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Modelling of Flash Flood Risk in Urban Areas

Junqiang Xia1,2, Roger A. Falconer1, Binliang Lin1 and Guangming Tan2

(1Hydro-environmental Research Centre, School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK)

(2State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China)

Abstract: In urban areas the impacts of flash floods can be very high due to these regions being

generally densely populated and containing vital infrastructure. Parts of the UK have been

particularly prone to such serious urban flooding in recent years, such as the 2004 Boscastle flood.

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. Therefore, it is

appropriate to estimate the potential flood risk to people and property for improved flood risk

management. In the current study, an integrated numerical model for estimating the flood risk in

urban areas is outlined herein, including the module for predicting the 2D hydrodynamic

characteristics of urban floods, together with a new module for predicting the flood risk to people

(including children and adults) and property (including vehicles and buildings). The hydrodynamic

module of this model 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 floods, with different reoccurrence frequencies. The predicted results for

different flood scenarios indicated that: (i) people would be swept away in the majority of the

flooded area for a flood with P = 1% (a return period of 100 years) , while they would be in danger

almost in all the flooded area for a high flood, with P = 0.25% (a return period of 400 years) or

0.1% (a return period of 1000 years); (ii) vehicles would be washed away from the parking area in

the centre of a car park during a flood with P = 1%, while they would also be flushed on the main

road and main street, and in the car park during a flood with P = 0.25 or 0.1% ; and (iii) there would

be no damage to buildings during a flood with P = 1%, but severe damage to buildings would be

likely to occur during high floods. Therefore, the developed integrated model can be used to predict

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the potential flood risk to people and property in urban areas, and these predictions can be used for

improved flood risk management.

Keywords: Floods & floodworks; Risk & probability analysis; Hydraulics & hydrodynamics

1 Introduction

A considerable change in the 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 16th August 2004 the coastal village of Boscastle in

North Cornwall, was devastated by a flash flood as a result of a series of torrential thunderstorm,

which deposited over 200 mm of rainfall within five hours, into a small rocky steep catchment. This

extreme event was caused by the combination of stationary cumulonimbus clouds, creating heavy

rain on the Valency Catchment, the saturation of the soil, due to antecedent rain generating high

runoff, and the steep nature of the catchment concentrating the flows in Boscastle (HR Wallingford,

2005). The observed water depths on the streets were more than 2 m, with high velocities carrying a

lot of 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 addition, about 116 vehicles were swept by the flow, and some of them

were washed out into the harbour. In another example, on 8th and 9th January 2005, Carlisle in

North-West England experienced widespread 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. Therefore significant reaches of the flood defences were

overtopped, which led to 2600 properties being flooded and with the estimated cost of damage

incurred being £450 million (EA, 2005). These typical floods have raised public and political

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awareness of urban flooding and have also highlighted the need to better understand and estimate

the flood risk in urban areas.

There now appears to be little doubt that global warming has played a significant role in

climate change, and international news about extreme urban flooding is being reported more

frequently. The Parliamentary Office of Science and Technology (POST) in the UK pointed out 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. Its impacts are expected to

increase if no policy changes are made (POST, 2007). A special report by a Foresight Programme

that the costs of urban flooding could rise to between £1-10 billion per annum by 2080 if no action

is taken to reduce the risks (Foresight Programme, 2004). Wheater (2006) reviewed the climate

change impacts on flooding and current guidelines for UK practice, and pointed out that floods

cannot be prevented but flood risk can be managed. Predicted results from the UK Climate Impacts

Programme UKCIP02 were presented by Hulme et al. (2002), which 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

the population and property in such regions, especially if no corresponding counter-measures are

taken in advance to cope with extreme flood events, such as the 2004 flash flood occurring in

Boscastle due to exceptional rainfall. 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 the 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 increases

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the risk, and urban flooding is also expected to occur more often due to future climate change.

Therefore, to define and estimate the hazard degree for people and property in urban areas is an

important component of good flood risk management, and usually consists 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 floodwaters, evacuation difficulty, and flood awareness of the local population

(Walsh et al., 1998). The processes of flood propagation in urban areas are often simulated by

two-dimensional (2D) hydrodynamic models (Liang et al. 2007; Soares-Frazao and Zech, 2008;

Hunter et al., 2008; Abderrezzak et al., 2009; Roca and Davison, 2010; Wang et al., 2010; Petaccia

et al., 2010). However, the estimation module of hazard degrees for people and property needs to be

integrated with the hydrodynamic module in order to predict the flood risk in urban areas, which is

the aim of the current study outlined in this paper.

In the current study, an integrated model for predicting the flood risk in urban areas is outlined

herein, including the module of simulating 2D hydrodynamic characteristics of urban floods and the

module of 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 reoccurrence frequencies.

2 Description of an integrated model

This section introduces an existing 2D hydrodynamic module, and the module of flood risk to

people (including children and adults) and property (including vehicles and buildings), together

with the quantification 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. More

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details of this model are given in Xia et al. (2010 a and b)

2.1 Module for 2D hydrodynamics

For flows in natural rivers, floodplain systems and urban catchments, a set of shallow water

equations for two-dimensional 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, a small vertical acceleration 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 given below:

t x y x y

U E G E G

S

(1)

where U = vector of conserved variables; E and G = convective flux vectors of flow in the x

and y directions, respectively; E and G = diffusive vectors related to the turbulent stresses in

the x and y directions, respectively; and S = source term including: bed friction, bed slope

and the Coriolis force. The above terms can be expressed in detail as:

hv

hu

h

U , 2 212

hu

hu gh

huv

E , 2 21

2

hv

huv

hv gh

G ,

0

xx

yx

E ,

0

xy

yy

G , and

( )

( )

s

bx fx

by fy

q

hfv gh S S

hfu gh S S

S (2)

where u , v = depth-averaged velocities in the x and y directions, respectively; h = total

water depth; sq = source (or sink) discharge per unit area ; g = gravitational acceleration; f =

the Coriolis acceleration due to the earth’s rotation; bxS and byS = bed slopes in the x and y

directions, respectively; fxS and fyS = friction slopes in the x and y directions, respectively;

and xx , xy , yx and yy = components of the turbulent shear stress over the plane. In this

model, a simple turbulence model was used to calculate the turbulent viscosity coefficient, and it is

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not applicable for simulating the complex separation and reattachment flows in local regions (Xia et

al., 2010a).

The module adopted a finite volume method to solve the governing equations based on an

unstructured triangular mesh. In this FVM model the study region was first divided into a set of

triangular cells, to form an unstructured computational mesh. A cell-centred finite volume method

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, the calculation of flow fluxes can be

treated as a locally one-dimensional 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 the scheme of 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), which 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 the wetting and drying processes due to rapid flooding. This model has been validated by

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

In this section, the module of flood risk to people and property is outlined briefly. In this

module, the estimation methods for the risk to people and vehicles in floodwaters were based on the

mechanical condition of sliding equilibrium (Keller and Mitsch, 1992; Xia et al., 2010c), and the

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

people in floodwaters needs to be understood by managers for urban floods. Therefore, it is

important to assess the degree of people stability in floodwaters. Previous studies on the assessment

method of people safety were carried out using two different approaches: (i) using empirical or

semi-quantitative criteria (ACER, 1988; Penning-Rowsell et al., 2005; Defra and EA, 2006), and (ii)

using formulae derived from the mechanical analysis based on experiments (Abt et al., 1989; Keller

and Mitsch, 1992; Lind et al., 2004; Jonkman and Penning-Rowsell, 2008). Jonkman and

Penning-Rowsell (2008) reported the results of new experiments on human instability in

floodwaters, based on studies reported by the Flood Hazard Research Centre (FHRC) in the UK.

These new results showed that floodwaters with low depths and high velocities are more dangerous

than suggested, based on the findings from previous experimental work. They discussed how

human instability can be related to two physical mechanisms: 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 the instability

mechanisms.

In this study, the more mechanics-based formula proposed by Keller and Mitsch (1992) 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, and given by:

8

2 r

cf d

FU

C A (3)

where rF = restoring force due to the friction; A = submerged area projected normal to the flow;

dC = drag coefficient; and f = density of water. According to Eq. (3), two curves were

presented between the product of the water velocity ( cU ) and the incoming depth ( h ) at the point of

human instability versus h , for a five year old child and an adult, under the condition of sliding

equilibrium.

Fig. 1 shows the instability curves for the child and the adult in floodwaters, and it can be seen

that there is a significant difference between the critical velocities for the child (i.e. 0.5 m/s) and the

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 condition (such as the local flow

pattern, terrain and visibility) and the subjective condition (such as the physical and psychological

status of a person). Moreover, these curves in Fig. 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 (Jonkman and Penning-Rowsell, 2008). Therefore, the curves in Fig. 1 just present a rough

estimation 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 Morris Mini car with the two back wheels being 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 (1992) conducted a series of experiments to study the stability conditions for

idealized Susuki Swifts, Ford Lasers and Toyota Corollas cars at 1:20 scale, and developed a simple

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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 by the authors for flooded vehicles, it

has been found that a completely water-tight 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 (Xia et al., 2010c). 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 windows

of the vehicle being 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 the floodwater flows around a vehicle parked on a road, the flow usually exerts three

forces on the vehicle, including: a lift force, a drag force and a buoyancy force. It is assumed that

the wheels of a vehicle are all locked against any movement as it parks on a road, 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 gravitational force. In the recent

study conducted by the authors (Xia et al., 2010c), all of the forces acting on a flooded vehicle were

analysed with the corresponding expressions for these forces being presented. According to the

theory of sliding equilibrium, the expression for the incipient velocity was then derived for

commonly used vehicles parking on flooded streets or roads. This formula is given as:

10

2 ( )c fc c

c f

hU g h

h

(4)

in which: c = density of the vehicle; ch = vehicle height; h = incoming water depth; and the

parameters and are related to the shape of the vehicle, the type of tyres and the road surface,

which could be determined from the flume measurements. This formula is valid for both fully and

partially submerged vehicles. A series of flume experiments were then conducted using three types

of scaled die-cast model vehicles, with two scales being tested for each type of vehicle. 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 this formula was validated using

the experimental data obtained for the large-scale model vehicles. Finally, the corresponding

incipient velocities obtained for various incoming depths were computed using this formula for

these three prototype vehicles, and the obtained instability curves for prototype vehicles are shown

in Fig. 2.

Fig. 2 indicates the relationship between the incoming water depth and corresponding incipient

velocity for different vehicles in floodwaters, according to the calculations using Eq. (4). It can be

seen from Fig. 2 that the Mini Cooper is the easiest vehicle to start sliding in floodwaters, and the

incipient velocity for each fully submerged vehicle ranges from 0.5 to 1.0 m/s. Therefore, Fig. 2 can

be used to preliminarily evaluate the degrees of vehicle stability in floodwaters, and it is useful for

assessing the flood hazard degrees of these various vehicles parking on flooded streets or roads.

However, it should be pointed out that the current formula, or Fig. 2, was based on relatively ideal

circumstances that the direction of the incoming flow was always facing the rear side of a vehicle

and the channel bed was always flat. For the assessment of instability thresholds of flooded vehicles

under real and more complex circumstances, more studies need to be conducted in order to enable a

practical application of the derived formula, including the effect of different incoming flow

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

collapse because of water pressure, scour of foundations, or a combination of these events. In

addition, debris carried by a flood in the form of trees, boulders or vehicles, 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, hydrodynamic actions, and erosion actions,

etc. 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 maximum 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.

Therefore, the simplified assessment matrix for the flood risk to buildings by Defra and EA

(2006) was introduced in the current study, as shown in Table 1. This matrix adopted an average of

hazard scale for each building type in each combination of depth difference and velocity (Kelman,

2002). The assessment matrix also can be approximately expressed by regression into a simple

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formula:

0.14 0.340.7HD U h (5)

in which U = velocity near the building walls; h = depth difference between water levels

outside and inside a building; and HD = hazard degree of the building in floodwaters. The hazard

degrees have been grouped into three damage categories, including some damage (HD ≤ 0.5),

severe damage (0.5 < HD < 0.98) and irreparable damage (HD ≥ 0.98). In the initial assessment, it

is difficult to calculate accurately the value of h without the detailed structure and layout of a

building, and it is assumed that h is approximately equal to half of 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 assessment of flood risk in local organisations such as

Enviroment Agency.

2.3 Quantification method of flood hazard degrees

In the current model the curves in Fig. 1 proposed by Keller and Mitsch (1992) were used to

evaluate the degree of people safety, and the incipient velocity formula from the recent study was

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

formulae based on the mechanics analysis to assess the degrees of safety of people and vehicles in

floodwaters. Although it is very difficult to accurately define 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 and is given by

1.0, / cHD Min U U (6)

in which HD = hazard degree for people or vehicles in floodwaters. People or vehicles will be safe

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if HD =0, namely, cU U ; while they will be in danger if HD approaches 1.0, namely cU U .

The values from Table 1 or Eq. (5) can be used directly to quantify the hazard degree of buildings in

floodwaters. However, these assessment methods in the model cannot account for the effect of flood

duration on the value of hazard degree.

3 Model tests

For the above outlined integrated model, the hydrodynamic module has been verified against

analytical solutions and experimental data for dam-break floods over simple bed topographies (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 verify further the hydrodynamic module, with the model

predictions being compared with laboratory experimental data and prototype surveyed wrack marks

for urban floods. Two test cases were undertaken including: (i) a dam-break flood through an

idealised city in a laboratory flume; and (ii) 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, and predicted results for the 2004

Boscastle flood can indirectly testify its estimation accuracy, with the details being presented in the

next section.

3.1 Dam-break flood through an idealised city

A series of laboratory experiments of dam-break flood flows through an idealised city were

carried out at the Civil Engineering Laboratory of the Université Catholique de Louvain, Belgium

(Soares-Frazao and Zech, 2008). The test case considered in this paper was conducted in a 36 m

long flume, having a width of 3.6 m. A gate was located between two impervious abutment blocks

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to simulate a breach. A sketch map of this experiment set-up is shown in Fig. 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 5×5 buildings, aligned

with the incoming flow direction. In this experiment the “building” consisted of impervious wooden

blocks of 0.30 m×0.30 m, while the “streets” were 0.10 m wide. The buildings in the experiment

were high enough in order not to be submerged by the flow. In these experiments several devices

were used to record the flow. Firstly, the water surface evolution was measured by means of several

resistive level gauges. Secondly, 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).

Fig. 4(a-d) shows the water level profiles along the longitudinal street located at y = 0.2 m, at

different times. It can be seen that the simulated water level profiles generally agree well with the

measurements. In Fig. 4a a hydraulic jump in front of the city was predicted at t = 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; and the predicted sequent

depth of hydraulic jump was about 22.0 cm, which was slightly greater than the measured depth. At

t = 10 s, it can be seen from Fig. 4d that the longitudinal street, located at y = 0.2 m, was fully

flooded and a depression occurred at the toe of the hydraulic jump. Fig. 5(a-d) shows the velocity

profiles along the longitudinal street, located at y = 0.2 m, at different times. It can be seen that the

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predicted depth-averaged velocities were not in close agreement with the measured surface

velocities, but the former could closely respond to the variation in the latter at different times. At t =

4 s, the predicted initial velocity of the hydraulic jump reached up to 2 m/s, and the predicted

sequent velocity of the hydraulic jump was less than 0.2 m/s. At t = 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 second test case undertaken was for the town of Boscastle, in the UK, and the key aim of

this study was to evaluate the calculation accuracy of predicting the hydrodynamic characteristics as

the real flash flood propagated through the urban area. This urban district is located in a small

mountain catchment with a steep and complex topography. On 16th August 2004 Boscastle was

devastated by a flash flood and heavy rainfall, which fell within five hours, into a small rocky

catchment. The flooding of the River Valency and its tributary, namely 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 300m AOD.

Therefore, the slope of the river is very steep. The catchment is predominantly rural, with

significant areas of woodland adjacent to the main river and its tributaries (Roca and Davison,

2010).

In this case study the computational domain is shown in Fig. 6, with the location of a car park

and main road also being marked. The River Valency enters this zone from the east, while the

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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, respectively, and the interval of flood recurrence was estimated to be 1

in 400 years according to the analysis of past floods (HR Wallingford, 2005). The total discharge

hydrograph for these two rivers is shown in Fig. 7, and the total peak discharge of this flood was

estimated to be 170 m3/s, including the discharge from the River Valency of 160 m3/s, and the

discharge from the tributary of about 10 m3/s. A rating curve between stage and discharge was used

at the downstream boundary, which was related to the local variation in sea level.

Fig. 8 indicates the distributions of water depths and velocities as the peak discharge arrived. It

can be seen from Fig. 8a that: (i) 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; and (ii) the blockage of the main bridge caused an abrupt rise in the water level

upstream of the bridge. The predicted depth-averaged velocities in the car park reached over 3-4

m/s (Fig. 8b), which meant that the vehicles that parked at this site could be washed away due to the

high velocities. Numerical results from Fig. 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 Fig. 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: (i) the mean water depth was about less than 3 m, with

the corresponding velocity being about 3-4 m/s in the car park at CS1; the mean depth on the right

17

riverine street was approximately 2 m, with the corresponding velocity being about 2-3 m/s at CS2.

Following the flood event a survey of wrack marks left by the flow on the buildings or

vegetation was undertaken. These flood marks provided a useful indicator of flood depths and can

be used to verify the performance of the numerical model. However, it should be noted that

uncertainties were associated with these wrack marks for such an extreme event (HR Wallingford,

2005). Fig. 10 shows a comparison between the predicted maximum water levels and flood tracks,

and the model predictions can generally be seen to have agreed well with these observations.

4 Application of the integrated model

As cited above global warming is known to have played a significant role in climate change,

which has caused an increase in the probability of occurrence of extreme floods in urban areas. In

this study Boscastle was selected as a study domain. The integrated model was then 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 = 1%), 1 in 400 years (i.e. P = 0.25%) and 1

in 1000 years (i.e. P = 0.1%). The corresponding peak discharges were about 60 m3/s, 170 m3/s and

290 m3/s, respectively. The discharge hydrograph for the P = 0.25% event was estimated from the

2004 flood event. The following predicted results just present a preliminary assessment of flood risk

to people and property under different floods, and they would be referred to the future management

of flood risk, which includes the distributions of maximum depths and hazard degrees, as well as

the temporal changes of flow conditions and risk at special sites.

4.1 Predicted maximum depths

Fig. 11 indicates the distributions of maximum depths under different flood events. In the case

18

of a 1 in 100 year flood event, the maximum depth was predicted to be less than 1.5 m across the

majority of the flooded area and to be less than 0.80 m in the car park (Fig. 11a). For the case of a 1

in 1000 year flood event, the maximum depth was predicted to be greater than 2 m in the car park

and to be over 4.0 m on the main road (Fig.11b). For such an extremely high flood event, both the

riverine streets and the Valency street were predicted to be fully flooded, and the predicted

maximum depth would exceed 1.2 m on the surface of the blocked main bridge. At the sites of the

main road and car park, the maximum velocities were predicted to be greater than 4 m/s, which

responded well to large water depths. Therefore, such an extremely high flood would lead to severe

loss of human life and property due to the occurrence of both large depths and high velocities.

4.2 Predicted flood risk to people

In the simulation for a flood, the value of HD for people at a cell for each time step was calculated

using the curves in Fig. 1 and Eq. (6), and then the maximum value of HD at each cell over the simulation

period was predicted. Thus, the maximum values of hazard degree for people at all cells in the study domain

were obtained. Fig. 12 shows the distributions of maximum risk to adults under different flood events,

and the people in the red zones could be in danger since the values of HD in these zones were

predicted to approach 1.0.

It can be seen from Fig. 12 that: (i) for the 1 in 100 year event, people in the majority of the

flooded area would be in danger and be swept away during the flash flood due to the relatively large

depths and high velocities, and however, people standing on the Valency street could be safe (Fig.

12a); (ii) 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 (Fig. 12b), therefore the potential flood risk to

people would be severe even if the flood with the frequency of 1% occurred in Boscastle, and

similar results were also obtained for the 1 in 400 years flood. The predicted distribution of risk to

people also indirectly verified that the estimation accuracy of instability curves for people in Fig. 1

was acceptable, because tens of local residents were rescued by helicopters during the 2004 flash

flood.

19

4.3 Predicted flood risk to property

The distributions of maximum risk to vehicles of the Pajero Jeep type under different flood

events are shown in Fig. 13. In this figure, the maximum values of flood hazard degree for the

vehicle were calculated by Eqs.(4) and (6), and the vehicles parking in the red zones could be swept

away because the flow velocities using the hydrodynamic model were predicted to be equal to, or

greater than, the corresponding incipient velocities using Eq.(4).

It can be seen from Fig. 13 that: (i) for the 1 in 100 year flood event, the Pajero Jeep vehicle

would be safe in the majority of the main street and the car park due to the relatively shallow depths

and low velocities; (ii) for the 1 in 400 year flood event, namely the 2004 flood, the values of risk

within the majority of flooded cells were predicted to be equal to 1.0, especially at the location of

the car park and in the region downstream of the main bridge, and therefore the vehicles parking at

these sites would be swept away by the flow. The survey conducted after this flood indicated that

lots of vehicles in the car park were washed away by this extreme flood, which also indirectly

testifies the predictive accuracy of the hydrodynamic model and the assessment method of the flood

risk to vehicles. Therefore, the layout of a car park in a steep mountain catchment needs to be

designed with considerable attention to detail in any flood risk management system. For example,

warning signs can be provided advising that if a particular flood frequency occurs then the vehicles

in the car park are likely to be swept away by the flow, and under these circumstances vehicles will

not be permitted to use the car park under such a flood or vehicles will be removed.

The distributions of maximum risk to buildings for different flood events are shown in Fig. 14.

As mentioned above, these simulated results are only provided as an indicative assessment of the

damage to buildings for different flood events, and cannot account for the effect of different

building types on the hazard degree. For the 1 in 100 year flood, all of the buildings were predicted

20

to be safe in this study domain (Fig.14a). However, for high floods (i.e. P = 0.25% and P = 0.1%),

the buildings near the main road were predicted to be damaged by the flow (Fig. 14b), which

accorded with the report of damaged buildings during the 2004 flood.

4.4 Temporal changes in flood risk at a specific site

Fig. 15a and b indicates the temporal variations in the flood risk to people and property under

different floods at a specific site of P1. P1 is located between the main road (B3263) and the

building near the channel. For the 1 in 100 year flood, the maximum depth at this site was predicted

to be about 1.2 m, with the corresponding velocity being 1.2 m/, where only children and the Mini

Cooper vehicle would be in danger during this flood (Fig. 15a). For the 1 in 1000 year flood, the

maximum depth at this site was predicted to be about 4.0 m, with the corresponding velocity being

predicted to be 2.5 m/s (Fig. 15b). It also can be seen from Fig. 15b that the predicted arrival times

for people and vehicle instability were different, but both were predicted to be in danger of being

washed away by the flood as the peak discharge reached the site. The Mini Cooper would start to be

unstable at t = 0.9 h, while the Pajero Jeep would start to be moved at t = 1.9 h. The most severe

damage to this building would occur at t = 4.0 h. Therefore, it can be concluded from these model

predictions that extreme flash floods occurring in such steep and complex catchments would cause

serious damage to both people and property due to the large water depths and high velocities.

5 Conclusions

The 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. Therefore, it is desirable to conduct flood risk analysis predictions in urban areas

using numerical models to improve flood risk management for the future. In this study, an

21

integrated numerical model has been outlined to estimate the flood risk in urban areas, including a

2D hydrodynamic module and a module for 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. Finally, the recent flood event in Boscastle, in the UK, was selected as a

study to test the applicablility of the model, and the integrated model was applied to estimate the

flood risk to people and property in this area. Model predictions indicated that: (i) for the 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 depths and vehicles would be swept away only in the

centre of the car park, while there would be no damage to local buildings; (ii) for the 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, the limited damage to buildings near the main road would occur; and

(iii) for the 1 in 1000 year flood event, severe risk to people and property would occur in all of the

flooded area during such an extremely high flood event. Therefore, the predicted results for

different flood events from such model predictions can be used by government, local agencies and

authorities, and emergency services associated with planning for future extreme flood events.

Acknowledgements

The 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 provided by the Environmental

Agency, with the postflood surveys being undertaken by Halcrow Group Limited. The contributions

of both the organizations and individuals involved are gratefully acknowledged. In addition, this

work was partly supported by the Programme for New Century Excellent Talents in University

22

from the Chinese Ministry of Education (Grant No. NCET-10-0619), and by the National Basic

Research Program of China (2007CB714102/6). Lastly, the authors would like to thank the

reviewers for their constructive and thorough comments which have led to improvements in the

paper.

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1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

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

)

Child

Adult

Fig. 1 Instability curves for a child and adult in floodwaters (Keller and Mitsch, 1992)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0h (m)

Uc

(m/s

)

Pajero Jeep

BMW M5

Mini Cooper

Fig. 2 Relationships between the incoming water depth and incipient velocity for three vehicles (Xia et al., 2010c)

Table 1 Flood damage degree matrix for buildings (Defra and EA, 2006)

Depth difference (m) Velocity

(m/s) 0 0.5 1 1.5 2

0.0 0.0 0.40 0.60 0.86 0.96 1.0 0.0 0.40 0.72 0.88 0.96 2.0 0.0 0.50 0.84 0.94 0.98 3.0 0.0 0.50 0.86 0.96 1.00 4.0 0.0 0.60 0.90 0.98 1.00 5.0 0.0 0.72 0.96 1.00 1.00 6.0 0.0 0.84 1.00 1.00 1.00

2

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=0.2m

Fig. 3 Sketch map of an idealised city in a flume

(a) t = 4s

0.0

0.1

0.2

0.3

4 5 6 7 8x (m)

h (m

)

Exp.Cal.

(b) t = 5s

0.0

0.1

0.2

0.3

4 5 6 7 8

Exp.Cal.

(c) t = 6s

0.0

0.1

0.2

0.3

4 5 6 7 8

Exp.Cal.

(d) t = 10s

0.0

0.1

0.2

0.3

4 5 6 7 8

Exp.Cal.

Fig. 4 Water level profiles along the longitudinal street located at y=0.2 m at different times

(a) t = 4s

0.0

1.0

2.0

4 5 6 7 8

Exp.Cal.

(b) t = 5s

0.0

1.0

2.0

4 5 6 7 8

Exp.Cal.

(c) t = 6s

0.0

1.0

2.0

4 5 6 7 8x (m)

U (

m/s

)

Exp.Cal.

(d) t = 10s

0.0

1.0

2.0

4 5 6 7 8

Exp.Cal.

Fig. 5 Velocity profiles along the longitudinal street located at y=0.2 m at different times

3

209600 209700 209800 209900 210000 210100 210200 210300

91200

91250

91300

91350

91400

Jordan Valency

car park

P1

x (m)

y (m

)

Valency St

main road

Channel

bridge

N

Fig. 6 Sketch map of Boscastle

0

60

120

180

240

300

0 1 2 3 4 5 6Time (h)

Dis

char

ge (

m3 /s

)

P=1%

P=0.25% (2004 Flood)

P=0.1%

Qmax=290 m3/s

Qmax=170 m3/s

Qmax=60 m3/s

Fig. 7 Inflow discharge hydrographs with different flood frequency

Fig. 8 Distributions of depths and velocities at the time of peak discharge

209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

914000.1 0.2 0.5 1 1.5 2 2.5 3 3.5 4

(a) Depth (m)CS

2

CS

1

xx

209600 209700 209800 209900 210000 210100 21020050

00

50

00

50

000.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

(b) Velocity (m/s)CS

2

CS

1

xx

4

Fig. 9 Simulated water level and velocity profiles at typical sections

4

6

8

10

12

14

16

18

20

4 6 8 10 12 14 16 18 20

Observed flood track (m)

Pre

dic

ted

ma

xim

um

leve

l (m

)

Fig. 10 Comparison between the predicted maximum water levels and observed flood tracks

Fig. 11 Distributions of maximum water depths

209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

0.1 0.2 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4Maximum depth(m)

(a) P = 1%

9600 209700 209800 209900 210000 210100 210200

0.1 0.2 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4Maximum depth(m)

(b) P = 0.1%

Distance for the right side (m)

Bed

orW

ater

Lev

el(m

)

Vel

ocity

(m/s

)

20 40 60 80 1006

8

10

12

14

16

18

20

0

2

4

6

8

10

12

Bed level

Water level

Velocity

(1)

(2)

(1) = Car Park(2) = Channel

(a) CS1

Distance from the right side (m)

Bed

orW

ater

Lev

el(m

)

Vel

ocity

(m/s

)

10 20 30 40 50 60 700

3

6

9

12

15

0

2

4

6

8

10

12

Bed level

Water level

Velocity

(1) (2)

(1) = Channel(2) = Riverine street

(b) CS2

5

Fig. 12 Distributions of maximum hazard degrees for people

Fig. 13 Distributions of maximum hazard degrees for vehicles

Fig. 14 Distributions of maximum hazard degrees for buildings

Fig. 15 Temporal changes in the flood risk to people and property at P1

209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Hazard degree of adults

(a) P = 1%

09600 209700 209800 209900 210000 210100 2102000

0

0

0

0

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Hazard degree of adults

(b) P = 0.1%

209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Hazard degree of Pajero Jeeps

(a) P = 1%

209600 209700 209800 209900 210000 210100 21020050

00

50

00

50

00

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Hazard degree of Pajero Jeeps

(b) P = 0.25%

Time (h)

Dep

th(m

)

Haz

ard

degr

ee

0 1 2 3 4 5 60

0.8

1.6

2.4

3.2

4

0

0.2

0.4

0.6

0.8

1

Depth

MiniCP

PajeroJP

Child

Adult

Building

(b) P = 0.1%

Time (h)

Dep

th(m

)

Haz

ard

degr

ee

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

Depth

MiniCP

PajeroJP

Child

Adult

Building

(a) P = 1%

209600 209700 209800 209900 210000 210100 21020050

00

50

00

50

00

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Hazard degree of buildings

(b) P = 0.1%

209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Hazard degree of buildings

(a) P = 1%