# The Fraction of Broken Waves in Natural Surf Zones

## TL;DR

This study quantifies the fraction of broken waves (Qb) in natural surf zones using remote sensing, in-situ data, and machine learning, revealing high variability influenced by environmental factors and improving theoretical models.

## Contribution

It introduces a novel quantification method for Qb across multiple beaches, linking it to environmental parameters and enhancing existing theoretical models.

## Key findings

- Qb varies significantly with tidal and infragravity energy levels.
- Existing models poorly predict Qb, but accuracy improves with Weibull distribution.
- Qb correlates with beach morphodynamics and environmental forcing.

## Abstract

This paper presents a novel quantification of the fraction of broken waves (Qb) in natural surf zones using data from seven wave-dominated Australian beaches. Qb is a critical, but rarely quantified, parameter for parametric surf zone energy dissipation models which are commonly used as coastal management tools. Here, Qb is quantified using a combination of remote sensing and in-situ data. These data and machine learning techniques enable quantification of Qb for a substantial dataset (>350,000 waves). The results show that Qb is a highly variable parameter with a high degree of inter- and intra-beach variability. Such variance could be explained (at least partially) by correlations between Qb and environmental parameters. Tidal variations drive changes in Qb of up to 70% for a given local water depth (h) on steep beaches, and increased infragravity energy levels decreased terminal values of Qb by about 20%. The links between Qb and environmental forcing lead to the development of a correspondence between Qb and the Australian beach morphodynamic model. Qb is larger for a given normalized depth (h/Hs, where Hs is offshore wave height) for dissipative beaches than for intermediate beaches. Finally, when comparing data to existing models, three commonly used theoretical formulations for Qb are observed to be poor predictors with errors of the order of 40%. Existing theoretical Qb models are shown to improve (revised errors of the order of 10%) if the Rayleigh probability distribution that describes the wave height is in these models is replaced by the Weibull distribution.