Treatment of precipitation uncertainty in rainfall-runoff modelling: a fuzzy set approach

The uncertainty in forecasted precipitation remains a major source of uncertainty in real time flood forecasting. Precipitation uncertainty consists of uncertainty in (i) the magnitude, (ii) temporal distribution, and (iii) spatial distribution of the precipitation. This paper presents a methodology for propagating the precipitation uncertainty through a deterministic rainfall-runoff-routing model for flood forecasting. It uses fuzzy set theory combined with genetic algorithms. The uncertainty due to the unknown temporal distribution of the precipitation is achieved by disaggregation of the precipitation into subperiods. The methodology based on fuzzy set theory is particularly useful where a probabilistic forecast of precipitation is not available. A catchment model of the Klodzko valley (Poland) built with HEC-1 and HEC-HMS was used for the application. The results showed that the output uncertainty due to the uncertain temporal distribution of precipitation can be significantly dominant over the uncertainty due to the uncertain quantity of precipitation.