Data‐based mechanistic modelling and the rainfall‐flow non‐linearity

Abstract Although rainfall‐flow processes have received much attention in the hydrological literature, the nature of the non‐linear processes involved in the relationship between rainfall and river flow still remains rather unclear. This paper outlines the first author's data‐based mechanistic (DBM) approach to model structure identification and parameter estimation for linear and non‐linear dynamic systems and uses it to explore afresh the non‐linear relationship between measured rainfall and flow in two typical catchments. Exploiting the power of recursive estimation, state dependent non‐linearities are identified objectively from the time series data and used as the basis for the estimation of non‐linear transfer function models of the rainfall—flow dynamics. These objectively identified models not only explain the data in a parametrically efficient manner but also reveal the possible parallel nature of the underlying physical processes within the catchments. The DBM modelling approach provides a useful tool for the further investigation of rainfall‐flow processes, as well as other linear and non‐linear environmental systems. Moreover, because DBM modelling uses recursive estimation, it provides a powerful vehicle for the design of real‐time, self‐adaptive environmental management systems. Finally, the paper points out how DBM models can often be interpreted directly in terms of dynamic conservation equations (mass, energy or momentum) associated with environmental flow processes and stresses the importance of parallel processes in this connection.