Potential theory

In this chapter we will introduce the reader to the techniques of the Boundary Element Method applied to simple Laplacian problems. Most classical applications refer to electrostatic and magnetic fields, but the Laplacian operator also governs problems such as Saint-Venant torsion, irrotational flow, fluid flow through porous media and the added fluid mass in fluidstructure interaction problems. This short list, to which it would be possible to add many other physical problems governed by the same equation, is an indication of the importance of the numerical treatment of the Laplacian operator. Potential theory has pioneered the use of BEM since the papers of Jaswon and Hess. An interesting introduction to the topic is given by Cruse. In the last five years a renaissance of integral methods has been detected. This can be followed in the books by Jaswon and Symm and by Brebbia or Brebbia and Walker.In this chapter we shall maintain an elementary level and follow a classical scheme in order to make the content accessible to the reader who has just started to study the technique. The whole emphasis has been put on the socalled "direct" method because it is the one which appears to offer more advantages. In this section we recall the classical concepts of potential theory and establish the basic equations of the method. Later on we discuss the discretization philosophy, the implementation of different kinds of elements and the advantages of substructuring which is unavoidable when dealing with heterogeneous materials.

A bivariate return period based on copulas for hydrologic dam design: accounting for reservoir routing in risk estimation

A multivariate analysis on flood variables is needed to design some hydraulic structures like dams, as the complexity of the routing process in a reservoir requires a representation of the full hydrograph. In this work, a bivariate copula model was used to obtain the bivariate joint distribution of flood peak and volume, in order to know the probability of occurrence of a given inflow hydrograph. However, the risk of dam overtopping is given by the maximum water elevation reached during the routing process, which depends on the hydrograph variables, the reservoir volume and the spillway crest length. Consequently, an additional bivariate return period, the so-called routed return period, was defined in terms of risk of dam overtopping based on this maximum water elevation obtained after routing the inflow hydrographs. The theoretical return periods, which give the probability of occurrence of a hydrograph prior to accounting for the reservoir routing, were compared with the routed return period, as in both cases hydrographs with the same probability will draw a curve in the peak-volume space. The procedure was applied to the case study of the Santillana reservoir in Spain. Different reservoir volumes and spillway lengths were considered to investigate the influence of the dam and reservoir characteristics on the results. The methodology improves the estimation of the Design Flood Hydrograph and can be applied to assess the risk of dam overtopping

Irrigation efficiency and water-policy implications for river-basin resilience

Rising demand for food, fiber, and biofuels drives expanding irrigation withdrawals from surface water and groundwater. Irrigation efficiency and water savings have become watchwords in response to climate-induced hydrological variability, increasing freshwater demand for other uses including ecosystem water needs, and low economic productivity of irrigation compared to most other uses. We identify three classes of unintended consequences, presented here as paradoxes. Ever-tighter cycling of water has been shown to increase resource use, an example of the efficiency paradox. In the absence of effective policy to constrain irrigated-area expansion using "saved water", efficiency can aggravate scarcity, deteriorate resource quality, and impair river basin resilience through loss of flexibility and redundancy. Water scarcity and salinity effects in the lower reaches of basins (symptomatic of the scale paradox) may partly be offset over the short-term through groundwater pumping or increasing surface water storage capacity. However, declining ecological flows and increasing salinity have important implications for riparian and estuarine ecosystems and for non-irrigation human uses of water including urban supply and energy generation, examples of the sectoral paradox. This paper briefly considers three regional contexts with broadly similar climatic and water-resource conditions – central Chile, southwestern US, and south-central Spain – where irrigation efficiency directly influences basin resilience. The comparison leads to more generic insights on water policy in relation to irrigation efficiency and emerging or overdue needs for environmental protection.