Handling uncertainty in extreme or unrepeatable hydrological processes—the need for an alternative paradigm

*Correspondence to: Malcolm Anderson, School of Geographical Sciences, University of Bristol, University Road, Bristol BS8 1SS, UK. E-mail: m.g.anderson@bristol.ac.uk The conventional approach to assessing uncertainty in a hydrological model involves comparing model predictions with a test dataset of measurements. Typically, both the dataset and the model predictions will be represented as a time series of precise measurements, even though it is acknowledged that field measurements have associated inaccuracies and, more significantly, a model cannot be expected to make an exact prediction of a hydrological phenomenon. By comparing predicted and measured time series it is possible to extract, often multiple, measures of the distance (in length or time) between model prediction and measurement, which is thought of as residual uncertainty. This conventional characterization also applies to the GLUE methodology (Beven and Binley, 1992), in which multiple model runs with multiple parameter sets, after some preselection on ‘behavioural’ grounds, are conditioned according to the distance between predicted and measured response. However, we believe that there are a number of classes of problems in hydrological processes that require different approaches towards uncertainty estimation. Figure 1 illustrates the dimensions on which hydrological problems can be classified, following a general classification for modelling problems proposed by Blockley (1980). The base (and rather special) case is the situation in which there are precise simultaneous measurements of the phenomenon of interest and the model prediction of that phenomenon. However, often the most interesting hydrological problems are where there are no simultaneous measurements and predictions. This may, for example, be because the phenomenon of interest is extremely rare (such as an extreme flood) or unrepeatable (such as a hydrologically activated landslide). The situation is analogous to the problem that occupies engineers responsible for high reliability systems: how is the probability of a nuclear reactor meltdown or the collapse of a long-span suspension bridge to be estimated when there may be no instances of the event of interest, and even if there are, the population is hopelessly small in statistical terms? Even if relevant measurements are available they may not be recorded in precise terms. Measurements may only be bounded, as would be the case with a discrete measurement device (any digital device), or may be described in linguistic terms, as is the case in a linguistic soil classification. Finally, the available measurements may only be partially relevant to the