Recent developments in predictive uncertainty assessment based on the model conditional processor approach

Abstract. The work aims at discussing the role of predictive uncertainty in flood forecasting and flood emergency management, its relevance to improve the decision making process and the techniques to be used for its assessment. Real time flood forecasting requires taking into account predictive uncertainty for a number of reasons. Deterministic hydrological/hydraulic forecasts give useful information about real future events, but their predictions, as usually done in practice, cannot be taken and used as real future occurrences but rather used as pseudo-measurements of future occurrences in order to reduce the uncertainty of decision makers. Predictive Uncertainty (PU) is in fact defined as the probability of occurrence of a future value of a predictand (such as water level, discharge or water volume) conditional upon prior observations and knowledge as well as on all the information we can obtain on that specific future value from model forecasts. When dealing with commensurable quantities, as in the case of floods, PU must be quantified in terms of a probability distribution function which will be used by the emergency managers in their decision process in order to improve the quality and reliability of their decisions. After introducing the concept of PU, the presently available processors are introduced and discussed in terms of their benefits and limitations. In this work the Model Conditional Processor (MCP) has been extended to the possibility of using two joint Truncated Normal Distributions (TNDs), in order to improve adaptation to low and high flows. The paper concludes by showing the results of the application of the MCP on two case studies, the Po river in Italy and the Baron Fork river, OK, USA. In the Po river case the data provided by the Civil Protection of the Emilia Romagna region have been used to implement an operational example, where the predicted variable is the observed water level. In the Baron Fork River example, the data set provided by the NOAA's National Weather Service, within the DMIP 2 Project, allowed two physically based models, the TOPKAPI model and TETIS model, to be calibrated and a data driven model to be implemented using the Artificial Neural Network. The three model forecasts have been combined with the aim of reducing the PU and improving the probabilistic forecast taking advantage of the different capabilities of each model approach.