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
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