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Summary: In this paper a statistical procedure to model joint probability distributions of wave height and wind speed and -setup will be critically reviewed on its performance.

This paper introduces the use of copulas for flood probability analysis applied to the Huangpu River during barrier closure. The Huangpu River meanders through the downtown area of Shanghai City and connects the westward-located Tai Lake with the Yangtze River estuary. Storm surges of a typhoon passing the offshore region of Shanghai in combination with high tide is the main cause for flooding of the Huangpu River with inundation of the downtown area as a result. By the year 2010, Shanghai should be protected for floods with a frequency of 1:1000 years. As re-heightening of the present floodwalls alongside the river to meet this demand is not a sustainable solution anymore, the Shanghai Municipal Government is investigating the feasibility to protect Shanghai with a storm surge barrier in the mouth of the river. However, typhoons not only bring storm surges but also torrential rainfall to the area. These intense rains temporarily increase the runoff into the Huangpu River substantially, and since the river is the main drainage route in the area, flooding of the river during barrier closure may occur after all. The objective of this study is to analyze the flood probability of the Huangpu River during barrier closure due to upstream discharges into the river. The paper shows that copulas have proven to be useful in flood probability analyses when limited data is available in which only the marginal distribution functions are known.

For risk-based design of flood defence systems it is necessary to know the probability of failure of the system. This can only be derived if the probability of occurrence of the loads on the flood defence is known. Hydraulic loads caused by typhoons such as water levels and wave characteristics are mutually dependent and this has to be included in their joint probability density functions. This paper describes a method to derive the dependent joint probability density functions of hydraulic loads resulting of typhoons for a bay in Japan. An example is given on how to apply the derived probability function of loads to the design and failure analysis of a flood defence.

The objective of this paper is to describe the hydraulic climate of the Southern North- Sea by statistical models and physical laws for wave heights, wind setup, wave periods and wind speed. The focus is on the selection and calibration of parametric physical models for the use in the description of the joint probability distribution of hydraulic loads. For the validation and calibration of these models, observations have been used. An application is presented about the Rotterdam harbour extension.

In this paper it is investigated whether flood risks of an existing area in the Netherlands can be determined with different risk measures. An overview is given of risk measures used in the field of quantitative risk analysis. Furthermore, a case study is described, in which a flood risk analysis is performed. The results of these risk calculations are compared to existing standards and the risks of other activities in the Netherlands.

On the basis of quantitative reliability analysis of flood defence systems, two design methods are developed. The first is reliability-based design, where the optimal geometry of a flood defence system is obtained by minimising the cost of construction under a constraint on the probability of flooding of the protected area. Reliability-based design is an integral part of the second design method, risk-based design. In risk-based design, the appropriate flooding probability of a protected area is obtained by comparing the cost of protection with the risk reduction that is obtained. A case study illustrates the application of both methods.

Time records of the surface elevation measured by four Waverider buoys in the Mediterranean Sea off the coast of Spain have been analysed to inspect the statistics of crest heights and wave heights. By concatenating the normalised records we obtained a long, quasi-stationary record of 10,000,000 waves, permitting a verification of the Rayleigh distribution and its theoretical variations at rather low levels of probability (wave heights up to 10 times the standard deviation of the surface elevation). The crest heights were almost perfectly Rayleigh distributed over the entire range of observation. The distribution of the wave heights is close to a Rayleigh distribution with scale factor 0.88 (rather than 1 as in the conventional Rayleigh distribution), but it is better approximated with a Weibull distribution with a shape factor 2.162 (rather than 2, as for a Rayleigh distribution). Supplementary observations with laser altimeters in the North Sea (10,000 waves) showed nearly identical results in the range of overlap (the normalised crest heights were slightly higher, showing a nonlinear behaviour).

This paper aims at probabilistic investigation of various possible failure mechanisms which often experience by coastal flood defence structures under the impact of sea loads. The factors that affect structure performance are usually varied. In order to undertake an effective assessment of overall reliability of the coastal flood defences it is essential to have a thorough knowledge and understanding of all possible failure modes and their contribution to the total failure probability of the whole system. All failure mechanism of these structures often relate with various stochastic variables. Sensitivity analysis is therefore necessary to perform in order to see the importance of these variables for each certain failure mode. Application of the method is made for a case study of coastal sea dikes in Vietnam.