On the determination of the temporal and spatial evolution of extreme events

Abstract

The current computations of the Hydraulic Boundary Conditions rely mostly on the distribution of the basic variables at the peak of the storms. As a means of improving the quality of the numerical modelling with a view towards the 2017 assessment, it is envisaged that the numerical models (e.g. the wave model) will in the future use time and space evolving wind fields and fields of the relevant variables (in the case of the wave model: offshore wave conditions, water levels and eventually currents) associated with extreme wind speeds. With these time and space evolving fields the numerical models will produce a set of time evolving hydraulic loads along the water defences. The distributions of these loads are then to be used in probabilistic models in order to compute failure probabilities. One needs therefore to be able to model the temporal and spatial evolution of the multivariate extreme events (wind, waves and water levels in a storm), up to a certain realistic level of detail and according to the needs and capabilities of the numerical and probabilistic models. There are many possibilities as to how the temporal and spatial evolution of an extreme event can be described. There are also varying levels of detail in which this can be achieved. Given the many possible ways in which this could be done, it was deemed necessary to consult two leading experts in extreme value theory, Prof. Laurens de Haan and Prof. Richard L. Smith for advice on how to approach the problem. The request for advice and their proposals are given in this report. Both experts have recommended the use of max-stable processes. Prof. de Haan proposes a semiparametric method derived by him especially for this purpose, which involves the extreme value analysis of the time series at each grid point, in order to determine the Generalized Pareto Distribution parameters for each grid point, and further a non-parametric approach to model the time and space evolution of each (say, 10,000 year) extreme event, by lifting the observed storms exceeding a certain threshold. Prof. Smith proposes a parametric and a semi-parametric method. The semi-parametric method shares some similarities with the method derived by Prof. de Haan, differing in particular in the way temporal and spatial evolution extreme events are selected. The proposed parametric method, although already applied to model spatial extremes, has not yet been applied to model their temporal evolution; some work is still needed in order to find appropriate models and be able estimate their parameters. Furthermore, it is also not clear whether such models, which use only a very limited number of parameters, will be able to realistically describe the complexity of storm fields. We recommend that the methods proposed by Prof. De Haan and Prof. Smith be tested and assessed using the available ERA-40 wind data and, furthermore, that the sensitivity of the results to different choices of the proposed parametric and semi-parametric models be studied.