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 ?

Study Area Rhine catchment – Germany Rhein Maxau Rhein Worms Rhein Kaub 1901 – 1999 Rhein Andernach 1901 – 1999 Mosel Cochem 1901 – 1999 Lahn Kalkofen 1901 – 1999 Neckar Plochingen

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 Randomness rejected for 6 out of 7

3. Understanding discharge series Goal: Equilibrium state Discharge: –Excess water –Meteorological origin –„Deterministic“ reaction

Principle

Signal to be explained

Bodrog – CP07 (362% Increase)

Tisza CP10 (462% increase)

The 100 largest observed floods of the Tisza at Vásárosnamény with the corresponding CPs.

Simulation Directly from CPs –

CP sequences Observed ( ) GCM simulated Historical simulated Semi-Markov chain (persistence)

Llobregat – observed CPs

Llobregat – KIHZ CPs

Summary and conclusions Hydrological extremes –Strongly influenced –Difficult to analyse –Not independent

Relationship between series Indicator series:

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

Principle

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 changes Tisza

Frequency of CP10 (Tisza)

Relationship between extremes Correlation (daily) Correlation (Maxima) Rank correlation Correlation (dQ+) Tisza - Szamos Tisza - Bodrog Szamos - Bodrog