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

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.

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.

Cite this paper

nullT. Tirabassi, D. Moreira, M. Vilhena and C. Costa, "Comparison between Non-Gaussian Puff Model and a Model Based on a Time-Dependent Solution of Advection-Diffusion Equation,"*Journal of Environmental Protection*, Vol. 1 No. 2, 2010, pp. 172-178. doi: 10.4236/jep.2010.12021.

nullT. Tirabassi, D. Moreira, M. Vilhena and C. Costa, "Comparison between Non-Gaussian Puff Model and a Model Based on a Time-Dependent Solution of Advection-Diffusion Equation,"

References

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[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.

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[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.

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[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.

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[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.

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[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.

[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.