ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-10-267-2010 Stochastic fields method for sub-grid scale emission heterogeneity in mesoscale atmospheric dispersion models Cassiani M. 1 Vinuesa J. F. 2 Galmarini S. 2 Denby B. 1 Norwegian Institute for Air Research (NILU), 2027 Kjeller, Norway European Commission – DG Joint Research Centre, Institute for Environment and Sustainability, 21020 Ispra, Italy 13 01 2010 10 1 267 277 This is an open-access article ditributed 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. This article is available from http://www.atmos-chem-phys.net/10/267/2010/acp-10-267-2010.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/10/267/2010/acp-10-267-2010.pdf

The stochastic fields method for turbulent reacting flows has been applied to the issue of sub-grid scale emission heterogeneity in a mesoscale model. This method is a solution technique for the probability density function (PDF) transport equation and can be seen as a straightforward extension of currently used mesoscale dispersion models. It has been implemented in an existing mesoscale model and the results are compared with Large-Eddy Simulation (LES) data devised to test specifically the effect of sub-grid scale emission heterogeneity on boundary layer concentration fluctuations. The sub-grid scale emission variability is assimilated in the model as a PDF of the emissions. The stochastic fields method shows excellent agreement with the LES data without adjustment of the constants used in the mesoscale model. The stochastic fields method is a stochastic solution of the transport equations for the concentration PDF of dispersing scalars, therefore it possesses the ability to handle chemistry of any complexity without the need to introduce additional closures for the high order statistics of chemical species. This study shows for the first time the feasibility of applying this method to mesoscale chemical transport models.

 References % vor jede Referenz Bakosi, J., Franzese, P., and Boybeyi, Z.: Joint PDF modelling of turbulent flow and dispersion in an urban street canyon, Bound.-Lay. Meteorol., 131(2), 245–261, 2009. Bougeault, P. and Lacarrére, P.: Parameterization of orography induced turbulence in a mesobeta-scale model, Mon. Weather Rev., 117, 1872–1890, 1989. Cassiani, M., Franzese, P., and Giostra, U.: A PDF micromixing model of dispersion for atmospheric flow Part I: development of the model, application to homogeneous turbulence and to neutral boundary layer, Atmos. Environ., 39(8), 1457–1469, 2005a. Cassiani, M., Franzese, P., and Giostra, U.: A PDF micromixing model of dispersion for atmospheric flow. Part II: application to convective boundary layer, Atmos. Environ., 39(8), 1471–1479, 2005b. Cassiani, M., Radicchi, A., and Giostra, U.: Probability density function modelling of concentration fluctuation in and above a canopy layer, Agr. Forest Meteorol., 133, 153–165, 2005c. Cassiani, M., Radicchi, A., Albertson, J. D., and Giostra, U.: An efficient algorithm for scalar PDF modelling in incompressible turbulent flow; numerical analysis with evaluation of IEM and IECM micro-mixing models, J. Comp. Phys., 223(2), 519–550, 2007a. Cassiani, M., Radicchi, A., and Albertson, J. D.: Modelling of concentration fluctuations in canopy turbulence, Bound.-Lay. Meteorol., 122(3), 655–681, 2007b. Clappier, A.: A correction method for use in multidimensional time-splitting advection algorithms: Application to two- and three-dimensional transport, Mon. Weather Rev., 126, 232–242, 1998. Cuijpers, J. W. M. and Duynkerke, P. G.: Large eddy simulations of trade wind with cumulus clouds, J. Atmos. Sci., 50, 3894–3908, 1993. Cuijpers, J. W. M. and Holtslag, A. A. M.: Impact of skewness and nonlocal effects on scalar and buoyancy fluxes in convective boundary layers, J. Atmos. Sci., 55, 151–162, 1998. Dixon, N. S. and Tomlin, A. S.: A Lagrangian stochastic model for predicting concentration fluctuations in urban areas, Atmos. Environ., 41, 8114–8127, 2007. Dopazo, C. and O'Brien, E. E.: An approach to the auto ignition of a turbulent mixture, Acta Astronaut., 1, 1239–1266, 1974. Dopazo, C., Valiño, L., and Fuego, F.: Statistical description of the turbulent mixing of scalar fields, Int. J. Modern Phys. B, 11(25), 2975–3014, 1997. Fox, R. O.: Computational models for turbulent reacting flows, Cambridge University Press, Cambridge, 419~pp., 2003. Gardiner C. W.: Handbook of stochastic methods for physics chemistry and the natural sciences, Springer-Verlag, 442~pp., 1983. Garmory, A., Richardson, E. S., and Mastorakos, E.: Micromixing effects in a reacting plume by the Stochastic Fields method, Atmos. Environ., 40, 1078–1091, 2006. Garmory, A., Britter, R. E., and Mastorakos, E.: Simulation of the evolution of aircraft exhaust plumes including detailed chemistry and segregation, J. Geophys. Res., 113, D08303, doi:10.1029/2007JD009104, 2008. Galmarini, S., Vinuesa, J.-F., and Martilli, A.: Modeling the impact of sub-grid scale emission variability on upper-air concentration, Atmos. Chem. Phys., 8, 141–158, 2008. Hauke, G. and Valiño, L.: Computing reactive flows with a field Monte Carlo formulation and multi-scale methods, Comput. Methods Appl. Mech. Eng., 193, 1455–1470, 2004. Heinz, S.: Statistical Mechanics of Turbulent Flows, Springer Verlag Berlin Heidelberg, Germany, 214~pp., 2003. Lewellen, W. S. and Sykes, R. I.: Analysis of Concentration Fluctuations from LIDAR Observations of Atmospheric Plumes, J. Clim. Appl. Meteorol., 25, 1145–1154, 1986. Luhar, A. K. and Sawford, B. L.: Micromixing modelling of mean and fluctuating scalar fields in the convective boundary layer, Atmos. Environ., 39, 6673–6685, 2005. Martilli, A.: Numerical study of urban impact on boundary layer structure: sensitivity to wind speed, urban morphology, and rural soil moisture, J. Appl. Meteorol., 41, 1247–1266, 2002. Mustata, R., Valiño, L., Jimenez, C., Jones, W. P., and Bondi, S.: A probability density function Eulerian Monte Carlo field method for large eddy simulations: Application to a turbulent piloted methane/air diffusion flame (Sandia D), Combustion and Flame, 145, 88–104, 2006. Pope, S. B.: PDF methods for turbulent reactive flows, Prog. Energy Combust. Sci., 11, 119–192, 1985. Pope, S. B.: Turbulent Flows, Cambridge University Press, Cambridge, 806 pp, 2000. Sabel'nikov, V. and Soulard, O.: Rapidly decorrelating velocity-field model as a tool for solving one-point Fokker-Planck equations for probability density functions of turbulent reactive scalars, Phys. Rev. E, 72(1), 016301, doi:10.1103/PhysRevE.72.016301, 2005. Sawford, B. L.: Micro-Mixing Modelling of Scalar Fluctuations for Plumes in Homogeneous Turbulence, Flow Turb. Combust., 72, 133–160, 2004. Sawford, B. L.: Lagrangian stochastic modelling of chemical reaction in a scalar mixing layer, Bound.-Lay.. Meteorol., 118(1), 1–23, 2006. Siebesma, A. P. and Cuijpers, J. W. M.: Evaluation of parametric assumptions for shallow cumulus convection, J. Atmos. Sci., 52, 650–666, 1995. Valiño, L.: A field Monte Carlo formulation for calculating the probability density function of a single scalar in a turbulent flow, Flow Turbul. Combust., 60, 157–172, 1998. Vilà-Guerau de Arellano, J. and Cuijpers, J. W. M.: The chemistry of a dry cloud: the effects of radiation and turbulence, J. Atmos. Sci., 57, 1573–1584, 2000. Vilà-Guerau de Arellano, J., Dosio, A., Vinuesa, J.-F., Holtslag, A. A. M., and Galmarini, S.: The dispersion of chemically reactive species in the convective boundary layer, Meteorol. Atmos. Phys., 87, 23–28, 2004. Villermaux, J. and Devillon J. C.: Représentation de la coalescence et de la redispersion des domaines de ségrégation dans un fluide par un modèle d'interaction phénoménologique. In proc. Second Int. Symp. On Chemical Reaction Engineering, New York, Elsevier, 1972. Yee, E., Wilson, D. J., and Zelt, B. W.: Probability Distributions of Concentration Fluctuations of a Weakly Diffusive Passive Plume in a Turbulent Boundary Layer, Bound.-Lay. Meteorol., 64, 321–354, 1993.