How much physical complexity is needed to model flood inundation?

Two-dimensional flood inundation models are widely used tools for flood hazard mapping and an essential component of statutory flood risk management guidelines in many countries. Yet, we still do not know how much physical complexity a flood inundation model needs for a given problem. Here, three two-dimensional explicit hydraulic models, which can be broadly defined as simulating diffusive, inertial or shallow water waves, have been benchmarked using test cases from a recent Environment Agency for England and Wales study, where results from industry models are also available. To ensure consistency, the three models were written in the same code and share subroutines for all but the momentum (flow) and time-stepping calculations. The diffusive type model required much longer simulation times than the other models, whilst the inertia model was the quickest. For flows that vary gradually in time, differences in simulated velocities and depths due to physical complexity were within 10% of the simulations from a range of industry models. Therefore, for flows that vary gradually in time, it appears unnecessary to solve the full two-dimensional shallow water equations. As expected, however, the simpler models were unable to simulate supercritical flows accurately. Finally, implications of the results for future model benchmarking studies are discussed in light of a number of subtle factors that were found to cause significant differences in simulations relative to the choice of model.

[1]  Paul D. Bates,et al.  An adaptive time step solution for raster-based storage cell modelling of floodplain inundation , 2005 .

[2]  B. Sanders.  Evaluation of on-line DEMs for flood inundation modeling , 2007 .

[3]  Paul D. Bates,et al.  A comparison of three parallelisation methods for 2D flood inundation models , 2010, Environ. Model. Softw..

[4]  P. Bates,et al.  Identifiability of distributed floodplain roughness values in flood extent estimation , 2005 .

[5]  B. Sanders,et al.  Unstructured mesh generation and landcover-based resistance for hydrodynamic modeling of urban flooding , 2008 .

[6]  Angelo Leopardi,et al.  Two-dimensional modeling of floods to map risk-prone areas , 2002 .

[7]  Robin K. S. Hankin,et al.  Bayesian calibration of a flood inundation model using spatial data , 2011 .

[8]  R. Lamb,et al.  A fast two-dimensional floodplain inundation model , 2009 .

[9]  C. Sampson,et al.  Benchmarking urban flood models of varying complexity and scale using high resolution terrestrial LiDAR data , 2011 .

[10]  P. Bates,et al.  Predicting floodplain inundation: raster‐based modelling versus the finite‐element approach , 2001 .

[11]  Pilar García-Navarro,et al.  A numerical model for the flooding and drying of irregular domains , 2002 .

[12]  P. Bates,et al.  Benchmarking 2D hydraulic models for urban flooding , 2008 .

[13]  Gareth Pender,et al.  Benchmarking of 2D hydraulic modelling packages , 2010 .

[14]  Sandra Soares Frazao,et al.  Computation of the ‘isolated building test case’ and the ‘model city experiment’ benchmarks , 2003 .

[15]  Heiko Apel,et al.  Flood risk analyses—how detailed do we need to be? , 2009 .

[16]  P. Bates,et al.  Two dimensional diffusion wave modelling of flood inundation using a simplified channel representation , 2004 .

[17]  P. Bates,et al.  A simple raster-based model for flood inundation simulation , 2000 .

[18]  P. Bates,et al.  Distributed whole city water level measurements from the Carlisle 2005 urban flood event and comparison with hydraulic model simulations , 2009 .

[19]  A. Paquier,et al.  Modeling floods in a dense urban area using 2D shallow water equations , 2006 .

[20]  Giuseppe T. Aronica,et al.  2D Multilevel Model for Flood Wave Propagation in Flood-Affected Areas , 1998 .

[21]  Roger Alexander Falconer,et al.  Comparison between TVD-MacCormack and ADI-type solvers of the shallow water equations , 2006 .

[22]  V. Guinot,et al.  Flux and source term discretization in two‐dimensional shallow water models with porosity on unstructured grids , 2006 .

[23]  J. Neal,et al.  Evaluating a new LISFLOOD‐FP formulation with data from the summer 2007 floods in Tewkesbury, UK , 2011 .

[24]  Timothy Fewtrell,et al.  Parallelisation of storage cell flood models using OpenMP , 2009, Environ. Model. Softw..

[25]  Peter M. Atkinson,et al.  The use of remotely sensed land cover to derive floodplain friction coefficients for flood inundation modelling , 2007 .

[26]  Jason P. Antenucci,et al.  A three dimensional model of Cryptosporidium dynamics in lakes and reservoirs: A new tool for risk management , 2004 .

[27]  P. Bates,et al.  Evaluation of 1D and 2D numerical models for predicting river flood inundation , 2002 .

[28]  M. Horritt.  Calibration of a two‐dimensional finite element flood flow model using satellite radar imagery , 2000 .

[29]  Pietro Prestininzi,et al.  Suitability of the diffusive model for dam break simulation: Application to a CADAM experiment , 2008 .

[30]  Stuart N. Lane,et al.  Urban fluvial flood modelling using a two‐dimensional diffusion‐wave treatment, part 2: development of a sub‐grid‐scale treatment , 2006 .

[31]  P. Bates,et al.  Comparing the performance of a 2‐D finite element and a 2‐D finite volume model of floodplain inundation using airborne SAR imagery , 2007 .

[32]  Julien Lhomme,et al.  Testing a new two‐dimensional flood modelling system: analytical tests and application to a flood event , 2010 .

[33]  M. Werner,et al.  A comparison of flood extent modelling approaches through constraining uncertainties on gauge data , 2004 .

[34]  P. Bates,et al.  Evaluating the effect of scale in flood inundation modelling in urban environments , 2008 .

[35]  D. Mason,et al.  Image processing of airborne scanning laser altimetry data for improved river flood modelling , 2001 .

[36]  S. Lane,et al.  A comparison of one‐ and two‐dimensional approaches to modelling flood inundation over complex upland floodplains , 2007 .

[37]  Roger Alexander Falconer,et al.  Simulation of rapidly varying flow using an efficient TVD–MacCormack scheme , 2007 .

[38]  I. Villanueva,et al.  Linking Riemann and storage cell models for flood prediction , 2006 .

[39]  James Brasington,et al.  Reduced complexity strategies for modelling urban floodplain inundation , 2007 .

[40]  Jim W. Hall,et al.  National-scale Assessment of Current and Future Flood Risk in England and Wales , 2005 .

[41]  W. J. Syme,et al.  Dynamically linked two-dimensional/one-dimensional hydrodynamic modelling program for rivers, estuaries & coastal waters , 1992 .

[42]  P. Bates,et al.  A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling. , 2010 .