Nonparametric estimation of aggregated Sobol’ indices: Application to a depth averaged snow avalanche model

Abstract

Avalanche models are increasingly employed for elaborating land-use maps and designing defense structures, but they rely on poorly known parameters. Careful uncertainty assessment is thus required but difficulty arises from the nature of the outputs of these models, which are commonly both functional and scalar. Hence, so far in the avalanche field, few sensitivity analyses have been performed. In this work, we propose to determine the most influential inputs of an avalanche model by estimating aggregated first-order Sobol’ indices. We propose a nonparametric estimation procedure based on the Nadaraya–Watson kernel smoother, which allows to estimate the aggregated Sobol’ indices from a given random sample of small to moderate size. Due to the limited size of the sample, the kernel estimation is biased. Therefore, we propose a bootstrap based bias correction before selecting the bandwidth by cross-validation. To estimate the aggregated Sobol’ indices, we reduce the dimension of the output using principal components analysis. After different test cases showing the efficiency of our approach, it is applied to a real avalanche case. Results show that the friction parameters and the snow depth in the release zone are the most influential parameters determining the avalanche characteristics.