Figure 3 . Quantitative assessment of the beach-face slope
estimation technique. a) 1:1 plot illustrating the comparison
between in situ measurements of the beach-face slope (x-axis) and
satellite-derived estimates (y-axis) at the eight test sites (total of
39 cross-shore transects). The horizontal bars represent one standard
deviation from the average in situ slope and indicate the degree
of temporal variability in beach-face slope at each transect.b) Synthetic analysis showing that the accuracy of the method
declines with decreasing tidal range to beach-face slope ratio TR/tanβ.
The orange contours represent the Normalised Mean Absolute Error (NMSE)
for each combination of tidal range and beach-face slope based on 100
synthetic shoreline time-series (described in Supporting Information
S4). The two black dashed lines indicate respectively a ratio of tidal
range to beach-face slope of 10 and 20. The dots indicate the tidal
range and average beach-face slope at each of the eight test sites.
4 Regional-scale application: Eastern Australia and California USA
coastlines
To demonstrate how this technique can be applied over large spatial
scales, an example application at the regional scale along two stretches
of coastline is presented here: the Eastern Australian coastline
(~1800 km) and the California USA coast
(~1500km). The methodology described in Section 2 was
applied at 100 m alongshore-spaced intervals at sandy beaches along both
coasts; in Eastern Australia this resulted in a total of 13,624
beach-face slope estimates; in California 8,147. The results are shown
in Figures 4a and 4b and the complete dataset is available as an
interactive web dashboard in the Data Availability section below. The
regional-scale distributions of beach-face slopes are depicted in Figure
4c. In both Eastern Australia and California approximately 80% of
time-averaged slopes are between 0.04 and 0.08, with the corresponding
means of 0.062 (SE Australia) and 0.068 (California).
As a pointer to where the new availability of broad-scale beach slope
information may find further application, an empirical relationship
between beach-face slope and sediment size D50 was
recently derived by Bujan et al. (2019) based on 2,144 individual field
measurements. This equation can now be employed along the Eastern
Australian and Californian coastlines to convert the beach-face slope
estimates to the equivalent grain size (D50) and obtain
an estimate of the distribution of sediment grain sizes for beaches
occurring along the full extent of both regions (see inset in Figure
4c). The detailed analyses of beach-face slope and sediment size
distributions at regional scales are outside the scope of this letter,
but this example demonstrates the significant potential of this
technique to provide beach-face slope estimates as well as sediment size
distributions at the global scale.