(1986). For more information on analytical approaches, reference is made to USACE (1986) or any text on

probability and statistics.

(3) Synthetic method.

(a) The synthetic method is based on the assumption that a particular event can be characterized by

several descriptive (component) parameters, and that the probability associated with each of those parameters

can be used to determine the joint probability of the total event. For example, tropical storm events were

described by parameters such as radius to maximum wind, maximum wind, pressure deficit, etc. It is assumed

that the frequency of the event can be described by the frequencies associated with each parameter.

(b) The most commonly used form of the synthetic approach is the Joint Probability Method (JPM).

The assumption basic to the JPM is that the probability of occurrence of a given storm event can be written

as the product of the probabilities corresponding to each storm parameter and that the probabilities for each

parameter are independent. For example, a common assumption is that the storm can be described by five

storm parameters. If the parameters are statistically independent, then the joint probability density function

for the five-dimensional set is the product of the individual probability density functions, i.e.,

(II-5-24)

where *f*D, fR, etc., represent the pdf for the central pressure deficit *D *(far-field pressure *p*n less central pressure

(with respect to some specified location) of the eye of the storm *L*. The JPM has been widely used in the past

for storm surge analyses. Details are well-documented in USACE (1986) and the reader is referred to that

document for a more detailed description.

(4) Empirical simulation technique.

(a) Introduction. Few locations have an adequate historical database of storm events from which to

develop reliable stage-frequency relationships. The JPM is subject to error because it is based on simplifying

assumptions of parameter independence, and specifying the pdf of each parameter according to parametrically

based relationships. The empirical simulation technique (EST) is a statistical resampling scheme that uses

historical data to develop joint probability relationships among the various storm parameters. These

relationships are based on data derived from actual storm events. There are no simplifying assumptions

concerning the pdf's; the interdependence of parameters is computed directly from the respective parameter

interdependencies contained in the historic data. In this manner, probabilities are site-specific, do not depend

on fixed parametric relationships, and do not assume parameter independence. Thus, the EST is "distribution-

free" and nonparametric. There are presently two approaches to applying the EST. The first approach is a

multi-parameter simulation approach developed for application to tropical events. The second is a single-

parameter approach developed for use in extratropical events. EST applications for tropical and extratropical

events are discussed briefly below.

(b) EST - tropical storm application.

(1) The multi-parameter EST Program (Scheffner et al. 1999) utilizes historic data to generate a large

number of multi-year simulations of possible future hurricane storm events for a specific location. The

approach is based on resampling and interpolation of data contained in a database of events derived from

historic events. The ensemble of simulations is consistent with the statistics and correlations of past storm

activity at the site, but allows for random deviations in behavior that are likely to occur in the future.

Water Levels and Long Waves

II-5-47

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