Approaches to uncertainty quantification in groundwater modelling for geological disposal of radioactive waste

The issue of safely dealing with radioactive waste has been addressed in several countries by opting for a geological disposal solution, in which the waste material is isolated in a subsurface repository. Safety assessments of such facilities require an in-depth understanding of the environment they are constructed in. Assessments are commonly underpinned by simulations of groundwater flow and transport, using numerical models of the subsurface. Accordingly, it is imperative that the level of uncertainty associated with key model outputs is accurately characterised and communicated. Only in this way can decisions on the long-term safety and operation of these facilities be effectively supported by modelling.

In view of this, a new approach for quantifying uncertainty in the modelling process has been applied to hydrogeological models for the UK Low Level Waste Repository, which is constructed in a complex system of Quaternary sediments of glacial origins. Model calibration was undertaken against a dataset of observed groundwater heads, acquired from a borehole monitoring network of over 200 locations. The new methodology comprises an evolution of the calibration process, in which greater emphasis is placed on understanding the propagation of uncertainty. This is supported by the development of methods for evaluating uncertainty in the observed heads data, as well as the application of mathematical regularisation tools (Doherty, 2018) to constrain the solution and ensure stability of the inversion. Additional information sources, such as data on the migration of key solutes, are used to further constrain specific model parameters. The sensitivity of model predictions to the representation of heterogeneity and other geological uncertainties is determined by smaller studies. Then, with the knowledge of posterior parameter uncertainty provided by the calibration process, the resulting implications for model predictive capacity can be explored. This is achieved using the calibration-constrained Monte Carlo methodology developed by Tonkin and Doherty (2009).

The new approach affords greater insight into the model calibration process, providing valuable information on the constraining influence of the observed data as it pertains to individual model parameters. Similarly, characterisation of the uncertainty associated with different model outputs provides a deeper understanding of the model’s predictive power. Such information can also be used to determine the appropriate level of model complexity; the guiding principle being that additional complexity is justified only where it contributes either to the characterisation of expert knowledge of the system, or to the model’s capacity to represent details of the system’s behaviour that are relevant for the predictions of interest (Doherty, 2015). Finally, the new approach enables more effective communication of modelling results – and limitations – to stakeholders, which should allow management decisions to be better supported by modelling work.

References:

• Doherty, J., 2015. Calibration and Uncertainty Analysis for Complex Environmental Models. Watermark Numerical Computing, Brisbane, Australia. ISBN: 978-0-9943786-0-6.
• Doherty, J., 2018. PEST Model-Independent Parameter Estimation. User Manual Part I. 7^th Edition. Watermark Numerical Computing, Brisbane, Australia.
• Tonkin, M. and Doherty. J., 2009. Calibration-constrained Monte Carlo analysis of highly parameterized models using subspace techniques. Water Resources Research, 45, W00B10.