Latin Hypercube Sampling of Gaussian random field for Sobol' global sensitivity analysis of models with spatial inputs and scalar output

The variance-based Sobol' approach is one of the few global sensitivity analysis methods that is suitable for complex models with spatially distributed inputs. Yet it needs a large number of model runs to compute sensitivity indices: in the case of models where some inputs are 2D Gaussian random fields, it is of great importance to generate a relatively small set of map realizations capturing most of the variability of the spatial inputs. The purpose of this paper is to discuss the use of Latin Hypercube Sampling (LHS) of geostatistical simulations to reach better efficiency in the computation of Sobol’ sensitivity indices on spatial models. Sensitivity indices are estimated on a simple analytical model with a spatial input, for increasing sample size, using either Simple Random Sampling (SRS) or LHS to generate input map realizations. Results show that using LHS rather than SRS yields sensitivity indices estimates which are slightly more precise (smaller variance), with no significant improvement of bias.