REDUCING UNCERTAINTY IN EXTREME WAVES AND STORM SURGES USING A COMBINED EXTREME VALUE MODEL AND WAVELETS

Panagiota Galiatsatou, Panayotis Prinos

Abstract


In the present study the wavelet transform is combined with non-stationary statistical models for extreme value analysis, to provide more reliable and more accurate return level estimates. The continuous wavelet transform is first used to detect the significant “periodicities” of the wave height and storm surge signals under study by means of the wavelet global and scale-averaged power spectra and then it is used to reconstruct the part of the time series, represented by these significant and prominent features. A non-stationary point process is utilized to model the extremes. A time varying threshold with a period of one year and having an approximately uniform crossing rate throughout the year is used. The reconstructed part of the series variability representing the significant non-stationarities of each signal is incorporated in the both the location and the scale parameters of the point process model, together with selected harmonic functions, formulating a number of candidate extreme value models. The quality of the fitted models is assessed by means of the Akaike Information Criterion, as well as by means of diagnostic quantile plots. The models which incorporate the reconstructed part of the wavelet transform in their location parameter, as a separate component of the parameter without any scaling coefficient, result in narrower return level confidence intervals and therefore tend to reduce uncertainty in extrapolated extremes.

Keywords


wavelet transform; statistically significant periodicities; non-stationary point process; uncertainty

References


Butler, A. 2005. Statistical modelling of synthetic oceanographic extremes, Ph.D. Thesis, Lancaster University, London, UK.

Callaghan, D.P., P. Nielsen, A. Short R. and Ranasinghe. 2008. Statistical simulation of wave climate and extreme beach erosion, Coastal Engineering, 55(5), 375-390.http://dx.doi.org/10.1016/j.coastaleng.2007.12.003

Coles, S. 2001. An introduction to statistical modelling of extreme values, Springer Series in Statistics

Coles, S. and J. Tawn. 1996. A Bayesian analysis of extreme rainfall data, Applied Statistics, 45(4), 463-478.http://dx.doi.org/10.2307/2986068

Coles, S. and J. Tawn. 2005a. Bayesian modeling of extreme surges on the UK east coast, Philosophical Transactions of the Royal Statistical Society A, 363, 1387-1406.http://dx.doi.org/10.1098/rsta.2005.1574

PMid:16191656

Coles, S. and J. Tawn. 2005b. Seasonal effects of extreme surges, Stochastic Environmental Research and Risk Assessment, 19, 417-427.http://dx.doi.org/10.1007/s00477-005-0008-3

Egozcue, J.J., V. Pawlowsky-Glahn and M.I. Ortego. 2005. Wave-Height Hazard Analysis in Eastern Coast of Spain: Bayesian Approach Using Generalized Pareto Distribution, Advances in Geosciences, 2, 25-30.http://dx.doi.org/10.5194/adgeo-2-25-2005

Farge, M. 1992. Wavelet transforms and their applications to turbulence, Annual Review of Fluid

Mechanics, 24, 395-457, doi:10.1146/annurev.fl.24.010192.002143http://dx.doi.org/10.1146/annurev.fl.24.010192.002143

FLOODsite: Integrated Flood Risk Analysis and Management Methodologies. 2004-2009, European Research Project, FP6, www.floodsite.net

Galiatsatou, P. 2009. Statistical estimation methods for extreme events simulation. Applications to storm surge, rainfall and wave data, PhD Dissertation, Division of Hydraulics and Environmental Engineering, Department of Civil Engineering, A.U.Th, Greece (in greek)

Galiatsatou, P. and P. Prinos. 2011, Modeling non-stationary extreme waves using a point process and wavelets, Stochastic Environmental Research and Risk Assessment, 25(2), 165-183.http://dx.doi.org/10.1007/s00477-010-0448-2

Huerta, G. and B. Sanso. 2007. Time varying models for extreme values, Environmental and Ecological Statistics, 14, 285-299.http://dx.doi.org/10.1007/s10651-007-0014-3

Kijewski-Correa, T. and A. Kareem. 2007. Performance of wavelet transform and empirical mode decomposition in extracting signals embedded in noise, Journal of Engineering Mechanics, ASCE, 133(7), 849-852http://dx.doi.org/10.1061/(ASCE)0733-9399(2007)133:7(849)

Liu, P.C. and A.V. Babanin. 2004. Using wavelet spectrum analysis to resolve breaking events in the wind wave time series, Annales Geophysicae, 22, 3335-3345.http://dx.doi.org/10.5194/angeo-22-3335-2004

Markovic, D. and M. Koch. 2005. Wavelet and scaling analysis of monthly precipitation extremes in Germany in the 20th century: Interannual to interdecadal oscillations and the North Atlantic

Oscillation influence, Water Resources Research, 41, W09420, doi: 10.1029/2004WR003843http://dx.doi.org/10.1029/2004WR003843

Massel, S.R. 2001. Wavelet analysis for processing of ocean surface wave records, Ocean Engineering, 28, 957-987.http://dx.doi.org/10.1016/S0029-8018(00)00044-5

Méndez, F.J., M. Menéndez, A. Luce-o and I.J. Losada. 2006 Estimation of the long-term variability of extreme significant wave height using a time-dependent Peak Over Threshold (POT) model.

Journal of Geophysical Research, 11, C07024. doi:10.1029/2005JC003344.http://dx.doi.org/10.1029/2005JC003344

Méndez, FJ, M. Menéndez, A. Luce-o, R. Medina and N.E. Graham. 2008. Seasonality and duration in extreme value distributions of significant wave height, Ocean Engineering, 35, 131-138.http://dx.doi.org/10.1016/j.oceaneng.2007.07.012

Menéndez, M., F.J., Méndez, C. Izaguirre, A. Luce-o and I.J. Losada. 2009. The influence of seasonality on estimating return values of significant wave height, Coastal Engineering, 56, 211-219.http://dx.doi.org/10.1016/j.coastaleng.2008.07.004

Menéndez, M., F.J. Méndez, I.J. Losada and N.E. Graham. 2008. Variability of extreme wave heights in the northeast Pacific Ocean based on buoy measurements, Geophysical Research Letters, 35, Morgan, M.G. and M. Henrion. 1990. Uncertainty: a guide to dealing with uncertainty in quantitative risk and policy analysis, Cambridge University Press, New York. L22607. doi: 10.1029/2008GL035394http://dx.doi.org/10.1029/2008GL035394

Pandey, M.D., P.H.A.J.M. van Gelder and J.K. Vrijling. 2001. The estimation of extreme quantiles of wind velocity using L-Moments in the Peaks-Over-Threshold approach, Structural Safety, 23, 179-192.http://dx.doi.org/10.1016/S0167-4730(01)00012-1

Prinos, P., Th. Koftis, and P. Galiatsatou. 2010. Wavelet analysis of wave propagation over Posidonia Oceanica, Proceedings of Coastlab10 Conference, Barcelona, Spain (full paper in CD-ROM)

Sánchez-Arcilla, A., D. Gonzalez-Marco, N. Doorn and A. Kortenhaus. 2008. Extreme values for coastal, estuarine and riverine environments, Journal of Hydraulic Research, 46(2), 183-190.http://dx.doi.org/10.1080/00221686.2008.9521953

Smith, R. L. 1989. Extreme value analysis of environmental time series: an example based on ozone data (with discussion), Statistical Science, 4, 367-393.http://dx.doi.org/10.1214/ss/1177012400

Torrence, Ch. and G. P. Compo. 1998. A practical guide to wavelet analysis, Bulletin of the American Meteorological Society, 79(1), 61-78.http://dx.doi.org/10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2

Torrence, C. and P. Webster. 1999. Interdecadal changes in the ENSO-Moonsoon System, Journal of Climate, 12, 2679-2690.http://dx.doi.org/10.1175/1520-0442(1999)012<2679:ICITEM>2.0.CO;2

van Gelder, P.H.A.J.M. 1999. Statistical methods for the risk-based design of civil structures, PhD Dissertation, The Netherlands

van Gelder, P.H.A.J.M. and C. Mai. 2008. Distribution functions of extreme sea waves and river discharges, Journal of Hydraulic Research, 46(2), 280-291.http://dx.doi.org/10.1080/00221686.2008.9521961

Zachary, S., G. Feld, G. Ward and J. Wolfram. 1998. Multivariate extrapolation in the offshore environment, Applied Ocean Research, 20, 273-295, doi:10.1016/S0141-1187(98)00027-3.http://dx.doi.org/10.1016/S0141-1187(98)00027-3


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