The theory of complex-valued random fields was already used in Geostatistics to describe vector data with two components. However, in the literature, there are various contributions focused only on modeling their spatial evolution, while the temporal perspective was analyzed separately or used to model time-varying complex covariance models. Thus, in this context it is surely challenging to propose some advances in modeling the joint spatial and temporal behavior of vector data with a reasonable representation on a complex domain.

In this paper, after introducing the fundamental aspects of the complex formalism of a spatio-temporal random field and some approaches for building new families of spatio-temporal models, the spatio-temporal complex modeling of current data observed in the US East and Gulf Coast is deeply discussed and the results regarding a comparative analysis between two different complex-valued covariance models are also presented.

复值随机场理论已经在地统计学中用于描述具有两个分量的矢量数据。然而，在文献中，有各种贡献仅集中在对其空间演化进行建模，而时间视角则单独分析或用于对时变复杂协方差模型进行建模。因此，在这种情况下，提出一些在复杂域上具有合理表示的矢量数据的联合空间和时间行为建模的进展肯定是具有挑战性的。

在本文中，在介绍了时空随机场的复杂形式的基本方面以及构建新的时空模型族的一些方法之后，美国东部和墨西哥湾沿岸观测到的当前数据的时空复杂建模进行了深入讨论，并提出了两种不同复值协方差模型之间的比较分析结果。