Table 1 Model parameters, control parameters and average barrier elevation for VBI

Barrier island	\(\overline{{h}_{0}}\)	\(\frac{{\sigma }_{{h}_{0}}}{\overline{{h}_{0}}}\)	\(\overline{H}\)	\(\frac{{\sigma }_{H}}{\overline{H}}\)	G_d	\({\overline{T}}_{d}\)	λ_r	\(\overline{S}\)	\({\lambda }_{0}^{+}\)	\({\overline{S}}^{+}\)	\({\overline{h}}_{{{{\rm{meas}}}}}\)	\({\overline{h}}_{{{{\rm{pred}}}}}\)
N. Met	0.32	0.32	2.1	0.17	0.17	10.5	18	0.3	61	0.18	0.39	0.35
Smith	0.42	0.52	2.1	0.17	0.19	8.8	18	0.3	39	0.18	0.61	0.55
Cedar	0.38	0.26	2.1	0.17	0.27	6.4	18	0.3	32	0.17	0.58	0.73
Parr.	0.47	0.42	1.3	0.22	0.36	2.3	18	0.3	8.7	0.36	0.84	0.71
S. Met	0.75	0.60	1.9	0.42	0.34	3.4	18	0.3	5.0	0.26	2.10	1.84
Hog	1.30	0.21	2.1	0.17	0.22	3.6	18	0.3	0.9	0.37	1.92	2.07

Estimated model parameters: mean \(\overline{{h}_{0}}\) (m) and rescaled standard deviation \({\sigma }_{{h}_{0}}/\overline{{h}_{0}}\) of the base elevation, mean \(\overline{H}\) (m) and rescaled standard deviation \({\sigma }_{H}/\overline{H}\) of the maximum dune height, maximum dune growth rate G_d (m yr⁻¹), mean dune formation time in the absence of dune erosion \(\overline{{T}_{{\rm {d}}}}(yr)=(\overline{H}-\overline{{h}_{0}})/{G}_{{\rm {d}}}\), mean frequency λ_r (yr⁻¹) and size \(\overline{S}\) (m) of HWEs overtopping the reference beach elevation. Control parameters \({\lambda }_{0}^{+}\) and \({\overline{S}}^{+}\) (Eqs. (4) and (5)). Measured and predicted mean barrier elevation (m), \({\overline{h}}_{{{{\rm{meas}}}}}\) and \({\overline{h}}_{{{{\rm{pred}}}}}\) respectively.

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