## 7 Modelling Odour Dispersion  
Information on emissions, meteorological and topographical data can be used to model the dispersion of odorous substances. Both the spatial and temporal variability in odour concentrations can be simulated. The method of obtaining these data can vary, from estimation to measurement. There are various approaches to modelling atmospheric dispersion. Three basic types can be distinguished: Gaussian, Lagrangian and Eulerian models. The simplest are the Gaussian models, which assume both the emission plume and the meteorological conditions to be constant over time. The software models AER-MOD, LODM, STING and OdiGauss are based on them [47]. In most cases, they do not take windless and weak wind conditions into account. They are usually used to estimate the average annual and hourly pollutant concentrations. An example of an equation based on the Gaussian model that represents the odour concentration at equilibrium in three spatial dimensions (x, y, z) is shown below (Equation (9)):  
\[S_{(x,y,z)}=\frac{\mathrm{E}}{2\pi\sigma_{y}\sigma_{z}u_{h}}.exp\left(-\frac{ y^{2}}{2\sigma_{y}^{2}}\right)\cdot\left[exp\left(-\frac{(z-h)^{2}}{2\sigma_{z}^{2}} \right)+exp\left(-\frac{(z+h)^{2}}{2\sigma_{z}^{2}}\right)\right] \tag{9}\]  
where  
\(S_{(x,y,z)}\)--odour concentration at a point with coordinates \(x\), \(y\), \(z\) (\(\mathrm{ou/m^{3}}\));  
\(E^{\bullet}\)--odour emission rate (\(\mathrm{ou/s}\));  
\(h\)--emission height (\(\mathrm{m}\));  
\(u_{h}\)--mean wind speed in the atmospheric layer from \(z=0\) to \(z=h\);  
\(\sigma_{\gamma}\)--horizontal dispersion coefficient (y-direction), calculated according to [PERSON] [120] based on atmospheric stability classes defined by [PERSON] [121] and  
\(\sigma_{z}\)--vertical dispersion coefficient (z-direction), calculated according to [PERSON] [122], based on atmospheric stability classes defined by [PERSON] [120]. When a Gaussian model is applied to a time series of weather conditions, the results can be viewed as integrated quasi-dynamic representations (e.g., repeating hourly dispersion calculations over a year). Pollutant dispersion in Lagrangian models combines stochastic effects as well as including deterministic factors. Based on the measured or estimated odour emission and the simulation of the spread of particles in the atmosphere according to the Lagrangian dispersion model, the impression value at certain points distant from the emission source is predicted depending on the wind speed and direction [118]. Such models can be used under low-wind conditions [54] and are computationally intensive and resource-intensive [114,121]. In addition, there are hybrid models that include both Lagrangian and Gaussian approaches and are known as puff models (e.g., CALPUFF) [47]. They characterise the dispersion of pollutants using clouds with a constant volume (so-called puffs). The concentration values in these clouds are determined by the Gaussian method, while the paths they follow are determined by the Lagrangian method. Eulerian models (grid models, 3-D models) are mathematically the most advanced and therefore more accurate. The dispersion calculations are carried out in a three-dimensional area. Eulerian models (e.g., CALGRID, ModOdour) make it possible to calculate the average pollutant concentration at certain receptor points, even for turbulent flows [47,123]. The disadvantage of Eulerian models is the considerable need for computing resources (higher operating costs) [114,123]. Regardless of the model, the necessary input data are topographical and orographic data or meteorological data such as temperature, humidity and air pressure, wind speed and direction, precipitation or solar radiation [47]. Odour emission measurements can be carried out using the dynamic olfactometry method, e.g., according to the EN 13725 standard, the VDI 3880 and VDI 3884-1 guidelines. The disadvantage of the dispersion modelling method is that for some sources, such as diffuse sources or area sources, the emission value is difficult to determine.