# Sea level return periods: What are they and how do we use them in SurgeWatch?

By Ivan Haigh

Introduction
The ‘100-year flood’ is a term many of us are used to hearing, and will be a phrase particularly familiar for those who live in flood prone areas. Using return periods like this is the standard way of describing the severity and likelihood of floods, as well as other events like hurricanes, earthquakes, droughts and heat waves. Such terms help us to make sense of extreme weather, but what technically are return periods, why do we use them, how are they calculated, how accurate are they and why do we refer to them on the SurgeWatch website? These are questions, among others, that we address in this article.

What are return periods?
Return periods, often called recurrence intervals, convey information about the likelihood (or probability) of rare events such as coastal floods happening. Return periods in our case refer to the average length of time between sea levels of given heights (which in other contexts could be replaced by any measurable parameter such as river flow or rainfall).

Return periods refer to the average amount of time between a specific sea level return level  being exceeded at a particular location. However, it is a mistake to think that if a 1 in 100 year sea level occurred this year, it would be another 100 years before we see a similar event of the same magnitude. A 1 in 100 year sea level could occur twice (or more) in the same year; or equally not at all in that period of time. Hence, it is best to think of a 1 in 100 year sea level as a level that has a 1% (i.e. 1/100) chance of occurring in any given year, regardless of when the last similar event was. Put another way, it is 10 times less likely to occur than a sea level with a return period of 1 in 10 years (i.e. a 10% probability of occurring in a given year).

It is for this reason that another measure, the annual exceedance probability (AEP), is often quoted in place of a return period. This is the probability of exceeding a specified sea level in any year and is the inverse of the return period. A 1 in 100 year sea level return period has an annual exceedance probability of 1%, whereas a 1 in 200 year sea level has an annual exceedance probability of 0.5%.

Why do we use return periods?
Return periods are used by engineers, scientists and policy makers to estimate the likelihood and severity of extreme events, such as flooding. Assessing the risk of these events for human populations provides a means to allocate defences and their levels, or to decide upon proposed developments in the floodplain. Return periods are part of an array of decision support tools that can be used to make judgements where there is inevitable compromises between cost and safety. Knowledge of sea level return periods is vital for assessing and prioritising the known threat to growing coastal communities.  At present, it is estimated that around 2.5 million properties and £150 billion of assets are exposed to coastal flooding in the UK. These numbers are projected to increase as sea levels continue to rise and development in the floodplain continues. Therefore, estimating the risk of extreme events (and how they might change) to human populations in low-lying coastal areas is tremendously important.

Return periods provide guidance for planning – for example the Environment Agency’s flood maps are based upon land elevation that it specified by return levels. Return periods have been especially important for informing the design of coastal defences and flood barriers, like the Thames Barrier. Here in the UK coastal defences are commonly designed to provide protection against a storm event with a return period of 1 in 200 years (Note this is dependent on a cost/benefit analysis so it is not always provided to this level). In the Netherlands, where a large proportion of people live below mean sea level, dikes are built to provide protection against an event with a return period of 1 in 10,000 years.

How are return periods calculated?
Return periods are estimated using a statistical analysis applied to sea level observations. The branch of statistics upon which analysis methods are based is called extreme value analysis or extreme value theory. Extreme value analyses allow us to estimate the probability of events that are more extreme than those in the dataset. For example at a particular site we might have sea level measurements for 30 years, but then need to estimate what extreme sea levels might occur over the next 100 years (given the 30-year record). Extreme value theory provides the basis that enables extrapolations of this type.

Over the last 60 years, several different methods have been developed and refined for estimating sea level return periods, many of them developed by UK scientists. I describe and compare these different methods in detail in a scientific paper I wrote in 2010 that can be read here. Several of the more recent methods utilize the results of numerical models to help improve the accuracy of return periods spatially all around the coast, particularly at locations where there are no sea level records are available.

In the UK, the most recent national guidance for sea level return periods is provided by a study commissioned by the Environment Agency that was released in 2011. The report, which describes this study, can be obtained here. This work is based on the best available statistical techniques and up-to-date sea level datasets (most from the UK National Tide Gauge Network) available and provides sea level return period estimates every 2 km around the entire coastline of England, Scotland and Wales. Estimates will be improved with time as more data becomes available and methods continue to be improved.

How accurate is a return period?
Return periods, whilst based on current state-of-the-art methods and best available data, are only estimates and thus come with a varying level of uncertainty. This uncertainty largely stems from the effectiveness of the statistical expressions used to determine the distribution of sea level heights through time, and the quality and quantity of the sea level data used, which varies with each site. The larger the return period, the further the extrapolation from the observed dataset, and thus the larger the uncertainty is.

The return period estimates provided by the Environment Agency commissioned study are listed with uncertainty bands. These uncertainty bands represent 95% confidence intervals. For sites with long and good quality sea level records the uncertainty intervals for 1 in 1 year return periods are typically ±0.1 m, for 1 in 10 year return periods are ±0.2 m and for 1 in 100 year return periods are ±0.3 m. For sites with shorter sea level records the confidence intervals are much larger.

Why do we get varying estimates at different coastal locations for the same event?
Return period estimates are typically based on site-specific sea level data. Each tide gauge location will experience different sea level heights due to several factors including (but not limited to) storm track, local bathymetry, and tidal conditions. Consequently, return period estimates are unique for each site. Two sites near to each other on an open stretch of coastline might have very similar return periods for a particular level. Whereas, two sites in an estuary, or along a complex coastline, might have very different return periods for a certain level, as tidal and storm surge characteristics can vary significantly over short distances. Therefore, if return periods are provided for the mouth of an estuary, or along complex coastlines, it should not be automatically assumed that these are applicable for locations nearby.

How do we account for sea level rise?
When calculating return periods it is assumed that the probability of the event occurring does not vary over time and is independent of past events. However, sea level rise influences estimates by increasing the height of mean sea level, which makes an ‘extreme’ sea level (by present standards) a more frequent occurrence in the future (i.e. lowering the return period).

It is for this reason that the long-term trend in mean sea level observed over the 20th century and early part of the 21st century is removed from sea level observations prior to undertaking extreme value analyses. The Environment Agency return periods are relative to a baseline level, which corresponds to the average sea level for the year 2008. At locations that have undergone a rise in mean sea level over the duration of the record, sea levels before 2008 would have a higher return period, and lower return period thereafter. When designing a flood defence it is therefore important that projections of mean sea level rise are factored into the calculations.

How and why do we use return periods in SurgeWatch?
On the SurgeWatch website we use the information provided by the Environment Agency commissioned study (which as we mentioned earlier is based on what is presently regarded as the best available statistical techniques and data) to assign return periods to the high sea levels recorded during each of the events we have identified. We stress again that these return periods are only estimates and have uncertainties associated with them. As new estimates become available in the future, we will update the values listed on the site.

Sea level height (relative to a datum) varies considerably around the UK due to differences in mean tidal range. For example, high water at Avonmouth in the Bristol Channel can reach over 13 mCD, while high water at Bournemouth will be closer to 2 mCD.  Because of this large difference, we do not use maximum sea level heights in SurgeWatch but instead use return periods so that we can directly compare the sea level from different sites during the same event, and for a series of historical events.

We stress also that at present SurgeWatch only lists the heights and return periods of ‘still’ water levels, as recorded by tide gauges. Still water level is the average sea level at any instance due to the combination of mean sea level, tides and storm surges, but excluding the local variation due to waves and wave setup. Waves and wave setup are very important factors for coastal flooding. Return periods for wave heights can be estimated using similar methods and it is possible to calculate the joint probability of still water level and wave heights of a certain magnitude. In the context of any coastal flood event, waves may generate a very different ‘event’ return period if included within an extremes analysis – as demonstrated in this paper. Furthermore, multiple variables (e.g. sea level, waves, river levels, and the duration of each variable) can be combined to define extreme events – as discussed in this paper). Unfortunately, wave records are much shorter than tide gauge records, and this is the main reason we do not yet report wave data (significant wave height, wave period etc.) in SurgeWatch. However, in the future we do plan on extending our analysis to include information about waves during the events we have identified.

Other useful articles on return periods: