# Case Studies

## The Challenge

When planners are developing coastal flood defences, they have to consider to what height they should build a sea wall so that the probability of flooding over a pre-specified future period is sufficiently small. The observed sea-level can be split into three different components; the mean sea-level, the tidal level and the surge level. The first captures the long-term changes in global water and local land levels, the second is caused by periodic forces such as the pull of the moon, and the third is an annual cycle induced by the seasonal pattern on the local climate.

Traditionally, methods to estimate sea levels have concentrated on the trend in mean sea-level, whilst assuming that the remaining two components are stationary (i.e., that they do not change over time). Since extreme sea-levels occur when there is a large storm surge at the same time as a high tide, these methods leave out potentially important cyclical effects of the tide and surge levels.

## The Approach

Extreme value analysis (EVA) is used to provide reliable estimates of the frequency of extreme sea-levels. Using historical data of sea-levels, a statistical model is fitted that not only incorporates knowledge of changes in long-term mean sea level, but also of the tidal and surge components of sea-level and how they interact (for more details see here). This model can then be used to provide estimates of sea-levels for specified return periods; for example, a 1 in 50 year extreme sea-level event is estimated to be 3 metres. It is often the case that planners need to account for extremes that are not observed within the available historical data (for example a 1 in 100 or 1000 year event, given a set of data that are 30 years in length); EVA provides a means of extrapolating predictions of extreme sea levels for return periods that are larger than the period of available data.

## The Value

Incorporating all of the processes that affect extreme sea-levels into a statistical model results in far more reliable estimates since, for example, excluding tidal levels can result in substantial underestimation of extreme sea-level. This means that planners can use the resulting estimates with greater confidence that they are not underestimating the levels which they should plan for.