This paper presents an inverse modelling procedure to estimate the location and release rate
of atmospheric pollution. The input to this model requires measured pollution concentration
at a minimum of three observation sites on the ground and meteorological conditions 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 for a non-steady point
source model. 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 using an optimisation routine such as MATLAB’s lsqnonlin and at each
iteration, the linear subproblem is solved to estimate the linear parameters. Finding the linear
parameters is an ill-posed problem and consequently its solution is extremely sensitive to errors
in the data. Tikhonov regularisation, which stabilises the process of the solution, is used
to overcome the ill posedness of the problem and the regularisation parameter is estimated
using the properties of the non-linear L-curve, linear L-curve and generalised cross validation.
Finally, the accuracy of the model is examined by imposing normally-distributed relative noise
into concentration data generated by the forward model.
Kathirgamanathan, P., McKibbin, R., McLachlan, R.I. (2003), Source release-rate estimation of atmospheric pollution from a non-steady point source - Part 2: Source at an unknown location, Research Letters in the Information and Mathematical Sciences, 5, 85-118