Low-lying reef-lined coasts are vulnerable to coastal flooding. While fringing reefs usually protect coastal communities from moderate storms by dissipating incoming wave energy, they can exacerbate flooding during strong events with energetic waves. Low-frequency waves (0.001-0.04 Hz) play an important role in coastal hazards, dominating nearshore reef flat wave patterns. Furthermore, low-frequency resonance on reef flats has been suggested to exacerbate coastal hazards. Despite expanding knowledge of wave dynamics on coral reefs, the transient characteristics of low-frequency resonant oscillations on reef flats have not been extensively researched, and no methods currently exist for analyzing this phenomenon in field observations.

This thesis introduces a new methodology for assessing transient characteristics of resonant and energetic low-frequency oscillations using the Hilbert-Huang transform. The study is based on a 5-month dataset from a cross-shore transect of a reef at Roi-Namur in the Marshall Islands, where the reef geomorphology corresponds to a natural frequency in the very low-frequency range (VLF, 0.001-0.005 Hz).

The findings indicate that resonance in the dataset typically had a short persistence, with a median and 90th duration of approximately 5 and 10 minutes respectively. Normalised with the period of the oscillations, which have a typical frequency of 0.0035 Hz, these durations are equal to approximately 1 and 2 wave oscillations. While these results are consistent with previous notions about the potentially short durations of resonance for this particular reef and dataset, they contradict suggestions that resonance is associated with a build-up over several wave periods. Comparison of resonance durations with instances of coastal flooding at the site shows that resonance occurred for about 1 hour within a 24-hour recording period during overwash and large runup events, but also at other times. The duration of energetic VLF oscillations, in general, was more closely linked to the severity of coastal flooding events. While resonance did not directly correspond to coastal flooding, it was observed that energetic VLF oscillations persisted for longer durations under (close to) resonant conditions.

These results suggest the critical role of energetic VLF waves in coastal hazards, while resonance may be of secondary importance. However, it is important to acknowledge the limitations of this study, which focused on a single dataset from a specific reef geometry and included short-duration recordings (34 minutes). Moreover, this study demonstrates the application of the Hilbert-Huang transform for analysing sea surface elevation signals recorded at a coral reef.

The insights gained from this research underscore the importance of considering both energetic VLF oscillations and resonance in coastal hazard assessment. Future investigations should explore factors influencing the persistence of such oscillations, like the characteristics of incoming wave forcing, to enhance coastal hazard prediction. Furthermore, the Hilbert-Huang transform offers a versatile framework for exploring more aspects regarding the time-varying and non-linear behaviour of waves on coral reefs.

The methodology framework proposed in this study facilitates the bulk analysis of extensive field data and longer sea surface elevation recordings, enabling further exploration of reef morphology and hydrodynamic controls on the persistence of energetic and resonant VLF oscillations.