Source release rate estimation of atmospheric pollution from a non-steady point source – Part 2: Source at an unknown location

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.