Identification and classification of very low frequency waves on a coral reef flat

Very low frequency (VLF, 0.001–0.005 Hz) waves are important drivers of flooding of low‐lying coral reef‐islands. In particular, VLF wave resonance is known to drive large wave runup and subsequent overwash. Using a 5 month data set of water levels and waves collected along a cross‐reef transect on Roi‐Namur Island in the Republic of the Marshall Islands, the observed VLF motions were categorized into four different classes: (1) resonant, (2) (nonresonant) standing, (3) progressive‐growing, and (4) progressive‐dissipative waves. Each VLF class is set by the reef flat water depth and, in the case of resonance, the incident‐band offshore wave period. Using an improved method to identify VLF wave resonance, we find that VLF wave resonance caused prolonged (∼0.5–6.0 h), large‐amplitude water surface oscillations at the inner reef flat ranging in wave height from 0.14 to 0.83 m. It was induced by relatively long‐period, grouped, incident‐band waves, and occurred under both storm and nonstorm conditions. Moreover, observed resonant VLF waves had nonlinear, bore‐like wave shapes, which likely have a larger impact on the shoreline than regular, sinusoidal waveforms. As an alternative technique to the commonly used Fast Fourier Transformation, we propose the Hilbert‐Huang Transformation that is more computationally expensive but can capture the wave shape more accurately. This research demonstrates that understanding VLF waves on reef flats is important for evaluating coastal flooding hazards. Key Points: Very low frequency (0.001–0.005 Hz) waves on a reef flat can be categorized into four classes A new method identifies very low frequency wave resonance that occurred with high water levels and long incident wave periods Maximum nearshore very low frequency wave heights and observed flooding were driven by resonance