What if just one wave is enough to cause disaster? (part 2): A look at the extreme runup events of 16 January 2016 on US Coast!

We’ve all heard stories of waves “reaching the car park” or “rushing past the treeline out of nowhere”. In January 2016, those tales became hard scientific evidence.

The paper by Li et al. (2023) gives us a case study: multiple extreme wave runup events occurring almost simultaneously across over 1000 km of the US Pacific Northwest coast – no earthquake, no asteroid, no warning. Just ocean.

So, over coffee and spectral plots, here’s what Li and their team set out to investigate, how they did it, and why this paper is a treat for anyone passionate about coastal dynamics and long waves.

What did they ask?

Can extreme wave runup events – the sort that resemble tsunamis – be generated solely by energy transfer from offshore wave groups to infragravity waves?

And more provocatively: can these match the magnitude of tsunamis, meteotsunamis, or shelf resonance? Spoiler: yes – and then some.

What was the goal?

To demonstrate, using real observations, that there is a fourth plausible mechanism to trigger extreme runup: energy transfer from carrier waves to bound infragravity waves. And that this alone can cause damaging inland incursions. Plus, they offer a predictive tool. Solid stuff.

How did they do it?

  • Videos taken by eyewitnesses
  • Injury and rescue reports
  • NOAA tide gauges (1-minute and 6-minute intervals)
  • Offshore NDBC buoys (wave spectra, height, period)
  • Deep-ocean DART pressure sensors (tsunami-quality data)
  • Detailed spectral analysis and theoretical models

All of this precisely aligned in space and time. Coastal fieldwork meets wave physics with flair.

What did they find?

  • No strong atmospheric anomalies → not a meteotsunami
  • Shelf resonance at 17–22 minutes was present but not dominant
  • Main spectral peak during the event was ~5 minutes → matches group periods
  • Offshore buoys showed sudden energy increase in <0.06 Hz band just before the events
  • DART sensors detected reflected IG waves hours after coastal runup → amplified at shore

They modelled infragravity wave shoaling and showed that wave groups with 25 s carrier waves can amplify significantly, shoaling with low dissipation and setting up standing IG waves. The result? Runup on par with tsunamis, no quake required.

What do they discuss?

  • Trapped fetch: when the fetch moves along with wave groups, allowing them to grow in period and height
  • Bound infragravity waves: under gentle slopes like the Pacific North West (PNW), shoaling can follow a \( h^{-2.5} \) law
  • DART observations: reflected IG waves were larger than the incoming ones → amplification occurred nearshore

To evaluate how much infragravity (IG) wave energy was reflected near the shoreline, Li et al. (2023) used the dimensionless parameter \( \beta_H \), originally introduced by van Dongeren et al. (2007), defined as:

\[ \beta_H = \frac{h_x}{\omega} \sqrt{\frac{g}{H_{\mathrm{IG}}}} \]

where:

  • \( h_x \) is the nearshore bed slope,
  • \( \omega \) is the angular frequency of the infragravity wave \((\omega = 2\pi / T_{\mathrm{IG}})\),
  • \( g \) is gravitational acceleration, and
  • \( H_{\mathrm{IG}} \) is the significant height of the infragravity wave near the shore.

This parameter characterises the balance between wave steepness and frequency in the IG band and serves as a control on whether IG waves are mostly dissipated or reflected. To estimate the reflection coefficient \( R \), Li et al. applied a simplified linear relation: \[ R = 0.5 \cdot \beta_H \] Using this, they evaluated two different wave scenarios: one with a 10-second carrier wave period and another with a 25-second period. The results were striking. For the 25-second case, they found \( R = 0.79 \), meaning the IG waves were highly reflective with minimal dissipation. In the 10-second case, \( R = 0.42 \), indicating that most IG energy dissipated before reflection.

This contrast explains a key observation: during the 16 January 2016 event, DART sensors offshore detected stronger reflected IG waves than incoming ones. The implication is that the long-period swell generated bound IG waves that shoaled with low dissipation and high reflectivity, sustaining powerful oscillations in the coastal zone. This mechanism helps explain how extreme runup can occur in mild slope environments without any tsunami or strong weather trigger.

Predictive method?

Yes. They propose a metric using negative spectral moments:

\[ \frac{\sqrt{m_{-4}}}{\mathrm{mean}\left( \sqrt{m_{-4}} \right)} \]

This ratio correlates well with extreme coastal water level variability. It offers a simple, operationally feasible way to identify high-risk IG events based on offshore buoy data. Physically, this simple expression gives enormous weight to low-frequency energy in the wave spectrum. By focusing on the negative spectral moments, it becomes highly sensitive to the presence of anomalous infragravity (IG) energy. It's essentially a low-frequency magnifying glass — perfect for flagging subtle but dangerous wave group dynamics that traditional bulk parameters might miss.

Although Li et al. (2023) did not define a fixed universal threshold, they observed that during the extreme runup events of 16 January 2016 and 18 January 2018, this ratio reached values as high as 2.5 to 3.0 times above the long-term mean. These spikes stood out clearly in the dataset, indicating a strong low-frequency anomaly consistent with elevated infragravity energy near the coast. In practical terms, this suggests that values above ~2.5× the mean may serve as a useful dynamic threshold, tailored to each location's background conditions. That said, a personal concern remains: while the metric is conceptually powerful, most spectral wave models (such as WAVEWATCH III) still struggle to represent the low-frequency tail accurately. Although newer versions include infragravity parameterisations, they are computationally costly and not yet widely operational. This makes real-time implementation challenging — especially in places without high-resolution buoy data.

What does this change?

  • Extreme runup doesn’t need earthquakes – just long-period swell and the right slope
  • Relevant for Chile, California, Japan, New Zealand – all coastal regions exposed to long-period Pacific swells
  • IG waves need to be taken seriously in design and coastal hazard models
  • Seasonality matters: winter = larger waves with longer periods = higher IG potential

Coastal coffee takeaway

This isn’t just a paper – it’s a call to rethink how we anticipate and model extreme runup. The sea doesn’t have to roar to strike; sometimes it just hums in long low tones… and then climbs the beach further than you thought possible.

Beautifully combining nonlinear wave theory, spectral analysis and field data, this paper adds a new tool to the coastal engineer’s toolbox – and reminds us to watch the quiet ones.

Full reference

Li, C., Özkan-Haller, H. T., García Medina, G., Holman, R. A., Ruggiero, P., Jensen, T. M., Elson, D. B., & Schneider, W. R. (2023). 
Observations of extreme wave runup events on the US Pacific Northwest coast. 
Natural Hazards and Earth System Sciences, 23, 107–126. https://doi.org/10.5194/nhess-23-107-2023

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