Wave Runup

Sandy coastal systems are highly dynamic and under the combined forces of waves, winds, currents, and water levels are prone to many hazards that threaten valuable ecological, recreational, and commercial resources. Coastal erosion and backshore flooding, two primary hazards to these regions, are both largely governed by local extreme total water levels (TWL) which are defined as the combination of mean sea level, tides, non-tidal residuals including storm surge, and wave runup. The magnitudes of the various components of the TWL are influenced by atmospheric conditions (e.g., pressure, wind), oceanic parameters (e.g., wave height), and coastal morphology (e.g., beach slope). In some settings, such as the US West Coast, the wave-induced components of TWL typically dominate the overall TWL signal, particularly during extreme high water events. The wave induced portion of the TWL, runup, consists of two distinct components. Wave setup is the increase in mean water level due to gradients in radiation stresses whereas swash is the time-varying variance around the setup.

Traditionally, empirical metrics have been widely adopted by scientists and management agencies to predict the wave induced components of TWL. However, recent studies have recognized limitations in applying these empirically based formulae where complex morphologies, such as sandbars, are prevalent (e.g., Cox et al., 2013; Stephens et al., 2011). In many locations throughout the world, including Japan, the Netherlands, and the US, a systematic trend of interannual net offshore sandbar migration(NOM) has been observed whereby bars form in the inner nearshore, migrate seaward across the surf zone, and eventually decay offshore in cyclic patterns (Walstra et al., 2012). The presence of a sandbar that has migrated offshore could result in breaking occurring far from the shoreline during storm conditions and significantly different surf zone and intertidal hydrodynamics relative to a case with no offshore bar. Therefore the stage of the NOM has implications for the risk of coastal flooding and erosion.

Given the importance of the morphologic profile on nearshore hydrodynamics, I have been applying wave models to explore the variance in water elevations imposed by seasonal and interannual variability in barred beach morphology. Recently I have been focusing in particular on how setup, infragravity swash, and runup vary for select locations in the Columbia River Littoral Cell (OR/WA, USA) based on different stages of the net offshore bar migration cycle. Specifically, I have been applying XBeach (xbeach.org), an open-source, phase-average to investigate these morphodynamic processes.

Here is a video of temporal and spatial variability in the water surface for one of the CRLC profiles as numerically predicted from XBeach:

Here you see waves propagating in to shore and as the wave train reaches the shoreline there is a large uprush on to the dry beach. The runup is simply the furthest extent of the water surface on the beach at a particular cross shore location at any given time. We can easily interrogate the model output to build a time series of the runup, from which we calculate important metrics such as infragravity component of swash and the R2% value.

We can run these type of simulations for a wide range of wave conditions to explore exactly how runup varies under different morphologies and under different wave conditions. As we would expect runup increases with increasing wave height and wave period, as shown in the figure below (for CRLC transect 66 in 2011).2011_R2_2

For a storm wave of 8 m at 12 s (the Pacific Northwest usually sees about 3 such magnitude events per year), there is significant variability in the potential responses at the shoreline:

ts_8M_14SIn fact we find that depending on the sandbar and beach morphology that there is potential variability of ~0.5m in the vertical extent of the water surface for those particular wave conditions. That may not sound like much, but on low sloping beaches such as in the CRLC that could lead to the additional flooding of ~50m of land. During a large storm event that could mean the difference between the dune toe being impacted/eroded or not.

Runup is a pretty important topic for coastal hazards and development. As this work indicates it is clear from a numerical modeling framework that local features of the morphology are critical to accurately assessing the hazard at any given site. Yet there is much more to understand about the feedbacks between morphology and nearshore hydrodynamics. This work is still ongoing in pursuit of more fully synthesizing how we can account for the variability in nearshore morphology on total water levels, especially under extreme storm events.

Check out my International Coastal Symposium (ICS 2014) conference proceedings paper or my poster from the Young Coastal Scientists and Engineers Conference (2014) to find out more:

ICS Paper

YCSEC Poster