Contributions to the calibration and global sensitivity analysis of snow avalanche numerical models

Keywords :

• Bayesian inference
• aggregated Sobol’ indices
• aggregated Shapley effects
• given data estimation method
• dimension reduction

Snow avalanche is a natural hazard defined as a snow mass in fast motion. Since the thirties, scientists have been designing snow avalanche models to describe snow avalanches. However, these models depend on some poorly known input parameters that cannot be measured. To understand better model input parameters and model outputs, the aims of this thesis are (i) to propose a framework to calibrate input parameters and (ii) to develop methods to rank input parameters according to their importance in the model taking into account the functional nature of outputs. Within these two purposes, we develop statistical methods based on Bayesian inference and global sensitivity analyses. All the developments are illustrated on test cases and real snow avalanche data.
First, we propose a Bayesian inference method to retrieve input parameter distribution from avalanche velocity time series having been collected on experimental test sites. Our results show that it is important to include the error structure (in our case the autocor- relation) in the statistical modeling in order to avoid bias for the estimation of friction parameters.
Second, to identify important input parameters, we develop two methods based on variance based measures. For the first method, we suppose that we have a given data sample and we want to estimate sensitivity measures with this sample. Within this pur- pose, we develop a nonparametric estimation procedure based on the Nadaraya-Watson kernel smoother to estimate aggregated Sobol’ indices. For the second method, we con- sider the setting where the sample is obtained from acceptance/rejection rules correspond- ing to physical constraints. The set of input parameters become dependent due to the acceptance-rejection sampling, thus we propose to estimate aggregated Shapley effects (extension of Shapley effects to multivariate or functional outputs). We also propose an algorithm to construct bootstrap confidence intervals. For the snow avalanche model application, we consider different uncertainty scenarios to model the input parameters. Under our scenarios, the release avalanche position and volume are the most crucial in- puts.
Our contributions should help avalanche scientists to (i) account for the error structure in model calibration and (ii) rank input parameters according to their importance in the models using statistical methods.

President:

PR Véronique Maume-Deschamps (Université Lyon 1)

Directors:

• Nicolas Eckert (INRAE Grenoble )
• PR Clémentine Prieur (UGA )

Raporteurs:

• PR Bruno Sudret (ETH Zürich )
• Jean-Thomas Fischer (BFW Innsbruck )

Examinators:

• Sébastien Da Veiga (Safran Tech. )
• PR Eric Parent (AgroParisTech )
• Guillaume Evin (INRAE Grenoble )