Use of simple analytical solutions in the calibration of Shallow Water Equations debris flow models

Abstract. Modelling debris flow propagation requires numerical models able to describe the main characteristics of the flow, like velocity or inundation extent. Due to the complex physics involved, every numerical model is dependent from a set of parameters whose influence on the results is often not evident. In this contribution we propose simple analytical solutions based on the monophasic Shallow Water Equations for some of the most used rheological models (O'Brien Julien, Voellmy, Bingham and Bagnold) implemented in monophasic (FLO-2D, RAMMS, HEC-RAS, TELEMAC-2D) and biphasic commercial software (TRENT2D). These simplified solutions and their asymptotic uniform-flow like relationship are useful on one hand to speed up the calibration process, limiting the need to perform multiple simulations with unrealistic set of parameters and on the other hand as a benchmark for existing numerical methods. To further guide the calibration, a Sobol's sensitivity analysis has been performed to highlight which parameters of the considered equations have the most influence on the flow velocity. Finally, as an example of application, the proposed methodology is validated on a real debris flow event occurred in Italy.