Global sensitivity analysis for models with spatially dependent outputs
Article first published online: 18 NOV 2010
Copyright © 2010 John Wiley & Sons, Ltd.
Volume 22, Issue 3, pages 383–397, May 2011
How to Cite
Marrel, A., Iooss, B., Jullien, M., Laurent, B. and Volkova, E. (2011), Global sensitivity analysis for models with spatially dependent outputs. Environmetrics, 22: 383–397. doi: 10.1002/env.1071
- Issue published online: 15 APR 2011
- Article first published online: 18 NOV 2010
- Manuscript Accepted: 5 AUG 2010
- Manuscript Revised: 30 JUL 2010
- Manuscript Received: 4 NOV 2009
- computer experiment;
- Gaussian process;
- functional data;
- radionuclide migration
The global sensitivity analysis of a complex numerical model often calls for the estimation of variance-based importance measures, named Sobol' indices. Metamodel-based techniques have been developed in order to replace the CPU time-expensive computer code with an inexpensive mathematical function, which predicts the computer code output. The common metamodel-based sensitivity analysis methods are well suited for computer codes with scalar outputs. However, in the environmental domain, as in many areas of application, the numerical model outputs are often spatial maps, which may also vary with time. In this paper, we introduce an innovative method to obtain a spatial map of Sobol' indices with a minimal number of numerical model computations. It is based upon the functional decomposition of the spatial output onto a wavelet basis and the metamodeling of the wavelet coefficients by the Gaussian process. An analytical example is presented to clarify the various steps of our methodology. This technique is then applied to a real hydrogeological case: for each model input variable, a spatial map of Sobol' indices is thus obtained. Copyright © 2010 John Wiley & Sons, Ltd.