Our study examines the issues associated with the use of deterministic methods for flood hazard mapping and proposes a novel, more reliable approach. The aim of this study is to enhance comprehension of the uncertainty surrounding the assessment of flood hazard mapping concerning a 500-year flood. Our research emphasizes the significance of utilizing probabilistic methodologies that consider uncertainty and warns against neglecting these methods. The findings are important because they reveal the drawbacks of deterministic approaches and the need for a more comprehensive and trustworthy method for estimating flood hazard (Figure 1).

Figure 1. a It displays a graph showing the probability distribution of flooded areas. It includes two peaks and lines representing different levels of flooding and their associated probabilities. The figure compares a deterministic approach (green dashed line) with different levels of stochastic flooding (pale-pink, dark-pink, and dark-red lines). The F-statistic indicates the level of disagreement between deterministic and stochastic flooding at a 0.5 confidence level. b The figure also shows the 500-year flood area at a 0.5 confidence level, as well as the limits of deterministic and stochastic flooding at 0.95.

 We argue that deterministic methods have been overused and that, when probabilistic approaches are employed, they regularly fail to account for all uncertainties, resulting in a fragmented strategy. To remedy these flaws, we propose a new, fully integrated system for predicting flood hazard that takes into consideration all uncertainties sources. This system is especially pertinent for the third cycle (2022-2027) of European Floods Directive implementation. The findings of our study have considerable importance as they exhibit the constraints of deterministic techniques in evaluating the hazard posed by floods and highlight the urgent demand for a more all-encompassing and trustworthy approach. The findings can additionally assist decision-makers make better-informed decisions.

 We use a brand-new, fully integrated system for predicting flood hazard to better understand the uncertainties and their impact on the third cycle of the European Floods Directive. We employed a variety of methods. To evaluate the influence of each uncertainty source on flood hazards, a local sensitivity analysis was conducted. The spatial impact of all uncertainties at the level of individual cells was analyzed using a technique known as global sensitivity analysis. The Monte Carlo method was used for developing probabilistic maps, which are required for a reliable evaluation of flood hazard. Then, convergence analysis was utilized to confirm the reliability of the results and identify areas of inconsistency. These methodologies were chosen because they provide an in- depth knowledge of the inherent uncertainty in flood hazard assessment. They also emphasize the drawbacks of deterministic methods and the need for probabilistic flood hazard mapping. Overall, probabilistic techniques give a thorough and reliable insight into the uncertainty involved with flood hazard assessment.

 Despite the fact that water depth and flow velocity did not always converge at the cell level, obtaining consistent results required a large number of simulations, which slowed down the analysis. The research additionally found that achieving consistent outcomes in regions encompassing complex geometries, such as urban areas, riverbanks, and islands, might pose a challenge or necessitate a substantial quantity of simulations (Figure 2).

 Figure 2. a It shows the convergence of flooded area outcomes (water depth and flow velocity) based on a confidence bound (CB) with a specific width and length. The orange CB represents unstable simulations, the pale-gray line indicates model stability, and the green CB represents stable simulations. b It displays the percentage of cells that converged in each simulation for water depth and flow velocity outcomes. c It shows stochastic 500-year flood map control, highlighting cells that converged on water depth and flow velocity in green, those that did not in yellow, cells that did not converge on flow velocity in red, and cells that did not converge on water depth in blue.

 The results demonstrated substantial differences between deterministic and probabilistic methodologies. Depending on the methodology employed, our study revealed that the flooding area is extremely variable and subject to substantial uncertainty. Our study highlights the relevance of probabilistic mapping and the repercussions of disregarding it. In order to assure effective flood risk management, they also emphasize the need for a thorough and reliable understanding of the uncertainties in flood hazard prediction.

 The findings of our investigation could be relevant in improving the decision-making procedures regarding the allocation of resources, implementation of risk reduction strategies, and preparedness for flood disasters. Consequently, based on the potential flood paths and magnitude depicted on the maps, authorities can prioritize areas with high flood risks for infrastructure enhancements or create more effective evacuation plans. Understanding flood hazard may encourage the general public to take preventative measures, such as purchasing flood insurance or adopting home flood protection measures. It can also influence urban planning and development, thereby assisting to prevent or reduce flood risk. Thus, areas with a significant risk of flooding may be designated as non-residential or ecological spaces. Understanding flood hazard can contribute to the development of more resilient communities that can endure and recuperate from flood events.

 Our study concludes that probabilistic methods should supplant deterministic methods for flood hazard prediction in order to more precisely account for uncertainties. We determined that traditional methodologies are not sufficiently reliable, which could have a substantial impact on the implementation of the European Floods Directive. The study also emphasizes the significance of a completely integrated system for flood risk prediction. These findings may help policymakers and urban planners make better decisions on flood risk management and boost urban areas' flood resilience.