Flood Inundation Modelling Model Choice and Proper Application

Integrated Flood Risk Analysis and Management Methodologies

FLOOD INUNDATION MODELLING MODEL CHOICE AND PROPER APPLICATION

Date February 2009

Report Number T08-09-03 Revision Number 3_3_P01

Task Leader Deltares | Delft Hydraulics (Delft)

FLOODsite is co-funded by the European Community Sixth Framework Programme for European Research and Technological Development (2002-2006) FLOODsite is an Integrated Project in the Global Change and Eco-systems Sub-Priority Start date March 2004, duration 5 Years Document Dissemination Level PU Public PU PP Restricted to other programme participants (including the Commission Services) RE Restricted to a group specified by the consortium (including the Commission Services) CO Confidential, only for members of the consortium (including the Commission Services)

Co-ordinator: HR Wallingford, UK Project Contract No: GOCE-CT-2004-505420 Project website: www.floodsite.net

Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

DOCUMENT INFORMATION

Title Flood Inundation Modelling – Model Choice and Proper Application Lead Author Nathalie Asselman Paul Bates, Simon Woodhead, Tim Fewtrell, Sandra Soares-Frazão, Yves Contributors Zech, Mirjana Velickovic, Anneloes de Wit, Judith ter Maat, Govert Verhoeven, Julien Lhomme Distribution Public Document Reference T08-09-03

DOCUMENT HISTORY

Date Revision Prepared by Organisation Approved by Notes 22/11/07 1_0_P02 NA Deltares |Delft Initial draft 25/02/08 1_1_P35 SSF UCL 01/08/08 1_2_P02 NA Deltares|Delft results on Scheldt and Thames 23/11/08 1_3_p02 NA Deltares|Delft results on Brembo included 3/12/08 1_4_P15 PB UniBris General edit 10/12/08 1_5_p35 SSF-MV-YZ UCL 11/12/08 1_6_p01 JL HRW additional results on Thames 15/12/08 2_0_P02 NA Deltares|Delft final draft 22/01/09 2_1_P03 AK LWI comments 03/02/09 3_0_P02 NA Deltares|Delft incl. comment theme leader 10/02/09 3_1_P35 SSF UCL update on Brembo 22/02/09 3_2_P02 NA Deltares|Delft final report 25/3/09 3_3_P01 J Bushell HR Final formatting for publication Wallingford

ACKNOWLEDGEMENT

The work described in this publication was supported by the European Community’s Sixth Framework Programme through the grant to the budget of the Integrated Project FLOODsite, Contract GOCE-CT- 2004-505420.

DISCLAIMER

This document reflects only the authors’ views and not those of the European Community. This work may rely on data from sources external to the members of the FLOODsite project Consortium. Members of the Consortium do not accept liability for loss or damage suffered by any third party as a result of errors or inaccuracies in such data. The information in this document is provided “as is” and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information at its sole risk and neither the European Community nor any member of the FLOODsite Consortium is liable for any use that may be made of the information.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 ii Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

SUMMARY

The EU Directive on the assessment and management of flood risks obliges the EU member states to develop flood risk maps. In areas where data on floods are scarce, inundation models are indispensable. In order to obtain reliable flood risk maps, it is important that a proper type of inundation model is selected and that the models are applied properly. Task 8, entitled “Flood inundation modelling”, supports flood risk managers in the selection and application of inundation models.

The report starts with some theoretical background on the suite of available model types, from 1D, through quasi-2D, 1D-2D linked and 2D models, that can be used for a variety of applications. The theory on model parameterization is discussed as well.

Additional information on model choice and application is derived from the models developed for three pilot sites that consisted of the Scheldt estuary in the Netherlands, the Thames estuary in the U.K. and the Brembo river in Italy.

The theoretical background together with the results of the pilot sites have resulted in an overview of guidelines on the most relevant models for a variety of applications as well as on the correct application of each model type in terms of data requirements and setting parameters such as 2D cell size. The guidelines are reported in Chapter 9 of this report and can also be regarded as a short summary.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 iii

Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

CONTENTS

Document Information ii Document History ii Acknowledgement ii Disclaimer ii Summary iii Contents v

1. Introduction 1 1.1 The FLOODsite project 1 1.2 Task 8 of the FLOODsite project 1 1.3 Report outline 2

2. Flood modelling techniques 3 2.1 Introduction: the need for inundation modelling 3 2.2 Flow processes in compound channels 3 2.3 Numerical modelling tools 5 2.3.1 Three-dimensional models (3D) 6 2.3.2 Two-dimensional models (2D and 2D+) 6 2.3.3 One-dimensional models (1D) 7 2.3.4 Coupled one-dimensional/two-dimensional models (1D+ and 2D-) 9 2.3.5 Zero-dimensional or non-model approaches (0D) 10

3. Model parameterization, validation and uncertainty analysis 13 3.1 Boundary condition data 13 3.2 Initial condition data 13 3.3 Topography data 13 3.4 Friction data 14 3.5 Model data assimilation 15 3.6 Calibration, validation and uncertainty analysis 16

4. Models used in Task 8 19 4.1 Introduction 19 4.2 LISFLOOD-FP 19 4.3 UCL / SV1D and SV2D 23 4.3.1 Concept and numerical approach 23 4.3.2 Additional features 24 4.3.3 Calibration and validation 25 4.4 SOBEK 29 4.4.1 Concept and numerical approach 29 4.4.2 Additional features 31 4.4.3 Calibration and validation 32 4.5 Infoworks 2D 34 4.5.1 Overview of the 1D engine 34 4.5.2 Overview of the 2D engine 34 4.5.3 Overview of the linking method 35 4.5.4 Description of the analytical tests 35 4.5.5 Results from the analytical tests 36 4.6 Rapid Flood Spreading Model (RFSM) 36 4.6.1 Overview of the RFSM concept 36 4.6.2 Description of the multiple spilling and friction approach 38

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 v Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

4.6.3 Overview of the spilling algorithm 40

5. Simulating flow in flat agricultural areas located along estuaries or coasts: the Scheldt pilot site 41 5.1 Description of the study area and the available data 41 5.2 Model development 44 5.2.1 SOBEK 44 5.2.2 SV2D 45 5.3 Model comparison 46 5.3.1 Introduction 46 5.3.2 Comparison of SV2D and SOBEK 2D 47 5.3.3 Comparison of a quasi-2D or 1D+ and a full 2D approach 52 5.4 Additional research questions 53 5.4.1 Impact of breach initiation and breach growth 53 5.4.2 Impact of the schematisation of buildings 55 5.4.3 Impact of wind 58 5.4.4 Impact of hydraulic roughness 60 5.4.5 Impact of uncertainties in boundary conditions 63

6. Simulating flow in urban areas located along estuaries or coasts: the Thames pilot site 67 6.1 Study area and available data 67 6.2 Model development 69 6.2.1 LISFLOOD-FP 69 6.2.2 SOBEK 69 6.2.3 Infoworks 69 6.2.4 RFSM 70 6.3 Model comparison 70 6.3.1 Comparison of SOBEK and LISFLOOD-FP 70 6.3.2 Comparison of Infoworks and SOBEK 73 6.3.3 Comparison of RFSM and Infoworks 77 6.4 Additional research questions 79 6.4.1 The impact of the schematisation of buildings 79 6.4.2 The impact of grid cell size 83 6.4.3 The impact of hydraulic roughness 85 6.4.4 The impact of wind 87 6.4.5 The impact of the schematisation of tunnels 88

7. Simulating flow in steep mountainous rivers: the Brembo site 93 7.1 Study area and available data 93 7.1.1 The study area 93 7.1.2 Available data 95 7.2 Model development 100 First- order upwind scheme (Orsa1D-Roe) 102 First-order Lax-Friedrich type scheme (SANA) 103 7.3 Model comparison 104 7.3.1 Introduction 104 7.3.2 Results at selected cross sections 104 7.3.3 Results along the river at selected times 110 7.3.4 Maximum water level 116 7.3.5 Conclusion 118 7.4 Additional research questions 118

8. Simulating flow in urban areas: flume data 119 8.1 Introduction 119 8.2 Experimental data 119

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 vi Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

8.2.1 Dam-break flow against an isolated obstacle 119 8.2.2 Dam-break flow in an idealised urban district 121 8.3 Porosity concept 123 8.4 Numerical simulations using detailed and simplified models 124 8.5 Conclusions 126

9. Synthesis / guidelines 127 9.1 Introduction 127 9.2 Model choice 127 9.2.1 Model complexity 127 9.2.2 Some available software packages 129 9.3 Model application 130 9.4 Recommendations 132

10. References 135

Tables Table 2.1 Overview of existing types of hydraulic models (After Table 2 from G. Pender et al. (2006)). 11 Table 4.1 Details of the analytical tests 35 Table 4.2 Description of the two other routinely used commercial hydraulic softwares 35 Table 5.1 Summary of numerical simulations 46 Table 6.1 Model efficiency for different versions of the SOBEK model 72 Table 6.2 Model efficiency of the SOBEK model using different calculation time steps 72 Table 6.3 Cell statistics for the flood extent comparison between Infoworks and Sobek. 75 Table 6.4 Fit indicators for the comparison between Infoworks and Sobek. 75 Table 6.5 Computational indicators for the comparison between Infoworks and Sobek. 76 Table 6.6 Computational indicators for the comparison between Infoworks and RFSM. 78 Table 6.7 Cell statistics for the flood extent comparison between Infoworks and RFSM. 78 Table 6.8 Fit indicators for the comparison between Infoworks and RFSM. 78 Table 7.1 Stage-discharge relation for the downstream section 98 Table 7.2 Maximum level water recorded along the river 99 Table 9.1 Overview of hydraulic model types and their application 130

Figures Figure 4.1 Representation of a breach in SV2D. Cell interfaces in contact with the sea boundary condition are indicated as thick black line in the inset. 25 Figure 4.2 Experimental set-up and initial conditions, all dimensions in metres 26 Figure 4.3 Comparison between experimental and numerical flow profiles. 27 Figure 4.4 Channel with 90° bend – Plane view (dimensions in m) 28 Figure 4.5 Experimental and computed (2D model) flow profiles: (a) t = 3 s, (b) t = 5 s, (c) t = 7 s, (d) t = 14 s 28 Figure 4.6 Staggered grid for unsteady channel flow or pipe flow 30 Figure 4.7 Schematisation of the Hydraulic Model: a) Combined 1D/2D Staggered Grid; b) Combined Continuity Equation for 1D2D Computations 30 Figure 4.8 Delft University of Technology dyke break: top view and side view of the experiment layout (Liang et al., 2004) 32 Figure 4.9 Comparison of measured and simulated water levels using the experiment carried out by Delft University of Technology (Duinmeijer, 2002). 33 Figure 4.10 Comparison of measured and simulated position of the front of the flood at different time steps (Duinmeijer, 2002). 33 Figure 4.11 View of the defence system with the Impact Zones and Impact Cells (based on Gouldby et al. 2008). 37 Figure 4.12 Principles and key features of the Impact Zones (based on Gouldby et al. 2008). 37

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 vii Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 4.13 Flowchart of the RFSM algorithm (a) and description of the different spilling/merging steps (b). 38 Figure 4.14 Description of the spilling rules in the earlier RFSM. 39 Figure 4.15 Link between the IZ shape and the dynamic filling effects. 39 Figure 4.16 Example of two Volume-Level curves. 39 Figure 4.17 Description of the spilling rules in the latest version of RFSM, with the combined role of multiple spilling (MSTol) and friction (Sf). 40 Figure 5.1 Location of the study area (a) in the Netherlands, (b) detailed topography, (c) aerial photograph (source: Google earth) 41 Figure 5.2 Flooded polders in Zuid Beveland during the 1953 storm surge. Arrows represent dike breaches. Polders 3, 4a, 6, 8, 9a, 9b, 9c, 11 were flooded by breaches occurring in the primary dikes, polders 4b, 5, 12 were flooded by failure of secondary dikes and polders 7 and 10 were flooded because drainage was obstructed (source: Rijkswaterstaat & KNMI, 1961) 42 Figure 5.3 Primary and secondary dikes schematised in the elevation model. Primary dikes are visualised by the green lines, secondary dikes are shown by pink lines. The blue line represents a small dike for which no detailed elevation data were available. Its height was estimated using the laser altimetry data. The elevation of the area is shown in brown colours, the range varies from about NAP -1.5 m (dark brown) to NAP +1.5 m (orange). 43 Figure 5.4 Observed water levels in the Western Scheldt at Waarde and Bath 43 Figure 5.5 Distribution of the roughness coefficient ks: light colours indicate low roughness and dark colours indicate high roughness. 44 Figure 5.6 Representation of a breach in SV2D. Cell interfaces in contact with the sea boundary condition are indicated as thick black line in the inset 46 Figure 5.7 Comparison points for the predicted water level and velocity by the numerical models 47 Figure 5.8 Computed results at comparison point P1: (a) water level and (b) velocity 47 Figure 5.9 Computed water level at point P4 48 Figure 5.10 Computed results at comparison point P7: (a) water level and (b) velocity 48 Figure 5.11 Computed results at comparison point P8: (a) water level and (b) velocity 49 Figure 5.12 Maximum water level (in m+NAP) (a) SOBEK, (b) SV2D instantaneous breaching, (c) SV2D progressive breaching 49 Figure 5.13 Water arrival time (in hours) computed with (a) SOBEK, (b) SV2D instantaneous breaching and (c) SV2D progressive breach opening. 50 Figure 5.14 Arrival time (in hours) of maximum water depth computed with (a) SOBEK, (b) SV2D instantaneous breaching and (c) SV2D progressive breach opening. 51 Figure 5.15 Water levels (m +NAP) computed with the 2D and quasi 2D application of SOBEK for model comparison location 1 (a) and location 4 (b) 52 Figure 5.16 Schematisation of 3 polders in 2D (upper half) and quasi 2D (lower half). Red and green lines represent low sections in secondary dikes between the polders. The green section is lower than the red section. 53 Figure 5.17 Breach growth according to the original SOBEK model 54 Figure 5.18 Computed water levels behind the breach in the Reigersbergsche polder (including locations 7 and 8) 54 Figure 5.19 Moment of first inundation Reigersbergsche Polder (a) progressive breach growth (b) instantaneous breaching 55 Figure 5.20 Water depths computed with a coarse grid (a), a finer grid and solid buildings (b) and a finer grid with very high roughness values representing buildings (c) 56 Figure 5.21 Moment of first inundation computed a coarse grid (a), a finer grid and solid buildings (b) and a finer grid with very high roughness values representing buildings (c) 57 Figure 5.22 Flow velocities computed with a coarse grid (a), a finer grid and solid buildings (b) and a finer grid with very high roughness values representing buildings (c) 58 Figure 5.23 The influence of wind on the computed maximum water depth 59

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 viii Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 5.24 Difference in water depth (m) between the simulation with wind force 10, direction west, and the simulation without wind 60 Figure 5.25 Difference in water depth (m) between simulations with a uniform roughness of n=0.06 sm-1/3 and n=0.03 sm-1/3 61 Figure 5.26 Difference in water depth (m) between simulations with a uniform roughness of n=0.06 sm-1/3 and n=0.03 sm-1/3 (location numbers are shown in Figure 5.7, location 1/4 is near the breach in the secondary dike between locations 1 and 4) 62 Figure 5.27 Difference in inflow through the breach (m/s) between simulations with a uniform roughness of n=0.06 sm-1/3 and n=0.03 sm-1/3 (location 1 and 7 represent flow into polders with location numbers 1 and 7, location ¼ respresent the flow through the breach in the secondary dike between locations 1 and 4) 62 Figure 5.28 Water level time-series used for the sensitivity analysis. Peak water levels correspond with T4000 water levels according to the Dutch approach (darkblue line) and the Belgian approach (pink line) (source: Asselman, et al., 2007). 64 Figure 5.29 Comparison of flood extent computed with SOBEK using different boundary conditions: (a) T4000 water level according to the Dutch approach, (b) T4000 water level according to the Belgian approach. 64 Figure 6.1 Map of the indicative tidal flood risk area of the Thames Region highlighting the Greenwich study area. Data courtesy of EA Thames region. 67 Figure 6.2 Aerial photograph of the study area. The Millennium dome and the Thames barrier are clearly visible. (source: Google earth) 68 Figure 6.3 Differences in water depths computed with LISFLOOD-FP and SOBEK using a high resolution 5 m DEM. light grey colours represent areas where LISFLOOD-FP computes greater depths. In dark grey areas SOBEK predicts larger depths. 70 Figure 6.4 Difference in time of first wetting using digital elevation models with a mesh of 5 m (a) and 10m (b). Green = LISFLOOD-FP is faster, red = SOBEK is faster. 71 Figure 6.5 Difference in flood extent between Infoworks and Sobek. 74 Figure 6.6 Difference in flood depth between Infoworks and Sobek (calculated as IW minus Sobek). 74 Figure 6.7 Local difference in flood extent due to the buildings representation. 75 Figure 6.8 Aerial photograph of buildings represented in Figure 6.7(source: Google earth) 76 Figure 6.9 Difference in flood extent between Infoworks and RFSM (5 m grid). 78 Figure 6.10 Difference in flood extent between Infoworks and RFSM (2 m grid). 79 Figure 6.11 Flooded area for the 5m grid with (brown) or without buildings (green). 80 Figure 6.12 Difference in computed maximum water depth between the 5m grid with and without buildings. Red/yellow colours represent areas where the DEM without buildings results in greater depths; in blue coloured areas the DEM with buildings predicts larger depths. 80 Figure 6.13 Differences between the flood extent with buildings (brown) or without buildings (green) for the different grid resolutions: (a) 5m, (b) 10m, (c) 25m, (d) 50m 81 Figure 6.14 Locations selected for detailed model output (a) in the northeast, (b) in the northwest 82 Figure 6.15 Computed water depths at locations in the north-eastern part of the study area: (a) 5m grid without buildings, (b) 5m grid with buildings 82 Figure 6.16 Computed water depths at locations in the north-western part of the study area: (a) 5m grid without buildings, (b) 5m grid with buildings 82 Figure 6.17 Water depth and flood extent computed with SOBEK using different grid resolution: (a) 5m (b) 10m, (c) 25m, (d) 50m (buildings are included as solid objects). 83 Figure 6.18 The flooded area in the 5 and the 25m grid size. The 5m grid is on top and represented by the brown colour. The 25m grid is in green, which represents the calculated water depth. 84 Figure 6.19 Computed water depths at locations in the northwestern part of the study area: (a) 5m grid without buildings, (b) 10m grid without buildings, (c) 5m grid with buildings, (d) 10m grid with buildings. 85

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 ix Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 6.20 Difference in time of inundation as computed with different roughness coefficients of manning = 0.035 s/m1/3 and 0.07 s/m1/3. Yellow colours indicate a delay in inundation when a roughness value of 0.07 s/m1/3 is used. 86 Figure 6.21 Computed water depths at four locations in the study area using different roughness coefficients(a) manning = 0.035 s/m1/3, (b) 0.07 s/m1/3. 86 Figure 6.22 Difference in maximum water depth between the SOBEK simulations with and without wind (wind velocity 30 m/s, coming from the north). Red/yellow colours indicate larger water depths when wind is not accounted for, blue colours imply greater depths when wind is accounted for. 87 Figure 6.23 Difference in computed water depth with and without schematisation of the tunnel crossing the Thames 89 Figure 6.24 Computed water depths after breach formation on the west side of the study area 89 Figure 6.25 Difference in computed water depth with and without schematisation of the tunnel crossing the Thames 90 Figure 6.26 Computed delay in time of inundation caused by flow through the tunnel crossing the Thames 90 Figure 7.1 Location of the Brembo River in the Italian Alps and plan view of the Brembo River with the major tributaries of the Adda river 93 Figure 7.2 Flood of the Brembo river 94 Figure 7.3 Profile of the thalweg and examples of steep and adverse slopes 94 Figure 7.4 Enlargements and constrictions of the sections 95 Figure 7.5 aerial photo of a part of the Brembo, with the location of some sections 95 Figure 7.6 Cross section at km 7.979, where the 1D field data are different from the new DEM data 96 Figure 7.7 Cross section at km 10.281, where the 1D field data are different from the new DEM data 97 Figure 7.8 Upstream hydrograph 97 Figure 7.9 Initial water level along the Brembo river 98 Figure 7.10 Map of the towns crossed by the Brembo where the maximum water levels were recorded 99 Figure 7.11 Cross section which arise a difficulty 100 Figure 7.12 Situation of the 4 points of comparison in the profile of the thalweg of the Brembo 105 Figure 7.13 Details of the thalweg in the surrounding of the four points of comparison 105 Figure 7.14 Evolution of water level zw in function of time at point x = 7.791 km 106 Figure 7.15 Evolution of discharge Q in function of time at point x = 7.791 km 106 Figure 7.16 Evolution of water level zw in function of time at point x = 24.413 km 107 Figure 7.17 Evolution of discharge Q in function of time at point x = 24.413 km 107 * Figure 7.18 Comparison between the mass flux Qi+1/ 2 and the momentum Q 108 * Figure 7.19 Evolution of discharge Q (and mass flux Qi+1/2 for SV1D) in function of time at point x = 24.413 km 108 Figure 7.20 Evolution of water level zw in function of time at point x = 36.852 km 109 Figure 7.21 Evolution of water level zw in function of time at point x = 48.446 km 109 Figure 7.22 picture of the water level after 8h around point 2 (x = 24.413) 110 Figure 7.23 detailed graph of the water level, bed level, Froude number and flow velocities near section 2, computed with the SOBEK model 111 Figure 7.24 Cross sections near section 2 111 Figure 7.25 picture of the water level after 8h with additional cross-sections around point 2 112 Figure 7.26 Schematisation of yz-cross sections (blue dots are yz points given by the user, the bold line represents the actual cross section and the dotted line the cross section used by the model 113 Figure 7.27 Water level after 9h around point 3 (x = 36.852 km) 113 Figure 7.28 Water level after 41h around point 4 (x = 48.446 km) 114 Figure 7.29 Picture of the discharge after 8h 114 Figure 7.30 Picture of the Froude number after 9h between x = 20 km and x = 30 km 115

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 x Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 7.31 Picture of the Froude number after 9h between x = 30 km and x = 40 km 115 Figure 7.32 picture of the maximum water level between x = 13 km and x = 20 km 116 Figure 7.33 Picture of the maximum water level between x = 20 km and x = 28 km 117 Figure 7.34 picture of the maximum water level between x = 28 km and x = 37 km 117 Figure 7.35 picture of the maximum water level between x = 37 km and x = 50 km 118 Figure 8.1 Channel and building dimensions (m) 120 Figure 8.2 Computed image of the flow at time t = 1 s 120 Figure 8.3 Computed image of the flow at time t = 3 s 121 Figure 8.4 Computed image of the flow at time t = 10 s 121 Figure 8.5 Experimental set-up and channel dimensions in (m)(a) plane view, (b) cross section 122 Figure 8.6 Hydraulic jump upstream of the urban district for case 1 122 Figure 8.7 Water-surface profiles along the central longitudinal street located at y = 0.2 m: experimental (•) and numerical results computed using a coarse 2T (dotted line) and a fine 10T mesh (continuous line) for (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s 123 Figure 8.8 Water level - Porosity and roughness models compared to 2D model and to experiments: aligned case, t = 8 s. 125 Figure 8.9 Water level - Porosity and roughness models compared to 2D model and to experiments: aligned case, t = 10 s. 125 Figure 8.10 Velocity - Porosity and roughness models compared to 2D model and to experiments: aligned case, t = 10 s. 126

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 xi Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

1. Introduction

1.1 The FLOODsite project

Flooding is the most widely distributed of all natural hazards across Europe with floods from rivers, estuaries and the sea threatening many millions of people in Europe. Floods cause distress and damage wherever they happen and insurance company data show that the financial impact of flooding has increased significantly since 1990.

In April 2007, the Parliament and Council of the European Union agreed the wording on a new European Directive on the assessment and management of flood risks. The Integrated Project FLOODsite is listed as one of the European actions which support the Directive.

FLOODsite is an interdisciplinary project integrating expertise from physical, environmental and social sciences, as well as spatial planning and management. The project has over 30 research tasks across seven themes, including pilot applications in Belgium, the Czech Republic, France, Germany, Hungary, Italy, the Netherlands, Spain and the UK. FLOODsite is an “Integrated Project” in the Global Change and Ecosystems priority of the Sixth Framework Programme of the European Commission. It commenced in 2004 and runs to 2009.

Flood risk management is a process which comprises pre-flood prevention, risk mitigation measures and preparedness, backed up by flood management actions during and after an event. Within the boundaries of FLOODsite, the Integrated Project is delivering advances in several areas of direct relevance to the three main activities of the Directive: • preliminary flood risk assessment; • the preparation of flood risk maps; • the preparation (and implementation) of flood risk management plans.

1.2 Task 8 of the FLOODsite project

In situations of flood risk, authorities need to make decisions concerning the management and evacuation strategies to apply. However, in order to prepare evacuation plans, or to assess potential damage, information is needed on inundation patterns, including water depths, flow velocities and timing of inundation. This information can be derived using inundation models.

The outcome of inundation models also is required for long-term planning. Long-term planning is an integral part of developing sustainable flood risk management policies and intervention measures. In particular, it enables decision makers to explore strategies, set targets, question the status quo and to determine the merits of innovative ideas. Flood inundation models are essential in the development of a framework for long-term planning of flood risk management.

For non experienced modellers it often is difficult to determine what type of model they should apply. And even if the right model choice is made, it can remain difficult to apply the model in a proper way. Questions that often arise concern the grid cell size to be used in case of a 2D model, the processes

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 1 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 that should be included (such as breach growth, wind effects and evaporation), or the best way to schematise a complex area.

The main purpose of Task 8 and this report is therefore to give guidance to engineers, researchers, and practitioners regarding the appropriate selection and correct application of 1D and 2D models for the purpose of flood inundation modelling.

1.3 Report outline

Chapter 2 describes the suite of available model types, from 1D, through quasi-2D, 1D-2D linked and 2D models, which can be used for a variety of applications. Model parameterization is discussed in chapter 3. An outline of the numerical models that are applied under Task 8 of the Floodsite project is given in chapter 4. The models are applied to three pilot sites. The results of the Scheldt pilot sites are described in chapter 5. Chapters 6 and 7 focus on the Thames estuary and the Brembo river, respectively. Computer simulations of flume experiments are reported in chapter 8. The report concludes with an overview of guidelines on the most relevant models for a variety of applications as well as on the correct application of each model type in terms of data requirements and setting parameters such as 2D cell size.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 2 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

2. Flood modelling techniques

2.1 Introduction: the need for inundation modelling

There are two main reasons to undertake numerical modelling of floodplain flow:

• first as an alternative to laboratory experiments or field data to improve understanding of the processes involved in floodplain flow; and • second to obtain predictions of quantities useful for the management of floodplain systems, e.g. discharge, water surface elevation, inundation extent and flow velocity.

In this context a model consists of a user’s best estimate of the processes that are perceived to be relevant to the application, and may be tested by comparison to analytical solutions, scale models or field data. Physical realism is of utmost importance in the first class of application, whereas for flood management the emphasis may be on computational efficiency.

Compound channel flows are fully turbulent over a wide range of space scales and unsteady in time, but it is computationally prohibitive to simulate flows with this level of complexity. Fortunately, the processes perceived by modellers to be relevant to the accurate simulation of floodplain flow for a particular purpose are typically a small subset of the known physical mechanisms. The key step in selecting an appropriate numerical modelling framework for floodplain flows is therefore to identify those processes that are relevant to a particular modelling problem and decide how these can be discretized and parameterised in the most computationally efficient manner.

This chapter describes the classes of model available for flood modelling and their limits of applicability. A more extensive review is given in a separate report of Task 8 (i.e. Woodhead et al., 2006).

2.2 Flow processes in compound channels

Flood basins normally consist of a main channel and one or two adjacent floodplain areas. When a flood wave exceeds bank full height, water will travel rapidly over the low lying floodplains. During a flood the floodplain may either act as storage or an additional means of conveyance. In the language of fluid dynamics a flood is a long, low amplitude wave passing through a compound channel with complex geometry. The size of the flood wave will be important when coming to select an appropriate flood management tool, in the very largest basins such waves may be ~103 km long and only ~10 m deep, and may take several months to traverse the whole system. Flood waves are translated downstream with speed or celerity, c [LT-1], and attenuated by frictional losses such that in downstream sections the hydrograph (the variation of discharge, Q [L-3T-1] with time, t [T]) is flattened out.

Even before bank full height is exceeded there are already many in-channel processes to consider, each with characteristic length scales. At the scale of the channel planform shear layers form at the junction between the main flow and slower moving dead zones (Hankin et al., 2001). At the scale of the channel cross-section there are secondary circulations (Bridge and Gabel, 1992; Nezu et al., 1993). Finally, turbulent eddies range from heterogeneous structures at the scale of roughness elements and obstructions on the bed (Ashworth et al., 1996; McLelland et al., 1999; Shvidchenko and Pender, 2001), down through the turbulent energy cascade (Hervouet and Van Haren, 1996), to the Kolmogorov length scale, η [L], where turbulent kinetic energy is dissipated. The smallest eddies may be only ~10-2 mm across, and the grid size required to include such processes in flood inundation models makes this infeasible for most real applications.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 3 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

When bank full height is exceeded and compound flow ensues, in addition to the above processes new physical mechanisms come into play. The principal mechanisms are momentum exchange between the fast moving channel and slower floodplain flow (Knight and Shiono, 1996) and interaction between meandering channel flows and flow on the floodplain (Sellin and Willetts, 1996). The channel- floodplain momentum exchange occurs across a shear layer which is manifest as a series of vortices with vertically aligned axes (Sellin, 1964; Fukuoka and Fujita, 1989; Shiono and Knight, 1991). Ervine and Baird (1982) conclude that failure to account for the momentum exchange can lead to errors of up to ±25% in the discharge calculated using uniform flow formulae such as the Manning and Chezy equations. Further vigorous momentum exchange occurs during out-of-bank flow in meandering compound channels (see Sellin and Willetts, 1996 for a discussion). Here water spills from the downstream apex of channel bends and flows over meander loops before interacting with channel flow in the next meander. These three-dimensional interactions modify secondary circulations within the channel and represent an additional energy loss in the near channel area. Floodplain flows beyond the meander belt will not be subject to such energy losses and this region may provide a route for more rapid flow conveyance. The impact of these additional energy losses will be at a maximum at some shallow overbank stage, when the interaction between main channel and floodplain is at its greatest (Knight and Shiono, 1996), before slowly decreasing as depth increases and the whole floodplain and valley floor begins to behave as a single channel unit.

Away from the near channel zone water movement on the floodplain may be more accurately described as a typical shallow water flow (i.e. one where the width:depth ratio exceeds 10:1) as the horizontal extent may be large (up to several kilometres) compared to the depth (usually less than 10m). Such shallow water flows over low-lying topography are characterised by rapid extension and retreat of the inundation front over considerable distances, potentially with distinct processes occurring during the wetting and drying phases (see Nicholas and Mitchell, 2003). Correct treatment of this moving boundary problem is therefore important both to capture adequately the shallow water energy losses (which may be high due to large relative roughness) and because flood extent is a common prediction requirement from hydraulic codes.

Flow interactions with micro-topography (see Walling et al., 1986), vegetation (Lopez and Garcia, 2001) and structures (Meselhe et al., 2000) may all be important, thereby giving a complex modelling problem. In particular, where the floodplain acts as a route for flow conveyance rather than just as storage, energy losses are typically dominated by vegetative resistance. Yet despite a small number of pioneering studies (see for example Kouwen, 1988; Nepf, 1999; Ghisalberti and Nepf, 2002; Wilson and Horritt, 2002), the interaction between plant form, plant biomechanics, energy loss and turbulence generation is at present relatively poorly understood (see Wilson et al., 2005). Moreover, many numerical models of floodplain flow assume that the channel bed is fixed over the course of the event, and for very large floods this may not be the case as embankment failure or geomorphic change may considerably affect the flow field.

Whilst overbank flow in compound channels is clearly a two-dimensional process, many practical floodplain management questions only require the prediction of water levels at particular points of interest. In such cases, the modeller is primarily concerned with the downstream routing of flow through a compound cross-section, and may be less concerned to represent floodplain flow and storage accurately. Here, the flow processes of interest are one-dimensional in the down-valley direction and one-dimensional models may therefore be used to represent such flows. Whilst this is often considered a gross simplification of the flow field (see Knight and Shiono, 1996), one can justify the approach by assuming that the additional approximations involved in continuing to treat out-of-bank flow as if it were one-dimensional are small compared to other uncertainties (for a discussion see Ali and Goodwin, 2002). Alternatively, one can attempt to correct one-dimensional flow routing methods to account for the additional energy losses and/or mass transfers (see Knight and Shiono, 1996) or develop hybrid schemes that combine one dimensional modelling for channel flows with a two- dimensional treatment of the floodplain (see Bates and De Roo, 2000).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 4 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Lastly, whilst typical hydraulic models do not consider water exchanges with the surrounding catchment, for whole catchment modelling or flood inundation simulation over long river reaches such exchanges may, at particular times, become important (e.g. Stewart et al., 1999; Woessner, 2000). Such processes include direct precipitation or runoff to the floodplain surface (e.g. Mertes, 1997), evapotranspiration losses, so called bank-storage effects (Pinder and Sauer, 1971; Squillace, 1996) resulting from interactions between the river water and alluvial groundwaters contained within the hyporheic zone (Stanford and Ward, 1988; Castro and Hornberger, 1991; Wroblicky et al., 1998), subsurface contributions to the floodplain groundwater from adjacent hill slopes (e.g Bates et al., 2000; Burt et al., 2002) and flows along preferential flow paths, such as relict channel gravels, within the floodplain alluvium (e.g. Haycock and Burt, 1993; Poole et al., 2002). Over particular reaches and in particular environments, integration of some or all of these processes with flood routing models may be required and necessitate complex modelling structures (e.g. Stewart et al, 1999, Kohane, and Welz, 1994) which may be difficult to fully parameterize.

2.3 Numerical modelling tools

Pender et al. (2006) divide hydraulic models for compound channels into classes according to the maximum dimensionality of the processes represented and the addition (or omission) of other flow processes, (see Table 2.1). It is clear that for particular problems different classes of models will be appropriate. In this section we discuss some details of numerical modelling and how the classifications given in Table 2.1 relate to the numerical scheme used.

Excepting 0D models, for which no physical laws are included, all hydraulic models are derived from the three-dimensional Navier-Stokes momentum equation which for an incompressible fluid of constant density may be expressed as:

Du ρ = −∇p + μ∇ 2u + F [1] Dt where ρ is the fluid density [ML-3]; u is the velocity [LT-1]; t is the time [T], p is the pressure [ML-1T-2]; μ is the viscosity [ML-1T-2] and F is the set of source terms (e.g. friction, gravity and coriolis) to be included in the specification of a particular problem.

Combining the Navier-Stokes equation with the equation of continuity:

∇.u = 0 [2] gives a system of equations that can be solved to yield the three-dimensional velocity vector u=(u,v,w), where u, v and w are the three components of u in the x, y and z directions respectively, and pressure, p, for a given point in time and space. In free surface models the pressure is typically replaced with the flow depth, h [L].

In theory these equations can be used to fully describe any open channel flow. However, to capture the details of turbulent flows (which can be as small as 10-2 mm) requires a very fine discretization both in space and time. In practice, we are often not interested in the velocity field at all scales but the mean flow properties. Reynolds (1895) averaging can be used to split each variable (say u) into a mean vector (ū) and a random variation about it (u’). Assuming the random variation averages to zero over some integration period we replace all components with their equivalent mean vector, this yields the Renolds Averaged Navier-Stokes equations (RANS). As a consequence, new terms representing shear stress on the mean flow due to turbulence appear in equation [1]. Values for the Reynolds stresses must be provided (by introducing some turbulence model) to close the RANS equations.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 5 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

2.3.1 Three-dimensional models (3D)

Representation of the three-dimensional processes, that dominate in the near channel region, requires a three-dimensional solution of the RANS equations that in turn necessitates an approximate numerical technique such as finite differences, finite elements or finite volumes. A number of codes are available for problems such as sediment transport and flow-vegetation interaction, where three-dimensional process representation is deemed important (e.g. CFX, FLUENT and PHOENIX).

The computational cost involved in three-dimensional codes means the modeller must trade off between cell or element size, the domain size and the complexity of the turbulence closure scheme employed. However, three-dimensional models for compound channels at scales of practical interest are feasible as evidenced by the work of Stoesser et al. (2003) who applied a steady state 3D RANS model with k-ε turbulence closure to a 3.5 km reach of the upper river Rhine using 198 114 cells within a finite volume code. Higher order turbulence modelling approaches for three-dimensional flow in compound channels has also been attempted and methods include algebraic stress (Shao et al., 2003) and Large Eddy Simulation (Thomas and Williams, 1995) schemes. However these approaches are computational expensive and have thus far only been applied to channels of regular geometry. Even when it is possible for 3D models with higher order turbulence closure to be applied to complex natural geometry, they may be hard to parameterise due to lack of calibration data.

For dynamic simulations of floodplain flow with three-dimensional models additional approximations need to be introduced to deal with the changing domain extent in both horizontal and vertical dimensions. To date, however, none of the available methods provides a complete solution to this problem. For example, models which use a deformable mesh (Feng and Perić, 2003) or the σ- transform (Stoesser et al., 2003) to discretize the grid in the vertical may suffer from stability problems during dynamic shallow water flows as with these methods the upper boundary of the computational domain moves with the water free-surface. If the number of vertical grid layers remains fixed, then cell height-length ratios may become highly distorted as water depth, h, approaches zero. For this reason most dynamic codes use the Volume of Fluid (VoF) method (Ma et al., 2002) to track the horizontal moving boundary in whilst retaining fixed vertical grid increments. The VoF method calculates the proportion of each 3D cell filled with water (1 for fully wet cells, 0 for cells that are fully dry and a value between 0 and 1 for partially wet cells) in order to track accurately the position of the surface and horizontal boundaries on a fixed grid in a computationally efficient manner. However, even with this method avoidance of distorted cells for flows with horizontal extent 100-10000 m and depths generally much less than 1-10 m still requires numerical grids that are horizontally very highly resolved and which are likely to incur a prohibitive computational cost.

Thus, to date most three-dimensional numerical models of compound channel flow have not been applied to problems with significant changes in domain extent over low gradient floodplains. Neither may three-dimensional approaches be necessary, as for many scales of compound channel flows the two-dimensional shallow water approximation may be adequate. For these reasons, dynamically varying flows in compound channels have, to date, typically been treated with two-dimensional models.

2.3.2 Two-dimensional models (2D and 2D+)

Two-dimensional approaches typically use depth averaged velocity obtained by integrating the Reynolds Averaged Navier-Stokes equations over the flow depth. Examples are the St. Venant equations, which assume a hydrostatic pressure distribution, or the Boussinesq equations, which do not (see Hervouet and Van Haren, 1996). For example, the St. Venant equations are given in non- conservative form as:

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 6 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Continuity equation

∂h → ⎯⎯→ → + u .grad (h) + hdiv(u ) = 0 [3] ∂t d d

Momentum equations

→ ⎯⎯→ ⎯⎯→ ∂ud ∂h ∂ Z f + u .grad (u ) + g − div(vt .grad (u )) = S x − g [4] ∂t d d ∂x d ∂x → ⎯⎯→ ⎯⎯→ ∂vd ∂h ∂ Z f + u d .grad (v ) + g − div(vt .grad (v )) = S y − g [5] ∂t d ∂y d ∂y

-1 Where ud,vd are the depth-averaged velocity components [with dimensions LT ] in the x and y 2 -1 cartesian directions [L]; Zf is the bed elevation [L]; vt is the kinematic turbulent viscosity [L T ]; Sx,Sy are the source terms (friction, coriolis force and wind stress) and g is the gravitational acceleration [LT-2].

Equations [3] to [5] can then be solved using some appropriate numerical procedure (see Wright, 2005) and turbulence closure (see Sotiropoulos, 2005) to obtain predictions of the water depth, h, and the two components of the depth-averaged velocity, ud and vd. The Shallow Water equations are most often applied to flows that have a large areal extent compared to their depth and where there are large lateral variations in the velocity field. They are thus well suited to the computation of overbank flood flows in compound channels, tides, tsunamis or even dam breaks (see Hervouet and Van Haren, 1996). Whilst two-dimensional models cannot fully represent the complex flow processes in the near channel region of a compound channel, they will still capture certain aspects of these processes. Here, the modeller assumes that this is sufficient to reproduce the particular flow features that are of interest for the problem in hand at a given scale. Moreover, two-dimensional schemes can also more easily represent moving boundary effects and may therefore be of more use for simulating problems where inundation extent changes dynamically through time (see Bates and Horritt, 2005).

The 2D class of models includes full solutions of the two-dimensional St. Venant or shallow water equations (Gee et al., 1990; Feldhaus et al., 1992; Bates et al., 1998; Nicholas and Mitchell, 2003) and simplified shallow water models (see for example Molinaro et al., 1994) where certain terms, such as inertia, are omitted from the controlling equations. Each of these equations sets can be discretized using structured or unstructured grids, and it may even be possible to allow the grid to deform to follow the moving inundation front through time (Benkhaldoun and Monthe, 1994). However the computational cost in re-meshing and problems with numerical stability mean that, to date, fixed grid approaches have been preferred. Also fixed grids, being cheaper computationally, may allow finer spatial resolution meshes to be employed which may be a considerable advantage given the complexity of floodplain topography.

Simpler methods for attempting to represent two-dimensional flow are storage cell codes, which are really a hybrid of one-dimensional and two-dimensional approaches. Storage cell codes are classified as 1D+ or 2D- depending on the way floodplain flow is represented, these methods are discussed further in Section 2.3.4.

2.3.3 One-dimensional models (1D)

Most simply, for flow routing problems floodplain flow can be treated as one-dimensional in the down-valley direction. An equation for one-dimensional channel flow can be derived by considering mass and momentum conservation between two cross sections Δx apart. This yields the well-known one-dimensional St. Venant or shallow water equations:

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 7 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Conservation of momentum

∂Q ∂()Q 2 / A ⎛ ∂h ⎞ + + gA⎜ + S f − So ⎟ = 0 [6] ∂t ∂x ⎝ ∂x ⎠ where Q is the flow discharge [L3T-1]; A is the flow cross-section area [L2], g is the gravitational -2 -1 -1 acceleration [LT ], Sf is the friction slope [LL ] and So is the channel bed slope [LL ].

Conservation of mass

∂Q ∂A + = q [7] ∂x ∂t

Where q is the lateral inflow or outflow per unit length [L2T-1].

Equations [6] and [7] have no exact analytical solution, but with appropriate boundary and initial conditions they can be solved using numerical techniques (e.g. Preissmann, 1961; Abbott and Ionescu, 1967) to yield estimates of Q and h in both space and time. The river reach in one-dimensional St. Venant models is discretized as a series of irregularly spaced cross-sections. Boundary conditions typically consist of the inflow hydrograph at the upstream cross section and, for sub-critical flow, the stage hydrograph at the downstream boundary. For critical flow where the Froude number,

Fr = u gh , exceeds 1, information from the downstream boundary cannot propagate upstream and no boundary condition need therefore be prescribed. These equations form the basis of most standard commercial hydraulic modelling software such as HEC-RAS, MIKE11, ISIS and SOBEK.

Horritt and Bates (2002) demonstrate for the simulation of a large flood event over a 60 km reach of the River Severn, UK that one-dimensional, simplified two-dimensional and full two-dimensional models perform equally well in simulating flow routing and inundation extent given uncertainties over inflow, topography and validation data. This suggests that although gross assumptions are made regarding the flow physics incorporated in a one-dimensional model applied to out-of-bank flows, the additional energy losses can be compensated for using a calibrated effective friction coefficient.

One-dimensional approaches that attempt to correct for some of these additional energy losses are reviewed by Knight and Shiono (1996, p155-159) and are based on subdividing the channel in the streamwise direction and then calculating the conveyance in each section using uniform flow formulae. The sub-area conveyances are then summed to give the total conveyance. Knight and Shiono (1996) identify three main variations on the channel division method which aim to simulate the channel-floodplain interaction more exactly. These are: (1) modification of the sub-area wetted perimeters (Wormleaton et al., 1982); (2) calculation of discharge adjustment factors for each sub-area based on a ‘coherence’ concept (Ackers, 1993) and (3) quantification of the apparent shear stresses on the sub-area division lines (Knight and Hamed, 1984). However, these methods have been developed to estimate the depth-discharge rating curve at particular cross-sections and are largely yet to be incorporated in standard flood routing models. One exception here is the LISFLOOD-FF model of De Roo et al. (2001). Here, a correction of the Manning roughness value is applied to simulate the momentum exchange, which occurs across the shear layer between main channel and floodplain flows.

These 1D codes are more appropriate when the width of the floodplain is no larger than 3 times the width of the main river channel and are not separated from the channel by embankments (Pender et al., 2006). One of the major disadvantages of this approach is that floodplain flow is assumed to be parallel to the channel, although as noted above cross-section conveyance can be computed by separating the cross-sections into a series of panels between which a separate conveyance is performed.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 8 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

2.3.4 Coupled one-dimensional/two-dimensional models (1D+ and 2D-)

Whilst one-dimensional codes are computationally efficient, they do suffer from a number of drawbacks when applied to floodplain flows. These include the inability to simulate lateral spreading of the flood wave, the lack of a continuous treatment for topography and the subjectivity of cross- section location. Whilst all of these constraints can be overcome with higher order codes, the computational cost of running a two or three dimensional simulation may be high. Consequently, recent research has begun to examine hybrid one-dimensional/two-dimensional codes that seek to combine the best of each model class (see for example Bladé et al., 1994; Estrela and Quintas, 1994; Bechteler et al., 1994, Romanowicz et al., 1996; Bates and De Roo, 2000; Venere and Clausse, 2002; Dhondia and Stelling, 2002).

Such models typically treat in-channel flow with some form of the one-dimensional St. Venant equations, but treat floodplain flows as two-dimensional using a storage cell concept first described by Cunge et al. (1980). Here the floodplain is discretized as a series of regions, with flows between regions calculated using analytical uniform flow formulae such as the Manning equation. Initially, this approach was implemented in standard one-dimensional river routing packages such as ISIS (Wicks et al., in press) by defining the storage cells as large polygonal areas (surface areas of ~100-101 km2) representing discrete flooding compartments (e.g. polders, storage basins etc) that are subjectively identified by the user. In Table 2.1 these are classified as 1D+ codes, examples being Infoworks RS, Mike 11 and SOBEK which can actually be used in either 1D or 1D+ modes.

Recent developments in topographic data capture have, however, allowed high (cell size ~100 m) resolution Digital Elevation Models of floodplain areas to be produced. This has allowed storage cells to be discretized as a high resolution grid (storage cells with surface area 10-5-10-4 km2), for example the LISFLOOD-FP raster flood routing model of Bates and De Roo (2000). We classify these codes as 2D- in Table 2.1. LISFLOOD-FP treats in–channel flow using either the simplified kinematic or diffusion wave forms of equations [6] and [7]. Floodplain flows are similarly described in terms of continuity and mass flux equations, discretized over a grid of square cells, which allows the model to represent 2-D dynamic flow fields on the floodplain. Flow between two cells is assumed simply to be a function of the free surface height difference between those cells (Estrela and Quintas, 1994):

1 2 h5 3 ⎛ hi−1, j − hi, j ⎞ i, j flow ⎜ ⎟ [8] Qx = ⎜ ⎟ Δy n ⎝ Δx ⎠

Water depths in each cell are then updated at each time step based on the sum of the fluxes over the four faces of the cell. dhi, j Q i−1, j − Q i, j + Q i, j−1 − Q i, j = x x y y [9] dt ΔxΔy where hi,j is the water free surface height at the node (i,j), Δx and Δy are the cell dimensions, n is the 1/3 -1 effective grid scale Manning’s friction coefficient [L T ] for the floodplain, and Qx and Qy describe the volumetric flow rates between floodplain cells. Qy is defined analogously to equation [8]. The flow depth, hflow, represents the depth through which water can flow between two cells, and is defined as the difference between the highest water free surface in the two cells and the highest bed elevation (this definition has been found to give sensible results for both wetting cells and for flows linking floodplain and channel cells.) This approach is similar to diffusive wave propagation, but differs marginally due to the de-coupling of the x- and y- components of the flow. While this approach does not accurately represent diffusive wave propagation, it is computationally simple and has been shown to give very similar results to a more accurate finite difference discretization of the diffusive wave equation (Horritt and Bates, 2001a).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 9 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Equation [8] is also used to calculate flows between floodplain and channel cells, allowing floodplain cell depths to be updated using equation 12 in response to flow from the channel. These flows are also used as the source term, q, in the channel flow sub-model (see equation [7]), effecting the linkage of channel and floodplain flows. Thus only mass transfer between channel and floodplain is represented, and this is assumed to be dependent only on relative water surface elevations. While this neglects effects such as channel-floodplain momentum transfer and the effects of advection and secondary circulation on mass transfer, it is the simplest approach to the coupling problem and should reproduce the dominant behaviour of the real system.

Such cellular approaches are capable of high-resolution application to relatively long river reaches up ~102 km in length and may provide an alternative to one-dimensional codes. For example, the LISFLOOD-FP storage cell code has been successfully used to model flow routing along a 60 km reach of the River Severn in the UK (see Horritt and Bates, 2002) and a 35 km reach of the River Meuse in The Netherlands (see De Roo et al., 2003).

2.3.5 Zero-dimensional or non-model approaches (0D)

In certain situations one may not even need a model at all to predict inundation extent. Given gauged water surface elevations along a reach, or water surface elevations predicted on the basis of flood frequency analysis, one can perform a similar interpolation to that used by Werner (2001). This approximates the flood wave as a plane (or series of planes) which are intersected with the DEM to give extent and depth predictions. Bates and De Roo (2000) compared this method to two-dimensional storage cell and full two-dimensional hydraulic models for a 35 km reach of the River Meuse, The Netherlands and found that in certain situations the planar approximation performed almost as well as hydraulic modelling. In this application, the methods were used to simulate the January 1995 event 3 -1 (Qpeak = ~2700 m s , 1 in 63 year recurrence interval) and validated by comparison to air photo imagery of flood extent taken at around the time of maximum flooding. For regions close to gauging stations where the recorded water level was used as a height control, the planar approximation achieved accuracy of 81% pixels correctly predicted as wet or dry, compared to 85% for a two- dimensional storage cell model. Away from the gauging station the planar approximation performed less well, and using a hydraulic model produced a better result in all circumstances examined, even if at times this difference was marginal. Clearly, the planar approximation will work well for reaches that are short compared to the wavelength of the flood and where there is good gauged data to constrain the position of the plane. Even in these circumstances, however, lack of mass conservation will mean that areas are predicted as flooded that are not hydraulically connected to the channel. Nevertheless, this may be a useful method under some circumstances, and provides a benchmark level of performance that all hydraulic models should exceed to be considered skilful.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 10 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Table 2.1 Overview of existing types of hydraulic models (After Table 2 from G. Pender et al. (2006)). Method Description Application Example Inputs Outputs Computation Models time (as of 2006) 0D No physical Broad scale ArcGIS DEM Inundation extent Seconds laws assessment of flood Delta mapper Upstream and water depth included in extents and flood water level by intersecting simulations. depths. Downstream planar water water level surface with DEM

1D Solution of Design scale Mike 11 Surveyed Water depth and Minutes the 1D St modelling which can HEC-RAS cross sections average velocity Venant be of the order of 10s SOBEK-CF of channel and at each cross equations. to 100s of km Infoworks RS floodplain section depending on (ISIS) Upstream Inundation extent catchment size. discharge by intersecting hydrographs predicted water Downstream depths with DEM stage Downstream out- hydrographs flow hydrograph

1D+ 1D plus a Design scale model- Mike 11 As for 1D As for 1D models Minutes to storage cell ling which can be of HEC-RAS models hours approach to the order of 10s to Infoworks RS the simu- 100s of km depending (ISIS) lation of on catchment size, flood plain also potential for flow. broad scale application if used with sparse cross-section data. 2D- 2D minus Broad scale modelling LISFLOOD- DEM Inundation extent Hours the law of or urban inundation FP Upstream Water depths con- depending on cell discharge Downstream servation of dimensions. hydrographs outflow momentum Downstream hydrograph for the flood stage plain flow. hydrographs 2D NC Solution of Design scale TUFLOW DEM Inundation extent Hours to days the two- modelling of the order Upstream Water depths dimensional of 10s km. May have discharge Depth-averaged shallow the potential for use in hydrographs velocities at each wave broad scale modelling Downstream computational equations – if applied with very stage node non coarse grids. Not hydrographs Downstream conservative suitable to model outflow form transcritical and dam hydrograph break flows. 2D C Solution of Same as 2D NC plus Mike 21 DEM Inundation extent Hours to days the two- the ability to model TELEMAC Upstream Water depths dimensional accurately SOBEK-OF discharge Depth-averaged shallow transcritical flows, Delft-FLS hydrographs velocities wave dam break and fast Infoworks Downstream Downstream equations - transient flows. stage outflow conservative hydrographs hydrograph form 2D+ 2D plus a Predominantly coastal TELEMAC DEM Inundation extent Days solution for modelling applica- 3D Upstream Water depths vertical tions where 3D velo- Delft-3D discharge u, v and w velocities city profiles are hydrographs velocities for each using important. Has also Inlet velocity computational cell continuity been applied to reach distribution Downstream only. scale river modelling Downstream outflow problems in research stage hydrograph projects. hydrographs

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 11 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Method Description Application Example Inputs Outputs Computation Models time (as of 2006) 3D 3D solution Local predictions of CFX DEM Inundation extent Days of the three- three-dimensional FLUENT Upstream Water depths dimensional velocity fields in main PHEONIX discharge u, v and w Reynolds channels and hydrographs velocities and averaged floodplains. Inlet velocity turbulent kinetic Navier and turbulent energy for each Stokes kinetic energy computational cell equations. distribution Downstream Downstream outflow stage hydrograph hydrographs

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 12 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

3. Model parameterization, validation and uncertainty analysis

Section 2.3 has made clear the variety of models available for floodplain flow modelling. Choice of model has been shown to depend on the scale of the problem, the computational resources available and the needs of the user. However, any model is only as good as the data used to parameterize, calibrate and validate it, and in this section the data sources available for floodplain flow models are discussed along with the methods available to assimilate these data into hydraulic models. The data required by any hydraulic model are principally: (1) boundary condition data; (2) initial condition data; (3) topography data; (4) friction data and (5) hydraulic data for use in model validation. validation. Whilst models should be selected based on the characteristics of the problem in hand, it is also clear that models of different complexity have different data requirements, and in practice this may constrain user choice in model selection.

3.1 Boundary condition data

Boundary condition data consist of values of each model independent variable at each boundary node and at each time step for unsteady simulations. For one and two-dimensional codes these can typically be assigned either from stage or discharge measured at river gauging stations or must be measured in the field by the user. The precise data required depends on the model and the reach hydraulics, but for sub-critical flow will, as a minimum, consist of the flux rate into the model across each inflow boundary and the water surface elevation at each outflow boundary. These requirements reduce to merely the inflow flux rates for super-critical flow problems as when the Froude number Fr > 1 information cannot propagate in an upstream direction. Rating curves may provide an alternative means of parameterizing the outflow water surface elevation in certain models. In addition, 3D codes require the specification of the velocity distribution at the inlet boundary and values for the turbulent kinetic energy. In most cases, hydrological fluxes outside the channel network, e.g. surface and subsurface flows from hill slopes adjacent to the floodplain and infiltration of flood waters into alluvial sediments, are ignored (for a more detailed discussion see Stewart et al., 1999).

3.2 Initial condition data

Initial conditions for a hydraulic model consist of values for each model dependent variable at each computational node at time t=0. In practice, these will be incompletely known, if at all, and some additional assumptions will therefore be necessary. For steady state (i.e. non-transient) simulations any reasonable guess at the initial conditions is usually sufficient, as the simulation can be run until the solution is in equilibrium with the boundary conditions and the initial conditions have ceased to have an influence. However, for dynamic simulations this will not be the case and whilst care can be taken to make the initial conditions as realistic as possible, a ‘spin up’ period during which model performance is impaired will always exist. For example, initial conditions for a flood simulation in a compound channel are often taken as the water depths and flow velocities predicted by a steady state simulation with inflow and outflow boundary conditions at the same value as those used to commence the dynamic run. Whilst most natural system are rarely in steady state, careful selection of simulation periods to coincide their start with near steady state conditions can minimise the impact of this assumption.

3.3 Topography data

Topography is frequently considered the key data set for flow routing and inundation modelling. High resolution, high accuracy topographic data are essential to shallow water flooding simulations over low slope floodplains with complex micro-topography, and such data sets are increasingly available from a variety of remotely mounted sensors. Traditionally, hydraulic models have been parameterised

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 13 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 using ground survey of cross sections perpendicular to the channel at spacings of between 100 and 1000 m. Such data are accurate to within a few millimetres in both the horizontal and vertical and integrate well with one-dimensional hydraulic models. However, ground survey data are expensive and time consuming to collect and of relatively low spatial resolution. They hence require significant interpolation to enable their use in typical two- and three-dimensional models, whilst in one- dimensional models the topography between cross-sections is effectively ignored and results are sensitive to cross-section spacing (e.g. Samuels, 1990). Moreover, topographic data available on national survey maps tends to be of low accuracy with poor spatial resolution in floodplain areas. For example in the UK, Nationally available contour data are only recorded at 5m spacing to height accuracy of ±1.25m and for a hydraulic modelling study of typical river reach Marks and Bates (2000) report finding only 3 contours and 40 unmaintained spot heights within a ~6 km2 floodplain area. When converted into a DEM such data lead to relatively low levels of inundation prediction accuracy in hydraulic models (see Wilson and Atkinson, 2005).

Considerable potential therefore exists for more automated, broad-area mapping of topography from satellite and, more importantly, airborne platforms. Three techniques which currently show reasonable potential for flood modelling are aerial stereo-photogrammetry (Baltsavias, 1999; Lane, 2000; Westaway et al., 2003), airborne laser altimetry or LiDAR (Krabill et al., 1984; Gomes Pereira and Wicherson, 1999) and airborne Synthetic Aperture Radar interferometry (Hodgson et al., 2003). Radar interferometry from sensors mounted on space-borne platforms, and in particular the Shuttle Radar Topography Mission (SRTM) data (Rabus et al., 2003), may in the future provide a viable topographic data source for hydraulic modelling in large, remote river basin where the flood amplitude is large compared to the topographic data error.

LiDAR in particular has attracted much recent attention in the hydraulic modelling literature (Marks and Bates, 2000; Bates et al., 2003; French, 2003; Charlton et al., 2003). Major LiDAR data collection programmes are underway in a number of countries, including The Netherlands and the UK, where so far approximately 20% of the land surface area in England and Wales has been surveyed. In the UK, helicopter-based LiDAR survey is also beginning to be used to monitor in detail (~0.2 m spatial resolution) along critical topographic features such as flood defences, levees and embankments. LiDAR systems operate by emitting pulses of laser energy at very high frequency (~5-100KHz) and measuring the time taken for these to be returned from the surface to the sensor. Global Positioning System data and an onboard Inertial Navigation System are used to determine the location of the plane in space and hence the surface elevation. As the laser pulse travels to the surface it spreads out to give a footprint of ~0.1m2 for typical operating altitude of ~800m. On striking a vegetated surface, part of the laser energy will be returned from the top of the canopy and part will penetrate to the ground. Hence, an energy source emitted as a pulse will be returned as a waveform, with the first point on the waveform representing the top of the canopy and the last point (hopefully) representing the ground surface. The last returns can then be used to generate a high resolution ‘bare earth’ DEM.

3.4 Friction data

Friction is usually the only unconstrained parameter in a hydraulic model. Two and three-dimensional codes which use a zero equation turbulence closure may additionally require specification of an ‘eddy viscosity’ parameter which describes the transport of momentum within the flow by turbulent dispersion, however this prerequisite disappears for most higher order turbulence models of practical interest. Hydraulic resistance is a lumped term that represents the sum of a number of effects: skin friction, form drag and the impact of acceleration and deceleration of the flow. These combine to give an overall drag force Cd, that in hydraulics is usually expressed in terms of resistance coefficients such as Manning’s n and Chezy’s C and which are derived from uniform flow theory. This assumes that the rate of energy dissipation for non-uniform flows is the same as it would be for uniform flow at the same water surface (friction) slope. The precise effects represented by the friction coefficient for a particular model depend on the model’s dimensionality, as the parameterization compensates for energy losses due to unrepresented processes, and the grid resolution. Thus, the extent to which form

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 14 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 drag is represented depends on how the channel cross-sectional shape, meanders and long profile are incorporated into the model discretization. Similarly, a high-resolution discretization will explicitly represent a greater proportion of the form drag component than a low-resolution discretization using the same model. Complex questions of scaling and dimensionality hence arise which may be somewhat difficult to disentangle. Certain components of the hydraulic resistance are, however, more tractable. In particular, skin friction for in-channel flows is a strong function of bed material grain size, and a number of relationships exist which express the resistance coefficient in terms of the bed material median grain size, D50 (e.g. Hey, 1979). Equally, on floodplain sections where conveyance rather than storage processes dominate, the drag due to vegetation is likely to form the bulk of the resistance term (Kouwen, 2000). Determining the drag coefficient of vegetation is, however, rather complex, as the frictional losses result from an interaction between plant biophysical properties and the flow. For example, at high flows the vegetation momentum absorbing area will reduce due to plant bending and flattening. To account for such effects Kouwen and Li (1980) and Kouwen (1988) calculated the Darcy-Weisbach friction factor f for short vegetation, such as floodplain grasses and crops, by treating such vegetation as flexible, and assuming that it may be submerged or non- submerged. f is dependent on water depth and velocity, vegetation height and a product MEI, where M is the number of stems per unit area, E is the stem modulus of elasticity and I is the stem area’s second moment of inertia. Whilst MEI often cannot be measured directly, it has been shown to correlate well with vegetation height (Temple, 1987).

Similar to topography, ground survey of grain size and vegetation parameters is extremely time consuming and, recently, research has begun to consider the use of remotely sensed techniques to determine certain of the above data. For example, photogrammetric techniques to extract grain size information from ground-based or airborne photography are currently under development (Butler et al., 2001). Similarly, recent research developments allow extraction of specific plant biophysical parameters from LiDAR data. For vegetation > 4m in height, this latter technique uses the timing difference between the first and last points on the returned LiDAR waveform to determine the height of the canopy. For vegetation < 4m the method uses the local standard deviation of the last return heights. Cobby et al. (2000 and 2001) demonstrate that the height of short vegetation up to 1.4m high can be estimated with such a technique to 0.14m rmse. Taller vegetation (>10m) is subject to greater height estimation error (~2-3m) as canopies are typically denser and it is less likely that the laser pulse will penetrate the full depth of the canopy, however for the purpose of determining hydraulic resistance this is less of a problem. Given that other plant biophysical properties, e.g. MEI, correlate with plant height, Mason et al. (2003) have presented a methodology to calculate time and space distributed friction coefficients for flood inundation models directly from LiDAR data. Much further work is required in this area, however such studies are beginning to provide methods to explicitly calculate important elements of frictional resistance for particular flow routing problems. This leads to the prospect of a much reduced need for calibration of hydraulic models and therefore a reduction in predictive uncertainty.

3.5 Model data assimilation

Increasing use of the above remote sensing techniques has caused a rapid shift in hydraulic modelling from a data-poor to a data-rich and spatially complex modelling environment with attendant possibilities for model testing and development. Despite an increase in computational power, the relative resolution of model and topography data has now reversed for most codes typically used to simulate flood inundation at the reach scale (see Bates and De Roo, 2000 for a review). A newly emergent research area is therefore how to integrate such massive data sets with lower resolution numerical inundation models in an optimum manner that makes maximum use of the information content available. This is the direct opposite to the problem that most environmental modellers have traditionally faced (see Grayson and Blöschl, 2001 for a general discussion).

For example, Marks and Bates (2000) describe the integration of a LiDAR data set with a two- dimensional hydraulic model where the unstructured mesh discretization was derived independent of

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 15 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 the topography. The topography was then assimilated into the model in an a posteriori step using weighted nearest neighbour interpolation to assign an elevation value to each computational node. This is typical of finite element mesh construction in many fields, but may not produce a mesh that captures those attributes of the original surface that are critical to the modelling problem in hand and may also lead to high data redundancy. To overcome these problems, Bates et al. (2003) describe a processing chain for high resolution data assimilation into a lower resolution unstructured model grid. This consists of: (1) variogram analysis to determine significant topographic length scales in the model; (2) identification of topographically significant points in this data set; (3) incorporation of these points into an unstructured model grid that provides a quality solution for the relevant numerical solver and (4) use of the data left over from the mesh generation process to parameterize the Bates and Hervouet (1999) sub-grid scale algorithm for dynamic wetting and drying. This method is demonstrated for the case of LiDAR topographic data but is general to any data type or model discretization. Cobby et al (2003) take this process further and develop an automatic mesh generator that produces an unstructured grid refined according to vegetation features (hedges, stands of trees etc) on the floodplain identified automatically from LiDAR. These methods show some promise, however much further work is required in this area to more fully analyse the numerical quality of meshes generated by competing techniques.

Similarly for friction parameters, Mason et al. (2003) use an area-weighting method to calculate area- effective frictional resistance from the high resolution height information contained in LiDAR data. This method aims to yield model parameters that are appropriate to the particular discretization used, rather than being scale and discretization independent, although this has yet to be fully tested.

3.6 Calibration, validation and uncertainty analysis

In all but the simplest cases (for example, the planar free-surface ‘lid’ approach of Puech and Raclot, 2002), some form of calibration is required to successfully apply a floodplain flow model to a particular reach for a given flood event. Calibration is undertaken in order to identify appropriate values for parameters such that the model is able to reproduce observed data and, as previously mentioned, typically considers roughness coefficients assigned to the main channel and floodplain and values for turbulent eddy viscosity, νt. , if a zero-equation turbulence closure is used. Though these values may sometimes be estimated in the field with a high degree of precision (Cunge, 2003), it has proven very difficult to demonstrate that such ‘physically-based’ models are capable of providing accurate predictions from single realisations for reasons discussed in the critiques of Beven (1989, 1996, 2001) and Grayson et al. (1992). As such, values of parameters calculated by the calibration of models should be recognised as being effective values that may not have a physical interpretation outside of the model structure within which they were calibrated. In addition, the process of estimating effective parameter values through calibration is further convoluted by a number of error sources inherent in the inundation modelling process which cast some doubt on the certainty of calibrated parameters (Aronica et al., 1998; Horritt, 2000; Bates et al., 2004). Principally, these errors relate to the inadequacies of data used to represent heterogeneous river reaches (i.e. geometric integrity of floodplain topography and flow fluxes along the domain boundaries) but also extends to the observations with which the model is compared during calibration and the numerical approximations associated with the discrete solution of the controlling flow equations. The model will therefore require the estimation of effective parameter values that will, in part, compensate for these sources of error (Romanowicz and Beven, 2003).

Given that the number of degrees of freedom in even the simplest of numerical models is relatively large, it is no surprise that many different combinations of effective parameter values may fit sparse validation data equally well. Such equifinality in floodplain flow modelling has been well documented (see, for example, Romanowicz et al., 1994, 1996; Aronica et al., 1998, 2002; Hankin et al., 2001; Romanowicz & Beven, 2003; Bates et al., 2004) and uncertainty analysis techniques, based on the Generalised Likelihood Uncertainty Estimation (GLUE) of Beven & Binley (1992), have been developed and applied in response. Based on Monte Carlo simulation, GLUE explicitly recognises this

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 16 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 equifinality and seeks to make an assessment of the likelihood of a set of effective parameter values being an acceptable simulator of a system when model predictions are compared to observed field data. In studies reported thus far, this level of ‘acceptability’ has typically been calculated by considering the deviation of simulated variables from one of the following classes of observed data (according to the terminology of Bates & Anderson (2000)):

External and internal bulk flow measures – for example, time series of stages and/or discharges recorded continuously at river gauging stations. Routinely available in national flow archives, these data have proven utility in testing the wave routing behaviour of flood models (for example, Cunge et al., 1980; Klemeš, 1986) and have shown to be replicable by even the simplest of numerical schemes (Horritt and Bates, 2002). As Dietrich (2000) notes “if the goal of a modelling exercise is to predict solely the time evolution of some bulk property of a complex system then spatial lumping (or spatial integration) can be invoked to filter out spatial variability”. As such, they are unlikely to provide a sufficiently rigorous test for competing model parameterisations (i.e. sets of effective parameter values) within spatially distributed schemes capable of directly simulating hydraulic patterns. Nevertheless, automatic collection of these data, often at hourly intervals or less, may provide records of sufficient temporal resolution to reasonably evaluate dynamic model performance and/or identify compensating errors operating within the model structure (for example, Bates et al., 1998). However, given the considerable intermediate distances between gauging stations, internal observations are typically much less common than external ones. Clearly, bulk flow data, while being an important source of observational data, have only limited strength as a stand-alone piece of evidence for the evaluation of hydraulic models and are sometimes of questionable accuracy, particularly for large out- of-bank flows (Bates & Anderson, 2000). Recourse must therefore be made additional sources of data, such as spatially distributed fields of model state variables (i.e. vector and point scale data) to further discriminate between competing models.

Vector data, for example, instantaneous observations of flood extent, either processed from remotely- sensed data (Horritt, 1999) or ground-survey methods (Simm, 1993), which may be considered an approximation to the zero water depth contour. Observational data of this type has the advantage that for relatively flat floodplain topography small changes in water surface elevation can result in large changes in shoreline position. Hence, in order to replicate a flood shoreline adequately a model must generate, either directly or through secondary interpolation, an accurate distributed field of the flow depth. In studies thus far, inundation extent has proven a useful test of model performance as it is both a relatively sensitive measure and its simulation requires a model capable of dealing with dynamic wetting and drying over complex topography (for example, Bates et al., 1997; Horritt, 2000; Bates & De Roo, 2000). However, during events where the valley is entirely inundated, and the flood shoreline is constrained mostly by the slopes bounding the floodplain, changes in water levels may produce only small changes in flood extent (Horritt and Bates, 2001a and b). In these instances, internal validation based on hydrometric data may prove a more exacting test of model performance than extent data. Furthermore, inundation data have typically been limited to one synoptic view per event due to the limited temporal resolution of satellite-borne imaging radars and thus provide only single ‘snapshots’ of inundation extent which do not allow adequate checking of the inundation dynamics simulated by the model.

Point scale data – for example, water levels recorded discretely during post-event surveys or velocities measured in the field. Maximum water levels can often be observed after the recession of a flood event, either as high-water marks on surviving structures or as trash or wracklines deposited at the limit of maximum inundation, and have been used in isolation as calibration data in a number of studies (for example, Aronica et al., 1998; Beven, 1989). However, Lane et al. (1999) have drawn attention to the potential dangers of using these data for calibration purposes, observing that variables simulated by the model are integrated over both space and time and, as such, are rarely reconcilable with point scale observations collected in the field.

While it is clear from the preceding discussion that each class of observed data has some value in the calibration and uncertainty estimation processes, it also apparent that the limitations of each data

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 17 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 source are such that, when used in isolation, they may preclude any definitive judgements to be made about model performance. These limitations may be considered in direct relation to the dimensionality of the respective data sources and their failure to provide explicit definition in higher dimensions – for example, vector data which may be considered two-dimensional in space but zero-dimensional in time. However, by making use of more than one type of observational data in the calibration process we should (hopefully) be able to overcome the inherent spatial or temporal limitations of any single source.

To date, only very limited attempts to calibrate distributed models against more than one particular data type have been made. Horritt and Bates (2002) tested the predictive performance of three industry-standard hydraulic codes on a 60 km reach of the River Severn, UK using independent calibration data from hydrometric and satellite sources. They found that all models were capable of simulating inundation extent and floodwave travel times to similar levels of accuracy at optimum calibration, but that differences emerged according to the calibration data used when the models were used in predictive mode due to the different model responses to friction parameterisations. However, Horritt and Bates (2002) did not consider either the potential for combining both data sources in the calibration process or the uncertainties associated with the model predictions.

Multiple observation data sets for historical flood events are still exceedingly rare and, as such, the potential value of additional observations in the calibration process has yet to be explored in the case of floodplain flow models. Furthermore, the use of uncertainty estimation techniques during this conditioning process allows the relative value of individual (sets of) observations to be precisely quantified in terms of the reduction in uncertainty over effective parameter specification (cf. Beven & Binley, 1992; Hankin et al., 2001). Interpretation of these uncertainty measures may also provide guidance over how much and of what type of observed data would be required to achieve given levels of uncertainty reduction in simulated variables.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 18 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

4. Models used in Task 8

4.1 Introduction

This chapter describes the numerical codes that are used in Task 8 to develop flood models for the pilot sites. Following the classification given in Table 2.1 we have a variety of OD, 1D, 2D- and 2D codes as these are most immediately appropriate for modelling dynamic wave routing and floodplain inundation. We exclude 3D models for the analysis at this stage as these are too computationally demanding for practical application and significant mesh distortion problems when applied to shallow water flows. Summary characteristics of the selected models are given in the table below.

Type of model software package characteristics of software package 1D • SOBEK-1D • 1D Saint-Venant equations, finite-volumes • SV1D • 1D Saint-Venant equations, finite-volumes pseudo 2D • Rapid Flood Spreading model • flood storage cells type model without time- stepping 2D- • LISFLOOD-FP • Research level (i.e. non-commercial) code that solves in-channel flow using 1D kinematic routing and floodplain flow using an analytical approximation to a 2D diffusion wave, with stability maintained through the adaptive time stepping scheme of Hunter et al. (2005b) 2D • SOBEK-1D2D • Saint Venant equations, structured mesh, finite volumes • SV2D • 2D shallow-water equations, structured and unstructured mesh, finite-volumes • Infoworks 2D • Saint-Venant equations, unstructured mesh, finite volumes

The applied models are described in more detail below.

4.2 LISFLOOD-FP

Raster-based storage cell codes, such as the LISFLOOD-FP model of Bates and De Roo (2000), solve a continuity equation relating flow into a cell and its change in volume:

i, j i−1, j i, j i, j−1 i, j ∂h Q x − Q x + Q y − Q y = [10] ∂t Δx Δ y and a momentum equation for each direction where flow between cells is calculated according to Manning’s law (only the x direction is given here):

1 2 h 5 3 ⎛ h i−1, j − h i, j ⎞ i, j flow ⎜ ⎟ [11] Q x = ⎜ ⎟ Δ y n ⎝ Δx ⎠ where h i,j is the water free surface height at the node (i, j), Δx and Δy are the cell dimensions, n is the Manning’s friction coefficient, and Qx and Qy describe the volumetric flow rates between floodplain cells. Qy is defined analogously to equation [11]. The flow depth, hflow, represents the depth through which water can flow between two cells, and is defined as the difference between the highest water

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 19 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 free surface in the two cells and the highest bed elevation. These equations are solved explicitly using a finite difference discretization of the time derivative term: t+Δt i, j t i, j t i−1, j t i, j t i, j−1 t i, j h − h Q x − Q x + Q y − Q y = [12] Δt Δx Δ y where th and tQ represent depth and volumetric flow rate at time t respectively, and Δt is the model time step.

The model time step is set by the user, however too large a time step was found to result in ‘chequerboard’ oscillations in the solution which rapidly spread and amplify, rendering the simulation useless. Ironically, these oscillations occur most readily in areas with low free surface gradients, where we might expect obtaining a solution to be easiest. For this reason, a flow limiter was found to be required in order to prevent instabilities in areas of very deep water, by setting a maximum flow between cells. This flow limit was fixed so as to prevent ‘over’ or ‘undershoot’ of the solution, and is a function of flow depth, grid cell size and time step:

i, j i−1, j i, j ⎛ i, j Δx Δ y ()h − h ⎞ ⎜ ⎟ [13] Q x = min ⎜Q x , ⎟ ⎝ 4 Δt ⎠

This value is determined by considering the change in depth of a cell, and ensuring it is not large enough to reverse the flow in or out of the cell at the next time step. This limiter replaces fluxes calculated using Manning’s equation with values dependent on model parameters, and hence when the flow limiter is in use floodplain flows are sensitive to grid cell size and time step, and insensitive to Manning’s n.

In tests of the code conducted to date validation data has largely consisted of gauged hydrometric data and single ‘snapshot’ images of near-maximum flood extent derived from air photo data and satellite- borne and airborne Synthetic Aperture Radars. The LISFLOOD-FP model has been tested within a simple calibration framework against inundation and hydrometric data for the Rivers Thames (Horritt and Bates, 2001a) and Severn (Horritt and Bates, 2001b; 2002) in the UK and the Meuse (Hunter et al., 2005a; Bates and De Roo, 2000) in The Netherlands and compared to two alternative hydraulic models; a planar approximation to the water surface (in effect not a model at all) and a standard two- dimensional finite element scheme. In all cases LISFLOOD-FP equalled or outperformed the alternatives when simulations of inundation extent were compared, even when the grid resolution was comparable.

Despite their ability to successfully replicate this maximum flood extent data, the simplifying assumptions made in the development of storage cell codes do lead to a number of theoretical and practical constraints to their usage. Firstly, when the flow limiter (equation [7]) was invoked for a significant proportion of the domain the model was found to lack any meaningful sensitivity to floodplain friction and seemed to be over-sensitive to channel friction (Horritt and Bates, 2002). Use of the flow limiter also means that the results are not independent of the space and time step selected by the modeller. While this result is common in both explicit and implicit (Romanowicz and Beven, 2003) formulations of storage cells schemes and is in agreement with the hypothesis of Cunge et al. (1980) - that the floodplains act primarily as additional storage, while the main body of the wave is transported by the main channel - it should not be overlooked as a potentially erroneous artefact of the model structure. A consequence of this sensitivity is that predictive performance of the model may be adversely affected (Horritt and Bates, 2002). Hence even though the optimum calibration for two events may be drawn from a similar region of the parameter space, steep gradients within this space may mean that when calibrated parameters from one event are used to predict another, the absolute model performance may vary markedly. In other words optimum parameter sets need only differ by a small amount to be considered non-stationary between events. Secondly, when applied without

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 20 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 calibration (i.e. single-realisation deterministic mode), LISFLOOD-FP can be shown to under predict markedly both the spatially-distributed (i.e. inundation extent, flood depths) and bulk (i.e. wave volume, travel time) flood characteristics within the domain when compared with other modelling approaches (Werner and Lambert, 2007).

As a solution to the above problems Hunter et al. (2005b) have recently proposed a modified version of the LISFLOOD-FP based on adaptive time stepping. This approach seeks to remove the need to invoke the flow limiter (equation [13]) by finding the optimum time step (large enough for computational efficiency, small enough for stability) at each iteration. Stability depends on water depth, free surface gradients, Manning’s n and grid cell size and thus varies in time and space during a simulation.

This method uses an analysis of the governing equations and their analogy to a diffusion system to calculate the largest stable time step. Equations [10] and [11] are essentially discretizations of the continuity and momentum equations:

∂h + ∇⋅ q = 0 [14] ∂t

1 2 h 5 3 ∂h 1 2 h 5 3 ∂h q = ± flow , q = ± flow [15] x n ∂x y n ∂y where qx and qy are components of the flow per unit width. Equation [15] differs from the usual definition of Manning’s equation in 2D shallow water models in that the two components are decoupled, but this has been found to have negligible effect on model predictions (Horritt and Bates, 2001a). The sense of the flow is determined by whether the free surface gradient is positive or negative. Combining equations [14] and [15] we obtain:

−1 2 ∂h h 5 3 ∂h −1 2 ∂2h h 5 3 ∂h ∂2h − flow − flow ± ∂t 2 n ∂x ∂x2 2 n ∂y ∂y2 142444444 43444444 Diffusion Terms [16]

1 2 5 h 2 3 ∂h 1 2 ∂h 5 h 2 3 ∂h ∂h flow flow ± flow flow = 0 3 n ∂x ∂x 3 n ∂y ∂y

The terms with the second spatial derivatives make up the diffusion part of the equation, and will dominate when free surface gradients are small and stability problems are likely to arise. The solution is unlikely to mirror the behaviour of classical diffusion problems since the diffusion coefficient varies in space and time, and is anisotropic, but we can use the analogy to estimate the most efficient time step. For the diffusion equation:

∂h ⎛ ∂2h ∂2h ⎞ − α ⎜ + ⎟ = 0 [17] ⎜ 2 2 ⎟ ∂t ⎝ ∂x ∂y ⎠ and its explicit discrete counterpart on a square grid (subscripts are spatial grid locations, superscripts time): h t+1 − h t α i, j i, j − ()h t + h t + h t + h t − 4 h t = 0 [18] Δt Δ x 2 i+1, j i−1, j i, j+1 i, j−1 i, j

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 21 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 a von Neumann stability analysis produces the following time step condition:

Δ x2 Δt ≤ [19] 4 α

t At equality, the h ij terms in equation [18] cancel, and it becomes the well known Jacobi relaxation approach to the solution of Laplace’s equation, where the value at a node is iteratively replaced by the mean of neighbouring values. This would imply that an optimal time step for the hydraulic model at a specific location is given by:

1/2 Δ x2 ⎛ 2 n ∂h 1/2 2 n ∂h ⎞ Δt = min ⎜ , ⎟ [20] 4 ⎜ h 5 3 ∂x h 5 3 ∂y ⎟ ⎝ flow flow ⎠

We thus arrive at an expression for the time step similar in form to that used by Werner & Lambert (2007) but larger by a factor of 2. In Werner & Lambert (2007) the time step was set to allow small chequerboard oscillations to decay down to a flat free surface, whereas in this analysis we counter the build up of these oscillations directly, and hence can use a larger time step. A scheme that uses this criterion can be implemented by searching the domain for the minimum time step value and using this to update h. The time step will thus be adaptive and change during the course of a simulation, but is fixed in space at each time step.

A problem with this approach is that there is no lower bound on the time step. As free surface gradients tend to zero (standing water), α tends to infinity and hence the time step also tends to zero. Furthermore, as flow reverses during the transition between the wetting and drying phases, the time step is driven to zero, causing the model to ‘stall’. For a fully dynamic model, some way of dealing with this pathological behaviour as surface gradients tend to zero is required. This is avoided by introducing a linear scheme that is applied to cells where free surface elevations in neighbouring cells differ by less than a specified threshold, hlin (Cunge et al., 1980) the flow equation then becomes:

1 2 h 5 3 ⎛ Δ x ⎞ ⎛ ∂h ⎞ flow ⎜ ⎟ [21] qx = ⎜ ⎟ ⎜ ⎟ n ⎝ h lin ⎠ ⎝ ∂x ⎠ with a similar expression for qy. For cells where this linearised flow equation is applied, an equation similar to equation [20] above is used to determine the time step.

Hunter et al. (2005b) tested this new adaptive time step (ATS) formulation against analytical solutions for wave propagation over flat and planar slopes and showed a considerable improvement over the original fixed time-step version of the model. Moreover, the ATS scheme was shown to yield results that were independent of grid size or choice of initial time step and which showed an intuitively correct sensitivity to floodplain friction over spatially-complex topography.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 22 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

4.3 SV1D and SV2D

4.3.1 Concept and numerical approach

The flood modelling tools SV1D and SV2D were developed for research purposes at the Université catholique de Louvain (UCL, Belgium) for fast transient flow simulations (Soares-Frazão, 2002). The main applications concern dam-break flows, with a special focus on irregular topographies and complex environments such as urban areas.

The one-dimensional model SV1D solves the Saint-Venant equations written in the following form, where the bed slope source terms S0 and the I2 term related to widening and narrowing of the cross- sections have been combined in a single term as in [22b], representing the derivative of the static moment I1 for a constant water level z

∂ A ∂Q + = 0 [22a] ∂t ∂ x

∂Q ∂ ⎛ Q 2 ⎞ ∂ + ⎜ + g I ⎟ = g I − g AS [22b] ⎜ 1 ⎟ ( 1 z ) f ∂ t ∂x ⎝ A ⎠ ∂x

These equations are discretised by a finite-volume scheme, with a lateralised HLL scheme (Fraccarollo et al., 2003) for the fluxes. Writing the topographical source terms as in [22b] ensures equilibrium at rest.

The SV2D model is based on a finite-volume numerical scheme solving the two-dimensional shallow- water equations on unstructured meshes (usually triangular cells). The fluxes are computed using Roe’s scheme (Alcrudo and Garcia-Navarro, 1993). The bed slope source terms are treated in a lateralised way (Soares Frazão, 2002), which is somewhat similar to an upwind treatment. This technique appears to be very robust and yields good results on irregular topographies such as the present one. The friction term is computed using Manning’s formula.

In two-dimensional conservative vector form, the Saint-Venant shallow-water equations stating mass and momentum conservation read:

∂U ∂F()U ∂G()U + + = S [23] ∂t ∂x ∂ y with the variables defined as

⎛ h ⎞ ⎛ uh ⎞ ⎜ ⎟ ⎜ ⎟ U = ⎜uh⎟ F = ⎜u2h + gh2 2⎟ [24a,b] ⎜ ⎟ ⎜ ⎟ ⎝vh ⎠ uvh ⎝ ⎠ ⎛ vh ⎞ ⎛ 0 ⎞ ⎜ ⎟ ⎜ ⎟ G = ⎜ uvh ⎟ S = ⎜ gh ()S0x − S fx ⎟ [24c,d] ⎜ 2 2 ⎟ ⎜ ⎟ v h + gh 2 ⎜ ⎟ ⎝ ⎠ ⎝ gh ()S0 y − S fy ⎠

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 23 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

In equations [23] and [24] h is the water depth, uh and vh the unit discharge in the x- and y-direction respectively, S0x and S0y the bed slope in the x- and y-direction respectively and Sfx and Sfy the components of the friction slope, computed using Manning’s formula.

The finite-volume scheme is built upon an integral form of equations [22], [23] and [24], yielding the generalised expression for non-Cartesian grids (Toro, 1999):

nb n+1 n Δt −1 * Ui = Ui − ∑ Tj Fj ()U j L j + Si Δt [25] Ω i j =1

where Ωi is the cell-base area, Lj the j-interface length and nb the number of cell interfaces (3 for triangular cells). The vectors U and F(U) express U and F in terms of normal and tangential velocity components, un and vt, attached to the considered interface, using a transformation matrix T, where nx and ny are the components of the outwards unit vector normal to the interface:

⎛1 0 0 ⎞ ⎛ h ⎞ ⎛ h ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ U = T U = ⎜0 n n ⎟ ⎜uh⎟ = ⎜u h⎟ [26] ⎜ x y ⎟ ⎜ ⎟ ⎜ n ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝0 − ny nx ⎠ ⎝ vh⎠ ⎝ vt h ⎠

The flux normal to the interface becomes:

⎛ u h ⎞ ⎜ n ⎟ F ()U = ⎜ u2 h + gh2 2 ⎟ [27] ⎜ n ⎟ ⎜ ⎟ ⎝ un vt h ⎠

The problem is thus solved by computing the mass and momentum fluxes in the direction normal to each interface, and then combining those fluxes to obtain the mass and momentum balance over each cell.

The normal fluxes are computed using Roe’s scheme adapted to the shallow water equations (Alcrudo and Garcia-Navarro, 1993), taking into account the wave propagation celerity of the system.

4.3.2 Additional features

Breaching can be taken into account in a simplified way, i.e. without exact morphological modelling of the breach growth. Rather, the final width of the breach can be specified, and the adaptation towards this final width is achieved either instantaneously opening or progressively. For example, if the progressive opening is assumed to take place over 24 h, with a decreasing opening rate, this progressive growth is taken into account in the computational model by multiplying the flux passing through each cell of the breach by a coefficient α varying in time from 0 to 1:

⎛ 1 ⎞ α = 2 ⎜1− ⎟ [28] ⎝ t 86400 +1⎠ where t is the time in seconds.

According to the known final breach width, the user selects the computational cells concerned with the breaching. These cells are located on dykes and thus appear with a higher bed elevation in the

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 24 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 discretised model of the area (Figure 4.1). Once the breaching starts, the bed elevation in the concerned computational cells is suddenly set to the final bed elevation.

Figure 6 shows an example of this: the dyke can be identified as computational cells with a higher bed elevation. The exact location of the breach and its final length are indicated as a black line superimposed on the computational grid (inset of Figure 4.1). Then, the computational cells selected to pertain to breach are marked by a cross. The selection must be such that water is allowed to flow from the sea to the polder. The figure also shows by means of a thick black line the cell interfaces through which water will flow from the sea boundary condition to the inside of the computational domain. The coefficient α was used to simulate the progressive opening of the breach is applied to the numerical fluxes calculated through these interfaces.

Figure 4.1 Representation of a breach in SV2D. Cell interfaces in contact with the sea boundary condition are indicated as thick black line in the inset.

4.3.3 Calibration and validation

Calibration of the SV2D model is not required, as there are no specific parameters to calibrate. Rather, for some applications, sensitivity analyses have to be carried out to define the best approximation for friction coefficients, or breach growth rates, for example.

Validation of the model was achieved by comparing the numerical results to analytical solutions for dam-break flows (Soares-Frazão, 2002), and by numerous comparisons with experimental data. Two examples of this latter type of validation are presented: a one-dimensional dam-break flow over a triangular bottom sill (Soares-Frazão, 2007) and a two-dimensional dam-break flow in a channel with a 90° bend (Soares-Frazão and Zech, 2002).

Dam-break flow over a triangular bottom sill

The experimental set-up is sketched in Figure 4.2. The channel has a rectangular cross section. It is 5.6 m long and 0.5 m wide, with glass walls. The upstream reservoir extends over 2.39 m and is initially filled with 0.111 m of water at rest. Downstream from the gate, the channel is dry up to the bump. The initial water head against the gate is thus h0 = 0.111 m. The symmetrical bump is 0.065 m high and has bed slopes of ± 0.14. Downstream from the bump, a pool contains 0.02 m of water at rest, and a wall closes the downstream end of the channel.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 25 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 4.2 Experimental set-up and initial conditions, all dimensions in metres

The gate separating the reservoir from the channel can be pulled up rapidly by means of a counterweight and pulley system that allows simulating an instantaneous dam break.

Available data for this test case consist in water level evolution in time at 3 measurement points and water profiles measured by digital-imaging techniques. A more detailed description can be found in Soares-Frazão (2007).

This test case was simulated using the SV2D model, and some results are reported in Soares-Frazão et al. (2002). This test case was computed on a 0.01-m mesh, in order to represent the bump as a series of steps with a sufficiently small height, compatible with the small water depth on the slopes. The results are first-order accurate in space, and were obtained with a CFL number of 0.9.

Comparisons with the experimental water-surface profiles are shown in Figure 4.3, for t = 1.8 s, t = 3.0 s, t = 3.7 s and t = 8.4 s. At t = 1.8 s (Figure 4.3a), the front wave is running up the upstream slope of the bump. The water level is well reproduced by the numerical model, but the front wave propagates slightly too fast on the slope. In the downstream pool, the computed water profile is perfectly horizontal, showing that the water stays well at rest, even on the slope. However, a discrepancy can be observed between the measured and computed water levels in the downstream pool, even though water there is at rest. This is due to an inaccurate measurement, as the calibration of the cameras was inaccurate when they were placed at the downstream end of the channel.

At time 3.0 s (Figure 4.3b), the bore formed by the reflection against the upstream slope of the bump is propagating back into the upstream direction. The numerical results are in agreement with the measurements, both for the water levels and the bore position. In the downstream pool, the bore formed at the arrival of the fast dam-break wave in the water at rest is also well reproduced by the numerical model. This latter bore then is reflected against the downstream wall (Figure 4.3c) and it appears that the numerical model overestimates this propagation speed. The more important discrepancies between numerical results and experiments are observed in the downstream pool, where complex processes occur, with multiple wave reflections. However, globally, the numerical scheme is able to reproduce these features.

At time 8.4 s, the bore formed by the second reflection against the downstream wall passes over the crest of the bump, in the upstream direction (Figure 4.3d). The computed water levels are in agreement with measurements, showing that this process is well captured by the numerical scheme.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 26 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

(a) t = 1.8 s

(b) t = 3 s

(d) t = 8.4 s Figure 4.3 Comparison between experimental and numerical flow profiles.

Dam-break flow in a channel with a 90° bend

This test case is described in Soares-Frazão and Zech (2002). The experiments intend to document the here-above description of the phenomenon in the case of a 90° bend. Figure 4.4 illustrates the experimental set-up, located in the Civil Engineering Department of the Université catholique de Louvain, Belgium. The upstream reservoir has dimensions of 2.44 m × 2.39 m, the channel is rectangular, 0.495 m wide, with glass walls, the upstream reach is about 4 m long and the downstream reach, after the bend, is about 3 m long. The channel bed level is 0.33 m above the upstream reservoir bed level. The downstream end of the channel is open (free chute). The initial water level in the reservoir is 0.25 m above the channel bottom. The channel bed is initially dry; its Manning roughness was measured under steady flow conditions as 0.011. The sudden rise of the gate separating the upstream reservoir from the channel simulates the dam break.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 27 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 4.4 Channel with 90° bend – Plane view (dimensions in m)

The flow was imaged by cameras above the flume for velocity measurements and through the glass walls for water-level measurements. Besides digital-imaging techniques, the water level evolution at 6 measurement points along the channel was measured (Soares-Frazão and Zech, 1999).

Comparisons of measured and computed water profiles along the outer wall of the clume at different times (3 s, 5 s, 7 s and 14 s) are shown on Figure 4.5. The bend zone, located between abscissa 6.31 m and 7.3 m, is indicated by two vertical lines.

Figure 4.5 Experimental and computed (2D model) flow profiles: (a) t = 3 s, (b) t = 5 s, (c) t = 7 s, (d) t = 14 s

The computed results show a good overall agreement with the measured profiles. At t = 3 s (Figure 4.5a), the front has reached the bend and the reflection has just occurred. The important rise of the water level due to the reflection against the bend appears in the computation but comparisons with the experiment are not possible at this early stage as the splashing effects make the free surface fuzzy. The

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 28 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 column of water, still fed by the water coming from the reservoir, transforms into a secondary dam- break-like front in the downstream direction and into a bore travelling back in the upstream direction. At t = 5 s (Figure 4.5b), the downstream front has already reached the free end of the channel, while the bore slowly recedes in the upstream reach. The water level is well reproduced, but a slight delay appears in the bore position. The numerical bore travels slightly slower than the real one, which is particularly clear on Figure 4.5c (t = 7 s). At t = 14 s (Figure 4.5d), the bore has almost reached the reservoir. After drowning in this, the flow becomes much slower, and attains an almost steady state, consisting in a progressive emptying of the reservoir.

4.4 SOBEK

4.4.1 Concept and numerical approach

SOBEK is a hydraulic modelling software package developed by Deltres | Delft Hydraulics (formerly known as WL | Delft Hydraulics) that consists of several modules. The modules used for inundation modelling are the Overland Flow module (SOBEK-2D) and the Channel Flow module (SOBEK-1D).

SOBEK is based upon the solution of the full de Saint Venant equations (de Saint Venant, 1871), presented in a slightly adapted form as follows:

∂A ∂Q t + = q [29] ∂∂txlat

1 ∂∂QQ2 ∂ζ QQ { +( )+} +=0 [30] gA∂∂ t x A ∂ x K 2

2 where At is the cross-sectional area representative for storage over a control volume (m ), t the time 3 (s), Q the discharge (m /s), x the position along the channel axis (m), qlat the lateral discharge per unit length of channel (m2/s), A the flow conveying cross-sectional area (m2), ζ the water level above a selected horizontal reference plane (m) and K the channel conveyance (m3/s).

In SOBEK the numerical solution of the de Saint Venant equations is based upon an implicit formulation on a staggered numerical grid. This offers great advantages in the numerical stability and robustness, in particular through the time step controller implemented in the numerical algorithm. On the staggered grid the dependent variables Q and ζ are defined alternatingly at successive grid points along the x-axis. On the so-called non-staggered schemes the variables Q and ζ would be defined jointly at every grid point. At first sight this last definition offers advantages through the availability of the state variables discharge and water level at the same points along the channel axis. It has been shown, however, that the staggered grid approach offers distinct advantages over non- staggered grids by guaranteeing the convergence of numerical solutions and the better ability to handle flooding and drying of grid sections, as shown by Stelling et al. (1998).

The numerical solution of the de Saint Venant Equations [29] and [30] in SOBEK is based upon their Eulerian form per unit width of channel. Without lateral inflow, wind stress and for constant width profiles, the equations are:

∂∂ς ()uh +=0 [31] ∂∂tx and

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 29 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

∂∂u ς uu ++adv g + c =0 [32] ∂∂txhf where ζ is the water level defined as ζ = h+zb with h defined as the local water depth (m) and zb as the local bottom level (m), u the flow velocity (m/s), adv the advective term (m/s2) and cf the dimensionless bottom friction coefficient.

Figure 4.6 Staggered grid for unsteady channel flow or pipe flow

Referring to Figure 4.6 and to Stelling and Duinmeijer (2003) for further details, the staggered grid approach requires that alternatingly at ζ- and u-points, equations [31] and [32] are applied. (see also Abbott (1979), Cunge et al. (1980), Hirsch (1990) and Toro (1999)). The advective term is set such that momentum conservation is ensured, except in strong contractions, where energy conservation is applied. For profiles with height varying width, the non-linear equation [29] is solved through Newton iteration.

SOBEK Overland Flow consists of a 2-dimensional modelling system based on the Navier-Stokes equations for depth-integrated free surface flow. All equations are solved through a fully implicit finite difference formulation for all terms in the Navier-Stokes equations, based upon a staggered grid. The special way in which the convective momentum terms have been formulated allows for the computation of mixed sub- and supercritical flows. Based upon this formulation it is also possible to compute the behaviour of standing and moving hydraulic jumps. For these computations to be robust and accurate there is no need to introduce artificial viscosity.

In combination with the 2D modelling system, SOBEK is able to handle 1D elements such as (small) water courses and hydraulic structures. In this 1D-2D combination, the 2D overland flow, including the obstructing effects of embankments and natural levees, is simulated through the 2D equations of SOBEK Overland Flow, while the sub-2Dgrid gullies and the hydraulic structures are modelled with SOBEK Channel Flow. Both modelling systems produce implicit finite difference equations, which are also linked through an implicit formulation for joint continuity equations at locations where both modelling systems have common water level points, as shown in Figure 4.7.

a b Figure 4.7 Schematisation of the Hydraulic Model: a) Combined 1D/2D Staggered Grid; b) Combined Continuity Equation for 1D2D Computations

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 30 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

The main advantages of combination of flow in the 1D and 2D domain are: • 2D grid steps can usually be significantly larger, as no refinement of the 2D grid is required for the correct representation of hydraulic structures and gullies; • as a result, the simulations will run much faster for a comparable level of accuracy; • a wide variety of hydraulic structure descriptions can be used; • robustness and accuracy.

The Overland Flow and the Channel Flow modules of SOBEK are based upon the same numerical principles and both allow for extremely stable and robust computations. In the first place this is based upon the properties of the numerical schemes applied. In the second place, a number of checks are made at every step in the computation to prevent physically unrealistic results, such as negative water depths. If such a constraint is not satisfied, the time step will be reduced. Such a procedure is also applied in the flooding and drying of cells in the Overland Flow module. Every time only one neighbouring computational cell can be wetted or dried, otherwise the time step will be reduced to satisfy this criterion.

The robustness and accuracy of the numerical schemes follow to a large extent from the particular way in which the convective momentum terms have been discretized. The formulation implemented also suppresses the development of oscillating velocity directions at irregular model boundaries. Here the finite difference scheme offers the same robust behaviour as models which follow irregular boundaries with their grid contours, such as curvilinear grids and finite elements. Of particular interest is the strict volume conservation. This feature is of particular importance in the simulation of transport of pollutants.

4.4.2 Additional features

SOBEK offers several additional features that can be used for inundation modelling. The main features are: • Simulating breach growth; • Rainfall and evaporation; • Wind set up.

Breach growth can be simulated using three approaches: 1. location, timing and breach size prescribed by the user. In this case SOBEK only computes the breach growth in time until the maximum width is reached. 2. location and timing prescribed by the user, breach width computed by SOBEK. SOBEK computes breach width B (m) in time (t), as a function of the difference in water level on both sides of the breach H (m) and the critical flow velocity for erosion (uc in m/s): gH0,5 1,5 ⎛⎞0,04. g Bt=+1, 3 log⎜⎟ 1 [33] uucc⎝⎠ 3. location and timing are determined by SOBEK, breach width equals cell size. This method allows for the application of a criterion for failure. The Real Time Control module of SOBEK (RTC- module) checks for each time step whether this criteria is met. Different criteria can be applied such as the exceedence of water levels or flow velocities, either instantaneous or during a certain time period. The width of the breach does not vary in time, but equals the width of a grid cell.

Flooding due to heavy rainfall can be accounted for. The same applies to the impact of evaporation. Evaporation can play an important role at locations where flooding last for months and evaporation losses are high. An example of an area where this option was prerequisite is the Doñana wetland in southern Spain. The rainfall distribution is assumed homogeneous over the area of interest.

The impact of strong winds on water levels can be simulated as well. This is of importance when vast areas are flooded under storm conditions.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 31 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

4.4.3 Calibration and validation

For proof of accuracy, comparison of results has been made with experimental studies, both with published data and obtained through own laboratory experiments. A dyke break flood onto a flat, horizontal basin has been undertaken in the Fluid Mechanics Laboratory of Delft University of Technology, the Netherlands (Liang et al., 2004). Figure 4.8 illustrates the experimental layout, which consists of a closed reservoir containing water of initial depth equal to 0:6 m separated by a solid dyke wall from a flat basin. The basin was initially dry or contained still water to a low depth (0:05m for the case considered here). A gate opening of 40cm represented the breach, and was located in the middle of the dyke. The dyke-break was modelled by lifting the gate at a constant speed of about 16 cm/s. According to Duinmeijer (2002), the basin has a smooth concrete bed corresponding to a Manning roughness coefficient of 0:012 ms−1/3. Reflective boundary conditions are imposed at all solid walls.

Figure 4.8 Delft University of Technology dyke break: top view and side view of the experiment layout (Liang et al., 2004)

Figure 4.9 shows the progress of the flood wave as observed from above. The upper part of the figure shows the image taken with a camera above the flume. The lower part shows the computed water levels at the same time step. The flood spreads from right to left. The figure shows that the computed front of the flood (b) is at the same position as the measured front (a). The same applies to the location of the hydraulic jump (comparison of c and d). Even the reflection from the walls is simulated correctly (comparison of e and f).

Figure 4.10 shows the measured and computed front of the flood wave at different time steps. From both figures it can be concluded that the model reproduces the experimental results accurately and that it is capable of simulating sub-critical flow, super-critical flow and hydraulic jumps. Wetting and drying of cells in the models does not cause any instabilities either.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 32 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

a e

d b

Figure 4.9 Comparison of measured and simulated water levels using the experiment carried out by Delft University of Technology (Duinmeijer, 2002).

Figure 4.10 Comparison of measured and simulated position of the front of the flood at different time steps (Duinmeijer, 2002).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 33 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

4.5 Infoworks 2D

A new version of InfoWorks RS-2D has been recently developed by Wallingford Software to couple a powerful 2D engine with a widely used 1D engine. Comprehensive testing of this new modelling package has been undertaken by HR Wallingford in order to: • check the numerical robustness of the model, • ensure the software meets the requirements of the engineering studies in terms of usability,

The testing procedure includes simulations of theoretical tests for which an analytical solution is known and the simulation of a real flood event in Boscastle (Lhomme et al. submitted). Only the analytical tests are presented here.

4.5.1 Overview of the 1D engine

The 1D component of InfoWorks RS-2D is widely used by practitional engineers and can simulate flows in channels or conduits, as well as hydraulic structures such as weirs, sluices, pumps (Wallingford Software 2008). Within this component the Saint-Venant equations are used as the mathematical representation of 1D flow :

⎧∂A ∂Q ⎪ + = q ∂t ∂x [34] ⎨∂Q ∂(uQ) ∂h ⎪ + + gA = gA()S − S ⎩ ∂t ∂x ∂x 0 f where A is the wetted cross-sectional area, Q is the discharge, QL is the lateral discharge per unit length, u is the velocity, h is the water depth, S0 and Sf are respectively the bottom slope and the friction slope.The solution algorithm is based on the Preissmann four-point implicit finite difference scheme (Preissmann 1961). After the discretisation, the 1D system is solved by inverting a sparse matrix. Because the numerical scheme is implicit, there is no time-step condition and the time-step is fixed by the user.

4.5.2 Overview of the 2D engine

The 2D engine used in InfoWorks RS-2D is based upon the procedures described in (Alcrudo and Mulet 2005). The Shallow Water equations (SWE), i.e. the depth averaged version of the Navier- Stokes equations, are used for the mathematical representation of the 2D flow:

∂h ∂(hu) ∂(hv) + + = q [35] ∂t ∂x ∂y 1D ∂(hu) ∂ ∂(huv) + ()hu 2 + gh2 / 2 + = S − S + q u [36] ∂t ∂x ∂y 0,x f ,x 1D 1D ∂(hv) ∂(huv) ∂ + + ()hv2 + gh2 / 2 = S − S + q v [37] ∂t ∂x ∂y 0, y f , y 1D 1D where h is the water depth, u and v are the velocity respectively in the x and y direction, zb is the ground level, K is the Strickler friction coefficient, S0,x and S0,y are the bottom slope respectively in the x and y direction, Sf,x and Sf,y are the friction slope respectively in the x and y direction, q1D is the source discharge per unit area, u1D and v1D are the velocity components of the source discharge q1D respectively in the x and y direction.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 34 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

This conservative formulation of the SWE is discretised using an explicit finite volumes scheme. Roe’s Riemann Solver is used to calculate the fluxes at the interfaces between cells. The time-step is calculated in order to satisfy the Courant-Friedrichs-Lewy condition. This algorithm can be used with both structured and unstructured meshes and can represent rapidly-varying flows (shock capturing) as well as supercritical and transcritical flows.

4.5.3 Overview of the linking method

The 2D module of InfoWorks RS-2D can be linked with a 1D network which can be made of conduits (drainage system), channels or river stretches. The link between 2D cells and 1D stretches is made by the mean of lateral or in-line spills for 1D channels, and by the mean of manholes for 1D conduits. The discharge and momentum transfer between the 1D and 2D modules is similar to (Liang et al. 2007). The discharge is exchanged between the 1D module and the 2D module by relating QL and q1D in the equations [35] and [37]. For spills, the momentum is also passed by the 1D module to the 2D module with an assumption of critical flow to calculate u1D and v1D (last term of equations 36 and 37). The momentum is not passed by the 2D module to the 1D module, however the momentum corresponding to the amount of water transferred to the 1D module is dissipated to ensure conservation of momentum.

4.5.4 Description of the analytical tests

To test the performance of the 2D model component a series of idealised test cases with known analytical solutions is modelled. The specific tests are detailed in Table 4.1. The objective of the tests is to highlight any weakness in the 2D numerical solution by comparing the simulation results with the corresponding analytical solutions. It is possible to derive analytical or pseudo-analytical solutions for these tests as the test geometry and initial conditions are simple. If the model results compare well to the analytical solutions over the range of tests, this lends some confidence when applying the model in practice to problems involving: flow over relatively steep slope, supercritical and transcritical flows, hydraulic jumps, fast transient flows and flash floods.

Table 4.1 Details of the analytical tests Test ID Test description Analytical solution Aim of the test Water at rest over check the discretisation of the hydrostatic Test 1 N/A complex topography pressure and bed slope terms Linear dam-break with verify the robustness of the model in Test 2 Stocker (1957) initially wet bed supercritical and trans-critical flow Linear dam-break with similar to Test 2 but also allows to Test 3 Stocker (1957) initially dry bed investigate the management of dry cells Circular dam-break with Toro (2001), 2D version of Test 3, tests any sensitivity Test 4 initially dry bed LeVeque (2002) of the flow to direction Reflection of a wave in a Test 5 Gill (1982) check the conservation of energy closed basin (seiche test)

For each of these tests, the solution computed by InfoWorks RS-2D has been compared against the analytical solution. To evaluate the performance of InfoWorks RS-2D with respect to existing models, the results have also been compared with two other commercially available models that are commonly being applied in consultancy studies (Table 4.2).

Table 4.2 Description of the two other routinely used commercial hydraulic softwares Numerical scheme Formulation Mesh type FD model Finite Difference full SWE, non-conservative regular grid form FV model Finite Volume full SWE, conservative form unstructured mesh

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 35 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

4.5.5 Results from the analytical tests

The numerical results from the analytical tests are not presented here but can be found in (Gutierrez Andres et al. 2008, Lhomme et al. submitted). The five analytical tests conducted on the InfoWorks RS-2D software and the two other commercial models lead to the following conclusions. InfoWorks RS-2D performs well on the dambreak tests, including the dry bed tests. This means that the model can be used in practical situations where fast transient flows and wave propagation on dry ground occur (i.e. dambreak and flash floods). This performance can be attributed to the finite volume discretisation and conservative formulation used in the numerical scheme. InfoWorks RS-2D is performing similarly to the FV model and they both outperform the FD model on the dambreak tests. This is because InfoWorks RS-2D and the FV model use a conservative formulation of the SWE, whereas the FD model uses a non-conservative formulation. However it was noticed in the dambreak tests that InfoWorks RS-2D reproduces shock waves better than the FV model.

InfoWorks RS-2D does not perform well on the seiche test as it leads to wave attenuation, nor does the FV model, whereas the FD model produces acceptable results. This tends to show that finite volume schemes are not well suited for this test. However the seiche test is more relevant to modelling tidal propagation in estuaries.

4.6 Rapid Flood Spreading Model (RFSM)

Flood risk analysis involves the integration of a full range of loading, multiple defence system states and uncertainty related to the input parameters of the model. This type of analysis involves the simulation of many thousands of flood events. To keep model runtimes to practical levels an efficient yet robust flood inundation model is required. To meet these requirements a new model (called RFSM, Rapid Flood Spreading Model) has been developed by HR Wallingford (HR Wallingford, 2006, Gouldby et al. 2008, Lhomme et al. 2008).

4.6.1 Overview of the RFSM concept

The RFSM is a simplified hydraulic model that takes as input flood volumes discharged into floodplain areas from breached or overtopped defences (Figure 4.11). It then spreads the water over the floodplain accounting for the floodplain topography. The output from the model is a flood depth grid of the floodplain area resulting from the input volumes at each defence. The model was specifically developed to provide a fast solution to the flood spreading problem for use in probabilistic flood risk models that consider defence failures (i.e. where many model runs, involving different defence failure combinations, are required).

The pre-process divides the floodplain in elementary areas called Impact Zones (IZs). The IZs represent topographic depressions in the floodplain where the water accumulates in case of flooding (Figure 4.12). The characteristics of the IZs are also generated by the pre-processing tool (relations between a given IZ and its neighbours, level-volume curve of each IZ). The communication level (CL) of an impact zone defines the level at which water spills into a given neighbour IZ.

The RFSM spreads the flood volumes by filling the IZs adjacent to the input points and spilling the excess to the neighbour IZs. This filling/spilling process is repeated as long as some IZs have volume in excess. When two or more neighbour IZs have the same water level, they are merged into a unique IZ. When all the input volumes have been spread in the IZs and no IZ has excess volume, it is considered that the flood has reached its final state.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 36 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

This process can be summarized in 5 steps as shown in Figure 4.13 : − Step 1, the overtopped volume is passed to the IZ adjacent to the defense (IZ B). − Step 2, the water level is set to the first CL, this allows to calculate the volume stored in the IZ and the excess volume. The excess volume is spilled towards one or more neighbour IZs (IZ C). − Step 3, the water level in IZ C being set to the first CL, IZ C has the same water level as IZ B. − Step 4, IZs B and C are merged. The CLs of this merged IZ (IZ BC) are calculated and the water level is set to the first CL. The excess volume is calculated and spilled towards one or more neighbour IZs (IZ A). − Step 5, the water volume is lower than the capacity of the IZ and the process stops.

A key feature of the RFSM is the conditions that control the spilling of excess water from one IZ to the next. The next section presents in more detail the spilling conditions and the incorporation of friction influences in addition to the gravitational forces within the RFSM.

IZj+5 IZj+4 Impact Impact IZj Zones Cells (IC) (IZ)

IZj+1 IZj+2 IZ j+3 d6 d5 d4 d3 d1 d2 Flood River Defences

Figure 4.11 View of the defence system with the Impact Zones and Impact Cells (based on Gouldby et al. 2008).

Profile view Impact zone A Impact zone B

communication points

communication point accumulation points Plan view communication points

Slope direction Impact cells

accumulation points Figure 4.12 Principles and key features of the Impact Zones (based on Gouldby et al. 2008).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 37 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Inflow volumes Input volume from defence

Check capacity of active IZs c d

A B C Any Excess ? e f

NO YES g End Spill Excess Volume

to neighbour IZ(s) (a) (b) Figure 4.13 Flowchart of the RFSM algorithm (a) and description of the different spilling/merging steps (b).

4.6.2 Description of the multiple spilling and friction approach

In the original version of the RFSM (HR Wallingford, 2006, Gouldby et al. 2008,), an IZ with excess volume only spills towards the neighbour IZ with the lowest CL. If two or more neighbour IZs have a CL equal to the lowest CL, the excess volume is equally shared between them (Figure 4.14).

In order to improve the RFSM, it was recognized that the algorithm should incorporate more physical processes, like the dynamic effects during the filling of an IZ and the friction effects during the spreading (Lhomme et al. 2008).

Multiple spilling The approach chosen to represent the dynamic effects during the filling has been called Multiple Spilling. The spilling algorithm has been modified so that an IZ with excess volume can spill towards many neighbours not necessarily having the same CL.

In a given IZ, it is considered that the water level will not be limited to the first CL but will reach a higher level depending on the IZ characteristics. This additional water level is called Multiple Spilling Tolerance. The functional relationship between the tolerance parameter and the IZ shape can be explained as follows.

Consider the shape of the IZ as approximated by a cone (in profile view). If the cone has a wide aperture (Figure 4.15a), the water level in the impact zone will increase relatively slowly for any given input discharge. Conversely, if the cone has a small aperture (Figure 4.15b), the water level in the IZ will increase rapidly for the same input discharge. It is more likely that there will be spilling towards many neighbour IZs if the water level is rising rapidly.

The nature of the impact zone is captured within the RFSM through the Volume-Level relation (Figure 4.16). IZ 1 has a higher average Volume-Level slope than IZ 2, despite both having approximately the same capacity. Thus for a given input volume the level will increase more rapidly in IZ 1 than in IZ 2. So IZ 1 and IZ 2 can respectively be associated with the shapes in Figure 4.15 a and b.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 38 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

The tolerance for each IZ is then calculated using the model variable, referred to as MSTol (for Multiple Spilling Tolerance), as follows:

Level − Level MSTol = KTol × 2 1 [38] Volume2 where Level2 and Level1 are respectively the elevations of the first CL and the lowest point in the IZ (i.e. a notional depth of the IZ), Volume2 is the volume of water in the IZ when the water level reaches Level2, KTol is a constant parameter.

IZ 3 IZ 1 IZ 2 IZ 3 IZ 1 IZ 2 Excess Volume Excess Volume

Figure 4.14 Description of the spilling rules in the earlier RFSM.

(a) (b) Figure 4.15 Link between the IZ shape and the dynamic filling effects.

200 000 IZ 1 IZ 2 150 000 ) 3

100 000 Volume (m

50 000

0 4 6 8 10 12 14 Level (m) Figure 4.16 Example of two Volume-Level curves.

MSTol is considered as an additional depth of water in the IZ due to the dynamic effects during the filling. In reality the excess volume will be discharged in the first neighbour IZ over a certain time allowing the water level to rise above the first CL and then possibly reach the second CL. MSTol is calculated and applied by the analysis module (rather than by the pre-processing). This also avoids any modification of the CL and hence the CLs used in the RFSM remain a true representation of the DTM. To explore the sensitivity of the RFSM to the introduction of the MSTol parameter and in particular its sensitivity to the constant KTol, a significant number of sensitivity tests have been undertaken. These tests show that the RFSM is relatively insensitive to KTol and a default value of 1400 for KTol provides satisfactory results for all tested situations (when used in conjunction with the friction effects, see next section).

Friction An important process for floodplain flow models is surface friction. In particular, floodplain land cover causes friction which affects the movement of the flood wave. Typically a Manning friction

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 39 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 coefficient is used to capture this physical effect. The original RFSM made no allowance for friction, this was recognized as a significant omission in the case of low lying coastal floodplains where the flood extents were too large.

This short-coming has been addressed by linking the influence of the friction effect to the plan size of the flooded area. The larger the flooded area, the greater the friction effects are.

The friction effects are represented through a head-loss. This head-loss is added to the CL to give the threshold value that the water level needs to exceed before spilling (see next section). This head-loss is considered to be a function of the total wet area by the linear relationship:

S f = C f × Atotal [39]

2 -1 where Sf is the friction head-loss (m), Atotal is the flooded area (m ), Cf is a constant coefficient (m ). The friction head-loss is calculated for every iteration (an iteration being a single spilling/merging step) as the flooded area varies after each iteration. The friction head-loss is applied for spilling only towards empty IZs.

The sensitivity of the RFSM to the parameter Cf has been examined. Although the RFSM is relatively –9 sensitive to the parameter Cf, the value 10 has been found giving satisfactory results for all tested situations (when used in conjunction with the multiple spilling).

4.6.3 Overview of the spilling algorithm

The condition for spilling in the RFSM is as follows:

WaterLevel + MSTol ≥ CL + S f [40] where Water Level is set to the first Communication Level and CL is the considered Communication Level. This is illustrated in Figure 4.17. In Figure 4.17a, the sum of the water level and MSTol is higher than CLIZ1-IZ2+Sf, but lower than CLIZ1-IZ3+Sf. Then the spilling of the excess volume is done only towards IZ 2. In Figure 4.17b, the sum of the water level and MSTol is higher than CL+Sf for both neighbour IZs. So the spilling is done towards both IZs 2 and 3.

Sf MSTol Sf IZ 3 IZ 1 IZ 2

(a)

Sf MSTol Sf IZ 3 IZ 1 IZ 2

(b) Figure 4.17 Description of the spilling rules in the latest version of RFSM, with the combined role of multiple spilling (MSTol) and friction (Sf).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 40 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

5. Simulating flow in flat agricultural areas located along estuaries or coasts: the Scheldt pilot site

5.1 Description of the study area and the available data

Study area The Scheldt pilot site consists of the eastern part of Zuid Beveland, located in the Province of Zeeland, in the southwestern part of the Netherlands (green rectangle in Figure 5.1.a). It is located between the Western Scheldt to the south, and the Eastern Scheldt to the north (Figure 5.1.b). The area contains several smaller cities and villages, but is mainly used as agricultural land (Figure 5.1.c).

a b

c Figure 5.1 Location of the study area (a) in the Netherlands, (b) detailed topography, (c) aerial photograph (source: Google earth)

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 41 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

The elevation in Zuid Beveland east varies from about 1 m below mean sea level in the west to about 1 m above mean sea level in the east. The polders are separated by secondary dikes, which often were former sea dikes, but no longer have a primary sea-defence function. Another higher element in the landscape that affected the flood pattern in 1953 is the railway dike. The highway that presently forms an obstacle as well, was not yet present in 1953.

In February 1953, a huge storm was recorded on the North Sea. The strong north-westerly winds resulted in a storm surge peak that coincided with springtide high water. This resulted in extremely high water levels, especially at the southern part of the North Sea. During the storm and over the following days, some 150 dike breaches occurred in the primary sea defences, and large areas on the southwest side of the Netherlands were flooded. There, the storm led to the worst disaster ever (Slager, 1992; Gerritsen, 2005). The flooded polders in Zuid Beveland are shown in Figure 5.2.

Figure 5.2 Flooded polders in Zuid Beveland during the 1953 storm surge. Arrows represent dike breaches. Polders 3, 4a, 6, 8, 9a, 9b, 9c, 11 were flooded by breaches occurring in the primary dikes, polders 4b, 5, 12 were flooded by failure of secondary dikes and polders 7 and 10 were flooded because drainage was obstructed (source: Rijkswaterstaat & KNMI, 1961)

Available data The topographic description of the study site was obtained using laser altimetry data with a resolution of at least 1 point per 10 m². The elevation of embankments and secondary dikes were provided in more detail by local water boards. They are shown by the pink and green lines in Figure 5.3. The elevation data were used by Deltares | Delft Hydraulics to develop a digital elevation model (DEM). The grid size of the DEM is 50 m. This grid represents the situation in 2001. It was modified to represent the situation in 1953 by removing the elevation of the highway that did not yet exist in 1953. The average elevation of the fields was not corrected for compaction. The final grid is used by all flooding models.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 42 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 5.3 Primary and secondary dikes schematised in the elevation model. Primary dikes are visualised by the green lines, secondary dikes are shown by pink lines. The blue line represents a small dike for which no detailed elevation data were available. Its height was estimated using the laser altimetry data. The elevation of the area is shown in brown colours, the range varies from about NAP -1.5 m (dark brown) to NAP +1.5 m (orange).

Water levels during the 1953 storm surge were measured at different locations along the coast. Figure 5.4 shows the observed levels at Waarde and Bath (see locations in Figure 5.1). The peak of the storm occurred on February 1st in the early morning. These measurements were used as boundary conditions in the inundation models.

water level (m) 7 6 Waarde 5 Bath 4 3 2 1 0 -1 -2 -3 30/01 30/01 31/01 31/01 01/02 01/02 02/02 02/02 03/02 00:00 12:00 00:00 12:00 00:00 12:00 00:00 12:00 00:00 time (day/hour)

Figure 5.4 Observed water levels in the Western Scheldt at Waarde and Bath

For the breaches, only the final width and depth are known, but not the formation process and the evolution in time of the breach shape. Therefore, breaches were assumed to grow in 24 hours time with breach growth rates decreasing in time. The breach growth rates vary between the applied inundation models.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 43 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Roughness coefficients for the area were estimated by Deltares | delft hydraulics using land use maps of the area made in 1996. A very high value of ks was attributed to forests and urban areas and much lower values to grass land and arable fields. The values of ks range from 0.1 m to 10 m. Land use may have been different in 1953. Hence, corrections were made for forested and built-up areas using old topographical maps. No corrections were made for different types of arable land, because no data are available. Identical roughness values were used in all simulations.

Figure 5.5 Distribution of the roughness coefficient ks: light colours indicate low roughness and dark colours indicate high roughness.

5.2 Model development

5.2.1 SOBEK

Two models were developed using the SOBEK software package: • 2D model based on the DEM and roughness grid, with breaches being represented by a special kind of 1D channel, called dam break link, to simulate breach growth; • quasi 2D or 1D+ model with storage nodes representing the different polders that are linked using 1D channel sections, with weirs representing low parts in the secondary dikes. The elevation distribution of the storage nodes was derived from the DEM.

Breach growth The number, width and location of the breaches have a large effect on the inundation pattern. Accurate breach growth modelling therefore is of utmost importance. Information on final breach widths was provided by the ministry of public works in the Netherlands (see also Rijkswaterstaat & KNMI, 1961).

In SOBEK, breach growth is modelled in 2 phases. During the first phase the breach mainly grows in a vertical direction. The breach width increases during the second phase. This was simulated using the formula of Van Voogt (1985):

05. BB= maxb tt/ max g [41] in which B is the width at time t after initiation of failure and Bmax is the final width reached at time tmax. In consultation with Henk Verheij (Delft Hydraulics) and Paul Visser (TU Delft) it was assumed that the final width was reached after 24 hours. The discharge through the breach is computed using a standard weir formula, with discharge and contraction coefficients set equal to 1 (user choice).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 44 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

From various reports on the 1953 flood it appeared that many breaches continued to grow because of tidal in- and outflow. The breach near Ouwerkerk, at the island of Schouwe Duiveland, increased from 200 to 450 m in several weeks. A couple of months later the width was 600 m. This continuing growth was not accounted for in the SOBEK models as the simulations relate to the first 48 hours after failure.

Wind In the basic model schematization, wind was only accounted for in the water level time series used for the boundary conditions, but not on the inundation process. The impact of wind on the flooding of polders was studied in a sensitivity analysis (see Chapter 5.4.3).

5.2.2 SV2D

A 2D inundation model also was made using the UCL software package SV2D. The model used the same square grid and the same boundary conditions as the SOBEK model.

Breach growth Two breaching options were used in SV2D: • instantaneous opening; • progressive opening.

Progressive opening is assumed to take place over a duration of 24 h, with a decreasing opening rate. This progressive growth is taken into account in the computational model by multiplying the flux passing through each cell of the breach by a coefficient α varying in time from 0 to 1:

⎛ 1 ⎞ α = 2 ⎜1− ⎟ [42] ⎝ t 86400 +1⎠ where t is the time in seconds.

According to the known final breach width, the user selects the computational cells concerned with the breaching. These cells are located on dykes and thus appear with a higher bed elevation in the discretised model of the area. Once the breaching starts, the bed elevation in the concerned computational cells is suddenly set to the final bed elevation.

Figure 5.6 shows an example of this: the dyke can be identified as computational cells with a higher bed elevation. The exact location of the breach and its final length are indicated as a black line superimposed on the computational grid (inset of Figure 5.6). Then, the computational cells selected to pertain to breach are marked by a cross. The selection must be such that water is allowed to flow from the sea to the polder. The figure also shows by means of a thick black line the cell interfaces through which water will flow from the sea boundary condition to the inside of the computational domain. The coefficient α used to simulate the progressive opening of the breach is applied to the numerical fluxes calculated through these interfaces.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 45 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 5.6 Representation of a breach in SV2D. Cell interfaces in contact with the sea boundary condition are indicated as thick black line in the inset

5.3 Model comparison

5.3.1 Introduction

Four models were developed for the Scheldt pilot site. The characteristics of the models are summarised in Table 5.1. The model results are used to answer the following questions: • Do the SOBEK and SV2D numerical models produce the same results? • If not, can the differences be explained? • Does a 2D model produce different results from a quasi 2D or 1D+ model? • Can these differences be explained?

Table 5.1 Summary of numerical simulations Run Model Breach opening 1 SOBEK 2D Progressive 2 SOBEK quasi 2D Progressive 3 SV2D Instantaneous 4 SV2D Progressive

To compare the water levels and velocities predicted by the numerical models, 8 comparison points were selected in the flooded area (P1 through P8). Their locations are indicated in Figure 5.7. Besides these point comparisons, maps are also drawn from the numerical results to compare the extent of inundation, the maximum water levels and velocities, and the arrival times of water, peak level and peak velocity.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 46 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

2 1

4 8 7 3 6

Figure 5.7 Comparison points for the predicted water level and velocity by the numerical models

5.3.2 Comparison of SV2D and SOBEK 2D

Results Water levels and velocities computed at P1 are shown in Figure 5.8. From this figure it can be concluded that the applied breach growth options have a significant impact on the water levels reached during the passage of the first wave (Figure 5.8). With the assumption of instantaneous breach opening (SV2D inst), water flows so fast into the area that the level observed in the polder almost equals the level in the estuary. The runs with progressive breaching (SV2D prog) show significant damping caused by the breaching process. Flooding occurs somewhat quicker according to the SOBEK simulations than according to the SV2D model. This is caused by the minor differences in breach growth rates. However, once the breach is fully open, all computations give very similar results.

z w (m) V (m/s) 5 0.5 SOBEK SOBEK 4 SV2D inst SV2D inst 0.4 SV2D prog SV2D prog 3 0.3 2 0.2 1

0 0.1 t (h) -1 0 0 10203040 t (h) a 010203040b Figure 5.8 Computed results at comparison point P1: (a) water level and (b) velocity

Computed water levels at comparison point P4 are shown in Figure 5.9. When looking at the results it is important to keep in mind that this polder is flooded after failure of the secondary dike between P1 and P4. From Figure 5.9 it can be concluded that the three models produce significantly different results. Instantaneous breaching (SV2D inst) results in the highest water levels. This is caused by the fact that the water levels in P1 increased so rapidly that water started flowing over the secondary dike before the observed breaching time. In the other two runs, flooding of P4 starts after breaching of the secondary dike. According to SV2D flooding of P4 takes place about 17 hours after the start of the simulation. According to SOBEK this takes a few hours more. This difference is caused by the breach growth rate applied to simulate breach growth in the secondary dike.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 47 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

z w (m) 5 SOBEK 4 SV2D inst SV2D prog 3

0 t (h) -1 0 10203040

Figure 5.9 Computed water level at point P4

Model results for P7 and P8 are shown in Figure 5.10 and Figure 5.11. Both locations are situated in the same polder, but are divided by the railway that constitutes a kind of internal dike. Flooding of P7 occurs after failure of the primary sea dike, while P8 is flooded after overtopping of the railway dike.

The most rapid inundation is simulated by the SV2D model with instantaneous breaching. Water levels in the polder increase very rapidly and the railway dike is overtopped only a few hours after failure of the primary dike. According to SOBEK, P7 is flooded about 3 hours later. The water level is sufficiently high to overtop the railway dike, but computed water depths in P8 are limited. According to SV2D with progressive breaching, no flooding occurs during the first flood period. During the second period, water levels increase rapidly, which causes overtopping of the railway dike.

The velocity predictions by the three models are similar, except during the first hours after failure of the primary dike. The run that assumes instantaneous breaching results in a more rapid flooding and hence in much higher flow velocities at the moment when almost no flooding occurs in the other model runs. This is due to the fact that assuming instantaneous breaching results in simulating this process as a sudden dam-break, with a rapid front of water propagating in the downstream direction. From the second high tide onwards, the velocities become quite similar.

z w (m) V (m/s) 6 0.5 SOBEK SOBEK 5 SV2D inst 0.4 SV2D inst 4 SV2D prog SV2D prog 0.3 3 0.2 2

1 0.1 t (h) 0 0 t (h) 0 10203040 010203040 a b Figure 5.10 Computed results at comparison point P7: (a) water level and (b) velocity

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 48 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

z w (m) V (m/s) 5 0.5 SOBEK SOBEK SV2D inst 4 0.4 SV2D inst SV2D prog SV2D prog 3 0.3

2 0.2

1 0.1 t (h) 0 0 t (h) 0 10203040 0 10203040 a b Figure 5.11 Computed results at comparison point P8: (a) water level and (b) velocity

The maximum water levels in the inundated areas as obtained with the three modelling options are shown in Figure 5.12. As could already be seen from the comparison points P1 and P2, water levels during the first high tide are overestimated when instantaneous breaching is assumed. This results in overtopping of many secondary dikes and hence also overestimates the flood extent (Figure 5.12.b). Maximum water levels computed with SOBEK 2D and SV2D are quite similar, with differences of the order of 2 m depending on the assumption made for the breach opening process.

a b

c Figure 5.12 Maximum water level (in m+NAP) (a) SOBEK, (b) SV2D instantaneous breaching, (c) SV2D progressive breaching

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 49 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Water arrival times (i.e. start of inundation) in the area are shown in Figure 5.13. When instantaneous breaching is assumed, the flood progresses much more rapidly. All polders are flooded in less than 10 hours. The other runs give a more progressive flooding, with significant differences at two locations: (1) in the most eastern polder area, where water arrives some 5 hours later according to SV2D than according to SOBEK; and (2) in the central polder area (enclosing comparison point P4) where a low water level was already observed.

Because of the relatively rapid water level fluctuations in the sea, differences in breach growth rates have a major impact on modelling results. Indeed, with a too low breach growth rate, only a limited amount of water can flow into the polders during the first high tide. The major inflow then occurs during the second high tide. When instantaneous breach growth is assumed, a huge amount of water already flows into the polders during the first high tide.

a b

c Figure 5.13 Water arrival time (in hours) computed with (a) SOBEK, (b) SV2D instantaneous breaching and (c) SV2D progressive breach opening.

Another important parameter in emergency planning is the time of occurrence of the maximum water depth. This is shown in Figure 5.14. When instantaneous breaching is assumed, water levels in the polders follow the water levels in the estuary. The time of occurrence of the maximum water levels therefore coincides with the time of the storm surge peak: i.e. during the first high tide. Progressive breaching results in a delay in the water levels in the polders. In this case maximum water levels are reached during the second high tide (or later when the polder is flooded through a breach in a secondary dike). The main differences in timing of maximum water levels are observed in the central polder enclosing point P4. This may be related to differences in breach formation for both the primary and secondary dikes.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 50 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

a b

c Figure 5.14 Arrival time (in hours) of maximum water depth computed with (a) SOBEK, (b) SV2D instantaneous breaching and (c) SV2D progressive breach opening.

Conclusions Differences between SOBEK and SV2D are related to (1) the choice of the simulation tool (numerical schemes) and (2) the simplified modelling of the breach growth process. 1. It was observed that both models (SOBEK and SV2D), although based on distinct numerical schemes, give similar results when run under similar conditions, i.e. on the same computational grid, with the same friction formula (as was done in this study). 2. The assumption regarding breach growth appears to be the key point in the case of Zuid Beveland, where the inundation is the consequence of a cascade of dike breaches. Considering instantaneous breaching gives the worst, thus the most conservative results, but these are too unrealistic for reasonable emergency planning. When considering progressive breach formation, the most important parameter is the breach growth rate. In the present study where the inundation comes from sea water subject to rather rapid level fluctuations, differences in breach growth rates have a major impact on modelling results.

This also implies that uncertainties in time of breach initiation (with respect to the peak time of the storm surge) and uncertainties in breach growth rates induce a high level of uncertainty in evaluating the time available for evacuation and rescue. Therefore, accurate breach growth models are required to simulate floods in tidal areas.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 51 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

5.3.3 Comparison of a quasi-2D or 1D+ and a full 2D approach

Results Differences between the 2D numerical models when applied to the Scheldt pilot site are small. Much larger differences are found between the 2D and quasi 2D or 1D+ application of SOBEK in the Scheldt pilot site. For locations that are situated close to the dike breach, the results are quite similar (Figure 5.15.a). For locations that are separated from the breach by a secondary dike very different results are obtained (see Figure 5.15.b).

) 4

3 2D 2 Quasi2D

water level(m+NAP 0

-1 01/02/1953 01/02/1953 02/02/1953 02/02/1953 00:00 12:00 00:00 12:00 time a

1.5 ) 1

0.5 2D Quasi2D 0

-0.5 water level(m+NAP

-1 01/02/1953 01/02/1953 02/02/1953 02/02/1953 00:00 12:00 00:00 12:00 time b Figure 5.15 Water levels (m +NAP) computed with the 2D and quasi 2D application of SOBEK for model comparison location 1 (a) and location 4 (b)

The main reason for the differences in polders that are separated by a secondary dike seems to be related to spatial differences in flooding in the first polder behind the breach. This is simulated in greater detail in the 2D model than in the quasi 2D model. This is explained in Figure 5.16. The upper part of Figure 5.16 represents 3 polders that are separated by secondary dikes. The green and red lines represent relatively low sections in the secondary dikes. The green section is lower than the red section. If the primary dike fails at the location represented by the black line it is very likely that water will first flow over the low section indicated by the red line. This will be simulated by the 2D model. Hence, according to the 2D model, polder B will be flooded before polder C. However, in the quasi 2D model, this spatial effect in polder A is not accounted for and water will start flowing over the lowest section in any of the surrounding dikes. Thus, according to the 2D model, polder C will be flooded before polder B.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 52 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

B A C

BAC

Figure 5.16 Schematisation of 3 polders in 2D (upper half) and quasi 2D (lower half). Red and green lines represent low sections in secondary dikes between the polders. The green section is lower than the red section.

Conclusions In case of the Scheldt pilot, the quasi 2D model produces different results than the fully 2D model, because the quasi 2D model lacks detail. The results therefore indicate that quasi 2D models can only successfully be applied if the flow pattern is known in advance, so that the model schematisation can be adjusted to it. This implies that quasi 2D models can relatively successfully be applied to river systems where the flow directions are known in advance. Application to relatively flat areas, where flow patterns may differ depending on the breach location, or where flow patterns are not very obvious, is likely to result in very inaccurate results.

5.4 Additional research questions

5.4.1 Impact of breach initiation and breach growth

Results The impact of breach growth rates on computed water depths was already noticed from the SV2D model results as shown in Figure 5.8 through Figure 5.14. A separate analysis for a single polder (the Reigersbergsche polder, including locations 7 and 8), carried out with the SOBEK model confirms these findings. Figure 5.17 shows the increase in breach opening (in m²) in time as applied in the original SOBEK model. The assumption that breach growth took place in 24 hours is clearly reflected in this figure. In the additional simulation it was assumed that the final breach width is reached in 1 hour. Figure 5.18 shows the computed water levels near the breach. The water level at the Western Scheldt is shown for comparison.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 53 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Dike break timeseries for Reigersbergsche Polder - Reference Case

800

700 Dike break Link 44 Dike break Link 45 600 Dike break Link 46

500

400

300 Opening area (m2) Opening area

200

100

0 01/02/1953 01/02/1953 01/02/1953 01/02/1953 02/02/1953 04:20:00 10:20:00 16:20:00 22:20:00 04:20:00 Date and time

Figure 5.17 Breach growth according to the original SOBEK model

Dike breach water level timeseries for Link 44

6 Case 1 - Inland flood wave 5 Case 4 - Inland flood wave Sea water level boundary condition 4

Water level (m+NAP) level Water 0 01/02/1953 01/02/1953 01/02/1953 01/02/1953 02/02/1953 02/02/1953 02/02/1953 02/02/1953 03/02/1953 -100:00 06:00 12:00 18:00 00:00 06:00 12:00 18:00 00:00

-2

-3 Date and time

Figure 5.18 Computed water levels behind the breach in the Reigersbergsche polder (including locations 7 and 8)

Figure 5.18 shows that instantaneous breach growth results in overestimated water levels as the water level in the polder almost equals the water level in the estuary. During the first high tide, water levels are overestimated by 1 to 1.5 m. During the following tidal cycles differences are smaller.

The rapid inflow that results from instantaneous breaching also leads to much more rapid flooding. This was already shown in Figure 5.14, and is confirmed by Figure 5.19. When the breach forms over more than 1 tidal cycle, it takes more than 12 hours to flood the entire polder. However, when instantaneous breaching is assumed, the entire polder is flooded in about 5 hours. When the model results are used for flood event management this means a 7 hour difference in the estimated time that is available for warning and rescue.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 54 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

0 - 4 hours 4 - 5 hours 5 - 6 hours 6 - 7 hours 7 - 8 hours 8 - 9 hours 9 - 10 hours 10 - 12 hours a b 12 - 24 hours Figure 5.19 Moment of first inundation Reigersbergsche Polder (a) progressive breach growth (b) instantaneous breaching

5.4.2 Impact of the schematisation of buildings

Introduction Most studies that aim at determining the maximum grid cell size to be used in inundation models for urban areas look at densely populated areas. In these models a large part, if not the entire model area is urbanised. The conclusion of these studies often is that the maximum grid cell size should not exceed 10 m, preferably less (see also chapter 6) as for European cities this is often the minimum gap distance between buildings. Grid sizes larger than this can artificially close routes for flow.

In the case of the Scheldt pilot area we look at a rural polder area in which small villages are present and we want to know how the flood spreads within the polder. Analysis were carried out to determine if a maximum grid cell size of 10 m is required to simulate the flooding process with sufficient detail.

Results Three SOBEK models were made using the following computational grids:

1. a relatively coarse grid (50m x 50m) in which buildings were schematised by increasing the hydraulic roughness of the entire urban areas (i.e. this is the model used for the previous simulations) 2. a fine grid in which buildings were schematised as solid 2D objects; 3. a fine grid in which the hydraulic roughness in streets was reduced and the roughness at grid cells that coincide with buildings was increased.

Figure 5.20 through Figure 5.22 show the results of the three models.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 55 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

a b

High : 5.7 m

c Low : 0.01 m Figure 5.20 Water depths computed with a coarse grid (a), a finer grid and solid buildings (b) and a finer grid with very high roughness values representing buildings (c)

The maps indicating maximum water depth and arrival time of the water (Figure 5.20 and Figure 5.21) do not shown any differences. Hence, the differences in model schematisation of the village do not affect the computed water depth or the arrival time.

The main differences between the three models concern computed flow velocities in individual streets (Figure 5.22). The 2D solid blocks force the flow to concentrate in the streets. This results in much higher flow velocities. The third method (with increased roughness values representing individual buildings) also results in higher flow velocities in the streets.

Conclusions The main conclusion is that if the user is interested in the flooding pattern that occurs in a rural area and the water depths that occur in villages, a coarse grid with grid cell sizes of more than 10 m is of sufficient detail and individual buildings do not have to be accounted for in the model schematisation. Only if the user is interested in flow velocities in the villages, smaller grids are needed and buildings should be schematised as 2D solid objects or by increasing the hydraulic roughness at the sites of buildings. The latter solutions results in smaller differences in flow velocities, but accounts for storage of water in buildings.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 56 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

a b

0 - 4 hours 4 - 5 hours 5 - 6 hours 6 - 7 hours 7 - 8 hours 8 - 9 hours 9 - 10 hours 10 - 12 hours c 12 - 24 hours Figure 5.21 Moment of first inundation computed a coarse grid (a), a finer grid and solid buildings (b) and a finer grid with very high roughness values representing buildings (c)

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 57 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

a b

0.0002 - 0.01 m/s 0.01 - 0.1 m/s 0.1 - 0.2 m/s 0.2 - 0.5 m/s 0.5 - 1 m/s c 1 - 2 m/s Figure 5.22 Flow velocities computed with a coarse grid (a), a finer grid and solid buildings (b) and a finer grid with very high roughness values representing buildings (c)

5.4.3 Impact of wind

Introduction Most inundation models do not account for the impact of wind. However, coastal flooding mainly occurs during storm surges, when strong winds prevail. Therefore, a number of calculations were made with different wind situations, changing the direction as well as the wind speed, in order to see the effect on the outcome of the calculations.

Results Figure 5.23 shows water depths for various wind forces and directions as computed with the SOBEK model. Figure 5.24 shows the difference in computed water depths between the simulation without wind and a simulation with wind force 10, coming from the west. In polders that are flooded through one or more breaches in the primary sea defence system, changes in water depths of about 0.3 m occur (upto 10% increase in water depth). However, when polders are flooded through a breach in a secondary dike, an increase in water level of about 0.65 m may occur when the polder is located downwind of the breach. As in the reference situation water depths were small, this is an increase in water depth of more than 50%.

The flow velocities do not change much due to strong winds. The time of inundation (hours after failure of the coastal dike) is also hardly effected by wind. Only when the progress direction of the

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 58 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 flood wave is in the same or opposite direction of the wind direction the time of inundation is affected by wind, but still not very significant.

Legend BASISmaxd 0 0.01 - 0.4 0.41 - 0.8 #* 0.81 - 1.2 ² 1.3 - 1.6 *# 1.7 - 2

#*#* 2.1 - 2.4 *

# *# 2.5 - 2.8 *# #* *# 2.9 - 3.2 3.3 - 3.6 3.7 - 4

* # 4.1 - 4.4 4.5 - 4.8

#* 4.9 - 5.2 5.3 - 8 *#*#*# zbbres53

#* #* #*

# * no wind

Legend NW10maxd 0 0.01 - 0.4 0.41 - 0.8 #* 0.81 - 1.2 ² 1.3 - 1.6 *# 1.7 - 2

#*#* 2.1 - 2.4 *

# *# 2.5 - 2.8 *# #* *# 2.9 - 3.2 3.3 - 3.6 3.7 - 4

* # 4.1 - 4.4 4.5 - 4.8

#* 4.9 - 5.2 5.3 - 8 *#*#*# zbbres53

#* #* #*

# * wind force 10, direction north-west

Legend W10maxd 0 0.01 - 0.4 0.41 - 0.8 #* 0.81 - 1.2 ² 1.3 - 1.6 *# 1.7 - 2

#*#* 2.1 - 2.4 *

# *# 2.5 - 2.8 *# #* *# 2.9 - 3.2 3.3 - 3.6 3.7 - 4

* # 4.1 - 4.4 4.5 - 4.8

#* 4.9 - 5.2 5.3 - 8 *#*#*# zbbres53

#* *# #*

* # wind force 10, direction west

Legend ZW10maxd 0 0.01 - 0.4 0.41 - 0.8 #* 0.81 - 1.2 ² 1.3 - 1.6 *# 1.7 - 2

#*#* 2.1 - 2.4 *

# *# 2.5 - 2.8 *# #* *# 2.9 - 3.2 3.3 - 3.6 3.7 - 4

* # 4.1 - 4.4 4.5 - 4.8

#* 4.9 - 5.2 5.3 - 8 *#*#*# zbbres53

#* *# #*

* # wind force 10, direction south-west Figure 5.23 The influence of wind on the computed maximum water depth

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 59 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 5.24 Difference in water depth (m) between the simulation with wind force 10, direction west, and the simulation without wind

Conclusion It is therefore concluded that wind can have a significant impact on computed water depths. Also the area which is flooded changes due to strong winds. If the wind direction is unfavourable the flooded area can increase significantly. For instance, strong winds may increase the volume of water flowing through breaches in secondary dikes when these breaches are located in the downwind direction. The wind set up depends on the fetch length. In this case the fetch length is about 5 km. The larger the polder, the longer the fetch length, which results in a higher wind set up.

Other meteorological factors, such as evaporation, have no significant effect on flooding simulations for the Scheldt, because the probability for flooding is highest during the winter season, when evaporation values are very low. However, in other areas evaporation can be an important process as well. This often is the case in extensive wetlands, where flooding occurs during the summer season, or that are located in a warmer climate. An example of such an area is the Doñana wetland in Spain. Here flooding occurs during the winter season. During the summer period, the wetland dries up, partly because water drains to an adjacent river, but for the main part because of high evaporation rates, which vary from 5 to 14 mm per day during the summer months. Measured evaporation rates indicate a total evaporation of about 0.7 m during the period April - July.

5.4.4 Impact of hydraulic roughness

Introduction The hydraulic roughness is known to have an effect on water levels. For instance, forests planted in flood plains along the Rhine branches in the Netherlands had to be compensated for by other measures like excavation of side channels or lowering of the flood plain surface. Compensation was required

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 60 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 because the flood plain forests increase the hydraulic roughness and hence result in higer water levels under extreme discharge conditions. For reasons of safety, measures were taken that increase the discharge capacity and in this manner compensated for the increased water levels caused by the flood plain forests.

The model of the Scheldt pilot site was used to study the impact of changes or uncertainties in hydraulic roughness on computed water levels.

Results Two simulations were carried out using the SOBEK model for the Scheldt. The first simulation used a uniform hydraulic roughness of 0.06 sm-1/3, while in the second simulation an n value of 0.03 sm-1/3 was applied. Figure 5.25 shows the difference in computed water depths between both runs. The positive values (orange colours) represent areas where the higher roughness values result in greater depths. As most areas in Figure 5.25 are green, it can be concluded that lower roughness values result in greater depths. This seems contradictory to the findings of river channels, but can be explained by the decreased inflow. Water levels in the estuary are identical in both model runs. However, the spreading of water in the polder is hampered in the simulation with higher roughness values. This reduces the water level slope through the breach and hence diminishes the inflow. This in turn results in lower water levels and shallower depths.

Figure 5.25 Difference in water depth (m) between simulations with a uniform roughness of n=0.06 sm-1/3 and n=0.03 sm-1/3

The decrease in maximum water depths also is visible in Figure 5.26. This figure also shows that the decrease in water depth is more pronounced in polders with smaller depths. At greater water depths, the impact of the hydraulic roughness is less. Differences of about 0.05 m are observed in polders with a maximum depths about 4 m. In polders with depths of less than 3 m differences are in the order of 0.2 m.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 61 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 5.26 also shows the delay in flooding (indicated by a small shift of the lines towards the right). The outflow of water during the ebb tidal period also decreases when higher roughness values are applied (see also Figure 5.27). This results in slightly greater depths at low tide.

4.5

3.5 1 mn=0.03 3 1 mn=0.06 1/4 mn=0.03 2.5 1/4 mn=0.06 4 mn=0.03 2 4 mn=0.06 water depthwater (m) 1.5 7 mn=0.03 7 mn=0.06 1

0.5

0 01/02/1953 00:00 01/02/1953 12:00 02/02/1953 00:00 02/02/1953 12:00 time

Figure 5.26 Difference in water depth (m) between simulations with a uniform roughness of n=0.06 sm-1/3 and n=0.03 sm-1/3 (location numbers are shown in Figure 5.7, location 1/4 is near the breach in the secondary dike between locations 1 and 4)

1500

1250

1000

750 1 mn=0.03 /s)

3 1 mn=0.06 1/4 mn=0.03 500 1/4 mn=0.06 7 mn=0.03 discharge (m 250 7 mn=0.06

0 01/02/1953 00:00 01/02/1953 12:00 02/02/1953 00:00 02/02/1953 12:00

-250

-500 time

Figure 5.27 Difference in inflow through the breach (m/s) between simulations with a uniform roughness of n=0.06 sm-1/3 and n=0.03 sm-1/3 (location 1 and 7 represent flow into polders with location numbers 1 and 7, location ¼ respresent the flow through the breach in the secondary dike between locations 1 and 4)

The only area where water levels increase when higher roughness values are applied is located behind the breach in the secondary dike between locations 1 and 4. The reason for this is that breach initiation in this secondary dike occurs during the falling limb of the hydrograph. Due to the delay in outflow,

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 62 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 water levels remain relatively high in polder 1. Higher water levels have a positive effect on the water level slope over the breach in the secondary dike, which results in relatively large discharges. The high roughness values in polder nr. 4 hinder rapid spreading of water away from the breach, which results in relatively great depths near the breach (location 1/4). At greater distance from the breach this effect is less pronounced.

The flood extent is not affected. This is due to the fact that the flood extent is mainly determined by the position of the secondary dikes.

Conclusions In the Scheldt pilot area, doubling of the hydraulic roughness results in differences in maximum water depth of about 0.05m to 0.2m (compared to an overall water depth of 1 to 4 m respectively). The difference depends on the water depth in the polder (the effect is more pronounced when water depths are low), and on the time of breaching. The time of breaching is especially important in polders flooded through a breach in the secondary dike.

Although uncertainties in hydraulic roughness affect computed water depths, the impact is less than for many other model parameters, such as breach growth rates and wind.

5.4.5 Impact of uncertainties in boundary conditions

Introduction Every hydraulic model needs boundary conditions. For models of rivers, the boundary conditions usually consist of a discharge time-series at the upstream model boundary and a water level time- series or stage-discharge relation at the downstream boundary. In the case of the Scheldt model, the boundary conditions consist of water level time series that are based on measured water levels during the flood of 1953. Uncertainties in measured water levels are relatively small. However, this type of model also is used to simulate flooding under more extreme conditions that have not yet happened. For instance, in the Netherlands the dikes are designed to resist a given design discharge or water level. In the case of the Scheldt pilot site the design water level is a water level with a probability of exceedence of 1:4000 per year. This water level is determined by applying statistical techniques to measured water levels and wave characteristics. As the measured time-series cover a much shorter time period this involves extrapolation, which results in a relatively large uncertainty.

To determine the impact of uncertainties in boundary conditions, two simulations were carried out. The first simulation uses boundary conditions determined with statistical techniques that are applied in the Netherlands. The second simulation uses boundary conditions obtained with the method applied in Belgium. Details on both methods are not reported here as we are merely interested in the impact of the differences in boundary conditions on the flooding pattern. More information can, however, be found in Asselman et al. (2007). The water level time series applied near one of the breaches is shown in Figure 5.28.

The sensitivity analysis was carried out with the SOBEK model. The same breaches were assumed as observed in the primary coastal dikes in 1953. Breaches in secondary dikes were not modelled. Flooding of polders that do not directly border the primary dike only occurs due to overflow of secondary dikes.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 63 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

T4000 maatgevend hoogwater Bres 1

7 MHW NL Bres 1 6 MHW BE Bres 1 5

0 Waterstand (mNAP) Waterstand -1

-2 -3 05/01/2010 00:00 06/01/2010 00:00 07/01/2010 00:00 08/01/2010 00:00 09/01/2010 00:00 Tijd

Figure 5.28 Water level time-series used for the sensitivity analysis. Peak water levels correspond with T4000 water levels according to the Dutch approach (darkblue line) and the Belgian approach (pink line) (source: Asselman, et al., 2007).

Results Two simulations were carried out using the SOBEK model for the Scheldt, using water level time- series obtained with the Dutch and Belgian methods. The difference in the results can be seen in Figure 5.29.

a b Figure 5.29 Comparison of flood extent computed with SOBEK using different boundary conditions: (a) T4000 water level according to the Dutch approach, (b) T4000 water level according to the Belgian approach.

The slightly higher water levels determined with the Dutch method, but especially the much higher water levels at low tide, result in larger water depths in polders that are flooded through a breach in the primary dike. In fact, water levels in most polders are just high enough to overflow the secondary dikes (Figure 5.29.a). The high water levels at low tide obstruct drainage of the polders. Therefore, the polders are still filled with water when the next high tide arrives, and water levels rise more rapidly.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 64 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

The secondary dikes are not over flown when the Belgian T4000 water levels are applied. This results in a significantly smaller flood extent (Figure 5.29.b).

Similar differences have been observed in flooding simulations carried out for the Rhine river in the Netherlands. Here, uncertainties in boundary conditions not only relate to the maximum water level, but also to the duration of the flood. Depending on the applied method to estimate flood duration, difference in inflow volumes of a factor 2 may occur. This results in large differences in the flood extent and the maximum water depths. In this case the discharge through the breach was not hindered by back water effects. If the flooded area is small and water levels behind the breach increase rapidly, the backwater effect may hinder the inflow, which will result in smaller differences.

Conclusion Uncertainties in boundary conditions (e.g. maximum water level, maximum discharge, duration of the storm surge or the period of high river discharge) can significantly effect computed water depths and flood extent. Differences especially are large in situations were computed water levels more or less equal the height of secondary dikes or other obstacles. Here, a relatively small increase in water levels may result in overflow of secondary dikes and in a much larger flood extent. It is therefore recommended always to perform a sensitivity analysis to estimate the effect of uncertainties in boundary conditions.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 65 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 66 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

6. Simulating flow in urban areas located along estuaries or coasts: the Thames pilot site

6.1 Study area and available data

Study area The Thames pilot site consists of the area near Greenwich and is located in the tidal flood risk area of the Thames region (Figure 6.1). London is home to 7.5 million people, with 1 million people and 300,000 properties in the tidal flood risk area (Dawson et al. 2005). The indicative tidal flood risk area for the Thames Region of the Environment Agency (EA) lies between Teddington Weir and Dart-ford Creek (approx. 116 km2) (Figure 1) and would be liable to frequent flooding from surge tides without the existing tidal walls and embankments. London is defended by a complex system of over 200 km of embankments and walls, the Thames Barrier and a suite of warning systems. However, recent development in London’s previously derelict docklands and the emergence of the new financial district around Canary Wharf combined with plans for significant future development over the next 15–30 years (ODPM 2005) poses significant questions over future flood risk.

The Greenwich embayment is chosen as a suitable study site indicative of defence integrity and urban topography and topology for the wider Thames region with tidal flood risk. The 11.5 km² embayment is characterised by areas of densely clustered terraced housing and large industrial units and machinery surrounded by substantial open spaces (Figure 6.2). Furthermore, the embayment incorporates significant assets, such as the O2 Arena and the Blackwall Tunnel.

Figure 6.1 Map of the indicative tidal flood risk area of the Thames Region highlighting the Greenwich study area. Data courtesy of EA Thames region.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 67 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 6.2 Aerial photograph of the study area. The Millennium dome and the Thames barrier are clearly visible. (source: Google earth)

Available data The Environment Agency provided the LiDAR data survey for this site, flown in March 1999 and collected at 1 m resolution. In order to increase the utility of LiDAR data, the EA have developed an in-house segmentation algorithm that delivers a DSM, a DTM and a mask of buildings and vegetation based on pattern recognition in the raw LiDAR signal. The EA also perform a significant amount of manual processing to remove bridges and elevated road sections that would otherwise form artificial blockages to flood propagation. This process generated two types of 1 m resolution digital elevation data:

• A Digital Surface Model with buildings left in; • A bare earth Digital Terrain Model with buildings and other surface artefacts removed

Unlike the Scheldt pilot site, where flooding was caused by widespread breaching, flooding is expected as a consequence of overtopping of the flood defence. According to Dawson et al. (2005) the contribution to total inundation volume from breaching is negligible compared to the inundation volume from overflow events when extreme sea level rise scenarios are considered. Furthermore, Gouldby et al. (2007) note that the flood defences along the River Thames are in good condition and thus breach events are less likely than overtopping. The overflow simulations that provided the inflow volumes used in the flooding simulations, were performed by HR Wallingford Ltd (Gouldby et al., 2007). The simulation of overtopping and breach scenarios for hydraulic modelling of individual flood embayments was conducted by HR Wallingford Ltd using a model based on the RASP procedure (Hall et al. 2003). This method involves the development of fragility curves which integrates a full range of loading conditions (water levels) with the performance and integrity of flood defences (Gouldby et al. 2007). Each defence section is considered independent and has a different resistance to flood loading which is characterised by structure type, crest level or condition. The fragility curve for each defence section, defined as a continuous random variable of defence failure conditional on the load, was derived from failure models for either overflow or piping, or a combination thereof. The occurrence of extreme water levels is defined as a continuous random variable associated with each defence section. The defence system state (failed/not failed) is calculated using a Monte Carlo

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 68 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 framework where the defence state is sampled with reference to the defence specific fragility curve for a given loading. Peak flow rates into the floodplain for each defence are calculated using the broad- crested weir equation and transformed to triangular hydrographs of duration equal to the breach duration (Gouldby et al. 2007).

These data were analysed by UniBristol to construct the LISFLOOD model. The LISFLOOD schematization was then used to develop the additional models.

6.2 Model development

6.2.1 LISFLOOD-FP

To build the terrain data sets used by LISFLOOD-FP, the 1 m resolution topography data were re- scaled using nearest neighbour sampling to generate DSM and DTM grids at 5, 10, 25 and 50 m resolution. These terrain representations were the used directly in the LISFLOOD-FP model.

In order to ensure consistent comparison of model results, boundary conditions in LISFLOOD-FP and all other models were schematised as similarly as possible although a few subtle differences remain which are unavoidable and detailed below.

The breach flows provided by HR Wallingford Ltd. (Gouldby et al. 2008, Floodsite Task 6 and 24), represent the volume of water flowing over the defence and/or through the breach over the duration of the event. Therefore, these flows should be input directly into any model representing the overland flow component of the flooding. Representing this process in LISFLOOD-FP is straightforward as a point source flux can be assigned at any given location in the domain such that the overtopping/breach flow is specified at the defence location.

6.2.2 SOBEK

SOBEK applies the same rectangular grids, with the same resolution, as LISFLOOD-FP. However, the breach flows were implemented slightly different. In SOBEK, the model is schematised such that a one dimensional (1D) channel with a prescribed bottom elevation routes the flow into the 2D domain. This option was required because of the large number of inflow points and the jagged boundary of the DEM. This option requires a certain amount of modeller skill and can be time consuming to implement. Generally the approach in SOBEK would be to apply 2D boundary nodes to simulate the inflow, or to model the Thames as a 1D river placed in a 2D grid. A flood-wave is modelled in the river and the interaction with the 2D grid is modelled by adding dike heights and breach-locations. SOBEK would then automatically compute the volume of water overtopping the flood defences.

6.2.3 Infoworks

The approach used here for the boundary and initial conditions is the same as used with SOBEK, i.e. only a 2D domain initially dry is considered. A set of input points associated with inflow volumes represent the breaches in the defence system. The inflow volumes are the same as used by SOBEK and LISFLOOD, the volumes are discharged over a duration of 10 minutes.

The 2D domain is meshed with triangular elements, the buildings are represented as impervious objects (voids) in the grid. The average size of the triangles is 24.5 m2. The DTM used to assign an elevation to the triangles is the same as the one used by SOBEK and LISFLOOD. The Manning friction coefficient is equal to 0.035 as in SOBEK.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 69 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

6.2.4 RFSM

The DTM used by RFSM (see section 4.6) to build the IZs is the same as the one used by all the other models. Two different grid sizes have been considered, 2 m and 5 m. Buildings are represented as impervious objects in the grid as in Infoworks. The inflow volumes are the same as used by all the other models, the volumes are instantly transferred to the IZs adjacent to the defences as there is no temporal evolution.

6.3 Model comparison

6.3.1 Comparison of SOBEK and LISFLOOD-FP

Results Flooding along the Thames estuary was simulated with SOBEK and LISFLOOD-FP using a high resolution 5 m DEM. At first glance, the model results look very much alike. However, locally differences in water depths are computed that are in the order of about 0.1 to 0.5 m maximum (Figure 6.3). Also, the flood extent is slightly different. Some locations are flooded according to the SOBEK model but not according to LISFLOOD-FP and vice versa.

Figure 6.3 Differences in water depths computed with LISFLOOD-FP and SOBEK using a high resolution 5 m DEM. light grey colours represent areas where LISFLOOD-FP computes greater depths. In dark grey areas SOBEK predicts larger depths.

One reason for the difference in water depths and flood extent seems related to the fact that SOBEK is able to model water inertia, while LISFLOOD-FP is not. When water overflows the embankments along the Thames, it plunges into the streets below. This results in a sort of wave that may overtop obstacles in or along the street. SOBEK is able to simulate this ‘plunging’ effect. According to the LISFLOOD-FP model, no water can flow over obstacles that exceed the elevation of the equilibrium water level. This results in different flow paths. According to LISFLOOD-FP water flows mainly through road paths, while according to the SOBEK simulations the water is divided over a larger number of pathways.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 70 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

difference first wetting sobek - lisflood (minutes) 30 min (sobek earlier) 20 - 30 min 10 - 20 min 5 - 10 min 3 - 5 min 1 - 3 min 0 - 1 min (sobek earlier) 0 - 1 min (lisflood earlier) 1 - 3 min 3 - 5 min 5 - 10 min 10 - 20 min (lisflood earlier) DEM (eaproc_10m) (meter to datum) High : 64,911

Low : -4,584

b Figure 6.4 Difference in time of first wetting using digital elevation models with a mesh of 5 m (a) and 10m (b). Green = LISFLOOD-FP is faster, red = SOBEK is faster.

Another difference between both models is that the flood propagation is generally quicker in LISFLOOD-FP than in SOBEK. This is likely to be caused by differences either in the way boundary conditions are assigned in the two models or differences in the in calculation scheme. For example in LISFLOOD-FP cells which contain water become instantaneously wet once water enters into them and hence the model can over predict the position of the real wetting front position by a maximum of 1 grid cell width. The difference in travel time of the flood is mostly a few minutes, but increases with increasing grid cell sizes as a result of the above identified effects. The results of the 5 m grid (Figure 6.4.a) show that in some cases SOBEK is fasters (indicated by the red colours), while at other locations LISFLOOD is faster (green colours). The 10 m grid shows an increase in green colours,

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 71 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 indicating that the number of locations where LISFLOOD-FP predicts a more rapid spreading of the flood increases (Figure 6.4.b). The few exceptions where SOBEK floods earlier than LISFLOOD –FP are caused by differences in flow pattern. At these locations, the flood propagation of SOBEK is through a different path, thus creating a shortcut to the path of the flood in LISFLOOD –FP. This is causing the sudden change from dark green to red. The path causing the shortcut is not shown in the Figure 6.4.b, since LISFLOOD –FP has no data on these locations and no difference was calculated by the software.

A last difference concerns model performance. SOBEK runs the simulations much faster than LISFLOOD-FP. This is related to the adaptive time step algorithm adopted in LISFLOOD-FP. For a simulation period of 50 minutes, LISFLOOD-FP needs a calculation time of 14 days when the 5 m grid is used on a 2.0 GHz Pentium4 Windows machine. This means a model efficiency of about 400 (running the model takes 400 times the duration of the simulation period). SOBEK requires about 18 minutes for the same simulation, when carried out on a Pentium 4 PC with 3600MHz (single core) processor and 4*512MB memory. This implies a model efficiency of about 0.4. In other words: when using the 5 m grid, SOBEK is 1000 times faster than LISFLOOD-FP. The lower efficiency at small grid sizes is a well known problem of storage cell models as to maintain stability according to the adaptive time stepping analysis of Hunter et al. (2005b) one requires a time step that is a quadratic function of grid cell size. Storage cell models were originally conceived for application at moderate (50-100 m) resolution where the lack of a numerical solution ensures greater efficiency than an equivalent full 2D model. The time step stability constraint reverses this efficiency advantage as the grid size is reduced and at 5 m the storage cell formulation typically requires very small time steps. For an explicit formulation this imposes a large penalty in terms of run time. Model efficiencies for the different SOBEK models are shown in Table 6.1.

Table 6.1 Model efficiency for different versions of the SOBEK model model run calculation time simulation period model efficiency 5m_buildings 00:18:51 00:50:00 0.38 5m no buildings 00:15:21 00:50:00 0.31 5m friction 0.07 00:14:48 00:50:00 0.30 10m buildings 00:02:25 00:50:00 0.05 10m no buildings 00:02:24 00:50:00 0.05 25m buildings 00:00:27 00:50:00 0.01 25m no buildings 00:00:31 00:50:00 0.01 50m buildings 00:00:30 00:50:00 0.01 50m no buildings 00:00:20 00:50:00 0.01 10m buildings (longer run) 00:11:32 08:00:00 0.02

The model efficiency is affected by the time step set by the user. The time step the user sets in SOBEK is the maximum length a time step may have in the simulation. When necessary, SOBEK reduces the time step internally to guarantee stability. The affect of the time step set by the user on the model efficiency was assessed using three different time steps (5, 10 and 20 seconds). The model efficiency increased when the computational time step was increased from 5 to 10 seconds. However, a further increase of the time step resulted in a slight reduction of the model efficiency (Table 6.2).

Table 6.2 Model efficiency of the SOBEK model using different calculation time steps model run calculation time simulation period model efficiency 10m buildings 5sec time step 00:03:06 00:50:00 0,062 10m buildings 10sec time step 00:02:24 00:50:00 0,048 10m buildings 20sec time step 00:02:03 00:50:00 0,041

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 72 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Conclusions At first sight LISFLOOD-FP and SOBEK produce similar results for the Thames pilot area. However, differences in computed water depth occur locally because SOBEK is capable of simulating inertia, while LISFLOOD-FP is not. Other differences concern the flood propagation, which is faster according to LISFLOOD-FP, and the model performance, with SOBEK having a much higher efficiency.

6.3.2 Comparison of Infoworks and SOBEK

Sobek and Infoworks have similar engines based on the resolution of the full shallow water equations. However the main difference between the two softwares is the meshing. Sobek uses a regular grid (with the possibility to nest different resolutions) whereas Infoworks uses a non-structured mesh made of triangles. This can generate differences between the two softwares in such a complex environment as urban areas where the street network and buildings need to be finely captured to ensure the best possible representation of flows. The comparison between the two softwares is made on the maximum water depth occurring during the first 50 minutes of the flood event in order to match with the comparison done in the previous section.

Some indicators have been used to compare the model outputs from Infoworks and Sobek : • the mean deviation between the Sobek depths and the Infoworks depths; • a fit indicator and a bias indicator to quantify the matching of the flood extent from both models (referred below as Fit and Bias, Bates and De Roo 2000); • a fit indicator to quantify the number of cells where the difference in the computed depths in small (referred below as FitDepth).

These indicators are calculated using the following relations: B Fit = [43] B ++CD

⎛⎞BC+ Bias=−⎜⎟ 1 [44] ⎝⎠BD+

α Fit = [45] Depth α + β + γ where B is the area wet in both models, C is the area wet in Infoworks but dry in Sobek, D is the area wet in Sobek but dry in Infoworks, A being the area dry in both models, α, β and γ are the number of cells that respect the following conditions:

α : dRFSM − dIW ≤ ε [46]

β : dRFSM − dIW < −ε [47]

γ : dRFSM − dIW > ε [48] where d is the computed depth and ε is a positive threshold value (expressed in meters). A Fit of 0 means that the two model extents have no cells in common (B = 0), hence a totally bad match between the two. A Fit of 1 means that the two model extents are exactly identical (C = D = 0), hence a perfect match.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 73 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

The two models give similar flood extent, however some differences can be locally observed (Figure 6.5). In some of the areas where only one model predicts flooding, the difference in water depth is small (Figure 6.6).

Figure 6.5 Difference in flood extent between Infoworks and Sobek.

Maximum depth deviation (m)

High : 1

Low : -1

differences in flood extent, but small differences in depths

differences in depths where ± Sobek only floods 0250 500 1,000 Meters

Figure 6.6 Difference in flood depth between Infoworks and Sobek (calculated as IW minus Sobek).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 74 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

The flood extent calculated by Sobek is larger than the extent calculated by Infoworks (Table 6.3). The average depth deviation between the two models is 2 mm (Table 6.4), showing that the difference in flood extent is not due to a difference in the final volumes. The Fit indicator is equal to 0.52, which is a reasonably high value, but a higher value could have been expected considering the similarities between the two models algorithms. The difference in water depth is smaller than 0.2 m for 57 % of the cells.

Those differences can only be attributed to the difference in the meshing. Sobek uses a regular grid, with the cell level is the ground level of the corresponding DTM cell. Infoworks uses triangular cells, where the cell level is calculated as the average between the elevations of the three vertices. The fact that the cells are different and that the representation of the topography in the model may slightly differ is likely to be responsible of the differences in the two model outputs.

Another source of differences comes from the representation of buildings in the mesh. Because of the unstructured mesh used in Infoworks, all the considered buildings are included in the mesh irrespective of their size. When a regular grid is used, like in SOBEK and LISFLOOD-FP, buildings and objects might be ignored in the mesh when their size is smaller than the grid resolution. Figure 6.7 illustrates this phenomenon with the magenta circle highlighting the area where Sobek predicts water flowing through the wall (see Google earth image in Figure 6.8). In this case, the wall seems to have a 2.5 m wide lean-to roof, and is not well represented by the rectangular grid with a resolution of 5 m.

Table 6.3 Cell statistics for the flood extent comparison between Infoworks and Sobek. Number of wet cells Both models wet (B) 12 053 InfoWorks only wet (C) 3 259 Sobek only wet (D) 7 873

Table 6.4 Fit indicators for the comparison between Infoworks and Sobek. Average Depth Fit Depth Fit deviation (m) Fit Bias ε = 0.1 m ε = 0.2 m Sobek vs. InfoWorks -0.002 0.52 -0.23 0.38 0.57

Comparison of flood extents Both models dry (A) Both models wet (B) IW2D only wet (C) Sobek only wet (D)

0±25 50 100 Meters

Figure 6.7 Local difference in flood extent due to the buildings representation.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 75 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 6.8 Aerial photograph of buildings represented in Figure 6.7(source: Google earth)

The computational times are indicated for the two models in Table 6.5. The SOBEK simulations were carried out on a PC with the following features Pentium 4, 3600MHz (single core) processor and 4*512MB memory. The Infoworks simulation was run on a PC with the following features: Pentium 4, 3 GHz CPU, 1.5 Gb RAM.

Table 6.5 Computational indicators for the comparison between Infoworks and Sobek. Calculation time Simulation time Model efficiency Number of cells InfoWorks 00:27:20 00:50:00 0.55 124 124 Sobek 00:18:51 00:50:00 0.38 121 874

Conclusions Differences between SOBEK and InfoWorks can mainly be attributed to the difference in the meshing: Sobek uses a regular grid, whereas Infoworks uses triangular cells. When a regular grid is used, like in SOBEK and LISFLOOD-FP, buildings and objects might be ignored in the mesh when their size is smaller than the grid resolution. In other words: application of regular grids requires a check on the schematisation of objects that are smaller than the grid cell size. These can be related to small buildings, but also to other (line) elements that may obstruct the flow, such as the wall in this case, or the secondary dikes in the Scheldt case. To increase the accuracy, it is also required to check all obstacles on openings. For instance, when a wall contains openings, or when tunnels or openings are present underneath secondary dikes, they should be schematised as well.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 76 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

6.3.3 Comparison of RFSM and Infoworks

The depths calculated by the RFSM are the final depths, thus the comparison with a hydrodynamic model needs to be made on the final depths rather than on the maximum depths as done in the previous sections. As Sobek and Lisflood were run for a simulation time of 50 minutes only, a 5 hours simulation has been run on Infoworks and is used as the reference for the comparison with the RFSM.

The performance of the RFSM has been assessed by using the following indicators: B Percentage of correct cells (PCC) = [49] B + C

D Percentage of incorrect cells (PIC) = [50] B + D

α Fit = [51] Depth α + β + γ where B is the area wet in both models, C is the area wet in IW2D but dry in RFSM, D is the area wet in RFSM but dry in IW2D, α, β and γ are the number of cells that respect the following conditions :

α : dRFSM − dIW ≤ ε [52]

β : dRFSM − dIW < −ε [53]

γ : dRFSM − dIW > ε [54] where d is the depth and ε is a positive threshold value (expressed in meters).

These statistics are different from those used for the comparison of SOBEK and Infoworks. The reason for this is that when comparing two similar software packages as Sobek and Infoworks, one can not say beforehand which model is better. Hence, the statistics used for that comparison help evaluating how the results match. However, when comparing RFSM and Infoworks, it is reasonable to consider that Infoworks is "right". Therefore the statistics used in this section use the Infoworsk results as a reference and calculate the percentage of cells that are correctly and incorrectly flooded.

Because of the simple algorithm used by the RFSM, the calculation time is very short (Table 6.6). The model efficiency for RFSM is given as indicative value using 5 hours for the simulation time although the notion of simulation time is not relevant with the RFSM. It should be noted that the RFSM calculation time includes the loading of the dataset in memory (60-70 % of the overall time in this test). The RFSM is designed to run in a flood risk analysis system involving thousands of runs, and the dataset loading is done only once. The spreading time is 6 s and 46 s respectively for the 5 m grid and 2 m grid.

The flood extent calculated by the RFSM is much larger than the extent calculated by Infoworks as shown in Table 6.7 and Figure 6.9 and Figure 6.16. The average deviation between Infoworks and RFSM confirms that the total volume is approximately the same in the two models (Table 6.8). The difference in water depth is smaller than 0.2 m between Infoworks and RFSM for 53 % of the cells for both grid resolution.

The differences between the RFSM and Infoworks outputs are due to (i) differences in the topography representation due to the mesh and the regular grid (as highlighted in the previous section, RFSM using a regular grid like Sobek), and (ii) differences in the spreading algorithm (as the algorithm in RFSM is simplified to allow for fast calculations).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 77 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Considering that the two grid resolutions 2 m and 5 m give overall very similar results and that the calculation time is much shorter with the 5 m grid, the 5 m resolution would be used on this site for a flood risk analysis.

Table 6.6 Computational indicators for the comparison between Infoworks and RFSM. Calculation time Simulation time Model efficiency Number of cells InfoWorks 02:39:00 05:00:00 0.53 124 124 RFSM (5 m) 00:00:25 N/A ~ 1E–03 121 874 RFSM (2 m) 00:01:55 N/A ~ 6E–03 761 502

Table 6.7 Cell statistics for the flood extent comparison between Infoworks and RFSM. Number of wet cells RFSM (5 m) RFSM (2 m) Both models wet (B) 6 113 39 969 InfoWorks only wet (C) 5 487 32 553 RFSM only wet (D) 8 039 48 774

Table 6.8 Fit indicators for the comparison between Infoworks and RFSM. Average Depth Fit Depth Fit deviation (m) PCC PIC ε = 0.1 m ε = 0.2 m RFSM 5 m vs. InfoWorks -0.001 0.53 0.57 0.34 0.53 RFSM 2 m vs. InfoWorks -0.002 0.55 0.55 0.34 0.52

Figure 6.9 Difference in flood extent between Infoworks and RFSM (5 m grid).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 78 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 6.10 Difference in flood extent between Infoworks and RFSM (2 m grid).

Conclusions The flood extent calculated by the RFSM is much larger than the extent calculated by Infoworks. The differences are due to (i) differences in the topography representation due to the mesh and the regular grid and (ii) differences in the spreading algorithm (as the algorithm in RFSM is simplified to allow for fast calculations).

6.4 Additional research questions

6.4.1 The impact of the schematisation of buildings

Results The previous model results were all based on a model in which buildings were schematised as solid objects in the 2D grid (DEM). The exclusion of the buildings in the DEM has a big effect on the spreading of the flood (Figure 6.11). At some locations, the flood travels much further inland when a DEM with buildings is used, because the flood follows a street. However, at other locations the flood reaches farther inland when a DEM without buildings is applied. This is partly because the street level is not well represented in the DEM with building, thus blocking the flow-path, and partly because water flows more easily through a wide channel (which is the case when no buildings are present in the raster) than through a small channel (such as streets when buildings are included). A very striking feature in Figure 6.11 is the Millennium dome, which is not flooded when buildings are modelled as 2D solid objects, but which is flooded when building, including the dome itself, are removed from the DEM. Differences in computed water depths can be about 0.25 m (Figure 6.12).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 79 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 6.11 Flooded area for the 5m grid with (brown) or without buildings (green).

Figure 6.12 Difference in computed maximum water depth between the 5m grid with and without buildings. Red/yellow colours represent areas where the DEM without buildings results in greater depths; in blue coloured areas the DEM with buildings predicts larger depths.

When comparing the difference with or without buildings for the other grid resolutions (Figure 6.13), it becomes clear that the observed difference for the 5 m DEM also are found for the 10 m DEM; e.g. preferential flow paths that coincide with streets result from the DEM with buildings, whereas the

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 80 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

DEM without buildings results in flow over larger areas (planes). No preferential flow through streets is observed in the results from the 25m and 50m because small streets are blocked or ‘averaged out’. The impact of a DEM without buildings here merely results in a further spreading of the water inland.

a b

c d Figure 6.13 Differences between the flood extent with buildings (brown) or without buildings (green) for the different grid resolutions: (a) 5m, (b) 10m, (c) 25m, (d) 50m

When choosing to model with or without buildings, one should keep in mind that when buildings are included, these buildings are modelled as solid blocks, which cannot contain any water. In reality, water will flow into the building, thus reducing the volume of the flood wave.

The impact of buildings on the computed water depths is shown in more detail in Figure 6.15 and Figure 6.16. When buildings are removed from the DEM, the water dissipates in all directions. This results in decreasing water depths with distance from the inflow (overtopping) location (Figure 6.15.a and Figure 6.16.a). However, when buildings are included in the DEM, the preferred flow through the streets results in different maximum water depths and in different timing of the maximum water depths (Figure 6.15.b). At location nr. 1 the water depth increases when buildings are included because the water is forced into relatively narrow streets. Preferred flow through streets reduces the travel time of the front of the flood wave. Between location 1 and 2 the time decreases from 18 minutes to 11 minutes. Between locations B and E the travel time reduces from 7 to 3 minutes.

The timing of flood waves from different streets can result in complex water depth time series. For instance, flood waves passing through two streets meet at location nr. 3. As the timing of the waves coming from the individual streets differs, two water level peaks can be seen in Figure 6.15.b. This pattern also is still visible at more downstream locations, such as location nr. 5.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 81 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

A B C D 4 E F

a b Figure 6.14 Locations selected for detailed model output (a) in the northeast, (b) in the northwest

0.15 0.30

0.12 0.25

1 0.20 1 0.09 2 2 0.15 3 3 0.06 4 0.10 5 water depth (m) water (m) depth 0.03 0.05

0.00 0.00 0 1020304050 0 1020304050 time (minutes) time (minutes) a b Figure 6.15 Computed water depths at locations in the north-eastern part of the study area: (a) 5m grid without buildings, (b) 5m grid with buildings

0.45 0.8 0.4 0.7 0.35 0.6 0.3 B 0.5 B 0.25 D 0.4 D 0.2 F 0.3 F 0.15 water depth (m) water depth (m) depth water 0.1 0.2 0.05 0.1 0 0 0.0 10.0 20.0 30.0 40.0 50.0 0.0 10.0 20.0 30.0 40.0 50.0 time (minutes) time (minutes) a b Figure 6.16 Computed water depths at locations in the north-western part of the study area: (a) 5m grid without buildings, (b) 5m grid with buildings

Conclusions The schematisation of buildings as 2D solid objects results in preferred flow through streets as long as the grid resolution is smaller than the width of the streets. At coarser resolutions the 2D buildings only obstruct the flow and prevent the flood wave from spreading inland.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 82 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

6.4.2 The impact of grid cell size

Results Four elevation models were used for the Thames pilot site. The resolution of the grids was 5m, 10m, 25m and 50m. The model results were compared. From the comparison it was concluded that differences in the grid cell size may lead to large differences in the flooded area.

a b

c d Figure 6.17 Water depth and flood extent computed with SOBEK using different grid resolution: (a) 5m (b) 10m, (c) 25m, (d) 50m (buildings are included as solid objects).

The largest difference in flood pattern is found between the grids with a 10m and a 25m resolution. The 10 m grid still exhibits the pattern of the roads, while this is not the case in the 25m grid. (see figure below). The model shows a significant degradation in model results at coarse resolutions compared to the high resolution benchmark. At coarser resolutions, roads can artificially be closed off, which results in different flow structures. This is apparent in Figure 6.18, where the results of the 5m grid (in brown) are printed on top of the results of the 25 grid (in green). The 5 m grid shows preferred flow through streets, while the 25 m grid shows wider areas that are flooded because the size of the streets is smaller than the grid cell size of the DEM.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 83 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 6.18 The flooded area in the 5 and the 25m grid size. The 5m grid is on top and represented by the brown colour. The 25m grid is in green, which represents the calculated water depth.

Even with the 10m grid results can be seriously affected if the street level is not accurately reproduced in the aggregated DEM. When the DEM without buildings is used, the resolution does not seriously affect the computed water depths (Figure 6.19 a and b). However, very different results are obtained for the DEMs with buildings schematised as 2D solid objects. In this case the differences seem related to major changes in elevation of the selected raster cells.

Conclusions Both the SOBEK and LISFLOOD-FP models predict significant degradation in model results at coarse resolutions compared to the high resolution benchmark. Specifically, results at 25 and 50 m suggest different flow structures emerge as the representation of urban structures in the digital elevation models (DEM) becomes more coarse. It is therefore concluded that inundation models for urban areas should apply a DEM with a grid cell size that is much smaller than the width of the streets. In many European cities this means that the grid cells size should be much smaller than 10m.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 84 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

0.50 0.50 0.45 0.45 0.40 0.40 0.35 0.35 0.30 C 0.30 C 0.25 D 0.25 D 0.20 E 0.20 E 0.15 0.15 water depth (m) water depth (m) 0.10 0.10 0.05 0.05 0.00 0.00 0 1020304050 0 1020304050 time (minutes) time (minutes) a b

0.7 0.4 0.6 0.35 0.3 0.5 0.25 0.4 C C D 0.2 D 0.3 E 0.15 E 0.2 water depth (m) water depth (m) depth water 0.1 0.1 0.05 0 0 0.0 10.0 20.0 30.0 40.0 50.0 0.0 10.0 20.0 30.0 40.0 50.0 time (minutes) time (minutes) c d Figure 6.19 Computed water depths at locations in the northwestern part of the study area: (a) 5m grid without buildings, (b) 10m grid without buildings, (c) 5m grid with buildings, (d) 10m grid with buildings.

6.4.3 The impact of hydraulic roughness

Results Analysis were carried out with the SOBEK model by modifying the hydraulic roughness from manning 0.035 s/m1/3 to manning = 0.07 s/m1/3.

As was to be expected the increase in hydraulic roughness slows down the spreading of the flood wave (Figure 6.20 and Figure 6.21). The delay is in the order of several minutes near the Thames river and increases to about half an hour further inland. The delay also is visible in the time series of computed water depths (Figure 6.21).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 85 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

0.30 0.30

0.25 0.25

0.20 1 0.20 1 2 2 0.15 0.15 3 3 0.10 5 0.10 5 water (m) depth water depth (m) 0.05 0.05

0.00 0.00 0 1020304050 0 1020304050 time (minutes) time (minutes) a b Figure 6.21 Computed water depths at four locations in the study area using different roughness coefficients(a) manning = 0.035 s/m1/3, (b) 0.07 s/m1/3.

Apart from a delay, small differences are also observed in flooding pattern because the increased roughness values increase the damping of the flood wave. Inertia has less effect when high roughness values are applied. The locations that are no longer flooded when higher roughness values are applied are the same locations as those that are not flooded according to the LISFLOOD-FP model.

Although variations in hydraulic roughness affect the computed water depths and flood extent, doubling the horizontal roughness has a smaller effect than increasing the grid cell size from 5m to 10m. In other words: uncertainties in the hydraulic roughness effect the model results less than application of a DEM with an incorrect resolution! The relatively small affect of the hydraulic roughness found here corresponds with the findings of the Scheldt model runs (Chapter 5.4.4)

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 86 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Conclusions The impact of increased roughness values on the model results is twofold. Increased roughness values • delay the progress of the flood wave; • have a minor effect on the water depth; • result in slightly different flow directions as the inertia becomes less important (due to damping effects).

Overall it is concluded that the impact of uncertainties in hydraulic roughness is less than errors caused by the application of the a DEM with a too low resolution.

6.4.4 The impact of wind

Results The impact of wind on the model results was studied by simulating storm winds of 11 Beaufort (30 m/s) coming from the north. The results indicate that the storm has little effect on the computed water depths and inundation pattern. The set-up generally is less than 0.05 m (Figure 6.22). The orientation of the streets does not have a large effect on wind set-up. Set-up against large buildings seems to be more important.

Figure 6.22 Difference in maximum water depth between the SOBEK simulations with and without wind (wind velocity 30 m/s, coming from the north). Red/yellow colours indicate larger water depths when wind is not accounted for, blue colours imply greater depths when wind is accounted for.

Conclusions In urban areas, wind seems to have a minor effect on computed water depths. In this case study, uncertainties in roughness values, grid resolution and model code all have a much greater impact on the results.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 87 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

6.4.5 The impact of the schematisation of tunnels

Introduction A large tunnel underneath the Thames is located in the study area. The entrance is about 200m south of the Millennium dome. The most western tunnel pipe is flooded according to the model. However, as the tunnel itself was not schematised, the flooding merely consisted of large water depths at the entrance of the tunnel (i.e. where the elevation of the road is lower than the surrounding area). SOBEK offers the possibility to model the impact of the tunnel by schematising the tunnel as a 1D channel with a rectangular cross section. The size of the cross section can correspond exactly with the true measures of the tunnel pipes. Also the slope and the hydraulic roughness can be modelled accurately. The entrance and exit of the tunnel can be connected to the 2D grid so that water can flow in and out of it.

A sensitivity analysis was carried out using the SOBEK model with a 5 m resolution DEM. The tunnel pipes where schematised as rectangular cross sections with a width of 6 m and a height of 5 m. In reality the size may differ from the size adopted here, but for a sensitivity analysis this was regarded sufficient. The entrance of the tunnel is located at the lowest visible point of the road leading to it. The exit of the tunnel, at the opposite site of the Thames, is schematised as a storage node. As no accurate elevation data were available for the left bank of the Thames, a similar elevation distribution as in the study area covered by the model was adopted for the storage node. This is accurate enough for a sensitivity analysis.

Results Maximum water depths in the study area coincide with the passage of the flood wave. This means that water depths increase rapidly when the front of the flood wave arrives, but decrease again some 20 minutes later (see for instance Figure 6.16.a and Figure 6.19).

The height of this flood wave is not affected by water flow through the tunnel. In other words, modelling of water flow through the tunnel does not affect water depths upstream of the tunnel (Figure 6.23). Differences only occur near the entrance of the tunnel.

If the inflow of water from the Thames into the study area would have been higher (for instance because of breaching instead of overtopping) and the area inland/downstream of the tunnel would have been flooded as well, a larger effect could be expected here. This situation is shown in Figure 6.24. In this simulation a breach is assumed at the western side of the study area, causing an inflow with a short peak discharge of 250 m3/s. It was assumed that measures were taken to decrease the inflow to 50 m3/s within one hour and stop the inflow completely within 4 hours. This is a conservative assumption as the inflow in most breaching studies, such as the Scheldt pilot, is much larger. Figure 6.24 shows that the larger inflow volume indeed results in a larger flood extent.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 88 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 6.23 Difference in computed water depth with and without schematisation of the tunnel crossing the Thames

a Figure 6.24 Computed water depths after breach formation on the west side of the study area

The simulation with breaching was used to simulate the impact of the tunnel. Figure 6.25 shows the decrease in water depths caused by the flow through the tunnel. The computed maximum discharges through the tunnel pipes were 70 m3/s through the most western tunnel pipe and 50 m3/s through the eastern pipe. The ‘loss’ of water through the tunnel affected water depths downstream of the tunnel. Here water depths decreased by about 0 to 0.5 m.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 89 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

b Figure 6.25 Difference in computed water depth with and without schematisation of the tunnel crossing the Thames

The flow through the tunnel also affected the time of first inundation (Figure 6.26). No delay is observed upstream of the tunnel. Downstream of the tunnel the delay varies from 15 minutes to half an hour. At greater distances the delay can increase up to several hours.

Figure 6.26 Computed delay in time of inundation caused by flow through the tunnel crossing the Thames

Conclusion Tunnels can have a significant impact on water depths and flood extent. In the Thames study area, simulation of flow through the tunnel under the Thames resulted in reduced water depths and a delay in the spreading of water on the right bank, i.e. the area where the breach occurred. Also, flow through the tunnel will cause inundation on the left bank, which otherwise would have remained dry.

The importance of tunnels also is known from model simulations in the Netherlands. Especially in the western part of the Netherlands, where the elevation often is several meters below mean sea level, many secondary dikes or other obstacles are present (canal dikes, railway dikes, etc.). These obstacles

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 90 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 significantly affect the flooding pattern as they stop the flood. However, in reality many openings such as tunnels and aqueducts are present that enable the flow to pass the dikes. Accurate simulation of water flow through these openings is of the utmost importance.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 91 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 92 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

7. Simulating flow in steep mountainous rivers: the Brembo site

7.1 Study area and available data

7.1.1 The study area The Brembo is a 50 km long river situated in Nothern Italy, in the Lombardy Region. It springs from the Bergamo Alps, then is fed by some water courses, and flows into the Adda river at the border between the provinces of Bergamo and Milan (Figure 7.1).

L=50 km

L=98 km

L=131 km

Figure 7.1 Location of the Brembo River in the Italian Alps and plan view of the Brembo River with the major tributaries of the Adda river

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 93 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 7.2 Flood of the Brembo river

Many floods occur along the Brembo river, and they are often disastrous. One of the worst was in June 1987 (Figure 7.2).

The Brembo River is an interesting case to test numerical models because of its geometrical complexity. The river bed presents a lot of steep and adverse slopes, as illustrated in Figure 7.3 showing the bed profile. The Brembo springs at an altitude of 481 m, and flows into the Adda river at an altitude of 131 m. The bed slope is steeper in the upstream part of the river. The cross sections also present successive enlargements and constrictions. Figure 7.4 shows several successive the cross sections, indicated by the black line. The blue line indicates the widening and narrowing of the channel width.

The objective of this study is to reproduce the flood of June 2006 for which detailed and accurate data are available. The numerical results will be compared with the available measurements so that it will be possible to judge the quality of the methods used to simulate such flows.

Figure Figure 7.3 Profile of the thalweg and examples of steep and adverse slopes

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 94 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 7.4 Enlargements and constrictions of the sections

7.1.2 Available data

The data were provided by the research unit of Pavia University, coordinated by Prof L. Natale. These data can be divided in two main sets: the data used as input of the models, and the data that are used to verify the numerical results. The input data are the topography of the area, the hydrograph at the upstream section, which serves as upstream boundary condition, and the water elevation and discharge along the river, which serves as an initial condition. Data that are available for comparison with the results of the numerical simulations consist of measured water levels at some locations.

Topographical data

Aerial photographs as illustrated in Figure 7.5 are available, along with two sets of measurements of the topography. The first one comes from a field survey and provides one-dimensional cross-sections. It will be referred to herein as “1D field data”. The second set was collected later and consists of LIDAR measurements that were used to construct a two-dimensional Digital Elevation Model (DEM). It will be referred to as “new DEM”. This section is dedicated to the description of the topography and the comparison between the two types of the available data.

Figure 7.5 aerial photo of a part of the Brembo, with the location of some sections

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 95 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Collecting the 1D field data consists in measuring the depth of the water at some cross sections along the water course. There were 274 cross sections with an average distance between cross-sections of 180 m. The measures were then expressed in function of the same common reference to obtain the bed elevation. The major drawback of this method is that there can be human errors, so the data must be used carefully. Also, at some locations, the measured cross sections are not wide enough to cover the whole extent of flooded land.

The new DEM was obtained by LIDAR measurements. It consists in sending a LASER ray from a plane. The ray is reflected as it reaches an obstacle like the ground or a water surface, and the reflected ray is picked up by the transmitter. The time of one travel transmitter – obstacle – transmitter is proportional to the distance between the obstacle and the transmitter, so this distance can be deduced. As the ray is reflected also by water, the river should be dry to measure the elevation of its bed, which is almost the case in the dry season. These measurements give the ground elevation over a grid of 2m × 2m. The covered zone extends over the major bed, so it is large enough to simulate a flood. A drawback of the method is that the bridges and other control structures prevent the LASER ray to reach the ground beneath. This is solved by removing the points situated in such places and replacing them by an interpolation of the points around. But this is a source of imprecision. Moreover, undesirable obstacle, such as trees or houses, cannot always be removed.

Comparison between the two data sets

At some locations, significant discrepancies were observed between the two data sets, as illustrated in the next examples. Figure 7.6 shows a cross section situated at a control structure (km 7.979), it can thus be expected that the cross-section there be rectangular, which is not the case in the new DEM data. This is probably the results of the interpolation process used when the LASER ray reaches an obstacle. So in this case, it was chosen to trust to the 1D field data.

z (m)

y (m)

Figure 7.6 Cross section at km 7.979, where the 1D field data are different from the new DEM data

Another example is illustrated in Figure 7.7. Here the 1D field data give a narrower cross section than the new DEM data. This is probably due to a measurement error while measuring the cross sections in the field, so in this case the new DEM data should be used.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 96 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

z (m)

y (m)

Figure 7.7 Cross section at km 10.281, where the 1D field data are different from the new DEM data

In general, the new DEM is more reliable than the 1D field data because of the possible human error. But when there is a control structure, it is often better to trust to the 1D field data. Indeed, in this case, the elevations from the DEM come from an interpolation of the points around and may be imprecise, while the data from the survey have been measured in situ by a team who saw the cross section and knew what it looked like.

Flow data

The upstream hydrograph (km zero) illustrated in Figure 7.8 constitutes the upstream boundary condition. It was recorded during the flood of 25th June 06 during 41 hours.

Figure 7.8 Upstream hydrograph

The initial conditions are taken as a steady flow with a discharge of 94.5 m³/s, corresponding to the first value of the inflow hydrograph. At the downstream end, a stage-discharge relation for the last section is used (Table 7.1), resulting in a water level of 133.31 m. The initial water profile is illustrated in Figure 7.9. It should be noted that in the realty, there are a number of tributaries along the Brembo river, that add discharge into the river. However, their discharge during the flood is not known, and for the sake of simplicity, it was chosen to neglect these tributaries in the present study.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 97 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Table 7.1 Stage-discharge relation for the downstream section h(m) Q(m3/s) 0.00 0.00 1.00 22.20 1.50 57.16 2.00 133.04 2.50 258.50 3.00 431.08 3.50 686.12 4.00 1164.93 4.50 1911.15 5.00 2946.64

500

450 z (m) San Pellegrino 400 Ambra Spino 350 Zogno

300 Villa d’Almè 250 Briolo

200 Roncola

150 Filago Brembate 100 0 1020304050 x (km)

Figure 7.9 Initial water level along the Brembo river

Available measurements

After the flood, the maximum level reached by the water was recorded in each town crossed by the Brembo River. These levels are shown in Table 7.2, and the towns are shown in the map of Figure 7.10.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 98 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Table 7.2 Maximum level water recorded along the river

Number Location Distance from spring (km) h max (m) 1 San Pellegrino 14.879 7.66 2 San Pellegrino 15.230 5.42 3 San Pellegrino 15.900 5.78 4 San Pellegrino 16.448 3.69 5 Ambra Spino 18.601 6.60 6 Zogno 20.479 5.52 7 Zogno 21.015 4.60 8 Sedrina 24.239 6.37 9 Villa d’Almè 30.192 5.04 10 Ponte di Briolo 34.963 8.79 11 Briolo 35.185 8.99 12 Ponte S.Pietro 36.368 5.67 13 Ponte S.Pietro 36.696 6.36 14 Roncola 39.282 5.31 15 Filago 44.426 7.70 16 Vivion (Brembate) 47.358 16.34 17 Brembate di Sotto 47.659 13.78 18 Brembate di Sotto 48.003 7.01

San Pellegrino Terme

Sedrina Ambra Spino

Zogno

Vila d’Almè Briolo

Ponte San Pietro

Roncola

Filago

Brembate

Figure 7.10 Map of the towns crossed by the Brembo where the maximum water levels were recorded

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 99 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

7.2 Model development

Challenges for the numerical models

As already mentioned, this test case presents features that challenge the numerical models: the very steep slope, with some adverse slopes, and the sudden enlargements and constrictions at some locations. Besides, there is another issue that might cause problems to 1D numerical models, or at least that deserve some caution from the modeller.

Cross section at km 1.776 illustrated in Figure 7.11 presents a double thalweg. If the water level lies between the two dotted lines, there are two possible wetted areas: the water flow could take place entirely in the left part, which is the original bed, or in both parts. In reality, during a flood, the river remains in the original bed, and overflows in the other part of the section only if the water level becomes higher than the intermediate crest. Then the river would make a secondary thalweg, with different water levels and velocities.

Usually, pure one-dimensional models are not able to properly account for such situations, and the water level is distributed from the beginning of the flood between the two thalwegs. If a detailed simulation of such areas is required, applying a local two-dimensional model would be the solution.

Figure 7.11 Cross section which arise a difficulty

The data were applied to develop four numerical models using the following packages: • SOBEK-1D, that is described in section 4.4 • SV1D, briefly described in section 4.3, for which a more detailed description is provided below • ORSA1D-Roe, developed at the University of Pavia (Petaccia, 2003) • SANA 1D, developed at the Universities of Rome and Pavia (Natale and Savi, 1992)

SV1D

This model solves the one-dimensional shallow-water equations written in fully conservation form as

∂ A ∂Q + = 0 [55] ∂t ∂ x

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 100 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

∂Q ∂ ⎛ Q 2 ⎞ ∂ + ⎜ + g I ⎟ = g I − g AS [56] ⎜ 1 ⎟ ()1 z f ∂t ∂x ⎝ A ⎠ ∂x

With A the wetted area, Q the discharge, I1 the static moment of the cross-section with wetted area A and with the topographical source term ∂ ∂ x (I1 z ) standing for the spatial variation of the first moment at a constant water level z ( ∂z ∂x = 0 ). This term arises by writing (Soares-Frazão, 2002)

∂ I 2 + AS 0 = ()I1 z [57] ∂x In this way, only one expression is to be discretised to represent the topographical source terms and the distinction between the bed slope term S0 and the cross-section widening term I2 is avoided. Whilst there are some advantages to write the equations in this way in very irregular topographies (Capart et al., 2003), some care must be taken over very steep slopes with low water depths. This will be illustrated in the applications to the Brembo case.

Equations (1-2) can be written in vector form as

Ut + Fx = S [58] ⎛ Q ⎞ ⎛ A⎞ ⎜ ⎟ ⎛ Q ⎞ ⎛ 0 ⎞ with U = ⎜ ⎟ , F = Q 2 = ⎜ ⎟ , S = ⎜ ⎟ ⎜Q⎟ ⎜ + g I ⎟ ⎜ Σ ⎟ ⎜ ∂ ∂ x()g I − gAS ⎟ ⎝ ⎠ ⎝ A 1 ⎠ ⎝ ⎠ ⎝ 1 z f ⎠

The finite-volume discretisation reads

Δt U n+1 = U n − ()F* − F* + SΔt [59] i i Δx i+1/ 2 i−1/ 2 * * Where Fi+1 2 and Fi−1 2 are the numerical fluxes at the interfaces between cells. These are calculated using HLL approach with a lateralized treatment for the topographical source term (Fraccarollo and Capart, 2003).

The HLL fluxes read λ+ λ− λ+ λ− F* = F − F − ()U − U [60] i+1/ 2 λ+ − λ− i λ+ − λ− i+1 λ+ − λ− i i+1

The wave speeds λ+ and λ- are defined by

+ λ = max()Vi + ci ,Vi+1 + ci+1,0 [61] − λ = min()Vi − ci ,Vi+1 − ci+1,0 [62]

Where V = Q/A is the flow velocity and c = g A B is the celerity with B the width of the cross- section at the free-surface.

The topographical source term is discretized in a lateralized way as

∂ 1 ()g I1 = (()gI1 − ()gI1 ) [63] ∂x z Δx zi i+1/ 2 zi i−1/ 2

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 101 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

With λ+ λ− [64] ()gI1 = + − ()gI1 − + − (gI1 ) zi i+1/ 2 λ − λ zi i λ − λ zi i+1

Orsa1D-Roe and SANA

The model solves the shallow water equations coming from the mass and momentum balance equations (Cunge et al 1980):

∂U ∂F + = S [65] ∂t ∂x ⎛ Q ⎞ ⎛ A⎞ ⎛ 0 ⎞ ⎜ 2 ⎟ ⎜ ⎟ U = ⎜ ⎟ F = ⎜ Q ⎟ S = ⎜ ⎟ [66] ⎝Q⎠ ⎜ + gI1 ⎟ gA()S0 − S f + gI2 ⎝ A ⎠ ⎝ ⎠ where x is the spatial co-ordinate measured along the channel, t the time, Q the discharge, Α the wetted area, g the gravitational acceleration, S0 the bottom slope, Sf the friction slope. The terms I1 and I2 are related to the hydrostatic pressure force:

h h ∂b I = ()()h −η b x,η dη , I = ()h −η dη [67] 1 ∫ 2 ∫ ∂x 0 0 h is the water depth and b(x,η) the width of the cross section at the distance x and height η, above the channel bed.

The system of equations (1) is solved by means of two explicit, finite-volume schemes. The computational domain is divided in a temporal-spatial computational mesh. Each point is represented n n by a pair (xi, t ), where xi represents the position in space and t the time level. The geometric variables (A, I1, I2, etc) are evaluated directly from the cross sections and any numerical function is used to interpolate the topographic features, as adopted by several Authors (Garcia Navarro et al, 1999; Aureli et al; 2000; Sanders, 2001).

First- order upwind scheme (Orsa1D-Roe)

This scheme is based on finite-volume discretization:

n+1 n Δt * * Ui = Ui − ()Fi+1/ 2 − Fi−1/ 2 [68] Δx assuming Roe’s approximated Jacobian of the flux (Roe 1981). The numerical fluxes F are computed as

* 1 n n 1 ~k k ~k Fi−1 / 2 = ()Fi + Fi+1 − ⋅ ai+1 / 2 ⋅αi+1 / 2 ⋅ ei+1 / 2 [69] 2 2 ∑ k=1,2 with ⎡ n n ~n n n ⎤ 1,2 1 n n (Qi +1 − Qi )− ui +1/ 2 (Ai +1 − Ai ) [70] α = ⎢()Ai +1 − Ai ± ⎥ i +1/ 2 2 ⎢ ~n ⎥ ⎣ (ci +1/ 2 ) ⎦

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 102 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 and ⎛ 1 ⎞ ~1,2 ~n ~n 1,2 ⎜ ⎟ ai+1/ 2 = ui+1/ 2 ± ci+1/ 2 , ei+1/ 2 = ⎜ ~1,2 ⎟ [71] ⎝ai+1/ 2 ⎠ ∂F The eigenvalues a and the eigenvectors e of the Jacobian matrix J = depend on the flow velocity u ∂U and celerity c:

An u n + An u n n n ~ n i+1 i+1 i i ~ n I1i+1 − I1i ui+1/ 2 = [72a] ci+1/ 2 = g [72b] n n An − An Ai+1 + Ai i+1 i

In order to avoid non-physical discontinuities (zero eigenvalues), that are incompatible with the entropy principle, the absolute value of the eigenvalues of J is modified by defining the quantity:

ε k = max o, a~k − ak , ak − a~k i+1/ 2 [ ( i+1/ 2 i ) ( i+1 i+1/ 2 )] [73] k = 1,2

The new absolute value of each eigenvalue in equation [60] is defined as:

⎧ a~k if a~k ≥ ε k k ⎪ i+1/ 2 i+1/ 2 i+1/ 2 Ψ = (k = 1,2) [74] i+1/ 2 ⎨ k ~k k ⎪ε if a < ε ⎩ i+1/ 2 i+1/ 2 i+1/ 2

First-order Lax-Friedrich type scheme (SANA)

This is a semi-implicit first-order scheme applied on a staggered grid; the momentum equation is written according to the characteristics of the flow in the current node. This scheme, developed by Natale and Savi (1992) modifying the scheme proposed by Sielecky (Vreugdenhil 1989), is intuitive from the physical point of view and easy to implement. The momentum equation is fully explicit and reads:

n+1 n Qi+1/ 2 = Qi+1/ 2 − Δt ⋅ M i+1/ 2 − Δt [75] − (gIi+1 − gIi−1)+ Δt ⋅ Si+1/ 2 Δxi+1/ 2 where ⎛ n n ⎞ n 1 ⎜ Q2 Q2 ⎟ ⎪⎧0 if F ≥ 1 M = ⋅ − s = i+1/ 2 i+1/ 2 ⎜ ⎟ ⎨ n Δxi+1/ 2+s ⎜ Aˆ Aˆ ⎟ ⎪1 if F < 1 ⎝ i+1/ 2+ s i−1/ 2 ⎠ ⎩ i+1/ 2 ˆ n n n Ai+1/ 2 = 0.5⋅ (Ai + Ai+1) [76]

The continuity equation is implicit and reads:

n+1 n Δt n+1 n+1 Ai = Ai − ()Qi+1/ 2 − Qi−1/ 2 [77] Δxi

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 103 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

The source terms are schematised in the pointwise approach (Brufau et al, 2000)

n2Qn+1 Qn+1 zi+1 − zi−1 n i i S0i = − and S f = [78] 2Δx i n n4 / 3 Ai Ri where n is the Manning roughness coefficient. For the converging-diverging flume the I2 term is schematised as

1 2 bi+1 − bi−1 I = ⋅ h [79] 2 2 i 2Δx

where b is the flume width. For the Lax-Friedrich type scheme, the source term in the momentum equation is discretised as:

ˆ g Si+1/ 2 = gAi+1/ 2 ()S0 − S f + ()I2 − I2 i +1/ 2 i +1/ 2 i+1 i Δxi+1/ 2 [80]

7.3 Model comparison

7.3.1 Introduction

The numerical models were compared under the following conditions: • Cross-sections: the original “1D field data” were used. For some cross sections with incomplete data, a “vertical” wall is assumed at the end of the cross section. The validity of this assumption is checked during the simulation process: what is the water depth, if any, against this virtual vertical wall, or, in other words, is the extent of the flooded area underestimated? • Initial conditions: a constant discharge of 94.5 m³/s is applied in the river reach, and the downstream level is defined by the stage-discharge relation at the downstream section. This results in a downstream water level of 133.31. • Boundary condition: Upstream: discharge Q(t) as provided in Figure 7.8. Downstream: stage-discharge relation as provided in Table 7.1. • Friction: a constant Manning coefficient of 0.04 is assumed for all cross-sections.

Computed water levels, discharges and Froude numbers were compared at selected times and locations. Besides, the maximum water level was compared to field data. However, this latter comparison has to be taken with some care, as the discharge from the tributaries was neglected.

7.3.2 Results at selected cross sections

In this section, zw(t) and Q(t) computed by the models are compared at four selected points. These points are situated at x = 7.791 km, 24.413 km, 36.852 km and 48.446 km, which are places where the geometry of the river bed is quite irregular (Figure 7.12 and Figure 7.13).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 104 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

600 z (m) Thalweg 500 Points of comparison

400

300

200

100

0 0 1020304050 x (km)

Figure 7.12 Situation of the 4 points of comparison in the profile of the thalweg of the Brembo

Point x = 7.791 km Point x = 24.413 km

440 300

430 290

420 280

410 270

400 260

390 250 6 6.5 7 7.5 8 8.5 23 23.5 24 24.5 25 25.5

Point x = 36.852 km Point x = 48.446 km

170 230

220 160

210 150

200 140

190 130 180 120 35 35.5 36 36.5 37 37.5 47 47.5 48 48.5 49 49.5

Figure 7.13 Details of the thalweg in the surrounding of the four points of comparison

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 105 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 7.14 and Figure 7.15 show the evolution of the water level and of the discharge as functions of time at the first comparison point located at x = 7.791 km. ROE gives the highest water level, while the discharge is very similar for all models.

422.5 zw (m) SV1D SOBEK 422.0 ORSA1D SANA 421.5

421.0

420.5

420.0 0 5 10 15 20 25 30 35 40 t (h)

Figure 7.14 Evolution of water level zw in function of time at point x = 7.791 km

600 Q (m³/s) Hydrogram 500 SV1D SOBEK 400 ORSA1D SANA 300

200

100

0 0 5 10 15 20 25 30 35t (h) 40

Figure 7.15 Evolution of discharge Q in function of time at point x = 7.791 km

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 106 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

287 zw (m) SV1D 286 SOBEK 285 ORSA1D 284 SANA 283 282 281 280 279 278 277 0 5 10 15 20 25 30 35t (h) 40

Figure 7.16 Evolution of water level zw in function of time at point x = 24.413 km

700 Hydrogram Q (m³/s) SV1D 600 SOBEK ORSA1D 500 SANA

400

300

200

100

0 0 5 10 15 20 25 30 35 40 t (h)

Figure 7.17 Evolution of discharge Q in function of time at point x = 24.413 km

The second comparison point (x = 24.413 km) is located immediately downstream of a scour hole caused by the presence of a bridge inducing a local narrowing of the cross-section. The computed water levels (Figure 7.16) are much more different from one model to another, with differences up to 6 m. The reason for this difference is discussed in more detail in the text near Figure 7.22. It can be observed that the discharges also show significant discrepancies between the models (Figure 7.17). More precisely, the agreement between SOBEK and SANA is good, while ORSA1D and SV1D show different results, with unrealistic features: an initial discharge less than the prescribed value of 94 m³/s for SV1D and a higher peak discharge than the inflow hydrograph for ORSA1D.

These observed differences in the computed discharge by the finite-volume schemes ORSA1D and SV1D were investigated by analysing the discharge profile over the river for a selected time. This is illustrated in Figure 7.18 for a reach around comparison point 2. The variable Q of Equation [56] does in fact represent the momentum and not the discharge flowing from one computational cell to another.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 107 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

* This latter value, which is in fact the actual discharge, is represented by the mass flux Qi+1/2 in the finite-volume scheme. This is a feature that is specific to finite-volume schemes. The value of the momentum Q is irregular (Figure 7.18) because it is strongly influenced by the topographic source terms that play an important role in the present case. It must be pointed out that in cases where the * topography is more regular, the differences between the momentum Q and the mass flux Qi+1/2 become negligible.

After 8h

800

Momentum Q 600 * Mass Flux Qi+1/2Qi+1/ 2

400 Point 2

200

Momentum and mass flux (m³/s) 0 0 10000 20000 30000 40000 50000 x (m)

-200

-400

-600

* Figure 7.18 Comparison between the mass flux Qi+1/ 2 and the momentum Q

* Figure 7.17 can thus be modified by considering the mass flux Qi+1/ 2 for SV1D, yielding the results presented in Figure 7.19: the correspondence between SOBEK, SANA and SV1D is now much better. Similar results would be obtained with ORSA1D.

600 Q (m³/s) Hydrogram 500 SV1D SOBEK SANA 400

300

200

100

0 0 5 10 15 20 25 30 35 40 t (h)

* Figure 7.19 Evolution of discharge Q (and mass flux Qi+1/2 for SV1D) in function of time at point x = 24.413 km

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 108 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

The computed water levels are further compared for the comparison points located at x = 36.852 km (Figure 7.20) and x = 48.446 km (Figure 7.21). Again, like for the comparison point located at x = 24.413 km (Figure 7.16), there are some important discrepancies, that will be discussed in the next section.

209.0 zw (m) SV1D SOBEK 208.6 ORSA1D SANA

208.2

207.8

207.4

207.0 0 5 10 15 20 25 30 35t (h) 40

Figure 7.20 Evolution of water level zw in function of time at point x = 36.852 km

148 zw (m) 147.8 147.6 SV1D 147.4 SOBEK 147.2 ORSA1D SANA 147 146.8 146.6

146.4 146.2 146 0 5 10 15 20 25 30 35t (h) 40

Figure 7.21 Evolution of water level zw in function of time at point x = 48.446 km

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 109 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

7.3.3 Results along the river at selected times

The computed free-surface profiles were compared at selected times, namely t = 8 h, t = 9 h, t = 11 s and t = 41 h. Time t = 8 h corresponds to the peak of the inflow hydrograph. At t = 9 h, the maximum discharge propagates along the river.

As already outlined, the computed results show significant differences at x = 24.413 km. A close-up view of the water level around this point showing the results of all models is shown inFigure 7.22, after 8 h, thus corresponding to the inflow peak discharge. The large differences in water depth observed in Figure 7.16 are clearly visible and seem related to an increase in water level that is predicted by SV1D and Orsa1D-Roe and is not, or less clearly in SOBEK and SANA.

300 z (m) SV1D zb 295 ORSA1D Point 2 SANA 290 SOBEK

285

280

275

270 23 23.5 24 24.5 25 25.5 x (km)

Figure 7.22 picture of the water level after 8h around point 2 (x = 24.413)

Figure 7.23 shows the results of the SOBEK model for this same location. The slope of the river bed is large between km 24 and 24.4. After km 24.4 the river bed slope is reversed. The width of the cross sections also varies rapidly (Figure 7.24). The width of the river only is about 17 m at section 2. Upstream and downstream of this location the river is much wider.

What seems to happen according to the SOBEK model is that the Froude number is greater than 1 upstream of location 2 (steep slope, limited depth, large velocities). Near location 2 the cross section is very narrow, this results in an increase in flow velocity. However, due to the scour hole the depth increases as well. This results in a decreasing Froude number and hence in a hydraulic jump. The small increase in water level at the beginning of the scour hole might reflect this. Further downstream the channel widens again and flow velocities decrease. The 'transport' of impulse causes a minor increase in water level (10 cm) when the slope of the bed level reverses.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 110 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

6 290 ) 5 287

4 284 Froude number velocity 3 281 water level bed level

2 278 +OD) (m elevation

1 275 Froude velocitynumber and (m/s Froude Flow

0 272 23.9 24.1 24.3 24.5 24.7 24.9 distance (km)

Figure 7.23 detailed graph of the water level, bed level, Froude number and flow velocities near section 2, computed with the SOBEK model

320

310

300 174 m upstream 118 m upstream 0 m (=section 2) 290 236 m downstream elevation (m+OD) elevation

280

270 0 255075100125150 width (m)

Figure 7.24 Cross sections near section 2

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 111 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

300 zb z (m) SV1D 295 ORSA1D_C

290 SANA

SOBEK 285

280

275

270 23 23.5 24 24.5 25 25.5x (km) 26

Figure 7.25 picture of the water level after 8h with additional cross-sections around point 2

Looking now more closely at the results provide by the finite-volume schemes ORSA1D and SV1D, it appears that the predicted water level is unrealistic. As illustrated in Figure 7.24, there is an important widening of the cross section near point 2 (x = 24.413 km). After performing some steady-flow simulations by means of dedicated steady-flow softwares, it was observed that that flow in this area should be close to the critical depth, but always subcritical, thus without any hydraulic jump. The erroneous results of SV1D and ORSA1D-Roe were thus suspected to be due to the too coarse description of the topography. Indeed, contrarily to SOBEK, these models compute the results only based on the provided topography, without interpolating automatically any additional computational points. If more computational points are required for the accuracy of the results, they should be added in the description of the computational domain.

Therefore, based on the steady-flow simulations, a convergence study was performed: additional cross-sections were added in this area to refine the computational grid locally. The new results for Orsa1D-Roe and SV1D with the additional cross sections are shown in Figure 7.25: SV1D and ORSA1D converge towards the same results, close to the results obtained by SANA without any additional cross-section, nor automatic interpolation. The sudden elevation of the water level has disappeared. The results provided by SOBEK, with automatically interpolated cross sections, provided a lower water elevation. This is probably due to the fact that, as mentioned earlier, SOBEK predicat a supercritical flow in this area, contrarily to the other models for which the flow remains subcritical.

Other aspects should also be taken into consideration for the observed differences in computed water level:

1. The way the yz-profiles are interpolated by the software. Several software packages do not interpolate between yz points given in the description of the cross section. This results in the type of schematization as shown in Figure 7.26a. Other models interpolate the yz-coordinates in a manner indicated in Figure 7.26b. 2. Interpolation between cross sections. Several models interpolate cross sections to compute water levels at water level locations. To compute flow velocities at location between the water level points, the cross section either upstream or downstream of the reach is used. In situations with rapidly varying cross sections, such as is the case in the Brembo river and certainly near section 2,

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 112 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

this may cause errors. SOBEK also interpolates the cross sections to the location where the velocity is computed. A sensitivity analysis for the Rhine model showed that this new approach resulted in water level differences of 30 cm. Given the large variability in the cross sections in the Brembo river, differences could be even larger here.

a b Figure 7.26 Schematisation of yz-cross sections (blue dots are yz points given by the user, the bold line represents the actual cross section and the dotted line the cross section used by the model

Figure 7.27 shows the water profile after 9h, in a reach where comparison point x = 36.852 km is located. The thalweg is very irregular between x = 34.5 km and x = 37 km, due to a deep scouring that occurred immediately downstream from a bridge located at x = 35.713 km. The results computed by the four different models are reasonably close to each other, except at x = 35 km where SV1D and Roe predict a very strong elevation of the free surface. Figure 7.28 shows water levels computed after 41 hours.

Figure 7.29 shows the discharge as a function of the abscissa after 8 h. As explained above, it must be noted that for the finite-volume schemes SV1D and Orsa1D-Roe, the discharge is provided by the * values of the mass flux Qi+1/ 2 between each computational cell.

z (m) 250

SV1D 240 zb Point 3 Roe 230 SANA SOBEK 220

210

200

190 30 32 34 36 38x (m) 40

Figure 7.27 Water level after 9h around point 3 (x = 36.852 km)

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 113 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

170 zb z (m) 165 SV1D ORSA1D 160 SANA Point 4 155 SOBEK Point 4 150

145

140

135

130

125

120 47 47.5 48 48.5 49 49.5 x (km)

Figure 7.28 Water level after 41h around point 4 (x = 48.446 km)

Q (m³/s) 600

500

400

300

200 Mass flux - SV1D Mass flux - Orsa1D - Roe 100 SOBEK SANA x (km) 0 0 1020304050

Figure 7.29 Picture of the discharge after 8h

Figure 7.30 and Figure 7.31 show the computed Froude number between x = 20 km and x = 30 km and x = 30 and x = 40 km, respectively, after 9 h. The bed level is also indicated in the figure. In the regions of local steep slopes, the flow is supercritical and the Froude number reaches values greater than one. But outside this area the flow regime is mainly subcritical.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 114 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

320 2 Fr (-) 1.8 300 z (m) Point 2 1.6

1.4 zb 280 SV1D 1.2 Roe 260 1 SANA SOBEK 0.8 240 0.6

0.4 220 0.2

200 0 20.017 21.015 22.846 24.1753 25.893 27.294 28.483 29.658 x (km)

Figure 7.30 Picture of the Froude number after 9h between x = 20 km and x = 30 km

250 3.5 Fr (-) 240 3 z (m) zb 230 2.5 SV1D 220 Roe 2 210 SANA SOBEK 1.5 200 1 190 0.5 180

170 0

160 -0.5

150 -1 30.0563 31.702 33.993 35.288 36.207 37.1005 38.556 40.664 x (km)

Figure 7.31 Picture of the Froude number after 9h between x = 30 km and x = 40 km

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 115 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

7.3.4 Maximum water level

Finally, the predicted maximum water levels reached during the flood are compared with field measurements collected at 16 stations along the river (Figure 7.32). This comparison is only qualitative, as it must be recalled that the discharge coming from the tributaries was neglected in this study.

For clarity, the results are presented for 3 reaches: x = [km 13 - 20] in Figure 7.32, x = [km 20 - 28] in Figure 7.33, x = [km 28-37] in Figure 7.33 and x = [km 37-50] in Figure 7.34. There is a good overall agreement between the models, and, as assumed, the maximum water level is underestimated by the models, due to the fact that inflow from the tributaries was neglected. The maximum water level measured at x = 47.358 km is very high and is probably due to a measurement error.

z (m) Thalweg 365 zw max measured SV1D 355 Roe SANA 345 SOBEK

335

325

315

305 13 14 15 16 17 18 19 20 x (km)

Figure 7.32 picture of the maximum water level between x = 13 km and x = 20 km

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 116 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

320 z (m) Thalweg zw max measured 310 SV1D Roe 300 SANA SOBEK 290

280

270

260

250 20 21 22 23 24 25 26 27 28 x (km)

Figure 7.33 Picture of the maximum water level between x = 20 km and x = 28 km

z (m) Thalweg 260 zw max measured 250 SV1D Roe 240 SANA SOBEK 230

220

210

200

190 28 30 32 34 36 x (km)

Figure 7.34 picture of the maximum water level between x = 28 km and x = 37 km

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 117 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

z (m) Thalweg 200 zw max measured 190 SV1D Roe 180 SANA SOBEK 170

160

150

140

130 37 39 41 43 45 47 49 x (km)

Figure 7.35 picture of the maximum water level between x = 37 km and x = 50 km

7.3.5 Conclusion

Simulation of a flood in a steep mountain reach requires a particular attention to the way the terms representing the topography (the source terms) are represented and discretised in the numerical scheme. Especially, it was shown that in some models a too coarse discretisation in areas where the topography shows strong variations may lead to erroneous results. Interpolation of cross sections is required. This was highlighted by a local convergence study after performing steady-flow simulations by means of a steady-flow tool and imposing a representative constant discharge.

7.4 Additional research questions

Additional research efforts should be devoted to a better understanding of the consequences of the choice made to represent the topographical source terms. At the current stage, it is not possible to identify the cases where the “integrated” approach provides better results than the traditional one (i.e S0 and I2). Moreover, although many efforts were devoted to the discretisation of these source terms, it is not yet completely clear why upwind-type approaches (like the lateralised treatment used in SV1D for example) provide in some cases results that may vary significantly from the classical centred approach (like in ORSA1D-Roe or SANA).

These additional research questions were not treated in this study.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 118 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

8. Simulating flow in urban areas: flume data

8.1 Introduction

The flooding of urbanised areas constitutes a major threat for population, especially if no counter- measures are planned to cope with this situation. This is likely to occur when an inundation results from unexpected or uncommon events such as the breaking of a dam or a dike, or a flash flood after an exceptional rainfall. Some examples of such recent events were particularly impressive: Flooding of the cities along the River Llobregat, in November 1982, Spain; the 1988 catastrophic inundation of Nîmes, France, following heavy rainfall, and the 2005 flooding of New-Orleans, USA, following the Katrina hurricane. Such events may result in more damages in small cities along torrents with a huge discharge variation because the city itself participates to the flow path, inducing sudden level rise and hazardous velocities, as was experienced at Vaison-la-Romaine, France, in September 1992 due to heavy rainfalls or in Longarone, downstream of the Vajont Dam, Italy, in October 1963 due to slope failure in the dam reservoir inducing a huge wave over the dam.

A characteristic of such floods is that the flow paths in urban districts are dictated by the layout of buildings and streets rather than by the river thalweg. This induces complex flow features, with water levels possibly higher than would have resulted without the presence of the city.

Results of past studies conducted by UCL in this field focus on the influence of an urban district on fast-transient flows, typically dam-break flows. Among other, they include experimental investigation of dam-break flow against an isolated obstacle (Soares-Frazão and Zech, 2007) and in an idealised urban district (Soares-Frazão and Zech, 2008). To simulate theses flows, different techniques were used and compared (Petaccia et al., submitted): resolution of the full two-dimensional shallow-water equations, use of an artificially increased roughness for the urban area, and use of a porosity concept (Guinot and Soares-Frazão, 2006).

8.2 Experimental data 8.2.1 Dam-break flow against an isolated obstacle

The experiments were carried out in the Civil Engineering Laboratory of the Université catholique de Louvain (UCL) in Belgium. The channel and building dimensions are indicated in Figure 8.1. The channel is about 36 m long, with a rectangular cross section except near the bed, where this section is cut to form a trapezoidal shape. A gate separates the upstream part of the channel, representing the reservoir, from the downstream part, representing the valley. The gate is located between two impermeable fixed blocks and the cross section between those abutments is rectangular and narrower than the channel cross-section. The channel bed is horizontal. From former experiments in this facility, a Manning friction coefficient was estimated as n = 0.010.

The initial conditions for the experiment consist in a water depth in the upstream reservoir h0 = 0.40 m and a thin layer of 0.02 m of water in the channel. To simulate the dam break, the gate separating the reservoir from the channel is pulled up rapidly, resulting in an instantaneous dam break.

Following the rapid opening of the gate, the strong dam-break wave reflects against the building, and the flow separates, forming a series of shock waves crossing each other. A wake zone can be identified just downstream from the building, surrounded by cross waves. After a fast transient phase, the flow features a slower evolution, following the progressive emptying of the reservoir. Also, re-circulation zones can be identified between the building and the walls.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 119 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 8.1 Channel and building dimensions (m)

This description of the flow is illustrated by means of Figure 8.2 to Figure 8.4. For sake of clarity, these are not immediately gained from experiments, but from computed results (Noël et al., 2003), which have been compared successfully to the measurements (Soares-Frazão et al., 2003), in such a way that they provide a good overview of the flow features. Figure 8.2 shows the free-surface elevation at t = 1 s, clearly featuring the two-dimensional spreading of the flood wave.

Figure 8.2 Computed image of the flow at time t = 1 s

At t = 3 s, the reflection of the wave against the building has occurred and results in the formation of an oblique hydraulic jump (Figure 8.3). The circular front wave also reflects against the side walls of the channel and lateral jumps are formed. Figure 5 shows the flow after 10 s: the hydraulic jump formed by the reflection against the building recedes in the upstream direction. The separation of the flow around the building and the wake zone can also be identified.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 120 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Figure 8.3 Computed image of the flow at time t = 3 s

Figure 8.4 Computed image of the flow at time t = 10 s

Available measurements for this test case consist in water level evolution at 6 measurement points and surface-velocity field measured by digital-imaging techniques. A detailed description of the data can be found in Soares-Frazão and Zech (2007).

8.2.2 Dam-break flow in an idealised urban district

The experiments were conducted at the Hydraulics Laboratory of the Civil and Environmental Engineering Department of the Université catholique de Louvain, Belgium. The test channel was 36 m long and 3.6 m wide, with a horizontal bed and a trapezoidal tailwater cross section (Figure 8.5). A gate was located between two impervious abutment blocks to simulate a breach. The initial reservoir water level was 0.40 m; the downstream reach was wetted with a thin layer of 0.011 m water. The reason for this initial wetting was the imperfect tightness of the gate and the impossibility to completely dry the channel bed before conducting an experiment. The Manning friction coefficient for the channel was assessed to 0.010 sm-1/3 by steady-flow experiments without the blocks and the gate. The expansion flow just downstream of the gate was two-dimensional from the narrow passage between the abutment blocks to the wider tailwater section.

The layout of the city in the experiments was idealised in the sense that it does not aim at being a scale model of an existing area. However, the ratio between building and street widths was chosen from aerial views of Brussels (Belgium), showing that 1/3 was a realistic value. Also, the buildings in the experiment had to be high enough in order not to be submerged by the flow.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 121 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

(a)

(b) Figure 8.5 Experimental set-up and channel dimensions in (m)(a) plane view, (b) cross section

Two different layouts of a simplified city were studied in the laboratory channel, namely a square city layout of 5 × 5 buildings (1) aligned with the approach flow direction, and (2) the street orientation turned by 22.5° relative to the approach flow direction. While the aligned case features a symmetric configuration, the skew case was chosen to illustrate a situation where the flow is no more symmetric around the urban district, but still keeping a preferential flow direction.

Observations of the flow in the aligned case indicated that the flow rises at the city front before entering the streets, after the wave impact that is similar to the impact against a single obstacle. A hydraulic jump forms at the impact section (Figure 8.6), with the water level locally higher than without the presence of the buildings. A wake zone developed immediately downstream of the city.

Figure 8.6 Hydraulic jump upstream of the urban district for case 1

Available measurements for this test case consist in water-level evolution at 64 measurement points and surface-velocity field measured by digital-imaging techniques. A detailed description of the data can be found in Soares-Frazão and Zech (2008).

Different unstructured computational grids were used to simulate the flow. Results are shown here for the 2T mesh (average of 2 triangular cells over the width of each street) and 10T mesh (average of 10 triangular cells over the width of each street). Figure 8.7 shows the water-surface profile computed at times t = 4, 5, 6 and 10 s in a street close to the channel axis (y = 0.20 m). The overall agreement between the numerical and experimental results is good. The coarse and the fine meshes give similar results at times t = 4 s (Figure 8.7.a) and t = 5 s (Figure 8.7.b). Later (Figure 8.7.c and d), significant

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 122 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 differences appear between the two numerical models. For example, the depression and the hydraulic jump at the entrance of the urban district (x = 5.20 m) is absent in the coarse mesh (2T) result.

(a) (b)

Figure 8.7 Water-surface profiles along the central longitudinal street located at y = 0.2 m: experimental (•) and numerical results computed using a coarse 2T (dotted line) and a fine 10T mesh (continuous line) for (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s

8.3 Porosity concept

In the approach initially proposed by Lhomme (2006) and Guinot and Soares-Frazão (2006), further developed and applied by Soares-Frazão et al. (2008), the hydraulic behavior of urban zones is accounted for via a porosity concept aimed at large-scale modeling of such urban areas. The porosity φ thus represents the average ratio of the land area not covered by buildings and thus available for water storage and water flow in case of inundation. The land area is parted in zones with various degrees of urbanization: for instance, one zone with high building density (with an averaged weak value of the porosity φ) another one considered as semi-urbanized (intermediate value of φ) and the residual zone assumed as not urbanized (φ = 1). This repartition just requires a rough description of the urban fabric without precise discrimination of the land use. Using the porosity concept, the governing equations in two dimensions of space can be written in conservation form as follows (Soares-Frazão et al. 2008)

∂ U ∂F ∂G + + = S [81] ∂t ∂ x ∂ y where the conserved vector variable U, the fluxes F and G and the source term S are defined as

⎡ φh ⎤ ⎡ φhu ⎤ ⎡ φhv ⎤ ⎡ 0 ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 2 2 U = ⎢φhu⎥ F = ⎢φ(hu + gh / 2)⎥ G = ⎢ φhuv ⎥ S = ⎢S p,x − Sl,x ⎥ [82] ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ φhv ⎢ φhuv ⎥ 2 2 ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣⎢φ(hv + gh / 2)⎦⎥ ⎣S p,y − Sl,y ⎦

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 123 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 where g is the gravitational acceleration, h is the water depth, u and v are the x- and y-velocity components, respectively, Sp,x and Sp,y are the source terms arising from the part of the pressure balance not accounted for in the flux terms F and G (i.e. bottom slopes and porosity variations) in the x- and y-directions, respectively, Sl,x and Sl,y are the source terms arising from head losses (friction and eddy losses) in the x- and y-directions, respectively. The logic of [82] is to consider that only a fraction of the total volume h dx dy is filled by water (storage porosity) and also that the momentum and pressure gradients only exert on a fraction of the total surface h dx or h dy (conveyance porosity). In the model proposed by Guinot and Soares-Frazão (2006), the two types of porosity were assumed to be equal to the same value φ.

The pressure balance consists of three parts. The first one is due to the change in water depth and is included in the flux terms F and G. The two other ones are expressed in the source terms Sp,x and Sp,y

∂z h2 ∂φ S = −φ gh b + g p,x ∂x 2 ∂x [83] ∂z h2 ∂φ S = −φ gh b + g p,y ∂y 2 ∂y where zb is the bottom level. The first term on the right–hand side of Equation [83] accounts for the horizontal component of the bottom reaction. The second term accounts for the change in cross- section width associated to the building and structure layout. This second term only exists at the limit between zones of distinct φ values.

The source terms Sl,x and Sl,y account for two types of head loss. The first, assumed to obey Manning’s law, is the classical head loss due to friction. The second expresses the eddy losses due to the multiple wave reflections and changes in the flow regime between the obstacles in the porous zone.

2 ⎡ n ζ x ⎤ 2 2 Sl,x = φ gh ⎢ 4/ 3 + ⎥ u u + v ⎣h 2g L⎦ [84] 2 ⎡ n ζ y ⎤ 2 2 Sl,x = φ gh ⎢ 4/ 3 + ⎥ v u + v ⎣h 2g L⎦ where n is Manning friction coefficient and ζx and ζy are head loss coefficient components that account for the urban singularities in the x- and y-directions respectively, L is the length of the considered domain, in such a way that the eddy losses are averaged on this length to form an equivalent energy slope.

Equations [81] and [82] are solved by a finite-volume scheme where the fluxes are calculated by an adapted HLL approach (Guinot and Soares-Frazão 2006).

8.4 Numerical simulations using detailed and simplified models

The flow experiment in an idealised urban district was simulated using a detailed meshing of each street, as illustrated before, and using two simplified approaches (Petaccia et al., submitted): (i) a higher friction and (ii) the porosity approach. In the porosity approach, a given porosity φ is assigned to any computational cell pertaining to the urban zone, without specifically discriminating streets or blocks, while φ = 1 for cells outside the urban fabric. In the same way, in the roughness approach, all the urban cells are affected by a fictitious higher roughness n, while the zones outside the city present a common value of the roughness coefficient. Both approaches are thus crude, in such a way that the meshing used for those approaches is a coarse one.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 124 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Results for the aligned case are illustrated in Figure 8.8. The water depth results inside a main street of both porosity and roughness models are compared to the reference 2D finite-volume model and to the experimental values.

The location of the hydraulic jump in front of the urban district is captured by all the methods, which was expected for the roughness method for which this location served in the calibration process. The magnitude of the jump is underestimated by the simplified approaches at t = 8 s, but seems correct at t = 10 s (Figure 8.9). Unsurprisingly, the jump in the first street at the entrance of the city is not reproduced by the simplified models. However the general water profile is satisfactory, mainly by the porosity model. That means that the distributed head losses, as well frictional as eddy losses, are representative of the hydraulic effect of the urban pattern. The wake effect at the exit of the city is well captured by the porosity approach although the water rise is too fast. In contrast, the roughness model delays the jump in the city wake. The main advantage of the porosity model compared to the roughness one relies on the ability of the porosity model to take into consideration a specific head loss at the entrance and at the exit of the city while the roughness model only adapts the average friction losses along the urban area.

Looking at the corresponding velocity profile (Figure 8.10 for t = 10 s) the simplified models do not reproduce the measured values. This is not unexpected, since the ‘velocity’ in both simplified model is only a fictitious one, assuming that the flow occupies the whole area without discerning the blocks and the streets.

0.25 h (m)

0.20

experiments 0.15 2D model n = 0.60 porosity 0.10

0.05

x (m) 0.00 0246810

Figure 8.8 Water level - Porosity and roughness models compared to 2D model and to experiments: aligned case, t = 8 s.

0.25

0.20 experiments 2D model n = 0.60 0.15 porosity

0.10

0.05

0.00 0246810

Figure 8.9 Water level - Porosity and roughness models compared to 2D model and to experiments: aligned case, t = 10 s.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 125 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

2.50 V (m/s) experiments 2.00 2D model n = 0.60 porosity 1.50

1.00

0.50

x (m) 0.00 0246810 Figure 8.10 Velocity - Porosity and roughness models compared to 2D model and to experiments: aligned case, t = 10 s.

8.5 Conclusions The applied methods (detailed mesh of streets, higher friction, porosity) to reproduce the flume data on urban flooding indicate the following: • the applied cell size should be about 1/10th of the width of the streets to obtain very accurate predictions of water levels and flow velocities; • when the cell size equals about half the street width hydraulic jumps or other complex features may not be reproduced accurately; • a friction approach (i.e. increasing the hydraulic roughness of areas occupied by buildings) can successfully be applied if one is interested in water levels only; computed velocities are seriously under estimated; • a disadvantage of the roughness approach is that the model needs to be calibrated and that unrealistic values need to be applied; • the porosity approach, in which the porosity is a measure of the open space in cities, results in slightly better water level estimates than the friction approach, but velocity estimates still are seriously underestimated.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 126 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

9. Synthesis / guidelines

9.1 Introduction The first decision to make when developing an inundation model regards the type of model to apply. Different types of models exist: one-, two- or three-dimensional (1D, 2D, 3D). For each model type, different software packages are available. The first part of this chapter deals with the question of what level of model complexity is required (1D, 2D, 3D). Software packages that can be used to develop inundation models with the required complexity are described.

After having decided on the model type and software package, the user needs to decide on the model schematisation (e.g. model resolution and schematisation of buildings and other features like bridges, etc.) and the processes to account for (wind set up, evaporation, etc.). These issues are dealt with in the second part of this chapter.

9.2 Model choice 9.2.1 Model complexity

3D models Three-dimensional models are especially appropriate for the representation of near channel processes where three dimensional processes are deemed important. 3D models are not commonly applied to simulate flood plain flow because the discretisation of the grid causes problems when water flow becomes very shallow (if the number of vertical cells is fixed, a very high horizontal grid resolution is required to cope with shallow water depths). For similar reasons they often cause problems when applied to floods characterized by significant changes in domain extent. Other reasons why 3D models are not commonly used for inundation modelling is that they may require very detailed boundary condition data (i.e. horizontal and vertical velocity and kinetic energy distributions at all inlets) and that computational costs are high as well.

2D models Two-dimensional models are most often applied to flows that have a large areal extent compared to their depth and where there are large lateral variations in the velocity field. They are thus well suited to the computation of overbank flood flows in compound channels, tides, tsunamis or even dam breaks. Moreover, two-dimensional schemes can also more easily represent moving boundary effects and may therefore be of more use for simulating problems where inundation extent changes dynamically through time.

2D models can use structured (e.g. square) or unstructured (e.g. triangular or irregular shaped) grids. Structured grids can be generated more easily. Moreover the results can easily be processed in GIS- packages. Unstructured grids are very suitable for areas with irregular topography and with obstacles with varying orientations so that the cell boundaries can follow the lining of the objects (e.g. houses along the streets in urban areas). Structured grids require relatively small cells to compensate for the jagged street boundaries.

1D models One-dimensional codes are more appropriate when the width of the floodplain is no larger than 3 times the width of the main river channel and is not separated from the channel by embankments. A shortcoming of 1D models for the simulation of flood plain flow is that flow in floodplains is assumed parallel to the main channel. They are unable to simulate lateral spreading of water. However mass and momentum exchanges can be accounted for in some recent models like the Exchange discharge model (EDM, Bousmar and Zech 1999) or the “Independent Subsection Method” (ISM, Proust 2005).

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 127 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Other situations that require special attention when modelled in 1D are: • River confluences, where water from one river can flow over the floodplain into the other river; • Flood plains that locally are characterised by storage of water rather than flow; • Rapidly varying cross section widths, this requires a large number of cross sections at short intervals; • Rivers with a multiple channel system where the connectivity between the different channels is complex.

1D models can also be applied in quasi-2D mode. Large areas are schematized as user-defined polygonal 1D storage cells that are linked through 1D channels. Quasi 2D models have successfully been applied to river environments where the flow direction is known. However, in areas where the flow pattern is more complex or where spreading of water over relatively flat areas is important, quasi- 2D models may produce less accurate results. Moreover, schematizing the floodplain using polygonal storage cell requires substantial operator skill and does not allow for emergent behaviour as the only floodplain flow paths that can operate have been explicitly specified by the user.

Spatial variations in water depths can also be obtained by extrapolating computed water levels of 1D models to a large area and intersecting this water level plane with a digital elevation model (DEM). This method, however, can produce unrealistic results if (1) flood plain flow or storage is not accounted for by the 1D model, (2) no check is made on the required connection between the flooded cell and the water body that causes the flooding, and (3) flooded cells in sloping terrains are connected with the main water body via cells that are located downstream of the flooded cell (here, flooding via downstream cells can only be caused by backwater effects).

1D models are often selected because they seem less complex than 2D models. However, the above remarks show that in areas with irregular topographies and complex or varying flow patterns, application of a 1D model is much more difficult than application of a 2D model.

Coupled 1D/2D models Coupled 1D/2D models become more popular as they have the advantage of combining computational efficient 1D models that are suitable for the simulation of flow in channels with 2D models that are more appropriate for the simulation of flood plain flows. By modelling relatively small and complex channels in 1D, the computational 2D grid for the simulation of flood plain flow can be coarser then with ordinary 2D models. Coupled models also enable the user to simulate flow through tunnels, viaducts and other structures in a simple manner.

The model choice thus depends on the scale of the problem and the characteristics of the flow (e.g. wide and shallow, or relatively narrow and deep; flood extent varying with time or rather constant boundaries). However, the available data also plays an important role. For instance, it is of no use to apply a 3D or 2D model when the only available topographical data consists of cross sections taken at irregular or large intervals.

Model complexity, calibration and the ability of available validation data to discriminate conclusively between model types For any given situation there are therefore a variety of modelling tools that could be applied to compute floodplain inundation and a variety of space and time resolutions at which these codes could be applied. All codes make simplifying assumptions and only consider a reduced set of the processes known to occur during a flood event. Hence, all models are subject to a degree of structural error that is typically compensated for by calibration of the friction parameters. Calibrated parameter values are not, therefore, physically realistic, as in estimating them we also make allowance for a number of distinctly non-physical effects such as model structural error and any energy losses or flow processes which occur at sub-grid scales. Calibrated model parameters are therefore area-effective, scale dependent values which are not drawn from the same underlying statistical distribution as the equivalent at-a-point parameter of the same name. Thus, whilst we may denote the resistance coefficient in a wide variety of hydraulic models as “Manning’s n”, in reality the precise meaning of

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 128 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 this resistance term changes as we change the model physical basis, grid resolution and time step. For example, a one-dimensional code will not include frictional losses due to channel meandering in the same way as a two-dimensional code. In the one-dimensional code these frictional losses need to be incorporated into the hydraulic resistance term. Similarly, a high-resolution discretization will explicitly represent a greater proportion of the form drag component than a low-resolution discretization using the same model. Little guidance exists on the magnitude of such effects and some of the differences so generated may be subtle. However complex questions of scaling and dimensionality do arise which may be difficult to disentangle. In general, as the dimensionality increases and grid scale is reduced we require the resistance term to compensate for fewer unrepresented processes and: (i) the model sensitivity to parameter variation reduces; and (ii) the calibrated value of the resistance term should converge towards the appropriate skin friction value.

With calibration it is also likely that many different types of model may fit available calibration data equally well (yet give different results in prediction). In this case it becomes difficult to conclusively discriminate between model types and determine precisely the correct model type for a particular application. As a consequence the above choices have, in reality, a degree of ambiguity, and a case can often be made for the application of quite widely differing models to solve a particular problem.

9.2.2 Some available software packages

Only a limited number of software packages were used in this study: • 2D models were developed in LISFLOOD-FP, SOBEK-2D and SV2D; • quasi 2D models were developed using SOBEK-1D and the rapid flooding model; • 1D models were constructed with SOBEK-1D, SV1D, SANA and ORSA1D-Roe.

The following limitations are observed for the different packages:

• SOBEK-2D and SV2D, although based on distinct numerical schemes, give similar results for the Scheldt pilot area when run under similar conditions, i.e. on the same computational grid, with the same friction formula and same inflow hydrographs. • The assumption regarding breaching appears to be the key point in this case study, where the inundation is the consequence of a cascade of dike breaches. The most important parameters are the time of breach initiation (with respect to the peak time of the storm surge) and the breach growth rate. In the present study where the inundation comes from sea water subject to rather rapid level fluctuations, differences in breach growth rates have a major impact on modelling results. • In case of the Scheldt pilot, the quasi 2D model produces different results than the fully 2D model, because the quasi 2D model misses detail on for instance the spreading of the water. The results therefore indicate that quasi 2D models can only successfully be applied if the flow pattern is known in advance, so that the model schematisation can be adjusted to it. This implies that quasi 2D models can relatively successfully be applied to river systems where the flow directions are known in advance. Application to relatively flat areas, where flow patterns may differ depending on the breach location, or where flow patterns depend on the water depth and are not very obvious, is likely to result in very inaccurate results. • The LISFLOOD-FP model was able to match reasonably well the results of the more complex SOBEK code for areas of the Greenwich model where local inertial effects do not have an impact (as the LISFLOOD-FP formulation does not include these terms). Similar to Hunter et al. (2008) we found that local inertial effects generally do not have a marked effect on flood propagation speeds and flood extent prediction, but can have an impact on flood depths locally. • As previously noted, for fine resolution grids the computational efficiency advantage of the LISFLOOD-FP type models over full shallow water solvers reverses and research is currently underway at the University of Bristol to address this problem.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 129 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Table 9.1 gives an overview of the type of hydraulic models that can be used depending on the characteristics of the area and on the available data

Table 9.1 Overview of hydraulic model types and their application Area characteristics examples data applicable models Wide, relatively flat areas low land rivers with wide detailed data available (laser 2D models with structured with natural or agricultural floodplains, river delta’s, altimetry terrain data, or unstructured grids. land use estuaries with large flood channel bathymetry infor- Storage-cell approach also plains mation, land use data, usable if limited discharge accurate boundary condi- through the floodplains tions. Data for model (mainly storage) validation) detailed topographical data 1D model with approximate missing storage cells Steep sloping rivers with detailed data available 2D models coping with large floodplains transcritical flows detailed topographical data 1D models coping with missing, cross sections transcritical flows and available preferably shock-capturing Steep sloping rivers with 1D or 2D models coping narrow floodplains with transcritical flows If available, 1D model with mass and momentum exchanges between subsections Urban areas cities along rivers, estuaries detailed data available (laser 2D models, with full shallow or coasts altimetry terrain data, digital water models where local map data, accurate boundary inertial effects are important. conditions. Data for model 2D storage cell models validation) currently give reasonable results but at high computational cost.

9.3 Model application

Grid and time step resolution In developing a model for a particular site, choices also need to be made about the discretization of space and time. These will clearly depend on the resolution of available terrain data, the length scales of terrain features in the domain and the length and time scales of relevant flow processes. With the development over the last decade of high resolution mapping technologies such as airborne scanning laser altimetry, terrain data are usually available at scales much finer than it is computationally possible to model over wide areas. However, deciding which terrain and flow length scales need to be incorporated in a model is a much more subjective choice. Clearly, as spatial resolution is increased particular terrain and flow features will no longer be adequately represented, and the impact of these sub-grid scale effects on the model predictions will need to be parameterized

Grid resolutions in rural areas with a gentle/regular/… topography can be coarser than grids developed for areas with a more complex topography or urban areas. The minimum grid resolution that is required for flood simulations in urban areas depends on the characteristics of the city (e.g. size of the streets) and on the required information.

In general, less resolution is required if only water level is to be predicted, finer resolution if the velocity field is also required for flood characterisation.

In particular, in urban areas, if the user is interested in water depths only, the minimum grid cell size should equal half to once the width of the streets (e.g. 5 to 10 m in most European cities). In rural

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 130 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420 areas where villages make up a small part of the total model area, larger cells can be used. Water depths in urban areas can also be computed quite accurately by increasing the hydraulic roughness or by adopting a porosity approach.

When information on flow velocities is required, the grid cell size should always be smaller than the width of the streets. This requirement applies to vast urban areas as well as for small rural villages. Increasing the hydraulic roughness or application of the porosity approach does not result in accurate velocity estimates.

Breach initiation and growth The timing of breach initiation and the breach growth rate determine to a large extent the volume of water that flows into an area. This implies that breach initiation and growth have a very large effect on computed water depths and flood extent. Unfortunately, breach initiation and growth are difficult to forecast and simulate, due to the complex mechanisms involved and to the stochastic character of breaching initiation. The advice therefore is to always carry out a sensitivity analysis to determine the uncertainties in the model results related to uncertainties in breach initiation (timing) and growth rate. The latest science on breach growth is reported in the final report of Task 6 (Report T06-08-02).

Wind effect In open areas, such as flood plains used as grass land or polders used for agricultural purposes, water depths can significantly be affected by wind. In open areas with fetch lengths of about 5 km, wind set- up during storms can be in the order of 0.5 m.

Wind has less effect in large urban areas. The pilot site along the Thames estuary indicated changes in water depth in the order of 5 cm or less.

Other meteorological factors Other meteorological factors, such as evaporation, have no significant effect on flooding simulations for the Scheldt, because the probability for flooding is highest during the winter season, when evaporation values are very low. However, in other areas evaporation can be an important process as well. This often is the case in extensive wetlands, where flooding occurs during the summer season, or that are located in a warmer climate. An example of such an area is the Doñana wetland in Spain. Here flooding occurs during the winter season. During the summer period, the wetland dries up, partly because water drains to an adjacent river, but for the main part because of high evaporation rates. The inundation model developed for this area had to include evaporation.

Hydraulic roughness Hydraulic models require information on the hydraulic roughness, which is related to the type of land use. In the case of spatially varying hydraulic roughness values, the roughness may affect the flow pattern as the flow chooses that pathway with the steepest slope, but also with the minimal resistance. The hydraulic roughness also has an effect on the celerity of the flood wave and the computed water depths and flow velocities. Results from the pilot areas, however, show that the impact of uncertainties in the hydraulic roughness is much less than uncertainties in breach initiation and growth, wind or errors in the DEM. However, it should be noted that we have here only examined a limited number of sites and other studies have drawn subtle different conclusions. For example, Hunter at al. (2008) have shown for 2D modelling of urban areas that if a LiDAR-based DEM is available then hydraulic roughness has a much greater impact on the model than DEM errors. This is also likely to be true of the Greenwich application although there was not time within FLOODsite to address this specific issue at this test site.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 131 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

9.4 Recommendations

Breaching The assumption regarding breaching appears to be the key point in the study of the Scheldt pilot site, where the inundation is the consequence of a cascade of dike breaches. The most important parameters are the time of breach initiation (with respect to the peak time of the storm surge) and the breach growth rate. This implies that uncertainties in time of breach initiation and breach growth rates induce a high level of uncertainty in evaluating the time available for evacuation and rescue. Therefore, accurate breach growth models are required to simulate floods in tidal areas. A subject of further research would be to implement the breach growth models developed under FLOODsite Task 6 in the inundation models and use those for further sensitivity analysis.

More thorough benchmark For a more thorough benchmark on inundation models, additional work should be undertaken on collecting better model validation data. The benchmark carried out in this study consists of a comparison of model results. As no accurate validation data are available, it is impossible to tell which model produces the most accurate results.

It could also be considered to use flume experiments for benchmark purposes, as this is the only way to eliminate uncertainties in for instance boundary conditions that may seriously affect the model results. For instance, a large data set exists for a flood along the River Eden in the UK, including the urban area of Carlisle. Aerial photographs of flood extent exist as well. However, as with all large floods there are questions over the accuracy of the discharge time series recorded at gauging stations during the event. An underestimation of the river discharge will result in an underestimation of the flood extent by the inundation models. This means that if the flood extent is used as a criterion to evaluate the models, the most accurate model will probably not be evaluated as such. Flume experiments have the advantage that the relevant data can be measured with a much higher accuracy.

A further way to overcome the problems of currently available field data sets would be to undertake a dedicated field monitoring programme during a future flood event using a combination of remote sensing and ground survey teams. This is logistically difficult, but ultimately may be the only way to address fundamental uncertainties concerning the fluid dynamics of real-world urban inundation

In the future we would like to carry out a benchmark together with the other research groups, such as the Flood Risk Management Research Consortium in the UK. This would enable a comparison of a much larger number of software packages.

Solid transport Another important issue, not accounted for in most of the models is the solid transport associated to the flood flow. In some case, this transport may constitute a worse hazard than the water wave itself. In turn the solid transport may affect seriously the topography and worsen the flood in terms of water depth and local velocities. There exist some successful attempts to model this kind of phenomenon in simple situations like straight channels. Applicability to real-life situation requires heavy efforts of research.

Boundary conditions From the additional sensitivity analysis reported in the final report of Task 8, it was concluded that uncertainties in boundary conditions can significantly affect the flood extent and water depths. In the Scheldt case, uncertainties in maximum water levels were in the order of 10 cm. However, differences in ebb water levels were much larger and appeared especially important in explaining the differences in simulated flood characteristics. This highlights the need for increased knowledge on water level time series over a longer period of time, instead of focussing on peak storm surge water levels only.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 132 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Other research questions Other particular questions are still not completely solved and thus worth of further research efforts and developments: • For one-dimensional approach: • more accurate estimation of interaction between main channel and floodplains • improved representation of distributed in- or outflow along rivers • improved modelling of bifurcations and confluences • optimal techniques for cross-section interpolation where required by the complexity of the river geometry • For two-dimensional approach: • better definition of boundary conditions • development of porosity concepts for simplified urban areas representation • adapted turbulence models for shear stresses characterisation between cells • dealing with the computational limitations of storage cell models on fine grids • For three-dimensional approach: • improvement of methods to determine water surface even in case of rapid variation in time and/or space

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 133 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 134 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

10. References

Abbott, M.B. 1979. Computational Hydraulics. Pitman, London. Abbott, M. and Ionescu, F. 1967. On the numerical computation of nearly horizontal flows. Journal of Hydraulic Research, 5 (2), 97-117. Ackers, P. 1993. Stage-discharge functions for 2-stage channels – the impact of new research. Journal of the Institution of Water and Environmental Management, 7 (1), 52-61. Alcrudo, F. and Mulet-Marti, J. 2005. Urban inundation models based upon the Shallow Water equations. Numerical and practical issues. In F. Benkhaldoun, D. Ouazar & S. Raghay (eds), Proceedings of Finite Volumes for Complex Applications IV. Problems and Perspectives. Hermes Science. pp 1-12. Alcrudo, F. & Garcia-Navarro, P. 1993. A High-Resolution Godunov-Type Scheme in Finite Volumes for the 2D Shallow-Water Equations. Int. J. Numer. Methods in Fluids, 16, 489-505. Ali, S. and Goodwin, P. 2002. The predictive ability of 1D models to simulate floodplain processes. In Falconer, R.A., B. Lin, E.L. Harris and C.A.M.E. Wilson, (eds), Hydroinformatics 2002: Proceedings of the Fifth International Conference on Hydroinformatics. Volume One: Model development and data management, IWA Publishing, London, 247-252. Aronica, G., Bates, P.D. and Horritt, M.S. 2002. Assessing the uncertainty in distributed model predictions using observed binary pattern information within GLUE. Hydrological Processes, 16, 2001-2016. Aronica, G., Hankin, B.G. and Beven, K.J., 1998. Uncertainty and equifinality in calibrating distributed roughness coefficients in a flood propagation model with limited data. Advances in Water Resources, 22 (4), 349-365. Ashworth, P.J., Bennett, S.J., Best, J.L. and McLelland, S.J. 1996. Coherent flow structures in open channels. John Wiley and Sons, Chichester, UK, 733pp. Asselman, N., Coen, L., Diermanse, F., Groeneweg, J., Jeuken, C., Peeters, P., Pereira, F., Sperna Weiland, F., Vanlede, J., Viaene, P. 2007. Koploperproject LTV-O&M-Thema Veiligheid - deelproject 2: Sterkte-zwakte analyse van de methoden waarmee de maatgevendecondities en de fysische gevolgen van overstromingen langs het Schelde estuarium worden bepaald in Nederland en in Vlaanderen. Report WL|Delft Hydraulics Z4384. Aureli, F., Mignosa, P. and Tomirotti, M., 1999. Numerical simulation and experimental verification of dam-break flows with shocks. J. Hydraul. Res., 38(3), pp. 197–206. Baltsavias, E.P. 1999. A comparison between photogrammetry and laser scanning. ISPRS Journal of Photogrammetry and Remote Sensing, 54 (2-3), 83-94. Bates, P.D. and Anderson, M.G., 2000. Validation of hydraulic models. In M.G. Anderson and P.D. Bates (eds), Model Validation, Perspectives in Hydrological Science, John Wiley & Sons, Chichester, UK, 325-356, Bates, P.D. and De Roo, A.P.J. 2000. A simple raster-based model for floodplain inundation. Journal of Hydrology, 236, 54-77. Bates, P.D. and Hervouet, J.-M. 1999. A new method for moving boundary hydrodynamic problems in shallow water. Proceedings of the Royal Society of London, Series A, 455, 3107-3128. Bates, P.D. and Horritt, M.S. (this volume). Modelling wetting and drying processes in hydraulic models. In Bates, P.D., Lane, S.N. and Ferguson, R.I. (eds), Computational Fluid Dynamics: applications in environmental hydraulics, John Wiley and Sons, Chichester, UK. Bates, P.D., Horritt, M.S, Aronica, G. and Beven, K.J., (in press). Bayesian updating of flood inundation likelihoods conditioned on flood extent data, Hydrological Processes. Bates, P.D., Horritt, M.S., Smith, C. and Mason, D., 1997. Integrating remote sensing observations of flood hydrology and hydraulic modelling. Hydrological Processes, 11, 1777-1795. Bates, P.D., Marks, K.J. and Horritt, M.S. 2003. Optimal use of high-resolution topographic data in flood inundation models. Hydrological Processes, 17, 5237-557. Bates, P.D., Stewart, M.D., Desitter, A., Anderson, M.G., Renaud J.-P. and Smith, J.A. 2000. Numerical simulation of floodplain hydrology. Water Resources Research, 36, 2517-2530. Bates, P.D., Stewart, M.D., Siggers, G.B., Smith, C.N., Hervouet, J.-M. and Sellin, R.H.J. 1998. Internal and external validation of a two-dimensional finite element model for river flood simulation. Proceedings of the Institution of Civil Engineers, Water Maritime and Energy, 130, 127-141.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 135 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Bechteler, W., Hartmaan, S. and Otto, A.J. 1994. Coupling of 2D and 1D models and integration into Geographic Information Systems (GIS). In: White W.R. and Watts J. (eds.), Proceedings of the 2nd International Conference on River Flood Hydraulics, John Wiley and Sons, Chichester; UK, 155-165. Benkhaldoun, F. and Monthe, L. 1994. An adaptive nine-point finite volume Roe scheme for two-dimensional Saint Venant equations. In P. Molinaro and L. Natale (eds), Modelling flood propagation over initially dry areas, American Society of Civil Engineers New York, 30-44. Beven, K.J and Binley, A., 1992. The future of distributed models: model calibration and uncertainty prediction. Hydrological Processes, 6, 279-298. Beven, K.J., 1989. Changing ideas in hydrology - The case of physically-based models. Journal of Hydrology, 105, 157-172. Beven, K.J., 1996. A discussion in distributed modelling. In J.-C. Refsgaard and M.B. Abbott (eds), Distributed Hydrological Modelling, 289-295, Kluwer Academic Publishers, The Netherlands. Beven, K.J., 2001. Rainfall-Runoff Modelling: The Primer, John Wiley & Sons, Chichester, UK, 372 pp. Bladé, E., Gómez, M. and Dolz, J. 1994. Quasi-two dimensional modelling of flood routing in rivers and flood plains by means of storage cells. In P. Molinaro and L. Natale (eds), Modelling of flood propagation over initially dry areas, American Society of Civil Engineers, New York, 156-170. Bousmar D., Zech Y. 1999. Momentum transfer for practical flow computation in compound channels. Journal of Hydraulic Engineering, ASCE, 1999, 125 (7), 696-706. Bridge, J.S. and Gabel, S.L. 1992. Flow and sediment dynamics in a low sinuosity, braided river – Calamus River, Nebraska sandhills. Sedimentology, 39 (1), 125-142. Brufau, P., Garcia-Navarro, P., Ghilardi, P., Natale, L. and Savi, F., 2000. 1D Mathematical Modeling of Debris Flow. J. Hydraul. Res./De Recherches Hydrauliques, 38(6), pp. 435–446. Burt, T.P., Bates, P.D., Stewart, M.D., Claxton, A.J., Anderson, M.G. and Price, D.A. 2002. Water table fluctuations within the floodplain of the River Severn, England. Journal of Hydrology, 262, 1-20. Butler, J.B., Lane, S.N. and Chandler, J.H. 2001. Automated extraction of grain-size data from gravel surfaces using digital image processing. Journal of. Hydraulic Research, 39 (5), 519-529. Capart; H., Eldho, T.I., Huang; S.Y., Young; D.L. and Zech, Y. 2003. Treatment of Natural Geometry in Finite Volume River Flow Computations. Journal of Hydraulic Engineering, 129(5), pp. 385-393 Castro N.M. and Hornberger G.M. 1991. Surface-subsurface water interactions in an alluviated mountain stream channel. Water Resources Research, 27, 1613-1621. Charlton, M.E., Large, A.R.G. and Fuller, I.C. 2003. Application of airborne LiDAR in river environments: The River Coquet, Northumberland, UK. Earth Surface Processes and Landforms, 28 (3), 299-306. Cobby, D.M., Mason, D., Horritt, M.S. and Bates, P.D., (2003). Two-dimensional hydraulic flood modelling using a finite element mesh decomposed according to vegetation and topographic features derived from airborne scanning laser altimetry. Hydrological Processes, 17, 1979-2000. Cobby, D.M., Mason, D.C. and Davenport, I.J. 2001. Image processing of airborne scanning laser altimetry for improved river flood modelling. ISPRS Journal of Photogrammetry and Remote Sensing. 56(2), 121–138. Cobby, D.M., Mason, D.C., Davenport, I.J. and Horritt, M.S. 2000. Obtaining accurate maps of topography and vegetation to improve 2D hydraulic flood models. Proceedings of the EOS/SPIE Symposium on Remote Sensing for Agriculture, Ecosystems, and Hydrology II, Barcelona, 25-9 Sept., 125-136. Coe, M.T., Costa, M.H., Botta, A. and Birkett, C. 2002. Long-term simulations of discharge and floods in the Amazon Basin. Journal of Geophysical Research – Atmospheres, 107 (D20), art. no. 8044. Cunge, J.A., 2003. Of data and models. Journal of Hydroinformatics, 5(2), 75-98. Cunge, J.A., Holly, F.M. Jr. and Verwey, A. 1980. Practical aspects of computational river hydraulics, Pitman, London, 420pp. Dawson, R.J., Hall, J.W., Sayers, P., Bates, P.D. and Rosu, C. 2005. Sampling-based flood risk analysis for fluvial dike systems. Stochastic Environmental Research and Risk Assessment, 19, 388-402. De Roo, A., Odijk, M., Schmuck, G., Koster, E. and Lucieer, A. 2001. Assessing the effects of land use changes on floods in the Meuse and Oder catchment. Physics and Chemistry of the Earth Part B – Hydrology, Oceans and Atmospheres, 26 (7-8), 593-599.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 136 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

De Roo, A.P.J, Bartholmes, J., Bates, P.D., Beven, K., Bongioannini-Cerlini, B., Gouweleeuw, B., Heise, E., Hils, M., Hollingsworth, M., Holst, B., Horritt, M., Hunter, N., Kwadijk, J., Pappenburger, F., Reggiani, P., Rivin, G., Sattler, K., Sprokkereef, E., Thielen, J., Todini, E. and Van Dijk, M. 2003. Development of a European Flood Forecasting System. International Journal of River Basin Management, 1 (1), 49-59. De Saint-Venant, B. 1871. Theorie du mouvement non permanent des eaux. Comptes rendus des séances de l'Académie des Sciences, 73 (3), 147-154. Defina, A. 2000. Two-dimensional shallow flow equations for partially dry areas. Water Resources Research, 36 (11), 3251-3264. Defina, A., D’Alpaos, L. and Matticchio, B. 1994. A new set of equations for very shallow water and partially dry areas suitable to 2D numerical models. In P. Molinaro and L. Natale (eds), Modelling flood propagation over initially dry areas, New York: American Society of Civil Engineers, 72-81. Dhondia, J.F. and Stelling, G.S. 2002. Application of one-dimensional-two-dimensional integrated hydraulic model for flood simulation and damage assessment. In Falconer, R.A., B. Lin, E.L. Harris and C.A.M.E. Wilson, (eds), Hydroinformatics 2002: Proceedings of the Fifth International Conference on Hydroinformatics. Volume One: Model development and data management, IWA Publishing, London, 265-276. Dietrich, C.R., 2000. On simulation, calibration and ill-conditioning with application to environmental system modelling, in M.G. Anderson and P.D. Bates (eds), Model Validation, Perspectives in Hydrological Science, John Wiley & Sons, Chichester, UK, 77-116 Duinmeijer, S.P.A. 2002. Verification of Delft FLS. Technical Report, Delft University of Technology. Ervine, D.A. and Baird, J.I. 1982. Rating curves for rivers with overbank flow. Proceedings of the Institution of Civil Engineers Part 2 – Research and Theory. 73, 465-472. Estrela T and Quintas L. 1994. Use of GIS in the modelling of flows on floodplains. In White HR and Watts J (eds), Proceedings of the 2nd International conference on river flood hydraulics, John Wiley and Sons, Chichester; UK, 177- 189. Feldhaus, R., Höttges, J., Brockhaus, T. and Rouvé, G. 1992. Finite element simulation of flow and pollution transport applied to a part of the River Rhine. In: Falconer, R.A,. Shiono, K. and Matthews, R.G.S (Eds.), Hydraulic and environmental Modelling; Estuarine and River Waters, Ashgate Publishing, Aldershot, 323-344. Feng, Y.T. and Perić, D. 2003. A spatially adaptive linear space-time finite element solution procedure for incompressible flows with moving domains. International Journal of Numerical Methods in Fluids, 43, 1099-1106. Fraccarollo, L., Capart, H. and Zech, Y.A., 2003. Godunov method for the computation of erosional shallow water transients. International Journal for Numerical Methods in Fluids, 41(9): pp. 951-976 French, J.R. 2003. Airborne LiDAR in support of geomorphological and hydraulic modelling. Earth Surface Processes and Landforms, 28 (3), 321-335. Fukuoka, S. and Fujita, K., 1989. Prediction of flow resistance in compound channels and its application to the design of river courses. Proceedings of the Japan Society of Civil Engineers. Garcia-Navarro, P., Fras, A. and Villanueva, I., 1999. Dam-break flow simulation: some results for one-dimensional models of real cases. Journal of Hydrology, 216 (3-4), pp. 227-247 Gee, D.M., Anderson, M.G. and Baird, L. 1990. Large scale floodplain modelling. Earth Surface Processes and Landforms, 15, 512-523. Gerritsen, H. 2005. What happened in 1953? The Big Flood in the Netherlands in retrospect. Phil. Trans. R. Soc. A, 363, 1271-1291. Ghisalberti, M. and Nepf, H.M. 2002. Mixing layers and coherent structures in vegetated aquatic flows. Journal of Geophysical Research – Oceans, 107 (C2), art. no. 3011. Gill, A.E. (1982). Atmosphere–Ocean Dynamics. Academic Press. Gomes-Pereira LM and Wicherson R.J. 1999. Suitability of laser data for deriving geographical data: a case study in the context of management of fluvial zones. Photogrammetry and Remote Sensing, 54: 105-114. Gouldby, B., P. Sayers, O. Tarrant, and D. Kavanagh 2007. Thames Estuary 2100: Performance based asset management. Technical Report IA8/10, HRWallingford. Gouldby, B, Sayers P, Mulet-Marti J, Hassan M and Benwell D 2008. A methodology for regional-scale flood risk assessment. Proceedings of the Institution of Civil Engineers, Water Management, 161(3), 169–182.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 137 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Grayson, R. and Blöschl, G. 2001. Spatial patterns in catchment hydrology: observations and modelling. Cambridge University Press, Cambridge, UK, 416pp. Grayson, R.B., Moore, I.D. and McMahon, T.A., 1992. Physically-based hydrologic modelling: II. Is the concept realistic? Water Resources Research, 28 (10), 2659-2666. Guinot V., Soares-Frazão S. 2006. Flux and source term discretisation in two-dimensional shallow water models with porosity on unstructured grids. International Journal for Numerical Methods in Fluids, 50 (3): 309-345. Gutierrez Andres, J., Lhomme, J., Weisgerber, A., Cooper, A., Gouldby, B., Mulet-Marti, J. (2008). Testing and application of a practical new 2D hydrodynamic model. In Samuels P., Huntington S., Allsop W. and Harrop J. (eds), Proceedings of the FloodRisk 2008 Conference, Taylor and Francis Group, London. Hall, J.W., R. J. Dawson, P. B. Sayers, C. Rosu, J. B. Chatterton, and R. Deakin 2003. A methodology for national scale flood risk assessment. Proceedings of the Institution of Civil Engineers-Water and Maritime Engineering, 156(3), 235-247. Hankin, B.G., Hardy, R., Kettle, H. and Beven, K.J., 2001. Using CFD in a GLUE framework to model the flow and dispersion characteristics of a natural fluvial dead zone. Earth Surface Processes and Landforms 26 (6), 667-687. Haycock N.E and Burt T.P. 1993. Role of floodplain sediments in reducing the nitrate concentration of subsurface runoff: A case study in the Cotswolds, UK. Hydrological Processes, 7, 287-295. Hervouet, J.-M. and Van Haren, L. 1996. Recent advances in numerical methods for fluid flows. In Anderson, M.G., Walling, D.E. and Bates, P.D. (Eds), Floodplain processes. John Wiley and Sons, Chichester, 183-214. Hey, R. D. 1979. Flow Resistance in Gravel Bed Rivers. American Society of Civil Engineers, Journal of Hydraulics Division, 105(4), 365-379. Hodgson, M.E., Jensen, J.R., Schmidt, L., Schill, S. and Davis, B. 2003. An evaluation of LIDAR- and IFSAR-derived digital elevation models in leaf-on conditions with USGS Level 1 and Level 2 DEMs. Remote Sensing of the Environment, 84 (2), 295-308. Horritt, M.S. and Bates, P.D. 2001a. Predicting floodplain inundation: raster-based modelling versus the finite element approach. Hydrological Processes, 15, 825-842. Horritt, M.S. and Bates, P.D. 2001b. Effects of spatial resolution on a raster based model of flood flow. Journal of Hydrology, 253, 239-249. Horritt, M.S. and Bates, P.D. 2002. Evaluation of 1-D and 2-D numerical models for predicting river flood inundation. Journal of Hydrology, 268, 87-99. Horritt, M.S., 1999. A statistical active contour model for SAR image segmentation. Image and Vision Computing, 17, 213-224. Horritt, M.S. 2000. Calibration of a two-dimensional finite element flood flow model using satellite radar imagery. Water Resources Research, 36 (11), 3279-3291. HR Wallingford 2006, Rapid Flood Spreading Methodology (RFSM), Environment Agency, Thames Estuary 2100 Report, DT4. Hunter, N.M., Bates, P.D., Horritt, M.S., De Roo, A.P.J. and Werner, M.G.F. 2005a. Utility of different data types for calibrating flood inundation models within a GLUE framework. Hydrology and Earth Systems Sciences, 9 (4), 412- 430. Hunter, N.M., Horritt, M.S., Bates, P.D., Wilson, M.D. and Werner, M.G.F. 2005b. An adaptive time step solution for raster-based storage cell modelling of floodplain inundation. Advances in Water Resources, 28 (9), 975-991. Ip, J.T.C., Lynch, D.R. and Friedrichs, C.T. 1998. Simulation of estuarine flooding and dewatering with application to Great Bay, New Hampshire. Estuarine Coastal and Shelf Science, 47 (2), 119-141. Kawahara, M. and Umetsu, T. 1986. Finite element method for moving boundary problems in river flows. International Journal of Numerical Methods in Fluids, 6, 365-386. Klemeš, V., 1986. Operational testing of hydrologic simulation models. Hydrological Sciences Journal, 31, 13-24. Knight D.W. and Shiono K. 1996. River channel and floodplain hydraulics. In : Floodplain Processes, Anderson M.G., Walling D.E. and Bates P.D. (eds.), John Wiley and Sons, Chichester, 139-182. Knight, D.W. and Hamed, M.E. 1984. Boundary shear in symmetrical compound channels. American Society of Civil Engineers, Journal of Hydraulic Engineering, 110(10), 1412-1430.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 138 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Kohane, R. and Welz, R. 1994. Combined use of FE models for prevention of ecological deterioration of areas next to a river hydropower complex. In Peter, A. Wittum, G., Meissner, U., Brebbia, C.A., Gray, W.G and Pinder, G.F., (eds), Computational methods in water resources X, Kluwer, The Netherlands, Volume 1, 59-66. Kouwen, N. 1988. Field estimation of the biomechanical properties of grass. Journal of. Hydraulic Research, 26(5), 559-568. Kouwen, N. 2000. Closure of ‘Effect of Riparian Vegetation on Flow Resistance and Flood Potential.’ American Society of Civil Engineers, Journal of Hydraulic Engineering, 126(12), 954. Kouwen, N. and Li, R.M. 1980, Biomechanics of vegetative channel linings. American Society of Civil Engineers, Journal of Hydraulics Division, 106(6), 713-728. Krabill, W.B., Collins, J.G., Link, L.E., Swift, R.N and Butler, M.L. 1984. Airborne laser topographic mapping results. Photogrammetric Engineering and Remote Sensing, 50, 685-694. Lane, S.N. 2000. The measurement of river channel morphology using digital photogrammetry. Photogrammetric Record, 16 (96), 937-957. Lane, S.N., Bradbrook, K.F., Richards, K.S., Biron, P.M. and Roy, A.G., 1999. The application of computational fluid dynamics to natural river channels: three-dimensional versus two-dimensional approaches, Geomorphology 29, 1-20. Leclerc, M., Bellemare, J.-F., Dumas, G. and Dhatt, G. 1990. A finite element model of estuarine and river flows with moving boundaries. Advances in Water Resources, 13, 158-168. LeVeque, R.J. (2002) Finite Volume Methods for Hyperbolic Problems. Cambridge University Press. Liang, Q., Borthwick, A. G. L. and Stelling, G. 2004. Simulation of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids. International journal for numerical methods in fluids 46, 127–162 Liang, D., Falconer, R.A., Lin, B. 2007. Linking one- and two-dimensional models for free surface flows. Proceedings of the Institution of Civil Engineers - Water Management, 160(3), pp 145-151. Lhomme, J. 2006. Modélisation des inondations en milieu urbain: approches unidimensionnelle, bidimensionnelle et macroscopique. PhD thesis (in French), Université Montpellier 2, France. Lhomme, J., Sayers, P., Gouldby, B., Samuels, P., Wills, M., Mulet-Marti, J. 2008. Recent development and application of a rapid flood spreading method. In Samuels P., Huntington S., Allsop W. and Harrop J. (eds), Proceedings of the FloodRisk 2008 Conference, Taylor and Francis Group, London. Lhomme, J., Gutierrez Andres, J., Weisgerber, A., Davison, M., Mulet Marti, J., Cooper, A., Gouldby, B. submitted. Testing a new hydraulic model - Analytical tests and application to a flood event. Submitted to Journal of Flood Risk Management. Liang, Q., Borthwick, A. G. L., Stelling, G. 2004. Simulation of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids. International Journal for Numerical Methods in Fluids, 46 (2), 127 – 162. Lopez, F. and Garcia, M.H. 2001. Mean flow and turbulence structure of open-channel flow through non-emergent vegetation. American Society of Civil Engineers, Journal of Hydraulic Engineering, 127 (5), 392-402. Lynch, D.R. and Gray, W.G. 1980. Finite element simulation of flow deforming regions. Journal of Computational Physics, 36, 135-153. Marks, K. and Bates, P.D. 2000. Integration of high resolution topographic data with floodplain flow models. Hydrological Processes, 14, 2109-2122. Mason, D., Cobby, D.M., Horritt, M.S. and Bates, P.D., 2003. Floodplain friction parameterization in two-dimensional river flood models using vegetation heights derived from airborne scanning laser altimetry. Hydrological Processes, 17, 1711-1732. McLelland, S.J., Ashworth, P.J., Best, J.L. and Livesey, J.R. 1999. Turbulence and secondary flow over sediment stripes in weakly bimodal bed material. American Society of Civil Engineers, Journal of Hydraulic Engineering, 125 (5), 463-473. Mertes, L.A.K., 1997. Documentation and significance of the perirheic zone on inundated floodplains. Water Resources Research, 33, 1749-1762. Meselhe, E.A., Weber, L.J., Odgaard, A.J. and Johnson, T. 2000. Numerical modeling for fish diversion studies. American Society of Civil Engineers, Journal of Hydraulic Engineering, 126 (5), 365-374. Molinaro, P., Di Filippo, A. and Ferrari, F. 1994. Modelling of flood wave propagation over flat dry areas of complex topography in presence of different infrastructures. In P. Molinaro and L. Natale (eds), Modelling of flood propagation over initially dry areas, American Society of Civil Engineers, New York, 209-225.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 139 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Nepf, H.M. 1999. Drag, turbulence, and diffusion in flow through emergent vegetation. Water Resources Research, 35 (2), 479-489. Nezu, I., Tominaga, A. and Nakagawa, H. 1993. Field-measurements of secondary currents in straight rivers. American Society of Civil Engineers, Journal of Hydraulic Engineering, 119 (5), 598-614. Nicholas, A.P. and Walling, D.E. 1997. Modelling flood hydraulics and overbank deposition on river floodplains. Earth Surface Processes and Landforms, 22, 59-77. Noël B., Soares Frazão S., Zech Y. 2003. Computation of the ‘isolated building test case’ and the ‘model city experiment’ benchmarks. in EC Contract EVG1-CT-2001-00037 IMPACT Investigation of Extreme Flood Processes and Uncertainty, Proceedings 3rd Project Workshop, Louvain-la-Neuve, Belgium 5-7 November 2003 (CD-ROM), European Commission, Brussels, 18 pages ODPM, 2005. Delivering growth in Thames Gateway and the Growth Areas. Office of The Deputy Prime Minister Technical Report, London, UK. Pender, G. 2006. Briefing: Introducing Flood Risk Management Research Consortium. Proceedings of the Institution of Civil Engineers, Water Management, 159 (WM1), 3-8. Petaccia G., 2003, “Propagazione di onde a fronte ripido per rottura di sbarramenti in alvei naturali”, Phd Thesis, in Italian Petaccia G., Soares-Frazão S., Savi F., Natale L., Zech Y. Simplified versus detailed two-dimensional approaches to transient flow modeling in urban areas, Journal of Hydraulic Engineering, submitted Pinder, G.E. and Sauer, S.P. 1971. Numerical simulation of flood wave modification due to bank storage effects. Water Resources Research, 7, 63 - 70. Poole, G.C., Stanford J.A., Frissell, C.A. and Running, S.W. 2002. Three-dimensional mapping of geomorphic controls on flood-plain hydrology and connectivity from aerial photos. Geomorphology, 48 (4), 329-347. Preissmann, A. 1961. Propagation of translatory waves in channels and rivers. In Proceedings of the 1st Congress de l’Association Francaise de Calcul, Grenoble, France, 433-442. Proust, S. 2005. Non-uniform flows in compound channels: effect of floodplain-width variations. PhD-Thesis of INSA de Lyon, n°2005-ISAL-0083, 362 p., Lyon, France. (www.lyon.cemagref.fr/doc/these/proust/index.shtml) Puech, C. and Raclot, D. 2002. Using geographical information systems and aerial photographs to determine water levels during floods. Hydrological Processes, 16, 1593–1602. Rabus, B., Eineder, M., Roth, A. and Bamler, R. 2003. The shuttle radar topography mission - a new class of digital elevation models acquired by spaceborne radar. ISPRS Journal of Photogrammetry and Remote Sensing, 57 (4), 241- 262. Reynolds, O. 1895. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philosophical Transactions of the Royal Society, 186A, 123-164. Rijkswaterstaat and KNMI 1961. Verslag over de stormvloed van 1953 (Report on the 1953 Flood). ’s-Gravenhage: Staatsdrukkerij en Uitgeverijbedrijf, 714 pp. Roe, P. L., 1981. Approximate Riemann solvers, parameter vectors and difference scheme. J. Comp. Phys., 43, 357- 372. Romanowicz, R. and Beven, K. 2003. Estimation of flood inundation probabilities as conditioned on event inundation maps. Water Resources Research, 39 (3), art. no. 1073. Romanowicz, R., Beven, K.J. and Tawn, J. 1996. Bayesian calibration of flood inundation models. In Anderson M.G., Walling D.E. and Bates P.D. (eds.), Floodplain Processes, John Wiley and Sons, Chichester, UK, 333-360. Romanowicz, R.J., Beven, K.J. and Tawn, J.A. 1994. Evaluation of predictive uncertainty in nonlinear hydrological models using a Bayesian Approach. In V. Barnett and F. Turkman (eds), Statistics for the Environment (2), Water Related Issues, John Wiley & Sons, Chichester, UK. 297-318. Samuels, P.G. 1990. Cross section location in one-dimensional models. In W.R. White (ed), International Conference on River Flood Hydraulics. John Wiley and Sons, Chichester, 339-350. Sanders, B.F. 2001. High-resolution and non-oscillatory solution of the St. Venant equations in non-rectangular and non-prismatic channels. Journal of Hydraulic Research, 39 (3), pp. 321–330. Sellin R.H.J. and Willets B.B. 1996. Three-dimensional structures, memory and energy dissipation in meandering compound channel flow. In Anderson M.G., Walling D.E. and Bates P.D. (eds.), Floodplain Processes, John Wiley and Sons, Chichester, 255-298.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 140 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Sellin, R.H.J. 1964. A laboratory investigation into the interaction between the flow in the channel of a river and that over its floodplain. La Houille Blanche, 7, 793-801. Shao, X.J., Wang, H. and Chen, Z. 2003. Numerical modelling of turbulent flow in curved channels of compound cross-section. Advances in Water Resources, 26 (5), 525-539. Shiono, K. and Knight, D.W. 1991. Turbulent open-channel flows with variable depth across the channel. Journal of Fluid Mechanics, 222, 617-646. Shvidchenko, A.B. and Pender, G. 2001. Macroturbulent structure of open-channel flow over gravel beds. Water Resources Research, 37 (3), 709-719. Simm, D.J., 1993. The deposition and storage of suspended sediment in contemporary floodplain systems: A case study of the River Culm, Devon. PhD Thesis, University of Exeter, 347 pp. Slager, K. 1992. De ramp (The disaster), 2nd edn. Amsterdam: Uitgeverij Atlas, 557 pp. Soares-Frazão S., Zech Y. 1999. Effects of a sharp bend on dam-break flow. Proceedings 28th IAHR Congress, Graz, Austria (CD-ROM proceedings), Technical University Graz, Institute for Hydraulics and Hydrology, 7 pages. Soares-Frazão, S. 2002. Dam-break induced flows in complex topographies. Theoretical, numerical and experimental approaches. PhD Thesis. Louvain-la-Neuve: UCL, Belgium. Soares Frazão S., Zech Y. 2002. Dam-break in channels with 90° bend. Journal of Hydraulic Engineering, American Society of Civil Engineers (ASCE), 128 (11): 956-968. Soares-Frazão S., de Bueger C., Dourson V., Zech Y. 2002. Dam-break wave over a triangular bottom sill. Proceedings River Flow 2002 Conference, Louvain-la-Neuve, Belgium, September 2002, Balkema, Vol. 1, pp. 437- 442. Soares Frazao S., Noël B., Spinewine B., Zech Y. 2003. The isolated building test case : results from the IMPACT benchmark. in EC Contract EVG1-CT-2001-00037 IMPACT Investigation of Extreme Flood Processes and Uncertainty, Proceedings 3rd Project Workshop, Louvain-la-Neuve, Belgium 5-7 November 2003 (CD-ROM), European Comission, Brussels, 14 pages Soares Frazão S. 2007. Experiments of dam-break wave over a triangular bottom sill. Journal of Hydraulic Research, Vol. 45 Extra Issue, pp. 19-26. Soares Frazão S., Zech Y. 2007. Experimental study of dam-break flow against an isolated obstacle. Journal of Hydraulic Research, Vol. 45 Extra Issue, pp. 27-36. Soares Frazão S., Zech Y. 2008. Dam-break flow through an idealised city, Journal of Hydraulic Research, in press Soares Frazão S., Lhomme J., Guinot V., Zech Y. 2008. Two–dimensional shallow water model with porosity for urban flood modelling, Journal of Hydraulic Research, in press. Sotiropoulos, F. (2005). Introduction to statistical turbulence modelling for hydraulic engineering flows. In Bates, P.D., Lane, S.N. and Ferguson, R.I. (eds), Computational Fluid Dynamics: applications in environmental hydraulics, John Wiley and Sons, Chichester, UK. Squillace, P.J. 1996. Observed and simulated movement of bank storage water. Groundwater, 34, 121-134. Stoker, J.J. (1957) Pure and Applied Mathematics, Vol. 9 Water Waves, The Mathematical Theory and Applications, Institute of Mathematical Sciences, New York University, U.S.A Srokosz, M., 1997, Ocean surface currents and waves and along-track interferometric SAR. Proceedings of a Workshop on Single-pass Satellite Interferometry, Imperial College, London, 22 July 1997. Stanford, J.A. and Ward, J.V. 1988. The hyporheic habitat of river ecosystems. Nature, 335, 64-66. Stelling, G. S. and Duinmeijer, S.P.A. 2003. A staggered conservative scheme for every Froude number in rapidly varied shallow water flows. Int. J. Numer. Meth. Fluids, 43, 1329–1354 . Stewart, M.D., Bates, P.D. Anderson, M.G., Price, D.A. and Burt, T.P. 1999. Modelling floods in hydrologically complex lowland river reaches. Journal of Hydrology, 223, 85-106. Stoesser, T., Wilson, C.A.M.E. and Bates, P.D. and Dittrich, A. 2003. Application of a 3D numerical model to a river with vegetated floodplains. Journal of Hydroinformatics, 5, 99-112. Tchamen, G.W. and Kawahita, R.A. 1998. Modelling wetting and drying effects over complex topography. Hydrological Processes, 12, 1151-1183.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 141 Task 8 Flood Inundation Modelling D8.1 Contract No:GOCE-CT-2004-505420

Temple, D.M. 1987. Closure of ‘Velocity distribution coefficients for grass-lined channels’. American Society of Civil Engineers, Journal of Hydraulic Engineering, 113(9), 1224-1226. Thomas, T.G. and Williams, J.J.R. 1995. Large-Eddy Simulation of turbulent flow in an asymmetric compound open channel. Journal of Hydraulic Research, 33 (1), 27-41. Toro, E.F. 1999. Riemann solvers and numerical methods for fluid dynamics. Springer, Berlin, Germany. Toro, E.F. 2001. Shock-Capturing Methods for Free-surface Shallow Flows. Wiley, Chichester. Venere, M. and Clausse, A. 2002. A computational environment for water flow along floodplains. International Journal of Computational Fluid Dynamics. 16 (4), 327-330. Vreugdenhil, C.B. 1989. Computational Hydraulics: An Introduction. Springer, 182 pp Walling, D.E., Bradley, S.B. and Lambert, C.P. 1986. Conveyance loss of suspended sediment within a floodplain system. IAHS Publication, 159, 119-132. Wallingford Software (2008) Infoworks 9.5 RS/CS Help. Werner, M.G.F. 2001. Impact of grid size in GIS based flood extent mapping using a 1D flow model. Physics and Chemistry of the Earth Part B – Hydrology, Oceans and Atmospheres, 26 (7-8), 517-522. Werner, M.G.F. and Lambert, M.F. (in press). Evaluation of modelling approaches for river reach scale inundation modelling. Journal of Hydraulic Research. Westaway, R.M., Lane, S.N. and Hicks, D.M. 2003. Remote survey of large-scale braided, gravel-bed rivers using digital photogrammetry and image analysis. International Journal of Remote Sensing, 24 (4), 795-815. Wicks, J., Mocke, R., Bates, P.D., Ramsbottom, D., Evans, E. and Green, C. (in press). Selection of appropriate models for flood modelling. Proceedings of the 38th DEFRA Annual Flood and Coastal Management Conference, Department of Food and Rural Affairs, London, UK. Wilson, C.A.M.E. and Horritt, M.S. 2002. Measuring the flow resistance of submerged grass. Hydrological Processes, 16 (13), 2589-2598. Wilson, C.A.M.E., Stoesser, T. and Bates, P.D. (2005). Modelling of open channel flow through vegetation. In Bates, P.D., Lane, S.N. and Ferguson, R.I. (eds), Computational Fluid Dynamics: applications in environmental hydraulics, John Wiley and Sons, Chichester, UK. Wilson, M and Atkinson, P. (2005). The use of elevation data in flood inundation modelling: a comparision of ERS interferometric SAR and combined contour and differential GPS data. Journal of River Basin Management, 3 (1), 3- 20. Woessner, W.W. 2000. Stream and fluvial plain ground water interactions: re-scaling hydrogeologic thought. Groundwater, 38, 423-429. Woodhead, S., Asselman, N., Zech, Y., Soares-Frazão, S., Bates, P., Kortenhaus, A. 2006. Evaluation of Inundation Models – limits and capabilities of models. FLOODsite report T08-06-01. Wormleaton, P.R., Allen, J. and Hadjipanos, P. 1982. Discharge assessment in compound channel flow. American Society of Civil Engineers, Journal of Hydraulics Division, 108(HY9), 975-993. Wright, N. (2005). Numerical solution and discretization schemes for CFD models. In Bates, P.D., Lane, S.N. and Ferguson, R.I. (eds), Computational Fluid Dynamics: applications in environmental hydraulics, John Wiley and Sons, Chichester, UK. Wroblicky, G.J., Campana, M.E., Valett, H.M. and Dahm, C.N. 1998. Seasonal variation in surface-subsurface water exchange and lateral hyporheic area of two stream-aquifer systems. Water Resources Research, 34, 317-328.

T08_09_03_Flood_inundation_modelling_D8_1_V3_3_P01.doc 26 03 2009 142