[7] To assess whether or not the observed shifts in shoreline response are consistent with the observed changes in Atlantic wave climate, we utilize a numerical model [*Ashton et al*., 2001] to determine the response of a modeled cuspate coastline forced by a changing wave climate. Because the model has been described in detail previously [*Ashton and Murray*, 2006a], we include only critical components here.

#### Model Description

[8] The flux of wave-driven sediment Q_{s} moving parallel to a local shoreline is given by

where *H*_{b} is the breaking-wave height, *φ*_{b} is the breaking wave angle, and *θ* is the local shoreline angle. The parameter *K*_{1} is an empirical constant set to 0.4 m^{1/2}/s [*Ashton et al*., 2001]. Conservation of sediment implies that gradients in this flux of alongshore sediment will alter the position, *η*, of the coastline as

where *D* is the cross-shore depth over which sediment is deposited or eroded, and *x* is the alongshore coordinate. The calculations of shoreline angle are made considering local shoreline orientation.

[9] Waves are forced in the model from a given offshore angle and then refracted across assumed shore parallel contours until a breakpoint has been reached. With complex coastline shapes, protruding portions of shoreline can shadow other shoreline segments from some wave-approach directions. Sediment transport does not occur on shadowed shoreline segments.

[10] Model experiments [*Ashton and Murray*, 2006a] show coastline shape depends primarily on two wave-climate parameters: the proportion of wave influences from “high-angle” waves (those with angles between offshore wave crests and the shoreline greater than approximately 45°) which affects the cross-shore/alongshore aspect ratio of coastline shapes; and the asymmetry (the proportion of wave influences from the left, looking offshore) which affects the asymmetry of coastline shapes. These two parameters combine to define a four-binned depiction of wave climate.

#### Wave Forcing

[11] Since historical records of offshore wave conditions from buoy data are incomplete and do not extend as far back in time as our observations of shoreline change (~30 years vs. ~160 years), we have used wave climates based on data from recent decades to represent historical wave conditions.

[12] We force the model with a wave climate that is derived from wave records for U.S. Army Corps of Engineers Wave Information Study hindcasts (*WIS*, based on 1980 – 1999, wis.usace.army.mil/wis.html, stations 507, 508, and 509). Forcing with any of the *WIS* wave climates results in a large-scale cuspate coastline roughly similar to that found along the Carolina coast (supporting information). Using WIS station data as a starting point, we run a series of simulations, varying the distribution of incoming wave angles, to search for the wave climate that produces a cuspate shoreline in the model that most closely matches the present coastline (Figure 3), (i.e., the “best fit” wave climate).

[13] In the coastline model, a new offshore incident wave angle is chosen every model day from a probability distribution function representing the wave climate. Because the model involves the simplified assumption of wave transformations over shore-parallel contours, the most appropriate location to collect wave data to force the model is at the seaward limit of the shoreface. However, because wave-shadowing effects are important along a complex-shaped coastline, wave data from any single shallow-water location is not representative of wave conditions affecting the whole coastline. On the other hand, wave transformations between the edge of the continental shelf and the seaward limit of the shoreface are not included in model simulations, so that deeper-water WIS stations (e.g., stations 507, 508, and 509), while providing a more representative wave climate, are also not fully appropriate as model input (supporting information). Therefore, although we generate a reference probability distribution for daily incoming wave directions based on WIS data (from station 509, the best of the three deeper-water stations, see supporting information), we then alter that climate to produce the best fit wave climate (supporting information).

[14] In generating the reference distribution, we utilize the WIS hourly records of significant wave height and mean wave direction to generate a probability distribution consisting of four equally spaced wave-angle bins, where angles represent the relative angle between incident waves and the general trend of the coastline along the Carolina coast [*Ashton and Murray*, 2006a]. We weigh the contribution from each wave observation in such a way that the probability of choosing waves from each wave-angle bin corresponds to the relative contribution of waves from those wave angles to alongshore sediment flux [*Ashton and Murray*, 2006b, supporting information].

[15] Previous authors [*Komar and Allan*, 2008] have documented an increase in wave height from wave events that occur in the summer months, especially when filtered for waves above 3 m in height. Specifically, for NOAA buoy 41002 located offshore of Charleston, South Carolina, these authors found that large, summer wave height events, which correspond to hurricanes, are increasing at a rate of 0.054 m/yr. We incorporate this in model forcing by adjusting the probability distributions such that all summer month wave heights above 3 m are increased by 2.7 m (representing application of the trend over 50 years). Based on the directions from which summer waves higher than 3 m approach in the WIS station 509 data, the adjustment in wave height produces an increase of 0.03 in the wave asymmetry and a decrease of 0.02 in the wave highness [*Ashton and Murray*, 2006b] (supporting information). (Using the smaller trend in hurricane wave height observed for the Hatteras Buoy produces qualitatively the same results; supporting information.) We apply the corresponding change to the four probability bins of the best fit wave climate to simulate an increase in hurricane waves (Figure 3a). The wave-angle bins 0 to 90 represent waves approaching from the left, when looking offshore (relative to the overall coastline orientation), and the increase in the wave influences from 0 to 45 degrees shifts the imbalance between influences from left-approaching and right-approaching waves. (The increased waves from the left, or E - NE, are generated by onshore-directed winds on the northern flanks of nearby hurricanes. Note that *Slott et al*. [2006] incorrectly assumed a relative increase in waves from the right in a scenario of increasing hurricane strength; supporting information.)

[16] We then compare the pattern of shoreline erosion and accretion that occurs in response to the altered wave climate with the case in which the model was forced with an unaltered wave climate (Figure 3, and supporting information). Results using the best fit wave climate (Figure 3c) show that the shift in wave climate results in increases in erosion updrift of capes and decreases in erosion downdrift of capes. This response is consistent, in both spatial pattern and magnitude, with the shifts in shoreline-change patterns identified in the observational record of shoreline position. This shift in shoreline-change patterns alters overall coastline shape by increasing the asymmetry of the cuspate form, which is consistent with an increasingly asymmetric wave climate. (Mechanistically, a relative increase in the sediment flux near the cape tip on the updrift side, and a corresponding decrease on the downdrift side, result in increased sediment-flux divergence on the updrift flank and increased sediment-flux convergence on the downdrift flank).