Numerical Optimization Techniques in Air Quality Modeling: Objective Interpolation Formulas for the Spatial Distribution of Pollutant Concentration

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Abstract
A technique is proposed for objection interpolation of the air quality distribution over a region in terms of sparse measurement data. Empirical information provided by the latter is effectively combined with knowledge of atmospheric dispersion functions of the type commonly used in source-oriented air quality models, to provide improved estimates of the concentration distribution over an extended region. However, the technique is not primarily source-oriented since, in contrast to the real source distribution of a source-oriented model, it utilizes fictitious or pseudò sources that are estimated in terms of the measured air quality data. This involves the use of interpolation functions that are computed using numerical optimization techniques based on the method of least squares. Due to the large number of different “weather” states that affect the atmospheric dispersion of pollution, considerable computation is required, although the bulk of this can be done in advance, so that the final interpolation from the measured values only requires very simple calculation. Thus the proposed method has the potential for application on a real-time basis. In addition to the mathematical formulation of the problem, this preliminary study includes some numerical experiments, using a current multiple source EPA air quality model, to illustrate the technique that is proposed.

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