Thesis (Ph. D. (Statistics)) -- University of Limpopo, 2016. / Statistics of extremes has seen much growth both in theory and application since its early theoretical developments almost a century ago in the 1920s and its first major applications to real-life problems pioneered by Emil Gumbel in the early 1940s. Although the theory and applications of extreme value theory (EVT) have been extensively advanced and utilised in most developed countries,intermsofapplicationslittlehasbeendoneinmanydevelopingcountries in Africa despite the abundance of areas of applications and raw data in some ofthesecountries. Inhydrology,thechoiceoffloodfrequencyprobabilitydistributions for a particular site or region remains the subject of ongoing research. The work contained in this thesis is a contribution towards this area and it addresses this problem in one of the developing and economically challenged countries in Africa, Mozambique, in the lower Limpopo River basin (LLRB). The LLRB is a basin characterised by extreme natural hazards, alternating between extreme floods and severe droughts. ThisthesisisbasedonanextensiveapplicationofEVTtoextremefloodheights data in the LLRB of Mozambique at three sites: Chokwe, Combomune and Sicacate hydrometric stations. Two fundamental approaches of EVT, block maxima and peaks-over-threshold (POT), are used in this thesis. Recent theoretical results by Ferreira and de Haan (2015) have shown that despite its inefficiency due to data lost as a result of blocking, the block maxima approach is more efficient in a number of situations than the POT approach, and the two approaches are quite comparable for large sample sizes. A number of ii candidate distributions are investigated for their goodness-of-fit to the annual daily maximum flood heights in a block maxima realisation at each site. The findings reveal that the GEV distribution is the most appropriate distribution to apply in the LLRB and the distribution can be recommended as the likelihood function for regional and spatial extremes flood frequency analysis in the basin. The thesis addresses the issue of cumulative effects on daily flood heights through a comparative analysis of six annual maxima moving sums. The findings demonstrate that the six annual maxima time series models are notsignificantlydifferentbasedonthecharacteristicsconsideredinthisthesis. In an attempt to reduce uncertainties in the estimates, a Bayesian Markov chain Monte Carlo (MCMC) approach with a conjugate prior and a GEV likelihood function is used to model the tails of the extreme flood heights in the basin. The findings reveal that the addition of prior information in Bayesian MCMC substantially reduces uncertainties in the estimates and improves precision in the predicted extreme floods. The r largest order statistics models developed in this thesis are generally promising and the standard errors of the estimates of the parameters are substantially reduced. In order to account for climate change impact, nonstationary models are considered with the longterm trend and seasonal oscillation index (SOI) (a meteorological variable indicator) as covariates of the parameters of the GEV distribution and the generalised Pareto distribution (GPD). Among the major contributions of this thesis is a proposed procedure for the determination of the 8 days window period used in extracting independent r largest order values within the same year for the r largest order statistics approach. A summary of the key findings and contributions of this thesis are given in Chapter 9. Moreover, contributions by the study topic in each chapter are given at the end of each chapter. / DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoEMaSS) of South Africa

Model-based reservoir management systems are indispensable for determining an optimal water resources management in river basins with multipurpose reservoirs. A recently developed management system will be described, using evolutionary algorithms to optimize both event-based and long-term operation of a reservoir system concerning multiple objectives with different units of measurement (Money, Dimensions, Ecology). The result are sets of so-called Pareto optimal solutions which represent the most useful compromises and can serve as a transparent information base for decision-making. In order to improve the ecological performance of multipurpose reservoirs, a dynamic operating scheme is implemented, which ensures that reservoir releases correspond to natural flow variability as far as possible. In addition water quality problems during the flood discharge and the release from selected layers of the water body will be discussed in brief.

Dams are amongst the most important components of water resource systems. In many places the water regulated by and stored in dams is essential to meet the development objectives of water supply, flood control, agriculture (i.e. irrigation and livestock), industry, energy generation and other sectors. Previous studies (Gourbesvive, 2008) indicate that in the next 30 years water use will increase by 50% in the world. By 2025 about 4 billion people will live under conditions of severe water stress. Continuous deterioration in water quality in most developing countries is additional challenge. Therefore, development of priority water infrastructures and improvements of water management have essential and complementary roles in contributing to sustainable growth and energy reduction in developing countries like Sweden. One way of improving water management is through increasing the efficiency of utilization of dam reservoirs (Bosona, 2010). Reservoir operation is a complex task involving numerous hydrological, technical, economical, environmental, institutional and political considerations. There is no general algorithm that covers all type of reservoir operation problems. The choice for techniques usually depends on the reservoir specific system characteristics, data availability, the objectives specified and the constraints imposed. Goal of the mathematical modelling and simulation of a physical system is to provide the user with the relevant information used in design and/or management decision-making. However, in the absence of adequate foresight and planning for adverse impacts, past dam construction has often resulted in devastating effects for ecosystems and the livelihoods of affected communities. In this project with Hec-ResSim simulation model four reservoirs in Ore River Basin and 3 reservoirs in Lule River Basin in different location in Sweden are considered and by new operation rules, model is simulated. With consideration of two high floods event model is calibrated and new operation rules for flood control and hydropower melioration was rendered and suggested.

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This is a research report that discusses some continuous and discrete modeling techniques. The report applies these techniques to the analysis of Canal 38 (Kissimmee River) part of Central and South Florida Flood Control District. The analysis is based on recorded data for defining the physical systems parameters. Established parameters are mathematically related to define a descriptive model for Canal 38. The modeling procedure of 'trial and error' is used to assemble the model with measures of merit, the integral square error, and root mean squared error. General simulation considerations are discussed for application of the mathematical model.

Infrastructure plays an instrumental role in the shaping of the landscape across many scales and is a critical human component within the landscape, yet these systems have tended to ignore the function of appearance and aesthetics in their design. Consequently, the relationship between our infrastructure, the environment, and us has become increasingly opaque. The majority of the vast infrastructure systems that weave throughout the landscape promote a mono-functional agenda which is relegated to the background of our everyday experiences. By investigating the traditional methods of designing infrastructure, we can begin to understand how to integrate aesthetics into the design of infrastructure. This is explored through one of the largest infrastructure systems in the United States; flood control. Flood control infrastructure in is an extensive system that has formed a protective barrier between human and natural processes for over 200 years. Its largest component, the levee, is an elegantly simple structure that contains many layers of significant cultural and historic aesthetic narratives. This thesis focuses on the levee as an infrastructure that mediates between natural processes and human development and studies how it can perform aesthetically to convey new meaning and value. What is the potential of the levee to become expressive in our lives, and be designed in such a way to move us? This new infrastructural paradigm explores the implications of utilizing aesthetics as an expressive and significant function of levee design that can inform and inspire the public and define a new dialogue between man, nature, and technology. / Master of Landscape Architecture

An investigation into the transient impacts of flood loadings on earthen embankments was conducted. Two embankments were instrumented and monitored over a period of four years. One of these embankments was a levee located along the Mississippi River just north of Cairo, Illinois. The other embankment was part of a catchment basin at the Engineer Research and Development Center located in Vicksburg, MS. Tensiometer and porous block sensors were used to monitor the pore water pressures in the embankments. It was found that when measuring the field soil water retention, tensiometers were more responsive than porous block sensors at low suctions; although, at shallower depths, the tensiometer performance was limited during periods of extended drying. It was shown that during the start of flooding, pore water pressures in the embankment soils were near −10 kPa at depths less than 2 m, which was greater than the normally assumed hydrostatic conditions. An investigation into flood hydrographs collected from across the United States showed that flood durations could be hundreds of days long. These hydrographs were collected over a period of 10 years. It was found that the recorded peak flood stage exceeded the major flood stage 11% of the time. An uncouple transient seepage model of a 2015 Mississippi River flood event that occurred at the Cairo levee showed that an uncoupled model could simulate the field measurements; however, the material properties that resulted in the most accurate simulation differed from those measured in the laboratory. Soil water retention characteristics of the embankment soils were assessed, and it was found that laboratory measured soil water retention curves could be used to bracket field measurements. Slope stability analyses were performed as a proxy to assessing the progression of the wetting front in the levees. Accounting for the increase in shear strength due to the presence of matric suction resulted in minimal impacts to stability factors of safety for levee embankments during flood loadings. The results of this investigation will help to improve the reliability of transient seepage analyses and provides guidance for future embankment monitoring investigations. / Doctor of Philosophy / An investigation into the movement of flood water through flood control embankments was conducted. Typically, analysis of this phenomenon is performed independent of the effects of time. For this investigation, the impacts of time were considered. When considering the effects of time dependent loadings, an initial distribution of water pressures must be considered. Typical assumptions regarding these distributions were investigated using four years of sensor measurements from two embankments. These measurements were also used to investigate appropriate material properties when considering saturated and unsaturated soil properties necessary for these analyses. Results show that typical assumptions may not be appropriate regarding initial water pressure distributions. Additionally, recommendations for assigning material properties were provided and it was found that these types of analyses can simulate flood loadings, but a range of material properties must be explored to understand the full range of performance. The impact of these results will lead to better predictions of embankment performance during flood loadings.

Geosynthetic tubes filled with water are considered. The tubes can be used in applications to resist rising floodwaters. They can also be used to form breakwaters and protect shores from erosion. This thesis considers single and stacked tubes resting on a rigid and deformable foundation resisting rising hydrostatic headwater. Experiments were carried out to determine the behavior of a three-tube stacked configuration resting on a sand foundation. This study was a continuation of previous work on unstacked tubes. Many tests were performed to determine the deformation and stability of the system. A geosynthetic drain was placed beneath the tubes to prevent piping. The objective was to cause failure of the system in a sliding manner and formulate a hypothesis according to the placement of the drain beneath the tubes. In order to cause a sliding failure, a strapping system was developed to try and prevent the tubes from rolling. A single tube at rest, filled with water but with no external hydrostatic pressure, was considered for analysis first. The tube rested on a rigid foundation and was assumed to be infinitely long. The friction between the tube and the foundation was neglected, and the bending stiffness of the tube was assumed to be negligible. The tube material was assumed to be inextensible. Mathematica was used to solve the system of equations and compute the unknowns. Excel was used to plot the data and observe the behavior of the tubes. An analysis was also performed on a single tube with an apron attached, resting on a rigid foundation. The apron was attached on the rising headwater side to increase stability. The assumptions for the tube at rest were also applied in this analysis. Two cases were derived and analyzed: a case where the internal hydrostatic pressure remains constant, and a case where the cross-sectional area remains constant. For the second case, the internal pressure changes as the floodwater level rises. The results from this study demonstrated that water-filled tubes, stacked or with an apron attached, can be an effective alternative method to sandbags in resisting floodwaters. / Master of Science

A water-filled geomembrane tube is considered for the purpose of temporary flood protection. With proper design, this tube can be a cheap and efficient breakwater, temporary levee, or cofferdam. This thesis considers a single tube resting on clay and sand foundations. A finite difference program, FLAC, is used in the numerical analyses. The tube is assumed to be infinitely long, and it is modeled two-dimensionally. Beam elements are used to model the tube. The tube is inflated with water. The hydrostatic pressure in the tube is converted to point loads and applied at the beam nodes in the direction perpendicular to the chord connecting two adjacent nodes. Two of FLAC's built-in soil models are used: elastic and Mohr-Coulomb. The Mohr-Coulomb model is used in all the cases except the preliminary analyses, in which the elastic soil model is used. The Mohr-Coulomb soil model is able to model the soil's nonlinear stress-strain and path-dependent deformation behavior. A tube without external water is placed on clay with various shear strengths to study how the clay consistency affects the height and the stresses in the tube. A tube with external water on one side is placed on medium dense sand. A wooden block is placed on the side opposite the floodwater. Three types of block geometry and two sizes are studied. The floodwater level is increased until the system fails. Three failure modes, rolling, sliding, and piping, are studied. The effect of pore pressure on these failure modes is examined. The influence of a filter placed under part of the tube and block is also investigated. The tube's tensile forces, shear forces, moments, and settlements are included. Soil stresses and pore pressures at the soil-tube interfaces are computed. The cross-section of the tube at various external water levels, and the pore pressures in the soil, are calculated. These results are compared with experimental results that were obtained by graduate students in geotechnical engineering at Virginia Tech. / Master of Science

Benefits from a flood control project that accrue to a landowner are defined as the amount the landowner is willing to pay for the reduction in flood risk. The primary method utilized by the U.S. Army Corps of Engineers to estimate a residential landowner's benefits is the property damages avoided method. Only under a set of restrictive assumptions will this method accurately estimate landowner willingness to pay. Therefore, several alternative techniques, such as the hedonic price method, are approved for use by the Corps but it is not known how they compare. The purpose of this study is to examine the benefit measures from the property damages avoided and hedonic price methods and two new measures, restricted willingness to pay (RWTP) and restricted willingness to accept (RWTA). The measures RWTP and RWTA are biased estimates of willingness to pay (WTP) and willingness to accept (WTA) where the direction of the bias is known. In addition, the methods that calculate these measures, the RWTP and RWTA methods, do not require data on income or an aggregator for the prices of all goods not in the analysis. Benefit estimates from the hedonic price and RWTP methods provide upper and lower bounds on WTP for non-marginal reductions in flood risk and converge for marginal reductions. / Master of Science