Variable K-theory model for the dispersion of air pollutants in low-wind conditions in the surface-based inversion

A variable K-model has been proposed for the dispersion in low winds in the surface-based inversion by expressing the eddy diffusivities as a linear function of downwind distance from the source. The resulting partial differential equation with variable coefficients along with the physically relevant boundary conditions is solved analytically. For the accuracy of the so-obtained solution, an analysis of the convergence and error estimation has been carried out. It is shown that the series converges absolutely. An upper bound for the error based on the partial sum of the series is estimated and it is described that the error tends to zero as the number of terms in the expansion are sufficiently large.The solution has been used to simulate the field tracer data sets collected from Hanford and IIT diffusion experiments in stable and unstable conditions, respectively. It predicts 41% cases in stable and 35% cases in unstable conditions within a factor of two to observations.