Extremes from scarce data: The role of Bayesian and scaling techniques in reducing uncertainty

Abstract

This paper deals with the analysis of extreme wave heights and their uncertainties. The main purpose is to assess confidence intervals using a conventional extreme value, and a Bayesian approach. It is shown how the introduction of an a priori information helps to bound the upper confidence limit. The analysis is performed with wave-height data recorded off the Spanish Catalan coast (NW Mediterranean) and wave-height data from the Dutch coast (North Sea). An analysis with natural-scale and log-transformed wave-height time series has been performed. This scale selection is proven to be advantageous for naturally bounded variables and also better captures some distribution features. The paper ends with a discussion on how the different techniques can be used to select a statistically robust threshold for an extreme event definition. This affects the evaluation of risk in low-lying coastal areas, associated to variables controlling flooding and erosion risks.

Keywords:

• Extremes
• scaling
• selection
• threshold
• wave