Time varying complex covariance functions for oceanographic data

In Geostatistics, vector data with two components, such as measures for wind field, electromagnetic field and ocean currents can be appropriately modeled by recalling the theory of complex-valued random fields. This is especially suitable for describing phenomena whose variables are expressed in the same unit of measurement and refer to homogeneous quantities. In this paper, a first approach useful for taking into account the temporal profile of complex data is described. After introducing the fundamental aspects of the complex formalism of a random field indexed in time, a new class of models apt to include the temporal component is proposed. A case study on a vector data set regarding surface ocean currents is provided. In particular, these data, derived from high frequency radar systems, were collected during the 30th of April 2016, from 207 stations along the US East and Gulf Coast. The complex covariance function, indexed in time, is estimated and modeled, then it is used for prediction purposes. A numerical analysis is also proposed in order to evaluate the consistency of the time varying complex model.