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Climate Risk and Climate Change

Climate Risk and Climate Change. Manfred Mudelsee Climate Risk Analysis, Hannover, Germany Alfred Wegener Institute, Bremerhaven, Germany. Potsdam, September 2010 Millennium Flood, July 1342 (Stadtarchiv Nürnberg). Climate.

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Climate Risk and Climate Change

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  1. Climate Risk and Climate Change Manfred Mudelsee Climate Risk Analysis, Hannover, Germany Alfred Wegener Institute, Bremerhaven, Germany Potsdam, September 2010 Millennium Flood, July 1342 (Stadtarchiv Nürnberg)

  2. Climate Solomon et al. (Eds.) (2007) Climate Change 2007: The Physical Science Basis. Cambridge Univ. Press

  3. Climate Dresden, river Elbe  long-term  mean and variability Brückner (1890) Geographische Abhandlungen 4:153 Hann (1901) Lehrbuch der Meteorologie, Tauchnitz Köppen (1923) Die Klimate der Erde: Grundriss der Klimakunde, de Gruyter Global Runoff Data Centre, Koblenz

  4. Climate Risk Dresden, river Elbe  mean and variability risk and extremes Gardenier & Gardenier (1988) In: Encyclopedia of statistical sciences 8:141, Wiley Mudelsee (2006) DKKV/ARL Workshop

  5. Climate Change Dresden, river Elbe  climate risk change? Solomon et al. (Eds.) (2007) Climate Change 2007: The Physical Science Basis. Cambridge Univ. Press

  6. Estimation Climate Risk Estimation  risk changes Climate Risk Test Examples

  7. Estimation {t(i), x(i)} sample (time series) n sample size q parameter q estimator CIq,12 = [ql; qu] confidence interval 12 confidence level seq standard error E[q ],biasq expectation, bias n i=1 ^ ^ ^ ^ ^ ^ ^

  8. Estimation PDF “Estimates without error bars are useless.” Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  9. Estimation Simple problem  derive CI analytically (e.g., mean estimation, t distribution of q) Advanced problem  resample data: bootstrap, Bayesian ^ Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  10. Estimation: Bootstrap Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  11. Estimation: Bootstrap resample data  shape Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  12. Estimation: Bootstrap resample data  shape resample data blocks  shape, persistence Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  13. Climate Risk Estimation I Data type Parametric model  Block maxima  Generalized Extreme Value distribution (GEV)  Peaks over  Generalized Pareto threshold (POT) distribution (GP) p tail probability, risk 1/p return period (time units) xp return level u threshold

  14. Climate Risk Estimation I GEV distribution GEV distribution, time-dependent Coles (2001) An Introduction to Statistical Modeling of Extreme Values. Springer Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  15. Climate Risk Estimation I GEV distribution GEV distribution, time-dependent “Recent achievements ...”  use of covariates  multivariate: difficult Coles (2001) An Introduction to Statistical Modeling of Extreme Values. Springer Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  16. Climate Risk Estimation II Elbe, winter, class 2–3 m = 64, h = 35 yr

  17. Climate Risk Estimation II nonparametric: kernel estimation l occurrence rate, risk per time unit (Poisson process) h bandwidth T time K kernel function Tout extreme event date m number of extremes Elbe, winter, class 2–3 m = 64, h = 35 yr Diggle (1985) Applied Statistics 34:138

  18. Climate Risk Estimation II Elbe, winter, class 2–3 m = 64, h = 35 yr Bootstrap resample (with replacement, same size)

  19. Climate Risk Estimation II Elbe, winter, class 2–3 m = 64, h = 35 yr Bootstrap resample (with replacement, same size)

  20. Climate Risk Estimation II Elbe, winter, class 2–3 m = 64, h = 35 yr Bootstrap resample (with replacement, same size) 2nd Bootstrap resample

  21. Climate Risk Estimation II Elbe, winter, class 2–3 m = 64, h = 35 yr Bootstrap resample (with replacement, same size) 2nd Bootstrap resample 10 000 Bootstrap resamples

  22. Climate Risk Estimation II Elbe, winter, class 2–3 m = 64, h = 35 yr Bootstrap resample (with replacement, same size) 2nd Bootstrap resample 10 000 Bootstrap resamples

  23. Climate Risk Estimation II 90% confidence band Elbe, winter, class 2–3 m = 64, h = 35 yr Cowling et al. (1996) Journal of the American Statistical Association 91:1516

  24. Climate Risk Estimation II more maths  CI construction  bandwidth selection  boundary bias correction 90% confidence band Elbe, winter, class 2–3 m = 64, h = 35 yr Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  25. Climate Risk Estimation II “Recent achievements ...”  uncertain timescales (Tout*), paleoclimate  hybrid model 90% confidence band Elbe, winter, class 2–3 m = 64, h = 35 yr Smith (1989) Statistical Science 4:367

  26. Climate Risk Test: Cox–Lewis H0: “Constant occurrence rate, l(T).” H1: “Increasing occurrence rate.” U test statistic Under H0, statistic U Tout extreme event date (“POT data”) is standard normally distributed. m number of extremes [T(1); T(n)] observation interval n sample size Cox & Lewis (1966) The Statistical Analysis of Series of Events. Methuen

  27. Climate Risk Test: Cox–Lewis H0: “Constant occurrence rate, l(T).” H1: “Increasing occurrence rate.” U test statistic Under H0, statistic U Tout extreme event date (“POT data”) is standard normally distributed. m number of extremes [T(1); T(n)] observation interval n sample size Cox & Lewis (1966) The Statistical Analysis of Series of Events. Methuen

  28. Climate Risk Test: Cox–Lewis H0: “Constant occurrence rate, l(T).” H1: “Increasing occurrence rate.” U test statistic Under H0, statistic U Tout extreme event date (“POT data”) is standard normally distributed. m number of extremes [T(1); T(n)] observation interval n sample size Cox & Lewis (1966) The Statistical Analysis of Series of Events. Methuen

  29. Climate Risk Test: Mann–Kendall H0: “Constant trend (mean).” H1: “Increasing trend.” Kendall (1938) Biometrika 30:81 Mann (1945) Econometrica 13:245

  30. Climate Risk Test: Mann–Kendall Zhang et al. (2004) Journal of Climate 17:1945 Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  31. Climate Risk Test: Monte Carlo start simulation prescribed prescribed l(T) PDFs end simulation empirical power = #(H1) / nsim generate time series test H0 vs. H1

  32. Climate Risk Test: Monte Carlo nsim = 90000 n sample size significance level = 0.10 mtrue prescribed number of extremes sepower = 0.001 k scaling parameter l(T) ~ T1/k–1 Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  33. Climate Risk Test “Recent achievements ...”  use Cox–Lewis, not Mann–Kendall Zhang et al. (2004) Journal of Climate 17:1945 Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  34. Examples Floods: Elbe, Oder Mudelsee et al. (2003) Nature 425:166

  35. Examples Wildfires, Canada Girardin & Mudelsee (2008) Ecological Applications 18:391 Girardin et al. (2009) Global Change Biology 15:2751 Canadian Forest Service

  36. Examples Hurricanes, Boston Besonen et al. (2008) Geophysical Research Letters 35:L14705 Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  37. Examples Myth “Extremes are by definition rare.”  Consider a two-state system

  38. Climate change  Climate risk change? 1. Estimates: give error bars 2. Tests: use Cox–Lewis, not Mann–Kendall 3. Future achievements:  better estimators  systematic application, data/models, small scale • floods • hurricanes

  39. Climate change  Climate risk change? 1. Estimates: give error bars 2. Tests: use Cox–Lewis, not Mann–Kendall 3. Future achievements:  better estimators  systematic application, data/models, small scale • floods • hurricanes Thank you!

  40. Appendix

  41. Climate Risk Test: Mann–Kendall Appendix H0: “Constant trend (mean).” H1: “Increasing trend.” x(3) x(1) x(2) x(2) x(4) x(3) x(1) x(4) U test statistic U’ #(interchanges) Under H0, statistic U n sample size is normally distributed. Kendall (1938) Biometrika 30:81 Mann (1945) Econometrica 13:245

  42. Climate Risk Test: Monte Carlo Appendix Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  43. Climate Risk Test: Monte Carlo Appendix Mudelsee (2010) Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer

  44. Climate Risk Test: Monte Carlo Appendix n sample size mtrue prescribed number of extremes, shifted (1.0) chi-squared in lognormal AR(1) noise k scaling parameter for upwards trend, l(T) ~ T1/k–1 Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards trend,” divided by nsim = 90000, se = 0.001; significance level: 0.10.

  45. Climate Risk Test: Monte Carlo Appendix n sample size mtrue prescribed number of extremes, shifted (1.0) chi-squared in lognormal AR(1) noise k scaling parameter for upwards trend, l(T) ~ T1/k–1 Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards trend,” divided by nsim = 90000, se = 0.001; significance level: 0.10.

  46. Climate Risk Test: Monte Carlo Appendix n sample size mtrue prescribed number of extremes, shifted (1.0) chi-squared in lognormal AR(1) noise k scaling parameter for upwards trend, l(T) ~ T1/k–1 Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards trend,” divided by nsim = 47500, se = 0.001; significance level: 0.05.

  47. Climate Risk Test: Monte Carlo Appendix n sample size mtrue prescribed number of extremes, shifted (1.0) chi-squared in lognormal AR(1) noise k scaling parameter for upwards trend, l(T) ~ T1/k–1 Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards trend,” divided by nsim = 47500, se = 0.001; significance level: 0.05.

  48. Climate Risk Test: Monte Carlo Appendix n sample size mtrue prescribed number of extremes, shifted (3.0) chi-squared in lognormal AR(1) noise k scaling parameter for upwards trend, l(T) ~ T1/k–1 Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards trend,” divided by nsim = 90000, se = 0.001; significance level: 0.10.

  49. Climate Risk Test: Monte Carlo Appendix n sample size mtrue prescribed number of extremes, shifted (3.0) chi-squared in lognormal AR(1) noise k scaling parameter for upwards trend, l(T) ~ T1/k–1 Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards trend,” divided by nsim = 90000, se = 0.001; significance level: 0.10.

  50. Climate Risk Test: Monte Carlo Appendix n sample size mtrue prescribed number of extremes, shifted (3.0) chi-squared in lognormal AR(1) noise k scaling parameter for upwards trend, l(T) ~ T1/k–1 Empirical power: #(simulations) where H0: “no trend” is rejected against H1: “upwards trend,” divided by nsim = 47500, se = 0.001; significance level: 0.05.

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