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System Identification, Environmental Modelling, and Control System Design pp 341–366Cite as

Identification and Representation of State Dependent Non-linearities in Flood Forecasting Using the DBM Methodology

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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.

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Notes

  1. 1.

    A common addition to the scheme described above is an adaptive gain module. This module is not included in the results presented in this chapter but for completeness a brief description follows. An adaptive gain module assumes that the forecast value is scaled by a probabilistic, non-stationary gain whose value is conditioned by the mismatch between observed and forecast output. A NVR hyperparameter for the adaptive gain module determines how quickly the gain reacts to this mismatch. It is usual to set a low NVR value so that in operation the adaptive gain responds sluggishly and can correct for the slow accumulation of model error. This mechanism provides a simple means to correct for scenarios such as seasonal variation in catchment dynamics. Full details of the adaptive gain module can be found in Young [22].

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Acknowledgements

This research was carried out as part of RPA9 and SWP1 of the Flood Risk Management Research Consortium (FRMRC) phases 1 and 2. The principal sponsors of FRMRC are: the Engineering and Physical Sciences Research Council (EPSRC) in collaboration with the Environment Agency (EA), the Northern Ireland Rivers Agency (DARDNI), the United Kingdom Water Industry Research (UKWIR) Organisation, the Scottish Government (via SNIFFER), the Welsh Assembly Government (WAG) through the auspices of the Defra/EA, and the Office of Public Works (OPW) in the Republic of Ireland. For details of the FRMRC, see http://www.floodrisk.org.uk.

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Authors and Affiliations

  1. Lancaster Environment Centre, Lancaster University, Lancaster, UK

    Keith J. Beven, David T. Leedal, Paul J. Smith & Peter C. Young

Authors
  1. Keith J. Beven
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  2. David T. Leedal
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  3. Paul J. Smith
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  4. Peter C. Young
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Correspondence to Keith J. Beven .

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Editors and Affiliations

  1. Computer Engineering, RMIT University, Swanston Street 10, Melbourne, 3000, Victoria, Australia

    Liuping Wang

  2. Centre de Recherche en, Automatique de Nancy, Université Nancy I, Vandoeuvre-les-Nancy CX, France

    Hugues Garnier

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Beven, K.J., Leedal, D.T., Smith, P.J., Young, P.C. (2012). Identification and Representation of State Dependent Non-linearities in Flood Forecasting Using the DBM Methodology. In: Wang, L., Garnier, H. (eds) System Identification, Environmental Modelling, and Control System Design. Springer, London. https://doi.org/10.1007/978-0-85729-974-1_17

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  • DOI: https://doi.org/10.1007/978-0-85729-974-1_17

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  • Online ISBN: 978-0-85729-974-1

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