Evaluation of rainfall thresholds through entropy: influence of bivariate distribution selection

Floods cause severe damage worldwide in terms of human injury and have severe economic consequences, causing landslides, road accidents and inundation of agricultural areas. Non-structural flood protection strategies offer the possibility to protect the land, preventing flood event effects. In particular, early warning systems can inform of flood occurrences. These systems can be based on the evaluation of a rainfall threshold value that is the rainfall amount that determines a critical discharge in a given river cross-section. The alert is issued if the observed or forecast rainfall equals the threshold value without the support of online real-time rainfall-runoff forecasting systems. The critical rainfall threshold values are evaluated by a probabilistic methodology, considering the joint cumulative distribution of cumulated rainfall and the corresponding peak discharge, for different durations. To estimate the joint distributions two approaches are considered: the meta-Gaussian and the copula functions. The rainfall threshold values are estimated for the Mignone River basin (Italy). Results show that both joint distribution functions perform well in estimating the rainfall threshold values, as found from reliability analysis. In particular, the copula-based approach leads to issuing the alert in advance.