Gaussian models, dispersion parameters

The aim of dispersion models is the prediction of atmospheric dilution of pollutants in order to prevent or avoid nuisance. Established dispersion models, designed for the large scale of industrial air pollution have to be modified to the small scale of agricultural pollutions. An experimental setup is described to measure atmospheric dilution of tracer gas under agricultural conditions. The experimental results deliver the data base to identify the parameters of the models, For undisturbed airflow modified Gaussian models are applicable. For the consideration of obstacles more sophisticated models are necessary,... 

Weber, A. H. (1976). Atmospheric Dispersion Parameters in Gaussian Plume Modeling, EPA-600/4-76-030A. U.S. Environ. Prot. Agency, Washington, D.C. 

It is apparent from equations 3.2.4-3.2.7 that the determination of the concentration field is dependent on the values of the Gaussian dispersion parameters a, (or Oy in the fully coupled puff model). Drawing on the fundamental result provided by Taylor (1923), it would be expected that these parameters would relate directly to the statistics of the components of the fluctuating element of the flow velocity. In a neutral atmosphere, the factors affecting these components can be explored by considering the fundamental equations of fluid motion in an incompressible fluid (for airflows less than 70% of the speed of sound, airflows can reasonably be modeled as incompressible) when the temperature of the atmosphere varies with elevation, the fluid must be modeled as compressible (in other words, the density is treated as a variable). The set of equations governing the flow of an incompressible Newtonian fluid at any point at any instant is as follows ... 

Calculations of model spectra (distribution functions/(6jj) of chemical shifts of protons) using Gaussian functions and parameters of dispersion of peaks from the experimental NMR spectra (or theoretical estimations) as described in Chapter 10. Such approach allows us to calculate appropriate NMR spectra of large systems. This information can be used for more reliable and detailed analysis of the experimental NMR spectra. 

A significant merit of the dispersion model is some experimental correlations for the Peclet number. There are no such direct correlations for the parameters of the Gamma or Gaussian or other similar models. 

The retention time tRjin and the second moment for the Gaussian profile (Eq. 6.61) have been replaced by variables indexed with g . These parameters tg and og must be optimized by curve fitting. Equation 6.143 is only suitable for symmetric peaks. Analytical solutions of, for example, the transport dispersive model (which describes asymmetric band broadening only for a very low number of stages) are not suited to describing the asymmetry often encountered in practical chromatograms. Thus, many different, mostly empirical functions have been developed for peak modeling. A recent extensive review by Marco and Bombi (2001) lists over 90 of them. 

---