Use of simple analytical solutions in the calibration of shallow water equation debris flow models

Abstract. Modelling debris flow propagation requires numerical models able to describe the main characteristics of the flow, such as velocity or inundation extent. Due to the complex physics involved, every model is dependent on 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 (SWEs) for some of the most used rheological models (O'Brien and Julien, Voellmy, Bingham and Bagnold) implemented in monophasic (FLO-2D, RAMMS, HEC-RAS, TELEMAC-2D) and biphasic (TRENT2D) commercial software. These simplified solutions and their asymptotic uniform-flow-like relationship are useful, on the 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' sensitivity analysis has been performed to highlight which parameters of the considered equations influence the flow velocity the most. Finally, as an example of application, the proposed methodology is validated on a real debris flow event that occurred in Italy.