Abrupt changes in the Earth’s
climate system: opportunities
and challenges for changepoint detection
Claudie Beaulieu
Example: The Nile problem Annual discharge of the Nile River at Aswan
4500
Discharge (m3/s)
4000
3500
3000
2500
2000
1500
1000
1860
1880
1900
1920
Year
Cobb (1978)
1940
1960
1980
2 Outline
•  Abrupt change nomenclature •  Specific examples of applica8ons –  Ar8ficial climate shi9s -­‐ precipita8on –  Terrestrial ecosystems -­‐ land uptake of carbon dioxide –  Timing of paleoclimate transi8ons •  Discussion of challenges and opportuni8es 3 Types of abrupt changes
Abrupt change Ar8ficial shi9 Unforced Forced e.g. due to changes in the
measurement procedures
Red noise or bimodality e.g. North Atlantic Oscillation
Driver shi9 -­‐ response shi9 e.g. climate shift leads to
an ecosystem shift
Threshold e.g. increasing anthropogenic
pressure pushes the system
to cross a threshold
4 Driver – response relationship
The change in the response
is much larger than the
change in the forcing (IPCC,
2007).
Adapted from Andersen et al., 2008
5 Example: regime shifts in the
Pacific Ocean
Scheffer et al., 2001
6 Example: regime shifts in the
Pacific Ocean
“Red noise and regime shifts”
Rudnick and Davis, 2003
Scheffer et al., 2001
7 Example: Vegetation cover over the
Sahara Scheffer et al., 2001
8 Potential abrupt change under
anthropogenic forcing
Lenton et al., 2008
9 Example 1: Artificial shifts in
precipitation
Opportunity: improve data
underlying assessment of climate
and ecosystem change
Challenge: adapting statistical
techniques to specific problems
Observed trends
Intergovernmental Panel on Climate Change, 2007 11 Observed trends
Problem with instrumental 1me series: Changes in the measurement procedures Intergovernmental Panel on Climate Change, 2007 12 Problems with observations
Inhomogeneous
Closer to the ’true’ precipitation
1600
Ptot (mm)
1400
1200
1000
800
600
1920
1940
1960
Year
1980
Photo courtesy of Lucie Vincent, Environment Canada 2000
13 Homogenization techniques
Change point methods extended to detect ar1ficial shi:s only Restric1ve techniques: •  At most one shi9, •  Normality, independence, … Large number of techniques available. Choice depends on: •  Network density (possible to find neighbour series?) •  Metadata (available?) •  Variable (temperature or precipita8on) •  Sta8s8cal proper8es (normality, autocorrela8on, …) Compara1ve studies: •  Temperature: Ducré-­‐Robitaille et al. (2003), Menne & Williams (2005), DeGaetano (2006), Reeves et al. (2007) •  Precipita8on Artificial shifts in precipitation series
Comparison study to iden1fy the most promising methods. Total annual precipita1on series were generated (100-­‐year long) Types of series generated •  No shi9 •  With a single shi9 in the mean •  With mul8ple shi9s in the mean 1800
•  Three neighbour series 1600
Ptot (mm)
1400
1200
1000
800
600
400
0
20
40
60
Position (year)
80
100
*9HC@>IJ9
Results: series with a single shift
0()*
07+,
07.'
078,
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415'
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012*
+,-/
+,-.
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Well-­‐posi)oned shi.: posi)on detected ± 2 years far from the real posi)on !"
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Results: series with a single shift
p=prior probability of no-­‐change p=0.01
p=0.5
50
0
3
2.5
2
1.5
1
Magnitude 0.5
85
6575
55
3545
1525 Position
50
0
3
2.5
2
1.5
1
Magnitude 0.5
0
Beaulieu et al., 2010 100
Shifts (%)
100
Shifts (%)
Shifts (%)
100
p=0.99
85
6575
55
3545
1525 Position
50
100
50
0
3
2.5
2
1.5
1
Magnitude 0.5
85
6575
55
3545
1525 Position
Example 2: Abrupt change in
the terrestrial carbon cycle
Opportunity: gain better
understanding of the underlying
processes
Challenge: distinguish different
types of change
Carbon cycle
19 Carbon sources and sinks 1959-2010
Sources
Sinks
Land use 1.2 Pg C/yr Fossil fuel 5.6 Pg C/yr Atmospheric growth rate 3 Pg C/yr Ocean and land sink 3.7 Pg C/yr Between 1959 and 2010, 45% of each year’s CO2
emissions remained in the atmosphere on
average; the rest was absorbed by carbon sinks
on land and in the oceans.
Le Quéré et al., 2009; Ballantyne et al. 2012 20 Net land uptake
Net land uptake = fossil fuel emissions -­‐ CO2 atmospheric growth rate -­‐ ocean uptake )
(
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!
$
Fossil fuel emissions 4
2
CO2 atmospheric growth rate 1970
1980
1990
Year
2000
3
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6
0
1960
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Ocean uptake (Pg C/yr)
./012341567-8
'
agr (Pg C/yr)
8
2
1
0
1960
Le Quéré et al. (2007)
Lovenduski et al. (2008)
Rodgers et al. (2008)
Wetzel et al. (2005)
1970
1980
1990
Year
2000
21 Land sink 1959-2010
Sarmiento et al. (2010) analysis suggests an increase of approximately 0.9 Pg C/yr around 1988-­‐1989 Sarmiento et al., 2010 22 Models considered
Shift in the mean
60
40
40
40
20
20
20
0
0
0
−20
−20
−20
−40
20 30 40 50
Time
Shift in the mean and variance
60
10
10
20 30 40
Time
Linear trend
−40
50
60
40
40
40
20
20
20
Y
60
Y
Y
Y
60
−40
0
0
0
−20
−20
−20
−40
20 30 40 50
Time
Shift in the intercept and trend
60
10
40
Y
Shift in the variance
60
Y
Y
Constant mean
20
0
−20
−40
10
20 30
Time
40
50
−40
10
20 30
Time
40
50
−40
10
20 30 40
Time
Shift in the intercept
50
10
50
20 30
Time
40
We use an informa)on criterion to iden)fy the )ming of the change and to discriminate between the models with or without changes. We can also integrate covariate effects and/or autocorrela)on in the model (Beaulieu et al., 2012a). 23 Best models
Mean net land uptake Atmospheric growth rate Beaulieu et al. (2012b) 24 Estimate of the shift
Mean net land uptake Shi. in 1988 1.2 Pg C/yr Shi. in 1988 0.9 Pg C/yr Beaulieu et al. (2012b) 25 Regions where the productivity
increased
NPP differences between 1990-­‐2008 and 1982-­‐1989 a c b Only significant differences are shown (t-test, 5% critical level).
26 Example 3: Timing of major
transitions in paleoclimate
time series
Opportunity: better understand
the past
Challenge: additional layer of
uncertainty using proxy data
Change-points in paleo-proxy records
Beaulieu et al. (2012a; Rodgers et al., 2011) 28 Discussion on opportunities
and challenges
Opportunities
•  Remove ar8ficial signals from data underlying assessment of global environmental change •  Detect, characterize and monitor shi9s in climate and ecosystem 8me series •  Contribute to beher understanding of the mechanisms leading to environmental shi9s 30 Potential for monitoring climate
For monitoring, we need to detect the shi: soon a:er it occurred. Simula1on study to inves1gate how long it takes to detect a shi: a:er it occurred. Synthe1c series •  start in 1960 (lots of instrumental series of observa8ons that started around this 8me) •  shi9 in 1990 (evidence for large scale-­‐shi9 around 1990 in the carbon cycle, in cloud and aerosols, intensifica8on of the hydrological cycle over land) Search for a shi: and decide whether a model with a shi: is beRer using two different decision rules: SIC( p) < SIC (n)
SIC( p) = min {SIC(k), k = 2,..., n − 2}
SIC( p) + c α < SIC (n)
Beaulieu et al. (2012a) Challenges
•  Extending exis8ng techniques to be less restric8ve (e.g. autocorrela8on, distribu8on) •  Tailor new methods to environmental data and global change problems •  Account for addi8onal layer of uncertainty of the data sets and provide uncertainty for the 8ming of the change 33 Distinguish between different types
of changes
Evidence of piecewise linear and step-­‐like changes in global temperature •  need sta8s8cs to iden8fy, quan8fy and understand temporal evolu8on Seidel & Lanzante (2004) 34 Detecting shifts in extremes
Extremes •  Heavy rainfall •  Floods •  Droughts •  Heat waves Take shi:s into account when assessing the risk of future extremes (e.g. Villarini et al., 2009) Zhao & Chu (2010) 35 Detecting a threshold
Toms and Lesperance, 2003
36 Multivariate change-point detection
Beaugrand et al., 2008
37 Uncertainty
IPCC, 2007 38 Communication
•  Choosing an appropriate sta8s8cal methodology and comparing the op8ons is challenging •  Gaining a good understanding of the phenomena to do a meaningful analysis 39 Acknowledgements
•  Jorge L. Sarmiento et al., Atmospheric and Oceanic Sciences, Princeton University •  Wolfgang Buermann, University of Leeds •  Jie Chen, University of Missouri •  Taha B.M.J. Ouarda (University of Quebec and Masdar MIT) and Ousmane Seidou (University of Ohawa) 40