The Influence of Dune Aspect Ratio, Beach Width and Storm Characteristics on Dune Erosion for Managed and Unmanaged Beaches

Dune height is an important predictor of dune impact during a storm event given that taller dunes have a lower likelihood of being overtopped. However, the temporal dominance of the wave collision regime, wherein significant volume loss (erosion) from the dune will occur through dune retreat without the dune being overtopped, 15 suggests that dune width must also be considered when evaluating the vulnerability of dunes to erosion. We use XBeach, a numerical model that simulates hydrodynamic processes, sediment transport, and morphologic change during a storm, to analyze dune erosion as a function of dune aspect ratio (i.e., dune height versus dune width) for storms of varying intensity and duration. We find that low aspect ratio (low and wide) dunes lose less volume than high aspect ratio (tall and narrow) dunes during longer storms, especially if they are fronted by a narrow beach. During 20 more intense storms, low aspect ratio dunes experience greater erosion as they are more easily overtopped than high aspect ratio dunes. In managed scenarios where sand fences are used to construct a “fenced” dune seaward of the existing “natural” dune, we find that the fenced dune effectively prevents the natural dune behind it from experiencing any volume loss until the fenced dune is sufficiently eroded, reducing the magnitude of erosion of the natural dune by up to 50%. We also find that beach width exerts a significant influence on dune erosion; a wide beach offers the 25 greatest protection from erosion in all circumstances regardless of dune morphology or storm characteristics. These https://doi.org/10.5194/esurf-2020-79 Preprint. Discussion started: 10 November 2020 c © Author(s) 2020. CC BY 4.0 License.

extend the beach profile to the buoy depth of 30.5 m. The height of the reference dune was increased (decreased) in 20% intervals as: where Hf is the post-stretch dune height, Hr is the height of the reference dune, and stretch is a multiple of 20 between -60 and 60. Every increase (decrease) in dune height is paired with a decrease (increase) in dune width such that: 115 where Wf is the post-stretch dune width, Wr is the reference dune width. This method of simultaneously modifying dune height and width allowed for dune volume to be conserved (and therefore essentially held constant across simulations) and resulted in a suite of beach profiles with aspect ratios (i.e., dune height divided by dune width) ranging from 0.02 to 0.27 and dune volumes between 50.6 and 53.5 m 3 /m. 120 We adjusted the position of the dune on the profile to create four different cross-shore configurations: 1) dune toe (Dlow) positions aligned, 2) dune crest (Dhigh) positions aligned, 3) dune heel (Dheel) positions aligned, and 4) dune toe (Dlow) positions aligned with a sand-fenced dune seaward of it (Figure 2A-D). Simulations with the Dlow position aligned ensured that all dunes share the same beach morphology, thereby controlling for the effects of beach slope on wave runup (i.e., Stockdon et al., 2006). Simulations with the Dhigh positions aligned may be more representative of a 125 more natural setting in which wider beaches are backed by taller dunes. Simulations with Dheel positions aligned may be more representative of a managed shoreline, where the dunes are widened seaward and thus share a common heel position regardless of dune height. In both the Dhigh and Dheel aligned scenarios, the beach width increases proportionally to the aspect ratio of the dune. The fourth configuration ( Figure 2D) represents a dune complex that arises when sand fences are placed on managed shorelines. The fenced profiles consist of the dune profiles in which 130 the Dlow position was aligned ( Figure 2A) and the addition of a gaussian curve on the seaward side of the dune to represent a typical fenced dune shape (Itzkin et al., 2020).
To demonstrate that the synthetic dunes are consistent with observed morphologies, and that it is reasonable to hold the volume constant for a dune while modifying its aspect ratio, we compared the aspect ratios and volumes of the synthetic dune profiles with those of LiDAR-derived dune profiles from Bogue Banks measured between 1997 135 and 2016 ( Figure 3). The aspect ratios of dunes on Bogue Banks range up to approximately 1.08 and 89.4% of all profiles fall within the range of aspect ratios of our synthetic profiles. While all of the lidar data is extracted in locations where dunes are present, the lowest aspect ratios explored in this study are essentially flat, representing conditions in https://doi.org/10.5194/esurf-2020-79 Preprint. Discussion started: 10 November 2020 c Author(s) 2020. CC BY 4.0 License. which a dune is absent. Dune volumes on Bogue Banks range up to 350 m 3 /m with the modelled value representing the 80 th percentile. Given the relatively weak relationship between dune volume and dune aspect ratio (with the aspect 140 ratios used in this study having a wide range of associated volumes; Figure 3), maintaining a relatively constant dune volume while varying the dune aspect ratio in our model simulations is reasonable.

Synthetic Storm Hydrographs
We created a set of synthetic storms for use in the model simulations by using Hurricane Matthew as a reference storm and then increasing its duration by up to 48 hours ( Figure 4). Hurricane Matthew moved northward 145 along the North Carolina coast on the afternoon of October 8, 2016, generating approximately 1 m of storm surge and significant wave heights (Hs) of approximately. 7.5 m. To capture the full spin up, peak, and relaxation of the storm, we used wave (Hs, Tp, Direction) and tide data for October 7-10, 2016, from the nearest NOAA National Data Buoy Center (NDBC) buoy (41159; Onslow Bay, NC; depth = 30.5 m) and NOAA tide gauge (Station CLKN7; Beaufort, NC). We used linear wave theory to transform the wave parameters to the 30.5 m depth contour to account for shoaling 150 and refraction with the transformed wave data used as input for XBeach.
To represent a longer duration storm than the base storm, we used the Hurricane Matthew storm time series to identify a 12-hour window centered on the timing of peak storm surge. We then interpolated all hydrodynamics (i.e., Hs, Tp, direction, and SWL) within this temporal window onto a +12hr, +18hr, +24hr, +36hr, and +48hr temporal "grid," effectively increasing the storm's duration by up to two days. We held constant the spin up (rising hydrograph) 155 and relaxation (falling hydrograph) of the storm for all simulations. For all storm durations, we created a version in which the surge is unmodified (1.0x), decreased by 50% (0.5x), and increased by 50% (1.5x). In total, this yielded 18 different synthetic storms (Figure 4).
The duration of our synthetic storms varied from 73 hr to 122 hr, and the surge in our synthetic storms varied from ~0.5 m to ~1.25 m. This compares favorably to other storms that have recently affected the North Carolina coast, 160 including Tropical Storm Joaquin (duration ~144 hours) and Hurricane Florence (Duration ~48 hours) ( Figure 5).
Water levels during Tropical Storm Joaquin were elevated for 6 days, which is comparable to the total duration of the +48 hr storm time series. Peak surge during Hurricane Florence was ~1.6 m, a similar order of magnitude to the maximum storm surge we used in the synthetic time series.

Foredune Erosion Simulations 165
https://doi.org/10.5194/esurf-2020-79 Preprint. Discussion started: 10 November 2020 c Author(s) 2020. CC BY 4.0 License. dunes were only inundated during the longest, most-intense storms ( Figure 7L). Overall, the trends in erosion from fenced scenarios showed a systematic decline in erosion of up to 50% compared to the unfenced scenarios.
In addition to sand volume lost from the dune, we calculated the overwash volume as the difference in sand volume behind the dune after the storm. Differences in overwash volume between the fenced and unfenced scenarios are only relevant when overwash/inundation are experienced. Thus, under low storm intensity scenarios, overwash 225 volume is zero. For moderate intensity storms, only the unfenced natural dunes experienced inundation, resulting in a positive difference in overwash volume between the fenced and unfenced simulations ( Figure 8A). For the most intense storms up to ~50 m 3 /m more overwash volume is experienced by the dunes without fences ( Figure 8B).

Beach Width Effects on Dune Erosion
Given that wave runup and erosion during a storm is lower for wider, more gently sloping beaches (i.e., 230 Ruggiero, Holman, & Beach, 2004;Stockdon et al., 2006;Straub et al., 2020), we were interested in analyzing the separate effects of beach width on dune erosion (Figure 9). In particular, for dunes in which dune toes are aligned, beach width would be held constant for all aspect ratios and thus would not affect the outcome for erosion. However, because crest and heel aligned dunes can vary in their beach morphology depending on aspect ratio, this difference leads to wider beaches and might explain decreased erosion for high aspect ratio dunes. We also note that because the 235 dune toe elevation is consistent across simulations, the beach width is inversely related to the beach slope in our simulations.
In all the simulations, regardless of dune configuration, there was a significant decrease in the amount of erosion as the width of the beach increased (Figure 9). For example, for any given beach width, the dune volume loss was similar in both the crests-aligned and heels-aligned scenarios despite the variability in dune morphology. 240 Additionally, the sensitivity of the dune to decreases in storm duration was inversely proportional to the beach width such that dunes fronted by wide beaches were noticeably less sensitive to increases in storm duration than dunes fronted by narrow beaches (Figure 9). This same trend was observed when analyzing increases in storm intensity; the increase in dune volume loss as surge elevation increased is much less in the cases of wider beaches (Figure 9). All of the dunes that were completely inundated (Figure 7) were fronted by narrow beaches during long, intense storms 245 ( Figure 9).