General Impression

The authors revisit a problem that has been known for a while, i.e. that the dynamic gas-aerosol partitioning of between gas-phase ammonia and nitric acid one the one hand and particulate ammonium nitrate on the other causes fluxes that are non-conserved with height for the interacting compounds and particulate matter as a whole. I fully agree that most ambient flux measurements are affected by this process and cannot and should not be used to derive the deposition velocity of particles at the ground, even at only small contributions from ammonium nitrate. Whilst it is worthwhile reiterating this message which is widely ignored, partially because it is difficult to deal with, unfortunately, this paper neither provides a full review of the subject nor does it add many new insights to the discussion already in the literature, provide a quantification of the impact of aerosol evaporation or offer a solution to the problem. The main new angle it adds, is framing the problem as a non-linearity between flux and concentration. This I agree has not been done before, but I am also not sure it helps (see below). 

In addition, there are some omissions, questionable assumptions and inconsistencies in the paper that would need to be addressed prior to publication.

The authors should take note of the study of (Ryder, 2010) which applied a more sophisticated model to the Speuld dataset, amongst others. I admit that this is unfortunately not very accessible via literature searches. Also not mentioned is the study by Van Oss et al. (1998) who also simulated the Speuld dataset. There is a lot of other literature not cited in the paper (see also below), including a relatively recent study over forest (Katata et al., 2020).

Overall, I feel this paper is not publishable in its current form. It would either need to be significantly extended to become a more complete review of the subject or the analysis of the modelling would need to be expanded to provide more guidance of how to deal with the problem. In either case the modelling would need to be redone incorporating a kinetic constraint on the attainment of the equilibrium (see below) and consideration of temperature gradients (if not already done).

Major comments

1.    I am not sure the modelling and measurement communities have different definitions for Vd. The modelling community uses the form F = (-) Vd x C to derive the flux from the modelled concentration, the measurement community uses the equation Vd = (-) F/C to derive Vd from flux measurements, often for use in models. This Vd is meant to be the same, that is usually the rationale for making the measurements. There are a number of reasons why the flux measured at a certain height above the surface does not represent the processes at the surface, such as advection,  storage and, for non-inert compounds, chemical conversion. These errors need to be corrected for or shown to be negligible. The measurement community measuring fluxes of NH3, HNO3, NH4+ or NO3- is getting increasingly aware of this, but the community measuring particle number fluxes less so. I do not think that this is due to a difference in definition; it is a problem of awareness and lack of solutions to deal with the problem. 

2.    The authors specifically comment on Nemitz et al. (2009) explicitly mentioning the problem, but still calculating Vd. This is no different in this paper which also deals with the problem and then calculates a deposition velocity (Fig. 2f), and refers to the measured deposition velocities as Vds (Fig. 1). This entity is explained in the caption, but (as a symbol) also has a clearly defined meaning from which this paper diverges. It is difficult to get away from these inconsistencies. Papers that are aware of the problem often use the term “apparent deposition velocity” or “local deposition velocity”. I agree that maybe a different symbol is needed by the community to distinguish this from the Vd that describes the deposition process at the ground. Here the authors use subscript “a” as an option. What might be more important, however, is that the associated text correctly describes how to interpret the presented values of Vd and what they really represent.  

3.    The paper is not framed in the context of what the models are being used for. Total aerosol deposition is not normally a metric of interest. The main interest is in surface PM2.5 concentrations (for health impacts) and in total nitrogen deposition (for ecosystem impacts). For the former, deposition is considered a loss process for the PM2.5 (and/or its chemical components) from the atmosphere. For this purpose it is of secondary importance whether the removal of the ammonium nitrate is due to actual deposition to the surface or evaporation, and the concept of an “apparent” or “effective” deposition velocity may suffice and is arguably the appropriate loss term to use (except for the fact that the non-mechanistic treatment of the process then does not allow for tracking of the gas phase compounds and their potential to reform NH4NO3 further aloft). If the goal is to quantify nitrogen deposition, the evaporation matters and as does the fate of the ammonia and nitric acid. How much of it is deposited and how much is transported upwards (line 188) and how can this be estimated?

4.    The paper needs to distinguish from the start between two related but different effects: the impact of aerosol evaporation on (a) bulk deposition fluxes, e.g. of nitrate mass or total PM mass, and (b) the impact on size segregated particle flux measurements measured over a specified size bin. The authors acknowledge the second effect in the paragraph starting in line 260, but ignore it in their attempt to reproduce the fluxes measured at Speuld (Fig. 1), which is impacted by exactly that effect as previously shown (Ryder, 2010). In this context, I am not convinced the (size-segregated) Speuld dataset can be reproduced with a bulk model. It needs a model that explicitly simulates the change in the particle size distribution. 

5.    The analysis in the paper assumes chemical equilibrium to be instantaneous, but concedes that this is probably not the case and later discuss potential kinetic constraints and time-scales. This is critical. If there were no constraint on evaporation then there would never be any NH4NO3 near the ground where concentrations of NH3 and HNO3 converge towards 0. Without a kinetic constraint the effect is overestimated. The authors omit to mention that kinetic constraints have been used in virtually all other model studies of this effect, either deploying rate constants (Kramm and Dlugi, 1994) or a relaxation time scale towards equilibrium (e.g. Brost et al., 1988; Van Oss et al., 1998; Nemitz and Sutton, 2004). So why is this neither used here? At a time scale of 1000s evaporation likely starts to become unimportant given that transport timescales are smaller; e.g. see timescale analysis of Wolff et al. (2010). In fact, equilibrium is not usually maintained even at the measurement height with concentrations affected by conditions further aloft (e.g. Aan de Brugh et al., 2012).

6.    From a modelling perspective, the problem is that (a) aerosol evaporation is an unresolved subgrid process in atmospheric chemistry and transport models which do not have the vertical resolution to calculate the thermodynamic partitioning according to the vertical concentration and temperature (and RH) gradients near the ground and (b) these models assume aforementioned equilibrium. Maybe it should be stated in these terms. 

7.    The paper identifies a problem, but does not offer a solution. If the deposition concept is not applicable, what should be used in its stead? For example, the EMEP model acknowledges aerosol evaporation as a non-resolved process within the model and uses a parameterisation of an “effective deposition velocity” for the constituents of ammonium and nitrate (Simpson et al., 2012; Eq. (68) and associated text). This has been developed by fit to nitrate flux measurements (apparent deposition velocity). This is a first approximation that should be improved with time. In terms of nitrogen deposition it implicitly makes the assumption that the ammonia and nitric acid that are liberated during evaporation are in fact deposited. 

8.    The text suggests that the reduction in gas-phase concentrations towards the ground, caused by their deposition (and in particular of HNO3; line 166), is the main driver of evaporation. The model results of  (Ryder, 2010) suggest that at Speuld this effect is only responsible for about half of the evaporation, the remainder being driven by increases in temperature (and equilibrium vapour pressures) near the ground and inside the canopy. In other words, even if NH3 and HNO3 did not deposit at all there would still be a driver for evaporation. Clearly, this varies over the day as the temperature gradients change. Are the temperature gradient accounted for in the model?

9.    Whilst I fully agree that the evaporation complicates the relationship between the surface (and also the measured) flux and concentration, field observations are unlikely to show a linear relationship for a number of reasons. Vd is not a simple function of u* (as implied by some of the parameterisations including that reflected in Fig. 4), but also atmospheric stability (as discussed in the paper), size distribution, surface roughness (which might change with footprint and wind direction) etc. In addition, measurement uncertainty complicates any relationship. As the paper correctly describes, the traditional deposition velocity concept relies on fluxes being constant with height and therefore does not apply to reactive compounds. Because Vd is effectively the slope between flux and concentration, it automatically follows that the relationship also becomes less meaningful and proportionality breaks down. I am not sure this is an independent observation / statement.

Other Scientific Comments

10.    Eq. (1) – Even in the standard use of the deposition velocity, it is a function of height (because the Ra component changes with height), whilst the flux is constant with height. For clarity it might be worth indicating explicit height dependencies where they apply, i.e. F = Vd(z) / C(z).  

11.    It doesn’t seem right that in the model NH3 deposits faster than HNO3 (line 186) and the deposition parameterisation needs checking. The opposite should be the case as stated in line 219-220. 

12.    The Wesely et al. (1985) parameterisation was derived for sulfate which is non-volatile, so this probably not the best reference to back up the fact that the stability-dependence is due to evaporation. In fact it highlights that at least a component of this dependence is not due to evaporation, unless the sulfate measurements are somehow affected by the presence of nitrate or the changing particle size. 

13.    Line 301 – How is this performance quantified? Often models are evaluated mainly for O3 and total PM2.5. 

14.    Line 71. Whilst the data of Nemitz et al. (2002) could be made to agree with wind tunnel studies by tuning the parameters in the Slinn (1982) model, in hindsight it is likely that they were also affected by ammonium nitrate evaporation not explicitly accounted for in the analysis. 

15.     Fig 1 legend: the description of Vds as the “apparent deposition velocity compensated for aerodynamic resistance” does not seem right. Vd is height dependent and Vds is the surface value, more accurately at the aerodynamic roughness height, zo, i.e. Vds = Vd(zo). 

16.    Line 113. I am not familiar with the thermodynamic module used in SILAM and the references here do not shed light on it. The reference to Mozurkewich (1993) and discussion throughout the paper suggest that ammonium nitrate is treated as a pure compound, whilst in reality NH3 and HNO3 will form their individual vapour pressures above (usually aqueous) mixed aerosols. Whilst this will not change the qualitative results, ignoring the interaction with sulfate and chloride will over-estimate the vapour pressures. This simplification and its implications should at least be mentioned.

17.    Line 116. Maybe clarify that it is the upward flux FROM THE SURFACE (or emission) the model cannot represent. It can likely represent upward fluxes at higher heights.

18.    Line 120. How closely did the model represent measured concentrations of individual compounds during the Speuld campaign? Some concentrations were published (Erisman et al., 1996; Wyers and Duyzer, 1997).

19.    Line 156. This sounds like the conditions favoured active production whilst they actually favoured evaporation. Maybe rephrase “high enough for particulate NH4NO3 to be present”. 

20.    Line 186. Several studies have found apparent reduced deposition of HNO3 (in fact this observation prompted some of the early investigations in the subject). The more extreme observation of upward flux of HNO3 is likely also the impact of evaporation being instantaneous in this particular model. 

Technical Corrections

•    Throughout the paper there are spaces lacking between numbers and their units as well as different units, e.g. 1ms^-1 should read 1 m s^-1; the meaning is different.

•    Units for Vd vary between mm/s, cm s^-1 and 10-2 m s^-1

•    Line 32. Missing “of” in “regardless of the presence”

•    Line 89 should probably better read “The role of ammonium nitrate formation in modifying particle fluxes has been studied …”

•    Fig. 1 – the style of the units and parentheses in the y-axis labels varies across subplots. 

References

Aan de Brugh, J.M.J., Henzing, J.S., Schaap, M., Morgan, W.T., van Heerwaarden, C.C., Weijers, E.P., Coe, H., Krol, M.C., 2012. Modelling the partitioning of ammonium nitrate in the convective boundary layer. Atmos. Chem. Phys. 12, 3005-3023.

Brost, R.A., Delany, A.C., Huebert, B.J., 1988. Numerical Modeling of Concentrations and Fluxes of HNO3, NH3, and NH4NO3 near the Surface. J Geophys Res Atmos 93, 7137-7152.

Erisman, J.W., Draaijers, G., Duyzer, J., Hofschreuder, P., Van Leeuwen, N., Roemer, F., Ruijgrok, W., Wyers, P., Gallagher, M., 1996. Particle deposition to forests - summary of results and application. Atmos Environ 31, 321-332.

Katata, G., Matsuda, K., Sorimachi, A., Kajino, M., Takagi, K., 2020. Effects of aerosol dynamics and gas–particle conversion on dry deposition of inorganic reactive nitrogen in a temperate forest. Atmos. Chem. Phys. 20, 4933-4949.

Kramm, G., Dlugi, R., 1994. Modelling of the vertical fluxes of nitric acid, ammonia and ammonium nitrate. J Atmos Chem, 319-357.

Nemitz, E., Sutton, M.A., 2004. Gas-particle interactions above a Dutch heathland: III. Modelling the influence of the NH3-HNO3-NH4NO3 equilibrium on size-segregated particle fluxes. Atoms Chem Phys 4, 1025-1045.

Ryder, J., 2010. Emission, deposition and chemical conversion of atmospheric trace substances in and above vegetation canopies. School for Earth, Atmospheric and Environmental Sciences University of Manchester, Manchester, p. 241.

Simpson, D., Benedictow, A., Berge, H., Bergström, R., Emberson, L.D., Fagerli, H., Flechard, C.R., Hayman, G.D., Gauss, M., Jonson, J.E., Jenkin, M.E., Nyíri, A., Richter, C., Semeena, V.S., Tsyro, S., Tuovinen, J.P., Valdebenito, Á., Wind, P., 2012. The EMEP MSC-W chemical transport model - technical description. Atmos. Chem. Phys. 12, 7825-7865.

Van Oss, R., Duyzer, J., Wyers, P., 1998. The influence of gas-to-particle conversion on measurements of ammonia exchange over forest. Atmos Environ 32, 465-471.

Wolff, V., Trebs, I., Foken, T., Meixner, F.X., 2010. Exchange of reactive nitrogen compounds: concentrations and fluxes of total ammonium and total nitrate above a spruce canopy. Biogeosciences 7, 1729-1744.

Wyers, G.P., Duyzer, J.H., 1997. Micrometeorological measurement of the dry deposition flux of sulphate and nitrate aerosols to coniferous forest. Atmos Environ 31, 333-343.

Referee Comment on “Deposition velocity concept does not apply to fluxes of ambient aerosols” by Rostislav Kouznetsov, Mikhail Sofiev, Andreas Uppstu, and Risto Hänninen

Description of aerosol dry deposition in chemical transport models (CTM) is associated with rather large uncertainties. Though wet scavenging of aerosols remains in general the main removal mechanism of aerosols from the atmosphere, the sound parameterisation of dry deposition efficiency is important for accurate modelling of their life times and range of transport (but also the contamination of ecosystems). Typically, the CTMs use dry deposition velocities (Vd, assuming constant fluxes proportional to the concentration) to parameterise the removal of aerosols (and gases) from the atmosphere by dry deposition, which are experimentally determined. In the manuscript, the authors look into the issue related to the breach of proportionality between the fluxes and concentrations, in particular due to gas-aerosol transformation of ammonium nitrate. The authors use SILAM model to demonstrate that the differences between Vd for ammonium nitrate based on wind-tunnel experiment  and apparent Vd from field studies can be explained by the semi-volatile nature of NH4NO3 and the dominant role of HNO3 and NH3 depositions rates. The importance of taking into account NH4NO3 evaporation during its deposition has been/will be growing as the formation of ammonium sulphate goes down following SOx emission reductions, so that more ammonia remains available for formations of ammonium nitrate. 

Overall evaluation. The authors have done a good job formulating, demonstrating and discussing the issue, but unfortunately there is rather little practical outcome and recommendations on how to deal with the identified problems (given the paper estimates quite an abundance of ammonium nitrate in Europe and indicates its potentially frequent presence in PM2.5?

Could the authors suggest better solutions for the application of Vd in the case of semi-volatile (ammonium nitrate) aerosols i.e. whether and how the “apparent Vd” from field measurements could be used in a sound way? Alternatively, could a model representation of the apparent Vd  be proposed? Actually the paper anticipates that the authors would (L. 105)  “..suggest an approach to bridge the gap between observed apparent deposition velocities and deposition parametrisations based on Eq. (1)”. 

It would also be advisable to show the effect of accounting for gas-aerosol partitioning during aerosol deposition on model results on a regional (European) scale. What is the seasonality of this effect? Does it help to improve the model performance.

My recommendation would be that the paper can be published after the authors complete the manuscript in line with the suggestions in the evaluation above and also attend to the following comments.

Detailed comments:

1. L. 96 - “The goal…  explore the discrepancy between different experimental studies of Vd”  sounds like exaggeration.
2. L. 120-124 - was emissions for 1993 used for these simulations? If not, please comment on the uncertainties
3. L. 135 - what season this simulation was representative of?’
4. Section 3:

• Fig. 1 (b) and L. 138 - is that so that different diameters of NH4NO3 were assumed in the simulations in sec. 3 and 4: 0.3 um and 0.7 um? Any particular reason?  Does SILAM model simulate size resolved Vd?
• Fig. 1 (a, b) - I assume that 0.3 um for NH4NO3 from SILAM’s was assumed in order to correspond with particle sizes of 0.1-0.4um in deposition timeseries  from Gallagher et. al (1997). The latter is actually for particle number, where the smallest particles are said to probably be sulphate (and the smallest particles determine Vd due to their large number) - does that inconsistency matter for your findings/conclusions?
• Fig. 1 (a, b) - I assume that 0.3 um for NH4NO3 from SILAM’s was assumed in order to correspond with particle sizes of 0.1-0.4um in deposition timeseries  from Gallagher et. al (1997). The latter is actually for particle number, where the smallest particles are said to probably be sulphate (and the smallest particles determine Vd due to their large number) - does that inconsistency matter for your findings/conclusions?
• What height the SILAM results in Fig. 1 are representative of?

      6. L. 284 (Fig. 4) - Do you have model results showing that the PM in the lower cluster does not contain any ammonium nitrate indeed?

Minor comments:

1. L. 3 - “ A brief overview” instead of We analyse
2. L. 39 - define Vd,a
3. L. 162 - why not NH3?
4. L. 186 and 220 - explain the different (contrary) assumptions with respect to deposition efficiency?