Directional Spectra-Based Clustering for Visualizing Patterns of Ocean Waves and Winds

The energy distribution of wind-driven ocean waves is of great interest in marine science. Discovering the generating process of ocean waves is often challenging and the direction is the key for a better understanding. Typically, wave records are transformed into a directional spectrum which provides information about the wave energy distribution across different frequencies and directions. Here, we propose a new time series clustering method for a series of directional spectra to extract the spectral features of ocean waves and develop informative visualization tools to summarize identified wave clusters. We treat directional distributions as functional data of directions and construct a directional functional boxplot to display the main directional distribution of the wave energy within a cluster. We also trace back when these spectra were observed, and we present color-coded clusters on a calendar plot to show their temporal variability. For each identified wave cluster, we analyze wind speed and wind direction hourly to investigate the link between wind data and wave directional spectra. The performance of the proposed clustering method is evaluated by simulations and illustrated by a real-world dataset from the Red Sea. Supplementary materials for this article are available online.

风驱海浪的能量分布是海洋科学领域广受关注的研究方向。探明海浪的生成过程往往极具挑战，而波向是深化认知的关键要素。通常，海浪观测记录会被转换为方向谱（directional spectrum），该谱可提供不同频率与方向下的海浪能量分布信息。为此，本文提出一种面向多组方向谱的时序聚类新方法，用于提取海浪谱特征，并开发了兼具信息价值的可视化工具，以归纳已识别的海浪簇。我们将方向分布视为以波向为自变量的函数数据，构建了方向函数箱线图（directional functional boxplot），用以展示单个簇内海浪能量的核心方向分布特征。此外，我们回溯了各方向谱的观测时刻，并通过日历图（calendar plot）上的颜色编码簇来呈现其时间变异性。针对每个已识别的海浪簇，我们对每小时的风速与风向数据进行分析，以探究风场数据与海浪方向谱之间的关联机制。本文通过模拟实验对所提聚类方法的性能开展了评估，并以红海（Red Sea）的真实数据集作为示例进行了验证。本文的补充材料可在线获取。