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How steep a beach is can dictate the way the beach interacts with the incoming ocean waves and therefore is of paramount importance for coastal scientists and engineers, coastal flood modelers and swim-safety officers. However, despite its importance, it is impractical to obtain reliable estimates of the ‘typical’ beach-face slope along large lengths of sandy coastlines (100’s to 1000’s of km) because of the logistics that would be necessary to visit many sites repeatedly to obtain these measurements. This letter describes a new technique to estimate the beach-face slope in the absence of field observations, relying instead on long-term publicly available satellite observations and a global tide model. This technique is then applied to 1000’s of beaches along the coastlines of Eastern Australia and California in the USA.
1 Introduction
The beach face is the most seaward region of the subaerial beach, where remaining ocean wave energy, following dissipation across the surf zone, is converted to potential energy in the form of wave runup and setup (Stockdon et al., 2006). The steepness of the beach face is closely related to grain size (Bujan et al., 2019), with gravel beaches typically adopting a steeper beach face (tanβ > 0.1) and finer sand beaches a flatter beach face (tanβ ~ 0.01-0.1). It is one of the key parameters controlling the elevation of wave runup and total swash excursion at the shoreline, processes that are of primary concern for assessing coastal inundation hazards along the coastal boundary (Senechal et al., 2011; Stockdon et al., 2007). The beach-face slope is also a useful proxy for surf zone morphology (Harley et al., 2015), which in the absence of difficult-to-obtain surf-zone bathymetric measurements, can inform surf-zone hydrodynamics (Battjes, 1974) such as wave breaker type (i.e., spilling, plunging or surging waves), wave set-up across the surf zone (Stephens et al., 2011), as well as beach swimmer safety (Short et al., 1993).
While the beach-face slope can be readily measured at individual beaches using conventional survey techniques, beach-face slope estimates at large spatial scales (i.e., regional, national or global) has to-date remained a core challenge. More significantly, while in recent decades Airborne Lidar (Stockdon et al., 2002) and UAV-based photogrammetry (Turner et al., 2016a) have considerably increased our ability to collect coastal topographic data over large spatial scales, applying these remote sensing methods across the intertidal profile and swash zone remains a challenge due to episodic submergence by the tide and wave run-up. The absence of large-scale datasets of beach-face slope estimates has been reported as a key limitation in the development of operational coastal inundation forecasting systems at the national scale (e.g., O’Grady et al., 2019) as well as in quantifying the contribution of wave run-up and setup at the shoreline relative to global sea-level-rise (Melet et al., 2018; Vitousek et al., 2017). Notably, these and other studies have attempted to overcome this limitation by assuming a global-constant beach-face slope of tanβ = 0.1 (or slope-independent runup formulations), an approach which has been challenged by peers (e.g., Aucan et al., 2019). In this context, a new method to estimate the typical beach-face slope across large spatial scales is needed.
This letter presents and demonstrates an innovative method to obtain estimates of the beach-face slope across the globe using satellite-derived shorelines. This approach follows recent efforts combining 30 years of satellite-derived shorelines with tidal models to create intertidal digital elevation models at the national scale (Bishop-Taylor et al., 2019a; Tseng et al., 2017). However, whereas these recent approaches obtain an approximation of the intertidal zone by assuming that the intertidal morphology at all coastal locations remains constant over time, this new approach inherently incorporates the highly dynamic nature of the intertidal zone that is observed at many sites worldwide, making it robust to the wide range of coastal environments found globally. To illustrate, Figure 1 highlights the challenges of estimating the beach-face slope at a dynamic beach where, as a result of naturally occurring cross-shore shoreline variability, the intertidal beach profile cannot be simply reconstructed from multiple shoreline observations at different tidal stages. This is due to the significant scatter induced by the dynamic beach profile, necessitating a more robust approach to estimate the beach-face slope.
A rigorous validation is presented of this new technique using both real and synthetic test cases ranging in slope, tidal range and wave energy. The automated method is then applied across 1000’s of beaches along the coastlines of Eastern Australia and California, USA, to determine the distribution of beach-face slopes along these two coastlines located on opposite sides of the Pacific.