nansen environmental and remote sensing center methods for diagnosing extreme climate events in...
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Nansen Environmental andRemote Sensing Center
Methods for diagnosing extreme climate events in
gridded data sets
D. J. Steinskog
D. B. Stephenson, C. A. S. Coelho and C. A. T. Ferro
Mines Paris, Fontainebleau, 20 March 2007
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Outline
• What are extremes in climate?• Short info about R and RCLIM• Methods for looking at extremes in
gridded datasets• Future development• Conclusions
Nansen Environmental andRemote Sensing Center
Climate extremes
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What is an extreme in meteorology?
• Large meteorological values– Maximum value (i.e. a local extremum)– Exceedance above a high threshold– Record breaker (threshold=max of past values)
• Rare event (e.g. less than 1 in 100 years – p=0.01)
• Large losses (severe or high-impact)(e.g. $200 billion if hurricane hits Miami)risk = p(hazard) x vulnerability x exposure
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Examples of wet and windy extremes
Extra-tropical cyclone
Hurricane
Polar low
Extra-tropical cyclone
Convective severe storm
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Examples of dry and hot extremesDrought
Wild fire
Dust storm
Dust storm
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IPCC 2001 definitionsSimple extremes:
“individual local weather variables exceeding critical levels on a continuous scale”
Complex extremes:“severe weather associated with particular climatic phenomena, often requiringa critical combination of variables”
Extreme weather event:“An extreme weather event is an event that is rare within its statistical referencedistribution at a particular place. Definitions of "rare" vary, but an extremeweather event would normally be as rare or rarer than the 10th or 90th percentile.”
Extreme climate event:“an average of a number of weather events over acertain period of time which is itself extreme (e.g.rainfall over a season)”
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Future changes in extremes?
IPCC 2001: Possible scenarios of extremes
Nansen Environmental andRemote Sensing Center
R and RCLIM
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R – Short intro
• RCLIM make use of R, a powerful statistical tool.
• R is freely available, and can be used on most computer platforms
• It is a huge community working with and on R.
• R can be downloaded from www.r-project.org
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RCLIM-initiative
• Part of Workpackage 4.3 ENSEMBLES: Understanding Extreme Weather and Climate Events
• Progress:– Spring 2005: Initiative started– March 2006: Delivery finished and
methods made public– Future: More methods to be included,
especially for daily datasets.
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RCLIM-initiative• Main motivation
– Climate analysis requires increasingly good statistical analysis tools.
• Aims– Develop statistical methods and write user
friendly functions in the R language for describing and exploring weather and climate extremes in gridded datasets, making efficient use of the already existing packages.
• Webpage– http://www.met.reading.ac.uk/cag/rclim/
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RCLIM-initiative• The RCLIM initiative will develop functions
for: – Reading and writing netcdf gridded datasets – Exploratory climate analysis in gridded datasets – Climate analysis of extremes in gridded datasets – Animating and plotting climate analysis of
gridded datasets
• Team: – David Stephenson, Caio Coelho, Chris Ferro and
Dag Johan Steinskog
Nansen Environmental andRemote Sensing Center
Statistical methods
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European heat wave 2003Estimated total mortality: 35000-50000
Effects on crops, both negative and positive
This extreme wheather was caused by an anti-cyclone firmly anchored over the western European land mass holding back the rain-bearing depressions that usually enter thecontinent from the Atlantic ocean. This situation was exceptional in the extended length of time (over 20 days) during which it conveyed very hot dry air up from south of the Mediterranean.
2003 event can be used as an analog of future summers in coming decades (Beniston, GRL 2004)
It is very likely (confidence level >90%) that human influence has at least doubled the risk of a heatwave exceeding this threshold magnitude (Stott et.al., Nature 2004)
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Data used in this presentation
• Monthly mean gridded surface temperature (HadCRUT2v)
• 5 degree resolution• January 1870 to December 2005• Summer months only: June July August• Grid points with >50% missing values and
SH are omitted.– Special focus on the 2003 summer heat wave
in Europe
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Mean temperature
-150 -100 -50 0 50 100 1500
20
40
60
80
a) Mean temperature
0 5 10 15 20 25 30 35Celsius
Central Europe(12.5ºE, 47.5ºN)
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Standard Deviation
-150 -100 -50 0 50 100 150
02
04
06
08
0
b) Standard deviation
0 0.5 1 1.5 2 2.5 3 3.5 4Celsius
-150 -100 -50 0 50 100 150
02
04
06
08
0
b) Standard deviation
0 0.5 1 1.5 2 2.5 3 3.5 4Celsius
Standard Deviation
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For sufficiently large thresholds, the distributionof values above a sufficiently large threshold u
approximates the Generalized Pareto Distribution (GPD):
Model for tails: peaks-over-threshold
1
Pr( | ) 1 ( ) 1x u
X x X u F x
Shape = -0.4 – upper cutoff
Shape = 0.0 – exponential tail
Shape = 10 – power law tail
Probability density function
(1 ) /
1 1/
0 ( ) ~ 0 when /
0 ( ) ~
>0 ( ) ~
x
f x x u
f x e
xf x
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Example: Central England Temperature
n = 3082 values
Min = -3.1C Max = 19.7C
90th quantile: 15.6C
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Location parameter: u=15.6C
Maximum likelihood estimates:Scale parameter: 1.38 +/- 0.09CShape parameter: -0.30 +/- 0.04C
Upper limit estimate:
GPD fit to values above 15.6C
1
1)|Pr(
ux
uXxX
Cu 3.20
Nansen Environmental andRemote Sensing Center
1870-2005 time series of summer (June-July-August) monthly mean temperatures for a grid point in
Central Europe (12.5ºE, 47.5ºN)
= 15.2ºC
75th quantile (uy,m = 16.2ºC) 2003 exceedance
Excess (Ty,m – uy,m)
Long term trend (Ly,m) JJAT
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Time varying threshold
year
Tem
pera
ture
(Cel
sius
)
2001 2002 2003 2004 2005 2006
-50
510
1520 a)
Year
T-u
(Cel
sius
)
1880 1900 1920 1940 1960 1980 2000
-4-2
02
JJA pts & trend+seasonal terms Excesses
Flexible approach that gives exceedances 25% of months
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Time mean of 75% threshold
-150 -100 -50 0 50 100 150
02
04
06
08
0
b) Mean threshold
0 5 10 15 20 25 30 35 40Celsius
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Mean of the excesses
-150 -100 -50 0 50 100 1500
20
40
60
80
a) Mean of excesses
0 0.5 1 1.5 2 2.5Celsius
( | )1
E X u X u
Large over extra-tropical land regions
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GPD scale parameter estimate
-150 -100 -50 0 50 100 150
02
04
06
08
0
a) Scale parameter
0 0.5 1 1.5 2 2.5
1
1)|Pr(
ux
uXxX
Large over extra-tropical land regions
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GPD shape parameter estimate
Generally negative finite upper temperature limit
-150 -100 -50 0 50 100 150
02
04
06
08
0
b) Shape parameter
-0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9
1
1)|Pr(
ux
uXxX
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-150 -100 -50 0 50 100 150
02
04
06
08
0c) Upper bound of excesses
0 2 4 6 8 60 10000Celsius
Upper limit for excesses
Largest over high-latitude land regions
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Return periods for August 2003 event
-150 -100 -50 0 50 100 150
02
04
06
08
0
a) August 2003: Excesses above 75% threshold
0 1 2 3 4Celsius
-150 -100 -50 0 50 100 150
02
04
06
08
0
b) August 2003: Return period
1 5 10 50 150 500years
Central Europe return period of 133 years (c.f. Schar et al 46000 years!)
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The role of large-scale modes
-150 -100 -50 0 50 100 150
02
04
06
08
0
b) Scale ENSO covariate parameter
-1.3 -0.9 -0.5 -0.1 0.3 0.5 0.7 0.9 1.1 1.3
1̂
1
0 1 0
Pr( | ) 1
log
x uX x X u
y
ENSO effect on temperature extremes in NH
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Teleconnections between extremes
14 16 18 20
17
18
19
20
21
Central Europe temperature(Celsius)
West
Nort
h A
tlantic t
em
pera
ture
(Cels
ius)
a)
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Central Europe temperarure empirical probability
West
Nort
h A
tlantic t
em
pera
ture
em
piric
al pro
babili
ty
b)
14 16 18 20
14
15
16
17
18
19
20
Central Europe temperature(Celsius)
West
Russia
tem
pera
ture
(Cels
ius)
c)
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Central Europe temperarure empirical probability
West
Russia
tem
pera
ture
em
piric
al pro
babili
ty
d)
Coles et al., Extremes, (1999)
2log Pr( )1
log Pr(( ) & ( ))
Y u
X u Y u
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-150 -100 -50 0 50 100 150
02
04
06
08
0
b) Chi bar (75th quantile) Central Europe
-0.4 -0.1 0.1 0.4 0.7 1
1-point association map for extreme events
Coles et al., Extremes, (1999)
2log Pr( )1
log Pr(( ) & ( ))
Y u
X u Y u
association with extremes in subtropical Atlantic
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Future development of RCLIM and methods
• Methods for data with high temporal correlation will be introduced (e.g. daily dataset)
• Quantile regression to estimate the thresholds?
• Improve the plotting procedure – filled contours and projections
• Feedback on other methods that could be included is wanted!
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Conclusions• Huge potential of doing extremes on
gridded datasets• Simple extremes can be analysed using
peaks-over-threshold methods• Extremes do not have a unique definition• Future work include testing the methods
on daily datasets and develop new methods for data with high autocorrelation with special focus on Arctic region
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Reference
Coelho, C. A. S., C. A. T. Ferro, D. B. Stephenson and D. J. Steinskog; Exploratory tools for the analysis of extreme weather and climate events in gridded datasets, Submitted to Journal of Climate
Contact info: David Stephenson, [email protected]
Dag Johan Steinskog, [email protected]
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Thank you for your attention!