Ocean Dynamics

, Volume 65, Issue 4, pp 509–521 | Cite as

A new hybrid model for filling gaps and forecast in sea level: application to the eastern English Channel and the North Atlantic Sea (western France)

  • Imen TurkiEmail author
  • Benoit Laignel
  • Nabil Kakeh
  • Laetitia Chevalier
  • Stephane Costa


This research is carried out in the framework of the program Surface Water and Ocean Topography (SWOT) which is a partnership between NASA and CNES. Here, a new hybrid model is implemented for filling gaps and forecasting the hourly sea level variability by combining classical harmonic analyses to high statistical methods to reproduce the deterministic and stochastic processes, respectively. After simulating the mean trend sea level and astronomical tides, the nontidal residual surges are investigated using an autoregressive moving average (ARMA) methods by two ways: (1) applying a purely statistical approach and (2) introducing the SLP in ARMA as a main physical process driving the residual sea level. The new hybrid model is applied to the western Atlantic sea and the eastern English Channel. Using ARMA model and considering the SLP, results show that the hourly sea level observations of gauges with are well reproduced with a root mean square error (RMSE) ranging between 4.5 and 7 cm for 1 to 30 days of gaps and an explained variance more than 80 %. For larger gaps of months, the RMSE reaches 9 cm. The negative and the positive extreme values of sea levels are also well reproduced with a mean explained variance between 70 and 85 %. The statistical behavior of 1-year modeled residual components shows good agreements with observations. The frequency analysis using the discrete wavelet transform illustrate strong correlations between observed and modeled energy spectrum and the bands of variability. Accordingly, the proposed model presents a coherent, simple, and easy tool to estimate the total sea level at timescales from days to months. The ARMA model seems to be more promising for filling gaps and estimating the sea level at larger scales of years by introducing more physical processes driving its stochastic variability.


Sea level forecast Astronomical tides Nontidal residual surges ARMA Sea level pressure 



The first thanks are granted to the CNES and TOSCA program of SWOT for financial support. The authors would like to thank the anonymous reviewers for their careful reading and their valuable comments that helped to improve this work. Many thanks also to the Spanish Government-EU FEDER for partially funding this research (research project CTM2012-35398).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Imen Turki
    • 1
    Email author
  • Benoit Laignel
    • 1
  • Nabil Kakeh
    • 2
  • Laetitia Chevalier
    • 1
  • Stephane Costa
    • 3
  1. 1.UMR CNRS 6143 Continental and Coastal Morphodynamics ‘M2C’ University of RouenMont-Saint-Aignan CedexFrance
  2. 2.Department of Applied PhysicsUniversitat Politècnica de Catalunya-Barcelona TechBarcelonaSpain
  3. 3.University of Caen Low Normandy, Geophen UMR-CNRS LETGNormandyFrance

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