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Linear time-varying models to investigate complex distributed dynamics: A rainfall-runoff example

Author

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  • Norton, J.P.
  • Chanat, J.G.

Abstract

Many processes with distributed, non-linear dynamics may be modelled adequately over suitable time and spatial scales by low-order, linear, time-invariant models, but the limitations of such models must be examined. For example, catchment rainfall-runoff models taking pulse-response peak, steady-state gain and recession time constant as time-invariant are useful in assessing water availability, but may not be capable of capturing short-term response well. This paper employs models of a catchment in Virginia, USA, to illustrate how insight into shorter-term dynamics, non-linearities and other unmodelled behaviour can be obtained by allowing selected linear model parameters to vary with time. Those parameters are treated as random walks, estimated recursively by a long-established optimal smoothing algorithm. Attention is paid to interaction between gain and dominant time constant through the transfer function denominator coefficients, and to the role of a time-varying output offset term in the model.

Suggested Citation

  • Norton, J.P. & Chanat, J.G., 2005. "Linear time-varying models to investigate complex distributed dynamics: A rainfall-runoff example," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(1), pages 123-134.
    • Handle: RePEc:eee:matcom:v:69:y:2005:i:1:p:123-134
    DOI: 10.1016/j.matcom.2005.02.029
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