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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.