Surface ocean currents are often of interest in environmental monitoring. These vectorial data can be reasonably treated as a finite realization of a complex-valued random field, where the decomposition in modulus (current speed) and direction (current direction) of the current field is natural. Moreover, when observations are also available for different time points (other than at several locations), it is useful to evaluate the evolution of their complex correlation over time (rather than in space) and the corresponding modeling which is required for estimation purposes. This paper illustrates a first approach where the temporal profile of surface ocean currents is considered. After introducing the fundamental aspects of the complex formalism of a random field indexed in time, a new class of models suitable for including the temporal component is proposed and applied to describe the time-varying complex covariance function of current data. The analysis concerns ocean current observations, taken hourly on 30 April 2016 through high frequency radar systems at some stations located in the Northeastern Caribbean Sea. The selected complex covariance model indexed in time is used for estimation purposes and its reliability is confirmed by a numerical analysis.

在环境监测中，地表洋流经常引起人们的兴趣。这些矢量数据可以合理地视为复值随机场的有限实现，其中，当前场的模量（当前速度）和方向（当前方向）的分解是自然的。此外，当观测值也可用于不同的时间点（而不是在几个位置）时，评估其复杂的相关性随时间（而不是在空间中）的演变以及估算目的所需的相应建模是有用的。本文说明了第一种方法，其中考虑了地表洋流的时间分布。在介绍了按时间索引的随机字段的复杂形式主义的基本方面之后，提出了一种适用于包含时间分量的新型模型，并将其应用于描述当前数据的时变复协方差函数。该分析涉及洋流观测，该观测于2016年4月30日每小时通过位于东北加勒比海某些站点的高频雷达系统进行。选择的按时间索引的复协方差模型用于估计目的，其可靠性通过数值分析得到确认。