Assessing the representativity of NH 3 measurements inﬂuenced by boundary-layer dynamics and the turbulent dispersion of a nearby emission source

. This study presents a ﬁne-scale simulation approach to assess the representativity of ammonia (NH 3 ) measurements in the proximity of an emission source. Close proximity to emission sources ( < 5 km) can introduce a bias in regionally representative measurements of the NH 3 molar fraction and ﬂux. Measurement sites should, therefore, be located a signiﬁcant distance away from emission sources, but these requirements are poorly deﬁned and can be difﬁcult to meet in densely agricultural regions. This study presents a consistent criterion to assess the regional representativity of NH 3 measurements in proximity to an emission source, calculating variables that quantify the NH 3 plume dispersion using a series of numerical experiments at a ﬁne resolution (20 m). Our ﬁne-scale simulation framework with explicitly resolved turbulence enables us to distinguish between the background NH 3 and the emission plume, including realistic representations of NH 3 deposition and chemical gas–aerosol transformations. We introduce the concept of blending distance based on the calculation of turbulent ﬂuctuations to systematically analyze the impact of the emission plume on simulated measurements, relative to this background NH 3 . We perform a suite of systematic numerical experiments for ﬂat homogeneous grass-lands, centered around the CESAR Observatory at Cabauw, to analyze the sensitivity of the blending distance, varying meteorological factors, emission/deposition and NH 3 dependences. Considering these sensitivities, we ﬁnd that NH 3 measurements at this measurement site should be located at a minimum distance of 0.5–3.0 and 0.75–4.5 km from an emission source for NH 3 molar fraction and ﬂux measurements, respectively. The simulation framework presented here can easily be adapted to local conditions, and paves the way for future ammonia research to integrate simulations at high spatio-temporal resolutions with observations of NH 3 concentrations and ﬂuxes.

chemical transformation and model resolution influence the relationships between emission and receptor. To this end, we indroduce and analyze the concept of a blending-distance (BD), i.e. the horizontal distance at which the emission plume can be considered well-mixed with respect to the background NH 3 . With the concept of blending-distance, we aim to provide an estimate of the minimum required distance from a typical NH 3 emission source for regionally representative measurements.

NH 3 turbulent dispersion in DALES
To understand the variations of the NH 3 budget due to turbulence and heterogeneous sources and sinks of ammonia, our approach is two folded: (a) explicit simulation of processes that govern turbulent dispersion and mixing of NH 3 and (b) identifying their individual contributions to the NH 3 molar fraction and surface-atmosphere exchange. For the former, we use the large-eddy simulation technique with a high resolution to solve explicitly turbulence. To this end, we conduct our numerical ex-to represent a typical 80 dairy cow barn as a surface emission source (Theobald et al., 2012) with an emission flux of 45 ppb m s -1 (about 32 µg m -2 s -1 ) over an area of 800 m 2 .
We identify the individual contributions of ammonia sources to the NH 3 molar fraction and surface-atmosphere exchange, 90 with each source of NH 3 represented by a unique scalar. In this study, these sources are identified as a background molar fraction (NH 3,bg ) and the NH 3 emission plume (NH 3,plume ) from a surface emission source. The sum of these two unique scalars represents the total atmospheric ammonia (NH 3,total ), as would be observed by in-field observations. Here, we modify DALES v4.2 to force the NH 3,plume molar fraction to zero at both x-edges of the domain (west and east), preventing circulation of the emission plume in x-direction. 95 Further modifications to DALES v4.2 are made to include the remaining processes governing the variability of the atmospheric ammonia budget. The scalar surface flux (F total ), representing surface atmosphere exchange, is divided between a flux acting on the background scalar (F bg ) and another flux acting on the emission plume scalar (F plume ). The magnitude of these two fluxes is weighted by their respective molar fractions (NH 3,bg and NH 3,plume ) relative to the total NH 3 molar fraction, e.g.
N H 3,total F total for NH 3,bg .

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The final modification adds an additional term to be added to the change in the scalar molar fraction ( S dt ). This modified change in the scalar molar fraction reads: dS dt + R chem 3600 S, with R chem representing the gain/loss rate in % hour -1 and subscript S representing the scalar molar fraction, which can be substituted by either NH 3,plume or NH 3,bg .

Numerical experiments
We simulate the meteorological conditions observed on 8 May 2008 at the CESAR -Ruisdael Observatory (https://ruisdael-observatory. 105 nl/cesar/) in the Netherlands (51.971 o N, 4.927 o E), as described by aan de Brugh et al. (2013) and Barbaro et al. (2014Barbaro et al. ( , 2015. This case is selected as it is widely studied and includes measurements of the NH 3 molar fraction. In May 2008, the intensive observational campaign IMPACT/EUCAARI was held, which included ammonia concentration measurements by a MARGA system (aan de Brugh et al., 2012;Mensah et al., 2012) and several additional meteorological variables, including vertical profiles and radiosondes (Kulmala et al., 2011). The model is initialized following the conditions as described by Barbaro 110 et al. (2014). The case can be characterized as typical clear-sky, fair-weather conditions with an absence of large-scale heat advection. The initial and prescribed meteorological values of the reference experiment can be found in Barbaro et al. (2014) Table 1, where the experiment is called CESAR2008.
In the morning, a 1500 m residual layer leads to a very rapid growth of the CBL around 10:30 CEST, up to roughly 1800 m. In the afternoon (12:30 -17:00 CEST), CBL growth is weak and the thermodynamic conditions remain relatively constant 115 (Barbaro et al., 2014). Therefore, we only study the turbulent dispersion in the afternoon, when the impact of boundary layer dynamics on the NH3 budget is minimal. The wind speed is moderate at 5.5 to 7 m s -1 in the afternoon, resulting in strong shear production near the surface and a strong momentum entrainment at the CBL top. The convective time scale (τ ) in the more hour. We do so to minimize impact of earlier entrainment on the one-hour moving average used to calculate statistics during the analysis phase. The analysis phase therefore starts at 14:00 CEST until the collapse of the CBL around 17:00 CEST.
The analysis phase is the focus of this study and when we analyze the impact of the emission plume on (simulated) point measurements of the NH 3 concentration and flux.

Quantifying the emission plume impact on NH 3 measurements 130
Inspired by the plume observation study by Mylne and Mason (1991), we introduce three variables to assess the presence of the emitted NH 3 plume and relevance of the plume fluctuations to nearby observations. These variables, intermittency factor (I), fluctuation intensity (fI) and NH 3 flux (F), are all defined by fluctuations in the NH 3 molar fraction. Fluctuations in the NH 3 molar fraction result from turbulent mixing of differences in NH 3 , caused by local sinks and sources. NH 3 fluctuations are therefore found in the background molar fraction as a result of ammonia-poor air near the surface (deposition) and top of 135 the CBL (entrainment). NH 3 fluctuations are further enhanced in proximity of surface heterogeneous surfaces. A strong local emission source (e.g. a dairy barn) as presented in this study, will cause an emission plume as the enhanced NH 3 molar fraction is mixed with the background molar fraction through turbulent mixing. Turbulent models like DALES explicitly resolve this turbulent mixing at high spatial-temporal resolution and can provide valuable information in the interpretation of in-field observations where surface heterogeneity plays an important role. 140 We first introduce the intermittency factor (I) to quantify the detectability of the emission plume. Intermittency is defined as the proportion of time during which the plume molar fraction is above the detection limit of instruments typically used to measure atmospheric ammonia, as seen in Fig. 1 and Eq. 1, where N is the number of timesteps.
Note that the intermittency is calculated for each individual grid point during the analysis window (14:00 -17:00 CEST) at 10 145 s temporal resolution. We set the NH 3 detection limit at 0.25 ppb, similar to the detection limit of the miniDOAS instrument used in the Dutch ammonia monitoring network (Berkhout et al., 2017). The concept of intermittency cannot be applied to NH 3,bg or NH 3,total , as the background molar fraction always exceeds 0.25 ppb in our numerical experiments, which would result in an intermittency of 1. We therefore only calculate the intermittenct for NH 3,plume to analyze the detectability of the emission plume. and 1 respectively, based on the mean NH3,total, standard deviation (light purple) and NH3 detection limit (dotted black).
The second variable, fluctuation intensity (fI), determines the magnitude of the NH 3 fluctuations, i.e. NH 3 standard deviation (σ NH3 ), relative to the mean NH 3 molar fraction (N H 3 ). Fluctuation intensity is defined following Eq. 2: The fluctuation intensity quantifies the level of turbulent mixing. High fI indicates that there are large fluctuations in the measured NH 3 which can introduce a positive bias in measurements. In the field of plume dispersion, high fI is found close 155 to the source where plume meandering dominates the mixing process (Dosio and Vilà-Guerau de Arellano, 2006), or at the edge of the emission plume as a result of lateral entrainment of air from outside the plume (Mylne and Mason, 1991;Gailis et al., 2007;Ražnjević et al., 2021). When analyzing the fluctuation intensity of NH 3,total , we have a consistent reference for the fluctuation intensity in NH 3,bg . Comparing the fI for the total ammonia (fI total ) to the fI for the background ammonia (fI bg ), enables us to quantify the relative impact of the emitted NH 3 plume to simulated measurement. When fI total is of the same 160 order of magnitude as fI bg , we consider the emission plume indistinguishable from the background NH 3 , i.e. the plume is well mixed.
Note that Fig. 1 shows a downward trend in NH 3,bg and NH 3,total , resulting from surface deposition and the loss by chemical gas-aerosol transformations. To minimize the impact of this downward trend on σ NH3 , we detrend the simulated molar fraction by subtracting a 1 hour leading moving average (NH 3,MA ), following Eq. 3 and shown in Fig. 1. The detrended molar frac-165 tion (NH 3,detrend ) is assumed to only represent turbulent fluctuations and is used to calculate the standard deviation to derive fluctuation intensity. By using NH 3,detrend to calculate σ NH3 , the fluctuation intensity follows from Eq. 4.
Finally, we introduce the 30 minute NH 3 flux, studied to mimic the in-field ammonia eddy-covariance flux measurements 170 and calculated following Eq. 5. The flux presented in this study is the average 30 minute flux, for each individual grid point, over the analysis phase between 14:00 and 17:00 CEST.

The concept of blending-distance
We use the fluctuation intensity and flux to quantify the impact of the emission plume on the simulated NH 3 molar fraction and flux measurements, by introducing the concept of blending-distance. The blending-distance is based on the percentage change (PC X ) in the simulated NH 3 measurements resulting from the emission plume, i.e. the percentage change between NH 3,total and NH 3,bg . PC X is calculated following Eq. 6, where X can be substituted by either fI or F.
Based on this percentage change, we define a threshold for which we assume that the impact of the emission plume is 180 negligible. The blending-distance (BD X , is defined as the maximum distance at which PC X drops below the threshold level (e.g. PC X < 10%), following Eq. 7.
In this study, we present blending-distances based on an arbitrary set of threshold levels, ranging from 5% to 50%.
The concept of blending-distance is applied to the fluctuation intensity (BD fI ) and the NH 3 flux (BD F ) to quantify the impact 185 on the simulated NH 3 measurements of NH 3 molar fraction and flux respectively. For context, we also present the intermittency in Sect. 3.2 to quantify the detectability of the plume.

Blending-distance sensitivity
A key aspect of the study is to determine the sensitivity of the concept of the blending-distance to variations in meteorological and NH 3 pollution factors. We study the sensitivity of blending-distance for fluctuation intensity and NH 3 flux by varying the   core of the Cartesius supercomputer system for one hour).
The sensitivity study is structured from large-scale processes to small scale processes and modelling numerics. Starting with mesoscale processes, we vary the geostrophic wind speed to study the impact of the atmospheric stability on blending-distrance, i.e. a shear or convection dominated CBL. Atmospheric stability plays a key role in turbulent mixing of local sources (emission) and sinks (entrainment and deposition), affecting both the fluctuations in the background molar fraction and the mixing of the 200 emission plume (Dosio et al., 2003). Next, we study the sensitivity of BD to different levels of the background NH 3 at the start of the analysis window, representing different levels of regional NH 3 pollution. Additionally, varying the background levels of ammonia changes the NH 3 inversion at the top of the CBL, affecting the impact of entrainment. Next, the emission strength is varied, in order to study the local effect of different emission strengths.
Furthermore, we study the sensitivity of both BD fI and BD F to NH 3 deposition and the chemical gas-aerosol transformation.

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These are dynamic processes, i.e. experiencing clear diurnal and seasonal variability, mainly related to temperature, humidity and pollution levels (Wichink Kruit et al., 2010;van Zanten et al., 2010;aan de Brugh et al., 2013). Our simulation approach, with a simplified representation of deposition and chemistry, allows us to distinctly study the role of these two processes.
Finally, we study the sensitivity of BD to choices made in the numerical setup of the experiments. We vary the height of the  (Heus et al., 2010). When we aim for a TKE res of 75% at all three (vertical) resolutions, we find TKE res of 76%, 95% and 96% for the low, middle and high resolution at 37.5 m (36.25 m for high resolution). Additionally, it is also expected that varying the measurement height will gain practical insight for in-field observations. Finally, the sensitivity of the blending-distance to 3 Results

Qualitative analysis of the NH 3 emission plume impact
The concept of blending-distance is based on fluctuations in the NH 3 molar fraction. To better understand the sources of these NH 3,bg (purple) and NH 3,plume (light purple). Here we find that the large NH 3,total fluctuations are mainly ascribed to NH 3,plume .
As discussed in Sect. 2.3, fluctuations are also found in the background concentration, NH 3,bg , leading to a non-zero fluctuation intensity for the background molar fraction. The high-frequency fluctuations in NH 3,total and NH 3,bg are filtered out when 225 averaging over 30 minutes, the typical averaging time of in-field observations. Such turbulent fluctuations could be interpreted as noise in the raw measurement data of in-field observations.
The Now that we understand the source of the NH 3 fluctuations, we take a closer look at the emission plume without any 235 background NH 3 . We only calculate fI for NH 3,plume for N H 3,plume > 1 10 -5 . The xy plot in Fig. 3a shows low fI in the plume center (≈ 2) and a strong increase near the plume edges, up to fI ≈ 18. This is echoed by the plume transects, as they shows the typical "U-shape" found for Gaussian plumes (Mylne and Mason, 1991;Gailis et al., 2007;Ražnjević et al., 2021). These high fI values at the edges of the plume are a result of very low average molar fractions combined with low intermittency. This leads to a high standard deviation, relative to the very low averaged molar fraction, at the plume edges. Without background 240 NH 3 , it is at the edges of the plume that in-plume lateral entrainment of ammonia-free air happens, diluting the emission plume by turbulent mixing.
The intermittency cross-section in Fig. 3b shows that maximum I is only a little over 0.3, resulting from the meandering of the plume. Figure 3b also shows that, with an NH 3 detection limit of 0.25 ppb, the plume can be detected up to a distance of about 2.5 km from the source.

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The cross-section of fI changes dramatically when analyzing NH 3,total , the sum of NH 3,bg and NH 3,plume . With the addition of a non-zero background molar fraction, fI can be calculated over the whole domain, as shown in Fig. 3c. Now, we find a much lower fluctuation intensity, with a maximum of 0.08 for NH 3,total compared to 18 for NH 3,plume . The U-shape in shown in the transect of Fig. 3a is replaced by an approximately Gaussian shape, with the highest fluctuation intensities at the centreline of the plume. This centreline fI decreases with distance from the source and becomes indistinguishable from the out-of-plume fI 250 after approximately 1 km distance, i.e. a rough estimate for BD fI .
Finally, Fig. 3d shows that the emission plume leads to a positive flux (emission) for NH 3,total in proximity of the emission source, while the flux is negative (deposition) outside the plume. Note that significant fluctuations are found in the flux over the full domain, with σ F,bg = 0.006 ppb m s -1 (prescribed F sfc. = -0.045 ppb m s -1 ) for NH 3,bg . Similar to fI total in Fig. 3c

Quantitative analysis of the NH 3 emission plume impact
We apply the concept of blending-distance in Fig. 4 to the main variables that characterize the NH 3 evolution: fluctuation in- indicating that the highest values for fI, F and I are generally found at the plume centreline, though with uncertainties. 265 We interpret the calculation of the blending-distance based on 3 arbitraty threshold levels (5%, 25% and 50%) for fI and F, shown in Fig. 4a and b. The distance at which the maximum value of PC X drops below the threshold level is the blending- distance. The sensitivity of BD to these thresholds will be discussed in detail in Sect. 3.3, using Fig. 5 and 6. Additionally, we show the intermittency in Fig. 4c to show that the emission plume is quantifyable up to over 2.6 km distance.
Starting with the fluctuation intensity (Fig. 4a), PC fI peaks at a relative change of about 300%, caused by the NH 3 emission 270 plume. BD fI decreases non-linearly from 1.5 km to 1 km with the thresholds increasing from 5% to 25%. We can therefore infer from BD fI that, while the NH 3 plume is still quantifiable, the change in fluctuation intensity caused by the plume is < 5% at 1.5 km or less, depending on wind direction.

Sensitivity of blending-distance to meteorological and NH 3 pollution variables
We study the sensitivities of BD fI and BD F to a range of meteorological, NH 3 pollution parameters and model resolution and simulated measurement height (Table 1). The results of the sensitivity study are shown in Fig. 5 and 6 for an arbitrary set of threshold ranging from 5% (orange dashed) to 50% (orange dotted), representing the maximum acceptable difference in fI and F caused by the emission plume in %.

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Starting with BD fI , Fig. 5 shows that BD fI ranges roughly between 0.5 and 2.5 km; an indicating of the minimum distence for NH 3 molar fraction measurements. There is a negative correlation between BD fI and the choice in threshold, i.e. increasing the threshold level decreases BD fI . We generally find that BD fI decreases nonlinearly by approximately 0.5 km when increasing the threshold level from 5% to 50%, halving BD fI . We discuss the individual variables of Fig The geostrophic wind speed (u g ) is one of the main drivers of turbulent mixing and transport of the plume (Dosio et al., 2003;Vrieling and Nieuwstadt, 2003;Dosio and Vilà-Guerau de Arellano, 2006). Figure 5 shows that BD fI is only weakly sensitive to u g , showing a weak positive correlation between the two. By varying u g we move from a convection-driven boundary layer (u g = 2 m s -1 ) to more shear-driven meteorological conditions (u g = 10 m s -1 ). In a convection-driven boundary layer, 295 turbulent mixing is rather weak and the NH 3 emission plume rises from the surface as convection plumes are the main drivers of turbulent mixing. Under these conditions, in-plume molar fractions are very high, but horizontal transport of the emission plume is weak, resulting in a low BD fI . For shear-driven conditions, the NH 3 emission plume tends to stick to the surface as the increased horizontal wind speed enhances horizontal transport and turbulent mixing. The enhanced horizontal transport and emission plume sticking to the surface should significantly increase BD fI , but the enhanced turbulent mixing counteracts these 300 processes by reducing the NH 3,plume molar fraction and fluctuations. This is exactly what is shown in Fig. 5 and explains why the sensitivity of BD fI increases for lower threshold levels (5%), as smaller plume fluctuations will reach long dinstances in shear-driven conditions.
One panel below, Fig. 5 shows a weak negative correlation between BD fI and the initial background molar fraction (C bg ), i.e.
the regional level of NH 3 pollution. Increasing C bg enhances the fluctuations in the CBL by entrainment, increaing σ bg from 305 0.13 ppb (C bg = 5 ppb) to 0.38 ppb (C bg = 25 ppb). The relative weight of the NH 3,plume fluctuations (σ plume ) decreases as a result, leading to slightly lower BD fI .
At the local scale, Fig. 5  on the other hand, directly affects the vertical NH 3 molar fraction gradient near the surface, increasing fI bg for increasing D and reducing BD fI . We only briefly touch upon the chemical conversion rate (R), as Fig. 5 shows that varying R does not significantly affect BD fI . R is applied uniformly to the 3D domain and has little effect on turbulent mixing. resolution is sufficient to infer the blending-distance.
Finally, Fig. 5 shows two regimes in the sensitivity of BD fI to the simulated measurement height (H). For the 50% threshold, BD decreases by about 300 m with height up to 60 m. Above 60 m, there is a transition where BD fI rapidly goes to zero. In this second regime, the simulated measurements are located above the plume centreline. From there on, fI plume rapidly decreases with height until PC fI does not reach the 50% threshold and BD fI becomes zero. This rapid decrease is a result of the similated 320 measurements being located above the emission plume, as the height of plume does not reach above 150 m for the first 1.5 km horizontal distance. The height of this transition increases with decreasing threshold levels as the thresholds become more sensitive to smaller NH 3,plume fluctuations. Figure 6 shows the results of the sensitivity study for BD F (Table 1). Both the blending-distance for molar fraction measurements (BD fI ) and for flux measurements (BD F ) can be interpreted as a inverse footprint analysis, as we estimate the area affected by the emission source. The results of the sensitivity study of BD F however, could differ from the sensitivity study of BD fI . The footprints for flux and molar fraction measurements are not the same and footprint for flux measurements are smaller than those of molar fraction measurements (Rannik et al., 2000;Kljun et al., 2003;Vesala et al., 2008). However, comparing BD fI to the footprint of NH 3 molar fraction measurements is not straightforward, as BD fI is based on the NH 3 fluctuation intensity, not the molar fraction. It is therefore interesting to determine whether the results of the sensitivity study of BD F will 330 differ compared to the results of BD fI .
When analyzing Fig. 6, we find that there are indeed differences between BD F and BD fI . BD F is significantly longer, ranging from 1.0 to 3.5 km, indicating that NH 3 flux measurements are more sensitive to the emission plume. Note that we removed the results for D = 0 ppb m s -1 . Here, F bg approaches zero, resulting in infinitely large PC F and unrealistic BD F values.
One of main differences between BD F and BD fI are found in the sensitivity to the threshold levels (5% to 50%). BD F is more 335 sensitive to the different threshold levels compared to BD fI . This is in agreement with the results shown in Fig. 4b, where we discussed that PC F is significantly larger than PC fI , with a significanlty longer tail as well. Despite these differences, the same arbitrary set of thresholds are used for both BD fI and BD F . As a result, the non-linear effect of the aforementioned long tail in PC F (Fig. 4b) increases BD F for low threshold levels.
Significant differences between BD F and BD fI are also found in the sensitivity to the geostrophic wind speed (u g ) and the 340 simulated measurement height (H). Both variables directly affect the footprint of the simulated flux measurements. In sheardriven turbulent conditions (high u g ), the footprint of the measurement is elongated compared to convective conditions. This reduces the width of the footprint and lengthens the up-wind distance at which the emission source can be measurement, thus increasing BD F . Increasing H also increases the footprint of the measurements, but there is no elongation of the footprint. As a result, BD F has a strong positive correlation to u g but is only weakly correlated to H.

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There are also strong similarities between the sensitivity of BD F and BD fI . Both Fig. 5 and 6 show that the blending-distance is only weakly sensitive to the chemical reaction rate (R), initial background molar fraction (C bg ) and te model resolution (∆).
For both molar fraction and flux measurements, the emission strength (E), deposition (D) and the geostrophic wind speed (u 3 are the driving variables of the blending-distance.

Uncertainty on the blending-distance estimation
The blending-distance cannot be captured by a single number. The turbulent dispersion of the emission plume is chaotic by nature and driven by a wide range of factors. We therefore carry out a systematic analysis on how these factors, as well as the model resolution, influence the the relationships between emission and the simulated in-field measurements. Additionally, the chaotic nature of turbulence introduces uncertainty in the blending-distances presented in this study, visualized and discussed in 355 Sect. 3.1, where random spatial variability is seen in the fluctuation intensity and flux of NH 3,bg . This introduces an uncertainty in the blending-distance which is especially pronounced in the analysis of the NH 3 flux, as discussed in Sect. 3.2.
Furthermore, there is a downside to of our simplified representation of chemical transformations, in that it is applied uniformly to the 3D domain. In reality, the equilibrium molar fractions for these chemical transformations are related to temperature and humidity and results in a near-surface NH 3 gradient of the NH 3 molar fraction (aan de Brugh et al., 2013).

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Therefore, we are likely to underestimate the role of chemical transformations and overestimate BD fI , as turbulent mixing of this near-surface gradient increases fI bg .
Finally, we filter out the impact of boundary-layer dynamics and variations in the thermodynamic variables with our choice of analysis window, from 14:00 and 17:00 CEST. Bourndary-layer dynamics are especially relevant in the morning, when entrainment is one of the dominant processes driving the NH 3 diurnal variability (Wichink Kruit et al., 2007;Schulte et al., 365 2021). As shown in Fig. 2, entrainment leads to large fluctuations in NH 3,bg , increasing fI bg and leading to a shorter BD fI .
Despite these uncertainties, the blending-distance provides a valuable first esitmate for the minimum distance required for measurements taken in proximity of a typical NH 3 emission source.

Blending-distance for passive tracers
Evaluating the blending-distance results against typical literature on plume dispersion is a complex exercise. These studies 370 generally focus on the release of passive scalars in an unpolluted environment, with only few studies researching (near) surface releases (Cassiani et al., 2020). Normalization of both distance from the source as the plume molar fraction further complicates the interpretation of literature. We can make a rough estimate of blending-distance, using the modelled in-plume molar fraction by Dosio et al. (2003) and Dosio and Vilà-Guerau de Arellano (2006), which rapidly decreases for a convection-driven boundary layer (−z/L ≥ 40 and u * /w * ≤ 0.2) at the surface up to roughly 6 km distance, after which it levels off. This 375 distance approximately doubles for shear-driven boundary layers (−z/L ∼ 40 and u * /w * ∼ 0.46). The observations by Mylne and Mason (1991) and the large-edy simulation results of Dosio et al. (2003) show that the in-plume fluctuation intensity also decreases with distance, but levels after roughly 15 km distance from the emission source.
These rough estimates of 6 to 15 km distance are significantly larger than the blending-distances presented in this study. Such long distances between source and measurement site would not make feasible requirements in densely agricultural regions, but 380 are likely an overestimation of the blending-distance. These estimates are based on the molar fraction and fI of the emission plume, with no representation of background ammonia levels. The latter is especially important, as we show in Sect. 3.1 and 3.2 that the impact of the emission plume rapidly decreases relative to the turbulent background ammonia, while the emission plume itself can be detected for several kilometers as indicated by the intermittency.

Blending-distance for ammonia 385
Articles on ammonia measurements in close proximity of an emssion source implicitly include all relevant processes. Such studies could also provide a qualitative, perhaps more realistic, evaluation of the NH 3 blending-distance results presented here. In-field measurements show that the NH 3 molar fraction exponentially decreases with distance from the source, with measurements close to the background molar fraction after 300 to 500 m (Fowler et al., 1998;Sommer et al., 2009;Shen et al., 2016). Similar results were obtained in an intercomparison study of short-range atmospheric dispersion models by Theobald and W). However, such measurements are typically arranged in a few lines downwind of the source, with only a handful of measurements over a distance of 300 to 1000 m. At these short distances, plume dispersion is dominated by meandering of the plume (Nieuwstadt, 1992) and the in-plume molar fraction measurements are underestimated as a result, especially given the averaging times of these measurements ranging from several hours up to multiple weeks.

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Finally, we can evaluate our findings against measurement site requirements of air quality networks. The Dutch air quality network and the EMEP (European Monitoring and Evaluation Programme) network do set requirements on the minimum distance from emission sources, no references to scientific studies are provided. Back in 1990, the Dutch network required a minimum distance for NH 3 sites of 300 -500 m from NH 3 point or area sources, depending on source strength (Boermans and Erisman, 1990). This is in line with the literature on measurements in proximity of emission sources discussed earlier, but 400 closer than the blending-distances presented here. Currently, no hard requirements are in place in the Netherlands, although the potential impact of NH 3 sources is still recognized . At a European level, EMEP measurement sites require a 2 km minimum distance for measurements nearby stabling of animals and manure application, depending on the number of animals and field size (Schaug, 1988;EMEP/CCC, 2001). This 2 km distance is in line with our recommendations.
However, the blending-distance presented in this study indicate that distances below 2 km could also be sufficient to assure the 405 measurement site to be regionally representative.

Towards an NH 3 virtual testbed
This study is the first which specifically addresses the regional representativity of ammonia measurements in proximity of an emission source. The systematic analysis presented in Fig. 5 and 6 can be used as a reference when interpreting in-field NH 3 measurements. Additionally, the simulation framework can be applied for individual locations and study the representativity 410 of (potential new) measurement sites under the local conditions, using the concept of blending-distance. The framework presented here can be expanded to include multiple sources, each with an unique passive scalar, as well as heterogeneous surface conditions (Ouwersloot et al., 2011), to simulate the local NH 3 conditions. The DALES model has proven to be flexible, allowing for simulations of a convective, sheared convective, stable and cloud topped boundary layer (Verzijlbergh et al., 2009;Heus et al., 2010).The fine scale simulation framework will be included in the Ruisdael Observatory, a nationwide observatory 415 for measurements and modelling of the atmosphere and air quality, but can be used at any location where topography does not play an important role. The simulation framework can be a powerful tool in future ammonia research, e.g. in preparation of (emission) measurement campaigns or to improve interpretation of NH 3 (flux) measurements. Furthermore, we want to stress that the simulation framework is not limited to ammonia, but can be used for any gas for which the relevant processes occur at high spatio-temporal resolution. The fine scale simulation framework will be included in the Ruisdael Observatory 420 (https://ruisdael-observatory.nl), a Dutch nationwide observatory for measurements and modelling of the atmosphere and air quality, but can be used at any location where topography does not play an important role.
We recommend to expand the simulation framework to create a testbed to study NH 3 at high spatio-temporal resolution, including all processes relevant to the NH 3 diurnal variability. The main additions should be a dynamic parameterization of the surface-atmosphere exchange, e.g. DEPAC (van Zanten et al., 2010), and a thermodynamic chemistry module, e.g.
ISORROPIA version 2 (Fountoukis and Nenes, 2007). With these additions, on top of the existing possibility to distinguish between background and emitted NH 3 , the fine scale simulation framework with explicitly resolved turbulence will be well suited to study short-range dispersion of ammonia, e.g. deposition in close proximity to emission sources. Such studies are typically performed using models where turbulence is parameterized or using Gaussian plume models (Loubet et al., 2006;Sommer et al., 2009;. Furthermore, the addition of a thermodynamic chemistry module can lead 430 to new insights on NH 3 flux measurements. The equilibrium molar fractions of the NH 3 gas-aerosol transformations depend on the atmospheric temperature and humidity, resulting in a near-surface molar fraction gradient. This gradient leads to an underestimation of the NH 3 deposition flux of about 0.02 µg m -2 s -1 when using the flux-gradient method (Nemitz et al., 2004).
With these additions to the simulation framework, the virutal NH 3 testbed can be used improve the interpretation of NH 3 flux measurements.

Conclusions
This paper presents a fine scale simulation framework with which we assess the regional representativity of NH 3 molar fraction and flux measurements in proximity of a typical NH 3 emission source. We aim to translate concepts from the fields of plume dispersion and fine scale simulations to a practical application in the field of NH 3 measurements, including realistic representations of NH 3 surface-atmosphere exchange and chemical gas-aerosol transformations. The concept of a blending-distance 440 is introduced to systematically analyze the impact of the emitted NH 3 on simulated measurements, relative to a background concentration. Following this approach, we define a first-order estimate of a minimum distance requirement between regional representative measurements and a typical NH 3 emission source.
By means of fine scale simulation of atmospheric NH 3 , we investigate the representativity of NH 3 measurements from kilometer to meter scales in proximity of a typical emission source. The fine scale simulation framework presented has proven 445 to be a powerful and flexible tool for future research on ammonia, or any gas for which the relevant processes occur at high spatio-temporal resolution. The simulation framework with explicitly resolved turbulence not only enables us to quantify the variability in NH 3 measurements, but also to analyze and quantify the individual contribution of the emitted NH 3 . The concept of blending-distance presents a consistent criterium, based on second order statistics, for the minimum distance at which the impact of the emitted NH 3 is estimated to be indistinguishable from the variability of the background NH 3 . A systematic 450 analysis of the blending-distance shows a strong sensitivity to the emission strenght, deposition and the threshold level used in the calculation, and to the stability of the (convective or shear dominated) boundary layer. Furthermore, we find that the blending-distances differ for NH 3 molar fraction and flux measurements, with flux measurements being more sensitive to the NH 3 emission plume. Following this sensitivity analysis, we conclude that NH 3 measurements should be taken at a minimum distance of 0.5 -2.5 km or 1 -3.5 km distance from an emission source, for measurements of the NH 3 molar fraction or flux