Christoph Mudersbach, Juergen Jensen


In this paper, a non-stationary extreme value analysis approach is introduced in order to determine coastal design water levels for future time horizons. The non-stationary statistical approach is based on the Generalized Extreme Value (GEV) distribution and a L-Moment parameter estimation as well as a Maximum-Likelihood-estimation. An additional approach considers sea level rise scenarios in the non-stationary extreme value analysis. All the methods are applied to the annual maximum water levels from 1849-2007 at the German North Sea gauge at Cuxhaven. The results show, that the non-stationary GEV approach is suitable for determining coastal design water levels.


extreme value statistics; non-stationary time series; design levels

Full Text:



Butler, A., Heffernan, J. E., Tawn, J. A., and Flather, R. A. (2007) Trend estimation in extremes of synthetic North Sea surges. Journal of the Royal Statistical Society: Series C (Applied Statistics), 56 (4), 395-414.

Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. Springer, London.

Coles, S.G. and Tawn, J. (1990) Statistics of coastal flood prevention. Phil. Trans. R. Soc. Lond. A, 332, 457-476.

Cunderlik, J.M. and Burn, D.H. (2003) Non-stationary pooled flood frequency analysis. Journal of Hydrology, 276, 210-223.

El Adlouni, S., Ouarda, T.B.M.J., Zhang, X., Roy, R., and Bobée, B. (2007) Gerneralized maximum likelihood estimators for the nonstationary generalized extreme value model. Water Resources Research, 43, W03410.

Grossmann, I., Woth, K. and von Storch, H. (2007) Localization of global climate change: Storm surge scenarios for Hamburg in 2030 and 2085. Die Küste, 71.

Gumbel, E. J. (1958) Statistics of Extremes. Columbia University Press, New York.

Hawkes, P.J., Gonzales-Marco, D., Sanchez-Arcilla, A., and Prinos, P. (2008) Best practice for the estimation of extremes: A review. Journal of Hydraulic Research, 46, Extra Issue 2, 324-332.

Hosking, J.R.M. and Wallis, J.R. (1997) Regional frequency analysis. Cambridge University Press, Cambridge.

Hundecha, Y., St-Hilaire, A., Ouarda, T.B.M.J., El Adlouni, S., and Gachon, P. (2008) A nonstationary Extreme Value Analysis for the Assessment of Changes in Extreme Annual Wind Speeds over the Gulf of St. Lawrence, Canada. Journal of Applied Meteorology and Climatology, 47, 2745-2759.

Jensen, J. (1985) Über instationäre Entwicklungen der Wasserstände an der Deutschen Nordseeküste, Dissertation, Technische Universität Braunschweig (in German)

Jensen, J. and Mudersbach, Ch. (2007) Zeitliche Änderungen in den Wasserstandszeitreihen an den Deutschen Küsten. Berichte zur deutschen Landeskunde, 81 (2), 99-112 (in German).

Jevrejeva, S., Moore, J.C., and Grinsted, A. (2010) How will sea level respond to changes in natural and anthropogenic forcings by 2100? Geophysical Research Letters, Vol. 37, L07703

Katz, R.W., Parlange, M.B., and Naveau, P. (2002) Statistics of extremes in hydrology. Advances in Water Resources, 25, 1287-1304.

Khaliq, M.N., Ouarda, T.B.M.J., Ondo, J.-C., Gachon, P. and Bobee, B. (2006) Frequency analysis of a sequence of dependent and/or non-stationary hydro-meteorological observations: A review. Journal of Hydrology, 329, 534-552.

Kotz, S. and Nadarajah, S. (2000) Extreme Value Distribution - Theory and Applications. Imperial College Press, London.

Meehl, G.A., T.F. Stocker, W.D. Collins, P. Friedlingstein, A.T. Gaye, J.M. Gregory, A. Kitoh, R.

Knutti, J.M. Murphy, A. Noda, S.C.B. Raper, I.G. Watterson, A.J. Weaver, and Z.-C. Zhao, 2007: Global Climate Projections. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S.,D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M. Tignor and H.L. Miller (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

Mendez, F. J., Menendez, M., Luceno, A., and Losada, I. J. (2007) Analyzing monthly extreme sea levels with a time-dependent GEV Model. Journal of Atmospheric and Oceanic Technology, 24, 894-911.

MLR (2001) Generalplan Küstenschutz - Integriertes Küstenschutzmanagement in Schleswig-Holstein, Ministerium für ländliche Räume, Landesplanung, Landwirtschaft und Tourismus des Landes Schleswig-Holstein (in German).

Mudersbach, C. and Jensen, J. (2010) Nonstationary extreme value analysis of annual maximum water levels for designing coastal structures on the German North Sea Coastline, Journal of Flood Risk Management 3 (2010), 52-62

Müller-Navarra, S., Bork, I., Jensen, J., Koziar, Ch., Mudersbach, Ch., Müller, A., and Rudolph, E. (2006) Modellstudien zur Sturmflut und zum Hamburg-Orkan 1962, Hansa, 12, Hamburg, 72-88 (in German)

Nogaj, M., Parey, S., and Dacunha-Castelle, D. (2007) Non-stationary extreme models and a climatic application. Nonlinear Processes in Geophysics, 14, 305-316.

Pugh, D. (2004) Changing Sea Levels - Effects of Tides, Weather and Climate. Cambridge University Press, Cambridge.

Rao, A.R. and Hamed, K.H. (2000) Flood frequency analysis. CRC Press, New York.

Ribereau, P., Guillou, A., and Naveau, P. (2008) Estimating return levels from maxima of nonstationary random sequences using the Generalized PWM method. Nonlinear Processes in Geophysics, 15, 1033-1038.

Salas, J.D. (1993) Analysis and Modelling of Hydrologic Time Series. In Maidment, D.R. (Ed.): Handbook of Hydrology, McGraw-Hill Inc., New York.

Strupczewski, W.G., Singh, V. P., and Feluch, W. (2001) Non stationary approach to at-site flood frequency modelling 1: Maximum likelihood estimation. Journal of Hydrology, 248, 123-142