# Development and Evaluation of a Fluctuating Plume Model for Odor Impact Assessment
###### Abstract  
For environmental odor nuisance, it is extremely important to identify the instantaneous concentration statistics. In this work, a Fluctuating Plume Model for different statistical moments is proposed. It provides data in terms of mean concentrations, variance, and intensity of concentration. The 90 th percentile peak-to-mean factor, \(R_{90}\), was tested here by comparing it with the experimental results (Uttenweiler field experiment), considering different Probability Distribution Functions (PDFs): Gamma and the Modified Weibull. Seventy-two percent of the simulated mean concentration values fell within a factor 2 compared to the experimental ones: the model was judged acceptable. Both the modelled results for standard deviation, \(\sigma_{C}\), and concentration intensity, \(I_{c}\), overestimate the experimental data. This evidence can be due to the non-ideality of the measurement system. The propagation of those errors to the estimation of \(R_{90}\) is complex, but the ranges covered are quite repeatable: the obtained values are 1-3 for the Gamma, 1.5-4 for Modified Weibull PDF, and experimental ones from 1.4 to 3.6.  
odor impact assessment; dispersion modelling; peak-to-mean; concentration fluctuation; fluctuating plume model +
Footnote †: journal: _Applied Sciences_  
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From a practical point of view, when interest is focused to Air Pollution and the related main pollutants (e.g., NO\({}_{2}\), CO, SO\({}_{2}\), O\({}_{3}\), PM\({}_{10}\), PM\({}_{2.5}\), and C\({}_{6}\)H\({}_{6}\)), the task is limited to the knowledge of the average concentration. Actually, for this purpose, models of various complexity are now available, both Eulerian [13; 14] and Lagrangian [15]. Things are different when dealing with environmental odors. In this case, peaks concentration of a vast set of (odorous) substances mixed in the ambient air are conveyed to the human olfactory system through every respiratory act of extremely short duration, which can last the order of 5 s [16; 17]. If the instantaneous concentration of these substances in the inhaled air exceeds a certain threshold, the individual perceives a sensation [18]. While usually odorous gases do not create direct toxicological effects on health [19; 20], they cause discomfort and malaise, headache, nausea, joint pain, pain in the arms or legs and a feeling of fullness in the stomach [21]. In this case, both measurements and modelling predictions of the concentration of odorous gases should be aimed at identifying the statistics of the instantaneous concentration. Starting from instantaneous concentration measurements gathered in a suitable averaging period (for instance 1 h), practical possibilities to identify the peak hourly concentration \(C_{p}\) are, for example:  
* \(C_{p}=C_{m}+\sigma\), where \(C_{m}\) is the hourly mean value and \(\sigma\) its standard deviation [22]
* \(C_{p}\) equal to the maximum value of the instantaneous concentration in the considered averaging period [23]
* As an appropriate \(p^{th}\) percentile of the instantaneous concentration at each point of the spatial domain [24]  
A historical scientific challenge was the objectification of the subjective sensation of odor [25]. For this reason, the measurement of odors requires specific methods [26; 27]. There are many regulations for Air Pollution, but olfactory pollution is typically treated differently. As previously mentioned, the trend in space and time of the instantaneous concentration of a gaseous species is very irregular. For instance, the sensation of smell is perceived mostly in hours when the PBL turbulence is low and therefore the atmospheric stability is high, i.e., at evening and early morning [17; 28]. In these situations, the use of an atmospheric dispersion model appears to be crucial [29; 30; 31]. As a matter of fact, the majority of environmental odor legislations around the world lean upon models [32; 33].