detecting human influence on extreme daily temperature at regional scales

WCRP Extremes Workshop - 27-29 Sept 2010 Detecting human influence on extreme

daily temperature at regional scales

Photo: F. Zwiers (Long-tailed Jaeger)

Francis Zwiers1, Xuebin Zhang2, Yang Feng2

1Pacific Climate Impacts Consortium, University of Victoria, Victoria, Canada2Climate Research Division, Environment Canada, Toronto, Canada

Outline

WCRP Extremes Workshop - 27-29 Sept 2010

• Introduction• Changes in the mean

state• An analog for extremes• Example application• Discussion

Photo: F. Zwiers

Introduction• The causes of changes in mean temperatures

have been robustly attributed on global and regional scales

• The literature on the causes of changes in extreme temperature is still developing

• Principal study was by Christidis et al (2005)– Warmest night ANT influence robustly detected– Coldest day, coldest night ANT less robustly

detected– Warmest day ANT not detected

• Recent work strengthens these results, extends to all four extreme temp indices and to regions

WCRP Extremes Workshop - 27-29 Sept 2010

Evaluateamplitudeestimates

Observations1946-56

Model

1986-96

XY Total least squares regression in reduced dimension space

XYFiltering and projection onto reduceddimension space

Evaluate goodness of

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WCRP Extremes Workshop - 27-29 Sept 2010

• Have a Gaussian setup

),(~| XXY

Space-time observations vector (decadal means)

Space-time signal matrix (one column per signal)

Vector of scaling factors

Covariance structure

YX

WCRP Extremes Workshop - 27-29 Sept 2010

From a statistical perspective

• Ultimate small sample problem• Fingerprints to look for are from models.

• Error covariance structure also from models (eg., control runs)

• Do generalized linear regression (optimize signal-to-noise ratio)

• Take some aspects of signal uncertainty into account using either a total least squares or errors-in-variables approach

WCRP Extremes Workshop - 27-29 Sept 2010

A few features

Photo: F. Zwiers

TXGEVXY ),,(~| Space-time vector of annual extremes

Space-time signal matrix (one column per signal)

Vector of scaling factors

Vector of scale parameters

Vector of shape parameters

YX

Note that these are vectors

WCRP Extremes Workshop - 27-29 Sept 2010

An extremes analogue

Photo: F. Zwiers

Photo: F. Zwiers (Arctic Tern)

• Amount of high quality, gridded daily data is limited

• Assume that the location parameter varies with time and space (e.g., due to external forcing)

• Assume that scale and shape parameters constant in time

• Unable to explicitly represent spatial or temporal dependence

• Unable to reduce dimension so as to include only scales where variability of extremes is well simulated

WCRP Extremes Workshop - 27-29 Sept 2010

A few features / limitations

• Typically have ensembles of 20th century simulations from a given model – M ensemble members M annual extremes per year

• Assume that signal changes slowly– If roughly constant within decades 10M annual extremes per

decade

• Fit GEV to these decadal samples at grid boxes• Retain the decadal fields of location parameter estimates

as signal• Average across multiple models to reduce signal

uncertainty• Currently consider only one signal at a time (either ALL or

ANT)

How do we get the signal?

WCRP Extremes Workshop - 27-29 Sept 2010

• Observed annual temperature extremes• TNn (annual minimum daily minimum temperature)• TNx (annual maximum daily minimum temperature)• TXn (annual minimum daily maximum temperature)• TXx (annual maximum daily maximum temperature)

– HadEX, compiled by Alexander et al. 2006– Dataset covers 1946-2000; we analyze 1961-2000

• Simulated annual temperature extremes– ANT – 7 models, 25 simulations– ALL – 3 models, 11 simulations

What extremes do we consider?

• Observations from HadEX, Alexander et al., 2006• Express signal in decade j at gridbox k as

• Note that same scaling factor β is used everywhere

• Obtain mle for β by profile likelihood technique

N

j l k

kjkkljk

k

k k

X

Nl

1

10

1

,,)1(10 ))}ˆ

(1log()1

1(

)log(10{

kjk ,̂

WCRP Extremes Workshop - 27-29 Sept 2010

How do we fit the GEV to obs?

• From internal variability– Block bootstrap on observations using 5-year blocks– For a given signal, resample residuals, re-estimate β

• Includes ENSO timescale• Does not include lower frequency timescales • Do not resample in space, so variability in re-estimated β’s

reflects effects of spatial dependence

• Signal uncertainty due to model simulated internal variability– Block bootstrap on model output

• Compare with approximate confidence intervals from profile likelihood

• Check goodness of fit

WCRP Extremes Workshop - 27-29 Sept 2010

How do we assess uncertainty?

Results: Global

TNn

TXn

TNx

TXx

Coldest night

Coldest day

Warmest night

Warmest day

WCRP Extremes Workshop - 27-29 Sept 2010

Results: Regional

WCRP Extremes Workshop - 27-29 Sept 2010

WCRP Extremes Workshop - 27-29 Sept 2010

TNn

TXn

TNx

TXx

Coldest night

Coldest day

Warmest night

Warmest day

Implied change in waiting times (1990’s vs 1960’s)

• Spatial smoothing of signal, scale, shape• Attempt to separate two signals• Unable to optimize• Need better approach for taking signal

uncertainty into account – what is the parallel to TLS/EIV?

• Should be able to calculate FAR directly• Potentially a constraint on future extremes

WCRP Extremes Workshop - 27-29 Sept 2010

Refinements / Discussion

WCRP Extremes Workshop - 27-29 Sept 2010

Photo: F. ZwiersThe End Photo: F. Zwiers