An Inverse Methodology to Estimate the Flow Released from a Levee Breach

When a levee breach occurs a remarkable volume of water is released causing the inundation of an extended area. To accurately reproduce the flooding resulting from the failure, the discharge over time leaving the river must be known. This flow rate is conditioned by many factors such as: 1. the river water levels in proximity of the failure; 2. the geometry of the breach and its evolution in time; 3. the water level of the flooded area that can produce backwater effects and thus reduce the leaving flow rate or in some case reverse the flow; and 4. the provisional works aimed at fixing the failure. However, from a practical point of view, many of the previous data are hardly known and usually the only available information is the position and the finally geometry of the breach and sometimes its opening time. But, if gauging stations are located in proximity of the failure, the water levels observed upstream and mainly downstream the levee breach are affected by the discharge leaving or eventually re-entering the river. In this work, a Bayesian inverse methodology to estimate the discharge time series leaving a levee breach based on the water levels recorded downstream and/or upstream the failure site is proposed. Prior information, in forms of geostatistical functions, regularizes the solution. The required simulation of the forward problem, able to reproduce the river flow routing and the discharge leaving the breach, has been accomplished by means of the 1D HEC-RAS model. The Uniform Later Flow boundary condition of HEC-RAS has been used to simulate the flow leaving/entering the river across the breach. Synthetic examples with and without the above mentioned back water effects and provisional works has been used to test the procedure. Different levee breaches modeled by means of a lateral weir with movable gates has been simulated to collect the synthetic level data then used in the inverse procedure. The methodology was able to accurately reproduce the flow released by the levee breaches in all cases. The procedure has been also tested on a real case study of the tragically famous inundation of the Polesine Region (Italy) occurred in 1951 and caused by three contiguous levee breaches of the Po river. The estimated discharge leaving the breaches and consequently the total volume of water released is in accordance with other literature studies.