Analysis and prediction of significant wave height series using complex network methods

Significant wave height (SWH) is a key parameter for characterizing ocean waves, whose dynamic features directly affect sea-state prediction, navigation safety, and marine engineering design. This paper, for the first time, applies the visibility graph algorithm from complex network theory. Each data point in a 10-year SWH series from Station 42001 in the Gulf of Mexico is mapped to a network node. Edges are formed between nodes based on visibility criteria, constructing a visibility graph, whose topological characteristics are then analyzed to uncover dynamic patterns difficult to capture using traditional statistical methods. The results indicate that the passages of hurricanes ‘LILI’, ‘RITA’, and ‘IKE’ correspond to nodes with the highest degrees, significantly impacting SWH. The SWH visibility graph exhibits scale-free properties, with the original time series showing long-term positive correlation (Hurst index is 0.715). Community division reveals that nodes within the same community cluster consecutively in time, reflecting the persistence of wave height patterns. Furthermore, this study integrates complex networks and time-series structural information to weight nodes, and Node similarities are computed using Jensen-Shannon divergence to build a time-series prediction model. For single-point and multi-point predictions, the mean absolute errors are 0.492 03 (single-point) and 0.465 80 (multi-point), respectively, demonstrating superior performance compared to other network-based prediction models.