Extreme value analysis of tropical cyclone trapped-fetch waves

Many of the extreme ocean wave events generated by tropical cyclones (TCs) can be explained by examining one component of the spectral wave field, the trapped-fetch wave (TFW). Using a Lagrangian TFW model, a parametric model representation of the local TC wind fields, and the National Hurricane Center's hurricane database archive, a dataset of TFWs was created from all TCs in the Atlantic Ocean, Gulf of Mexico, and Caribbean Sea from 1851 to 2005. The wave height at each hourly position along a TFW trajectory was sorted into 2 degrees x 2 degrees latitude -longitude grid squares. Five grid squares (north of Hispaniola, Gulf of Mexico, Carolina coast, south of Nova Scotia, and south of Newfoundland) were used to determine if extreme value theory could be applied to the extremes in the TFW dataset. The statistical results justify accepting that a generalized Pareto distribution (GPD) model with a threshold of 6 m could be fitted to the data: the datasets were mostly modeled adequately, and much of the output information was useful. Additional tests were performed by sorting the TFW data into the marine areas in Atlantic Canada, which are of particular interest to the Meteorological Service of Canada because of the high ocean traffic, offshore drilling activities, and commercial fishery. GPD models were fitted, and return periods and the 95% confidence intervals (CIs) for 10-, 15-, and 20-m return levels were computed. The results further justified the use of the GPD model; hence, extension to the remaining grid squares was warranted. Of the 607 grid squares successfully modeled, the percentage of grid squares with finite lower (upper) values for the 10-, 15-, and 20-m return level CIs were 100 (80), 94 (53), and 90 (16), respectively. The lower success rate of 20-m TFW CIs was expected, given the rarity of 20-m TFWs: of the 5 713 625 hourly TFW points, only 13 958, or 0.24%, were 20 m or higher. Overall, the distribution of the successfully modeled grid squares in the data domain agreed with TFW theory and TC climatology. As a direct result of this study, the summary datasets and return level plots were integrated into application software for use by risk managers. A description of the applications illustrates their use in addressing various questions on extreme TFWs.