ABSTRACTS 'Extreme Discharges' - CHR-KHR

Some comments on the estimation of extreme floods
Annegret Thieken
Bruno Merz
Heiko Apel
Engineering Hydrology, GeoForschungsZentrum Potsdam
Telegrafenberg, D-14473 Potsdam, Germany
thieken@gfz-potsdam.de
The estimation of flood hazard is often based on an extreme value analysis of discharge data. Such estimations
are, however, rather uncertain (e.g. Merz & Thieken, 2005). Fig. 1 shows that large uncertainty bounds result if
various distribution functions are adapted to a series of annual maximum floods (from 1880 to 1999) at the Cologne
gauge on the river Rhine. Therefore, the question arises how this uncertainty can be reduced. Two different
approaches are followed up for the gauges Cologne and Rees on the river Rhine.
At the Cologne gauge historic flood events listed in Krahe (1997) were considered. Flood events of 1497, 1342
and 1374 with water levels (according to the current gauge level) of 11.50 m, 11.53 m, and 13.30 m, respectively,
clearly exceed the largest observed flood events in the time period 1880 to 1999. Discharges were obtained
using the current rating curve. Owing to the morphological and hydraulic changes in the river bed the
calculated discharges are very uncertain.
The return periods of these events were estimated following the guidelines of DVWK (1999). The results are
given in Table 1. Thus, the largest flood of 1374 can be classified as a 1000-year flood. Its magnitude is well
estimated by the Generalised Logistic, the Gumbel or the Log-normal distribution in Fig. 1.
Furthermore, an upper bound was assessed using different methods: the classification of maximum floods of
Francou & Rodier (1967), the estimation of floods with large return periods after Kleeberg & Schumann (2001)
and an envelop curve of maximum observed floods using data of Stanescu (2002) and other sources. In addition,
Lammersen (2004) assessed a maximum flood at the Cologne gauge by means of modelling techniques. The
resulting values are summarised in Table 1. On the basis of these data some distribution functions shown in
Fig. 1 can be ruled out, e.g. the Weibull distribution.
At the Rees gauge that is situated downstream of the Cologne gauge the probabilistic model of Apel et al. (2004,
2005) was applied. The model consists of a flood frequency analysis at the Cologne gauge, a generation of typical
flood waves and discharges from the tributaries Ruhr and Lippe, a routing module as well as an estimation
and simulation of possible levee breaches between the gauges Cologne and Rees.
In Fig. 2 the flood frequency analysis for the Rees gauge is contrasted to the results of the probabilistic model of
Apel et al. (2004, 2005). Since levee breaches are included in the probabilistic model, it is capable of calculating
an upper bound of the flood discharge. The upper bound of the probabilistic model is consistent with the results
of Lammersen (2002). However, the data and modelling requirements of the probabilistic model are lower.
It is suggested that the results of flood frequency analyses should be complemented with simple estimation
methods in order to reduce uncertainty. If more time and data are available a simple probabilistic model gives a
good assessment of an upper bound of flood discharge.
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