Comparison between Non-Gaussian Puff Model and a Model Based on a Time-Dependent Solution of Advection-Diffusion Equation

Tiziano Tirabassi, Davidson M. Moreira, Marco Tullio Vilhena, Camila Pinto da Costa

.

DOI: 10.4236/jep.2010.12021                

Abstract

A comparison between a non-Gaussian puff model and an advanced time-dependent model to simulate the pollutant dispersion in the Planetary Boundary Layer is presented. The puff model is based on a general technique for solving the K-equation, using the truncated Gram-Charlier expansion (type A) of the concentration field and finite set equations for the corresponding moments. The other model (named ADMM: Analytical Dispersion Multilayers Model) is an semi- analytical solution to the time-dependent two-dimensional advection-diffusion equation based on a discretization of the PBL in N sub-layers; in each sub-layers the advection-diffusion equation is solved by the Laplace transform technique, considering an average value for eddy diffusivity and the wind speed. A preliminary performance evaluation is shown in the case of continuous emission from an elevated source in a variable boundary layer. Both models were able to correctly reproduce the concentration field measured and so to be used as operative air pollution models.

Keywords

Advection-Diffusion Equation, Air Pollution Modeling, Analytical Solution, Puff Models

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. P. Arya, “Air Pollution Meteorology and Dispersion,” Oxford University Press, Oxford, 1999, p. 310.
[2]	P. Zannetti, “Air Quality Modeling III,” The EnvironComp Institute and Air & Waste Management Association, Fremont, 2008, p. 485.
[3]	S. R. Hanna, G. A. Briggs, J. Deardoff, B. A. Egan, F. A. Gifford and F. Pasquill, “AMS Workshop on Stability Classification Schemes and Sigmas Curves – Summary of Recommendations,” Bulletin of the American Meteorological Society, Vol. 58, No. 12, 1977, pp. 1305-1309.
[4]	G. A. Briggs, “Plume Rise Predictions,” Lectures on Air Pollution and Environmental Impact Analyses, Workshop Proceedings, American Meteorological Society, Boston, 29 September-3 October 1975, pp. 59-111.
[5]	S. R. Hanna, “Lateral Dispersion from Tall Stacks,” Journal of Climmate Applied Meteorology, Vol. 25, No. 10, 1986, pp. 1426-1433.
[6]	R. Berkowicz, H. R. Olesen and U. Torp, “The Danish Gaussian Air Pollution Model (OML): Description, Test and Sensivity Analysis in View of Regulatory Applications,” In: C. De Wispelaere, F. A. Schiermeier and N. V. Gillani, Ed., Proceedings of NATO-CCMS 16th International Meeting on Air Pollution, Modelling and its Applications, Plenum Press, New York, 1986, pp. 453-481.
[7]	B. M. Bowen, “Long-Term Tracer Study at Los Alamos, New Messico. Part II: Evaluation and Comparison of Several Methods to Determinate Dispersion Coefficients,” Journal of Appied Meteorology, Vol. 33, No. 11, 1994, pp. 1236-1254.
[8]	J. J. Erbrink, “Use of Boundary-Layer Meteorological Parameters in the Gaussian Model ‘Stacks’,” Bounary- Layer Meteorology, Vol. 74, No. 3, 1995, pp. 211-235.
[9]	M. Mohan and T. A. Siddiqui, “An Evaluation of Dispersion Coefficients for Use in Air Quality Models,” Bounary- Layer Meteorology, Vol. 84, No. 2, 1997, pp. 177-205.
[10]	B. J. Tsuang, “Quantification on the Source/Receptor Relationship of Primari Pollutants and Secondary Aerosols by a Gaussian Plume Trajectory Model: Part I – Theory,” Atmospheric Environment, Vol. 37, No. 28, 2003, pp. 3981- 3991.
[11]	A. J. Cimorelli, S. G. Perry, A. Venkatram, J. C. Weil, R. J. Paine, R. B. Wilson, R. F. Lee, W. D. Peters and R. W. Brode, “AERMOD: A Dispersion Model for Industrial Source Applications. Part I: General Model Formulation and Boundary Layer Characterization,” Journal of Appied Meteorology, Vol. 44, No. 5, 2005, pp. 682-693.
[12]	J. S. Scire, D. G. Strimaitis and R. J. Yamartino, “A User’s Guide for the CALPUFF Dispersion Model,” Version 5, Earth Tech Inc., Lowell, 2000. http://www.src. com/calpuff/calpuff1.htm
[13]	A. P. van Ulden, “A Surface-Layer Similarity Model for the Dispersion of a Skewed Passive Puff near the Ground,” Atmospheric Environment, Vol. 26, No. 4, 1992, pp. 681- 692.
[14]	M. Sharan and M. Modani, “A Two-Dimensional Ana- lytical Model for the Dispersion of Air-Pollutants in the Atmosphere with a Capping Inversion,” Atmospheric Environment, Vol. 40, No. 19, 2006, pp. 3479-3489.
[15]	T. Tirabassi, “Operational Advanced Air Pollution Mode- ling,” Pure and Applied Geophysics, Vol. 160, No. 1-2, 2003, pp. 5-16.
[16]	R. Lupini and T. Tirabassi, “Solution of the Advection- Diffusion Equation by the Moments Method,” Atmospheric Environment, Vol. 17, No. 5, 1983, pp. 965-971.
[17]	T. Tirabassi and U. Rizza, “Boundary Layer Paramete- rization for a Non-Gaussian Puff Model,” Journal of Appied Meteorology, Vol. 36, No. 8, 1997, pp. 1031-1037.
[18]	D. M. Moreira, P. V. F. Neto and J. C. Carvalho, “Ana- lytical Solution of the Eulerian Dispersion Equation for Nonstationary Conditions: Development and Evaluation,” Environmental Modelling and Software, Vol. 20, No. 9, 2005, pp. 1159-1165.
[19]	M. Kendall and A. Stuart, “The Advanced Theory of Statistic,” Charles Griffin, London, 1977, pp. 1-472.
[20]	A. H. Stroud and D. Secrest, “Gaussian Quadrature Formulas,” Prentice-Hall, Englewood Cliffs, 1996, p. 320.
[21]	D. M. Moreira, G. A. Degrazia and M. T. Vilhena, “Dis- persion from Low Sources in a Convective Boundary Layer: An Analytical Model,” Il Nuovo Cimento, Vol. 22C, No. 5, 1999, pp. 685-691.
[22]	C. Mangia, D. M. Moreira, I. Schipa, G. A. Degrazia, T. Tirabassi and U. Rizza, “Evaluation of a New Eddy Dif- fusivity Parameterisation from Turbulent Eulerian Spectra in Different Stability Conditions,” Atmospheric Environment, Vol. 36, No. 1, 2002, pp. 67-76.
[23]	D. M. Moreira, M. T. Vilhena, J. C. Carvalho and G. A. Degrazia, “Analytical Solution of the Advection-Diffusion Equation with Nonlocal Closure of the Turbulent Diffusion,” Environmental Modelling and Software, Vol. 20, No. 10, 2004, pp. 1347-1351.
[24]	C. P. Costa, M. T. Vilhena, D. M. Moreira and T. Tirabassi, “Semi-Analytical Solution of the Steady Three- Dimensional Advection-Diffusion Equation in the Planetari Boundary Layer,” Atmospheric Environment, Vol. 40, 2006, pp. 5659-5669.
[25]	I. Troen and L. Marth, “A Simple Model of the Atmos- pheric Boundary Layer; Sensitivity to Surface Evapora- tion,” Bounary-Layer Meteorology, Vol. 37, No. 1-2, 1986, pp. 129-148.
[26]	J. Pleim and J. S. Chang, “A Non-Local Closure Model for Vertical Mixing in the Convective Boundary Layer,” Atmospheric Environment, Vol. 26, No. 6, 1992, pp. 965- 981.
[27]	J. H. Seinfeld and S. N. Pandis, “Atmospheric Chemistry and Physics,” John Wiley & Sons, New York, 1998, p. 1326.
[28]	G. Tangerman, “Numerical Simulations of Air Pollutant Dispersion in a Stratified Planetary Boundary Layer,” Atmospheric Environment, Vol. 12, No. 6-7, 1978, pp. 1365- 1369.
[29]	P. K. Kythe, P. Puri and M. R. Schäferkotter, “Partial Differential Equations and Mathematics,” CRC Press, Boca Raton, 2002, p. 440.
[30]	S. E. Gryning and E. Lyck, “Atmospheric Dispersion from Elevated Sources in an Urban Area: Comparison between Tracer Experiments and Model Calculations,” Journal of Climate and Applied Meteorology, Vol. 23, No. 4, 1984, pp. 651-660.
[31]	S. E. Gryning, A. A. M. Holtslag, J. S. Irwin and B. Siversten, “Applied Dispersion Modelling Based on Me- teorological Scaling Parameters,” Atmospheric Environment, Vol. 21, No. 1, 1987, pp. 79-89.
[32]	D. M. Moreira, M. T. Vilhena, D. Buske and T. Tirabassi, “The GILTT Solution of the Advection-Diffusion Equa- tion for an Inhomogeneous and Nonstationary PBL,” Atmospheric Environment, Vol. 40, No. 17, 2006, pp. 3186- 3194.
[33]	S. R. Hanna, “Confidence Limit for Air Quality Models as Estimated by Bootstrap and Jacknife Resampling Me- thods,” Atmospheric Environment, Vol. 23, No. 6, 1989, pp. 1385-1395.
[34]	H. R. Olesen, “Datasets and Protocol for Model Validation,” International Journal of Environment and Pollution, Vol. 5, No. 4-6, 1995, pp. 693-701.