Authors:
Tran Vi-vi Élodie Perrin | Ecole des Mines de Saint Etienne | France
Olivier Roustant | INSA de Toulouse | France
Jeremy Rohmer | BRGM | France
Jean-Philippe Naulin | CCR | France
Olivier Alata | Laboratoire Hubert Curien, UMR CNRS 5516 | France
In the present communication, we aim at (1) generalizing the existing Sobol indices (SI) for model with multivariate outputs with spatial dependencies; (2) proposing a procedure to apply it, in the case of high-dimensional spatial output with strong discontinuities. For objective (1), Lamboni et al. (2011) proposed a synthetic criterion, by averaging the SI of the coordinates of the first eigenvectors, weighted by the associated eigenvalues. However, other functional basis (wavelets, splines ...) are more adapted to take into account the spatial nature of the data and their features characteristics, such as smoothness. Therefore, our contribution is to extend this criterion for any type of basis. For objective (2), we decompose the data on a functional basis. For time saving, there is a need to restrict the SI estimates on the most informative coefficients. Our contribution is to propose a criterion to select them. However, when spatial data contained strong discontinuities, the number of kept basis can still be high. To reduce further the dimension, we use functional PCA, which is equivalent to apply PCA on a functional basis using its metric. We introduce how to calibrate this decomposition (functional basis decomposition, number of eigenvectors, ...). Finally, the application case is for coastal flooding at a French site for which maps of 40 000 pixels have to be processed. Our method shows faster and more accurate results than using standard PCA.