Wave setup over a Pacific Island fringing reef

Abstract

[1] Measurements obtained across a shore-attached, fringing reef on the southeast coast of the island of Guam are examined to determine the relationship between incident waves and wave-driven setup during storm and nonstorm conditions. Wave setup on the reef flat correlates well (r > 0.95) and scales near the shore as approximately 35% of the incident root mean square wave height in 8 m water depth. Waves generated by tropical storm Man-Yi result in a 1.3 m setup during the peak of the storm. Predictions based on traditional setup theory (steady state, inviscid cross-shore momentum and depth-limited wave breaking) and an idealized model of localized wave breaking at the fore reef are in agreement with the observations. The reef flat setup is used to estimate a similarity parameter at breaking that is in agreement with observations from a steeply sloping sandy beach. A weak (∼10%) increase in setup is observed across the reef flat during wave events. The inclusion of bottom stress in the cross-shore momentum balance may account for a portion of this signal, but this assessment is inconclusive as the reef flat currents in some cases are in the wrong direction to account for the increase. An independent check of fringing reef setup dynamics is carried out for measurements at the neighboring island of Saipan with good agreement.

Wind and Wave Setup Contributions to Extreme Sea Levels at a Tropical High Island: A Stochastic Cyclone Simulation Study for Apia, Samoa

“…Wave setup tends to be the dominant process, particularly at coastal locations adjacent to shore-parallel reef crests such as the Mulinu'u Peninsula. At such locations, the results presented here closely approximate a number of analytic/empirical solutions of wave setup which assume straight and parallel alongshore topography and wave conditions, e.g., [8,43,44]. In particular, water levels within several hundred meters shoreward of the reef crest fronting the Mulinu'u Peninsula (e.g., the "reef" location) simulated by the wave forcing ensemble are within approximately 10 centimetres of the solution described by Becker et al [44], which is plotted for comparison with model output in Figure 9.…”

“…Ensemble (wave forcing, baseline, and SLR scenarios) significant wave heights (Hs, red) and water levels (WL, blue), along a transect through the "reef" location (shown in Figure 5); offshore is on the left side, landward direction towards the right; topography (Z) is indicated with a black line. The analytic estimate of wave setup described by Vetter et al [8] and Becker et al [44], based on Hs from the Apia model, is plotted with black circles, with the caveat that breaking parameter λb is set to 1.0 (consistent with the Apia model), rather than varying with water level.…”

“…Wave dissipation and subsequent wave setup over reefs have been shown to be sensitive to hydraulic bed roughness (fw) and the wave breaking index (λb), defining the water depth at which waves will break, i.e., Hb = hλb where Hb is breaking wave height, h is water depth. In keeping with a number of studies [8,33,35,36], we implement a spatially-varying fw grid with roughness lengths equivalent to 0.15 m in reef areas and 0.02 in sandy areas [37], and set the λb to 1.0 based on mean fore-reef bottom slope according to the empirical relationship of Raubennheimer [38].…”

“…These contributions have a morphological dependence: storm surge tends to be the dominant contributing factor on wide-shelved continental coastlines, and wave setup is often assumed to contribute less than 10% to the total water level (e.g., [5,6]). Wave setup and run-up, on the other hand, have been shown to be an important contributor to extreme sea levels, particularly along steep-shelved coastlines and narrow fringing reefs that characterize many small islands and atolls, e.g., [6][7][8][9]. In addition, whereas the cyclone-induced storm surge tends to be concentrated in the region of maximum onshore winds close to the cyclone center, wind-waves propagate with little loss of energy over the deep ocean, and so can increase the scale and duration over which damaging coastal impacts occur during a TC event [10].…”

Mapping wave set-up near a complex geometric urban coastline

“…This is perhaps why users of the SWAN model broadly believe that the set-up height is in the range of 10-15 % of the offshore wave height (Filipot and Cheung, 2012;Nayak et al, 2012). On the other hand, in particular conditions, the set-up may reach about 1/3 of the offshore wave height (Vetter et al, 2010), and extreme values of set-up up to 2 m above the offshore water level have been observed being influenced by large storm waves (Heidarzadeh et al, 2009). A subtle but important impact of wave set-up under very rough seas is an increase in the water level at the entrance of wave-dominated inlets or lagoons (Bertin et al, 2009;Irish and Canizares, 2009;Torres-Freyermuth et al, 2012), a process that may considerably enhance the dangers, e.g.…”