Recent hurricanes in the Gulf of Mexico (e.g., Ivan, Dennis, Katrina, Rita and Ike) were observed to develop wave conditions that were near or exceeded the predicted 100-year conditions. As a result, many offshore facilities, as well as coastal infrastructure, which were designed to withstand the 100-year condition, were damaged. New estimates of extreme conditions, which incorporate recently observed maxima, are needed to provide better guidelines for design of coastal and offshore structures. Berek et al. (2007) have used modeled data to develop new criteria, but these estimates can be very sensitive to the data and to the statistical methods used in the development. Berek's estimates also do not cover the entire Gulf of Mexico. We have developed updated estimates of the 100-year extreme wave conditions for the entire Gulf of Mexico using a more comprehensive approach. First, the applicability of standard parametric wind models was examined and appropriate adjustments to the Rankine vortex model were developed to reduce the wind field errors during hurricane conditions. The adjusted winds reduced the error by up to 25 percent compared to the original Rankine vortex model. To obtain reliable wave data, merged wind fields were generated using the NCEP/NCAR Reanalysis 1 project modeled wind data for background wind and the parametric wind model for hurricane conditions. Next, the SWAN wave model was used for the 51-year period from 1958 to 2008 along with multiple statistical methods (Gumbel, Weibull and GEV-Generalized Extreme Value distribution). The effect of the recent hurricane season (2004-2008) shows that maximum 100-year wave height values and their distribution changes. A resampling technique (bootstrap) is used to evaluate and select the optimum statistical method to estimate more appropriate extreme wave conditions.

Thesis (MScEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Tropical cyclones are synoptic scale rotating storms capable of generating intense wind speeds and rainfall with potentially devastating social and economic consequences. In addition to abnormally high winds and rainfall, the associated storm surge and extreme waves can lead to severe coastal erosion, damage to coastal property and inundation. A good understanding of the risk exposure to these events is therefore of great importance to planners and designers of coastal infrastructure in vulnerable regions. Probabilistic approaches have been routinely adopted for the calculation of extreme tropical cyclone induced wind speeds, with significant developments in these techniques over the last few decades. While the application of these approaches has become widely adopted in regions such as the North Atlantic, North Pacific and South Pacific Oceans, relatively little attention has been paid to the South-West Indian Ocean. This thesis focusses on the quantification of the risk exposure to tropical cyclones over the South-West Indian Ocean, using current state-of-the-art techniques. The primary results of the thesis are extreme wind speed maps at various return periods of interest for engineering design. Best track data for the South-West Indian Ocean, as archived by the Joint Typhoon Warning Centre (JTWC), has been used as the primary dataset forming the basis of this study. These data provide estimates of the location and intensity of historical tropical cyclones at six hourly intervals. Location data are provided as estimates of longitude and latitude of the eye, while intensity data are provided as estimates of the maximum sustained surface (10 m elevation) wind speed and/or minimum central pressure. The modelling of tropical cyclone wind fields has been carried out using both the Holland (1980) and the Willoughby et al. (2006) parametric wind field models. Using the limited information available in the best track data as input to the model, surface wind fields which reasonably resemble those of actual storms have been generated. Both considered parametric wind field models have been shown to yield reasonable wind speeds and directions when compared with measurements. Of the two considered models the Willoughby et al. (2006) model has been shown to provide the best fit to historical wind speed measurements. Extreme value analyses of tropical cyclone induced wind speeds based on historical data alone have been shown to lead to potentially large errors, owing to the small sample size of the historical data. This highlights the need to augment the historical database through a probabilistic approach. Largely following the methods described in Powel et al. (2005) and Emanuel et al. (2006), a synthetic track model for the South-West Indian Ocean has been developed. The objective of the synthetic track model is to simulate thousands of years of tropical cyclone tracks, thereby circumventing errors induced by small sample sizes in the available historical best track data. The synthetic track model developed as part of this study is a Markov chain model, capable of simulating track propagation and intensity evolution along the track, from track genesis through to termination. The model is purely statistical, based on properties derived from the historical best track data. Adjustments have however been made to account for physical limitations such as those imposed by the equator and the maximum potential intensity which an event can attain. The statistical characteristics of synthetic tracks have been shown to agree well with those of the historical population. Applying the Willoughby et al. (2006) wind field model along synthetic tracks has enabled the simulation of 5 000 years of tropical cyclone induced wind speeds at any location of interest in the South-West Indian Ocean. Applying calculations on a 1 degree geographical grid, wind speed maps corresponding to return periods of 50, 100, 200 and 500 years have been generated for the South-West Indian Ocean. Extreme wind speeds along coastal regions provide valuable input for the design of coastal infrastructure in the region. / AFRIKAANSE OPSOMMING: Tropiese siklone is sinoptiese orde roterende storms wat in staat is om aansienlike windspoed en reënval, tot gevolg te hê met potensiële vernietigende sosiale en ekonomiese gevolge. Benewens die abnormale sterk winde en hoë reënval kan die verwante stormdeinings en vloedgolwe lei tot ernstige kus-erosie, skade aan kusfront-eiendom en oorstromings. ‘n Goeie begrip van die risiko-blootstelling aan hierdie gebeurtenisse is daarom van groot belang vir die beplanners en ontwerpers van kus-infrastruktuur in kwesbare gebiede. As gevolg van die beduidende ontwikkeling van probabilistiese benadering tot die berekening van windspoed wat veroorsaak word deur ekstreme tropiese siklone, word hierdie tegnieke huidiglike op ‘n roetine basis aangewend. Terwyl die toepassing van hierdie benaderings wyd aanvaar word in gebiede soos die Noord-Atlantiese, Noordelike- en Suidelike Stille Oseaan, word relatief min aandag gegee aan die Suid-Westelike Indiese Oseaan. Hierdie tesis fokus op die kwantifisering van die risiko-blootstelling aan tropiese siklone in die Suid-Westelike Indiese Oseaan met die gebruik van die huidige gevorderdste tegnieke. Die primêre resultaat van die tesis is uiterste wind spoed kaarte vir ‘n verskeindenheid herhaal periodes wat van belang in vir engenieursontwerp. Beste roete-ata vir die Suid-Westelike Indiese Oseaan, soos voorsien deur die Gesametlike Tifoon Waarskuwing Sentrum (JTWC), is gebruik as die primêre data stel wat die basis vorm van hierdie studie. Hierdie data gee die beste skattings van die ligging (lengte- en breedtegraad), en intensiteit (maksimum volgehoue oppervlak (10m hoogte) wind spoed en/of sentrale druk tekort) van historiese tropiese siklone teen ses-uurlikse intervalle. Die modelering van tropiese sikloon windvelde was uitgevoer met die gebruik van die Holland (1980) en die Willoughby et al. (2006) parametriese windveldmodelle. Met die gebruik van beperkte inligting wat beskikbaar is in die beste roete data as invoer vir die model, was oppervlak wind velde gegenereer wat ‘n billike ooreenstemming het met die van werklike storms. Beide tegnieke se parametriese windveldmodelle is al bewys om redelike akkurate windspoed en windrigtings te lewer in vergelyking met waargenome waardes. Van die twee modelle het die Willoughby et al. (2006) model se resultate die beste ooreenstemming gewys met historiese wind spoed metings. Dit is al uitgewys dat uiterste waarde-analises van tropiese sikloon veroorsaakte windspoed moontlik kan lei tot groot foute in die resultate as gevolg van die klein monster-grootte van die historiese data. Dit beklemtoon die noodsaaklikheid om die historiese databasis aan te vul met behulp van probabilistiese metodes. Die metodes soos beskryf deur Powel et al. (2005) en Emanuel et al. (2006) is hoofsaaklik gebruik om ‘n sintetiese roete-model vir die Suid-Westelike Oseaan te ontwikkel. Die doelwit van die sintetiese roete model is om duisende jare se tropiese sikloonroetes te produseer, en in effek foute te vermy as gevolg van die gebruik van klein monster groottes van die beskikbare historiese beste roete data. Die sintetiese roete model wat tydens hierdie studie ontwikkel is, is ‘n Markov kettingmodel wat in staat is om die roete verspreiding asook die evolusie van intensiteit saam die roete te simuleer vanaf die onstaan tot die beëindiging van die sikloon se roete. Die model is suiwer statisties en is gebasseer op die eienskappe soos afgelei vanaf die historiese beste roete data. Aanpassings is gemaak om rekening te hou van die fisiese beperkings soos die wat opgelê word deur die ewenaar en die maksimum potensiële intensiteit wat ‘n sikloon kan bereik. Dit is voorgelê dat die statistiese einskappe van die sintetiese roetes goed saamstem met die van die historiese populasie. Die toepassing van die Willoughby et al. (2006) wind veld model langs die sintetiese roetes het dit moontlik gemaak om 5000 jaar se windspoed, wat veroorsaak is deur tropiese siklone, te genereer by enige ligging wat van belang is in die Suid-Westelike Indiese Oseaan. Met berekeninge wat op ‘n 1 grade geografiese ruitnet gedoen is, is windspoedkaarte vir herhaal periodes van 50, 100, 200 en 500 jaar opgestel vir die Suid-Westelike Indiese Oseaan. Die uiterste wind spoed in kusgebiede gee waardevolle invoer vir die ontwerp van kus-infrastruktuur in die omgewing.

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