# Estimation of spatio-temporal wave grouping properties using Delaunay triangulation and spline techniques

## TL;DR

This paper introduces a novel method combining Delaunay triangulation and spline techniques to compute more realistic, non-symmetric wave envelopes, improving wave group detection over traditional symmetric methods.

## Contribution

The paper presents a new approach for wave envelope estimation that captures non-symmetry, using local maxima/minima, Delaunay triangulation, and tensor-product splines, applicable to simulated and real data.

## Key findings

- Accurately reproduces simulated wave behavior
- Detects non-symmetry in wave envelopes
- Effective on radar-measured wave data

## Abstract

Wave groups can be detected and studied by using the wave envelope. So far, the method used to compute the wave envelope employs the Riesz transform. However, such a technique always produces symmetric envelopes, which is only realistic in the case of linear waves. In this paper we present a new method to compute the wave envelope providing more realistic results. In particular, the method allows to detect non-symmetry in the wave envelope, something useful, for instance, when detecting groups of high waves. The method computes first the local maxima and minima of the sea surface, and then determines the wave envelope by combining discrete methods, namely the use of the Delaunay triangulation, and tensor-product splines. The proposed method has been applied to simulated wave fields, and also to wave elevations data measured by an X-band radar. The obtained results correctly reproduce the behavior of the simulated waves.