Comparison of two model based approaches for areal rainfall estimation in urban hydrology

We introduce and compare two different approaches to estimate mean areal rainfall intensity in urban catchments. Both methods are based on the same lumped hydrological model that is calibrated beforehand. The first method uses a reverse model, i.e. an inverse formulation of a rainfall–runoff model. Rainfall intensities and their uncertainties are estimated from runoff data only. The second method estimates parameters of a rainfall error model using a Bayesian approach. It requires measurements of both runoff and rainfall. Although the two approaches are conceptually rather different, they address the same issue – the quantification of areal rainfall intensities and their related measurement errors – and a comparison is hence of interest. The merits and faults of the two methods are discussed. Results show that both methods provide best estimates of hyetographs with maximum intensities and total depths in a realistic order of magnitude, whereas the uncertainty of rainfall estimated with the reverse model is rather large.