In oceanography, modeling wave fields requires the use of statistical tools capable of handling the circular nature of the {data measurements}. An important issue in ocean wave analysis is the study of height and direction waves, being direction values recorded as angles or, equivalently, as points on a unit circle. Hence, reconstruction of a wave direction field on the sea surface can be approached by the use of a linear-circular regression model, viewing wave directions as a realization of a circular spatial process whose trend should be estimated. In this paper, we consider a spatial regression model with a circular response and several real-valued predictors. Nonparametric estimators of the circular trend surface are proposed, accounting for the (unknown) spatial correlation. Some asymptotic results about these estimators as well as some guidelines for their practical implementation are also given. The performance of the proposed estimators is investigated in a simulation study. An application to wave directions in the Adriatic Sea is provided for illustration.

翻译：在海洋学中，波浪场建模需要使用能够处理数据测量圆形性质的统计工具。海洋波浪分析中的一个重要问题是研究波高和波向，其中方向值以角度形式记录，或等价地以单位圆上的点表示。因此，海面波向场的重建可通过线性-圆形回归模型实现，将波向视为需估计趋势的圆形空间过程的实现。本文考虑具有圆形响应变量和多个实值预测变量的空间回归模型。我们提出了考虑（未知）空间相关性的圆形趋势面非参数估计方法，给出了这些估计量的渐近性质及其实用实施指南。通过模拟研究验证了所提出估计量的性能，并以亚得里亚海波向数据为例进行说明。