Inverse Modelling for Identifying the Origin and Release rate of Atmospheric Pollution -An Optimisation Approach

Abstract

This paper describes a mathematical modelling technique which may be used to identify the origin and release history of a polluting gas released into the atmosphere from a point source. The inputs to this model are: pollution concentration measurements made at ground locations downstream, wind speed and transport parameters. The inverse model is formulated as a non-linear least-squares minimisation problem coupled with the solution of an advection-dispersion equation for a non-steady point source. The minimisation problem 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. Since the minimisation problem has a combination of linear and non-linear parameters, the problem is solved in two steps. Non-linear parameters are found by constructing an iterative procedure and, at each iteration, the linear parameters are calculated. The optimal value of the regularisation parameter is obtained by incorporating the L-curve criterion from linear inverse theory in conjunction with maintaining a steady increase in the regularisa¬tion parameter from one iteration to the next. Finally, the accuracy of the model is examined by imposing a normally-distributed relative noise into concentration data generated by the forward model.