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

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.