1. 1. Improving statistical models for ood risk assessment 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 October 2016
2. 2. Motivation Credit: BBC NEWS Credit: Barry Hankin, JBA Consulting
3. 3. KTP Project Two year project between JBA Consulting, JBA Trust and Lancaster University Aim of the project is to improve the efciency and applicability of statistical models for ood risk assessment Incorporate rainfall information into the existing models for ood risk assessment Challenges relate to data availability and quality
4. 4. Motivation What is the probability of multiple locations observing a 1 in 100 year ood event? What is the probability that a location will simultaneously experience an extreme rainfall and river ow event?
5. 5. Motivation What is the probability of multiple locations observing a 1 in 100 year ood event? What is the probability that a location will simultaneously experience an extreme rainfall and river ow event? F = (F1, . . . , Fd ) are observations of river ow X = (X1, . . . , Xn) are observations of rainfall We can model the joint dependence between river ow and rainfall
6. 6. Motivation Can t a statistical model to the river ow gauges to provide us with predictions of plausible future ood events Need predictions of the future ood events at ungauged locations qq q q q q q 51.5 52.0 52.5 53.0 4 3 2 Longitude Latitude 50 100 150 ReturnPeriod
7. 7. Motivation Can t a statistical model to the river ow gauges to provide us with predictions of plausible future ood events Need predictions of the future ood events at ungauged locations Existing statistical method interpolates through using river ow information Limitations: Missing data Lack of nearby gauges qq q q q q q 51.5 52.0 52.5 53.0 4 3 2 Longitude Latitude 50 100 150 ReturnPeriod
8. 8. Data
9. 9. Data comparison qqqq q q qqqqq qq q qqqq qq qq q q q qq q q q q q q q q q q q q q q qq q q q q q q q q q q q qq q q q qq q q qq q qqqqqq q q qqqqqqqqqq qqqq q qqqqqqqqqqqqqqqqqqqq q qq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqq q qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqq qq q q q q qqqqqqq q qqqq qqq q q qq q q q q q q q qqqqqqq q qqqq q q q qq q q q q q q qq qqqqqqqq q q q q q q q qqqqq q q q q q q q q qqq q q qqq q qq q q qqq q q q q qqq q q q qqqqqqqqqqqqqqqqqqqqqq q q q q q qq q q q qq q q q q qq q q q q q q q q q q q qqq q q q q q q q q qqqqqqq q q qq q qq q q q qqqqqqqqqqqqqqqq q q q q q qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqq q qq q qqqqqqqqqqqqqq qqqqqqqqqqqqq qqq q qqqqqqqq qq qqqqqqqqqqqq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq q q qq q qqqqqq q qqq qqqqqq q q qqqqqqqqqq q q q q qq q qq q q q q qqq q qq q q q q q q q qqqqqqqqqqqqqqqqqqqqqqq q q q q q q q q q q qqqqqqq q q q q q q 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Data comparison q qqq q q qqq qq qq q q qqq qq q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q qqq q q q q q q qq q q qqq qqqqqqqqqqqqq qq q qq qqqqq q q qqqqqqqqqqqq qqq q q q q qq qqq q q qqqqqq qq qqq qqqq qq q qq q q q qq q q qq q q q qqq qqq q qq q qq q q q qq q q q q q q qq q q q qq q q qq q q q q q q qq q q q q q q q q q q q qq q q q q q q q q qq qqq qqqqqq q q q q q q q qqqq q q q q q q q q q q q q q q qq q q qq q q qq q q q q qq q qqq q q q q q q qq q qq qq q q q qq q qq q q qqqq q q q q q qq q q qq q q q q q qqq q q q qq q q q qq qq q q q q q q qqqqqqqq q q q q qqq q q qqqq q q qq q q q qq q q q q qqqqq q q q q qqq q q q q qq q q qqqqqqqqqqqqqqqqq qqqqqq q q q q q q q q q q q qq q q qq q q q q q q q q q q q q qqq qq qqq q q q qqqqqq q q q q qq qqq q q q qqqqqqqq qqqq qqqq q q q q qqqqqqqqqq qqqqqqqqq qqqqqqqqqq q q qq q q q q qq q q q q q qq q q qqqq q qq qqq q q q q qqqq q q qqq q qq qq q q qq qq q qqq q q q qqq q q q qqq q q q qq q q q q q q q q q qq q q q q qq q 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qqqq q q qq q q q qq qqqq q qqqqqqqqqqq qqqqq q q qq q q q q q q q q qq q q q q q q q q qqqqqqq q q q q q q q q qq qqqqqqqqqqq q q q q q qq q q q q qq q qqqqqqqq q q qqqq q qqqqqqq q q qqq q qqq q qqq qqqq q q q qq q qqq q qq q qqq q qqq q q q q qq qq qqqqq q q qq qqq qq q q qq q q qq q q qq qqqqqq qqq qqqq q q qqq q q qqq q q qq q q q q q q q q qqqq q qq q q q qq q qqqqq q q q qqqq qqq q qqq qq qq q qq q qq q q qq q q q q qq qqqqq q q qqq q q qq q q qqqq q q q q q q q q q qqqqq q qqq q q qq qq qq qqq q q q q qqqq q q q q q q q q q q qqq q q qqq q qqq qq q q q qqqq q qqqqqq q q q qq q q
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Data comparison qqqq qq qqqqq qq q qqqqqqqq q q q q q q q q q q q q q q q q q q q qq q q q q q q q qqq q qq q qq qq q q qqq qqqqqqqqqqqqqqqqqq qqqqq q qqqqqqqqqqqqqqqqqq q q qq qqqq q qqqqqq qqqqq qqqq qq q qq q q q qq q q qq q q q qqq qqq q qq q qq q q q qq q q q q q q qqq q q qq q q qq qq q q q q qq q q q q q q q q q q q qq q q q q q q q q qq qqq q qqqq q q q q q q q q qq qq q q q q q q q q q q q q qq qq q q q q q q qq q q q q q q q qq q q q q q q q qq q qq qq q q q qq q qq q q qq qq q q q q q q q q q qq q q q q q qqqq q q qqqq q qq qq q q q q q qqqqqqqqqq q q q qqq q q qqqqq q qq qq q qqqqqq qq qqq qq q q qqq q q q q qqq q qqqqqqqqqqqqqqqqqqqqqqqq q q q q qqq q q q qq q q qq qq q q q q q q q q q q qqqqq qqq q q q qqqqqqqq q q qq q qq q q qqqqqqqqqqqqqqqqq q q q q qqqqqqqqqqqqqqqqqqq q qqqqqqqqq qq qqq q qqqq q q q q q q qq q qqqq q qq qqq q q q q qqqq q q q qq q qq qq q q qq qqq qqq q q q qqq q q qqqq q q q qq q q q q qq q q q qq q q q q qq q q q q q q q q q q q qq q qq qqq q q qq 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qqqqqq qq q q q qq q qqqqq qq qqqqq qqq q qqqq q qq qqq q qq q q qq q q q q qq qqqqq q q qqq q q qq q q q qqqq q q q q q q q q qqqqq q qqqq q qq qq qq qqqq q q qqqqq q q q qq q q qqq qqq q qqq q q qqq qq q q q q q qq q q q q q qqqq q qqqqqqq q q qq q qq q q q q qqqqqqqqq q q q q q q q q qq q q q qqqq qq q qq q qqqqqqqqqqq q qq qqqqq q q qq q q q q qqqqqqqqqqqqqqqqqqq q q qqq qqqq qq q q qqq qqqqqqqqqqqqqqqqq qqqqq q q q qqqqqqqqqqqq q qqqq qqqq q qq qq qqq q qqq q q q q q qq qq q q q qqqq q qq qq q q q q qq q q q qqq q q q q q q q q q q q q qq q q qq q q q qq q q q q q qq q qqqq q q q qq q q q q qq q qq q q q q q q q qq q q qqq q q q q q q q q q q q qq q q q q qqq q q q qq q qq q q q q qqqqqqqqq qqqqqqq qqqq qq q q qqq qq qqqq qqqqqqqqqqqqqqqqq qq q q qqq qq qqq qqq qqqqq q q q q q qq q qqqq q q qqqq q q qq q qq q q q q q qqqqqqqqqqqq q q q q q q q q qqqqqq q q q q q qq q qq q q qqqqqqqqqqqqqqq q qqqq q q qqqqqqqqq qqq q q q qqqqqqq q q qqq q q q qqqqqqq q q qqq q q q qq q qqqq q q q q q q q q qqqq q q q q q q q qq q q qq q q q q q q qq q q q q q q qq q q q q q qq qqq q qq q q q q q qq qq q q q q q qq q q q q q q q q qq q q q q q q q q q q qqq q q q qq q q q q q q q q qqq q q q q q q qq q qq q q q q q q q q q q q qq q q qqq q q qq q q q qq q q qqq q qqq q qqqqq q q qqq q q qq qqqq q q qq q q qq qq q qqqq q q qqqq q q qqqqq qqq qq q qq q qqq q qqq qqq q qqq q q q qqq q q q qqq q q qqq q q qqqq q q q qqqqqqqqq q qqqq q qqqqqq qqqqqq q qqqq q q q qqqqqq q qqq q qqq q q qqqqq qq qq q q q qqqqqqqqq q q q qqqq q q q qqq qq q qqq qq q q q q q q qq q q q q qqqq qq q q qqqqqqqq qqqqqqqqqqq q qq q q qq qq q q q q qqq q qqqq qq q q q q q qq q qq q qq q qq qq q q q q qq q q q q q qqqqqqqqqqqqqq q qqqqqq q qqqqq qq qq q qqq q q q q q q q qqqqqqqqqq q qqqq q q qq q qqq q q q qqqqq q q q qqq qq qqqq qq q q qqqqqqqq qq q qqq q q q qqqqqqqqq qq qq q q qq q q q q q q q q q q q q q qq q q qq q q qq qq q q q q q qq q q qqq
12. 12. Modelling Strategy Chosen model: Adopt the conditional extreme value model of Heffernan and Tawn (2004) Examples of applications to ood risk management include Keef et al. (2009), Lamb et al. (2010) and Keef et al. (2013) Capable of handling high dimensional data sets 5 0 5 10 50510 Y1 Y2 q q q q q qqqq q q q q q q qq q qq q q qq q q q q q q q q q q q qq q q q q q qq q q q qqqqqqq q q q q q q q q qq q qq qqqqqqqqq q qqq q q qqq q qq q q q q q q qq qqqq q qq q q q q qq q q q q q q q q qqqqqqqqqqq qq q q q qqqqqq q q q q q qq q q qq q qqq qqqqqqqqqqqqqqqqq q q q q q q q qqqqqqqqqqqqq q qq q q q q q q q q q q q qq q q q q q q q qqq q q qq qq qqqq q q q q q qq q qqqqq q qqq qqq q qq qq q q q qqqqqqqqqqqqqq q qqq q q q qq q q q q q qq q q q q q qqqqqqqqqqqqq qq qqqqq qqqq q q qq q qqqqqqq qqqq q q q q qq q q q q q q q q q q q q q qqqq q qqqqqqq qqq qqqqq q q q qqqq qqqqqqqqqqq q q qq q q qqqq q q qq qq q q q q qqq q qqqq q qq q q q q q q q qq q q q q q q q q q q q q q qq q q q q qqq q q q q q q q q q qqq qqq q q q q q q q q q qq qqqq qqqqqq qq qqq q q q q q q q q q q q q q q q q q q q q q q q qqqqq q q q q q q q q q q q q qq q q q q q qqqqqqqqqqqqqqqqqqqqqqqqqqq q q q qq q qq qq qq q q qqqqqqqqqq q q 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