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 1 Dept. Mathematics and Statistics, Lancaster University, Lancaster, UK 2 JBA Trust, Broughton Hall, Skipton, UK 3 Lancaster Environment Centre, Lancaster University, UK 4 JBA Risk Management, Broughton Hall, Skipton, UK July 2016

Motivation Credit: Barry Hankin, JBA Consulting Credit: BBC NEWS

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 of 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 = ( F 1 , . . . , F d ) are observations of river flow • X = ( X 1 , . . . , X n ) are observations of 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 ( Y 2 > y | Y 1 > y ) > 0 as y → ∞ • Asymptotic independence P ( Y 2 > y | Y 1 > y ) → 0 as y → ∞ , where Y 1 and Y 2 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 ( Y 2 > y | Y 1 > y ) > 0 as y → ∞ • Asymptotic independence P ( Y 2 > y | Y 1 > y ) → 0 as y → ∞ , where Y 1 and Y 2 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 ( Y 1 , Y 2 ) • Y 1 is the conditioning variable • Y 2 is the response of interest at a given site Y 2 = α Y 1 + Y β 1 Z , for Y 1 > v • − 1 ≤ α ≤ 1 and −∞ < β < 1 are the dependence parameters of the model • Z is the non-zero mean residual variable independent of Y 1 • Over observations have IID values of Z denoted by Z 1 , . . . , Z m • Use the empirical distribution of these Z values to estimate the distribution of Z

Conditional extreme value model Heffernan and Tawn (2004) Y 2 = α Y 1 + Y β 1 Z , for Y 1 > v α =0.95 β =-0.26 α =0.60 β =0.40 8 8 * * * * 6 6 * * * * * * * * * * * * * * * * * * * * * * * * * * 4 * * 4 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Y 2 * * * * Y 2 * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 2 * * * * * * * * * * * * * 2 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * 0 * * * * * * * * * ** * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * 0 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * −2 * * −2 * * * * −2 0 2 4 6 8 −2 0 2 4 6 8 Y 1 Y 1

Conditional extreme value model Heffernan and Tawn (2004) We are now interested in extreme river flow at Y = ( Y 1 , . . . , Y d ) If we select Y 1 as our initial conditioning location β | 1 Y − 1 = α | 1 Y 1 + Y Z | 1 , for Y 1 > v 1 where Z | 1 ∼ G | 1 is the residual and Z | 1 Y 1 = |