Source parameter estimation of atmospheric pollution from accidental releases of gas : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Palmerston North, New Zealand
This thesis presents the development of an inverse model that may be used to estimate the source term parameters for a polluting gas released into the atmosphere from a point above the ground. The model uses measured pollution concentrations at observation sites on the ground as well as meteorological data such as wind speed and cloud cover. The inverse model is formulated as a least- squares minimisation problem coupled with the solution of an advection-diffusion equation. The least-squares technique allows quantification of the uncertainty of the calculated estimates, which in turn allows estimation of the uncertainty of the simulation model predictions. The minimisation problem where the pollutants are released instantaneously is well-posed and the source term is calculated with reasonable accuracy. However, the problem with a non-steady extended release source is ill-posed; consequently, its solution is extremely sensitive to errors in the measurement data. Tikhonov's regularisation, which stabilises the solution process, is used to overcome the ill-posedness of this problem. The optimal value of the regularisation parameter in the problem is estimated using both the linear and non-linear L-curve criterion, and a generalised cross-validation approach. The accuracy of the model is examined by using simulated concentration data (generated by the forward model) to which normally-distributed relative noise has been added, as well as some real experimental data.