# Development and Evaluation of a Fluctuating Plume Model for Odor Impact Assessment
###### Abstract
The outputs of the dispersion models used in Air Pollution assessment and forecast are usually the hourly-mean concentrations \(C_{m}\), but this information is not sufficient to describe completely the nature of an odor nuisance process [34; 35]. To consider the variability of the ambient odor concentration within the period of 1 hour, a constant peak-to-mean factor \(C_{p}/C_{m}\) (also P/M) is usually provided by authorities [36; 37; 38]. As an example, the German legislation prescribes that all olfactory considerations of a modelling type, \"Must be made considering an appropriate peak concentration\". The Standard requires that the hourly average concentration obtained from the model is simply multiplied by a constant numerical factor equal to 4 [36; 37]. Differently, all the regional guidelines present in Italy, suggest the value of 2.3 [38; 39; 40]. Unluckily, the experimental data show that a huge amount of physical phenomena have an effect on concentration fluctuations, demonstrating that the choice of a constant parameter is a very simplified approach [41]. Different simple methods for the calculation of this \"peak-to-mean\" factor can be found in literature; it is worth mentioning the constant peak-to-mean [36], the peak-to-mean variable only depending on atmospheric stability [42] and the one variable with stability and distance downwind the emission source [43; 44]. Obtaining the sub-hourly percentile (and so the peak concentration) of a passive substance via dispersion model is not a trivial challenge. An alternative approach, available for Gaussian models is the consideration of recalculated lateral dispersion coefficients, in order to make them able to estimate ambient concentrations with averaging times shorter that 10 min [45; 46]. However, the use of new models able to assess the mean concentration and variance, based on the physical laws describing the transport and dispersion in air of a substance, treated as a stochastic variable, appears the most recently debated methodology for the identification of peak concentrations (however defined, but linked to the statistical characteristics of the instantaneous concentration). In [PERSON] et al. (2019) [PERSON] et al. (2019) an updated and exhaustive review of the modelling methods that can be used for odor modelling has been presented, and the most suitable methods to represent real situations seem to be those based on a Lagrangian framework. The most used philosophy to solve the problem of estimating a sub-hourly percentile is to hypothesize a priori a realistic PDF for the passive concentration. Experimental evidences show that, for this purpose, it is sufficient to consider a two-parameter PDF that asymptotically reduces to an exponential distribution near the source and a Log-Normal distribution at great downwind distances ([PERSON] and [PERSON], 2019). Weibull distribution and especially Gamma distribution own these adaptability features. Since a two-parameter distribution is completely known once the mean value and the variance are obtained, this closure hypothesis means that, to describe the concentration fluctuations, and therefore to determine the desired percentile, it is sufficient to reconstruct the mean and the concentration variance. One of the most interesting model is the Fluctuating (or Meandering) Plume model, originally proposed in qualitative terms by [PERSON] (1959) [PERSON] (1959). In [PERSON] et al. (2000) [PERSON] et al. (2000), the logical evolution of this modelling philosophy over the years is shown and a version based on Lagrangian Particle Modelling is described in detail. Further works have been published about this topic ([PERSON] and [PERSON], 2000; [PERSON] and [PERSON], 2001; [PERSON] and [PERSON], 2002). Within these studies, a Lagrangian version of the Fluctuating Plume is proposed, which provides extremely realistic reconstructions of the instantaneous concentration statistics. Unlucky, the complexity of the models proposed hinders their application for regulatory or screening evaluations. The work of [PERSON] et al.