{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T20:49:28Z","timestamp":1760820568851,"version":"3.40.5"},"reference-count":21,"publisher":"Copernicus GmbH","issue":"10","license":[{"start":{"date-parts":[[2013,10,16]],"date-time":"2013-10-16T00:00:00Z","timestamp":1381881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nat. Hazards Earth Syst. Sci."],"abstract":"<jats:p>Abstract. A distinguishable feature of overland tsunami propagation is the incorporation of solids within the flow column, either sediment from the natural environment or remains from built infrastructure. This article describes a 2DH (two-dimensional horizontal) mathematical model particularly suited for tsunami propagation over complex and dynamic geometries, such as river and estuarine mobile beds. The discretization scheme is based on a finite-volume method using a flux-splitting technique featuring a reviewed Roe\u2013Riemann solver, with appropriate source-term formulations to ensure full conservativeness. The model is validated with laboratory data and paleo-tsunami evidence. As a forecasting application, it is applied to a tsunami scenario in the Tagus estuary, an effort justified by the numerous catastrophic tsunamis that are known to have struck this location over the past two millennia. The obtained results show that, despite the significant differences in Lisbon's layout and morphology, a 1755-like tsunami would still inflict a devastating impact on this major city.\n                    <\/jats:p>","DOI":"10.5194\/nhess-13-2533-2013","type":"journal-article","created":{"date-parts":[[2013,10,16]],"date-time":"2013-10-16T08:06:26Z","timestamp":1381910786000},"page":"2533-2542","source":"Crossref","is-referenced-by-count":5,"title":["A shallow-flow model for the propagation of tsunamis over complex geometries and mobile beds"],"prefix":"10.5194","volume":"13","author":[{"given":"D. A. S.","family":"Conde","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6381-703X","authenticated-orcid":false,"given":"M. A. V.","family":"Baptista","sequence":"additional","affiliation":[]},{"given":"C.","family":"Sousa Oliveira","sequence":"additional","affiliation":[]},{"given":"R. M. L.","family":"Ferreira","sequence":"additional","affiliation":[]}],"member":"3145","published-online":{"date-parts":[[2013,10,16]]},"reference":[{"key":"ref1","unstructured":"Andrade, C., Freitas, M. C., Miranda, J. M., and Baptista, M. A.: Recognizing Possible Tsunami Sediments In The Ultradissipative Environment Of The Tagus Estuary, in: Proceedings of the International Conference on Coastal Sediments 2003, Florida, USA, 18\u201323, 2003."},{"key":"ref2","doi-asserted-by":"crossref","unstructured":"Bagnold, R. A.: An approach to the sediment transport problem from general physics, United States Department of Interior, Geological Survey, Professional Paper 442-I, 1966.","DOI":"10.3133\/pp422I"},{"key":"ref3","doi-asserted-by":"crossref","unstructured":"Baptista, M. A. and Miranda, J. M.: Revision of the Portuguese catalog of tsunamis, Nat. Hazards Earth Syst. Sci., 9, 25\u201342, https:\/\/doi.org\/10.5194\/nhess-9-25-2009, 2009.","DOI":"10.5194\/nhess-9-25-2009"},{"key":"ref4","doi-asserted-by":"crossref","unstructured":"Baptista, M. A., Miranda, J. M., Omira, R., and Antunes, C.: Potential inundation of Lisbon downtown by a 1755-like tsunami, Nat. Hazards Earth Syst. Sci., 11, 3319\u20133326, https:\/\/doi.org\/10.5194\/nhess-11-3319-2011, 2011.","DOI":"10.5194\/nhess-11-3319-2011"},{"key":"ref5","doi-asserted-by":"crossref","unstructured":"Canelas, R., Murillo, J., and Ferreira, R. M. L.: Two-dimensional depth-averaged modelling of dam-break flows over mobile beds, J. Hydraul. Res., online first, https:\/\/doi.org\/10.1080\/00221686.2013.798891, 2013.","DOI":"10.1080\/00221686.2013.798891"},{"key":"ref6","unstructured":"Canelas, R. J. F.: 2D Mathematical Modeling of Discontinuous Shallow Sediment-laden Flows, Master's thesis, Instituto Superior Tecnico \u2013 Technical University of Lisbon, Portugal, 2010."},{"key":"ref7","unstructured":"Chapman, S. and Cowling, T. G.: The Mathematical Theory of Non-Uniform Gases, 3rd Edn., Cambridge University Press, Cambridge, UK, 1970."},{"key":"ref8","unstructured":"Conde, D. A. S.: A tsunami in Lisbon. Where to run?, Master's thesis, Instituto Superior Tecnico \u2013 TU Lisbon, Portugal, 2012."},{"key":"ref9","doi-asserted-by":"crossref","unstructured":"Ferreira, R. M., Franca, M. J., Leal, J. G., and Cardoso, A. H.: Mathematical modelling of shallow flows: Closure models drawn from grain-scale mechanics of sediment transport and flow hydrodynamics, Can. J. Civil. Eng., 36, 1604\u20131621, 2009.","DOI":"10.1139\/L09-033"},{"key":"ref10","unstructured":"Ferreira, R. M. L., Leal, J. G., and Cardoso, A. H.: Conceptual model for the bedload layer of gravel bed stream based on laboratory observations, in: River Flow, Balkema, Taylor and Francis Group, 1, 947\u2013956, 2006."},{"key":"ref11","doi-asserted-by":"crossref","unstructured":"Jenkins, J. T. and Richman, M. W.: Plane simple shear of smooth inelastic circular disks: the anisotropy of the second moment in the dilute and dense limits, J. Fluid Mech., 192, 313\u2013328, 1988.","DOI":"10.1017\/S0022112088001879"},{"key":"ref12","doi-asserted-by":"crossref","unstructured":"LeVeque, R.: Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002.","DOI":"10.1017\/CBO9780511791253"},{"key":"ref13","doi-asserted-by":"crossref","unstructured":"Luis, J. F.: Mirone: A multi-purpose tool for exploring grid data, Comput. Geosci., 33, 31\u201341, 2007.","DOI":"10.1016\/j.cageo.2006.05.005"},{"key":"ref14","unstructured":"Meyer-Peter, E. and Muller, R.: Formulas for bedload transport, in: Proceedings of the 2nd Meeting of the International Association for Hydraulic Structures Research, Stockholm, Sweden, Appendix 2, 39\u201364, 1948."},{"key":"ref15","doi-asserted-by":"crossref","unstructured":"Murillo, J. and Garcia-Navarro, P.: Weak solutions for partial differential equations with source terms: application to the shallow water equations, J. Comput. Phys., 229, 4327\u20134368, https:\/\/doi.org\/10.1016\/j.jcp.2010.02.016, 2010.","DOI":"10.1016\/j.jcp.2010.02.016"},{"key":"ref16","doi-asserted-by":"crossref","unstructured":"Pope, S. B.: Turbulent Flows, Cambridge University Press, Cambridge, 2000.","DOI":"10.1017\/CBO9780511840531"},{"key":"ref17","unstructured":"Shi, S. and Smith, D. E.: Coastal Tsunami Geomorphological Impacts And Sedimentation Processes: Case Studies Of Modern And Prehistorical Events, in: Int. Conf. on Estuaries and Coasts, Hangzhou, China, 189\u2013198, 2003."},{"key":"ref18","doi-asserted-by":"crossref","unstructured":"Soares-Frazao, S. and IAHR Working Group for Dam-break flows: Dam-break flows over mobile beds: experiments and benchmark tests for numerical models, J. Hydraulic Res., 50, 364\u2013375, https:\/\/doi.org\/10.1080\/00221686.2012.689682, 2012.","DOI":"10.1080\/00221686.2012.689682"},{"key":"ref19","unstructured":"Stoker, J.: Water Waves: The mathematical theory with applications, Interscience Publishers, New York, USA, 1957."},{"key":"ref20","unstructured":"Toro, E.: Shock-Capturing Methods for Free Surface Shallow Flows, Wiley, New York, USA, 2001."},{"key":"ref21","doi-asserted-by":"crossref","unstructured":"Vazquez-Cendon, M. E.: Improved treatment of source terms in upwind schemes for the shallow water equations with irregular geometry, J. Comput. Phys., 148, 497\u2013526, https:\/\/doi.org\/10.1006\/jcph.1998.6127, 1999.","DOI":"10.1006\/jcph.1998.6127"}],"container-title":["Natural Hazards and Earth System Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/nhess.copernicus.org\/articles\/13\/2533\/2013\/nhess-13-2533-2013.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,24]],"date-time":"2021-01-24T07:19:56Z","timestamp":1611472796000},"score":1,"resource":{"primary":{"URL":"https:\/\/nhess.copernicus.org\/articles\/13\/2533\/2013\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,16]]},"references-count":21,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2013]]}},"URL":"https:\/\/doi.org\/10.5194\/nhess-13-2533-2013","relation":{},"ISSN":["1684-9981"],"issn-type":[{"type":"electronic","value":"1684-9981"}],"subject":[],"published":{"date-parts":[[2013,10,16]]}}}