Benchmarking of flood inundation extent using various dynamically linked one‐ and two‐dimensional approaches

An accurate representation of linking processes between one-dimensional (1-D) and two-dimensional (2-D) models is of particular importance for many flood-modelling projects. This paper provides a comparison of 1-D/2-D linking methods used to simulate a hypothetical embankment failure. Comparisons were made by implementing 1-D/2-D linked models using two different 1-D/2-D linking methods, namely water levels and discharges, using both the alternating direction implicit (ADI) and total variation diminishing (TVD) 2-D numerical schemes widely used in flood models such as Flood Modeller Pro (http://www.floodmodeller.com). The flood inundation levels and extent predicted by each numerical scheme were similar when the discharge method was used to link the models, whereas they were dependent on the numerical scheme when the water-level method was used. Consequently, where decisions affecting public safety are informed by the modelling, such as evacuation following a breach, it is recommended that the discharge-linking method should be used for linking models.

[1]  T. Namiki,et al.  A new FDTD algorithm based on alternating-direction implicit method , 1999 .

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

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

[4]  Steven J. Burian,et al.  Assessment of GPU computational enhancement to a 2D flood model , 2011, Environ. Model. Softw..

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

[6]  Guus S. Stelling,et al.  SOBEK ONE DIMENSIONAL – TWO DIMENSIONAL INTEGRATED HYDRAULIC MODEL FOR FLOOD SIMULATION – ITS CAPABILITIES AND FEATURES EXPLAINED , 2004 .

[7]  S. Lane,et al.  Urban fluvial flood modelling using a two‐dimensional diffusion‐wave treatment, part 1: mesh resolution effects , 2006 .

[8]  Roger Alexander Falconer,et al.  Water Quality Simulation Study of a Natural Harbor , 1986 .

[9]  Roger Alexander Falconer,et al.  Hydro-environmental modeling of the proposed Severn barrage , 2010 .

[10]  Bettina N. Bockelmann-Evans,et al.  Comparison of hydro-environmental impacts for ebb-only and two-way generation for a Severn Barrage , 2014, Comput. Geosci..

[11]  A Ervine,et al.  MODELLING A RIVER CHANNEL WITH DISTANT FLOODBANKS. , 1999 .

[12]  G. Strang.  On the Construction and Comparison of Difference Schemes , 1968 .

[13]  M. Werner,et al.  Impact of grid size in GIS based flood extent mapping using a 1D flow model , 2001 .

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

[15]  P. Bates,et al.  Effects of spatial resolution on a raster based model of flood flow , 2001 .

[16]  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 .

[17]  X. Fang,et al.  AN INTEGRATED ONE‐DIMENSIONAL AND TWO‐DIMENSIONAL URBAN STORMWATER FLOOD SIMULATION MODEL 1 , 2006 .

[18]  C. Chatterjee,et al.  Comparison of hydrodynamic models of different complexities to model floods with emergency storage areas , 2008 .

[19]  D. Kay,et al.  Development of a modelling tool to quantify faecal indicator levels in Cardiff Bay , 2002 .

[20]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

[21]  Alessandro Dal Palù,et al.  GPU-enhanced Finite Volume Shallow Water solver for fast flood simulations , 2014, Environ. Model. Softw..

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

[23]  Derek M. Causon,et al.  A TVD MacCormack scheme for transcritical flow , 2001 .

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

[25]  D. Liang,et al.  Linking one- and two-dimensional models for free surface flows , 2007 .

[26]  R A Falconer,et al.  Hydro-environmental modelling for bathing water compliance of an estuarine basin. , 2002, Water research.

[27]  Pilar García-Navarro,et al.  Dam-break flow simulation : some results for one-dimensional models of real cases , 1999 .

[28]  Benedict D. Rogers,et al.  Mathematical balancing of flux gradient and source terms prior to using Roe's approximate Riemann solver , 2003 .

[29]  Valerio Caleffi,et al.  Finite volume method for simulating extreme flood events in natural channels , 2003 .

[30]  Guus S. Stelling,et al.  Practical Aspects of Accurate Tidal Computations , 1986 .

[31]  R. Falconer,et al.  Integrating 1D and 2D hydrodynamic models for flood simulation , 2006 .

[32]  F. Sotiropoulos,et al.  Three-dimensional numerical model for open-ehannels with free-surfaee variations , 2000 .

[33]  Bettina Nicole Bockelmann-Evans,et al.  Far-field modelling of the hydro-environmental impact of tidal stream turbines , 2012 .

[34]  Hans Middelkoop,et al.  Flood management along the Lower Mississippi and Rhine Rivers (The Netherlands) and the continuum of geomorphic adjustment , 2008 .

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

[36]  Flood Management Strategy for the Upper and Middle Odra River Basin: Feasibility Study of Raciborz Reservoir , 2005 .

[37]  G. Umgiesser,et al.  Hydrodynamic and salinity modeling of the Venice channel network with coupled 1-D–2-D mathematical models , 2001 .

[38]  Michiel Blind,et al.  OpenMI Document Series: Part B - Guidelines for the OpenMI (Version 1.0). IT Frameworks (HarmonIT) Contract EVK1-CT-2001-00090 , 2005 .