statistical analysis of abrupt climate changes * instituto de hidráulica ambiental, ihcantabria,...
TRANSCRIPT
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?)
CLIVAR-ES, Madrid, Feb-2009
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
CLIVAR-ES, Madrid, Feb-2009
The basic idea..METHODOLOGY
Poisson distribution Pareto distribution
FREQUENCY INTENSITY
(Rare events process) (Abrupt changes require a minimum magnitude)
CLIVAR-ES, Madrid, Feb-2009
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
CLIVAR-ES, Madrid, Feb-2009
Stationary process Non-Stationary process
The probability that a ACC happens, of a magnitude, varies through time
METHODOLOGY
CLIVAR-ES, Madrid, Feb-2009
METHODOLOGY
Identifying ACC events..
CLIVAR-ES, Madrid, Feb-2009
2T
2T2T2T
METHODOLOGY
Identifying ACC events..
CLIVAR-ES, Madrid, Feb-2009
METHODOLOGY
Poisson distribution Pareto distribution
FREQUENCY INTENSITY
Statistical Model
1/
( ; ) 1 1x
F x
0
( ; )!
( )
x
T
p t ex
t dt
CLIVAR-ES, Madrid, Feb-2009
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
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
CLIVAR-ES, Madrid, Feb-2009
METHODOLOGY
• Isolation• Eccentricity• Obliquity• Precession
Potential covariates
CLIVAR-ES, Madrid, Feb-2009
METHODOLOGY
Potential covariates
CLIVAR-ES, Madrid, Feb-2009
METHODOLOGY
0
0 1
( ; ) ( )
2 cos
orbitalparameter f orbital parameter
tT
Potential covariates
CLIVAR-ES, Madrid, Feb-2009
METHODOLOGY
0
0 1
( ; ) ( ) ( ) ( ) ( )
2 cos
I E O Pparameter I t E t O t P t
tT
Potential covariates
M1
M2
M3
(5 parámetros)
To obtain the simplest possible model (following the principle of parsimony) that fits the data sufficiently well:
STEPWISE PROCEDURE
CLIVAR-ES, Madrid, Feb-2009
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
CLIVAR-ES, Madrid, Feb-2009
APPLICATION 1
Data
SST time series in Alborán Sea
Martrat et al., 2004
CLIVAR-ES, Madrid, Feb-2009
APPLICATION 1
Data
ACC warm events
CLIVAR-ES, Madrid, Feb-2009
APPLICATION 1
Data
ACC cold events
CLIVAR-ES, Madrid, Feb-2009
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
CLIVAR-ES, Madrid, Feb-2009
APPLICATION 1
Results
FREQUENCY MODEL
CLIVAR-ES, Madrid, Feb-2009
APPLICATION 1
Results
FREQUENCY MODEL
Warming events:
Cooling events:
Isolation (0ºN)
Slope of Isolation (45ºN) + Obliquity + Eccentricity
CLIVAR-ES, Madrid, Feb-2009
APPLICATION 1
Results
INTENSITY MODEL
Main covariate:
Eccentricity(- gradient)
Mean value
90% quantile
CLIVAR-ES, Madrid, Feb-2009
APPLICATION 2
Data
• (~atmosferic temperature) time series in Greenland18O
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), …
CLIVAR-ES, Madrid, Feb-2009
APPLICATION 2
A possible periodic component ?
In spite of the differences, a periodic component should be detected both proxies
CLIVAR-ES, Madrid, Feb-2009
APPLICATION 2
A possible periodic component ?
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
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?
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.