Probability is the chance of occurrence of one event compared to the population of all possible events. The probability is normally computed for a particular event or outcome. Therefore, probability is subject to the definition of an event as well as the methodology of computing a probability. It is quite important to note here that the probability of flooding may be quite different to the probability of some stage or discharge being exceeded in a river. Flooding is modified by the effects of flood defence and drainage systems.

It is important to recognise that even in well defined statistical system the estimation of a probability of an event will itself be uncertain. In poorly defined environmental systems, with many and various sources of uncertainty, this uncertainty might be significant. This is best illustrated here in the context of flood frequency. Risk maps require the definition of a discharge with a particular probability (0.01 in any year or 100 year return period for fluvial flooding). There are very few sites with discharge records of a length of 100 years in the UK. For a good statistical estimate of the 100 year event, even longer records would be required, with the additional assumption that the climatic forcing and the catchment characteristics are stationary. Thus, especially for sites with shorter record lengths, the estimation of the 100 year event will require a model (generally a fitted distribution for this type of problem) but there will be uncertainty as a result of choosing the form of distribution and extrapolating the data to longer return periods on the basis of a small sample. Current practice generally requires the estimation of only a best estimate of the discharge for a given return period. Best practice would require that the uncertainty due to both model choice and extrapolation be estimated. Well-established statistical, and continuous simulation, methods of flood frequency estimation allow this.

The Flood Estimation Handbook (FEH) (1999) gives guidance on how to apply both peaks over threshold and annual maximum methodologies of frequency estimation (but the FEH software does not estimate uncertainty in, for example, the T year flood as a standard procedure). For further definitions of probability and flood frequency analysis the reader is referred to Sayers et al. (2002), p 7 and 10, box 2.1 and 2.2 respectively.

The previous two sections demonstrate that the computation of risk is in fact a combination of two probability distributions. The consequence as well as the probability are uncertain and are combined to a risk prediction. There are many different sources of uncertainty and estimating the net effect on predictions will depend on the assumptions made. Thus a more detailed understanding of the sources and propagation of uncertainties through prediction systems is required.

References

CEH, 1999. Flood Estimation Handbook, Centre for Ecology and Hydrology.

Sayers, P.B., Gouldby, B.P., Simm, J.D., Meadowcroft, I. and Hall, J., 2002. Risk, Perfromance and Uncertainty in Flood and Coastal Defence - A Review, DEFRA/Environment Agency - Flood and Coastal Defence R&D Programme, Wallingford.

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Risk and Uncertainty (Description and Definition)