Linear rainfall-runoff system identification with ramifications for modelling catchment processes

The convolution assumption between excess rainfall and runoff provides a framework in which catchment runoff can be predicted with reasonable accuracy and moderate computational cost. Associated with it, the deconvolution problem of estimating unitgraph ordinates from rainfall-runoff events involves a matrix with a particularly simple structure. This matrix structure is used here as a basis on which the ill-posed nature of deconvolution is analysed. As a result, based on a simple transform of the excess rainfall data, a very simple criterion is derived to test the degree to which deconvolution may yield a unit hydrograph estimate displaying spurious oscillations of large magnitude. This has practical implications as the solution to an ill-posed problem can be very sensitive to errors in the model and the data and therefore may need to be stabilized. Illustration of these issues is provided using published rainfall-runoff data.