Incident, infragravity and very low frequency wave motions on an atoll reef platform

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Abstract

Coral reefs are hard structures that front many coasts in tropical and subtropical climates and protect them against wave attack and erosion. Despite reducing incoming wave energy by up to 98%, coral reefs are not a guarantee that mainland or island coasts are safe from being flooded. This was demonstrated by a series of wave-driven flooding events in 2008, that caused widespread damage to infrastructure and freshwater resources at islands in the western Pacific Ocean (e.g. Micronesia, the Marshall Islands, Kiribati, Papua New Guinea and the Solomon Islands). In particular atoll islands were exposed as they are only 2-5m above sea level. Atolls are typically ring shaped and enclose a lagoon in the center. The actual landmass is small and therefore offers little space for rainwater to accumulate under the subsurface and form a fresh water lens. Coastal managers are concerned that future overwash events may get more frequent due to climate change related sea levels rise and thereby cause permanent salinification of the natural fresh water sources. The United States Geological Survey (USGS), the National Oceanographic and Atmospheric Administration (NOAA) and the University of Hawaii jointly initiated an investigation on the processes that are involved in the flooding of atoll islands. Eventually, research aims at the prediction of hazardous flooding events by utilizing computer models. Plenty of nearshore processes have been described for reef systems in general, however, few studies have been devoted to the understanding of wave run-up. For sandy beaches the latter is typically a combination of wave induced set-up, incident short wave and incident infragravity swash. In case of coral reefs the physics behind wave run-up can get far more complex. On reefs with a steep reef face and long shallow flats, strong amplification or even resonance of low frequency harmonics have been observed, both of which are likely to increase surf beat. During a field experiment at the Kwajalein atoll between 3-Nov-2013 and 13-Apr-2014, hydrodynamic data were collected by the USGS to study run-up at a typical atoll reef with a steep fore reef (1:18) and a long horizontal reef flat. In previous research these data have been used to force one dimensional XBeach models and to subsequently validate the model performance with respect to set-up, short and long wave heights and wave run-up on the beach. The models performed well with exception of the reproduced wave run-up that was systematically underestimated. The current study continued on this subject, i.e. investigating wave run-up at Kwajalein atoll. The report was divided into two parts. For the first part, subharmonic wave motions were analyzed using the available field data. For the second part wave run-up was reexamined with one dimensional (non-hydrostatic and surfbeat) XBeach models. More specifically, the purpose of the data analysis was to get a detailed description of the (long) wave hydrodynamics and to find out how major run-up events distinguish themselves from the ordinary situation. Focal points were: Generation mechanism associated with subharmonic motions across the reef site and the amplification of very low frequencies (VLF) on the reef flat. Subsequently, 1D-XBeach modelling plugged in on the open question whether run-up would eventually be predictable by XBeach. Roi-Namur was shown to be sensitive to wave climates with long peak periods, that generally induced strong VLF amplification across the reef flat. Concurrently, fundamental resonant periods were strikingly similar to the most energetic VLFs observed on the inner reef flat. Tidal differences also impacted the combined low frequency (LF) energy inshore as the response was larger during high tide. Instead of bound long wave release, evidence was found that free long waves were generated by a moving breakpoint. This was also confirmed by high values of the relative bedslope parameter. Further investigation of the breakpoint mechanism moreover suggested that the relative effectiveness of generating infragravity (IG) waves varied for different wave conditions, which was explained by changes in the length of the breakpoint excursion. It was found that non-hydrostatic models used in the first Kwajalein study underrated wave induced set-up because the mean sea level (MSL) was imposed 0.5 m too low on the model boundary. Taking this water level offset into account, the performance of XBeach-Surfbeat (XB-SB) was compared to XBeach-Non-hydrostatic (XB-NH). The former captured enough physics to compete with the non-hydrostatic XBeach mode in terms of the representation of wave induced set-up, short wave heights and long wave heights. However, XB-SB fell short on the prediction of run-up, which is a crucial weakness since the models are ultimately meant to estimate just that. Furthermore, two distinct ways of boundary forcing were tried, i.e. with measured spectra or idealized JONSWAP spectra. Bulk LF energy was best reproduced by models that were forced with measured spectra. Onset of idealized JONSWAP spectra introduced erroneously high LF amplitudes at the fore reef. This problem could be improved upon by changing the value of the peak enhancement factor. Run-up heights were well reproduced by non-hydrostatic simulations, in contrast to simulations with XB-SB that underestimated them. It was reasoned that incident short wave swash in XB-NH was key to better run-up predictions. Combining the findings of the data and model analyses it could be concluded that both LF waves as well as nonlinear solitary waves significantly contribute to wave run-up on the beach.

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