Air pollution monitoring: Development of ammonia (NH 3 ) dynamic reference gas mixtures at nmol/mol levels for improving the lack of traceability of measurements

. The measurement of ammonia (NH 3 ) in ambient air is a sensitive and priority topic due to its harmful effects on 10 human health and its impact on ecosystems. NH 3 emissions have continuously increased over the last century in Europe, because of intensive livestock practices and enhanced use of nitrogen-based fertilizers. European air quality monitoring networks monitor atmospheric NH 3 amount fractions. However, the lack of stable reference gas mixtures (RGMs) at atmospheric amount fractions to calibrate NH 3 analyzers is a common issue of the networks, which results in data that are not accurate, traceable and, thus, geographically comparable. In order to cover this lack, LNE developed, in close collaboration 15 with the company 2M PROCESS, a gas reference generator to generate dynamically NH 3 RGMs in air. The method is based on gas permeation and further dynamic dilution to obtain an amount fraction range between 1 and 400 nmol/mol (also well known as ppb; 1 ppb (NH 3 )  to 0.7 µg/m 3 ) to cover the NH 3 amount fractions measured in ambient air (immisions), as well as the operating range of the NH 3 analysers used by the monitoring networks. The calibration of the elements of the generator against LNE primary standards ensures the traceability of the RGMs to the international system of units. Furthermore, the 20 highly accurate flow and oven temperature measurements of the reference generator, together with the associated calibration procedure defined by LNE, guarantee relative expanded uncertainties of the calibration of the NH 3 analyzers

on gas permeation and further dynamic dilution to obtain an amount fraction range between 1 and 400 nmol/mol (also well known as ppb; 1 ppb (NH3)  to 0.7 µg/m 3 ) to cover the NH3 amount fractions measured in ambient air (immisions), as well as the operating range of the NH3 analysers used by the monitoring networks. The calibration of the elements of the generator against LNE primary standards ensures the traceability of the RGMs to the international system of units. Furthermore, the 20 highly accurate flow and oven temperature measurements of the reference generator, together with the associated calibration procedure defined by LNE, guarantee relative expanded uncertainties of the calibration of the NH3 analyzers lower than 2 % (coverage factor =2). This result is very satisfactory considering the low NH3 amount fraction levels (1 to 400 nmol/mol) and the phenomena of adsorption and desorption, especially in the presence of traces of water on the surfaces in contact. A bilateral comparison was organized between METAS and LNE, consisting on the calibration of a PICARRO G2103 gas analyzer by 25 both national metrology institutes (NMI). The results highlighted the good agreement between the NH3 reference generators developed by the two institutes and allowed to validate both LNE's reference generator and calibration procedure. The development of the NH3 reference generator has already raised great interest within the French air quality monitoring networks (AASQA). Since the end of 2020, LNE calibrated several NH3 analysers from the French air quality monitoring networks (AASQA) using the newly developed SI-traceable RGMs. The enhanced number of calibrations provided, may increase the 30 comparability, accuracy and traceability of the NH3 measurements carried out on the French territory. Since the end of 2020, LNE calibrated several NH3 analyzers of the networks. These requests shows the interest of the AASQA in the development of this new gas reference generator to guarantee the traceability of measurements carried out on the French territory.

Introduction
Measuring ammonia (NH3) in ambient air is a sensitive and priority topic because of its harmful effects on human health 35 andnegative effects on ecosystems even at low amount fractions (i.e. atmospheric level, <100 nmol/mol).. Ammonia is the main precursor of atmospheric acid neutralization and therefore affects the long-range transport of sulfur dioxide (SO2) and nitrogen oxide(s) (NOx). Moreover, atmospheric NH3 contributes to the formation and stabilization of suspended particles (PM10, PM2.5 and aerosols) (Holmes, 2007), which have adverse human health effects such as premature deaths. In 2016, estimations suggested 4.2 million premature deaths worldwide caused by suspended particles (WMO, 2018). In addition, the 40 deposition of ammonia on particle-borne molecules contributes to the eutrophication and acidification of soils and fresh water (Schöpp et al., 2003;Pinder et al., 2008) and thus to the degradation of soil and water quality. These phenomena therefore have negative effects on biodiversity and ecosystems.
Main sources of atmospheric NH3 are anthropogenic, such as fossil fuel combustion, power plants, vehicular exhaust and agricultural activities (Behera et al., 2013;Wu et al., 2020). The latter accounts for about 60 % of the total NH3 global emissions 45 (Clarisse et al., 2009), according to inventories and chemical transport models, such as GEOS-Chem, that allows to select different grid sizes (e.g. 2° x 2.5° (Clarisse et al., 2009;Paulot et al., 2014)). Organic emissions from livestock, applications of organic, mineral and organo-mineral fertilizers on crops are the main agricultural sources of NH3. In Europe, the European Union (EU) agricultural sector accounts for 93% of European NH3 emissions (EEA, 2020). However, recent studies based on isotopic nitrogen suggest that the contribution of nonagricultural sources to NH3 emissions are greater than the agricultural 50 ones in certain urban regions (Feng et al., 2022;Gu et al., 2022). Despite the management strategies adopted by EU, NH3 emissions have continuously increased since 1990 (Aksoyoglu et al. 2020;Warner et al., 2017;Behera et al., 2013;Van Damme et al., 2021), mainly due to the development of intensive agricultural practices and the associated use of nitrogenbased fertilizers (Aksoyoglu et al., 2020).
Air pollution spreads across national borders and over long distances. This is why ammonia was included in the 1999 55 Gothenburg Protocol, revised in 2012 (UNECE, 2012), which is part of the Convention on Long-range Transboundary Air Pollution (United Nations, 1999). The protocol was established with the aim of reducing acidification, eutrophication and ozone concentrations by setting emission ceilings to be met by 2010. Following the revision of the Gothenburg Protocol, the Directive (EU) 2016/2284 (European Commission, 2016), defines national emission ceilings for each Member State, in particular for NH3. As NH3 is recognized as a precursor of secondary inorganic aerosols, controlling its emissions is important 60 to reduce PM2.5 and PM10 concentrations (Holmes, 2007;Clappier et al., 2021). Bessagnet et al. (2014), who used three different chemistry transport models, showed an underestimation of the formation of ammonium particles (e.g. ammonium nitrate or sulfate) and concluded that NH3 had a much greater role than initial estimates. Contrary to the emission ceilings, no limit or threshold value is defined for NH3 in ambient air in the European Directives. With regard to the protection of ecosystems, particularly of the vegetation, NH3 concentration Critical Levels (CLEs) ─ based on measurements and 65 observations ─ were set by the International Cooperative Programme (ICP) Vegetation of the United Nations Economic Commission for Europe (UNECE) in 1988. The updated NH3 CLE for the protection of lichens is 1 µg/m 3 and 3 µg/m 3 for higher order plants (annual means under real conditions). A monthly critical level of 23 µg/m 3 was also provisionally adopted to take into account possible high peaks in emissions during periods of manure application (e.g. in spring) (Cape et al., 2009).
Despite the importance of measuring ammonia for monitoring ambient air quality, neither the Directive (EU) 2016/2284 nor 70 the Ambient Air Quality Directive 2008/50/EC (European Commission, 2008) provides recommendations for reliable measurements. In particular, recommendations on method selection, instrument calibration (procedures, frequencies, reference gas mixtures (RGMs) to be used, etc.), maximum allowed expanded uncertainty, quality assurance and quality control procedures (QA/QC), as well as guidelines on an infrastructure to ensure the metrological traceability of measurements are lacking. 75 Available NH3 measurement techniques are very diverse and include direct and indirect methods, with and without sample preconcentration steps. Direct methods of making real-time measurements are based on spectroscopic techniques such as cavity ring-down spectroscopy (CRDS) (Martin et al., 2016). Examples of indirect methods are active sampling using denuders or on-line gas-liquid interactions systems (e.g. MARGA, AIRMONIA) (von Bobrutzki et al., 2009;Nair and Yu, 2020) and passive samplers consist of using passive samplers (EN17346, 2020;Braban et al., 2018;EN, 2020) or active sampling using 80 denuders or on-line gas-liquid interactions systems (e.g. MARGA, AIRMONIA) (Bobrutzki et al., 2009) that are exposed to ambient air for a certain period of time. During this period, NH3 is collected on a support impregnated with reagent (acid-base reaction), which is then analyzed after extraction by ion chromatography, colorimetry, chemiluminiscence or flow injection analysis among others (Tang et al., 2001, colorimetry, chemiluminiscence or flow injection analysis among others). The selection of an appropriate method generally depends on the concentration levels to be measured in ambient air, the desired 85 spatial and temporal representativeness and the restrictions to be taken into account (e.g. installation in the field, investment and operating costs). Since NH3 is not regulated in ambient air, these methods are often poorly characterized and they do not allow reliable and comparable measurements taking into account effective quality assurance and quality control procedures (QC/QA) (calibration, traceability, maximum allowed expanded uncertainty, etc.) even if some methods are based on established standard (ex: passive sampling in standard (EN17346, 2020)). For example, direct methods based on spectroscopic 90 techniques are characterized by metrological performances that vary significantly among themselves, especially in terms of accuracy and resolution. In addition, the sampling systems and the control of relative humidity ̶ key points in ammonia measurements ̶ are not adequate. Furthermore, the lack of traceability of the measurements to the International System of Units (SI-traceability) performed with these instruments is highlighted, as stable RGMs in gas cylinders at low amount fractions (i.e. ambient air level; 0 -< 500 nmol/mol) are not commercially available. Reasons for that are the reactivity of 95 ammonia with the inner walls of the cylinder and the phenomena of adsorption and desorption, especially in the presence of water traces (Martin et al., 2016). This lack of SI-traceability therefore may affect the quality and credibility of NH3 amount fraction values measured in ambient air by national air quality monitoring networks in Europe as well as the spatio-temporal comparability of data across countries.
In this paper, we describe a developed NH3 reference generator, based on permeation and further dynamic dilution, which 100 can generate NH3 RGMs at low amount fractions between 1 and 400 nmol/mol to cover the NH3 amount fractions measured in ambient air (immission), as well as the operating range of the NH3 analysers used by the monitoring networks. Moreover, we present the set-up of a calibration method for NH3 analyzers and the validation of the calibration method through a comparison with METAS (Swiss National Metrology Institute). This new reference generator will contribute to fulfil the lack of traceability, improving thus the accuracy and comparability of NH3 datasets. was to provide traceable NH3 amount fractions in the environmentally relevant range of 0 -500 nmol/mol (Pogány et al., 2016). Within the project, two solutions were investigated to generate NH3 amount fractions from 1 to 400 nmol/mol. One solution was based on the production of gravimetric RGMs in gas cylinders at an amount fraction of 10 µmol/mol followed by a dynamic dilution using mass flow controllers. The other one was based on gas permeation with a double dynamic dilution stage (METAS, 2017). 115 The gravimetric method for preparing RGMs consists of introducing the pure constituent compounds of the RGMs into a cylinder under vacuum, and determining then the quantities of each constituent by weight differences (ISO6142-1, 2015).
Thus, this method is traceable to the international system by kg and allows the assessment of uncertainties of amount fractions.
The problem linked to this method is to obtain stable gas mixtures over time. Indeed, NH3 is a compound that is very easily adsorbed on the internal walls of the cylinder, as shown in the study carried out during the MetNH3 project on different 120 materials (Pogány et al., 2016). This study shows Teflon-perfluoroalkoxy (Teflon-PFA) or SilcoNert® 2000 materials lead to the lowest NH3 adsorption. As part of the same project, the Dutch National Metrology Institute (VSL) carried out a stability study on NH3 gas mixtures at 10 µmol/mol in cylinders treated by different processes. The obtained results showed that the stability of the amount fraction of the gravimetrically prepared gas mixtures at 10 μmol/mol of NH3 was not completely satisfactory, especially since it was subsequently necessary to dilute this gas mixture dynamically to obtain the desired low 125 amount fractions (nmol/mol).
The principle of the gas permeation technique (ISO6145-10, 2008) is based on the permeation of a pure chemical compound through a semi-permeable membrane. This technique is particularly used for the generation of dynamic RGMs of gaseous compounds that are reactive or not very stable over time (e.g. sulfur dioxide (SO2), nitrogen dioxide (NO2)). During the MetNH3 project, METAS selected the permeation technique to generate NH3 RGMs. The developed portable device was based 130 on the implementation of a permeation tube in a temperature-regulated oven and on mass flow controllers allowing to dilute dynamically the pure NH3 from the permeation tube to the desired amount fractions. All parts in contact with NH3 were inert due to a SilcoNert® 2000 coating to avoid adsorption effects (Vaittinen et al., 2018). The results obtained by METAS during the study showed a very good stability (standard deviation lower than 1.5%) in the generation of NH3 with short response times (lower than 60 min), even at very low amount fractions. 135 The project results showed that it is therefore possible to generate low amount fractions of NH3 by limiting the adsorption of this compound with coatings such as SilcoNert® 2000. The use of gas permeation provides an NH3 amount fraction range compatible with measurements in ambient air with relative uncertainties of less than 3%. The French NMI LNE has therefore chosen this technique for developing the NH3 reference generator, used for calibrating analyzers over their analytical range.
This technique has been used by LNE for many years for molecules such as SO2sulfur dioxide, NO2nitrogen dioxide or even 140 more recently for traces of water vapor which are not stable in gas cylinders at these low amount fractions.

Principle of the permeation method
Permeation tubes consist of a polymeric membrane (usually polytetrafluoroethylene (PTFE) or a copolymer of tetrafluoroethylene and hexafluoropropylene (FEP)) through which a small amount of pure analyte (NH3) will permeate 145 (Lucero, 1971). The most common type is a small, sealed tubular device, which contains the analyte (e.g. NH3) in liquid form.
A very small but stable flow (hundreds of ng/min) of ammonia in gaseous phase is emitted through the permeable membrane when the temperature is constant. This emission or permeation rate depends on the physical characteristics of the permeable membrane, on the permeability of the analyte through the membrane, on the temperature of the permeation tube and on the partial pressure across the membrane. The permeation rate of the tube is determined by measuring its mass loss over time using 150 a microbalance with a resolution of 1 µg and applying the BORDA weighing method (Gläser et al., 2009) under controlled temperature conditions using a temperature sensor with a resolution of 0.01°C and a standard deviation of 0.05°C to guarantee the traceability to the SI. The tube placed in a temperature-and flow-controlled stream of inert dilution gas (see Fig. 1) allows to generate an ammonia gas mixture, which is stable in terms of amount fraction at trace levels (nmol/mol).

170
The compound (e.g. NH3) permeates through the membrane (blue wave shapes) at specific permeation rates (qm), which are mainly temperature dependent. Grey arrows represent the dilution input flow (qv) of the gas (e.g. nitrogen, synthetic air) used to generate reference gas mixtures at different amount fractions depending on the flow (qv). The bicolor arrows represents the input flow (qv) of the generated reference gas mixture (RGM) at specific amount fraction (ꭓ). regulator (EL-Press; Bronkhorst, Netherlands) and a touch-sensitive graphic interface for automatic control of all the elements (see Fig. 2). The temperature is only a control value, but not an entry parameter for the determination of the permeation rate.

Description of the NH3 reference generator
After the weighing of the tube, it is replaced in the oven exactly at the same position; in this way, the influence of the temperature gradient has not to be taken into account. All parts (tubings, oven and MFCs) in contact with NH3 are coated with SilcoNert® 2000 in order to limit the adsorption 190 of NH3 on the walls as much as possible. The ammonia permeation tube (99.98 % purity; Fine Metrology S.r.l.s., Italy) is placed inside the temperature-controlled oven at 30.00°C ± 0.01°C, which is flushed with purified dry air (on-line gatekeeper CE2500KF04R; ENTEGRIS, USA) at 100 ml/min (id1). The first dilution stage consists of two MFCs (id1 and id2) with a measurement range of respectively 120 ml/min and 10 l/min allowing the generation of amount fractions from 400 to 60 nmol/mol (also depending on the permeation rate of the tube) with a back pressure regulator (1 bar relative) (id5) for regulating 195 the gas pressure in the permeation oven. The second dilution stage is composed of two MFCs (id3 and id4) with a measurement range of respectively 120 ml/min and 10 l/min leading to amount fractions between 50 and 1 nmol/mol. All MFCs are calibrated against very accurate flowmeters (Molbloc/Molbox TM from Fluke Calibration, WA, USA) previously calibrated by the dynamic gravimetric method at LNE. An integrated software (graphical interface), which allows automatic control of MFCs, calculates the amount fraction of the gas generated as well as its associated uncertainty. Figure 3 shows the different elements 200 of the reference generator and their functions during the generation of NH3 at the first and second stages. The ammonia amount fraction xNH3 generated by the reference generator, in nmol/mol, can be estimated according Eq. (1): 210 Here, qm is the permeation rate of the tube in ng/min, M is the molar mass of ammonia in g/mol, qv is the total air flow in l/min and Vn is the normal molar volume of the dilution gas in l/mol (273.15 K and 1.013 bar).

Calculation of the permeation rate of ammonia tube and the associated uncertainty
The nominal permeation rate (provided by Fine Metrology) of the ammonia tube was (462 ng/min ± 5 %) at 215 30 °C. The tube was weighed monthly to account for effects of temperature variation and temporal stability on the determination of the amount of pure NH3 emitted (i.e. permeation rate).

Determination of the permeation rate
The rate of permeation − (in ng/min) of the tube used in this study between day i and day j was calculated according to Eq. (2): 220 where,

PNH3
purity of the liquid NH3 in the permeation tube m mass loss of the tube between day i and day j (in g) t period of time for the mass loss Δm between day i and day j (in min) 225 correction accounting for the stability of the temperature in the oven (in ng/min) correction associated to the reproducibility of the weighing procedure (in ng/min) − stability of the permeation rate over time (in ng/min)

NH3 purity (PNH3)
The pure compound in liquid form contained in the permeation tube was supplied by the company Sigma Aldrich. The certificate of analysis provided by the manufacturer stated a purity greater than 99.98 %, being water vapor as the major impurity. The purity was considered to be equal to 0.9999 with a standard uncertainty calculated according Eq. (3) (uniform law): 235 (3)

Mass loss of the tube (m)
The calculation of the standard uncertainty of the tube mass loss between day i and day j took into account the following uncertainty sources: mass standards, balance resolution and accuracy, weighing repeatability, air density and volume of the tube. 240

Period of time for the mass loss (t)
The standard uncertainty of the period during which the mass loss was determined was calculated by applying a uniform law given by Eq. (4): (4)

Stability of temperature (CT) 245
The stability of the oven temperature is equal to 0.05 °C. The correction accounting for the stability of the temperature in the oven was considered as equal to zero. However, an uncertainty is associated with it, which was calculated using a range of the variations of the oven temperature equal to 0.05 °C. AsSince the influence of temperature on the permeation rate of the tube is of the order of 8 % per degree, considering a uniform law (Eq. (5)), the standard uncertainty was:

Reproducibility of the weighing procedure (CR)
The reproducibility of the tube weighing process was estimated by weighing periodically a permeation tube with a stable permeation rate during 3 months. The reproducibility correction was considered as zero and the associated uncertainty was evaluated as being equal to 0.2 % of the permeation rate. The reproducibility standard uncertainty was calculated according to 255 Eq. (6):

Evolution of the permeation rate over time ( − )
The permeation tube was placed in the oven of the reference generator at a temperature of 30.00 °C ± 0.05 °C; it was weighed regularly to calculate its permeation rate over a period of two years. Table 1 summarizes the different determinations 260 of the permeation rate of the tube (using Eq. (2)) as well as the associated uncertainties. The results obtained over two years showed that the permeation rate of the NH3 tube was stable over time with the exception 265 of the first few months, which is quite usual when putting a new permeation tube into an oven ("tube maturation"). Figure 4 illustrates the change in the permeation rate of the tube over time. The error bars correspond to the expanded uncertainty (k = 2) on the determination of the permeation rate of the tube. The stability over time of the permeation rate ( − ) was considered as equal to zero. Its standard uncertainty ( − ), 275 in ng/min, was calculated by considering the maximum deviation found between the last three determinations of the tube permeation rate (Eq. (7)):

Uncertainty budget of the NH3 permeation rate
The uncertainty budget on the NH3 permeation rate was calculated using the standard uncertainties determined previously and by applying the law of propagation of uncertainties expressed in the Guide to the expression of uncertainty in measurement (GUM) (JCGM, 2008) on the equation 2. One example is summarized in Table 12. 285 Table 12: Uncertainty budget of one of the permeation rates used in this study. The contribution, in percentage, of each variable to the overall uncertainty is indicated in the column Weight. The last row shows the permeation rate value and its expanded uncertainty; k is the coverage factor of the uncertainty.

Determination of the amount fraction of the generated RGMs
The developed reference generator has two dilution stages, the first one for "higher" amount fractions (400 nmol/mol to 60 nmol/mol) and the second one for lower amount fractions (50 nmol/mol to 1 nmol/mol). NH3 amount fractions in the RMGs generated by the reference generator can be estimated applying Eq. (8)

Determination of the standard uncertainties of the amount fractions of the generated RGMs
The variance on the NH3 amount fraction in the generated RGMs was determined using the law of propagation of 315 uncertainty expressed in the Guide to the expression of uncertainty in measurement (GUM) (JCGM, 2008). Standard uncertainties of the NH3 amount fraction of the generated RGMs were as follows:  Standard uncertainty of the permeation rate ( ( − )) was calculated as described in section 4.3  Standard uncertainty of the NH3 molar mass (u(M)) was determined with data from the IUPAC document (IUPAC, 320

2013)
 Standard uncertainties of the flow rates (u(qva), u(qvb), u(qvc) and u(qvd)) were determined using the results obtained during the calibration of the MFCs at LNE. These standard uncertainties take into account the uncertainty of the linearity (u(linearity), which was estimated according a model WLS RegPoly developed by LNE (Yardin, 2013), the (u(durability)) as shown in Eq. (10):  Standard uncertainty of the normal molar volume (u(Vn)), which is given in the CODATA document (Mohr, 2014)  Standard uncertainty of the residual NH3 amount fraction in the dilution air (u(Imp)). The dilution gas (Alphagaz 2 from Air Liquide) was purified by means of an Entegris filter (CE2500KF04R). According to the specifications of 330 the Entegris filter (CE2500KF04R)dilution gas (Alphagaz 2 from Air Liquide), the residual NH3 amount fraction was less than 10 pmol/mol. The NH3 residual amount fraction was considered to be equal to 0.005 nmol/mol with a standard uncertainty Because the dilution gas was further purified by means of an Entegris filter, the residual amount fraction was considered to be equal to 0.005 nmol/mol. The standard uncertainty was estimated following Eq.

Summary of the uncertainty budget of the amount fractions of the generated reference gas mixtures
The uncertainty budget of the NH3 amount fractions generated by the reference generator was calculated from the standard uncertainties determined previously and by applying the law of propagation of uncertainties. Two examples at the extreme points of the generation range of the reference generator are summarized in Tables 23 and 34. 340 Table 23: Uncertainty budget of the amount fraction of one of the ammonia RGMs generated after the first dilution stage. The contribution, in percentage, of each variable to the overall uncertainty is indicated in the column Weight. The last row shows the amount fraction value and its expanded uncertainty; k is the coverage factor of the uncertainty.  These results highlighted that the main source of uncertainty of the NH3 reference amount fractions generated after the single dilution (first stage from 400 to 60 nmol/mol) was linked to the calculation of the permeation rate of the tube and to the measurement of the air dilution flow rate (MFC -id2). After the second dilution step (< 60 nmol/mol), the weight of the 355 uncertainties was more evenly distributed among the uncertainty of the permeation rate, the flow rates (MFCs -id2, id3 and id4) and the residual NH3 impurities in the dilution air. The expanded relative uncertainties of the generated amount fractions were between 1 and 2 % over the whole range.

Characterization of the calibration method of NH3 analyzsersCharacterization of the calibration method of analyzers
We determined the repeatability, reproducibility and uncertainty budget of the calibration procedure in order to characterise 360 it. For that purpose, 6.1. Calibration procedure of NH3 analyzers Tthe reference generator was permanently switched on during the characterization and the NH3 permeation tube was continuously flushed by a synthetic air flow at 100 ml/min. NH3 amount fractions between 0 and 400 nmol/mol were generated during 2 hours for each amount fraction level using the reference generator. The average of the generated amount fractions 365 and the average of the readings of the analyzer to be calibrated were calculated over the last 30 minutes along with their standard deviations.

Determination of the repeatability of the calibration method
To evaluate the repeatability of the calibration methodfollowing the procedure indicated in the air quality standards as for example in NF EN 14211 (2012)at different amount fractions, nine amount fraction levels were generated in the range 370 between 1 and 400 nmol/mol. The software of the developed reference generator calculated, every ten seconds, the amount fraction of NH3 generated according to the set parameters (permeation rate, molar mass, purity, etc.), and the measured flow rates (MFCs) and oven temperature (taking into account temperature variations). Table 45 shows the standard deviations calculated over the last 30 minutes of generation for the amount fractions range between 1 nmol/mol and 400 nmol/mol. The relative standard deviation of the generated amount fractions at all generation levels was less than 0.1 %, indicating a very good stability of the flow rates and a good temperature control. A standard uncertainty of the repeatability equal to 0.1 % 380 (id. ( ) = 0.001 × x ) was retained and combined with the uncertainty calculated for the reference generator (cf. paragraph 5.3).

Determination of the reproducibility of the calibration method
LNE used METAS ammonia analyzer, based on cavity ring-down spectroscopy (G2103, Picarro Inc., CA, USA), for a 385 bilateral comparison. This device is specifically manufactured for the measurement of NH3. Moreover, the analyzer was upgraded in 2019, when the cavity and the sampling handling were replaced by SilcoNert® 2000 coated elements, thus limiting adsorptions. The analyzer required an inlet flow rate of 1.8 l/min, which was provided by an external diaphragm vacuum pump (N920AP.29.18, KNF Neuberger Inc., NJ, USA) and was calibrated without particles filter. The tests were performed using Air Alphagaz2 (Air Liquide) purified with ENTEGRIS filter and 1/4 in. coated (SilcoNert® 2000) stainless steel tubing. In 390 order to quantify the reproducibility standard deviation on the calibration of an NH3 analyzer, the calibration of the Picarro G2103 analyzer was performed 4 times on different days between 20 and 125 nmol/mol (amount fractions are limited by the sampling flow rate of the analyzer). The calibration function was determined for each of the calibrations using the RegPoly software developed at LNE. This software allowed the integration of uncertainties of the X and the Y axis. The procedure was the same as when determining repeatability: generation during 2 hours and calculation of the amount fractions average and 395 associated standard deviations over the last 30 minutes. Tables 56 and 67 summarize the results obtained.   The reproducibility of the determination of the calibration function was around 0.05 % (Table 67). A reproducibility uncertainty increased to 0.1 % (id. ( ) = 0.001 × x ) was considered in the uncertainty budget. 405

Uncertainty budget of the calibrated amount fractions
The expanded uncertainty (k = 2) of the calibrated NH3 amount fractions (UNH3) in nmol/mol was calculated using Eq. (12): 3 = 2 * √ 2 ( ) + 2 ( ) + 2 ( ) where, 2 ( ) variance of the NH3 amount fraction calculated by the software of the reference generator (in nmol/mol) 2 ( ) repeatability variance of the calibration method in nmol/mol 415 2 ( ) reproducibility variance of the calibration method in nmol/mol Table 78 shows the final uncertainties obtained over the range of amount fractions generated by the reference generator. The uncertainty budget of the NH3 reference amount fractions highlighted that over an amount fraction range between 1 and 400 nmol/mol, the relative expanded uncertainties was between 1.1 % and 1.6 %. This uncertainty may vary slightly over time depending mainly on the uncertainties of the permeation rate of the NH3 tube and the MFC calibrations. Nevertheless, taking into account the experience acquired at LNE on the weighing of permeation tubes and on the calibration of MFCs, the 425 relative expanded uncertainties would remain less than 2 % (k = 2) over the whole range studied. It should be noted that for the amount fractions obtained after the first dilution stage, the associated uncertainty was mainly linked to the uncertainty of the permeation rate and the dilution flow rate. For the amount fractions generated after the second dilution stage, the main uncertainties were those of the NH3 tube permeation rate, the two dilution flow rates (id3 and id4) and the flow rate taken from the first stage (id2). The uncertainty of the amount fraction of the NH3 impurities present in the dilution gas could represent 430 up to 10 % of the final uncertainty for very low amount fractions. Figure 5 shows schematically the distribution of the different uncertainty sources for NH3 calibrated amount fractions from 1 nmol/mol (second stage) and 400 nmol/mol (first stage).   (14)).
where k is the coverage factor (k = 2), u(b) is the uncertainty of the determination of b (RegPoly) and std is the standard 470 deviation of the 4 determinations of b (LNE).
The normalized deviation (En) between the slopes of the regression lines determined by METAS and by LNE, was equal to 0.54 (Table 910). This value lower than 1 demonstrated the good agreement between the NH3 reference generators developed by METAS and by LNE. This comparison validated the LNE reference generator and the analyzer's calibration method. analyzers. To ensure the reliability of the NH3 measurements performed by these analyzers LNE developed a metrological calibration procedure. The calibration procedure consists of generating dynamic RGMs at different ammonia amount fractions (at least 5 levels in synthetic air) on the measurement range defined by the AASQA (between 1 to 400 nmol/mol) using the reference generator. These RGMs are then injected in NH3 analyzers and, for each level, the reference amount fraction and the reading are compared. Figure 6 presents AAn example of NH3 analyser calibration performed for monitoring networks is 490 shown in Fig. 6, for the NH3 analyzer number 2244-AHDS2115 (G2103, Picarro Inc., CA, USA) over an amount fractionthe range from 1 nmol/mol to 300 nmol/mol. The standard deviations over the last 30 minutes were calculated and given in Figure   6. Figure 6: Stability of the ammonia reference amount fractions (blue line) and of the analyzer readings (orange close circles) over the range from 1 nmol/mol to 300 nmol/mol. The relative standard deviation of the analyser readings is lower than 0.5% for all the generated amount fraction levels.
These results demonstrate a very high stability of the ammonia reference amount fraction calculated from the measurement of the various parameters of the reference generator (MFCs flow rates, oven temperature). It can be noted that the MFC 500 regulation is very fast, as suggested by the immediate response time when changing the setpoint. Furthermore, the results show a high stability of the flow rates over time, because no drift in the calculated amount fraction is observed and its standard deviation is less than 0.1 % for the whole range. This highlights the good quality of the MFCs and oven temperature control.
Analysis of the NH3 amount fractions read by the analyzer shows a low standard deviation on the measurements (0.5 %).  By the end of 2020, LNE calibrated seven NH3 analyzers set up by four French networks in monitoring stations. The calibration results determined by LNE for each analyzer are given in Table 101. The results summarized in Table 101 show that the calibration can be very different from one to another NH3 analyzer of the same trademark and model up to an accuracy error of 4 %. The calibration process is therefore unavoidable to ensure the 520 reliability of NH3 measurements performed in ambient air by the monitoring networks to ensure their spatiotemporal comparability. These calibration tests also demonstrated the good linearity of all NH3 analyzers with correlation coefficients between 0.9994 and 1.000.

Conclusion
This study led to the development of a reference generator for ammonia in air based on the dynamic generation method by 525 gas permeation over a range of amount fractions from 1 to 400 nmol/mol, in close collaboration with the company 2M PROCESS according to the specifications established by LNE. The reference generator integrates a real-time calculation of the ammonia generated amount fractions (1 to 400 nmol/mol) and its associated expanded uncertainties and allows the calibration of NH3 analyzers in an automatic way. All parameters and measurements carried out are stored in a downloadable file so that they can be easily processed in Excel files. The characterization of this reference generator led to relative expanded 530 uncertainties of the ammonia reference amount fractions in the reference gas mixtures lower than 2 % (k = 2). This result is very satisfactory considering the very low levels of the amount fractions of interest and the potential ammonia adsorption/desorption on the surfaces in contact.
The bilateral comparison organized by LNE and METAS consisted used a PICARRO G2103 gas analyzer as transfer standard of the calibration of a PICARRO G2103 gas analyzer by both institutesbased on a robust spectroscopic method and set up in a lot of AASQA monitoring stations., Both institutes generated which used reference gas mixtures generated dydynamically by two different reference generators and used the above-mentioned PICARRO as comparator. The normalized deviation between the slopes of the regression lines determined by METAS and by LNE was equal to 0.5, which highlights the good agreement between the dynamic NH3 reference generators developed by METAS and by LNE. This comparison allowed the validation of LNE's reference generator and the analyzer calibration method developed. 540 Furthermore, the tests carried out during this study showed the importance of the internal surface treatment of calibrated analyzers in order to limit ammonia adsorption strongly.
The application of these findings, together with the use of the newly developed NH3 SI-traceable RGMs by the French air quality monitoring stations within AASQA, may promote the accuracy, comparability and traceability of NH3 measurements carried out in France. Since the end of 2020, several French air quality monitoring networks have requested LNE to calibrate 545 their NH3 analyzers, enabling them to guarantee the traceability and accuracy of measurements performed in France.
Data availability. Research data could be made available after review of the request.
Author contribution. TM and CS conceived the idea, methods and experimental design of the study; MI calibrated, calculated the uncertainty and provided the analyzer for the validation; CS designed the reference generator, carried the experiments out, analysed the data and calculated the uncertainties of the measurements; TM led the writing of the manuscript; CS, SV, MI, CP 550 and BN contributed critically to the drafts. All authors gave final approval for publication.
Competing interests. The authors declare that they have no conflict of interest.