Probabilistic rainfall thresholds for flood forecasting: evaluating different methodologies for modelling rainfall spatial correlation (or dependence)



Rainfall threshold (RT) method is one of the evolving flood forecasting approaches. When the cumulative rainfall depth for a given initial soil moisture condition intersects the threshold rainfall curve, the peak discharge is expected to be equal or greater than the threshold discharge for flooding at the target site. Besides the total rainfall depth, spatial and temporal distribution of rainfall impacts the flood peak discharge and the time to peak. To revisit a previous study conducted by the authors, in which spatially independent rainfall pattern was assumed, the spatial distribution of rainfall was simulated following a Monte Carlo approach. The structure of the spatial dependence among sub-watersheds' rainfalls was taken into account under three different scenarios, namely independent, bivariate copula (2copula) and multivariate Gaussian copula (MGC). For each set of generated random dimensionless rainfalls, the probabilistic RT curves were derived for dry moisture condition. Results were evaluated with both historical and simulated events. For the simulated events, threshold curves were assessed by means of categorical statistics, such as hit rate, false rate and critical success index (CSI). Results revealed that the best performance based on the CSI criterion corresponded to 50% curve in 2copula and MGC scenarios as well as 90% curve in the independent scenario. The recognition of 50% curve in 2copula and MGC scenarios is in agreement with our expectations that the mean probable curve should have the best performance. Moreover, the proposed inclusion of spatially dependent rainfall scenario improved the performance of RT curves by about 25% in comparison with the presumed spatially uniform rainfall scenario. Copyright © 2011 John Wiley & Sons, Ltd.