advanced metrics of extreme precipitation events

Advanced metrics of extreme precipitation eventsOlga Zolina

Meteorologisches Institut der Universität Bonn, GermanyP.P.Shirshov Institute of Oceanology, Moscow, Russia

Complexity of extreme precipitation, definitions and uncertainties of metrics

Absolute extremes: use of raw data vs application of extreme value statistics

Relative extremeness: empirical and PDF-based indices

Problem of precipitation timing: duration of wet periods

Perspectives

MeteorologischesInstitut

Universit tBonn

ä

Outline:

Workshop on extreme climate events, September 2010 Paris

Complexity of precipitation process implies the complexity in estimation of precipitation extremes

Many more (compared to the other variables) metrics are needed to characterize it

Methods for estimation of extremes need to account for clustering in space and in time

Timing of the event is essential and should be accounted for both methods and data

Precipitation is an event-like phenomenon, clustered in space and in time, it is not aclassical scalar, like temperature or pressure 20 km

20 km

Datarequirement

s

Methodrequirement

sWorkshop on extreme climate events, September 2010 Paris

for treshhold=10 mm/day

in Stenslese - 3 days

in Bulken - 11 days

95%=12 mm/day2 days

95%=22 mm/day3 days

How to define what is extreme precipitation: uncertanties of metrics

Stensele, Sweeden

Bulken,Norway

JJA, 1982

0 10 20 30 40 50 60 70 80 90da y s

0

10

20

30

40

mm

/da

y

0

10

20

30

409 daystotal=35.3mmintensity=3.9mm/day

4 daystotal=22.0mmintensity=5.5mm/day

95% for 1950-2007 period =21.4 mm/dayBulken: 3 days, R95pTOT=33.021%Stensele: 0 days, R95pTOT=0%


Approaches for estimating precipitation extremes

Absolute extremes

Extremeness (relative extremes)

Time- (area-)integrated extremes

Raw data – based

• Intensities• Maxima• Peaks over threshold

Contribution of the wettest days to totals

from empirical distributions

ETCCDI RxTOT index

Wet spell durations and associated

intensities & extremes

PDF –based

Percentiles of the theoretical

PDFs

IVD vs EVD


derived from theoretical PDFs

Intensity-duration-frequency (IDF)

distributionsFrom engineering

hydrology to climate


Absolute extremes: IVD vs EVD

PDF for the core (IVD, e.g. Gamma) may not capture the extremes accurately EVD (e.g. GEV, GPD) may be strongly constrained by the threshold chosen and overestimate extremes “fetishism of heavy tails”

Is the concept “absence of evidence is not evidence of absence” always valid?

Gamma

GPD

Maraun et al. 2010

Cambridge

Daily precipitation is a time-integrated value, not an elementary event, difficulties in applying extreme statistics

30

40

50

60

70

-10 0 10 20 30 40 50 60

-10 0 10 20 30 40 50 60

30

40

50

60

70

1 to 60 60 to 70 70 to 80 80 to 90 90 to 100 100 to 150 150 to 200 200 to 300 300 to 400 400 to 20000mm/day

<6060-70

70-80

80-9090-100

100-150

150-200

200-300

300-400>400

30

40

50

60

70

-10 0 10 20 30 40 50 60

-10 0 10 20 30 40 50 60

30

40

50

60

70

1 to 60 60 to 70 70 to 80 80 to 90 90 to 100 100 to 150 150 to 200 200 to 300 300 to 400 400 to 20000mm/day

<6060-70

70-80

80-9090-100

100-150

150-200

200-300

300-400>400

Overall record for Europe is 543 mm/day (Gard, France, 08.09.2002)


1898-2009 maxima of daily precipitation

100-yr returns from GEV distribution

Zolina 2010

Absolute precipitation extremes:observed changes in 95% percentile of

precipitation

-10--6 -6--4 -4--2 -2-0 0-2 2-4 4-6 6-10 %

significant at 95% level

1951-2000 JJA

1951-2000 DJF

Zolina et al. 2005, Geophys. Res. Lett.

Zagreb

95th percentile

mean intensity

Changes in extremes differ from those in totals Absolute extremes grow with seasonality in Western Europe


Seasonality in extreme precipitation trendsover Germany 1950-2004

-1

00 t

o -

10

-10

to -

5

-5 t

o -

4

-4 t

o -

3

-3 t

o -

2

2 to

3

3 to

4

4 to

5

5 to

10

10

to

100

<-10

-10 -

-5

-5 -

-4

-4 -

-3

-3 -

-22 -

33 -

44 -

55 -

10> 1

0 %

6 8 10 12 14

48

50

52

54

6 8 10 12 14

48

50

52

54

P95

6 8 10 12 14

48

50

52

54

6 8 10 12 14

48

50

52

54

intensity

4 8

5 0

5 2

5 4

6 8 1 0 1 2 1 4

6 8 1 0 1 2 1 4

4 8

5 0

5 2

5 4

D J F

6 8 1 0 1 2 1 4

4 8

5 0

5 2

5 4

6 8 1 0 1 2 1 4

4 8

5 0

5 2

5 4

J J A

10 20 30 40 50 60 70 80 90 100

Precipitation classes (%)

-5

-4

-3

-2

-1

0

1

2

3

4

5

Li n

ear

tre n

d (

%)

10 20 30 40 50 60 70 80 90 100

Precipitation classes (%)

-5

-4

-3

-2

-1

0

1

2

3

4

5

Li n

ea

r tr

en

d (

%)


-1

00 t

o -

7

-7 t

o -

6

-6 t

o -

5

-5 t

o -

4

-4 t

o -

2

3 t

o 4

4

to

5

5 t

o 6

6

to

7

7 t

o 8

8

to

100

48

50

52

54

6 8 10 12 14

48

50

52

54

48

50

52

54

6 8 10 12 14

6 8 10 12 14

48

50

52

54

6 8 10 12 14

48

50

52

54

6 8 10 12 14

6 8 10 12 14

48

50

52

54

DJF MAM

JJA SON

(c)

%DJF JJA

95% significance level

DJF

Zolina et al. 2008, J. Geophys. Res.

JJA YEAR



Absolute extremes



Raw data – based




ETCCDI RxTOT index



PDF –based


PDFs

IVD vs EVD







Absolute extremes and relative extremeness

Analyzing interannual changes, it is critical to know how much the fraction contributed by the uppermost wet days has changed

Limitations of the empirical indices are associated with the finite number of wet days in sample (R95totfalls to zero) Need to extent index of relative extremeness to the theoretical distributions

Zolina et al. 2009, J. Hydrometeorol.

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000y e a rs

0

10

20

30

40

50

%0

10

20

30

40

50

R95pTOT Sodankyla, Finland, (26.65E, 67.37N) DJF


Distribution of fractional contribution (DFC) of daily precipitation to the total

yxxPyPn

iii )()(

1

xi, i=1, ...n is the daily precipitation, n is the number of wet days

n

iiii xxy

1

1)1(1 )1()(])1[(

)()(

nyy

n

nyF

DFC for Gamma distribution

),1,,1(

)1()(])1[(

)()(

12

)1(

ynF

yyn

nyC n

),,,(12 ycbaF - Gaussian hypergeometric function

PDF:

CDF:

Zolina et al. 2009, J. Hydrometeorol.

R95tt index instead of R95tot


0.

4 to

0.5

0.

5 to

0.6

0.

6 to

0.7

0.

7 to

0.8

0.

8 to

0.9

0.

9 to

1

-20 -10 0 10 20 30 40 50 60

-20 -10 0 10 20 30 40 50 60

30

40

50

60

70

30

40

50

60

70

-20 -10 0 10 20 30 40 50 6030

40

50

60

70

30

40

50

60

70

-20 -10 0 10 20 30 40 50 6030

40

50

60

70

30

40

50

60

70

(a)

(b)

(c)

YEAR

DJF

JJA

Corellation R95tt vs R95tot

Relative precipitation extremeness:PDF-based vs empirical index

New index exhibits significant differences compared to the traditional index and may also show different variability patterns

R95tt DJF

-1

00 t

o -

4

-4 t

o -

3

-3 t

o -

2

-2 t

o -

1.5

-1

.5 t

o -

1

1 to

1.5

1.

5 to

2

2 to

3

3 to

4

4 to

100

-20 -10 0 10 20 30 40 50 60

-20 -10 0 10 20 30 40 50 60

30

40

50

60

70

30

40

50

60

70

-20 -10 0 10 20 30 40 50 6030

40

50

60

70

30

40

50

60

70

-20 -10 0 10 20 30 40 50 60

-20 -10 0 10 20 30 40 50 60

30

40

50

60

70

-20 -10 0 10 20 30 40 50 6030

40

50

60

70

(a) (b)

(c) (d)

R95tt DJF

R95tt JJA

R95ttMAM

R95ttSON

-20 -10 0 10 20 30 40 50 6030

40

50

60

70

30

40

50

60

70

-20 -10 0 10 20 30 40 50 6030

40

50

60

70

(e) (f)

R95tt-R95tot DJF

R95tt-R95tot JJA

R95tot DJF1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

years

0

10

20

30

40

50

%

0

10

20

30

40

50Sodankyla, Finland (26.65°E, 67.37°N)

DJFR95totR95tt

Sondakyla, Finland26.65E, 67.37N, DJF

Linear trend, % per dec

Linear trend, % per dec



Absolute extremes



Raw data – based




ETCCDI RxTOT index



PDF –based


PDFs

IVD vs EVD







0 5 10 15 20 25 30

days

0

5

10

15

20

25

30

mm

/da

y

0

5

10

15

20

25

30

Duration of precipitation: essential metric for estimation extremes

For design purposes a critical metric is the precipitation accumulated during consecutive days or over area Time-integrated extremes may not correlate with the magnitude of extremes for single days

IDF (Intensity-duration-frequency)-distributions: developed in engineering hydrology, however for minute- and hourly time scales only, not yet applied to climate studies

Madsen, 2002, Wat. Res. Res.

IDFs for Vietnam

IDFs for CopenhagenWP=3 daysMax = 27.1mmTotal = 32.8mm

WP=12 daysMax = 6.2mmTotal = 51.5mm


0 5 10 15 20 25 30 35 40 45 50fraction of wet days due to wet spells (%)

0 5 10 15 20 25 30 35 40 45 50ocurrence of wet spells (%)

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005years

-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.10.00.10.40.60.81.01.21.41.61.82.0-0.2-0.6-1.0-1.8-2.0 0.2 0.6 1.0 1.4 2.0-1.4 1.8

12

123456789

1011

dura

tion

of w

et s

pells

(day

s) 12

123456789

1011

a

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5linear trend in the fracion of wet days

b c

Changes in the duration of European wet periods

normalized occurrence anomalies

Zolina et al. 2010, Geophys. Res. Lett.

Net effect of the number of wet days(Monte-Carlo simulation of the growing

number of wet days, % per decade)

1% 2% 3%

0.17±0.10 0.31±0.19 0.47±0.25

It is not the effect of changingnumber of wet days!!!

Linear trend in the WP duration: 1950-2008


How changing wet spells affect precipitation

-1

00 t

o -

3

-3 t

o -

2

-2 t

o -

1

-1 t

o 0

0

to 1

1

to 2

2

to 3

3

to 1

00< - 3

- 3 - - 2- 2 - - 1

- 1 - 00 - 1

1 - 22 - 3 > 3

- 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0

- 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0

3 0

4 0

5 0

6 0

7 0

3 0

4 0

5 0

6 0

7 0

- 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0

- 1 0 0 1 0 2 0 3 0 4 0 5 0 6 03 0

4 0

5 0

6 0

7 0

Linear trends in fractional contrbution of extremes to the total

Short WPs (<2 days) Long WPs (>2 days)


Changes in the IDF distrbutions for daily preciptiation in Europe (1950-2009)

0 4 8 1 2 1 6 2 0 2 4 2 8m e a n i n t e n s i t y ( m m / d a y )

1

2

3

4

5

6

7

8

9

1 0

5 1 0

4 0

6 0

1 0 0

2 03 0

8 0

1 2 0

1 5 0

b

- 6

- 4

- 2

- 1

1

2

4

6

0 4 8 1 2 1 6 2 0 2 4 2 8m e a n i n t e n s i t y ( m m / d a y )

1

2

3

4

5

6

7

8

9

1 0

dura

tion

of w

et s

pells

(day

s)

5

6 0

4 0

1 0

1 5 0

8 0

1 2 0

1 0 0

2 03 0

a


Intensity-durationdistribution for

Central Germany

Acc. precipitation

Linear trends in time-integrated precipitationfor all European stations (% per decade)

All wet periods Extremes (95th percentile)

Longer wet periods imply stronger extremes!Workshop on extreme climate events, September 2010 Paris

Conclusions and perspectives

Absolute extremes:

Existing methods are quite accurate, however more close look is needed on the approaches to estimation of very rare events Absolute extremes show primarily growing intensity over Europe (up to 5% per

decade) but for most regions spatial patterns are noisy and significance is low There is a clear seasonality in long-term trends of Central European

precipitation extremes: more extremes in winter and less in summer Relative extremeness:

New R95tt index allows to overcome the problem of the finite number of wet days in the raw time series of daily precipitation Compared to R95tot index, new R95tt index shows more homogeneous trend

pattern with the trends being statistically significantly larger in the Central and Eastern Europe Duration of wet spells:

During the last 60 years European wet spells have become longer by about 15-20%. Lengthening was not caused by the net effect of wet days Extreme precipitation associated with longer wet spells have intensified

by 12-18%, while extremes associated with short wet spells became weaker


Thank you

Soja & Starkel, 2007, Geomorph.

4-month (1998) daily precipitation In Cherrapunji

Extreme precipitation season (summer 1998) andcatastrophic flood and land slide in Ladakh,

Himalay


advanced metrics of extreme precipitation events

Documents

totals absolute extremes

estimation of extremes

wettest days

climate absolute extremes

intensities maxima peaks

ivd vs evd pdf

integrated extremesraw

timeintegrated value