Approaches to the measurement of uncertainty in geoscience data modelling

Broadly speaking, geoscientific investigations involve observations or measurements of the natural environment and, through modelling and interpretation, produce an understanding of the objects within the geosphere and the natural processes governing it. The absolute value of the measurements arising from the modelling and interpretation are critically important but equal importance must be given to the confidence that can be placed upon the measurement in terms of how closely it mimicks reality. The aims of this study are to review current methodologies for measurement of uncertainty, to make recommendations for a practical approach to uncertainty measurement within the BGS and to give some practical examples of how this might be achieved.
The major sources of uncertainty in geoscience were found to be:
• Variability - the inherent natural variability that exists in geological objects and processes that exists independently of geoscientist’s investigations;
• Measurement uncertainty - the uncertainty arising from imperfections in the measurement procedure;
• Sampling uncertainty - arising from the process of making a measurement at a specific spatial location and takes account of whether the measurement is truly representative of the area/volume being sampled;
• Modelling Uncertainty - the uncertainty at this interpretive stage is a combination of the uncertainties of all of the input parameters and the uncertainty introduced through the data interpretation itself.
The methods used for estimating uncertainty were found to fall into three broad categories:
• The analytical approach - this uses rigorous statistical theory to propagate combined uncertainties through the mathematical functions that use the measured inputs to produce the modelled output.
• Computationally intensive approaches - this procedure requires that the model is calculated a number of times, each time a small change is made to the input parameters (representative of the natural uncertainty of that parameter). The result of each run of the model is stored and, with the use of suitable strategies for the choice input parameter changes, the distribution of results for the repetitions will be representative of the uncertainty in the model.
• Measurement of uncertainty on subjective and semi-quantitative data. - in geoscience applications there are many examples where semi-quantitative data is an important input parameter for modelling. Geological interpretation is a good example of subjective information. Borehole logs and geological maps produced by different geologists will be different according to their experience and background, data from these sources is then digitised and can end up as an input to a solid geology model.
Examples of applying selected measurement uncertainty strategies to three different geoscience data models have been presented. These are:
i) Bootstrap resampling of synthetic borehole data
ii) Bootstrap resampling of coal-field borehole data
iii) Bootstrap resampling on a geostatistical interpretation of G-base arsenic data From the literature review and the modelling examples a philosophy and strategy for the measurement of uncertainty in BGS geoscience data modelling has been proposed:
• Equal importance should be given to the measurement of uncertainty as is given to the final model.
• It is critical to have a multidisciplinary team with expert representatives from each stage of the modelling project providing information on the uncertainty of each step of the process and to ensure that that emphasis is placed on obtaining good uncertainty estimates for those inputs that critically affect the model outcome.
• There should be a defined mechanism for all geoscience modelling projects that allows all sources of uncertainty within the project to be recorded in a formalised manner. A suitable tool for this is the use of cause and effect diagrams.
• Geoscience data models include both quantitative and subjective/semi-quantitative inputs and outputs. The authors suggest that bootstrap-resampling and fuzzy logic approaches respectively are suitable methods for producing robust estimates of uncertainty on these two types of data.
• The final estimate of uncertainty on any model must include contributions from all of the significant sources of uncertainty identified by the cause and effect diagram of the project.