A polder-boezem system consists of a (large) number of polders that pump their drainage water into a network of watercourses and lakes. A few large pump stations then pump the drainage water into rivers or the sea. In some cases a sluice gate is used when water levels allow it. A receding horizon control algorithm for a polder-boezem system is presented where the selection of the control action is based on a prescribed order of use for the different states of available pumps and sluices. It is an extension of an earlier algorithm that operated boezem pump stations only. A further extension is proposed that will allow inclusion of the control of polder pumps. Arguments are presented to support the claim that, from the point of view of transparency, this algorithm is better suited to the control of polder-boezem systems than receding horizon control with a traditional objective function.

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A first prototype of a Python package that can generate input for, perform runs of, and the analyse output of the Delft3D FM 1D2D simulation software corresponding to both simple and complex canal networks is demonstrated. The package can, for instance, generate input files for a canal system with a wide range of friction values and a range of variations on the design cross sections and structures used. It can then start parallel Delft3D runs for these input files. Finally, results can be analysed from Python. Results are presented for the rise time associated with a step change in the discharge for a prismatic canal with a trapezoidal cross section and either a weir or a gate at the downstream end. The size of the step change, the parameters of the cross section, the friction, and the canal slope are varied.

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The dependency structure between hydrological variables is of critical importance to hydrological modelling and forecasting. When a copula capturing that dependence is fitted to a sample, information on the uncertainty of the fit is needed for subsequent hydrological calculations and reasoning. A new method is proposed to report inferential uncertainty in a copula parameter. The method is based on confidence curves constructed with the use of a pseudo maximum likelihood estimator for the copula parameter. The method was tested on synthetic data and then used as a tool in two hydrological examples. The first examines the probability of major floods in two locations on the Rhine River and its tributaries in the same calendar year. In the second example, rainfall–runoff from a karst region in Tunisia was analysed to determine a confidence interval for the delay between precipitation and runoff.

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The representation of uncertainty in results is an important aspect of statistical techniques in hydrology and climatology. Hypothesis tests and point estimates are not well suited for this purpose. Other statistical tools, such as confidence curves, are better suited to represent uncertainty. Therefore three parametric methods to construct confidence curves for the location of a sudden change in the properties of a time series, a change point (CP), are analyzed for three distributions: log-normal, gamma, and Gumbel. Two types of change are considered: a change in the mean and a change in the standard deviation. A question that confidence curves do not answer is how likely the null hypothesis of ‘no change’ is. A possible statistic to help answer this question, denoted by Un, is introduced and analyzed. It is compared to the statistic that underlies the Pettitt test. All methods perform well in terms of coverage and confidence set size. One method is based on the profile likelihood for a CP, the other two, first defined in this article, on the pseudolikelihood for a CP. The main advantage of the pseudolikelihood over the profile likelihood lies in the much lower computational cost. The confidence curves generated by the three methods are very similar. In a limited test on time series of measurements found in the literature, the methods gave results that largely matched those reported elsewhere. Some results are also given for an order one autoregressive series with a lognormal marginal distribution.

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Analysis of existing data is the first step in preparing for human modification of natural water systems or existing water infrastructure. Time series of environmental measurements form an important part of that data. Such an analysis has as its aim the determination of the future operating conditions of the modified system. The dependence between time series is important both for normal operation and for the evaluation of risks in extreme situations. One way to study this dependence is through the use of copulas. But because the analysis is statistical in nature, its results, in this case the copula parameters, contain a certain amount of uncertainty. In this paper we demonstrate an approach that can be used to represent that uncertainty in cases where the dependence is modeled by a copula. The method is based on the confidence curve concept, that is it provides confidence sets for the parameter at all confidence levels. The use of confidence curves for copula parameters is a recent development. The confidence curve construction method uses a pseudo likelihood to avoid having to fit marginals to the data. This pseudo likelihood is then used to construct a confidence curve. The method was applied to annual maximum river discharge data for different tributaries of the Rhine to see how these are correlated. @en

The availability of water resources is declining, while the demand for water continues to increase for the agricultural sector and drinking water supply in the context of climate change hazards, such as the increasing frequency of extreme weather events (drought, floods). In fact, several studies show that droughts occur more and more frequently, with a duration varying from one month to a few years. Therefore, monitoring these droughts would help in the management of groundwater in the short and medium term and thus would enhance adaptation to climate change. For this purpose, several indices allowing the prediction and characterization of these droughts have been proposed by researchers. Among these, two indices were selected: SPEI (Standardized Precipitation Evapotranspiration Index) and SGI (Standardized Groundwater Index). SPEI makes it possible to take into account precipitation and evapotranspiration on different time scales which facilitates the analysis of drought impact on water resource demands. The same is true for SGI, which allows analysis of the water table level. The objective of this work is to calculate each of these indices for several boreholes in Tunisia to assess correlations between SPEI and SGI, to project SPEI over several horizons under climate change and to predict the evolution of the SGI thanks to the correlations. Correlation between SPEI and SGI time series was examined using three different copula families, Frank, Gumbel and Clayton. Copulas were fitted to a 2D data set consisting of the SPEI time series and the time shifted SGI time series for different lag times. The Kendall @en

In almost all practical applications of control, technological and economical consid -erations impose limits on communication speed, frequency of communication, and frequency of actuator adjustment. Such limits turned the analysis of sampled data systems into a flourishing field. Water systems pose a particular challenge: the systems are networks of canals and reservoirs spread over large areas, and the actuators are relatively large and exposed to the elements. In this study, a theorem on the local exponential stability of sampled data systems with variable control time step and variable delay in the communication between the non-linear continuous time process and the non-linear discrete time controller is presented. To illustrate the application of the theorem, it is applied to a simple water system.

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Management of water systems is becoming more and more complex; this creates opportunities for the application of control theory. These opportunities are the subject of a course on operational water management given to students of the water management department, Delft University of Technology, over the past 15 years. Traditional examples in control theory courses are taken from industry and do not easily map to water systems, so examples were developed that use water systems to illustrate control theory concepts. This provided the students with a link between control theory and water management practice.

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Networks of open channels form an important category of environmental systems. They are used not only to transport irrigation and drainage water, but also as highways for barges transporting raw materials and goods. Automatic control of these systems poses specific problems. A local stability analysis for an open canal that is split into several parts by sluice gates under discrete time control is proposed. Theoretical justification is provided, and the method is tested for a simple controller. The method allows the examination of local stability of a series of canals when equipped with a controller from a large class, linear and non-linear. The analysis is based on the analysis of the eigenvalues of a matrix derived from the controlled system that is small enough to allow for parameter optimization.

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The problem of smoothing dry weather inflow variations for a Waste Water Treatment Plant (WWTP) that receives sewage from multiple mixed sewer systems is formulated. A first rough control algorithm that uses branch and bound is presented. The control algorithm uses a form of Model Predictive Control. Trials showed that the algorithm had trouble satisfying two constraints that were initially regarded as ‘soft’ constraints. As a result, a closer look was taken at the feasibility of the problem. A family of simpler problems were derived to do so. These auxiliary problems made it possible to show that for a given subclass feasibility was strongly dependent on the choice of problem parameters.

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In this paper, a method based on Approximate Empirical likelihood ratio and a Deviance function combined with bootstrapping (AED-BP) is proposed to construct a confidence curve for the location of a change point. The method is compared with a method based on parametric Profile Likelihood and a Deviance function combined with Monte Carlo simulation (PLD-MC). A confidence curve provides a representation of the uncertainty in the outcome of the change point analysis. To evaluate the practical usability of confidence curves constructed by AED-BP, its properties were examined and its performance was compared to that of PLD-MC. The methods were applied to both synthetic and real data. Synthetic data were generated from three parametric distributions: Fréchet with a constant shape parameter, log-normal, and gamma distributions. The real data are the hydrometeorological data analysed in other studies. The change points found in the original publications are used as a reference in this present paper. The results show that AED-BP has a performance that is similar to PLD-MC, but has an advantage in that it is not necessary to select a distribution family for the data. The AED-BP results on the Annual Maximum Runoff series for the stations Yichang and Hankou along the Yangtze river are among the first that show a possible effect of the presence of the Three Gorges dam.@en

Several commonly-used nonparametric change-point detection methods are analysed in terms of power, ability and accuracy of the estimated change-point location. The analysis is performed with synthetic data for different sample sizes, two types of change and different magnitudes of change. The methods studied are the Pettitt method, a method based on the Cramér von Mises (CvM) two-sample test statistic and a variant of the CUSUM method. The methods differ considerably in behaviour. For all methods the spread of estimated change-point location increases significantly for points near one of the ends of the sample. Series of annual maximum runoff for four stations on the Yangtze River in China are used to examine the performance of the methods on real data. It was found that the CvM-based test gave the best results, but all three methods suffer from bias and low detection rates for change points near the ends of the series.

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This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through online media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focused on the process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come.@en

Arguments are presented in favor of modeling sewer systems and in particular Dutch sewer systems as a sampled data system with events. Basic limitations on controlling these systems when ignoring their hybrid nature are stated. The traditional control scheme for the Dutch systems is given as an example of event driven local control. Basic limitations on systems using a sampled data approach without an event driven component are derived. To provide context a brief description of a sampled data controller for a sewer system based on set-point tracking is given. This is followed by an explanation of how the absence of event driven control limits its effectiveness.

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When investigating the hydrological cycle one does not always have the luxury of perfect knowledge. Moreover, searching for possible causes for changes in the behaviour of hydrological variables can be like looking for a needle in a haystack. Statistical tools can help to restrict our search to certain parts of that haystack, provided we have some idea of the probability of not looking in the right place. This work considers change points in hydrological time series. Numerous papers have been published on non-stationarity in hydrological time series and several methods have been developed to solve the problems related to it, such as the detection and quantification of the change including change-point and trend. Change points in hydrological time series are often the consequence of human behaviour such as urbanization, deforestation, change on land-use and the construction of large waterrelated projects. Many techniques, both parametric and non-parametric, have been proposed to infer the position of , but most of them concentrate on detection of the presence of a change point and providing a specific value for its location on the basis of a given probability bound. In this research confidence distributions are used to find and express the uncertainty about its position. The results are compared to those of commonly used tests: a Cramér von Mises statistic-based test, Pettitt’s test, and the Lee-Heighinian test. All methods are applied to a large number of simulated data series and the results are compared. @en

Many Dutch sewer networks are combined sewer systems, they carry both storm water and foul water. They consist of multiple sub-networks, linked by pumps into a tree structure with the Waste Water Treatment Plant as its root. Within sub-networks sewage transport is by gravity driven flow. Usually the original design assumed local control. Later changes, additions and extensions sometimes reduced the effectiveness of the original design. In these cases central control can improve the performance of the system without costly new construction. We apply two algorithms from graph theory, one is based on stable flows in time, the other on quickest evacuation flows. Results on local control are included to provide a lower bound on performance. A linear programming problem based of a perfect forecast of the whole event provides an upper bound on performance.@en