Transcript Advanced metrics of extreme precipitation events Olga Zolina Meteorologisches Institut Universitä t Bonn Meteorologisches Institut der Universität Bonn, Germany P.P.Shirshov Institute of Oceanology, Moscow, Russia Outline:  Complexity of.

Advanced metrics of extreme precipitation events
Olga Zolina
Meteorologisches
Institut
Universitä t
Bonn
Meteorologisches Institut der Universität Bonn, Germany
P.P.Shirshov Institute of Oceanology, Moscow, Russia
Outline:
 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
Workshop on extreme climate events, September 2010 Paris
Complexity of precipitation process implies the
complexity in estimation of precipitation extremes
Precipitation is an event-like phenomenon,
clustered in space and in time, it is not a
classical scalar, like temperature or pressure
20 km
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
Data
requirements
20 km
Method
requirements
Workshop on extreme climate events, September 2010 Paris
JJA, 1982
Stensele,
Sweeden
Bulken,
Norway
40
How to define what is extreme precipitation:
uncertanties of metrics
95% for 1950-2007 period =21.4 mm/day
Bulken: 3 days, R95pTOT=33.021%
Stensele: 0 days, R95pTOT=0%
for treshhold=10 mm/day
in Stenslese - 3 days
in Bulken - 11 days
30
mm/day
40
9 days
total=35.3mm
intensity=3.9mm/day
30
4 days
total=22.0mm
intensity=5.5mm/day
95%=22 mm/day
3 days
20
20
95%=12 mm/day
2 days
10
10
0
0
0
10
20
30
50
40
60
70
80
90
days
Workshop on extreme climate events, September 2010 Paris
Approaches for estimating precipitation extremes
Absolute
extremes
• Intensities
Raw data – • Maxima
• Peaks over
based
threshold
PDF –
based
Percentiles of
the theoretical
PDFs
IVD vs EVD
Extremeness
(relative extremes)
Time- (area-)
integrated
extremes
Contribution of the Wet spell durations
wettest days to totals
and associated
from empirical
intensities &
distributions
extremes
ETCCDI RxTOT
index
Intensity-durationContribution of the
frequency (IDF)
wettest days to totals
distributions
derived from
From engineering
theoretical PDFs
hydrology to
climate
Workshop on extreme climate events, September 2010 Paris
50
50
Absolute extremes: IVD vs EVD
40
 PDF40 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
30
and30 overestimate
extremes
 “fetishism
of heavy
tails”
-10
0
10
20
30
40
50
60
Is the concept “absence of evidence is
not evidence of absence” always valid?
<60
60-70
70-80
Cambridge
GPD
80-90
90-100
100-150
150-200
Gamma
200-300
300-400
>400
1898-2009 maxima of daily precipitation
1 to 60
60 to 70
70 to 80
<60
1 to 60
80
90to 70
60-70 to 60
70-80
70 to 80
90
to
100
80 to 90
80-90
90-100
100 to90 150
to 100
100-150
100 to 150
150
to
200
150-200
150 100-yr
to 200returns from GEV distribution
to 300
200-300
200 to200300
300 to 400
300-400
300
to
mm/day
400400
to 20000
>400
mm/day
400 to 20000
Maraun et al. 2010
Daily precipitation is a time-integrated value,
not an elementary event, 
difficulties in applying extreme statistics
Overall record for Europe is 543 mm/day
(Gard, France, 08.09.2002)
Zolina 2010
Workshop on extreme climate events, September 2010 Paris
Absolute precipitation extremes:
observed changes in 95% percentile of precipitation
Zagreb
1951-2000 DJF
95th percentile
mean intensity
1951-2000 JJA
-10--6
-6--4
-4--2
-2-0
significant at 95% level
0-2
2-4
4-6
6-10
%
 Changes in extremes differ from those in totals
 Absolute extremes grow with seasonality in
Western Europe
Zolina et al. 2005, Geophys. Res. Lett.
Workshop on extreme climate events, September 2010 Paris
Seasonality in extreme precipitation trends
over Germany 1950-2004
48
48
6
14
DJF
DJF
54
6
8
54
52
52
52
50
50
50
48
48
48
8
12
JJA
JJA
54
10
10
14
JJA
54
4
10
12
5
DJF
4
Linear trend (%)
3
Linear trend (%)
6
2
1
0
-1
SON
YEAR
54
52
52
52
50
50
50
50
50
48
48
10
6
12
8
14
JJA
48
48
6
10
8
12
14
6
8
10
10
12
6
12
54
48
14
8
14
10
intensity
54
-7 -8
6 7
%54
significant at 95% level
1
52
52
0
-1
-3
-3
-4
-4
50
-5
Precipitation classes (%)
10
14
52
2
-2
10 20 30 40 50 60 70 80 90 100
8
12
54
3
-2
-5
8
6
10
54
52
14
8
<-7 7
-6 -6
-5 -5
- 4 -4
-2
2
-4
4
-5
5
-6
5
8
14
6
P95
(c)
6
12
8
12
>
10
-100 to -7
-7 to -6
-6 to -5
-5 to -4
-4 to -2
3 to 4
4 to 5
5 to 6
6 to 7
7 to 8
8 to 100
8
48
10 20 30 40 50 60 70 80 90 100
Precipitation classes (%)
95% significance level
-100 to -10
-10 to -5
-5 to -4
-4 to -3
-3 to -2
2 to 3
3 to 4
4 to 5
5 to 10
10 to 100
6
6
50
48
Zolina
et al.102008, J.12Geophys.
Res.
8
14
Workshop on extreme climate events, September 2010 Paris
Approaches for estimating precipitation extremes
Absolute
extremes
• Intensities
Raw data – • Maxima
• Peaks over
based
threshold
PDF –
based
Percentiles of
the theoretical
PDFs
IVD vs EVD
Extremeness
(relative extremes)
Time- (area-)
integrated
extremes
Contribution of the Wet spell durations
wettest days to totals
and associated
from empirical
intensities &
distributions
extremes
ETCCDI RxTOT
index
Intensity-durationContribution of the
frequency (IDF)
wettest days to totals
distributions
derived from
From engineering
theoretical PDFs
hydrology to
climate
Workshop on extreme climate events, September 2010 Paris
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
W
R
, Rwj  Rwn 95
R95pTOT
Rj
Sodankyla, Finland, (26.65E, 67.37N) DJF
50
50
40
40
30
30
20
20
10
10
0
0
%
R95tot  100 w1
wj
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
years
Zolina et al. 2009, J. Hydrometeorol.
Limitations of the empirical indices are associated
with the finite number of wet days in sample (R95tot
falls to zero)  Need to extent index of relative
extremeness to the theoretical distributions
Workshop on extreme climate events, September 2010 Paris
Distribution of fractional contribution (DFC)
of daily precipitation to the total
n
 xi
yi  xi
i 1

P ( y )  P ( x i


x
)

y

i

i 1

n
xi, i=1, ...n is the daily precipitation, n is the number of wet days
DFC for Gamma distribution
(n )
F
(
y
)

y 1 (1  y ) ( n 1) 1
PDF:
[( n  1) ]( )
(n )
 y (1  y ) ( n 1) 
CDF: C ( y ) 
[( n  1) ]( )
 F21 (1, n ,   1, y )
1
2
F (a, b, c, y)
- Gaussian hypergeometric function
R95tt index instead of R95tot
Zolina et al. 2009, J. Hydrometeorol.
Workshop on extreme climate events, September 2010 Paris
Relative precipitation extremeness:
PDF-based vs empirical index
-10
0.4
0.5
0.6
0.7
0.8
0.9
to
to
to
to
to
to
0.5
0.6
0.7
0.8
0.9
1
40
0
10
20
0.
7
0. 0.8
8
-0
.9
6
5
7
0. 0. 0.
< 5- 60. 0.
30
0.
9
40
50
30
60
-20
70
.0
-1
-10
0
Linear trend, % per dec
10
20
30
40
50
60
-20
50
40
40
(a)
-10
0
10
20
30
40
50
60
70
R95tt
JJA
60
(c)
30
-20
-10
%
-10
10
20
30
40
50
40
50
40
50
R95tt DJF
R95tt
SON
1985
1990
1995
40
50
60
-10
(d)
-20
-10
0
10
20
30
R95tt-R95tot
JJA
60
50
40
Linear trend, % per dec
2000
(e)
30
-20
30
-100 to -4
-4 to -3
-3 to -2
-2 to -1.5
-1.5 to -1
1 to 1.5
1.5 to 2
2 to 3
3 to 4
4 to 100
1980
30
10
0
years
0
(b)
-20
70
40
1975
20
20
0
1970
10
R95tt-R95tot
DJF
50
10
0
30
60
20
1965
50
40
40
70
1960
40
50
40
30
1955
30
50
R95tot
R95tt
1950
20
0
10
New index exhibits significant differences
compared to the traditional index and may
also show different variability patterns
20
30
40
50
60
30
R95tot DJF
(f)
-20
-10
0
10
20
30
<
-4 -4
-3 -3
-2 - 2
-1 -1.
.5 5
1 -1
-1
1. .5
5
2 2
3 3
-4
>
4
40
30
60
50
Sondakyla, Finland
Sodankyla,
Finland
(26.65°E,
67.37°N)
26.65E, 67.37N,
DJF
DJF
10
70
Corellation R95tt vs R95tot
50
0
60
50
30
-20
-10
R95tt
MAM
R95tt
DJF
60
70
Workshop on extreme climate events, September 2010 Paris
Approaches for estimating precipitation extremes
Absolute
extremes
• Intensities
Raw data – • Maxima
• Peaks over
based
threshold
PDF –
based
Percentiles of
the theoretical
PDFs
IVD vs EVD
Extremeness
(relative extremes)
Time- (area-)
integrated
extremes
Contribution of the Wet spell durations
wettest days to totals
and associated
from empirical
intensities &
distributions
extremes
ETCCDI RxTOT
index
Contribution of the
Intensity-durationwettest days to totals
frequency (IDF)
derived from
distributions
theoretical PDFs
From engineering
hydrology to
climate
Workshop on extreme climate events, September 2010 Paris
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
30
30
WP=3 days
Max = 27.1mm
Total = 32.8mm
25
25
20
mm/day
IDFs for Vietnam
IDFs for Copenhagen
20
WP=12 days
Max = 6.2mm
Total = 51.5mm
15
15
10
10
5
5
0
0
0
5
10
15
days
20
25
30
Madsen, 2002, Wat. Res. Res.
IDF (Intensity-duration-frequency)-distributions:
developed in engineering hydrology, however
for minute- and hourly time scales only, not yet
applied to climate studies
Workshop on extreme climate events, September 2010 Paris
Changes in the duration of European wet periods
normalized occurrence anomalies
fraction of wet days due to wet spells (%)
duration of wet spells (days)
0
5 10 15 20 25 30 35 40 45 50
12
11
10
9
8
7
6
5
4
3
2
1
a
0
5 10 15 20 25 30 35 40 45 50
ocurrence of wet spells (%)
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
12
11
10
9
8
7
6
5
4
3
2
1
c
b
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
years linear trend in the fracion of wet days
-2.0
0.00.10.40.60.81.01.21.41.61.82.0
1.4
1.8
0.6
1.0
2.0
-1.4-1.0-0.8
-2.0-1.8-1.6
-1.8-1.4-1.2
-1.0-0.6-0.4
-0.6-0.1-0.2
0.2
It is not the effect of changing
number of wet days!!!
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
Linear trend in the WP duration: 1950-2008
Zolina et al. 2010,
Geophys. Res. Lett.
Workshop on extreme climate events, September 2010 Paris
How changing wet spells affect precipitation
Linear trends in fractional contrbution of extremes to the total
-10
0
10
20
30
40
50
-10
60
0
10
20
30
40
50
60
70
70
70
60
60
60
50
50
50
40
40
30
-10
0
10
20
30
40
50
60
-10
0
10
20
30
40
50
60
30
<
-3 -3
-2 -2
-1 -1
-0
01-1
2-2
3
>3
30
40
Long WPs (>2 days)
-100 to -3
-3 to -2
-2 to -1
-1 to 0
0 to 1
1 to 2
2 to 3
3 to 100
Short WPs (<2 days)
Workshop on extreme climate events, September 2010 Paris
Changes in the IDF distrbutions for daily preciptiation
in Europe (1950-2009)
Linear trends in time-integrated precipitation
for all European stations (% per decade)
Intensity-duration
distribution for
Central Germany
All wet periods
duration of wet spells (days)
10
Extremes (95th percentile)
a
b
10
9
9
6
8
8
4
7
7
2
6
150
150
6
1
5
120
120
5
-1
4
100
100
4
-2
3
80
80
3
-4
2
60
60
40
30
20
40
30
20
2
-6
1
5
0
10
5
10
1
4 8 12 16 20 24 28 0 4 8 12 16 20 24 28
mean intensity (mm/day)
mean intensity (mm/day)
significant at 95% level
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
Workshop on extreme climate events, September 2010 Paris
Thank you
Extreme precipitation season (summer 1998) and
catastrophic flood and land slide in Ladakh, Himalay
Soja & Starkel, 2007, Geomorph.
4-month (1998) daily
precipitation In Cherrapunji
Workshop on extreme climate events, September 2010 Paris