Natural Hazards

, Volume 80, Issue 1, pp 103–125 | Cite as

Simulation of the January 2014 flood on the Secchia River using a fast and high-resolution 2D parallel shallow-water numerical scheme

  • Renato Vacondio
  • Francesca Aureli
  • Alessia Ferrari
  • Paolo Mignosa
  • Alessandro Dal Palù
Original Paper


The capability of a GPU-parallelized numerical scheme to produce accurate and fast simulations of floodings induced by levee breaches in large domains, adopting high-resolution digital terrain maps, is investigated. The good predictive skills of the presented 2D shallow-water model were proven with regard to the inundation caused by a levee breach that occurred on the Secchia River, Italy, in January 2014. The numerical computations were carried out on a domain of about 180 km2 adopting a Cartesian grid of approximately 7.2 M cells with size 5 m. The results of the simulation were validated against several field data and observations, including a high-resolution synthetic aperture radar image. A ratio of simulation to physical times of about 1/15 was achieved; this kind of simulation tool opens up new perspectives in the devising and implementing of flood event management strategies for civil protection purposes and with the aim of minimizing the economic loss.


Flood Shallow water Levee breach Flood hazard 



Interregional Agency for the Po River (AIPo) and personnel directly involved in the management of the emergency are gratefully acknowledged for providing a large amount of field data and observations. We acknowledge the CINECA Award P-FLOOD2-HP10CHAL0S, 2014, under the ISCRA initiative for the availability of high-performance computing resources and support. Luigi Romenghi is gratefully acknowledged for shooting and providing the aerial views of the flooding. The authors are grateful to the editor and the anonymous reviewers for the valuable suggestions and constructive comments on the early version of this manuscript.


  1. Aureli F, Mignosa P (2004) Flooding scenarios due to levee breaking in the Po River. In: Proceedings of the ICE—water management, vol 157(1), 1 Mar 2004Google Scholar
  2. Aureli F, Mignosa P, Ziveri C, Maranzoni A (2006) Fully-2D and quasi-2D modeling of flooding scenarios due to embankment failure. In: International conference on fluvial hydraulics—river flow 2006, Lisbon, 6 Sept 2006 through 8 Sept 2006Google Scholar
  3. Aureli F, Maranzoni A, Mignosa P, Ziveri C (2008) A weighted surface-depth gradient method for the numerical integration of the 2d shallow water equations with topography. Adv Water Resour 31:962–974CrossRefGoogle Scholar
  4. Bates P, De Roo APJ (2000) A simple raster-based model for flood inundation simulation. J Hydrol 236:54–77CrossRefGoogle Scholar
  5. Bladé E, Gómez-Valentin M, Dolz J, Aragón-Hernández JL, Corestein G, Sánchez-Juny M (2012) Integration of 1D and 2D finite volume schemes for computations of water flow in natural channels. Adv Water Resour 42:17–29CrossRefGoogle Scholar
  6. Brodtkorb AR, Saetra ML, Altinakar M (2012) Efficient shallow water simulations on GPUs: implementation, visualization, verification, and validation. Comput Fluids 55:1–12CrossRefGoogle Scholar
  7. Caleffi V, Valiani A, Zanni A (2003) Finite volume method for simulating extreme flood events in natural channels. J Hydraul Res 41:167–177CrossRefGoogle Scholar
  8. Crossley A, Lamb R, Waller S (2010) Fast solution of the Shallow Water Equations using GPU technology. In: Proceedings of the British hydrological society 3rd international symposium, Newcastle, 13–19 July 2010Google Scholar
  9. De la Asunción M, Castro MJ, Fernández-Nieto E, Mantas JM, Acosta SO, González-Vida JM (2013) Efficient GPU implementation of a two waves TVD-WAF method for the two-dimensional one layer shallow water system on structured meshes. Comput Fluids 80(2013):441–452CrossRefGoogle Scholar
  10. Di Baldassarre G, Uhlenbrook S (2012) Is the current flood of data enough? A treatise on research needs for the improvement of flood modelling. Hydrol Process 26:153–158. doi: 10.1002/hyp.8226 CrossRefGoogle Scholar
  11. Di Baldassarre G, Castellarin A, Brath A (2009) Analysis of the effects of levee heightening on flood propagation: example of the River Po, Italy. Hydrol Sci J 54(6):1007–1017CrossRefGoogle Scholar
  12. Domeneghetti A, Vorogushyn S, Castellarin A, Merz B, Brath A (2013) Probabilistic flood hazard mapping: effects of uncertain boundary conditions. Hydrol Earth Syst Sci 17(8):3127–3140CrossRefGoogle Scholar
  13. Dottori F, Di Baldassarre G, Todini E (2013) Detailed data is welcome, but with a pinch of salt: accuracy, precision, and uncertainty in flood inundation modeling. Water Resour Res 49:6079–6085. doi: 10.1002/wrcr.20406 CrossRefGoogle Scholar
  14. Gallegos HA, Schubert JE, Sanders BF (2009) Two-dimensional, high-resolution modeling of urban dam-break flooding: a case study of Baldwin Hills, California. Adv Water Resour 32(8):1323–1335, ISSN 0309-1708.
  15. Gejadze IYu, Monnier J (2007) On a 2D’zoom’ for the 1D shallow water model: coupling and data assimilation. Comput Methods Appl Mech Eng 196:4628–4643CrossRefGoogle Scholar
  16. Hallegatte S, Green C, Nicholls RJ, Corfee-Morlot J (2013) Future flood losses in major coastal cities. Nat Clim Change 3:802–806CrossRefGoogle Scholar
  17. Horritt MS, Bates PD (2002) Evaluation of 1D and 2D numerical models for predicting river flood inundation. J Hydrol 268(1–4):87–99CrossRefGoogle Scholar
  18. Jongman B, Hochrainer-Stigler S, Feyen L, Aerts JCJH, Mechler R, Botzen WJW, Bouwer LM, Pflug G, Rojas R, Ward PJ (2014) Increasing stress on disaster-risk finance due to large floods. Nat Clim Change 4:264–268CrossRefGoogle Scholar
  19. Kurganov K, Petrova G (2007) A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system. Commun Math Sci 5(1):133–160CrossRefGoogle Scholar
  20. Lacasta A, Morales-Hernández M, Murillo J, García-Navarro P (2014) An optimized GPU implementation of a 2D free surface simulation model on unstructured meshes. Adv Eng Softw 78:1–15. doi: 10.1016/j.advengsoft.2014.08.007 CrossRefGoogle Scholar
  21. Lacasta A, Juez C, Murillo J, García-Navarro P (2015) An efficient solution for hazardous geophysical flows simulation using GPUs. Comput Geosci 78:63–72. doi: 10.1016/j.cageo.2015.02.010 CrossRefGoogle Scholar
  22. Leskens G, Brugnach M, Hoekstra AY, Schuurmans W (2014) Why are decisions in flood disaster management so poorly supported by information from flood models? Environ Model Softw 53:53–61CrossRefGoogle Scholar
  23. Liang Q, Borthwick AGL (2009) Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography. Comput Fluids 38:221–234CrossRefGoogle Scholar
  24. Macchione F (2008) Model for predicting floods due to earthen dam breaching. I: formulation and evaluation. J Hydraul Eng 134:1688–1696CrossRefGoogle Scholar
  25. Macchione F, Rino A (2008) Model for predicting floods due to earthen dam breaching. II: comparison with other methods and predictive use. J Hydraul Eng 134:1697–1707CrossRefGoogle Scholar
  26. Marks K, Bates P (2000) Integration of high-resolution topographic data with floodplain flow models. Hydrol Process 14:2109–2122. doi: 10.1002/1099-1085 CrossRefGoogle Scholar
  27. Masoero A, Claps P, Asselman NEM, Mosselman E, Di Baldassarre G (2013) Reconstruction and analysis of the Po River inundation of 1951. Hydrol Process 27:1341–1348CrossRefGoogle Scholar
  28. Mason DC, Schumann GJP, Neal JC, Garcia-Pintado J, Bates PD (2012a) Automatic near real-time selection of flood water levels from high resolution synthetic Aperture Radar images for assimilation into hydraulic models: a case study. Remote Sens Environ 124:705–716CrossRefGoogle Scholar
  29. Mason DC, Davenport IJ, Neal JC, Schumann GJP, Bates PD (2012b) Near real-time flood detection in urban and rural areas using high-resolution Synthetic Aperture Radar images. IEEE Trans Geosci Remote Sens 50(8):3041–3052CrossRefGoogle Scholar
  30. Mazzoleni M, Bacchi B, Barontini S, Di Baldassarre G, Pilotti M, Ranzi R (2014) Flooding hazard mapping in floodplain areas affected by piping breaches in the Po River, Italy. J Hydrol Eng 19(4):717–731CrossRefGoogle Scholar
  31. Morales-Hernández M, García-Navarro P, Burguete J, Brufau P (2013) A conservative strategy to couple 1D and 2D models for shallow water flow simulation. Comput Fluids 81:26–44CrossRefGoogle Scholar
  32. Morales-Hernández M, Lacasta A, Murillo J, Brufau P, García-Navarro P (2014) A Comparative study of accuracy and performance between a fully 2D GPU based and a 1D-2D coupled numerical model in a real river. In: Proceedings of international conference on hydroinformatics, HIC, 2014, New York CityGoogle Scholar
  33. Murillo J, García-Navarro P (2010) Weak solutions for partial differential equations with source terms: application to the shallow water equations. J Comput Phys 229(11):4327–4368. doi: 10.1016/ CrossRefGoogle Scholar
  34. Murillo J, García-Navarro P (2012) Augmented versions of the HLL and HLLC Riemann solvers including source terms in one and two dimensions for shallow flow applications. J Comput Phys 231(20):6861–6906. doi: 10.1016/ CrossRefGoogle Scholar
  35. Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I—a discussion of principles. J Hydrol 10(3):282–290. doi: 10.1016/0022-1694(70)90255-6 CrossRefGoogle Scholar
  36. Rogers BD, Borthwick AGL, Taylor PH (2003) Mathematical balancing of flux gradient and source terms prior to using Roes approximate Riemann solver. J Comput Phys 192:422–451CrossRefGoogle Scholar
  37. Sanders BF, Schubert JE, Detwiler RL (2010) Parbrezo: a parallel, unstructured grid, Godunov-type, shallow-water code for high-resolution flood inundation modeling at the regional scale. Adv Water Resour 33(12):1456–1467, ISSN 0309-1708Google Scholar
  38. Schubert JE, Sanders BF (2012) Building treatments for urban flood inundation models and implications for predictive skill and modeling efficiency. Adv Water Resour 41:49–64. doi: 10.1016/j.advwatres.2012.02.012 CrossRefGoogle Scholar
  39. Schubert JE, Sanders BF, Smith MJ, Wright NG (2008) Unstructured mesh generation and landcover-based resistance for hydrodynamic modeling of urban flooding. Adv Water Resour 31(12):1603–1621CrossRefGoogle Scholar
  40. Schumann GJP, Bates PD, Neal JC, Andreadis KM (2014) Fight floods on a global scale. Nature 507:169CrossRefGoogle Scholar
  41. Smith LS, Liang Q (2013) Towards a generalised GPU/CPU shallow-flow modelling tool. Comput Fluids 88:334–343. doi: 10.1016/j.compfluid.2013.09.018 CrossRefGoogle Scholar
  42. Soares-Frazao S, Lhomme J, Guinot V, Zech Y (2008) Two-dimensional shallow-water model with porosity for urban flood modelling. J Hydraul Res 46(1):45–64CrossRefGoogle Scholar
  43. Toro E (1999a) Shock capturing methods for free surface shallow water flows. Wiley, New YorkGoogle Scholar
  44. Toro E (1999b) Riemann solvers and numerical methods for fluid dynamics. Springer, BerlinCrossRefGoogle Scholar
  45. Vacondio R, Dal Palù A, Mignosa P (2014) GPU-enhanced finite volume shallow water solver for fast flood simulations. Environ Model Softw 57:60–75CrossRefGoogle Scholar
  46. Valiani A, Begnudelli L (2006) Divergence form for bed slope source term in shallow water equations. J Hydraul Eng 132:652–665CrossRefGoogle Scholar
  47. Vázquez-Cendón ME (1999) Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J Comput Phys 148(2):497–526CrossRefGoogle Scholar
  48. Viero DP, D’Alpaos A, Carniello L, Defina A (2013) Mathematical modeling of flooding due to river bank failure. Adv Water Resour 59:82–94CrossRefGoogle Scholar
  49. Zhou J, Causon D, Mingham C, Ingram D (2001) The surface gradient method for the treatment of source terms in the shallow-water equations. J Comput Phys 168:1–25CrossRefGoogle Scholar
  50. Zhu YH, Visser PJ, Vrijling JK (2004) Review on embankment dam breach modeling. Taylor and Francis Group, London, pp 1189–1196Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Renato Vacondio
    • 1
  • Francesca Aureli
    • 1
  • Alessia Ferrari
    • 1
  • Paolo Mignosa
    • 1
  • Alessandro Dal Palù
    • 2
  1. 1.Department of Civil and Environmental Engineering and ArchitectureUniversity of ParmaParmaItaly
  2. 2.Department of Mathematics and Computer ScienceUniversity of ParmaParmaItaly

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