** Odours are typically released into the atmosphere as diffuse emissions from area and volume sources, whose detailed quantification in terms of odour emission rate is often hardly achievable by direct source sampling. Indirect methods, involving the use of micrometeorological methods in order to correlate downwind concentrations to the emission rates, are already mentioned in literature, but rarely found in real applications for the quantification of odour emissions.**

The instrumentation needed for the development of micrometeorological methods has nowadays become accessible in terms of prices and reliability, thus making the implementation of such methods to industrial applications more and more interesting.

M. Invernizzi ^{1} , B.J. Lotesoriere ^{1} , R. Sozzi ^{2} , S. Sironi ^{1}, L. Capelli ^{1*}

1 Politecnico di Milano, Department of Chemistry, Materials, and Chemical Engineering “Giulio Natta”, P.za Leonardo da Vinci 32, 20133 Milan, Italy.

2 Independent Researcher, 20133 Milan, Italy.

** Competing interests:** The author has declared that no competing interests exist.

**Academic editor:** Carlos N. Díaz

** Content quality:** This paper has been peer reviewed by at least two reviewers. See scientific committee here.

** **** Citation:*** M. Invernizzi , B.J. Lotesoriere, R. Sozzi, S. Sironi, L. Capelli, 2021. Micrometeorological methods for the indirect quantification of odour emissions*

*, 9th IWA Odour& VOC/Air Emission Conference, Bilbao, Spain, www.olores.org.*

** Copyright:** 2021 Olores.org. Open Content Creative Commons license. It is allowed to download, reuse, reprint, modify, distribute, and / or copy articles in olores.org website, as long as the original authors and source are cited. No permission is required from the authors or the publishers.

** ISBN:** 978-84-09-37032-0

** Keyword: **Odour Emission Rate, complex sources, area sources, eddy covariace, gradient method.

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### Abstract

Odours are typically released into the atmosphere as diffuse emissions from area and volume sources, whose detailed quantification in terms of odour emission rate is often hardly achievable by direct source sampling. Indirect methods, involving the use of micrometeorological methods in order to correlate downwind concentrations to the emission rates, are already mentioned in literature, but rarely found in real applications for the quantification of odour emissions.

The instrumentation needed for the development of micrometeorological methods has nowadays become accessible in terms of prices and reliability, thus making the implementation of such methods to industrial applications more and more interesting. For this reason, this work aims to provide an overview of micrometeorological methods and investigate their effective applicability to odours, thereby providing a short description of the physics related to such methods and analysing the relevant scientific literature.

The theoretical basis of these methods is presented, and their advantages and disadvantages are discussed. Moreover, their applicability to the estimation of odour emissions is discussed by providing some suggestions about the suitable ways to evaluate the most critical parameters needed for the calculation of the odour emission rate.

### 1. Introduction

In many cases, odour emissions are not related solely to conveyed sources, but rather to other types of diffuse sources, which are often more critical from the point of view of the odour impact, because of their low dispersion capacity (Capelli et al., 2011).

Among the different types of complex odour sources, passive area sources are by far the ones that have been studied the most. In principle, two main strategies exist for evaluating emission rates from passive area sources (Capelli et al., 2013):

- direct measurements using an enclosure of some sort, i.e. so-called “hood methods”. In this case, emission rates are derived from the data regarding the concentration of the compounds of interest measured in the samples collected at the outlet of the sampling device combined with the dimensions of the device and the operating conditions;
- indirect measurements using micrometeorological methods, where emission rates are derived from simultaneous measurements of wind velocities and concentrations across the plume profile downwind of the source.

There are some scientific publications proving the scarce effectiveness of hood methods to evaluate emissions from extended or inhomogeneous area sources. For instance, in the case of landfills, because of the limited dimensions of flux chambers or wind tunnels, they tend to underestimate emissions (Mønster et al., 2019).

Despite being often mentioned as an alternative to hood methods also for odour sampling, the practical applications of micrometeorological methods for the indirect estimation of odour emissions is extremely rare. Nonetheless, the recent scientific progress is raising the interest towards the application of micrometeorological methods, mainly because the instrumentation needed for their implementation (i.e. 3D sonic anemometers and sensor systems for continuous odour/ or odorant concentration measurements) have become more reliable and affordable in terms of cost.

Thus, the aim of this work is to explore the applicability of micrometeorological methods to the indirect estimation of odour emissions, thereby relying on the available scientific papers discussing the application of such methods to the emissions of different odorous compounds, such as NH_{3}, H_{2}S and VOCs.

### 2. Theoretical background

#### 2.1 The Monin-Obukhov Similarity Theory

The amazing result of the theory of Similarity formulated by Andrei Monin and Alexander Obukhov is that the vertical profile of each characteristic variable of the surface layer (SL), suitably scaled and rendered dimensionless, is given by a universal function, which depends exclusively on the stability parameter z/L, where L is the so-called “Monin-Obukhov length”. This parameter condenses in itself both the mechanical and the convective turbulence that acts in the SL (Foken, 2006).

#### 2.2 Definition of micrometeorological methods and turbulent flux

In extreme synthesis, a micrometeorological method is a method that, based on the instantaneous measurements of the three components of the wind speed (u, v, w), the friction velocity (u*), the turbulent flow of sensible heat (H_{0}), and the Monin-Obukhov length (L), which can all be obtained by a triaxial sonic anemometer, enables to calculate the flux of a passive chemical species as:

Applying the Reynolds’ decomposition, this can be reformulated as:

Where F_{C} is the vertical turbulent flux of the target chemical at the measurement point, and w’ and c’ are the turbulent contributions (i.e. instantaneous fluctuations around its mean value) of the vertical wind component and the concentration, respectively.

Two main families of micrometeorological methods can be identified.

- One first family of methods is based on the definition of turbulent flux. These methods involve the direct detection of the trend in time of w(t) (by means of a triaxial ultrasonic anemometer) and of c(t) and the calculation of the covariance of the two signals, and are called “Eddy-Covariance methods”.
- The second method is based on the Monin-Obukhov Similarity Theory (briefly explained in Section 2.3), and on the measurement of the average concentration of the scalar at, at least, two different heights. This method is called “Gradient Method”.

We are aware of the existence of other micrometeorological methods that have been proposed for the indirect estimation of emission fluxes (Padro, 1993; Sjöblom and Smedman, 2004; Sozzi et al., 2001), however, because of their importance, and because they are the most frequently used, here we decided to focus to the Eddy-Covariance (EC) and the Gradient methods (GM).

### 3. Overview of micrometeorological methods

#### 3.1 Eddy-Covariance methods

The “complete” EC method is the most direct method to asses F_{C}: it is based on the direct quantification of the covariance of high-frequency w and c. It is based on the use of a triaxial sonic anemometer, able of providing the instantaneous values of u, v, w, u*, H 0 and L, and of a fast-analyser for the chemical species under investigation (Aubinet et al., 2012). The main shortcoming of this method lies in the availability of instrumentation able to measure high frequency concentration fluctuations (in the range of 10 Hz). Due to this technological limitation, EC has often been used for the measurement of H_{2}O, CO_{2}, NH_{3}, N_{2}O, O_{3} and CH_{4} (e.g., Ferrara et al., 2012; Smith et al., 1994) while few works are available for H_{2}S and Volatile Organic Compounds (VOC) (e.g., Spirig et al., 2005).

Because of the limited availability of high-frequency measuring instruments, with the purpose of using slow response analysers systems alternative methods to the complete EC have been developed, but based on a similar logic, such as the Eddy Accumulation (EA) methods.

The True Eddy Accumulation (TEA) assumes to send small air samples taken almost instantaneously (i.e. 0.1 s) from the measurement volume of the sonic anemometer, and with a sampled volume linearly proportional to |w|, into two different tanks, depending on whether at the sampling moment w i is positive (updraft) or negative (downdraft). In such conditions, it can be demonstrated that the flux F_{C} can be obtained as:

Where W is the average of the modulus of the N w_{i} values, c^{+} and c^{−} are the average concentrations of air sampled in the two tanks (updraft and downdraft).

The greatest difficulty encountered in the construction of a TEA apparatus is the need for a system capable of capturing almost instantaneously a volume of air directly and linearly proportional to the modulus of w.

If using a sampling system that still withdraws air into two different tanks with high frequency (linked to the sonic value of w), but with a constant flow, which thus does not need to be linearly dependent on |w|: this technique is called Relaxed Eddy Accumulation (REA). In this case, the flux can be obtained as:

Where c^{+} and c^{−} are the average concentrations of air sampled in the two tanks (updraft and downdraft), σ_{w} is the sample standard deviation of the vertical component w measured by the sonic anemometer, while b represents an appropriate proportionality factor, which is often given a value of 0.6. Indeed, the correct setting of the value of b is one of the critical aspects for the implementation of the REA (Amman and Meixner, 2002). A handy way to obtain a value for b is to assume a complete scalar similarity between the sonic temperature and the gas considered. In this case, the ultrasonic anemometer provides fast measurements of the temperature and hence allows to implement an eddy correlation, thus giving the b parameter can be computed independently from the type of compound.

#### 3.2 Gradient method

The Gradient Method (GM) is the oldest micrometeorological method, but it is still employed for substances for which the concentration measurement requires laboratory techniques or low-response analysers (Maier and Schack-Kirchner, 2014). Based on similarity considerations, the vertical turbulent flow F_{C} can be expressed as:

where k is the von Karman’s constant and Ф_{C} is the gradient universal stability function. By integrating the previous equation between two different measurement heights z_{1} and z_{2} , it is possible to reformulate the expression for the calculation of F_{C} as a function of easily measurable variables:

where Ψ_{C} is the profile universal stability function, whose analytical form can be considered as known.

Thus, the minimum items needed for the implementation of a measurement system based on the GM are:

- a 3D ultrasonic anemometer/ thermometer providing the average wind speed and direction, u*, H
_{0}, and the stability parameter z/L; - the measurements of the concentration at two heights z
_{1}and z_{2}; - a conventional analyser for the scalar, not necessarily fast-response, but with an adequate accuracy and resolution to measure the concentration difference: ∆C=C(z
_{2})-C(z_{1}).

Based on the review conducted by Högström (1988) it is possible to define the most recent stability functions to be used in convective (z/L<0) and in weakly stable (0<z/L<0.8) situations. Only in the last two decades, thanks to the experimental observations collected at Arctic and Antarctic bases, it has been possible to obtain clear information for the definition of the stability functions in very stable situations (0.8<z/L<50) and in extremely stable situations (z/L>50), which can be found in the work by Gryanik et al. (2020).

Another critical aspect for the application of the GM is the choice of the measurement heights, which shall be comprised within the SL. It should be highlighted that, in some of the papers analysed (e.g., Darmais et al., 2000; Todd et al., 2005), the measurements were carried out at three different heights or more, even if, in the end, the gradient is always evaluated between only two levels. Even though the use of more than two heights limits the risk to have ambiguous results, especially in the case of chemically reactive species or close to rough surfaces, where a constant flux layer may be perturbed, it has a direct impact on the sampling strategy, thus involving either an alternating sampling at two or three heights or simultaneous sampling, which means having a sampling system at each level.

#### 3.3 Comparison of methods

Table 1 summarizes the main pros and cons of the two methods here discussed.

Method |
Pros |
Cons |

REA | - It is an attractive method for the quantification of odorous substances since the measurement of the average concentrations can be achieved using slow response analysers. - Even if the technique is based on the evaluation of the updraft and downdraft concentrations, the measurement height is unique. |
- There is no standardization for the method, especially in the instrumental setup, and in the choice of the most appropriate proxy scalar to be used for the quantification of the b parameter. - Dealing with a difference in concentration, numerical errors are always present, especially if the flow is low the uncertainty can be enormous. |

GM | - It is the most robust and solid method since it is applicable even in the most complex situations. - It is suitable for all the compounds for which the concentration measurement requires laboratory techniques or low-response automatic analysers. - Although it is necessary to measure concentration at two different heights, it has been proven that it is possible to use a single analyser for non-simultaneous measurements; hence, calibration discrepancies between the instruments are eliminated. |
- The footprint is poorly defined since two diverse heights for the concentration difference are requested, which can be very large considering that it must be measurable. - A measurement “deadband” is given by the intrinsic uncertainty of the instrument. In the case of a single analyser the uncertainty is unique for the two measurement heights, while if two analysers are used and the measured concentrations are similar, it is not possible to know which is greater. - Dealing with a difference in concentration, numerical errors are unavoidable, since the calibration of the instrument is never perfect. |

### 4. Conclusions

Based on the remarkable and promising results reported by several authors, micrometeorological methods represent an attractive and potentially feasible alternative to hood methods.

Their mathematical reformulation of the REA and GM allows to demonstrate that both methods are based on the use of a triaxial ultrasonic anemometer, and on the measurement of a difference in concentration (∆C).

However, a standardisation of the experimental facilities needed for the implementation of such methods is missing, especially regarding their application to VOC measurements.

One aspect that remains unexplored is the possibility to directly measure odour concentration instead of the concentration of single odorous substances for the implementation of such methods.

Future works should thus focus on the determination of the minimum accuracy and resolution requirements for potential odour analysers to be applied in specific situations, as for instance the evaluation of odour fluxes from landfills.

### 5. References

Ammann, C., Meixner, F. 2002. Stability dependence of the relaxed eddy accumulation coefficient for various scalar quantities. J Geophys Res-Atmos, 107(D8), ACL7-1.

Aubinet, M., Vesala, T., Papale, D. 2012. Eddy Covariance - A Practical Guide to Measurement and Data Analysis. Springer, Dordrecht.

Capelli, L., Sironi, S., Del Rosso, R., Céntola, P., Rossi, A., Austeri, C. 2011. Olfactometric approach for the evaluation of citizens' exposure to industrial emissions in the city of Terni, Italy. Sci Total Environ 409, 595-603.

Capelli, L., Sironi, S., Del Rosso, R. 2013. Odor sampling: techniques and strategies for the estimation of odor emission rates from different source types. Sensors 13, 938-955.

Darmais, S., Dutaur, L., Larsen, B., Cieslik, S., Luchetta, L., Simon, V., Torres, L. 2000. Emission fluxes of VOC by orange trees determined by both relaxed eddy accumulation and vertical gradient approaches. Chemosph-Glob Chang Sci 2, 47–56.

Ferrara, R. M., Loubet, B., Di Tommasi, P., Bertolini, T., Magliulo, V., Cellier, P., Eugster, W., Rana, G. 2012. Eddy covariance measurement of ammonia fluxes: Comparison of high frequency correction methodologies. Agr Forest Meteorol 158, 30-42.

Foken, T. 2006. 50 Years of the Monin–Obukhov Similarity Theory. Bound-Lay Meteorol 119, 431–447.

Gryanik, V.M., Lüpkes, C., Grachev, A., Sidorenko, D. 2020. New Modified and Extended Stability Functions for the Stable Boundary Layer based on SHEBA and Parametrizations of Bulk Transfer Coefficients for Climate Models. J Atmos Sci 77, 2687–2716.

Högström, U. 1988. Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation. Bound-Lay Meteorol 42, 55–78.

Maier, M., Schack-Kirchner, H. 2014. Using the gradient method to determine soil gas flux: A review. Agr Forest Meteorol 192, 78-95.

Mønster, J., Kjeldsen, P., Scheutz, C. 2019. Methodologies for measuring fugitive methane emissions from landfills–A review. Waste Manage 87, 835-859.

Padro, J. 1993. An investigation of flux-variance methods and universal functions applied to three land-use types in unstable conditions. Bound-Lay Meteorol 66, 413-425.

Sjöblom, A., Smedman, A.S. 2004. Comparison between eddy-correlation and inertial dissipation methods in the marine atmospheric surface layer. Bound-Lay Meteorol 110, 141-164.

Smith, K. A., Clayton, H., Arab, J. R. M., Christensen, S., Ambus, P., Fowler, D., Hargreaves, K.J., Skiba, U., Harris, G.W., Wienhold, F.G., Klemedtsson, L., Galle, B. 1994. Micrometeorological and chamber methods for measurement of nitrous oxide fluxes between soils and the atmosphere: Overview and conclusions. J Geophys Res-Atmos 99, 16541-16548.

Sozzi, R., Rossi, F., Georgiadis, T. 2001. Parameter estimation of surface layer turbulence from wind speed vertical profile. Environ Modell Softw 16, 73-85.

Spirig, C., Neftel, A., Ammann, C., Dommen, J., Grabmer, W., Thielmann, A., Schaub, A., Beauchamp, J., Wisthaler, A., Hansel, A. 2005. Eddy covariance flux measurements of biogenic VOCs during ECHO 2003 using

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Todd, R. W., Cole, N. A., Harper, L. A., Flesch, T. K., Baek, B. H. 2005. Ammonia and gaseous nitrogen emissions from a commercial beef cattle feedyard estimated using the flux-gradient method and N: P ratio analysis. In Proceedings of the Symposium on State of Science: Animal and Waste Management, San Antonio, Texas (CD-ROM).