This paper discusses basic issues in hydrological modelling and flood forecasting, ranging from the roles of physically-based and data-driven rainfall runoff models, to the concepts of predictive uncertainty and equifinality and their implications. The evolution of a wide range of hydrological catchment models employing the physically meaningful and data-driven approaches introduces the need for objective test beds or benchmarks to assess the merits of the different models in reconciling the alternative approaches. In addition, the paper analyses uncertainty in models and predictions by clarifying the meaning of uncertainty, by distinguishing between parameter and predictive uncertainty and by demonstrating how the concept of equifinality must be addressed by appropriate and robust inference approaches. Finally, the importance of predictive uncertainty in the decision making process is highlighted together with possible approaches aimed at overcoming the diffidence of end-users.

This paper briefly discusses the nature, the causes and the role of predictive uncertainty in flood forecasting and proposes a novel approach to its estimation. Following the definition of predictive uncertainty, its importance in the decision process is highlighted in relation to the different sources of errors (model, parameter, observations, boundary conditions) that affect flood forecasting. Moreover, the paper briefly analyses the importance of using a full predictive uncertainty, obtained by marginalising the parameter uncertainty, instead of the predictive uncertainty conditional to a single parameter set. Finally, a new Model Conditional Processor (MCP) for the assessment of predictive uncertainty is then proposed as an alternative to the Hydrologic Uncertainty Processor (HUP) introduced by Krzysztofowicz as well as to the Bayesian Model Averaging (BMA) approach due to Raftery et al. The new MCP approach, which aims at assessing, and possibly reducing, predictive uncertainty, allows combination of the observations with one or several models’ forecasts in a multi‐Normal space, by transforming observations and model forecasts in a multivariate Normal space by means of the Normal Quantile Transform. The results of the new approach are shown for the case of the River Po in Italy, and compared with the results obtainable both with the HUP and the BMA.

The paper introduces a new technique based upon the use of block-Kriging and of Kalman filtering to combine, optimally in a Bayesian sense, areal precipitation fields estimated from meteorological radar to point measurements of precipitation such as are provided by a network of rain-gauges. The theoretical development is followed by a numerical example, in which an error field with a large bias and a noise to signal ratio of 30% is added to a known random field, to demonstrate the potentiality of the proposed algorithm. The results analysed on a sample of 1000 realisations, show that the final estimates are totally unbiased and the noise variance reduced substantially. Moreover, a case study on the upper Reno river in Italy demonstrates the improvements in rainfall spatial distribution obtainable by means of the proposed radar conditioning technique. Keywords: Rainfall, meteorological radar, Bayesian technique, block-Kriging, Kalman filtering

In 2000, the resilience and failure indices were introduced as a convenient and compact tool to express respectively water-distribution network (WDN) surplus and deficit in satisfying users’ demand, in terms of delivered power. In their original formulation, the mentioned indices, originally thought as WDN design tools, were developed only considering the demand-driven modeling approach, which would include pumps but not leakage. This paper extends the formulation of both indices and presents a generalized expression, more convenient for use when dealing with pressure-driven modeling and capable of including the effect of leakage. Following the original concept, the generalized indices were developed by calculating the power dissipated in the network as a function of the difference between the total power inserted through source nodes and pumps and the net delivered power, whereas the leakage-related power is considered as a loss similarly to the internally dissipated one. Applications to WDN anal...