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STATISTICAL ANALYSIS OF ABRUPT CLIMATE CHANGES. Melisa Menéndez*; I. J. Losada; F. J. Méndez; J. Grimalt; M. Canals; B. Martrat. * Instituto de Hidráulica Ambiental, IHCantabria, Universidad de Cantabria. future. ?. t. Frequency (a). ?. t. Intensity (b). We are interested on.
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STATISTICAL ANALYSIS OF ABRUPT CLIMATE CHANGES Melisa Menéndez*; I. J. Losada; F. J. Méndez; J. Grimalt; M. Canals; B. Martrat. * Instituto de Hidráulica Ambiental, IHCantabria, Universidad de Cantabria
future ? t Frequency (a) ? t Intensity (b) We are interested on.. Studying the Abrupt Climate Changes (ACC) events in the past • Modeling the occurrence of ACC (Frequency) • Modeling the abrupt Temperature changes (Intensity) • Quantifying the influence of possible forcings • Analyze time variations of interest (cycles?)
METHODOLOGY Randomvariable, X Stochasticprocess • The basic idea.. Sample Tª time (bp) Cumulative distribution function ↔ Probability density function cdf pdf
METHODOLOGY • The basic idea.. INTENSITY FREQUENCY Pareto distribution Poisson distribution (Abrupt changes require a minimum magnitude) (Rare events process)
METHODOLOGY • But…..Is it a stationary process? Number of ACC ACC has characteristics that change systematically through the time
METHODOLOGY Non-Stationary process Stationary process The probability that a ACC happens, of a magnitude, varies through time
METHODOLOGY • Identifying ACC events..
METHODOLOGY • Identifying ACC events..
METHODOLOGY • Statistical Model INTENSITY FREQUENCY Pareto distribution Poisson distribution
METHODOLOGY • Statistical Model FREQUENCY Poisson distribution Occurrence rate varies through time INTENSITY Pareto distribution Magnitude of Tª change varies through time
METHODOLOGY • Potential covariates 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 • Isolation • Eccentricity • Obliquity • Precession
METHODOLOGY • Potential covariates
METHODOLOGY • Potential covariates
METHODOLOGY • Potential covariates To obtain the simplest possible model (following the principle of parsimony) that fits the data sufficiently well: STEPWISE PROCEDURE M2 M1 (5 parámetros) M3
METHODOLOGY • Statistical Model: Fitness Maximum likelihood estimation To study statistical significance of covariates: profile likelihood technique
APPLICATION 1 • Data SST time series in Alborán Sea Martrat et al., 2004
APPLICATION 1 • Data ACC warm events
APPLICATION 1 • Data ACC cold events
APPLICATION 1 • Results FREQUENCY MODEL Main covariate: • Isolation
APPLICATION 1 • Results FREQUENCY MODEL
APPLICATION 1 • Results FREQUENCY MODEL Warming events: • Isolation (0ºN) Cooling events: • Slope of Isolation (45ºN) • + Obliquity • + Eccentricity
APPLICATION 1 • Results INTENSITY MODEL Main covariate: • Eccentricity (- gradient) Mean value 90% quantile
APPLICATION 2 • Data • (~atmosferic temperature) time series in Greenland
APPLICATION 2 • A possible periodic component ? Schulz, M. (2002); Rahmstorf, S (2003); Ditlevsen et al., (2005, 2007); Rohling et al., (2003), … Does it exist the 1470 cycle? ACC warm events
APPLICATION 2 • A possible periodic component ? In spite of the differences, a periodic component should be detected both proxies
APPLICATION 2 • A possible periodic component ?
Conclusions • 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. • Further works • Other forcings /covariates ??? • Other proxies with high resolution?
STATISTICAL ANALYSIS OF ABRUPT CLIMATE CHANGES Melisa Menéndez*; I. J. Losada; F. J. Méndez; J. Grimalt; M. Canals; B. Martrat. * Instituto de Hidráulica Ambiental, IHCantabria, Universidad de Cantabria