Estimation of the Maximum Concentration for Non-Gaussian Under Using Different Schemes of Dispersion Parameters for Isotopes

In this paper, we have calculated of the maximum concentration for non-Gaussian and maximum downwind distance under using different schemes of dispersion parameters for isotopes. We have compared between maximum predicated, concentrations for non-Gaussian under using different schemes of dispersion parameters for I131 and Cs137 via observed and maximum downwind distance. *Corresponding author: Essa KSM, Mathematics and Theoretical Physics, NRC, Atomic Energy Authority, Cairo, Egypt, Tel: 989378212956; E-mail: mohamedksm56@yahoo.com Received June 23, 2015; Accepted July 08, 2015; Published July 18, 2015 Citation: Essa KSM, Elsaid SEM (2015) Estimation of the Maximum Concentration for Non-Gaussian Under Using Different Schemes of Dispersion Parameters for Isotopes. J Civil Environ Eng 5: 178. doi:10.4172/2165-784X.1000178 Copyright: © 2015 Essa KSM, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


Introduction
Atmospheric dispersion modeling refers to the mathematical description of contaminant transport in the atmosphere. The term dispersion in this context used to describe the combination of diffusion (due to turbulent eddy motion) and advection (due to the wind). Analytical and approximate solutions for the atmospheric dispersion problem have been derived under wide range of simplifying assumptions, as well as various boundary conditions and parameter dependencies. These analytical solutions are especially useful to engineers and environmental scientists who study pollutant transport, since they allow parameter sensitivity and source estimation studies to be performed [1].
Both our scientific understanding and technical developments have greatly increased by the use of empirical, analytical and numerical models to predict the air pollution concentration in atmosphere. For this purposed, the advection -diffusion equation has been largely applied in operational atmospheric dispersion models, in principal, from this equation it is possible to obtain the dispersion from a source given appropriate boundary and initial conditions plus knowledge of the mean wind velocity and concentration turbulent fluxes [2].
The advection-diffusion equation has largely calculated in operational atmospheric dispersion models to predict mean concentrations of contaminants in the planetary boundary dispersion from a continuous point source given appropriate boundary and initial conditions as well as knowledge of the mean wind velocity and concentration turbulent fluxes.
Many turbulent dispersion studies are relating to the specification of these turbulent fluxes to allow the solution of the averaged advection -diffusion equation, this procedure used to know as the closure of the turbulent diffusion problem.
In this paper, we have calculated of the maximum concentration for non-Gaussian and maximum downwind distance under using different schemes of dispersion parameters for isotopes. We have compared between maximum predicated, concentrations for non -Gaussian under using different schemes of dispersion parameters for I 131 and Cs 137 via observed and maximum downwind distance.

Non-Gaussian distributions
The concentration from a continuous point source of strength Q with interference from the ground at a mean wind speed U using non-Gaussian plume formula as follows [3]: Where: C is the mean concentration of the effluent at a point (x, y, z), (Bq/m 3 ).
Q is the source strength (Bq).
U is the mean wind speed (m/s).
X, y, z refer to a downwind, crosswind and vertical coordinate system at the center of the moving cloud. Σ i (i=x, y, z) are the plume dispersion coefficients in the x, y and z directions respectively (m) [4,5].
Exp(-x λ/U) is the radioactive decay for the specified nuclide.
Maximum mean concentration of the effluent concentration occurs when ∂C n /∂x=0 which gives: From which we get Multiply the equation (3) in x 2, we get: From which we get Substituting from equation (5)

Dispersion parameters schemes
We select the four different methods namely, power law , Briggs, Irwin and standard method for calculating σ y and σ z to select the most accurate one [6], as follows.

A-Power-law method
In this method, σ y and σ z can be calculated from the following formula:  Table 1.

B-Standard method
In this method, σ y and σ z are in the form: Where r, s, p and q are constants depending on the atmospheric stability. These values are explained in Table 2

C-Briggs method
In this method, σ y and σ z can be calculated from the Tables 3-6 according to Briggs [7].

D-Irwin method
In this method, σ y and σ z are taking the following formula:     Briggs (1973) for σ y (x) and σ z (x).        concentrations for non-Gaussian under using different schemes of dispersion parameters for Cs137 are shown in Figure 3. It is clear the most values of predicated and maximum concentrations agreement with observed data in cases of standard, Briggs and Irwin methods, while in case power law method the values of maximum concentration are best from predicated concentration with observed data.

Power law method
The comparison between observed and predicated, maximum concentration via maximum downwind distance for non-Gaussian under using different schemes of dispersion parameters for Cs137 are shown in Figure 4. It is clear in cases of Briggs and Irwin methods the values of observed and predicated concentrations are best from maximum concentrations with maximum downwind distance, while, in cases power law and standard methods the values of predicated concentration are best from observed and maximum concentrations with maximum downwind distance.

Conclusions
The maximum concentration for non-Gaussian and maximum downwind distance under using different schemes of dispersion parameters for isotopes has evaluated. Comparison between maximum predicated concentrations for non-Gaussian under using different schemes of dispersion parameters for I131 and Cs137 via observed and maximum downwind distance are calculated.