Modelling flash flood risk in urban areas

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Proceedings of the Institution of Civil Engineers

Water Management 164 June 2011 Issue WM6

Pages 267–282 doi: 10.1680/wama.2011.164.6.267

Paper 1000061

Received 01/07/2010 Accepted 27/01/2011

Keywords: floods & floodworks/hydraulics & hydrodynamics/risk &

probability analysis

ICE Publishing: All rights reserved

Water ManagementVolume 164 Issue WM6

Modelling flash flood risk in urban areasXia, Falconer, Lin and Tan

Modelling flash flood risk inurban areasj1 Junqiang Xia

Professor of RIver Engineering, State Key Laboratory of WaterResources and Hydropower Engineering Science, Wuhan University,Wuhan, China

j2 Roger A. FalconerHalcrow Professor of Water Management, Hydro-environmentalResearch Centre, School of Engineering, Cardiff University, Cardiff,UK

j3 Binliang LinProfessor of Hydro-environmental Engineering, Hydro-environmentalResearch Centre, School of Engineering, Cardiff University, Cardiff,UK

j4 Guangming TanProfessor of River Management, State Key Laboratory of WaterResources and Hydropower Engineering Science, Wuhan University,Wuhan, China

j1 j2 j3 j4

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

contain vital infrastructure. Parts of the UK have been particularly prone to serious urban flooding in recent years,

such as Boscastle in 2004. 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. This paper

outlines an integrated numerical model for estimating flood risk in urban areas. The model includes a module for

predicting the two-dimensional hydrodynamic characteristics of urban floods and a new module for predicting the

flood risk to people (both children and adults) and property (including vehicles and buildings). The hydrodynamic

module of this model was verified against laboratory experimental data and real flood tracks in urban areas. The

integrated model was also applied to predict the flood risk to people and property for the Boscastle 2004 floods,

with different recurrence frequencies. The developed integrated model can be used to predict the potential flood risk

to people and property in urban areas and such predictions can be used as a rough assessment in improving flood

risk management.

1. IntroductionA considerable change in climatic and meteorological conditions

in recent years has led to an increasing probability of urban

flooding and the UK has recently experienced a number of

serious urban flood events. For example, on 16 August 2004 the

coastal village of Boscastle in north Cornwall was devastated by

a flash flood as a result of a series of torrential thunderstorms that

deposited over 200 mm of rainfall within 5 hours into a small,

rocky, steep catchment. This extreme event was caused by the

combination of stationary cumulonimbus clouds creating heavy

rain on the River Valency catchment, saturation of the soil due to

antecedent rain generating high runoff and the steep nature of the

catchment concentrating flows in Boscastle (HRW, 2005). Ob-

served water depths on the streets were more than 2 m, with high

water velocities carrying debris and vehicles, which caused

significant damage to buildings. About 60 buildings were flooded,

some completely destroyed, and more than 100 people were

rescued by helicopter, without any fatalities occurring. In addi-

tion, about 116 vehicles were swept by the flow and some of

them were washed out into the harbour. In another example, on 8

and 9 January 2005, Carlisle in northwest England experienced

widespread heavy rainfall of up to 164 mm in 24 h. The flood

was estimated to have a return period of 150 years, whereas the

flood defences were cited to be designed for 1 in 20–70 year

return period events. Significant reaches of the flood defences

were overtopped, leading to the flooding of 2600 properties; the

estimated cost of damage incurred was £450 million (EA, 2005).

These events raised public and political awareness of urban

flooding and also highlighted the need to better understand and

estimate flood risk in urban areas.

International news about extreme urban flooding is also being

reported more frequently. The UK Parliamentary Office of

Science and Technology (POST, 2007) noted that urban flooding

due to drainage systems being overwhelmed by rainfall is

estimated to cost £270 million per year in England and Wales,

with 80 000 homes being at risk; these impacts are expected to

increase if no policy changes are made. A special report by the

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UK Foresight programme (DTI, 2004) stated that the costs of

urban flooding could rise to between £1 billion and £10 billion

per annum by 2080 if no action is taken to reduce risks. Wheater

(2006) reviewed climate change impacts on flooding and current

guidelines for UK practice, and reported that floods cannot be

prevented but flood risk can be managed. Predicted results from

the UK climate impacts programme (UKCIP02) (Hulme et al.,

2002) showed that flood risk over the UK can be expected to

increase, with a potential increase of 20% in the magnitude of

floods by 2050. Therefore, future flooding in urbanised areas is

expected to constitute a major threat to both population and

property in such regions, especially if no corresponding counter-

measures are taken in advance to cope with extreme flood events

such as occurred in Boscastle in 2004. It is therefore necessary to

conduct an initial assessment of flood risk in flood-prone urban

areas.

Urban flooding is often caused by rainfall overwhelming local

drainage capacity. The risk of flooding is defined as a function of

both the probability of a flood occurrence and its impacts. In

urban areas, the impacts caused by floods can be very high

because the areas affected are densely populated and contain vital

infrastructure. Continuing development in flood-prone areas in-

creases the risk, and urban flooding is also expected to occur

more often due to future climate change. Therefore, defining and

estimating the hazard degree for people and property in urban

areas are important components of good flood risk management,

and usually consist of modelling the hydrodynamic characteristics

of urban floods and estimating the flood risk to people and

property. Flood hazard is usually associated with many elements,

including the stability of people, vehicles and buildings in flood-

waters, evacuation difficulty and flood awareness of the local

population (Walsh et al., 1998). The processes of flood propaga-

tion in urban areas are often simulated by two-dimensional (2D)

hydrodynamic models (Abderrezzak et al., 2009; Hunter et al.,

2008; Liang et al., 2007; Petaccia et al., 2010; Roca and Davison,

2010; Soares-Frazao and Zech, 2008; Wang et al., 2010). How-

ever, the estimation module of hazard degrees for people and

property needs to be integrated with the hydrodynamic module in

order to predict flood risk in urban areas.

An integrated model for predicting flood risk in urban areas is

outlined here, including a module for simulating 2D hydrody-

namic characteristics of urban floods and a module for estimating

the flood risk to people and property. The hydrodynamic module

was then verified against laboratory experimental data and real

flood tracks in urban areas. Finally, the integrated model was

applied to predict the flood risk to people and property for the

Boscastle flood, and for various flood events, with different

recurrence frequencies.

2. Integrated modelThis section introduces an existing 2D hydrodynamic module, a

module for flood risk to people (including children and adults)

and property (including vehicles and buildings), and a quantifica-

tion method of their corresponding flood hazard degrees, which

comprises an integrated model capable of predicting the flood

risk to people and property in urban areas. The model is

explained in more detail by Xia et al. (2010a; 2010b).

2.1 Module for 2D hydrodynamics

For flows in natural rivers, floodplain systems and urban catch-

ments, a set of shallow-water equations for 2D flows over a

horizontal plane can be deduced, with these flows meeting most

of the key underlying hypotheses, including a hydrostatic pressure

distribution, a free surface and a relatively small bed slope (Tan,

1992). The depth-averaged 2D shallow-water equations used in

the current model can be written in a general conservative form

as

@U

@ tþ @E

@xþ @G

@ y¼ @ ~EE

@xþ @ ~GG

@ yþ S

1:

where U is a vector of conserved variables, E and G are

convective flux vectors of flow in the x and y directions respec-

tively, ~EE and ~GG are diffusive vectors related to turbulent stresses

in the x and y directions respectively and S is a source term that

includes bed friction, bed slope and the Coriolis force. The above

terms can be expressed in detail as

U ¼h

hu

hv

24

35

2a:

E ¼hu

hu2 þ 12gh2

huv

24

35

2b:

G ¼hv

huv

hv2 þ 12gh2

24

35

2c:

~EE ¼0

�xx� yx

24

35

2d:

~GG ¼0

�xy� yy

24

35

2e:

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S ¼0

gh(Sbx � S fx)

gh(Sby � S fy)

24

35

2f:

where u and v are depth-averaged velocities in the x and y

directions respectively, h is water depth, g is gravitational accelera-

tion, Sbx and Sb y are bed slopes in the x and y directions

respectively; Sf x and Sf y are friction slopes in the x and y

directions respectively, and �xx, �xy, � yx and � yy are components of

the turbulent shear stress over the plane. In this model, a simple

turbulence model was used to calculate the turbulent viscosity

coefficient; it is not applicable for simulating the complex separa-

tion and reattachment flows in local regions (Xia et al., 2010a).

The module adopted a finite-volume method (FVM) to solve the

governing equations based on an unstructured triangular mesh. In

the FVM model the study region was first divided into a set of

triangular cells to form an unstructured computational mesh. A

cell-centred FVM was then adopted in the model, in which the

average values of the conserved variables are stored at the centre

of each cell, with the three edges of each cell defining the

interface of a triangular control volume. At an interface between

two neighbouring cells, calculation of flow fluxes can be treated

as a locally one-dimensional (1D) problem in the direction

normal to the interface; thus the fluxes can be obtained by an

approximate Riemann solver. In the current model, a Roe’s

approximate Riemann solver with a monotone upstream scheme

for conservation laws (MUSCL) was employed for evaluating the

normal fluxes across the cell interface (Van Leer, 1979), with a

procedure of predictor–corrector time stepping being used to

provide second-order accuracy in both time and space (Tan,

1992). Furthermore, a refined procedure for treating wetting and

drying fronts was used (Xia et al., 2010a); this was based on an

algorithm developed for a regular grid finite-difference model

(Falconer and Chen, 1991). This method has been shown to be

effective in simulating wetting and drying processes due to rapid

flooding. The model was validated with existing analytical

solutions and experimental data of dam-break flows on initially

dry beds with simple bed topography (Xia et al., 2010a).

2.2 Module of flood risk to people and property

Estimation methods for the risk to people and vehicles in flood-

waters were based on the mechanical condition of sliding

equilibrium (Keller and Mitsch, 1993; Xia et al., 2010c). The

method for risk to buildings (Defra and EA, 2006) was an

indicative assessment taken from an average of damage scale for

each building type proposed by Kelman (2002).

2.2.1 Estimation of flood risk to people

The danger to people caused by a flood varies both in time and

place across a flood-prone area, and also changes for different

body shapes and weights. The variation in the hazard degree for

people in floodwaters needs to be understood by managers for

urban floods. It is therefore important to assess the degree of

people stability in floodwaters. Previous studies on the assessment

of people safety were carried out using two different approaches:

(a) empirical or semi-quantitative criteria (ACER, 1988; Defra

and EA, 2006; Penning-Rowsell et al., 2005)

(b) formulae derived from mechanical analysis based on

experiments (Abt et al., 1989; Jonkman and Penning-Rowsell,

2008; Keller and Mitsch, 1993; Lind et al., 2004).

Based on studies reported by the UK Flood Hazard Research

Centre, Jonkman and Penning-Rowsell (2008) reported the results

of new experiments on human instability in floodwaters. These

results showed that floodwaters with low depths and high

velocities are more dangerous than previously suggested, based

on the findings from previous experimental work. They discussed

how human instability can be related to two physical mechan-

isms: moment instability and friction instability. They reported

that it is difficult to determine human instability in floodwaters,

which is influenced by a range of factors such as the height and

mass of a person and instability mechanisms.

In this study, the more mechanics-based formula proposed by

Keller and Mitsch (1993) was used to estimate the stability

degree of people in floodwaters. Based on the mechanism of

friction instability, this formula established a force balance of a

person on a flooded street or road, linking the buoyant force,

weight, frictional resistance and drag force due to flowing water

Uc ¼2Fr

rfCdA

� �1=2

3:

where Fr is the restoring force due to friction, A is the submerged

area projected normal to the flow, Cd is the drag coefficient and

rf the density of water. According to Equation 3, two curves

were presented between the incoming depth h and the flow

velocity Uc at the point of human instability for a 5-year old

child and an adult, under the condition of sliding equilibrium, as

shown in Figure 1.

Figure 1 shows that there is a significant difference between the

critical velocities for a child (i.e. 0.5 m/s) and an adult (i.e.

2.2 m/s) for an incoming depth of 0.6 m. It should be pointed out

that whether a person standing in floodwater is in danger or not

depends on the objective conditions (such as local flow pattern,

terrain and visibility) and subjective conditions (e.g. the physical

and psychological status of that person). Moreover, the curves in

Figure 1 just account for the mode of friction instability, instead

of the mode of moment instability, and it is assumed that friction

instability is the dominating instability mechanism for flows with

shallow depths and large velocities based on the analysis of

Jonkman and Penning-Rowsell (2008). Furthermore, the effect of

bed slope on the stability degree of people in floodwaters is not

considered in Equation 3 or Figure 1. Therefore, the curves in

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Figure 1 can only present a rough estimate of the risk to a generic

person in floodwaters.

2.2.2 Estimation of flood risk to vehicles

Existing studies on the stability limit of vehicles in floodwaters

are limited. Gordon and Stone (1973) investigated the stability of

a small car with its two rear wheels locked against movement.

The vehicle stability condition was obtained when the horizontal

force was just balanced by the product of the measured vertical

reaction force and the coefficient of friction. Keller and Mitsch

(1993) conducted theoretical research into the stability conditions

for three idealised cars at 1:20 scale, and developed a simple

method for estimating the forces exerted on a stationary vehicle

in floodwaters and the corresponding incipient velocity formula

for a partially submerged vehicle. In the existing experimental

studies on the stability condition of flooded vehicles, the results

obtained were only applicable to partially submerged vehicles

and the stability threshold for fully submerged vehicles was not

considered. According to more recent experiments on flooded

vehicles by the authors (Xia et al., 2010c), it was found that a

completely watertight vehicle was too idealised in a real event of

urban flooding and the coefficients of friction and drag usually

changed with different incoming water depths. In practice, the

water outside a vehicle usually fills the inside space of the vehicle

as the stage of the floodwater rises. This phenomenon is gradual

in time when the vehicle windows are closed. Furthermore, the

flow and the vehicle are initially aligned parallel to the road axis,

but when the vehicle is moved by the flow it tends to position

itself transversally to the flow when meeting an obstacle in its

path. However, the flume experiments conducted by the authors

did not account for such a complex phenomenon.

As floodwater flows around a parked vehicle, the flow usually

exerts three forces on the vehicle – a lift force, a drag force and

a buoyancy force. It can also be assumed that the wheels of a

vehicle parked on a road are locked against any movement, and

thus a frictional force will be produced to resist the vehicle from

sliding on the road surface. Therefore, the stability of a flooded

vehicle is controlled by the above four forces, plus the gravita-

tional force. In the recent study conducted by the authors (Xia et

al., 2010c), all of the forces acting on a flooded vehicle were

analysed and the corresponding expressions for these forces were

presented. According to the theory of sliding equilibrium, an

expression for the incipient velocity was derived for commonly

used vehicles parking on flooded streets or roads

Uc ¼ Æh

hc

� ��

2grc � rf

rf

� �hc

� �1=24:

in which rc is the density of the vehicle, hc is the height of the

vehicle, h is the incoming water depth and parameters Æ and �are related to the shape of the vehicle, the type of tyres and the

road surface, which can be determined from flume measurements.

This formula is valid for both fully and partially submerged

vehicles. A series of flume experiments was then conducted using

scaled die-cast models of three vehicles, with two scales tested

for each type of vehicle (434 all-terrain vehicle (ATV), executive

saloon and small family car). The experimental data obtained for

the small-scale model vehicles were used to determine the two

parameters in the derived formula and the predictive accuracy of

the formula was validated using experimental data obtained for

large-scale model vehicles. Finally, the corresponding incipient

velocities obtained for various incoming depths were computed

using the formula for the three prototype vehicles.

Figure 2 shows the relationships between incoming water depth

and corresponding incipient velocity for the three vehicles in

floodwaters according to Equation 4. The figure shows that the

small family car is most likely to start sliding in floodwaters and

the incipient velocity for each fully submerged vehicle ranges

from 0.5 to 1.0 m/s. Figure 2 can thus be used to preliminarily

evaluate degrees of vehicle stability in floodwaters, and is useful

for assessing the flood hazard degrees of various vehicles parking

on flooded streets or roads. However, it should be pointed out that

Equation 4 (or Figure 2) was based on the relatively ideal

circumstances that the direction of the incoming flow was always

facing the rear of the vehicle and the channel bed was always flat.

For an assessment of instability thresholds of flooded vehicles

under real and more complex circumstances, more studies need

to be conducted, including the effect of different incoming flow

directions on the incipient motion of vehicles and the effect of

different bed slopes on the values of incipient velocity.

2.2.3 Estimation of flood risk to buildings

Buildings are potential places of refuge during floods and are

frequently used by people in flood-prone areas. The partial or

complete failure of buildings in which people might shelter to

provide safe refuge is consequently a significant factor in

determining the potential number of deaths resulting from flood-

ing in extreme circumstances (Defra and EA, 2006). Buildings

can collapse because of water pressure or scour of foundations,

or a combination. In addition, debris (e.g. trees, boulders or

0

1·0

2·0

3·0

4·0

0 0·2 0·4 0·6 0·8 1·0 1·2 1·4 1·6 1·8 2·0h: m

Uc:

m/s

ChildAdult

Figure 1. Instability curves for a child and adult in floodwaters

(Keller and Mitsch, 1993)

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vehicles) carried by a flood can cause severe damage to buildings.

Kelman and Spence (2004) presented an overview of flood

characteristics with respect to their applicability for estimating

and analysing direct flood damage to buildings.

Flood actions on buildings include hydrostatic actions, hydro-

dynamic actions and erosion. However, the main flood actions are

the depth difference between water levels outside and inside a

building and the velocity near the building walls. Kelman (2002)

proposed matrices for damage to buildings based on the maxi-

mum flood depth difference and the maximum flood velocity.

Five potential levels of damage were assigned to different

combinations of depth differences and velocities, from minor

water contact and infiltration to irreparable structural damage.

However, such complex matrices for damage to buildings are not

necessary in the initial assessment of flood risk.

A simplified assessment matrix for flood risk to buildings (Defra

and EA, 2006) was therefore used in the current study (Table 1).

This matrix adopted an average hazard scale for each building

type in each combination of depth difference and velocity

(Kelman, 2002). The assessment matrix can also be approxi-

mately expressed by regression into a simple formula

HD ¼ 0:7U 0:14˜h0:345:

in which U is flow velocity near the building walls, ˜h is the

depth difference between water levels outside and inside the

building and HD is the hazard degree of the building in flood-

waters. Hazard degrees have been grouped into three damage

categories: some damage (HD < 0.5); severe damage

(0.5 , HD, 0.98); irreparable damage (HD > 0.98). In an initial

assessment, it is difficult to calculate ˜h accurately without

knowing the detailed structure and layout of the building, and it

is assumed that ˜h is approximately equal to half the depth at a

cell. It should be pointed out that such a matrix is an indicative

assessment of the damage that will occur to buildings in urban

areas and it cannot include the effect of different types of

building. However, it is often accepted for a preliminary assess-

ment of flood risk by local organisations such as the Environment

Agency.

2.3 Quantification method of flood hazard degrees

In the current model, the curves in Figure 1 proposed by Keller

and Mitsch (1993) were used to evaluate the degree of people

safety and the incipient velocity formula from the recent study

(Xia et al., 2010c) was used to assess the degree of vehicle safety.

The model therefore adopts formulae based on mechanics ana-

lysis to assess the degrees of safety of people and vehicles in

floodwaters. Although it is very difficult to define accurately the

hazard degree for people and vehicles, it can be concluded that a

person or vehicle will be swept away as the incoming velocity

approaches or exceeds the corresponding critical velocity. Thus,

the following expression is used to quantify the corresponding

degree of hazard for people or vehicles

HD ¼ Min 1:0, U=Ucð Þ6:

People or vehicles will be safe if HD ¼ 0 (U � Uc) while they

will be in danger if HD approaches 1.0 (U > Uc). The values

from Table 1 or Equation 5 can be used directly to quantify the

hazard degree of buildings in floodwaters. However, these assess-

ment methods in the model cannot account for the effect of flood

duration on the HD values.

3. Model testsFor the integrated model outlined above, the hydrodynamic

module has been verified against analytical solutions and experi-

mental data for dam-break floods over simple bed topography

(Xia et al., 2010a). However, the paths of flood propagation in

urban areas are complex due to the irregular layout of buildings

and streets, which leads to some special flow characteristics

including higher water levels and transient flows between two

buildings. Therefore, two series of model tests were undertaken

in this study to further verify the hydrodynamic module, with the

ATVExecutive saloonSmall family car

0

1·0

2·0

3·0

4·0

0 0·5 1·0 1·5 2·0 2·5 3·0h: m

Uc:

m/s

Figure 2. Relationship between incoming water depth and

incipient velocity for three vehicle types (Xia et al., 2010c)

Velocity: m/s Depth difference: m

0 0.5 1.0 1.5 2.0

0 0 0.40 0.60 0.86 0.96

1 0 0.40 0.72 0.88 0.96

2 0 0.50 0.84 0.94 0.98

3 0 0.50 0.86 0.96 1.00

4 0 0.60 0.90 0.98 1.00

5 0 0.72 0.96 1.00 1.00

6 0 0.84 1.00 1.00 1.00

Table 1. Flood damage degree matrix for buildings (Defra and EA,

2006)

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model predictions being compared with laboratory experimental

data and prototype surveyed wrack marks for urban floods. Two

test cases were undertaken:

(a) a dam-break flood through an idealised city in a laboratory

flume

(b) the Boscastle flash flood occurring in August 2004.

With regard to the module of estimating flood risk to people and

property, measured data are not available to directly verify the

accuracy of the model predictions. Predicted results for the 2004

Boscastle flood can, however, indirectly testify its estimation

accuracy and details are presented in Section 4.

3.1 Dam-break flood through an idealised city

A series of laboratory experiments was carried out at the civil

engineering laboratory of the Universite Catholique de Louvain,

Belgium (Soares-Frazao and Zech, 2008). The test case consid-

ered in this paper 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 Figure 3. The initial water depth in the

reservoir was 0.40 m and 0.011 m in the downstream reach. The

layout of the city in the experiment was idealised in the sense

that a square city was composed of 5 3 5 buildings, aligned with

the incoming flow direction. In this experiment the ‘buildings’

were impervious wooden blocks of 0.30 3 0.30 m; the ‘streets’

were 0.10 m wide. The buildings in the experiment were high

enough in order not to 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. In the test case, the study domain

was divided into 17 689 unstructured triangular cells and the

mesh was refined just around these buildings of the idealised city,

with an area constraint of about 4 cm2 being used. A free-slip

boundary condition was applied at all side walls, with a free

outflow boundary condition being used at the downstream outlet.

A Manning roughness value of 0.01 m�1=3s was set according to

steady-flow experiments without the blocks and the gate (Soares-

Frazao and Zech, 2008).

Figure 4 shows the water level profiles along the longitudinal

street at y ¼ 0.2 m at different times; the simulated water level

profiles generally agree well with the measurements. In Figure

4(a) a hydraulic jump in front of the city was predicted at t ¼ 4 s,

which accorded with the visualised phenomenon. The predicted

initial depth of the hydraulic jump was about 2.7 cm, which was

slightly less than the measured depth of 3.3 cm; the predicted

sequent depth of hydraulic jump was about 22.0 cm, which was

slightly greater than the measured depth. At t ¼ 10 s (Figure

4(d)) the longitudinal street located at y ¼ 0.2 m was fully

flooded and a depression occurred at the toe of the hydraulic

jump. Figure 5 shows the velocity profiles along the longitudinal

street (again at y ¼ 0.2 m) at different times. It can be seen that

the predicted depth-averaged velocities were not in close agree-

ment with the measured surface velocities, but the former could

closely respond to variation in the latter at different times. At

t ¼ 4 s, the predicted initial velocity of the hydraulic jump

reached 2 m/s and the predicted sequent velocity of the hydraulic

jump was less than 0.2 m/s. At t ¼ 10 s, the predicted velocity

was about 1.4 m/s near the exit of the idealised city, due to the

presence of a hydraulic jump. Furthermore, simulations with

different mesh sizes for this case study indicated that the effect of

mesh refinement on improving the quality of the results was

limited. In general, the hydrodynamic module predicted the

complex flow characteristics as the dam-break flood flows

propagated through the idealised city in the flume.

3.2 Flash flood in Boscastle

The key aim of this study was to evaluate the calculation

accuracy of predicting hydrodynamic characteristics as the real

flash flood propagated through the urban area of Boscastle. This

district is located in a small mountain catchment with steep and

x: m

y: m

�8 �6 �4 �2 0 2 4 6 8�3

�2

�1

0

1

2

3

Initial depth 0·4 m� Initial depth 0·011 m�

y 0·2 m�

Figure 3. Sketch of idealised city in a flume

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0

0·1

0·2

0·3

(a)

h: m

Exp.Calc.

0

0·1

0·2

0·3

(b)

h: m

Exp.Calc.

0

0·1

0·2

0·3

(c)

h: m

Exp.Calc.

0

0·1

0·2

0·3

4 5 6 7 8x: m(d)

h: m

Exp.Calc.

Figure 4. Water level profiles at y ¼ 0.2 m along the longitudinal

street at different times: (a) t¼ 4 s; (b) t¼ 5 s; (c) t¼ 6 s; (d) t¼ 10 s

(a)0

0

0

1

1

1

2

2

2

Exp.Calc.

(b)

Exp.Calc.

(c)

U (m

/s)

Exp.Calc.

U: m

/sU

: m/s

U: m

/s

4 5 6 7 80

1

2

x: m(d)

Exp.Calc.

U: m

/s

Figure 5. Velocity profiles at y ¼ 0.2 m along the longitudinal street

at different times (a) t¼ 4 s; (b) t¼ 5 s; (c) t¼ 6 s; (d) t¼ 10 s

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complex topography. On 16 August 2004, Boscastle was devas-

tated by a flash flood due to heavy rainfall that fell within 5 h into

a small rocky catchment. Flooding of the River Valency and its

tributary the River Jordan caused significant damage to the town

of Boscastle. The Valency River has a catchment area of

approximately 20 km2. Its main branch is 7 km long and the

catchment rises to 300 m AOD. The slope of the river is therefore

very steep. The catchment is predominantly rural, with significant

areas of woodland adjacent to the main river and its tributaries

(Roca and Davison, 2010).

The computational domain of this case study is shown in Figure

6, with the locations of a car park and main road marked. The

River Valency enters this zone from the east while the tributary

of the River Jordan flows into this domain from the south. The

study domain was divided into about 54 192 equilateral triangular

cells, with each cell area being 2 m2. The eastern boundary of the

domain was set as an inflow boundary for the River Valency and

the western boundary was set as the downstream boundary. The

different discharge hydrographs were specified as the inflow

boundaries of the two rivers and the interval of flood recurrence

was estimated to be 1 in 400 years according to analysis of past

floods (HRW, 2005). The total discharge hydrograph for these two

rivers is shown in Figure 7; the total peak discharge of the flood

was estimated to be 170 m3/s, including discharges from the

River Valency of 160 m3/s and the tributary of about 10 m3/s. A

rating curve between stage and discharge was used at the down-

stream boundary, which was related to the local variation in sea

level.

Figure 8 indicates the distributions of water depths and velocities

as the peak discharge arrived. It can be seen from Figure 8(a)

that:

(a) roads and riverine streets were flooded by this extreme event,

with the depth on the main road being greater than 2.0 m,

which accorded well with the visually observed depth

(b) the blockage of the main bridge caused an abrupt rise in

water level upstream of the bridge.

The predicted depth-averaged velocities in the car park reached

over 3–4 m/s (Figure 8(b)), meaning that vehicles parked on this

site could be washed away. Numerical results from Figure 8

indicate many changes between subcritical and supercritical flows

in the channel and floodplains. At the time of the peak discharge,

supercritical flows were predicted in the car park and on the

blocked main bridge. Simulated water level and velocity profiles

at typical sections are shown in Figure 9. Section 1 (CS1) is

located 200 m downstream of the inflow boundary, crossing the

car park, while section 2 (CS2) is located 170 m upstream of the

outlet. It can be seen that:

x: m

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Bridge

Jordan Channel

Valency St

Main road

Car park

Valency

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y: m

Figure 6. Sketch map of Boscastle (Basemap #Googlemaps)

0

60

120

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300

0 1 2 3 4 5 6Time: h

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char

ge: m

/s3

P � 1%P 0·25%(2004 Boscastle flood)

�

P 0·1%�

Qmax3290 m /s�

Qmax3170 m /s�

Qmax360 m /s�

Figure 7. Inflow discharge hydrographs for different flood

frequencies

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(a) the mean water depth was less than 3 m, with the corresponding

velocity being about 3–4 m/s in the car park at CS1

(b) the mean depth on the right riverine street was approximately

2 m, with the corresponding velocity being about 2–3 m/s at

CS2.

Following the flood event, a survey was undertaken of wrack

marks left by the flow on buildings or vegetation. These flood

marks provided a useful indicator of flood depths that could be

used to verify the performance of the numerical model, although

it should be noted that uncertainties were associated with these

wrack marks after such an extreme event (HRW, 2005). Figure 10

shows that the predicted maximum water levels generally agree

well with the observed flood tracks.

4. Application of the integrated modelThe integrated model was used to simulate the impact of flash

floods in Boscastle under different inflow discharges, for various

flood frequencies, and then to assess the corresponding risk to

people and property in floodwaters. Three discharge hydrographs

were considered at the inflow boundaries, with the different flood

frequencies being of the order of 1 in 100 years (i.e. P ¼ 1%), 1 in

400 years (P ¼ 0.25%) and 1 in 1000 years (P ¼ 0.1%). The

corresponding peak discharges were about 60, 170 and 290 m3/s

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Depth: m

Velocity: m/s

(a)

(b)

CS

2

CS

1C

S1

CS

2

Figure 8. Distributions of (a) depths and (b) velocities at the time

of peak discharge (Basemap #Googlemaps)

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respectively. The discharge hydrograph for the P ¼ 0.25% event

was estimated from the 2004 flood event. The following predicted

results only present a preliminary assessment of flood risk to

people and property under different floods; however, such results

could be used to inform future management of flood risk, including

distributions of maximum depths and hazard degrees, as well as

temporal changes in flow conditions and risk at special sites.

4.1 Predicted maximum depths

Figure 11 indicates the distributions of maximum depths under

different flood events. In the case of a 1 in 100 year flood event

(Figure 11(a)), the maximum depth was predicted to be less than

1.5 m across the majority of the flooded area and less than

0.80 m in the car park. For the case of a 1 in 1000 year flood

event (Figure 11(b)), the maximum depth was predicted to be

greater than 2 m in the car park and over 4.0 m on the main road.

In the case of an extreme flood event, both the riverine streets

and Valency street were predicted to be fully flooded, with the

maximum depth predicted to exceed 1.2 m on the surface of the

blocked main bridge. At the main road and car park sites, the

maximum velocities were predicted to be greater than 4 m/s.

Therefore, such an extremely high flood would lead to severe loss

of human life and property due to the occurrence of both large

water depths and high velocities.

4.2 Predicted flood risk to people

In the flood simulations, the HD value for people at a cell for

each time step was calculated using the curves in Figure 1 and

Equation 6 and then the maximum HD at each cell over the

simulation period was predicted. Thus, the maximum values of

HD for people at all cells in the study domain were obtained

(Figure 12). The distributions of maximum risk to adults under

different flood events in Figure 12 indicate that:

(a) for the 1 in 100 year event, people in the majority of the

flooded area would be in danger of being swept away during

a flash flood due to the relatively large depths and high

velocities; however, people standing on Valency Street could

be safe (Figure 12(a))

(b) for the 1 in 1000 year event, people across all of the flooded

area would be swept away during the flood due to the

extremely high velocities (Figure 12(b)).

Therefore the potential flood risk to people would be severe even

if a flood with a frequency of 1% occurred in Boscastle; similar

results were also obtained for the 1 in 400 year flood. The

predicted distribution of flood risk to people indirectly verified

that the estimation accuracy of instability curves for people in

Figure 1 is acceptable because tens of local residents were

rescued by helicopters during the 2004 flash flood (a 1 in

400 year flood).

(a)

Distance from the right-hand side: m(b)

Bed

or w

ater

leve

l: m

Bed

or w

ater

leve

l: m

Velo

city

: m/s

Velo

city

: m/s

20 40 60 80 1008

10

12

14

16

18

20

0

2

4

6

8

10

12

Bed levelWater levelVelocity

(A)

(B)

(A) Car park�

(B) Channel�

10 20 30 40 50 60 702

4

6

8

10

12

14

0

2

4

6

8

10

12

Bed levelWater levelVelocity

(A) Channel�(B) Riverine street�

A B

Figure 9. Simulated water level and velocity profiles at sections

(a) CS1 and (b) CS2

4

6

8

10

12

14

16

18

20

4 6 8 10 12 14 16 18 20Observed flood track: m

Pred

icte

d m

axim

um le

vel:

m

Figure 10. Comparison of predicted maximum water levels and

observed flood tracks

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4.3 Predicted flood risk to property

The distributions of maximum risk to 434-type vehicles under

different flood events are presented in Figure 13, based on

Equations 4 and 6. Figure 13 shows that:

(a) for the 1 in 100 year flood event, this type of vehicle would

be safe in the majority of the main street and the car park due

to the relatively shallow depths and low velocities

(b) for the 1 in 400 year flood event (i.e. the actual 2004 flood),

HD values in the majority of flooded cells were predicted to

be equal to 1.0, especially in the car park and the region

downstream of the main bridge; vehicles parked at these sites

would be swept away by the flow.

A survey conducted after the Boscastle flood indicated that many

vehicles in the car park were indeed washed away in this extreme

event; this also indirectly testifies the predictive accuracy of the

hydrodynamic module and the assessment method of flood risk to

vehicles. The layout of any car park in a steep mountain

catchment therefore needs to be designed with considerable

attention to detail in any flood risk management plan. For

example, warning signs could be provided advising motorists that

vehicles in the car park are likely to be swept away if a particular

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CS2

(a)

(b)

Maximum depth: m

Maximum depth: m

0·8 2·82

Figure 11. Distributions of maximum water depths: (a) P ¼ 1%;

(b) P ¼ 0.1% (Basemap #Googlemaps)

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frequency flood occurs and that, under these circumstances,

vehicles will not be permitted to park.

The distributions of maximum risk to buildings for different flood

events are shown in Figure 14. As mentioned earlier, these

simulated results are only provided as an indicative assessment of

damage to buildings for different flood events and cannot account

for the effect of different building types on the values of HD. For

a 1 in 100 year flood, all the buildings were predicted to be safe

in this study domain (Figure 14(a)). However, for high floods (i.e.

P ¼ 0.25 and 0.1%), buildings near the main road were predicted

to be damaged by the flow (Figure 14(b)). Again, this agrees with

reports of buildings actually damaged during the 2004 flood.

4.4 Temporal changes in flood risk at a specific site

Figure 15 indicates the temporal variations in flood risk to people

and property under different floods at the specific site of P1,

located between the main road (B3263) and the building near the

channel. For the 1 in 100 year flood (Figure 15(a)), the maximum

depth at this site was predicted to be about 1.2 m with the

corresponding velocity being 1.2 m/s: children and small family

cars would be in danger during a flood of this severity. For the 1

in 1000 year flood (Figure 15(b)), the maximum depth was

predicted to be about 4.0 m, with a corresponding velocity of

2.5 m/s. Figure 15(b) also shows that the predicted arrival times

for people and vehicle instability were different, but both were

predicted to be in danger of being washed away as the peak

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(a)

(b)

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Hazard degree of adults

Hazard degree of adults

Figure 12. Distributions of maximum hazard risk to people:

(a) P ¼ 1%; (b) P ¼ 0.1% (Basemap #Googlemaps)

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discharge reached the site. Small family cars were predicted to

start to be unstable at t ¼ 0.9 h, while 434 ATVs would begin to

move at t ¼ 1.9 h. The most severe building damage would occur

at t ¼ 4.0 h. It can thus be concluded from these model predic-

tions that extreme flash floods occurring in such a steep and

complex catchment would cause serious damage to both people

and property due to the large water depths and high velocities.

5. ConclusionsThe impacts caused by flash floods can be very high in densely

populated urban areas and the future occurrence probability of

urban flooding is likely to increase due to global warming and

climate change. Flood risk predictions in urban areas are there-

fore important in improving future flood risk management.

This paper has outlined an integrated numerical model to

estimate flood risk in urban areas. The model includes a 2D

hydrodynamic module and a module for estimating flood risk to

people and property. Laboratory experimental data and real flood

tracks in urban floods were used to verify the accuracy of the

hydrodynamic module. The 2004 flood event in Boscastle, UK,

was selected as a case study and the integrated model was applied

to estimate flood risk to people and property in this area. Model

predictions indicated the following.

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(b)

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Hazard degree of Pajero Jeeps

Hazard degree of Pajero Jeeps

Figure 13. Distributions of maximum hazard risk to 434-type

vehicles: (a) P ¼ 1%; (b) P ¼ 0.25% (Basemap #Googlemaps)

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(a) For a 1 in 100 year flood event, people standing on the main

road and in the car park would be in danger of becoming

unstable due to the relatively large water depths. Vehicles in

the centre of the car park would be swept away, but there

would be no damage to local buildings.

(b) For a 1 in 400 year flood event, people and vehicles would be

swept away on the main road and riverine streets, as well as

in the car park. In addition, limited damage to buildings near

the main road would occur.

(c) For a 1 in 1000 year flood event, people and property (both

vehicles and buildings) throughout the flooded area would be

at severe risk.

The results for different flood events from such model predictions

therefore offer a rough assessment of the flood risk to people and

property in urban areas. Simulations such as those presented here

would be useful to governments, the emergency services and

local agencies and authorities associated with planning for future

extreme flood events.

AcknowledgementsThe research reported in this paper was conducted as part of the

flood risk management research consortium (phase II) supported

by the UK Engineering and Physical Sciences Research Council

(GR/S76304). The bathymetric data for the Boscastle study were

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Hazard degree of buildings

Hazard degree of buildings

Figure 14. Distributions of maximum hazard risk to buildings:

(a) P ¼ 1%; (b) P ¼ 0.1% (Basemap #Googlemaps)

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provided by the Environmental Agency, with post-flood surveys

undertaken by Halcrow Group Limited. The contributions of both

the organisations and individuals involved are gratefully acknowl-

edged. This work was partly supported by the programme for

new century excellent talent in university of the Chinese Ministry

of Education (NCET-10-0619) and by the national basic research

program of China (2007CB714102/6), and by the Natural Science

Foundation of China (Grant no. 50739003).

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(a)

Dep

th: m

HD

0 1 2 3 4 5 60

0·3

0·6

0·9

1·2

1·5

0

0·2

0·4

0·6

0·8

1·0DepthSmall car4 4 ATV�

ChildAdultBuilding

Time: h(b)

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HD

0 1 2 3 4 5 60

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1·0

Figure 15. Changes in flood hazard risk to people and property at

P1: (a) P ¼ 1%; (b) P ¼ 0.1%

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