Accounting for Field-Scale Dry Deposition in Backward Lagrangian Stochastic Dispersion Modelling of NH 3 Emissions

A controlled ammonia (NH3) release experiment was performed at a grassland site. The aim was to quantify the effect of dry deposition between the source and the receptors (NH3 measurement locations) on emission rate estimates by means of inverse dispersion modelling. NH3 was released for three hours at a constant rate of Q = 6.29 mg s−1 from a grid of 36 orifices spread over an area of 250 m2. The increase in line-integrated NH3 concentration was measured with open-path optical miniDOAS devices at different locations downwind of the artificial source. Using a backward Lagrangian stochastic (bLS) dispersion model (bLSmodelR), the fraction of the modelled release rate to the emitted NH3 (QbLS/Q) was calculated from the measurements of the individual instruments. QbLS/Q was found to be systematically lower than 1, on average between 0.69 and 0.91, depending on the location of the receptor. We hypothesized that NH3 dry deposition to grass and soil surfaces was the main factor responsible for the observed depletion of NH3 between source and receptor. A dry deposition algorithm based on a deposition velocity approach was included in the bLS modelling. Model deposition velocities were evaluated from a ‘big-leaf’ canopy resistance analogy. Canopy resistances (generally termed Rc) that provided QbLS/Q = 1 ranged from 75 to 290 s m−1, showing that surface removal of NH3 by dry deposition can plausibly explain the original underestimation of QbLS/Q. The inclusion of a dry deposition process in dispersion modelling is crucial for emission estimates, which are based on concentration measurements of depositing tracers downwind of homogeneous area sources or heterogeneously-distributed hot spots, such as, e.g., urine patches on pastures in the case of NH3.


Introduction
Estimation of trace gas emission from confined source areas on a local scale (i.e.receptor (measurement) distance to sources less than 500 m) using the combination of inverse dispersion modelling with either concentration or flux measurements is a widespread method, especially in the agricultural sector (e.g.Coates et al., 2017;Felber et al., 2015;Laubach et al., 2008;Laubach et al., 2012;Loubet et al., 2010;Sintermann et al., 2011).
In particular, the combination of concentration measurements with backward Lagrangian stochastic (bLS) modelling is a convenient way of emission estimation that has spurred its utilization in the past decade (Wilson et al., 2012).Flesch et al. (2004) present details of a surface-layer bLS model that has been embedded in the framework of the frequently used software 'WindTrax' 1 .A variety of trace gases, such as e.g.methane (CH4) or

Backward Lagrangian Stochastic Dispersion Model
The employed bLS model is a first-order Lagrangian stochastic dispersion model based on Flesch et al. (2004) that is run in backward mode (i.e.backward in time) assuming horizontally homogeneous and vertically inhomogeneous, Gaussian turbulence.The vertical profiles of the wind speed and the turbulence statistics are based on Monin-Obukhov Similarity Theory (MOST).
The relation between the emission rate (  ) of a homogeneous surface area and the corresponding concentration increase () at a receptor location, is calculated as where  TD is the vertical velocity at touchdown and  is the total number of trajectories in the model run that have been released and calculated back-in-time from the receptor location.The sum consists of all touchdowns inside of the emitting area.The concentration increase  represents the difference between the concentration with and without the source present.The latter is often referred to as background concentration.
For the numerical discretization, the mixed implicit-explicit Euler scheme described in Flesch et al. (1995) is used.The trajectories are reflected perfectly at an effective ground level, taken as the level of the roughness length  0 above the displacement height , such that the covariance of the wind components is retained.The initialization of the wind components at release from the receptor location is done using an orthogonal projection procedure 2 that has been adapted for three correlated components.This guarantees a Gaussian distribution of initial wind components with a covariance matrix given by cov where  * is the friction velocity (Section 2.4.3.) and   2 ,   2 and   2 are the variances of the along-wind, the crosswind and the vertical wind components.

Basic Principle
The deposition modelling is coupled to the dispersion modelling as a concentration modifying process that acts on each touchdown occurring outside of the predefined source areas (Figure 1).
Figure 1.Illustration of the deposition modelling in the bLSmodelR.The trajectory touchdowns (indicated by circles) at -2.5 sec and -2.7 sec are inside the source area and not affected by deposition modelling; those at -1.9 sec and 0.0 sec are outside the source area where deposition occurs in the model.
The flux () between the absorbing surface (at the notional height  0 ′ ) and the model effective ground level  =  +  0 , the level where touchdowns occur in the bLS model, can be approximated by the product of an exchange velocity  ex , active through the quasi-laminar viscous sub-layer, and the difference between the concentration at the absorbing surface  {+ 0 } and the concentration at the model surface  � 0 ′ � :  =  ex � � 0 ′ � −  {+ 0 } �. (3) The super-positioning of concentrations in the bLS model (i.e. the concentration of a single trajectory can be written as the sum of concentration contributions from the background and the different sources: it is assumed, that the increase in  � 0 ′ � � Sources due to already deposited molecules from the source areas can be neglected.Thus, it holds that  � 0 ′ � � Sources = 0 and Equation ( 4) can be written as where  TD is used as synonym for  {+ 0 } � Sources , the modelled concentration at touchdown of the trajectory.
Since  TD is strictly positive, the right-hand side of Equation ( 5) is always negative, i.e. a downward directional deposition flux   , and the exchange velocity represents in fact a surface deposition velocity   * :

Integration of Dry Deposition in the bLS Model
The integration of Equation ( 6) into the model when a touchdown occurs outside the source areas is done straightforward as where  can be regarded as vertical extension of the notional volume where the deposition takes place.Thus, at each touchdown, the concentration is decreased by where  >TD is the concentration after and  <TD the concentration before a touchdown occurs.The 'residence time'  TD (i.e. the amount of time that the trajectory is below  0 , in the deposition relevant volume) is given as and thus or equivalent, when dividing both sides by the source strength : The deposition pathway inside emitting areas is switched off, i.e. no deposition is modelled.The concentration after the touchdown occurred is only affected by the usual increase due to the source area emission rate, thus: if the touchdown occurs inside the source areas.
The modelled / ratio for a single trajectory  is given as the cumulative sum over all touchdowns  ∈ {1, … , }, starting at the first (i.e.first in time) touchdown inside the source: with The final modelled / ratio is given as the average value of all trajectories:

Structure and Implementation of bLSmodelR
The bLS model by Flesch et al. (2004) together with the deposition algorithm was implemented into an R (R Core Team, 2018) package called bLSmodelR (Supplement S1, current version available at https://www.agrammon.ch/documents-to-download/blsmodelr/).The deposition algorithm was included in the bLSmodelR package as a post-processing function that allows the modelling of the dry deposition additionally to the dispersion modelling.It provides reduced / ratios due to the user defined dry deposition velocity, where the bLS model needs to be run first in normal mode, i.e. without the dry deposition mechanism included.
The bLSmodelR package makes use of several different available R packages.A complete list of all packages that bLSmodelR depends on can be found on the above-mentioned homepage.Amongst the most important ones are used mainly due to CPU time, the packages snowfall (Knaus, 2015) and snow (Luke et al., 2016) for simple parallelization of calculation processes, Rcpp (Eddelbuettel and François, 2011) for the simple implementation of the core model's C++ code (i.e. the calculation of the individual trajectories) and data.table(Dowle and Srinivasan, 2017) for fast calculation in the model framework.

Experimental Site
The experiment took place on September 22 nd , 2014 at a grassland site (46°59'06"N / 07°04'35"E) in the Seeland region, Switzerland.The release started at 10h40 local time and lasted until 13h42.The sward was treated with a broad-spectrum herbicide (glyphosate) one week before the release experiment.The height of the canopy was estimated as 9.6 cm on average with a rising plate pasture meter (RPM; Filip's Manual Folding Plate Meter, NZ Agriworks Ltd t/a Jenquip, Feilding, NZ).
During the experiment, the wind direction varied between NE to E (45° to 103°), where the only obstacles upwind of the setup was a hedge of lower height at approx.140 m and on the eastern end, a group of tall trees at approx.200 m distance.The terrain was horizontally flat and homogeneous within 140 m upwind of the artificial source.There were two farms located within a range of 1 km, one farm at 700 m distance NE (42°) with pasture next to the farm buildings and another farm at 500 m distance SSE (163°).

Artificial Source
The artificial source included a gas distributor unit at the center where 12 branches consisting of polyamide tubes (6 mm outer diameter x 4 mm inner diameter, Legris, Parker Hannifin) were attached radially forming a hexagonal geometry (Figure 2).Each branch contained 3 critical flow orifices (100 μm diameter, stainless steel, LenoxLaser, USA) in series with 3 m distance between neighboring orifices.The source grid covered a notional circular area of approximately 250 m 2 .The gas bottle with a nominal NH3 to N2 mixing ratio of 4.97% (±2% rel., CarbaGas, CH) was placed 20 m away from the source orifices.The constant release rate of 10 Ln min -1 was regulated and measured by a mass flow controller (red-y smart controller, Voegtlin Instruments AG, CH).The NH3 total release rate of the source was given as 6.28 mg NH3 s -1 (174.6 µg NH3 s -1 per orifice).The response time of the source, i.e. the time between the switching-on of the flow and the reaching of the total NH3 release rate at the exit (orifices), is in the order of minutes.

Velocity Field and Model Dispersion
The high frequency fluctuations of 3D wind components along with the sonic temperature were measured at 10 Hz using an ultrasonic anemometer (WindMaster™Pro, Gill Instruments Limited, Lymington, UK).Since the raw data of the WindMaster™Pro series includes a bug produced by the firmware they were corrected according to the indications communicated by Gill instruments3 .The ultrasonic anemometer (denominated 'Sonic') was placed next to the NH3 measurements at a height of 1.25 m above ground level (a.g.l.) and oriented towards magnetic north using a geological compass.The orientation of the Sonic was corrected by the magnetic declination, i.e. the deviation of the magnetic north to the geographic north.A bubble level was used to align the Sonic in the vertical axis.The raw data from the Sonic was averaged on a 10-minute basis.The wind vector was rotated twice to provide a wind vector with components ,  and , representing the along-wind, crosswind and vertical velocity, respectively.The first rotation in the horizontal adjusted the x-axis to the 10-minute mean wind direction and the second rotation was done afterwards around the new y-axis until the mean vertical wind equaled zero.All Sonic data were linearly detrended.
The roughness length ( 0 ) was calculated from the theoretical wind profile according to Monin-Obukhov similarity theory (MOST): with the friction velocity given as and the stability correction function for momentum as defined in Flesch et al. (2004): where The calculation is based on the rotated wind components  and , where the overbar represents their temporal average and the prime denotes the deviation from the average value  � and  � , respectively. represents the geometric height (i.e. the height above ground),   is the von Kármán constant (defined as 0.4) and  is the Obukhov-Length.The displacement height  was taken to be 2/3 of the canopy height, resulting in  = 6.4 cm.The value of  0 was estimated in an iterative procedure solving Equation ( 16) for  0 by providing  �,  * and  from sonic anemometer measurements.
The bLS model was run by supplying direct measurements of the wind statistics   ,   ,   implying a varying Kolmogorov coefficient ( 0 ) and related to that, a varying eddy diffusivity equivalent of the model.

Concentration Measurement
The NH3 concentrations in the ambient air were determined with miniDOAS instruments described in detail by Sintermann et al. (2016).They are open-path (thus sample inlet-free) optical devices that measure the concentration of NH3, sulfur dioxide (SO2) and nitric oxide (NO) as line-integrated averages over a measurement path between a light source and a detector (spectrometer) by UV absorption in the wavelength range of 200 to 230 nm.The light path is returned by a retroreflector typically at 10 to 50 m from the light source to keep the light source and the detector at the same location in an actively ventilated, temperature stabilized box (Figure 3).
The four miniDOAS were placed 15 m downwind (location denominated near) of the source center at three heights (0.5 m, 1.25 m and 3.0 m) and 70 m downwind (location denominated far) of the source center at a height of 1.2 m (Figure 4).The measurement paths were approx.70 m (i.e.distance between box and reflector ≈ 35 m) for all miniDOAS instruments.The positions of all instruments and the individual orifices were recorded by a Global Positioning System (GPS Trimbel R8 GNSS, approx.precision 10 cm).

Background Concentration
The background concentration for each individual miniDOAS instrument was linearly interpolated from the concentration measurement before and after the release.The concentration measurements during daytime several days before and after the release experiment with wind from the north easterly sector (the prevailing wind direction during the release experiment) showed little variation over time and a linear interpolation of the background concentration seems appropriate for the short time of the release.

Recovered Fraction of the Tracer Gas
The ratio of the modelled to the emitted release rate (i.e. the recovered fraction of NH3 by the model) was calculated as where   is the contribution of the background concentration to the measured total concentration   , both in μg NH3 m -3 ,  src is the emission rate of the source in μg NH3 m -2 s -1 and �   � � sim is the modelled / ratio in s m -1 calculated from Equation (1) if dry deposition was not included or Equation (15) if deposition was included in the model run.For the model calculation of �   � � sim the source area was defined as 36 circular areas of 5 cm radius, all emitting with equal strength of  src = 22.24 mg NH3 m -2 s -1 .
The ratio  bLS / is equivalent to the ratio between the measured net concentration and the modelled concentration  bLS / = (  −   )  bLS ⁄ where the modelled concentration is given as

Surface Deposition Velocity
For each estimate of the recovery rate  bLS / (i.e. each interval at each location), the near-surface deposition velocity (  * ) (Section 2.2.) was evaluated by running the model deposition post-processing with different values of   * and its optimum was estimated from these results.The values of   * that were provided as input to the bLS dry deposition modelling were approximated by a resistances approach (Sutton et al., 1995), where   * is modelled as the inverse of the sum of a series of different resistances to deposition: and   represent transfer resistances below the aerodynamic surface ( +  0 ), with   the pseudolaminar boundary layer resistance and   a bulk (big-leaf) canopy resistance, respectively.The aerodynamic resistance (  ) usually included in resistance schemes is not included in Equation ( 21), since   * is defined between  +  0 and the absorbing surface ( 0 ′ ), and, therefore,   is already implicitly accounted for in bLS dispersion modelling.
To estimate the effective magnitude of   * , based on the assumption that dry deposition was the main reason for the observed incomplete recovery rates,   was varied from 0 to 500 s m -1 in steps of 50 s m -1 .In a first step, the optimum of   (henceforth referred to as   1 ) was estimated with local polynomial regression (R function loess) from the post-processed results such that  bLS / = 1.This yields a 'best estimate' of   anywhere in the range between 0 and ∞ s m -1 .In a second step, the corresponding optimum of   * was calculated from Equation ( 21).
The pseudo-laminar resistance   was calculated following Garland (1977) as where  0 is the roughness length,  * the friction velocity,  the kinematic viscosity of air and  the molecular diffusivity of NH3 in air.The temperature and pressure dependence of the diffusion coefficient was approximated according to the Chapman-Enskog theory of gas diffusion (Cussler, 2013): where  is the actual air pressure and  is the actual air temperature.The standard diffusion coefficient of ammonia in air ( 0 = 0.20487 cm 2 s -1 at  0 = 1 atm and  0 = 273 K) is calculated as the average of the values summarized in Tang et al. (2014).

Meteorological Conditions and Dispersion Parameters
On the day of the experiment, the weather was sunny with a steady easterly wind.During the release, the air temperature increased from 15.5 to 18.9 °C with an average of 17.6 °C, whereas the relative humidity dropped from 61% to 43% (average: 51%) (Figure 5e).The 10-minute averaged wind speed at 1.25 meters above ground level from the sonic anemometer measurements ranged from 1.7 to 2.7 m s -1 (average: 2.2 m s -1 ) with wind directions ranging between 45° and 103° with an average of 74° (Figure 5c).

SO2 Plume
Simultaneous to the NH3 concentration, the concentration of NO and SO2 were recorded with the miniDOAS instruments.An SO2 plume originating from the eruption of the Icelandic volcano Bárðarbunga passed the location from 08h00 (local time) to 17h00 (Sintermann et al., 2016), raising the SO2 concentration from 20 to 70 µg m -3 during the NH3 release with highest concentration just at the end of the release experiment (Figure 5f).There was no detectable difference in the SO2 concentration between the three miniDOAS systems close to the NH3 source, but the instrument at position far was higher by roughly 10%.

NH3 Concentration
The average increase in the measured NH3 concentration during the NH3 release period amounted to 39.7 μg m -3 (near/bottom), 22.6 μg m -3 (near/middle), 6.3 μg m -3 (near/top) and 2.7 μg m -3 (far) (Figure 5a-b).The standard deviation  NH3 of the measured concentration increased from 0.5 μg m -3 , 0.3 μg m -3 , 0.2 μg m -3 and 0.8 μg m -3 before and after the release to 11.5 μg m -3 , 6.0 μg m -3 , 3.2 μg m -3 and 2.3 μg m -3 during the release for the near/bottom, near/middle, near/top and far measurement location, respectively.The standard deviation of the NH3 concentration at position far during the release phase was of the same order as the average increase above background concentration.The instruments' random errors (i.e. the standard error (SE) of the coefficient estimates from the instrument's curve fitting, reflecting the quality of the measurement) averaged to 0.3 μg m -3 , 0.5 μg m -3 , 0.3 μg m -3 and 0.6 μg m -3 during the release and changed only marginally from background concentration measurements.The measured background concentration immediately before and after the release was around 4 μg m -3 .All instruments showed a similar temporal behavior in the measured concentration, with a residual tailing of the concentration above background after the gas flow through the source stopped, i.e. the NH3 concentration did not instantaneously drop to background unlike the case for CH4 (data not shown).

Recovered Fractions of NH3 without Deposition Modelling
The calculated recovered fractions  bLS / from the standard model runs are shown in Figure 6.The average  bLS / was significantly below 1 for each instrument, estimated as 0.88 (near/bottom), 0.91 (near/middle), 0.83 (near/top) and 0.69 (far).The corresponding standard deviations  / were smaller in the case of larger fractions recovered, i.e. 0.11 (near/bottom, number of intervals n = 18), 0.12 (near/middle, n = 18), versus 0.19 (near/top, n = 18) and 0.19 (far, n = 17).One interval (from 12h10 to 12h20) from the measurement at position far showed a very high recovery rate ( bLS / = 4.4) exceeding the average  bLS / by approx.20 times the standard deviation, indicative of large measurement or modelling errors and thus excluded from the further analysis.The SE of the individual  bLS / estimates (i.e. on an interval basis) were calculated from error propagation.They were also smaller in the case of the larger recovered fractions, i.e. 0.05 (near/bottom), 0.06 (near/middle), versus 0.10 (near/top) and 0.31 (far).The error propagation assumed independent error contributions from a) the NH3 release rate with an SE of the NH3 release rate assumed to be 5% of the absolute release rate, b) the concentration measurement (individual SE given by the miniDOAS instruments), c) the background concentration estimation (SE assumed to be 0.5 μg m -3 ) and d) the model calculation of the / ratio (SE given by the bLS model output).estimates.One interval from the measurement at position far (12h10 to 12h20,  bLS / = 4.4) was excluded from the analysis.

Canopy Resistance and Surface Deposition Velocity
When considering the ensemble of all intervals, the   values that were required to raise the uncorrected  bLS / values closest to 1 (  1 ) and the corresponding average surface deposition velocities (  * � ) were 280 s m - 1 , (  * � = 0.34 cm s -1 ) for position near/bottom, 290 s m -1 (  * � = 0.33 cm s -1 ) for position near/middle, 120 s m -1 (  * � = 0.74 cm s -1 ) for position near/top and 75 s m -1 (  * � = 1.11 cm s -1 ) for position far.Figure 7 shows the numerical impact of the investigated range of   (and   * � ) values on the calculated  bLS /.The maximum deposition possible (  = 0 s m -1 ) resulted in  bLS / averages between 1.6 and 2.0.  1 is reduced from 290 s m -1 at position near/middle to 120 s m -1 at position near/top by roughly 60%, the corresponding surface deposition velocity   * is enhanced by a factor 1.2, whereas the recovery rate is only decreased by about 8% (from 0.91 to 0.83).This is not a contradiction, but reflects the fact that the modelled removal of emitted NH3 molecules needs to be higher by a factor of 1.8.
Regarding the results from individual intervals, the medians of   * were 0.28 cm s -1 (near/bottom), 0.42 cm s -1 (near/middle), 0.67 cm s -1 (near/top) and 1.06 cm s -1 (far).Values of   1 with the corresponding surface deposition velocities for each interval are given in Table A1 of the Appendix.

Recovered Fraction of NH3 without Deposition Modelling
The recovered fractions  bLS / for the standard model runs showed similar patterns with time of the release experiment at the four measurement locations (Figure 6) averaging over all intervals between 0.69 and 0.91 times the expected release rate  src .The variation in between different intervals was small ( / between 0.11 and 0.19) and compared well to previously published results (e.g.Table A1 in Harper et al., 2010).
For the instrument at position far, there are a few factors that explain the larger uncertainty compared to the other instruments, which are: 1. the higher sensitivity of  bLS / to errors in the calculated average wind direction at 70 m downwind of the source, 2. measurement at the plume edge (Figure 8) and with that a. the higher sensitivity of  bLS / due to the smaller increase in the measured concentration above the background concentration (resulting in a higher sensitivity to the interpolation of the background concentration and to the concentration measurement itself) and b. the higher sensitivity of  bLS / due to the smaller value of �   � � sim .
The latter two also introduce a higher uncertainty in the results of near/top compared to near/middle and near/bottom, since location near/top was most of the time at the edge of the emission plume.Wind is blowing from east (β = 97°), i.e. from right to left.Right: Modelled concentration distribution in the horizontal plane at height 1.2 m a.g.l. between 12h10 and 12h20, assuming an emission rate identical to the source release of 6.29 mg NH3 s -1 .
In previous experiments with CH4 as a passive tracer using the same artificial source grid as in this study, we observed  bLS / values with averages of 0.96 and 1.04 under comparable conditions (see Supplement S2).
While there are different possible causes for the low values of  bLS / in the present study (e.g. the parametrization of the model dispersion that is reflected i.a. by the value of  0 ), we focus on the hypothesis that the systematically lower  bLS / values in this study are related to the dry deposition removal of NH3 between source and receptor.

Deposition Modelling
The canopy resistance   can be modelled as the inverse of the sum of the inverse of resistances to the stomatal exchange (usually termed   ) and the uptake to non-stomatal surfaces (e.g.ground surface, plant cuticle, etc.), usually termed   (Flechard et al., 2010).Because the sward of the entire experimental site was treated with glyphosate one week prior to the measurements, an absence of stomatal activity can be assumed (  = ∞ s m -1 ).Therefore, the experimentally-derived   values in the context of the present study mostly describe the magnitude of   .Average   1 values that explained the observed  bLS / are compatible with the   parameterization by Massad et al. (2010) (several hundred s m -1 at low relative humidity), and the resulting surface deposition velocities   * of 0.33 to 1.11 cm s -1 do not disagree with the deposition velocity ranges published in Schrader and Brümmer (2014).It needs to be mentioned that Schrader and Brümmer reviewed deposition velocity values at a certain, unknown reference height above the canopy and their reported values of 0.1 to 1.8 cm s -1 (average: 0.9 cm s -1 ) for semi-natural land use would a) increase by a certain amount if corrected down to a height of  +  0 but also b) decrease by a certain amount if corrected for the absence of stomatal activity.
The individual estimates of   1 show a comparable inter-quartile range from 127 to 526 s m -1 and from 148 to 1182 s m -1 for positions near/low and near/middle and, similarly, for positions near/top and far a comparable inter-quartile range from 35 to 501 s m -1 as well as from 26 to 314 s m -1 .These wide ranges reflect the turbulence-induced variability and do not indicate a physical variability of the deposition processes from one interval to the next.Furthermore, the assumption of a constant deposition velocity over time and space can be questioned.Close to the source, the elevated deposition momentarily enhances the NH3 loading of plant and soil surfaces, which may lead to a non-zero surface equilibrium concentration.This translates physically into an increased effective surface resistance, which will induce a negative feedback on further deposition over time.Further away from the source, this surface charging-up effect is less pronounced due to a less intense exposure of the absorbing surface to NH3.As a result, the deposition velocity is expected to rise with increasing measurement distance to the source, but the effect is not accounted for in the model.
The canopy resistance also depends on the physical and chemical conditions of the absorbing surfaces e.g.water content, surface temperature or pH, possibly driven by atmospheric acid gas (SO2, HNO3, HCl, etc.) and aerosol concentrations (Flechard et al., 2013).The correlation between the recovery rate and the measured relative humidity, air temperature and SO2 concentration can be seen (Supplement S3), however, the effects are rather weak and possibly attenuate each other.
After the interruption of the gas flow through the source, the NH3 concentration did not instantaneously drop to background concentration, in contrast to the immediate response of the CH4 concentration observed in a different, comparable release experiment (data not shown).As the miniDOAS instruments measure NH3, NO and SO2 open-path, their response to the actual concentration in the air is instantaneous.Therefore, the delay in the NH3 concentration decrease is not an instrument artefact but points towards a temporal storage of NH3 during the release phase (Sutton et al., 1998).This temporal storage is not considered by the deposition modelling where NH3 is assumed to absorb irreversibly.Therefore, the modelled values of   likely represent lower bounds of   .
For any source that consists of small emission hot spots such as the artificial source with 36 point sources (or to be accurate, 36 tiny source areas) at ground level, the fraction of the emission that is deposited very close to the source is high.If we compare this fraction between a setup with the artificial source and a comparable setup with a homogeneously emitting circular source, the model shows that measurements very close to, or even above the artificial source will be significantly different for the two model runs (Figure 9).It can then be surmised that in the case of say, a circular slurry patch in actual field emission experiments, the fraction of dry deposited NH3 between the source and receptors with the same geometry to the total emitted NH3 would be much smaller (by a factor of more than 3 in the example of Figure 9).Conversely, our multiple hotspot artificial source can be compared with a cattle-grazed or sheep-grazed field, in which very significant dry deposition will occur over the unsoiled grass patches in-between urine hotspots (Bell et al., 2017).Loubet et al. (2006) investigated different release experiments on grassland sites and found cumulative deposition of the released NH3 within 200 m to be between 4% and 34%.They exhibited similar findings, with largest deposition flux close to the source and a (rather) fast drop in the deposition flux with distance.These findings are consistent with the expected deposition fluxes due to the vertical mixing of the plume with time downwind of a (surface) source.

Conclusions
Micrometeorological flux measurements always produce net flux estimates.In the case of surfaceinteracting trace gases like NH3, a significant part can be deposited downwind of a source.For the interpretation of the flux estimates, it is hence important to distinguish between: • the net emission from the footprint-related area (comprising the field of interest as well as the surrounding area), • the net emission from confined areas (the field of interest with well-defined boundaries), and • the net emission from hot spots within such an area (e.g.urine patches in a pasture field as investigated in Bell et al. (2017)).
In the latter two cases, when emissions measurements are performed downwind of confined source areas such as e.g.pasture areas or farm buildings which include livestock housings or manure stores, the resulting emission rates excluding dry deposition removal will underestimate the gross emissions, if the target is to evaluate emissions from the individual hot spots such as individual buildings.The estimated emission will represent the net flux from the area defined by the source area (net emission of NH3) plus the area between source and receptor (deposition of NH3).Including a dry deposition algorithm in the dispersion modelling is needed to correct for this systematic error.This applies not only for emission estimation in inverse dispersion modelling based on concentration measurements, but also for flux-footprint calculations as used in the Eddy-Covariance and the Flux-Gradient method, where the net flux from the entire footprint area is estimated from vertical flux measurements.
Furthermore, the results from this study show that for upscaling the emission from urine patch models (e.g.Giltrap et al., 2017;Móring et al., 2017), dry deposition inclusion is mandatory when comparing the modelled net emission from an entire pasture area to flux measurements.

( 4 )
With respect to the source-receptor relationship, only the flux related to the source emission is needed and the terms that are related to the background concentration are discarded without any loss of information.Further, Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 3 March 2018 doi:10.20944/preprints201803.0026.v1

Figure 2 .
Figure 2. Schematic of the artificial source setup.Black/grey circles with crosses: orifices; black lines: polyamide tubes.

Figure 3 .Figure 4 .
Figure 3. Three miniDOAS instruments located at the release site, 15 m downwind of the source center (position near).The distances between the boxes containing the light source and the detector (picture foreground) and the reflectors (picture background) were approx.35 m.The measurement heights were 0.5 m (near/bottom), 1.25 m (near/middle) and 3.0 m (near/top) above ground.

Figure 5 .
Figure 5. Overview on the measured variables during the release experiment.Thin/thick lines show the 1-/10minute averages of the measurements.Black vertical dotted lines indicate the start at 10h40 and the end at 13h42 (local time) of the NH3 release.Panels (top to bottom): a) Measured NH3 concentration increase above background for the miniDOAS instruments at position near: light grey: near/bottom; grey: near/middle; black: near/top.b) Measured NH3 concentration increase above for the miniDOAS instruments at position far.c) Wind direction β in ° from N (black lines) and wind speed U in m s -1 (grey lines) measured with the sonic anemometer at 1.25 m a.g.l.. d) Friction velocity  * in m s -1 (black line) and Obukhov Length L in m (grey line) as calculated on a 10-minute basis.e) Air temperature T in °C (black line) and relative humidity RH in % (grey line) measured at 1.25 m a.g.l.. f) Ensemble of the SO2 concentration measurements from the individual instruments.The SO2 plume from the Bárðarbunga volcano passed the experimental area during the NH3 release.

Figure 6 .
Figure 6.Calculated recovery rates  bLS / from model runs without accounting for deposition.The order of the instrument position is given (within an interval) from left (darkest grey) to right (lightest grey) as near/bottom, near/middle, near/top and far.Vertical lines indicate the 95% confidence region of the individual

Figure 7 .
Figure 7. Sensitivity of the  bLS / ratio to the canopy resistance   and the average of the corresponding surface deposition velocities   * � (secondary x-axis on top).Points and vertical lines indicate the average  bLS / over all intervals with the associated 95% confidence intervals.The line is showing the local polynomial regression estimate.

Figure 8 .
Figure 8. Left: Modelled concentration footprint for instrument far at time 12h10 to 12h20.The results from this interval were excluded from the analysis for location far.The grey areas indicate the spatial distribution of the relative contribution of surface fluxes to the concentration at position far (i.e. the concentration footprint).Wind is blowing from east (β = 97°), i.e. from right to left.Right: Modelled concentration distribution in the horizontal plane at height 1.2 m a.g.l. between 12h10 and 12h20, assuming an emission rate identical to the source release of 6.29 mg NH3 s -1 .

Figure 9 .
Figure 9. Modelled cumulative, cross-wind integrated fraction of emission (in %) that is deposited up to a distance downwind of the source, in the case of a multiple-orifice artificial source versus the case of a true circular area source (e.g.homogeneous slurry patch) of the same size.The atmospheric conditions were taken from measurement interval 6 (11h30 to 11h40).A model deposition velocity   * of 0.35 cm s -1 was used.