1. No category

Extreme hydro-meterological events
and their probabilities;
a non-parametric resampling approach
Jules Beersma
Colloquium
Meteorology and Air Quality
22 March 2007
Outline
• Introduction
• The principle of time series resampling
• Applications (wet & dry)
• Conclusions
Colloquium MAQ, 22 March 2007
2
Introduction
Many hydrological applications require long
simultaneous time series of:
• Various locations (multi-site)
• Various meteorological variables (multivariate)
Non-parametric resampling
N0 assumptions about distributions, spatial, temporal
and mutual dependencies needed
Parametric time series modelling
Often needs unrealistic assumptions about distributions
and about the various dependencies
Colloquium MAQ, 22 March 2007
3
Time series resampling
Historical rainfall series
5
1
0
2 20 10 0
5 30 0
value (mm)
Resampling with
replacement = Bootstrap
Simulated rainfall series
0
5
1 20 10 30 10 0
0
0
…
Simulated series
>>
Historical series
Colloquium MAQ, 22 March 2007
4
Time series resampling
Historical rainfall series
5
1
0
2 20 10 0
5 30 0
value (mm)
Largest 4-day amount: 45 mm
Simulated rainfall series
0
5
1 20 10 30 10 0
0
0
…
Largest 4-day amount: 70 mm
Colloquium MAQ, 22 March 2007
5
Time series resampling
Is the persistence of the historical series
reproduced by the resampled series?
(Temporal correlation or autocorrelation)
Conditional bootstrap to include persistence in
simulated time series:
Nearest-neighbour resampling
Colloquium MAQ, 22 March 2007
6
Nearest-neighbour resampling (with persistence)
Historical rainfall series
5
1
0
2 20 10 0
5 30 0
Simulated rainfall series
0
5
1 20 10 30 10 0
value (mm)
Nearest-neighbour
resampling =
conditional bootstrap
0
0
Colloquium MAQ, 22 March 2007
…
7
Time series resampling (sum up)
• Bootstrap (random sampling)
(Efron, 1979)
• Nearest-neighbour resampling
(conditional bootstrap to include persistence)
(Young, 1994;
Lall and Sharma, 1996)
Colloquium MAQ, 22 March 2007
8
Applications
z
Extreme precipitation in the Rhine basin
(Rainfall generator for the Rhine basin)
z
Probability of drought in the Netherlands
(National drought study = ‘Droogtestudie Nederland’)
Colloquium MAQ, 22 March 2007
9
Rainfall generator for the Rhine basin
Historical data:
1961–1995: daily P and T for 34 stations
Simulated data (NN-resampling):
10 ×1000 years: daily P and T for 34 stations
and
daily P and T for 134 subbasins
Colloquium MAQ, 22 March 2007
10
34 stations
in the
Rhine basin
(CHR data)
X
Colloquium MAQ, 22 March 2007
X
11
HBV Districts
Erft
Lahn
Lippe
Lower Rhine
Main
Middle Rhine
Moselle
Nahe
Neckar
Ruhr
Schweiz
Sieg
Upper Rhine
Upper Rhine 2
134 Subbasins
(input for
hydrological
model)
100
76
77
75
99
98
97 74
72
70 96 101
T needed for
evaporation,
snow melt and
accumulation
Staatsgrenze
Gewässer
71
73
95
66
69
94
64
67
90
52
55
50
35
89
92
51
34
91
93
60
36
37
88
63
53 59
54
33
65
68
15
23
61
56
85 84
32
25
47
82
To obtain large river
discharges at Lobith
extreme ~10-day
precipitation sums
are needed over a
large area
79
45
48
41
24
81 12
46
11
10
80
115
40
7
78
5
117
114
16
9
113
44
19
17
18
13
43
42
21
83
31
58
49
14
20
27
30
57
22
26
29
86
87
62
28
8
4
116
6
2
110
3
39
106
38
105
111
109
108
112
1
104 103
102
107
132
122
120
134
133
121
131
130
129
126
125
N
119
128
127
124
123
100
118
Colloquium MAQ, 22 March 2007
0
100 Kilometer
12
Results for the Rhine basin
0.5
0.9
0.99
0.999
-lnColloquium
[-ln (P)]MAQ,
and 22
P March
= 1 –2007
1/T
13
‘Niederrhein’ study
Rainfall generator Rhine
Hydrological models subbasins
Hydraulic model Rhine
Extreme discharges ‘Niederrhein’
Colloquium MAQ, 22 March 2007
14
‘Niederrhein’
study
(NordrheinWestfalen)
Lobith
Andernach
“Grenzüberschreitende
Auswirkungen von
extremem Hochwasser
am Niederrhein”
Colloquium MAQ, 22 March 2007
15
Results ‘Niederrhein’ study
1995 and simulated discharge waves at Andernach
1995
18000
HW1
16000
HW2
HW3
14000
Discharge [m3/s]
HW4
12000
HW5
HW6
10000
HW7
8000
HW8
6000
4000
2000
0
1
5
9
13
17
21
Colloquium MAQ, 22 March 2007
Time [Days]
25
29
16
Conclusions rainfall generator Rhine basin
z
Rainfall generator produces for the
Rhine basin precipitation series
with realistic multi-day extremes
Colloquium MAQ, 22 March 2007
17
Conclusions rainfall generator Rhine basin
z
z
Rainfall generator produces for the
Rhine basin precipitation series
with realistic multi-day extremes
The largest simulated multi-day
extremes are larger than historically
observed
Colloquium MAQ, 22 March 2007
18
Conclusions rainfall generator Rhine basin
z
z
Rainfall generator produces for the
Rhine basin precipitation series
with realistic multi-day extremes
The largest simulated multi-day
extremes are larger than historically
observed
In combination with a
hydrological/hydraulic model higher
(and wider) discharge waves are
simulated
Colloquium MAQ, 22 March 2007
1995
18000
HW1
16000
HW2
HW3
14000
HW4
Discharge [m3/s]
z
12000
HW5
HW6
10000
HW7
8000
HW8
6000
4000
2000
0
1
5
9
13
17
21
25
Time [Days]
19
29
Applications
z
Extreme precipitation in the Rhine basin
(Rainfall generator for the Rhine basin)
z
Probability of drought in the Netherlands
(National drought study = ‘Droogtestudie Nederland’)
Colloquium MAQ, 22 March 2007
20
National drought study
• Probability of summer drought Netherlands
• Regional differences in summer drought
Colloquium MAQ, 22 March 2007
21
National drought study
z
z
Precipitation deficit:
cumulative difference between potential evaporation
and precipitation (E - P)
•
Summer half year:
Annual evaporation
•
•
1971-2000
1 April - 30 September
NE
•
• NW
(growing season)
•
•
z
z
•
Six districts
P: 18 stations, E: De Bilt
•
CW
•
•
De Bilt
•
• SW
•
0
•
50 km
Colloquium MAQ, 22 March 2007
•
CE
mm
SE •
•
510 - 525
525 - 540
540 - 555
555 - 570
570 - 585
585 - 600
600 - 615
22
National drought study
Historical data:
1906–2000: daily P and E (Makkink evaporation derived
from sunshine duration)
Prior to the frequency analysis the daily values are
converted into decade values (10-day values)
Simulated data (NN-resampling):
100 000 years: decade values of E - P (for 6 districts)
Colloquium MAQ, 22 March 2007
23
National drought study
Colloquium MAQ, 22 March 2007
24
National drought study
NN-resampling with long-term persistence
Colloquium MAQ, 22 March 2007
25
Precipitation deficit for 6 districts
How certain are
these curves?
Colloquium MAQ, 22 March 2007
26
Bootstrap uncertainty
NN-resampling + bootstrap uncertainty
Generate 95-year
bootstrap samples
from 95 years of
historical data:
Use 95-year
bootstrap samples
as input for
NN-resampling:
1st bootstrap
sample
NN-resampling
100 000 years
2nd bootstrap
sample
NN-resampling
100 000 years
:
:
N th bootstrap
sample
NN-resampling
100 000 years
Colloquium MAQ, 22 March 2007
27
Bootstrap uncertainty
NN-resampling + bootstrap uncertainty
Generate 95-year
bootstrap samples
from 95 years of
historical data:
Use 95-year
bootstrap samples
as input for
NN-resampling:
1st bootstrap
sample
NN-resampling
100 000 years
2nd bootstrap
sample
NN-resampling
100 000 years
:
N thN=499
bootstrap
:
NN-resampling
100 000 years
sample
bootstrap
samples
Colloquium MAQ, 22 March 2007
28
Resampling + bootstrap uncertainty
N=50
Colloquium MAQ, 22 March 2007
29
Resampling + bootstrap uncertainty
N=100
Colloquium MAQ, 22 March 2007
30
Resampling + bootstrap uncertainty
N=200
Colloquium MAQ, 22 March 2007
31
Resampling + bootstrap uncertainty
N=499
Colloquium MAQ, 22 March 2007
32
Bootstrap standard errors
Colloquium MAQ, 22 March 2007
33
Bootstrap standard errors
Parametric model with
curvature in upper tail
fitted to the historical
annual maxima (same
curvature parameters for all
six districts)
Colloquium MAQ, 22 March 2007
34
Bootstrap standard errors
499 x 100 000 year
10 000 samples
Colloquium MAQ, 22 March 2007
35
Conclusions national drought study
z
Large relative uncertainty (s.e.)
near curvature of probability
distribution
Colloquium MAQ, 22 March 2007
36
Conclusions national drought study
z
z
z
Large relative uncertainty (s.e.)
near curvature of probability
distribution
Relative uncertainty (s.e.) of NNresampling for long return periods
smaller than that of the parametric
model
Large increase in uncertainty with
parametric model is due to
uncertainty of model parameters
Colloquium MAQ, 22 March 2007
37
General conclusions
z
z
z
z
Time series resampling offers an opportunity
to simulate unprecedented multi-day extreme
events from either historical or physically
modelled daily data
It even provides the (exceedance) probabilities of
such unprecedented events
In short, time series resampling is an effective
method to prolong ‘existing’ time series
(especially for multivariate and/or multi-site time
series)
Uncertainty of time series resampling can be
addressed with (second) bootstrap
Colloquium MAQ, 22 March 2007
38
Time series resampling
is definitely useful for
hydrological applications
PhD defense April 23,
2007, 1.30 pm
Wageningen Aula
Colloquium MAQ, 22 March 2007
39