Abstract
Estimation of extreme wave height across the oceans is important for marine safety and design, but is hampered by lack of data. Buoy and platform data are geographically limited, and though satellite observations offer global coverage, they suffer from temporal sparsity and intermittency, making application of standard methods of extreme value estimation problematical. A possible strategy in the face of such difficulty is to use extra model assumptions to compensate for lack of data. In this spirit we report initial exploration of an approach to estimation of extreme wave heights using crossings methods based on a log-Gaussian model. The suggested procedure can utilize either intermittent satellite data or regular time series data such as obtained from a buoy, and it is adapted to seasonal variation in the wave height climate. The paper outlines derivation of the method and illustrates its application to data from the Atlantic and Pacific oceans. A numerical comparison is made with the results of an annual maximum analysis for sites at which both satellite and buoy data are available. The paper concludes with a discussion of the applicability of the new approach, its relationship to other extreme value methods and desirable directions for further development.
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References
Anderson, C.W., Carter, D.J.T., Cotton, P.D.: Wave climate variability and impact on offshore design extremes. Shell International Report. Available from http://clive-anderson.staff.shef.ac.uk/waves.pdf (2001)
Azais, J.-M., Wschebor, M.: Level Sets and Extrema of Random Processes and Fields. Wiley, Hoboken (2009)
Baxevani, A., Rychlik, I., Wilson, R.: A new method for modelling the space variability of significant wave height. Extremes 8, 267–294 (2005)
Baxevani, A., Caires, S., Rychlik, I.: Spatio-temporal statistical modelling of significant wave height. Environmetrics 20, 14–31 (2008)
Bleistein, N., Handelsman, R.A.: Asymptotic Expansions of Integrals. Dover Publications, New York (1986)
Caires, S., Sterl, A.: 100-year return value estimates for ocean wind speed and significant wave height from the ERA-40 data. J. Climate 18, 1032–1048 (2005)
Challenor, P., Cotton, P.D.: Trends in Topex Significant Wave Height Measurement. Available as a pdf document at http://www.soc.soton.ac.uk/JRD/TOPtren/TOPtren.pdf (1999)
Cook, N.J.: Towards better estimates of extreme winds. J. Wind Eng. Ind. Aerodyn. 9, 295–323 (1982)
de Haan, L.: On Regular Variation and its Application to the Weak Convergence of Sample Extremes. Math. Centre Tract, vol. 32. Mathematisch Centrum, Amsterdam (1970)
Fisher, R.A., Tippett, L.H.C.: Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proc. Camb. Philos. Soc. 24, 180–190 (1928)
Leadbetter, M.R., Lindgren, G., Rootzén, H.: Extremes and Related Properties of Random Sequences and Processes. Springer, Heidelberg (1983)
Marcus, M.B.: Level crossings of a stochastic process with absolutely continuous sample paths. Ann. Probab. 5, 52–71 (1977)
Pickands, J.: Asymptotic properties of the maximum in a stationary Gaussian process. Trans. Am. Math. Soc. 145 75–86 (1969)
Rychlik, I.:. Extremes, rainflow cycles and damage functionals in continuous random processes. Stoch. Process. Their Appl. 63, 97–116 (1996)
Rydén, J.:. Estimation of return values: consequences of missing observations. Int. J. Math. Educ. Sci. Technol. 39, 357–363 (2008)
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Rychlik, I., Rydén, J. & Anderson, C.W. Estimation of return values for significant wave height from satellite data. Extremes 14, 167–186 (2011). https://doi.org/10.1007/s10687-010-0117-3
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DOI: https://doi.org/10.1007/s10687-010-0117-3