View
215
Download
0
Category
Tags:
Preview:
Citation preview
Hydrological extremes and their meteorological
causes
András Bárdossy
IWS
University of Stuttgart
1. Introduction
• The future is unknown• Modelling cannot forecast• We have to be prepared • Extremes used for design
– Wind – storm– Precipitation– Floods
2. Hydrological extremes
• Assumption:The future will be like past was• „True“ for rain and wind • Less for floods
– Influences:• River training• Reservoirs• Land use
Choice of the variable:
• Water level – Important for flooding– Measurable– Strongly influenced
• Discharges (amounts)– Less influenced “natural” variable– Less important– Difficult to measure
Cross section
2. Statistical assumptions
• Annual extremes• Seasonal values
(Summer Winter)• Partial duration series
Independent sample Homogeneous
Future like past ?
TN HQaaaQFQQtQ 3211 ,,)(,...,)(
Study Area
• Rhine catchment – Germany
Rhein Maxau 1901 - 1999
Rhein Worms 1901 - 1999
Rhein Kaub 1901 – 1999
Rhein Andernach 1901 – 1999
Mosel Cochem 1901 – 1999
Lahn Kalkofen 1901 – 1999
Neckar Plochingen 1921 - 1999
Independence
• Independence temporal changesAre there any unusual time intervals?• Tests
– Permutations and Moments– Autocorrelation (Bartlett)– Von Neumann ratio Test
Negative Tests – only rejection possible
Permutations
Randomness rejected for 6 out of 7
randomness test to- Comparison
moments random ))(()),(()),((
sequencedifferent ))(()),...,1((
series mixedrandomly
intervals for time (i) Moments )(),(),(
maAnnualmaxi )(),...,(),...1(
3i2i1i
3i2i1i
tmtmtm
TQQ
tmtmtm
TQtQQ
3. Understanding discharge series
• Goal: Equilibrium state• Discharge:
– Excess water– Meteorological origin– „Deterministic“ reaction
Principle
0 100 200 300 400
Tim e (days)
-80
-40
0
40
80
120
Dis
char
ge (
m3 /
s)
W eather
C atchm ent
Signal to be explained
0 100 200 300 400
Tim e (days)
0
20
40
60
Dis
char
ge (
m3 /
s)
Bodrog – CP07(362% Increase)
Tisza CP10(462% increase)
The 100 largest observed floods of the Tisza at Vásárosnamény 1900-1999 with the corresponding CPs.
Simulation
Directly from CPs –
dependent CP )(
))1(()(
ticdeterminis -Reaction )(
random - eDisturbanc )(
)()()(
tQ
tQFtQ
tQ
tQ
tQtQtQ
P
N
N
P
NP
CP sequences
• Observed (1899-2003)
• GCM simulated
• Historical simulated
• Semi-Markov chain (persistence)
0 10000 20000 30000
Time (days)
0
400
800
1200
1600
Dis
char
ge (
m3/s
)Llobregat – observed CPs
Llobregat – KIHZ CPs 1691-1781
0 10000 20000 30000
Time (days)
0
400
800
1200
1600
2000
Dis
char
ge (
m3/s
)
Summary and conclusions
• Hydrological extremes – Strongly influenced– Difficult to analyse– Not independent
Relationship between series
• Indicator series:
p
pp QtQ
QtQtI
)( if 1
)( if 0)(
4. Probability distributions
• Choice of the distribution– Subjective– Objective statistical testing
• Kolmogorow-Smirnow
• Cramer – von Mises
• Khi-Square
• More than one not rejected (?!)
Significance of the results
1. Select random subsample (80 values)
2. Perform parameter estimation for subsample
3. Calculate design floods
4. Repeat 1-3 N times (N=1000)
5. Calculate mean and range for design flood
Bootstrap results
M M M L M L S Q L M P W M
10000
11000
12000
13000
14000
15000 Andernach Q 100Gum belGEVPearson 3
Principle
0)( if weather toRelated
)1()()(
)(CP from )(
tQ
tQtQtQ
ttQ
0 100 200 300 400
Tim e (days)
0
20
40
60
80
100
Dis
char
ge (
m3 /
s)
Downscaling
• Parameter estimation:– Maximum likelihood
– Explicit separation of the data (CPs)
• Simulation:– For any given sequence of CPs
• Observed gridded SLP based
• NN based historical
• KIHZ based historical
• Extreme value statistics
Signal to be explained
0 100 200 300 400
Tim e (days)
0
20
40
60
Dis
char
ge (
m3 /
s)
Discharge changes Tisza
0 100 200 300 400
-1500
-1000
-500
0
500
1000
1500
Q
(m
3 /s
)
Frequency of CP10 (Tisza)
1950 1960 1970 1980 1990 2000
0
0.04
0.08
0.12
0.16
Fre
qu
en
cy
Relationship between extremes
Correlation
(daily)
Correlation
(Maxima)Rank
correlationCorrelation
(dQ+)
Tisza - Szamos 0.79 0.48 0.63 0.57
Tisza - Bodrog 0.70 0.40 0.49 0.48
Szamos - Bodrog 0.60 0.49 0.50 0.31
Recommended