The empirical method for the determination of apparent water losses, using the assessment of consumption patterns and the laboratory testing of water meters, is compared against alternative methods of comparative billing and meter change analyses for one of the largest water utilities in South Africa. Using the empirical method, apparent losses are estimated to have an average value of 12% of the billed volume with a range from 9.4% to 14.6% that is dependent on meter size ratios. This overlaps with the estimates, of 8%−10% for a utility with direct feed good quality water but high meter age (> 10 yr) and low accuracy, currently proposed in some studies and used by industry. The estimate from the comparative billing analysis method is 14% and it is sensitive to how the data is processed and analysed. The meter change method yielded an estimate of 4.7% for only a subset of the data. Both results of the alternative methods are in line with previous studies, with the comparative billing analysis performing better, but requiring further refinement for better accuracy and repeatability. The empirical method remains the gold standard in assessing apparent water losses but is undoubtedly very laborious, expensive and out of reach of the budget of many utilities. The development and validation of alternative methodologies therefore holds great promise but these are substantially reliant on comprehensive meter information and credible billing datasets which are rarely available in most utilities in Africa.

Despite wide acceptance of the IWA water balance as the basis of managing water losses, experience suggests that there are difficulties with its application. For apparent losses assessment, the traditional approach of deriving consumption profiles and testing water meters exceeds the resources of many utilities. While a few studies have explored alternative methodologies, these have largely not been validated and are susceptible to reproducibility and interpretation difficulties. This paper introduces an improved comparative billing analysis method that combines data preparation techniques, clustering analysis and classical regression analysis on monthly billing data of a water utility in Johannesburg, South Africa. Using the method, an average estimate of apparent losses due to metering errors of 8.2% was found against the best-case scenario of 9.4% using field investigations and laboratory tests, which also measure meter under-registration that the proposed methodology does not cater for. The validated results were possible at a fraction of the cost and effort, while also providing better insight into the underlying consumption patterns. The results show that data-driven discovery processes are viable alternatives for improved assessment and management of water losses.

When pollution spills occur, they impact on the quality of water in underlying aquifers. Such spills can be modelled as instantaneous pollution sources, and estimating their strengths from the concentration plumes they produce is an inverse problem which is addressed in this paper by the Green element method (GEM). Estimating the strengths of such spills, making use of the concentration data at various locations and times, is an inverse problem whose solution is often associated with non-uniqueness, non-existence and instability. Here the GEM is used to predict the strengths of pollution spills from measured concentration data at internal observation points. The performance of the methodology is illustrated using two numerical examples in which the contaminant plumes are from multiple point and distributed pollution sources. Single and multiple episodes of pollution injections are accommodated in both examples. It is observed that GEM is more accurate in predicting the strengths of distributed instantaneous pollution sources than point sources because of the discontinuities of the latter in both the spatial and temporal dimensions.

Multiple agricultural water management (AWM) technologies are being promoted worldwide in rainfed agro-ecological production systems, such as the Limpopo River Basin, to close the yield gap, enhance food security and reduce poverty, but evidences on yield gains and environmental impacts are varied. This paper conducts a review of the performance of AWM technologies against conventional farmer practices to produce adequate evidence on cereal yield and field runoff changes. With the interrogation of literature from 1980 to 2013 using seven AWM groupings, enough evidence was found that AWM technologies can deliver substantial benefits of increased crop yield and water productivity with reduced environmental impacts. Using random effects model, the standardized mean difference (SMD) of yield between AWM and control was 0.27, while SMD of water productivity was 0.46, indicating the effectiveness of the technologies (SMD > 0). Subgroup analyses showed greatest yield responses on silty-clay-loam, clay-loam and sandy soils compared to clay and loam-sandy soils, and higher yield increase under low rainfall regime (200–500 mm) than under high rainfall regime (500–800 mm). Large yield change variations for different AWM technologies present a huge opportunity for meeting the existing yield gaps and enhancing coping capacity in dry years and under climate change.

Evaluating pollution sources from limited concentration data of their contaminant plumes in groundwater systems is an inverse problem that presents computational challenges because of its ill-posedness. In this work, the Green element method (GEM) is used to solve inverse contaminant transport problems in 2-D orthotropic homogeneous aquifers. The GEM discretization of the differential equation produces an over-determined, ill-conditioned global matrix that is decomposed by the singular value decomposition method and solved by the least square method with Tikhonov regularization. Five test cases of pollution sources of unknown strengths are used to evaluate the performance of GEM. The results indicate that the current methodology is capable of correctly predicting the strength of pollution sources and the historical concentration plumes that they produce. However, the computation accuracy is influenced by the location of the observation points in relation to the source, data errors of observed concentrations, the transport mode, and the value of the Courant number used in the simulations. Data errors at observation points influence more significantly the GEM prediction of the pollution source strength than the concentration plume, while numerical artefacts of dispersion and oscillations observed in direct solutions of advection-dominant transport cases are also evident in inverse modelling.

The mappings of poverty and food insecurity were carried out for the rural districts of the four riparian countries (Botswana, Mozambique, South Africa and Zimbabwe) of the Limpopo river basin using the results of national surveys that were conducted between 2003 and 2013. The analysis shows lower range of food insecure persons (0–40%) than poverty stricken persons (0–95%) that is attributable to enhanced government and non-government food safety networks in the basin countries, the dynamic and transitory nature of food insecurity which depends on the timings of the surveys in relation to harvests, markets and food prices, and the limited dimension of food insecurity in relation to poverty which tends to be a more structural and pervasive socio-economic condition. The usefulness of this study in influencing policies and strategies targeted at alleviating poverty and improving rural livelihoods lies with using food insecurity mappings to address short-term socio-economic conditions and poverty mappings to address more structural and long-term deprivations. Using the poverty line of $1.25/day per person (2008–2013) in the basin, Zimbabwe had the highest percentage of 68.7% of its rural population classified as poor, followed by Mozambique with 68.2%, South Africa with 56.1% and Botswana with 20%. While average poverty reduction of 6.4% was observed between 2003 and 2009 in Botswana, its population growth of 20.1% indicated no real poverty reduction. Similar observations are made about Mozambique and Zimbabwe where population growth outstripped poverty reductions. In contrast, both average poverty levels and population increased by 4.3% and 11%, respectively, in South Africa from 2007 to 2010. While areas of high food insecurity and poverty consistently coincide with low water availability, it does not indicate a simple cause–effect relationship between water, poverty and food insecurity. With limited water resources, rural folks in the basin require stronger institutions, increased investments and support to enable them generate sufficient income from their rain-fed farming livelihood to break out of the poverty cycle.

Pollution source identification in groundwater contaminant transport using limited concentration data of the contaminant plume is an inverse problem. In this paper, we develop a numerical-optimization approach that utilizes the green element method (GEM) and the shuffled complex evolutionary (SCE) technique to identify pollution source strengths and recover the concentration distribution of the plume for contaminant transport in groundwater systems. Two test cases are used to evaluate our proposed methodology: 1D transient case with an analytical solution and 2D transient hypothetical case that mimics a real life situation. The results indicate that the proposed methodology gives good estimates of the release history and the historical distribution of the plume even in the presence of observation and parameter errors.

The solutions to inverse heat conduction problems (IHCPs) are provided in this paper by the Green element method (GEM), incorporating the logarithmic fundamental solution of the Laplace operator (Formulation 1) and the timedependent fundamental solution of the diffusion differential operator (Formulation 2). The IHCPs addressed relate to transient problems of the recovery of the temperature, heat flux and heat source in 2-D homogeneous domains. For each formulation, the global coefficient matrix is over-determined and ill-conditioned, requiring a solution strategy that involves the least square method with matrix decomposition by the singular value decomposition (SVD) method, and regularization by the Tikhonov regularization method. Comparisons of the two formulations are made using five numerical examples of transient IHCPs. Using the same spatial and temporal discretizations, the GEM with the logarithmic fundamental solution is generally more superior in accuracy and computational speed than the formulation with the time-dependent fundamental solution.

Using family balance (i.e., combined net farm and non-farm incomes less family expenses), an output from an integrated model, which couples water resource, agronomic and socio-economic models, its sensitivity and uncertainty are evaluated for five smallholder farming groups (A E) in the Olifants Basin. The crop management practiced included conventional rainfed, untied ridges, planting basins and supplemental irrigation. Scatter plots inferred the most sensitive variables affecting family balance, while the Monte Carlo method, using random sampling, was used to propagate the uncertainty in the model inputs to produce family balance probability distributions. A non-linear correlation between in-season rainfall and family balance arises from several factors that affect crop yield, indicating the complexity of farm family finance resource-base in relation to climate, crop management practices and environmental resources of soil and water. Stronger relationships between family balance and evapotranspiration than with in-season rainfall were obtained. Sensitivity analysis results suggest more targeted investment effort in data monitoring of yield, in-season rainfall, supplemental irrigation and maize price to reduce family balance uncertainty that varied from 42% to 54% at 90% confidence level. While supplemental irrigation offers the most marginal increase in yields, its wide adoption is limited by availability of water and infrastructure cost. (C) 2014 Elsevier Ltd. All rights reserved.

In two spatial dimensions, inverse heat conduction problems of temperature, heat flux and heat source recovery are solved in homogeneous and heterogeneous media for steady and transient cases by the Green element method (GEM). The formulation of GEM employed is presented in Taigbenu (2012) [27] and it uses a second-order difference expression to approximate the internal normal fluxes and, therefore, gives accuracy comparable to the flux-based formulation. The Tikhonov regularization with the singular value decomposition (SVD) are used to solve in a least square sense the over-determined, ill-conditioned discrete equations arising from the element-by-element implementation of the singular integral equations. With seven numerical examples, the numerical characteristics of the GEM are evaluated for inverse problems where it is required to recover the temperature, heat flux and heat source from available data. In some of the examples, the performance of the formulation is evaluated when random errors are introduced into the measured data. Excellent results are obtained from the simulated numerical examples, and more especially that these results are obtained with coarse grids.

Inverse contaminant transport problems, unlike direct problems, may result in non-unique and unstable solutions because of the ill-conditioned nature of the coefficient matrix.In this work the Green element method (GEM) is used to solve steady inverse contaminant transport problems.The ill-conditioned, overdetermined system of equations that arises from the Green element discretization is solved by the least square method with the singular value decomposition technique and Tikhonov regularization.Two examples of steady inverse contaminant transport problems with constant and variable velocity are simulated by GEM with good prediction obtained for the concentration and fluxes.

Continuous developments and investigations in flow predictions are of interest in watershed hydrology especially where watercourses are poorly gauged and data are scarce like in most parts of Africa. Thus, this paper reports on two approaches to generate local monthly runoff of the data-scarce Semliki watershed. The Semliki River is part of the upper drainage of the Albert Nile. With an average annual local runoff of 4.622 km3/annum, the Semliki watershed contributes up to 20% of the flows of the White Nile. The watershed was sub-divided in 21 sub-catchments (S3 to S23). Using eight physiographic and meteorological variables, generated from remotely sensed acquired datasets and limited catchment data, monthly runoffs were estimated. One ordination technique, the Principal Component Analysis (PCA), and the tree cluster analysis of the landform attributes were performed to study the data structure and spot physiographic similarities between sub-catchments. The PCA revealed the existence of two major groups of sub-catchments – flat (Group I) and hilly (Group II). Linear and nonlinear regression models were used to predict the long-term monthly mean discharges for the two groups of sub-catchments, and their performance evaluated by the Nash-Sutcliffe Efficiency (NSE), Percent bias (PBIAS) and root mean square error to the standard deviation ratio (RSR). The dimensionless indices used for model evaluation indicate that the non-linear model provides better prediction of the flows than the linear one.

Research has largely been driven by the quest for innovation, new knowledge and improving the general wellbeing of the human race. Monumental challenges that plague humanity tend to, from time to time, shape research and take it to new heights, and one of such is the global water crisis [1,2]. To restate the obvious that water is the basis of life and the engine for social and economic growth, water resource engineering research attempts to address challenges related to: (i) how water of sufficient quantity and quality can be made available to meet various competing sectoral demands; (ii) how development and exploitation of the resource can be carried out in a sustainable manner so that its benefits extend to future generations; (iii) what adaptation and mitigating measures can be put in place to minimize the impacts of global climate change. This paper, therefore, presents trends in four areas of research in water resources engineering that focus on the paradigm shifts in water supply and sanitation, integrated modeling in order to give quantitative expression to integrated water resources management (IWRM), thereby achieving a more defined space for decision making, new and emerging cost-effective water treatment technologies, and research developments in adaptation measures to climate change.

Computerised integrated models from science contribute to better informed and holistic assessments of multifaceted policies and technologies than individual models. This view has led to considerable effort being devoted to developing integrated models to support decision-making under integrated water resources management (IWRM). Nevertheless, an appraisal of previous and ongoing efforts to develop such decision support systems shows considerable deficiencies in attempts to address the hydro-socio-economic effects on livelihoods. To date, no universal standard integration method or framework is in use. For the existing integrated models, their application failures have pointed to the lack of stakeholder participation. In an endeavour to close this gap, development and application of a seasonal time-step integrated model with prediction capability is presented in this paper. This model couples existing hydrology, agronomy and socio-economic models with feedbacks to link livelihoods of resource-constrained smallholder farmers to water resources at catchment level in the semi-arid Olifants subbasin in South Africa. These three models, prior to coupling, were calibrated and validated using observed data and participation of local stakeholders. All the models gave good representation of the study conditions, as indicated by the statistical indicators. The integrated model is of general applicability, hence can be extended to other catchments. The impacts of untied ridges, planting basins and supplemental irrigation were compared to conventional rainfed tillage under maize crop production and for different farm typologies. Over the 20years of simulation, the predicted benefit of untied ridges and planting basins versus conventional rainfed tillage on surface runoff (Mm3/year) reduction was 14.3% and 19.8%, respectively, and about 41–46% sediment yield (t/year) reduction in the catchment. Under supplemental irrigation, maize yield improved by up to 500% from the long-term average yield of 0.5 t/ha. At 90% confidence interval, family savings improved from between US$ 4 and US$ 270 under conventional rainfed to between US$ 233 and US$ 1140 under supplemental irrigation. These results highlight the economic and environmental benefits that could be achieved by adopting these improved crop management practices. However, the application of various crop management practices is site-specific and depends on both physical and socio-economic characteristics of the farmers.

Most watersheds in the developing world lack appropriate data for hydrological studies. At the same time, accuracy and reliability in flow predictions at both temporal and spatial scales are very important for water resources planning and development. Thus, adequate consideration about the reliability in the prediction of flow should be incorporated into decision making by water practitioners. Sensitivity analysis has been used as part of uncertainty estimation methods by indicating where focus should be directed in order to reduce uncertainty associated with predictive models. Hence, this paper reports on the step-wise sensitivity analyses performed on two models for predicting flows of the Semliki watershed in the equatorial Nile basin. The Semliki watershed is part of the upper drainage of the Albert Nile and contributes up to 20% of the water flowing in the White Nile. Using the 90m SRTM Digital Elevation Model (DEM), the watershed was subdivided into 21 sub catchments (S3–S23) in order to capture the spatial dynamics. Eight landscape and meteorological attributes generated from remotely acquired datasets and limited ground information for each sub catchment were used as predictors at the monthly time step in the two predictive models. From clustering and ordination, two groups (hilly and flat) of sub-catchments, related to their landscape attributes, were identified and subsequently used for the analyses. The first predictive model assumed linearity between sub-catchments attributes and flow, while the second model assumed nonlinearity. The results indicate that predicted flows by the linear model were more sensitive to landscape variables than the nonlinear one for the flat sub-catchments, and conversely for the hilly sub-catchments. The order of sensitivity of the variables in the linear model, starting with the most sensitive, is the stream length, followed by drainage density, and then maximum elevation. This was observed for both the flat and hilly sub-catchments. The nonlinear model in flat sub catchments indicated however that the weighted-average elevation was the most sensitive variable, followed by the stream length, the drainage density and the NDVI. Rainfall, commonly considered one of the most important drivers in hydrological processes, is found not to be very sensitive in the models’ flow predictions, and this may be attributable to the conceptual construct of the models and/or the humid nature of the study area.

The 2-D formulation of the Green element method (GEM) which approximates the internal normal directional fluxes by difference expressions in terms of the field variable had been recognized to be fraught with errors that comprise its accuracy. However, this approach is computational attractive because there is only one degree of freedom at every node, the system matrix is slender, and it does require additional compatibility relationships. There have been attempts to reduce the numerical errors of this original GEM formulation by the use of flux-based formulations which essentially retain the internal fluxes but at the expense of those attractive numerical features. Here the original GEM is revisited and shown that, with difference approximation of the internal normal fluxes whose error is of the order of the square of the size of the element, its accuracy is greatly enhanced to a level comparable to the flux-based formulations. This approach is demonstrated on regular domains with rectangular elements and irregular domains with triangular elements using six examples that cover steady, transient, linear and nonlinear potential flow and heat transfer problems in homogeneous and heterogeneous media.

Water paucity remains a major threat to poverty, hunger alleviation as well as sustainable development. Innovative water technologies such as rainwater harvesting (RWH) have the potential to improve rural water supply and contribute to the provision of the first 6kl of water consumed monthly. RWH can also be the solution to South Africa food security by increasing water productivity of dryland agriculture and enabling homestead gardening. Although used for decades in South Africa, rainwater harvesting (RWH) is still far from being utilised to its full potential as unresolved challenges prevent its wide scale adoption. The paper presents the challenges and opportunities to the upscaling of RWH in South Africa. Key challenges preventing the nationwide expansion of RWH are the current water related legislations, the lack of finances and the absence of a national umbrella body that coordinates. While opportunities lie in the worth of knowledge gathered by research projects, funded over the last two decades, on the biophysical and socio-economic impacts of RWH.

This revisit of the stream-aquifer problem is based on a recent flux-based Green element formulation which offers more accurate solutions than previous formulations presented in Taigbenu (2003). Its accuracy also surpasses those provided by finite element and finite difference methods using grids that are coarser. As in all Green element formulations, the current formulation is predicated on the singular boundary integral theory that is implemented in an element-by-element fashion. What is new in the current formulation is that it calculates the fluxes at all nodes and not only at external nodes. While this approach exhibits much improved accuracy, its drawback lies with handling an increased number of unknowns. This drawback is, however, compensated for by the fewer elements required to achieve accuracies comparable to other conventional numerical methods. In this paper, it is demonstrated that with between 20% and 30% of elements used in finite element and finite difference models, comparable accuracy is achieved with this formulation. The main significance of the current computational technique is that it preserves the flux calculations in a manner that is consistent with the stream-aquifer interaction problem.