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
Politecnico di Milano
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
Politecnico di Milano
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
Politecnico di Milano
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 5.32: Differences in water depth for mesh sizes 60 m and 80 m (route No. 2) ....................... 151
Figure 5.33: Differences in water depth for mesh sizes 60 m and 80 m (route No. 3) ....................... 152
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 5.37: Differences in water depth for lower and higher inflow hydrographs (route No. 2) ...... 155
Figure 5.38: Differences in water depth for lower and higher inflow hydrographs (route No. 3) ...... 155
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 5.42: Differences in water depth for roughness height (Ks) 0.3 m and 2 m (route No. 2) ...... 158
Figure 5.43: Differences in water depth for roughness height (Ks) 0.3 m and 2 m (route No. 3) ...... 159
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).
2
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
3
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).
4
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
7
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”.
10
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.
11
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.
12
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
14
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
Mike 21
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
16
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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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)
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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.
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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
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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.
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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).
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(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)
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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)
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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:
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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)
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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)
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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
114
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
115
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
116
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 depth at 5 sec
Water depth at 6 sec
Water depth at 10 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
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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(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
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 4.30: 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
128
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
132
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
133
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:
135
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
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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.
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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
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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
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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)
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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
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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)
Mesh size 40 m (after 60 min) Mesh size 80 m (after 60 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.
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Mesh size 80 m (after 30 min) Mesh size 100 m (after 30 min)
Mesh size 80 m (after 240 min) Mesh size 100 m (after 240 min)
Figure 5.28: Comparison between the flood extension of mesh sizes 80 m and 100 m
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
Mesh size 60 m (after 60 min) Mesh size 80 m (after 60 min)
Mesh size 60 m (after 240 min) Mesh size 80 m (after 240 min)
Figure 5.29: Comparison between the flood extension of mesh sizes 60 m and 80 m
(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
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10 min after the flood 60 min after the flood
120 min after the flood
240 min after the flood
Figure 5.31: Differences in water depth for mesh sizes 60 m and 80 m (route No. 1)
10 min after the flood 60 min after the flood
120 min after the flood
240 min after the flood
Figure 5.32: Differences in water depth for mesh sizes 60 m and 80 m (route No. 2)
152
10 min after the flood 60 min after the flood
120 min after the flood
240 min after the flood
Figure 5.33: Differences in water depth for mesh sizes 60 m and 80 m (route No. 3)
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
153
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)
Lower bound hydrograph (after 60 min) Higher bound hydrograph (after 60 min)
Lower bound hydrograph (after 240 min) Higher bound hydrograph (after 240 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
10 min after the flood 60 min after the flood
240 min after the flood
480 min after the flood
Figure 5.36: Differences in water depth for lower and higher inflow hydrographs (route No. 1)
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10 min after the flood 60 min after the flood
240 min after the flood
480 min after the flood
Figure 5.37: Differences in water depth for lower and higher inflow hydrographs (route No. 2)
10 min after the flood 60 min after the flood
240 min after the flood
480 min after the flood
Figure 5.38: Differences in water depth for lower and higher inflow hydrographs (route No. 3)
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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.
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Roughness height (Ks) = 0.3 m (after 60 min) Roughness height (Ks) = 2 m (after 60 min)
Roughness height (Ks) = 0.3 m (after 120 min) Roughness height (Ks) = 2 m (after 120 min)
Roughness height (Ks) = 0.3 m (after 480 min) Roughness height (Ks) = 2 m (after 480 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
10 min after the flood 60 min after the flood
240 min after the flood
480 min after the flood
Figure 5.41: Differences in water depth for roughness height (Ks) 0.3 m and 2 m (route No. 1)
10 min after the flood 60 min after the flood
240 min after the flood
480 min after the flood
Figure 5.42: Differences in water depth for roughness height (Ks) 0.3 m and 2 m (route No. 2)
159
10 min after the flood 60 min after the flood
240 min after the flood
480 min after the flood
Figure 5.43: Differences in water depth for roughness height (Ks) 0.3 m and 2 m (route No. 3)
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.
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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
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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)
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Grand Hotel Della Posta located in Piazza Garibaldi
Building category 3 (Multi-storey building with basement)
Residential building in Lungo Mallero Luigi Cadorna
Building category 3 (Multi-storey building with basement)
Residential building in Lungo Mallero Luigi Cadorna
Building category 3 (Multi-storey building with basement)
Residential building in Lungo Mallero Luigi Cadorna (In front of Eiffel Bridge)
Building category 4 (Multi-storey building without basement)
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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
Building category 3 (Multi-storey building with basement)
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).
175
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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