Preservation of rainfall properties in stochastic disaggregation by a simple random cascade model

Abstract

We analyse properties of a simple discrete multiplicative random cascade model for rainfall disaggregation in urban hydrology. Two types of cascade models (canonical and microcanonical) are applied to the stochastic fine graining of rainfall observations into high resolution data. In particular, we analyse the disaggregation of 1280-min into 10-min data for a 20-year record period (Zurich raingauge, 1979–1998). Differences between the models and parameter estimation techniques are explored on simulated data with a special focus on three important properties of observed rainfall: distribution, intermittency, and extremes. The canonical models are overall better at preserving the distribution of rainfall at the 10-min scale. It is demonstrated that the growth of intermittency across scales is preserved well with all studied models. The ability of the models to reproduce rainfall extremes is a fundamental requirement in disaggregation. The studied models preserved annual rainfall maxima satisfactorily for short durations; however, the performance deteriorated for longer durations. The canonical models performed substantially better in capturing the variability in rainfall. The results are encouraging considering the parsimonious nature of the models and simple parameter estimation.