modelling extreme flood events and associated...

Professor Roger A. Falconer FREng Professor of Water Management and

Past President of IAHR (2011-15)

Hydro-environmental Research Centre

School of Engineering, Cardiff University

Modelling Extreme Flood Events

and Associated Processes

• Flooding essentially a natural process we need to live

with rivers, climate change and increasing storm events

Flooding not only be caused by high rainfall also poor

drainage, groundwater saturation, debris flows etc.

Flooding usually also leads to water pollution large loss

of life in many countries due to epidemiological outbreaks

Flooding damage extent often exacerbated by:

Inadequate data, poor warning systems and planning

Inadequate defences and insufficient upstream storage

Use of crude modelling tools and inexperienced operators

General

Floods are on the Rise

Floods Cause Loss of Life

Floods Bring Misery and Stress

Floods Bring Contamination

Cumbria Floods 2016 – Short Steep River Basin

Somerset Levels 2014 – Mild Slope River Basin

• Increasing concern of flooding along steep river basins and levee breeches – particularly in Wales

• Traditional 2-D and 1-D models not ideal for such flows and need refining for trans- and supercritical flows

• Full shallow water equations solved using a finite volume scheme on a collocated grid

• Model also refined to include surface and sub-surface flow interactions and extended to include floodplain flows in urban regions

Overview of Research for Steep Catchments

DIVAST-ADI vs. DIVAST-TVD

Dam-Break Problem

h 1

h 0

DIVAST-ADI vs. DIVAST-TVD

6

8

10

De

pth

(m)

0

50

100

150

200

x (m)

0

50

100

150

200

y (m)

h0 = 5 m

= 10-6 m2/s

6

8

10

De

pth

(m)

0

50

100150

200

x (m)

0

50

100

150

200

y (m)

h0 = 5 m

= 10-6 m2/s

DIVAST-ADI DIVAST-TVD

Dyke Break Experiment (TU Delft)

Gate

Dyke Break Experiment

Dyke Break Experiment

Time (s)

De

pth

(m)

0 5 10 15 200

0.05

0.1

0.15

Measured

Computed

Time (s)

De

pth

(m)

0 5 10 15 200

0.05

0.1

0.15

Measured

Computed

Time (s)

De

pth

(m)

0 5 10 15 200

0.05

0.1

0.15

Measured

Computed

Time (s)

De

pth

(m)

0 5 10 15 200

0.05

0.1

0.15

Measured

Computed

• Three modelling approaches considered:

Modelling buildings as solid blocks making buildings impervious

Remove buildings and increase local roughness not ideal

for water quality predictions

Remove buildings and treat as porous media better for

predicting water quality in buildings

Refined Treatment of Buildings

Flood Building Interaction

Unit: m

10

20

100 300

20

0

100

Dyke

Square Building

Reservoir

Manning’s n = 0.015

Flood Building Interaction 1 – Solid Building

Model Building

as solid block

Without Building

Flood Building Interaction 2 – High Roughness

n = 0.01 n = 0.03

n = 0.1 n = 5.0

Flood Building Interaction 3 – Porous Media

K = 250 m/s K = 50 m/s

K = 1 m/s K = 10 m/s

Flood Building Interaction – Water Levels

Time (s)E

levatio

n(m

)

0 60 120 1800

0.05

0.1

0.15

0.2

0.25

n=0.011

n=0.03

n=0.1

n=0.2

n=0.5

n=5.0

Solid

Time (s)

Ele

vatio

n(m

)

0 60 120 1800

0.2

0.4

0.6

0.8

Solid

n=5.0

n=0.5

n=0.2

n=0.1

n=0.03

n=0.011

Time (s)

Ele

vatio

n(m

)

0 60 120 1800

0.05

0.1

0.15

0.2

K=250

K=50

K=20

K=10

K=5

K=1

Solid

Time (s)

Ele

vatio

n(m

)

0 60 120 1800

0.2

0.4

0.6

0.8

Solid

K=1

K=5

K=10

K=20

K=50

K=250

Before Building After Building

Flood Inundation of Glasgow

Without buildings With buildings

City in Scotland prone to urban flooding

Flood Inundation of Glasgow

Porous media and solid block methods

Without buildings With buildings

Interaction Between Flood and Buildings

Water depth variance at G3:

t (min)

Ele

vatio

n(m

)

0 30 60 90 12023.6

23.8

24.0

24.2

24.4

Local high roughness method

K=0.1 m/s, Φ=0.8

K=0.1 m/s, Φ=0.5

Solid block method

• Small picturesque town in South West of UK

• Short river basin with steep valley terrain similar to

many river basins in Wales and Northern England

• Up to 200 mm rainfall fell in 5 hr and predicted to have 1 in 400 yr return period event

• Extensive damage to properties, bridges, highways and other infrastructure

• One of best recorded extreme flood events in UK with trans- and super-critical flows

Boscastle Flood 2004

View of Boscastle and Valency Valley

Determine type of model scheme most appropriate for predicting key parameters for extreme flood events

Three different schemes compared:

Simplified DIVAST (i.e. NI – No Inertia)

Standard DIVAST (i.e. ADI – Alternating Direction Implicit)

DIVAST – TVD (i.e. Total Variation Diminishing)

• Case studied: 2004 Boscastle flash flood

• Predicted main flood parameters (i.e. water elevations and flood inundation extent) compared with observed data

Model Study Objectives

Boscastle Study Domain

River Valency

Predicted Flood Simulation (TVD Scheme)

Flood Inundation Extent Predictions

Cases

NI – No Inertia

ADI – Alternating Direction Implicit

TVD – Shock Capturing

Predicted and Measured Water Levels

Models can be extended to include treatment of buildings on floodplains using surface/subsurface models offering

attractive options for flood modelling (e.g. health impact)

For rivers with trans- or supercritical flows, or levee breeches, then need to use more complex models and replicate hydrodynamic processes more accurately

Computational models with shock capturing algorithms provide more accurate predictions of flood elevations

Debris and vehicles can increase flood risk by blocking bridges and culverts to reduce local discharges

Summary

Wrong exit Debris flow problem

Study first undertaken to determine incipient velocity for fully submerged vehicles

Subsequent studies undertaken for partially submerged vehicles based on:

Based on physics derived formulae

Flume experiments based on similarity laws

Parameter determination and formulae validation

Based on incipient velocity for prototype vehicles

Incipient Velocity for Vehicles in Floodwaters

Formula Derivation

Different forces acting on a partially submerged vehicle

FR

FG

FN

U

FD

FG : Effective weight

FD: Drag force

FN : Normal force

FR: Frictional force

2

[ ( )] [ ( )]2f

bd d f c c c c c c f f f

uC a h b a l b h R h

g

2c c cb c f

d d f f

a hu gl R

a C h

(1 )( )f

yu U

h

2f c c

c c f

c f f

h hU gl R

h h

1

1

c

b d d

a

a C a

α, β = Parameters, to be calibrated using flume experiments;

Uc = Incipient velocity for a partially submerged vehicle.

D RF F

Flume Experiments for Vehicle Instability

Experiments conducted in HRC flume Cardiff University. Flume: 15 m long, 1.20 m wide and 1.00 m deep, plastic bed and glass sides

To estimate critical conditions for prototype vehicles - scaled model vehicles used, with 3 similarity laws used to design flume experiments

Partially submerged vehicle test Experimental test flume

Prototype can be analysed from experiments if similarity occurs with: form (geometric), motion (kinematic) and force (dynamic) .

Scale ratios of model experiments

Design of Flume Experiments

Flow and dimensions used typical for Taff

0

0 . 2

0 . 4

0 . 6

0 . 8

1

1 . 2

1 . 4

1 . 6

0 0 . 0 1 0 . 0 2 0 . 0 3 0 . 0 4h ( m )

U(

m/s

)

180°

0°

(a) Ford Focus

Uc (

m/s

)

hf (m)

U

U

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0.01 0.02 0.03 0.04h (m)

U(m

/s)

180°

0°

(b) Ford Transit

Uc

(m/s

)

hf (m)

U

U

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.01 0.02 0.03 0.04h (m)

U(m

/s)

180°

0°

(c) Volvo XC90

Uc

(m/s

)

hf (m)

U

U

Depth-incipient velocity relationships for partially submerged vehicles

Incipient Velocity for Prototype Vehicles

Incipient velocities for

partially submerged

vehicles in floodwaters

estimated using two

methods: (i) using

model scale ratios, (ii)

computations based

on derived formulae

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7hf (m)

Uc

(m/s

)

Eq.(12)(Ford Focus ST)

Eq.(12) (Ford Transit)

Eq.(12)(Volvo XC90)

Eq.(13)(Ford Focus ST)

Eq.(13)(Ford Transit)

Eq.(13)(Volvo XC90)

Ford Focus ST

Ford Transit

Volvo XC90

Comparison between estimated incipient velocities using two different approaches

Assessment of People Safety

Previous studies carried out using two approaches:

Empirical or semi-quantitative criteria Stability analysis validated by experimental data

Instability curves for child and adult in floodwaters

Keller and Mitsch (1992) established balanced forces acting on a flooded person:- buoyancy, weight, frictional resistance and drag due to flow:-

0.5

2 rc

f d

FU

C A

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 2.0

h (m)

Uc

(m/s

)

Child

Adult

Fr = restoring force due to friction;

A = submerged area normal to flow;

Cd = drag coefficient .

Similar approach adopted to previous study on incipient velocity for vehicles

Current study for partially submerged people

Formula derivation

Flume experiments following similarity laws

Parameter determination and formula validation

Estimation of incipient velocity for prototype people

Incipient Velocity for People in Floodwaters

Formula Derivation

186 tests undertaken in China using 1:5.54 scale models

Different forces acting on partially submerged person

FG : Effective weight

FD: Drag force Fb: Buoyancy force

FN : Normal force

FR: Frictional force

O

y

x

ufh

dL

gL

NF

DF

GF

toppling

u

Fb

y

x

(b) (a)

1 12 22 2

( ) cos sin ( )( )f p

p

p f f p f p

h m a bU a m b

h h h h h（）

0Gy gy Gx gx D dF L F L F L

Critical condition for toppling instability, given by moment

around pivot point O :

Giving for velocity v. depth:-:

where: α, γ = coefficients (see paper), mp = body mass,

hp = body height, hf = flow depth,

a1,a2,b1,b2 = body shape coefficients

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0.2 0.4 0.6 0.8 1 1.2hf (m)

Uc(

m/s

)

Flat ground(Exp.)

Flat ground(Cal.)

1:50 slope(Exp.)

1:25 slope(Exp.)

1:25 slope(Cal.)

1:25 slope(Cal.)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0.2 0.4 0.6 0.8 1.0 1.2hf (m)

Uc

(m/s

)

Flat ground

Slope 1:50

Slope 1:25

(a) (b)

Scaled Incipient Velocity vs. Depth

Adult Child

Empirical or Semi-quantitative Criteria

Defra (2003) in UK use simple method to assess flood hazard based on velocity, depth and debris:

HR = flood hazard rating;

H = depth of flooding (m);

U = velocity of floodwaters (m/s);

DF = debris factor (= 0, 1, 2 varies

with probability that debris will

lead to greater hazard)

( 1.5)HR h U DF

Determination of Hazard Degree

U = depth-averaged velocity in a cell (m/s); h = flow depth in a cell (m); Uc = critical velocity for depth (h) for vehicle or people(m/s);

HD = Hazard degree for vehicle or people in floodwaters

Safe if HD=0, Dangerous if HD =1.0

HD=Min(1.0, U/Uc)

Expression used to determine degree of hazard:-

Incipient velocity formula from our studies used to assess vehicle and people safety

Comparison of Hazard Formulae

Model Application

1. Glasgow flood in the UK

2. Boscastle flood in the UK

Map of a small urban area in Glasgow

0

2

4

6

8

10

12

0 600 1200 1800 2400 3000 3600

Time(s)

Dis

charg

e(m

3/s

)

Point X0 = Inflowing location

Points X1-X4= Comparison sites

Qmax=10 m3/s Glasgow

Predicted maximum water depth distribution

Predicted maximum velocity distribution

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Maximum water depth (m)

Frame 001 01 Dec 2009 MaximumZ/U/SF

Distributions of hazard degree for vehicles: (a) Pajero; (b) MiniCooper

(a) (b)

Distributions of hazard degree for people: (a) Children; (b) Adults

(a) (b)

Boscastle Flood

Water depths on streets over 2 m, with high velocities transporting debris and cars

Over 100 vehicles washed away, but no fatalities

Valency

Jordan

Car Park

P1

P2

P3

P4

209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

91450

91500

91550

91600

Frame 001 29 Nov 2009 MaximumZ/U/SF

Domain showing upstream and downstream boundaries

1

2

3

4

5

6

7

8

0 100 200 300 400 500

Discharge (m3/s)

Sta

ge(m

)

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10

Time (h)

Dis

char

ge(m

3/s

)

Rating curve Discharge hydrograph

Outlet

Inlet

Flood Frequency

0.25%=400 Years

Distribution of water depth and velocity at Qpk

209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

91450

91500

91550

91600

0.1 0.2 0.5 1 1.5 2 2.5 3 3.5 4Depth (m)4m/s

CS

2

CS

1

Frame 001 29 Nov 2009 Hydrodynamic Results in Nodes

CS2 CS1

Distance for the right side (m)

Bed

or

Wat

erL

evel

(m)

Vel

oci

ty(m

/s)

0 20 40 60 80 100 120

0

6

12

18

24

30

36

0

2

4

6

8

10

12

Bed level

Water level

Velocity

Frame 001 01 Dec 2009 HYD-VP Hazard Degree

Distance from the right side (m)

Bed

or

Wat

erL

evel

(m)

Vel

oci

ty(m

/s)

0 10 20 30 40 50 60 70 80 90

0

3

6

9

12

15

18

0

2

4

6

8

10

12Bed level

Water level

Velocity

Frame 001 01 Dec 2009 HYD-VP Hazard Degree

209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

91450

91500

91550

91600

0.01 0.1 0.2 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4Maximum depth(m)


209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

91450

91500

91550

91600

0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4Maximum velocity (m/s)


Maximum water depth

Maximum velocity

Comparison between predicted peak levels and flood tracks

4

6

8

10

12

14

16

18

20

4 6 8 10 12 14 16 18 20

Observed flood tracks (m)

Pre

dic

ted

ma

xim

um

le

ve

l (m

)

Hazard degree for vehicles: (a) Pajero; (b) MiniCooper

209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

91450

91500

91550

91600

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


(b) Car Park

209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

91450

91500

91550

91600

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


(a) Car Park

Hazard degree for people: (a) Children; (b) Adults

209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

91450

91500

91550

91600

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


209600 209700 209800 209900 210000 210100 21020091150

91200

91250

91300

91350

91400

91450

91500

91550

91600

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


(a)

(b)

Conclusions

• Accurate modelling of flooding in steep catchments and levee breaches requires shock capturing models and DIVAST-TVD provides engine for Flood Modeller Pro

• Novel treatment of buildings using high roughness or low porosity and Darcy flow attractive for modelling floods

• New formulae developed for critical velocity of vehicles and people under flood conditions

• New formulae developed for flood hazard risk based on

fundamental physics vis-à-vis empirical formulae

• Models tested successfully for two sites predicting hazard levels for people and vehicles new algorithms provided

Thank You

Professor Roger A. Falconer Email: [email protected]

modelling extreme flood events and associated...

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