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.