Bayesian estimation of levee breach progression in natural rivers

During severe flood events, sometime, levee breaches occur in a river reach causing the flooding of the surrounding area. Most levee failures are not instantaneous but they gradually evolve over a period of time: the initial breach progressively increases its depth and enlarges its width. After the failure takes place, even if its location can be known, the breach progression is hard to be recovered. However, if one or more sites monitored with level gauges are located downstream the failure site, the breach time evolution leaves an imprint in these water levels. The knowledge of the breach progression can be useful to better understand the effective dynamics of the failure and to evaluate the breach flood wave in order to simulate the flooding process for forensic purposes among others. In this work an inverse methodology to estimate the progression of an occurred levee breach in a natural river using water level data available at monitored stations downstream the failure is presented. The methodology is based on a Bayesian approach to the inverse problem coupled with geostatistical models to describe the structure of the unknown breach time evolution. The methodology requires a forward hydraulic model of the considered river reach able to accurately reproduce not only the flow routing processes but also the levee breach in terms of progression and outflow discharge. In this work, a 1D forward model (USACE HEC-RAS river analysis system) that solves the unsteady flow De Saint Venant equations has been used. A simplified description of both the depth and the width time evolution of the levee breach has been considered. The methodology has been tested by means of synthetic examples of several levee breaches considering different stressing flood waves and different locations of the observed water levels used as input for the inverse procedure. The results highlight the reliability of the procedure in estimating the progression of the levee breach and consequently the volume of water released. Further studies will be conducted considering more complex descriptions of the levee breaches and the flow field using also 2D flooding models.