Dissertations / Theses on the topic 'Streamflow – Swaziland – Mathematical models'

The purpose of this study is to develop a method for predicting monthly flow duration curves for ungaged basins that are suitable for estimating average annual flow, and installed capacity and average annual energy generation at potential sites for hydropower development. The procedures were tested by developing monthly rainfall duration curves for five sample watersheds and then developing flow duration curves from the rainfall data. The methods were evaluated by comparing the predicted monthly flow duration curves to daily and monthly flow duration curves based on field data from the selected sites because a plant's potential energy output can be computed directly from a flow duration curve. The methods tested fit duration curves based on field data reasonably well and are suitable for preliminary evaluation of hydropower developments in ungaged basins.

Many hydrologic basins in the southwest have seen their perennial streamflows turn to ephemeral, their riparian communities disappear or be jeopardized, and their aquifers suffer from severe overdrafts. Under -management of ground -water exploitation and of conjunctive use of surface and ground waters are the main reasons for these events.

A finite element numerical model is developed for the modeling of coupled surface-water flow and ground-water flow. The mathematical treatment of subsurface flows follows the confined aquifer theory or the classical Dupuit approximation for unconfined aquifers whereas surface-water flows are treated with the kinematic wave approximation for open channel flow. A detailed discussion of the standard approaches to represent the coupling term is provided. In this work, a mathematical expression similar to Ohm's law is used to simulate the interacting term between the two major hydrological components. Contrary to the standard approach, the coupling term is incorporated through a boundary flux integral that arises naturally in the weak form of the governing equations rather than through a source term. It is found that in some cases, a branch cut needs to be introduced along the internal boundary representing the stream in order to define a simply connected domain, which is an essential requirement in the derivation of the weak form of the ground-water flow equation. The fast time scale characteristic of surface-water flows and the slow time scale characteristic of ground-water flows are clearly established, leading to the definition of three dimensionless parameters, namely, a Peclet number that inherits the disparity between both time scales, a flow number that relates the pumping rate and the streamflow, and a Biot number that relates the conductance at the river-aquifer interface to the aquifer conductance. The model, implemented in the Bill Williams River Basin, reproduces the observed streamflow patterns and the ground-water flow patterns. Fairly good results are obtained using multiple time steps in the simulation process.

A finite element numerical model is developed for the modeling of coupled surface-water flow and ground-water flow. The mathematical treatment of subsurface flows follows the confined aquifer theory or the classical Dupuit approximation for unconfined aquifers whereas surface-water flows are treated with the kinematic wave approximation for open channel flow. A detailed discussion of the standard approaches to represent the coupling term is provided. In this work, a mathematical expression similar to Ohm's law is used to simulate the interacting term between the two major hydrological components. Contrary to the standard approach, the coupling term is incorporated through a boundary flux integral that arises naturally in the weak form of the governing equations rather than through a source term. It is found that in some cases, a branch cut needs to be introduced along the internal boundary representing the stream in order to define a simply connected domain, which is an essential requirement in the derivation of the weak form of the ground-water flow equation. The fast time scale characteristic of surface-water flows and the slow time scale characteristic of ground-water flows are clearly established, leading to the definition of three dimensionless parameters, namely, a Peclet number that inherits the disparity between both time scales, a flow number that relates the pumping rate and the streamflow, and a Biot number that relates the conductance at the river-aquifer interface to the aquifer conductance. The model, implemented in the Bill Williams River Basin, reproduces the observed streamflow patterns and the ground-water flow patterns. Fairly good results are obtained using multiple time steps in the simulation process.

A Disaggregation model was tested for arid land stream flow generating. The test was performed on data from Black River, near Fort Apache, Arizona. The model was tested in terms of preserving the relevant historical statistics on both monthly and daily levels, the monthly time series were disaggregated to a random observation of their daily components and the daily components were then reaggregated to yield monthly values. A computer model (DSGN) was developed to perform the model implementation. The model was written and executed on the Macintosh plus personal computer Data from two months were studied; the October data represented the low flow season, while the April data represented the high flow season. Twenty five years of data for each month was used. The generated data for the two months was compared with the historical data.

The basic concepts of hydrologic forecasting using the Streamflow Synthesis And Reservoir Regulation Model of the U.S. Army Corps of Engineers, auto-regressive-moving-average time series models (including Greens' functions, inverse functions, auto covariance Functions, and model estimation algorithm), and the Kalman filter (including state space modeling, system uncertainty, and filter algorithm), were explored. A computational experiment was conducted in which the Kalman filter was applied to update Mehama local basin model (Mehama is a 227 sq. miles watershed located on the North Santiam River near Salem, Oregon.), a typical SSARR basin model, to streamflow measurements as they became available in simulated real time. Among the candidate AR and ARMA models, an ARMA(l,l) time series model was selected as the best-fit model to represent the residual of the basin model. It was used to augment the streamflow forecasts created by the local basin model in simulated real time. Despite the limitations imposed by the quality of the moisture input forecast and the design and calibration of the basin model, the experiment shows that the new stochastic methods are effective in significantly improving the flood forecast accuracy of the SSARR model.

Relationships between thunderstorm and watershed variables and runoff from or within semiarid watersheds at Walnut Gulch, Arizona were examined. Variables showing greater sensitivity to basin and storm size were better flow predictors. Stepwise regression with three increasingly nonlinear algebraic models showed mean storm depth was the best simple predictor of runoff. Predictions improved using storm volume, a product of storm depth and areal extent. Initial runoff to streams was best described as a highly nonlinear function of storm and watershed variables. Runoff from a basin was a more linearized function of similar variables. The above differences were ascribed to channel transmission losses, reductions in runoff moving down initially dry channels. For a given basin and small storms, loss to runoff ratios exceeded 10:1 and were highly variable. Ratios were similar and less than 0.5:1 for storms centrally located over a basin and generating sufficient initial runoff to minimize flow variation due to losses. Losses increased disproportionately with basin size. Antecedent rainfall and first summer flows also affected rainfall runoff relationships in a differential manner. Wet conditions enhanced runoff more from larger versus smaller storms. First summer flows were less than expected probably because of higher soil infiltration and channel losses at the onset of summer storms. Overall, as storm size decreased or basin area increased, initial runoff was more often a localized phenomenon and downstream flow more dependent on storm depth, extent, location, and seasonal timing and basin channel losses, but less dependent on antecedent rainfall. Consequently, storm depth accounted for only 60% to 70% of the variation in flows while storm volume, antecedent rainfall, channel losses, and first summer flows explained 80% to 90%. Finally, oversimplifying storm or watershed variables or analytical methods led to errors in assessing their affect on runoff. It was also determined that current arguments supporting a recommendation to delete smaller, frequent annual floods to better fit remaining data to flood frequency curves were oversimplified. Distributed rainfall - runoff models with channel losses and regional storm depth - area - frequency data may be the way to develope flood curves for semiarid basins with short runoff records.

This study presents a new Lagrangian model for predicting dynamics and transport in rivers and shallow water flows. A hydrostatic model is developed for the prediction of rivers and floodplain flow and lateral interactions between them. The model is extended to the Boussinesq weakly non-linear, non-hydrostatic model for the simulation of solitary waves and undular bores. A model for advection-diffusion transport of tracers in open channel flow is also presented. The simulation results are compared against an analytical solution and published laboratory data, field data and theoretical results. It is demonstrated that the Lagrangian moving grid eliminates numerical diffusion and oscillations; the model is dynamically adaptive, providing higher resolution under the wave by compressing the parcels (grid). It also allows flow over dry beds and moving boundaries to be handled efficiently. The hydrostatic model results have shown that the model accurately simulates wave propagation and non-linear steepening until wave breaking. The model is successfully applied to simulate flow and lateral interactions in a compound channel and flood wave movement in a natural river. The non-hydrostatic model has successfully reproduced the general features of solitary waves such as the balance between non-linearity and wave dispersion and non-linear interactions of two solitary waves by phase-shift. Also, the model successfully reproduced undular bores (high frequency short waves) from a long wave and the predicted maximum height of the leading wave agreed very well with the published results. It is shown that the simple second order accurate Lagrangian scheme efficiently simulates dispersive waves without any numerical diffusion. Lagrangian modeling of advection-diffusion transport of Gaussian tracer distributions, top hat tracer distributions and steep fronts (step function) in steady, uniform flow has provided exact results and has shown that the scheme allows the use of a large time step without any numerical diffusion and oscillations, including for the advection of steep fronts. The scheme can handle large Courant numbers (results are presented for Cr = 0 to 20) and the entire range of grid Peclet numbers from zero to infinity. The model is successfully applied to tracer transport due to flow induced by simple waves, solitary waves and undular bores

The National Water Act (Act 36 of 1998) provides for an ecological Reserve as the quantity (flow) and quality of water needed to protect aquatic ecosystems. While there are methods available to quantify the ecological Reserve in terms of flow, methods of linking flow to water quality are lacking. Therefore, the research presented in this thesis investigated various modelling techniques to estimate the effect of flow on water quality. The aims of the research presented in this thesis were: Aim 1: Can the relationship between flow and water quality be accurately represented by simple statistical models? Aim 2: Can relatively simple models accurately represent the relationship between flow and water quality? Aim 3: Can the effect of diffuse sources be omitted from a water quality model and still obtain realistic simulations, and if so under what conditions? Aim 4: Can models that solely use historical monitoring data, accurately represent the relationships between flow and water quality? In Chapter 3, simple Q-C regressions of flow and water quality were investigated using Department of Water Affairs (DWA) historical monitoring data. It was found that while flow versus salinity regressions gave good regression fits in many cases, the Q-C regression approach is limited. A mechanistic/statistical model that attempted to estimate the point and diffuse signatures of nutrients in response to flow was developed in Chapter 4 using DWA historical monitoring data. The model was verified as accurate in certain case studies using observed point loading information. In Chapter 5, statistical models that link land cover information to diffuse nutrient signatures in response to flow using DWA historical data were developed. While the model estimations are uncertain due to a lack of data, they do provide an estimation of the diffuse signature within catchments where there is flow and land cover information available. Chapter 6 investigates the extension of an existing mass-balance salinity model to estimate the effect of saline irrigation return flow on in-stream salinity. The model gave accurate salinity estimates for a low order stream with little or no irrigation within its catchment, and for a permanently flowing river within a catchment used extensively for irrigation. Chapter 7 investigated a modelling method to estimate the reaction coefficients involved in nitrification using only DWA historical monitoring data. Here, the model used flow information to estimate the residence time of nutrients within the studied river reaches. While the model obtained good estimations of nitrification for the data it was applied to, very few DWA data sets were suitable for the model. Chapter 8 investigated the ability of the in-stream model QUAL2K to estimate nutrient concentrations downstream of point and diffuse inputs of nutrients. It was found that the QUAL2K model can give accurate results in cases where point sources dominate the total nutrient inputs into a river. However, the QUAL2K simulations are too uncertain in cases where there are large diffuse source inputs of nutrients as the load of the diffuse inputs is difficult to measure in the field. This research highlights the problem of data scarcity in terms of temporal resolution as well as the range of constituents measured within DWA historical monitoring data for water quality. This thesis in addition argues that the approach of applying a number of models is preferable to applying one model to investigate the research aims, as particular models would be suited to particular circumstances, and the development of new models allowed the research aims of this thesis to be explored more thoroughly. It is also argued that simpler models that simulate a few key processes that explain the variation in observed data, are more suitable for implementing Integrated Water Resource Management (IWRM) than large comprehensive water quality models. From this research, it is clear that simple statistical models are not adequate for modelling the relationship between flow and water quality, however, relatively simple mechanistic models that simulate a limited number of processes and water quality variables, can provide accurate representations of this relationship. Under conditions where diffuse sources are not a major factor within a catchment, models that omit diffuse sources can obtain realistic simulations of the relationship between flow and water quality. Most of the models investigated in this thesis demonstrate that accurate simulations of the relationships between flow and water quality can be obtained using solely historical monitoring data.

Reliability and accuracy of the forcing data plays a vital role in the Hydrological Streamflow Prediction. Reliability of the forcing data leads to accurate predictions and ultimately reduction of uncertainty. Currently, Numerical Weather Prediction (NWP) models are developing ensemble forecasts for various temporal and spatial scales. However, it is proven that the raw products of the NWP models may be biased at the basin scale; unlike model grid scale, depending on the size of the catchment. Due to the large space-time variability of precipitation, bias-correcting the ensemble forecasts has proven to be a challenging task. In recent years, Ensemble Pre-Processing (EPP), a statistical approach, has proven to be helpful in reduction of bias and generation of reliable forecast. The procedure is based on the bivariate probability distribution between observation and single-value precipitation forecasts. In the current work, we have applied and evaluated a Bayesian approach, based on the Copula density functions, to develop an ensemble precipitation forecasts from the conditional distribution of the single-value precipitation. Copula functions are the multivariate joint distribution of univariate marginal distributions and are capable of modeling the joint distribution of two variables with any level of correlation and dependency. The advantage of using Copulas, amongst others, includes its capability of modeling the joint distribution independent of the type of marginal distribution. In the present study, we have evaluated the capability of copula-based functions in EPP and comparison is made against an existing and commonly used procedure for same i.e. meta-Gaussian distribution. Monthly precipitation forecast from Climate Forecast System (CFS) and gridded observation from Parameter-elevation Relationships on Independent Slopes Model (PRISM) have been utilized to create ensemble pre-processed precipitation over three sub-basins in the western USA at 0.5-degree spatial resolution. The comparison has been made using both deterministic and probabilistic frameworks of evaluation. Across all the sub-basins and evaluation techniques, copula-based technique shows more reliability and robustness as compared to the meta-Gaussian approach.

Several different approaches are applied in low flow frequency analysis. Each method's theory and application is explained. The methods are (1) physically based recession model dealing with time series, (2) log-Pearson type III and mixed log-Pearson type III using annual minimum series, (3) Double Bounded pdf using annual minimum series, (4) Partial Duration Series applying truncated and censored flows. Each method has a computer program for application. One day low flow analysis was applied to 15 stations, 10 perennial streams and 5 intermittent streams. The physically based method uses the exponential baseflow recession with duration, initial recession flow, and recharge due to incoming storm as random variables, and shows promise as an alternative to black box methods, and is appealing because it contains the effect of drought length. Log-Pearson is modified to handle zero flows by adding a point mass probability for zero flows. Another approach to zero flows is the Double Bounded probability density function which also includes a point mass probability for zero flows. Maximum likelihood estimation is used to estimate distribution parameters. Partial Duration Series is applied due to drawbacks of using only one low flow per year in annual minimum series. Two approaches were used in Partial Duration Series (i) truncation, and (ii) censorship which represent different low flow populations. The parameters are estimated by maximum likelihood estimation.
M.S.

Semi-distributed hydrological models are often used for streamflow forecasting, hydrological climate change impact assessments, and other applications. In such models, basins are broken up into hydrologic response units (HRUs), which are assumed to have a relatively homogenous response to precipitation. HRUs are delineated in a variety of ways, and the procedure used may impact model performance. HRU delineation procedures have been researched, but it is still not clear how important these subdivision schemes are or which delineation methods are most effective. To start addressing this knowledge gap, this project investigated whether or not HRU size has a significant effect on streamflow simulation at the mouth of a watershed. To test this, 30 gaged, relatively unimpaired western U.S. basins were each modeled with 6 HRU sets of different sizes using the Precipitation Runoff Modeling System (PRMS). To isolate size as a variable, HRUs were delineated using stream catchments. For each basin, streams were defined with 6 different threshold levels, producing HRUs of differing sizes. Nineteen model parameters were derived for each HRU using nationally consistent GIS datasets, and all other model parameters were left at default values. Climate inputs were derived from a national 4-km2 gridded daily climate dataset. After calibration, 4 goodness-of-fit metrics were calculated for daily streamflow for each HRU set. Uncalibrated model performance was generally poor for a variety of reasons, but comparison of the models was still informative. Results for the 30 basins across the 6 HRU size classes showed that HRU size did not significantly impact model performance across all basins. However, in basins that had less total precipitation and higher elevation, sensitivity of model performance to HRU subdivision levels was slightly greater, though not significantly so. Findings indicate that, in most basins, little subdivision may be required for good model performance, allowing for desirable simplicity and fewer degrees of freedom without sacrificing runoff simulation accuracy.

The existing theories for predicting longitudinal dispersion in straight open channels have long been recognized as inadequate when applied to natural rivers. These theories tend to grossly underestimate dispersion in real streams since an important mixing mechanism due to nonuniform river cross-section variations is not explicitly taken into account. Recognizing the important role of stream irregularities on solute transport and the analytical difficulties of classical deterministic analysis, we develop a stochastic approach for analyzing solute transport in natural streams. Variations in river width and bed elevation are conveniently represented as one-dimensional random fields, characterized by their autocorrelation functions. Advection and dispersion due to the combined effect of turbulent diffusion and nonuniform flow are described by the stochastic solute transport equation. When boundary variations are small and statistically homogeneous, a stochastic spectral technique is used to obtain closed-form stochastic solutions. In particular, closed-form expressions are obtained for effective mean solute transport velocity and effective dispersion coefficient reflecting mixing due to flow variations both within the river cross-section and in the streamwise direction. The results show that the mean behavior of solute transport in a statistically irregular stream can be described as a gradient dispersion process. The effective mean transport velocity in natural rivers is smaller than that in a corresponding uniform channel, and the effective longitudinal dispersion coefficient in natural rivers can be considerably greater than that of uniform open channels. The discrepancy between uniform channels and natural rivers increases rapidly as the variances of river width and bed elevation increase, especially when the mean flow Froude number is high.

This research focuses on the estimation of the impacts of climate change on water yield, streamflow extremes, and the streamflow regimes in the Cline River Watershed, and consequently, water availability for hydropower generation in this area. The Cline River Watershed comprises the flow into Lake Abraham, the reservoir for Bighorn Dam, is part of the upper North Saskatchewan River basin (UNSRB). This objective was achieved by parameterizing the ACRU agro-hydrological modelling system. After parameterization was complete, ACRU output was calibrated and verified against available observed data, including temperature, snow water equivalent, glacier mass balance, potential evapotranspiration, and streamflow data. After ACRU was properly verified, five selected climate change scenarios to estimate impacts of climate change in this area. Overall water yields are projected to increase over time. A large shift in seasonality is likely the biggest impact climate change will have on water resources in the Cline River Watershed.
xii, 126 leaves : ill., maps ; 29 cm

Climatic conditions (precipitation, evapotranspiration, available soil moisture, and temperature) are important variables when considering cumulative storm streamflow for a watershed. The objective of this study was to determine what climatic conditions, if any, could be used to mathematically model cumulative storm streamflow for an extensively-drained small agricultural watershed in northwest Delaware County, Indiana. A water-level recorder was installed in Killbuck Creek during autumn 2002, spring, summer, and autumn 2003 and 2004. To determine discharge, velocity measurements were collected following US Geological Survey (USGS) methods and two rating curves (high and low flow) were constructed. Simple linear regressions were performed using cumulative streamflow as the dependent variable and precipitation, evapotranspiration, available soil moisture, temperature, and runoff as independent variables. Multiple linear regressions were used to examine combinations of the independent variables. Cumulative streamflow was most related to precipitation (r2 = 0.23 and p < 0.001) and least related to temperature (r2 = 0.03 and p < 0.5). The multiple linear regression from the combination of precipitation, runoff, and temperature provided the most accurate cumulative streamflow simulation (R2 = 0.53 and p < 0.001). Multiple linear regressions using climatic variables can be used to estimate cumulative streamflow for an agricultural watershed.
Department of Natural Resources and Environmental Management

This thesis develops a one-dimensional version of a new data driven model of turbulence that uses the KL expansion to provide a spectral solution of the turbulent flow field based on analysis of Particle Image Velocimetry (PIV) turbulent data. The analysis derives a 2nd order random field over the whole flow domain that gives better turbulence properties in areas of non-uniform flow and where flow separates than the present models that are based on the Navier-Stokes Equations. These latter models need assumptions to decrease the number of calculations to enable them to run on present day computers or super-computers. These assumptions reduce the accuracy of these models. The improved flow field is gained at the expense of the model not being generic. Therefore the new data driven model can only be used for the flow situation of the data as the analysis shows that the kernel of the turbulent flow field of undular hydraulic jump could not be related to the surface waves, a key feature of the jump. The kernel developed has two parts, called the outer and inner parts. A comparison shows that the ratio of outer kernel to inner kernel primarily reflects the ratio of turbulent production to turbulent dissipation. The outer part, with a larger correlation length, reflects the larger structures of the flow that contain most of the turbulent energy production. The inner part reflects the smaller structures that contain most turbulent energy dissipation. The new data driven model can use a kernel with changing variance and/or regression coefficient over the domain, necessitating the use of both numerical and analytical methods. The model allows the use of a two-part regression coefficient kernel, the solution being the addition of the result from each part of the kernel. This research highlighted the need to assess the size of the structures calculated by the models based on the Navier-Stokes equations to validate these models. At present most studies use mean velocities and the turbulent fluctuations to validate a models performance. As the new data driven model gives better turbulence properties, it could be used in complicated flow situations, such as a rock groyne to give better assessment of the forces and pressures in the water flow resulting from turbulence fluctuations for the design of such structures. Further development to make the model usable includes; solving the numerical problem associated with the double kernel, reducing the number of modes required, obtaining a solution for the kernel of two-dimensional and three-dimensional flows, including the change in correlation length with time as presently the model gives instant realisations of the flow field and finally including third and fourth order statistics to improve the data driven model velocity field from having Gaussian distribution properties. As the third and fourth order statistics are Reynolds Number dependent this will enable the model to be applied to PIV data from physical scale models. In summary, this new data driven model is complementary to models based on the Navier-Stokes equations by providing better results in complicated design situations. Further research to develop the new model is viewed as an important step forward in the analysis of river control structures such as rock groynes that are prevalent on New Zealand Rivers protecting large cities.

Problems in the water sector range from degradation and depletion of water resources as a result of the impacts of land based anthropogenic activities, to the impacts of natural hydrological disasters and floods, while inadequate availability of water is at the core of most water related disputes in arid and semi-arid areas at local, regional, national and international levels. In the past, finding practical solutions for these problems fell neatly within the traditional scope of water resources management, which hinged almost entirely on economic viability of engineering oriented endeavors. However, a new set of management challenges has arisen following the high priority nowadays given to equity in water allocation and the protection of the natural environment above other issues. These new challenges have created a need for devising and adopting suitable management approaches, especially that would take social considerations into account. One of the approaches that provides promise relative to the new directions in dealing with contemporary water issues is integrated water resources management (IWRM). One objective of this study was to critically review the definitions and the fundamental principles of IWRM with the view of determining its applicability in developing countries and highlighting difficulties that may be faced regarding the adoption and implementation of this integrated approach. Swaziland is atypical example ofa developing country that is engulfed by the diverse water resources issues highlighted above and is currently engaged in updating water management legislation. Hence, Swaziland's experiences were used to put in perspective the key points and barriers regarding the adoption and implementation of IWRM. The catchment, the recommended spatial unit of IWRM, poses the first practical barrier, as catchments often cross both political and administrative boundaries, thereby creating the need for many water management problems to be solved across catchments with international security issues, cultural issues, different levels of development and different hydroclimatic regimes. The successful implementation of IWRM depends on effective participation of stakeholders. Lack of information flow between stakeholders of different backgrounds limits informed participation. Therefore, it is necessary to develop tools such as decision support systems (DSSs) that will foster easier multilateral information flow and aid decision making. IWRM requires information which itself should be managed in an integrated manner and be readily accessible. This is not always the case in developing countries with shortage of funds for data collection, manipulation and storage as well as adequately trained and experienced staff With the shortage of sufficiently long and reliable hydrological data for water management, the alternative is to synthesize records through hydrological modelling. Another objective of this study was to evaluate and test the suitability of the ACRU modelling system, a daily time-step agrohydrological model, to simulate catchment level hydrological processes and land use impacts as part of the assessment studies which form an integral part of integrated water resources management. ACRU was set up for the Mbuluzi, a 2958 km2 catchment in Swaziland. The catchment was subdivided into 40 sub catchments, after which the model was used for assessing both the impacts of land use and management changes on runoff yields and available water resources by evaluating present and future sectoral water demands, determining whether river flow from Swaziland into Mozambique meets the quantitative requirements of the international agreement existing between the two countries, and evaluating sediment yield and its spatial and temporal variation as well as its response to potential changes in land management. The physical-conceptual structure of the model, its multi-level adeptness regarding input information requirements, coupled with in-built decision support systems and generic default values make ACRU a suitable modelling tool in developing countries, as it makes it possible to obtain reasonable simulations for a range of levels of input information. Together with the model's multi-purpose nature, the ability of simulating ''what if scenarios", which was utilised in this study, makes it useful in the generation of information for IWRM. Future research needs which were identified include finding means of encouraging effective communication between scientists, water managers and other stakeholders, who may be "lay people". There is a need to conduct research that will lead to equipping ACRU with sediment routing and deposition algorithms, as well as routines to account more explicitly for dam operating rules and ecological issues, which would render its output even more useful in IWRM than the model's present structure allows.
Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 2001.

Submitted in fulfillment of the requirements of the Degree of Master of Technology: Civil Engineering, Durban University of Technology, 2014.
Streamflow modelling remains crucial to decision-making especially when it concerns planning and management of water resources systems in water-stressed regions. This study proposes a suitable method for streamflow modelling irrespective of the limited availability of historical datasets. Two data-driven modelling techniques were applied comparatively so as to achieve this aim. Genetic programming (GP), an evolutionary algorithm approach and a differential evolution (DE)-trained artificial neural network (ANN) were used for streamflow prediction in the upper Mkomazi River, South Africa. Historical records of streamflow and meteorological variables for a 19-year period (1994- 2012) were used for model development and also in the selection of predictor variables into the input vector space of the models. In both approaches, individual monthly predictive models were developed for each month of the year using a 1-year lead time. Two case studies were considered in development of the ANN models. Case study 1 involved the use of correlation analysis in selecting input variables as employed during GP model development, while the DE algorithm was used for training and optimizing the model parameters. However in case study 2, genetic programming was incorporated as a screening tool for determining the dimensionality of the ANN models, while the learning process was further fine-tuned by subjecting the DE algorithm to sensitivity analysis. Altogether, the performance of the three sets of predictive models were evaluated comparatively using three statistical measures namely, Mean Absolute Percent Error (MAPE), Root Mean-Squared Error (RMSE) and coefficient of determination (R2). Results showed better predictive performance by the GP models both during the training and validation phases when compared with the ANNs. Although the ANN models developed in case study 1 gave satisfactory results during the training phase, they were unable to extensively replicate those results during the validation phase. It was found that results from case study 1 were considerably influenced by the problems of overfitting and memorization, which are typical of ANNs when subjected to small amount of datasets. However, results from case study 2 showed great improvement across the three evaluation criteria, as the overfitting and memorization problems were significantly minimized, thus leading to improved accuracy in the predictions of the ANN models. It was concluded that the conjunctive use of the two evolutionary computation methods (GP and DE) can be used to improve the performance of artificial neural networks models, especially when availability of datasets is limited. In addition, the GP models can be deployed as predictive tools for the purpose of planning and management of water resources within the Mkomazi region and KwaZulu-Natal province as a whole.

A disappointingly large proportion of the citizens of developing countries remain excluded from services provided by formal financial enterprises. This segment of the market, often referred to as the bottom of the economic pyramid (BOP), is subjected to a host of barriers which prevent it from accessing traditional financial services. In society, money does not only represent material value, but it is also a social construct through which all members of societies express themselves. Hence these, often poor, members of developing societies consequently attain access to credit through alternative modes of financing – one of which is the financial cooperative. Financial cooperatives play a dual role in society; they provide an economic vehicle for individuals and also a platform for social interaction for its members, thereby building social capital within the society. The existence of social capital within a society increases the members’ ability to solve communal problems. Unfortunately, an inadequate amount of research has been done to aid our understanding of this, and indeed other, alternative financing models. This paper seeks to begin to address this by investigating the competitive advantage and critical success factors of financial cooperatives in Swaziland. To this end, a qualitative research with an exploratory approach was conducted, as this approach was found most appropriate to provide new insights on the key phenomena that was being investigated. Consequently, 24 in-depth interviews at five different levels of involvement with cooperatives in Swaziland were conducted. The interviews provided rich data which was analysed using content and frequency analysis. This study found that successful financial service providers serving the market at the BOP provide a solution that has an appropriate balance between functional and social features. Financial cooperatives as a means of financial service was found to be suitably designed to meet the needs of the underserved financial service market. The Financial Services Acquisition Journey model was developed from the research findings. In graphic form, this model offers an integrated representation on how to ensure enhanced customer experience whilst providing financial services for the underserved financial services market.
Dissertation (MBA)--University of Pretoria, 2014.
zkgibs2015
Gordon Institute of Business Science (GIBS)
Unrestricted

Natural stream systems contain a variety of flow geometries which contain flow separation, turbulent shear layers, and recirculation zones. This work focuses on streams with dead zones. Characterized by slower flow and recirculation, dead zones are naturally occurring cutouts in stream banks. These dead zones play an important role in stream nutrient retention and solute transport. Previous experimental work has focused on idealized dead zone geometries studied in laboratory flumes. This work explores the capabilities of computational fluid dynamics (CFD) to investigate the scaling relationships between flow parameters of idealized geometries and the time scales of transport. The stream geometry can be split into two main regions, the main stream flow and the dead zone. Geometric parameters of the dead zone as well as the bulk stream velocity were varied to determine a scaling relationship for the transport time scales. These flow geometries are simulated using the RANS turbulence model with the standard k-ω closure. The standard first order dead zone model is expanded to a two region model to accommodate the multiple time scales observed in the simulation results. While this model currently has limited predictive capability, it provides physical insight into the functional dependence of the dead zone time scales. LES is used to evaluate the performance of the Reynolds Averaged Navier-Stokes (RANS) turbulence model and to describe the anisotropic turbulence characteristics. The differences between the time averaged flow field for Large Eddy Simulation (LES) and RANS was determined to have a significant impact on passive scalar transport.
Graduation date: 2012

Many techniques have been developed over the years in first world countries for the estimation of flood hydrographs from small catchments for application in design, management and operations of water related issues. However, relatively little attention has been directed towards the transfer and adaptation of such techniques to developing countries in which major hydrological decisions are crucially needed, but in which a scarcity of quality hydrological data often occurs. As a result, hydrologists and engineers in developing countries are frequently unable to alleviate the problems that extreme rainfall events can create through destructive flood flows or, alternatively, they do not possess the appropriate tools with which to design economically viable hydraulic structures. Eritrea is a typical example of a developing country which faces difficulties in regard to the adaptation of an appropriate design flood estimation technique for application on small catchments. As a result, the need has arisen to adapt a relatively simple and robust design flood model that can aid hydrologists and engineers in making economic and safe designs of hydraulic structures in small catchments. One objective of this study was, therefore, to review approaches to hydrological modelling and design flood estimation techniques on small catchments, in order to identify the barriers regarding their adaptation, as well as to assist in the selection of an appropriate technique for application, in Eritrea. The southern African adaptation of the SCS (i.e. Soil Conservation Service) design hydrograph technique, which has become a standard method for design flood estimation from small catchments in that region, was selected for application on small catchments in Eritrea for several reasons. It relies on the determination of a simple catchment response index in the form of an initial Curve Number (CN), which reflects both the abstraction characteristics and the non-linear stormflow responses of the catchment from a discrete rainfall event. Many studies on the use of SCS-based hydrological models have identified that adjustment of the initial CN to a catchment's antecedent soil moisture (ASM) to be crucial, as the ASM has been found to be one of the most sensitive parameters for accurate estimates of design flood volumes and peak discharges. In hydrologically heterogeneous regions like Eritrea, the hypothesis was postulated that simulations using a suitable soil water budgeting procedure for CN adjustment would lead to improved estimates of design flood volumes and peak discharges when compared with adjustments using the conventional SCS antecedent moisture conditions (SCS-AMC) method. The primary objective of this dissertation was to develop a surrogate methodology for the soil water budgeting procedure of CN adjustment, because any direct applications of soil water budgeting techniques are impractical in most parts of Eritrea owing to a scarcity of adequate and quality controlled hydrological information. It was furthermore hypothesised that within reasonably similar climatic regions, median changes in soil moisture storage from the socalled "initial" catchment soil moisture conditions, i.e. LIS, were likely to be similar, while between different climatic regions median LISs were likely to be different. Additionally, it was postulated that climatic regions may be represented by a standard climate classification system. Based on the above hypotheses, the Koppen climate classification, which can be derived from mean monthly rainfall and temperature information, was first applied to the 712 relatively homogeneous hydrological response zones which had previously been identified in southern Africa. A high degree of homogeneity of median values of LIS, derived by the daily time step ACRU soil moisture budgeting model, was observed for zones occurring within each individual Koppen climate class (KCC) - this after a homogeneity test had been performed to check if zones falling in a specific KCC had similar values of median LIS. Further assessment within each KCC found in southern Africa then showed that a strong relationship existed between LIS and Mean Annual Precipitation (MAP). This relationship was, however, different between KCCs. By developing regression equations, good simulations of median LIS from MAP were observed in each KCC, illustrating the potential application of the Koppen climate classification system as an indicator of regional median LIS, when only very basic monthly climatological information is available. The next critical task undertaken was to test whether the estimate of median LIS from MAP by regression equation for a specific Koppen climate class identified in southern Africa would remain similar for an identical Koppen climatic region in Eritrea. As already mentioned, LIS may be determined from daily time step hydrological soil moisture budget models such as ACRU model. The performance of the ACRU stormflow modelling approach was, therefore, first verified on an Eritrean gauged research catchment, viz. the Afdeyu, in order to have confidence in the use of values of LIS generated by it. A SCS-ACRU stormflow modelling approach was then tested on the same catchment by using the new approach of CN adjustment, termed the ACRU-Koppen method, and results were compared against stormflow volumes obtained using the SCS-AMC classes and the Hawkins' soil water budgeting procedures for CN adjustment, as well as when CNs remain unadjusted. Despite the relatively limited level of information on climate, soils and land use for the Afdeyu research catchment, the ACRU model simulated both daily and monthly flows well. By comparing the outputs generated from the SCS model when using the different methods of CN adjustment, the ACRU-Koppen method displayed better levels of performances than either of the other two SCS-based methods. A further statistical comparison was made among the ACRU, the SCS adjusted by ACRU-Koppen, the SCS adjusted by AMC classes and the unadjusted SCS models for the five highest stormflows produced from the five highest daily rainfall amounts of each year on the Afdeyu catchment. The ACRU model produced highly acceptable statistics from stormflow simulations on the Afdeyu catchment when compared to the SCS-based estimates. In comparing results from the ACRU-Koppen method to those from the SCS-AMC and unadjusted CN methods it was found that, statistically, the ACRU-Koppen performed much better than either of the other two SCS based methods. On the strength of these results the following conclusions were drawn: • Changes in soil moisture storage from so-called "initial" catchment soil moisture conditions, i.e. L1S, are similar in similar climatic regions; and • Using the ACRU-Koppen method ofCN adjustment, the SCS-SA model can, therefore, be adapted for application in Eritrea, for which Koppen climates can be produced from monthly rainfall and temperature maps. Finally, future research needs for improvements in the SCS-ACRU-Koppen (SAK) approach in light of data availability and the estimation ofL1S were identified. From the findings of this research and South African experiences, a first version of a "SCSEritrea" user manual based on the SAK modelling approach has been produced to facilitate its use throughout Eritrea. This user manual, although not an integral part of this dissertation, is presented in its entirety as an Appendix. A first Version of the SCS-Eritrea software is also included.
Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2004.

Demands on the water resources of South Africa are ever increasing owing to population growth and increased development of urban, peri-urban and rural communities. Problems in terms of water quantity and quality are likely to be experienced during baseflow recessions. It is therefore imperative that water resources managers not only understand these baseflow periods of streamflow, but are able to model them with confidence. Research for this study thus included a comprehensive literature survey of the factors which affect baseflow as well as the approaches that previous studies have utilised to analyse and model baseflow recession. The primary aims of this study were to establish a streamflow database, to construct master recession curves (MRCs) for each catchment under consideration, evaluate the assumption that South African rivers recede exponentially, to determine a representative set of catchment characteristics for use in the baseflow recession analysis, to attempt to explain the MRC trends using these catchment characteristics and to investigate the feasibility of establishing a rule based model for baseflow recession. A streamflow database for South Africa was therefore established. This consisted initially of 202 catchments which were deemed to be recording natural streamflow. MRCs were established for 134 of these catchments. Those MRCs which were established indicate that the majority of South African rivers do not conform to an exponential model of recession. In order to account for the trends defined by the MRCs, catchment area, average catchment slope, drainage density, mean annual precipitation, rainfall concentration, rainfall seasonality, two independent estimates of groundwater recharge and a geological index were calculated for each catchment. Limited success was achieved when the data set was divided into subsets in order to group catchments with similar baseflow recession responses. The geological composition of the catchments appeared to provide the best results in that those trends exhibited by the MRCs could be explained by the types and proportions of the lithologies present. Owing to the lack of readily useable results it was concluded that until further results were forthcoming the development of a rule based model for baseflow recession analysis in South Africa would be premature. The establishment of a readily accessible database containing streamflows and associated catchment characteristics lends itself to future research.
Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 1997.

This thesis describes the development of a decision support tool to be used in the operation of Vanderkloof Dam on the Orange River so that the supply of water to the lower Orange River can be optimised. The decision support tool is based on a hydrodynamic model that was customised to incorporate real time data recorded at several points on the river. By incorporating these data into the model the simulated flows are corrected to the actual flow conditions recorded on the river, thereby generating a best estimate of flow conditions at any given time. This information is then used as the initial conditions for forecast simulations to assess whether the discharge volumes and schedules from the dam satisfy the water demands of downstream users, some of which are 1400km or up to 8 weeks away. The various components of the decision support system, their functionality and their interaction are described. The details regarding the development of these components include: • The hydraulic model of the Orange River downstream of Vanderkloof Dam. The population and calibration of the model are described. • The modification of the code of the hydrodynamic engine so that real time recorded stage and flow data can be incorporated into the model • The development of a graphical user interface to facilitate the exchange of data between the real time network of flow gauging stations on the Orange River and the hydraulic model • The investigation into the effect of including the real time data on the simulated flows • Testing the effectiveness of the decision support system.
Thesis (M.Sc.)-University of Natal, Durban, 2002.