nansen environmental and remote sensing center methods for diagnosing extreme climate events in...

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


Outline

• What are extremes in climate?• Short info about R and RCLIM• Methods for looking at extremes in

gridded datasets• Future development• Conclusions


Climate extremes


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


Examples of wet and windy extremes

Extra-tropical cyclone

Hurricane

Polar low

Extra-tropical cyclone

Convective severe storm


Examples of dry and hot extremesDrought

Wild fire

Dust storm

Dust storm


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)”


Future changes in extremes?

IPCC 2001: Possible scenarios of extremes


R and RCLIM


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


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.


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/


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


Statistical methods


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)


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


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)


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


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


Example: Central England Temperature

n = 3082 values

Min = -3.1C Max = 19.7C

90th quantile: 15.6C


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


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


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


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


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


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


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


-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


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!)


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


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


-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


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!


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


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]


Thank you for your attention!

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