1. STATISTICAL ANALYSIS OF ABRUPT CLIMATE CHANGES * Instituto de Hidráulica Ambiental, IHCantabria, Universidad de Cantabria Melisa Menéndez*; I. J. Losada; F. J. Méndez; J. Grimalt; M. Canals; B. Martrat.

2. CLIVAR-ES, Madrid, Feb-2009 We are interested on..  Modeling the occurrence of ACC (Frequency)  Modeling the abrupt Temperature changes (Intensity) Studying the Abrupt Climate Changes (ACC) events in the past t t Frequency (a) Intensity (b) future ? ? Quantifying the influence of possible forcings Analyze time variations of interest (cycles?)

3. CLIVAR-ES, Madrid, Feb-2009 METHODOLOGY  The basic idea.. time (bp) Sample Cumulative distribution function ↔ Probability density function cdf pdf Random variable, X Stochastic process Tª

4. CLIVAR-ES, Madrid, Feb-2009  The basic idea.. METHODOLOGY Poisson distribution Pareto distribution FREQUENCY INTENSITY (Rare events process) (Abrupt changes require a minimum magnitude)

5. CLIVAR-ES, Madrid, Feb-2009  But….. Is it a stationary process? Number of ACC ACC has characteristics that change systematically through the time METHODOLOGY

6. CLIVAR-ES, Madrid, Feb-2009 Stationary process Non-Stationary process The probability that a ACC happens, of a magnitude, varies through time METHODOLOGY

7. CLIVAR-ES, Madrid, Feb-2009 Analysis of time series Statistical Model | Non-stationary theory | select best model / Fit | Inference / bias | Model checking Climatic information Climatic variability METHODOLOGY 1.Identifying ACC events 2.Probability distribution 3.Time-dependent parameters 4.Potential covariates 5.Regression model 6.Fitness 7.Select best model 8.Model cheking

8. CLIVAR-ES, Madrid, Feb-2009 METHODOLOGY  Identifying ACC events..

9. CLIVAR-ES, Madrid, Feb-2009 METHODOLOGY  Identifying ACC events..

10. CLIVAR-ES, Madrid, Feb-2009 METHODOLOGY  Identifying ACC events..

11. CLIVAR-ES, Madrid, Feb-2009 METHODOLOGY  Identifying ACC events..

12. CLIVAR-ES, Madrid, Feb-2009 METHODOLOGY Poisson distribution Pareto distribution FREQUENCY INTENSITY  Statistical Model

13. CLIVAR-ES, Madrid, Feb-2009 METHODOLOGY  Statistical Model Poisson distribution Pareto distribution FREQUENCY Occurrence rate varies through time Magnitude of Tª change varies through time INTENSITY

14. CLIVAR-ES, Madrid, Feb-2009 Climatic Theory of Milankovitch Milankovitch cycles are the collective effect of changes in the Earth's movements upon its climate This theory explains climatic changes by orbital parameters: axial tilt METHODOLOGY  Potential covariates

15. CLIVAR-ES, Madrid, Feb-2009 METHODOLOGY Isolation Eccentricity Obliquity Precession  Potential covariates

16. CLIVAR-ES, Madrid, Feb-2009 METHODOLOGY  Potential covariates

17. CLIVAR-ES, Madrid, Feb-2009 METHODOLOGY  Potential covariates

18. CLIVAR-ES, Madrid, Feb-2009 METHODOLOGY  Potential covariates M1M1 M2M2 M3M3 (5 parámetros) To obtain the simplest possible model (following the principle of parsimony) that fits the data sufficiently well: STEPWISE PROCEDURE

19. CLIVAR-ES, Madrid, Feb-2009 Maximum likelihood estimation To study statistical significance of covariates: profile likelihood technique METHODOLOGY  Statistical Model: Fitness

20. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 1  Data SST time series in Alborán Sea Martrat et al., 2004

21. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 1  Data ACC warm events

22. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 1  Data ACC cold events

23. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 1  Results FREQUENCY MODEL Main covariate:  Isolation

24. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 1  Results FREQUENCY MODEL

25. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 1  Results FREQUENCY MODEL Warming events: Cooling events:  Isolation (0ºN)  Slope of Isolation (45ºN)  + Obliquity  + Eccentricity

26. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 1  Results INTENSITY MODEL Main covariate:  Eccentricity (- gradient) Mean value 90% quantile

27. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 2  Data (~atmosferic temperature) time series in Greenland

28. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 2  A possible periodic component ? Does it exist the 1470 cycle? ACC warm events Schulz, M. (2002) ; Rahmstorf, S (2003); Ditlevsen et al., (2005, 2007); Rohling et al., (2003), …

29. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 2  A possible periodic component ? In spite of the differences, a periodic component should be detected both proxies

30. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 2  A possible periodic component ?

31. CLIVAR-ES, Madrid, Feb-2009 APPLICATION 2  A possible periodic component ? profile likelihood technique

32. CLIVAR-ES, Madrid, Feb-2009  Conclusions  Further works Los modelos estadísticos se han aplicado satisfactoriamente para el estudio de la influencia de forzamientos externos y la detección de periodicidades en los ACC. Los resultados obtenidos indican la influencia de la Insolación terrestre en los ACC ocurridos en el pasado, así como una relación de su señal con la latitud en función de si el ACC es un calentamiento/enfriamiento. El estudio realizado permite identificar cuantitativamente la influencia de los parámetros orbitales en los ACC. Se ha detectado la presencia de una periodicidad en torno a los 1500 ±200 años en los registros obtenidos de testigos de hielo en Groenlandia. Other forcings /covariates ??? Other proxies with high resolution?

33. STATISTICAL ANALYSIS OF ABRUPT CLIMATE CHANGES * Instituto de Hidráulica Ambiental, IHCantabria, Universidad de Cantabria Melisa Menéndez*; I. J. Losada; F. J. Méndez; J. Grimalt; M. Canals; B. Martrat.