Assessing Uncertainty when Predicting

Extreme Flood Processes

Risk & Uncertainty (IMPACT WP5)

Overview• Aims & Objectives

• Defining Uncertainty

• Expressing Uncertainty

• Sources of Uncertainty

• Combining Uncertainty

• Conclusions

• Where are we now?

• The way forward

Uncertainty

Aims & Objectives

The typical problem to be solved is:

• Typically modelling undertaken for flood risk assessment, emergency planning etc. offers a prediction of likely conditions with no guidance upon the accuracy and reliability of the prediction.

• One example: The peak of a flood may be predicted to arrive after 3 hours, but is that prediction 3 hours plus / minus 10 minutes, or 3 hours plus / minus 1 hour?

• The problem to be solved is predicting the accuracy and uncertainty of individual modelling and combined modelling results.

• How do you deal with uncertainty?

Risk & Uncertainty

Objectives• Creation of an advisory group drawn from

industry, to advise on R&D direction, and in particular outputs

• Assessment of model prediction uncertainty at start / mid / finish of project within each theme area

– Theme leader responsibility

• Application of models to a combined case study (real or virtual) near completion of the project to demonstrate predictive abilities and uncertainty

• Guidelines / implications of modelling uncertainty in relation to application of modelling results

Uncertainty

Defining Uncertainty

“Uncertainty is a general concept that reflects our lack of sureness about something or someone, ranging from just short of complete sureness to an almost complete lack of conviction about an outcome”

NRC (2000) ‘Risk analysis and Uncertainty in Flood Reduction Studies’. National Research Council (US). National Academic Press.

Uncertainty

Expressing Uncertainty - examples• Deliberate vagueness – ‘There is a high chance of

breaching’

• Ranking without quantifying – ‘Option A is safer than Option B’

• Stating possible outcomes without stating likelihoods – ‘It is possible the embankment will breach’

• Probabilities of events or outcomes – ‘There is a 10% chance of breaching’

• Range of variables and parameters – ‘The design flow rate is 100 cumecs +/- 10%’

• Confidence intervals – ‘There is a 95% chance that the design flow rate lies between 90 and 110 cumecs’

• Probability distributions (see example)

Uncertainty

An example of uncertainty affecting the end user...BCR for two flood defence options (say)

BCR Option B > BCR Option A --> Option B is better?

But

Uncertainty information shows that Option B has a higher chance of achieving a BCR < 1

If the decision maker places a greater importance on BCR > 1, then Option A may become the preferred choice

Uncertainty

Sources of Uncertainty

Uncertainty

Combining Uncertainty

Consider three approaches:

• General approach

– Root mean square of uncertainty

• Simulation approach

– Uncertainty expressed as probability distribution

– Integrate through Monte Carlo techniques

• Sensitivity testing

– variation in parameters

– appropriate prior to more thorough techniques (1 & 2)

Uncertainty

Sensitivity Testing

Two approaches:

• HR BREACH model probability distribution for factor of safety in bank stability calculations

– Distribution represents ‘all’ uncertainty

• Basic sensitivity assessment

– Vary each parameter in turn

– Assess sensitivity at different levels

Uncertainty

Sensitivity Testing - HR BREACH

Factor of Safety Probability Distribution Functions

0

0.25

0.5

0.75

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Factor of safety

Pro

bab

ity o

f fai

lure

Poor

Good

V. Good

DeterministicApproachEqual Probability

low

er li

mit

Up

pet

lim

it

Risk & Uncertainty

Sensitivity testing - HR Breach Example

Risk & Uncertainty

Sensitivity testing - HR Breach Example

Risk & Uncertainty

Sensitivity Testing - Basic ParametersCD Varation

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000 3500

Time (s)

Flo

w (

m3

/s)

Base (cd = 1.5)

1.6

1.7

1.8

Risk & Uncertainty

Sensitivity Testing - Basic ParametersManning's n Varation

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000 3500

Time (s)

Flo

w (

m3

/s)

Base (n = 0.03)

0.02

0.04

Risk & Uncertainty

Sensitivity Testing - Basic ParametersD50 Varation

0

100

200

300

400

500

600

0 1000 2000 3000 4000 5000 6000

Time (s)

Flo

w (

m3

/s)

Base (D50 = 2.5 mm)

1

5

Risk & Uncertainty

Sensitivity Testing - Basic ParametersAngle of Friction Varation

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000 3500

Time (s)

Flo

w (m

3/s

)

Base (Phi = 30)

20

40

Uncertainty

Conclusions (1)• Consideration of uncertainty provides the

decision maker with additional information on which to base a decision. Consideration of uncertainty can therefore lead to different and more justifiable decisions than studies that do not include uncertainty.

Uncertainty

Conclusions (2)

Uncertainty can stem from a variety of different sources. These sources can be generally categorised under two headings:

Natural Variability Knowledge Uncertainty

(These two categories are known by a variety of different names)

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Conclusions (3)

Uncertainty can be presented or expressed and handled in a variety of different ways.

To facilitate incorporating uncertainty within the IMPACT project, specific (methodical) practices will be agreed

(see paper for initial approach)

Uncertainty

Where are we now? Where are we going?• Reviewed concepts

• Identified three levels of approach

• Starting with simplest - sensitivity analyses

• Starting with breach; expanding to flood propagation and sediments

• Implement more detailed analysis as time and funding permits

• Seeking end user feedback on this approach