Spatial Estimation Using Universal Kriging with Training Images
Résumé
Universal kriging relies on a random function model formulation whereby the regionalized variable is decomposed into a trend and residual component. While the theory is well established, the actual practice of UK remains challenging in particular when dealing with complex trend cases, large datasets and/or difficult to infer spatial covariance functions. In this paper, we reformulate the least-square formulation of UK in the presence of an exhaustive image (termed training image), deemed representative for the spatial variation of the modeling domain. We demonstrate how this new form of universal kriging with training images (UK-TI) need not rely on a random function model and can be written in a purely empirical form, directly lifting the required estimates from the training image. We present Monte Carlo studies comparing traditional UK with this new form under various complex trend variation. We present applications to various environmental data sets and propose fast implementations in the Fourier domain.