Group 2

E treme

hot spells

Mari JonesChristiana PhotiadouDavid KeelingsCandida DewesMerce Castella

2

Motivation

• Examine extreme hot temperatures in Europe and their drivers:– Blocking Index– North Atlantic Oscillation– El Niño-Southern Oscillation (BEST index)

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Russia July 2010

http://earthobservatory.nasa.gov/IOTD/view.php?id=47880

4

Data Sets

Barcelona: 1926-2010Oslo: 1937-2010Oxford: 1853-2010Moscow: 1949-2010Trier: 1948-2010

Blocking: 1961-2000NAO: 1848-2010ENSO-SST: 1871-2010

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-20 0 20 40

40

50

60

70

Oxford

Oslo

Trier

Barcelona

Moscow

Atmospheric blocking

relationship between temperature and precipitation anomalies (Rex 1951, Trigo et al. 2004)

… sustained, quasi-stationary, high-pressure systems that disrupt the prevailing westerly circumpolar flow

Height of tropopause (2 pvu *):

• elevated tropopause associated with strong negative potential vorticity anomalies ( > -1.3 pvu )

* [10-6m2s-1K kg-1]

Sillmann, 2009

Atmospheric blockingPotential Vorticity (PV) - based blocking indicator

Blocking detection method (Schwierz et al. 2004):

• Identification of regions with strong negative PV anomalies between 500-150hPa

• PV anomalies which meet time persistence (> 10 days) and spatial criteria (1.8*106km2) are tracked from their genesis to their lysis

Sillmann, 2009

Excesses over Thresholds

0 20 40 60 80 100 120

05

1015

2025

Days

Pre

cip

itatio

n [

mm

]

v = 1mm

u = 16.8mm

Stationary Point Process

• Frequency of Events: Poisson Process

• Magnitude of excess: GPD

9

Threshold Selection

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31 32 33 34 35

-10

10

30

Threshold

Mo

difi

ed

Sca

le

31 32 33 34 35

-1.0

0.0

0.5

Threshold

Sh

ap

e

10

Model fitting

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Stationary Model

Non-Stationary Model Blocking Non-Stationary Model ENSO

Non-Stationary Model NAO

Stationary Point Process

Parameters for JJA Maximum temperaturelocation

MLE estimates of the GEV parameters transformed to give the parameters of the Poisson model and GPD:

σu = σ + ξ(u – μ)Λ = (t2-t1)[1+ξ (z-μ)/σ ]-1/ξ

Non-stationary Point ProcessDo the atmospheric driving conditions improve the

statistical mode fits?

stationary Point Process non-stationary Point Process

COV – time dependent covariate

As before derive GPD parameters from GEV estimates

e.g. Atmospheric blocking as covariate (CAB)

Statistical modelingModel selection

Model choice

Deviance Statistic:

where nllh0(M0) is the neg. log-likelihood of simple model

nllh1(M1) is the neg. log-likelihood of more complex model

*

* degrees of freedom

Model µ σ λ Distribution functions d.f.

0 0 0 0 F(x) ~ GPD(μ,σ) G(x) ~Pois(λ) 3

1 CAB 0 CAB F(x|CAB(t)=z) ~ GPD(μ(z),σ) G(x|CAB(t=z)) ~Pois(λ(z))

4

2 CAB CAB CAB F(x|CAB(t)=z) ~ GPD(μ(z),σ(z)) G(x|CAB(t)=z) ~Pois(λ(z))

5

Non-stationary Point ProcessComparison of models

15

Discussion

• Resolution of Blocking index is too low• JJA Summer only may miss some events• Attributing excess temperatures to one driver

alone is too simplistic multiple covariates?• Hot spells (consecutive days of excess) may be

more interesting• Similarly considering relative importance of

minimum temperatures and relative humidity

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Issues…

• Data limitations (blocking only available JJA)• Familiarity with R packages

– Fitting covariates– Calculating return levels under non-stationarity– Mapping

• Time!

ASP Summer Colloquium Project#223 June 2011