Dam break flow modelling with uncertainty analysis

The failure of a large dam may result in catastrophic floods in the downstream valley. However, past experience has revealed that loss of life and damage can be drastically reduced if crisis management is planned in advanced, including early-warning systems, organized communication and structural measures. This requires a fairly good knowledge of the inundation characteristics likely to be induced in case of a failure.
Predictions of flood waves induced by dam failure are affected by a considerable level of uncertainty. Due to the extreme nature of such events, numerical models can hardly be calibrated and validated. Flow resistance parameterizations are designed for ranges of flow properties which significantly differ from those occurring during dam break flows. Large amounts of debris may also be transported by the flow and the details of the failure scenario remain usually unknown, such as sequence of dislodgement of dam wall fragments or breach formation time (e.g., Dewals et al. 2011). Nonetheless, most dam break flow studies so far have been conducted without systematic uncertainty nor sensitivity analyses. This is partly due to the high computational cost of the multidimensional flow models used to simulate dam break flows on natural topography.
We present here the simulation of a real dam break flow with a systematic analysis of the uncertainty resulting from the roughness coefficient, the failure hydrograph and topographic data. The flow simulations have been conducted with the model WOLF 2D developed at the University of Liege. It solves the fully dynamic shallow-water equations based on a finite volume scheme and a self-developed flux-vector splitting (Erpicum et al. 2010a; Erpicum et al. 2010b). Monte-Carlo simulations have been used to perform the uncertainty analysis. The two-dimensional flow model is computationally too costly to perform a high number of repeated runs, as needed for Monte Carlo simulations. Therefore, a “reduced complexity model” has been set up, in the form of multidimensional Hermite polynomials. The method developed by Isukapalli et al. (Isukapalli et al. 2004) indicates the number of simulations of the complete model needed to calibrate the polynomials, as well as the parameter values to be used in these calibration runs. The methodology has been tested for a real dam break which occurred in Spain in 1982 (Alcrudo and Mulet 2007) and for which a number of observations are available (mainly maximum water depths at different locations in a town).
The presentation will show the applicability and efficiency of the methodology, which is readily available for real-world analyses. Such uncertainty analysis for dam break flows disclose crucial information for practical risk management. In particular, they reveal that the uncertainty ranges on maximum water depth and time of arrival of the front are not symmetric (overestimation vs. underestimation) and very unevenly distributed in space.