Natural Hazards

, Volume 91, Issue 1, pp 267–285 | Cite as

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

  • F. G. Schmitt
  • A. Crapoulet
  • A. Hequette
  • Y. Huang
Original Paper


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.


Surge Return times Sea level Scaling Intermittency 



We thank Denis Marin for the making of Fig. 2. Observations from the tide gauge of Dunkirk are the property of SHOM and the Grand Port Maritime de Dunkirk; observations from the Calais tide gauge are the property of SHOM, the Region “Hauts de France” and of the port of Calais; observations from the Boulogne-sur-Mer tide gauge are the property of SHOM, the Region “Hauts de France-Nord-Pas de Calais Picardie” and of the port of Boulogne-sur-Mer. These datasets are available on the Web site of the reference network of tide gauge observations ( The reviewers are thanked for their comments and recommendations that helped improve the manuscript. Y.X is partially sponsored by the National Natural Science Foundation of China (under Grant Nos. 11332006 and 11732010) and by the Fundamental Research Funds for the Central Universities (Grant No. 20720150075). Y.X. and F.G.S. are partially funded by the Sino-French (NSFC-CNRS) joint research project LATUMAR (No. 11611130099, NSFC China, and PRC 2016-2018).


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Univ. Lille, Univ. Littoral Cote d’Opale, UMR 8187, LOG, Laboratoire d’Océanologie et de GéosciencesCNRSWimereuxFrance
  2. 2.State key Laboratory of Marine Environmental Science, College of Ocean and Earth SciencesXiamen UniversityXiamenChina

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