A multi-site approach to risk assessment for the insurance

A multi-site approach to risk assessment for the insurance industry

Linda Speight

Supervisors: Jim Hall, Chris Kilsby, Paul Kershaw

[email protected] HydroPredict, Prague 2010

Outline

• Introduction

• Methodology

– Modelling extreme events

– Flood defences

• Calculating Risk

• Conclusions

Catastrophe Models

Premium = AAL + Risk Load + Expense Load

AIR model output

Aims and Objectives

To develop a method for multi-site concurrent damages due to weather related extremes

FLOODsite 2007 Flood (BBC News)

Spatial dependencies

at multiple scales

Methodology

Statistical modelling of

extreme events

Statistical modelling of

flood defence failure

Process based

modelling of water level &

floodplain inundation

Multiple sites nested in national framework

Deterministic calculation of

damage

Sum damage across all sites

For each site

Damage per site conditional on event

For each event

Repeat until

P(breach sequence)

→ 0

Sample breach widths

Simulate crest height and defence

reliability

Sample breach

failure state

Sample sequence of defence failure.

Hydraulic modelling of water level and

flow through breach

Estimate peak flows and

hydrographs

Simulate extreme event across network

Hydraulic modelling for breach sequence

Calculate

damage

Floodplain inundation modelling Estimate probability of

breach sequences

Hydraulic modelling of water level assuming

no breaching

For each site


For each event

Repeat until

P(breach sequence)

→ 0



reliability

Sample breach

failure state



flow through breach


hydrographs



Calculate

damage


breach sequences


no breaching

Modelling extreme events

• Aim – Spatial dependency

between events

– Large scale model for UK

– Good representation of extremes

• Method – Conditional dependence

model of Heffernan and Tawn (2004) applied by Keef et al (2009)

Y|X, x > ux

a = strength of dependences

b = changing dependence

Z = residuals

Y = a(x) + b(x)Z

Y = set of gauges

X = conditional gauge

x = daily mean flow

ux = threshold

Example application

· = observed

below threshold

o = observed

o = simulated

55026

55023

5500854022

54019

54002

54001

28046

28018

Sum damage across all sites

For each site


For each event

Repeat until

P(breach sequence)

→ 0



reliability

Sample breach

failure state



flow through breach


hydrographs



Calculate

damage


breach sequences


no breaching

Estimating peak flows at site

Peak flow conversion methods

• Shape of hydrograph

• Catchment characteristics

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14 16 18 20 22 24

Flo

w(m

3/s

)

Time (h)

Daily mean flow Hydrograph Flood Peak

Ungauged site transfer methods

• Analogue sites

• Weighted by distance and catchment characteristics

For each site


For each event

Repeat until

P(breach sequence)

→ 0



reliability

Sample breach

failure state



flow through breach


hydrographs



Calculate

damage


breach sequences


no breaching

Flood defence system

Characterised by

• Design standard

• Construction type

Defence wall SOP = 100 years

Embankment SOP = 25 years

Embankment SOP = 5 years

d1 d2 d3

High ground

Floodplain

Novel aspects

• No restriction on length

• Consideration of upstream breaches

Sampling crest heights

Autocorrelation function for crest height =

f (defence type, age, condition, data quality)

6

6,1

6,2

6,3

6,4

6,5

6,6

6,7

6,8

6,9

7

0 10 20 30 40 50 60 70 80 90 100

Cre

st h

eig

ht

(m)

Chainage (m)

design crest level defence A - old embankment Defence B - sea wall

Defence reliability

• Initiation

– Fragility curves

– Type

Photos from FLOODsite

Fragility curve from Hall et al (2003)

– Condition

– Sequencing

Sampling breaches

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

6

6,1

6,2

6,3

6,4

6,5

6,6

6,7

6,8

6,9

7

0 20 40 60 80 100

P(f

ailu

re)

Elev

atio

n (

m)

Chainage (m)

P(varying failure) crest height water level breaches

Autocorrelation function for strength =

f (defence type, age, condition)

Breach widths

FLOODsite

• Growth Rate

– Materials

– Floodplain type

– Amount of water

– Sequencing

• Max width

Case study Observed

values

Assumed

values Source

Elbe 20m to 200m

Median 20m

Log normal

width mean of

64m

De Kok and

Grossmann

2010

Lower Rhine Width 100 –

400m

Apel et al

2004

Lower Rhine Width 50 -

150m

Kamrath et al

2006

UK RASP

method

Function of load

and defence

length

Hall et all

2003

Netherlands Largest 520m

wide and 36m

deep

Muir-Wood

and Bateman

2005

River Po Normal Width:

100m - 300m

Depth:

0.5m - 4m

Govi and

Turitto 2000

For each site


For each event

Repeat until

P(breach sequence)

→ 0



reliability

Sample breach

failure state



flow through breach


hydrographs



Calculate

damage


breach sequences


no breaching

For each site


For each event

Repeat until

P(breach sequence)

→ 0



reliability

Sample breach

failure state



flow through breach


hydrographs



Calculate

damage


breach sequences


no breaching

Damage

• Raster based floodplain inundation model depths

• Depth-damage curves

damage

-1

-0,75

-0,5

-0,25

0

0,25

0,5

0,75

1

1,25

1,5

1,75

2

2,25

2,5

2,75

3

0 50 100 150 200 250 300 350 400 450 500

Dep

th M

etr

es

Damage £/m2

Penning-Roswell et al (2006) BBC News

Risk

Risk = Probability x Consequence

P(Imax,i,j|Fi,j|OTi,j ,Bi,j , BWi,j|Lj,i,Ci,j,Ri,j |Qi,j | Xi )

Imax,i,j = maximum inundation depth across site j for event i

Risk


P(OTi,j) = f(Ci,j, Li,j)

P(Bi,j) = f(Ci,j, Li,j , Ri,j , OTi,j)

P(BWi,j) = f(type, material, Li,j)

Fi,j = Flow over or through defence


Risk


Xi = Large scale spatial event

P(Li) = f(upstream breaches, Qi,j)

Ci, Ri = f(type, age, condition) Qi,j = Inflow to hydraulic model


Conclusions

• Integrated system model

• Detail nested in national scale

• Consider risk load

– If modelling of flood defences is poor how much impact does this have?

– Which areas could flood at the same time / where are we over exposed?

• Future...

– Sensitivity testing

– Resilience measurers

Informed decision!

Thank you

Linda Speight

Civil Engineering & Geosciences

Newcastle University, UK

[email protected]

mailto:[email protected]

1. Extreme data at conditional gauge

2. Extreme dependence between gauges

Fit Generalised

Pareto

• Shape (β)

• Scale (ε)

• threshold

Modelling extreme events (2)

Solid lines: parametric

Dashed lines:

nonparametric (residuals)

Fit dependence model

References

Hall, J. W., R. Dawson, et al. (2003). A methodology for national-scale flood risk assessment. Proceedings of the Institution of Civil Engineers-Water and Maritime Engineering, 156: 235-247

Heffernan and Tawn (2004) A conditional approach to modelling multivariate extreme values. Journal of the Royal Statistical Society Series B, 66(3), 497-547

Keef, C., Lamb, R., et al. (2009a) Spatial coherence of flood risk – Methodology report. Science Report – SC060088/SR., Environment Agency

Keef, C., Svensson, C., et al. (2009b) Spatial dependence in extreme river flows and precipitation for Great Britain. J. Hydrology, 378, 240-252.

Keef, C., Tawn, J., et al. (2009c) Spatial risk assessment for extreme river flows. Journal of the Royal Statistical Society Series C- Applied Statistics 58(5), 601-618.

Penning-Roswell et al (2006) The benefits of flood and coastal risk management: a manual of assessment techniques, Middlesex University FHRC

Documents

A multi-site approach to risk assessment for the insurance