[M-IS07] Geophysical particulate gravity current

[MIS07-P06] A study for hazard mapping method with polynomial chaos quadrature method to quantify uncertainty inputs for depth-averaged granular flow model

*Takahiro Tanabe¹ (1.National Research Institute for Earth Science and Disaster Resilience)

Keywords:Avalanch, Hazard map, Uncertainty propagation

Avalanche model with shallow-water equation are powerful tools to predict the runout area. In the input of avalanche model, there include various kinds of uncertainties, such as friction coefficient, fluid viscosity, and initial conditions. Recently, the numerical model has been utilized to hazard mapping (Dalbey et. al., 2008; Tierz et al., 2018). In order to obtain useful hazard map with the numerical model, it is required that the uncertainty of input should be taken into account. The hazard map, which considers the uncertainties is known as probabilistic hazard map. These input uncertainties are propagated to outputs via the model, which is called uncertainty propagation.
In this presentation, we assume that the input uncertainties are able to be represented with uniform distributions. To evaluate the uncertainties propagation, polynomial chaos quadrature method is employed, and introduce its application in this presentation. The output of the numerical model is represented as a linear function of the orthogonal polynomials of input variables with uncertainties under the assumption. The comparison of the hazard map between PCQ and classical Monte Carlo method reveals the advantage of PCQ, which converges faster in a few parameters case and has practical application to arbitrary input distributions.

Reference
Dalbey, K., Patra, A.K., Pitman, E.B., Bursik, M.I., and Sheridan, M.F. (2008), J. Geophys. Res., 113, B05203.
Tierz, P., Stefanescu, E.R., Sandri, L., Sulpizio, R., Valentine, G.A., Marzocchi, W. and Patra, A.K. (2018), J. Geophys. Res. Solid Earth, 123, 6299-6317.