  Global sensitivity analysis of complex numerical models can be performed by
calculating variance-based importance measures of the input variables, such as
the Sobol indices. However, these techniques, requiring a large number of model
evaluations, are often unacceptable for time expensive computer codes. A well
known and widely used decision consists in replacing the computer code by a
metamodel, predicting the model responses with a negligible computation time
and rending straightforward the estimation of Sobol indices. In this paper, we
discuss about the Gaussian process model which gives analytical expressions of
Sobol indices. Two approaches are studied to compute the Sobol indices: the
first based on the predictor of the Gaussian process model and the second based
on the global stochastic process model. Comparisons between the two estimates,
made on analytical examples, show the superiority of the second approach in
terms of convergence and robustness. Moreover, the second approach allows to
integrate the modeling error of the Gaussian process model by directly giving
some confidence intervals on the Sobol indices. These techniques are finally
applied to a real case of hydrogeological modeling.
