Climate change, hydrodynamical models & extreme sea levels Adam Butler Janet Heffernan Jonathan Tawn Lancaster University Department of Mathematics &

Slides:

Advertisements

Similar presentations

Copula Representation of Joint Risk Driver Distribution

Advertisements

Introduction to modelling extremes

Cointegration and Error Correction Models

Analysis of multivariate transformations. Transformation of the response in regression The normalized power transformation is: is the geometric mean of.

Exploratory methods to analyse output from complex environmental models Exploratory methods to analyse output from complex environmental models Adam Butler,

Active Appearance Models

Probabilistic Analysis of Hydrological Loads to Optimize the Design of Flood Control Systems B. Klein, M. Pahlow, Y. Hundecha, C. Gattke and A. Schumann.

4 th International Symposium on Flood Defence Generation of Severe Flood Scenarios by Stochastic Rainfall in Combination with a Rainfall Runoff Model U.

Budapest May 27, 2008 Unifying mixed linear models and the MASH algorithm for breakpoint detection and correction Anders Grimvall, Sackmone Sirisack, Agne.

STAT 497 APPLIED TIME SERIES ANALYSIS

19. September 2003 Int.Conference Earth Systems Modelling1 Climatic Extremes and Rare Events: Statistics and Modelling Andreas Hense, Meteorologisches.

Extremes ● An extreme value is an unusually large – or small – magnitude. ● Extreme value analysis (EVA) has as objective to quantify the stochastic behavior.

Climate Change and Extreme Wave Heights in the North Atlantic Peter Challenor, Werenfrid Wimmer and Ian Ashton Southampton Oceanography Centre.

Quantitative Methods for Flood Risk Management P.H.A.J.M. van Gelder $ $ Faculty of Civil Engineering and Geosciences, Delft University of Technology THE.

PHYC Environmental Physics Climate, Climate Change Nuclear Power and the Alternatives.

Statistical analysis and modeling of neural data Lecture 5 Bijan Pesaran 19 Sept, 2007.

Extreme Value Analysis, August 15-19, Bayesian analysis of extremes in hydrology A powerful tool for knowledge integration and uncertainties assessment.

1 Multivariate Normal Distribution Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication/ Graduate Institute of Networking.

School of Information Technologies The University of Sydney Australia Spatio-Temporal Analysis of the relationship between South American Precipitation.

Bayesian networks Classification, segmentation, time series prediction and more. Website: Twitter:

Detecting change in UK extreme precipitation using results from the climateprediction.net BBC Climate Change Experiment 11th International Meeting on Statistical.

Climate change, extreme sea levels & hydrodynamical models

Some advanced methods in extreme value analysis Peter Guttorp NR and UW.

Why Model? Make predictions or forecasts where we don’t have data.

University of Colorado Boulder ASEN 5070: Statistical Orbit Determination I Fall 2014 Professor Brandon A. Jones Lecture 14: Probability Wrap-Up and Statistical.

Extreme Value Techniques Paul Gates - Lane Clark & Peacock James Orr - TSUNAMI GIRO Conference, 15 October 1999.

Lévy copulas: Basic ideas and a new estimation method J L van Velsen, EC Modelling, ABN Amro TopQuants, November 2013.

Extreme values and risk Adam Butler Biomathematics & Statistics Scotland CCTC meeting, September 2007.

Designing for Global Warming Orson P. Smith, PE, Ph.D. School of Engineering.

Statistical approach Statistical post-processing of LPJ output Analyse trends in global annual mean NPP based on outputs from 19 runs of the LPJ model.

An exploration of the relationship between productivity and diversity in British Grasslands Adam Butler & Janet Heffernan, Lancaster University Department.

A Survey of Statistical Methods for Climate Extremes Chris Ferro Climate Analysis Group Department of Meteorology University of Reading, UK 9th International.

Extreme value statistics Problems of extrapolating to values we have no data about Question: Question: Can this be done at all? unusually large or small.

BioSS reading group Adam Butler, 21 June 2006 Allen & Stott (2003) Estimating signal amplitudes in optimal fingerprinting, part I: theory. Climate dynamics,

Feng Zhang and Aris Georgakakos School of Civil and Environmental Engineering, Georgia Institute of Technology Sample of Chart Subheading Goes Here Comparing.

Statistical Analyses of Extremes from a Regional Climate Model Chris Ferro Climate Analysis Group Department of Meteorology University of Reading Royal.

Simulation Study for Longitudinal Data with Nonignorable Missing Data Rong Liu, PhD Candidate Dr. Ramakrishnan, Advisor Department of Biostatistics Virginia.

Identification of Extreme Climate by Extreme Value Theory Approach

Spatial oceanographic extremes Adam Butler (Lancaster University), talk at RSC2003 Coworkers: Janet Heffernan, Jonathan Tawn, Roger Flather Data supplied.

Statistics What is the probability that 7 heads will be observed in 10 tosses of a fair coin? This is a ________ problem. Have probabilities on a fundamental.

Evaluating the ability of climate models to simulate extremes Eric Robinson Natalie McLean Christine Radermacher Ross Towe Yushiang Tung Project 6.

New approaches in extreme-value modeling A.Zempléni, A. Beke, V. Csiszár (Eötvös Loránd University, Budapest) Flood Risk Workshop,

WCRP Extremes Workshop Sept 2010 Detecting human influence on extreme daily temperature at regional scales Photo: F. Zwiers (Long-tailed Jaeger)

Options and generalisations. Outline Dimensionality Many inputs and/or many outputs GP structure Mean and variance functions Prior information Multi-output,

Chris Ferro Climate Analysis Group Department of Meteorology University of Reading Extremes in a Varied Climate 1.Significance of distributional changes.

Stats Term Test 4 Solutions. c) d) An alternative solution is to use the probability mass function and.

Stochastic Hydrology Random Field Simulation Professor Ke-Sheng Cheng Department of Bioenvironmental Systems Engineering National Taiwan University.

26134 Business Statistics Week 4 Tutorial Simple Linear Regression Key concepts in this tutorial are listed below 1. Detecting.

Multiple comparisons problem and solutions James M. Kilner

Bootstrapping James G. Anderson, Ph.D. Purdue University.

NOAA Northeast Regional Climate Center Dr. Lee Tryhorn NOAA Climate Literacy Workshop April 2010 NOAA Northeast Regional Climate.

Introduction to emulators Tony O’Hagan University of Sheffield.

How many iterations in the Gibbs sampler? Adrian E. Raftery and Steven Lewis (September, 1991) Duke University Machine Learning Group Presented by Iulian.

26134 Business Statistics Week 4 Tutorial Simple Linear Regression Key concepts in this tutorial are listed below 1. Detecting.

Application of Extreme Value Theory (EVT) in River Morphology

Basics of Multivariate Probability

Why Model? Make predictions or forecasts where we don’t have data.

32931 Technology Research Methods Autumn 2017 Quantitative Research Component Topic 4: Bivariate Analysis (Contingency Analysis and Regression Analysis)

Multiple Random Variables and Joint Distributions

Why Stochastic Hydrology ?

Ruth Doherty, Edinburgh University Adam Butler & Glenn Marion, BioSS

Change in Flood Risk across Canada under Changing Climate

Considerations in Using Climate Change Information in Hydrologic Models and Water Resources Assessments JISAO Center for Science in the Earth System Climate.

Adam Butler, Biomathematics and Statistics Scotland

Stochastic Hydrology Random Field Simulation

forecasts of rare events

Generalized Spatial Dirichlet Process Models

Environmental Statistics

Identification of Extreme Climate by Extreme Value Theory Approach

Presentation transcript:

Climate change, hydrodynamical models & extreme sea levels Adam Butler Janet Heffernan Jonathan Tawn Lancaster University Department of Mathematics & Statistics

The problem

Introduction Understanding the impacts of climate change upon extreme sea levels. l Understanding spatial variation in impacts. Use statistical ideas of spatial statistics and extreme value theory (Smith, 2002). l Attempt to build physically realistic models. l Applications: flood defence, offshore engineering, insurance…

Hydrodynamical models

POL models < 35km NEAC grid < 12km NISE grid V V

Observed climate inputs Run using observational climate data. Model run for period Run on NICE and NEAC grids. l Reasonable fit to observational data (Flather, 1987). Test for evidence for a linear temporal trend in extreme values.

Climate sensitivity Generate 30-year long sequences of model output under two hypothetical climate scenarios: 1“Current” CO 2 levels 2Double “current” CO 2 levels Sequences are stationary. Climate inputs generated using the ECHAM-4 climate model. We will construct parametric models. Interest is in comparing the parameter estimates obtained under the two scenarios.

Univariate extremes

The GEV distribution Blockwise maxima converge to a GEV (Generalized Extreme Value) distribution :  is the shape parameter. l Conditions for convergence include: independence or weak dependence stationarity (Leadbetter, 1987).

Modelling extremes General ideas l Ignore distribution of original data. l Can model maxima using GEV distribution. l Alternative approaches to extremes exist: e.g. threshold methods (Coles, 2001). Application to the POL data l Model the annual maxima at each site. l Assume independence between sites.

Previous findings l Surge residuals l Changes (cm) in 50 year surge levels for the NISE grid. l Estimates exhibit spatial variability.

Spatial extremes

Multivariate extremes Componentwise maxima l Multivariate Extreme Value Distribution l Nonparametric or parametric estimation ? Parametric approaches Marginal and dependence characteristics. The Multivariate Logistic Distribution l Alternative parametric models (Tawn, ?) l Physically motivated subsets

Multivariate logistic distribution

Spatial extremes Assume smooth spatial variation in GEV parameters. This implies spatial coherence. Assume that observations at neighbouring sites are spatially dependent. Use a multivariate approach to extremes, with one dimension for each site. Benefits Improved efficiency in parameter estimation. l Interpretable estimates of spatial structure. l Allows extrapolation to ungauged sites. Enables regional-level estimates to be derived.

Current work

Marginal or joint estimation? Bivariate case, GEV margins, logistic dependence. l Three possible methods for estimation: joint likelihood (“joint”), product of marginal likelihoods (“marginal”) robust version of “marginal” approach Marginal approach results in reduced efficiency if there is dependence. How large is this effect ? Simulation study. l See: Shi, Smith & Coles (1992), Barao & Tawn (1999).

Conclusions Further work l “Bivariate efficiency” study l Comparison of approaches to spatial extremes l POL data: extremal trends l POL data: climate sensitivity l Scottish rainfall data…? Statistical significance l Application of modern extreme value methods in an applied context l High dimensionality

Questions ?