A main purpose in a frequency or extreme value analysis is to obtain an estimate for some hydraulic or hydrologic quantity (e.g. a water level or a discharge at some location) that corresponds to a given return period. In traditional methods of frequency analysis observations are used. These are statistically extrapolated when estimates of extremes are desired for return periods much longer than the time period covered by the data. To overcome limitations in such traditional methods, GRADE (Generator of Rainfall And Discharge Extremes) can be used as an alternative. In GRADE a chain of mathematical models is used for the generation of ‘arbitrary’ long term time series of discharges in a river system. Such GRADE systems are presently available for the rivers Rhine and Meuse.
The main issue addressed in this report is the derivation of the uncertainty that should be assigned to the estimates that GRADE produces for discharge extremes. These uncertainties in the by GRADE computed discharges are derived from uncertainties in GRADE’s model components.
One of these components is formed by the temporally long term and spatially distributed weather (rainfall and temperature) series. The uncertainty in this component is here quantified by means of an ensemble of synthetically generated series of length 20,000 years. As a matter of the construction (using a stochastic weather generator) the variability in this ensemble reflects the current climate uncertainty.
The hydrological HBV models form a second source of uncertainty in the GRADE system. The uncertainty in these hydrological models is also quantified by means of an ensemble. This ensemble consists of five sets of HBV model parameter-combinations, which reflect the model parameter uncertainty of the HBV model.
Uncertainties in the hydrodynamic SOBEK models that are used for the routing of (extreme) flows along the main river channel are a third source of uncertainty. In the present work these uncertainties are not yet taken into account, however.
For every combination of the synthetic weather series and a set of HBV-parameters a GRADE simulation of 20,000 years is carried out. In the report below it is described how the results of these GRADE computations are combined to obtain the uncertainty in the estimates of the extreme discharges.
This uncertainty analysis has been applied to derive the uncertainties in the GRADE estimates of extreme discharges of the Rhine at Lobith and the Meuse at Borgharen. The results are illustrated by means of discharge frequency curves for return periods up to 50,000 year. It is also verified to what extent the (uncertainties in) the various model components in GRADE contribute to the total uncertainty in the discharges. Moreover for the Rhine the effects of taking upstream flooding into account are established. On the basis of SOBEK models with and without flooding it is found that flooding significantly reduces the Lobith discharges for return periods longer than about 50 year. For example, for a return period of 10,000 year this reduction amounts about 4000 m3/s. At the same time the width of the confidence bands is also (and even much more substantially) reduced.
In a separate variational (rather than uncertainty) analysis the sensitivity of extreme Lobith discharges on uncertain parameters in the upstream flooding mechanisms is examined.
HFP van den Boogaard, M Hegnauer, JJ Beersma. GRADE Uncertainty Analysis