Applied Mathematics

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Applied Mathematics at the University of Adelaide is one of the leading groups in teaching and research in Australia. Members conduct internationally recognized research into a wide range of Applied Mathematics. The research within Applied Mathematics can be loosely grouped into the following areas.

  • Biomedical Engineering
  • Fluid Dynamics
  • Optimisation
  • Stochastic Modelling
  • Teletraffic Research

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Browsing Applied Mathematics by Author "Adamson, P."

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    Bivariate stochastic modelling of ephemeral streamflow
    (John Wiley & Sons Ltd, 2002) Cigizoglu, H.; Adamson, P.; Metcalfe, A.
    AbstractStreamflow time series in arid and semi‐arid regions can be characterized as a sequence of single discrete flow episodes or clusters of hydrographs separated by periods of zero discharge. Here, two point process models are presented for the joint occurrence of flow events at neighbouring river sites. The first allows for excess clustering by adding autocorrelated errors to an empirically derived seasonally varying probability of an event and is extended to the case of the joint occurrence of flow events in two catchments. The second approach is to explicitly model the occurrences of clusters of events and the bivariate point process of event occurrences within them at both sites. For the two models, the magnitude of event peaks are assumed to be drawn from continuous distributions with seasonally varying parameters. Rises and recessions in discharge are interpolated between the peaks using regression estimates of hydrographs. The models are fitted to mean daily flows at two sites in Namibia and demonstrated to provide realistic simulations of the hydrology. Copyright © 2002 John Wiley & Sons, Ltd.
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    Relationships between the El-Nino southern oscillation and spate flows in southern Africa and Australia
    (European Geosciences Union, 2004) Whiting, J.; Lambert, M.; Metcalfe, A.; Adamson, P.; Franks, S.; Kuczera, G.
    The flow records of arid zone rivers are characterised by a high degree of seasonal variability, being dominated by long periods of very low or zero flow. Discrete flow events in these rivers are influenced by aseasonal factors such as global climate forcings. The atmospheric circulations of the El-Niño Southern Oscillation (ENSO) have been shown to influence climate regimes across many parts of the world. Strong teleconnections between changing ENSO regimes and discharges are likely to be observed in highly variable arid zones. In this paper, the influence of ENSO mechanisms on the flow records of two arid zone rivers in each of Australia and Southern Africa are identified. ENSO signals, together with multi-decadal variability in their impact as identified through seasonal values of the Interdecadal Pacific Oscillation (IPO) index, are shown to influence both the rate of occurrence and the size of discrete flow episodes in these rivers.
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    The Mekong - applications of value at risk (VaR) and conditional value at risk (CVaR) simulation to the benefits costs and consequences of water resources development in a large river basin
    (Elsevier Science BV, 2007) Webby, R.; Adamson, P.; Boland, J.; Howlett, P.; Metcalfe, A.; Piantadosi, J.
    Conditional value at risk (CVaR) was developed as a coherent measure of expected loss given that actual loss exceeds some value at risk (VaR) threshold. To date the concept has been primarily used to support quantitative risk assessment for investment decisions and portfolio management, using stochastic financial models to minimise the risk of unacceptable monetary loss. Intriguingly, the models and concepts are potentially adaptable to water resources planning and operational problems. This paper explores the application of CVaR within the context of identifying the risk of macro-economic damage to the fishery resources of Tonle Sap given reduced volumes of flow on the mainstream Mekong during the flood season. Emphasis is placed on simulating the linkages between the seasonally available flows in the Mekong mainstream, Tonle Sap water levels, annual fish catch and its economic value. We present scenarios using real hydrological and fish catch data along with exploratory concepts of contingency fund costs in terms of national and international aid requirements. The objective is to estimate the potential economic loss at a prescribed level of probability and to illustrate how VaR and CVaR may be calculated in this context. We demonstrate the properties of these risk measures through their behaviour under continuous and discontinuous loss distributions. We show that CVaR has advantages over VaR even under a relatively simple modelling approach. In the case where a loss distribution has discontinuities, VaR is potentially a poor measure of risk as it can vary unacceptably with a small increase in probability level. CVaR is stable in these situations. Here we find that when the loss distribution is continuous the CVaR is only marginally higher than the VaR. However, for the more realistic model where the loss distribution is discontinuous, the CVaR is substantially greater. We demonstrate the potential use of these two risk measures on a simple set of models of the Tonle Sap fishery in Cambodia. The sustainability of this fishery is crucial to the country in order to avoid even further dependence on international donor aid. Estimating the financial risk to which the national government and potential aid donors might be exposed given any damage to the fishery is the essence of this exploratory study of VaR and CVaR. © 2006 Elsevier B.V. All rights reserved.