Uncertainty in urban flood damage assessment due

to urban drainage modelling and depth-damage

curve estimation

G. Freni, G. La Loggia and V. Notaro

ABSTRACT

G. Freni (corresponding author)

G. La Loggia

V. Notaro

Dipartimento di Ingegneria Idraulica ed

Applicazioni Ambientali,

Universita degli Studi di Palermo,

Viale delle Scienze—Edificio 8,

Palermo 90128,

Italy

E-mail: freni@idra.unipa.it;

glal@idra.unipa.it;

notaro@idra.unipa.it

Due to the increased occurrence of flooding events in urban areas, many procedures for flood

damage quantification have been defined in recent decades. The lack of large databases in most

cases is overcome by combining the output of urban drainage models and damage curves linking

flooding to expected damage. The application of advanced hydraulic models as diagnostic, design

and decision-making support tools has become a standard practice in hydraulic research and

application. Flooding damage functions are usually evaluated by a priori estimation of potential

damage (based on the value of exposed goods) or by interpolating real damage data (recorded

during historical flooding events). Hydraulic models have undergone continuous advancements,

pushed forward by increasing computer capacity. The details of the flooding propagation process

on the surface and the details of the interconnections between underground and surface

drainage systems have been studied extensively in recent years, resulting in progressively more

reliable models. The same level of was advancement has not been reached with regard to

damage curves, for which improvements are highly connected to data availability; this remains

the main bottleneck in the expected flooding damage estimation. Such functions are usually

affected by significant uncertainty intrinsically related to the collected data and to the simplified

structure of the adopted functional relationships. The present paper aimed to evaluate this

uncertainty by comparing the intrinsic uncertainty connected to the construction of the damage-

depth function to the hydraulic model uncertainty. In this way, the paper sought to evaluate the

role of hydraulic model detail level in the wider context of flood damage estimation. This paper

demonstrated that the use of detailed hydraulic models might not be justified because of the

higher computational cost and the significant uncertainty in damage estimation curves. This

uncertainty occurs mainly because a large part of the total uncertainty is dependent on depth-

damage curves. Improving the estimation of these curves may provide better results in term of

uncertainty reduction than the adoption of detailed hydraulic models.

Key words | flood damage, flood modelling, modelling uncertainty, urban flood

INTRODUCTION

Localflooding is a recurrentproblemformanycities inEurope

whose sewers and storm water systems are often affected by

surcharging problems, pipe deterioration and construction

flaws due to a combination of aging infrastructures and

growing urbanisation (Ugarelli et al. 2005). Evaluation and

management of flood risk in urban areas has become a major

theme in recentandcurrentengineering researchandpractice,

among others: Bouma et al. (2005); Dawson et al. (2005);

doi: 10.2166/wst.2010.177

2979 Q IWA Publishing 2010 Water Science & Technology—WST | 61.12 | 2010

Apel et al. (2006);Barroca et al. (2006);Grunthal et al. (2006);

Hall et al. (2006); Chen et al. (2008);Dawson et al. (2008).

Given the high spatial concentration of people and

values in cities, the potential damage from floods is

extraordinarily high: even small-scale floods may lead to

considerable damage. Continuing urban development in

flood-prone areas increases these risks. Riverbanks and

lakesides have become preferred living spaces: most of the

large urbanised centres around the world are located in

valleys and flood plains or on coasts (WMO/GWP 2008).

Although the terminology occasionally differs, flood

damage in the literature is mostly categorised first as direct

and indirect damage and second as tangible and intangible

damage. This classification system was presented first by

Parker & Green (1987). In practical applications, analysis is

focused on tangible damage because it can be easily

estimated based on monetary costs and can be related to

hydraulic variables, such as flooding depth or velocity

components (Penning-Rowsell et al. 2003; Merz et al. 2004;

Meyer & Messner 2006; Nascimento et al. 2006).

Flood damage is usually correlated with three kinds of

data in order to extrapolate expected damage once certain

variables are known:

† hydrologic-hydraulic data, such as the flooding depth

above the ground elevation (Dutta et al. 2003), the

combination of water depth and velocity (Abt et al. 1989;

Nanıa et al. 2002), or the flooding duration (Dutta et al.

2003; Meyer & Messner 2006). Such variables permit

evaluation of the flooding severity as well as its

distribution in space and time.

† physical data, represented by land use, building charac-

teristics and types, number of storeys, house furniture,

etc. (Jonkman et al. 2008); and

† economic data, such as the social and economic

conditions of the analysed area and information about

monuments (Oliveri & Santoro 2000).

Most often, the expected damage is calculated by the

mean of depth-damage functions (Wind et al. 1999;National

Research Council 2000; Dutta et al. 2003; Apel et al. 2006;

Nascimento et al. 2006; Hardmeyer & Spencer 2007;

Dawson et al. 2008), which usually show the total damage

of valuable property (e.g. buildings, cars, roads) or its

relatively damaged share as a function of inundation depth.

Depth-damage functions are typically obtained from

systematically applied survey procedures, but they can also

be derived from analysis of insurance claims data or

historical flood data, considering the possible damage

ratio based on the given flood depths. The damage functions

are usually based on the evaluation of damages occurring in

large catchments and caused by river floods, coastal floods

and flash floods. Very few methodologies have focused on

local floods in small urban watersheds that occur due to

zenithal or pluvial waters and are usually related to sewer

system failures or to the insufficient capacity of sewer inlets

to capture surface runoff. Although the involved flood

volumes and the related damages are often not very

harmful, consistent economical losses and, consequently,

damages for people can be produced in the long term due to

the high frequency of this kind of failure event.

The depth-damage function’s applicability is limited to

data used for interpolation unless a mathematical model is

used for scenario analysis. In recent years, several pro-

cedures have been proposed in the literature for assessing

flood damages in urbanised watersheds by combining the

flood depth-damage curves and the output of urban flood

models (Dawson et al. 2008; Jonkman et al. 2008; Prince &

Vojinovic 2008). The adoption of flooding propagation

models provides some advantages, allowing for the analysis

of several potential flood scenarios (Mark et al. 2004) and

the effectiveness of mitigation measures (Freni & Oliveri

2005). Mark et al. (2004) discussed the advantages and

limitations of urban flood modelling, highlighting the fact

that in practical applications, simplified approaches are

most likely adopted for reducing computational efforts and

coping with insufficient system information. Such

approaches are based mainly on 1-D De Saint Venant

(DSV) equations according to the dual-drainage concept

(Djordjevic et al. 1999; Leandro et al. 2009). In these

simplified approaches, sewer flow is modelled using a 1-D

model coupled with a 1-D surface network model of open

channels (streets, pedestrian lawns, etc.) and ponds for

floodable areas, among others: Despotovic et al. (2002);

Merz et al. (2004); Chen et al. (2005); Djordjevic et al.

(2005); Lipime Kouyi et al. (2009). Such approaches are less

computationally demanding than more complex models,

but they cannot represent the complexity of flooding

propagation in open spaces where the process is general

2980 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

multi-dimensional. In these cases, 1-D/2-D models are

used, coupling 1-D DSV equations for the underground

sewer system and 2-D flooding propagation on the

catchment surface, among others: Hsu et al. (2000); Ettrich

et al. (2005); Schmitt et al. (2005); Carr & Smith (2007);

Smith et al. (2006); Chen et al. (2007); Lipime Kouyi et al.

(2009). Independent of the detail level of model equations,

many studies have been carried out regarding the simu-

lation of the linking element between the two network

systems. Some studies identify dynamic vertical interactions

between major and minor systems through manholes or

groups of gully inlets. Most of the models developed so far

model the linkage between subsurface and surface net-

works as a weir or an orifice (Mark et al. 2004; Nasello &

Tuccairelli 2005; Kawaike & Nakagawa 2007), a combi-

nation of both or simply as a sink (Aronica & Lanza 2005;

Aronica et al. 2005). Other studies take into account the

possibility of multiple inlets and the reduction clogging

factor for study of grate sag inlets (Almedeij et al. 2006) or

the use of multiple linking element to model the linkage

between the sewer manhole and the surface (Carr & Smith

2007; Leandro et al. 2009).

In addition, progress has been made in wrapping urban

drainage models with sophisticated interfaces and

gluing routines to link them with Geographical Information

Systems (GIS) in order to automatically create a detailed

representation of the overland flow network that can

interact with the minor system (Maksimovic et al. 2009;

Gironas et al. 2010).

As described previously, mathematical models have

been much improved in recent years, while the correlation

between damage and flooding characteristics has been

mainly limited to simplified regression laws. For this

reason, a detailed analysis of the urban flooding phenom-

ena may not be justifiable when the goal of analysis is

evaluation of the expected damage related to a given

flooding event. In this case, uncertainty related to flood

damage evaluation can be high due to the accumulation of

uncertainty sources (e.g. intrinsic uncertainty of collected

data, uncertainty due to the regression approach) con-

nected with the depth-damage- curves. Finally, flooding

data are often not available for each part of the urban

watershed and can be greatly affected by measurement

errors (Freni et al. 2006).

In the present study, uncertainty connected with the

evaluation of the depth-damage curve has been estimated

and compared with the uncertainty provided by the

adoption of modelling approaches providing different levels

of complexity. This paper aims to highlight the importance

of a correct balance of those instruments (models, regres-

sion curves) that are use for expected damage forecasting in

order to obtain reliable results without adopting costly but

useless detailed models.

The analysis was applied to a real case study of the

“Centro Storico” catchment in Palermo (Italy): a highly

urbanised area about 2.5 km2 affected by local surface

flooding due to drainage system insufficiency, for high

frequency rainfalls.

MATERIALS AND METHODS

Local flooding modelling in urban areas

Several phenomena can produce urban flooding, includ-

ing inundations from natural water bodies, direct surface

runoff and overflows and surcharges from sewer net-

works. Sometimes one of these phenomena is dominant

and can be considered alone; in other cases, flooding is

the result of the complex interaction of these factors.

Such complexity reflects on the adopted modelling

approaches that can be derived from existing urban

drainage models, including, among others, MOUSE by

Lindberg et al. (1989), InfoWorks by Bouteligier et al.

(2001) and SWMM by Huber & Dickinson (1988). or it

can be specifically built for flooding analysis. The 1-D/2-D

approaches enable more realistic analysis of the overland

flows, especially during extreme flooding events in which

flood flows are not confined to road and street profiles,

but require a higher level of spatial detail and increased

computational capacity. The 1-D/1-D approach involves a

simple numerical scheme and is less computationally

demanding than the 1-D/2-D approach (Paquier et al.

2003; Lhomme et al. 2006), but requires pre-defined

surface flooding pathways and flooding areas. The 1-D/1-D

approaches are more widely used in practical applications

and were also adopted for the present study given the

absence of wide-open spaces in the analysed case and

2981 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

the fact that flooding originated from sewer surcharge. In

the present study, two approaches have been adopted,

both based on the SWMM model: one simple and

computationally parsimonious (model 1) and the other

more detailed and resource-demanding (model 2).

Model 1

In the parsimonious approach, a distributed “non-linear

reservoir” model is adopted to simulate surface runoff,

taking into account both the surface storage and the

infiltration phenomenon.

Concerning surface storage, a constant hydrological

loss, concentrated at the beginning of the rainfall event, is

applied: different unit losses have been considered for

pervious surfaces and for impervious ones. The infiltration

is simulated using the Horton equation.

The rainfall-runoff routing is solved by coupling the

continuity Equation (Equation (1)) and the Manning

Equation (Equation (2)):

S›hs

›t¼ Sip 2 Q ð1Þ

Q ¼1

nLðhs 2 h0Þ5=3s1=2s ð2Þ

where Q is the surface runoff; S is the sub-catchment surface

area; i p is the net rainfall intensity; L is the sub-catchment

width; ss is the sub-catchment average slope; hs and h0 are,

respectively, the water depth and the depression storage

depth on sub-catchment surface; and n is the Manning

roughness coefficient.

Since the problems of drainage systems hydraulic

insufficiency must be analysed with the need to take into

account backwater and/or surcharge phenomena into the

sewer pipes, a mathematical model is adopted here that

Sewer manhole

Street inlets

Street curb

Sewer pipe

Floodedsewer manhole

Fictive basin

Weir(Eq. 5)

Weir(Eq. 5)

Sewer flow(Eqs. 3,4)

Catchment runoff(Eqs.1,2)

Figure 1 | Surface storage-weir approach.

2982 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

Sewer manhole

Streetinlets

Street curb

Sewer pipe

Flooded sewer manhole

Street channel

Sewer flow(Eqs. 3,4)

Catchment runoff(Eqs. 1,2)

Surface flow(Eqs. 3,4)

Seweroverflow

Surface flow(Eqs. 3,4)

Seweroverflow

Figure 2 | Dual drainage approach (Djordjevic et al. 1999).

“Centro Storico” catchment

Upstream watersheds

Sewer pipes

15

1413

121110

9

87

6

5

43

21

RG

RG Rain Gauge

Flooded area

PALERMO

13°18’ 59.05’’E

38°0

4’ 3

9.41

’’N

38°07’ 23.03’’ N

13°23’ 52.18’’ E

“Centro Storico”catchment

Upstreamwatersheds

Figure 3 | The “Centro Storico” catchment of Palermo (Italy).

2983 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

solves the complete 1-D De Saint Venant Equations

(Equations (3) and (4)):

A›v

›xþ v

›A

›xþ

›A

›t2 q ¼ 0 ð3Þ

›h

›xþ

v

g

›v

›xþ1

g

›v

›tþ

vq

gA¼ s 2 J ð4Þ

where g is the gravity acceleration, s is the sewer slope, J is

the unit resistant force, q is the inflowing discharge per unit

length, v is the stream velocity, h is the water depth and A is

the cross-section area.

In model 1, the surface drainage system (street net-

works, squares, parking lots, etc.) is simulated according to

two basic functions: a storage function and a transport

function. More specifically, the surface storage-weir

approach (Figure 1) has been adopted in order to analyse

the temporal and spatial distribution of surface flooding

(Freni et al. 2002).

The model inserts a storage structure (“fictive basin”) on

top of every sewer manhole. When the underground

drainage system is surcharged and the water depth in the

manhole rises above ground level, the generated flooding

volume is stored in the fictive basin. The propagation of

flooding volumes on the catchment surface is approximated

by a series of weirs added to connect the fictive basins on

the surface. The fictive links are built on the basis of the real

hydraulic connection on the catchment surface and ground

levels. This approach allows for propagation of the flooding

volume from the upstream manholes to the downstream

ones until it resides in the depressed manholes of the

catchment. It is then disposed of to the underground

drainage system when the system is no longer surcharged.

Fictive basins are dimensioned, taking into account the real

floodable area around the selected manhole.

The propagation phenomena are simulated through the

application of a weir function, as follows (Equation (5)):

Qw ¼ CwLwhw þ v2

w

2g

!3=2

2v2

w

2g

!3=224

35 ð5Þ

where Cw is the discharge coefficient, Lw is the weir

transverse length, hw is the driving head on the weir, and

vw is the approach velocity, which in this case is equal

to zero.Table

1|

His

tori

cal

rain

fall

eve

nts

Unit

Floodingevent

Para

mete

r1

23

45

67

89

10

Data

even

td/m

/y25/1

0/9

308/0

1/9

501/1

2/9

518/0

9/9

626/0

9/9

605/1

0/9

612/0

8/9

722/0

8/9

725/0

9/9

707/1

2/9

7

Duration

hm

s14.05.03

19.05.02

13.17.03

15.01.00

6.19.01

10.55.01

12.18.20

15.33.30

10.34.02

16.29.50

Mea

nrainfallintensity

mm

h21

7.27

8.67

6.79

20.20

24.39

9.02

19.45

38.70

3.47

9.53

Med

ianrainfallintensity

mm

h21

5.66

8.21

5.20

12.34

13.77

7.74

14.55

18.88

3.32

7.83

Min.non-nullrainfallintensity

mm

h21

2.11

1.23

3.77

1.83

1.22

1.65

2.66

1.10

0.81

1.87

Max.rainfallintensity

mm

h21

144.9

144.89

172.08

125.54

212.73

111.03

115.02

271.42

135.64

100.66

Standard

dev

iation

mm

h21

Rain

volume

mm

60.51

33.55

49.77

16.38

19.91

44.85

47.36

47.50

20.34

39.59

Rain

return

period

years

83

43

34

10

20

23

2984 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

The definition of propagation functions is conceptual

and is better fitted to analysing limited flooding where the

flow regime in the streets is not affected by dynamic

phenomena (backwater, wave attenuation). Moreover, the

presence of low water levels and relatively low flow rates

along the major system makes the model almost insensitive

to weir parameters.

This approach does not require significant information

about the major system (e.g. the surface drainage system,

streets and squares), and its computational cost is not much

higher than the related drainage network model, but its

responses can be highly erroneous because surface flooding

propagation is simulated by highly simplified Equations

(linear functions of the flooding volume, weir equations).

Therefore, the applicability of the method is reduced to

frequent limited flooding phenomena and problems for

which a detailed analysis is not needed (such as pre-design

or planning procedures).

Model 2

The more detailed approach to urban flooding modelling

adopted in the present study is a full 1-D/1-D dual drain-

age model (Djordjevic et al. 1999; Leandro et al. 2009).

Surface runoff is simulated by the same Equations

(Equations (1) and (2)) presented in model 1. The under-

ground and surface drainage systems are schematised in a

unique network made by two sets of channels dynamically

interconnected by way of the sewer manholes (Figure 2),

in which flooding volumes can be stored. The flow into the

underground pipes and surface channels is simulated by

solving the complete 1-D De Saint Venant Equations

(Equations (3) and (4)).

This approach can be used to examine a wider range

of problems, from frequent and limited local flooding to

a global system surcharge with high water levels on the

streets and high discharges. Flooding velocity is taken into

account, and surface backwater propagation can be

Table 2 | Historical flooding events locations and maximum flooding water depths

Parameter Unit Flooding water depth

Flooding event 1 2 3 4 5 6 7 8 9 10

Flooding location Mean flooding water depth

1 cm 130 130 160 170 180 140 230 200 130 140

2 cm 50 47 80 130 107 50 58 37 45 0

3 cm 0 40 60 45 70 50 80 60 35 0

4 cm 54 30 30 77 45 50 67 97 50 0

5 cm 60 60 80 70 60 60 70 80 70 0

6 cm 30 40 30 40 35 40 30 55 40 0

7 cm 40 28 28 35 0 30 28 0 28 0

8 cm 30 40 50 93 80 30 67 57 30 0

9 cm 45 70 50 50 50 35 50 40 30 0

10 cm 28 30 28 25 0 0 28 40 30 0

11 cm 30 30 40 28 28 40 28 30 30 0

12 cm 50 50 70 70 50 50 70 70 50 70

13 cm 50 40 50 45 50 50 40 40 50 50

14 cm 40 30 70 50 35 40 35 40 30 0

15 cm 0 0 30 0 0 30 33 40 0 0

Mean flooding depth cm 36.21 44.33 57.07 61.87 52.67 46.33 60.93 59.07 43.20 17.33

Median flooding depth cm 18.32 28.55 34.14 43.14 46.21 29.55 50.30 45.13 28.59 40.08

Standard deviation cm 40.00 40.00 50.00 50.00 50.00 40.00 50.00 40.00 35.00 0.00

2985 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

analysed by means of complete DSV equations. The basic

disadvantage of this approach lies in the high dendriticity of

the network structure, which may lead to model instability.

Moreover, even if this modelling approach can improve

accuracy, it requires good knowledge of the surface street

network (cross-sections, slopes, etc.) and significant com-

putational resources.

Description of the study area

The “Centro Storico” catchment of Palermo (Italy) is the

oldest part of the city and is highly urbanised (Figure 3). It is

about 2.5 km2, consisting of about 88% impervious areas

(mainly buildings, roads and squares) and a few pervious

areas, mostly fragmented into public parks and courtyards

in mansions and religious buildings that are often spread

along the main roads.

The analysed catchment is one of the largest old city

centres in Europe and also one of the richest and most

varied in terms of historical buildings. The most common

land use in the area is for residential dwellings, but the

area also contains many monuments and other estates

with cultural or artistic significance, including over 500

palaces, churches, convents, and monasteries, plus seven

theatres.

The whole catchment is drained by a very old (about

120 years) drainage system and has a total pipe length of

about 56 km. It receives both storm and waste water from

upstream less urbanised watersheds; local surface flooding

due to the system insufficiency often occurs for high

frequency rainfalls (La Loggia et al. 1998).

The monitoring campaign

The study area currently experiences frequent flooding

occurring less than annually, even in cases of low water

depth and low consequent damages. Over a five-year period

(1993–1997), the municipality coordinated a monitoring

campaign in which data about rainfall, network flows,

surface flooding and consequent damage were monitored

by the concurrent efforts of the municipality, fire brigades,

Palermo University and insurance companies. Ten histori-

cal rainfall events have been recorded by the Palermo Parco

d’Orleans rain gauge (University Campus), which is locatedTable

3|

Best

ow

ed

insu

ran

cep

rem

ium

sd

iffere

nti

ate

db

yth

ety

pe

of

dam

aged

pro

pert

y

Floodingevent

Para

mete

rUnit

12

34

56

78

910

Data

even

td/m

/y25/1

0/9

308/0

1/9

501/1

2/9

518/0

9/9

626/0

9/9

605/1

0/9

612/0

8/9

722/0

8/9

725/0

9/9

707/1

2/9

7

Noco

mpen

sationrequests

(properties)

711

23

20

14

10

20

14

90

Totalbuildingdamage

e185.375

173.757

350.051

693.979

362.806

163.365

417.220

322.436

105.754

0.00

Noco

mpen

sationrequests

(veh

icles)

39

48

61

62

47

51

59

50

49

8

Totalveh

icle

damage

e277.212

392.329

450.266

627.051

418.868

347.691

445.468

455.706

308.043

67.848

2986 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

in the analysed area and has been in operation since 1991.

Relevant network surcharges and local flooding for these

events were also observed. Rainfall data were recorded with

a temporal resolution equal to 1min. The characteristics

and statistics of the main rainfall events are presented in

Table 1. The return period was estimated by means of

statistical analysis of the rainfall annual maxima available

at the rain gauge.

In order to obtain an accurate and reliable data set of

these historical flooding events and the related damages,

data from fire brigades and insurance companies have been

integrated.

For each flooding event, fire brigades provided flooding

information such as the flooded area and locations along

with related water depth, duration, flooding volumes and

information about damaged properties and objects. Fifteen

Table 4 | Model performance indicators

Indicator Acronym Formulation

Normalised mean square error NMSE NMSE ¼N21

PN

iðPi2OiÞ

2

h iðOPÞ

Root mean square error RMSE RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiN21

PNi ðPi 2 OiÞ

2q

Ration between RMSE and MSE RMSE/MSE RMSE=MSE ¼ N21PN

i ðPi 2 OiÞ2

h i21=2

Unsystematic RMSE RMSEu RMSEu ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiN21

PNi ðPi 2 �PÞ2

q

Fractional bias FB FB ¼ 2ð �O 2 �PÞ=ð �O þ �PÞ

Fractional variance FS FS ¼ 2 s2o 2 s2

p

� �= s2

o þ s2p

� �

Predictions within a factor of two of observations FA2 Fraction of data contained in the interval 0.5Oi , Pi , 2.0Oi

Determination coefficient R2 R2 ¼ 12

PN

iðPi2OiÞ

2

h iPN

iðOi2

�OÞ2h i

N is the number of observations; Pi and Oi represent the predicted and observed values, respectively; the overscored variables represent average values and sp and so represent the

standard deviations of predictions and observations, respectively.

y = 1.1221x + 1.4232

0

50

100

150

200

250

(a) (b)

0 50 100 150 200 250

Mea

sure

d flo

odin

g de

pths

(cm

)

0

50

100

150

200

250

Mea

sure

d flo

odin

g de

pths

(cm

)

Simulated flooding depths (cm)

0 50 100 150 200 250

Simulated flooding depths (cm)

y = 1.0668x – 2.9136

Figure 4 | Comparison of simulated and measured flooding depths for model 1 (a) and model 2 (b).

2987 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

flooded areas were located and investigated. Data were

collected by means of visual inspections during and after the

rainfall event. The maximum flooding water depth recorded

by fire brigades in flooded areas during each event is

presented in Table 2.

Insurance companies provided data related to the

capitalised damages based on the premium bestowed by

the insurance company once a request for compensation

was received. By comparing the two data sources, it was

possible to determine the economic damage (insurance

data) connected to all objects subjected to flooding (fire

brigade data). The premiums bestowed by the insurance

companies are presented in Table 3 differentiated by the

type of damaged property (mainly vehicles and movable

goods in buildings and properties).

In terms of expected damage, each flooding event affects,

on average, 13 properties and 47 vehicles, with average

damages equal to 277.470/00 and 379.050/00 Euros, respect-

ively. The medians of expected damage are slightly lower for

property (253.900/00 Euros) and slightly higher for vehicles

(405.600/00 Euros). The distribution of damage data is quite

wide (especially for properties); the standard deviations are in

the sameorderofmagnitudeof theaveragevalues (192.160/00

Euros for property damage and 146.000/00 Euros for

vehicles). This may be explained by the larger variability of

exposed goods in properties and buildings that increases the

uncertainty connected to the prediction of expected damage.

Flooding hydraulic characteristics were used for cali-

brating the two mathematical models. Damage data were

used to compute depth-damage curves for both single

locations and the whole area. Damage and flooding data

were used to construct depth-damage-functions.

Validation of the two mathematical

modelling approaches

The two hydraulic models were compared both visually by

means of q-q plots and using some standard performance

indicators often adopted in literature (Saltelli et al. 2000;

Chang & Hanna 2005; Thielena et al. 2008). The indicators

adopted in the present study were all based on the analysis

of residuals between model estimations and observed data

because the aim of the study is to evaluate the errors

introduced in the expected damage by means of the

hydraulic model and the depth-damagecurve. Analysis of

the models’ performance was conducted in three steps: first,

y = 867.85x0.8409

R2 = 0.9277

0

20

40

60

80

100

(a) (b)

0 50 100 150 200 250

Dam

age

(Eur

os)

× 1000

Dam

age

(Eur

os)

× 1000

Measured flooding depth (cm)

0 50 100 150 200 250

Measured flooding depth (cm)

95%quantile

5% quantile5% quantile

y = 1035.7x0.511

R2 = 0.726

0

5

10

15

20

25

95%quantile

Figure 5 | Depth-damage curves for building furniture (a) and vehicles (b): red lines represent quantiles of the 25 curves obtained by excluding data derived from one flooding

location or from one flooding event.

Table 5 | Performance of hydraulic models

NMSE RMSE RMSE/MSE RMSEu FB FS FA2 R2

Model 1 0.082 12.96 0.077 12.07 0.1455 0.1515 0.826 0.890

Model 2 0.019 6.74 0.15 6.38 0.00633 0.0777 0.853 0.970

2988 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

the estimation of flooding water levels was evaluated by

comparing the ability of the two proposed models to fit

measured flooding data; second, the depth-damage -curves

were introduced to evaluate the performance with damage

estimation; finally, uncertainty was introduced in the

analysis by reducing the flooding damage dataset and

obtaining alternative depth-damage curves. Table 4 shows

the adopted indicators and their formulations.

RESULTS AND DISCUSSION

Initially, the two models were calibrated according to

flooding depth registered in the area (Table 2). Details of

the calibration process are not reported in the present paper

for the sake of conciseness; they can be found in Freni et al.

(2006). Figure 4 shows the comparison between the two

models and the recorded data. The agreement of the

detailed model and the recorded data is generally higher,

especially with regard to higher flooding depths, which are

evidently underestimated by the simplified approach. Both

models underestimated the observed flooding depths, as

demonstrated by the interpolating lines presented in

Figure 4. The simplified model 1 has an average over-

estimation of 12%, while the detailed model 2 overestima-

tion is in the range of 6–7%. These results are largely

acceptable in practical applications, and the low value of

the interpolating line intercept is another confirmation of

the models’ good adaptation to observed data. The better fit

of the detailed model was confirmed by the model

performance indicators presented in Table 4. In both

cases, most of the model error was unsystematic as

demonstrated by the comparison of RMSE and RMSEu;

its overestimation tendency is confirmed by the positive

values of FB. More than the 80% of the model predictions

reside in the range between 50% and 200% of the

observations, confirming the reliability of the models.

The main differences between the two modelling

approaches may be found not only in the error differences,

but also in the increased dispersion between predictions

and observations as demonstrated by FB and FS values.

In the second part of the study, the depth-damage

curves were estimated and then applied to the modelled

flooding depths in order to determine whether the same

considerations provided above can be transferred to flood

Table 6 | Performance of models after the integration of depth-damage curves

NMSE RMSE RMSE/MSE RMSEu FB FS FA2 R2

Model 1 0.0928 4682.19 0.014 4297.81 20.021 0.199 0.582 0.717

Model 2 0.0544 3902.35 0.016 3707.18 20.010 0.1118 0.696 0.778

Table 7 | Total damage estimated by the simplified (model 1)and detailed (model 2) models (Euros £ 1,000)

Model 1 Model 2

Flooding event Best fit curve Uncertainty range Best fit curve Uncertainty range

1 432.5 390.1–485.1 465.4 423.2–501.5

2 567.3 504.3–623.3 583.5 515.5–635.2

3 690.4 608.5–760.3 740.3 630.4–830.4

4 1,150.5 894.2–1,321.3 1350.2 950.3–1,520.2

5 780.3 701.3–820.3 810.2 730.4–840.3

6 532.3 490.2–582.2 562.1 510.2–603.6

7 852.7 795.3–912.3 856.2 793.4–916.3

8 769.2 710.5–850.3 802.2 726.4–860.9

9 404.6 336.1–423.5 414.5 350.1–443.4

10 61.6 43.4–78.4 71.6 52.6–88.5

2989 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

damage estimation. Depth-damage curves were interpolated

by power laws using the least squares minimisation

approach. Data for vehicles and movable goods on proper-

ties were interpolated separately (Figure 5). The agreement

between the interpolation law and available data is good,

but the diffusion of experimental points around the curves

was high, signalling that modelling results may deteriorate

when integrating depth-damage curves and hydraulic

models. Table 6 shows the performance of the models

after such integration.

As expectable, errors increased when the depth-damage

curves were added to the hydraulic model. Comparison of

RMSE in Tables 5 and 6 is not useful because the order of

magnitude of damage was much higher than water depth.

Comparison of normalised indicators (NMSE and RMSE/

MSE) showed higher values in Table 6 than in Table 5, thus

demonstrating the deterioration of modelling results. The

models tended towards underestimation of observed

damage mainly because the overestimation tendency of

hydraulic model was compensated and overwhelmed by the

underestimation of the depth-damage curves (Figure 5(b)).

FA2 and R2 showed less successful adaptation of the model

to observed data, but the differences between the two

modelling approaches were preserved. The adoption of a

detailed model still seems advantageous.

Because of the high uncertainty related to the esti-

mation of depth-damage curves, the final part of the study

was dedicated to this aspect and to the main source of

uncertainty related to data availability. The damage database

was factiously reduced by the “leave-one-out” approach:

25 families of curves were obtained by excluding information

drawn from one flooding location or one flooding event.

Figure 5 shows the resulting uncertainty bands (red lines) for

the 5% and 95% quantiles. The uncertainty on the estimation

of depth-damage curves was relevant and fell in the range of

40%of the average estimated damage value. Table 7 shows the

computed damage for each flooding event and the uncertainty

range linked to the selection of the depth-damage curve.

The detailed model was able to better estimate

measured damage considering the depth-damage curve

obtained for the whole dataset. The uncertainty ranges fell

between 10% and 30% depending on the analysed event;

their extension did not depend greatly on the adopted

model. The uncertainty was higher than the increased

modelling accuracy provided by the detailed approach

(model 2); for this reason, the use of simplified models

can be encouraged, especially when taking into account

their reduced computational needs. The uncertainty bands

provided by the two modelling approaches intersect,

indicating that if some of the observed damage data was

used only for model 1 and not for model 2, the simplified

approach would provide better results than the detailed

one. This result does not mean that the simplified approach

should be preferred more generally, but simply shows that

additional damage data is more valuable than the

implementation of a more detailed model.

CONCLUSIONS

The present paper discussed the use of numerical modelling

for evaluating the expected damage resulting from urban

flooding. The use of simplified or detailed modelling

approaches was discussed in terms of their ability to best

fit hydraulic and damage data against the uncertainty

inherent in the evaluation of flooding depth-damage curves.

The study drew some interesting conclusions that are

summarised here:

† The advantages provided by the detailed modelling

approach (model 2) result from lower errors in the

prediction of flooding depths and fewer predictions

being far from the observed values.

† The integration of depth-damage curves and the hydrau-

lic model produces errors that are sometimes higher than

the hydraulic model alone; this partially reduces the

advantages of the detailed approach. Normalised per-

formance indicators that, in the first comparison based

on hydraulic variables, are much better for the detailed

approach, show smaller differences when depth-damage

curves are added. This reduces the appeal of detailed

modelling approaches and highlights the importance

of a reliable estimation of the depth-damage curves.

† Uncertainty connected with historical damage data can

be sufficiently relevant such that the use of detailed

models provides no relevant advantages; the use of

simplified approaches can be suggested unless more

reliable data about damage are available. In the present

application, the two applied models differed in terms of

2990 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

their accuracy in fitting measured flooding depths: the

simplified model (model 1) generated modelling errors

nearly two times those provided by the detailed model

(model 2).

† The uncertainty bands in depth-damage curves are in the

range of 40%–50% of the average value, depending on

the analysed water depths. Such uncertainty propagates

to the evaluation of damage in single flooding locations

that can be underestimated or overestimated of 20%-

30% depending on the curve adopted and, consequently,

on available damage data.

† The use of detailed modelling approaches thus has to

be weighted accurately with the uncertainty provided by

data availability, bearing in mind that the advantages

provided by detailed models may be largely absorbed by

the uncertainty in damage estimation; thus, the

additional computational costs of such approaches may

not be justified.

† Uncertainty analysis is shown to be an important tool

not only for estimating the reliability of a modelling

response, but also for selecting the most appropriate

model for application in a specific uncertain context.

REFERENCES

Abt, S. R., Wittler, R. J. & Taylor, A. 1989 Predicting human instability

in flood flows. Proceedings of the 1989 National Conference on

Hydraulic Engineering. ASCE, New York, pp. 70–76.

Almedeij, J., Alsulaili, A. & Alhomoud, J. 2006 Assessment of grate

sag inlets in a residential area based on return period and

clogging factor. J. Environ. Manage. 79(1), 38–42.

Apel, H., Annegret, W., Thieken, H., Merz, B. & Bloschl, G. 2006

A probabilistic modelling system for assessing flood risks.

Nat. Hazards 38(1–2), 79–100.

Aronica, G. T. & Lanza, L. G. 2005 Drainage efficiency in urban

areas: a case study. Hydrol. Process. 19(5), 1105–1119.

Aronica, G., Freni, G. & Oliveri, E. 2005Uncertainty analysis of the

influence of rainfall time resolution in the modelling of urban

drainage systems. Hydrol. Process. 19(5), 1055–1071.

Barroca, B., Bernardara, P., Mouchel, J. M. & Hubert, G. 2006

Indicators for identification of urban flooding vulnerability.

Nat. Hazards Earth Syst. Sci. 6(4), 553–561.

Bouma, J. J., Francois, D. & Troch, P. 2005 Risk assessment

and water management. Environ. Modell. Softw. 20,

141–151.

Bouteligier, R., Vaes, G., Berlamont, J., van Assel, J. & Gordon, D.

2001 Water quality model set-up and calibration—a case study,

The Autumn WaPUG Conference, Blackpool, UK.

Carr, R. S. & Smith, G. P. 2007 Linking of 2D and pipe hydraulic

models at fine spatial scales. Water Practice Technol. 2(2),

doi:10.2166/wpt.2007.038.

Chang J. C. & Hanna S. R. 2005 Technical Descriptions and User’s

Guide for the BOOT Statistical Model Evaluation Software

Package, Version 2.0. George Mason University 4400

University Drive, MS 5B2 Fairfax, VA 22030-4444.

Chen, A. S., Hsu, M. H., Chen, T. S. & Chang, T. J. 2005 An

integrated inundation model for high development urban

areas. Water Sci. Technol. 51(2), 221–229.

Chen, A. S., Djordjevic, S., Leandro, J. & Savic, D. 2007 The urban

inundation model with bidirectional flow interaction between

2D overland surface and 1D sewer networks. Proceedings of

Novatech 2007: Sixth International Conference on Sustainable

Techniques and Strategies in Urban Water Management, June

25–28 2007, Lyon, France. pp. 465–472.

Chen, J. C., Ning, S. K., Chen, H. W. & Shu, C. S. 2008 Flooding

probability of urban area estimated by decision tree and

artificial neural network. J. Hydroinformatics 10(1), 57–67.

Dawson, R. J., Hall, J. W., Sayers, P. B., Bates, P. D. & Rosu, C.

2005 Sampling-based flood risk analysis for fluvial dike

systems. Stoch. Environ. Res. Risk Anal. 19(6), 388–402.

Dawson, R. J., Speight, L., Hall, J. W., Djordjevic, S., Savic, D. &

Leandro, J. 2008 Attribution of flood risk in urban areas.

J. Hydroinformatics 10(4), 275–288.

Despotovic, J., Petrovic, J. & Jacimovic, N. 2002 Measurement,

calibration of rainfall-runoff models and assessment of the

return period of flooding events at urban catchment Kumodraz

in Belgrade. Water Sci. Technol. 45(2), 127–133.

Djordjevic, S., Prodanovic, D. &Maksimovic, C. 1999 An

approach to simulation of dual drainage. Water Sci. Technol.

39(9), 95–103.

Djordjevic, S., Prodanovic, D., Maksimovic, C., Ivetic, M. & Savic,

D. 2005 SIPSON-Simulation of interaction between pipe flow

and surface overland flow in networks. Water Sci. Technol.

52(5), 275–283.

Dutta, D., Herath, S. & Musiake, K. 2003 A mathematical model for

flood loss estimation. J. Hydrol. 277, 24–49.

Ettrich, N., Steiner, K., Thomas, M. & Rothe, R. 2005 Surface

models for coupled modelling of runoff and sewer flow in

urban areas. Water Sci. Technol. 52(2), 25–33.

Freni, G. & Oliveri, E. 2005Mitigation of urban flooding:

a simplified approach for distributed stormwater

management practices selection and planning. Urban Water

2(4), 215–226.

Freni, G., Schilling, W., Saegrov, S., Milina, J. & Konig, A. 2002

Catchment -Wide Efficiency Analysis of Distributed Stormwater

Management Practices: The Case Study of Baerm, Norway.

Proceedings of 9th International Conference on Urban Storm

Drainage, 8–13 September, Portland, Oregon, USA.

Freni, G., La Loggia, G., Notaro, V. & Oliveri, E. 2006 Reliability

of sewer system performance analysis. Proceedings of

32nd Congress of IAHR, the International Association of

Hydraulic engineering & Research, Venezia, 1–6 June 2007,

p. 208.

2991 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

Gironas, J., Niemann, J. D., Roesner, L. A., Rodriguez, F. &

Andrieu, H. 2010 Evaluation of methods for representing

urban terrain in storm-water modelling. J. Hydrologic Eng.

15(1), 1–14.

Grunthal, G. W., Thieken, A. H., Schwarz, J., Radtke, K. S.,

Smolka, A. & Merz, B. 2006 Comparative risk assessments for

the city of Cologne—Storms, floods, earthquakes. Nat. Hazards

38(1–2), 21–44.

Hall, J., Dawson, R., Speight, L., Djordjevic, S., Savic, D. &

Leandro, J. 2006 Attribution of flood risk in urban areas.

Proceedings of 7th International Conference on

Hydroinformatics, Nice.

Hardmeyer, K. & Spencer, M. A. 2007 Using risk-based analysis

and geographic information systems to assess flooding

problems in an urban watershed in Rhode Island. Environ.

Manage. 39(4), 563–574.

Hsu, M. H., Chen, S. H. & Chang, T. J. 2000 Inundation simulation

for urban drainage basin with storm sewer system. J. Hydrol.

234(1–2), 21–37.

Huber, W. C. & Dickinson, R. E. 1988 Storm Water Management

Model-SWMM, Version 4 User’s Manual. US Environmental

Protection Agency, Athens Georgia, USA.

Jonkman, S. N., Bockarjovab, M., Kokc, M. & Bernardinid, P. 2008

Integrated hydrodynamic and economic modelling of flood

damage in the Netherlands. Ecol. Econ. 66, 77–90.

Kawaike, K. & Nakagawa, H. 2007 Flood disaster in July 2006 in the

Matsue city area and its numerical simulation. Proceedings of

32nd Congress of IAHR-Harmonizing the Demands of Art and

Nature in Hydraulics, IAHR, Venice, Italy.

La Loggia, G., Oliveri, E., Freni, G. & Giangrasso, G. 1998 Analisi

della consistenza di una rete di drenaggio urbano attraverso

l’uso di modelli a base fisica. Proceedings of Conference

on “Risorse idriche ed impatto ambientale dei deflussi urbani”,

18–20 Nov., Cagliari, Italy.

Leandro, J., Chen, A. S., Djordjevic, S. & Savic, D. A. 2009

A comparison of 1D/1D and 1D/2D coupled (sewer/surface)

hydraulic models for urban flood simulation. J. Hydraulic Eng.

135(6), 495–504.

Lhomme, J., Bouvier, C., Mignot, E. & Paquier, A. 2006 One

dimensional GIS-based model compared to two-dimensional

model in urban floods simulations. Water Sci. Technol.

54(6–7), 83–91.

Lindberg, S., Nielsen, J. B. & Carr, R., 1989 An integrated PC

modelling system for hydraulic analysis of drainage systems.

Proceedings of The first Australian Conference on technical

computing in the water industry: Watercomp ’89, Melbourne,

Australia.

Lipime Kouyi, G., Fraisse, D., Riviere, N., Guinot, V. & Chocat, B.

2009 One-dimensional modelling of the interactions between

heavy rainfall-runoff in an urban area and flooding flows from

sewer networks and rivers. Water Sci. Technol. 60(4), 927–934.

Maksimovic, C., Prodanovic, D., Boonya-aroonnet, S., Leitao, J.,

Djordjevic, S. & Allitt, R. 2009 Overland flow and pathway

analysis for modelling of urban pluvial flooding. J. Hydraulic

Res. 47(4), 512–523.

Mark, O., Weesakul, S., Apirumanekul, C., Boonya Aroonnet, S. &

Djordjevic, S. 2004 Potential and limitations of 1D

modelling of urban flooding. J. Hydrol. 299(3–4),

284–299.

Merz, B., Kreibich, H., Thieken, A. & Schmidtke, R. 2004

Estimation uncertainty of direct monetary flood damage to

buildings. Part of special issue “landslide and

flood hazards assessment”. Nat. Hazards Earth Syst. Sci. 4,

153–163.

Meyer, V. & Messner, F. 2006 Flood damage, vulnerability and

risk perception—challenges for flood damage research. Book

series NATO Science Series: IV: Earth and Environmental

Sciences. ISSN 1568-1238. Volume 67—Flood Risk

Management: Hazards, Vulnerability and Mitigation Measures.

Publisher -Springer Netherlands. DOI 10.1007/978-1-4020-

4598-1. ISBN 978-1-4020-4596-7 (Print) 978-1-4020-4598-1

(Online).

Nanıa L., Gomez, M. & Dolz, J.2002 Analysis of risk associated to

the urban runoff. Case study: city of Mendoza, Argentina.

Proceedings of 9th International Conference on Urban Storm

Drainage, 2002, Portland, USA.

Nascimento, N., Baptista, M., Silva, A., Lea Machado, M., Costa de

Lima, J., Goncalves, M., Silv, A., Dias, R. & Machado, E. 2006

Flood-damage curves: Methodological development for the

Brazilian context. Water Pract. Technol., 1(1) doi: 10.2166/

WPT.2006.022.

Nasello, C. & Tucciarelli, T. 2005 Dual multilevel

urban drainage model. J. Hydraulic Eng.—ASCE 131(9),

748–754.

National Research Council 2000 Risk Analysis and Uncertainty in

Flood Damage Reduction Studies. National Academy Press,

Washington DC.

Oliveri, E. & Santoro, M. 2000 Estimation of urban structural flood

damages: the case study of Palermo. Urban Water J. 2,

223–234.

Paquier, A., Tanguy, J. M., Haider, S. & Zhang, B. 2003

Estimation des niveaux d’inondation pour une crue eclair en

milieu urbain: comparaison de deux modeles

hydrodynamiques sur la crue de Nımes d’Octobre 1988.

Rev. Sci. Eau. 16(1), 79–102.

Parker, D. J. & Green, C. H. 1987 Urban flood protection Benefits.

A Project Appraisal Guide, Aldershot.

Penning-Rowsell, E., Johnson, C., Tunstall, S., Tapsell, S., Morris, J.,

Chatterton, J., Coker, A., & Green, C. 2003 The Benefits of

flood and coastal defence: techniques and data for 2003.

Flood Hazard Research Centre, Middlesex University.

Prince, R. K. & Vojinovic, Z. 2008 CASE STUDY-Urban

flood disaster management. Urban Water J. 5(3),

259–276.

Saltelli, A., Tarantola, F. & Campolongo, F. 2000 Sensitivity

analysis as an ingredient of modeling. Stat. Sci. 15(4),

377–395.

Schmitt, T. G., Thomas, M. & Ettrich, N. 2005 Assessment of urban

flooding by dual drainage simulation model RisUr-Sim.

Water Sci. Technol. 52(5), 257–264.

2992 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010

Smith, M. B. 2006 Comment on ‘Potential and limitations of 1D

modeling of urban flooding’ by O. Mark et al. [J. Hydrol. 299

(2004) 284–299]. J. Hydrol. 321(1–4), 1–4.

Thielen, D. R., San Jose, J. J., Montes, R. A. & Lairet, R. 2008

Assessment of land use changes on woody cover and

landscape fragmentation in the Orinoco savannas using fractal

distributions. Ecol. Indic. 8(3), 224–238.

Ugarelli, R., Freni, G., Di Federico, V., Liserra, T., Maglionico, M.,

Pacchioli, M., Prax, P., Sægrov, S. & Schulz, N. 2005

Evaluation of rehabilitation impact on hydraulic and

environmental performance of sewer systems (WP3 CARE-S

Project). Proceedings of 10th International Conference on

Urban Drainage—Copenhagen (Denmark).

Wind, H. G., Nierop, T. M., de Blois, C. J. & de Kok, J. L. 1999

Analysis of flood damages from the 1993 and 1995 Meuse

floods. Water Resour. Res. 35(11), 3459–3465.

WMO/GWP Associated Programme on Flood Management 2008

Urban Flood Risk Management—A Tool for Integrated Flood

Management Version 1.0. APFM Technical Document N. 11,

Flood Management Series.

2993 G. Freni et al. | Uncertainty in urban flood damage assessment Water Science & Technology—WST | 61.12 | 2010