control operation of the barrier are optimized. Finally, conclusions and future work are presented.

A schematic graph of the Rhine Delta is shown in

The flooding types are divided into three categories in

The Rhine-Meuse Delta in the Netherlands.

Gauge stations.

Gauge station | Unit | Period (years) |
---|---|---|

Hook of Holland | High sea water level (m MSL one high water recording at every tide cycle) | 1887–2009 |

Lobith | Mean daily discharge (m^{3}/s) |
1901–2009 |

Rotterdam | Water level (m MSL one high water recording at every tide cycle) | 1940–2009 |

(

Flooding types and the function of the Maeslant Barrier: (

In order to obtain statistically significant results for the flood frequency analysis in Rotterdam, the following steps are undertaken (

(1) To investigate the historical observations in order to detect and remove trends and discontinuities.

(2) To derive the probability density functions for annual maximum sea levels and their corresponding Rhine flows.

(3) To examine the degree of correlation between the above sea levels and Rhine flows.

(4) To develop an exceedance probability function of the Rotterdam water level using the above probability functions and ‘Equal Level Curves’.

(5) To work out the exceedance joint probability function using Monte Carlo Simulations.

(6)To repeat steps 2 to 6 to build up future sea level rising scenarios.

Flow chart of methodology.

A detailed hydrodynamic model of the delta, calibrated every five years, has been developed [

Equal Level Curves approach is a simple steady state function, which can simulate the highest water level at Rotterdam by up-down boundary conditions during one tidal period.

where _{basin}_{sea}_{river}_{mouth}_{river}

The parameters in Equation (1) are estimated using historical data. For practical reasons, only the product of _{mouth}_{mouth}^{2}.

In

Comparison of the observed and simulated water levels at Rotterdam.

With the available parameter _{mouth}

Equal Level Curves for Rotterdam.

Observation of water level at Rotterdam and Hook of Holland.

To consider the effect of the Maeslant Barrier closure, the operation control is combined with Equal Level Curves. During the storm surge, the high sea level is kept out of the basin by closing the Maeslant Barrier. Afterwards the water level behind the barrier will rise because the Rhine flow is stored here. The water level in the basin after the barrier closure becomes:

where _{basin}_{basin,c}_{river}_{basin}

_{basin,c}_{basin,c}

The parameters of these four equations are estimated by system identification on historical measurements according to Equation (1). The time unit of

The parameter _{basin}

The flow of the small branch of the Rhine towards the North and the Meuse flow are considered in order to get more accurate values of _{basin}^{3}/s, the daily mean discharge of the Meuse was 148 m^{3}/s and the water level at Rotterdam rose from 0.70 to 1.12 m during the 15 hour closure. In _{basin}^{2}.

Given a certain storm surge event, the closure duration of the barrier _{s}_{c}_{s}_{s}_{c}_{s}_{s}_{s}_{c}_{s}^{3}/s, respectively [

Rotterdam water level during the closure event of November 9, 2007.

The operation control of the Maeslant Barrier.

In order to execute Equation (2) in the simulations, the following assumptions are applied to the sea level boundary:

First, the design hydrograph of high sea level in Hook of Holland is considered. The sea level consists of the astronomical tide, the wind set up and the mean sea level. The mean sea level is 0 m MSL. The assumption is that the astronomical tide and the wind set up are independent but their peak values coincide.

Wind set up is a dynamic process and its variation with time could be roughly approximated by Equation 9 [

_{wmax}_{wmax}

The astronomical tide is assumed to be a sinusoidal wave. Its amplitude and duration are selected by a yearly mean value: The peak to peak amplitude _{a}

Second, in the simulation, _{basin}_{basin}

In the flood frequency analysis, the annual maximum sea levels and the corresponding Rhine flows are chosen, since the Rotterdam water level is mostly influenced by the sea water level. First, these data are tested; second, their probability density functions (PDF) are estimated; third, their relationship is estimated. Finally the exceedance joint probability function of the Rotterdam water level is derived.

The behavior and course of a river or sea condition may change considerably over long time periods due to artificial or natural causes, and therefore several tests must be executed to check whether all observations from hydrologic events come from the same population. The Mann Kendall test is commonly applied to assess the significance of trends in hydro-meteorological time series such as stream flow, temperature and precipitation (e.g., [

In

Tests on the annual maximum sea level at Hook of Holland.

Annual maximum sea level in Hook of Holland | Trend test | Jump test | |
---|---|---|---|

Test (at the significance level 0.05) | Mann Kendall test | Spearman’s rank correlation coefficient method | Jump test |

Null hypothesis (H_{0}) |
No trend | No trend | No abrupt points |

P-value | 0.0058 | 0.0054 | 0.1318 |

Reject H_{0} |
Yes | Yes | No |

Tests on the corrected annual maximum sea level at Hook of Holland.

Annual maximum sea level in Hook of Holland | Trend test | Jump test | |
---|---|---|---|

Test | Mann Kendall test | Spearman’s rank correlation coefficient method | Jump test |

Null hypothesis (H_{0}) |
No trend | No trend | No abrupt points |

P-value | 0.71 | 0.69 | 0.21 |

Reject H_{0} |
No | No | No |

Tests on Rhine flow at Lobith.

Rhine flow in Lobith | Trend test | Jump test | |
---|---|---|---|

Test | Mann Kendall test | Spearman’s rank correlation coefficient method | Jump test |

Null hypothesis (H_{0}) |
No trend | No trend | No abrupt points |

P-value | 0.98 | 0.96 | 0.16 |

Reject H_{0} |
No | No | No |

The PDF of the annual maximum sea level is calculated. According to the extreme value theory, the annual maximum sea level belongs to one General Extreme Value distribution [

where the value of

The daily mean Rhine flow that corresponds to the annual maximum sea level fits the lognormal distribution according to the Kolmogorov-Smirnov test and the Anderson-Darling test. The other reason to choose the lognormal distribution is that it is still possible to generate some extreme peak values for Rhine discharge, and subsequently the combination of a surge tide and Rhine peak flow is possible to include. The Maximum Likelihood Method is used to estimate the parameters of the lognormal distribution. Then the PDF becomes:

where the value of ^{3}/s; the value of ^{3}/s; ^{3}/s.

Return period of the sea levels at Hook of Holland.

The annual maximum sea levels and their corresponding daily Rhine flows are plotted in

In order to get the exceedance joint probability function of the Rotterdam water level, PDFs of annual maximum sea levels and the corresponding daily Rhine flow (Equations (11) and (12)) are chosen. These two variables are independent. The relationship is given by Equation 13:

In which: Ω is the complement area of (1 – Ω), which is the shadow area in _{basin}_{sea}_{river}_{basin}_{sea}_{river}_{sea}_{river}

An analytical method for calculating Equation (13) is infeasible. Instead, Monte Carlo Simulations offer a more flexible way to estimate the exceedance probability (e.g., [

Annual maximum sea levels against corresponding Rhine flows.

Integration for the exceedance probability of a particular H_{basin}.

Future climate change is taken into consideration, but in this research attention is only paid to sea level rise. There are two sets of scenarios given by Royal Netherlands Meteorological Institute (KNMI) [

The scenarios of mean sea level rise.

Year | Mean Sea Level Rise (m) |
---|---|

2050 | 0.35 |

2100 | 0.85 |

Large enough combination samples of sea level and Rhine discharge are generated by Monte Carlo Simulation according to Equations (11) and (12). The ‘Equal Level Curves’ described in

The operation of the Maeslant Barrier effectively reduces the flood frequency. In the scenario of 2010, due to the barrier, the return period of 3.0 m MSL is increased from 10.9 years to about 2,400 years. The return period of other high water levels is also increased. For example, the return period of 4.0 m MSL water level (the design safety level) is increased from 609 years to 46,950 years.

However, future sea level rise will increase the flood frequency significantly, and therefore the return periods of all the water levels will drop largely. For example, the return period of 3.0 m MSL will reduce from 10.9 years to 3.23 years in 2050 and to 1.10 years in 2100. The return period of a 4.0 m MSL water level (the design safety level) will reduce from 609 years to 141 years in 2050 and to 19 years in 2100.

The operation of the barrier can partly compensate the effect of the future sea level rise. According to the current operation, the barrier will increase the return period of 4.0 m MSL water level from 141 years to 16,420 years in 2050 and from 19 years to 3849 years in 2100. In conclusion the barrier reduces the flood frequency effectively for the present situation and for future sea level rise scenarios.

Return period at different scenarios.

When a storm surge is approaching, it is of vital importance to decide whether and when to close the Maeslant Barrier in advance. The operation of the closure process depends on three parameters: first, the closing level _{c}_{s}_{s}^{3}/s). The sensitivity tests for the three parameters show how much the water levels are influenced.

In _{s}_{s}_{s}_{s}_{s}

The sensitivities to the flood frequency for _{c}_{s}

Return periods for different values of _{s}

This article demonstrates how the operation of a storm surge barrier can strongly influence the flood frequency in a delta area. According to the model in this paper, under the current Maeslant barrier operation system, a water level of 4.0 m in Rotterdam will be reached with a return period of 46,948 years in 2010, 16,420 years in 2050, 3,849 years in 2100. In the future, the port of Rotterdam will be closed once every 3.2 years in 2050 and once every 1.1 years in 2100 under the current control operation (_{s}_{s}_{s}_{s}

Further improvements in the study are necessary, especially to give absolute answers to the area under investigation. These improvements are as follows:

(1) The uncertainty in Equal Level Curves and in the statistic analysis of extreme North Sea level will be investigated.

(2) Instead of the Equal Level Curves approach, a more advanced numerical hydrodynamic model should be applied.

(3) Both the sea level and Rhine discharge are not a constant peak value of a certain duration. In this research a semi-unsteady sea level boundary condition seems to be an overestimation. A design hydrograph of the sea level at Hook of Holland is preferred. The sea level consists of several variables like the wind set-up and the astronomical tide; the former occurs randomly and the other occurs deterministically. The phase difference between them is statistically important. In other words, an improved probability analysis of the hydraulic boundary conditions is required.

(4) Considering the effects of the control parameters in the operation in an integrated manner, constraints on other objectives such as navigation and fresh water supply will influence the parameters. Moreover, instead of one barrier in the mouth of a simplified estuary, there are several barriers and flood gates in the Rhine delta, with different operational controls. All these barriers and other hydraulic structures define a whole system, where an advanced model predictive controller should be applied [