Air pollution models play a vital role in understanding environmental impact, but ensuring model accuracy comes with significant computational expense. To balance this
trade off, we investigate multi-fidelity approaches that mix costly high-fidelity simulations with inexpensive approximations to achieve efficient and reliable predictions.
This thesis develops methods for uncertainty quantification of advection–diffusion
models, focusing on variance reduction. We study how uncertainty in advection, diffusion, and source strength affects pollutant transport, and design efficient strategies
to estimate means, confidence intervals, and sensitivity indices.
A two-dimensional advection–diffusion equation is discretised using finite element
methods. Using Monte Carlo estimation, we confirm that computed mean-squared
errors agree with theory, and extend the method with bootstrapped confidence intervals, providing reliable uncertainty estimates at lower cost.
Variance reduction is achieved through new control variate methods. Building on
control variates methods which allow control variates with unknown means, we introduce the control variates with estimated means and budget control (CVB) method
which incorporates an explicit budget. Both methods are analysed, showing significant accuracy gains over standard Monte Carlo. We also propose a multi-fidelity
bootstrap estimator, combining CVB with confidence intervals to produce consistently smaller intervals. We test numerical and data-informed surrogate models and
find that neural network approximations are the most suitable as a control variate.
For sensitivity analysis, we compare standard Sobol index estimators and introduce a CVB based alternative that lowers variance while preserving confidence interval coverage. We extend the CVB multi-fidelity bootstrap estimator to find
confidence intervals for Sobol indices. Applied to the advection–diffusion model, this
method enables parameter ranking with smaller budgets.
Finally, we extend the model to dimensional form with realistic input distributions and more uncertain parameters. Wind speed, diffusion, source strength, and
wind direction are represented by Weibull, log-normal, gamma, and von Mises distributions respectively, with surrogates tested as low-fidelity models.
| Date of Award | 23 Feb 2026 |
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| Original language | English |
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| Awarding Institution | - University Of Strathclyde
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| Sponsors | University of Strathclyde |
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| Supervisor | John MacKenzie (Supervisor) & Alison Ramage (Supervisor) |
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