Quadrature-based approach for the efficient evaluation of surge hazard

The Joint Probability Method (JPM) has been used for hurricane surge frequency analysis for over three decades, and remains the method of choice owing to the limitations of more direct historical methods. However, use of the JPM approach in conjunction with the modern generation of complex high-resolution numerical models (used to describe winds, waves, and surge) has become highly inefficient, owing to the large number of costly storm simulations that are typically required. This paper describes a new approach to the selection of the storm simulation set that permits reduction of the JPM computational effort by about an order of magnitude (compared to a more conventional approach) while maintaining good accuracy. The method uses an integration scheme called Bayesian or Gaussian-process quadrature (together with conventional integration methods) to evaluate the multi-dimensional joint probability integral over the space of storm parameters (pressure, radius, speed, heading, and any others found to be important) as a weighted summation over a relatively small set of optimally selected nodes (synthetic storms). Examples of an application of the method are shown, drawn from the recent post-Katrina study of coastal Mississippi.