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-diusio n 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.

[1]  C. W. Groetsch,et al.  Inverse Problems in the Mathematical Sciences , 1993 .

[2]  T. Skaggs,et al.  Recovering the History of a Groundwater Contaminant Plume: Method of Quasi‐Reversibility , 1995 .

[3]  R. H. Myers.  Classical and modern regression with applications , 1986 .

[4]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[5]  Robert McKibbin,et al.  Source Release-Rate Estimation of Atmospheric Pollution from a Non-Steady Point Source at a Known Location , 2004 .

[6]  Douglas W. Oldenburg,et al.  Automatic Estimation of the Trade-off Parameter In Nonlinear Inverse Problems Using the GCV And L-curve Criteria , 2000 .

[7]  E. Haber,et al.  A GCV based method for nonlinear ill-posed problems , 2000 .

[8]  William P. Ball,et al.  Application of inverse methods to contaminant source identification from aquitard diffusion profiles at Dover AFB, Delaware , 1999 .

[9]  T. Ulrych,et al.  Minimum Relative Entropy Inversion: Theory and Application to Recovering the Release History of a Groundwater Contaminant , 1996 .

[10]  Per Christian Hansen,et al.  Rank-Deficient and Discrete Ill-Posed Problems , 1996 .

[11]  Z. J. Kabala,et al.  Recovering the release history of a groundwater contaminant using a non-linear least-squares method. , 2000 .

[12]  J. Kevorkian,et al.  Partial Differential Equations: Analytical Solution Techniques , 1990 .

[13]  T. Skaggs,et al.  Recovering the release history of a groundwater contaminant , 1994 .

[14]  E. Palazzi,et al.  Diffusion from a steady source of short duration , 1982 .

[15]  H. R. Busby,et al.  Practical inverse analysis in engineering , 1997 .

[16]  P. H. Gudiksen,et al.  The Use of Nonlinear Regression Analysis for Integrating Pollutant Concentration Measurements with Atmospheric Dispersion Modeling for Source Term Estimation , 1993 .

[17]  Analyzing the nonlinear L-curve , 1998 .

[18]  Brian J. Wagner,et al.  Simultaneous parameter estimation and contaminant source characterization for coupled groundwater flow and contaminant transport modelling , 1992 .

[19]  Bithin Datta,et al.  Identification of Pollution Sources in Transient Groundwater Systems , 2000 .

[20]  John T. Suttles,et al.  Air Pollution Model Parameter Estimation Using Simulated LIDAR Data , 1977 .

[21]  P. Kathirgamanathan,et al.  Source Term Estimation of Pollution from an Instantaneous Point Source , 2002 .