v = (v1 , v2, v3 ,..., v N )
(21)
In the case of typhoons, pertinent input vectors include: the central pressure
deficit, the radius to maximum winds, minimum distance from the eye of the
storm to the location of interest, forward speed of the eye, and the tidal phase
during the event. These values can be defined for each specific location and
correspond to each particular historical or hypothetical event of the total set of
storm events used in the study.
The second class of vectors involve some selected response resulting from
the N-dimensional parameterized storm, i.e.,
r = (r1, r2 , r3 ,..., rM )
(22)
For typhoons, response vectors can include maximum storm surge, shoreline
erosion, dune recession, wind-generated wave height and period, bottom erosion,
overtopping rate, or any response that can be attributed to the passage of the
storm. The maximum total water-surface elevation, resulting from the combined
tide and storm surge, is the response vector of interest.
Although response vectors are related to input vectors
v⇒r
(23)
the interrelationship is highly nonlinear and involves correlation relationships
which cannot be directly defined, i.e., a nonparametric relationship. For
example, in addition to the storm-input parameters, storm surge is a function of
local bottom topography, shoreline slope and exposure, ocean currents, etc., as
well as their spatial and temporal gradients. It is assumed that these combined
properties are implicit in the response vector. For the case of storm surge along
the coast of Guam, atmospheric and hydrodynamic models are applied to
compute response vectors as a function of the input vectors and local bottom
topography together with shoreline configuration. Other response vectors such as
sediment transport, shoreline response, and dune recession require application of
additional models.
Historical data for storms can be characterized as
[vi ; i = 1,..., I ]
(24)
where I is the number of historical storm events. For example, let vi have dv
components
vi = ℜdv
(25)
29
Chapter 3
Modeling Approach
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