Combining Statistical and Expert Evidence within the D-S Framework: Application to Hydrological Return Level Estimation
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  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.
KeywordsReturn Period Flood Risk Generalize Extreme Value Return Level Belief Function
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