Simulation of Pollutant Dispersion in the Atmosphere by the Laplace Transform: The ADMM Approach

Abstract

Transport and diffusion models of air pollution are based either on simple tech-nique, such as the Gaussian approach, or on more complex algorithms, such as thenumerical solution of air dispersion differential equation, based on K-theory. TheGaussianequationisaneasyandfastmethodwhich,however,cannotproperlysim-ulate complex nonhomogeneous conditions. The K-theory can accept virtually anycomplex meteorological input, but generally requires numerical integration whichis computationally expensive and is often affected by large numerical advectionerrors. Conversely, Gaussian models are fast, simple, do not require complex me-teorological input, and describe the diffusive transport in an Eulerian framework,making easy use of the Eulerian nature of measurements.For these reasons they are still widely used by the environmental agencies allover the world for regulatory applications. However, because of their well knownintrinsic limits, the reliability of a Gaussian model strongly depends on the waythe dispersion parameters are determined on the basis of the turbulence structure ofthe Planetary Boundary Layer (PBL) and the model’s ability to reproduce exper-imental diffusion data. The Gaussian model has to completed by empirically de-termined standard deviations (the so called “sigmas”) while some commonly mea-surable turbulent exchange coefficient has to introduce in the advection-diffusionequation.Analytical solutions to the complete advection-diffusion equation cannot begiven but in a few specialized cases (Tirabassi, 2003), and numerical solutions areexpansive and cannot be easily “interpreted” as the simple Gaussian model. Asa consequence, the major part of applications to practical problems are currentlydone by using the Gaussian model, and great deal of empirical work has been donedo determinate the “sigmas” appropriate to the PBL under various meteorologi-cal conditions and to extend the basic formulation of this model and its range ofapplicability (Zannetti, 1990).