Geometric Constraints on Long-Term Barrier Migration: From Simple to Surprising



Considerations of mass conservation, sediment budgets, and geometry lead to insights regarding how barriers respond to sea-level rise. We begin with relatively simple insights, which facilitate more surprising conclusions as more complicated cases are considered. The simplest case assumes: (1) a constant depth beyond which sediment transport is negligible; (2) a lack of gradients in net long-term alongshore sediment flux that add or remove sediment; (3) shoreface erosion into a substrate that produces sediment which is all sufficiently coarse to remain in the nearshore system; and (4) a spatially uniform slope across which a barrier migrates (i.e., the substrate slope). In this case, the migration trajectory for the barrier shorelines—the ratio between the rates of sea-level rise and landward transgression—parallels the average slope of the barrier and shoreface profile (the surface over which active sediment transport occurs). In the next simplest case, substrates composed partly of fine sediment (which is lost to the nearshore system when the substrate is eroded) cause a reduction of the slope of the migration trajectory, because more landward migration is required for each increment of sea-level rise in this case. Gradients in net alongshore sediment transport also cause adjustments to the migration trajectory (although the adjustment depends on the rate of relative sea-level rise). Analysis shows that even with a gradient in net alongshore sediment transport, in the long term, barrier geometry adjusts until the trajectory parallels the (spatially uniform) slope of the substrate. When a barrier is eroding into material that was deposited in back-barrier bay or marsh environments, surprising results come from considerations of geometry and conservation of mass. In this case, the effects of substrate slope on barrier migration trajectory become indirect and time-lagged. In addition, depending on the relative compositions of marsh and bay deposits, feedbacks tend to either produce a stable bay/marsh width and barrier geometry, or a runaway widening or narrowing of the back-barrier environment. When substrate slope (or alongshore-transport gradients or substrate composition) varies as the barrier migrates landward, numerical investigation is required to determine how the migration trajectory varies with time.


Generalized Bruun Rule Barrier migration Substrate slope Shoreface depth Equilibrium profile Overwash Geometry Barrier evolution Shoreline erosion Numerical modeling Analytical modeling Conservation of mass Barrier response to sea-level rise Barrier migration trajectory Back-barrier depth 



The authors thank Dylan McNamara and Michael Kinsela for helpful reviews and feedback that assisted in improving this manuscript.


  1. Barkwith A, Thomas CW, Limber PW, Ellis MA, Murray AB (2014) Coastal vulnerability of a pinned, soft-cliff coastline. Part I, assessing the natural sensitivity to wave climate. Earth Surf Dyn 2:295–308CrossRefGoogle Scholar
  2. Brenner OT, Moore LJ, Murray AB (2015) The complex influences of back-barrier deposition, substrate slope and underlying stratigraphy in barrier island response to sea-level rise: insights from the Virginia Barrier Islands, Mid-Atlantic Bight, U.S.A. Geomorphology 246:340–350. CrossRefGoogle Scholar
  3. Bruun P (1962) Sea-level rise as a cause of shore erosion. J Waterw Harb Div 88(1):117–132Google Scholar
  4. Cowell PJ, Roy PS, Jones RA (1995) Simulation of large-scale coastal change using a morphological behaviour model. Mar Geol 126(1–4):45–61CrossRefGoogle Scholar
  5. Cowell PJ, Stive MJ, Niedoroda AW, de Vriend HJ, Swift DJ, Kaminsky GM, Capobianco M (2003) The coastal-tract (part 1): a conceptual approach to aggregated modeling of low-order coastal change. J Coast Res 19(4):812–827Google Scholar
  6. Davidson-Arnott RG (2005) Conceptual model of the effects of sea level rise on sandy coasts. J Coast Res 21(6):1166–1172CrossRefGoogle Scholar
  7. Dean RG (1977) Equilibrium beach profiles: US Atlantic and Gulf coasts. Department of Civil Engineering and College of Marine Studies, University of DelawareGoogle Scholar
  8. Dean RG (1991) Equilibrium beach profiles: characteristics and applications. J Coast Res 7(1):53–84Google Scholar
  9. Dean RG, Maurmeyer EM (1983) Models for beach profile response. In: Komar PD (ed) CRC handbook of coastal processes and erosion. CRC Press, Boca Raton, pp 151–165Google Scholar
  10. Donnelly C, Kraus N, Larson M (2006) State of knowledge on measurement and modeling of coastal overwash. J Coast Res 224:965–991CrossRefGoogle Scholar
  11. Duran Vinent O, Moore LJ (2015) Barrier island bistability induced by biophysical interactions. Nat Clim Chang 5(2):158–162CrossRefGoogle Scholar
  12. Fearnley S, Miner MD, Kulp M, Bohling C, Penland S (2009) Hurricane impact and recovery shoreline change analysis of the Chandeleur Islands, Louisiana, USA: 1855–2005. Geo-Mar Lett 29:455–466CrossRefGoogle Scholar
  13. Fredsøe J, Deigaard R (1992) Mechanics of coastal sediment transport, vol 3. World Scientific, SingaporeGoogle Scholar
  14. Hallermeier RJ (1981) A profile zonation for seasonal sand beaches from wave climate. Coast Eng 4:253–277CrossRefGoogle Scholar
  15. Lazarus E, Ashton A, Murray AB, Tebbens S, Burroughs S (2011) Cumulative versus transient shoreline change: dependencies on temporal and spatial scale. J Geophys Res Earth Surf 116(F2):2156–2202. CrossRefGoogle Scholar
  16. Leatherman SP (1979) Migration of Assateague Island, Maryland, by inlet and overwash processes. Geology 7(2):104–107CrossRefGoogle Scholar
  17. Lee GH, Nicholls RJ, Birkemeier WA (1988) Storm-driven variability of the beach-nearshore profile at Duck, North Carolina, USA, 1981–1991. Mar Geol 148(3):163–177Google Scholar
  18. Lorenzo-Trueba J, Ashton AD (2014) Rollover, drowning, and discontinuous retreat: distinct modes of barrier response to sea-level rise arising from a simple morphodynamic model. J Geophys Res Earth Surf 119(4):779–801CrossRefGoogle Scholar
  19. Magliocca NR, McNamara D, Murray AB (2011) Long-term, large-scale effects of artificial dune construction along a barrier island coastline. J Coast Res 27:918–930CrossRefGoogle Scholar
  20. Marani M, D’Alpaos A, Lanzoni S, Carniello L, Rinaldo A (2007) Biologically-controlled multiple equilibria of tidal landforms and the fate of the Venice lagoon. Geophys Res Lett 34:L11402. CrossRefGoogle Scholar
  21. Mariotti G., Fagherazzi S (2010) A numerical model for the coupled long-term evolution of salt marshes and tidal flats. J Geophys Res Earth 115(F1)Google Scholar
  22. McBride RA et al (1992) Analysis of barrier shoreline change in Louisiana from 1853 to 1939. In: Williams SJ et al (eds) Miscellaneous 1-2150-A. U.S. Geological Survey, RestonGoogle Scholar
  23. McNamara, D. E., Werner, B. T. (2008). Coupled barrier island–resort model: 1. Emergent instabilities induced by strong human-landscape interactions. J Geophys Res Earth 113(F1).Google Scholar
  24. Moore LJ, List JH, Williams SJ, Stolper D (2010) Complexities in barrier island response to sea level rise: insights from numerical model experiments, North Carolina Outer Banks. J Geophys Res Earth 115(F3)Google Scholar
  25. Moore LJ, Patsch K, List JH, Williams SJ (2014) The potential for sea-level-rise-induced barrier island loss: insights from the Chandeleur Islands, Louisiana, USA. Mar Geol 355:244–259CrossRefGoogle Scholar
  26. Ortiz AC, Ashton AD (2016) Exploring shoreface dynamics and a mechanistic explanation for a morphodynamic depth of closure. J Geophys Res Earth Surf 121(2):442–464CrossRefGoogle Scholar
  27. Penland S, Sutter JR, Boyd R (1985) Barrier island arcs along abandoned Mississippi River deltas. Mar Geol 63:197–233CrossRefGoogle Scholar
  28. Rogers LJ, Moore LJ, Goldstein EB, Hein CJ, Lorenzo-Trueba J, Ashton AD (2015) Anthropogenic controls on overwash deposition: evidence and consequences. J Geophys Res Earth 120(12):2609–2624CrossRefGoogle Scholar
  29. Rosati JD, Dean RG, Walton TL (2013) The modified Bruun Rule extended for landward transport. Mar Geol 340:71–81CrossRefGoogle Scholar
  30. Roy PS, Cowell PJ, Ferland MA, Thom BG (1994) Wave-dominated coasts. In: Carter RWG, Woodroffe CD (eds) Coastal evolution: late quaternary shoreline morphodynamics. Cambridge University Press, Cambridge, pp 121–186Google Scholar
  31. Sallenger AH Jr (2000) Storm impact scale for barrier islands. J Coast Res 16(3):890–895Google Scholar
  32. Sallenger A, Wright CW, Lillycrop J (2007) Coastal-change impacts during Hurricane Katrina: an overview. In: Kraus N, Rosati JD (eds) Coastal sediments ‘07: proceedings of the sixth international symposium on coastal engineering and science of coastal sediment processes. American Society for Civil Engineers, Reston, pp 888–896CrossRefGoogle Scholar
  33. Stive MJ, De Vriend HJ (1995) Modelling shoreface profile evolution. Mar Geol 126(1–4):235–248CrossRefGoogle Scholar
  34. Stockdon HF, Holman RA, Howd PA, Sallenger AH (2006) Empirical parameterization of setup, swash, and runup. Coast Eng 53(7):573–588CrossRefGoogle Scholar
  35. Stolper D, List JH, Thieler ER (2005) Simulating the evolution of coastal morphology and stratigraphy with a new morphological-behaviour model (GEOMBEST). Mar Geol 218(1–4):17–36CrossRefGoogle Scholar
  36. Storms JE (2003) Event-based stratigraphic simulation of wave-dominated shallow-marine environments. Mar Geol 199(1–2):83–100CrossRefGoogle Scholar
  37. Storms JE, Weltje GJ, Van Dijke JJ, Geel CR, Kroonenberg SB (2002) Process-response modeling of wave-dominated coastal systems: simulating evolution and stratigraphy on geological timescales. J Sediment Res 72(2):226–239CrossRefGoogle Scholar
  38. Valvo LM, Murray AB, Ashton A (2006) How does underlying geology affect coastline change? An initial modeling investigation. J Geophys Res Earth Surf 111(F2):F02025CrossRefGoogle Scholar
  39. Wolinsky MA, Murray AB (2009) A unifying framework for shoreline migration: 2. Application to wave-dominated coasts. J Geophys Res Earth Surf 114(F01009). doi:

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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Division of Earth and Ocean Sciences, Nicholas School of the Environment, Center for Nonlinear and Complex SystemsDuke UniversityDurhamUSA
  2. 2.Department of Geological SciencesUniversity of North Carolina at Chapel HillChapel HillUSA

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