A process-based transfer function approach to model tile-drain hydrographs

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Tile-drain response to rainfall events is determined by unsaturated vertical flow to the water table, followed by horizontal saturated water movement. In this study, unsaturated vertical movement from the redistribution of water is modelled using a sharp-front approximation, and the saturated horizontal flow is modelled by an approximate solution to the Boussinesq equation. The unsaturated flow component models the fast response that is associated with the presence of preferential flow paths. By convoluting the responses of the two components, a transfer function is developed that predicts tile-drain response to unit amounts of infiltrated water. It is observed that the unsaturated flow component can be cast in a form that is linear in a power function of the infiltrated depth. Since the approach is process based, model parameter definitions are easily identified with soil properties at the field scale. Furthermore, it is demonstrated that the transfer function model parameters can be estimated from moment analysis. Using superposition, the transient tile-drain response to arbitrary amounts of infiltrated water can be constructed. Comparison with data measured from the Water Quality Field Station show that this approach provides a promising method for generating tile-drain response to rainfall events.

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