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