Defining single extreme weather events in a climate perspective

Defining single extreme weather events in a climate perspective

Julien Cattiaux, Aurélien Ribes

Centre National de Recherches Météorologiques, Toulouse, France.

[email protected]|@julienc4ttiaux

Riederalp 2019 Extremes Workshop | 19–23 March 2019

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Context

The analysis of single extreme weather events relates to:

−climate monitoring;

−physical understanding;

−estimation of return periods;

−attribution to climate change.

For the latter, one compares the probability of the event occurring:

−in thefactualworld (p1);

−in acounter-factualworld, e.g. non-anthropized (p0).

One defines the Risk Ratioand the Fraction of Attributable Riskas:

RR= p₁ p0

and FAR= p₁−p₀ p1

=1− 1 RR

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The four steps of event definition

1. Select the variable (X).

Usually straightforward — not crucial here.

2. Define the class of events.

Here, traditional "risk-based" approach, i.e. eventsequally or more intense thanthe observed one: Pr{X ≥x0}withx0the event value.

N.B. Alternative "storyline" approach: eventsof about the same intensity— not appropriate for probabilistic framework since:Pr{x0−ε≤X≤x0+ε}−→^ε→00.

3. Define the level of conditioning.

Pr{X ≥x0|Y ∈Ω}withY a concurrent climate variable(e.g. SST, atmospheric circulation, ENSO)or the time of the year(e.g. winter heat wave)?

Here only thecalendar conditioningis explored (relevant for climate monitoring).

4. Define the spatio-temporal scale.

The main topic of this talk.

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Why spatio-temporal scale matters

Example of the European heat-wave of summer 2003 (EHW03):

−Stott et al. (2004): EHW03 becomes acoldextreme after 2050.

−Beniston (2007): EHW03 remains ahotevent in 2100.

The difference? Seasonal/Europeanvs. daily/localtemperature anomalies.

a) JJA T Europe

Stott et al., Nature, 2004 (SRES A2 scenario).

b) Daily T Basel

Beniston, GRL, 2007 (SRES A2 scenario).

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Why spatio-temporal scale matters

Example of the European heat-wave of summer 2003 (EHW03):

−Stott et al. (2004): EHW03 becomes acoldextreme after 2050.

−Beniston (2007): EHW03 remains ahotevent in 2100.

The difference? Seasonal/Europeanvs. daily/localtemperature anomalies.

Temperature (°C)

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b) Daily T Paris

June July August

1 10 20 1 10 20 1 10 20 30 10

15 20 25 30 35

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Average 1961−1990 JJA 2003

Perc. 2070−2099 (RCP8.5) P1 P10 P50 P90 P99

Temp. anomaly wrt. 1961−1990 (°C)

1900 1950 2000 2050 2100

−2 0 2 4 6 8 10

12a) JJA T Europe E−OBS

CMIP5 HIST+RCP8.5 (61 members)

Cattiaux and Ribes, BAMS, 2018 (RCP8.5 scenario).

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Choice of spatio-temporal scale

Most of the time: arbitrary.

Authors use predefined areas(e.g. a local station, a national territory)and periods(e.g., a day, a month, a season), and/or their own expertise.

Problem #1: this may not faithfully portray the event / be biased by our perception.

Problem #2: different definitions of the "same" event may lead to different attribution statements(see EHW03 example).

—

Our idea: select the scale at which the event has been the most extreme, i.e. minimize the factual probability:

p1= Pr

X^(t1)≥xt1 ,

withX^(t1)the random variable describing the temperature distribution at timet1=2003, andxt1the observed 2003 value.

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Optimizing the time window

Example: DailyT at Paris-Montsouris station for Jun-Jul-Aug 2003.

Data: Météo-France.

Question: Over which time window is the anomaly the most extreme?

1. Aug 11 (1 day);

2. Aug 5–12 (1 week);

3. Aug 2–17 (2 weeks);

4. August (1 month);

5. June (1 month);

6. Jun-Jul-Aug (1 season).

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Optimizing the time window

−we consider the observed time seriesxt& the climate changext^∗at this location;

−we correct for climate change before and aftert1=2003: x_t^(t1)=xt−(xt^∗−xt^∗1);

−we estimatep1fromx_t^(t1), assumingX^(t1) follows a Gaussian distribution;

−we also estimatep0by correcting wrt. t0=1950 (our counter-factual world).

2003

290292294296298300302

T Paris for Aug 1 − Aug 10

Temperature (K)

Years

1950 1960 1970 1980 1990 2000 2010

291.0 291.5

292.0 N.B.x_t^∗= smoothed multi-model mean of CMIP5

JJA temperatures (common to all time windows but location-dependent).

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Optimizing the time window

−we consider the observed time seriesxt& the climate changext^∗at this location;

−we correct for climate change before and aftert1=2003: x_t^(t1)=xt−(xt^∗−xt^∗1);

−we estimatep1fromx_t^(t1), assumingX^(t1) follows a Gaussian distribution;

−we also estimatep0by correcting wrt. t0=1950 (our counter-factual world).

2003

290292294296298300302

T Paris for Aug 1 − Aug 10

Temperature (K)

●

Years

●

1950 1960 1970 1980 1990 2000 2010

291.0 291.5

292.0 N.B.x_t^∗= smoothed multi-model mean of CMIP5

JJA temperatures (common to all time windows but location-dependent).

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Optimizing the time window

−we consider the observed time seriesxt& the climate changext^∗at this location;

−we correct for climate change before and aftert1=2003: x_t^(t1)=xt−(xt^∗−xt^∗1);

−we estimatep1fromx_t^(t1), assumingX^(t1) follows a Gaussian distribution;

−we also estimatep0by correcting wrt. t0=1950 (our counter-factual world).

2003

290292294296298300302

T Paris for Aug 1 − Aug 10

Temperature (K)

●

Years

●

1950 1960 1970 1980 1990 2000 2010

291.0 291.5 292.0

2003

290 295 300 305

T Paris pdf for Aug 1 − Aug 10

Temperature (K) 10−day calendar (gauss)

N.B.x_t^∗= smoothed multi-model mean of CMIP5 JJA temperatures (common to all time windows but location-dependent).

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Optimizing the time window

−we consider the observed time seriesxt& the climate changext^∗at this location;

−we correct for climate change before and aftert1=2003: x_t^(t1)=xt−(xt^∗−xt^∗1);

−we estimatep1fromx_t^(t1), assumingX^(t1) follows a Gaussian distribution;

−we also estimatep0by correcting wrt. t0=1950(our counter-factual world).

2003

290292294296298300302

T Paris for Aug 1 − Aug 10

Temperature (K)

●

Years

●

1950 1960 1970 1980 1990 2000 2010

291.0 291.5 292.0

2003

290 295 300 305

T Paris pdf for Aug 1 − Aug 10

Temperature (K) 10−day calendar (gauss) 10−day calendar (gauss) 1950

N.B.x_t^∗= smoothed multi-model mean of CMIP5 JJA temperatures (common to all time windows but location-dependent).

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Optimizing the time window

The most extreme anomaly is found forAug 5–12(p₁=4×10⁻⁶, 250 000 y).

1 10 20 1 10 20 1 10 20

June July August

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 25 30 35 40 45 60 75 92

a) p1 Paris JJA2003 Calendar

Central day

Duration in days

X

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0.5 0.2 0.1 0.05 0.02 0.01 0.005 0.002 0.001 5e−04 2e−04 1e−04 5e−05 2e−05 1e−05 5e−06

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Calendar vs. annual maxima

The calendar approach is relevant for climate monitoring (seasonal context), butthe obtainedp₁should not be interpreted as a formal return period.

Alternative approach: consider x_t^(t1) as the time series of annual maxima, (now assuming thatX^(t1) follows a Gumbel distribution).

N.B. The question becomes: Over which time window is the anomalytemperaturethe most extreme?

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Calendar vs. annual maxima

The calendar approach is relevant for climate monitoring (seasonal context), butthe obtainedp₁should not be interpreted as a formal return period.

Alternative approach: considerx_t^(t1) as the time series ofannual maxima, (now assuming thatX^(t1) follows a Gumbel distribution).

2003

290 295 300 305

T Paris pdf for Aug 1 − Aug 10

Temperature (K) 10−day calendar (gauss)

10−day annual max (gev)

N.B.The question becomes: Over which time window is theanomalytemperaturethe most extreme?

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Calendar vs. annual maxima

The most extreme temperature is found forAug 4–12(p1=0.008, 125 y). Hot anomalies distant from the annual cycle peak disappear(e.g. June).

110 20 1 10 20 110 20

June July August

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 25 30 35 40 45 60 75 92

a) p1 Paris JJA2003 Calendar

Central day

Duration in days

X

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0.5 0.2 0.1 0.05 0.02 0.01 0.005 0.002 0.001 5e−04 2e−04 1e−04 5e−05 2e−05 1e−05 5e−06

1 10 20 1 10 20 1 10 20

June July August

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 25 30 35 40 45 60 75 92

b) p1 Paris JJA2003 Annual−maxima

Central day

Duration in days

X

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0.5 0.2 0.1 0.05 0.02 0.01 0.005 0.002 0.001 5e−04 2e−04 1e−04 5e−05 2e−05 1e−05 5e−06

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A compromise: local maxima

Idea : limit the search of annual maxima to a calendar neighborhood, i.e.

considerx_t^(t1) as the time series oflocal maxima.

Here we use±7 days; similar to what is done for establishing record values.

110 20 1 10 20 110 20

June July August

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 25 30 35 40 45 60 75 92

a) p1 Paris JJA2003 Calendar

Central day

Duration in days

X

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0.5 0.2 0.1 0.05 0.02 0.01 0.005 0.002 0.001 5e−04 2e−04 1e−04 5e−05 2e−05 1e−05 5e−06

110 20 1 10 20 110 20

June July August

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 25 30 35 40 45 60 75 92

b) p1 Paris JJA2003 Annual−maxima

Central day

Duration in days

X

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0.5 0.2 0.1 0.05 0.02 0.01 0.005 0.002 0.001 5e−04 2e−04 1e−04 5e−05 2e−05 1e−05 5e−06

1 10 20 1 10 20 1 10 20

June July August

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 25 30 35 40 45 60 75 92

c) p1 Paris JJA2003 Local−maxima

Central day

Duration in days

X

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0.5 0.2 0.1 0.05 0.02 0.01 0.005 0.002 0.001 5e−04 2e−04 1e−04 5e−05 2e−05 1e−05 5e−06

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