Understanding and communicating widespread flood risk Ross Towe 1 , - - PowerPoint PPT Presentation

Understanding and communicating widespread flood risk

Ross Towe 1,2 Jonathan Tawn 1 Rob Lamb 1,3 Chris Sherlock 1 Ye Liu 4

• 1Dept. Mathematics and Statistics, Lancaster University, Lancaster, UK

2JBA Trust, Broughton Hall, Skipton, UK 3Lancaster Environment Centre, Lancaster University, UK 4JBA Risk Management, Broughton Hall, Skipton, UK

July 2016

Motivation

Credit: BBC NEWS Credit: Barry Hankin, JBA Consulting

KTP Project

• Two year project between JBA and Lancaster University
• JBA are an engineering and environmental consultancy firm

founded in 1995

• Aim of the project is to improve the efficiency and applicability
• f statistical models for flood risk assessment
• Challenges relate to data availability and quality

Motivation

What is the probability of multiple locations observing a 1 in 100 year flood event? What is the probability that a location will simultaneously experience an extreme rainfall and river flow event?

Motivation

What is the probability of multiple locations observing a 1 in 100 year flood event? What is the probability that a location will simultaneously experience an extreme rainfall and river flow event?

• F = (F1, . . . , Fd) are observations
• f river flow
• X = (X1, . . . , Xn) are observations
• f rainfall
• We can model the joint dependence

between river flow and rainfall

Data

Data comparison

Data comparison

Data comparison

Statistical model

Considerations:

• Need a statistical model that handles both asymptotic

dependence and independence:

• Asymptotic dependence

P(Y2 > y|Y1 > y) > 0 as y → ∞

• Asymptotic independence P(Y2 > y|Y1 > y) → 0 as y → ∞,

where Y1 and Y2 have the same margins.

• Capable of handling high dimensional data sets

Statistical model

Considerations:

• Need a statistical model that handles both asymptotic

dependence and independence:

• Asymptotic dependence

P(Y2 > y|Y1 > y) > 0 as y → ∞

• Asymptotic independence P(Y2 > y|Y1 > y) → 0 as y → ∞,

where Y1 and Y2 have the same margins.

• Capable of handling high dimensional data sets

Chosen model:

• Adopt the conditional extreme value model of Heffernan and

Tawn (2004)

• Examples of applications to flood risk management include

Keef et al. (2009), Lamb et al. (2010) and Keef et al. (2013)

Conditional extreme value model

Heffernan and Tawn (2004)

• Data are on common Laplace margins
• Data are IID over vectors (Y1, Y2)
• Y1 is the conditioning variable
• Y2 is the response of interest at a given site

Y2 = αY1 + Y β

1 Z, for Y1 > v

• −1 ≤ α ≤ 1 and −∞ < β < 1 are the dependence

parameters of the model

• Z is the non-zero mean residual variable independent of Y1
• Over observations have IID values of Z denoted by Z1, . . . , Zm
• Use the empirical distribution of these Z values to estimate

the distribution of Z

Conditional extreme value model

Heffernan and Tawn (2004)

Y2 = αY1 + Y β

1 Z, for Y1 > v

α=0.95 β=-0.26

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * ** * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * ** * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * −2 2 4 6 8 −2 2 4 6 8 Y1 Y2

α=0.60 β=0.40

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * −2 2 4 6 8 −2 2 4 6 8 Y1 Y2

Conditional extreme value model

Heffernan and Tawn (2004)

We are now interested in extreme river flow at Y = (Y1, . . . , Yd) If we select Y1 as our initial conditioning location Y−1 = α|1Y1 + Y

β|1 1

Z|1, for Y1 > v where Z|1 ∼ G|1 is the residual and Z|1 | = Y1

Conditional extreme value model

Heffernan and Tawn (2004)

We are now interested in extreme river flow at Y = (Y1, . . . , Yd) If we select Y1 as our initial conditioning location Y−1 = α|1Y1 + Y

β|1 1

Z|1, for Y1 > v where Z|1 ∼ G|1 is the residual and Z|1 | = Y1 Estimate (α|1, β|1) through fitting (d − 1) regression models Obtain residuals Z|1 Z|1 = Y−1 − α|1Y1 Y

β|1 1

This procedure is repeated in turn for each of the d sites

Missing values

Simulation with missing values

Y−1 = ˆ α|1Y1 + Y

ˆ β|1 1

Z|1, for Y1 > v Heffernan approach:

• Resample from the residual distribution Z|1
• Assume that Z|1 ∼ ˆ

F is the empirical distribution function

• Cannot handle missing values
• Limited to combinations of the observed residuals

Simulation with missing values

Y−1 = ˆ α|1Y1 + Y

ˆ β|1 1

Z|1, for Y1 > v Heffernan approach:

• Resample from the residual distribution Z|1
• Assume that Z|1 ∼ ˆ

F is the empirical distribution function

• Cannot handle missing values
• Limited to combinations of the observed residuals

Proposed approach:

• Model the observed residual distribution by using a Gaussian

copula

• Assume that Zi ∼ ˜

Fi is a kernel smoothed distribution function

• Can handle missing values
• Limited extrapolation

Calculation of conditional probabilities

Example 1

Calculation of conditional probabilities

Example 1

Conditional probabilities can be used for flood risk management. For example, let Y(1) = max {Y2, . . . , Yd} and we can consider pp = P(Y(1) > yp|Y1 > yp), where yp is a sufficiently large value, i.e. a 1 in 100 year event

Calculation of conditional probabilities

Example 1

Conditional probabilities can be used for flood risk management. For example, let Y(1) = max {Y2, . . . , Yd} and we can consider pp = P(Y(1) > yp|Y1 > yp), where yp is a sufficiently large value, i.e. a 1 in 100 year event

Prob Observed Heffernan Gaussian copula p0.01 0 (NA) 0.053 (0.026, 0.116) 0.059 (0.027, 0.118) p0.002 0 (NA) 0.036 (0.017, 0.080) 0.039 (0.018, 0.085) p0.001 0 (NA) 0.031 (0.014, 0.070) 0.036 (0.016, 0.076) p0.0001 0 (NA) 0.023 (0.005, 0.031) 0.023 (0.007, 0.033)

Calculation of conditional probabilities

Example 2

Calculation of conditional probabilities

Example 2

Conditional probabilities can be used for flood risk management. For example, let Y(1) = max {Y2, . . . , Yd} and we can consider pp = P(Y(1) > yp|Y1 > yp), where yp is a sufficiently large value, i.e. a 1 in 100 year event

Prob Observed Heffernan Gaussian copula p0.01 NA NA 0.029 (0.007, 0.091) p0.002 NA NA 0.017 (0.002, 0.066) p0.001 NA NA 0.012 (0.001, 0.057) p0.0001 NA NA 0.006 (0.000, 0.024)

Further benefits of the Gaussian copula

How have JBA used this model?

• Global flood event set
• Construction of offshore flood defences
• Flood and coastal risk management for the Environment

Agency

• Evaluating flood risk to railway infrastructure
• National Flood Resilience Review

National Flood Resilience Review

• Consider gauges with at least 20

years of observations

• Model the spatial and temporal

dependence between the gauges

• Define an event to last for 7 days
• Use JBA Risk Management’s tool

JSheep to generate 10 000 years worth of events

National Flood Resilience Review

What is the chance of an extreme river flow occurring at one or more gauges, somewhere within the national river gauge network in any one year?

National Flood Resilience Review

What is the chance of an extreme river flow occurring at one or more gauges, somewhere within the national river gauge network in any one year?

10 50 100 500 1000 5000 10000 0.0 0.2 0.4 0.6 0.8 1.0 Return Period (years) Probability of observing at least 1 event in a given year

National Flood Resilience Review

What is the chance of an extreme river flow occurring at one or more gauges, somewhere within the national river gauge network in any one year?

10 50 100 500 1000 5000 0.0 0.2 0.4 0.6 0.8 1.0 Return Period (years) Probability of observing at least 1 event in a given year Modelled dependence Complete dependence Complete independence

National Flood Resilience Review

What is the chance of an extreme river flow occurring at one or more gauges, somewhere within the national river gauge network in n years?

5 10 50 100 500 5000 50000 0.0 0.2 0.4 0.6 0.8 1.0 Return Period (years) Probability of at least one event in M years 1 year 5 years 10 years 25 years 50 years

Local Resilience Forums (LRF)

What is the chance of an extreme river flow occurring in one or more LRFs, somewhere within the national river gauge network in any one year?

Local Resilience Forums (LRF)

What is the chance of an extreme river flow occurring in one or more LRFs, somewhere within the national river gauge network in any one year?

10 50 100 500 1000 5000 0.0 0.2 0.4 0.6 0.8 1.0 Return period (years) Probability of at least m regions 'flooded' in any given year m ≥ 1 m ≥ 2 m ≥ 3 m ≥ 4

Understanding uncertainty

• Analysis does not account for uncertainty
• Parametric bootstrap

Understanding uncertainty

• Analysis does not account for uncertainty
• Parametric bootstrap
• Sample from the event set by taking subsamples of 37 years

Understanding uncertainty

• For each subsample we generate a new event set
• Initially consider 5% of the gauges sampled according to their

LRF

Understanding uncertainty

What is the chance of an extreme river flow occurring at one or more gauges, somewhere within the national river gauge network in any one year?

10 50 100 500 5000 50000 0.0 0.2 0.4 0.6 0.8 1.0 Return period (years) Probability of at least 1 event in a given year All of the gauges 75% of the gauges 50% of the gauges 10% of the gauges 5% of the gauges

Understanding uncertainty

What is the chance of an extreme river flow occurring at one or more gauges, somewhere within the national river gauge network in any one year?

50 100 200 500 1000 2000 5000 10000 50000 0.0 0.1 0.2 0.3 0.4 Return period (years) Probability of at least 1 event in a given year All of the gauges 75% of the gauges 50% of the gauges 10% of the gauges 5% of the gauges

Predicting flood events anywhere

Predicting flood events anywhere

Concluding remarks

• Multivariate statistical model used to aid flood risk

assessment

Concluding remarks

• Multivariate statistical model used to aid flood risk

assessment

• Extensions to the statistical model include:
• Efficient approach to handle missing values

Concluding remarks

• Multivariate statistical model used to aid flood risk

assessment

• Extensions to the statistical model include:
• Efficient approach to handle missing values
• Output from the statistical model aided national review of

flooding

• Spatial interpolation of extreme values across the UK river

network will further aid the assessment of flood risk

Concluding remarks

• Multivariate statistical model used to aid flood risk

assessment

• Extensions to the statistical model include:
• Efficient approach to handle missing values
• Output from the statistical model aided national review of

flooding

• Spatial interpolation of extreme values across the UK river

network will further aid the assessment of flood risk

Thank you and any questions?

Rainfall locations

Number of gauges used to define an event

10 50 100 500 1000 5000 0.0 0.2 0.4 0.6 0.8 1.0 Return period (years) Probability of observing at least 1 event in a given year 1 gauge 2 gauges 5 gauges 10 gauges 20 gauges 30 gauges 50 gauges

Number of gauges used to define an event

10 50 100 500 1000 5000 0.0 0.2 0.4 0.6 0.8 1.0 Return period (years) Probability of observing at least 1 event in 10 years 1 gauge 2 gauges 5 gauges 10 gauges 20 gauges 30 gauges 50 gauges

Effective Number

P (X1 ≤ x, X2 ≤ x, . . . , X916 ≤ x) =

• 1 − 1

T m = 0.5,

5 10 50 100 500 1000 5000 0.0 0.2 0.4 0.6 0.8 1.0 Return Period (years) Probability of observing at least 1 event in a given year Modelled dependence Complete dependence Complete independence Effective number