The multi temporal/multi-model approach to predictive uncertainty assessment in real-time flood forecasting

This work extends the multi-temporal approach of the Model Conditional Processor (MCP-MT) to the multi-model case and to the four Truncated Normal Distributions (TNDs) approach, demonstrating the improvement on the single-temporal one. The study is framed in the context of probabilistic Bayesian decision-making that is appropriate to take rational decisions on uncertain future outcomes. As opposed to the direct use of deterministic forecasts, the probabilistic forecast identifies a predictive probability density function that represents a fundamental knowledge on future occurrences. The added value of MCP-MT is the identification of the probability that a critical situation will happen within the forecast lead-time and when, more likely, it will occur. MCP-MT is thoroughly tested for both single-model and multi-model configurations at a gauged site on the Tiber River, central Italy. The stages forecasted by two operative deterministic models, STAFOM-RCM and MISDc, are considered for the study. The dataset used for the analysis consists of hourly data from 34 flood events selected on a time series of six years. MCP-MT improves over the original models' forecasts: the peak overestimation and the rising limb delayed forecast, characterizing MISDc and STAFOM-RCM respectively, are significantly mitigated, with a reduced mean error on peak stage from 45 to 5 cm and an increased coefficient of persistence from 0.53 up to 0.75. The results show that MCP-MT outperforms the single-temporal approach and is potentially useful for supporting decision-making because the exceedance probability of hydrometric thresholds within a forecast horizon and the most probable flooding time can be estimated.