Classification of Uncertainty
The causes of uncertainty in the model results come from various sources: Natural meteorological variations too small or too complex to be measured; approximations in the model formulation; approximations in deriving data to input to the model; and bias due to the aims and limitations of the model. These sources of uncertainty are not uniquely defined, and the regions between them are hazy. Even so, following international consensus in the study of radioactive waste disposal (NEA, 1999), we can categorise uncertainty into the following classes:
Specifying the wind for a given half hour period has no unique definition - for instance one could use the average of the scalar wind or the vector wind, the 'average' could be the median, the arithmetic mean or the harmonic (inverse) mean. This uncertainty is increased further when one looks at other parameters, such as temperature and boundary layer height, as the variations in the different atmospheric model input parameters might be correlated.
Atmospheric dispersion models are idealisations of reality - for instance a Gaussian spread is often assumed. Whilst the model might be representative of the general evolution of a plume it cannot represent all the behaviour. Such simplifications are made in going from the real world to a 'conceptual model'. Similarly the representation of the effects of topography and buildings. The effect of local heat sources might not even be included in the dispersion model.
Scenario (Future) Uncertainty
When seeking to estimate the likely maximum values for future years there is an inherent uncertainty as to what the meteorology will be for that year. If conditions are 'good', as far as pollution episodes are concerned, then the maximum values will be reduced. Conversely it may be 'bad', leading to increased pollution. Such uncertainties about the future weather of a location can be termed 'scenario' uncertainty, as we do not know in detail the precise scenario to be modelled. Scenario Uncertainty a particular problem in modelling radioactive waste disposal as the future climate for the next hundred years, let alone the next hundred thousand years, is difficult to predict due to anthropogenic factors.
Natural Variability (Turbulence)
When two releases are made close to each other it is found that they do not behave identically, and tend to drift apart. During two periods of theoretically similar weather the behaviour of the plume will depend on the exact conditions during and after the release. This is predominantly due to atmospheric turbulence continually causing stochastic variations in the way that a contaminant plume is dispersed. Such natural variability can be reduced by taking ensemble averages, though even then there will be a limit to how far the uncertainty can be reduced.
Atmospheric dispersion models have been developed to predict particular results. Often it is the maxima that are most important, rather than the value at larger distances. This can lead to a bias in the results, as a model which seeks to perform well in one meteorological and release regime might not perform well under different conditions. Bias can also occur in the derivation of input data, for instance when interpreting data from the 'nearest' meteorological station.
Evaluation Data Uncertainty
For complex models one means of enhancing the model's usefulness is by using observed data. This introduces further uncertainties as the data used is itself both uncertain and not continuous in space or time. Thus there is no direct link between a model prediction and an observed value, as they will be representative of different volume and time averages. Observations are also liable to 'observational error', actually an uncertainty not an error.
In controlling and limiting uncertainty an analysis which leads to an understanding of the sources of uncertainty is only a first step. The next stage is, where possible, to quantify the the uncertainty. When a dominant component is parameter uncertainty then this can be done using Monte Carlo studies. In seeking to then reduce uncertainty sensitivity studies can be used to estimate how sensitive the model is to uncertainty in individual input parameters. This can then guide future work, including experimental or observational studies, so that the uncertainty in the most influential parameters can be reduced.
© 2000 Neill S Cooper
This page is available in French: La Classification de l'Incertitude
Estimates of the uncertainty in atmospheric dispersion models can be found here.