  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.
