Identification and representation of state dependent non-linearities in flood forecasting using the DBM methodology

Beven, Keith and Leedal, David and Smith, Paul and Young, Peter (2012) Identification and representation of state dependent non-linearities in flood forecasting using the DBM methodology. In: System Identification, Environmental Modelling and Control Systems Design :. Springer Verlag, London, pp. 341-366. ISBN 978-0-85729-973-4

Abstract

This paper addresses the issue of identifying a state dependent input nonlinearity in a Data Based Mechanistic (DBM) flood forecasting model based on the data rather than some prior conceptualisation of nonlinearity in the system response. Four forms of nonlinear function are presented. A power law may be useful when the input non-linearity is simple. The Radial Basis Function (RBF) network method is appropriate for systems that exhibit well defined but complex input non-linearities. The Piecewise Cubic Hermite Data Interpolation (PCHIP) method also provides the flexibility to map complex input non-linearity shapes while providing the ability to maintain a natural curve. Overfit to the calibration data is a risk in both RBF and PCHIP methods when a large number of knots are used. The Takagi-Sugeno Fuzzy Inference method, together with interactive tuning, provides an alternative approach that allows human-in-the-loop interaction during the parameter estimation process but is not optimal in any statistical sense. Future work will explore the use of these methods with continuous time transfer functions and optimisation of the nonlinear function at the same time as the transfer function.