ABSTRACTS 'Extreme Discharges' - CHR-KHR

Uncertainty in flood quantiles from basin and river models
Ferdinand Diermanse
Henk Ogink
WL Delft Hydraulics
P.O. Box 177, NL 2600 MH Delft, the Netherlands
Hendrik Buiteveld, RIZA
Institute for Inland Water Management and Waste Water Treatment (RIZA)
P.O.Box 9072, NL 6800 ED Arnhem, the Netherlands
ferdinand.diermanse@wldelft.nl
henk.ogink@wldelft.nl
h.buiteveld@riza.rws.minvenw.nl
Introduction
Without adequate flood defence structures, almost two-thirds of the Netherlands would be regularly flooded. To
prevent floods by the sea, rivers and lakes, an extensive system of river dikes and coastal-defence has been constructed
in the past. In the design of the dikes a safety level is defined of the order of 10 -3 to 10 -4 “failures” per
year. This frequency is based on both the economic value of the protected area and the extent of the threat. Related
to this safety level, the design of the dikes must be based on extreme hydraulic conditions, i.e. extreme
water levels, wave heights or wave periods. In practice these conditions are often derived in statistical form
where some type of extreme-value distribution function is fitted to observed data of extreme conditions. When
extrapolating to extreme events with a frequency of exceedance of 10 -3 to 10 -4 per year, the statistical uncertainties
inevitably are substantial.
Extreme value analysis: traditional approach
Most commonly statistical methods are used in extreme value analysis and a parameterised probability distribution
function is fitted to a set of observed extremes of the target variable. The distribution provides a one to one
relation between probabilities of (non)exceedence (which are equivalent to return periods) and the associated
level of the target variable (e.g. peak discharges). This relation can then be used for the prediction of extremes
for recurrence times that are far beyond the length of the data record. The popularity of such strictly statistical
methods is mainly due to the fact that they are easy to apply. For design purposes along the river Rhine the frequency
analysis of extreme discharges uses no less than five distribution functions: Gumbel, log-normal, Pearson-III,
general Pareto and exponential. An averaging procedure is applied to obtain a unified result.
The uncertainties in frequency analyses are generally expressed by confidence intervals. The traditional method
to estimate these intervals is to assume a Gaussian shaped confidence band for the parameters of the distribution
function. In this way the confidence intervals, or at least approximations, can be derived analytically. A problem
with this assumption is that it sometimes results in suspiciously wide confidence intervals. Furthermore, confidence
intervals can differ strongly for different distributions even if the goodness-of-fit is comparable. An example
of this is shown in Figure 1 where two functions (general Pareto and exponential) are derived from a
series of Peaks-Over-Threshold discharges for the Rhine at Lobith over the period 1901-2004. For a return period
of 1,250 years (which is the design criterion along the non-tidal part of the Rhine in the Netherlands) the
width of the confidence interval is 5,500 m 3 /s for the exponential distribution and 9,000 m 3 /s for the Pareto distribution.
Since both underestimation and overestimation of flood dangers can prove to be very costly, these
uncertainties are much larger than desired. Furthermore, these two numbers show that even the estimated uncertainties
are highly uncertain!
39