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APPENDIX B: EXTREME SEA LEVEL ESTIMATION

Method

The methods used to analyse the performance of coastal schemes differ from the fluvial flood prevention schemes. Sources of flooding are high water levels occurring from tidal and surge components and discharge from waves overtopping defence structures. These two conditions were estimated to provide hydraulic inputs to the performance analysis of the scheme under investigation.

Estimation of extreme water levels

Extreme sea levels were taken from those calculated from the Indicative River and Coastal Flood Maps (Scotland) ³⁷. These were calculated using the POL³⁸ (1997, Internal document No. 112) method for the spatial analysis of extreme sea levels on the UK coast. The method is based on analysis using observed data from coastal locations supplemented by calculated water levels hindcast from a numerical model using meteorological data input. These may then have been adjusted by trend figures based on Admiralty MHWS tide data for ports.

These extreme sea levels have also been adjusted to account for climate change to 2080 ³⁹.

Wave prediction

In the absence of measured wave data for a site of interest a number of empirical methods exist to predict wave characteristics in deep water. The recommended method for this analysis is the Donlan/ JONSWAP method ⁴⁰ which predicts significant wave height and wave period from fetch length and wind speed.

Where no information is available about the wave climate at a site it is considered that the longest straight line fetch is the most appropriate; producing the highest wave estimates. Although this will not result in conservative wave heights it is considered that this will give the most realistic figures.

Deep water wave characteristics for each fetch were calculated and checked for shallow water processes, where the wave speed is determined solely by water depth. The onset of shallow water processes depends on the water depth (d) in relation to the deep water wavelength. The deep water wavelength was estimated assuming small amplitude wave theory ⁴¹:

Estimate of shallow water wave characteristics

Reducing water depths lead to the transformation of incoming deep water waves by refraction, shoaling and eventually breaking. On the assumption that the wave period is constant, these processes affect the wave height and wavelength.

Refraction

Wave refraction is a consequence of the wave moving out of deep water. The portion of the crest in shallower water has its celerity reduced and is progressively turned parallel to the bed contours.

Refraction due to the bathymetry of the foreshore is difficult to assess without detailed bathymetric data. It was therefore generally assumed that incident wave fronts are parallel to the bed contours which are themselves parallel to the sea wall and no refraction takes place.

Shoaling

Shoaling is the increase in wave height and decrease in wavelength and wave speed caused as waves propagate in reducing water depths. Using linear wave theory, this effect can be expressed as a shoaling coefficient KS; the equation for is given in CIRIA 83 Rock Manual ⁴² as follows:

Inshore, the wavelength can be estimated using first order wave theory as follows:

These wavelengths were used to estimate the shoaling coefficient to give a new estimate of significant wave height at the toe of the any structure.

Wave breaking

As waves approach a shoreline, and the water becomes shallower, they may become unstable and break either through steepness induced breaking or depth induced breaking. In shoaling water breaking is usually caused by the latter but both should be considered.

Joint probability

Joint probability analysis is the consideration of the probability that two or more partially dependent variables take extreme values concurrently which, in the case of most coastal schemes, will be the probability of concurrent wave heights and sea levels. Analysis will usually involve some method of estimating the level of dependence between variables, and producing combinations of marginal return periods for each variable that together give a joint probability of occurrence equal to the design requirement. A number of combinations of marginal return periods or scenarios will produce a given design return period. A matrix or joint probability curves are usually produced to ascertain the maximum combined value for use in detailed design.

Joint probability is the subject of on-going research. H R Wallingford has produced an interim report ⁴³, as part of the DEFRA/Environment Agency Flood and Coastal Defence R & D Programme, to provide guidance on best practice on joint probability analysis. The interim report describes a simple method of constructing tables of joint exceedance extremes using existing information on marginal extremes and an estimate of the dependence between the variables.

The simplified method uses a correlation factor to describe the actual dependence relative to independence and full dependence. Tables of marginal return periods for given joint exceedance return periods of 1 year, 5 year, 20 years, 100 years and 500 years are provided for 5 correlation factors ranging from "none" to "supercorrelated" (Tables 3.1 to 3.5). Other joint return periods are interpolated from the tables. Guidance for assessing the correlation factor ( CF) is provided in tabular or map form for a number of variable pairs. Using the tables in the Interim Report, matrices of marginal return periods giving joint probabilities of 2 to 1000 years were produced.

Wave overtopping analysis

In addition to extreme tide levels, overtopping of the defence due to wave action was also assessed. Owen's overtopping method ⁴⁴ provides empirical equations to estimate overtopping discharge for various geometries and incident wave conditions. Account is taken of whether the approaching waves are reflecting or impacting when calculating the overtopping discharge. Guidance is given as to tolerable discharges depending on the presence of crest and downstream slope protection. Safe thresholds of overtopping for structural safety based on structure type, for functional safety based on access requirements and land use behind the structure are given.

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