where ℜ dv denotes a dv-dimensional space. From this historical data set, a subset
of storm events is selected
[v , j = 1,..., J ]
*
(26)
j
where J is the number of historical storms contained in the subset. The subset of
storms is representative of the entire set of historical storms and is referred to as
the training set. Furthermore, those storms comprising the training set are subse-
quently used as input to numerical models for computing the desired response
vectors. The set of v* usually includes historical events but may include histori-
j
cal storms with a deviation or perturbation, such as a typhoon with a slightly
altered path. Some historical events may also be deleted from the training set if
two events are nearly identical such that both would produce the same response.
Because the purpose is to fill parameter space ℜ, two similar events are
redundant.
The training set of storms can be augmented with additional storms con-
tained in the historical data set. Storm events augmenting the training set are
referred to as the statistical set of storms. Whereas numerical models are used for
calculating response vectors for those events in the training set, response vectors
for the statistical set of storms are interpolated using the training set response
vectors. Thus, stage-frequency relationships can be generated using the entire
historical data set without need of simulating all storms in that data set.
With the augmented storm data set (i.e., training and statistical storm sets),
the EST produces N simulations of a T-year sequence of events (typhoons), each
with their associated input vectors and response vectors. Because there are N-
repetitions of a T-year sequence of events, an error analysis of the results can be
performed with respect to median, worst, least, standard deviation, etc. The
following describes the procedures by which the input and response data are
used to produce multiple simulations of multiple years of events.
Empirical simulation
Two criteria are required of the T-year sequence of events. The first criterion
is that individual events must be similar in behavior to historical events in order
that the interrelationships among the input and response vectors remain realistic.
For example, a typhoon with high central pressure deficit and low maximum
winds is not a reasonable event the two parameters are not independent
although their exact dependency is unknown.
Simulation of realistic events is accounted for in the nearest-neighbor inter-
polation resampling technique developed by Borgman et al. (1992). A storm
event is identified by random sampling from the total storm population. The
procedure is equivalent to drawing and replacing random samples from the full
storm event population.
30
Chapter 3
Modeling Approach
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