Nonlinear dynamics of the sea level time series in the eastern English Channel

Coastal flooding due to surge events represents natural hazards with huge potential consequences for coastal regions. Sea level time series display variations on a large range of timescales, with a deterministic component associated with tidal variations and a stochastic component primarily associated with meteorological forcing, the non-tidal residual. The deterministic component can be evaluated using a model taking into account astronomical forcing and topographic information. The measured sea level is the sum of a slowly varying mean sea level component, the tidal term and the stochastic term. Here, we consider hourly time series recorded in the ports of Boulogne-sur-Mer, Calais, and Dunkirk, in the eastern English Channel. Measured data and modeled data, both provided by the SHOM (“Service hydrographique et océanographique de la marine,” hydrographic and oceanographic services of the French Navy), are analyzed using Fourier spectral analysis. The statistics of return times of extreme events are also estimated directly from the time series and compared between modeled and measured data. It is found that return times from tidal or measured time series are quite different for large thresholds and that they also have a very different Fourier power spectrum, the measured data having a power-law regime which is not found in the modeled tidal data. It is also shown, using Hilbert–Huang transform, that non-tidal residual time series are intermittent and possess multifractal scaling properties. Finally, water level non-tidal residual relationship is explored, and it is shown that the larger mean values of the surge (negative and positive parts) are obtained for the medium level of the tidal value.