EM 1110-2-1100 (Part II)
30 Apr 02
b. Stochastic time history.
(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
sequencing of wave and water level conditions is important in progressive beach erosion and recovery. Thus
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.
c. Extremal probability distribution functions
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.
d. Empirical simulation technique. The Empirical Simulation Technique (EST) offers a powerful tool
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).
e. Methods for fitting distributions to data. Selecting data for extremal analysis, estimating parameters
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.
Hydrodynamic Analysis and Design Conditions