1997 Floods and Rains in the Mirror of Extreme Value Theory

The Moravian floods in July 1997 have killed 49 people, affected 536 settlements, 29 000 houses and cost over 2.5 billion USD. A question arises whether the hydrological event (or the preceding meteorological one) can be predicted. In order to foresee the magnitude of catastrophic events we extrapolate historical data which has an impact on the construction in the vicinity of the rivers, insurance pricing and the general ecology of the river systems. A balance between underestimating the hazard and excessively conservative approach needs to be found as both could have tragic or costly outcomes. We present an application of Extreme Value Theory to daily precipitation data set from Northern Moravia and compare various aspects of the available estimators. We argue that when reasonable estimators are used, even events such as the 1997 one are assigned probabilities and return periods which are not unrealistic. We observe the impact of in(ex-)cluding the actual 1997 data point on the resulting estimators. Introduction The main flood risks in the Czech Republic are usually classified as: • snow melt period of December to April in combination with precipitation (typical of lowland and hilly parts of the Labe, Vltava and Morava catchments • longer duration events summer floods from regional rainfall lasting from 10 to 72 hours (rainfall intensified and prolonged by orographic (elevation) enhancement, smaller water volume and more abrupt than spring floods) • intense short-duration summer rainfall exceeding 44 mm per hour (flood peak occurring within hours of rainfall peak, small areas affected, around 100 km, flash floods are characteristic of small short streams after April-September thunderstorms) Previous to 2002, the most significant flood event in recent history is that of 6th to 9th July 1997 with long-lasting and intensive precipitation over the eastern quarter of the Czech Republic including Moravia and east Bohemia affected. Statistics and Extreme Value Theory have already become a standard tool for evaluation in hydrological and meteorological practice. [Coles and Dixon (1999)], [Coles et al.(2003)] and [Engeland et al.(2004)] are thorough examples of the state-of-the-art application. Being aware of the existence of complex hydrological/meteorological prediction models we do not claim to be able to link the two. We rather focus on the main cause of floods, i.e. precipitation, and claim that being aware of the possible range of precipitation outcomes may help in foreseeing the scale of catastrophic flood events. Data We have obtained a data set from the Czech Hydro-Meteorological Institute (CHMI) detailing daily precipitation values for 10 meteorological stations in Northern Moravia. We have excluded station KAST due to the short duration of measurements and therefore only work with 9 stations. Station KRNO is missing records for the period of the 1997 flood and is therefore also largely irrelevant for our study. The longest record spans across 45 years (January 1, 1960 to February 6, 2005) and the maximum daily precipitation at these stations was 214 mm. For most of the stations, the maximum precipitation in 1997 by far exceeded the previously known maxima. Table 1 gives summary statistics of this data set. Fitting Block Maxima Assuming the daily precipitation records at a given station X1, X2, . . .Xn are i.i.d (the same asypmtotic results hold for short-term dependence, see [Leadbetter et al.(1983)]), the maxima of this series WDS'05 Proceedings of Contributed Papers, Part I, 138–143, 2005. ISBN 80-86732-59-2 © MATFYZPRESS