Abstract
The evolution and more particularly the erosion of the coasts morphology is an important environmental subject. Both the study of the actual evolution of coasts via digital tools and their modelling for the sake of prediction are necessary. A study of the evolution of a section of the Algerian coastline with a geographical information system shows that erosion is the main factor for the shoreline evolution, in the absence of structures consolidating the beaches. Therefore, a qualitative numerical model of the erosion of a coastline is proposed. It relies on a coupling between a cellular automata sedimentation model and a bi-fluid hydrodynamical model based on the Lattice Boltzmann method. The current model is two-dimensional and simulates a cross-section of a virtual coastline. The virtual coastline exhibits a gradual erosion by the water, whose speed depends on the kind of perturbation applied on the water level.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Aidun CK, Clausen JR (2010) Lattice-Boltzmann method for complex flows. Annu Rev Fluid Mech 42:439–472
Avolio MV, Calidonna CR, Delle Rose M, Di Gregorio S, Lupiano V, Pagliara TM, Sempreviva AM (2012) A cellular automata model for soil erosion by water. In: Proceedings of ACRI 2012, Springer, Berlin, Heidelberg, vol LCNS 7495, pp 273–278
Benzi R, Succi S, Vergassola M (1992) The lattice Boltzmann equation: theory and applications. Phys Rep 222:145–197
Bhatnager P, Gross E, Krook M (1954) A model for collision process in gases. Phys Rev 94:511
Bordins P (2002) SIG: concepts, outils et données. Lavoisier, Cachan
Calidonna CR, Di Gregorio S, Gullace F, Gull D, Lupiano V (2016) Rusica initial implementations: simulation results of sandy shore evolution in Porto Cesareo, Italy. In: AIP conference proceedings, vol 1738(1), pp 480103. doi:10.1063/1.4952339
Chen S, Doolen G (1998) Lattice Boltzmann method for fluid flows. Ann Rev Fluid Mech 30:329–364
Chopard B, Droz M (1998) Lattice-gas cellular automata and lattice Boltzmann models: an introduction. Cambridge University Press, Cambridge
Chopard B, Luthi P, Masselot A, Dupuis A (2002) Cellular automata and lattice Boltzmann techniques: an approach to model and simulate complex systems. Adv Complex Syst 5–2:103–242
Coulthard TJ, Hicks DM, Wiel MJVD (2007) Cellular modelling of river catchments and reaches: advantages, limitations and prospects. Geomorphology 90:192–207
Dagorne A (1970) Remarques préliminaires sur la sédimentation pré-littorale en baie de Bou-Ismail (Ouest Alger). Ann algériens de géographie 7:73–78
D’Ambrosio D, Gregorio SD, Gabriele S, Gaudio R (2001) A cellular automata model for soil erosion by water. Phys Chem Earth Part B Hydrol Oceans Atmos 26(1):33–39
Dearing JA, Richmond N, Plater AJ, Wolf J, Prandle D, Coulthard TJ (2006) Modelling approaches for coastal simulation based on cellular automata: the need and potential. Phil Trans R Soc A 364:1051–1071
Ginzburg I (2005) Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation. Adv Water Resour 28(11):1171–1195
Ginzburg I (2007) Lattice Boltzmann modeling with discontinuous collision components: hydrodynamic and advection–diffusion equations. J Stat Phys 126–1:157–206
Ginzburg I, Steiner K (2003) Lattice Boltzmann model for free-surface flow and its application to filling process in casting. J Comp Phys 185:61–99
Hawick KA (2014) Modelling flood incursion and coastal erosion using cellular automata simulations. In: Proceedings of IASTED international conference on environmental management and engineering, IASTED, Banff, Canada, pp 1–8. URL http://www.hull.ac.uk/php/466990/csi/reports/0007/csi-0007.html
He X, Zou Q (1995) Analysis and boundary condition of the lattice Boltzmann BGK model with two velocities components. Los Alamos preprint, LA-UR-95-2293
Körner C, Pohl T, Rüde U, Thürey N, Hofmann T (2004) Lattice Boltzmann methods with free surfaces and their application in material technology. Technical report, Friedrich-Alexander-Universität Erlangen-Nürnberg—Institüt Fur Informatik (Mathematische Maschinen und Datenverarbeitung)
Körner C, Thies M, Hofmann T, Thürey N, Rüde U (2005) Lattice Boltzmann model for free surface flow for modeling foaming. J Stat Phys 121(1–2):179–196
Lätt J (2007) Hydrodynamic limit of lattice Boltzmann equations. Ph.D. thesis, University of Geneva, Switzerland. URL http://www.unige.ch/cyberdocuments/theses2007/LattJ/meta.html
Lätt J, Chopard B, Malaspinas O, Deville M, Michler A (2008) Straight velocity boundaries in the lattice Boltzmann method. Phys Rev E 77:056703
Luo W (2001) Landsap: a coupled surface and subsurface cellular automata model for landform simulation. Comput Geosci 27:363–367
Marcou O, El Yacoubi S, Chopard B (2006) A bi-fluid lattice Boltzmann model for water flow in an irrigation channel. In: Proceedings of ACRI 2006, Springer, pp 373–382
Marcou O, Chopard B, El Yacoubi S (2007) Modeling of irrigation canals: a comparative study. Int J Mod Phys C 18(4):739–748
Marcou O, Chopard B, El Yacoubi S, Hamroun B, Lefèvre L, Mendes E (2010) A lattice Boltzmann model for the simulation of flows in open channels with applications to flows in a submerged sluice gate. J Irrig Drain Eng 136(12):809–822. URL https://hal.archives-ouvertes.fr/hal-00580892
Marcou O, Chopard B, El Yacoubi S, Hamroun B, Mendes E, Lefèvre L (2013) A lattice Boltzmann model to study sedimentation phenomena in irrigation canals. Commun Comput Phys 13:880–899
Mennad M (2008) Approche des systèmes d’information géographique (SIG) pour l’analyse spatio-temporelle de la pollution marine des eaux côtières. Application à la baie d’Alger. Ph.D. thesis, Université des Sciences et de la Technologie Houari Boumediène
Succi S (2001) The lattice Boltzmann equation, for fluid dynamics and beyond. Oxford University Press, Oxford
Sukop M, Thorne D (2005) Lattice Boltzmann modeling: an introduction for geoscientists and engineers. Springer, Berlin
Wolf-Gladrow DA (2000) Lattice-gas cellular automata and lattice Boltzmann models: an introduction. Lecture notes in mathematics. Springer, Berlin
Yuan L (2008) A soil erosion model based on cellular automata. Int Arch Photogramm Remote Sens Spat Inf Sci 37(B6b):21–26
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Seghir, A., Marcou, O. & El Yacoubi, S. Shoreline evolution: GIS, remote sensing and cellular automata modelling. Nat Comput 17, 569–583 (2018). https://doi.org/10.1007/s11047-017-9638-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11047-017-9638-x