Worked example: Exploring model defects using linear analysis

Any groundwater model is riddled with imperfections. Do these compromise its decision-support utility? Linear analysis can answer this question.

Ideally, a groundwater model should be endowed with many parameters. These allow it to capture information on hydraulic property heterogeneity that is made available to it through history-matching. Assessment of post-history-matching parameter nonuniqueness is an indispensable component of model predictive uncertainty analysis. It is through associating uncertainties with decision-critical model predictions that risks accompanying contemplated courses of management action can be assessed.

Prediction uncertainties can be approximated using linear methods, wherein the action of a model is replaced by that of a matrix populated by model-output-to-parameter sensitivities. These methodologies can be fast, and they can be powerful. Furthermore, “parameters” that are not really parameters at all can be included in these analyses. These “parameters” can include aspects of a model that would not normally be adjusted through history-matching. These aspects can represent some of a model’s potential defects, particularly those which pertain to its boundaries which often represent, in simplified form, connections to wider systems. The contributions made by these “parameters” to the uncertainties of decision-critical predictions can be evaluated. If these are small compared with other sources of uncertainty that are, indeed, included in a model, then the model is ok – for the making of certain predictions at least.

Model defect analysis is illustrated using a model that was built to evaluate impacts of ongoing extraction from two wellfields that are situated near the south western margin of the Great Artesian Basin. Our GMDSI report discusses philosophies, methodologies, software, and a few implementation details in an easy-to-read way. Conclusions on the decision-support utility of the model are drawn.