  We assume a spatial blind source separation model in which the observed
multivariate spatial data is a linear mixture of latent spatially uncorrelated
Gaussian random fields containing a number of pure white noise components. We
propose a test on the number of white noise components and obtain the
asymptotic distribution of its statistic for a general domain. We also
demonstrate how computations can be facilitated in the case of gridded
observation locations. Based on this test, we obtain a consistent estimator of
the true dimension. Simulation studies and an environmental application
demonstrate that our test is at least comparable to and often outperforms
bootstrap-based techniques, which are also introduced in this paper.
