Identification of a Point of Release by Use of Optimally Weighted Least Squares

This paper addresses the parametric inverse problem of locating the point of release of atmospheric pollution. A finite set of observed mixing ratios is compared, by use of least squares, with the analogous mixing ratios computed by an adjoint dispersion model for all possible locations of the release. Classically, the least squares are weighted using the covariance matrix of the measurement errors. However, in practice, this matrix cannot be determined for the prevailing part of these errors arising from the limited representativity of the dispersion model. An alternative weighting proposed here is related to a unified approach of the parametric and assimilative inverse problems corresponding, respectively, to identification of the point of emission or estimation of the distributed emissions. The proposed weighting is shown to optimize the resolution and numerical stability of the inversion. The importance of the most common monitoring networks, with point detectors at various locations, is stressed as a misleading singular case. During the procedure it is also shown that a monitoring network, under given meteorological conditions, itself contains natural statistics about the emissions, irrespective of prior assumptions.