# Influence of water level on wave Transformation over La Saline fringing reef (La Réunion Island, France)

F Floc'H, W Bruch, E Cordier

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F Floc'H, W Bruch, E Cordier. Influence of water level on wave Transformation over La Saline fringing reef (La Réunion Island, France). Coastal Dynamics 2021, Jun 2021, Delft (Virtual Event), Netherlands. hal-04974728

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# Influence of water level on wave Transformation over La Saline fringing reef (La Réunion Island, France)

F. Floc'h¹, W. Bruch², E. Cordier³

1-Geosciences Ocean UMR6538 UBO/IUEM Plouzané, France

2- MIO, UMR 7294, Université de Toulon, France

3- OSU de La Réunion, UMS3365, 97490 Saint-Denis de La Réunion, France

## 1. Introduction

In many cases, coral reefs provide a natural protection against incident waves. It is now widely accepted that reef systems protect the coastline by inducing wave transformation in wave fields reaching the coastline through significant wave energy dissipation in the gravity part of the wave spectrum, induced by breaking at the reef crest and bottom friction over the shallow reef-flat. Combining sea level rise, more intense wave climate and bed roughness decrease would diminish the capacity of coral reef to defend the coastline. In fringing reefs, the lagoons are often narrower and shallower and bounded by the shore, the wave transformation processes are then slightly different than for atolls or barrier reefs having deeper and unbounded lagoons. The fringing reefs are typically divided in three morphological zones: a seaward reef-slope, a reef-flat which has a shallow and rough bottom extending to the coast, and a back-reef that is usually slightly deeper than the reef-flat, mainly made of biodetrital sands, and bounded by a carbonate beach at the shore. The transitional zone between the reef-flat and the external slope is named the reef crest. The wave actions on fringing reef systems have been shown to increase back-reef setup as well as beach wave runup, both contributing to flood risks on land shoreward and coastal erosion. Even in microtidal environment, the water level above the reef crest is supposed to be a key parameter to understand the wave transformation across the reef-flat, influencing the wave dissipation, the transfer to lower frequency waves, and the nearshore water levels (setup and runup).

## 2. Methods

The focus of this study is the La Saline coral reef, located in the West of La Réunion Island (France) in the Indian Ocean. The area is microtidal and frequently exposed to Southern Ocean swell as well as cyclonic events. The objective of this paper is to provide a better understanding of the coastal defense characteristics of the reef system according to Southern Ocean swell events of different magnitudes, and to quantify the influence of offshore water level. Field measurements were carried-out using pressure sensors placed on the reef slope (OFF station) and on the reef flat (MID station) during 53 days from 13-Mar-2017 to 05-May-2017. A numerical model (XBeach) was used for deeper understanding of wave transformation, wave setup and runup.

## 3. Results and discussion

The 53 days mean spectrum (Fig. 1a) confirms the energy transfer from the gravity to the lower frequency bands. The maximum of energy in VLF (Very Low Frequency) band is more than twice the maximum of energy in the IG band, with a large peak of energy at $9.10^{-4}$Hz (~18.5 min). A particularity is the presence of a double peak in the IG band, at 0.0076 Hz and 0.0150 Hz, reflecting possibly harmonic behavior. The long wave peaks at the reef-flat is evidence of wave transformation with the transfer of energy from higher to lower wave frequencies. The gravity waves are almost totally dissipated between the reef slope and the reef flat, except during particularly energetic events (Hs>4 m). In order to evaluate the influence of water level on the gravity wave dissipation over the reef, the analytical model of Lentz et al. (2016) is applied to our dataset considering breaking occurs at reef crest (Fig. 1b). Assuming a breaking ratio $\gamma = 0.55$ and a friction factor $f_w = 0.16$ leads to a good fit with our dataset ($R^2 = 0.98$ and RMSE = 0.5 cm). Even if $f_w$ is close to the lower limit of coral reef friction factor (reported in the literature as [0.1-2] range), the wave dissipation is shown to be strongly influenced by the bed friction due to coral cover in the reef flat. Besides this result demonstrate the reliability of Lentz et al. (2016) analytical model for fringing reef based on a water level including the reef-flat setup.

Over the reef slope, IG and VLF significant wave heights are shown proportional to incident
gravity wave power ($R2$ = 0.93 and 0.78 resp.). Over the reef flat, IG waves are slightly enhanced (by a factor 1.2) and VLF waves are increased by a factor 5. A slight modulation by the water level is observed, responsible for about 1% of the total variability of IG and VLF wave heights in the reef flat. The observed setup in the middle of the reef flat is explained at 97% by the incident wave height. The modulation by the tide is responsible of 10% of the setup variability. After having validated numerical results, the runup is also shown to be modulated by the water level, by 25%. Empirical laws are proposed for setup ($R2$ = 0.97) and runup ($R2$ = 0.93). The setup is maximum for high incident energy and low water level (Fig.1c). The runup is maximum for high incident energy and high water level (Fig.1c). Even if the numerical model reproduces correctly the wave dissipation and IG waves whatever the incident conditions are, the setup is well reproduced for mild conditions but underestimated by 20% during the 4 m-offshore wave height event. In the context of predicted increase of sea water levels in region of La Reunion Island in the near future of about 50 cm in 2100 (Hoegh-Guldberg et al., 2014), our study indicates that for an extreme event of 4 m-wave-height, this means an increase of 50 cm of the mean water level, added to a runup of 1.25 m caused by propagating waves of almost 40 cm inside the reef.

<figure><img src="image_2.png" /><figcaption>Figure 1. a) 53-days mean wave spectrum at reef slope (OFF, blue) and reef flat (MID, red) stations. b) Dissipation at the La Saline fringing reef as compared to the Lentz et al. (2016) dissipation model. c) In-situ and simulated reef setup and runup during 4 m-wave forcing.</figcaption></figure>

## Acknowledgements

This work was supported by Calhyco, RenovRISK, Geosciences Ocean lab (UMR6538), and LabexMER (ANR-10-LABX-19).

## References

S. Lentz, J. Churchill, K. Davis, J. Farrar, J. Pineda, V. Starczak 2016. "The characteristics and dynamics of wave-driven flow across a platform coral reef in the red sea". *Journal of Geophysical Research: Oceans* 121 (2) 1360-1376

Hoegh-Guldberg, O., R. Cai, E.S. Poloczanska, P.G. Brewer, S. Sundby, K. Hilmi, V.J. Fabry, and S. Jung. 2014, The Ocean. In: Climate Change 2014: Impacts, Adaptation, and Vulnerability. Part B: Regional Aspects. Contribution of WGII to the 5th Assessment IPCC Report on Climate Change, Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 1655-1731.