Figure 4 . Regional-scale application over SE Australia and
California. The mean beach-face slope is 0.062 for SE Australia and
0.068 for California, with both regions showing similar spread around
the mean (standard deviations of 0.019 and 0.024 respectively).a) Map of beach-face slopes estimated along 13’624 transects on
the SE Australian coastline. b) Map of beach-face slopes
estimated along 8’147 transects on Californian US west coast.c) Histogram of the distribution of beach-face slopes along the
two stretches of coastline (SE Australia and California). In the
top-right inset the equivalent sediment size distributions are obtained
with the empirical relationship from Bujan et al. (2019). The mean
D50 values are 0.26 and 0.29 mm respectively for SE
Australia and California, with an inter-quartile range (IQR) of 0.09 and
0.16 mm.
5 Conclusions
A novel methodology to estimate beach-face slopes from satellite-derived
shorelines and modelled tides is described here and evaluated along
eight diverse sandy/gravel beaches spanning a broad range of tidal
regimes, beach-face slopes and wave climates. This new technique employs
a variant of the Fourier transform, the Lomb-Scargle transform, to
identify the slope that, when used for tidal correction, minimises the
tidal energy in the shoreline time-series.
A comparison with in situ (beach survey) topographic data along
39 transects demonstrates that this technique is capable of estimating
the time-averaged beach-face slope in different coastal environments
ranging from macrotidal, gentle-sloping beaches, to microtidal
wave-dominated beaches. Further analysis using synthetic shoreline data
reveals that the accuracy of this method declines significantly when the
ratio between tidal range and beach-face slope is < 10.
Finally, an example application spanning a section of the Eastern
Australia and California USA coastlines demonstrates the capability of
this technique to estimate beach-face slopes over large spatial scales,
with the potential to now create and further investigate a global
dataset of beach-face slopes. It is anticipated that the future
availability of such a dataset will be a key variable to support global
studies on the impact of sea level rise and increased storminess along
world coastlines.
Acknowledgments
The authors would like to thank the multiple individuals and
organisations that made available the in situ beach slope data
used for validation in this study: Slapton Sands (UK) beach surveys were
obtained from the Channel Coastal Observatory
(https://www.channelcoast.org); Funding for the routine monitoring
at Narrabeen is provided by Northern Beaches Council, UNSW Research
Infrastructure Scheme, UNSW Faculty of Engineering Early Career Grant,
the NSW Adaptation Research Hub – Coastal Processes Node (Office of
Environment and Heritage), and the Australian Research Council
(LP0455157, LP100200348, DP150101339, LP170100161); Prof. A.D. Short
(Univ. of Sydney) provided the surveyed profiles at Moruya and Pedro
beaches; Chris Daly, Karin Bryan (University of Waikato) and Jennifer
Montano Munoz (Univ. of Auckland) kindly provided the surveyed data for
Tairua beach (New Zealand); Torrey-Pines (California) survey data was
compiled and made publicly available by the Scripps Institution of
Oceanography in Ludka et al. (2019); special thanks to Amaia Ruiz de
Alegria Arzaburu and Jesus Adrian Vidal Ruiz from the Autonomous
University of Baja California who generously shared beach slope data for
Ensenada beach, Mexico; the Duck (North Carolina) data set is maintained
by the U.S. Army Engineer Research & Development Centre, Coast &
Hydraulics Laboratory, Field Research Facility. Finally, FES2014 was
produced by Noveltis, LEGOS and CLS and distributed by AVISO+
(https://www.aviso.altimetry.fr)
with support from CNES (French National Centre for Space Studies). In
particular, the authors wish to acknowledge Frederic Briol for
developing the Python wrapper to FES2014, a fantastic tool for end
users. Thanks also to Sean Vitousek for his insightful comments and
suggestions. The lead author is supported by a UNSW Scientia PhD
scholarship.
Data availability
- The beach-face slope datasets for Eastern Australia and California can
be visualised and downloaded on an interactive web dashboard at
http://coastsat.wrl.unsw.edu.au/.
- The data sets have also been uploaded to the following open-access
Zenodo data repository https://doi.org/10.5281/zenodo.3747130.
- The codes to estimate beach slopes with this technique are available
in a Github repository (https://github.com/kvos/CoastSat.slope)
uploaded to Zenodo with the following DOI:
https://doi.org/10.5281/zenodo.3872443.
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