Wind velocity prediction through complex kriging: formalism and computational aspects

The formalism of complex random fields is suitable for describing, in a compact and unified way, vectorial data sets in two dimensions, such as wind fields, electromagnetic fields, as well as measurements derived from any two dimensional vectorial field. This representation is rarely considered in Geostatistics, although interesting applications can be found in environmental sciences and meteorology. Moreover, the lack of procedures for modeling a complex covariance function as well as the lack of specialized routines for computing predictions in the complex case have considerably restricted the applications of these techniques. In this paper, some essential aspects of the complex formalism and some computational developments associated with fitting a complex covariance function and predicting a complex-valued random field through an ad-hoc routine are discussed. An environmental application to wind data is provided, moreover, the consistency of the proposed methodology is demonstrated through a numerical study.