PREDICTION OF THE FATE OF POLLUTANTS IN RIVERS BY MEANS OF NONLINEAR VOLTERRA SERIES

The transport of a conservative soluble pollutant along a uniform channel is usually described by means of the well-known Advection-Dispersion Equation. To apply this equation to a practical scenario, the dispersion coefficient value for the reach is required. Since dispersion coefficients cannot be measured in-situ directly from a simple individual measurement, they have to be estimated from available experimental data. In this paper an alternative modelling approach is presented in which the transport of a conservative soluble pollutant in rivers is modelled by means of a non-linear Volterra series. The description of the system by the Volterra series is a generalization of the concept of the linear transfer function, which is of great importance in the analysis of linear systems. Data for this study were derived from a programme of 18 tracer experiments undertaken in the Murray Burn, which is a stream that flows through the Heriot-Watt University Campus at Riccarton in Edinburgh. A two-term nonlinear model was first fitted to the records of breakthrough curves from 10 randomly chosen experiments. Then the performance of the method was assessed by making predictions for the remaining 8 experiments. Predictions from a cascade of continuously stirred tank reactors and from Fischer's routing procedure were also obtained. The results obtained indicate that generally the simple nonlinear model gives better results than those obtained by the routing procedure and that it gives marginally better results than the cascade model. nonlinear Volterra series model in the form of a sum of convolution integrals, and a Fischer’s routing procedure with dispersion coefficients determined by means of a Multi-Layer Perceptron Artificial Neural Network or via linear regression. 2 MURRAY BURN EXPERIMENTS Between 1999 and 2001, 26 tracer experiments were performed on the Murray Burn, which is a small river that flows through the Heriot-Watt University Campus at Riccarton in Edinburgh. These experiments were undertaken at various flow rates in a 540m long reach. Each experiment consisted of the release of a tracer (Rhodamine WT) followed by the collection of tracer concentrations at up to 4 cross-sections. The tracer was injected to the river at the same place each time. In the first few experiments concentration measurements were collected only at the first two cross-sections, but in the later experiments three or four of the crosssections were used. In a few cases, equipment or human failure led to data not being successfully collected. Further information on the experiments is available in Burke (2002), Wallis and Manson (2005) or Wallis et al (2007). In the present paper models are used to predict the tracer concentration versus time profiles at the second cross-section using concentration measurements at the first crosssection. The distance between these two crosssections is about 137 meters. The data come from 18 experiments, which were considered to contain reliable data. 3 LINEAR DISPERSION MODEL A simple approach to modelling pollutant transport is a cascade of continuously stirred tank reactors as depicted in Fig. 1. This completely mixed system can be used to model pollutant concentration in sub-reaches of a natural watercourse. The mass balance equations for a conservative pollutant can be expressed in terms of concentrations (C), flows (Q) and volumes (V) as: Fig. 1. Cascade of continuously stirred tank reactors