Large Wave Direction Data Modeling Using Wrapped Spatial Gaussian Markov Random Fields

TL;DR

This paper introduces a wrapped Gaussian Markov random field model for large-scale spatial directional data, offering computational efficiency and improved predictive accuracy over existing methods, demonstrated through simulations and tsunami wave data analysis.

Contribution

The paper develops a novel WGMRF model that leverages sparse precision matrices for efficient spatial dependence modeling on the circle, suitable for high-resolution large spatial datasets.

Findings

WGMRF outperforms non-spatial models in predictive accuracy.

The approach significantly reduces computational complexity.

Application to Indian Ocean tsunami data validates model effectiveness.

Abstract

Statistical modeling of dependent directional data remains relatively underexplored, particularly in high-dimensional spatial settings. Existing approaches for spatial angular data primarily rely on wrapped Gaussian process (WGP) models, which provide a coherent framework for capturing spatial dependence on the circle. However, WGP-based methods become computationally challenging when the spatial domain is large, and observations are available at high resolution. This limitation is especially relevant in the analysis of large-scale geological and climate phenomena, such as tsunamis and hurricanes, where directional measurements (e.g., wave or wind directions) may be available over an entire ocean basin. To address these challenges, we propose a wrapped Gaussian Markov random field (WGMRF) model for large spatial directional datasets. By exploiting the sparse precision structure inherent in Gaussian Markov random fields, the proposed approach achieves substantial computational gains while preserving flexible spatial dependence on the circular scale. We discuss key properties of the model, including its identifiability and dependence characteristics. The model fitting involves standard Markov chain Monte Carlo techniques. Through extensive simulation studies and an application to the wave direction data across the Indian Ocean during the 2004 Indian Ocean Tsunami, we compare the proposed method with both a non-spatial wrapped Gaussian model and a low-rank WGP alternative. The results demonstrate that the WGMRF offers improved predictive performance and scalability in large-domain applications.