Gaussian process emulators for uncertainty analysis in groundwater flow

Stone, Nicola (2011) Gaussian process emulators for uncertainty analysis in groundwater flow. PhD thesis, University of Nottingham.

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Abstract

In the field of underground radioactive waste disposal, complex computer models are used to describe the flow of groundwater through rocks. An important property in this context is transmissivity, the ability of the groundwater to pass through rocks, and the transmissivity field can be represented by a stochastic model. The stochastic model is included in complex computer models which determine the travel time for radionuclides released at one point to reach another. As well as the uncertainty due to the stochastic model, there may also be uncertainties in the inputs of these models. In order to quantify the uncertainties, Monte Carlo analyses are often used. However, for computationally expensive models, it is not always possible to obtain a large enough sample to provide accurate enough uncertainty analyses. In this thesis, we present the use of Bayesian emulation methodology as an alternative to Monte Carlo in the analysis of stochastic models. The idea behind Bayesian emulation methodology is that information can be obtained from a small number of runs of the model using a small sample from the input distribution. This information can then be used to make inferences about the output of the model given any other input.

The current Bayesian emulation methodology is extended to emulate two statistics of a stochastic computer model; the mean and the distribution function of the output. The mean is a simple output statistic to emulate and provides some information about how the output changes due to changes in each input. The distribution function is more complex to emulate, however it is an important statistic since it contains information about the entire distribution of the outputs. Distribution functions of radionuclide travel times have been used as part of risk analyses for underground radioactive waste disposal. The extended methodology is presented using a case study.

Item Type:Thesis (PhD)
Supervisors:Cliffe, K.A.
Dryden, I.L.
Faculties/Schools:UK Campuses > Faculty of Science > School of Mathematical Sciences
ID Code:1989
Deposited By:Dr NA Stone
Deposited On:11 Oct 2011 10:54
Last Modified:11 Oct 2011 10:54

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