Alongshore variability in wave runup and inner surfzone wave conditions on an intermediate beach

Abstract

Alongshore and temporal variability in wave runup and inner surfzone wave conditions are investigated on an intermediate beach using lidar-derived elevation transect timeseries. The lidar scanners were deployed at two alongshore locations separated by $\sim$330 m at the U.S. Army Engineer Research and Development Center Field Research Facility in Duck, NC and collected 30 min (41 min) linescan time series at 7.1 Hz (5 Hz) each hour over an 11-day period before, during, and after Hurricane Matthew in October 2016. Runup and water surface-elevation time series at the estimated 0.5-m depth contour were used to determine the extreme runup $R_{2\text{\%}}$, the mean runup and inner surfzone water surface elevation, and the significant runup and inner-surf wave heights across sea-swell, infragravity, and all frequency bands. Offshore wave conditions were determined from an array of pressure gauges located in $\sim$8-m water depth. Results show that the significant wave height in the sea-swell frequency band $H_{SS}$ was intermittently depth-limited in the inner surf zone, with the ratio of significant sea-swell wave height in the inner surf zone to that in about 8-m depth ($H_{SS,ISZ}$/$H_{SS,8m}$) ranging from 0.42 to 1.31 during low-energy conditions and from 0.19 to 0.39 during high-energy conditions. Significant temporal variability in runup parameters was observed over the 11-day period, with $R_{2\text{\%}}$ ranging from 1.07 to 3.07 m at the southern lidar location and from 1.45 to 3.36 m at the northern lidar location. Alongshore differences in $R_{2\text{\%}}$ ranged from 0.00 to 0.90 m, with both $R_{2\text{\%}}$ and the significant swash height $R_{sig}$ typically larger at the northern lidar location. Alongshore variability in most inner surfzone and runup parameters was largest during low-energy offshore wave conditions when the inner surf zone was unsaturated, although this trend was weakest in $R_{2\text{\%}}$. The mean runup elevation $R_{mean}$ above the still water level was only weakly correlated with the wave-driven super-elevation of the water surface in the inner surf zone ($Z_{mean}$, R${}^2$ = 0.23), suggesting that wave-breaking-induced setup is only one factor contributing to $R_{mean}$. Although the significant sea-swell swash height $R_{SS}$ and alongshore differences in $R_{SS}$ were correlated with foreshore beach slope ${\beta }_{foreshore}$ (R${}^2$ = 0.59 and R${}^2$ = 0.70, respectively), $R_{2\text{\%}}$, $R_{mean}$, and alongshore variations thereof were uncorrelated with ${\beta }_{foreshore}$. $R_{2\text{\%}}$ and $R_{mean}$ were correlated with the significant wave height in the inner surf zone $H_{sig,ISZ}$ (R${}^2$ = 0.61 and R${}^2$ = 0.72, respectively), which is strongly influenced by wave dissipation patterns across the surf zone. These results suggest that while ${\beta }_{foreshore}$ affects the magnitude of swash oscillations about the mean, it has a smaller role in the total elevation reached by runup on intermediate beaches. Furthermore, the results illustrate the importance of surfzone bathymetry and the resulting temporal and alongshore variations of inner surfzone wave heights to the extreme and mean runup.