Variationally Optimized Numerical Analysis Equations for Urban Air Pollution Monitoring Networks

Abstract

Formulas are derived, and their characteristics examined, for the purpose of optimizing objectively contoured patterns of air pollution concentrations where the diffusion equation is used as a dynamical constraint in the interpretation of network observations. The low-pan filter characteristics of the method are also demonstrated. An adjustment routine equation is derived for optimally correcting continuity discrepancies between successive isopleth patterns, such as might be computed for an automatic display system. Analytical expressions are obtained which predict the degree of improvement expected in practical applications where discrepancies occur in the analysis due to the natural periodic concentration variations which occur at monitoring stations. A sample calculation shows that the mean square residual error over a region can be reduced to less than 10% of its original magnitude when the adjustment routine is applied with a realistic set of meteorological parameters. Such adjustment routines can be programmed into a computerized objective analysis method, and thus they can be applied with a high degree of automation and efficiency.