The kernel method to compute the intensity of segregation for reactive pollutants: Mathematical formulation

It is well known that turbulent dispersion influences chemical reactions and that computation of reactant concentrations or mean chemical reaction rates can suffer of serious error when small-scale atmospheric processes' effects on chemical transformation are neglected. A quantity that gives a measure of the influence of turbulent dispersion on second-order chemical reaction rates is the intensity of segregation. A nonparametric estimator based on the kernel method aimed at measuring the intensity of segregation is proposed. Numerical benchmark tests, in the case of a Gaussian plume, are performed to study the suitability of this technique. The estimator works well, especially for small and moderate separation from the plume centreline and generally in the smooth parts of the estimated function. The effective reaction rate is computed and the percentage error emerges to be less than 5% in the best estimation intervals, and less than 40% in the worst. A method to reduce percentage error is introduced and improved performances are observed. The estimator proposed turns out to be particularly suitable for Lagrangian air quality modelling because it permits conservation of the grid independence.