Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Over the last few decades, wave run up prediction has gained the interest of numerous researchers and every newly-published paper has aimed to predict wave run up with greater accuracy. Wave run up is defined as the vertical elevation reached by a wave's, front water edge as it runs up a beach, measured relative to the still water line. Wave run up is dependent on the incidental wave height, the wave period, the beach slope and the wave steepness. The majority of publications incorporate all of these factors, but some do not, which has led to numerous debates. The goal of this study is to do a re-assessment of previously published wave run up formulae, to obtain a more informed understanding about wave run up and the available predictive empirical formulae. The study also seeks to evaluate the Mather, Stretch & Garland (2011) formula. The method for undertaking this objective comprised a physical model test series with 10 regular wave conditions on a constant slope, being 1/24, performed with an impermeable floor. Also, a beach study in the field was done on Long Beach, Noordhoek, where run up measurements were taken for 30 minute intervals, resulting in five test conditions. A numerical model was employed in conjunction with the beach study to determine the local offshore wave parameters transformed from a deep water wave rider. This information was used to correlate the run up measurements with known wave parameters. Firstly, the physical model assessment was performed to provide a proper foundation for run up understanding. Plotting empirical normalised run up values (R2/H0 ) versus the Iribarren number for different formulae, a grouping was achieved with upper and lower boundaries. The physical model results plotted on the lower end of this grouping, resulted in prediction differences of more than 10%. These differences may have been caused by the unevenness of the physical model slope or the fact that only one slope had been tested. Despite this, the results fell within a band of wave run up formulae located on the lower end of this grouping. An assessment of the beach measurements in the field gave a better correlation than the physical model results when compared to normalised predicted wave run up formulae. These measurements also plotted on the lower end of the grouping, resulting in prediction differences of less than 10% for some empirical formulae. When comparing these empirical predictions to one another, the results demonstrate that the formulae comparing best with the beach measurements were Holman (1986) and Stockdon, Holman, Howd, & Sallenger Jr. (2006). Extreme over predictions were found by Mase & Iwagaki (1984), Hedges & Mase (2004) and Douglass (1992). Nielsen & Hanslow (1991) only compared best with the beach measurements and De la Pena, Sanchez Gonzalez, Diaz-Sanchez, & Martin Huescar (2012) only compared best to the physical model results. This study supports the formula proposed by Mather, Stretch, & Garland (2011). Applying their formula to the measured results presented a C constant of 3.3 for the physical model and 8.6 for the beach results. Both values are within the range prescribed by the authors. Further reasearch minimized the array of possible „C‟ values by correlating this coefficient to Iribarren numbers. „C‟ values between 3.0~5.0 is prescribed for low Iribarren conditions (0.25-0.4) and values between 7.0~10 for higher Iribarren conditions are 0.75-0.8. However, this formula is still open for operator erros whereby the „C‟ value has a big influence in the final result. The best formulae to use, from results within this thesis, is proposed by Holman (1986) and Stockdon et.al (2006). These formulae are not open to operator erros and uses the significant wave height, deep water wave length and the beach face slope to calculate the wave run up. / AFRIKAANSE OPSOMMING: Gedurende die afgelope paar dekades, het golf-oploop voorspellings die aandag van talle navorsers gelok en elke nuwe geskrewe voorlegging het gepoog om meer akkurate golf-oploop voorspellings te verwesenlik. golf-oploop kan definieer word as die vertikale elevasie bereik deur 'n golf se voorwaterkant soos dit op die strand uitrol, gemeet relatief vanaf die stilwaterlyn. golf-oploop is afhanklik van die invals-golfhoogte, die golfperiode, die strandhelling en die golfsteilheid. Die oorgrote mederheid publikasies uit die literaturr inkorporeer al hierdie faktore, maar sommige nie, wat groot debatvoering tot gevolg het. Die doel met hierdie studie is om vorige gepubliseerde golf- oploop formules te re-evalueer, om 'n meer ingeligte begrip van golf- oploop en beskikbare voorspellende formules te verkry. Die studie poog terselfdertyd ook om golf-opvolg tendense, uniek aan Suid Afrikaanse strande te evalueer deur die huidige formule wat tans hier gebruik word, te assesseer. Om hierdie doelwit te bereik, is gebruik gemaak van 'n fisiese model toets reeks bestaande uit 10 reëlmatige golfstoestande op 'n konstante ondeurlaatbaare strandhelling van 1/24. 'n Veldstudie was ook uitgevoer op Langstrand, Noordhoek, waar golf-oploopmetings met 30 minute tussenposes uitgevoer is, vir vyf toets-toestande. Tesame met die veldstudie, is 'n numeriese model aangewend om die gemete diepsee data nader ann die strand wat bestudeer is te transformeer. Hierdie inligting is benodig om 'n verband tussen tussen oploop-metings en bekende golf parameters te bepaal. Eerstens is die fisiese model assessering uitgevoer om 'n behoorlike basis vir die begrip van golfoploop in die veld te verkry. Deur die emperiese, genormaliseerde oploop waardes (R₂/H₀) vir verkeie formules teenoor die Iribarren getal te plot, is 'n groepering met hoër en laer grense gevind. Daar is gevind dat die fisiese modelwaardes op die laer grens plot, en het verskille met die emperiese waardes van meer as 10% getoon. Hierdie verskille is moontlik veroorsaak as gevolg van 'n oneweredige fisiese model strandhelling of deur die feit dat slegs een helling getoets is. Ten spyte hiervan, het die model oploop waardes binne die bestek van golf- oploop formules geval. Assessering van die veldmetings het 'n beter korrelasie as die fisiese modelresultate getoon, tydens vergelykings met genormaliseerde golf-oploop formules van die emperiese formules. Die oploop waardes van hierdie metings het ook geplot aan die laer grens van die groepering, met verskille van minder as 10% vir die meeste gevalle van die emperiese formules. Wanneer hierdie emperiese voorspellings vergelyk word, is gevind dat die formules wat die beste ooreenstem met die fisiese model, die van Holman (1986) en Stockdon, Howd, & Sallenger Jr. (2006) is. Die emperiese formules van Mase & Iwagake (1984), Hedges & Mase (2004) en Douglas (1992) het die golf-oploop oorvoorspel. Nielsen & Hanslow (1991) het slegs die beste met die strandmetings vergelyk, terwyl De la Pena, Sanchez Gonzalez, Diaz-Sanchez & Martin Huescar (2012) slegs die beste vergelyk het met die fisiese-model resultaat. Hierdie studie ondersteun die formule voorgestel deur Mather, Stretch, & Garland (2011). Deur hul formules op die gemete bevindings toe te pas, is 'n C konstante van 3.3 vir die fisiese model resultate, en 8.0 vir die stranduitlslae bepaal. Beide waardes lê binne die grense wat deur die outeurs voorgestel is. Verdere navorsing het getoon dat moontlike waardes vir die „C‟ konstante tussen 3.0 en 5.0 moet wees vir Iribarren waardes van tussen 0.25 en 0.4. Vir hoër Iribarren waardes, 0.75-0.8, moet die „C‟ kosntante tussen 7.0 en 10 wees; dog is die formule steeds oop vir operateur foute. Die hoofbevindinge van die tesis is gevind dat die beste golf-oploop formules, om tans te gebruik, die van Holman (1986) en Stockdon et.al (2006) is. Hierdie formules kan glad nie beinvloed word deur operateurs foute nie en maak gebruik van die invals golfhoogte, die golfperiode en die strandhelling om die golf-oploop te bepaal.

Este trabalho apresenta o cálculo da cota de inundação para a Enseada do Itapocorói e para a praia de Morro dos Conventos, litoral do Estado de Santa Catarina. Para atingir os objetivos desse trabalho, a cota de inundação foi calculada através da soma das marés meteorológica e astronômica e do wave run-up. Foi utilizada uma base de 60 anos (horária) de dados de marés e ondas, além de dados de batimetria e topografia das praias. Com o intuito de se obter dados mais realistas do wave run-up, os parâmetros ondulatórios da base de dados foram transferidos de águas profundas para próximo da costa com a utilização do modelo SWAN (Simulating Waves Nearshore). A Enseada do Itapocorói foi dividida em quatro setores (exposto, semiexposto, semiprotegido e protegido) em função dos diferentes graus de exposição à ação de ondas, sendo as equações calibradas para cada setor. A partir dos resultados para Enseada do Itapocorói, notou-se que quanto mais exposta a praia, melhor as equações existentes representavam o wave run-up, assim, para a praia de Morro dos Conventos foi utilizada a equação mais aceita na literatura sem calibração. A cota de inundação instantânea foi calculada para cada hora da série de 60 anos somando-se o wave run-up às marés astronômicas e meteorológicas. Sobre a série de cota de inundação instantânea, para ambas as áreas, foi calculada a cota atingida durante 50% do tempo e por eventos extremos com recorrência de 50, 100 e 200 anos. A estas foi adicionada a previsão de elevação do nível do mar de longo prazo para o mesmo período. A cota atingida durante 50% do tempo na Enseada do Itapocorói foi de 1,35 m no setor exposto, enquanto nos setores semiexposto, semiprotegido e protegido foi de 1 m, 0,9 m e 0,7 m respectivamente. Também, o setor exposto foi o que apresentou as maiores cotas atingidas, sendo 3,45 m, 3,85 m e 4,45 m com tempo de recorrência de 50,100 e 200 anos respectivamente. No setor semiexposto, os valores calculados foram de 2,85 m (50 anos), 3,25 m (100 anos) e 3,9 m (200 anos). No setor semiprotegido, as cotas com tempo de recorrência de 50, 100 e 200 anos foram de 2,65 m, 3,05 m, 3,75 m respectivamente. Já o setor protegido apresentou as menores cotas entre os setores, 2,4 m, 2,85 m e 3,5 m para 50, 100 e 200 anos de tempo de recorrência. Considerando a extensão da área costeira que possui um levantamento de topografia do terreno, 2,4 % da área é inundada durante 50% do tempo, subindo para 26%, 29% e 33% nos casos de recorrência com 50, 100 e 200 anos. A cota atingida na praia de Morro dos Conventos durante 50% do tempo é de 1,1 m, já as cotas calculadas para os tempos de recorrência de 50, 100 e 200 anos foram de 4,2 m, 4,6 m e 5,35 m respectivamente. E, da mesma forma, a área costeira com levantamento topográfico teve 15% de superfície é inundada em 50% do tempo, passando para 85%, 91% e 96% da área total analisada com 50, 100 e 200 anos de tempo de recorrência. A metodologia proposta neste trabalho contribui para o planejamento de zonas costeiras, à medida que indica áreas afetadas por inundação aos eventos extremos. A apresentação de cartas contendo esse tipo de informação em ambiente de SIG facilita a tomada de decisão e o entendimento da área por determinado evento extremo. / The goal of this study is to determine the inundation levels at Ensenada do Itapocorói and Morro dos Conventos beaches, located in Santa Catarina State. This was accomplished through the calculation of the inundation level as the sum of astronomical and meteorological tides and wave run-up. The database for this study included -60 years of hourly waves and tides, bathymetric and topographic data. The instantaneous sea level has been defined for each hour of the data series through the summation of astronomical and meteorological tides. To determine more realistic wave run-up data, the wave parameters have been propagated to shallower water using the SWAN (Simulating WAves Nearshore) model. Published equations were used and results were compared with measured data at a headland bay beach (Enseada do Itapocorói); furthermore, the equations have been calibrated for four sectors of the bay (exposed, semi-exposed, semi-protected and protected). Morro dos Conventos is an exposed beach, comparable to those for which the equations have been developed, so the raw, un-calibrated equations were applied for this site. The inundation level was calculated for each hour of the 60 year-long series by summing the run-up values to obtain the instantaneous level. Over the series of inundation levels, the area inundated during 50% of the time, and the return period for this inundation, have been calculated for 50, 100 and 200 years. The sea-level rise prediction for each calculated period has also been incorporated in order estimate the area likely to be inundated by future events. For Enseada do Itapocorói, the inundation level reached 50% of the time was 1,35 m in the exposed sector, 1 m in the semi-exposed sector, 0,9 m in the semi-protected sector and 0,7 in the protected sector. The exposed sector demonstrated the highest values of inundation, 3,45, 3,85 and 4,5 m for 50, 100 and 200 years of return period respectively. At the semi-exposed sector, the values calculated were 2,85 (50 years), 3,25 (100 years) and 3,9 (200 years) m. At semi-protected sector, inundation levels for the 50-, 100- and 200-year return period intervals were 2,65, 3,05 and 3,75 m, respectively. At the protected sector the lowest levels were reached: 2,4, 2,85 and 3,5 m for 50-, 100- and 200-year return period intervals. 2,4% of the total area for which topographic data is available would be inundated during 50% of the time, increasing to 26%, 29% and 33% for 50-, 100- and 200-year return periods. At Morro dos Conventos, the level of inundation reaches 1,1 m 50% of the time;, for 50,100 and 200 years the level rises to 4,2, 4,6 and 5,36 m respectively. Approximately 15% of the area for which topographic data is available would be area is inundated during 50% of the time, 85% with a 50 year return period, 91% with a 100-year period and 96% with a 200 year period.

Este trabalho apresenta o cálculo da cota de inundação para a Enseada do Itapocorói e para a praia de Morro dos Conventos, litoral do Estado de Santa Catarina. Para atingir os objetivos desse trabalho, a cota de inundação foi calculada através da soma das marés meteorológica e astronômica e do wave run-up. Foi utilizada uma base de 60 anos (horária) de dados de marés e ondas, além de dados de batimetria e topografia das praias. Com o intuito de se obter dados mais realistas do wave run-up, os parâmetros ondulatórios da base de dados foram transferidos de águas profundas para próximo da costa com a utilização do modelo SWAN (Simulating Waves Nearshore). A Enseada do Itapocorói foi dividida em quatro setores (exposto, semiexposto, semiprotegido e protegido) em função dos diferentes graus de exposição à ação de ondas, sendo as equações calibradas para cada setor. A partir dos resultados para Enseada do Itapocorói, notou-se que quanto mais exposta a praia, melhor as equações existentes representavam o wave run-up, assim, para a praia de Morro dos Conventos foi utilizada a equação mais aceita na literatura sem calibração. A cota de inundação instantânea foi calculada para cada hora da série de 60 anos somando-se o wave run-up às marés astronômicas e meteorológicas. Sobre a série de cota de inundação instantânea, para ambas as áreas, foi calculada a cota atingida durante 50% do tempo e por eventos extremos com recorrência de 50, 100 e 200 anos. A estas foi adicionada a previsão de elevação do nível do mar de longo prazo para o mesmo período. A cota atingida durante 50% do tempo na Enseada do Itapocorói foi de 1,35 m no setor exposto, enquanto nos setores semiexposto, semiprotegido e protegido foi de 1 m, 0,9 m e 0,7 m respectivamente. Também, o setor exposto foi o que apresentou as maiores cotas atingidas, sendo 3,45 m, 3,85 m e 4,45 m com tempo de recorrência de 50,100 e 200 anos respectivamente. No setor semiexposto, os valores calculados foram de 2,85 m (50 anos), 3,25 m (100 anos) e 3,9 m (200 anos). No setor semiprotegido, as cotas com tempo de recorrência de 50, 100 e 200 anos foram de 2,65 m, 3,05 m, 3,75 m respectivamente. Já o setor protegido apresentou as menores cotas entre os setores, 2,4 m, 2,85 m e 3,5 m para 50, 100 e 200 anos de tempo de recorrência. Considerando a extensão da área costeira que possui um levantamento de topografia do terreno, 2,4 % da área é inundada durante 50% do tempo, subindo para 26%, 29% e 33% nos casos de recorrência com 50, 100 e 200 anos. A cota atingida na praia de Morro dos Conventos durante 50% do tempo é de 1,1 m, já as cotas calculadas para os tempos de recorrência de 50, 100 e 200 anos foram de 4,2 m, 4,6 m e 5,35 m respectivamente. E, da mesma forma, a área costeira com levantamento topográfico teve 15% de superfície é inundada em 50% do tempo, passando para 85%, 91% e 96% da área total analisada com 50, 100 e 200 anos de tempo de recorrência. A metodologia proposta neste trabalho contribui para o planejamento de zonas costeiras, à medida que indica áreas afetadas por inundação aos eventos extremos. A apresentação de cartas contendo esse tipo de informação em ambiente de SIG facilita a tomada de decisão e o entendimento da área por determinado evento extremo. / The goal of this study is to determine the inundation levels at Ensenada do Itapocorói and Morro dos Conventos beaches, located in Santa Catarina State. This was accomplished through the calculation of the inundation level as the sum of astronomical and meteorological tides and wave run-up. The database for this study included -60 years of hourly waves and tides, bathymetric and topographic data. The instantaneous sea level has been defined for each hour of the data series through the summation of astronomical and meteorological tides. To determine more realistic wave run-up data, the wave parameters have been propagated to shallower water using the SWAN (Simulating WAves Nearshore) model. Published equations were used and results were compared with measured data at a headland bay beach (Enseada do Itapocorói); furthermore, the equations have been calibrated for four sectors of the bay (exposed, semi-exposed, semi-protected and protected). Morro dos Conventos is an exposed beach, comparable to those for which the equations have been developed, so the raw, un-calibrated equations were applied for this site. The inundation level was calculated for each hour of the 60 year-long series by summing the run-up values to obtain the instantaneous level. Over the series of inundation levels, the area inundated during 50% of the time, and the return period for this inundation, have been calculated for 50, 100 and 200 years. The sea-level rise prediction for each calculated period has also been incorporated in order estimate the area likely to be inundated by future events. For Enseada do Itapocorói, the inundation level reached 50% of the time was 1,35 m in the exposed sector, 1 m in the semi-exposed sector, 0,9 m in the semi-protected sector and 0,7 in the protected sector. The exposed sector demonstrated the highest values of inundation, 3,45, 3,85 and 4,5 m for 50, 100 and 200 years of return period respectively. At the semi-exposed sector, the values calculated were 2,85 (50 years), 3,25 (100 years) and 3,9 (200 years) m. At semi-protected sector, inundation levels for the 50-, 100- and 200-year return period intervals were 2,65, 3,05 and 3,75 m, respectively. At the protected sector the lowest levels were reached: 2,4, 2,85 and 3,5 m for 50-, 100- and 200-year return period intervals. 2,4% of the total area for which topographic data is available would be inundated during 50% of the time, increasing to 26%, 29% and 33% for 50-, 100- and 200-year return periods. At Morro dos Conventos, the level of inundation reaches 1,1 m 50% of the time;, for 50,100 and 200 years the level rises to 4,2, 4,6 and 5,36 m respectively. Approximately 15% of the area for which topographic data is available would be area is inundated during 50% of the time, 85% with a 50 year return period, 91% with a 100-year period and 96% with a 200 year period.

Este trabalho apresenta o cálculo da cota de inundação para a Enseada do Itapocorói e para a praia de Morro dos Conventos, litoral do Estado de Santa Catarina. Para atingir os objetivos desse trabalho, a cota de inundação foi calculada através da soma das marés meteorológica e astronômica e do wave run-up. Foi utilizada uma base de 60 anos (horária) de dados de marés e ondas, além de dados de batimetria e topografia das praias. Com o intuito de se obter dados mais realistas do wave run-up, os parâmetros ondulatórios da base de dados foram transferidos de águas profundas para próximo da costa com a utilização do modelo SWAN (Simulating Waves Nearshore). A Enseada do Itapocorói foi dividida em quatro setores (exposto, semiexposto, semiprotegido e protegido) em função dos diferentes graus de exposição à ação de ondas, sendo as equações calibradas para cada setor. A partir dos resultados para Enseada do Itapocorói, notou-se que quanto mais exposta a praia, melhor as equações existentes representavam o wave run-up, assim, para a praia de Morro dos Conventos foi utilizada a equação mais aceita na literatura sem calibração. A cota de inundação instantânea foi calculada para cada hora da série de 60 anos somando-se o wave run-up às marés astronômicas e meteorológicas. Sobre a série de cota de inundação instantânea, para ambas as áreas, foi calculada a cota atingida durante 50% do tempo e por eventos extremos com recorrência de 50, 100 e 200 anos. A estas foi adicionada a previsão de elevação do nível do mar de longo prazo para o mesmo período. A cota atingida durante 50% do tempo na Enseada do Itapocorói foi de 1,35 m no setor exposto, enquanto nos setores semiexposto, semiprotegido e protegido foi de 1 m, 0,9 m e 0,7 m respectivamente. Também, o setor exposto foi o que apresentou as maiores cotas atingidas, sendo 3,45 m, 3,85 m e 4,45 m com tempo de recorrência de 50,100 e 200 anos respectivamente. No setor semiexposto, os valores calculados foram de 2,85 m (50 anos), 3,25 m (100 anos) e 3,9 m (200 anos). No setor semiprotegido, as cotas com tempo de recorrência de 50, 100 e 200 anos foram de 2,65 m, 3,05 m, 3,75 m respectivamente. Já o setor protegido apresentou as menores cotas entre os setores, 2,4 m, 2,85 m e 3,5 m para 50, 100 e 200 anos de tempo de recorrência. Considerando a extensão da área costeira que possui um levantamento de topografia do terreno, 2,4 % da área é inundada durante 50% do tempo, subindo para 26%, 29% e 33% nos casos de recorrência com 50, 100 e 200 anos. A cota atingida na praia de Morro dos Conventos durante 50% do tempo é de 1,1 m, já as cotas calculadas para os tempos de recorrência de 50, 100 e 200 anos foram de 4,2 m, 4,6 m e 5,35 m respectivamente. E, da mesma forma, a área costeira com levantamento topográfico teve 15% de superfície é inundada em 50% do tempo, passando para 85%, 91% e 96% da área total analisada com 50, 100 e 200 anos de tempo de recorrência. A metodologia proposta neste trabalho contribui para o planejamento de zonas costeiras, à medida que indica áreas afetadas por inundação aos eventos extremos. A apresentação de cartas contendo esse tipo de informação em ambiente de SIG facilita a tomada de decisão e o entendimento da área por determinado evento extremo. / The goal of this study is to determine the inundation levels at Ensenada do Itapocorói and Morro dos Conventos beaches, located in Santa Catarina State. This was accomplished through the calculation of the inundation level as the sum of astronomical and meteorological tides and wave run-up. The database for this study included -60 years of hourly waves and tides, bathymetric and topographic data. The instantaneous sea level has been defined for each hour of the data series through the summation of astronomical and meteorological tides. To determine more realistic wave run-up data, the wave parameters have been propagated to shallower water using the SWAN (Simulating WAves Nearshore) model. Published equations were used and results were compared with measured data at a headland bay beach (Enseada do Itapocorói); furthermore, the equations have been calibrated for four sectors of the bay (exposed, semi-exposed, semi-protected and protected). Morro dos Conventos is an exposed beach, comparable to those for which the equations have been developed, so the raw, un-calibrated equations were applied for this site. The inundation level was calculated for each hour of the 60 year-long series by summing the run-up values to obtain the instantaneous level. Over the series of inundation levels, the area inundated during 50% of the time, and the return period for this inundation, have been calculated for 50, 100 and 200 years. The sea-level rise prediction for each calculated period has also been incorporated in order estimate the area likely to be inundated by future events. For Enseada do Itapocorói, the inundation level reached 50% of the time was 1,35 m in the exposed sector, 1 m in the semi-exposed sector, 0,9 m in the semi-protected sector and 0,7 in the protected sector. The exposed sector demonstrated the highest values of inundation, 3,45, 3,85 and 4,5 m for 50, 100 and 200 years of return period respectively. At the semi-exposed sector, the values calculated were 2,85 (50 years), 3,25 (100 years) and 3,9 (200 years) m. At semi-protected sector, inundation levels for the 50-, 100- and 200-year return period intervals were 2,65, 3,05 and 3,75 m, respectively. At the protected sector the lowest levels were reached: 2,4, 2,85 and 3,5 m for 50-, 100- and 200-year return period intervals. 2,4% of the total area for which topographic data is available would be inundated during 50% of the time, increasing to 26%, 29% and 33% for 50-, 100- and 200-year return periods. At Morro dos Conventos, the level of inundation reaches 1,1 m 50% of the time;, for 50,100 and 200 years the level rises to 4,2, 4,6 and 5,36 m respectively. Approximately 15% of the area for which topographic data is available would be area is inundated during 50% of the time, 85% with a 50 year return period, 91% with a 100-year period and 96% with a 200 year period.

In this study, the semi-empirical approach is introduced to accurately estimate the probability distribution of complex non-linear random variables in the field of wavestructure interaction. The structural form of the semi-empirical distribution is developed based on a mathematical representation of the process and the model parameters are estimated directly from utilization of the sample data. Here, three probability distributions are developed based on the quadratic transformation of the linear random variable. Assuming that the linear process follows a standard Gaussian distribution, the three-parameter Gaussian-Stokes model is derived for the second-order variables. Similarly, the three-parameter Rayleigh-Stokes model and the four-parameter Weibull- Stokes model are derived for the crests, troughs, and heights of non-linear process assuming that the linear variable has a Rayleigh distribution or a Weibull distribution. The model parameters are empirically estimated with the application of the conventional method of moments and the newer method of L-moments. Furthermore, the application of semi-empirical models in extreme analysis and estimation of extreme statistics is discussed. As a main part of this research study, the sensitivity of the model statistics to the variability of the model parameters as well as the variability in the samples is evaluated. In addition, the sample size effects on the performance of parameter estimation methods are studied. Utilizing illustrative examples, the application of semi-empirical probability distributions in the estimation of probability distribution of non-linear random variables is studied. The examples focused on the probability distribution of: wave elevations and wave crests of ocean waves and waves in the area close to an offshore structure, wave run-up over the vertical columns of an offshore structure, and ocean wave power resources. In each example, the performance of the semi-empirical model is compared with appropriate theoretical and empirical distribution models. It is observed that the semi-empirical models are successful in capturing the probability distribution of complex non-linear variables. The semi-empirical models are more flexible than the theoretical models in capturing the probability distribution of data and the models are generally more robust than the commonly used empirical models.

Restlöcher ausgekohlter Braunkohlentagebaue werden aus landeskulturellen und ökonomischen Gründen wasserwirtschaftlich als Speicher, Hochwasserrückhaltebecken, Klärteiche, Wassergewinnungsanlagen sowie zur Naherholung genutzt. Diese Restlöcher werden zum großen Teil von aus geschüttetem Abraum bestehenden Böschungen umschlossen. Bei Wasserspiegelschwankungen neigen diese unbefestigten Böschungen zum Rutschen. Als Folge dieser Böschungsrutschungen bilden sich auf der Wasseroberfläche Wellen, die eine beachtliche Größe erreichen können. Diese Schwallwellen übertreffen in ihren Ausmaßen die Windwellen in den Tagebaurestlöchern um ein Vielfaches. Um diese Erscheinungen vorausberechnen zu können, wurden im Hubert-Engels-Laboratorium der Sektion Wasserwesen Untersuchungen durchgeführt. Die Entwicklung einer allgemeingültigen Berechnungsmethode für die Schwallwelle bei der Bewegung eines Teiles der das Wasserbecken begrenzenden Böschung verlangt die Einführung erfassbarer Parameter wie der Breite der rutschenden Böschung, den zeitlichen Verlauf der Wasserverdrängung sowie Tiefen- und Lageverhältnisse des Beckens. Die dafür notwendigen Kennzahlen können nur näherungsweise bestimmt werden, so dass einfache Beckengeometrien, ein über die Rutschzeit gleich bleibender Verlauf der Wasserverdrängung und Erhaltung der Böschungskante einem Berechnungsverfahren zugrunde gelegt werden müssen. Für die Berechnung des Füllschwalles auf das ruhende Wasser sind einige Verfahren bekannt geworden, die auf eine gemeinsame Gleichung für die Berechnung der Schwallhöhe zurückzuführen sind. Für die ebene Ausbreitung des Füllschwalles über Ruhewasser ergeben sieh zwei prinzipielle Abflussmöglichkeiten: Auflösung in Wellen oder brandender Schwallkopf. Diese beiden Möglichkeiten sowie der Übergangsbereich werden durch FROUDE-zahlen festgelegt. Der Wellenkopf von Füllschwallwellen wird durch eine Einzelwelle gebildet. Die Rutschung einer Böschung wurde durch die gleichzeitige Horizontal- und Vertikalbewegung einer Platte nachgebildet. Die Bewegung der Platte, die entstehenden Wellen und die Kräfte auf Auflaufböschung wurden durch einen Oszillografen aufgezeichnet. Die Auswertung der Versuche ergab eine Übereinstimmung zwischen Messergebnissen und den Berechnungen nach den Gesetzen des Füllschwalls. Die sekundlich verdrängte Wassermenge pro Breiteneinheit und die Ruhewassertiefe bestimmen die entstehenden Schwallwellen. Ein Einfluss der vertikalen Bewegungskomponente ist im untersuchten Bereich nicht nachweisbar. Die dynamischen Kräfte auf die Abschlussböschung können durch den Impuls der Einzelwelle dargestellt werden. Die räumliche Ausbreitung der Schwallwellen wurde in einem Modell untersucht. Dabei wurde festgestellt, dass die größten Wellenhöhen in der Richtung der Bewegung der Platte auftreten, während die Wellenhöhen in seitlichen Ausbreitungsrichtungen kleiner sind. Berechnungsansätze für die maximale Wellenhöhe der front wurden ermittelt. Als Ergebnis wurde ein Berechnungsverfahren entwickelt, welches ausgehend von den Parametern dar Rutschung, die Eigenschaften der Schwallwellen einschließlich der durch sie hervorgerufenen Belastungen auf der Auflaufböschung ermöglicht. Mit diesem Berechnungsverfahren ist es möglich, Böschungen wirtschaftlich zu gestalten und schädliche Rückwirkungen auf das Staubecken durch Schwallwellen zu vermeiden. Bisher notwendige Kosten für eine sehr flache Gestaltung der Böschung können entfallen. Gleichzeitig bleibt ein größerer nutzbarer Stauraum erhalten. Die Digitalisierung der vorliegenden Arbeit durch die Sächsische Landesbibliothek - Staats- und Universitätsbibliothek Dresden (SLUB) wurde durch die Gesellschaft der Förderer des Hubert-Engels-Institutes für Wasserbau und Technische Hydromechanik an der Technischen Universität Dresden e.V. unterstützt.

[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] Wave run-up is the vertical uprush of water when an incident wave impinges on a free- surface penetrating body. For large volume offshore structures the wave run-up on the weather side of the supporting columns is particularly important for air-gap design and ultimately the avoidance of pressure impulse loads on the underside of the deck structure. This investigation focuses on the limitations of conventional wave diffraction theory, where the free-surface boundary condition is treated by a Stokes expansion, in predicting the harmonic components of the wave run-up, and the presentation of a simplified procedure for the prediction of wave run-up. The wave run-up is studied on fixed vertical cylinders in plane progressive waves. These progressive waves are of a form suitable for description by Stokes' wave theory whereby the typical energy content of a wave train consists of one fundamental harmonic and corresponding phase locked Fourier components. The choice of monochromatic waves is indicative of ocean environments for large volume structures in the diffraction regime where the assumption of potential flow theory is applicable, or more formally A/a < Ο(1) (A and a being the wave amplitude and cylinder radius respectively). One of the unique aspects of this work is the investigation of column geometry effects - in terms of square cylinders with rounded edges - on the wave run-up. The rounded edges of each cylinder are described by the dimensionless parameter rc/a which denotes the ratio of edge corner radius to half-width of a typical column with longitudinal axis perpendicular to the quiescent free-surface. An experimental campaign was undertaken where the wave run-up on a fixed column in plane progressive waves was measured with wire probes located close to the cylinder. Based on an appropriate dimensional analysis, the wave environment was represented by a parametric variation of the scattering parameter ka and wave steepness kA (where k denotes the wave number). The effect of column geometry was investigated by varying the edge corner radius ratio within the domain 0 <=rc/a <= 1, where the upper and lower bounds correspond to a circular and square shaped cylinder respectively. The water depth is assumed infinite so that the wave run-up caused purely by wave-structure interaction is examined without the additional influence of a non-decaying horizontal fluid velocity and finite depth effects on wave dispersion. The zero-, first-, second- and third-harmonics of the wave run-up are examined to determine the importance of each with regard to local wave diffraction and incident wave non-linearities. The modulus and phase of these harmonics are compared to corresponding theoretical predictions from conventional diffraction theory to second-order in wave steepness. As a result, a basis is formed for the applicability of a Stokes expansion to the free-surface boundary condition of the diffraction problem, and its limitations in terms of local wave scattering and incident wave non-linearities. An analytical approach is pursued and solved in the long wavelength regime for the interaction of a plane progressive wave with a circular cylinder in an ideal fluid. The classical Stokesian assumption of infinitesimal wave amplitude is invoked to treat the free-surface boundary condition along with an unconventional requirement that the cylinder width is assumed much smaller than the incident wavelength. This additional assumption is justified because critical wavelengths for wave run-up on a fixed cylinder are typically much larger in magnitude than the cylinder's width. In the solution, two coupled perturbation schemes, incorporating a classical Stokes expansion and cylinder slenderness expansion, are invoked and the boundary value problem solved to third-order. The formulation of the diffraction problem in this manner allows for third-harmonic diffraction effects and higher-order effects operating at the first-harmonic to be found. In general, the complete wave run-up is not well accounted for by a second-order Stokes expansion of the free-surface boundary condition and wave elevation. This is however, dependent upon the coupling of ka and kA. In particular, whilst the modulus and phase of the second-harmonic are moderately predicted, the mean set-up is not well predicted by a second-order Stokes expansion scheme. This is thought to be caused by higher than second-order non-linear effects since experimental evidence has revealed higher-order diffraction effects operating at the first-harmonic in waves of moderate to large steepness when k < < 1. These higher-order effects, operating at the first-harmonic, can be partially accounted for by the proposed long wavelength formulation. For small ka and large kA, subsequent comparisons with measured results do indeed provide a better agreement than the classical linear diffraction solution of Havelock (1940). To account for the complete wave run-up, a unique approach has been adopted where a correction is applied to a first-harmonic analytical solution. The remaining non-linear portion is accounted for by two methods. The first method is based on regression analysis in terms of ka and kA and provides an additive correction to the first-harmonic solution. The second method involves an amplification correction of the first-harmonic. This utilises Bernoulli's equation applied at the mean free-surface position where the constant of proportionality is empirically determined and is inversely proportional to ka. The experimental and numerical results suggest that the wave run-up increases as rc/a--› 0, however this is most significant for short waves and long waves of large steepness. Of the harmonic components, experimental evidence suggests that the effect of a variation in rc/a on the wave run-up is particularly significant for the first-harmonic only. Furthermore, the corner radius effect on the first-harmonic wave run-up is well predicted by numerical calculations using the boundary element method. Given this, the proposed simplified wave run-up model includes an additional geometry correction which accounts for rc/a to first-order in local wave diffraction. From a practical view point, it is the simplified model that is most useful for platform designers to predict the wave run-up on a surface piercing column. It is computationally inexpensive and the comparison of this model with measured results has proved more promising than previously proposed schemes.

Restlöcher ausgekohlter Braunkohlentagebaue werden aus landeskulturellen und ökonomischen Gründen wasserwirtschaftlich als Speicher, Hochwasserrückhaltebecken, Klärteiche, Wassergewinnungsanlagen sowie zur Naherholung genutzt. Diese Restlöcher werden zum großen Teil von aus geschüttetem Abraum bestehenden Böschungen umschlossen. Bei Wasserspiegelschwankungen neigen diese unbefestigten Böschungen zum Rutschen. Als Folge dieser Böschungsrutschungen bilden sich auf der Wasseroberfläche Wellen, die eine beachtliche Größe erreichen können. Diese Schwallwellen übertreffen in ihren Ausmaßen die Windwellen in den Tagebaurestlöchern um ein Vielfaches. Um diese Erscheinungen vorausberechnen zu können, wurden im Hubert-Engels-Laboratorium der Sektion Wasserwesen Untersuchungen durchgeführt. Die Entwicklung einer allgemeingültigen Berechnungsmethode für die Schwallwelle bei der Bewegung eines Teiles der das Wasserbecken begrenzenden Böschung verlangt die Einführung erfassbarer Parameter wie der Breite der rutschenden Böschung, den zeitlichen Verlauf der Wasserverdrängung sowie Tiefen- und Lageverhältnisse des Beckens. Die dafür notwendigen Kennzahlen können nur näherungsweise bestimmt werden, so dass einfache Beckengeometrien, ein über die Rutschzeit gleich bleibender Verlauf der Wasserverdrängung und Erhaltung der Böschungskante einem Berechnungsverfahren zugrunde gelegt werden müssen. Für die Berechnung des Füllschwalles auf das ruhende Wasser sind einige Verfahren bekannt geworden, die auf eine gemeinsame Gleichung für die Berechnung der Schwallhöhe zurückzuführen sind. Für die ebene Ausbreitung des Füllschwalles über Ruhewasser ergeben sieh zwei prinzipielle Abflussmöglichkeiten: Auflösung in Wellen oder brandender Schwallkopf. Diese beiden Möglichkeiten sowie der Übergangsbereich werden durch FROUDE-zahlen festgelegt. Der Wellenkopf von Füllschwallwellen wird durch eine Einzelwelle gebildet. Die Rutschung einer Böschung wurde durch die gleichzeitige Horizontal- und Vertikalbewegung einer Platte nachgebildet. Die Bewegung der Platte, die entstehenden Wellen und die Kräfte auf Auflaufböschung wurden durch einen Oszillografen aufgezeichnet. Die Auswertung der Versuche ergab eine Übereinstimmung zwischen Messergebnissen und den Berechnungen nach den Gesetzen des Füllschwalls. Die sekundlich verdrängte Wassermenge pro Breiteneinheit und die Ruhewassertiefe bestimmen die entstehenden Schwallwellen. Ein Einfluss der vertikalen Bewegungskomponente ist im untersuchten Bereich nicht nachweisbar. Die dynamischen Kräfte auf die Abschlussböschung können durch den Impuls der Einzelwelle dargestellt werden. Die räumliche Ausbreitung der Schwallwellen wurde in einem Modell untersucht. Dabei wurde festgestellt, dass die größten Wellenhöhen in der Richtung der Bewegung der Platte auftreten, während die Wellenhöhen in seitlichen Ausbreitungsrichtungen kleiner sind. Berechnungsansätze für die maximale Wellenhöhe der front wurden ermittelt. Als Ergebnis wurde ein Berechnungsverfahren entwickelt, welches ausgehend von den Parametern dar Rutschung, die Eigenschaften der Schwallwellen einschließlich der durch sie hervorgerufenen Belastungen auf der Auflaufböschung ermöglicht. Mit diesem Berechnungsverfahren ist es möglich, Böschungen wirtschaftlich zu gestalten und schädliche Rückwirkungen auf das Staubecken durch Schwallwellen zu vermeiden. Bisher notwendige Kosten für eine sehr flache Gestaltung der Böschung können entfallen. Gleichzeitig bleibt ein größerer nutzbarer Stauraum erhalten. Die Digitalisierung der vorliegenden Arbeit durch die Sächsische Landesbibliothek - Staats- und Universitätsbibliothek Dresden (SLUB) wurde durch die Gesellschaft der Förderer des Hubert-Engels-Institutes für Wasserbau und Technische Hydromechanik an der Technischen Universität Dresden e.V. unterstützt.

In this work we review 12 years of developments in the field of residual based discretizations for hyperbolic problems and their application to the solution of the shallow water equations. Fundamental concepts related to the topic are recalled and he construction of second and higher order schemes for steady problems is presented. The generalization to time dependent problems by means of multi-step implicit time integration, space-time, and genuinely explicit techniques is thoroughly discussed. Finally, the issues of C-property, super consistency, and wetting/drying are analyzed in this framework showing the power of the residual based approach.