Abstract
Estimation of extreme sea levels and waves for high return periods is of prime importance in hydrological design and flood risk assessment. The common practice consists of inferring design levels from the available observations and assuming the distribution of extreme values to be stationary. However, in the recent decades, more concern has been given to the integration of the effect of climate change in environmental analysis. When estimating defense structure design parameters, sea level rise projections provided by experts now have to be combined with historical observations. Due to limited knowledge about the future world and the climate system, and also to the lack of sufficient sea records, uncertainty involved in extrapolating beyond available data and projecting in the future is considerable and should absolutely be accounted for in the estimation of design values.
In this paper, we present a methodology based on evidence theory to represent statistical and expert evidence in the estimation of future extreme sea return level associated to a given return period. We represent the statistical evidence by likelihood-based belief functions [7] and the sea level rise projections provided by two sets of experts by a trapezoidal possibility distribution. A Monte Carlo simulation allows us to combine both belief measures to compute the future return level and a measure of the uncertainty of the estimations.
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References
Apel, H., Thikeken, A.H.: Flood risk assessment and associated uncertainty. Natural Hazards and Earth Sysem Sciences 4, 295–308 (2004)
Aickin, M.: Connecting Dempster-Shafer belief functions with likelihood based inference. Synthese 123, 347–364 (2000)
Barnard, G.A., Jenkins, G.M., Winsten, C.B.: Likelihood inference and time series. Journal of the Royal Statistical Society 125(3), 321–372 (1962)
Coles, S.G., Dixon, M.J.: Likelihood based inference for extreme value models. Extremes 2, 5–23 (1999)
Cox, D.R.: Some problems connected with statistical inference. Ann. Math. Statistics 29, 357–372 (1958)
Denoeux, T.: Maximum likelihood estimation from uncertain data in the belief function framework. IEEE Transactions on Knowledge and Data Engineering (to appear), doi:10.1109/TKDE.2011.201
Edwards, A.W.F.: Likelihood. University Press, Baltimore (1972)
Fisher, R.A.: Inverse Probability and the use of likelihood. Proceedings of the Cambridge Philosophical Society 28, 257–261, CP3 (1932)
Gumbel, E.J.: The statistics of extremes. Colombia University Press, New York (1958)
IPCC Forth Assessment Report (2007), http://www.ipcc.ch/publications_and_data/publications_and_data_reports.shtml
Jenkinson, A.F.: The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Quart. J. Roy. Meteo. Soc. 81, 158–171 (1955)
Merz, B., et al.: Flood risk curves and uncertainty bounds. Natural Hazards 51, 437–458 (2009)
Pfeffer, W., Harper, J., O’Neel, S.: Kinematic constraints on glacier contribution to 21st century sea level rise. Science 321, 1340–1430 (2008), doi:10.1126/science.1159099
Purvis, M.: Probabilistic methodology to estimate future coastal flood risk due to sea level rise. Coastal Engineering 55, 1062–1073 (2008)
Rhamstorf, S.: A semi empirical approach to projecting future sea level rise. Science 315, 368–370 (2007)
Shafer, G.: A mathematical Theory of Evidence. Princeton University Press (1976)
Shafer, G.: Belief Functions and Parametric Models. Journal of the Royal Statistical Society. Series B. 44, 322–352 (1982)
Xu, P., et al.: Uncertainty analysis in statistical modeling of extreme hydrological events. Stochastic Environmental Research and Risk Assessment 24, 567–578 (2010)
Wasserman, L.: Belief functions and statistical inference. The Canadian Journal of Statistics 18, 183–196 (1990)
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© 2012 Springer-Verlag Berlin Heidelberg
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Ben Abdallah, N., Voyneau, N.M., Denœux, T. (2012). Combining Statistical and Expert Evidence within the D-S Framework: Application to Hydrological Return Level Estimation. In: Denoeux, T., Masson, MH. (eds) Belief Functions: Theory and Applications. Advances in Intelligent and Soft Computing, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29461-7_46
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DOI: https://doi.org/10.1007/978-3-642-29461-7_46
Publisher Name: Springer, Berlin, Heidelberg
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