Separating natural and epistemic uncertainty in flood frequency analysis

Although there are many sources of uncertainty it is important to recognise two basic kinds of uncertainty that are fundamentally different from each other: natural and epistemic uncertainty. Natural uncertainty stems from variability of the underlying stochastic process. Epistemic uncertainty results from incomplete knowledge about the process under study. The paper looks at the difference between these two kinds of uncertainty in flood frequency analysis. Natural uncertainty is incorporated in the distribution function of the annual maximum series from which the flood design criteria (e.g. annual failure probability, AFP) is derived. Sampling uncertainty and model uncertainty are two epistemic uncertainty sources. Sampling uncertainty is represented by probability distributions for AFP. The design criteria AFP is considered as random variable whereas the uncertainty of AFP depends on the knowledge of the analyst. It is shown how more data steepen the cumulative distribution function (cdf) of AFP, and, therefore, decrease the uncertainty about AFP. The uncertainty due to different distribution functions is incorporated by using probability bounds. They give a region within which the true but unknown distribution function is expected. The greater the uncertainty due to the distribution function type, the wider the bounds and the more difficult to make statements about frequencies of extreme events. By using a likelihood measure as indicator for the appropriateness of different distribution functions, distribution functions with low weights are eliminated. This considerably narrows the uncertainty bounds. This approach which separates between natural and epistemic uncertainty reveals the uncertainty which can be reduced by more knowledge (epistemic uncertainty) and the uncertainty which is not reducible (natural uncertainty).