Figure G1. ADCIRC grid for computing surface elevations and currents (Cont.)

(b) application of the Joint Probability Method (JPM). The design storm

approach basically involves selecting a severe historic storm event and using it to

define a worst case scenario. The disadvantage of this method is that the

frequency-of-occurrence of the design storm is usually not well known. There-

fore the selected event may impose a more stringent cap design condition than

necessary. Conversely, a worst case event may never have occurred at a specific

location, and the design storm could lead to an overdesigned cap. In either case,

the design storm event provides no information on frequency of occurrence and

does not provide any error bands for use in design analysis.

The general JPM approach to assigning frequency relationships begins with

parameterizing the storm that generated the effect of concern (e.g., wave height,

surge level, bottom current). For hurricanes, descriptive parameters include

maximum pressure deficit, maximum winds, radius to maximum winds, speed of

translation, and track. The JPM is based on the assumption that the probability

for each of the listed parameters can be modeled with empirical, or parametric,

relationships. The joint probability of occurrence for a given effect, such as

maximum surge, is defined as the probability of a particular storm event, com-

puted as the product of the individual storm parameter probabilities via these

assumed parametric relationships. This assumption is the primary basis of the

JPM method used in past studies (Myers 1975).

However, the parameters that describe tropical storms are not independent,

but are interrelated in some nonlinear sense (Ho et al. 1987). Because the

parameters are not independent, joint probability cannot be computed as the

product of individual parameter probabilities. Furthermore, it is generally

recognized that extratropical storms cannot be effectively parameterized, so

parametric probability relationships do not exist. Therefore, the JPM may not

provide accurate approximations for tropical storms and is not appropriate for

extratropical storms.

The empirical simulation technique (EST) is a statistical procedure for simu-

lating nondeterministic multiparameter systems such as tropical and extratropical

storms. The EST, which is an extension of the "bootstrap" statistical procedure

(Efron 1982; Efron 1990), overcomes the JPM limitations by automatically

incorporating the joint probability of the historical record. The bootstrap method

on which EST is based incorporates resampling with replacement, interpolation

based on a random walk nearest neighbor techniques with subsequent smoothing.

More detailed descriptions of EST can be found in Scheffner, Borgman, and

Mark (1993) and Borgman et al. (1992).

In EST, the various geometric and intensity parameters from storms are used

to create a large artificial population (several centuries) of future storm activity

(Borgman et al. 1992). The only assumption required for EST is that future

storms will be statistically similar to past storms. Thus, the future storms gener-

ated during EST simulations resemble the past storms but possess sufficient

variability to fill in the gaps in the historical data.

Appendix G Procedures for Conducting Frequency-of-Erosion Studies