Santiágo Beguería: Covariate-dependent modeling of extreme events by non-stationary Peaks Over Threshold analysis

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  • 1. Covariate-dependent modeling of extreme events by nonstationary Peaks Over Threshold analysis A review and a case study in Spain Santiago Beguería santiago.begueria@csic.es Estación Experimental de Aula Dei, Consejo Superior de Investigaciones Cientícas (EEADCSIC), Zaragoza, España Liberec, February 17th 2012(santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 1 / 52
  • 2. Motivation, I We all love the extreme value theory (EVT) applied to the analysis of climatic hazard: its elegant, simple, and provides useful and understandable results in terms of magnitude / frequency curves. The stationarity assumption, though, was an important limitation of the EVT. Relatively recent extensions of the EVT allow for non-stationary analysis (Coles, 2001), and an increasing number of authors are exploring their possibilities for the analysis of climatic hazard. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 2 / 52
  • 3. Motivation, I We all love the extreme value theory (EVT) applied to the analysis of climatic hazard: its elegant, simple, and provides useful and understandable results in terms of magnitude / frequency curves. The stationarity assumption, though, was an important limitation of the EVT. Relatively recent extensions of the EVT allow for non-stationary analysis (Coles, 2001), and an increasing number of authors are exploring their possibilities for the analysis of climatic hazard. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 2 / 52
  • 4. Motivation, I We all love the extreme value theory (EVT) applied to the analysis of climatic hazard: its elegant, simple, and provides useful and understandable results in terms of magnitude / frequency curves. The stationarity assumption, though, was an important limitation of the EVT. Relatively recent extensions of the EVT allow for non-stationary analysis (Coles, 2001), and an increasing number of authors are exploring their possibilities for the analysis of climatic hazard. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 2 / 52
  • 5. Motivation, II Most studies up to now focused on identifying temporal trends in the occurrence of extreme events, i.e. making time a covariate. In the last few years other covariates with an expected inuence on the occurrence of extreme events are being used, too > high relevance for the statistical downscaling of reanalysis or model data, which typically cannot be used for local impact studio. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 3 / 52
  • 6. Motivation, II Most studies up to now focused on identifying temporal trends in the occurrence of extreme events, i.e. making time a covariate. In the last few years other covariates with an expected inuence on the occurrence of extreme events are being used, too > high relevance for the statistical downscaling of reanalysis or model data, which typically cannot be used for local impact studio. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 3 / 52
  • 7. SummaryIn this talk I will present ongoing research on the relationship betweenextreme precipitation and teleconnection indices in Spain, usingnon-stationary EVT techniques. The talk is organized as follows: A review of non-stationary Peaks Over Threshold analysis Case study: relationship between teleconnection indices and extreme rainfall events in Spain Conclusions and future work (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 4 / 52
  • 8. SummaryIn this talk I will present ongoing research on the relationship betweenextreme precipitation and teleconnection indices in Spain, usingnon-stationary EVT techniques. The talk is organized as follows: A review of non-stationary Peaks Over Threshold analysis Case study: relationship between teleconnection indices and extreme rainfall events in Spain Conclusions and future work (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 4 / 52
  • 9. SummaryIn this talk I will present ongoing research on the relationship betweenextreme precipitation and teleconnection indices in Spain, usingnon-stationary EVT techniques. The talk is organized as follows: A review of non-stationary Peaks Over Threshold analysis Case study: relationship between teleconnection indices and extreme rainfall events in Spain Conclusions and future work (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 4 / 52
  • 10. SummaryIn this talk I will present ongoing research on the relationship betweenextreme precipitation and teleconnection indices in Spain, usingnon-stationary EVT techniques. The talk is organized as follows: A review of non-stationary Peaks Over Threshold analysis Case study: relationship between teleconnection indices and extreme rainfall events in Spain Conclusions and future work (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 4 / 52
  • 11. Short review of NSPOT analysis, I 200 150 Intensity (mm day-1) 100 50 0 1950 1960 1970 1980 1990 2000 2010 Time (n = 266)Peaks-over-threshold (POT) sampling: take only exccedances over a threshold, x − x0 (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 5 / 52
  • 12. Short review of NSPOT analysis, II 200 150 Intensity (mm day-1) 100 50 0 1950 1960 1970 1980 1990 2000 2010 Time (n = 266)Peaks-over-threshold (POT) sampling: take only exccedances over a threshold, x − x0 (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 6 / 52
  • 13. Short review of NSPOT analysis, IIIStationary POT: assuming independent inter-arrival times, the POT datafollows a Generalized-Pareto distribution.Probability of exceedance: −1/κ x − x0 P (X > x |X > x0 ) = 1 − λ 1 + κ (1) αQuantile corresponding to a return period T: κ α 1 XT = x0 + 1− (2) κ λT(beware of alternative conventions: x0 = u , α = σ, κ = ξ ) (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 7 / 52
  • 14. Short review of NSPOT analysis, IVApproaches for assessing non-stationarity in POT modeling: Split-sample approach (Li et al., 2005) Moving kernel (Hall and Tajvidi, 2000) Non-stationary POT (NSPOT) modeling (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 8 / 52
  • 15. Short review of NSPOT analysis, GPar distribution Return period curves, V 2500 NAO− 2000 1500 daily EI NAO+ 1000 500 0 1 2 5 10 20 50 100 return period (years)Split-sample approach: independent models for positive and negative phases of NAO (Angulo et al., 2011). (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 9 / 52
  • 16. Short review of NSPOT analysis, VI 2110 ´ S. BEGUERIA et al. X287 X164 0.00 0.02 0.04 0.06 0.08 0.10 0.00 0.05 0.10 0.15 0.20 0.25 1930 1950 1970 1990 2010 1930 1950 1970 1990 2010 X9198 X2234 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1930 1950 1970 1990 2010 1930 1950 1970 1990 2010 Figure 6. Model uncertainty: time variation of the 10-year return period event intensity standard error (mm by a nonparametric NSPOT d−1 ) model (dots), a linear NSPOT model (solid line), a high order polynomial NSPOT model (short-dashed line) and a stationary POT modelMoving kernel approach: time variability in the stations. Location of the stations a moving Figure 1. of the previous 20 years of (long-dashed line) in four P10 quantile, based on is shown in windowdata (Beguería et al., 2011). by more than 50% (e.g. series X164). The time evolution and the most parsimonious (i.e. with the lowest polyno- of q10 depended on the evolution (santiago.begueria@csic.es) of both α (scale) and mial order) was chosen. Following this approach, statis- 10 / 52 NSPOT with covariates Liberec, 17/02/2012
  • 17. Short review of NSPOT analysis, VIIStationary POT: −1/κ x − x0 P (X > x |X > x0 ) = 1 − λ 1 + κ αNon-stationary POT: −1/κ(c ) x − x0 (c ) P (X > x |X > x0 , C ) = 1 − λ(c ) 1 + κ(c ) (3) α(c ) (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 11 / 52
  • 18. Short review of NSPOT analysis, VIIISome examples of NSPOT analysis of climatic variables: Time dependence of T and P (Smith, 1999) Nogaj et al. (2006) time trends of T extremes over the NA region Laurent and Parey (2007), Parey et al. (2007), T extremes in France Méndez et al. (2006), trends and seasonality of POT wave height Yiou et al. (2006) trends of POT discharge in the Czech Republic Abaurrea et al. (2007) trends of POT T in the IP Acero et al. (2011), Beguería et al. (2011), trends in POT P, IP Friederichs (2010), Kallache et al. (2011), downscaling of POT P based on reanalysis / GCM data Tramblay et al. (2012), covariation between POT P extremes and atmospheric covariates, SE France (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 12 / 52
  • 19. Teleconnections aecting precipitation in IP, IThe North Atlantic Oscillation (NAO). (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 13 / 52
  • 20. Teleconnections aecting precipitation in IP, IIThe North Atlantic Oscillation (NAO). (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 14 / 52
  • 21. Teleconnections aecting precipitation in IP, IIIThe Mediterranean Oscillation (MO, Palutikof 2003). (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 15 / 52
  • 22. Teleconnections aecting precipitation in IP, IVThe Mediterranean Oscillation (MO, Palutikof 2003). (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 16 / 52
  • 23. Teleconnections aecting precipitation in IP, VThe Western Mediterranean Oscillation (WEMO, Martín-Vide and López-Bustins 2006). (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 17 / 52
  • 24. Teleconnections aecting precipitation in IP, VIThe Western Mediterranean Oscillation (WEMO, Martín-Vide and López-Bustins 2006). (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 18 / 52
  • 25. Teleconnections aecting precipitation in IP, VII 1.5 1.5 q q q q q q q q q q q q q q 1.0 1.0 qq qq q qq qqq qq q q q q q q qq q qq q q qq q q q q q q q q q q qq q q q qq q q q q q q qq q q q q q q q qqq q q q q q q q qq q q q q q q q q q q q q q qq qq q q q q q q q q q q q q qq q q q q q qq q qq q q qq q q qq q qq q q q q qq q 0.5 0.5 q q q qqq q q q q q q q q q q qq q qqqq qqq q qq q q q qq q q qq qq qq q q q qqqq q qqq q q q q qqqq q q q q qq q q q qq qq q q q q q qq q q q q qq qq q q qq q qqqqq qq qqq q q qqq q q q q q qq q q qq q qq q q qqqq qq q qqqq q q q qq q q q q q qq q q qqq q q qq q q q q qq q q qqq q q qq q q qqqq q q qq q q q qq q q qqq qq qq q qqq q q q q q q q qq q q q qq q q qq q q q qqq q qqqq q q qqq qq q qqq q q q q q q q q q q q q q q qqq qq q qq qqqq qq q q q q q qq q q qqqq q qqqq q q qq q q q q q q q qq qq qqqqq qq qqqqq q qq q q qq qqqqqq q q qq q qq q q q q qq qq qq qqq q q qq q qq q q q q q q qqqqq q q q q q q qqqq qq qqq q q qqq q qq qq q q q NAOi NAOi q qqqqqqq qq qqqq q q q q q q q q qq qq qq q q q qq qqqqqqqqqqqq q q q q q q q qq qqqq qqqq qqqqqqq qq q qq q qqq qq qq q q q q q q q q q q qqqqqq q qqq q q q q q q qq q 0.0 0.0 q qq q q q q q qq q q q q q q qq qq qq q q q q q q qqq qqqq q qqqq q qqq qq q q q q q q qq qq q qqqqqqq q qq qq q qq q q qq q q q q q q q q q q qq q q q q qqq qq qqqq qq qq qqqq qqq q q q qq q qq q q q q q q qq q qq qq q q q q q qqqqqqqqq q q q qq qqq q q qqqq q q q qqq q qq q q q q qq qq q q q qqqq qq q q qq q qq q q q q qqq qq q q qqq q q qq q q qq q q q q q qq q qq q qq q q q q q q qq q qqqqqq q qq q q qqq q q qq q qq q q q qq qq q q qqqq q q q q q q q qq qqqq qq q qq qq q q q q q qqq q q qq q q q q q q qq q q q q q q qq q qq qq q q q q q q qq qqq q q q q qq q q q qq q q q q q q q q q qq qq qqq q q q q qq q q qq q −0.5 −0.5 q qq q q q q q qqq q qq q q q qqq q q qqq qqqqqqq qq qqq q q q q q q qqqq q q qq q q qqqqq qq q q q q q qq q q q q qq q qq q q q qq qq q q qq q q qq q q q q q q qq qq qqq q qq q q q qq q q qq q qqqqq qq q q q qq q q q q qq qqq q q q q q qq q q q q q q q q q qq q qq q q q q qq q q qq q qq q q q q q q qq q qq q qqqqqq q q q q qqq q qq q q q q q q qq q q q q qqq q qq q q q q q q qq q q q q q qq q q qq q q q q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q qq q −1.5 −1.5 r2=0.21 r2=0.005 q q −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 MOi WEMOi 1.5 q 1.0 q q q qqq q qq q qq q q q q qq q qq qq q q q q q qqq q q q q qq q q qq qq q q q qq q q q qq q q q q q qq q q q q qq q 0.5 q qq q qq qqqq q qq q qq q q qqqq q q qq q q q qq q q q qq q q q q qqq q q qqq q q q qq qq q q q q q q q qq qq qq qq qqq q q q qq qq q q q q q q qq q q qqq qq q q qq q q qq qq qqq q q qqq q q qq q q qq qqq qq q qq q qqq qq q qq q q q q q q qqq q q qq WEMOi q q q q qqqq qqqqqq qq qqqq q q qqq q q q qq qqqq qq qqq qqq q qqq q q q q q q q q q q qqq q qq q q q qq qq qqqq qq qqqq q q q q q q q qq qq q q qq q q q qq q q qqqq qq qqqqqq qqqqq q qq q qq qq q q qq q qq q qqqq qq qqq q qq 0.0 q q q q q q q q q qq q q q q q q qqq q q q q q q q q q q q q q q q qq q q q q qq qq qq q qq qqq qqqq q q q q qqqq q q q q q q qqqq qqqq q qq q q qq qq q qq q q qq qq qq q qq qq qqqq qqq q q q qqqqq qq qqqqqqqqqq q q q q q qqq q q q q q qq q q q q q qq qq q q q qq q q q q q qq q qqqq qq qq q q q qq q q q q qqq q q q q q q q q qqq q qqqq q q qq qq q qqq q q −0.5 q q q q q q q q q q q q q qq q q q q qq q q q qq q q q q q q q q q qqq q q q q q q q q q q qq q q −1.5 r2=0.047 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 MOiCorrelations between teleconnection indices. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 19 / 52
  • 26. Dataset, I Stations network 4800000 q q q q q q q q qq q q q q q q q qq q q q q q q q q q q q q q 4600000 q q q q q q q q q q q q q q qq q q q q 4400000 q q q q q qq qq q q qq q q q q q 4200000 q q q q q q qq q q qq q q q q q q 4000000 q q q q106 stations, 58 daily precipitation 2e+05 reconstructed for6e+05 period 8e+05 0e+00 series 4e+05 the 1950-2009 1e+06 (source: AEMET). (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 20 / 52
  • 27. Dataset, IITeleconnection indices (Reykjavik, Padova, Lod and Gibraltar). Sources: http://www.cru.uea.ac.uk,http://www.ub.es. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 21 / 52
  • 28. Dataset, III 1 0 NAOi −1 −2 0 20 40 60 80 2 1 WEMOi 0 −1 −2 0 20 40 60 80 15 P (mm/day) 10 5 0 0 20 40 60 80 Time (days since 01/11/2001)Declustering: intensity and magnitude series and associated teleconnection indices. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 22 / 52
  • 29. Dataset, IV 1 0 NAOi −1 −2 0 20 40 60 80 2 1 WEMOi 0 −1 −2 0 20 40 60 80 20 P (mm/day) 10 5 0 0 20 40 60 80 Time (days since 01/11/2001)Declustering: intensity and magnitude series and associated teleconnection indices. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 23 / 52
  • 30. Dataset, V 1 0 NAOi −1 −2 0 20 40 60 80 20 P (mm/day) 10 5 0 0 20 40 60 80 Time (days since 01/11/2001) 2 1 WEMOi 0 −1 −2 0 20 40 60 80 20 P (mm/day) 10 5 0 0 20 40 60 80 Time (days since 01/11/2001)Declustering: intensity and magnitude series and associated teleconnection indices. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 24 / 52
  • 31. Dataset, VI 1 0 NAOi −1 −2 0 20 40 60 80 15 P (mm/day) 10 5 0 0 20 40 60 80 Time (days since 01/11/2001) 2 1 WEMOi 0 −1 −2 0 20 40 60 80 15 P (mm/day) 10 5 0 0 20 40 60 80 Time (days since 01/11/2001)Declustering: intensity and magnitude series and associated teleconnection indices. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 25 / 52
  • 32. Analysis, I > x |X > x0 ) = 1 − λ 1 + κ x −x0 −1/κM0: P (X α −1/κM1: P (X > x |X > x0 , C ) = 1 − λ 1 + κ x −x0 (c ) α(c ) x0 = β0 + βi c (4) α = γ0 γic (5) κ = δ (6) λ = ε (7)Likelihood ratio test: D = − 2 ( 1 (M1 ) − 0( M0 )) (8)distributed according to χ2 (with d.f. k k = 4). (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 26 / 52
  • 33. Analysis, IIR, package ismev (Stuart Coles, ported to R by Alec Stephenson)....m0 < gpd.t(xdat=dat, threshold=u, npy=rate)...uu < predict(lm(v∼cdat))m1 < gpd.t(xdat=dat, threshold=uu, npy=rate, ydat=cdat,sigl=1, siglink=exp) (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 27 / 52
  • 34. Analysis, III Histogram of tel$naoi Histogram of pnorm(tel$naoi) 4000 1000 1200 3000 800Frequency Frequency 2000 600 400 1000 200 0 0 -2 0 2 4 6 0.0 0.2 0.4 0.6 0.8 1.0 tel$naoi pnorm(tel$naoi)Covariates: NAOi and pnorm(NAOi) (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 28 / 52
  • 35. Example: Valencia, I Location of station: VALENCIA, X8416 4800000 4600000 4400000 q 4200000 4000000Spatial location 0e+00 5e+05 1e+06 (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 29 / 52
  • 36. Example: Valencia, II Threshold (u = q0.9 = 23.5, n = 229) 50 100 45 50 Return period (years) 40 25 Mean Excess 35 10 30 5 25 2 20 1 q q q q qqq qq q q qq q q q q q 10 20 30 40 50 60 70 80 q q q q q 50 q q q q q q q qq q q u q q q qStationary model: xed threshold (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 30 / 52
  • 37. Example: Valencia, III29) Stationary model (AIC=1875) 100 q 50 Return period (years) q 25 q q q 10 q q q q q q q q 5 q q q qq q q q q q q qqq q 2 q q qq q q qq q qq q qq qq q qq 1 q q q q qqq qq q q qq qq q q q 70 80 q q q q q 50 100 150 200 250 qq q q q q q q q q q q q q q Intensity (mm day−1) Intensity (mm) Intensity (days) Stationary model: quantile plot (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 31 / 52
  • 38. Example: Valencia, IV 200 q 35 q 30 150 q q Intensity (mm day−1) Scale parameter q q 25 q q q q q q q 100 qq qq qq q 20 q qq 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 q q 50 qq q q 15 q q q q q q q q q q q qq q q q qq qqqq q q qq q q q q q q qq qq q q q q q q q q q q q q qqq qq q q q q q q q qq q q q q q q q q q qqq q q q q q q q qq q q q q q qqqq qq q q q q q q q q qqq q q qq q q qqqq qq q q q q qqq q q q qq q q q q qq q q q q qq q q q q qq q qq q q q q qq q q q qq q qqq q q q q q q qq qqqq qqq q q q qqq q qq qq q qqq qq q q q qqq q qqq qq q q q q qq qq q qq q q qq q q q q qq q qq q qq q q q q q q q q q q qq qq q q q qqq q q q q qq q 10 q qq qq qqqqq qq q qqq q q q q q qq qq qq qqq qqq q qqq q qq qqq qqq q q q q qq qq q qq qq q q q q q q q qq q q qqq qq q qqq q q q q q qq q q qq q q q q q q qq q q q qqq q q q q qqq q q q qqqqqqqqqqqqq qqqqqqqqqq qqqqqq qqqqqqqqqq q qqqqqqqqqqq qqqq q qq qqq q qq qq q qq q q qqq qqqq q qqq q qqqq q q qqqq q q qqqqqqq qqqq qqqqq qqqqq qqqqqq qqq q qqq q q q qqqq qqqq qqqqq qq q q q q q q q q qqq q q q q qqqqqqqqq qqqqqqqqqqqqqqqqqq qqqqqqqqqqqqq qqqqqqqq q qqqqqqqqqqqqq qqq q q q q q q q qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq q q qq qqq q qq q qqqqqq q q q qq qq qq q qq q q q qqqqq q q qqqqqqqq qq qqq q qq qqqqqq qqqqqqqqqqqqqqqqqqqqqqqqqqq qqqqqqq q qq qqqqqqqq qqqqqqq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqqqqqqqqqq qqqqqqqqqqqqqqqqqq qq q q q q q q q q q q q qq q q q q q qq q q q q q q q qq qq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq q qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqq qqqqqqqqqqqqqqqqqqqqqqqqqq qq q qq q q qq qq q q q q q q qq q qqqqq qq q qq q q qqqqqqqqq qqqq qqqq q qqqq qqqqqqqq qq qqq qqqqqqq q q qqqqqqq qq qq q q qq q qq q qqqq qqq q qqq qq q qqq qqqqq qq q qqq q q qq qq q 0 0.0 0.2 0.4 0.6 0.8 1.0 WEMOi (n = 200) 100Non-stationary model: threshold model 100 2 1 0.5 0 −0.5 −1 −2 50 50 (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 32 / 52 s) s)
  • 39. Example: Valencia, V 35 30 Scale parameter 25 20 15 q q q qq q q qq q q q q qqq q 10q qqq qqq qqq qq q q q qq q qq qq qq qqqqqqqqqq qqqq q qq qqq q q qq qq q q qq q qqqqqqqqqqqqqqqqqqqqq q qqqqqqqq qqqq qqqqq q q qqqqqqqqqqq q qq q qqq qqqqqqqqq q q q qqqqqqqqqqqqq q qq 1.0 −2 −1 0 1 2 WEMOi (AIC=1569*) 100 Non-stationary model: scale parameter model −2 220 210 200 50 190 180 (santiago.begueria@csic.es) 0 17 160 NSPOT with covariates Liberec, 17/02/2012 33 / 52 )
  • 40. 0.0 0.2 0.4 0.6 0.8 1.0Example: Valencia, VI WEMOi (n = 200) 100 100 2 1 0.5 0 −0.5 −1 −2 50 50 Return period (years) Return period (years) 25 25 10 10 5 5 2 2 1 1 50 100 150 200 250 300 Intensity (mm day−1)Non-stationary model: quantile plot (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 34 / 52
  • 41. 1.0 −2 −1 0 1 2Example: Valencia, VII WEMOi (AIC=1569*) 100 −2 220 210 200 50 190 180 170 160 Return period (years) 25 150 140 130 120 10 110 100 90 5 80 70 60 50 2 40 30 1 300 −2 −1 0 1 2 WEMOiNon-stationary model: quantile plot (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 35 / 52
  • 42. q q q q q qExample: Valencia, VIII 20 20 150 50Scale parameter 150 50Scale parameter 150Intensity (mm day−1) qq q q q q Intensity (mm day−1) Intensity (mm day−1) Scale parameter q q q q q q q q q q q q q q 18 q q q q q q q q q q q q q 18 100 100 100 q q q qq q q q q q q q q qq qq q q q q q q qq q qq q q q qq q q q q q q 16 q q qq q q q q q q q q q qq q q q q q q q q q q qq q q q q qqq q q qq q q q q q q qq q qq q q q q q q q q qq q q q qq q qq qq q q 16 q q q q q qq q q q q q q q q q q q q q qqq qq q q q q qq q q q 50 q qq q q qq q q q q q q q q qq q q q qq q q q q q qq q q q q qq q q q q q q qq q q q q q qq q q q qq q qq q q q q q 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 qq q q q q qq q q q q q qq q q qq q q q q q q q q q q qq q q q qq q q q q q q qq q q q q q q qq q q q qqqqqq q q q q q qq q q qq q q qq q qq qq q q qq q q q qq q q q qq qq q qqq q qqq qq qqq q q q q q qq q qq q q qq q q q qq qqq q q q qq q q q q q q q q q qq q q q q q q q 14 q q qqq qq q q q q qq q q q q q qq q q qqqq q q qq q qq q qqqq q q q q q q qq q q q q q q q q q q qq qqq qq q q qqqqq q qq qq q q qqq q qq q q qq q q q q q q q q q qq q q qq qq q q qq qq q qq qqqq q q q q q q q q qqq q q qq q q qq qq q q q q q q q q q q q qq q q q qqq q q q qq qq q q q q q q q qq q q q q q q qqq qq q qqq q q q qq q qq q q q q q q q qq q q q qq q q q q q qq q q q qqq q qq q qq q q q q qqq q q qq qq qq q q qq qq q qqq q q qq qq q q q qq qq qq q q q qqqq q q q q qq q qqqq q q qqq q q q q q qq q q qq q qq q q qq q q q qqqq q q q q qq q q q qq q q q q q q q qq q q qq q qq qq q qqqq qqq qqqqq qqqqq qqqqq q qq qq qqqqq qq q q q qq qq qq qqq q qq q q q q qq q q q q q q q qq q q q q qq qq qq q qq qq qq q q q qq qq q q q q q q qq q q q qq q qq q qq qq q q qqq q q q q qq q q q qqqq q q qq q q qqqqqq q q q q q q qq qqqq qqq q qq qqq q qq qq q qqq qq q q q qqq q qq qq q q qqq q qq q q qq q qq q q q qq q q q q q q q qq q q q q qq q q qq q q q q q qq q q q q qqqq qqq q q qq qq qq qq q q q q qqqqqq qqq q qq qqq q qq qqqqq q qqqq qq q q qqqq q qqq q qqq q q q q qq qq q q q qq qq q q q qq q q qq qqq qqq qq q q qqqqq q qq q qq q q q q qq q qqqqqqqqq qqqq qq qq q q qqqq qqqqqqqq qq q q q qq q qq q qq q q q q qq q qq qq q qqq qq q qqq q q q q q qq qq q q qqqqq q qqq q qq qqq qqq q q qq q q q qqq q q q q q q q qqq qq q q q q q qqq q q qq qq q qq q q q q q qq q q qqq q q q q qqq q q q q q q qqq q qq q qqqq q q qqqqqq qq qq qq q qqqqq qqq qqqq qqq qq qqqq qq qq q qq q qq qq qqqqqqqqqqqqqqqqqqq qqqq qqqqqqqqqqqqqqqqq qqqqqqqqqqqq q qqq q qqqq qqqq q q qqq qq q q q q q qq qqq qq q qqqq q q q q q q q qqqq q qq qq q q q q q qq q q qqq qq qq q qqq qq qq qq qqq q q qq q qqq qq qq qqq qq qq q q q qq q q q qq q q q qq qqqq qqqqqqqqqqq q qqqqqqq qqqqqq qqqqqq q qq qq qqqqq qqqqqqqqq qqqqq q q qq q qqq qqq qq q q qqqqqqqq qqqqqqq q q qq q qq qqq qqqq qq q qq q q q q q qqqq q q q q q q q q q q qqq qqqqqqqqqq qqqqqqqqqq qqqqqq qqqqqqqqqqqqqqqqqqqqqqq qqqq q qq qqq q qq q q q qqq qq qqqq qqqq q qqq qqq qq q q qqqqq qq q qqq qqqq qqq q qqq qq qqq qq qqq q q qqq q qqq q q qqqqqq q qqqq qqq qq q qqqq qq q qq qq qq q qq q q qq qq qqq qq qqqq q qq q q qq qq q q qqqqqqqqqqqqqqqq q qqqqqqq qqq qqq qq qqqq qq q qqqq qqq q qq qqq qq qq q q qqqqqqqqq qqq q q qqqqqqq qqqqq qqq qqqqqqqq qq qq q qqqq q qqqq q qqqqqq q q q qqqq qqqq q q qqq q qqqq qqq q qqq q q qq q q qqqqqq q q qqqqqqqqqqqqqqqqqqqq qqqqqqqqqqqqqqqqq qqqqqqqqqqqq qqqqqqqqqqqqqqq q q qq q qqqqqqqqqq qqqq qqq qqqqqqqqqqqq qq qq qq qqq qqqqq q qqqqqqqqq qqqqqq q q q qqq q qqqqqqqqq qqqqq qq qqqqqqqqqqqqqqq qq qq qq qq qqq q qqqqq qqq q qqqq q qqqq qqq q qqq qqq qqqqq q q qq q qq q q qq qq q qq q q q q q q qq qqq qqqqqq qqqqqqq qqqqq qqq qq q q q qqqq qq q q qq q q q q q qq qq q q q q q q q q qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqqqqqqqqqqqqqqqqqqqqqqq qq q q qqqqqqqqqqqqqqqqqqqqqqqq qqq qqqqqqqqqqqqqqqqq qqqq q qqqqqqqqqqqqq qqq q qq qqqqq qq q qqqq q qqqq qqqqqqqq qq q q q q q q q qqqq qq qq q qq q q q q q q qqqqq q qq q q qqqqqqqqqqqq qq q q q q qq q q q q q qqqqqq q q q qqq qqqqqq q qqqqqqqq qq q qq q qqqq q q qqqqqqqqqqqq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqqqqq qqq qqqqq 14 qqqqqqqqqqqqqqqqqqq qqqqqqqqqq qqqqqqqqqqqqqqqq qqq q qqqqqqqq qqqqq qq q qq q qq q qq q qqq qqqqq qqqq q qq q q q q qqq qq qqqqqqqqqqqqqq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqqqq q qqqq q q qqq q qqqqqqqqqqqq q qqq qqq qq qq q q q q qqqq qqqq qqqqqq qqqq qqqqqqqqqqq qqqqqqqqqqqqq qqqqqqqqq qqq q q qqq qqqqqqqqqqqqq qqqqqq qqqq qqqq q qqqqqq qqqqq qqqqq qq qqqqqq qq qqqq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqq qqq qq q qq qqqq qqq qq q q qqqq qq q q qqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqqqqqqqqq qqqqqq q qqq q qqq q q q qqqq q q qq q qq q q qqqqqq qq q qq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqqqqq qqqqq q qqqqqqqqqq q q q qqqq q q qqqqqqq qq qqq qq qqqqqqqqqqqqqqqqqqqq q q q qq qqqqqqq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqqq q qq q qq q q qq q qq qq qq qqq qqq q q q q q q q q qq q qq q qqqqq qqqqq qqqqqqqq q qqqqqq qqq qq q q q q qq qq q q qq q q q qqqqq qq q qq q q q q qqq q q q q q qq q q qq qq qqqqqqqqq qqqqqq q qq q q qq q q qq qqqqqqq qq q q qqq q q q q q q q q qq q q qq q q q q q qq q qqq q q q q qq qqqqqqqqqqqqq qqqqqqqq q q qqq qq qqq q q qq q qqqq qqqqq qq q q qqqqqqq qqqqqq qqq qqqqq qq qqq qqqqqqqqq q qq q q qq q q q qq qqqq q q q q q q q q q qq q q q qq q q q q q q q q qq q q q q qqqqqqqqq qqqq qqqqqq q qqqqqqqq qqqqqq qqqqqqqqqq qqq qqqqqqqq qq qq q q qqqqqq q q q q qqqq q qqq q qq qq q qq qqq q q q qq qqq q q q q q qq q q q q qqqqq q qq qqqq q qq q qqq qq qq qq qq q q q q q q q q q q q qq q q q q qq qq q 0 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 −2 0.2 −1 0.4 0 0.6 1 0.8 2 1.0 0.0 −2 0.2 −1 0.4 0 0.6 1 0.8 2 1.0 NAOi (n = 221) MOi (n = 223) NAOi (AIC=1817*) WEMOi (n = 200) MOi (AIC=1831*) 100 100 100 100 100 −2 −1 −0.5 0 0.5 1 2 2 1 0.5 0 −0.5 −1 −2 2 1 210 0.5 0 −0.5 −1 −2 140 200 200 130 130 190 190 180 180 50 50 120 170 170 110 50 Return period (years) 50 Return period (years) 50 160 160 150 150 100Return period (years) Return period (years) Return period (years) Return period (years) 140 25 25 25 25 25 120 80 110 100 70 10 10 90 90 10 10 10 60 80 70 5 5 50 5 5 5 60 40 50 2 2 40 2 2 2 30 30 1 1 1 1 1 50 100 150 200 250 300 50 −2 100 150 −1 200 0 250 1 300 2 350 50 −2 100 −1 150 0200 250 1 300 2 Intensity (mm day−1) Intensity (mm day−1) NAOi Intensity (mm day−1) MOiNon-stationary model: NAO (left), MO (center), WEMO (right) (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 36 / 52
  • 43. Results: events magnitude, effect on q100 NAO I 4800000 4600000 4400000 4200000 4000000 x times 1.25 2 3 4 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06Eect of NAO on the 100-years return period event: (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 37 / 52
  • 44. Results: events magnitude,effect on q100 MO II 4800000 4600000 4400000 4200000 4000000 x times 1.25 2 3 4 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06Eect of MO on the 100-years return period event (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 38 / 52
  • 45. Results: events magnitude, III on q100 WEMO effect 4800000 4600000 4400000 4200000 4000000 x times 1.25 2 3 4 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06Eect of WEMO on the 100-years return period event (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 39 / 52
  • 46. Results: events intensity NAO effect on q100 MO effect on q100 WEMO effect on q1004800000 4800000 48000004600000 4600000 46000004400000 4400000 44000004200000 4200000 42000004000000 4000000 4000000 x times x times x times 1.25 1.25 1.25 2 2 2 3 3 3 4 4 4 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 Eect of NAO, MO and WEMO on the 100-years return period event (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 40 / 52
  • 47. Results: events magnitude, winter NAO effect on q100 MO effect on q100 WEMO effect on q1004800000 4800000 48000004600000 4600000 46000004400000 4400000 44000004200000 4200000 42000004000000 4000000 4000000 x times x times x times 1.25 1.25 1.25 2 2 2 3 3 3 4 4 4 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 Eect of NAO, MO and WEMO on the 100-years return period event (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 41 / 52
  • 48. Results: events magnitude, spring NAO effect on q100 MO effect on q100 WEMO effect on q1004800000 4800000 48000004600000 4600000 46000004400000 4400000 44000004200000 4200000 42000004000000 4000000 4000000 x times x times x times 1.25 1.25 1.25 2 2 2 3 3 3 4 4 4 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 Eect of NAO, MO and WEMO on the 100-years return period event (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 42 / 52
  • 49. Results: events magnitude, autumn NAO effect on q100 MO effect on q100 WEMO effect on q1004800000 4800000 48000004600000 4600000 46000004400000 4400000 44000004200000 4200000 42000004000000 4000000 4000000 x times x times x times 1.25 1.25 1.25 2 2 2 3 3 3 4 4 4 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 Eect of NAO, MO and WEMO on the 100-years return period event (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 43 / 52
  • 50. Results: threshold independence, I Threshold (u = q0.9 = 23.5, n = 229) Stationary model (AIC=2766) Threshold (u = q0.95 = 36.1, n = 113) Stationary model (AIC=1875) Stationary model (AIC=994) 50 100 100 100 60 q q q 25 30 35 (years) 45 50 50 50 Return period (years) Return period (years) 50 q q q 40 25 25 25 Mean Excess Mean Excess q q q q q q Return period q q q 40 10 10 10 q q q q q q q q q q q q q q q q q q q q q q 5 5 5 qq 30 q q q q q q q q q qq q qq q q qq q q qq qq qq qq q q q q qq qq qq q q q qqq q q q 2 2 2 q q qq q q q q q 20 q qq qq q q qq q q q 20 q q q q q q q q q q q q qq q qq q q q q q q q qq qq qq q q q q q q 1 1 1 q q q q q q q q qq q qq q qqq q qqq qqq qq q q qq q q qq qq q q q q q qq q q q q q q qq q80 10 q q q q q q 50 20 100 30 40150 50 200 60 250 70 80 300 10 q q q q q 5020 30 100 40 15050 60 200 70 25080 q q 50 100 150 200 250 q q qq q qq q q q qq q q q q q q q q qq q q q q q q q q Intensity (mm day−1) u q q q q Intensity (mm day−1) u Intensity (mm day−1) q qq q q q q q q Intensity (mm) Intensity (mm) Intensity (mm) q Intensity (days) Intensity (days) Intensity (days) Quantile plots for rainfall intensity in Valencia, thresholds at u=q85, u=q90 and u=q95 (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 44 / 52
  • 51. Results: threshold independence, II Intensity, non−stationary model Intensity, non−stationary model Intensity, non−stationary model 100 100 100 100 100 100 100180 0 250 160 20 200 0 180 200 140 210 70 20 230 240 300160 190 190 160 0 21 170 140 19060 180 220 280 2 170 150190 180 50 50 50 50 50 50 50 120 180 170 0 160 0 200 210 170 0 160 15 140 0 18 17 130 110 160 24 150 150 190 100 120 60 180 100 140 1 220 200 140 25 25 25 25 25 25 25 0 130 120 0 17090 Return period (years) Return period (years) Return period (years) Return period (years) Return period (years) Return period (years) Return period (years) Return period (years) 130 12 150 100 14 130 18 0 120 150 50 80 110 110 130 110 100 80 0 70 160 70 100 40 120 11 130 90 10 10 10 10 10 10 10 90 140 90 6080 80 60 100 110 50 80 120 70 90 80 50 5 5 5 5 5 5 5 50 60 90 100 60 50 40 70 40 60 80 60 70 50 30 40 2 2 2 2 2 2 2 60 30 30 40 403020 30 20 40 1 1 1 1 1 1 1 −2−2 −1−1 00 11 22 −2−2−2 −1−1−1 000 111 222 −2−2 −1−1 00 11 22 NAOi (AIC=1817*) WEMOi (AIC=2476*) NAOi (AIC=1033) WEMOi (AIC=1569*) MOi (AIC=2609*) WEMOi (AIC=1831*) MOi (AIC=953*) Quantile plots for rainfall intensity in Valencia, thresholds at u=q85, u=q90 and u=q95 (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 45 / 52
  • 52. Results: threshold independence, III NAO effect on q100 MO effect on q100 WEMO effect on q1004800000 4800000 48000004600000 4600000 46000004400000 4400000 44000004200000 4200000 42000004000000 4000000 4000000 x times x times x times 1.25 1.25 1.25 2 2 2 3 3 3 4 4 4 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 0e+00 2e+05 4e+05 6e+05 8e+05 1e+06 Eect of WEMO in rainfall magnitude, thresholds at u=q85, u=q90 and u=q95 (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 46 / 52
  • 53. −0.2Projected evolution of NAOi, MOi and WEMOi 1950 1960 1970 1980 1990 2000 0.1 0.2 −0.4 −0.3 0.0 −0.1 0.4 0.1 0.2 0.3 MOi 0.2 NAOi 1950 1960 1970 1980 1990 2000 2000 2020 2040 2060 2080 2100 0.4 WEMOi 0.2 −0.1 MOi −0.2−0.30.0 1950 1960 1970 1980 1990 2000 2000 2020 2040 2060 2080 2100 0.4 0.2 WEMOi 0.0 −0.2 −0.4 2000 2020 2040 2060 2080 2100Time variation of NAOi, MOi and WEMOi in the 21th Century, INMCM3.0 model output, 48-months convolution(envelope of SRES A1b, A2 and B1 scenarios) (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 47 / 52
  • 54. Conclusions and future work I NSPOT analysis is good at capturing the relationship between extreme precipitation processes and atmospheric circulation indices. The results are promising for a variety of applications, including short-term warning systems and the statistical downscaling of GCM/RCM outputs. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 48 / 52
  • 55. Conclusions and future work II Clustering methods based on the series of covariates (and not on P). Other covariates: synoptic scale airow parameters (direction, strength, vorticity), specic humidity, etc. Multi-covariate analysis. Spatial model: take advantage of spatial dependence to reduce uncertainty. (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 49 / 52
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  • 58. Thank you!santiago.begueria@csic.es (santiago.begueria@csic.es) NSPOT with covariates Liberec, 17/02/2012 52 / 52