A simple model to assess odour hours for regulatory purposes
Introduction
In several countries (e.g. Austria, Germany, Switzerland, Italy) odour assessments are based on so-called odour-hours defined by at least 6 min of perceivable odour concentrations. It is well known that dispersion models typically provide mean concentrations for averaging times of about 30–60 min. Different models for odour estimation can be found in the literature (e.g. Mussio et al., 2001, Lo Iacono, 2009, Dourado et al., 2014, Murguia et al., 2014). Modelling odour hours requires the determination of the 90th percentile of the corresponding cumulative frequency distribution. Often the 90th percentile is normalized by the hourly-mean concentration by defining , where is the hourly-mean concentration, and the 90th percentile. In Germany, the regulatory odour dispersion model AUSTAL2000G (GIRL, 2009) uses the simple relationship , which is based on the work of Janicke and Janicke (2004). This assumption is broadly used in Austria, too, and is currently implemented in the Lagrangian particle model GRAL (Oettl, 2015a). The advantages of setting are its robustness, and, as will be seen later in this work, its tendency to provide a conservative estimate for , which is generally eligible when applying (simple) models for regulatory purposes. Nevertheless, one might suppose that the magnitude of overestimation increases substantially with distance to sources or in case of overlapping plumes.
Piringer et al. (2016) use an empirical approach for assessing , which depends on atmospheric turbulence and the distance to the source. Though this model is certainly more appropriate from the theoretical point of view than using a constant factor, it has been strictly derived for a single point source only and cannot be applied for multiple sources. Furthermore it does not take into account cross-wind variability of .
Therefore, the aim of this work was to derive a simple model providing a better estimate for , but which is still applicable in licencing procedures. The concept of the approach is based on a simplified version of the advection-diffusion equation for the concentration variance , which serves determining by utilizing a representative probability density function (PDF) for the odour concentration. Many models have been developed for the second- or higher-order moments of the concentration PDF, starting from the two-particle models proposed by Thomson (1990) and Borgas and Sawford (1994) for idealized conditions (homogeneous, isotropic, and stationary turbulence). Another interesting approach, the so-called PDF method, was brought forward by Pope (1985) and Cassiani et al. (2005). Unfortunately, it is difficult to apply the model to real cases due to the large computational time required. On the contrary, the fluctuating plume model (Yee et al., 1994a, Yee et al., 1994b; Yee and Wilson, 2000; Luhar et al., 2000, Franzese, 2003, Mortarini et al., 2009, Ferrero et al., 2013) is less time expensive and can be used in real-world dispersion conditions, i.e. non-homogeneous boundary layers. Recently, Manor (2014) proposed a Lagrangian model, able to simulate the concentration-variance trajectories, and Ferrero et al. (2016) introduced a new parameterization for the dissipation variance for that kind of models. Concerning Eulerian models, it is worth mentioning the paper of Mavroidis et al. (2015) that used a computational fluid dynamics (CFD) model to calculate the concentration fluctuations and compared model results with a wind-tunnel experiment suggesting that the magnitude of concentration fluctuations are comparable with those of mean concentrations.
Sect. 2.1 deals with the selection of a proper PDF by analysing concentration-fluctuation observations of three different field studies. In Sect. 2.2, the derivation of the basic equations of the concentration-variance model are outlined, and sect. 3 presents a comparison of modelled and observed data.
Section snippets
Selection of a proper probability density function (PDF) for concentration fluctuations
A number of field studies concerning concentration fluctuations are reported in literature. Different PDFs have been proposed for fitting observed data. Mylne and Mason (1991), by investigating dispersing plumes originating from a ground-level point source, compared a clipped-normal distribution with an exponential one and found that the clipped-normal PDF represents most of the observed features (e.g. concentration intensity), but underestimates concentration intensity close to the
Model evaluation
The Uttenweiler and JU03 experiments were used to test the model's accuracy with regard to simulating the concentration-fluctuation intensity i and . It is planned to carry out similar model evaluations for other available datasets, such as the Sagebrush field campaign, in the future.
As tracer dispersion was influenced by buildings in both the Uttenweiler and JU03 experiments, microscale flow-field simulations had to be carried out prior to dispersion modelling. The GRAL model used in this
Conclusions
Based on previous works (Hsieh et al., 2007, Milliez and Carissimo, 2008, Manor, 2014, Ferrero et al., 2016) a simplified version for computing concentration variances has been derived. One of the crucial steps in the derivation was the neglecting of the transport and diffusion terms. The validity of this assumption has been tested by comparing modelled concentration-fluctuation intensities with observed ones, and by comparing the general spatial patterns with simulation results obtained by
Acknowledgements
We are very grateful to Prof. Dennis Finn, Air Resources Laboratory, Maryland, U.S., for providing the Sagebrush and Joint Urban 2003 data and for his useful directions. We would also like to thank all three anonymous reviewers for their precious comments, which helped a lot to improve this work.
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