Elements of the mathematical modeling in the control of pollutants emissions

Two models are presented in order to describe the dispersion of a primary and secondary pollutants in the atmosphere and control their emissions. The first of them is a simple box model whose analytical solutions permit to establish easily evaluated relations between the short-term and long-term controls of pollutants emissions and the model parameters. The dispersion of a primary and secondary pollutants emitted to the atmosphere by point, line and area sources is also simulated with a more general two-dimensional diffusion–advection-reaction model. The duality principle based on using the adjoint model is derived to formulate sufficient restrictions on the emission rates of different sources allowing to maintain mean concentrations of both pollutants in a zone below maximally admissible values (sanitary norms). A short-term control strategy using the solution to the adjoint model is suggested. The control (correction of emission rates) is implemented any time when the model forecast of at least one mean pollution concentration is unfavorable. The control strategy is optimal in that it minimizes the changes in the original emission rates. The minimization process is subjected to a restriction imposed with the duality principle. The optimal control parameters are obtained with an efficient algorithm of the successive orthogonal projections.