hazard modelling and risk assessment for urban flood scenario

Politecnico di Milano

M.Sc. in Civil Engineering for Risk Mitigation

Hazard Modelling and Risk Assessment

for Urban Flood Scenario

Supervisor:

Professor Alessio Radice

Co-supervisor:

Professor Scira Menoni

Thesis by:

Maryam Izadifar

Alireza Babaee

December 2015

Academic Year: 2014 - 2015


Hazard Modelling and Risk Assessment for Urban Flood Scenario

A Master thesis submitted to Department of Civil and Environmental Engineering in partial

fulfillment of the requirements for the degree of Master of Science in Civil Engineering for

Risk Mitigation.

Students: Supervisor:

Maryam Izadifar

Student ID: 814117 Professor Alessio Radice

Dept. of Civil and Environmental Engineering

Alireza Babaee Politecnico di Milano Student ID: 814217

Co-supervisor:

Professor Scira Menoni

Dept. of Architecture and Urban Studies


Abstract (English)

Flood is the most frequent and costly natural hazard, affecting the majority of the world’s

countries on a regular basis. Floods are categorized by river floods, flash floods, urban floods,

and floods from the sea in coastal areas. Studies of past flood events show that the majority of

losses arise in urban areas, due to impairment of structures, costs of business shut-down and

failure of infrastructure. Due to climate change, the occurrence of urban flooding is predicted

to increase.

This research is part of an integrated study for the hydrogeological risk evaluation in a

mountain environment, where an urban area is crossed by a mountain torrent in its

downstream course and is thus prone to flash floods. The urban area considered here is the

town of Sondrio in Northern Italy. The scope of this Master’s thesis is twofold. First,

hydraulic modelling has been conducted for the urban area and has been complemented with

sensitivity analyses in order to cope with uncertainties. Second, damage assessment has been

made for buildings located in the area flooded according to the hazard scenario.

Flood hazard is described by a flood scenario with assigned probability of exceedance,

represented by a statistical return period. The scenario is characterized by spatial distributions

of water depth and velocity. The propagation of a flood in urban area is strongly influenced

by the geometric and topographic features of the area. An adequate two-dimensional

description of the urban district is necessary for modelling. In this study, a finite-element

model (implemented by the software package River2D) was used for the hydraulic

computations. Validation of the modelling procedure was carried out reproducing laboratory

test for a dam-break wave propagation in an ideal town. In order to consider uncertainties of

modelling, sensitivity analyses were implemented for mesh size, groundwater parameters,

and bed roughness. The same approach for sensitivity analysis was taken for the hazard

modelling of the case study that led to generating the hazard map.

The risk level associated with the hydraulic scenario was defined as the expected flood

damage. Although flood damage assessment is an essential part of flood risk management, it

has not received as much scientific attention as flood hazard. In this study, after a

comprehensive review of existing approaches to damage evaluation, damage assessment was

carried out by the HAZUS-MH model. Buildings located in the flooded area were divided in

four different categories based on typical factors determining the vulnerability of buildings,

like the number of storeys and presence of basement. Finally, a damage rate was assigned

according to building type and the level of hazard, represented by the water depth computed

by the hydraulic model.

Keywords: Flood Hazard, Hydraulic Modelling, Risk, Damage Assessment,

Vulnerability, Sensitivity Analysis, Uncertainty.

Abstract (Italian)

Le alluvioni sono tra le calamità naturali più frequenti, nonché più estesamente distuibuite

su tutto il territorio mondiale. Si possono distinguere piene fluviali, più o meno repentine;

alluvioni in aree urbane; alluvioni in aree costiere. In questo contesto, le alluvioni in area

urbana conducono alle perdite economiche più elevate a causa della concentrazione di beni e

infrastrutture, noché dei danni indotti dal fermo delle attività. I cambiamenti climatici

lasciano presagire che gli eventi alluvionali in aree urbane siano destinati ad aumentare in

frequenza.

La ricerca qui presentata è parte di uno studio integrato volto alla quantificazione del

rischio idrogeologico in una cittadina montana attraversata da un corso d’acqua. Lo studio

considera la città di Sondrio, situata nell’Italia del nord e soggetta a pericolo alluvionale da

parte del fiume Mallero. La tesi affronta due temi principali. È stata in primo luogo condotta

una modellazione idraulica della piena urbana, nella quale svariati aspetti di incertezza sono

stati tenuti in conto tramite opportune analisi di sensitività. In secondo luogo, si sono stimati i

danni indotti dall’alluvione per lo scenario di pericolo considerato.

Il pericolo alluvionale è stato descritto da uno scenario corrispondente a un tempo di

ritorno di cento anni. Lo scenario di pericolo deve essere descritto da distribuzioni spaziali di

altezza e velocità d’acqua nell’area allagata. La propagazione della piena nell’area urbana

dipende ovviamente dalle caratteristiche topografiche e geometriche del sito, che devono

essere adeguatamente rappresentate. La modellazione idraulica è stata condotta tramite un

modello agli elementi finiti, implementato nel software River2D. Il modello è stato

preliminarmente validato riproducendo dei risultati sperimentali di letteratura, relativi alla

propagazione di un’onda di crollo attraverso una cittadina ideale realizzata in laboratorio.

Opportune analisi di sensitività hanno riguardato la discretizzazione geometrica, i parametri

del flusso sotterraneo e la scabrezza del fondo. Il medesimo approccio è stato usato anche per

modellare l’allagamento dell’area urbana nel caso-studio e arrivare a generare le mappe di

pericolo.

Il danno atteso a causa dello scenario è stato assunto quale misura del rischio idraulico.

La valutazione dei danni è stata oggetto di ricerche di minor respiro rispetto ai fenomeni

idraulici, nonostante rappresenti ovviamente una componente cruciale dell’analisi di rischio.

Dopo una rassegna dei modelli esistenti in letteratura, in questo lavoro è stato applicato il

modello HAZUS-MH. Gli edifici ricadenti nell’area allagata sono stati divisi in quattro

categorie sulla base della relativa vulnerabilità, rappresentata da caratteristiche chiave quali il

numero di piani o la presenza di scantinati. È stato quindi calcolato un tasso di danno sulla

base del tipo di edificio e delle forzanti idrauliche, rappresentate dall’altezza e velocità

d’acqua fornite dal modello idraulico.

Parole chiave: Pericolo alluvionale, Modelli idraulici, Rischio, Valutazione dei danni,

Vulnerabilità, Analisi di sensitività, Incertezza.

Abstract (Persian)

سيل از متداول ترين فجايع طبيعي در سراسر جهان بحساب مي آيد كه هر ساله در بسياري از : چکیده

كشورهاي دنيا خسارات فراواني به جا مي گذارد. سيل را مي توان در انواع سيل هاي رودخانه اي، سيل هاي ناگهاني،

لعات سيل هاي گذشته، بيشترين خسارات و سيل هاي ساحلي طبقه بندي كرد. با توجه به مطا سيالب هاي شهري،

ناشي از سيل ها در مناطق شهري اتفاق مي افتد كه به دليل وارد شدن خسارت به ساختمانها و زيرساخت هاي

شهري و تعطيلي كسب و كار است. امروزه با توجه به تغييرات آب و هوايي وقوع سيالب هاي شهري رو به افزايش

است.

طالعات جامعي است كه براي ارزيابي خطر وقوع سيل در يك منطقه شهري به نام اين تحقيق بخشي از م

ايتاليا انجام شده است. اين شهر در محيطي كوهستاني و در پايين دست رودخانه با خطر كشور سوندريو در شمال

بخش اول شامل وقوع سيل واقع شده است. در اين پايان نامه فوق ليسانس دو بخش مورد مطالعه قرارگرفته است.

نيز مدلسازي هيدروليكي سيل در يك منطقه شهري است كه در آن آناليز حساسيت به منظور كاهش عدم قطعيت

انجام شده است. در بخش دوم ارزيابي خسارت وارد شده به ساختمان هاي واقع در منطقه شهري مورد نظر با توجه

روليكي انجام شده است. به سناريوي آب گرفتگي احتمالي حاصل از مدلسازي هيد

خطر سيل مورد نظر بر اساس مدل سيلي با احتمال وقوع دوره بازگشت آماري تعريف شده است. هم چنين در

اين مدل توزيع فضايي عمق و سرعت آب نيز مد نظر قرار گرفته شده است. انتشار يك سيل در يك منطقه شهري

وگرافي منطقه است. براي مدلسازي هيدروليكي نياز به يك مدل به ميزان زيادي تحت تاثير وضعيت هندسي و توپ

( براي River2Dرم افزار نشده در دو بعدي است. در اين مطالعه از مدلي بر اساس روش اجزا محدود )استفاده

آزمايشگاهي براي يك مدل بازتوليد محاسبات هيدروليك استفاده شده است. سنجش اعتبار روش مدل سازي توسط

و به منظور لحاظ عدم قطعيت در مدل ه استانجام شدشهر ايده آل مدل يك شار موج حاصل از شكست سد در انت

زبري بستر اجرا شد. همچنين حساسيت براي اندازه شبكه بندي، پارامترهاي آب هاي زيرزميني، و آناليزسازي،

د مطالعه نيز استفاده شده است. مدل سازي سيل در شهر موردر حساسيت آناليزهمچنين از همين روش براي

در اين مطالعه ريسك به عنوان خسارت مورد انتظار از سناريوي سيل حاصل از مدل هيدروليك تعريف شده

داراي توجه تاكنون است. اگر چه ارزيابي خسارت سيل يك بخش اساسي از مديريت ريسك سيالب است، ولي

مطالعه پس از يك بررسي جامع از روش هاي موجود ارزيابي خسارات، علمي به اندازه خطر سيل نبوده است. در اين

انجام شد. ساختمانهاي واقع در منطقه آب گرفتگي در HAZUS-MHتوسط مدل اين مرحله از اين مطالعه

چهار دسته مختلف بر اساس عوامل عمومي تعيين كننده آسيب پذيري ساختمان ها، مانند تعداد طبقه و حضور

با توجه به نوع ساختمان و سطح خطر)عمق آب( حاصل از مدل خسارتيم شدند. در نهايت، نرخ زيرزمين تقس

هيدروليكي محاسبه شد.

، آناليز حساسيت، عدم قطعيت.خطر سيل، هيدروليك، ريسك، ارزيابي خسارت، آسيب پذيريکلمات کلیدی:

Acknowledgments

We would like to express our sincere gratitude and appreciation to our thesis supervisor

Professor Alessio Radice and co-supervisor Professor Scira Menoni for their continuous

guidance, support and encouragement throughout this research. We are very grateful to them

for the education and support they have provided.

Maryam Izadifar,

Alireza Babaee


December 2015

Table of Contents

Abstract (English) ........................................................................................................................ iii

Abstract (Italian) .......................................................................................................................... iv

Abstract (Persian) .......................................................................................................................... v

Acknowledgments ........................................................................................................................ vi

List of Tables ................................................................................................................................ x

List of Figures .............................................................................................................................. xi

1. INTRODUCTION .......................................................................................................................... 1

Aim of the Study ..................................................................................................................... 1 1.1.

Outline of the Thesis ............................................................................................................... 7 1.2.

2. BACKGROUND AND STATE OF THE ART.............................................................................. 9

Introduction ............................................................................................................................. 9 2.1.

Hazard Modelling ................................................................................................................... 9 2.2.

2.2.1. Modelling Aspects .......................................................................................................... 9

2.2.2. Software Packages for Hydraulic Modelling ................................................................ 13

2.2.3. Validation and Uncertainty in the Modelling ................................................................ 19

2.2.4. Application of 2D Numerical Modelling ...................................................................... 24

2.2.5. Roughness Effects ......................................................................................................... 28

State of the Art on Flood Risk Analysis................................................................................ 31 2.3.

2.3.1. European Flood Directive on the Assessment and Management of Flood Risks ......... 31

2.3.2. Floods and Climate ....................................................................................................... 33

2.3.3. Fundamental of Flood Risk Analyses ........................................................................... 38

2.3.4. Applications of Flood Damage Assessment ................................................................. 41

2.3.5. Fundamental of Flood Damage ..................................................................................... 42

2.3.6. Damage Functions......................................................................................................... 45

2.3.7. Direct Monetary Damages ............................................................................................ 47

2.3.8. Indirect Economic Damages ......................................................................................... 51

2.3.9. Damage Influencing Parameters ................................................................................... 52

2.3.10. Flood Actions on Buildings .......................................................................................... 54

2.3.11. Flow Velocity Effect ..................................................................................................... 57

2.3.12. Uncertainty of Flood Damage Assessment ................................................................... 59

2.3.13. Flood Damage Modelling ............................................................................................. 61

2.3.14. Available Flood Damage Assessment Models .............................................................. 61

2.3.15. Flood Damage Model Comparison ............................................................................... 66

3. RIVER2D HYDRODYNAMIC MODELLING ........................................................................... 75

Introduction ........................................................................................................................... 75 3.1.

2D Hydrodynamic Principles in River2D ............................................................................. 75 3.2.

Numerical Modelling Concepts ............................................................................................ 80 3.3.

3.3.1. Finite Difference Methods ............................................................................................ 81

3.3.2. Finite Element Methods ................................................................................................ 81

3.3.3. Finite Volume Methods ................................................................................................ 82

3.3.4. Computational Grids ..................................................................................................... 82

River2D Modelling Procedure .............................................................................................. 85 3.4.

River2D Bed ......................................................................................................................... 85 3.5.

River2D Mesh ....................................................................................................................... 87 3.6.

River2D ................................................................................................................................. 89 3.7.

River2D Applications ........................................................................................................... 94 3.8.

4. MODELLING OF THE IDEALISED CITY ................................................................................ 99

Introduction ........................................................................................................................... 99 4.1.

Experimental Test (Idealised City) ....................................................................................... 99 4.2.

Previous Applications of Idealised City for Validation of Modelling ................................ 103 4.3.

Development of Idealised City Model in River2D Package ............................................... 108 4.4.

Results of the Idealised City Modelling .............................................................................. 116 4.5.

4.5.1. Sensitivity Analysis for Mesh Size ............................................................................. 116

4.5.2. Sensitivity Analysis for Groundwater Parameters ...................................................... 120

4.5.3. Sensitivity Analysis for Roughness ............................................................................ 126

Conclusion for Modelling of the Idealised City .................................................................. 128 4.6.

5. HAZARD MODELLING FOR THE CASE STUDY ................................................................ 130

Introduction ......................................................................................................................... 130 5.1.

Uncertainties in Hydraulic Modelling of Urban Area ......................................................... 133 5.2.

Sondrio Model Description and Input Data ........................................................................ 136 5.3.

Monitoring Points and Monitoring Routes in the Sondrio Model ...................................... 139 5.4.

Sensitivity Analysis for Mesh Size ..................................................................................... 146 5.5.

Sensitivity Analysis for Inflow Discharge .......................................................................... 152 5.6.

Sensitivity Analysis for Roughness .................................................................................... 156 5.7.

Hazard Maps ....................................................................................................................... 159 5.8.

Conclusion for Hazard Modelling ....................................................................................... 163 5.9.

6. FLOOD RISK ASSESSMENT ................................................................................................... 165

Introduction ......................................................................................................................... 165 6.1.

Damage Functions and Limitations .................................................................................... 165 6.2.

Flood Damage Assessment in Italy and Limitations ........................................................... 166 6.3.

Sondrio Damage Assessment: Applied Damage Curve and Final Results ......................... 167 6.4.

Discussion and Conclusions ................................................................................................ 173 6.5.

7. CONCLUSION ........................................................................................................................... 176

References ................................................................................................................................. 181

List of Tables

Table ‎2.1: Classification of inundation models (Neelz and Pender, 2009) ........................................... 14

Table ‎2.2: Software packages for flood inundation modelling (Neelz and Pender, 2009) ................... 17

Table ‎2.3: Uncertainty sources considered in the modelling system (Apel et al., 2010) ...................... 23

Table ‎2.4: Manning’s n values according to Chow (1959) ................................................................... 29

Table ‎2.5: Contrasting traditional views with emerging perspectives on flood hazard and risk (adapted

from Merz et al. 2014) .......................................................................................................................... 34

Table ‎2.6: Advantages and disadvantages of relative and absolute damage functions (Merz et al.,

2010) ..................................................................................................................................................... 46

Table ‎2.7: Advantages and disadvantages of empirical and synthetic flood damage models (Merz et

al., 2010) ............................................................................................................................................... 47

Table ‎2.8: Possible classification of elements at risk based on economic sectors (Merz et al., 2010) . 50

Table ‎2.9: Damage influencing factors (Merz et al., 2010) .................................................................. 53

Table ‎2.10: Qualitative summary of the influence of impact parameters on flood damage (Kreibich et

al., 2009) ............................................................................................................................................... 58

Table ‎2.11: Studies of non-depth flood damage models (Kelman and Spence, 2004) ......................... 66

Table ‎2.12: Flood damage models qualitative comparison (Jongman et al., 2012) .............................. 69

Table ‎2.13: Flood damage models comparison for residential sectors (Merz et al., 2010) .................. 70

Table ‎2.14: Flood damage models comparison for industrial sectors (Merz et al., 2010) .................... 71

Table ‎2.15: Flood damage models comparison for agricultural sectors (Jongman et al., 2012) ........... 73

Table ‎3.1: Correlation between roughness height (𝐾𝑠), and Manning’s coefficient (n) ...................... 78

Table ‎4.1: 14 different bed geometries constructed for the Idealised City ......................................... 111

Table ‎4.2: Monitoring points along longitudinal street located at y = 0.2 m of Idealised City model 115

Table ‎4.3: Velocity comparison for roughness sensitivity analysis .................................................... 126

Table ‎5.1: Sources of uncertainty in urban flood hazard mapping (Domeneghetti et al., 2013) ........ 135

Table ‎5.2: Monitoring points in Sondrio model .................................................................................. 140

Table ‎5.3: Monitoring routes configuration ........................................................................................ 141

Table ‎5.4: Comparison between mesh sizes generated for Sondrio case study .................................. 147

Table ‎5.5: Hydrographs as upstream B.C. for Sondrio model ............................................................ 152

Table ‎5.6: Maximum water depth and velocity recorded in the monitoring points ............................ 160

Table ‎6.1: Damage rates according to USACE damage function and level of hazard (water depth) . 172

List of Figures

Figure 1.1: Increasing trend in global disaster losses (The World Bank, 2013 - Source: Munich RE) .. 2

Figure 1.2: Total number of disasters and losses (The World Bank, 2013 - Source: Munich RE) ......... 2

Figure 1.3: The role of natural hazards, exposure and vulnerability in disaster risk (IPCC, 2012) ........ 2

Figure 1.4: General methodology for hydrogeological risk evaluation .................................................. 6

Figure 2.1: The art and science of river engineering (Knight, 2013) .................................................... 10

Figure 2.2: Chart explaining the modelling procedure (DHI Water, 2014) .......................................... 20

Figure 2.3: Schematic structure of the IHAM model adopted for flood hazard estimation under

uncertainty conditions (Domeneghetti et al., 2013) .............................................................................. 21

Figure 2.4: Flood extent (dark grey) in the lower part of the catchment at time t = 30 minutes (left), t =

90 minutes (centre), t =150 minutes (right) (Dottori et al., 2014) ........................................................ 25

Figure 2.5: Depiction of a general 1D model of the river channel coupled with a 2D model of the

floodplain .............................................................................................................................................. 27

Figure 2.6: Mesh generation (left), water depth (right) by Mike 21 (Sameer and Dilnesaw, 2013) ..... 27

Figure 2.7: Three ways to define building roughness in 2D models (Alcrudo, 2002) .......................... 28

Figure 2.8: Land use classification and Manning’s n value distribution, left: Google satellite image,

middle: distributed Manning’s n value, right: single composite friction value (Ozdemir et al., 2013) 30

Figure 2.9: Drivers of flood risk change, dynamic risk and dynamic risk management (Merz et al.,

2014) ..................................................................................................................................................... 37

Figure 2.10: Detail of classification in flood damage assessments in relation to the main influencing

factors. ................................................................................................................................................... 49

Figure 2.11: Water levels and pressure distribution levels on building component (Kelman and

Spence, 2004) ........................................................................................................................................ 55

Figure 2.12: FLEMO model for water depth relationship with loss ratio (Jongman et al., 2012) ........ 62

Figure 2.13: Schematic display for qualitative assessment of the damage models (Jongman et al.,

2012) ..................................................................................................................................................... 68

Figure 3.1: a) Dam-break simulation on a structured square grid from Liang et al. (2006); b)

Boundary-fitted grid from Liang et al. (2007) ...................................................................................... 83

Figure 3.2: Unstructured mesh from Hunter et al. (2006) ..................................................................... 84

Figure 3.3: A sample .bed file with nodes, breaklines and triangulation displayed. ............................. 87

Figure 3.4: A sample mesh file with triangulation and boundaries displayed. ..................................... 89

Figure 3.5: a) introducing upstream hydrograph; b) transient modelling dialogue box; c) transient

output options dialogue box (River2D Manual, 2002) ......................................................................... 94

Figure 3.6: Topographic survey (up) and River2D mesh generation (down) (Bright, 2012) ............... 95

Figure 3.7: The layout of the reach (left) bed roughness heights over the reach for ice–covered

condition (right) (Katopodis and Ghamry, 2005) ................................................................................. 95

Figure 3.8: Sample result of 2D hydraulic modelling with River2D (BC hydro, Canada) ................... 96

Figure 3.9: 2D hydraulic modelling with River2D (Susitna-Watana Hydro, USA) ............................. 97

Figure 3.10: River2D mesh generation (left) and velocity result (right) (Chelminski, 2010) .............. 97

Figure 4.1: Experimental set-up and channel dimensions in (m) ........................................................ 100

Figure 4.2: Cross section (m) (except the inlet) .................................................................................. 100

Figure 4.3: Hydraulic jump upstream of the urban district (Soares-Frazao and Zech, 2008) ............. 101

Figure 4.4: Water-surface profiles along the central longitudinal street at y = 0.2 m: experimental data

(•), (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s, reproduced from Soares-Frazao and Zech (2008) . 102

Figure 4.5: Velocity along the central longitudinal street located at y = 0.2 m: experimental data (•),

(a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s, reproduced from Soares-Frazao and Zech (2008) ....... 102

Figure 4.6: Water level profiles at y = 0.2 m along the longitudinal street at different times: (a) t = 4 s;

(b) t = 5 s; (c) t = 6 s; (d) t = 10 s (Xia et al., 2011) ............................................................................ 104

Figure 4.7: Water velocity at y = 0.2 m along the longitudinal street at different times: (a) t = 4 s; (b) t

= 5 s; (c) t = 6 s; (d) t = 10 s (Xia et al., 2011) ................................................................................... 104

Figure 4.8: Inflow discharge hydrographs for different flood frequencies (Xia et al., 2011) ............. 105

Figure 4.9: Distributions of (a) depths (b) velocities at the time of peak discharge (Xia et al., 2011)105

Figure 4.10: Idealized city layouts: (a) Case 1; (b) Case 2 (Petaccia et al., 2010) ............................. 106

Figure 4.11: Coarse mesh used for the porosity and roughness approaches (Petaccia et al., 2010) ... 107

Figure 4.12: Water levels—RM model: aligned case, t=6 s (Petaccia et al., 2010) ............................ 107

Figure 4.13: Computed and observed water levels: aligned case, t=10 s (Petaccia et al., 2010) ........ 107

Figure 4.14: Sketch of dam break wave in a dry horizontal channel (Chanson, 2004) ...................... 108

Figure 4.15: Comparison between trapezoidal and rectangular shapes for the inlet section of the

Idealised City ...................................................................................................................................... 113

Figure 4.16: Specific points for defining city blocks in the Idealised City model .............................. 113

Figure 4.17: Defining blocks in the Idealised City model .................................................................. 113

Figure 4.18: Construction of dry bed for initial condition in River2D ............................................... 114

Figure 4.19: Monitoring points configuration in the Idealised City model ........................................ 115

Figure 4.20: Mesh size 70 cm with region refinement in the block position ...................................... 116

Figure 4.21: Water depth and velocity for mesh size 70 cm with region refinement in the blocks

position ................................................................................................................................................ 118

Figure 4.22: Sensitivity analysis for water-surface profiles and mesh size along the central

longitudinal street located at y = 0.2 m: experimental data (•), (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t =

10 s ...................................................................................................................................................... 119

Figure 4.23: Sensitivity analysis for velocity and mesh size along the central longitudinal street

located at y = 0.2 m: experimental data (•), (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s .................. 119

Figure 4.24: Sensitivity analysis for groundwater, water depth at 4 sec, water depth and velocity at 10

sec. ...................................................................................................................................................... 123

Figure 4.25: Sensitivity analysis for water-surface profiles and groundwater parameters along the

central longitudinal street located at y = 0.2 m: experimental data (•), (a) t = 4 s, (b) t = 5 s, (c) t = 6 s,

(d) t = 10 s ........................................................................................................................................... 124

Figure 4.26: Sensitivity analysis for velocity and groundwater parameters along the central

longitudinal street located at y = 0.2 m: experimental data (•), (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t =

10 s ...................................................................................................................................................... 124

Figure 4.27: Sensitivity analysis for water depth and groundwater parameters along the central

longitudinal street located at y = 0.2 m: experimental data (•), (a) x = 5 m, (b) x = 5.55 m, (c) x = 6.15

m, (d) x = 6.9 m .................................................................................................................................. 125

Figure 4.28: Sensitivity analysis for velocity and groundwater parameters along the central

longitudinal street located at y = 0.2 m: experimental data (•), (a) x = 5 m, (b) x = 5.55 m, (c) x = 6.15

m, (d) x = 6.9 m .................................................................................................................................. 125

Figure 4.29: Sensitivity analysis for water depth and roughness height along the central longitudinal

street located at y = 0.2 m: experimental data (•), (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s ........ 127

Figure 4.30: Sensitivity analysis for velocity and roughness height along the central longitudinal street

located at y = 0.2 m: experimental data (•), (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s .................. 127

Figure 5.1: Mallero basin (right) and its position in Italy and Lombardia region ............................... 131

Figure 5.2: Two parts of Sondrio connected with bridges over Mallero River (left), Mallero River

passing through Sondrio ends in Adda River (right) .......................................................................... 131

Figure 5.3: Sondrio in 1987 at Garibaldi Bridge (left), at bend before the bridge (right) ................... 132

Figure 5.4: Temporal evolution of the river bed and the water elevation at Garibaldi Bridge for 100-

year hydrograph (Ivanov, 2014).......................................................................................................... 132

Figure 5.5: Hydrographs of the flood with lower bound and higher bound scenarios, adapted from

Ivanov (2014) ...................................................................................................................................... 132

Figure 5.6: Mallero River looking toward south (left), HEC-RAS cross section for this part of the

river (right) .......................................................................................................................................... 136

Figure 5.7: a) Aerial view of Sondrio including buildings, b) River2D model generated for Sondrio

including building blocks, c) model dimensions and bed elevation variation .................................... 138

Figure 5.8: a) Inlet location (zoomed in the River2D model), b) initial water level vs bed level at inlet

position ................................................................................................................................................ 139

Figure 5.9: 8-hour hydrographs of the flood with lower bound and higher bound scenarios constructed

for River2D modelling of town Sondrio (derived from Figure 5.5) ................................................... 139

Figure 5.10: Schematic view for monitoring points in Sondrio model ............................................... 140

Figure 5.11: Three monitoring routes based on the highest discharge intensity in Y direction .......... 141

Figure 5.12: Three monitoring routes location on Sondrio map ......................................................... 141

Figure 5.13: Schematic view for monitoring routes configuration ..................................................... 141

Figure 5.14: Flood starting point (inlet position in the model) at Garibaldi Bridge ........................... 142

Figure 5.15: Three different direction of flood propagation along the monitoring routes .................. 142

Figure 5.16: Garibaldi Square (Piazza Garibaldi) starting place for flood routes 2 and 3 .................. 142

Figure 5.17: Via Alessi, first point of the route No. 1 (monitoring point No. 4) ................................ 143

Figure 5.18: Via Parolo, second point of the route No. 1 (monitoring point No. 8) ........................... 143

Figure 5.19: Via Parolo, third point of the route No. 1 (monitoring point No. 15) ............................ 143

Figure 5.20: Via Caimi, first point of the route No. 2 (monitoring point No. 9) ................................ 144

Figure 5.21: Via Caimi, second point of the route No. 2 (monitoring point No. 16) .......................... 144

Figure 5.22: Via Caimi, third point of the route No. 2 (monitoring point No. 28) ............................. 144

Figure 5.23: Corso Vittorio Veneto, first point of the route No. 3 (monitoring point No. 5) ............. 145

Figure 5.24: Corso Vittorio Veneto, second point of the route No. 3 (monitoring point No. 10) ...... 145

Figure 5.25: Piazzale Giovanni Bertacchi, third point of the route No. 3 (monitoring point No. 17) 145

Figure 5.26: Graphical representation for different mesh sizes in Sondrio model ............................. 147

Figure 5.27: Comparison between the flood extension of mesh sizes 40 m and 80 m ....................... 148

Figure 5.28: Comparison between the flood extension of mesh sizes 80 m and 100 m ..................... 149

Figure 5.29: Comparison between the flood extension of mesh sizes 60 m and 80 m ....................... 150

Figure 5.30: Water depth comparison between mesh sizes 60 m and 80 m, a) monitoring point No. 1

(Garibaldi Bridge), b) monitoring point No. 2 .................................................................................... 150

Figure 5.31: Differences in water depth for mesh sizes 60 m and 80 m (route No. 1) ....................... 151



Figure 5.34: Comparison for the flood extension in lower bound and higher bound hydrographs .... 153

Figure 5.35: Sensitivity analysis of inflow discharge with lower bound and higher bound at Garibaldi

Square, a) water depth, b) velocity ..................................................................................................... 154

Figure 5.36: Differences in water depth for lower and higher inflow hydrographs (route No. 1) ...... 154



Figure 5.39: Comparison between the flood extension for roughness height (Ks) 0.3 m and 2 m ..... 157

Figure 5.40: Sensitivity analysis for roughness height (Ks) at Garibaldi Square, a) water depth, b)

velocity ................................................................................................................................................ 157

Figure 5.41: Differences in water depth for roughness height (Ks) 0.3 m and 2 m (route No. 1) ...... 158



Figure 5.44: Final results for Sondrio model, a) water depth (m), b) water velocity (m/sec) ............. 161

Figure 5.45: Flood extension scenario in town Sondrio ..................................................................... 162

Figure 5.46: Water depth for flood scenario in Sondrio on Open Street map ..................................... 162

Figure 6.1: Flood damage function based on USACE (adapted from Molinari, 2014 c) ................... 168

Figure 6.2: Flood hazard map for town Sondrio ................................................................................. 168

Figure 6.3: Samples for building categories of town Sondrio ............................................................ 171

Figure 6.4: Damage map for flood scenario of town Sondrio ............................................................. 173

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Picture: Flood in New Orleans, USA, after hurricane Katrina, 2005

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Chapter 1

1. INTRODUCTION

Aim of the Study 1.1.

Overall losses from natural disasters have increasing trend in the last decades

(Figure 1.1). Some 87% of these reported disasters (18,200 events), 74% of losses (US$2,800

billion) and 61% of lives lost (1.4 million in total) were caused by weather extremes

(Figure 1.2). Development patterns, particularly population growth in high risk areas and

environmental degradation, continue to be the most important drivers of disaster risks (The

World Bank, 2013). However, since the 1960s, human-induced climate change has been

increasingly contributing to extreme events in the form of rising temperatures, changing

precipitation patterns (e.g., flash floods) and sea storms (IPCC, 2012).

Disaster risk is determined by the occurrence of a natural hazard (e.g., a flood), which

may impact exposed populations and assets (e.g., houses located in the flooded area).

Vulnerability is the characteristic of the population or asset making it particularly susceptible

to damaging effects (e.g., fragility of housing construction). According to IPCC (2012),

poorly planned development, poverty, environmental degradation and climate change are all

drivers that can increase the magnitude of this interaction, leading to larger disasters

(Figure 1.3).

Flood is the most frequent and costly natural hazard, affecting the majority of the world’s

countries on a regular basis (UNISDR, 2011; IPCC, 2012). Despite the decade-long effort of

United Nations towards natural disaster reduction through its program IDNDR (International

Decade Natural Disaster Reduction), no reduction in losses due to natural disasters has been

observed. Indeed there is evidence that flooding is getting more serious over time, in terms of

the number of floods and the damage (Munich Re, 2005) and the loss of life (EM-DAT) that

it has caused. Several studies state that increasing economic damage can be attributed to a

growth of population and wealth in flood prone areas (Barredo, 2009; Bouwer et al., 2010;

Kreft, 2011; UNISDR, 2011; Jongman et al., 2012).

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Figure 1.1: Increasing trend in global disaster losses (The World Bank, 2013 - Source: Munich RE)

Figure 1.2: Total number of disasters and losses (The World Bank, 2013 - Source: Munich RE)

Figure 1.3: The role of natural hazards, exposure and vulnerability in disaster risk (IPCC, 2012)

With increasing frequency and expenses of natural disasters, a standardized loss

estimation methodology for consistently compiling information about their economic impacts

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has become essential for all the concerned authorities for natural disaster reduction processes

(NRC, 1999).

If we note that flood risk can be defined as the probability and the magnitude of expected

losses that result from interactions between flood hazard and vulnerable conditions

(UNISDR, 2004), then losses assessment could be considered as the essential part of risk

mitigation (Elmer et al., 2010).

According to European Flood Directive (2007), ‘Flood’ means the temporary covering by

water of land not normally covered by water. This shall include floods from rivers, mountain

torrents (flash floods), urban floods, and floods from the sea in coastal areas, and may

exclude floods from sewerage systems. ‘Flood risk’ means the combination of the probability

of a flood event and of the potential adverse consequences for human health, the

environment, cultural heritage and economic activity associated with a flood event.

Despite decades of research, flood loss estimation is still a challenging task. Drawing on

recent research, a number of major problems can be identified among them, the question of

what specific damages under what circumstances are seen as significant? It is sensible that

people would choose risk management strategies according to their capacity to reduce

significant damages (Molinari et al., 2014 a).

Studies of past flood events show that the majority of losses arise in urban areas, due to

impairment of structures, costs of business shut-down and failure of infrastructure

(EA/CIRIA, 2001; The World Bank and ADB, 2010).

An estimate of losses from future natural hazards is essential to preparing for a disaster

and facilitating good decision making at the local, regional, state, and national levels of

government (Dutta et al., 2001).

Government agencies, insurance companies and research institutions in many countries

develop and use flood damage models to assess the expected economic flood impact. Overall,

the estimation of flood damage is an important component for flood risk mapping, land use

planning, cost-benefit analysis for optimal decision of flood mitigation measures, financial

appraisals for insurance sectors and comparative risk analyses (Kreibich et al., 2010;

Jongman et al., 2012).

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The concept of traditional flood protection is increasingly being replaced by

comprehensive risk management, which includes structural and non-structural measures

(Sayers et al., 2002; Hooijer et al., 2004). Hazard and risk maps are of particular importance

for planning purposes, risk awareness campaigns and the encouragement of private

preventive measures (Kreibich et al., 2009).

Traditionally, design standards and structural flood defence measures were the dominant

flood management approaches. Structural flood defence measures, such as dikes and

retention basins, were designed in order to control up to a certain, predefined design flood,

e.g. a 100-year flood. In recent years, this “flood control approach” has increasingly been

questioned. New concepts have been developed, usually referred to as “flood risk

management” (Merz et al., 2010). The level of protection is determined by broader

considerations than some predefined design flood while more emphasis is put on non-

structural flood mitigation measures. An important development in this context is a focal shift

from flood hazard to flood risk.

Flood policies traditionally concentrated on the control or reduction of flood hazard, i.e.

decreasing the probability of occurrence and intensity of flood discharges and inundations.

Flood risk management puts a much stronger emphasis on flood risk, where risk is defined as

damage that occurs or will be exceeded with a certain probability in a certain time period

(e.g. one year). Hence, damage aspects need to be taken into account in any deliberations on

flood risk management.

Although flood damage assessment is an essential part of flood risk management, it has

not received much scientific attention. The consideration of flood damage within the

decision-making process of flood risk management is still relatively new (Messner et al.,

2007). Compared to the wealth of methods and available information on flood hazard, flood

damage data are scarce and damage estimation methods are crude. This lack frequently leads

to transfer of damage data and damage assessment models in time, space and across damage

processes without sufficient justification (Merz et al., 2010).

Flood hazard is described by the exceedance probability of damaging flood situations in a

given area and within a specified period of time, and by the characteristics of the flood

situations, e.g., extent and depth of inundation (Apel et al., 2010).

5

In urban areas, the impacts of flash floods can be very severe as these regions are

generally densely populated and contain vital infrastructure. Due to climate change, the

occurrence of urban flooding is predicted to increase in the future, which is likely to lead to

increasing flood risk to people and property in urban areas. It is therefore appropriate to

estimate potential flood risk to people and property for improved flood risk management (Xia

et al., 2011).

The propagation of a flood wave in an urban area is strongly influenced by the geometric

and topographic features of a flood prone area. A complete two-dimensional (2D) description

of the urban district, including the actual geometry of streets and housing, can be considered

as the state-of-art approach (Hunter et al., 2008) even though some modifications have been

recently proposed to analyze flows over complex terrain without the limitations of mild slope

assumption usually used in depth-averaged models (Anh and Hosoda, 2007). Such an

accurate description requires heavy computational efforts and data from detailed land surveys

that are not always available. When these data are missing or inaccurate or the layout of the

urban fabric is only roughly known, a simplified model may be more appropriate (Petaccia et

al., 2010).

There are a number of commercial and public domain 2D models available. They are

based on a variety of numerical schemes and offer a range of graphical pre and post processor

modules. The fundamental physics is more or less common, however. All 2D models solve

the basic mass conservation equation and two (horizontal) components of momentum

conservation. Outputs from the model are two (horizontal) velocity components and a depth

at each point or node. Velocity distributions in the vertical are assumed to be uniform and

pressure distributions are assumed to be hydrostatic. 2D model schemes based on finite

difference, finite volume, and finite element methods are available. Each approach has

advantages and disadvantages.

This research is part of an integrated study for the hydrogeological risk evaluation in a

mountain environment, in which an urban area is located in the downstream of a mountain

torrent and is prone to flash flood event. The general methodology is depicted in Figure 1.4.

Results from hydrological part is a flood hydrograph for the mountain river. First part of the

hydraulic study is river modelling (with sediment transport and bed morphology). Ivanov

(2014) carried out a research as a Master’s thesis in Politecnico di Milano focused on the

geological part and river modelling with water and sediment transport processes. A return

6

period of 100 years used as hydrological input in that research. Ivanov (2014) showed

significant bed aggradation in river reach inside the city. In that research, water overwhelmed

the river bank and entered the city. Output hydrograph from river in that study is considered

as input boundary condition of this research.

Focus of this Master’s thesis is in the last two parts of this integrated research (red dashed

rectangle in Figure 1.4), including hydraulic modelling for urban area (2D modelling of water

propagation) and flood risk and damage assessment for a case study of Sondrio city.

The town of Sondrio is located in the Mallero catchments, which is situated on the

Southern flanks of the Alps in Northern Italy, near the Swiss-Italian border. The Mallero

catchment has a surface area of 320 km2 and is mountainous with the highest point being at

approximately 4,000 m above mean sea level. The lowest point in the catchment is

approximately 300 m above mean sea level at Sondrio. Sondrio is located on the alluvial fan

of the River Mallero just upstream of where the Mallero ends to the River Adda. The Mallero

is a ‘torrent river’ which passes through the center of Sondrio and is prone to generating flash

floods, which are a serious risk facing the town and its approximately 22,000 inhabitants. The

town is protected from flooding by dikes (i.e. concrete walls), however, the principal risk

arises from the danger of river bed aggradation, which can significantly reduce this level of

protection leading to the flood walls being overtopped.

Figure 1.4: General methodology for hydrogeological risk evaluation

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Outline of the Thesis 1.2.

This Master’s thesis consists of seven chapters. This chapter deals with general concepts

of flood hazard modelling and flood risk assessment and its particular significance in urban

areas. The methodology of this study is presented here.

Chapter two introduces state of the art in two main aspects of this study. First, in flood

hazard modelling by studying various software packages dealing with urban flood modelling,

modelling uncertainties, level of accuracy, roughness effects and etc. Second, studies related

to flood risk are listed. In this sense, flood risk management, flood and climate, uncertainties

in flood risk assessment, flood damage models and their comparison, etc. are evaluated.

Principals of two-dimensional hydraulic modelling including mathematical background

and numerical concepts are presented in the chapter three.

Chapter four is about hydraulic modelling of the Idealised City model and its results

including sensitivity analyses. The aim of this part of study is to validate our modelling

software for the next stage which is modelling of the case study.

Modelling a case study is presented in the chapter five. Case study is town Sondrio

located in Northern Italy. Various sensitivity analyses are conducted to have the most reliable

results in terms of flood propagation, water depth and velocity. Results for this part is hazard

maps for the case study.

Chapter six is about flood risk assessment. In this part flood damages for the case study is

evaluated by using hazard maps generated in the previous chapter. Focus of this part is on

damage assessment for buildings using HAZUS-MH model.

Chapter seven addresses our conclusion of this integrated study including modelling

aspects, hydraulic results in the Idealised City model as well as the Sondrio model, and flood

damage assessment of the case study.

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Picture: Flood in Rockhampton, Australia, 2011

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Chapter 2

2. BACKGROUND AND STATE OF THE ART

Introduction 2.1.

The purpose of this chapter is to define the context into which this thesis is framed and

the reasons that motivated this work. A comprehensive state of the art is collected in two

main parts. First, hazard modelling part, introducing hydraulic modelling aspects, software

packages, special aspects in uncertainties of hydraulic modelling and roughness effects.

Second, risk assessment part including European legislation in flood risk, flood and climate,

flood risk assessment uncertainties, and damage assessment models.

Hazard Modelling 2.2.

2.2.1. Modelling Aspects

It is often said that river engineering is an “art” as well as a “science”, and that modelling

should therefore take into account two distinct elements: “theoretical fluid mechanics” and a

multitude of “practical issues”. This is illustrated by following figure, taken from Nakato and

Ettema (1996), in which river engineering is envisaged as the joining together of two river

banks, one named “theoretical fluid mechanics” and the other “practical problems”.

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Figure 2.1: The art and science of river engineering (Knight, 2013)

In dealing with complex technical issues, and particularly when trying to explain an issue

to government officials or politicians, it is a good practice to pose the issue in the form of a

simple question with the key technical issues highlighted immediately afterwards.

According to Knight (2013), there are different questions arising:

Question 1 – What level of modelling is generally required?

There is generally a range of models available. It is essential that the user is able to select

the best model for each application and is aware of the shortcomings and uncertainties of the

chosen method.

Correct model selection and application will pay for itself many times over in terms of

improved accuracy and certainty in the results.

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Question 2 – What are the appropriate calibration parameters for use in 2D and 3D

models?

2D and 3D models can provide much improved flow and level predictions in many cases,

for example on floodplain flows. However, there are issues in model calibration that need

resolving.

The use of 2D and 3D models poses particular difficulties with respect to calibration. Not

only does the level of turbulence closure and the values for many turbulence coefficients have

to be specified, but also the time and effort spent on data handling increases proportionately.

Furthermore, there will often be a lack of any appropriate field data for suitable verification.

Question 3 – What is the role of computer software in learning about river engineering?

Useful in understanding certain issues, either through numerical experiments or through

applying a dedicated model to a case study. Both require a model for repetitive calculations in

order to investigate physical effects, boundary changes or calibration techniques. Helpful in

understanding fluid flow concepts through flow visualization of velocity or turbulence data,

showing videos of laboratory or natural phenomena, and transmitting teaching notes with

embedded pictures, graphs and comments, maybe on some rare and unusual events.

Question 4 – Why are laboratory experiments still needed when computers can do it all?

Laboratory studies sometimes provide the only way of gaining insights into the behavior

of complex flow patterns under controlled conditions, thereby enabling theoretical concepts

to be validated and numerical models to be developed securely.

Laboratory research often provides the primary data on many empirical coefficients used

in turbulence models, without which no closure is possible.

Question 5 – What is wrong with our estimates of flow and level and what will make them

better?

There is high uncertainty in flood levels for extreme flows predicted by models. One

reason for this is that models use simple roughness parameters, often only calibrated for

lower flows.

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There is uncertainty in deriving “design” flood flows in hydrology for a given return

period or frequency, because of poor understanding and extrapolation of stage–discharge

relationships.

Question 6 – What is the role of broad-scale modelling in catchment flood risk mapping?

There is an important role for broad-scale models, making the best use of available

technology, but recognizing the uncertainties associated with their application.

There is a need to integrate broad-scale models of different processes, hydraulic,

hydrological, flood risk, socio-economic and biological, into a system approach.

Question 7 – It looks good, but is it correct?

Outputs from numerical models often look impressive but the user must be able to assess

whether they are correct, preferably by some independent means.

The performance of hydraulic models is very dependent on the quality and quantity of

calibration data, and so there is a need to maximize the use of existing data and to understand

what additional data should be acquired.

Question 8 – Would an intelligent client save money by improving the job specification?

Clients should be aware of the risks and uncertainties associated with different methods

of hydraulic analysis in order to better assess and guide decisions.

Many client representatives have limited knowledge of hydraulics and rely on the

judgement of experts or their consultants.

Question 9 – What is eco-hydraulics, and why is it important?

There is a growing need to link hydraulics with ecosystems to ensure that hydraulically

acceptable solutions are acceptable from an environmental viewpoint.

Question 10 – What will be the problems and novel applications in 10 or 100 years’ time?

Present research must fulfill the requirements of future practitioners. Likely, future needs

must be kept under constant review and R & D programmes developed to match those needs.

It is not always sensible to try and second guess the future.

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2.2.2. Software Packages for Hydraulic Modelling

Knight (2013) notes that, it seems that at many places the idea that 2D must be “better”

than 1D and 3D even “better” than 2D has been extended to the idea that if there are more

computational points in the model then it is “better”. Indeed, to have some several hundred

thousand computational points in a model of a river and its floodplain may be topographically

more accurate (if the topographic representation is available at that small scale), but does not

at all guarantee that computed (approximate) results are nearer to the “true” solution of the

original equations. Even worse, because of such resolution the solution may deviate from the

hypotheses on which the original equations were built.

The hydraulic engineer has to select the right tool, for example, the appropriate 1D, 2D

and 3D model, for any particular job, and this demands considerably more knowledge and

understanding than was required in the past. Today, the questions that are likely to be asked

are: When should one adopt a 2D depth-averaged numerical model to represent the flow

physics, rather than a 1D model?

When one uses a 3D model, what type should it be and what level of turbulence closure is

appropriate? The experience of the modeler in using 2D and 3D models is now also

important, as different answers will be obtained by different users, not only due to subtle

differences in model type and calibration requirements but also according to what type and

version of commercial software is used.

Depth-averaged models are commonly used in practice. However, depth-averaging of

velocities in rivers, especially in sinuous and meandering channels, may lead to false

representation of actual flow patterns. For example, where the velocity vectors vary over the

depth, depth-averaging in a preferred direction will give misleading results, especially so

when used to calculate the discharge. Thus, in some circumstances, a 3D model might be

preferable, and so one has to ask at what stage should a 3D model be considered? The use of

hybrid models, such as a 1D river model with a 2D floodplain model, also raises a number of

technical issues.

It is worth noting at this point that higher dimensionality of a model does not necessarily

lead to better accuracy in the results. In certain cases, the opposite may be true.

Flood modelling methods currently in use can be divided into a number of approaches

presented in Table 2.1, characterized by their dimensionality or the way they combine

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approaches of different dimensionalities. The table provides a summary of the methods and

range of applications for each method.

Table 2.1: Classification of inundation models (Neelz and Pender, 2009)

Method Description Application Typical

computation

times

Outputs Example

Models

1D Solution of the one

dimensional St-

Venant equations.

Design scale modelling which can

be of the order of 10s to 100s of

km depending on catchment size.

Minutes Water depth, cross-section

averaged velocity, and

discharge at each cross

section. Inundation extents if

floodplains are part of 1D

model, or through horizontal

projection of water level.

Mike 11

HEC-RAS

ISIS

InfoWorks RS

1D+ 1D plus a storage

cell approach to the

simulation of

floodplain flow.

Design scale modelling which can

be of the order of 10s to 100s of

km depending on catchment size,

also has the potential for broad

scale application if used with

sparse cross-section data.

Minutes As for 1D models, plus water

levels and inundation extent

in floodplain storage cells.

Mike 11

HEC-RAS

ISIS

InfoWorks RS

2D- 2D minus the law of

conservation of

momentum for the

floodplain flow.

Broad scale modelling and

applications where inertial effects

are not important.

Hours Inundation extent

Water depths

LISFLOOD-FP

JFLOW

2D Solution of the two

dimensional

Shallow Water

Equations.

Design scale modelling of the

order of 10s of km. May have the

potential for use in broad scale

modelling if applied with very

coarse grids.

Hours or

days

Inundation extent

Water depths

Depth-averaged velocities

TUFLOW

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TELEMAC

SOBEK

InfoWorks-2D

2D+ 2D plus a solution

for vertical

velocities using

continuity only.

Predominantly coastal modelling

applications where 3D velocity

profiles are important. Has also

been applied to reach scale river

modelling problems in research

projects.

Days Inundation extent

Water depths

3D velocities

TELEMAC-3D

3D Solution of the three

dimensional

Reynolds averaged

Navier Stokes

equations.

Local predictions of

three-dimensional

velocity fields in main

channels and floodplains

Days Inundation extent

Water depths

3D velocities

CFX

According to Neelz and Pender (2009), three-dimensional methods derived from the 3D

Reynolds-averaged Navier-Stokes equations can be used to predict water levels and 3D

velocity fields in river channels and floodplains. However, significant practical challenges

remain to be overcome before such models can be routinely applied at the scale necessary to

support flood risk management decisions.

Hydrodynamic models based on the two-dimensional shallow water equations are classed

here as 2D approaches. A solution to these equations can be obtained from a variety of

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numerical methods (such as finite difference, finite element or finite volume) and use

different numerical grids (such as structured or unstructured) all of which have advantages

and disadvantages in the context of floodplain modelling. This issue is described in more

details in the next chapter.

One-dimensional models are based on some form of the one-dimensional St-Venant or

shallow water equations, which can be derived by integrating the Navier-Stokes equations

over the cross-sectional surface of the flow. The assumptions used in the derivation of the St-

Venant equations limit their use to where the direction of water movement is aligned to the

center line of the river channel. The technique has at least two disadvantages, namely that 1)

floodplain flow is assumed to be in one direction parallel to the main channel, which is often

not the case, and 2) the cross-sectional averaged velocity predicted by the St-Venant has a

less tangible physical meaning in a situation where large variations in velocity magnitude

exist across the floodplain.

In contrast with the 1D approach, the 1D+ approach involves the 1D approach to model

the main channel flow only. Floodplains are modelled as storage cells that can cover up to

several km2 and are defined only through a water level/volume relationship. The flow

between the 1D channel and these floodplain storage cells is modelled using discharge

relationships (for example based on weir flow equations). However, these models do not

include any momentum conservation on floodplains, meaning that water can be transferred

instantaneously from one end of the storage cell to the other. The 1D+ approach is also

referred to as “pseudo-2D” or “quasi-2D”.

The 2D- models are a class of model that encompasses: 1) 2D models based on a

simplified version of the 2D shallow water equations where some terms are neglected,

resulting in the kinematic and diffusive wave representations (approach used in JFLOW); 2)

models relying on square-grid digital elevation models and a simplified 1D representation of

the flow between the raster DEM cells (LISFLOOD-FP). In effect the latter approach is

similar to that adopted for the 1D+ approach, but usually with a much finer regular

discretization of the physical space. As with the 1D+ approach, momentum is not conserved

for the two-dimensional floodplain simulation in 2D- models.

Almost limitless possibilities exist to combine 1D, 2D and 3D modelling approaches. In

particular, a number of commercial software packages include the possibility to link a 1D

river model to 2D floodplain grids. This has become popular in recent years because it allows

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the modeler to take advantage of the established tradition of 1D river modelling while at the

same time modelling floodplains in two dimensions. This also results in computational

savings over structured fully 2D approaches where a finer grid would be required to correctly

represent the river channel geometry.

Neelz and Pender (2009) also reviewed different 2D hydraulic modelling packages

frequently used in urban flood modelling. According to them application of each modelling

package depends upon:

The physical processes simulated by the model’s mathematical formulation;

The approximate numerical method used to solve the mathematical formulation

within the modelling package;

The representation of the problem geometry on the numerical grid upon which the

numerical method is applied;

The representation of boundary conditions (inflows to and outflows from) to the

modelled domain;

The manner in which the 2D inundation model interfaces with other models of the

flood system, which can include river models and sewer models.

Table 2.2 provides a summary of the software packages included in their review,

according to the column number in the table:

The package name.

An indication of how much physics are modelled, that is, whether the full Shallow

Water Equations (SWE) are used or otherwise.

Some basic information about the numerical scheme.

Whether the code has shock-capturing capabilities.

The name of the developer.

Whether the package is available commercially, is an “internal” proprietary package

or is an academic research code.

Whether the package includes the possibility to link 2D and 1D modelling

approaches.

17

Table 2.2: Software packages for flood inundation modelling (Neelz and Pender, 2009)

Name Physics Further information on

numerical scheme

Shock

capturing

Developer Status Linkages

FINITE DIFFERENCE SCHEMES

TUFLOW SWE Alternating Direct. Implicit No BMT-WBM Commercial Own 1D river and pipes

solver

DIVAST SWE Alternating Direct. Implicit No Cardiff Univ. Research As part of ISIS 2D

DIVAST-TVD SWE Explicit TVD- MacCormack Yes Cardiff Univ. Research

ISIS 2D SWE Alternating Direct. Implicit No Halcrow Commercial Own 1D river solver

MIKE 21 SWE Alternating Direct. Implicit No DHI Commercial As part of MIKE FLOOD

MIKE FLOOD SWE MIKE 21 No DHI Commercial Own 1D river (MIKE 11)

and urban drainage

(MIKE URBAN) solvers

SIPSON/UIM SWE Alternating Direct. Implicit No U. of Exeter Research Own multiple linking

element

SOBEK SWE Implicit - Staggered grid Yes DELTARES Commercial Own 1D river solver,

vertical link

JFLOW Diffusive

wave

Explicit No JBA Internal

FINITE ELEMENT SCHEMES

TELEMAC 2D SWE No EDF Commercial

FINITE VOLUME SCHEMES

TELEMAC 2D SWE Tbc Yes EDF Commercial

MIKE 21 FM SWE Godunov based Yes DHI Commercial As part of MIKE FLOOD

MIKE FLOOD SWE MIKE 21 FM Yes DHI Commercial Own 1D river (MIKE 11)

and urban drainage

(MIKE URBAN) solvers

InfoWorks-RS SWE Roe’s Riemann solver Yes Wallingford

Software

Commercial Own 1D river solver

InfoWorks-CS SWE Roe’s Riemann solver Yes Wallingford

Software

Commercial Own 1D urban drainage

solver

HEMAT SWE Roe’s Riemann solver Yes Iran Wat. Res.

Cent. & Cardiff

Research

BreZo SWE Explicit- R Riemann solver Yes U. of California Research

TRENT SWE Explicit- R Riemann solver Yes Nottingham U. Research

OTHERS

LISFLOOD-FP Norm. Flow

in x and y

dir.

Explicit No U. of Bristol Research

RFSM Gravity only Volume filling algorithm No HR-

Wallingford

Internal Linked to other

components of national

FRA

Flowroute Diffusive

wave

Ambiental Internal No technical information

published.

Grid-2-Grid CEH No technical information

published.

Floodflow Microdrainage No technical information

published.

18

Neelz and Pender (2009) summarized their reviewed study as follows:

1. Where estimates of flood hazard are required, a modelling package based on the

shallow water equations should provide predictions of flood water velocity that are closer to

reality than those obtained from models based on simplified equations.

2. Where one is interested in predicting inundation extent at a broad scale, the

performance of models based on simplified equations should be compared with that of

models based on the shallow water equations applied on a coarse numerical grid.

3. For a range of practical applications, the choice of numerical scheme should be a

secondary consideration to the physical processes included in model equations.

4. The exception to point 3 may be where hydraulic conditions alternate between super

and subcritical flows; such circumstances can occur close to embankment failures, in dam

break flows following reservoir failures and during inundation of urban areas. In such

circumstances the literature suggests that shock capturing schemes will perform better. This

requires to be confirmed.

5. 2D hydraulic modelling packages using a variety of grid methods to represent problem

geometry are available. There is no clear evidence that these different techniques possess any

particular advantage for problems at a practical level, although there may be a preference for

structured grids due to the ease with which data from this configuration can be transferred to

and from GIS software.

6. The capacity to link to 1D modelling packages is essential for many applications as it

ensures best use of available models in terms of both theoretical application and re-use of

existing resources. Literature review has highlighted a number of alternative methods for

linking 1D and 2D models and an evaluation of these is required through a systemic

benchmarking exercise.

19

2.2.3. Validation and Uncertainty in the Modelling

One very simple interpretation of calibration is to adjust a set of parameters associated

with a computational science and engineering code so that the model agreement is maximized

with respect to a set of experimental data. One very simple interpretation of validation is to

quantify our belief in the predictive capability of a computational code through comparison

with a set of experimental data. Uncertainty in both the data and the code are important and

must be mathematically understood to correctly perform both calibration and validation.

Sensitivity analysis, being an important methodology in uncertainty analysis, is thus

important to both calibration and validation (Trucano et al., 2006).

There is a consensus in the scientific community that a proper risk analysis should

provide an indication of uncertainty, emphasizing how the identification of the optimal flood

risk management strategy can be pursued only if all major sources of uncertainty are

adequately taken into consideration and a quantification of their impacts is provided

(USACE, 1992).

The use of flood modelling tools in model-based projects follows a systematic procedure

such as the one shown in the following figure from Parkinson & Mark (2005). It involves the

following steps:

1. Planning and preparation (including an assessment of data requirements);

2. Acquire data, and formulate and build the model;

3. Model calibration and verification;

4. Evaluate the performance of the calibration and verification. If necessary repeat Steps 2

and 3 to improve model accuracy if it is not considered to be satisfactory;

5. Model application and assessment of results.

20

Figure 2.2: Chart explaining the modelling procedure (DHI Water, 2014)

New survey techniques provide a large amount of high-resolution data, which can be

extremely precious for flood inundation modelling. Such data availability raises the issue as

to how to exploit their information content to effectively improve flood risk mapping and

predictions. Dottori et al. (2013) discussed a number of important issues which should be

taken into account in works related to flood modelling. These include the large number of

uncertainty sources in model structure and available data; the difficult evaluation of model

results, due to the scarcity of observed data; computational efficiency; false confidence that

can be given by high-resolution outputs, as accuracy is not necessarily increased by higher

precision.

The effect of uncertain boundary condition was discussed by Domeneghetti et al. (2013).

Their study was focuses on a 50 km reach of River Po (Italy) and three major sources of

uncertainty in hydraulic modelling and flood mapping: uncertainties in (i) upstream and (ii)

downstream boundary conditions, and (iii) uncertainties in dike failures.

21

They analyzed the role of uncertain boundary conditions on flood hazard statements by

means of the Inundation Hazard Assessment Model (IHAM).

IHAM model is a hybrid probabilistic-deterministic model developed for flood hazard

assessment along protected river reaches considering dike failures. The model is comprised

of three main modules: an unsteady one-dimensional hydraulic model (1D model) for river

channel and area between dikes, a probabilistic dike breach model, which evaluates dike

system stability under hydraulic load conditions, and a 2D raster-based diffusive wave model

for the simulation of floodplain flow in the case of dike failures (Figure 2.3).

Figure 2.3: Schematic structure of the IHAM model adopted for flood hazard estimation under uncertainty

conditions (Domeneghetti et al., 2013)

The debate relative to the deterministic and probabilistic approach for flood hazard

estimation is still ongoing in the scientific community (Di Baldassarre, 2012; Di Baldassarre

et al., 2010; Montanari, 2007). Providing flood probability maps for the flood prone areas

appears to be an efficient way to visualize the likelihood of flooding and it also offers

additional information concerning the reliability of its estimation.

The scientific community is well aware of all risks associated with deterministic

statements (i.e. binary, yes or no kind of statements) when the system under study is

uncertain. Nevertheless, the output of numerical simulations as well as hydraulic and

hydrological input data are often used in practice and applied regardless of their uncertainty.

22

Probabilistic inundation maps are still scarcely adopted as additional assets by decision-

makers called to define flood protection strategies. This should mainly be attributed to a lack

of specific guidelines as well as to a limited ability of the scientific community to

communicate the meaningfulness and effectiveness of this kind of spatial representation of

flood hazard (Domeneghetti et al., 2013).

Another study about uncertainty in flood risk was carried out by Apel et al. (2010). In this

research, a dynamic-probabilistic method is proposed, which enables a cumulated flood risk

assessment of a complete river reach considering dike failures at all dike locations. The

model uses simple but computational efficient modules to simulate the complete process

chain of flooding. These modules are embedded into a Monte Carlo framework thus enabling

a risk assessment which is physically based thus mapping the real flooding process, and

which is also probabilistic and not based on scenarios. The model also provides uncertainty

estimates by quantifying various epistemic uncertainty sources of the hazard as well as the

vulnerability part in a second layer of Monte Carlo simulations. These uncertainty estimates

are associated to defined return intervals of the model outputs, i.e., the derived flood

frequencies at the end of the reach and the risk curves for the complete reach, thus providing

valuable information for the interpretation of the results. By separating single uncertainty

sources a comparison of the contribution of different uncertainty sources to the overall

predictive uncertainty in terms of derived flood frequencies and monetary risks could be

performed. This revealed that the major uncertainties are extreme value statistics, the length

of the data series used and the discharge-stage relation used for the transformation of

discharge into water levels in the river.

In their study, two basic kinds of uncertainty that are fundamentally different from each

other were considered: natural and epistemic uncertainty. Natural uncertainty stems from

variability of the underlying stochastic process, whereas epistemic uncertainty results from

incomplete knowledge about the system under study. It is often stated that natural uncertainty

is a property of the system, whereas epistemic uncertainty is a property of the analyst.

Different analysts, with different states of knowledge, different resources for obtaining

data etc., may have different levels of epistemic uncertainty regarding their predictions. The

central issue is that the differentiation in natural and epistemic uncertainty separates

uncertainty which can be reduced (epistemic uncertainty) and uncertainty which is not

reducible (natural uncertainty).

23

The input, i.e., the upstream boundary of the system is defined by a flood peak value, and

a typical normalized flood hydrograph, which is scaled to the flood peak. The attenuation and

translation of flood waves in the river reach was investigated by 1D hydrodynamic

simulations (HEC-RAS). 2D inundation simulations were performed every flow km to both

sides of the river. For these simulations a constant breach width of 100 m and a constant

outflow with water levels at the dike crest was assumed. The outflow through the breach was

calculated by a standard formula for broad crested weirs. The mean breach width of 70.3 m

was used for the risk assessment, whereas for the uncertainty assessment the standard

deviation of 31.5 m was additionally taken into account. Within the Monte Carlo framework

105 model runs were performed, i.e., 105 synthetic flood events were created for the reach.

The final aim of this study is an estimate of the predictive uncertainty of the model, which

includes data (DU), parameter (PU) and model (MU) uncertainties. According to Merz and

Thieken (2005) the different uncertainty sources considered for the predictive uncertainty

assessment can be categorized as epistemic. All three different types of uncertainty are

treated simultaneously and equally weighed for the assessment of the predictive uncertainty.

Table 2.3 lists the uncertainty sources considered along with a categorisation and short

description of the quantification.

Table 2.3: Uncertainty sources considered in the modelling system (Apel et al., 2010)

Hazard Risk assessment

Uncertainty

source Discharge

series (DU) Extreme value

statistics (MU, PU) Q-H-

relation

(PU)

Dike breach width

(MU, PU, DU) Inundation

depths

(DU)

Damage

estimation

(MU) Quantification two discharge

series of

different

length

weighed combined

variance of

quantile

estimators

variance

of

regression

parameters

statistically by

normal

distribution

with upper and

lower bounds

variance of

interpolated

inundation

depths

set of 3

different

damage

models

(DU = data uncertainty; PU = parameter uncertainty; MU = model uncertainty.)

24

2.2.4. Application of 2D Numerical Modelling

Dottori et al. (2014) studied a flash flood scenarios in urbanized catchments using 2D

hydraulic models. The assessment of flash flood hazard requires new modelling tools that can

reproduce both the rainfall-runoff processes in the catchment, and the flow processes in the

drainage network. In their paper they proposed the use of a simple two-dimensional hydraulic

model for analyzing a flood scenario in a small valley within the urban area of the city of

Bologna, Italy. The two-dimensional hydraulic model was therefore applied at catchment

scale, in order to simulate the possible effects of historical scenarios in the present catchment

configuration. Rainfall and runoff data measured during recent rainfall events were used to

calibrate model parameters.

They applied a simple two-dimensional hydraulic model, called CA2D (Dottori and

Todini, 2011), which has already been successfully applied for reproducing flow in urban

areas and over steep slopes (Dottori and Todini, 2013), and for simulating rainfall-runoff at

catchment scale.

For the application of the CA2D (acronym for “Cellular Automata Two-Dimensional”)

model, a digital elevation model (DEM) of the study area, at 2 m resolution, is used. The

DEM includes all the buildings located in the study area, which are represented as blocks

using roof-top height. To obtain the model computational grid, the original DEM was

resampled to a 4 m resolution, in order to provide acceptable model run times while

accurately reproducing the stream bed and the urban topography.

The maps in following figure show the flood extension computed by their model in the

urbanized portion of the catchment at different times.

25

Figure 2.4: Flood extent (dark grey) in the lower part of the catchment at time t = 30 minutes (left), t = 90

minutes (centre), t =150 minutes (right) (Dottori et al., 2014)

Sameer and Dilnesaw (2013) presented their study in flood modelling with 2D approach

for Toronto, Canada urban area. According to them, key components to developing flood

lines are:

1. Hydrology Modelling

2. Hydraulic Modelling

3. Flood Plain Mapping

Hydrology modelling identifies how much water flows down the river during various

storm events. Hydraulic modelling calculate water surface elevations to define flood plain

extents and velocities. In this part mostly 1D flows are contained within a defined valley and

flow in a longitudinal direction. In urban situations where flows are not contained and spill

(water moves in a longitudinal and lateral direction), 2D modelling is necessary. Three

different software were used in their study:

HEC-RAS

Delft3D

Mike Flood (Mike 11 & 21)

26

1D modelling solves energy. Its assumptions are: flow is parallel to main channels

(Unidirectional flow); constant water surface elevation on a given cross section. These

models are suitable for:

Confined flow and mostly unidirectional;

When no need of detailed velocities;

With many complex structures.

Advantages of 1D modelling are:

Accurate hydraulic description in rivers with 1D flow;

Less computational points relative to 2D model, i.e. less computational time;

Easy to analyze and extract results;

Hydraulic structures well represented.

Disadvantages of 1D modelling are:

Flow paths must be known beforehand;

No detailed flow descriptions in floodplains.

2D modelling solves mass and momentum. 2D models make no implicit assumptions

about flow direction or magnitude, discharge divisions in splitting channels, and the

discharge given inflow and outflow elevations can be calculated directly. These models are

suitable for:

Flow paths are not well defined or difficulty of visualizing the flow patterns;

Complex channel-floodplain interaction;

Threaded rivers and poorly confined flow;

Flood hazard, when detailed velocity and depth patterns are important;

Complicated nature of overflow along streets and between development;

Flow attenuation and floodplain storage are significant.

Advantages of 2D modelling are:

Realistic computation of velocities in any direction and determining watershed

sheet flow patterns, flow depth hazard to people;

Accounts for lateral variation in water surface elevations;

Better schematization of distributed flow in threaded rivers or unconfined flows;

27

Relatively easy to schematize model (i.e. can be quick to set up);

Beneficial to model impacts of obstructive fill.

Disadvantages of 2D modelling are:

Costly in computational time;

Requires fine grid in rivers/channels in order define conveyance accurately;

2D model results are limited by the accuracy of input data;

Resolution effects may be a problem.

Sameer and Dilnesaw (2013) believe coupling two types of models helps to take

advantage of the benefits from both 1D and 2D.

Figure 2.5: Depiction of a general 1D model of the river channel coupled with a 2D model of the floodplain

Figure 2.6: Mesh generation (left), water depth (right) by Mike 21 (Sameer and Dilnesaw, 2013)

28

2.2.5. Roughness Effects

Another critical issue in two-dimensional hydraulic modelling is to select a proper value

of roughness for the model. In general, there are three strategies for defining buildings:

a) Buildings as impervious blocks (blocked out);

b) Buildings as ground elevation;

c) Friction tuning.

These three strategies are depicted in Figure 2.7.

(a)

(b)

(c)

Figure 2.7: Three ways to define building roughness in 2D models (Alcrudo, 2002)

29

Shepherd et al. (2011) presented their research result about the effect of buildings and

surface roughness on 2D flood modelling. A 1D-2D model was produced using InfoWorks

CS, and an investigation of the sensitivity of the 2D surface model was carried out.

Surface roughness has been assessed by varying Manning’s n from 0.017 𝑆

𝑚13

, which

represents asphalt in reasonable condition, to 0.035 𝑆

𝑚13

, which represents coarse gravel or

pasture. This seems a realistic range of roughnesses for an urban center, although it would be

possible to find lower roughnesses where smooth concrete is used, or higher roughnesses for

longer grass or areas with significant degrees of planting.

Two methods of modelling buildings have been considered; firstly as voids in the mesh

(blocked out), which forces flow around the buildings, and secondly as porous polygons

raised by 0.3 m (ground elevation), to take account of an average building threshold, which

allows some flow into buildings. Finally, the combined effect of modelling buildings and

roads has been compared to the basic bare earth model.

Increasing the Manning coefficient from 0.017 to 0.035 showed that the maximum flood

depth is increased, as might be expected. The effect on the flooding extent was small and run

time differences between the two roughness simulations were negligible. When buildings

were modelled as porous polygons the flood extent within the buildings tends to reduce.

In addition, Manning’s n values according to Chow (1959) are in the table below.

Table 2.4: Manning’s n values according to Chow (1959)

Type Manning’s n value

Building 0.4

Forest 0.15

Shrub 0.1

River 0.05

Road 0.016

Crop/grass 0.035

No data 0.03

Ozdemir et al. (2013) carried out a research for evaluating scale and roughness effects in

urban flood modelling using terrestrial LiDAR data. They used LISFLOOD-FP hydraulic

model, using different high resolution terrestrial LiDAR data (10 cm, 50 cm and 1 m) and

roughness conditions (distributed and composite) in an urban area.

30

In densely urbanized areas where relatively smooth surfaces are found, the simulation of

surface water floods using a very fine resolution DEM (below 1 m) and very low friction

values (below Manning’s n = 0.020) may also cause numerical instabilities to arise in shallow

water models as these strictly only apply to slopes with gradients <10 %. They applied to the

models two types of friction coefficient, namely distributed Manning’s n and a single

composite friction coefficient for the entire domain (Figure 2.8).

In their study, Manning’s n values taken from Chow (1959) table were assigned to every

type of land use and then converted to 10 cm, 50 cm and 1 m raster data using the cell

centered method. As shown in Figure 2.8, Manning’s n values of 0.013, 0.015, 0.025 and

0.035 were assigned to asphalt road, brick, gravel and short grass surfaces respectively.

The second type of friction parameterization is a uniform composite, assigned to the

whole domain, for which the value of n = 0.013 was chosen because it represents the smooth

and impervious road surfaces that typically underlie flow paths taken by surface flood water

in urban areas.

Figure 2.8: Land use classification and Manning’s n value distribution, left: Google satellite image, middle:

distributed Manning’s n value, right: single composite friction value (Ozdemir et al., 2013)

In some other previous studies (Fewtrell et al., 2011; Sampson et al., 2012), a single fixed

composite friction coefficient has been used (n = 0.035). Small instabilities and increased

errors on predicted depth were noted by Bates et al. (2010) under low friction conditions (n <

0.03) that may be typical of skin frictions in urban areas. Fewtrell et al. (2011) tested

diffusive and inertial equations using terrestrial LiDAR data and a high single composite

friction value (n = 0.035) in urban areas.

31

State of the Art on Flood Risk Analysis 2.3.

2.3.1. European Flood Directive on the Assessment and Management of Flood Risks

According to European Flood Directive, floods have the potential to cause fatalities,

displacement of people and damage to the environment, to severely compromise economic

development and to undermine the economic activities of the community.

Floods are natural phenomena which can not be prevented. However, some human

activities (such as increasing human settlements and economic assets in floodplains and the

reduction of the natural water retention by land use) and climate change contribute to an

increase in the likelihood and adverse impacts of flood events.

It is feasible and desirable to reduce the risk of adverse consequences, especially for

human health and life, the environment, cultural heritage, economic activity and

infrastructure associated with floods. However, measures to reduce these risks should, as far

as possible, be coordinated throughout a river basin if they are to be effective.

The European Flood Directive has defined different types of flood: River floods, flash

floods, urban floods and floods from the sea in coastal areas.

In order to have an available and effective tool for information, as well as a valuable basis

for priority setting and further technical, financial and political decisions regarding flood risk

management, it is necessary to provide for the establishing of flood hazard maps and flood

risk maps showing the potential adverse consequences associated with different flood

scenarios, including information on potential sources of environmental pollution as a

consequence of floods. Following studies must be conducted:

Preliminary Flood Risk Assessment:

Based on available or readily derivable information, such as records and studies on long

term developments, in particular impacts of climate change on the occurrence of floods, a

preliminary flood risk assessment shall be undertaken to provide an assessment of potential

risks.

Flood Hazard Maps:

Flood hazard maps shall cover the geographical areas which could be flooded according

to the following scenarios:

32

(a) floods with a low probability, or extreme event scenarios;

(b) floods with a medium probability (likely return period ≥ 100 years);

(c) floods with a high probability, where appropriate.

For each scenario the following elements shall be shown:

(a) the flood extent;

(b) water depths or water level, as appropriate;

(c) where appropriate, the flow velocity or the relevant water flow.

Flood Risk Maps:

Flood risk maps shall show the potential adverse consequences associated with flood

scenarios in terms of the following:

(a) the indicative number of inhabitants potentially affected;

(b) type of economic activity of the area potentially affected;

(c) installations concerning integrated pollution prevention and control, which might

cause accidental pollution in case of flooding and potentially affected protected areas

(d) other information considers useful such as the indication of areas where floods with a

high content of transported sediments and debris floods can occur and information on other

significant sources of pollution.

Flood Risk Management Plans:

Flood risk management plans shall take into account relevant aspects such as costs and

benefits, flood extent and flood conveyance routes and areas which have the potential to

retain flood water, such as natural floodplains, the environmental objectives, soil and water

management, spatial planning, land use, nature conservation, navigation and port

infrastructure.

Flood risk management plans shall address all aspects of flood risk management focusing

on prevention, protection, preparedness, including flood forecasts and early warning systems

and taking into account the characteristics of the particular river basin or sub-basin.

33

Flood risk management plans may also include the promotion of sustainable land use

practices, improvement of water retention as well as the controlled flooding of certain areas

in the case of a flood event.

2.3.2. Floods and Climate

It is taken for granted that changes in climate or human interventions in catchments and

river systems may change flood hazard and, as a consequence, flood risk. Within this view,

floods are evaluated from a hazard perspective, focusing on hydrologic/hydraulic parameters

such as discharge, water level or inundation extent. Societal processes are often neglected,

which implicitly means they are assumed to be constant or, if random, a stationary process.

However, some socio-economic processes, like population growth and economic

development, may change at a faster pace than long-term physical changes (for example, the

impacts of climate change on discharge), and exposure and vulnerability to floods can be

highly dynamic. Against this background, societal processes need to be addressed within a

risk-based approach, where next to the hazard, societal exposure and vulnerability play a

decisive role. A particularly interesting question is how space–time variations in flood hazard

that may be related to climate variability and change intersect with the changing nature of the

flood exposure and vulnerability.

Merz et al. (2014) emphasize that the emerging view of climate–flood linkages is process

driven and seeks to understand and analyses flood events in the context of their long-term

history of variation – in magnitude, frequency, and seasonality – and within the climatic

framework of the global and regional atmospheric circulation patterns and processes that

drive changing combinations of meteorological elements at the catchment scale.

Table 2.5 contrasts the traditional narrow framing of floods with the broader perspective

that is emerging from an improved understanding of the climatic context of flood generation.

34

Table 2.5: Contrasting traditional views with emerging perspectives on flood hazard and risk (adapted from

Merz et al. 2014)

Aspect Traditional view Emerging Perspective

Understanding climate–flood linkages

Randomness Random: floods are random

events with flood magnitude

quantified by a probability

distribution.

Causal: flood occurrence and magnitude depend on a causal

network of processes in atmosphere, catchment and river

systems. A fraction of the flood variability is described by

deterministic processes: for example, by using climate

information as co-variates in flood probability distributions.

Spatial perspective Local: floods are events that

can be described fully by

processes on a catchment

scale.

Global: floods occur within the spatial framework of large-

scale circulation. Patterns and global climate mechanisms.

Natural variability

and floods

Stationary: flood

characteristics are

stationary and represent the

long-term natural variability

of the climate–catchment

system

Time-varying: flood characteristics change in time due to

climate variability at different timescales.

Temporal

perspective

Recent: flood characteristics

result from current catchment

characteristics and are

derived from recent

observations.

Long-term: flood characteristics result from the long-term

interplay of climate, geology, topography, vegetation

(biology), and humans. To fully understand floods,

this long-term interplay has to be disentangled

Randomness or causality?

Floods are typically seen as events that are generated by the random superposition of

processes in the atmosphere, catchment and river system. The idea of very strong or even

complete randomness prevails in the history of flood prediction.

Much effort has been spent on describing flood occurrence and magnitude by probability

distributions, a large share of the flood research has been focused on statistical aspects, and

the role of randomness has been emphasized. This avenue has been shaped by the pioneers of

flood frequency analysis; for example, in 1941 Emil Julius Gumbel mentioned the flood

estimation problem: “The author believes it is possible to give exact solutions, exactitude

being interpreted from the standpoint of the calculus of probabilities.” (Gumbel, 1941).

Local or global?

Frequently, floods have been understood as local phenomena, driven by the perspective of

flood management at the local level, e.g. at the municipal or county scale. Within the last two

decades there have been many attempts to reconcile the spatial frame of this societal lens

with the traditional hydrological view. Here, floods are considered through the local

35

catchment lens, and are shaped by catchment meteorology, hydrology and river processes.

The emerging view extends this spatial framework to the continental and global scale to

accommodate the interactions between local flooding and global climate mechanisms.

Stationary or time-varying random variables?

Traditional flood frequency analysis assumes stationarity. This assumption implies that

flood characteristics fluctuate around a constant value. It is assumed that the flood generating

processes remain constant in time, and that flood probability represents the long-term natural

variability of the climate–catchment system. Changes in flood characteristics are expected to

result from anthropogenic interventions in this system, such as human-induced climate

change, land-use change.

Recent or long term?

Traditionally, understanding of flood characteristics and flood frequency analysis have

been focused on data from the most recent decades, based on the idea that flood

characteristics result from current catchment characteristics. From a long-term perspective, it

must be recognized that flood characteristics are the result of an interplay of climate, geology,

topography, vegetation (biology) and humans.

Benefit of climate–flood linkages for flood risk management:

Merz et al. (2014) describes the benefit of an improved understanding of climate– flood

linkages for flood risk management. In the last two decades, flood change research has been

dominated by studies looking at changes in flood hazard, for instance due to human-induced

climate change (Feyen et al., 2012; Ott et al., 2013; Ward et al., 2014), land-use change or

river training (Bronstert et al., 2007). Today it is recognized that all risk elements are

dynamic through time, not only hazard (IPCC, 2012; Jongman et al., 2012). Bubeck et al.

(2012) show that societal responses are critical in understanding how vulnerability to floods

changes over time. This study surveyed 752 households along the Rhine in Germany that

experienced floods, with two major floods in 1993 and 1995. The results indicate that flood

damage mitigation measures were implemented by households gradually over time, with

major flood events being important triggers for accelerated implementation. Especially in the

aftermath of the severe flood in 1993, a remarkable increase in the number of measures

undertaken was observed.

36

Kuhlicke et al. (2011) analyze the social vulnerability of households to floods for three

European case studies. Using the definition of Blaikie et al. (1994), who understand

vulnerability as “the characteristics of a person or group in terms of their capacity to

anticipate, cope with, resist, and recover from the impact of a natural hazard”, they find that

social vulnerability to floods is not a static characteristic. It is highly dynamic and may

change even in the course of one single flood event. A household may be vulnerable in

certain event phases – anticipation, resistance and coping, recovery and reconstruction – and

not vulnerable in others.

Further, a single driver may influence different risk components. For example, the

societal perception of flood risk may be strongly influenced by a damaging flood, which may

trigger investments in structural flood defence, such as flood retention basins, and may

change flood hazard. In parallel, it may change exposure by flood-affected companies and

private households migrating out of heavily flooded areas, and vulnerability by triggering

private precaution in the flooded areas (Petrow et al., 2006; Kreibich et al., 2011).

In addition, spatio-temporal interdependencies between vulnerability, exposure and

hazard have to be expected. Current risk assessments, if they include dynamics at all, often

examine dynamics in one of the components, whereas the interdependencies could be crucial

(Di Baldassarre et al., 2013). For example, flood protection by dikes aimed at reducing the

flood hazard can lead to increased development behind dikes, thus increasing exposure, the

so-called levee effect (Tobin, 1995). In areas with high protection standards by dikes,

individuals and societies may have low risk perceptions, and thus be less prepared for floods;

in other words, they may have high vulnerability (Bubeck et al., 2012; Zaalberg and Midden,

2013).

Figure 2.9 illustrates the concept of dynamic flood risk and dynamic risk management,

based on the climate-informed risk management approach of Pizarro et al. (2009).

Since all components of risk vary in time, flood risk itself is dynamic. Some aspects of

flood risk dynamics may be predictable, many others not.

The predictability of the climate–flood link would allow for the portfolio of risk reduction

measures to be optimized. On the other hand, many future flood risk changes are expected to

be severe but are not predictable. In such cases robustness is an important criterion for

designing risk management strategies. Robustness describes how well a measure performs

37

under different possible but initially uncertain future developments. Flood-proofing strategies

– such as elevated configuration of buildings, sealing of buildings to prevent water entrance,

or the use of building materials in such a way that the impact of inundation is minimized –

are robust in the sense that these measures will lower the damage in the case of flooding,

regardless of the exact future development of the flood hazard (Merz et al., 2010). Another

example is the enhancement of risk awareness and self-protecting behavior of people at risk.

If residents are aware of their flood risk and of their possibilities to undertake effective

precautionary, adverse flood impacts will be reduced under different possible but initially

uncertain future developments. Risk reduction measures that are designed to be robust differ

from measures that are the result of an optimization for most likely future development. They

represent trade-offs and are associated with real or opportunity costs (Heltbert et al., 2009).

Hence, the degree of predictability of future changes in flood hazard and risk influences the

role that different criteria play in designing risk management measures (Blöschl et al., 2013).

Figure 2.9: Drivers of flood risk change, dynamic risk and dynamic risk management (Merz et al., 2014)

38

2.3.3. Fundamental of Flood Risk Analyses

Risk-oriented methods and risk analyses are gaining more and more attention in the fields

of flood design and flood risk management since they allow us to evaluate the cost

effectiveness of mitigation measures and thus to optimize investments (Resendiz- Carrillo

and Lave, 1990; USACE, 1996; Olsen et al., 1998; Al-Futaisi and Stedinger, 1999; Ganoulis,

2003; Hardmeyer and Spencer, 2007). Moreover, risk analyses quantify the risks and thus

enable (re-) insurance companies, municipalities and residents to prepare for disasters

(Takeuchi, 2001; Merz and Thieken, 2004).

The most common approach to define flood risk is the definition of risk as the product of

hazard, i.e. the physical and statistical aspects of the actual flooding (e.g. return period of the

flood, extent and depth of inundation), and the vulnerability, i.e. the exposure of people and

assets to floods and the susceptibility of the elements at risk to suffer from flood damage

(Mileti, 1999; Merz and Thieken, 2004). This definition is adopted in the European Flood

Directive (2007). Following this definition, meteorological, hydrological and hydraulic

investigations to define the hazard and the estimation of flood impact to define vulnerability

can be undertaken separately in the first place, but have to be combined for the final risk

analysis.

Clearly, risk quantification depends on spatial specifications (e.g. area of interest, spatial

resolution of data) and relies on an appropriate scale of the flood hazard and land-use maps.

For instance, for planning and cost-benefit analysis of flood-mitigation measures and for the

preparedness and mitigation strategies of different stakeholders (communities, companies,

house owners, etc.), very detailed spatial information on flood risk is necessary. For both the

hazard and vulnerability analyses a number of approaches and models of different complexity

levels are available, and many of them were used in scientific as well as applied flood risk

analyses and on different scales.

Hazard Analyses:

A flood is a general and temporary condition of partial or complete inundation of

normally dry land areas. Hazard analyses give an estimation of the extent and intensity of

flood scenarios and associate an exceedance probability to it (Merz and Thieken, 2004).

Flood hazard statements do not convey information about the consequences of such

events on society, built environment or natural environment. Since these consequences

39

depend, among others, on the intensity of the flood, hazard statements should extend beyond

flood frequency curves, i.e. they should provide information about flood intensity, such as

inundation depth or flow velocity which are usually associated with the selection of the

appropriate hydraulic model, as well as consideration of calibration and validation of the

models. Depending on the scale of the hazard or risk analysis, the complexity of models

applied range from simple interpolation methods to sophisticated and spatially detailed

models solving the shallow water equations in two dimensions. However, the correctness of

the models can usually be only qualitatively evaluated, because sufficient data on inundation

extent and depths for the calibration and validation of the models are lacking (Apel et al.,

2008).

Vulnerability analyses:

Vulnerability analyses are normally restricted to the estimation of detrimental effects

caused by the flood water like fatalities, business interruption or financial/economic losses.

Frequently, vulnerability analyses focus only on direct flood loss which is estimated by

damage or loss functions. One feature most flood loss models have in common is that the

direct monetary flood loss is a function of the type or use of the building and the inundation

depth (Smith, 1981; Krzysztofowicz and Davis, 1983; Wind et al., 1999; NRC, 2000; Green,

2003). Such depth-damage functions are seen as the essential building blocks upon which

flood loss analyses are based, and they are internationally accepted as the standard approach

to assessing urban flood loss (Smith, 1994).

Usually, building-specific damage functions are developed by collecting flood loss data in

the aftermath of a flood. Another data source is ‘‘what-if analyses’’ (ex-ante analysis), by

which the damage which is expected in case of a certain flood situation is estimated, e.g.

‘‘What damage would you expect if the water depth was 2 m above the building floor?’’. On

the basis of such actual and synthetic data, generalized relationships between damage and

flood characteristics have been derived for different regions (Green, 2003; Penning-Rowsell

et al., 2005; Scawthorn et al., 2006).

Recent studies have shown that estimations based on stage-damage functions may have a

large uncertainty since water depth and building use only explain a part of the data variance

(Merz et al., 2004). It is obvious that flood loss depends, in addition to building type and

water depth, on many factors, e.g. flow velocity, duration of inundation, availability and

40

information content of flood warning, precaution and the quality of external response in a

flood situation (Smith, 1994; Wind et al., 1999; Penning-Rowsell and Green, 2000; ICPR,

2001; Kelman and Spence, 2004; Kreibich et al., 2005). Some flood loss models include

parameters like flood duration, contamination, early warning or precautionary measures

(Penning-Rowsell et al. 2005; Buchele et al., 2006; Thieken et al., 2006). While the outcome

of most of the functions is the absolute monetary loss of a building, some approaches provide

relative loss functions, i.e. the loss is given in percentage of the building or content value

(Dutta et al. 2003; Thieken et al., 2006) or as index values, e.g. loss may be expressed as an

equivalent to the number of median-sized family houses totally destroyed. If these functions

are used to estimate the loss due to a given flood scenario, property values have to be

predetermined.

As outlined by Messner and Meyer (2005), flood loss estimation can be performed on

different scales: In small investigation areas with detailed information about type and use of

single buildings, micro-scale analyses can be undertaken. Here, flood loss is evaluated on an

object level, e.g. at single buildings. For bigger areas, a meso-scale approach is advantageous.

These approaches are based on aggregated land cover categories, which are connected to

particular economic sectors. Loss is then estimated by aggregated sectoral models.

Validation and Data Requirement:

Despite the large number of flood risk analyses, there is still no study present that

investigates the performance of different approaches and models compared to an actual flood

event. The reason for this is the scarcity of valuable calibration and validation data, for both

hazard and vulnerability models. For a thorough calibration and validation of any flood risk

analysis, numerous data sets are necessary. For the hazard side, which is usually covered by a

hydraulic model, this would ideally be:

• up- and downstream flow hydrographs;

• mapped inundation extents;

• recorded inundation depths, especially in urban areas;

• flow velocities in case of rivers with high flow velocities.

41

For the vulnerability side, the data demands depend on the type of flood loss considered

and the chosen modelling approach. Flood loss estimation is restricted to direct monetary

damage at residential buildings. Basically the following data sets are required:

• hazard data of the event: inundation extent and depths;

• exposure data: building inventory, especially the location of buildings;

• susceptibility data: building characteristics, and further data sets depending on the flood

loss model.

Comprehensive calibration and validation data sets like these are hardly available.

Damage data are rarely gathered, (initial) repair cost estimates are uncertain and data are not

updated systematically (Downton and Pielke, 2005), let alone the problem of obtaining

quality elevation and river morphology data.

2.3.4. Applications of Flood Damage Assessment

According to Merz et al. (2010), Flood damage assessments are gaining more importance

within this evolving context of decision-making in flood risk management. Flood Damage

Assessment is for:

– Assessment of flood vulnerability: elements at risk in flood-prone areas, e.g. households

or communities, are variably vulnerable to floods. For instance, communities which

experience floods on a more or less regular basis develop strategies for coping with such

events. Communities which are not “flood experienced” often neglect risk mitigation and,

hence, develop a higher vulnerability (Thieken et al., 2007; Kreibich and Thieken, 2009).

Knowledge about vulnerability of elements at risk is necessary for identifying appropriate

risk reduction measures, e.g. development of emergency plans and the undertaking of

emergency exercises.

– Flood risk mapping: flood risk mapping is an essential element of flood risk

management and risk communication. In many countries risk mapping is regulated by law.

The Flood Directive of the European Union, enacted in November 2007, requires member

states to create both flood hazard and flood risk maps. Although flood mapping is frequently

limited to mapping the flood hazard, there is a lively discussion on flood risk mapping,

42

including the potentially adverse effects on asset values, people and the environment (de

Moel et al., 2009).

– Optimal decisions on flood mitigation measures: safety against floods requires

resources. It should therefore be secured that these resources are well used economically.

This implies that the current flood risk has to be estimated, the potential risk reduction

options have to be determined, and benefits and costs of different options have to be

quantified and compared. For these steps towards cost-effective risk management, damage

assessments are an essential ingredient.

– Comparative risk analysis: in a wider context, flood risk reduction competes with other

policy fields dealing with risk reduction. For example, a municipality may be prone to

different types of natural hazards. A quantitative comparison of different risks within a

community or a region, e.g. risks due to flooding, windstorms and earthquakes, can be done

on the basis of consistent damage and risk estimates (Grunthal et al., 2006). On a wider

perspective, the allocation of resources devoted for safety against floods can be evaluated in

terms of the social willingness-to-pay (Pandey and Nathwani, 2004).

– Financial appraisals for the (re-)insurance sector: to calculate insurance premiums and

to guarantee solvency, expected economic damages and the Probable Maximum Loss (PML)

of the portfolios of insurers and re-insurers have to be estimated. The terms loss and damages

are often used interchangeably in the risk management of insurers. Acknowledging the

differences between economic as well as physical loss and damage – for example, a damaged

good is not necessary lost – we will restrict our usage of the term loss to either insurance

contexts or to losses in substance such as loss of life or loss of production.

– Financial appraisals during and immediately after floods: in the case of a flood event,

disaster management and governments need assessments of the flood damage, in order to

budget and co-ordinate decisions about damage compensation.

2.3.5. Fundamental of Flood Damage

Types of flood damages:

Types of damage are typically differentiated into direct and indirect damages, which may

be tangible or intangible (e.g. Parker et al., 1987; Messner et al., 2007; Meyer et al., 2012).

43

Direct damage is caused directly by the physical processes of the hazard (e.g. damages of

structures and inventories); while indirect ones are caused by the impact of the first category

(e.g. costs occurring at a longer period of time or a larger spatial scale to the disaster itself).

They can occur inside or outside of the hazard area and often with a time lag. The difference

between tangible and intangible damages is that the first can be valuated from a financial

point of view (all marketable goods and services), whereas the second cannot be assessed

from a monetary point of view, e.g. loss of life, damage to ecosystems (Andre et al., 2013;

Jongman et al., 2012). Direct and indirect damages can be subdivided into primary and

secondary categories.

It is worth mentioning that most studies are focused on direct-tangible damages and the

assessment of indirect and intangible losses, while very important, remains methodologically

difficult and because of this reason the application of damage assessments in practice is often

incomplete and biased. Furthermore, all parts of damage assessment entail considerable

uncertainties due to insufficient or highly aggregated data sources, along with a lack of

knowledge about the processes leading to damage (Elmer et al., 2010; Meyer et al., 2012).

While much effort is done to improve the hazard estimation leading to more accurate and

more reliable models, the estimation of flood damage is still crude and affected by large

uncertainties (Merz et al., 2004; Egorova et al., 2008; Freni et al., 2010; de Moel et al., 2011;

Meyer et al., 2013).

Spatial and Temporal Scales:

Flood damage assessments are performed on different spatial scales:

Micro-scale: the assessment is based on single elements at risk. For instance, in order to

estimate the damage to a community in case of a certain flood scenario, damages are

calculated for each affected object (building, infrastructure object, etc.).

Meso-scale: the assessment is based on spatial aggregations. Typical aggregation units are

land use units, e.g. residential areas, or administrative units, e.g. zip code areas. Their size is

in the order of magnitude of 1 ha to 1 km2 (Preference of reinsurance companies).

Macro-scale: large-scale spatial units are the basis for damage estimation. Typically,

administrative units are used, e.g. municipalities, regions, countries.

44

The classification in micro-, meso- and macro-scale is, on the one hand, related to the

spatial extent of the damage assessment. On the other hand, there is a methodological

distinction: Meso- and macro-scale approaches differ from micro-scale approaches in their

need for aggregation. Damages are assessed for aggregations of objects, e.g. land use units. In

order to compare different-scale methods, upscaling and downscaling procedures for the

different steps of damage assessment are necessary.

The results of a damage assessment depend on the spatial and temporal boundaries of the

study. For example, a flood might devastate a community. At the same time, nearby

communities might experience economic benefits, since the flood might trigger business and

orders that cannot be performed by the flood-affected companies.

Similar considerations hold concerning the temporal scale. Flood can cause long-term

consequences, such as health effects, which are not captured if a too short time horizon of the

damage assessment is chosen. The classification in micro-, meso- and macro-scale level has

no clear-cut boundaries, and different analysts may set the boundaries in a different way

(Merz et al., 2010).

Depreciated Values and Replacement Costs:

Depreciated values of durable consumer goods reflect the value of a good at the time

when the flood damage actually occurs, whereas replacement values usually involve some

form of improvement: “Old goods which are damaged during a flood are substituted by new,

more productive or better performing ones” (Penning-Rowsell et al., 2003). Using

replacement values overestimates the damage. Moreover it is not in line with the national

accounting where capital goods are depreciated based on a perpetual inventory of incoming

and outgoing capital goods. The evaluation of flood damages at full replacement costs would

systematically result in “values at risk” which are higher than the ones depicted in the

national accounts. Therefore, the basic rule for public policy appraisal is: use depreciated

values, not full replacement costs. Occasionally, the replacement of goods by improved new

ones can be cheaper than the repair of the goods in its original condition at the time when the

flooding occurred. This is often the case with consumer durables that recently went out of

production (e.g., single glass windows). For these types of goods replacement values should

be used in economic evaluation if they undercut the costs of repair or monetary compensation

at the depreciated original value (Merz et al., 2010).

45

2.3.6. Damage Functions

Ex-post and ex-ante, relative and absolute:

There are two general approaches for economic damage assessment as ex-post and ex-

ante. Ex-post assessments are carried out in the aftermath of the disaster for emergency

management or the coordination of early recovery issues, or later, for feedback on experience

concerning damage processes and costs. Also, it will be used to inform local or national

governments of the overall amount of induced damage and to provide a basis for calculating

levels of compensation and recovery support (McCarty and Smith, 2005; Karunasena and

Rameezdeen, 2010).

Ex-ante assessments, i.e. prior-event, aim to evaluate potential economic losses for

scenarios having probable hazard characteristics. Ex-ante assessment models are generally

calibrated with damage data from ex-post assessments. However, most economic analysis

guidelines mainly address ex-ante assessments, since ex-post assessments are not as well

developed. For ex-ante damage assessment purposes, a standard approach calls on damage

functions, also referred to as stage-damage curves or fragility curves (Messner et al., 2007).

These functions define the causal relationship between the intensity of hazard parameters

and a level of damage or loss for each class of assets and they can be expressed in terms of

absolute values of estimated costs or in relative damage in order to support governmental

decision making relating to alternative risk mitigation options (Jongman et al., 2012; Molinari

et al., 2014 a; Hasanzadeh, 2013). Table 2.6 compares the advantages and disadvantages of

relative and absolute damage functions.

46

Table 2.6: Advantages and disadvantages of relative and absolute damage functions (Merz et al., 2010)

Advantage Disadvantage

Relative

damage

functions

Simplicity, because many data sources on the value of

properties are available (Messner et al., 2007).

Better transferability in space and time, since they are

independent of changes in market values of individual

structures which may result from inflation, shifts in local

economy or development status (Krzysztofowicz and

Davis, 1983).

Applicable for different purposes (cost-benefits analyses

as well as PML-studies for insurances; only asset data

base has to be altered).

Values of the object assets are necessary.

Their estimation might bring in additional

uncertainty.

Absolute

damage

functions

No need for asset values, the estimated monetary damage

due to a given flood scenario results directly.

Need for regular re-calibration, e.g. damage functions

of Penning-Rowsell and Chatterton (1977) were re-

calibrated, reflecting larger investments in properties

and contents (Penning-Rowsell and Green, 2000).

Depend on the total value of the affected

Synthetic methods and empirical methods:

We can categorize the available approaches to synthetic methods and empirical ones.

While synthetic approaches rely on expert judgment, empirical approaches use damage data

derived from ex-post assessments of actual past events. Synthetic method appears more

theoretical, the second calls for a substantial effort in collecting ex-post damage information,

and such data sets are scarce (Jongman et al., 2012; Molinari et al., 2014 a). Both approaches

have advantages and disadvantages (Table 2.7).

47

Table 2.7: Advantages and disadvantages of empirical and synthetic flood damage models (Merz et al., 2010)

Advantage Disadvantage

Empirical

damage

models

Real damage information possesses a greater accuracy

than synthetic data (Gissing and Blong, 2004).

Effects of damage mitigation measures can be

quantified and taken into account in damage modelling

(Kreibich et al., 2005; Thieken et al., 2008).

Variability within one category and water depth is

reflected by the data and uncertainty can be quantified

(Merz et al., 2004).

Detailed damage surveys after floods are uncommon, so that

models may be based on poor quality data (Smith, 1994).

Paucity of information about floods of different magnitude

and often a lack of damage records with high water depth

require extrapolations (Smith, 1994; Gissing and Blong,

2004).

Transferability in time and space is difficult due to

differences in warning time, flood experience, building type

and contents (Smith, 1994).

Synthetic

damage

models

In each building, damage information for various

water levels can be retrieved (Penning-Rowsell and

Chatterton, 1977).

Approach does not rely on information from actual

flood events and can therefore be applied to any area

(Smith, 1994).

Higher level of standardization and comparability of

damage estimates

High effort is necessary to develop a detailed database

(inventory method) or undertake large surveys (valuation

survey method) to achieve sufficient data for each

category/building type (Smith, 1994).

What-if analyses are subjective, resulting in uncertain

damage estimates (Gissing and Blong, 2004; Soetanto and

Proverbs, 2004).

Mitigation actions are not taken into account (Smith, 1994).

Premises within one classification can exhibit large

variations which are not reflected by the data (Smith, 1994).

2.3.7. Direct Monetary Damages

The most frequently used procedure for the assessment of direct monetary flood damage

comprises three steps:

1. Classification of elements at risk by pooling them into homogeneous classes;

2. Exposure analysis and asset assessment by describing the number and type of elements

at risk and by estimating their asset value;

3. Susceptibility analysis by relating the relative damage of the elements at risk to the

flood impact.

This three-step procedure holds for the relative damage approach, where the damage

share or relative damage is used.

Alternatively, the absolute damage approach is based on the absolute monetary amount of

damages per risk element or unit (e.g. square meter). In this case, steps 2 and 3 are combined

within a single damage function (Merz et al., 2010).

48

Classification of elements at risk:

Depending on the spatial extent of the investigated inundation area and the chosen degree

of detail of the damage assessment, a large number of elements at risk has to be considered.

In general, it is not possible to assess the damage for each single object, because there is no

information on the damage behavior of each object and/or because such a detailed assessment

would require a huge effort. Therefore, elements at risk are pooled into classes, and the

damage assessment is performed for the different classes, whereas all elements within one

class are treated in the same way.

In most cases the classification is based on economic sectors, such as private households,

companies, infrastructure and agriculture, with a further distinction into sub-classes. This is

based on the understanding that different economic sectors show different characteristics

concerning assets and susceptibility. Furthermore, a pragmatic reason for using economic

sectors as a classification criterion is that economic data which are needed for estimating the

value of elements at risks are usually aggregated according to economic sectors. To be more

precise, the elements at risk within one economic sector may be very diverse. Therefore, most

damage assessments introduce sub-classes. For example, recently in Germany the damage

models FLEMOps and FLEMOcs have been developed for the private and the commercial

sector, respectively (Thieken et al., 2008; Kreibich et al., 2010). FLEMOps, the model for the

private sector, differentiates into three building type classes (one-family homes, semi-

detached houses, multi-family houses) and two building quality classes (low/medium quality,

high quality).

Similarly, FLEMOcs distinguishes among three classes concerning company size in

respect to the number of employees (1– 10, 11–100, >100 employees) and among four sub

sectors (public and private services, producing industry, corporate services, trade). Even with

such sub-classes the variability of objects within one sub-class is large. Therefore, asset

estimates and damage functions that are given for a certain sub-class are expected to describe

only a rather limited share of the variability that is observed in damage data. However, finer

classifications require more data and/or information which are usually not available. Also,

based on the objective classifications which are related to vulnerability of the structures, the

effective aspects of the hazard could vary as well. For instance, flood impact (i.e. Inundation

depth, Flow velocity, Duration of inundation, Contamination, Sediment, Rate of rise,

Frequency of inundation and Timing) varies between different sectors. Flood damage to

49

residential buildings is strongly dependent on the water depth of a flood, whereas for damage

to agricultural crops the time of flooding and the duration of the flood are important (Forster

et al., 2008). Figure 2.30 schematically depicts the relation between the detail of

classification and the main influencing factors.

Figure 2.10: Detail of classification in flood damage assessments in relation to the main influencing factors.

Table 2.8 gives a typical classification in economic sectors and short remarks on their

characteristics.

50

Table 2.8: Possible classification of elements at risk based on economic sectors (Merz et al., 2010)

Sector Examples Remarks

Private households

Residential buildings including

contents, garages, summer houses

etc., privately used vehicles

Majority of data sets and approaches exist for this sector.

Variation of assets and susceptibility is rather low compared to

other sectors

Industry,

manufacturing

Mining, metal processes, car and

mechanical engineering industry,

chemical industry, construction

industry, installers workshop,

carpentry, etc.

High variability and little data available. Transfer of asset values

and damage functions within sector is problematic. Booysen et

al. (1999) argue that it is not possible to develop standard

damage function for industries and that questionnaires have to be

provided for each industrial plant.

Services sector

Retail trade, wholesale trade, credit

and insurance institutions, hotel and

restaurant industry, lawyers, software companies, etc.

Rather high variability and little data available. Transfer of asset

values and damage functions within sector has to be done with

care.

Public sector

Education and culture (schools,

universities, theaters, etc.),

recreation and sports (campsite,

sports hall, etc.), administration,

health care and social welfare

(hospitals, nursing home, etc.),

churches.

High variability and little data available. Transfer of asset values

and damage functions within sector is problematic.

Lifelines and

infrastructure

Water supply, sewerage and

drainage, gas supply, power supply,

telecommunication, transportation

Little data available. Transfer of asset values and damage

functions possible within certain classes, e.g. unit values

and damage functions for roads of certain characteristics.

Agriculture

Loss of crops, damage to buildings,

contents, machinery; soil erosion,

loss of livestock

Methods and data availability comparatively good. Average

values per element at risk might be suitable in countries where

this sector has a small damage potential compared to other

sectors.

Others

Damage to flood defence structures;

clean-up costs, evacuation and

disaster management costs

Little data available. Average values are often used e.g. average

costs of evacuation (Penning-Rowsell and Green, 2000), but do

not hold in the context of multiple hazards (Pfurtscheller and

Schwarze, 2008).

Exposure analysis and asset assessment:

Exposure analysis identifies objects that are affected by a certain flood scenario. Exposed

objects are commonly extracted by intersecting land use data with inundation data by means

of operations within a geo information system. In order to achieve quantitative estimates of

the exposed value (or value at risk), asset values have to be estimated for all flood-affected

objects. Asset values depend on the type of the elements at risk, but also vary in time and

space (Merz et al., 2010).

51

Susceptibility analysis:

A central idea in flood damage estimation is the concept of damage functions. They relate

damage for the respective element at risk to characteristics of the inundation. These functions

represent the susceptibility of the respective element at risk, similar to dose-response

functions or fragility curves in other safety-relevant fields. Most flood damage models have

in common that the damage is obtained from type or use of the element at risk and the

inundation depth (Wind et al., 1999; NRC, 2000). Other parameters, like flow velocity,

duration of the inundation and time of occurrence are rarely taken into account. Such stage-

damage curves or depth-damage curves were proposed in the USA (White, 1945, 1964) and

they are seen as the standard approach to assessing urban flood damage (Smith, 1994).

2.3.8. Indirect Economic Damages

Indirect flood damages are induced by the direct impacts and transmitted through the

economic system. Indirect economic damage is necessarily attached to some form of

interruption of usual business but strictly different from the business interruption caused by

the direct physical impacts of flood water on production facilities. It is a secondary or trigger

effect caused by the interlinkages in the economic system (Cochrane, 2004). The magnitude

of indirect damage is determined by the boundaries in space and time of the damage

assessment.

Floods can also have long-term indirect impacts such as altered migration flows,

relocation of industries, depressed housing values, and altered government expenditures that

result from the new patterns of migration and regional development.

Evidence to date suggests that the indirect effects are more important in large disasters

than in smaller disasters.

Compared to direct effects, indirect damages are much more difficult to measure.

Additionally, there are limited available sources of data for measuring indirect damages.

Merz et al. (2010) suggested macro-economic damage models to study the effect of both,

direct and indirect economic flood damages with regard to their effects on performance

indicators of the national economy. In fact, macro-economic effects are a complementary

view to assess direct damages and indirect damages from a national perspective.

52

2.3.9. Damage Influencing Parameters

It is obvious that flood damage depends, in addition to the type of object and water depth,

on many factors. Some of these factors are flow velocity, duration of inundation, sediment

concentration, contamination of flood water, availability and information content of flood

warning, and the quality of external response in a flood situation. Although a few studies give

some quantitative hints about the influence of these factors (Smith, 1994; Wind et al., 1999;

Penning-Rowsell and Green, 2000; Kreibich et el., 2009; Thieken et al., 2005), there is no

comprehensive approach for including such factors in damage modelling.

Damage influencing factors can be differentiated into impact and resistance parameters

(Thieken et al., 2005). Impact parameters reflect the specific characteristics of a flood event

for the object under study, e.g. water depth, flow velocity, contamination. Impact parameters

depend on the kind and magnitude, resistance parameters depend on characteristics of the

flood prone objects. They depict the capability or incapability of an object to resist the flood

impact. Resistance parameters can be the object size or the type and structure of a building.

Also mitigation measures, former flood experience and early warning influence resistance.

Table ‎2.9 compiles damage influencing factors. Most of these damage influencing factors are

neglected in modelling, since they are very heterogeneous in space and time, difficult to

predict, and there is limited information on their (quantitative) effects. For instance, a gate

being opened could make the difference between high and low flow velocities and, as a

consequence, scour undermining a foundation or not (Kelman and Spence, 2004). Floating

and destruction of an oil-tank can make the difference between total damage of a building

due to severe contamination or marginal damage due to water contact only.

The influence of these factors on the damage was tested separately in most studies.

However, damage susceptibility depends on many factors, which are not independent from

each other. For example an early warning cannot work, if the meaning of the warning is not

recognized by the affected people due to a lack of preparedness, or if mitigation measures are

impossible due to an extreme flood impact. Thus, multivariate analyses are necessary.

However, such analyses undertaken by McBean et al. (1988) did not lead to clear-cut results

and let them conclude: “In all likelihood, the factors considered here and many others

combine to determine the level of flood damage that may be experienced in any household. It

does not however seem possible to develop a simple and practical predictive tool that

incorporates these factors”.

53

Table 2.9: Damage influencing factors (Merz et al., 2010)

Impact parameter

Parameter Description Selected references

Inundation depth The higher the inundation depth, the greater the

building and content parts which are damaged and the

stronger the buoyancy force.

CH2M Hill (1974); Black (1975), Sangrey et al.

(1975), Smith and Tobin (1979), Handmer (1986),

Smith (1991), Torterotot et al. (1992), Smith and

Greenaway (1994), Hubert et al. (1996), USACE

(1996), Islam (1997), Blong (1998), Zerger (2000),

Nicholas et al. (2001), Beck et al. (2002), Kato and

Torii (2002), Citeau (2003), Dutta et al. (2003),

Hoes and Schuurmans (2005), Penning-Rowsell et

al. (2005), Buchele et al. (2006), Kreibich and

Thieken (2008), Thieken et al. (2008)

Flow velocity The greater the velocity of floodwaters, the greater the

probability of structural pressure, scouring, etc. High

flow velocities can cause direct damage to crops and

may lead to soil degradation from erosion. Building

damage due to lateral

CH2M Hill (1974), Black (1975), Sangrey et al.

(1975), Smith and Tobin (1979), Handmer (1986),

McBean et al. (1988), Smith (1991), Smith and

Greenaway (1994), USACE (1996), Islam (1997),

Blong (1998), Zerger (2000), Nicholas et al.

(2001), Beck et al. (2002), Kato and Torii (2002),

Citeau (2003), Schwarz and Maiwald (2007, 2008),

Kreibich et al. (2009), Pistrika and Jonkman (2009)

Duration of inundation

The longer the duration of inundation, the greater the

saturation of building structure and contents, the

higher the effort for drying, the more severe the

anoxia of crops, increasing the probability of damage.

Smith and Tobin (1979), Handmer (1986), McBean

et al. (1988), Torterotot et al. (1992), Consuegra et

al. (1995), Hubert et al. (1996), USACE (1996),

Islam (1997), Nicholas et al. (2001), Kato and Torii

(2002), Citeau (2003), Dutta et al. (2003),

Penning-Rowsell et al. (2005), Forster et al. (2008)

Contamination The greater the amount of contaminants, the greater

the damage and the cleanup costs. Inclusion or

adsorption of contaminants may even lead to total

damage. Examples are the inclusion of small particles

in porous material impossible to remove, or the

dispersal of microorganisms in moist building

material requiring extensive clean up and disinfection.

Smith and Tobin (1979), Handmer (1986), USACE

(1996), Nicholas et al. (2001), Kreibich and

Thieken (2008), Thieken et al. (2008)

Debris/ sediments The presence of debris in floodwater, depending on its

amount, size and weight, increases the dynamical

forces which affect buildings and thus the potential

for structural damage. Sediment can damage flooring

and mechanical equipment and it may lead to an

increased effort for cleanup.

Handmer (1986), Penning-Rowsell et al. (1994),

Kato and Torii (2002)

Rate of rise As the rate of rise increases, it becomes increasingly

difficult to reduce flood damage.

Smith and Tobin (1979), Handmer (1986),

Penning-Rowsell et al. (1994)

Frequency of

inundation

Repeated flooding may have cumulative effects,

increasing the probability of damage. On the other

hand, preparedness significantly increases, leading to

reduced damage.

USACE (1996), Elmer et al. (2010)

Timing Floods occurring at night may be associated with

greater damage owing to ineffective warning

dissemination. Floods occurring during holidays may

see property owners absent and unable to take

damage-reduction measures. The time of year

(season) of flood occurrence with respect to crop

growth stages and critical field operations plays a

crucial role for the magnitude of agricultural damage.

Smith and Tobin (1979), Smith and Greenaway

(1984), Smith (1992), Smith (1992), Consuegra et

al. (1995), Yeo (1998), Citeau (2003), Dutta et al.

(2003),

54

Resistance parameter

Parameter Description Selected references

Business sector/

use of building

Sectors differ significantly in respect to exposed

assets as well as susceptibility. For instance, the

manufacturing sector has a relatively high damage

potential (high assets and business volumes) but a

relatively good preparedness status. In contrast,

preparedness is comparatively weak in the financial

and service sectors.

MURL (2000), ICPR (2001a), FEMA (2003),

Emschergenossenschaft and Hydrotec (2004),

Penning-Rowsell et al. (2005), Scawthorn et al.

(2006)

Building type Building type may significantly influence the degree

of damage. For instance, multistory buildings are

affected by a lower fraction in contrast to single-

storey buildings. Additionally, their relation of weight

to buoyancy force is advantageous.

Penning-Rowsell et al. (2005), Buchele et al.

(2006), Kreibich and Thieken (2008), Thieken et al.

(2008a)

Building material Building material reacts differently to exposure to

(contaminated) water, e.g. absorbents rates are

different. Additionally, drying of material as well as

decontamination is more or less difficult.

Building material affects also the weight of the

building and thus the danger of buoyancy.

Nicholas et al. (2001), Schwarz and Maiwald

(2007, 2008)

Precaution There are various precautionary measures, which are

able to reduce flood damage significantly. Examples

are constructur measures such as elevated building

configuration, use of suitable building material or

flood adapted interior fitting. Measures like flood

secure configuration of oil tanks or secure storage of

chemical can prevent contamination.

Kreibich et al. (2005), Buchele et al. (2006),

Kreibich and Thieken (2008), Thieken et al. (2008)

External response/

emergency

Emergency measures can be undertaken particularly

effective with sufficient warning time and low water

levels.

Such measures are for instance the dismounting of

fixed equipment/machinery, the relocation of

inventory, the sealing of openings to prevent water

from entering the building. Or quick drying or

disinfection which reduce mold building on walls.

Early warning Only if the warning time is sufficiently long and if the

content is comprehensible, emergency measures can

be undertaken efficiently.

McBean et al. (1988), NRE (2000), Penning-

Rowsell et al. (2005)

2.3.10. Flood Actions on Buildings

Kelman and Spence (2004) present an overview of flood actions on buildings. According

to them, flood actions describe acts which a flood could do directly to a building, potentially

causing damage. Full analysis of flood actions would permit damage from potential flood

events to be estimated and calculated more comprehensively and would allow the

uncertainties to be properly acknowledged.

55

Analyses of direct flood damage to buildings often focus on damage from water contact

and water depth that tend to be the flood characteristic most frequently analyzed in detail.

Some flood characteristics less commonly examined in detail with respect to their

applicability for estimating and analyzing the direct flood damage to buildings.

Damage may result from energy transfer, forces, or pressures leading to effects on

buildings including wall failure, doors being forced to open, glass breaking, roofs collapsing

or foundations being undermined. The iportant step towards this investigation is a thorough

understanding of what a flood could impose on a building in order to elicit a response from

the building. The following list and figure presents an overview of categorizing such flood

‘‘actions’’ according to Kelman and Spence (2004).

1. Hydrostatic actions (actions resulting from the water’s presence):

lateral pressure from flood depth differential between the inside and outside of a

building;

capillary rise.

Figure 2.11: Water levels and pressure distribution levels on building component (Kelman and Spence, 2004)

2. Hydrodynamic actions (actions resulting from the water’s motion):

velocity: moving water flowing around a building imparting a hydrodynamic

pressure;

velocity’s localized effects, such as at corners;

56

velocity: turbulence;

waves changing hydrostatic pressure;

wave breaking.

3. Erosion actions (water moving soil; the water’s boundary becomes dynamic and moves

into the adjacent solids).

4. Buoyancy action: the buoyancy force.

5. Debris actions (actions from solids in the water):

static actions;

dynamic actions;

erosion actions.

6- Non-physical actions:

chemical actions;

nuclear actions;

biological actions.

These categories indicate the current capability available for introducing more flood

actions to flood damage analysis. A poor capability for considering the flood actions over a

relatively large space scale does not necessarily imply low impact where they do manifest.

Therefore, more work is needed in order to fully understand how flood damage arises and,

hence, how flood damage may be prevented.

57

2.3.11. Flow Velocity Effect

Flow velocity is generally presumed to influence flood damage. However, this influence

is hardly quantified and virtually no damage models take it into account.

In these contexts, flood risk encompasses two aspects; on the one hand the flood hazard

characterized by its impact parameters such as water depth and its associated probability and

on the other hand vulnerability, often due to exposure and susceptibility of affected elements

(Mileti, 1999; van der Veen and Logtmeijer, 2005). Thus, besides meteorological,

hydrological and hydraulic investigations, such analyses require estimation of the

consequences of flooding, which is normally restricted to detrimental effects, i.e. flood

damage.

A central idea in flood damage estimation is the concept of damage functions or stage-

damage curves, which are internationally the standard approach to assess urban flood losses

(Smith, 1994). These damage models have in common that direct monetary damage, are

mainly related to the type or use of the building and the inundation depth (Smith, 1994; Merz

and Thieken, 2005). The strong focus on inundation depth as the main determinant for flood

damage might be due to limited information about other parameters characterizing the flood,

e.g. flow velocity. However, it implies that slowly rising riverine floods are taken as the

prototype for flooding (Kelman and Spence, 2004), despite the fact that torrential rain, flash

floods and groundwater flooding also cause significant damage. However, these flood types

and differences in damaging processes have rarely been analyzed.

It is generally accepted that the higher the flow velocity of the floodwater, the greater the

probability (and extent) of structural damage. USACE (1996) states that velocity is a major

factor in aggravating structure and content damage. High velocities limit the time available

for emergency measures (e.g. flood proofing by way of mobile protection elements) and

evacuation. The additional force of high velocities creates greater danger of foundation

collapse and forceful destruction of contents.

According to Kreibich et al. (2009), a strong influence of flow velocity on flood damage

could only be identified for structural damage of road infrastructure. Further, a significant

influence of flow velocity on the structural damage of residential buildings is suspected for

flow velocities above a certain critical lower bound analogous to the other impact parameters.

In contrast, the influence of flow velocity on monetary losses of residential buildings,

58

companies and road infrastructure, as well as on business interruption/ disruption duration

was weak to non-existent (Table 2.10).

The water depth and the energy head, which are highly correlated, have a medium to

strong influence on all investigated damage types, except on monetary losses of companies

and road infrastructure. Thus, the energy head is suggested as a suitable flood impact

parameter for reliable forecasting of structural damage to residential buildings above a critical

impact level of 2 m of energy head or water depth. Forecasting of structural damage to road

infrastructure should be based on the flow velocity alone. Water depth is an important

parameter for monetary loss estimation as it is commonly used in loss modelling. General

consideration of flow velocity in monetary loss modelling cannot be recommended on the

basis of their study. Damage modelling for companies needs a more detailed approach, at

least differentiating them according to economic sectors.

Table 2.10: Qualitative summary of the influence of impact parameters on flood damage (Kreibich et al., 2009)

Damage Types

Impact

Parameters

Structural damage

of residential

buildings

Structural damage

of road

infrastructure

Monetary loss to

residential

buildings

Business

interruption

and disruption

duration

Flow velocity NO STRONG WEAK NO

Water depth STRONG MEDIUM MEDIUM MEDIUM

Energy head STRONG MEDIUM MEDIUM WEAK

Indicator for flow

force WEAK STRONG WEAK NO

Intensity WEAK STRONG WEAK WEAK

59

2.3.12. Uncertainty of Flood Damage Assessment

Availability and reliability of damage data:

In comparison to other fields of water resources management, flood damage data are still

scarce. Only a few data sets are publicly available and little is known about data quality. The

lack of reliable, consistent and comparable damage data is seen as a major obstacle for risk

analyses and effective and long-term damage prevention. However, flood damage data are

needed at a variety of spatial scales (national, regional, local, object scale) to analyze

variations in damage and to investigate causal relations between the hazard characteristic and

the amount of damage (Downton et al., 2005).

Especially for the development of damage models, such as depth-damage curves, object-

oriented data are needed. Such data sets are, however, hardly available or accessible (Merz et

al., 2010).

Sources of uncertainty in damage modelling:

Damage modelling aims at predicting damages of potential future events or they are

geared towards financial appraisals during and immediately after floods. In both cases

damage models have to be transferred to another situation. These transfers can be grouped

into:

(1) transfer between elements at risks;

(2) transfer in time;

(3) transfer in space;

(4) transfer in spatial scale.

Each transfer is associated with uncertainty, in addition to the uncertainty and errors in

damage data collection (Merz et al., 2010).

Degree of uncertainty:

There is a large degree of uncertainty in the construction of the damage curves, the asset

values connected to these curves and the larger methodological framework (Merz et al., 2004;

Hall et al., 2005; Meyer and Messner, 2005; Messner et al., 2007; Apel et al., 2008; Freni et

al., 2010; Merz et al., 2010; de Moel and Aerts, 2011; Green et al., 2011; Ward et al., 2011).

60

Differences in the methodological framework of flood damage models are for example

apparent in the spatial scale (object- versus area-based), damage-function type (absolute

versus relative), damage classes, cost base (replacement cost versus depreciated cost) and the

number of hydrological characteristics included. Also, while some damage models are

constructed using empirical damage data, others are defined on expert judgement in

combination with artificial inundation scenarios (Jongman et al., 2012).

Moel and Aerts (2011) show that uncertainty in depth–damage curves and corresponding

asset values constitutes the most important factor in damage estimation, and has a much

stronger effect on the outcome than uncertainties in hydrological and land use (“assets at

stake”) inputs.

Sensitivity analysis:

It is possible to conduct sensitivity analysis to quantify the effect of uncertainties

associated with the modelling of flood damage. In the analysis two different types of

uncertainties can be distinguished:

Function uncertainty: Function uncertainty is defined as sensitivity of the outcome to

uncertainty in the shape of the depth–damage functions.

Value uncertainty: Value uncertainty relates to uncertainty in maximum damage values.

Function uncertainty are calculated by combining fixed maximum damage estimates with all

seven depth– damage functions. Following the same logic, value uncertainty were compared

by combining a fixed depth–damage function with all seven maximum damage values and

assessed the spread. Both types of uncertainty can be expressed in terms of the absolute and

relative difference between the highest and lowest damage estimates (Jongman et al. 2012).

61

2.3.13. Flood Damage Modelling

Jongman et al. (2012) state that the estimation of direct flood damage is a complex

process involving a large number of hydrologic and socioeconomic factors. The structure,

inputs and outputs of a specific damage model are defined not only by the available data, but

also by the purpose of the model. For example, while insurance companies model the

estimated insured damages, government agencies and academics are generally interested in

the accurate assessment of total economic losses.

In almost all models in use today, flood depth is treated as the determining factor for

expected damage, sometimes complemented by other parameters like velocity, duration,

water contamination, precaution and warning time (Messner et al., 2007; Merz et al., 2010;

Green et al., 2011). Some recently developed multi-parameter models are conceptual

(Nicholas et al., 2001) or developed (and validated) for specific areas, e.g. for Japan (Zhai et

al., 2005) or FLEMO for Germany (Kreibich et al., 2010). Thus, more research is needed on

their validation and transferability.

However, the internationally accepted and most common method for the estimation of

direct flood damage is still the application of depth–damage functions (Smith 1994; Kelman

and Spence, 2004; Meyer and Messner, 2005; Merz et al., 2010; Green et al., 2011). Depth–

damage functions represent relationships between flood depth and the resulting monetary

damage.

2.3.14. Available Flood Damage Assessment Models

Several countries around the world have damage assessment models developed by

responsible organizations. Mainly, these models are developed for cost-benefit analysis of

flood mitigation measurements. However, looking at the flood damage assessment of various

countries, some interesting differences can be observed. In most of these countries, it can be

observed that there is no standardization of such methodology and various methods are used

by different organizations (Dutta et al., 2001).

In this section a brief description of the focus, development and characteristics of the

different well-known flood damage models developed for simulating ex-ante flood is

provided.

62

FLEMO: The FLEMO model family has been developed at the German Research Centre

for Geosciences, mainly for flood risk analyses from the local to national scale and for the

estimation of direct tangible damage (Apel et al., 2009; Vorogushyn et al., 2012). FLEMO

family contains the rules for two different categories, Flood Loss Estimation MOdel for the

private sector (FLEMOps) and the rules for Flood Loss Estimation MOdel for the

commercial sector (FLEMOcs) (Kreibich et al., 2010). FLEMOps calculates the flood

damage using five different classes of inundation depth, three individual building types, two

classes of building quality, three classes of contamination and three classes of private

precaution (Thieken et al., 2008). FLEMOcs has a similar structure, it calculates the flood

damage using five classes of inundation depth, four different economic sectors, three classes

of company size in respect to the number of employees as well as three classes of

contamination and three classes of private precaution (Kreibich et al., 2010).

The models have been intensively validated on the micro- as well as on the meso-scale

using different data sets of repair costs at the scale of single buildings and whole

municipalities (Thieken et al., 2008).

Figure 2.12: FLEMO model for water depth relationship with loss ratio (Jongman et al., 2012)

63

Damage Scanner: The Damage Scanner is based on the economic values and depth–

damage curves of the HIS-SSM module (the standard method for the detailed estimation of

flood damage in the Netherlands), but as opposed to HIS-SSM works with aggregated land

use data instead of individual units. The Damage Scanner has been used for the estimation of

future flood risk under climate and land use changes and is mainly based on synthetic data,

using “what-if analyses” estimating the damage that would be expected in case of a certain

flood situation. Maximum damage values are based on replacement values. Indirect losses are

calculated as an additional 5% on top of the direct losses, and are consequently also subject to

depth–damage curves.

The Flemish: A model for flood damage estimation developed for the Flemish

Environmental Agency in Belgium is described by Vanneuville et al. (2006). Similar to the

Damage Scanner, the Flemish methodology is specifically designed for assessments on a

regional and national scale using aggregated land use data. The methodology has been

applied for identifying vulnerable areas and calculating efficient flood defense investments.

The maximum damage values in the Flemish model are based on national averages of

housing prices, surface areas and market values. Damage to residential content is assumed to

be 50% of the structural losses. Furthermore, indirect costs are included as a percentage on

top of the direct damage, ranging from 10% for agriculture to 40% for industry. The Flemish

model has a separate structure and content class for residential areas and there is only one

infrastructure and one industry (industry plus commerce) class. Also, the same as Damage

Scanner it has been used for the estimation of future flood risk mainly based on synthetic

data.

HAZUS-MH: The HAZUS Multi-Hazard model (FEMA, 2009; Scawthorn, 2006) is a

tool for the estimation of the potential economic, financial and societal effects of natural

hazards within the United States. HAZUS-MH besides flood includes wind and earthquake

hazards as well. The typical scales of application are city, county and state level. Over several

years, all inputs required for flood damage estimation such as: building data on the census

block level (including building type, number of floors, presence of a basement and date of

construction), data on an object level of infrastructure and high-potential facilities (e.g.

hospitals), a large number of nationally applicable depth–damage functions for buildings on

the basis of empirical damage data (as well as separate functions developed by USACE for

specific regions of the United States) and a separate user-defined module for the estimation of

indirect costs and larger economic effects of the flood event, were collected in the software.

64

Users of the HAZUS software have to choose the level of analysis (vary from using default

input data to extensive additional economic and engineering studies). Also, the user can

define the intensity and timing of the flood, early warning system and whether the losses

should be calculated on the basis of replacement or depreciated asset values.

USACE (1998) proposes a flood proofing matrix delineating thresholds believed to be

important for different damage scenarios:

f diff (flood depth differential [m]): shallow (< 0.9 m), moderate (0.9 to 1.8 m), or deep

(>1.8 m);

ν (velocity [m/s] ): slow ( < 0.9 m/s), moderate (0.9 to 1.5 m/s), or fast (>1.5 m/s);

Flash flooding: yes (less than 1 h) or no;

Ice and debris: yes or no;

Site location: coastal or riverine;

Soil type: permeable or impermeable;

Three sets of structural characteristics are also provided. Justification for the categories is

not provided, but USACE notes that most buildings would collapse for f diff > 0.9 m.

USACE (1998) further suggests that for f diff > 0.9 m, the building would need to be

designed to resist both hydrostatic and buoyancy forces. This f diff = 0.9 m threshold may

come from experimental results in USACE (1988). USACE describes water loads

(hydrostatic and hydrodynamic), debris impact loads, soil loads, wave loads, and uplift

pressures as factors in structural flood damage (Kelman and Spence, 2004).

Multi-Coloured Manual: The Flood Hazard Research Centre (FHRC) at Middlesex

University, London has completed extensive studies estimating UK flood damage. FHRC’s

work focuses on depth-damage curves using slow-rise depth. Their major publications are in

the form of manuals (N’Jai et al., 1990; Parker et al., 1987; Penning-Rowsell et al., 1992;

Penning-Rowsell and Chatterton, 1977; Suleman et al., 1988). These manuals provide depth-

damage curves for various land use categories and also consider two arbitrary flood

durations: less than 12 h, termed short, and more than 12 h, termed long (Kelman and Spence,

2004).

65

The Multi-Coloured Manual (MCM) is the most advanced method for flood damage

estimation within Europe (e.g. Penning-Rowsell and Chatterton, 1977; Penning-Rowsell et

al., 1992, 2010). The purpose of the MCM is explicitly defined for water support

management policy and assessment of the investment decisions (Penning-Rowsell et al.,

2010). For these purposes, Penning-Rowsell et al. (2010) have developed a wide range of

depth– damage relationships and additional methodologies for the estimation of the absolute

losses value of flooding. These relationships are developed for a wide variety of residential,

commercial and industrial buildings, using mostly synthetic analysis and expert judgment.

For each damage class, damage curves are available for different levels of maintenance and

the presence of a basement. Similar to HAZUS, the MCM is an object-based model that the

maximum damage per square meter estimates only reflects expected repair costs to buildings

and not damage to the surrounding land.

Rhine Atlas: In order to meet the performance targets in terms of risk reduction and flood

awareness, the Rhine Atlas damage model (RAM) was developed (ICPR, 2001). The RAM

has the least detailed classification system of the models included in this study by recognizing

only five land use classes. The depth–damage functions and the corresponding maximum

damage values were established on the basis of the empirical results and expert judgment

(ICPR, 2001). For the land use classes, residential, industrial and infrastructure, the RAM

applies both a structure and contents damage assessment. Since the RAM is developed to

estimate direct economic costs, all damage values are calculated on the basis of depreciated

values. Through a comparison with insurance data, the ICPR (2001) estimates that the

replacement values are approximately a factor 2 higher than depreciated values. Indirect

losses are not included in the RAM method.

JRC Model: In support of European policy on flood risk management, the European

Commission’s Joint Research Centre Institute for Environment and Sustainability (JRC-IES)

has developed a JRC damage model (Huizinga, 2007), which has been applied to estimate

trends in European flood risk under climate change (Feyen et al., 2011). The JRC Model

comprises differentiated relative depth–damage functions and maximum damage values for

all EU-27 countries. Properties are classified for five damage classes: residential,

commercial, industrial, roads and agriculture. As a result, the flood depth in every grid cell is

multiplied with a weighted average of relative depth–damage functions and maximum

damage values (Jongman et al., 2012).

66

In addition, There are other models also focused on depth, such as Smith and Greenaway

(1980) for Australia; DeGagne (1999) for Manitoba, Canada; and Smith et al. (1981) for

South Africa. Kelman and Spence (2004) also listed models that are working on more

parameters than water depth (Table 2.11).

Table 2.11: Studies of non-depth flood damage models (Kelman and Spence, 2004)

Reference

Geographic area

Flood hazard considered

Beck et al. (2002)

Black (1975)

USA CH2M Hill (1974)

Luxembourg

USA

Willamette Valley, OR, USA

Depth and velocity

Depth and velocity

Depth and velocity

Child of ANUFLOOD (1998),

Smith (1991), and Zerger (2000)

Australia Depth with velocity as an optional input.

Hubert et al. (1996)

Islam (1997)

France

Bangladesh

Depth and duration

Depth, duration, velocity, and salinity

Kato and Torii (2002) Japan Depth, sediment depth of deposited sediment,

and duration.

Sangrey et al. (1975) Elmira, NY, USA Depth and velocity

Smith and Greenaway (1994) Mackay, Queensland, Australia Depth, velocity, and wave height.

Torterotot et al. (1992) France Depth and duration

2.3.15. Flood Damage Model Comparison

Qualitative comparison of the damage models:

According to Jongman et al. (2012), the framework used for the qualitative assessment of

the damage models is presented in Figure 2.13. All models are assessed on three main

aspects: scale, input data and damage calculation. On the basis of preceding comparison

studies (Meyer and Messner, 2005; Messner et al., 2007; Merz et al., 2010), nine specific

characteristics are defined within these three categories that were compared between models:

Scale:

– Scale of application: the spatial scale of application for which the model is developed,

ranging from local to supra-national;

67

– Regional differentiation: the options for differentiation in parameters (such as

maximum damage values) between areas of analysis;

– Units of analysis: the units used for damage estimation, which can be the level of

individual objects or aggregated land use classes, or a combination of these;

Input Data:

– Hydrological characteristics: the inundation characteristics taken into account in

damage assessment, such as depth, duration, velocity and contamination;

– Data method: the method used in developing the damage models, either using

empirical data from past flood events or synthetic data from “what-if” analyses of a

simulated potential flood;

– Land use classification: the detail of the classification system used to differentiate

between various objects or land use types;

Damage Calculation:

– Cost base: the type of values on which the maximum damage per object or land use

class is based. The values can be expressed as either replacement costs, i.e. the

estimated new value of the object or class, or depreciated repair costs, i.e. an estimate of

the present-day cost of replacement or reparation.

– Empirical validation: the validation of the damage model after development on the

basis of reported flood damage data;

– Damage functions: the type of depth–damage function, which can represent either the

relative percentage loss with respect to a pre-defined maximum damage value or the

absolute monetary loss with depth.

68

Figure 2.13: Schematic display for qualitative assessment of the damage models (Jongman et al., 2012)

Jongman et al. (2012) summarized the characteristic of flood damage models in three

above mentioned aspects (Scale, Input Data, and Damage Calculation). In this regard, it

would be worth noting that: for estimating the direct flood losses, except HAZUS model

which consider duration, velocity, debris, rate of rise and timing, rest methods use only depth

as the hydrological input. Damage functions in most of the methods are relative.

These models are still crude in estimating the indirect consequences and they mostly have

focused on direct physical damages.

Except HAZUS and MCM models, they are not well flexible in cost base expression. Unit

of analysis in most of the models is considered as the surface area of the objects (Klijn et al.,

2007; Aerts et al., 2008; Aerts and Botzen, 2011; Jongman et al., 2012; Hasanzadeh, 2013).

Flood Damage Models

Scale

Input

Data

Damage

Calculation

Scale of

application

Regional

differentiation

Units of

analysis

Cost base

Empirical

validation

Damage

functions

Cost base

Empirical

validation

Damage

functions

69

Finally, there is an important difference in methods for the valuation of assets at risk.

FLEMO, DSM and the Flemish model value assets at replacement costs; MCM and RAM are

based on depreciated values; the JRC model is a mixture of both; and HAZUS allows the user

to choose which of the value types to use. An evaluation of the methodologies on the basis of

the parameters defined in the qualitative framework (Figure 2.13) is presented in Table 2.12.

Table 2.12: Flood damage models qualitative comparison (Jongman et al., 2012)

Damage

model

Scale of

application

Regional

differentiation

Units of

analysis

Hydrological

characteristics

Data

method

Number

of unit

classes

Cost base Empirical

validation Function Reference

FLEMO

Local

Regional

National

Local asset

values

Surface

area

Depth

Contamination

Empirical 5-10 Replacement

values

Yes Relative Thieken et

al. (2008)

Kreibich et

al. (2010)

Damage

Scanner

Regional

National

No Surface

area

Depth Synthetic 5-10 Replacement

values

No Relative Klijn et al.

(2007)

Flemish

Model

Regional

National

No Surface

area

Depth Synthetic 5-10 Replacement

values

No Relative Vanneuvill

e et al.

(2006)

HAZUS

-MH

Local

Regional

Local asset

values

Individual

objects

Surface

area

Depth

Duration

Velocity

Debris

Rate of rise

Timing

Empirical

Synthetic

>20 Replacement

values

Depreciated

values

Yes Relative FEMA

(2009)

MCM Local

Regional

No Individual

objects

Depth Synthetic >20 Depreciated

values

Limited Absolute Penning-

Rowsell et

al. (2010)

Rhine

Atlas

Local

Regional

No Surface

area

Depth Empirical

Synthetic

10-20 Depreciated

values

No Relative ICPR

(1998)

JRC

Model

Regional

National

European

GDP

normalization

area

Surface

area

Depth Empirical

Synthetic

Statistical

5-10 Replacement

values

Depreciated

values

No Relative Huizinga

(2007)

Different Economic Sectors and Model Comparison:

Residential Sector: Most flood damage data, analyses as well as damage models refer to

the residential sector. Here, only three models are presented exemplarily to illustrate different

development strategies, function types and number of parameters. As it has shown in the next

table, the model of the Multicoloured Manual for UK is based on synthetic damage data and

uses absolute damage functions (Penning-Rowsell et al., 2005). In contrast, FLEMOps is

based on empirical damage data and uses relative damage functions (Buchele et al., 2006;

70

Thieken et al., 2008). The relative damage model of the ICPR is based on a combination of

empirical and synthetic damage data (ICPR, 2001). The models differ greatly in the number

of influencing parameters used. The model of the ICPR exclusively takes the water depth into

account to estimate the immobile and equipment damage of settlements. The model of the

Multicoloured Manual takes into account 14 water depth levels and two duration classes

(Penning-Rowsell et al., 2005). Also, five house types, seven building periods and four

different social classes of the residence’ occupants are considered. FLEMOps differentiates

between five water depth classes, three contamination classes, three building types, two

building qualities and three precaution classes (Buchele et al., 2006; Thieken et al., 2008).

Table 2.13: Flood damage models comparison for residential sectors (Merz et al., 2010)

Models Country Data Method Functions Input Parameters Damage Type

Multicoloured UK Synthetic Absolute Water depth, flood

duration, building

type, building age

social class of the

occupants

Building fabric

items, household

Inventory

FLEMOps Germany Empirical Relative Water depth,

contamination, building

type, quality of building,

Building and

contents

ICPR Germany Empirical-

Synthetic

Relative Water depth Immobile,

equipment,

mobile

Industrial Sector: Models for the estimation of direct damages of companies differ based

on their development, their functions, the parameters they include and the damage types they

estimate. In regard of comparing models, while the HAZUS-MH distinguishes 16 main

company types with several sub-classes for damages to buildings, RAM (NRE, 2000) ,which

is a model of Australia that calculate damages in absolute values and express it in total for all

asset types, does only differentiate in companies smaller or larger than 1000 m2. Variations

between the models can also be found regarding the company size as resistance parameter.

HAZUS-MH includes a size factor in its object classification (e.g. small, medium, large

warehouses), Anuflood which is another Australian models and it is almost the same as

RAM, relates company size to the building floor space and FLEMOcs distinguishes three

sizes of companies in relation to their number of employees (Kreibich et al., 2010).

71

Also, some models separately estimate damages to different asset types, e.g. the functions

developed by the USACE, which are partly used in HAZUS-MH (FEMA, 2003; Scawthorn

et al., 2006), distinguish damages at buildings, inventory and equipment. FLEMOcs

distinguishesdamages at buildings, equipment and goods, products, stock (Kreibich et al.,

2010), the ICPR (2001) and the Saxon Agency of Environment and Geology (LfUG, 2005)

estimate separately damages to buildings, immobile inventory and mobile inventory. Other

models, e.g. Hydrotec (Emschergenossenschaft and Hydrotec, 2004) the same as Anuflood

(NR&M, 2002) and RAM (NRE, 2000), simply estimate the total damage of all asset types.

Table 2.14: Flood damage models comparison for industrial sectors (Merz et al., 2010)

Models

Country

Data Method

Functions

Input Parameters

Damage Type

Anuflood Australia Empirical Absolute water depth, object size,

object susceptibility

total

RAM Australia Empirical/

Synthetic

Absolute object size, object value, lead

time, flood experience

total

FLEMOcs Germany Empirical Relative water depth, contamination,

business sector, number of

employees, precaution

building and

equipment and

goods, products,

stock

MURL Germany Empirical Relative water depth, business sector building and

inventory

Hydrotec

Germany Empirical Relative water depth, business sector total

LfUG Germany Empirical/

Synthetic

Relative water depth or specific

discharge, business sector

building and

mobile and immobile

inventory

Multicoloured UK Synthetic Absolute water depth, flood duration,

object type, lead time

total

HAZUSMH USA Empirical/

Synthetic

Relative water depth, object type building and

equipment and

inventory

Infrastructure: Damage to infrastructure includes a variety of potentially affected

structures and different damage types. Potentially affected structures are public utilities

(lifelines) such as water supply, sewerage and drainage, gas and power supply and

telecommunication. Furthermore, damage to transportation facilities, particularly roads and

railways, belong to this damage sector. Also, sometimes essential facilities such as hospitals,

schools and fire brigades are considered in this sector as well. Besides direct damage to the

affected structures damages can occur due to a disruption of services, which have to be

considered as indirect damage. Damage due to disruption of utilities is in general a function

72

of physical and systemic (redundancy, transferability, interdependency) vulnerability of the

flooded structures and networks. With regard to damage to infrastructure, only few data and

no well-established models exist. Since damage is governed by many local factors,

uncertainties are very high (Dutta et al., 2003). Penning-Rowsell et al. (2005) further

recommend using the depth damage approach for assessing direct damage. However, due to

the site-specificity of utility works, no standard data are given in the Multicoloured Manual.

It is worth noting that in contrast to other sectors direct damage to transportation

infrastructure seems to be more influenced by flow velocity than by inundation depth

(Kreibich et al., 2009). Consequently, effects by erosion and debris flow (closure of bridges)

have to receive more attention. Due to the variety of structures a three-step filtering process

has been proposed with Multicoloured Manual:

Count relevant infrastructure assets at risk by assessing their sizes (e.g. length)

and values

assess the total risk for each infrastructure by roughly classifying the likelihood

of damage and the scale of impact as high, medium or low,

quantify damages for “high risk” and “very high risk” assets only

Similarly, in HAZUS-MH important lifeline components are selected for fragility

modelling. Impacts to system functionality, relative cost of the component and the overall

time to recover from damage are considered, as well (Scawthorn et al., 2006).

Agricultural sector: Flood damage in the agricultural sector includes losses of

agriculture products, farm houses and farm infrastructure (Dutta et al., 2003). The reduction

in yield and quality of agriculture products may require additional expenditure for sowing,

tillage, and the application of fertilizer and crop protective agents. Additionally, damage to

the soil that refers to a potential decrease in the quality of soil and a loss of soil structure due

to compaction or erosion might be relevant as well (Pivot et al., 2002). Total economic

damages in the agricultural sector are frequently much lower than those in urban areas.

Hence, damage evaluation is often neglected or only accounted for by using simple

approaches and rough estimates (Forster et al., 2008). A significant difference for damage

evaluating compare to other sectors is the importance of the time of occurrence of a flood

with respect to crop growth stages and critical field operations (Penning-Rowsell et al.,

2003). For example, flooding in July results in much higher damages for summer grain crops

73

just prior to harvesting than flooding in August just after harvesting. In most models, as

opposed to other flood variables, time of occurrence is considered.

Table 2.15: Flood damage models comparison for agricultural sectors (Jongman et al., 2012)

Models

Country

Data Method

Functions

Input Parameters

Citeau France Synthetic Relative Water depth, flood duration, flow velocity, submersion period, crop type

Neubert and Thiel

Germany Synthetic Relative Submersion period

MEDIS-Model Germany Empirical- Synthetic

Relative

Flood duration, submersion period, crop type

Dutta et al. Japan Empirical Relative Water depth, flood duration, submersion period, crop type

Hoes and Schuurmans

The Netherlands

Synthetic Relative Water depth

74

C

H

A

P

T

E

R

T

H

R

E

E Picture: Flood in Passau, Germany, 2013

75

CHAPTER 3

3. RIVER2D HYDRODYNAMIC MODELLING

Introduction 3.1.

This chapter dedicated to theoretical formulas and numerical concepts for two-

dimensional hydrodynamic modelling with River2D software. River2D is a two dimensional

depth averaged finite element hydrodynamic model that has been developed by the

University of Alberta. In addition, procedure of creating a geometry file, mesh file and

modelling in River2D are presented. At the end, some previous applications of this software

package are introduced.

2D Hydrodynamic Principles in River2D 3.2.

This section is intended to provide a brief background on the physics and numerical

procedures underlying 2D depth averaged hydrodynamic models. The practical value of this

background is that it helps explain the significance of the input parameters and also highlights

the limitations and expected reliability of the model results.

Depth averaged modelling is based on the basic physical principles of conservation of

mass and momentum and on a set of constitutive laws which relate the driving and resisting

forces to fluid properties and motions. Given a set of governing equations, there are two

essential steps in developing a computational model:

1. Discretization. The infinite number of equations for an infinite number of unknowns is

reduced to a finite number of equations at a finite number of mesh or grid points in space and

time. At this stage, calculus operations are reduced to algebraic operations.

2. Solution. A scheme or process is devised where the algebraic equations developed in

the first step can be solved for the unknown nodal values. The algebra is reduced to

arithmetic which can be translated into computer code.

76

There are a number of alternatives for each step. Common discretization methods include

finite difference, finite volume, and finite element methods. Solution methods include explicit

and implicit solvers, the latter of which depend on a variety of iterative or direct non-linear

and linear equation solution methods.

The result of the finite element method, or any other discretization method, is a set of

nonlinear algebraic equations for all the unknown depths and velocities. The process of

solving these equations is what is demanding of computer resources.

Most computer models of depth averaged flow solve for transient conditions, even if

steady state results are desired. This is a convenient way of providing a controlled and stable

iteration scheme from an arbitrary first guess or initial condition. Two approaches are

generally used, referred to explicit and implicit methods.

The hydrodynamic component of the River2D model is based on the two-dimensional,

depth averaged St. Venant Equations expressed in conservative form. These three equations

represent the conservation of water mass and of the two components of the momentum

vector. The dependent variables actually solved for are the depth and discharge intensities in

the two respective coordinate directions.

Conservation of mass:

𝜕𝐻

𝜕𝑡+

𝜕𝑞𝑥

𝜕𝑥+

𝜕𝑞𝑦

𝜕𝑦= 0

Conservation of x direction momentum:

𝜕𝑞𝑥

𝜕𝑡+

𝜕

𝜕𝑥(𝑈𝑞𝑥) +

𝜕

𝜕𝑦(𝑉𝑞𝑥) +

𝑔

2

𝜕

𝜕𝑥𝐻2 = 𝑔𝐻(𝑆0𝑥 − 𝑆𝑓𝑥) +

1

𝜌 (

𝜕

𝜕𝑥(𝐻𝜏𝑥𝑥)) +

1

𝜌 (

𝜕

𝜕𝑦(𝐻𝜏𝑥𝑦))

77

Conservation of y direction momentum:

𝜕𝑞𝑦

𝜕𝑡+

𝜕

𝜕𝑥(𝑈𝑞𝑦) +

𝜕

𝜕𝑦(𝑉𝑞𝑦) +

𝑔

2

𝜕

𝜕𝑦𝐻2 = 𝑔𝐻(𝑆0𝑦 − 𝑆𝑓𝑦) +

1

𝜌 (

𝜕

𝜕𝑥(𝐻𝜏𝑦𝑥)) +

1

𝜌 (

𝜕

𝜕𝑦(𝐻𝜏𝑦𝑦))

Where H is the depth of flow, 𝑈 and 𝑉 are the depth averaged velocities in the x and y

coordinate directions respectively. 𝑞𝑥 and 𝑞𝑦 are the respective discharge intensities which

are related to the velocity components through:

𝑞𝑥 = 𝐻𝑈

𝑞𝑦 = 𝐻𝑉

𝑔 is the acceleration due to gravity and 𝜌 is the density of water. 𝑆0𝑥 and 𝑆0𝑦 are the bed

slopes in the x and y directions; 𝑆𝑓𝑥 and 𝑆𝑓𝑦 are the corresponding friction slopes. 𝜏𝑥𝑥 𝜏𝑥𝑦,𝜏𝑦𝑥

and 𝜏𝑦𝑦 are the components of the horizontal turbulent stress tensor.

Basic assumptions are:

1. The pressure distribution in the vertical is hydrostatic. Generally, this limits accuracy

in areas of steep slopes and rapid changes of bed slopes. Roughly speaking, bed

features of horizontal size less than about 10 depths (typically dune bed forms) will

not be modeled accurately. Similarly, slopes in in the direction of flow in excess of

about 10% will not be modeled correctly.

2. The distributions of horizontal velocities over the depth are essentially constant. An

assumed velocity distribution may be used in the interpretation of the provided depth

average velocity, but the distribution is treated as constant by the internal calculations.

Specifically, information on secondary flows and circulations is not available.

3. Coriolis and wind forces are assumed negligible. For very large water bodies,

particularly for large lakes and estuaries, these forces may be significant.

78

The friction slope terms depend on the bed shear stresses, which are assumed to be related

to the magnitude and direction of the depth averaged velocity. In the x direction for example:

𝑆𝑓𝑥 = 𝜏𝑏𝑥

𝜌𝑔𝐻=

√𝑈2 + 𝑉2

𝑔𝐻𝐶𝑠2 𝑈

Where 𝜏𝑏𝑥 is the bed shear stress in the x direction and 𝐶𝑠 is a non-dimensional Chezy

coefficient. This coefficient is related to the effective roughness height, 𝐾𝑠, of the boundary,

and the depth of flow through. The relationship between roughness height (𝐾𝑠), and

Manning’s coefficient (n) is:

𝑛 = 𝐾𝑠

16

26

Correlation between roughness height (𝐾𝑠) in meter, and Manning’s coefficient (n) in

𝑠

𝑚13

used in this study are presented in Table 3.1.

Table 3.1: Correlation between roughness height (𝐾𝑠), and Manning’s coefficient (n)

𝑲𝒔 0.001 0.01 0.1 0.3 2

n 0.0122 0.0179 0.0262 0.0315 0.0432

The effective roughness height was chosen as the resistance parameter because it tends to

remain constant over a wider range of depth than does Manning's n. The effective roughness

height (in m) is the resistance parameter to be specified at every node in the mesh in the input

files.

Depth-averaged transverse turbulent shear stresses are modeled with a Boussinesq type

eddy viscosity formulation. For example:

79

𝜏𝑥𝑦 = 𝑣𝑡(𝜕𝑈

𝜕𝑦+

𝜕𝑉

𝜕𝑥)

Where, 𝑣𝑡 is the eddy viscosity coefficient. The eddy viscosity coefficient is assumed to

be composed of three components: a constant, a bed shear generated term, and a transverse

shear generated term.

𝑣𝑡 = 𝜀1 + 𝜀2 𝐻√𝑈2 + 𝑉2

𝐶𝑠+ 𝜀3

2 𝐻2√2𝜕𝐻

𝜕𝑥+ (

𝜕𝑈

𝜕𝑦+

𝜕𝑉

𝜕𝑥)2 + 2

𝜕𝑉

𝜕𝑦

Where ε1, ε2, and ε3 are user definable coefficients.

The default value for ε1 is 0. The default value for ε2 is 0.5. A typical value for ε3 is 0.1,

but this may be adjusted by calibration.

In performing a two-dimensional model evaluation, the depth of flow, as a dependent

variable, is not known in advance. The horizontal extent of the water coverage is therefore

unknown.

Significant computational difficulties are encountered when the depth is very shallow or

there is no water at all over a part of the modelled area. The River2D model handles these

occurrences by changing the surface flow equations to groundwater flow equations in these

areas. A continuous free surface with positive (above ground) and negative (below ground)

depths is calculated. This procedure allows calculations to carry on without changing or

updating the boundary conditions. In addition, modelled area selection and boundary

condition specification are greatly simplified. Specifically, the water mass conservation

equation is replaced by:

𝜕𝐻

𝜕𝑡=

𝑇

𝑆(

𝜕2

𝜕𝑥2(𝐻 + 𝑧𝑏) +

𝜕2

𝜕𝑦2(𝐻 + 𝑧𝑏))

80

Where T is the transmissivity, S is the storativity of the artificial aquifer and zb is the

ground surface elevation.

The transmissivity and storativity of the groundwater flow can be set by the user. The

transmissivity should be set to a low value such that the actual groundwater discharge is

negligible; the default is 0.1 m2/sec.

For a given area, the storativity is a measure of the volume of water the ground will

release per unit decline in the water table. The default storativity is set to 1 (storativity is

dimensionless). For accurate transient analysis or to speed up the groundwater response rate,

the storativity should be reduced.

The Finite Element method used in River2D’s hydrodynamic model is based on the

Streamline Upwind Petrov-Galerkin weighted residual formulation. In this technique,

upstream biased test functions are used to ensure solution stability under the full range of

flow conditions, including subcritical, supercritical, and transcritical flow. As a result, there is

no need for mixed (unequal order) interpolations or artificially large transverse diffusivities.

Using the Finite Element Method to solve the hydrodynamic equations results in a system

of non-symmetric, non-linear equations which can be solved by explicit or implicit methods.

In River2D, an implicit approach is taken which requires a simultaneous solution of the

system of equations. Because the system is non-linear, the Newton-Raphson iterative method

is employed.

Numerical Modelling Concepts 3.3.

This section provides a brief introduction to the numerical modelling approaches used in

inundation modelling software. It is limited to the techniques used to solve the shallow water

equations or some simplified form.

The first step in numerical modelling consists of replacing the differential equations such

as the shallow water equations by a set of algebraic equations which are relationships that

link variables calculated at a finite set of points in the space-time domain. The process of

representing space and time using such points and converting the differential equations into

algebraic equations is called discretization.

81

The many numerical methods in existence can be split into classes depending on the

discretization strategy, that is, the specific approach applied to do this. The great majority of

methods used to solve the shallow water equations fall into one of three discretization

strategies: finite difference, finite element, and finite volume methods.

3.3.1. Finite Difference Methods

Finite Difference (FD) methods rely on Taylor series expansions to express the value

taken by a variable (h, u, v and so on) at a given point, as a function of the values at

neighboring points and of local derivatives of increasing orders. These Taylor series are then

combined to yield approximate expressions for the derivatives involved in the shallow water

equations, as a function of a finite number of neighboring point values.

The accuracy of the approximations can be controlled by the order to which the Taylor

series expansions are developed (the order of the so-called truncation), which is also linked to

the number of neighboring points involved.

The implementation of finite difference methods is significantly more straightforward on

a structured grid, which is a computational grid that can effectively be represented on a

square matrix (in 2D applications). This explains to some extent why their popularity is

currently in decay in the academic community, as unstructured grids lend themselves better to

the modelling of environmental flows.

3.3.2. Finite Element Methods

In Finite Element (FE) methods, the solution space in divided into a number of elements

in 2D. In each element, the unknown variables are approximated by a linear combination of

piecewise linear functions called trial functions. There are as many such functions as there

are vertices defining the element, and each takes the value of one at one vertex and the value

of zero at all other vertices. A global function based on this approximation is substituted into

the governing partial differential equations. This equation is then integrated with weighting

functions and the resulting error is minimized to give coefficients for the trial functions that

represent an approximate solution (Wright, 2005).

82

Finite element methods benefit from a rigorous mathematical foundation, however, the

technique has not been used as much as other approaches in commercial software, perhaps

because it is less accessible conceptually and produces models that result in large run-times.

Also, generating meshes can be time-consuming when a suitable mesh generation tool is not

available (Sauvaget et al., 2000).

3.3.3. Finite Volume Methods

In the Finite Volume (FV) method, space is divided into so-called finite volumes, which

are 2D (in this context) regions of any geometric shapes. The shallow water equations (in

conservative form) are integrated over each control volume to yield equations in terms of

fluxes through the control volume boundaries. Flux values across a given boundary

(calculated using interpolated variables) are used for both control volumes separated by the

boundary, resulting in the theoretically perfect mass and momentum conservativeness of the

approach (a flux into a finite volume through a boundary is always equal to a flux out of a

neighboring one through the same boundary). In 1D, finite volume methods are equivalent to

finite difference methods.

3.3.4. Computational Grids

The numerical methods outlined above are implemented on a discretized representation of

space called either a mesh or grid. A grid is a collection of points (or vertices) where the

variables defining the flow condition (velocity, depth or water level) are computed through

solution of the systems of algebraic equations obtained from the discretization process. The

resolution of the grid refers to the distance between the vertices. Closely positioned vertices

give a fine grid and widely spaced vertices give a coarse grid. The resolution may also vary in

space. The computational efficiency of a numerical model is directly related to the number of

equations that need to be solved and therefore to the resolution of the grid.

A structured grid is (originally) a grid that can be conceptually represented on a

rectangular matrix (the numerical program can effectively make use of rectangular matrices

to store the flow variables involved in the computation). Any point in the matrix is physically

connected to the four points on either side. A structured grid where the vertices are physically

83

at regular intervals apart is called a structured square grid (Figure 3.1a). A boundary-fitted

grid is a structured grid that makes use of irregular intervals between vertices (Figure 3.1b).

Figure 3.1: a) Dam-break simulation on a structured square grid from Liang et al. (2006); b) Boundary-fitted

grid from Liang et al. (2007)

An unstructured grid is a grid that cannot be represented on a rectangular matrix

(Figure 3.2). The points that constitute such a grid are kept as lists of (x,y,z) coordinates and

details on how the points are connected to each other are recorded in a database. The flow

variables computed by the model are also stored in the form of lists. The attraction of

unstructured grid models lies in the possibility to follow irregular floodplain contours, and to

apply a non-uniform resolution. It can be refined locally to take into account fine features in

the flow, while keeping a low resolution in areas where refinement is not needed, thereby

ensuring optimal use of computer power. However, the finer areas usually dictate that a

smaller time step be used which can increase computation time.

84

Figure 3.2: Unstructured mesh from Hunter et al. (2006)

The choice of discretization strategy is linked to the choice of grid type. Finite difference

methods are suited to structured grids only, whereas most finite element and finite volume

methods have been designed with both structured and unstructured grids in mind.

Structured square grids have an obvious advantage over unstructured grids in that the

construction of the physical geometry of the grid is straightforward and entirely defined by a

small number of user-defined parameters, for example resolution, lower left corner

coordinates, and dimensions (alternatively, an irregular GIS defined outline can also be used).

The issue of grid generation for unstructured grids is much more complicated, and the

process can be time-consuming if a large amount of human intervention is necessary

(Sauvaget et al., 2000). Automatic grid generation techniques are not yet used to their full

potential in the context of floodplain flow modelling. However, significant advances in this

field in recent years are beginning to be used in such applications including in some

commercially available software (such as InfoWorks-RS 2D).

Modelling of inundation in urban areas faces specific difficulties. Urban flood flow

pathways are typically narrow in size and their modelling in detail requires a grid resolution

such that computation times are excessive for most applications. It is therefore preferable to

apply coarse grids combined with some sort of sub-grid treatment of the urban environment.

While the limitations of the approach in using roughness alone to account for the overall

effects of buildings on the flow have been shown, approaches where an attempt is made to

model the directional effect of the urban area on the flow are beginning to be proposed (Neelz

and Pender, 2009).

85

River2D Modelling Procedure 3.4.

The River2D model suite actually consists of four programs: R2D_Bed, R2D_Ice,

R2D_Mesh and River2D. All programs have graphical user interfaces that are supported by

any 32 bit version of Windows. R2D_Bed, R2D_Ice, and R2D_Mesh are graphical file

editors. R2D_Bed was designed for editing bed topography data while R2D_Ice is intended

for developing ice topographies to be used in the modelling of ice-covered domains. The

R2D_Mesh program is used for the development of computational meshes that will

ultimately be input for River2D.

These programs are typically used in succession. The normal modelling process would

involve creating a preliminary bed topography file (text) from the raw field data, then editing

and refining it using R2D_Bed. If an ice-covered domain were being modelled, R2D_Ice

would be used to develop ice topography. The resulting bed topography file is used (in

conjunction with an ice topography file where relevant) in R2D_Mesh to develop a

computational discretization as input to River2D.

River2D is then used to solve for the water depths and velocities throughout the

discretization. River2D is used also to visualize and interpret the results and perform

PHABSIM type fish habitat analyses. An iterative approach at various stages, including

modification of the bed topography (and ice topography), is usual.

Input files for River2D have the file extension .cdg. Use of R2D_Ice is only required

when modelling flow under an ice cover. In this case, an ice topography file (a text file with a

.ice file name extension) would be developed using R2D_Ice and then loaded into River2D

once the .cdg file for the domain has been opened.

River2D Bed 3.5.

R2D_Bed is a utility program intended for use with the River2D river modelling system.

R2D_Bed is an interactive and graphical bed topography file editor. The normal modelling

process would involve creating a preliminary bed topography file (text) from the raw field

data, then editing and refining it using R2D_Bed.

86

The River2D model family is based on the Triangulated Irregular Network (TIN)

methodology, including breaklines, for spatial interpolation of nodal parameters.

Input to, and output from, R2D_Bed model is in the form of bed topography files, usually

indicated with a .bed filename extension. These files are also input to the R2D_Mesh finite

element mesh generator program.

A single node is represented by a line in the .bed file and consists of a point number

(integer), x-coordinate (floating point number), y- coordinate (floating point number), bed

elevation (floating point number), bed roughness height (floating point number), and an

optional code (up to twenty alphanumeric characters), all separated by any number of spaces

or tabs.

The first, and simplest, method of defining breaklines is to enclose the points forming the

breakline in brackets. Curved brackets "(...)" indicate an "open" breakline, which starts at the

first point and ends at the last point. Square brackets, "[...]", indicate a closed breakline,

which starts and ends at the same point like a polygon. The closing point (same as the starting

point) should not be entered a second time.

Curly brackets, "{...}", are used to delineate default computational boundaries. Like the

square brackets, they delimit the points that make up a polygon. Any number of boundary

polygons may be defined with the following restrictions. The first polygon represents the

outer boundary, enclosing the overall area to be modelled. It must be defined with the points

proceeding in a counter-clockwise fashion around the polygon. The subsequent polygons

represent internal boundaries which are being excluded from the modelled domain, such as

islands. These polygons must be defined with the points proceeding in a clockwise fashion.

87

Figure 3.3: A sample .bed file with nodes, breaklines and triangulation displayed.

River2D Mesh 3.6.

The purpose of the R2D_Mesh program is to provide a relatively easy to use but effective

mesh generation facility for two dimensional depth-averaged finite element hydrodynamic

modelling. Essentially, a bed topography file, containing pointwise elevations and

roughnesses over the reach of interest, is taken as input to the R2D_Mesh program. The

points can be independent or connected in breaklines or featurelines. A finite element mesh is

defined interactively and graphically by the user with the aid of various tools. Finally, when

the user is satisfied, an input file for the River2D finite element hydrodynamic model is

generated. This file is complete and the flow solution may proceed directly although some

changes to the default run options may be desired.

In R2D_Mesh, the boundary is defined by graphically “drawing” a polygon around the

area to be modeled. First, select the “Define External Boundary” command under the

“Boundary” menu, then position the cursor and click boundary node positions. If there is

more than one inflow segment, each must be defined separately with its own discharge.

Selecting “Set Inflow by Area” under the “Boundary” menu allows the user to draw a “rubber

band” rectangle around a group of boundary segments and set the discharge for all selected

segments at once.

88

As with the inflow boundary condition, selecting “Set Outflow by Area” under the

“Boundary” menu allows the outflow elevation for a group of outflow boundary segments to

be set at one time. When defined, outflow segments are shown in blue.

Normally the boundary is discretized first. Select the “Boundary Nodes” item from the

“Generate” menu. A dialog appears which asks for the desired spacing. The default value of

1000 meters is generally adequate as intermediate points will be automatically generated as

required.

Generally, the objective is to provide a high node density in critical areas while having

lesser densities in unimportant or slowly varying areas.

The most basic fill option available is the Uniform Fill. Since this option places nodes

throughout the domain, the spacing chosen is usually the coarsest desired. The dialog box

first asks for a spacing and then for an angle. The spacing is used to set the location of the

nodes such that all nodes will be equidistant from each other in an equilateral triangular

pattern. The angle (between 0o and 90

o) is the pattern angle from the horizontal (x) direction.

The inserted nodes can be triangulated at any time with the “Triangulate” (icon)

command under the “Generate” menu. This command invokes a constrained Delauney

triangulation routine which gives the “best” possible triangles.

To make the triangles more regular in shape and to give a more gradual transition

between triangles of different sizes, the mesh should be smoothed. Select the “Smooth”

(icon) command from the “Generate” menu. The smoothing process moves each point to a

more central position with respect to neighboring points, as defined by the triangles. After the

points have been moved, the entire mesh is re-triangulated, to insure the best possible

triangulation. The smoothing process may be repeated as often as desired. The mesh will

become smoother and more regular, but the discretization contrast will gradually diminish.

The QI value displayed on the status line is a mesh Quality Index, which may be used as a

rough guide. The number presented is the minimum “triangle quality” value for all triangles

generated. The triangle quality is defined as the ratio of triangle area to circumcircle area (the

circle which passes through the three points defining the triangle) normalized to the

corresponding ratio for an equilateral triangle. Thus, an ideal mesh (all equilateral triangles)

would have a QI of 1.0. Real meshes will have a QI of less than one. Typical acceptable

values may be in the order of 0.15 to 0.5.

89

Once an acceptable mesh has been developed (or at any other time), it can be saved either

as a mesh or as a River2D input file by using the “Save As Mesh” or “Save As River2D Input

File” commands respectively under the “File” menu. The “Save As River2D Input File”

command saves the mesh in a River2D input file (.cdg extension) that is ready to be run.

Default values are supplied for all of the run parameters. These may be changed, if desired, in

the River2D model interface or by editing the resulting input file.

Figure 3.4: A sample mesh file with triangulation and boundaries displayed.

River2D 3.7.

In this part, main steps for running River2D in transient condition are described:

Initial Conditions:

For any transient simulation, initial conditions must be specified at every computational

node within the domain. When using River2D to obtain a steady state solution, we use

somewhat arbitrary initial conditions. This is because we are not concerned with the path the

model takes to get to the final steady state. In a transient simulation, the path is the solution,

so the initial conditions should represent the flow conditions in the domain at the time the

transient phenomenon enters the domain. Because it is unlikely that initial conditions will be

available from field data, it is common practice to use the model to obtain initial conditions.

90

This is accomplished by running the model to steady state with constant boundary

conditions that are equivalent to the boundary conditions just prior to the transient event.

Alternatively, the model can be run in transient mode from an arbitrary initial condition with

appropriate boundary conditions to the point in time when the desired simulation is to start.

Once initial conditions are set, the next step is to specify the boundary conditions for the

transient simulation.

Boundary Conditions:

Unsteady boundary conditions for subcritical flow usually take the form of discharge

hydrographs at inflow boundaries and stage (water surface elevation) hydrographs at outflow

boundaries. River reaches modelled with 2D models are typically around 10 channel widths

in length. Therefore, it is unlike that hydrographs will be available at the location of model

boundaries when simulating historical events. In these cases, a 1D flow model could be used

to obtain the necessary hydrographs. The 1D model could be developed such that it

incorporates the 2D reach and boundaries for the 1D model could be chosen to coincide with

gauging stations.

Setting the boundary condition at the inflow:

Choose Flow > Edit Flow Boundary…

Using your mouse, click on the inflow boundary (green line).

This will open the Edit Flow Boundary dialog box, shown as Figure 3.5a. Modify this

inflow so that its boundary condition is a discharge hydrograph.

Click on the radio button beside “Time Varying Discharge”.

Click on the active Browse button below this radio button. This will open File Open

dialog box.

The hydrograph file contains the discharge hydrograph for our hypothetical event. The

left column in this file is time in seconds in ascending order and the right column is the

corresponding discharge in m3/s.

For the outflow boundary condition a proper level of water is entered.

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Setting River2D Model Parameters for Transient Simulations River2D’s transient mode is

accessed through the Run Transient dialog box. At this point, open the Run Transient dialog

so that the contents of the box and specify appropriate values for model parameters are there.

Choose Flow > Run Transient.

The dialog box in Figure 3.5b will appear.

The Run Transient dialog box is quite similar to the Run Steady dialog box. However,

there are enough differences that a discussion of the different fields in this dialog is

warranted.

The "Present time" value is the point in time at which the model is currently running or

has stopped at. In contrast to steady mode, time cannot be loosely specified when using the

model in transient mode. The present time is used to set the model boundary conditions based

on input hydrographs (discharge and/or elevation) and to generate output at appropriate

times. It is recommended that the time only be reset at the beginning of a simulation. Since

our input hydrograph is defined starting at a time of 0 seconds, the present time should also

be set to 0.

"Final time" is the time at which execution of the hydrodynamic model will be stopped.

As in steady mode, execution is halted once the present time equals or exceeds the final time.

"Time step increment, Δt” is the size of the current time step. It may be set at the start of a

run, provided that it does not exceed the Goal time step increment. The program will

automatically adjust it downward or upward as necessary in order keep the solution within

the specified tolerance after every time step. If the model is running smoothly it should

remain at the value of the Goal time step increment.

"Goal Δt” is the user specified time step increment for the simulation. It is also the

maximum time step that the model will allow. This value is also used in defining when file

output from the analyses will be generated. For example, if the model is run with a goal Δt =

2, then the model will ensure that a solution is produced at t = 2, 4, 6, 8…etc., even if the

actual time step increment must be less than 2 to maintain stability.

At every time step, River2D solves a system of non-linear equations. This non-linear

system is solved by approximating it as a linear system and then iterating to a solution, with a

specified level of accuracy, using the Newton-Raphson technique.

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“# iterations per Δt” is simply an indicator of how many Newton-Raphson iterations were

required to achieve model convergence at the last time step.

“Max # of iterations per Δt” is a user specified setting that limits the number of Newton-

Raphson iterations for each time step. If the actual number of iterations reaches this value

before the solution change is within the tolerance criterion, then the time step will be rejected

and the time step increment will be reduced to half its current value.

"Solution tolerance" is a user specified value that controls the amount of solution

convergence required at every time step. At the end of each Newton-Raphson iteration, the

value of each solution variable (3 for each node) is compared to their respective values from

the previous iteration. If the change in all of the variables is less than the user specified

solution tolerance, then the time step is accepted. A larger value of tolerance will result in

fewer Newton Raphson iterations per time step. However, accuracy may be compromised and

numerical instabilities may occur. Testing has suggested that a value of 0.01 is appropriate.

“Implicitness, θ” is a user specified value that controls the way in which the model solves

the system of governing equations. A value of 0 indicates fully explicit while a value of 1

specifies fully implicit. The solution to the governing equations is most accurate when the

model is run semi-implicit, that is θ = 0.5. However, the solution is more stable with θ = 1.0.

"Total Inflow" and “Total Outflow” represent the total discharge flowing into and out of

the model, respectively. In a transient analysis these will change according to the transient

boundary conditions.

"Update display every -- time steps" is used to set how often the display updates. As

drawing the display takes some processor time away from the computations, it may be

advisable to limit the number of times that the screen is redrawn. We will use the default

value of 1 for this parameter.

The “Output Options” button simply opens the Transient Output Options Dialog box.

This dialog allows the user to select and customize output from the transient analysis.

There is one last parameter that should be set. This is the upwinding coefficient in the

finite element scheme. It is recommended that this coefficient be to a value of 0.25 for

transient simulations.

93

Select Options > Flow Options…This will open the Flow Options dialog box. Set the

upwinding coefficient to 0.25 and press “OK”.

Generating Output:

River2D is equipped to generate various types of output when running the model in

transient mode. Transient model output is specified and formatted using the Transient Output

Options dialog box. This dialog can be accessed either by clicking on the Output Options

button in the Run Transient dialog box or by selecting “Transient Output Options” in the

Options menu. We will now have a look at the various output formats and specify some

output for our simulation.

Click on the “Output Options” button in the Run Transient dialog box.

There are three possible types of transient output available to the user: video output, point

output, and cdg output. We will get River2D to generate a video output for our simulation.

Putting a check beside “Point Output”. This will enable the point output options. This

option allows the user to output transient model results at specified points. These output

points must be specified in a csv (Comma Separated Values) file.

Click on the first “Browse” button after the “Point Output” check point to locate the csv

file that contains the coordinates of the output points.

Navigate to the R2D_Transient folder, select the file entitled with .csv, and press “OK”.

The points in this file defined a transverse section through the reach.

Check beside all the options in the “Select output variables” group box.

In the “Variable output file prefix” edit box, type in a prefix.

Click on the second “Browse” button in this section of the dialog to select a folder to

place our point output file. Locate the R2D_Transient folder and press “OK”.

Specify a value in the edit box for “Output variable data every -- goal time steps”.

Click on the “Initialize Output” button and then click on the “Close”.

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(a) (b) (c)

Figure 3.5: a) introducing upstream hydrograph; b) transient modelling dialogue box; c) transient output options

dialogue box (River2D Manual, 2002)

River2D Applications 3.8.

There are some papers and reports about the different application of River2D software for

two-dimensional hydraulic modelling.

Wardman and McDaniel (2013) presented their study for validation of 2-D hydrodynamic

models. They used two different models:

1- River2D (free). Developed by the University of Alberta;

2- ADH (free). Developed by ERDC (Engineer Research and

Development Center, US Army Corps of Engineers).

Calibration of the numerical result was performed by velocity measurement (Large Scale

Particle Image Velocimetry). This method is image based and non-intrusive. These are key

results of their study:

Large scale 2D depth average models can provide reasonable approximations, but

are limited due to inherent assumptions;

Bed roughness, in the form of Ks or Manning’s n, is the primary variable which

affects velocity distribution.

95

Bright (2012) presented a research about fish habitant in rivers. They used specific

module of River2D for fish habitant study. Figure 3.6 shows the reconstruction of bed

(geometry) in River2D for their case study.

Figure 3.6: Topographic survey (up) and River2D mesh generation (down) (Bright, 2012)

Katopodis and Ghamry (2005) used River2D for ice cover analysis in Athabasca River,

Alberta, Canada. The ice module is incorporated into the River2D model to adjust or adapt

the hydraulics to account for the presence of an ice cover of known thickness and roughness.

Figure 3.7: The layout of the reach (left) bed roughness heights over the reach for ice–covered condition (right)

(Katopodis and Ghamry, 2005)

96

Another study with River2D presented in a report on Red River Valley water supply

(2003). This study focused on hydrologic and geomorphologic aspects of aquatic needs in the

Sheyenne River from Harvey, North Dakota. Fish habitant study performed and compared by

two packages of PHABSIM (the one dimensional hydrodynamic model,"1D") and River2D

(two dimensional hydrodynamic model, "2D").

For this study, the major advantage of River2D modelling over PHABSIM was the

attractive visual aids generated to display hydraulic and habitat results. However, River2D is

more labor intensive and expensive.

Figure 3.8 shows the result of another similar study in British Columbia, Canada

conducted by BC hydro.

Figure 3.8: Sample result of 2D hydraulic modelling with River2D (BC hydro, Canada)

Another application of River2D in ice-covered rivers presented by Susitna-Watana Hydro

in 2014. This results showed in Figure 3.9 are about an ice-covered river in Alaska, USA.

97

Figure 3.9: 2D hydraulic modelling with River2D (Susitna-Watana Hydro, USA)

Chelminski (2010) also used River2D for the evaluating of stream restorations. The river

in his study is in North Carolina.

Figure 3.10: River2D mesh generation (left) and velocity result (right) (Chelminski, 2010)

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Picture: Flood in Minot, North Dakota, USA, 2011

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CHAPTER 4

4. MODELLING OF THE IDEALISED CITY

Introduction 4.1.

This chapter is about the modelling of a sudden transient flow of the dam-break wave

type in an Idealised City in order to investigate the effects of flow depth and velocity on such

a city. A characteristic of urban 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.

An Experimental test was conducted by Soares-Frazão and Zech (2008) in Université

Catholique de Louvain for a square city layout of 5 × 5 buildings aligned with the approach

flow direction, so called “Idealised City”. In this experimental study, data were recorded

using water-level gauges and digital-imaging technique. These form a complete data set

available to validate numerical models aimed at transient flow modelling in complex

geometries. This research was part of the European FLOODsite project.

Experimental Test (Idealised City) 4.2.

A series of laboratory experiments were carried out at the civil engineering laboratory of

the Université Catholique de Louvain, Belgium (Soares-Frazao and Zech, 2008). The test

case that has been used in this Master’s thesis was conducted in a 36 m long flume, 3.6 m

wide. A gate was located between two impervious abutment blocks to simulate a breach.

A sketch map of the experimental set-up is shown in following figures. The initial water

depth in the reservoir was 0.40 m and 0.011 m in the downstream reach. 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

100

channel was assessed to 0.010 𝑠

𝑚13

by steady-flow experiments without the blocks and the

gate. The ratio between building and street widths was chosen from aerial views of Brussels

(Belgium), showing that 3 to 1 was a realistic value.

The layout of the city in the experiment was idealised in the sense that a square city was

composed of 5 × 5 buildings, aligned with the incoming flow direction. In this experiment the

buildings were impervious wooden blocks of 0.30 × 0.30 m; the streets were 0.10 m wide.

The buildings in the experiment were high enough in order to not be submerged by the flow.

Water surface evolution was measured by means of several resistive level gauges and the

surface velocity field was recorded using a digital-imaging technique to track the movement

of tracer particles on the free surface.

Figure 4.1: Experimental set-up and channel dimensions in (m)

Figure 4.2: Cross section (m) (except the inlet)

Observations indicated that the flow rises at the city front before entering the streets, after

wave impact that is similar to the impact against a single obstacle. A hydraulic jump forms at

the impact section (Figure 4.3), with the water level locally higher than without the presence

of the buildings.

101

Figure 4.3: Hydraulic jump upstream of the urban district (Soares-Frazao and Zech, 2008)

The free-surface profile along the left central street (y =0.20 m) includes a hydraulic jump

after 5 s (Figure 4.4b) following the flow reflection against the buildings, whereas the flow

depth in the city is still low. After 10 s (Figure 4.4d), the upstream hydraulic jump is still

present but the water level has significantly increased in the streets. The flow in the streets

has evolved from supercritical (with a control section near the street entrance) to subcritical

(with a control section at the street exit).

102

(a) (b)

(c) (d)

Figure 4.4: Water-surface profiles along the central longitudinal street at y = 0.2 m: experimental data (•), (a) t =

4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s, reproduced from Soares-Frazao and Zech (2008)

(a) (b)

(c) (d)

Figure 4.5: Velocity along the central longitudinal street located at y = 0.2 m: experimental data (•), (a) t = 4 s,

(b) t = 5 s, (c) t = 6 s, (d) t = 10 s, reproduced from Soares-Frazao and Zech (2008)

103

Previous Applications of Idealised City for Validation of Modelling 4.3.

Results of the study by Soares-Frazão and Zech (2008) has been used for the following

research by Xia et al. (2011) and Petaccia et al. (2010), as well.

Modelling of a flash flood risk in an urban area was studied by Xia et al. (2011).

According to them, the processes of flood propagation in urban areas are often simulated by

two-dimensional (2D) hydrodynamic models.

They conducted an integrated study for flood risk in an urban area stating by a validation

of their numerical model by the experimental results of Soares-Frazão and Zech (2008).

They presented the results of the validation of their hydraulic models in terms of water

level and water velocity by comparison with the above mentioned experimental study of

Idealised City (Figure 4.6 and Figure 4.7).

Research by Xia et al. (2011) continues after the validation, by modelling of one case

study of urban flood. Different flood hazard scenarios by considering different hydrograph

was used in their study. Figure 4.9 indicates theirs results in terms of distributions of water

depths and velocities as the peak discharge arrived.

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(a) (b)

(c) (d)

Figure 4.6: Water level profiles at y = 0.2 m along the longitudinal street at different times: (a) t = 4 s; (b) t = 5

s; (c) t = 6 s; (d) t = 10 s (Xia et al., 2011)

(a) (b)

(c) (d)

Figure 4.7: Water velocity at y = 0.2 m along the longitudinal street at different times: (a) t = 4 s; (b) t = 5 s; (c) t

= 6 s; (d) t = 10 s (Xia et al., 2011)

105

Figure 4.8: Inflow discharge hydrographs for different flood frequencies (Xia et al., 2011)

Figure 4.9: Distributions of (a) depths (b) velocities at the time of peak discharge (Xia et al., 2011)

Petaccia, et al. (2010) also followed the research about Idealised City. In their study,

simplified and detailed two-dimensional modelling approaches to transient flows in urban

areas, based on finite-volume solution of the shallow water equations, are compared. Through

the example of a dam-break flow in a simplified urban district for which accurate laboratory

data exist, various methods are compared:

106

The solution of the two-dimensional shallow water equations with a detailed

meshing of each street;

The use of a porosity concept to represent the reduction of water-storage and

conveyance in the urban area;

The representation of urban areas as zones with higher friction coefficient.

Accuracy and adequacy of each method are assessed through comparison with the

experiments. Among the simplified models, the porosity approach seems to be the most

adequate as head losses at the entrance and the exit of the city are considered.

Three 2D numerical models of different levels of accuracy and complexity were

considered. The detailed approach solves the shallow-water equations (SWEs) on a fine mesh

that represents any detail of the street network (detailed model or DM); a simplified approach

solves, on a coarse mesh, SWE with porosity terms that represent the water storage and

conveyance reduction of the urban area (porosity model or PM); another simplified approach,

still solving SWE on a coarse mesh, represents the urban area as an area with high roughness

(roughness model or RM). Following figures show the model and results of their study.

Figure 4.10: Idealized city layouts: (a) Case 1; (b) Case 2 (Petaccia et al., 2010)

107

Figure 4.11: Coarse mesh used for the porosity and roughness approaches (Petaccia et al., 2010)

Figure 4.12: Water levels—RM model: aligned case, t=6 s (Petaccia et al., 2010)

Figure 4.13: Computed and observed water levels: aligned case, t=10 s (Petaccia et al., 2010)

108

Development of Idealised City Model in River2D Package 4.4.

Since water level at initial condition and discharge are needed for the numerical

modelling, dam break calculation was used in order to derive these needed data from the

experimental study. Considering an ideal dam break surging over a dry river bed, the method

of characteristics may be applied to completely solve the wave profile as first proposed by

Ritter in 1892. The dam break may be idealized by a vertical wall that is suddenly removed

(Figure 4.14). After removal of the wall, a negative wave propagates upstream and a dam

break wave moves downstream.

Figure 4.14: Sketch of dam break wave in a dry horizontal channel (Chanson, 2004)

At the origin (x = 0), equations by Ritter predicts a constant water depth:

𝑑 (𝑥 = 0) =4

9 𝑑0

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Similarly the velocity at the origin is deduced:

𝑉 (𝑥 = 0) = 2

3 √𝑔𝑑0

After dam break, the flow depth and velocity at the origin are both constants, and the

water discharge at x = 0 equals:

𝑄 (𝑥 = 0) = 8

27 𝑑0 √𝑔𝑑0 𝐵

Where:

g = ground acceleration;

d0 = Water depth behind the gate before abrupt opening;

B = Gate width;

Considering B = 1 m, g = 9.81 m/s2, and d0 = 0.4 m, needed data are calculated:

𝑑 (𝑥 = 0) ≅ 0.18 𝑚

𝑉 (𝑥 = 0) ≅ 0.32 𝑚

𝑠

𝑄 (𝑥 = 0) ≅ 0.235 𝑚3

𝑠

Calculations were performed assuming a smooth rectangular channel, an infinitely long

reservoir and for a quasi-horizontal free surface. That is, bottom friction is zero and the

pressure distribution is hydrostatic. These conditions are not completely valid in this study,

however, since the channel and its inlet are rectangular and horizontal and bed roughness is

very low (n = 0.01 𝑠

𝑚13

), conditions are acceptable.

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As it was described in the previous chapter, the first step for modelling is to generate the

bed file. Since the model is very sensitive to the geometrical parameters, 14 different models

(without blocks) were created. At this stage, building blocks were not added to models in

order to reduce the complexity. In order to have positive coordinates in the model, the

coordinates in Y direction were added by 1.8 m.

Since the model with exact geometry of experimental test (Model No. 1) did not work

properly, following geometrical parameters was changed in order to reach a decent model for

the idealized city. Table 4.1 addresses these geometry changing and their result.

Inlet Shape

Elevation of side walls

Changing the configuration of thalweg

Enlarging width of the model

Increasing length of the model

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Table 4.1: 14 different bed geometries constructed for the Idealised City

Model Length

(m)

Wall elevation/

height (m)

Inlet shape Sections shape Worked

(Yes/No)

Comment

1 8 1 / 1

No Exact geometry

of the

experimental

test

2 8 101 / 1

No Elevated and

trapezoidal

inlet

3 8 105 / 5

No Higher walls

and wide

trapezoidal

sections

4 8 105 / 5

No Higher walls

and wide

rectangular

sections

5 8 101 / 1

No Single thalweg

for all sections

6 8 105 / 5

No Single thalweg

for all sections,

elevated and

high walls

7 8 101 / 1

No Wider sections

8 800 105 / 5

Yes Long model

with single

thalweg, high

walls

9 50 105 / 5

No Long model

and wide

rectangular

sections

10 100 105 / 5

No Long model

and wide

rectangular

sections

11 200 105 / 5

No Long model

and wide

rectangular

sections

12 500 105 / 5

Yes Long model

and wide

rectangular

sections

13 500 101 / 1

No Long model,

geometry of the

experimental

test, elevated

14 500 101 / 1

Yes Long model.

Elevated and

trapezoidal

inlet

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General notes for Idealised City geometrical models:

Although models No. 2, 3 and 4 were far from the experimented test, from

geometric point of view in inlet shape, elevation and height of walls, it was

beneficial to understand that these models do not work properly neither due to the

shape of inlet nor due to the elevation nor due to the height of side walls.

Although the original shape of Idealised City sections must be generated by two

thalweg lines, models No. 5 and 6 were created by a quasi-rectangular shape with

one thalweg at the bottom middle, for the sake of simplicity. These models proved

that the problem is not due to the shape of cross sections and place of thalweg.

First acceptable results were in the Model No. 8 with 800 meters of the length.

This model indicates the necessity of having high ratio between length and the

width of the model.

Models No. 9, 10, 11 and 12 created in order to find the minimum acceptable

length for the model. Based on these steps, 500 m was chosen for the model.

Model No. 13 with 500 meters and exact geometry of the inlet and other sections

was created. This model did not work properly and showed high values of velocity

in inlet position, which means this section needs simplification and the model is

very sensitive to sharp edged inlet shape.

The last model (No. 14), which worked properly, is basically the same as second

one with very high length. This model is chosen for next steps.

As a summary, there were two difficulties to make the geometry of the Idealised City that

are solved by model No. 14:

1) the shape of inlet must be trapezoidal;

2) model must be very long in order to avoid downstream boundary condition effect.

Since water level at inlet position for initial time is equal to 18 cm, the difference between

original rectangular shape and trapezoidal shape in Model No. 14, in terms of water

discharge, is negligible as it is shown in the following figure. Therefore, replacing the

trapezoidal shape instead of rectangular one is acceptable.

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Figure 4.15: Comparison between trapezoidal and rectangular shapes for the inlet section of the Idealised City

Next step is to add blocks for the Idealised City model. For this purpose, first

corresponding four points of each square block have to be entered in the text file. Figure 4.16

depicts the graphical view of the bed file with these predefined points. Then, using “Define

Interior Boundary Loop (CW)” option in R2D_Bed, 25 square blocks with 30 × 30 cm

dimension are defined (Figure 4.17).

Figure 4.16: Specific points for defining city blocks in the Idealised City model

Figure 4.17: Defining blocks in the Idealised City model

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Upstream boundary condition in Idealised City model is defined as a constant discharge

of 0.235 m3/s. Since model runs in transient mode rather than steady flow, this constant

discharge was introduced to the model by a hydrograph.

Initial condition for water depth was calculated equal to 18 cm. Model bed elevation is

100 m, therefore the initial water elevation was set to 100.18 m.

Downstream boundary condition is defined by the water elevation. In order to make a dry

condition for the initial step, water level is set to 0 m in downstream, which means water is

100 meter lower than the bed elevation of the model.

The conceptual idea behind River2D to make dry initial condition is given in Figure 4.18.

The dimensions of figure are just for the presentation and has no particular meaning in this

study. The figure shows how water flow evolution affects the negative water depth just in

front of the wave. In fact by propagation of water front, the level of water increases from

elevation lower than the bed elevation till water arrives to a certain point.

If water level at downstream had been chosen equal to bed level, the water level surface

of the model at initial condition would have been similar to the dotted red line in this figure,

which is not the right condition for dry bed.

Figure 4.18: Construction of dry bed for initial condition in River2D

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16 monitoring points are defined to record water depth and velocity along the central

longitudinal street located at y = 0.2 m of the model (Table 4.2 and Figure 4.19). These points

are exactly chosen according to the results of the experimental test (Figure 4.4).

It must be noted that in the experimental test all these 16 points were recorded for the

water level, however, some of them were chosen for velocity representation (Figure 4.4 and

Figure 4.5). Nevertheless, in our numerical modelling, all these points were used either for

water level or for the velocity results.

Since for our models positive coordinates were used, the Y direction has been shifted by

1.8 m. Therefore, central longitudinal street that was located at y = 0.2 m in the original

experimental model, is in y = 2 m in the River2D model. However, in order to compare the

results with the experiment, this street is still referred as y = 0.2 m in the following.

Table 4.2: Monitoring points along longitudinal street located at y = 0.2 m of Idealised City model

Point No. X Y Point No. X Y

1 4.1 0.2 9 5.95 0.2 2 4.4 0.2 10 6.15 0.2 3 4.7 0.2 11 6.35 0.2 4 5 0.2 12 6.55 0.2 5 5.15 0.2 13 6.75 0.2 6 5.35 0.2 14 6.9 0.2 7 5.55 0.2 15 7.25 0.2 8 5.75 0.2 16 7.7 0.2

Figure 4.19: Monitoring points configuration in the Idealised City model

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Results of the Idealised City Modelling 4.5.

4.5.1. Sensitivity Analysis for Mesh Size

Completing the bed file for the Idealised City model, mesh must be generated in

R2D_Mesh. For this purpose two strategies are chosen:

1) Fine mesh for all parts of the model;

2) Coarse mesh in all parts of the model with refinement in building block position.

Since the model bed has 500 meter length, making a very fine mesh means lots of nodes

and elements. The lowest possible value was 25 cm (distance between nodes on boundaries

and all inside the model). River2D could not open mesh files with lower values for this model

due to large number of nodes and elements.

Four models with different mesh sizes created as follows:

1) Mesh size 25 cm for all part of the model;

2) Mesh size 30 cm for all part of the model;

3) Mesh size 50 cm with refinement in block position;

4) Mesh size 70 cm with refinement in block position;

Refinement of mesh is additional step in River2D after loading the bed file in “Mesh

Edit” tab with the option “Region Refine” under the same tab. Figure 4.20 shows the mesh

different sizes in building block positions and the rest of model due to region refinement.

Figure 4.20: Mesh size 70 cm with region refinement in the block position

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The graphical evolution of water depth for mesh size 70 cm is depicted in Figure 4.21.

The numerical results of sensitivity analysis for water depth and velocity are presented in

Figure 4.22 and Figure 4.23. The following conclusion can be deduced by this study:

The most compatible results in terms of either water depth or velocity belong to

the largest mesh size (70 cm with refinement in block position);

The larger the mesh size, the faster the wave front (Figure 4.22);

The larger the mesh size, the faster the computational time;

Water front has not reached to the end of blocks for small mesh sizes (25 and 30

cm) after 10 sec (Figure 4.22 d);

Model with mesh size 25 cm, have lower values of water depth and velocity

comparing to the experimental test;

Model with mesh size 30 cm, have lower values of water depth (except at 10 sec)

and higher values of velocity comparing to the experimental test;

Almost all the models have the same shape of wave front comparing to the

experimental test, and there is a hydraulic jump at X = 5 m, where water hits the

first blocks;

Model with mesh size 70 cm has very similar results of water depth with the

experimental test, especially at the end of test (Figure 4.22 d);

Model with mesh size 70 cm has slightly higher water depth and lower velocity

comparing to the experimental results. Maximum water depth is very similar to

the experiment (e.g. Figure 4.22 a), which is around 20 cm;

Even the largest mesh size (70 cm) has slower wave front comparing to the

experiment (Figure 4.22 a, b);

Results in terms of water depth are also compatible with previous studies by Xia

et al. (2011) especially in 4 sec and 10 sec (Figure 4.6 and Figure 4.22 a, d);

All in all, we concluded that in order to have the most reliable result especially to

model a wave propagation with proper velocity, the highest value for the mesh

size must be selected. This means that in River2D by reducing the mesh sizes, not

only the computational time increases significantly, the wave front might become

slower than the reality, which might lead to a not reliable result, as it is shown for

this sensitivity especially for the mesh sizes 25 cm and 30 cm.

118

Water depth at 4 sec




Water velocity at 10 sec

Figure 4.21: Water depth and velocity for mesh size 70 cm with region refinement in the blocks position

119

(a) (b)

(c) (d)

Figure 4.22: Sensitivity analysis for water-surface profiles and mesh size along the central longitudinal street

located at y = 0.2 m: experimental data (•), (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s

(a) (b)

(c) (d)

Figure 4.23: Sensitivity analysis for velocity and mesh size along the central longitudinal street located at y =

0.2 m: experimental data (•), (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s

120

4.5.2. Sensitivity Analysis for Groundwater Parameters

There are two groundwater parameters inside River2D; storativity and transmissivity. In

this section, sensitivity analysis for these two parameters in the Idealised City model is

described.

Storativity (S): the volume of water that a permeable unit will absorb or expel from

storage per unit surface area per unit change in head. Storativity is a dimensionless property:

𝑆 = 𝐿3

𝐿2 × 𝐿

The volume of water that will be drained from or added to an aquifer as the head is raised

or lowered, is derived from:

𝑉 = 𝑆 × 𝐴 × ∆𝐻

Where A is the area overlying the aquifer.

Transmissivity (T): This is a measure of how much water can be transmitted horizontally

through a unit width of a fully saturated aquifer under a hydraulic gradient of 1.0.

Transmissivity is the product of the hydraulic conductivity and the saturated thickness of

the aquifer:

𝑇 = 𝑏 × 𝐾

T has units of L2/T.

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The default values for transmissivity and storativity in River2D are 0.1 and 1,

respectively. However, the user manual recommends that for accurate transient analysis or to

speed up the groundwater response rate, the storativity should be reduced.

Interaction between groundwater and surface water in the case of urban flooding is very

complex. Therefore, four combination for storativity and transmissivity are modelled:

1) Storativity = 1, Transmissivity = 1;

2) Storativity = 0.001, Transmissivity = 1;

3) Storativity = 1, Transmissivity = 0.1;

4) Storativity = 0.001, Transmissivity = 0.1.

Based on the result of mesh sensitivity analysis, the mesh size 70 cm with refinement in

block position was chosen.

Results from these four models are significantly different. Graphical representation of

water depth (at t = 4 sec and 10 sec) and velocity (at t = 10 sec) for these models are

compared in Figure 4.24. Difference between water front velocity and water extension in

these models are depicted.

Numerical results for water level and velocity are presented in Figure 4.25 and

Figure 4.26.

Another meaningful representations for water depth evolution in time for four points

along the central longitudinal street located at Y = 0.2 m (X = 5 m, 5.55 m, 6.15 m and 6.9 m)

are shown in Figure 4.27. The same representation for velocity evolution in time are

illustrated in Figure 4.28.

The following conclusion can be deduced for groundwater sensitivity analyses:

The most compatible results in terms of either water depth or velocity belong to

the model 4 (storativity = 0.001, transmissivity = 0.1). This result is in line with

the recommendation by River2D manual;

Models with higher value of storativity equal to 1 (models number 1 and 3), have

very slow wave front as it is depicted in Figure 4.24. This result also can be

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deduced from Figure 4.25, in which red and sky blue curves (belong to model 1

and 3) are moving slower than two others. This result can be seen in the

Figure 4.27 d, as well. In this figure, wave front has not reached to X=6.9 m (last

blocks), even after 10 sec. Therefore, having a very low value for storativity is

very crucial, especially in this model that is no actual interaction with

groundwater (experimental hydraulic flume was sealed);

Comparing between models number two and four, it is concluded that the default

value for transmissivity equal to 0.1 had the better result;

The lower the groundwater parameters, the faster the wave front. Velocity of wave

front was more sensible to the storativity in this case. However, as we decreased

the storativity three time more than the transmissivity, this result was expectable;

Models with higher transmissivity (models 1 and 2) have lower results for water

depth (Figure 4.25);

According to Figure 4.27 and Figure 4.28, models 2 and 4, with storativity equal

to 0.001, have more compatible water evolution for water depth comparing to the

experimental test, whereas only model 4 (storativity = 0.001, transmissivity = 0.1)

have comparable results of velocity for some points (e.g. X = 6.15 m);

Finally, storativity = 0.001 and transmissivity = 0.1 is suggested for next steps of

modelling according to the result of this sensitivity study.

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Model 1: Storativity = 1, Transmissivity = 1

Model 2: Storativity = 0.001, Transmissivity = 1

Model 3: Storativity = 1, Transmissivity = 0.1 Model 4: Storativity = 0.001, Transmissivity = 0.1

Figure 4.24: Sensitivity analysis for groundwater, water depth at 4 sec, water depth and velocity at 10 sec.

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(a) (b)

(c) (d)

Figure 4.25: Sensitivity analysis for water-surface profiles and groundwater parameters along the central

longitudinal street located at y = 0.2 m: experimental data (•), (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s

(a) (b)

(c) (d)

Figure 4.26: Sensitivity analysis for velocity and groundwater parameters along the central longitudinal street


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(a) (b)

(c) (d)

Figure 4.27: Sensitivity analysis for water depth and groundwater parameters along the central longitudinal

street located at y = 0.2 m: experimental data (•), (a) x = 5 m, (b) x = 5.55 m, (c) x = 6.15 m, (d) x = 6.9 m

(a) (b)

(c) (d)

Figure 4.28: Sensitivity analysis for velocity and groundwater parameters along the central longitudinal street

located at y = 0.2 m: experimental data (•), (a) x = 5 m, (b) x = 5.55 m, (c) x = 6.15 m, (d) x = 6.9 m

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4.5.3. Sensitivity Analysis for Roughness

In this section, results of sensitivity analysis for roughness in the Idealised City model is

presented. Since River2D accept roughness height (Ks) instead of Manning’s coefficient (n),

two different models were compared in this stage:

1) Model with roughness height 𝐾𝑠 = 0.01 m (Manning coefficient n = 0.0179 𝑆

𝑚13

)

2) Model with roughness height 𝐾𝑠 = 0.001 m (Manning coefficient n = 0.0122 𝑆

𝑚13

)

Models have mesh size 70 cm, storativity and transmissivity of 0.001 and 0.1

respectively. Manning coefficient (n) of the experimental test is 0.01 𝑆

𝑚13

. Therefore, the

second model has roughness value closer to the test. Figure 4.29 and Figure 4.30 present the

numerical results for two above mentioned models. The conclusion of this study is:

Results in terms of water depth and velocity are very similar and they did not

show significant difference by changing the roughness height. It should be noted

that the difference between these two models in Manning’s n is not very much,

therefore, this result is reasonable.

In the model with lower roughness height (Ks = 0.001), lower water depth was

expected. In Figure 4.29, results seem otherwise. In fact, in this study with lower

roughness height, wave front arrives faster and that is why it seems a bit higher in

some points.

Shapes of wave front for either models are very similar with exception for t = 10

sec (Figure 4.29 d).

It is difficult to differentiate between water velocity results of these two models

(Figure 4.30). Detailed comparison in following table showed that velocity values

for the second model (lower roughness) are higher in some points, as it was

expected.

Table 4.3: Velocity comparison for roughness sensitivity analysis

X = 5 m Model 1 (m/s) Model 2 (m/s) X = 5.55 m Model 1 (m/s) Model 2 (m/s)

t = 4 sec 0.189 0.234 t = 4 sec 0.510 0.524

t = 5 sec 0.193 0.238 t = 5 sec 0.569 0.571

t = 6 sec 0.199 0.246 t = 6 sec 0.552 0.575

t = 10 sec 0.263 0.278 t = 10 sec 0.610 0.614

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(a) (b)

(c) (d)

Figure 4.29: Sensitivity analysis for water depth and roughness height along the central longitudinal street


(a) (b)

(c) (d)

Figure 4.30: Sensitivity analysis for velocity and roughness height along the central longitudinal street located at

y = 0.2 m: experimental data (•), (a) t = 4 s, (b) t = 5 s, (c) t = 6 s, (d) t = 10 s

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Conclusion for Modelling of the Idealised City 4.6.

Based on the results of three sensitivity analyses performed namely mesh size,

groundwater parameters and roughness height, following conclusion are presented. These

results are used for the case study modelling in the next chapter.

The most compatible results in either water depth or velocity is for the mesh size

70 cm (the largest mesh size). Therefore in order to have decent wave front

velocity, largest possible mesh size should be selected in River2D. This result is in

contrast with the recommendation of some literature studies, in which the smallest

mesh size are suggested. Nevertheless, size of building and streets in urban

modelling should be taken into account, as in this model for the building block

position a refinement of mesh was performed.

Model with lowest values of groundwater parameters (storativity = 0.001 and

transmissivity = 0.1) had the closest results with the experiment. It was in line

with recommendations of the manual and reasonable as the experiment condition

(sealed hydraulic flume) had not any groundwater interaction.

Results for two roughness heights were very similar and both are close to the

experimental test. Comparison between two models showed that the higher the

roughness, the lower the velocity and the higher the water depth, as it was

expected.

All in all, numerical results proved that modelling of the Idealised City with

River2D led to reliable results and the modelling procedure was validated by the

experimental test. However, various difficulties to generate a proper geometry in

River2D package should be taken into consideration.

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Picture: Flood in Venice, Italy, 2012

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CHAPTER 5

5. HAZARD MODELLING FOR THE CASE STUDY

Introduction 5.1.

The town of Sondrio is located in the Mallero catchment, which is situated on the

Southern flanks of the Alps in Northern Italy, near the Swiss-Italian border (Figure 5.1).

Sondrio has approximately 22,000 inhabitants and is located on the alluvial fan of the River

Mallero just few hundred meters upstream of where the Mallero emerges into the Adda River

at approximately 280 m asl.

Numerous flood events have been recorded during the last century in the town of Sondrio.

Records show that major floods happened in 1911, 1927, 1951 (Molinari et al., 2013). It is

reported that a specifically intense one was the one in 1927. However, due to the

technological limitations of the time it happened, there are no available records that could

allow its in‐depth investigation. As it happened more recently, the event in Valtellina that

occurred in 1987 is probably the most famous one and investigations have been carried out

on its basis ever since. In this event the town was not flooded, however, due to sediment

transport and bed elevation, the river channel inside the city was almost full (Figure 5.3).

Following the event, an investigation started in order to better understand the features of

the hazard. The estimated peak was about 500 m3/s and the total duration of 60 hours (for

comparison; the 100-year peak discharge is 640 m3/s with the same duration). The sediment

transport led to aggradation of up to 5 m at the Garibaldi Bridge and more than 2 m at the

Eiffel Bridge (Radice and Elsayed, 2014).

Ivanov (2014) carried out a research as a Master’s thesis in Politecnico di Milano focused

on an attempt of integrated modelling of event‐scale water and sediment transport processes.

A return period of 100 years served as a definition of the intensity of the event and therefore,

the boundary conditions used for the different models were based on this value. This study

showed significant bed aggradation in river reach inside the city due to decreasing the bed

slope, especially around Garibaldi Bridge. In this scenario water overwhelms the river bank

131

at Garibaldi Bridge and enters the city. Temporal evolution of river bed and water elevation

at the Garibaldi Bridge is shown in Figure 5.4. Outflow hydrograph for this location

(Garibaldi Bridge) was constructed by standard weir formulas. For this purpose, due to

various sources of uncertainties, two different bounds (lower and higher) were introduced.

The final result by Ivanov (2014) is presented in Figure 5.5. These hydrographs are

considered as entry data for upstream boundary condition of this study.

Figure 5.1: Mallero basin (right) and its position in Italy and Lombardia region

Figure 5.2: Two parts of Sondrio connected with bridges over Mallero River (left), Mallero River passing

through Sondrio ends in Adda River (right)

Garibaldi Bridge

Eiffel Bridge

Marcora Bridge

Railway Bridge

Settimo Bridge

Pathway Bridge

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Figure 5.3: Sondrio in 1987 at Garibaldi Bridge (left), at bend before the bridge (right)

Figure 5.4: Temporal evolution of the river bed and the water elevation at Garibaldi Bridge for 100-year

hydrograph (Ivanov, 2014)

Figure 5.5: Hydrographs of the flood with lower bound and higher bound scenarios, adapted from Ivanov (2014)

Garibaldi Bridge

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Uncertainties in Hydraulic Modelling of Urban Area 5.2.

Sources of uncertainty in hydraulic modelling of urban area, which are all relevant in

Sondrio case study, could be summarized as follows:

1. Despite the great advances in survey techniques, topographic data may still be a

relevant source of uncertainty when data from ordinary survey techniques are used as

geometrical input.

2. Boundary conditions, in particular inflow, are a well-known source of uncertainty

(Brandimarte and Di Baldassarre, 2012). In flood events due to dyke or river bank

overtopping, reconstruction and location of flooding hydrographs is difficult, and the related

uncertainty may severely affect all the resulting simulations (Romanowicz and Beven, 2003);

(Bates, 2004); (Mignot et al., 2006); (Masoero et al., 2012). Also, river bank overtopping

may be increased by debris buildups in bridges (Neal et al., 2009).

3. In urban flood events, reproduction of the complex interactions between subsurface

drainage network and surface flow is another difficult task. Different authors have

investigated this issue using models that couple the sewer system with the surface flow (Hsu

et al., 2000; Smith, 2006; Gallegos et al., 2009; Neelz and Pender, 2010). However, during

flood events drainage systems rarely work under optimal condition and may be subject to

unpredictable local failures such as obstruction of manholes and pipes (it is difficult, if not

impossible, to make any sensible exact prediction of the time lags between the servicing of

the sewer system and the occurrence of major flooding). As a result, urban flooding may

occur due to the combined effect of sewer surcharging and surface flooding, adding further

uncertainty to reconstruction of flooding mechanisms (Neal et al., 2009).

4. During flood events, water flows typically interact with different small-scale features,

both fixed and moving. These include draining ditches, small embankments (Wright et al.,

2008; Bates et al., 2006), and walls (Yu and Lane, 2006) in rural areas; cars, fences, (Mignot

et al., 2006), road cambers, and curbs (Fewtrell et al., 2011) in urban landscapes. Some

features related to micro-topography may be included in model grid when high-resolution

data are available (Yu and Lane, 2006; Fewtrell et al., 2011), while the effect of vegetation

can be represented through resistance parameters, based on terrain heights (Schubert et al.,

2008). On the contrary, minor fixed obstacles, cars and other vehicles are much more difficult

to reproduce and are not generally considered in model grid, as they would be impossible to

134

characterize. However, the problem of their influence on local flow conditions should be

considered, especially when very fine mesh resolutions are used. For instance, cars may

partially obstruct narrow streets and contribute to forming debris roundups that can affect

overall flow processes (Mignot et al., 2006). This is especially dangerous in urban flood

events characterized by a high energy flow, as demonstrated by the recent catastrophic flood

event of November 2011 in Genoa, Italy (Cavallo et al., 2012), and, again, it is difficult, if not

impossible, to predict where cars will be parked at the time of flooding.

5. In urban areas, the interaction of buildings with flow processes is complex. Building

walls act as impervious obstacles, modifying and deflecting flow path (Chen et al., 2012);

(Schubert and Sanders, 2012). On the other hand, as flooding progresses buildings also

behave as porous media, as water normally enters inside buildings and fill them, producing

levels that tend to be similar to outside values (Mignot et al., 2006; Schubert et al., 2008;

Dottori and Todini, 2012). Therefore, their representation in model grid is not straightforward

as both these processes should be considered.

6. Especially in high energy flow conditions, transport and erosion processes, like debris

buildups, scour, damage, and collapse of buildings, can modify the configuration of the study

area and affect flow dynamics (Mignot et al., 2006; Gallegos et al., 2009).

Even when theoretical research works are carried out, modelers should always bear in

mind the practical use of their results. Hydraulic models can produce flood inundation maps

with extremely high precision, but these outputs need to be aggregated to a coarser scale to

obtain readable maps that can be useful for, say, evacuation plans or risk assessment. Indeed,

this loss of modelling detail can be advisable, the use of too high resolution outputs can

generate a false confidence on obtained results (Dottori et al., 2013). In other words, the

Keynesian view that it is better to be ‘‘approximately right, rather than precisely wrong.” is

very meaningful.

In practical applications, the assessment of inundation areas is usually carried out in a

deterministic fashion by means of hydraulic models. Those are first calibrated relative to a

specific historical flood event, and then used to estimate flood extents relative to different

(and typically higher) event magnitudes. This procedure, even when physically based and

numerically complex models are considered (e.g. fully 2-D model, etc.), relies on some

fundamental assumptions that may be summarized as follows:

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Capability of the model to correctly reproduce the hydraulic behavior of the river

and inundated floodplains;

Time stationarity of model parameters, i.e. the roughness coefficients calibrated

for a specific event are considered suitable for a range of flooding scenarios that

could differ significantly from the calibration event;

All hydraulic information (i.e. flow hydrographs, rating curves) are error-free.

The effects of uncertain (upstream and downstream) boundary conditions on flood hazard

assessment is still poorly understood. The effect of the downstream boundary condition on

the area of interest is reduced, if not completely removed, by extending the hydraulic model

far downstream of the area of interest. However, this expedient may be costly and time

consuming to implement, or difficult due to a lack of data (Domeneghetti et al., 2013).

Despite these different sources of uncertainties, the 2D modelling of urban areas could be

performed with acceptable level of accuracy with proper sensitivity analyses, in order to

identify and reduce the uncertainties.

Table 5.1: Sources of uncertainty in urban flood hazard mapping (Domeneghetti et al., 2013)

Modules Natural uncertainty Epistemic uncertainty

Hydrological

Analysis

annual maximum discharge;

flow hydrograph shape;

measurement error;

limited time series length;

statistical inference;

parameter estimation

peak discharge estimation;

flow hydrograph wave form;

Rating-

Curve

variation of river geometry in time; discharge measurement errors;

mathematical expression for rating-curve estimation;

number of pair used for rating-curve estimation;

methodology for rating-curve estimation;

interpolation/extrapolation errors;

Flood

Routing

variation of river geometry over time; error in model selection;

numerical simplification;

parameter calibration;

Dike

Stability

geometrical variation over space;

variation of geotechnical parameters in space;

final width and development time of levee

breaches;

measurements errors of levee geometry;

variability estimations of levee parameters

(permeability, material cohesion, etc.);

formalization of dike breach processes;

Flood

Dynamics

variability of surface roughness in space and

time due to variable land use;

error in model selection;

numerical simplification;

DEM inaccuracy;

parameter estimation;

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Sondrio Model Description and Input Data 5.3.

The Mallero passes through the center of Sondrio generating flash floods, which are a

serious risk facing the town. The town is protected from flooding by dikes (i.e. concrete

walls: Figure 5.6), the bank-full discharge is equivalent to 700 m3/s. However, the risk arises

from the danger of river bed aggradation, which can significantly reduce this level of

protection leading to the flood walls being overtopped.

According to Ivanov (2014), flood overwhelms left bank of the river at Garibaldi Bridge.

Therefore, in this study only east part of the city was modelled (left side of Mallero looking

from upstream to downstream).

Figure 5.7 (a) and (b) show how building blocks from the city map have been defined in

the model. Dashed polygon shows the interested part of the city that was used for

construction of building blocks. The buildings were also modelled by blocked out method, in

which water cannot enter the buildings.

(a) (b)

Figure 5.6: Mallero River looking toward south (left), HEC-RAS cross section for this part of the river (right)

Dealing with various sources of uncertainties, River2D model is constructed with

simplification of building blocks and extension of downstream boundary. Constructed model

is big in terms of its dimensions. The model has 1100 meter extension from north to south

and 1900 meter from east to west (Figure 5.7 c). Bed elevations varies from 286 m asl in the

downstream up to 313 m asl in the upper point. Downstream boundary condition, which is in

term of water level, was selected equal to 260 m to have dry initial condition.

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Based on Figure 5.7 (c) and Figure 5.8 (b), average bed elevation at inflow position is

about 304.7 m asl. Width of the inlet in Sondrio model is 22 meters and water level for initial

condition is introduced as 305 m asl. Therefore, as it is shown in Figure 5.8 (b), average

water depth for initial condition is 30 cm at the inflow.

Inflow discharge is based on the Mallero River outflow hydrographs shown in Figure 5.5.

These hydrographs have 34 hours duration. It was found that when the 34-hour hydrograph

was used, which started from zero value of discharge, the water propagation in the model was

very slow to develop from the inlet, gave very unreliable outcome and water disappeared

around inlet position instead of propagating downstream. Besides, if 34-hour hydrograph was

used, the model calculation time would be very longer. Therefore, it was decided to start from

four hours before the peak and to end four hours after the peak. Figure 5.9 shows 8-hour

hydrographs (upper bound and lower bound) used as upstream boundary condition in the

Sondrio model.

138

(a)

(b)

(c)

Figure 5.7: a) Aerial view of Sondrio including buildings, b) River2D model generated for Sondrio including

building blocks, c) model dimensions and bed elevation variation

1100 m

Inflow (Garibaldi Bridge)

1900 m

139

(a) (b)

Figure 5.8: a) Inlet location (zoomed in the River2D model), b) initial water level vs bed level at inlet position

Figure 5.9: 8-hour hydrographs of the flood with lower bound and higher bound scenarios constructed for

River2D modelling of town Sondrio (derived from Figure 5.5)

Monitoring Points and Monitoring Routes in the Sondrio Model 5.4.

Sondrio model is very big (1100 m × 1900 m) and water propagation is quite complex.

Therefore, a network of monitoring points including 36 points were introduced in the model,

as it is shown in Figure 5.10.

Inflow

140

Figure 5.10: Schematic view for monitoring points in Sondrio model

Table 5.2: Monitoring points in Sondrio model

Point No. X Y Point No. X Y

1 567120 5113400 19 567540 5113160

2 567060 5113350 20 567650 5113160

3 567205 5113355 21 566870 5113000

4 567080 5113280 22 567170 5112960

5 567220 5113280 23 567390 5112960

6 567310 5113280 24 567560 5113020

7 566940 5113250 25 567750 5113080

8 566990 5113210 26 566580 5112880

9 567110 5113150 27 566820 5112880

10 567200 5113180 28 567070 5112880

11 567340 5113200 29 567410 5112880

12 567500 5113270 30 566460 5112800

13 567600 5113290 31 566900 5112800

14 566770 5113100 32 567300 5112800

15 566980 5113090 33 567720 5112800

16 567100 5113040 34 566600 5112650

17 567200 5113060 35 567100 5112650

18 567370 5113100 36 567500 5112650

In addition, three specific routes are defined in order to better understand the water

propagation along main streets of the city. Selection of these routes was according to the

places with highest water discharge intensity in Y direction (Figure 5.11).

These routes also represent more meaningful results for flood propagation in time and

space. They pass from three main streets of the city (Figure 5.12).

Each monitoring route consists of three monitoring points as it is addressed in Table 5.3

and is illustrated in Figure 5.13.

141

Figure 5.11: Three monitoring routes based on the highest discharge intensity in Y direction

Figure 5.12: Three monitoring routes location on Sondrio map

Table 5.3: Monitoring routes configuration

Route No. No. of 1st Point No. of 2

nd Point No. of 3

rd Point Length (m)

1 4 8 15 235

2 9 16 28 270

3 5 10 17 220

Figure 5.13: Schematic view for monitoring routes configuration

142

Following pictures from Street View of Google Map show the starting point for the flood

scenario at Garibaldi Bridge and three monitoring routes along the streets of Sondrio.

Garibaldi square, which is the main square of the city, is the starting position for

propagation of flood into routes 2 and 3 (Figure 5.16).

Figure 5.14: Flood starting point (inlet position in the model) at Garibaldi Bridge

Figure 5.15: Three different direction of flood propagation along the monitoring routes

Figure 5.16: Garibaldi Square (Piazza Garibaldi) starting place for flood routes 2 and 3

Route 1

Route 2

Route 3

Route 2 Route 3

143

Flood route No. 1 starts in via Alessi (Monitoring point No. 4), and continues toward via

Parolo (Monitoring points No. 8 and 15). At the end of this route there is an open space

illustrated in Figure 5.19. Length of this route is 235 m and the width of streets varies from 6

to 12 m.

Figure 5.17: Via Alessi, first point of the route No. 1 (monitoring point No. 4)

Figure 5.18: Via Parolo, second point of the route No. 1 (monitoring point No. 8)

Figure 5.19: Via Parolo, third point of the route No. 1 (monitoring point No. 15)

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Flood route No. 2 is the place of water propagation from Piazza Garibaldi into Via Caimi

(Figure 5.16). This route starts in via Caimi (Monitoring point No. 9), and continues for about

270 m along this street including monitoring points No. 16 and 28. This is a straight 2-lane

street from north to south with about 8 m width.

Figure 5.20: Via Caimi, first point of the route No. 2 (monitoring point No. 9)

Figure 5.21: Via Caimi, second point of the route No. 2 (monitoring point No. 16)

Figure 5.22: Via Caimi, third point of the route No. 2 (monitoring point No. 28)

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Flood route No. 3 is the place of water propagation from Piazza Garibaldi into the corso

Vittorio Veneto (Figure 5.16). This route starts in corso Vittorio Veneto (Monitoring point

No. 5) and continues for about 220 m, passing from monitoring point No. 10, ends in an open

area of Piazzale Giovanni Bertacchi (Monitoring point No. 17). The railway station building

is a few meters after the end point of this route. Width of corso Vittorio Veneto is about 8 m.

Figure 5.23: Corso Vittorio Veneto, first point of the route No. 3 (monitoring point No. 5)

Figure 5.24: Corso Vittorio Veneto, second point of the route No. 3 (monitoring point No. 10)

Figure 5.25: Piazzale Giovanni Bertacchi, third point of the route No. 3 (monitoring point No. 17)

146

Sensitivity Analysis for Mesh Size 5.5.

In practice, especially for applications in urban environments, the optimal grid scale is

still under discussion and different opinions on this issue have been given.

Several authors (Schubert et al., 2008; Fewtrell et al., 2011; Schubert and Sanders, 2012)

have agreed that mesh size should be related to the average dimension of buildings and roads

in the test site.

The message that seems to emerge in many current research works is that ‘‘more

information (in terms of mesh resolution and topographic detail) will result in better model

performance.’’ This approach, which can be termed ‘‘reductionist,’’ may sometimes be

misleading, and generate confusion between the concepts of accuracy and precision.

In the field of hydraulic modelling, model precision can be related to the resolution of the

computation grid, where the variables of interest are computed, and the detail of governing

equations. On the other hand, model accuracy is defined as the ability of the model to

correctly reproduce the variables of interest, for instance, an observed flood extent map.

The two definitions only partially overlap. A certain level of precision is of course

necessary for model reliability, but beyond some limit (depending on the case) an increase of

precision does not necessarily imply greater accuracy (Dottori et al., 2013).

On the contrary, in our mesh sensitivity analysis for Idealised City, the larger mesh size

had the better result. Therefore, in this study, the more reliable results are being expected for

large mesh sizes rather small. However, it has to be a limit for enlarging the mesh size. In this

sense, very different sizes are compared in order to find the optimum size.

For Sondrio model 6 different mesh sizes generated; 20 m, 40 m, 60 m, 80 m, 100 m and

120 m. Table ‎5.4 gives a general idea for these models and their performance.

Calculation time are according to an typical computer with Core i3 CPU 2.3 GHz.

Figure 5.26 shows the geometrical differences in mesh sizes between these models.

Higher bound hydrograph (discharge maximum equal to 117 m3/s) and roughness height

(Ks) equal to 0.3 m were used for all models in this sensitivity analysis.

147

Table 5.4: Comparison between mesh sizes generated for Sondrio case study

Mesh

Size

(m)

Number

of

Nodes

Number

of

Elements

Mesh

Quality

Index (QI)

Calculation Time for

10 Min Flood (Min)

Estimated Calculation

Time for 8-hour Flood

(Hours)

Comments

20 4362 7353 0.078 360 288 (12 days) Flood wave is very slow

40 1565 2372 0.073 120 96 (4 days) Flood wave is very slow

60 978 1243 0.048 60 48 (2 days) Acceptable results

80 737 985 0.032 20 16 Acceptable results

100 612 834 0.003

5 4 Results were not reliable. Water

propagation stops after certain time

120 498

640

0.003

4 3.2 Results were not reliable. Water

propagation stops after certain time

Mesh size 20 m Mesh size 40 m 40

Mesh size 60 m Mesh size 80 m 40

Mesh size 100 m Mesh size 120 m

Figure 5.26: Graphical representation for different mesh sizes in Sondrio model

148

Water propagation in the two first models (mesh sizes 20 m and 40 m) is very slow. There

were the same results for very fine meshes in the Idealised City model in previous chapter.

Difference between water propagation speed for mesh sizes of 40 m and 80 m is shown in

Figure 5.27 qualitatively.

Mesh size 40 m (after 20 min) Mesh size 80 m (after 20 min)


Figure 5.27: Comparison between the flood extension of mesh sizes 40 m and 80 m

In addition, flood propagation in mesh sizes 100 m and 120 m is not realistic and its

extension does not grow after a certain time. Difference between water propagation for mesh

sizes of 80 m and 100 m is illustrated in Figure 5.28 qualitatively.

149




Therefore, the only two models with acceptable results are with mesh sizes 60 m and 80

m. Figure 5.29 shows the graphical comparison between these two models.

Results from the sensitivity analysis for mesh size in Idealised City model in the previous

chapter proved that the larger the mesh size, the faster the wave front, and the more truthful

results in River2D. Therefore, mesh size of 80 m was chosen in this study.

In fact, this model has a wave front that is slightly faster than the model with 60 m mesh

size, looking in to Figure 5.29.

Numerical comparison for these two models for three monitoring routes are presented in

Figure 5.31, Figure 5.32 and Figure 5.33. These graphs show that the water depth for these

two models are very similar. In the most of the records, mesh size 80 m show higher depth.

However, this result is mainly due to the faster wave front in larger mesh size, which led to

higher water depth in certain time and point.

Another important conclusion according to Figure 5.30 is that mesh size 60 m has more

fluctuation in the result, whereas in mesh size 80 m, except for the first calculation time, the

water depth increases almost linearly by time, due to increasing the inlet water discharge.

150




(a) (b)

Figure 5.30: Water depth comparison between mesh sizes 60 m and 80 m, a) monitoring point No. 1 (Garibaldi

Bridge), b) monitoring point No. 2

151

10 min after the flood 60 min after the flood

120 min after the flood


Figure 5.31: Differences in water depth for mesh sizes 60 m and 80 m (route No. 1)





152





Sensitivity Analysis for Inflow Discharge 5.6.

Based on Figure 5.9, there are two hydrographs to be introduced as upstream boundary

condition of the Sondrio model. In this section, Sondrio model with 80 m mesh size and

roughness height (Ks) equal to 0.3 m was selected for this sensitivity study.

Since the 8-hour hydrographs in Figure 5.9 have two linear parts, the introduction of these

hydrographs as an entry to the River2D is very straightforward (Table 5.5).

Table 5.5: Hydrographs as upstream B.C. for Sondrio model

Lower bound hydrograph Upper bound hydrograph

Time (sec) Discharge (m3/s) Time (sec) Discharge (m

3/s)

0 46 0 69

7200 57 7200 93

14400 68 14400 117

21600 63 21600 112

28800 58 28800 108

Graphical comparison for the water extension and depth for these two models are

illustrated in Figure 5.34. Result was expectable, the model with upper bound hydrograph has

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larger water extension. As it is shown in Figure 5.35, both water depth and velocity in the

model with upper discharge bound are higher. The same pattern can be seen in three

monitoring routes (Figure 5.36, Figure 5.37 and Figure 5.38).

Although peak water discharge in upper bound hydrograph is 1.72 times the peak water

discharge of lower bound hydrograph (117 m3/s vs 68 m

3/s), the difference in water depth of

two models is less. For instance, maximum water depth for the model with upper bound

hydrograph in monitoring points No 1, 2 and 4 are 0.71 m, 0.31 m and 1.78 m, respectively.

Maximum records for same points of the model with lower bound hydrograph are 0.49 m, 0.2

m and 1.57 m. The mean difference between the results for these three points is 1.38.

Lower bound hydrograph (after 20 min) Higher bound hydrograph (after 20 min)



Figure 5.34: Comparison for the flood extension in lower bound and higher bound hydrographs

154

(a) (b)

Figure 5.35: Sensitivity analysis of inflow discharge with lower bound and higher bound at Garibaldi Square, a)

water depth, b) velocity




Figure 5.36: Differences in water depth for lower and higher inflow hydrographs (route No. 1)

155









156

Sensitivity Analysis for Roughness 5.7.

Mesh size 80 m and higher bound input hydrograph (discharge maximum equal to 117

m3/s) were used for this sensitivity analysis.

Increasing the roughness height (Ks) coefficient from 0.3 m (n = 0.0315 𝑠

𝑚13

) to 2 m (n =

0.0432 𝑠

𝑚13

), showed that the maximum flood depth is increased, as it was expected. This

result is well shown in Figure 5.40 a, for one specific point and in three monitoring routes

(Figure 5.41, Figure 5.42 and Figure 5.43), as well.

Water extension in two models are very similar as it is illustrated in Figure 5.39. By

graphical comparison between these two models, we could conclude that the model with

higher roughness has a bit larger water extension.

Very important result from increasing the roughness is depicted in Figure 5.40. Model

with higher roughness ran very smoothly and without any fluctuation. Water depth increases

by time for first four hour and then decreases. Water depth evolution in this model as it

shown in Figure 5.40 a, has the same pattern as input hydrograph (Figure 5.9).

General conclusion for this study is that models in River2D with higher roughness height

(Ks) run faster (in terms of calculation time) and with less fluctuation. In fact, another models

with (Ks) coefficient equal to 0.1 m (n = 0.0262 𝑠

𝑚13

), 0.01 m (n = 0.0179 𝑠

𝑚13

) and 0.001 m (n

= 0.0122 𝑠

𝑚13

) were tested, as well. In those model, water extension was very small and results

were not compatible, therefore, results of those models were excluded from this study.

157

Roughness height (Ks) = 0.3 m (after 60 min) Roughness height (Ks) = 2 m (after 60 min)



Figure 5.39: Comparison between the flood extension for roughness height (Ks) 0.3 m and 2 m

(a) (b)

Figure 5.40: Sensitivity analysis for roughness height (Ks) at Garibaldi Square, a) water depth, b) velocity

158




Figure 5.41: Differences in water depth for roughness height (Ks) 0.3 m and 2 m (route No. 1)





159





Hazard Maps 5.8.

Based on the results of three sensitivity analyses namely for mesh size, roughness height

and inflow discharge, the selected model for construction of hazard maps, including water

depth and velocity, has the following basic characteristics:

Mesh size: 80 m;

Roughness height (Ks) = 2 m (equal to 0.043 Manning’ n);

Higher inflow hydrograph with peak discharge equal to 117 m3/s.

It should be taken into consideration that although lower roughness height (Ks) = 0.3 m

(equal to 0.0315 Manning’ n) were used for mesh size and inflow discharge sensitivity

analyses, model with higher value of roughness height was chosen. Because in this model the

values of water depth are higher and therefore the final hazard maps are in the safe side.

In order to generate the hazard maps, in one hand and in a quantitative approach

maximum recorded water depth and velocity in all the monitoring points were taken into

account (Table 5.6), in the other hand graphical representations like Figure 5.44 were used in

a qualitative way. In fact, the final result of the hazard maps (water depth and water velocity)

160

is a compromise between qualitative and quantitative methods. The reason is, basically the

monitoring points do not cover all the places and as it can be seen in Figure 5.44, some

places, especially close to buildings, have higher records for either depth or velocity

comparing to their adjacent monitoring points.

According to both recorded results and graphical results, three intervals for water depth

and three intervals for water velocity are defined.

Water depth intervals (m):

(0 ˂ h ≤ 0.5), (0.5 ˂ h ≤ 1.5), (1.5 ˂ h ≤ 2)

Water velocity intervals (m/s):

(0 ˂ v ≤ 1), (1 ˂ v ≤ 2.5), (2.5 ˂ v ≤ 3);

Table 5.6: Maximum water depth and velocity recorded in the monitoring points

Point No. Max water

depth (m)

Max water

velocity (m/s)

Point No. Max water

depth (m)

Max water

velocity (m/s)

1 0.8 1.4 19 0 0

2 0.54 1.14 20 0 0

3 0.56 0.59 21 0.37 0.71

4 2 0.91 22 0.4 1.15

5 0.24 0.83 23 0 0

6 0 0 24 0 0

7 0.7 0.59 25 0 0

8 1.04 1.16 26 0 0

9 0.91 0.25 27 0.27 0.59

10 0.6 0.94 28 2.16 1.17

11 0 0 29 0.07 0.38

12 0 0 30 0 0

13 0 0 31 0 0

14 0.41 0.17 32 0.08 0.05

15 0.63 1 33 0 0

16 0.14 1.71 34 0 0

17 0.08 2.5 35 0.94 0.68

18 0.14 0.42 36 0 0

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(a)

(b)

Figure 5.44: Final results for Sondrio model, a) water depth (m), b) water velocity (m/sec)

The reason for high values of water velocity in some block corners in Figure 5.44 b is the

contraction of flow in those places. The effect is local and not constant in time during the

flood duration (8 hours) of the modelling. Therefore, it is excluded for hazard map

generation.

In addition, most of the points with zero water depths and velocity in Table 5.6 are

located outside the flood extension zone.

There is an exception in Table 5.6 for water depth in monitoring point No. 28, which has

more than 2 meters water depth. The reason that in this point water depth is very high is

because of low ground level in the geometry of Sondrio model due to the underpass for the

railway line.

162

Flood extension overlapped on Google Earth map of town Sondrio is illustrated in

Figure 5.45. Total water extension calculated in the ArcGIS map is about 450,000 m2. Water

depth for the flood scenario in three above-mentioned groups is shown in Figure 5.46.

Figure 5.45: Flood extension scenario in town Sondrio

Figure 5.46: Water depth for flood scenario in Sondrio on Open Street map

163

Conclusion for Hazard Modelling 5.9.

In order to generate the hazard maps for the case study of town Sondrio, a model with

geometrical properties of the city and blocks was created. Afterward three sets of sensitivity

analyses performed to have the most reliable results. Two type of analyses are the same as the

Idealised City model namely for mesh size and roughness, and the results from that

modelling were used in this part of research as well.

First sensitivity analysis was carried out for the size of meshes. In this study 6 different

models with various mesh sizes from 20 m to 120 m were compared. Results showed that the

model with mesh size 80 m had the most acceptable results.

Second sensitivity analysis was devoted for the inflow discharge. Since the inflow

hydrographs from previous studies had been limited between an upper-bound (117 m3/sec)

and lower-bound (68 m3/sec), models with these two hydrographs compared in terms of water

depth and velocity. Result was entirely predictable and the upper-bound hydrograph with

higher values of water depth and velocity was selected for generating the hazard maps.

Finally, sensitivity analysis for roughness was performed for two values of roughness

height (Ks). As it was expectable, model with the higher value of the roughness height

showed higher water depth. Therefore, this model was picked for generating the hazard maps.

Besides, model with higher roughness height (Ks = 2 m equal to 0.043 Manning’ n) worked

very faster, in terms of calculation time, and showed results without any particular

fluctuation.

Hazard maps were generated for a model chosen by the above-mentioned analyses. The

results of this model are illustrated in Figure 5.44. Flood extension on Google Earth map for

this scenario is depicted in Figure 5.45. Water depth and water velocity were categorized in

three groups. Figure 5.46 shows the result on Open Street map.

164

Picture: Flood in Colorado, USA, 2013

C

H

A

P

T

E

R

S

I

X

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CHAPTER 6

6. FLOOD RISK ASSESSMENT

Introduction 6.1.

The approach to natural risk assessment has undergone radical change in the past few

decades, with a significant shift from a hazard-centred perspective to a much broader

understanding of risk (Weichelsgartner and Obersteiner, 2002).

In order to protect people and assets from the impact and consequences of floods, the

flood risk management plans based not only on various flood hazard scenarios, but also on

risk assessments are required, which must present the potential adverse consequences of

floods for human health, the environment, cultural heritage, and economic activity (European

Flood Directive, 2007). This requirement introduces the need to estimate the potential

damage and to identify the most appropriate definition and the methods for qualifying and

quantifying damage. In order to quantify flood risk, the expected damage is used as a unit of

measure.

The most widely used tool for estimating damage before an event are damage functions

relating a hazard parameter (generally flood depth) to a given class of exposed elements

characterised by certain vulnerability factors (Merz et al., 2010). These classes differ as to the

uses of various zones and types of building (industrial, residential, or commercial), and/or

with regard to features such as the number of floors, materials, and the existence and use of

basements (Molinari et al., 2014 b).

Damage Functions and Limitations 6.2.

Despite the large number of damage assessment models, a number of problems have been

highlighted regarding the use of damage functions: these include the limited transferability of

curves designed for one geographic area to another (Cammerer et al., 2013), and the

parameters used to characterise the hazard (Merz et al., 2004; Kelman and Spence, 2004), the

criteria used to value exposed land use and/or objects. Last but not least, there is general

agreement that the methods for developing and using damage functions are only relatively

166

stable and consistent for residential areas and buildings, while in the case of other assets, such

as industrial or commercial facilities and critical infrastructures, the methodologies are still at

a developmental stage. This is particularly the case when the most widely used tool for

assessing flood risk in terms of expected direct physical damage – damage functions – is

considered. The main reason for these problems is the scarcity of valuable calibration and

validation data, for both hazard and vulnerability models.

Moreover, usually there is a difference between observed damage and damage estimated

by each curve. This difference is due to the fact that depth–damage curves supply an average

value for the damage, even within a specific vulnerability class, so that singularity (i.e. the

damage for a specific building of a class) is hardly predicted. It is plausible that, if more than

few data were available for each vulnerability class, the average observed data for each class

would better fit with curve estimates. On the other hand, different curves supply different

estimates for the same damage, as to say that uncertainty in damage curve estimation is high

(Molinari et al., 2014 b).

Flood Damage Assessment in Italy and Limitations 6.3.

Unlike in the case of seismic risk, a standard procedure for flood damage data collection

and storage at a national scale has not been established yet in Italy, while the available

information is not easy to use in the development or validation of damage functions because

the information is provided in narrative form, so that the most significant data for validation

need to be reorganised into tables that are manageable for assessment purposes; also, because

the georeferencing of the data is rather poor and the description of the physical phenomena

that provoked the reported damage is not uniform in all cases.

Moreover, geographical and geomorphological contexts as well as those of territories

characterised by the differing urban patterns and building typologies that are typical of Italy

make it difficult either to generalise damage functions or to obtain large enough data sets to

achieve statistical relevance.

To sum up, the existing large-scale databases in Italy are too poor to support a

comparison between the results that would be obtained using damage functions from the

literature and actual damage recorded in past events; at least one of the three main factors to

167

be related – hazard, vulnerability, or damage – is always missing or too imprecise to develop

a comparison (Molinari et al., 2014 b).

Sondrio Damage Assessment: Applied Damage Curve and Final Results 6.4.

Damage assessment part of this research was conducted based on the analysis of

buildings in Sondrio, in which vulnerability data were collected according to the depth-

damage functions developed by the U.S. Army Corps of Engineers (USACE) related to the

HAZUS Multi-Hazard model.

The HAZUS flood model uses estimates of flood depth along with depth-damage

functions to compute the possible damage to buildings that may result from flooding. Two

inputs to the damage module are required to estimate building damage:

Number of building storey and presence of basement;

Depth of flooding at the building or area where the building is located.

The depth of flooding is determined using the flood hazard map. The extent and severity

of damage to structural components is estimated from the depth of flooding and the

application of the assigned depth-damage curve which expresses damage as a percentage of

replacement cost of the total value of the building.

This damage function applied at the local scale (micro-scale) and the assessment is based

on single elements (building). It represents direct, tangible, and short time damages for each

affected building, however the results considered as average for a group of similar buildings.

It is frequently noted that nominally similar buildings have experienced vastly different

damage and losses during a natural hazard.

In order to apply this method, the data needed are the building characteristics (occupancy

class, age, foundation type, presence of basement, number of floors and assumed first floor

elevation) and flood depth. However, for the purpose of this work which is conducting a

complementary sample study of appliying hazard map in order to generate a damage map, a

simplified USACE damage curve has been used for the case study. The damage curve is

shown in Figure 6.1.

168

Figure 6.1: Flood damage function based on USACE (adapted from Molinari, 2014 c)

First step to perform the damage assessment was to define the water depth levels in

ArcGIS. According to previous chapter, there are three levels of water depth. The extensions

of flood for each level are shown in Figure 6.2.

Figure 6.2: Flood hazard map for town Sondrio

169

Next step is to categorize the buildings located in the flood extension zone according to

the four types of USACE damage function:

Building category 1: One-storey building with basement;

Building category 2: One-storey building without basement;

Building category 3: Multi-storey building with basement;

Building category 4: Multi-storey building without basement.

Figure 6.3 shows a few samples for the type of buildings located in town Sondrio.

According to Menoni et al. (2012) the majority of buildings (68 %) in town Sondrio have

basement, and are highly vulnerable to flooding. In addition, based on a site visit, most of the

buildings located in the flooded zone are multi-storey. Therefore, the frequency of the

buildings in category 3 is higher than the others. The second common building type is

category 4.

Three sources for defining the building type used in this research are:

1- Site visit

2- Google Street View

3- A previous damage study for 50 buildings in town Sondrio (Molinari, 2014 c)

170

Grand Hotel Della Posta located in Piazza Garibaldi

Building category 3 (Multi-storey building with basement)

Residential building in Lungo Mallero Luigi Cadorna


Residential building in Lungo Mallero Luigi Cadorna


Residential building in Lungo Mallero Luigi Cadorna (In front of Eiffel Bridge)

Building category 4 (Multi-storey building without basement)

171

Residential building in Via Trento

Building category 4 (Multi-storey building without basement)

Sport Facility in Via Trento

Building category 2 (One-storey building without basement)

Train station of Sondrio in Piazza Bertacchi


Figure 6.3: Samples for building categories of town Sondrio

172

Based on the chosen damage function (Figure 6.1) and flood hazard map (Figure 6.2), the

following table for the damage rate corresponding to each type of building and water level

was created. The damage rates of this table is the base for generating the damage map

(Figure 6.4).

Table ‎6.1: Damage rates according to USACE damage function and level of hazard (water depth)

Damage (%)

Building Type Zone 1

(Max water depth = 2 m)

Zone 2

(Max water depth = 1.5 m)

Zone 3

(Max water depth = 0.5 m)

One storey with

basement (Cat 1)

68

58

37

One-storey without

basement (Cat 2)

61

53

28

Multi storeys with

basement (Cat 3)

50

43

27

Multi-storey without

basement (Cat 4)

43

36

18

Four levels of damage were defined for presentation in the damage map.

Damage Levels:

Very High (50 % ≤ Damage rate)

High (40 % ≤ Damage rate < 50 %)

Moderate (25 % ≤ Damage rate < 40 %)

Low (Damage rate < 25 %)

No expected damage (out of flood extension zone)

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Figure 6.4: Damage map for flood scenario of town Sondrio

Discussion and Conclusions 6.5.

Damage assessment procedure for the case study in the town of Sondrio permitted us to

point out certain fundamental weaknesses and problems associated with the way damage

functions are currently developed and applied.

As a matter of fact, finding that which damage model is more suitable to be applied on a

given area has been proven to be a challenging task.

The first issue is, despite the fact that the used curve is for micro-scale, it is not very

reliable when used for single buildings.

Second point is the damage models are very site-specific. They take into account the

characteristics of the exposed elements of a particular area, which in general change from

country to country, or even region to region. These characteristics are related to the type of

building, the materials and the type of construction. All of these features are known to change

from site to site. In fact using damage function developed for the United States, where the

construction materials and the architecture differs considerably from other countries such as

Italy can cause major uncertainty in the results.

174

The third problem is about the spatial scales. Most of the damage functions are based on

real data of past floods. In addition, these functions were obtained from large data sets during

very large events, for instance flood in large catchments of the U.S.A., while in Italy there are

generally much smaller catchment areas.

Furthermore, flood events are scattered across a wide spectrum between riverine and

mountain floods, for which, as suggested by Merz et al. (2004), water depth is not sufficient

to explain consequential damage.

To sum up, it can be stated that one of the main challenges for adapting damage models to

the local scale is the lack of data, but more precisely the lack of reliability of the data. It

obviously highlighted the need to make significant improvements to post flood event damage

surveys. The inconsistencies in, and poor performance levels of, disaster damage databases

on different scales (ranging from global to local) are the subject of debate in results, which is

also ongoing internationally (De Groeve et al., 2013).

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Picture: Flood in Alberta, Canada, 2013

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CHAPTER 7

7. CONCLUSION

We are all standing midstream in the river of knowledge. Like water in a river, the

knowledge we rely on flows from the past to the present, where our task is to add something

useful to it today, before it flows on to future generations, who will interpret it and develop it

yet further (Knight, 2013).

During the last decades, Europe suffered major damaging floods. Severe floods

reinforced the need for concerted action. The European Flood Directive published in 2007

with the requirement of carrying out a preliminary assessment to identify the river basins and

associated coastal areas at risk of flooding. For such zones there is a need to draw up flood

risk maps and establish flood risk management plans.

In this context, the main purpose of this thesis is providing the hazard and damage maps

for the case study of Sondrio which are the fundamental steps of providing flood risk maps

and flood risk management plans.

For this research a comprehensive literature review was carried out in two separated

aspects. First, in hydraulic engineering for subjects related to urban flood modelling,

including introduction of software packages available for urban flood simulation, their

capabilities and differences as well as their theoretical backgrounds related to 1D, 2D or 3D

calculation, modelling validation and how to cope with uncertainties throughout sensitivity

analyses of different key parameters like roughness, and previous modelling experiences for

urban flooding. Second, in diverse perspectives of flood risk assessment. In this part,

European Flood Directive and its definitions were introduced. Fundamental of flood risk

analysis and flood damage assessment were described. Flood damage functions were

introduced. Actions of flood on buildings and effective parameters of flood in damage

assessment were presented. Uncertainties in flood risk assessment were explained, and

available flood damage models were introduced and qualitatively compared.

177

Chapter three was dedicated to theoretical background of two-dimensional hydrodynamic

modelling especially in River2D software package. First, Shallow water equations, their

parameters and assumptions were introduced. Then, the most common discretization schemes

including finite difference, finite element, and finite volume were compared, and basic

concepts of mesh generation were introduced. River2D modelling procedure was introduced

in detail including the application of different modules of the package like R2D_Bed and

R2D_Mesh. For each module the modelling steps were defined with the corresponding

parameters. At the end of this chapter, a few samples of using River2D package for hydraulic

modelling were presented.

In order to validate the procedure of modelling and corresponding parameters of River2D,

a separate part of this research in chapter four was dedicated to a model called Idealised City

that is a sudden transient flow of the dam-break wave. The experimental test was conducted

in Université Catholique de Louvain in Belgium (Soares-Frazão and Zech, 2008) for a square

city layout of 5 × 5 buildings aligned with the approach of flow direction. In that

experimental test water surface evolution was measured by means of several level gauges and

the surface velocity field was recorded using a digital-imaging technique to track the

movement of tracer particles on the free surface. The recorded data was available and used to

compare with our modelling results.

To develop the bed file for the Idealised City model in R2D_Bed, 14 different models

were created. Basically, there were two main modifications to make the geometry of the

Idealised City. First, the shape of inlet must be trapezoidal. Second, model must be very long

in order to avoid downstream boundary condition effect. 16 monitoring points were defined

in the Idealised City model to record water depth and velocity during the modelling. Three

different sensitivity analyses were performed. First, for the mesh size, in which four models

were created. The most reliable result, which was very close to the experiment, was from the

largest mesh size. However, in that model mesh was refined in the building block positions to

have a reasonable ratio between mesh size and street size of that region. Second, groundwater

interaction was analysed. Four models with different values of storativity and transmissivity

were compared. The closest result was for the model with lowest values for these two

parameters. This result was expected considering that experimental flume was sealed,

therefore, groundwater interaction must have been the minimum in the modelling. Third,

sensitivity analysis for roughness through two models with different values of roughness

178

height. The results in this part was as expected and the model with lower roughness showed

lower water depth and higher water velocity.

Numerical results showed that modelling of the Idealised City with River2D led to

reliable outcomes and the modelling procedure was validated by the experimental test.

Results and conclusions of three sensitivity analyses for the Idealised City were crucial for

the next step of this research, in which a real case study of urban flood was modelled.

Chapter five was about modelling of the hazard scenario for the case study of town

Sondrio located in the Mallero catchments on the southern flanks of the Alps in Northern

Italy. The Mallero river passes through the center of Sondrio. The town is protected from

flooding by concrete dikes. However, the risk arises from the danger of river bed aggradation,

which can significantly reduce this level of protection.

Based on the results of a previous research, upstream boundary condition of the Sondrio

model was defined. In that study, a return period of 100 years was used for the modelling of

Mallero river flood and its bed aggradation. The study showed significant bed aggradation in

river reach inside the city especially around Garibaldi Bridge. In that scenario water

overwhelmed the river bank at Garibaldi Bridge and entered the city. Outflow hydrograph at

Garibaldi Bridge was constructed by standard weir formula. For this purpose, due to various

sources of uncertainties, two different bounds (lower and higher) were introduced as flood

outflow from Mallero river to town Sondrio. These 34-hour outflow hydrographs were used

in this research as input upstream boundary condition of the Sondrio model.

River2D model for town Sondrio was constructed with simplification of building blocks

and extension of downstream boundary. The model had about one kilometer extension from

north to south and two kilometers of extension from east to west. A network of monitoring

points including 36 points was introduced in the model. In addition, three specific routes were

defined in order to have better understanding of the water propagation along the main streets

of the city.

Three sets of sensitivity analysis were performed for the Sondrio model. First, 6 different

mesh sizes from 20 m to 120 m were generated. The first two models with mesh sizes of 20

m and 40 m showed very slow water propagation. The last two models with 100 m and 120 m

mesh sizes had unreliable results and water expansion was very small. Therefore, detailed

comparison between mesh sizes of 60 m and 80 m was carried out. Having the results of the

179

Idealised City modelling, the 80 m mesh size was selected. Because, in the Idealised City

modelling the model with larger mesh size showed the closest results comparing to the

experimental test. Second, two input hydrographs with peak discharge of 117 m3/s and 68

m3/s were compared. The result was expected and the model with higher peak discharge was

chosen due to higher level of water depth and water velocity. Third sensitivity analysis was in

roughness. Increasing the roughness height (Ks) coefficient from 0.3 m to 2 m showed that

the maximum flood depth was increased, as it was expected. Water extensions in the two

models were very similar, however, model with higher roughness height ran very smoothly

and without any fluctuation in the results.

According to the results of three sensitivity analyses namely for mesh size, inflow

discharge and roughness height, the selected model for construction of hazard maps had the

mesh size of 80 m, peak inflow discharge of 117 m3/s and roughness height (Ks) equal to 2

m. To generate the hazard maps, in one hand maximum recorded water depth and velocity in

all the monitoring points were taken into account, in the other hand, graphical results were

used. In fact, the final results of the hazard maps were a compromise between quantitative

and qualitative ways. Finally, three intervals for water depth and three intervals for water

velocity were defined.

Chapter six addressed the flood damage assessment for the scenario defined in the

previous chapter. HAZUS-MH model was chosen as the damage function in this study. The

HAZUS flood model uses estimates of flood depth along with depth-damage functions to

compute the possible flood damage to buildings. Two inputs to the damage module are

required to estimate building damage: number of storeys of the building and presence of

basement, and depth of flooding at the building or area where the building is located. The

depth of flooding was determined using the flood hazard map for the water depth. Based on

the HAZUS model, four building categories were selected as the representative of building

vulnerabilities. Finally, flood damage map was generated according to the damage rates

derived from the HAZUS model.

The damage map generated in chapter six was a sample application of risk assessment in

order to complete this research and to present a complete procedure including flood hazard

analysis and flood damage assessment. However, there were problems to perform the damage

assessment for the case study. First, despite the fact that the used curve is for micro-scale, it is

not very reliable when used for single buildings. Second, transferring curves from one site to

180

another without prior uncertainties checks. In this case, damage function developed in the

U.S.A was used in an Italian case study. Third, relates to the spatial scales. Most of the

damage functions are based on real data of past floods. In addition, these functions were

obtained from large data sets during very large events, for instance flood in large catchments

of the U.S.A., while in Italy there are generally much smaller catchment areas. Finally, flood

events are scattered across a wide spectrum between riverine and mountain floods, for which

water depth is not sufficient to explain consequential damage.

181

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