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There are at least as many definitions for uncertainty as have been quoted for risk. The Defra report (Sayers et al., 2002) defines it as “a general concept that reflects the lack of sureness about something, ranging from just a sort of complete sureness to an almost complete lack of conviction about an outcome”. This definition can be narrowed for uncertainty analysis, which aims to quantify the overall uncertainty associated with the response as a result of uncertainties in the model input/Parameters/structure/etc.
Traditionally, uncertainty is divided into natural (or aleatory) variability which refers to the randomness observed in nature and knowledge (or epistemic) uncertainty which refers to the state of knowledge of a physical system and our ability to measure and model it (an in depth discussion has been presented by Hall). It has been argued that only knowledge uncertainty can be used to reduce the overall uncertainty. Moreover, it has been stated that natural uncertainty is a property of the system, whereas epistemic uncertainty is a property of the analyst. This distinction is a valuable theoretical concept, however, it can be questioned if it is in most cases possible to distinguish between these two fundamental uncertainties. When (as commonly in science) knowledge is captured though an imperfect model or theory, the boundary between natural and knowledge uncertainties will be blurred and will change over time. Lack of understanding of a process, for example, might initially appear as natural variability; inclusion of that process into a formal model might then appear to shift some of the uncertainty into knowldege uncertainty.
In the estimation of flood frequency, it is common to fit a single statistical distribution to all the flood peak data that are available. This is despite the fact that different peaks might come from quite different physical mechanisms, each of which might have its own distribution (synoptic rainfall events, convective rainfall events, combined rain on snow events) and might not be easily represented as a single distribution. The dilemma then is that including such knowledge also makes the knowledge model more complex and consequently more difficult to calibrate with small data samples. The multiple sources of uncertainty involved in flood modelling processes for different applications will necessarily make it difficult to separate between these types of uncertainty in practice.
Nevertheless, any attempt to characterize knowledge uncertainty highlights the three key parts of any uncertainty analysis:
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Define what is uncertain in the modelling process (Sources of uncertainty) The various sources of uncertainty have to be identified and quantified. A methodology has to be chosen accordingly.
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Define how to quantify output uncertainty consequent on the sources of uncertainty The various sources of uncertainty have to be propagated through the modelling system
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Define how to condition the uncertainty estimate as data on model predicted variables become available Many uncertainty methods require a definition of model performance (e.g. how well does a model predicted variable compare to measurements, which may themselves be associated with uncertainty). Measures of model performance should lead to uncertainty constraint and refinement of risk estimates through model conditioning or rejection.
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References
Hall, J.W., Handling uncertainty in the hydroinformatic process. Hydroinformatics, 5(4): 215-232.
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)