Probabilistic Flood Hazard Maps: a Bayesian Approach

Abstract

Computing the likelihood of different events that might deal damage to built infrastructure and human lives is a key step in every rigorous risk analysis. Generally speaking, this is done by the mathematical concatenation of two models: (1) an events recurrence model, such as a rainfall or river discharge frequency model for the case of flood hazard; (2) a source-to-site model that describes how the event’s perturbation propagates to the sites of interest, such as an inundation model.

It is customary, in practice, to acknowledge that the probabilistic nature of hazards is given by the aleatory uncertainty of predicting future events as defined by the frequency curve of the recurrence model. In this sense, the classical approach consists in estimating the corresponding hazard map, that is the flood map, for events with different return periods: the 100-years flood map is the inundation for the 100-years river discharge. Somewhat less applied, but also widely studied, is the inclusion of epistemic uncertainties in the computation of the frequency curve (and return levels) that stem mainly from limited-length data and models of analysis. This results in uncertainty of rainfall or discharge quantities for a given return period selected for design or for inundation mapping for example. This yields in ‘uncertain’ or ‘probability of flood’ maps for each return period.

However, the inclusion of epistemic uncertainties in the inundation model on top of the uncertainties in the flow discharge frequencies is still scarcely studied. The objective of this work is to implement a rigorous Bayesian approach to account for epistemic uncertainties for river discharge frequency curves and the inundation model. Flood depths distributions are then obtained via Bayesian predictive sampling, and hazard maps are developed by marginally mapping Bayesian predictive flood depths for every point. We show how these maps compared to the classical maps and how epistemic uncertainties on the frequency curves and the flood model are aggregated to form the predictive curve. We also discuss the limitations of including epistemic uncertainties through uncertain hazard maps, and potential ways of providing useful information for damage and risk analysis that robustly include epistemic uncertainty.