(1) Applications such as long-term shoreline evolution depend partially on major storm events and

partially on a wide variety of day-to-day conditions that also influence sediment movement. Further, the

attention must be focussed on the long-term *time history *of conditions.

(2) A statistical framework is available for using a limited, but multi-year wave information base to

define statistical characteristics at the location and then synthesize an unlimited number of additional years

of information (Scheffner and Borgman 1992). The synthesized information matches the known information

in a statistical sense but includes random variability also present in the process.

conditions. Because these conditions are typically difficult to estimate accurately and they often have large

economic implications, a number of different probability distribution functions have been used to find a best

fit to available data (Figures II-8-2 and II-8-3). The Fisher-Tippett Type I and II (FT-I and FT-II)

distributions were derived from statistical theory of extremes, and hence are true extremal distributions. The

Weibull distribution with *k*=2 is equivalent to the Rayleigh distribution. The parameters *A, B, *and *k *are

known as the *scale, location, *and *shape *parameters, respectively (Table II-8-2). Typical values for the shape

parameter in coastal engineering applications (e.g. Goda 1988) are given along with the general distribution

functions. Expressions for the mean and standard deviation in terms of the distribution function parameters

and vice-versa are also included if they can be written in compact form. Of the distributions shown in

Figure II-8-3, choosing the Weibull distribution with *k*=0.75 clearly leads to the highest extremal estimates.

Choosing the Weibull distribution with *k*=2.0 leads to the lowest estimates. The FT-I distribution gives

estimates intermediate to the Weibull with *k *values of 1.0 and 1.4.

for estimating extreme responses, especially when multiple input parameters are important and the linkages

between inputs and response are complex. This technique makes use of relationships embedded in the input

information. There is no requirement for selecting distribution functions or assuming that input parameters

are mutually independent. The EST is described in Part II-5-5-b-(3) in relation to storm surge estimation.

In addition to providing the traditional stage-frequency relationship, the method gives valuable information

on variability about the mean relationship. The information can be used to assess the level of risk associated

with surge heights selected for design within the limits of the range of events simulated. The EST can be

extended to design applications besides storm surge, such as beach erosion caused by tropical storms (Farrar

et al. 1994).

in the distribution function, and choosing an extremal distribution function must be done carefully. Each of

these choices can significantly influence the estimated extreme values, especially those for very rare events.

(1) Data selection.

(a) Data used for extreme analysis should be taken only from significant events in the recorded time

history. Further, each data value should be from a different event to ensure statistical independence between

values. The events should be representative of the *type *of events (though of lesser intensity) expected to

cause the extremes of design concern. It is assumed that the statistics of extreme events are stationary over

the period of record and in the future (e.g. no systematic increase in number and severity of extreme storms

due to such possible effects as global warming). A full climatological data set (such as observations every

3 hr over 20 years) is not recommended for extreme analysis. Such data sets include multiple data values

from each major storm, and one or several very severe storms can dominate the extremes.

II-8-6

Hydrodynamic Analysis and Design Conditions

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