Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




J.R. Kramer


Numerical simulations are used to investigate the behaviour of a system, based on a set of initial conditions and assumptions about the processes involved. The complexity of a model's structure influences its output, which in turn affects predictive performance. The confidence accorded to a model's results is directly associated with the input uncertainties propagated and transformed through the model's structure. Understanding the relationship between modelling uncertainty and model complexity is important when using numerical simulation for decision-making purposes such as environmental risk assessment. Components of uncertainty are defined by modelling error and modelling sensitivity. Modelling error is defined as the difference between a model's predictions and actual observations from the system. Modelling sensitivity is defined as the change in model output, given a change in model input. Error and sensitivity are related to complexity in different ways. More complex models have more detailed mathematical descriptions of the system being simulated. They also have less error, but greater sensitivity, due to larger numbers of inputs (degrees of freedom) and interactions within the model's structure. Therefore, error decreases and sensitivity increases, with increasing model complexity. Model utility, U, is used to select among models of different complexities. U is defined by combining evaluations of error and sensitivity into a single, quantitative characteristic. Utility is weighted by the modeller to reflect the relative importance of error and sensitivity. The uncertainty/complexity relationship is determined for two systems (a simple sorption system, and a more complex 3-dimensional groundwater tracer transport system). Moderately complex models are the most utile of those studied. For the more complex groundwater system however, all models performed equally well (no difference in error), indicating that sensitivity was the only significant contributor to utility measurements. The uncertainty/complexity relationship derived for this system indicates that all the models studied might be more complex than the system warrants, and that simpler models should be investigated. While the uncertainty/complexity relationship exists for all models, inter-disciplinary models that combine two or more discrete systems (such as environmental-economic models) are of particular interest, due to the presence of discontinuities and incompatibilities between the different model types. An inter-disciplinary model is developed, involving the integration of an input-output economic model (which describes the flow of money to and from various sectors of an economy) with a physical model that describes the environmental impact of economic activity. Simple, linear input-output models, both with and without environmental extensions, are evaluated and compared for modelling uncertainty. The effect of adding an environmental extension (and therefore changing overall model complexity) is an increase in uncertainty of model output. Uncertainty is largest at low levels of economic activity. The uncertainty/complexity relationship is a useful diagnostic tool for the purposes of selecting among models of differing complexity. The trends of error and sensitivity can define the optimal threshold of complexity, where the improvement in fit of moving to more complex models is not worth the increased sensitivity. If the optimal complexity threshold is not within the set of models studied, the results can be used to determine whether to move to more or less complicated models before repeating the process. This way, the methods can be used iteratively to arrive at the "best" model for the job.

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