Martin F. Lambert

Drought Analysis Using Trivariate Copulas Conditional on Climatic States

Droughts are an inevitable consequence of meteorological variability, and the design of water resource infrastructure and management strategies to mitigate their effects requires assessment of the risk. Crucial characteristics of droughts are related to their peak intensities, durations, and severities. These variables are typically correlated and copulas provide a versatile means to model their dependence structure. In Australia, for example, drought severity is associated with the El-Nino Southern Oscillation. Data from two rainfall districts in New South Wales, one on the east and the other on the west of the Great Dividing Range, are considered. These rainfall data are categorized into three states, El-Nino, Neutral, and La-Nina, according to the prevailing Southern Oscillation Index. Gumbel-Hougaard copulas and t -copulas are fitted to the droughts in the three states. The copula parameters are estimated separately for each state, and the differences are analyzed. The goodness-of-fit of the Gumbel-Ho...

Experimental verification of the frequency response method for pipeline leak detection

This paper presents an experimental validation of the frequency response method for pipeline leak detection. The presence of a leak within the pipe imposes a periodic pattern on the resonant peaks of the frequency response diagram. This pattern can be used as an indicator of leaks without requiring the “no-leak” benchmark for comparison. In addition to the experimental verification of the technique, important issues, such as the procedure for frequency response extraction and methods for dealing with frequency-dependent friction are considered in this paper. In this study, transient signals are generated by a side-discharge solenoid valve. Non-linearity errors associated with large valve movements can be prevented by a change in the input parameter to the system. The optimum measuring and generating position for two different system boundary configurations—a symmetric and an antisymmetric system—are discussed in the paper and the analytical expression for the leak-induced pattern in these two cases is derived

Parameters affecting water-hammer wave attenuation, shape and timing—Part 1: Mathematical tools

This two-part paper investigates key parameters that may affect the pressurewaveform predicted by the classical theory ofwater-hammer. Shortcomings in the prediction of pressure wave attenuation, shape and timing originate from violation of assumptions made in the derivation of the classical waterhammer equations. Possible mechanisms that may significantly affect pressure waveforms include unsteady friction, cavitation (including column separation and trapped air pockets), a number of fluid–structure interaction (FSI) effects, viscoelastic behaviour of the pipe-wall material, leakages and blockages. Engineers should be able to identify and evaluate the influence of these mechanisms, because first these are usually not included in standard water-hammer software packages and second these are often “hidden” in practical systems. Part 1 of the two-part paper describes mathematical tools for modelling the aforementioned mechanisms. The method of characteristics transformation of the classical water-hammer equations is used herein as the basic solution tool. In separate additions: a convolution-based unsteady friction model is explicitly incorporated; discrete vapour and gas cavity models allow cavities to form at computational sections; coupled extended water-hammer and steel-hammer equations describe FSI; viscoelastic behaviour of the pipe-wall material is governed by a generalised Kelvin–Voigt model; and blockages and leakages are modelled as end or internal boundary conditions

A strategy for diagnosing and interpreting hydrological model nonstationarity

This paper presents a strategy for diagnosing and interpreting hydrological nonstationarity, aiming to improve hydrological models and their predictive ability under changing hydroclimatic conditions. The strategy consists of four elements: (i) detecting potential systematic errors in the calibration data; (ii) hypothesizing a set of “nonstationary” parameterizations of existing hydrological model structures, where one or more parameters vary in time as functions of selected covariates; (iii) trialing alternative stationary model structures to assess whether parameter nonstationarity can be reduced by modifying the model structure; and (iv) selecting one or more models for prediction. The Scott Creek catchment in South Australia and the lumped hydrological model GR4J are used to illustrate the strategy. Streamflow predictions improve significantly when the GR4J parameter describing the maximum capacity of the production store is allowed to vary in time as a combined function of: (i) an annual sinusoid; (ii) the previous 365 day rainfall and potential evapotranspiration; and (iii) a linear trend. This improvement provides strong evidence of model nonstationarity. Based on a range of hydrologically oriented diagnostics such as flow-duration curves, the GR4J model structure was modified by introducing an additional calibration parameter that controls recession behavior and by making actual evapotranspiration dependent only on catchment storage. Model comparison using an information-theoretic measure (the Akaike Information Criterion) and several hydrologically oriented diagnostics shows that the GR4J modifications clearly improve predictive performance in Scott Creek catchment. Based on a comparison of 22 versions of GR4J with different representations of nonstationarity and other modifications, the model selection approach applied in the exploratory period (used for parameter estimation) correctly identifies models that perform well in a much drier independent confirmatory period.

Discharge prediction in straight compound channels using the mixing length concept

A method for predicting the depth-discharge relationship in a compound channel is developed and applied to two different sets of experimental results. The method uses a mixing length formulation to account for the turbulent interaction between the main channel and the floodplain and the resulting momentum exchange. This momentum transfer tends to reduce the discharge in the main channel and increase the discharge on the floodplain. The net effect is a reduction in the overall discharge capacity of the compound channel. As a result, practical methods which can allow for the interaction effect are needed. In this formulation a variation of Prandtls mixing length hypothesis is applied to calculate the apparent shear stresses, indicative of the turbulent interaction, on the sides of small vertical elements which comprise the compound channel cross-section. The approach suggested is to use the mixing length approximation to calculate the correction for the momentum interaction effects that are neglected when ...

Parameters affecting water-hammer wave attenuation, shape and timing—Part 2: Case studies

This two-part paper investigates parameters that may significantly affect water-hammer wave attenuation, shape and timing. Possible sources that may affect the waveform predicted by classical water-hammer theory include unsteady friction, cavitation (including column separation and trapped air pockets), a number of fluid–structure interaction effects, viscoelastic behaviour of the pipe-wall material, leakages and blockages. Part 1 of this two-part paper presents the mathematical tools needed to model these sources. Part 2 of the paper presents a number of case studies showing how these modelled sources affect pressure traces in a simple reservoir-pipeline-valve system. Each case study compares the obtained results with the standard (classical) water-hammer model, from which conclusions are drawn concerning the transient behaviour of real systems

The simulation of an Australian reservoir using a phytoplankton community model: protech

The freshwater phytoplankton model protech was adapted to simulate an artificially destratified reservoir located in the Southern Hemisphere. The chosen site for validation was a drinking supply reservoir (Myponga reservoir, South Australia), which has a history of nuisance algal blooms and is regularly dosed with CuSO4 to control algal growth. An aerator is used at Myponga to limit stratification and two raft-mounted mechanical surface mixers (hereafter referred to as surface mixers) have been deployed to limit the growth of undesirable algae. New subroutines were incorporated into protech to simulate CuSO4 dosing and the surface mixers. The validation of protech against field data from Myponga reservoir, for the period 1 September 1999 to 1 September 2000, was successful and demonstrated that protech is readily adaptable to simulate different latitudes and to simulate highly managed water bodies.

Leak location in pipelines using the impulse response function

Current transient-based leak detection methods for pipeline systems often rely on a good understanding of the system—including unsteady friction, pipe roughness, precise geometry and micro considerations such as minor offtakes—in the absence of leaks. Such knowledge constitutes a very high hurdle and, even if known, may be impossible to include in the mathematical equations governing system behavior.An alternative is to test the leak-free system to find precise behavior, obviously a problem if the system is not known to be free of leaks. The leak-free response can be used as a benchmark to compare with behavior of the leaking system. As an alternative, this paper uses the impulse response function (IRF) as a means of leak detection. The IRF provides a unique a relationship between an injected transient event and a measured pressure response from a pipeline. This relationship is based on the physical characteristics of the system and is useful in determining its integrity. Transient responses of completely different shapes can be directly compared using the IRF. The IRF refines all system reflections to sharp pulses, thus promoting greater accuracy in leak location, and allowing leak reflections to be detected without a leak-free benchmark, even when complex signals such as pseudo-random binary signals are injected into the system. Additionally, the IRF approach can be used to improve existing leak detection methods. In experimental tests at the University of Adelaide the IRF approach was able to detect and locate leaks accurately.

Joint probability and design storms at the crossroads

Abstract The joint probability problem inherent in flood estimation is complex. Although the design storm approach has a long tradition it lacks the fundamental rigour of joint probability analysis. The use of average values for random inputs other than rainfall intensity and duration can be justified from a joint probability perspective provided variations in the input affect the peak flow density in a linear fashion. However, the assignment of the average value for initial conditions is problematic. A case study involving a detention basin demonstrates large biases arising from mis-specification of initial conditions in volume-sensitive systems. It is suggested that the current revision of ARR needs to articulate the shortcomings of the design storm approach, identify calibration strategies that ensure closure and give guidance about its reliability in different applications. Looking to the future, ARR needs to move towards event and total joint probability approaches that are underpinned by a rigorous joint probability framework. Continuous simulation is emerging as a practical tool and remains the most rigorous tool available. Event joint probability methods based on Monte Carlo simulation are computationally less demanding but require specification of the probability distribution of initial conditions. Stochastic rainfall models are on the verge of practical application to service Monte Carlo methods.

Detection of Distributed Deterioration in Single Pipes Using Transient Reflections

A number of different methods that use signal processing of fluid transients (water hammer waves) for fault detection in pipes have been proposed in the past two decades. However, most of them focus solely on the detection of discrete deterioration, such as leaks or discrete blockages. Few studies have been conducted on the detection of distributed deterioration, such as extended sections of corrosion and extended blockages. This is despite the fact that they commonly exist and can have a severe negative impact on the operation of pipelines. The research reported here proposes a method of detecting distributed deterioration by investigating the time-domain water hammer response trace from a single pipe with a deteriorated section. Through wave analysis using a step pressure input, a theoretical square-shaped perturbation is found to exist in the transient pressure trace as a result of distributed deterioration. The hydraulic impedance of this section can be derived from the magnitude of the reflected pressure perturbation, while the location and length of the corresponding deteriorated section can be determined by using the arrival time and duration of the perturbation. The proposed method has been validated by analyzing experimental data measured from a pipe with a section of wall thickness change.