Near real-time atmospheric contamination source identification by an optimization-based inverse method

In this article, we propose a method to identify contamination events (location and time of release) by enhancing a mathematical method originally proposed by Carasso et al. (Carasso, A., Sanderson, J.G. and Hyman, J.M., 1978, Digital removal of random media image degradation by solving the diffusion equation backward in time. SIAM Journal of Numerical Analysis, 15(4)). The method of the Marching-Jury Backward Beam/Plate Equation, applied earlier to groundwater problems, is enhanced and coupled to discrete Fourier transform processing techniques to solve a two-dimensional (2D) advection-dispersion transport problem with homogeneous and isotropic parameters backwards in time. (Atmadja, J. and Bagtzoglou, A.C., 2001a, Pollution source identification in heterogeneous porous media. Water Resources Research, 37(8), 2113-2125; Bagtzoglou, A.C. and Atmadja, J., 2003, The marching-jury backward beam equation and quasi-reversibility methods for hydrologic inversion: application to contaminant plume spatial distribution recovery. Water Resources Research, 39(2), 1038. Cornacchiulo, D. and Bagtzoglou, A.C., 2002, The marching-jury backward plate equation for contaminant plume spatial distribution recovery in two-dimensional heterogeneous media: Computational Issues, In: S.M. Hassanizadeh, R.J. Schotting, W.G. Gray and G.F. Pinder (Eds.) Computational Methods for Subsurface Flow and Transport (Netherlands: Elsevier Publishers) pp. 461-468. The difficulties associated with this ill-posed, inverse problem are well-recognized (Atmadja, J. and Bagtzoglou, A.C., 2001b, State-of-the-art report on mathematical methods for groundwater pollution source identification. Environmental Forensics, 2(3), 205-214). We, therefore, enhance the method by integrating an optimization scheme that takes as input parameters the stabilization parameter, the transport velocities, and the coefficient of diffusion. The objective function is set as an equally weighted sum of different mass and peak errors that can be calculated based on a combination of exhaustive contaminant coverage at specific points in time (e.g., lidar) and/or point data collected at a continuously monitored network of chemical sensors or biosensors, which may be stationary or mobile.