Cooper and Caulcott Ltd

Environmental Modelling Consultants

Sensitivity Studies

In general Sensitivity Analysis is the exploration of changes in some outcome of a calculation when the inputs to the calculation are altered. The primary reason for undertaking sensitivity studies is to assess the possible effect of uncertainty on the model results.

A second important use of sensitivity studies, which is for undertaking calculations to assess the effect of assumptions made within the model, and also to investigate model behaviour. By making an appropriate selection of a data value it is possible to consider the effect of some processes not included in the model.

Types of Sensitivity Analysis

A local sensitivity analysis is concerned with small changes about some central case (or cases) of interest. By its nature it is concerned with sensitivity to continuously variable (rather than discrete) aspects of the system. The local sensitivity about one location may be completely different from that about another location. Essentially, the objective of a local sensitivity analysis is to find the partial derivatives of the outcome with respect to the inputs at the point in question, and is thus primarily a tool in investigating model behaviour.

A global sensitivity analysis is concerned with the whole set of potential inputs and aims to give an overall indication of the way that the outcome varies, and in particular how the output varies in response to input variations within the range of parameter uncertainty. A global sensitivity analysis can display a non-linear response, and thus it can be incorrect to globally extrapolate the local results. Often within radioactive waste studies the uncertainty in some key parameter values (such as hydraulic conductivity and sorption coefficient) have uncertainties of an order of magnitude or more. In such circumstances it is unlikely that the global response is linear.

The simplest of sensitivity studies involves the variation of a single parameter value whilst all other values remain fixed. However, even a series of such studies will only investigate a tiny fraction of the parameter space, as it is ignores the simultaneous variation of two (or more) parameter values. If all variations are local, and therefore linear, then the effect of varying multiple parameters can be found by a suitable linear combination of the results for individual parameters. However, if the global response is non-linear then such linear combinations are no longer valid and muleiple parameter variations need to be considered.

Undertaking multiple parameter variations can easily lead to there needing to be an astronomical number of calculations. When a probabilistic (Monte Carlo) code is available such non-linear interactions can be studied by a random approach in which calculations are made at a randomly generated set of parameter values (in a specified set of ranges) and the results are statistically analysed to discover the sensitivities. Such multiple runs also allow global sensitivity studies to be undertaken, by ploting the calculated dose aginst the parameter value the sensitivity of teh results to that parameter can be visualised. Whilst the sampling of many parameter values can lead to the sensitivity to a single parameter not being so evident, it avoids the problems of single parameter sensitivity studies which can themselves be sensitive to the values of other parameters. Global sensitivity studies provide results which can be used to prioritise studies to reduce uncertainty, for example by focusing experimental studies on those radionuclides and locations which have the greatest contribution to the uncertainty in the peak risk

© 2000 Neill S Cooper
Last changed on June 12, 2000

Classification of the uncertainty in numerical models can be found here.

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