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.

在海洋学中，对波场建模需要使用能够处理数据测量的循环性质的统计工具。海浪分析中的一个重要问题是研究高度波和方向波，即以角度或等效地以单位圆上的点记录的方向值。因此，可以通过使用线性-圆形回归模型来对海面的波浪方向场进行重建，将波浪方向视为圆形空间过程的实现，应估计其趋势。在本文中，我们考虑具有循环响应和几个实值预测变量的空间回归模型。考虑到（未知）空间相关性，提出了圆形趋势面的非参数估计量。还给出了有关这些估计量的一些渐近结果，以及它们的实际实现准则。在模拟研究中研究了提出的估计量的性能。为了说明，提供了在亚得里亚海中波浪方向的应用。