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Chapter II. Extreme events
II.1. Introduction
Coastal zones are subject to storm events with associated extreme waves. Various parameters are
of interest, but in this study, emphasis is put on the return periods and their extreme waves,
which are important in the design of coastal defense structures such as seawalls and breakwaters.
This is done in order to provide sufficient protection against flooding or erosion to a desired
return level associated with a particular return period, for example 100 years (Thompson et al.
2009). Under or over design can lead to very costly consequences and even fatalities. Proper
statistical analyses of measured wave data of a time series are therefore required for these
estimations.
To achieve convincing results, we have opted to work, in this chapter with the theory of extreme
values.
II.2. Extreme value theory
Extreme value theory provides a framework that enables extrapolation in order to estimate the
probability of events that are more extreme than any that have already been observed (Coles
2001). In other words, it is used to determine bounds by estimating statistical models that fit the
extreme values of the observed data (Cornel Stander, 2015).
Although there are various statistical approaches for analyzing extreme values, they are typically
divided into two main categories: methods that consider maxima over fixed intervals (block
maxima approach) and methods that consider exceedances (peaks) above high thresholds based
on exceedances over a chosen threshold (u) is called the Points Over Threshold (POT) method
(Jacob, Neves, & Greetham, 2020).
These methods are illustrated in Figure II-1 (Cornel Stander, 2015) where the block maxima
approach is illustrated in the graph on the left and the POT approach is illustrated in the graph on
the right. The red dots indicate the values to be used for analysis. The block maxima (BM)
approach in extreme value theory (EVT) involves dividing the observation period into nonoverlapping periods of equal size and focusing on the maximum observation in each period.
Chapter II. Extreme events
II.1. Introduction
Coastal zones are subject to storm events with associated extreme waves. Various parameters are
of interest, but in this study, emphasis is put on the return periods and their extreme waves,
which are important in the design of coastal defense structures such as seawalls and breakwaters.
This is done in order to provide sufficient protection against flooding or erosion to a desired
return level associated with a particular return period, for example 100 years (Thompson et al.
2009). Under or over design can lead to very costly consequences and even fatalities. Proper
statistical analyses of measured wave data of a time series are therefore required for these
estimations.
To achieve convincing results, we have opted to work, in this chapter with the theory of extreme
values.
II.2. Extreme value theory
Extreme value theory provides a framework that enables extrapolation in order to estimate the
probability of events that are more extreme than any that have already been observed (Coles
2001). In other words, it is used to determine bounds by estimating statistical models that fit the
extreme values of the observed data (Cornel Stander, 2015).
Although there are various statistical approaches for analyzing extreme values, they are typically
divided into two main categories: methods that consider maxima over fixed intervals (block
maxima approach) and methods that consider exceedances (peaks) above high thresholds based
on exceedances over a chosen threshold (u) is called the Points Over Threshold (POT) method
(Jacob, Neves, & Greetham, 2020).
These methods are illustrated in Figure II-1 (Cornel Stander, 2015) where the block maxima
approach is illustrated in the graph on the left and the POT approach is illustrated in the graph on
the right. The red dots indicate the values to be used for analysis. The block maxima (BM)
approach in extreme value theory (EVT) involves dividing the observation period into nonoverlapping periods of equal size and focusing on the maximum observation in each period.