Date of Award

Summer 2009

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Civil & Environmental Engineering

Committee Director

David R. Brasco

Committee Member

Jaewan Yoon

Committee Member

John M. Klinck

Abstract

The scarcity of observations at any single location confounds the probabilistic characterization of tropical cyclone-generated storm surge hazards using annual maxima and peaks-over-threshold methods. The EST and the JPM are indirect approaches aimed at estimating the probability distribution of the response variable of interest (i.e. storm surge) using the probability distributions of predictor variables (e.g. storm size, storm intensity etc.). In the first part of this work, the relative performance of the empirical simulation technique (EST; Borgman et al., 1992) and the joint probability method (JPM; Myers, 1970) is evaluated via stochastic simulation methods. It is shown that the JPM has greater predictive capability for the estimation of the frequency of tropical cyclone winds, an efficient proxy for storm surge.

The traditional attractions of the EST have been its economy and ease of implementation; more efficient numerical approximation schemes such as Bayesian quadrature now exist, which allows for more cost effective implementation of the JPM. In addition, typical enhancements of the original EST approach, such as the introduction of synthetic storms to complement the historical sample, are largely ineffective. These observations indicate that the EST should no longer be considered a practical approach for the robust and reliable estimation of the exceedance probabilities of storm surge levels, as required for actuarial purposes, engineering design and flood risk management in tropical cyclone-prone regions. The JPM is, however, not applicable to extratropical storm-prone regions and nonstationary phenomena.

Additionally, the JPM requires the evaluation of a multidimensional integral composed of the product of marginal and conditional probability distributions of storm descriptors. This integral is typically approximated as a weighted summation of discrete function evaluations in each dimension and extended to D-dimensions by tensor product rules. To adequately capture the dynamics of the underlying physical process—storm surge driven by tropical cyclone wind fields—one must maintain a large number of explanatory variables in the integral. The complexity and cost of the joint probability problem, however, increases exponentially with dimension, precluding the inclusion of more than a few (≤4) stochastic variables. In the second part of the work, we extend stochastic simulation approaches to the classical joint probability problem.

The successful implementation of stochastic simulation to the storm surge frequency problem requires the introduction of a new paradigm: the use of a regression function constructed by the careful selection of an optimal training set from the storm sample space such that the growth of support nodes required for efficient interpolation remains nonexponential while preserving the performance of a product grid equivalent. Apart from retaining the predictive capability of the JPM, the stochastic simulation approach also allows for nonstationary phenomena such as the effects of climate change on tropical cyclone activity to be efficiently modeled. A great utility of the stochastic approach is that the random sampling scheme is readily modified so that it conducts empirical simulation if required in place of parametric simulation.

The enhanced empirical simulation technique attains predictive capabilities that are comparable with the JPM and the parametric simulation approach, while also retaining the suitability of empirical methods for application to situations that confound parametric methods, such as, application to extratropical cyclones and complexly distributed data. The parametric and empirical simulation techniques, together, will enable seamless flood hazard estimation for the entire coastline of the United States, with simple elaborations where needed to allow for the joint occurrence of both tropical and extratropical storms as compound stochastic processes. The stochastic approaches proposed hold great promise for the efficient probabilistic modeling of other multi-parameter systems such as earthquakes and riverine floods.

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DOI

10.25777/s56g-1j68

ISBN

9781109331301

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