Urban fluvial flood modelling using a two‐dimensional diffusion‐wave treatment, part 1: mesh resolution effects

High‐resolution data obtained from airborne remote sensing is increasing opportunities for representation of small‐scale structural elements (e.g. walls, buildings) in complex floodplain systems using two‐dimensional (2D) models of flood inundation. At the same time, 2D inundation models have been developed and shown to provide good predictions of flood inundation extent, with respect to both full solution of the depth‐averaged Navier–Stokes equations and simplified diffusion‐wave models. However, these models have yet to be applied extensively to urban areas. This paper applies a 2D raster‐based diffusion‐wave model to determine patterns of fluvial flood inundation in urban areas using high‐resolution topographic data and explores the effects of spatial resolution upon estimated inundation extent and flow routing process. Model response shows that even relatively small changes in model resolution have considerable effects on the predicted inundation extent and the timing of flood inundation. Timing sensitivity would be expected, given the relatively poor representation of inertial processes in a diffusion‐wave model. Sensitivity to inundation extent is more surprising, but is associated with: (1) the smoothing effect of mesh coarsening upon input topographical data; (2) poorer representation of both cell blockage and surface routing processes as the mesh is coarsened, where the flow routing is especially complex; and (3) the effects of (1) and (2) upon water levels and velocities, which in turn determine which parts of the floodplain the flow can actually travel to. It is shown that the combined effects of wetting and roughness parameters can compensate in part for a coarser mesh resolution. However, the coarser the resolution, the poorer the ability to control the inundation process, as these parameters not only affect the speed, but also the direction of wetting. Thus, high‐resolution data will need to be coupled to a more sophisticated representation of the inundation process in order to obtain effective predictions of flood inundation extent. This is explored in a companion paper. Copyright © 2005 John Wiley & Sons, Ltd.

[1]  Jacob Cohen.  A Coefficient of Agreement for Nominal Scales , 1960 .

[2]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[3]  J. Cunge,et al.  Practical aspects of computational river hydraulics , 1980 .

[4]  L. E. Link,et al.  Airborne laser topographic mapping results , 1984 .

[5]  M. Anderson,et al.  Large‐scale floodplain modelling , 1990 .

[6]  Nicole Goutal,et al.  TELEMAC: A new numerical model for solving shallow water equations , 1991 .

[7]  P. Bates,et al.  Modelling floodplain flows using a two-dimensional finite element model , 1992 .

[8]  A. Defina,et al.  A New Set of Equations for Very Shallow Water and Partially Dry Areas Suitable to 2D Numerical Models , 1994 .

[9]  P. Bates,et al.  INITIAL COMPARISON OF TWO TWO-DIMENSIONAL FINITE ELEMENT CODES FOR RIVER FLOOD SIMULATION. , 1995 .

[10]  Paul D. Bates,et al.  A preliminary investigation into the impact of initial conditions on flood inundation predictions using a time/space distributed sensitivity analysis , 1996 .

[11]  D. S Biggin.  A Comparison of ERS‐1 Satellite Radar and Aerial Photography for River Flood Mapping , 1996 .

[12]  B. Everitt.  The Cambridge Dictionary of Statistics , 1998 .

[13]  K. Richards,et al.  High resolution, two‐dimensional spatial modelling of flow processes in a multi‐thread channel , 1998 .

[14]  Stuart N. Lane,et al.  Hydraulic modelling in hydrology and geomorphology: a review of high resolution approaches , 1998 .

[15]  K. Richards,et al.  The application of computational fluid dynamics to natural river channels: three-dimensional versus two-dimensional approaches , 1999 .

[16]  Paul D. Bates,et al.  Development and testing of a subgrid-scale model for moving-boundary hydrodynamic problems in shallow water , 2000 .

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

[18]  P. Bates,et al.  Integration of high-resolution topographic data with floodplain flow models. , 2000 .

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

[20]  S. N. Lane,et al.  Application of Digital Photogrammetry to Complex Topography for Geomorphological Research , 2000 .

[21]  S. Lane,et al.  The Measurement of River Channel Morphology Using Digital Photogrammetry , 2000 .

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

[23]  Stuart N. Lane,et al.  REMOTE SENSING OF CLEAR-WATER, SHALLOW, GRAVEL-BED RIVERS USING DIGITAL PHOTOGRAMMETRY , 2001 .

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

[25]  H. Wheater.  Progress in and prospects for fluvial flood modelling , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

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

[27]  S. Lane,et al.  Remote survey of large-scale braided, gravel-bed rivers using digital photogrammetry and image analysis , 2003 .

[28]  Stuart N. Lane,et al.  Photogrammetric and laser altimetric reconstruction of water levels for extreme flood event analysis , 2003 .

[29]  Paul D. Bates,et al.  Floodplain friction parameterization in two‐dimensional river flood models using vegetation heights derived from airborne scanning laser altimetry , 2003 .

[30]  Derek B. Ingham,et al.  Numerical modeling of flow processes over gravelly surfaces using structured grids and a numerical porosity treatment , 2004 .