statistical analysis of abrupt climate changes * instituto de hidráulica ambiental, ihcantabria,...

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.

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?)


METHODOLOGY

The basic idea..

time (bp)

ª, Tti

Sample

Cumulative distribution function ↔ Probability density functioncdf pdf

( ) PrF x X x ( )dF

f xdx

Random variable, X

Stochastic process

Tª


The basic idea..METHODOLOGY

Poisson distribution Pareto distribution

FREQUENCY INTENSITY

(Rare events process) (Abrupt changes require a minimum magnitude)


But…..Is it a stationary process?

Núm

ero

de C

am

bio

s a

bru

pto

sN

umb

er o

f A

CC

ACC has characteristics that change systematically through the time

METHODOLOGY


Stationary process Non-Stationary process

The probability that a ACC happens, of a magnitude, varies through time

METHODOLOGY


METHODOLOGY

Identifying ACC events..


2T

2T2T2T

METHODOLOGY

Identifying ACC events..


METHODOLOGY

Poisson distribution Pareto distribution

FREQUENCY INTENSITY

Statistical Model

1/

( ; ) 1 1x

F x

0

( ; )!

( )

x

T

p t ex

t dt


METHODOLOGY

Statistical Model

Poisson distribution

Pareto distribution

FREQUENCY

covariatetimef

methrough ticte

)(

( )

cte through time

f time covariate

Occurrence rate varies through time

Magnitude of Tª change varies through time

INTENSITY


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


METHODOLOGY

• Isolation• Eccentricity• Obliquity• Precession



METHODOLOGY



METHODOLOGY

0

0 1

( ; ) ( )

2 cos

orbitalparameter f orbital parameter

tT



METHODOLOGY

0

0 1

( ; ) ( ) ( ) ( ) ( )

2 cos

I E O Pparameter I t E t O t P t

tT


M1

M2

M3

(5 parámetros)

To obtain the simplest possible model (following the principle of parsimony) that fits the data sufficiently well:

STEPWISE PROCEDURE


0

1

( ; ) ( ) log ( )Nt N

k i iit

t t dt t

Maximum likelihood estimation

To study statistical significance of covariates:profile likelihood technique

21 1 0 0 ,1

1( ) ( )

2 kM M

METHODOLOGY

Statistical Model: Fitness


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

Gdte Eccen Oblic Prece Inso

Warming 70.1% 45.6% 78.4% 91.3%

Cooling 57.2% 65% 38.9% 78.82%

Eccen Obliq Prece Grdte Inso


APPLICATION 1

Results

FREQUENCY MODEL


APPLICATION 1

Results

FREQUENCY MODEL

Warming events:

Cooling events:

Isolation (0ºN)

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 Greenland18O


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), …


APPLICATION 2


In spite of the differences, a periodic component should be detected both proxies


APPLICATION 2


NGRIP

α0

SIN COVARIABLE -63.7271 0.257

α0 α1 TCiclo 1470 con desfase 21.02 -63.2034 0.257 -0.069 3.734

α0 α1 TCiclo 1800 con desfase 68.63 -63.2196 0.2564 0.0727 3.6553

α0 α1 T ρCiclo 1000-2000 con desfase 93.87 -60.0287 0.256 0.189 1.392 3.8863

parámetrossignificancia(%) ( ; )kt

GISP2

α0

SIN COVARIABLE -44.5481 0.261

α0 α1 ρCiclo 1470 con desfase 99.6376 -38.928 0.252 0.241 0.875

α0 α1 ρCiclo 1800 con desfase 42.3223 -43.9978 0.2601 -0.0917 0.8521

α0 α1 T ρCiclo 1000-2000 con desfase 99.5801 -37.9309 0.2612 0.2586 1.4622 -0.1195

parámetrossignificancia(%) ( ; )kt


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?

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.

statistical analysis of abrupt climate changes * instituto de hidráulica ambiental, ihcantabria,...

Documents

cooling events

possible periodic component

acc warm eventsschulz

periodicidades en los

simplest possible model

climatic changes

quantile data

collective effect of