Transcript Hydrological extremes and their meteorological causes

Hydrological extremes
and their meteorological
causes
András Bárdossy
IWS
University of Stuttgart
1. Introduction
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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
Q(t )  Q1 ,..., QN  F (Q)  a1 , a2 , a3  HQT
• Annual extremes
• Seasonal values
(Summer Winter)
• Partial duration series
Independent sample
Homogeneous
Future like past ?
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 changes
Are there any unusual time intervals?
• Tests
– Permutations and Moments
– Autocorrelation (Bartlett)
– Von Neumann ratio Test
Negative Tests – only rejection possible
Permutations
Q(1),...Q(t ),..., Q(T )
Annualmaxi ma
mi (t1 ), mi (t 2 ), mi (t3 ) Moments (i) for time intervals
randomly mixed series
Q( (1)),..., Q( (T ))
mi ( (t1 )), mi ( (t 2 )), mi ( (t3 ))
different sequence
random moments
Comparison - to test randomness
Randomness rejected for 6 out of 7
3. Understanding discharge
series
• Goal: Equilibrium state
• Discharge:
– Excess water
– Meteorological origin
– „Deterministic“ reaction
Principle
120
Weather
Discharge (m3/s)
80
40
0
-40
Catchment
-80
0
100
200
Time (days)
300
400
Signal to be explained
Discharge (m3/s)
60
40
20
0
0
100
200
Time (days)
300
400
Bodrog – CP07
(362% Increase)
Tisza CP10
(462% increase)
4000
Discharge (m3/s)
3500
3000
2500
CP01
CP05
Other
2000
1500
1
10
100
Return period (years)
1000
The 100 largest observed floods of the Tisza at
Vásárosnamény 1900-1999 with the corresponding CPs.
Simulation
Directly from CPs –
Q(t )  QP (t )  QN (t )
QP (t )  Disturbanc e - random
QN (t )  Reaction - determinis tic
QN (t )  F (Q(t  1))
QP (t )  CP dependent
CP sequences
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Observed (1899-2003)
GCM simulated
Historical simulated
Semi-Markov chain (persistence)
Llobregat – observed CPs
Discharge (m3/s)
1600
1200
800
400
0
0
10000
20000
Time (days)
30000
Llobregat – KIHZ CPs 16911781
Discharge (m3/s)
2000
1600
1200
800
400
0
0
10000
20000
Time (days)
30000
Summary and conclusions
• Hydrological extremes
– Strongly influenced
– Difficult to analyse
– Not independent
Relationship
between series
• Indicator series:
0 if Q(t )  Q p
I p (t )  
1 if Q(t )  Q p
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
Andernach Q 100
Gumbel
GEV
Pearson 3
15000
14000
13000
12000
11000
10000
MM
MLM
LSQ
LM
PWM
Principle
Discharge (m3/s)
100
80
60
40
20
0
0
100
200
300
Time (days)
Q(t ) from CP(t )
Q(t )  Q(t )  Q(t  1)
Related to weather if Q(t )  0
400
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
Discharge (m3/s)
60
40
20
0
0
100
200
Time (days)
300
400
Discharge changes Tisza
1500

Q (m3/s)
1000
500
0
-500
-1000
-1500
0
100
200
300
400
Frequency of CP10 (Tisza)
0.16
Frequency
0.12
0.08
0.04
0
1950
1960
1970
1980
1990
2000
Relationship between extremes
Correlation Correlation
Rank
(daily)
(Maxima) correlation
Tisza Szamos
Tisza Bodrog
Szamos Bodrog
Correlation
(dQ+)
0.79
0.48
0.63
0.57
0.70
0.40
0.49
0.48
0.60
0.49
0.50
0.31