Reply to 'Bistability and the future of barrier islands'

Durán Vinent and Moore reply —

We thank Zinnert et al.¹ for the opportunity to elaborate further on the local nature of the bistability (that is, the tendency for islands to exist in alternate states under a given set of conditions) indicated by our numerical results². Because our model assumes uniform alongshore conditions (that is, does not consider alongshore variability) all of our conclusions apply strictly to the local barrier island elevation. In particular, the bistability of local island elevation is supported by the bimodal distribution of dune elevation along the Virginia Barrier Islands (figure 1e,f in ref. 2). Examples shown in figure 1a–d in ref. 2 correspond to sections of the island in a high or low elevation state, where we use the implicit convention of naming an island high (low) if its average elevation is above (below) the crossover elevation defined in fig. 1f. Although a detailed analysis of the spatial dynamics is beyond the scope of this work, there are two fundamental spatial scales suggested by our model² that are important in determining future barrier island state: the scale of the spatial variation of the vulnerability index (eq. (1) of ref. 2), which is the control parameter that determines whether island elevation is bistable and that quantifies the probability of dune recovery (figures 3e and 4 in ref. 2); and the spatial scale of alongshore variations in extreme water levels that erode dunes and drive a transition from a high to a low state. The stochastic alongshore variation of storm-induced erosion implies that both states can coexist spatially in a bistable system and at different scales, for example, at the scale of individual islands or at the scale of island segments, as observations suggest is the case for the Virginia Barrier Islands. In summary, because alongshore variability in processes and through history may prevent entire islands from existing in the low or high state, our concept of bistability applies most strictly to individual points or local sections of a barrier island.