# Concentration Fluctuations and Odor Dispersion in Lagrangian Models

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## Abstract

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## 1. Introduction

## 2. Lagrangian Stochastic Models

_{η}(approximately equal to the correlation time of the accelerations) and the Lagrangian time scale T

_{L}.

_{j}is an incremental Wiener process component, Gaussian distributed with zero mean and variance of

_{η}≤ dt ≤ T

_{L}, the following relationship can be considered [31]:

_{0}is a universal constant.

_{i}(t) as given by the Langevin equation in (Equation (1)), averaging and considering only the terms of the order of dt, leads to

## 3. Observations and Lagrangian Modeling of Concentration Fluctuation

#### 3.1. Experimental Results

^{85}Kr from a point source 1 m above ground level. Averaging time was 39 s and arcs of samplers were located at downwind distances of 200 and 800 m. They observed that the intensity of concentration fluctuations $i$ increased from about 1.5 on the plume axis to about 3.0 towards the edges under stable and slightly unstable atmospheric conditions.

^{85}Kr released from a ground-level point source in near-neutral and convective conditions. Furthermore, they established a reasonable linear relationship between p/m and $i$, whereby the largest observed values for $i$ were around 30. While Lung et al. (2002) [44] reported also increasing $i$ towards the edge of the plumes and decreasing values at larger distances, in contrary to the studies mentioned previously, they concluded that the Gamma- and Weibull pdfs provided a better fit to the data than did a log-normal distribution.

#### 3.2. Two-Particle Model

#### 3.3. Fluctuating Plume Model

#### 3.4. Pdf Micro-Mixing Model

#### 3.5. Volumetric Particle Approach

#### 3.6. Parameterizations

_{s}is the stoichiometric distance, which is the axial centerline location where the initial concentration of the reactant A emitted by the source was diluted to the initial background concentration of B (which remains constant outside the plume) and N

_{D}the Damköhler number, which represents the ratio between the time scales of turbulence and chemical reaction.

#### 3.7. Virtual Variance Sources

#### 3.8. Variance Dissipation Time Scale

_{d}.

_{c}. As a matter of fact, the plume can be divided into inner and outer scales. The outer scale corresponds to the scale over which the plume meanders and the inner scale is the relative spread of the plume. As a consequence, Sykes et al. (1984) [75] prescribed an inner scale from which they determined the dissipation time scale ${t}_{d}$. In particular they showed, as also stated by Sawford (1982) [76], that λ

_{c}should be initially proportional to the time t and then to t

^{3/2}. However, in these works, the time scale is obtained from both the length scale and a velocity scale, and the velocity scale actually depends on the length scale. Galperin (1986) [77] showed that the dissipation time scale grows linearly with time, and, if we consider the dissipation time scale as the life-time of the fluctuations, it should be smaller close to the source where the intense mixing causes rapid development and dissipation of the fluctuations. Proportionality between ${t}_{d}$ and the Lagrangian integral time scale was proposed by Bèguier et al. (1978) [78] and Warhaft and Lumley (1978) [79], and used by Andronopoulos et al. (2002) [80] and Milliez and Carissimo (2008) [81]. A similar relationship can be found in Yee et al. (2009) [63]. A proportionality coefficient equal to 22 was suggested by Manor (2014) [21]. It is worth to notice that Manor (2014) [21] parameterized ${t}_{d}$ as proportional to the local vertical Lagrangian time scale at a particle position. Ferrero et al. (2017) [22] proposed the following function for the dissipation time scale t

_{d}

_{*}= zi/U (zi is the boundary-layer depth and U is the freestream velocity), α

_{1}, α

_{2}are constants, ds is the source diameter, and hs is the source height. Since it has been demonstrated [22] that the observed concentration-variance dispersion by Fackrell and Robins (1982) [73] depend on both source size and height, a dependency on these two parameters was introduced in the parameterization for ${t}_{d}$. As t → 0 (i.e., for times just after emission) Equation (44) becomes a constant that depends on the Lagrangian time scale and the ratio between source diameter and height. As a matter of fact, the dimension of the plume close to the source is of the order of the source size and the eddies that can dissipate the concentration variance should have the same size. The second term in Equation (44) is needed to avoid that ${t}_{d}=0$ at t = 0 and hence that $\overline{{c}^{\prime}{\left(t+\mathsf{\Delta}t\right)}^{2}}=0$, while in contrast the fluctuations are larger close to the source. Naturally, the mean concentration field has the largest gradient near the source and, as a consequence, concentration fluctuations are highest there. Subsequently the dissipation time scale becomes proportional to the dispersion time.

## 4. Odor Dispersion

#### 4.1. Fluctuating Plume Models

#### 4.2. Lagrangian Stochastic Particle Models

_{m}calculated for an integration time of t

_{m}(1800 s) and the peak concentration C

_{p}for an integration time of t

_{p}(5 s). The exponent ‘a’ depends on atmospheric stability. Generally, Equation (45) gives relatively large values of ${\psi}_{0}$. Following Mylne (1992) [42], it is assumed that, due to turbulent mixing, the peak- to-mean factor is reduced with increasing distance from the source. The peak-to-mean factor in Equation (45) is modified by an exponential decaying function of the quantity T/t

_{L}, where T = x/u is the time of travel with distance x and the mean wind speed u, and t

_{L}is a measure of the Lagrangian time scale [42].

#### 4.3. Hybrid Lagrangian-Eulerian (Enrico)

#### 4.4. Puff Model (Enrico)

_{E}/m

^{3}for more than 2% of the hours in the year. It defines the maximum extent at which the CALPUFF model predicts there is reasonable cause of odor annoyance. The 3 ou

_{E}/m

^{3}98 percentile is the applicable odor impact criteria. De Melo et al. [92] compared AERMOD and CALPUFF with wind tunnel data simulating odor dispersion around a pig farm building complex. The results show that concentrations predicted by AERMOD are, in general, higher than those predicted by CALPUFF, especially regarding the maximum mean concentrations observed in the near field. Ranzato et al. [93] assessed the olfactory nuisance caused by an anaerobic treatment plant for municipal solid waste by means of two alternative techniques: the field inspection procedure and the atmospheric dispersion model CALPUFF.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Schauberger, G.; Piringer, M.; Knauder, W.; Petz, E. Odour emissions from a waste treatment plant using an inverse dispersion technique. Atmos. Environ.
**2011**, 45, 1639–1647. [Google Scholar] [CrossRef] - Hilderman, T.; Hrudey, S.; Wilson, D. A model for effective toxic load from fluctuating gas concentrations. J. Hazard. Mater.
**1999**, 64, 115–134. [Google Scholar] [CrossRef] - Crone, G.C.; Dinar, N.; van Dop, H.; Verver, G.H.L. A Lagrangian approach for modelling turbulent transport and chemistry. Atmosp. Environ.
**1999**, 33, 4919–4934. [Google Scholar] - Sawford, B.L.; Pinton, J.-F. A Lagrangian view of turbulent dispersion and mixing. In Ten Chapters in Turbulence; Davidson, P.A., Kaneda, Y., Sreenivasan, K.R., Eds.; Cambridge University Press: Cambridge, UK, 2013; Chapter 4; pp. 131–175. [Google Scholar]
- Thomson, D.J. Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech.
**1987**, 180, 529–556. [Google Scholar] [CrossRef] - Oettl, D.; Ferrero, E. A simple model to assess odour hours for regulatory purposes. Atmos. Environ.
**2017**, 155, 162–173. [Google Scholar] [CrossRef] - Thomson, D.J. A stochastic model for the motion of particle pairs in isotropic high-Reynolds-number turbulence, and its application to the problem of concentration variance. J. Fluid Mech.
**1990**, 210, 113–153. [Google Scholar] [CrossRef] - Borgas, M.S.; Sawford, B.L. A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence. J. Fluid Mech.
**1994**, 289, 69–99. [Google Scholar] [CrossRef] - Pope, S.B. PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci.
**1985**, 11, 119–192. [Google Scholar] [CrossRef] - Cassiani, M.; Franzese, P.; 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. Atmosp. Environ.
**2005**, 39, 1457–1469. [Google Scholar] [CrossRef] - Cassiani, M.; Radicchi, A.; Albertson, J.D.; 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.
**2007**, 223, 519–550. [Google Scholar] [CrossRef] - Leuzzi, G.; Amicarelli, A.; Monti, P.; Thomson, D. A 3D lagrangian micromixing dispersion model LAGFLUM and its validation with a wind tunnel experiment. Atmos. Environ.
**2012**, 54, 117–126. [Google Scholar] [CrossRef] - Yee, E.; Chan, R.; Kosteniuk, P.R.; Chandler, G.M.; Biltoft, C.A.; Bowers, J.F. Experimental Measurements of Concentration Fluctuations and Scales in a Dispersing Plume in the Atmospheric Surface Layer Obtained Using a Very Fast Response Concentration Detector. J. Appl. Met.
**1994**, 33, 996–1016. [Google Scholar] [CrossRef] - Yee, E.; Wilson, D.J. A comparison of the detailed structure in dispersing tracer plumes measured in grid-generated turbulence with a meandering plume model incorporating internal fluctuations. Bound.-Layer Meteorol.
**2000**, 94, 253–296. [Google Scholar] [CrossRef] - Luhar, A.; Hibberd, M.; Borgas, M. A skewed meandering-plume model for concentration statistics in the convective boundary layer. Atmos. Environ.
**2000**, 34, 3599–3616. [Google Scholar] [CrossRef] - Franzese, P. Lagrangian stochastic modeling of a fluctuating plume in the convective boundary layer. Atmos. Environ.
**2003**, 37, 1691–1701. [Google Scholar] [CrossRef] - Mortarini, L.; Franzese, P.; Ferrero, E. A fluctuating plume model for concentration fluctuations in a plant canopy. Atmos. Environ.
**2009**, 43, 921–927. [Google Scholar] [CrossRef] - Ferrero, E.; Mortarini, L.; Alessandrini, S.; Lacagnina, C. Application of a Bivariate Gamma Distribution for a Chemically Reacting Plume in the Atmosphere. Bound.-Layer Meteorol.
**2013**, 147, 123–137. [Google Scholar] [CrossRef] - Bisignano, A.; Mortarini, L.; Ferrero, E.; Alessandrini, S. Analytical offline approach for concentration fluctuations and higher order concentration moments. Int. J. Environ. Poll.
**2014**, 55, 58–66. [Google Scholar] [CrossRef] - Marro, M.; Nironi, C.; Salizzoni, P.; Soulhac, L. Dispersion of a passive scalar from a point source in a turbulent boundary layer. part ii: Analytical modelling. Bound.-Layer Meteorol.
**2015**, 156, 447–469. [Google Scholar] [CrossRef] - Manor, A. A stochastic single particle Lagrangian model for the concentration fluctuation in a plume dispersing inside an urban canopy. Bound.-Layer Meteorol.
**2014**, 150, 327–340. [Google Scholar] [CrossRef] - Ferrero, E.; Mortarini, L.; Purghè, F. A simple parameterization for the concentration variance dissipation in a Lagrangian single-particle model. Bound.-Layer Meteorol.
**2017**, 163, 91–101. [Google Scholar] [CrossRef] - Ferrero, E.; Oettl, D. An evaluation of a Lagrangian stochastic model for the assessment of odours. Atmos. Environ.
**2019**, 206, 237–246. [Google Scholar] - Durbin, P.A. A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech.
**1980**, 100, 279–302. [Google Scholar] [CrossRef] - Cassiani, M.; Giostra, U. A simple and fast model to compute concentration moments in a convective boundary layer. Atmos. Environ.
**2002**, 36, 4717–4724. [Google Scholar] [CrossRef] - Ferrero, E.; Mortarini, L.; Alessandrini, S.; Lacagnina, C. A fluctuating plume model for pollutants dispersion with chemical reactions. Int. J. Environ. Poll.
**2012**, 48, 3–12. [Google Scholar] [CrossRef] - Pope, S.B. Lagrangian pdf methods for turbulent flows. Ann. Rev. Fluid Mech.
**1994**, 26, 23–63. [Google Scholar] [CrossRef] - Pope, S.B. Turbulent Flows; Cambridge University Press: Cambridge, UK, 2000; 806p. [Google Scholar]
- Heinz, S. Statistical Mechanics of Turbulent Flows; Springer: Berlin/Heidelberg, Germany, 2003; 214p. [Google Scholar]
- Kernstein, A.L. Linear-eddy modelling of turbulent transport. Part. 6 Microstructure of diffusive scalar mixing fields. J. Fluid. Mech.
**1991**, 231, 361–394. [Google Scholar] [CrossRef] - Monin, A.S.; Yaglom, A.M. Statistical Fluid Mechanics: Mechanics of Turbulence; MIT Press: Cambridge, MA, USA, 1975; Volume 2, 874p. [Google Scholar]
- Gardiner, C.W. Handbook of Stochastic Methods; Springer: Berlin, Germany, 1990. [Google Scholar]
- Hinze, J.O. Turbulence; Mc Graw Hill: New York, NY, USA, 1975; 790p. [Google Scholar]
- Sawford, B.L.; Guest, F.M. Uniqueness and universality of Lagrangian stochastic models of turbulent dispersion. In Proceedings of the 8th Symposium on Turbulence and Diffusion, San Diego, CA, USA, 25–29 April 1988; pp. 96–99. [Google Scholar]
- Sawford, B.L. Reynolds number effects in Lagrangian stochastic models of turbulent dispersion. Phys. Fluids
**1991**, A3, 1577–1586. [Google Scholar] [CrossRef] - Sawford, B.L. Recent developments in the Lagrangian stochastic theory of turbulent dispersion. Bound.-Layer Meteorol.
**1993**, 62, 197–215. [Google Scholar] [CrossRef] - Hanna, S.R. Concentration fluctuations in a smoke plume. Atmos. Environ.
**1984**, 18, 1091–1106. [Google Scholar] [CrossRef] - Ramsdell, J.V.; Hinds, W.T. Concentration fluctuations and peak-to-mean concentration ratios in plumes from a ground-level continuous point source. Atmos. Environ.
**1971**, 5, 483–495. [Google Scholar] [CrossRef] - Jones, C.D. Statistics of concentration fluctuations in short range atmospheric diffusion. In Mathematical Modeling of Turbulent Diffusion in the Environment; Academic Press: New York, NY, USA, 1981; pp. 277–300. [Google Scholar]
- Mole, N.; Jones, C.D. Concentration fluctuation data from dispersion experiments carried out in stable and unstable conditions. Bound.-Layer Meteorol.
**1994**, 67, 41–74. [Google Scholar] [CrossRef] - Lewellen, W.S.; Sykes, R.I. Analysis of concentration fluctuations from Lidar observations of atmospheric plumes. J. Appl. Meteorol. Clim.
**1986**, 25, 1145–1154. [Google Scholar] [CrossRef][Green Version] - Mylne, K.R.; Mason, P.J. Concentration fluctuation measurements in a dispersing plume at a range of up to 1000m. Q. J. R. Meteorol. Soc.
**1991**, 117, 177–206. [Google Scholar] [CrossRef] - Mylne, K.R. Concentration fluctuation measurements in a plume dispersing in a stable surface layer. Bound.-Layer Meteorol.
**1992**, 60, 15–48. [Google Scholar] [CrossRef] - Lung, T.; Müller, H.J.; Gläser, M.; Möller, B. Measurements and Modelling of Full-Scale Concentration Fluctuations. Agrartech. Forsch.
**2002**, 8, E5–E15. [Google Scholar] - Finn, D.; Clawson, K.L.; Carter, R.G.; Rich, J.D.; Biltoft, C.; Leach, M. Analysis of Urban Atmosphere Plume Concentration Fluctuations. Bound.-Layer Meteorol.
**2010**, 136, 431–456. [Google Scholar] [CrossRef][Green Version] - Finn, D.; Clawson, K.L.; Eckman, R.M.; Carter, R.G.; Rich, J.D.; Strong, T.W.; Beard, S.A.; Reese, B.R.; Davis, D.; Liu, H.; et al. Project Sagebrush Phase 1. NOAA Technical Memorandum OAR ARL-268; 2015; 362p. Available online: https://www.arl.noaa.gov/documents/reports/ARL-TM-268.pdf (accessed on 8 July 2015).
- Finn, D.; Carter, R.G.; Eckman, R.M.; Rich, J.D.; Gao, Z.; Liu, H. Plume Dispersion in Low-Wind-Speed Conditions During Project Sagebrusch Phase 2, with Emphasis on Concentration Variability. Bound.-Layer Meteorol.
**2018**, 169, 67–91. [Google Scholar] [CrossRef] - Sawford, B.L. Turbulent relative dispersion. Ann. Rev. Fluid Mech.
**2001**, 33, 289–317. [Google Scholar] [CrossRef] - Gifford, F.A. Horizontal diffusion in the atmosphere: A Lagrangian-dynamical theory. Atmosp. Environ.
**1982**, 16, 505–512. [Google Scholar] [CrossRef] - Stapountzis, H.; Sawford, B.L.; Hunt, J.C.R.; Britter, R.E. Structure of the temperature field downwind of a line source in grid turbulence. J. Fluid Mech.
**1986**, 165, 401–424. [Google Scholar] [CrossRef] - Kaplan, H.; Dinar, N. A three-dimensional model for calculating the concentration distribution in inhomogeneous turbulence. Bound.-Layer Meteorol.
**1993**, 62, 217–245. [Google Scholar] [CrossRef] - Richardson, L.F. Atmospheric diffusion shown on a distance neighbour graph. Proc. Roy. Soc.
**1926**, 110, 709–737. [Google Scholar] [CrossRef][Green Version] - Gifford, F. Statistical properties of a fluctuating plume dispersion model. Adv. Geophys.
**1959**, 6, 117–137. [Google Scholar] - Pope, S.B. Turbulent Flows; Cambridge University Press: Cambridge, UK, 2001. [Google Scholar]
- Sawford, B.L. Micro-mixing modelling of scalar fluctuations for plumes in homogeneous turbulence. Flowturb. Comb.
**2004**, 72, 133–160. [Google Scholar] [CrossRef] - Dopazo, C.; Valiño, L.; Fueyo, N. Statistical description of the turbulent mixing of scalar fields. Int. J. Mod. Phys. B
**1997**, 11, 2975–3014. [Google Scholar] [CrossRef] - Dixon, N.S.; Tomlin, A.S. A Lagrangian stochastic model for predicting concentration fluctuations in urban areas. Atmosp. Environ.
**2007**, 41, 8114–8127. [Google Scholar] [CrossRef] - Postma, J.V.; Wilson, J.D.; Yee, E. Comparing two implementations of a micromixing model. Part I: Wall shear-layer flow. Bound.-Layer Meteorol.
**2011**, 140, 207–224. [Google Scholar] [CrossRef] - Cassiani, M. The volumetric particle approach for concentration fluctuations and chemical reactions in Lagrangian particle and particle-grid models. Bound.-Layer Meteorol.
**2013**, 146, 207–233. [Google Scholar] [CrossRef] - Kaplan, H. An estimation of a passive scalar variances using a one-particle Lagrangian transport and diffusion model. Phys. A Stat. Mech. Its Appl.
**2014**, 393, 1–9. [Google Scholar] [CrossRef] - Kaplan, H.; Olry, C.; Moussafir, J.; Oldrini, O.; Mahe, F.; Albergel, A. Chemical reactions at street scale using a Lagrangian particle dispersion model. Int. J. Environ. Poll.
**2014**, 55, 1–4. [Google Scholar] - Villermaux, E.; Duplat, J. Mixing as an aggregation process. Phys. Rev. Lett.
**2003**, 91, 184501. [Google Scholar] [CrossRef] [PubMed][Green Version] - Yee, E.; Wang, B.C.; Lien, F.S. Probabilistic model for concentration fluctuations in compact-source plumes in an urban environment. Bound.-Layer Meteorol.
**2009**, 130, 169–208. [Google Scholar] [CrossRef] - Marro, M.; Salizzoni, P.; Soulhac, L.; Cassiani, M. Dispersion of a Passive Scalar Fluctuating Plume in a Turbulent Boundary Layer. Part III: Stochastic Modelling. Bound.-Layer Meteorol.
**2018**, 167, 349–369. [Google Scholar] [CrossRef][Green Version] - Garmory, A.; Richardson, E.S.; Mastorakos, E. Micromixing effects in a reacting plume by the stochastic fields method. Atmos. Environ.
**2006**, 40, 1078–1091. [Google Scholar] [CrossRef] - Alessandrini, S.; Ferrero, E. A hybrid lagrangian–eulerian particle model for reacting pollutant dispersion in non-homogeneous non-isotropic turbulence. Phys. A
**2009**, 388, 1375–1387. [Google Scholar] [CrossRef] - Alessandrini, S.; Ferrero, E. An application of a Lagrangian particle model with chemical reactions to power plant pollution dispersion in complex terrain. In Air Pollution Modeling and its Application XX; Steyn, D.G., Rao, S.T., Eds.; Springer: New York, NY, USA, 2010; pp. 361–366. [Google Scholar]
- Alessandrini, S.; Ferrero, E. A Lagrangian particle model with chemical reactions: Application in real atmosphere. Int. J. Environ. Poll.
**2011**, 47, 97–107. [Google Scholar] [CrossRef][Green Version] - Alessandrini, S.; Balanzino, A.; Ferrero, E.; Riva, M. Lagrangian modelling evaluation of the NOx pollution reduction due to electric vehicles introduction. Int. J. Environ. Poll.
**2012**, 50, 200–208. [Google Scholar] [CrossRef] - Brown, R.J.; Bilger, R.W. Experiments on a reacting plume–1. Conventional concentration statistics. Atmos. Environ.
**1998**, 32, 611–628. [Google Scholar] [CrossRef] - Aguirre, C.; Vinkovic, I.; Simoens, S. A subgrid Lagrangian model for turbulent passive and reactive scalar dispersion. Int. J. Heat Fluid Flow
**2006**, 27, 627–635. [Google Scholar] [CrossRef] - Vilá-Guerau de Arellano, J.; Dosio, A.; Vinuesa, J.-F.; Holtslag, A.A.M.; Galmarini, S. The dispersion of chemically reactive species in the atmospheric boundary layer. Meteor. Atmos. Phys.
**2004**, 87, 23–38. [Google Scholar] [CrossRef] - Lewellen, W.S. Use of invariant modelling. In Handbook of Turbulence; Plenum Press: New York, NY, USA, 1977; Volume 180. [Google Scholar]
- Sykes, R.I.; Lewellen, W.S.; Parker, S.E. A turbulent-transport model for concentration fluctuations and fluxes. J. Fluid Mech.
**1984**, 139, 193–218. [Google Scholar] [CrossRef] - Fackrell, J.E.; Robins, A.G. Concentration fluctuations and fluxes in plumes from point sources in a turbulent boundary. J. Fluid Mech.
**1982**, 117, 1–26. [Google Scholar] [CrossRef] - Sawford, B.L. Comparison of some different approximations in the statistical theory of relative dispersion. Q. J. R. Meteorol. Soc.
**1982**, 108, 191–208. [Google Scholar] [CrossRef] - Galperin, B. A modified turbulence energy model for diffusion from elevated and ground point sources in neutral boundary layer. Bound.-Layer Meteorol.
**1986**, 37, 245–262. [Google Scholar] [CrossRef] - Bèguier, C.; Dekeyser, I. Launder BE Ratio of scalar and velocity dissipation time scales in shear flow turbulence. Phys. Fluids
**1978**, 21, 307–310. [Google Scholar] [CrossRef] - Warhaft, Z.; Lumley, J.L. An experimental study of the decay of temperature fluctuations in grid-generated turbulence. J. Fluid Mech.
**1978**, 88, 659–684. [Google Scholar] [CrossRef] - Andronopoulos, S.; Grigoriadis, D.; Robins, A.; Venetsanos, A.; Rafailidis, S.; Bartzis, J.G. Three-dimensional modeling of concentration fluctuations in complicated geometry. Environ. Fluid Mech.
**2002**, 1, 415–440. [Google Scholar] [CrossRef] - Milliez, M.; Carissimo, B. Computational fluid dynamical modeling of concentration fluctuations in an idealized urban area. Bound.-Layer Meteorol.
**2008**, 127, 241–259. [Google Scholar] [CrossRef] - Dourado, H.; Santos, J.M.; Reis Junior, N.C.; Mavroidis, I. Development of a fluctuating plume model for odour dispersion around buildings. Atmos. Environ.
**2014**, 89, 148–157. [Google Scholar] [CrossRef] - Mussio, P.; Gnyp, A.W.; Henshaw, P.F. A fluctuating plume dispersion model for the prediction of odour-impact frequencies from continuous stationary sources. Atmos. Environ.
**2001**, 35, 2955–2962. [Google Scholar] [CrossRef] - Piringer, M.; Knauder, W.; Petz, E.; Schauberger, G. Factors influencing separation distances against odour annoyance calculated by Gaussian and Lagrangian dispersion models. Atmos. Environ.
**2016**, 140, 69–83. [Google Scholar] [CrossRef] - Piringer, M.; Knauder, W.; Petz, E.; Schauberger, G. Use of ultrasonic anemometer data to derive local odour related peak-to-mean concentration ratios. Chem. Eng. Trans.
**2014**, 40, 103–108. [Google Scholar] - Smith, M.E. Recommended Guide for the Prediction of the Dispersion of Airborne Effluents; ASME: New York, NY, USA, 1973. [Google Scholar]
- Janicke, L.; Janicke, U.; Ahrens, D.; Hartmann, U.; Müller, W.J. Development of the odour dispersion model AUSTAL2000G in Germany. Environ. Odour Manag. Vdi-Ber.
**2004**, 1850, 411–417. [Google Scholar] - VDI 3788-1, Environmental meteorology—Dispersion of odorants in the atmosphere—Fundamentals. Available online: https://www.vdi.de/richtlinien/details/vdi-3788-blatt-1-umweltmeteorologie-ausbreitung-von-geruchsstoffen-in-der-atmosphaere-grundlagen (accessed on 29 November 2019).
- Oettl, D.; Kropsch, M.; Mandl, M. Odour assessment in the vicinity of a pig-fatting farm using field inspections (EN 16841-1) and dispersion modelling. Atmos. Environ.
**2018**, 181, 54–60. [Google Scholar] [CrossRef] - Scire, J.; Strimaitis, D.; Yamartino, R. A User’s Guide for the CALPUFF Dispersion Model; Earth Tech. Inc.: Concord, MA, USA, 2000; pp. 1–521. [Google Scholar]
- Murguia, W.; Pagans, E.; Barclay, J.; Scire, J. Case study: A comparison of predicted odour exposure levels in Barcelona using CALPUFF lite, CALPUFF NoObs and CALPUFF hybrid model. Chem. Eng. Trans.
**2014**, 40, 31–36. [Google Scholar] - De Melo, A.M.; Santos, J.M.; Mavroidis, I.; Reis, N.C., Jr. Modelling of odour dispersion around a pig farm building complex using AERMOD and CALPUFF. Comparison with wind tunnel results. Build. Environ.
**2012**, 56, 8–20. [Google Scholar] [CrossRef] - Ranzato, L.; Barausse, A.; Mantovani, A.; Pittarello, A.; Benzo, M.; Palmeri, L. A comparison of methods for the assessment of odor impacts on air quality: Field inspection (VDI 3940) and the air dispersion model CALPUFF. Atmos. Environ.
**2012**, 61, 570–579. [Google Scholar] [CrossRef]

**Figure 1.**Concentration signals observed in JU03 field campaign (IOP 188, release 5). The left panel shows the continuous source (black pentagon), and four selected fast gas analyzers (green circles, labeled a, b, c and d), coordinates are given in meters with the source at the origin. The right panel presents the corresponding concentration signals.

**Figure 2.**Modeled intensities of concentration fluctuations using Equation (48) near a point source indicated by the circle, and a wind direction from the left.

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Ferrero, E.; Manor, A.; Mortarini, L.; Oettl, D. Concentration Fluctuations and Odor Dispersion in Lagrangian Models. *Atmosphere* **2020**, *11*, 27.
https://doi.org/10.3390/atmos11010027

**AMA Style**

Ferrero E, Manor A, Mortarini L, Oettl D. Concentration Fluctuations and Odor Dispersion in Lagrangian Models. *Atmosphere*. 2020; 11(1):27.
https://doi.org/10.3390/atmos11010027

**Chicago/Turabian Style**

Ferrero, Enrico, Alon Manor, Luca Mortarini, and Dietmar Oettl. 2020. "Concentration Fluctuations and Odor Dispersion in Lagrangian Models" *Atmosphere* 11, no. 1: 27.
https://doi.org/10.3390/atmos11010027