Ammonia dry deposition is typically modeled using an electrical analogy based on a network of serial and parallel resistances. The two-layer model structure introduced by Nemitz et al. (2001) has been recognized as a good compromise between model complexity, ease of use, and accuracy of the resulting exchange fluxes (Flechard et al., 2013), and it is the foundation for the parameterization of Massad et al. (2010) that is used throughout this study. However, in the Massad et al. (2010) formulation the second (soil/leaf-litter) layer is essentially switched off for semi-natural ecosystems and managed ecosystems outside of management events because soil emissions are expected to be negligible in these cases. We therefore focus on the one-layer big-leaf model (Fig. 1) in this paper. For a list of variables used throughout this article, refer to Table S1 in the Supplement.

In the simplest form, the canopy resistance model (e.g., Wesely, 1989; Erisman and Wyers, 1993), surface–atmosphere fluxes are limited by three resistances in series: The aerodynamic resistance Ra{z-d} (s m-1) at the reference height z-d (m) (where z (m) is the measurement height above ground and d (m) is the zero-plane displacement height), the quasi-laminar boundary layer resistance Rb (s m-1), and the canopy resistance Rc (s m-1). While Ra{z-d} and Rb are mainly dependent on micrometeorological conditions, surface roughness, and chemical properties of the compound of interest, Rc is directly dependent on the characteristics of the vegetated surface. The inverse of the sum of these three resistances is called the deposition velocity, vd{z-d} (m s-1).

Rc is further split into a stomatal pathway with the stomatal resistance Rs (s m-1), and a non-stomatal (or cuticular) pathway with the non-stomatal resistance Rw (s m-1) (e.g., Erisman et al., 1994; Sutton et al., 1998). Stomatal exchange is usually modeled bidirectionally for ammonia in field scale studies and some CTMs, i.e., it is assumed that there is a non-zero gaseous ammonia concentration χs (µg m-3) in equilibrium with dissolved ammonia in the apoplastic fluid. This concentration is often called the stomatal compensation point, although strictly speaking the compensation point is only met when χs is approximately equal to the air ammonia concentration at the reference height χa{z-d} (µg m-3) and consequently the net flux Ft (µg m-2 s-1) is zero (Farquhar et al., 1980). The non-stomatal pathway is modeled unidirectionally in many parameterizations, i.e., the gaseous ammonia concentration in equilibrium with the solution on the external leaf surfaces χw (µg m-3) is assumed to be zero, although observational evidence indicates that this pathway is in fact bidirectional as well (e.g., Neirynck and Ceulemans, 2008). A canopy compensation point, χc (µg m-3), that integrates these two pathways can be calculated as (e.g., Sutton et al., 1995; modified to include χw) χc=χa{z-d}⋅Ra+Rb-1+χs⋅Rs-1+χw⋅Rw-1(Ra{z-d}+Rb)-1+Rs-1+Rw-1, and the total net flux of ammonia to or from the ecosystem, Ft (µg m-2 s-1) as Ft=-χa{z-d}-χcRa{z-d}+Rb, where by convention negative fluxes indicate deposition towards the surface and positive fluxes indicate emission. This is typically done on a half-hour basis for consistency with flux measurement practices. Ra{z-d} and Rb are here modeled after Garland (1977) as Ra{z-d}=u{z-d}u∗2-ΨHz-dL-ΨMz-dLk⋅u∗, and Rb=u∗-11.45⋅z0⋅u∗νair0.24⋅νairDNH30.8, where u{z-d} (m s-1) is the wind speed at the reference height, u∗ (m s-1) is the friction velocity, L (m) is the Obukhov length, k (–) is the von Kármán constant (k=0.41), ΨH (–) and ΨM (–) are the integrated stability corrections for entrained scalars and momentum, respectively, after Webb (1970) and Paulson (1970), z0 (m) is the roughness length, νair (m2 s-1) is the kinematic viscosity of air, and DNH3 (m2 s-1) is the molecular diffusivity of ammonia in air. Rs can be modeled using at least a light and temperature response function (e.g., Wesely, 1989), often with additional reduction factors accounting for vapor pressure deficit, soil moisture, and other environmental variables (e.g., Emberson et al., 2000). However, this study focuses on nighttime fluxes when non-stomatal fluxes are assumed to be dominant. If Rs is assumed to approach infinity at nighttime, all terms involving Rs in Eq. (1) collapse to zero.

The MNS model uses a minimum non-stomatal resistance Rw,min of 31.5 s m-1, which is further significantly increased when AR < 1, RH < 100 %, LAI < 1, and T≠0 ∘C (Fig. 2). For example, at AR = 0.5 and T=10 ∘C, the minimum allowed Rw at 100 % relative humidity lies between 163 and 282 s m-1 for an LAI range of 1 to 3 m2 m-2. It is evident from Table 1 of Massad et al. (2010) that AR < 1 is no rare occurrence, but compared to minimum measured Rw (ibid.) predicted values appear to be rather high. It should also be noted that in the MNS model, the deposition velocity can never reach the maximum limit allowed by turbulence vd,max{z-d} (m s-1): vd,max{z-d}=Ra{z-d}+Rb-1. The temperature-dependent parameterization of Γw in the WK model can lead to contrasting effects: When temperatures increase, the exponential decay function in Eq. (8) can completely counter the growth of Eq. (7). In other words, depending on NH3 air concentration levels, after a certain cut-off temperature the non-stomatal compensation point χw decreases (Fig. 2), although with a constant Γw an equilibrium shift towards gaseous ammonia would be expected to lead to a further exponential increase of χw. Consequently, when T is high and χw approaches zero, χc is canceled out in Eq. (9) and Rw,eff. becomes equal to the clean air Rw,WK (Eq. 6), which at 100 % relative humidity is as low as 2 s m-1.

Based on these considerations, we hypothesize that i.

The MNS model has a tendency to overestimate Rw and consequently to underestimate Ft, especially at sites with low acid ratios.

Non-stomatal resistance models are parameterized using flux measurements during reasonably turbulent, i.e., near-neutral or only slightly stable, nighttime conditions. When stomatal closure is high and therefore Rs≫Rw, we can assume that the canopy resistance Rc is approximately equal to Rw based on the single-layer model when the non-stomatal pathway is treated unidirectional: Rw,obs.≈-χa{z-d}Ft-(Ra{z-d}+Rb), where Rw,obs. (s m-1) is the observed non-stomatal resistance, and Ft is in µg m-2 s-1. Rw,obs. values were selected from turbulent nighttime conditions (e.g., Wichink Kruit et al., 2010), when Ra{z-d}+Rb < 200 s m-1, u∗ > 0.1 m s-1, and global radiation < 10 W m-2.

Existing datasets of flux measurements were used for a comparison of measured and modeled Rw. These measurements were conducted at two peatland sites, Auchencorth Moss (AM) in the United Kingdom, and Bourtanger Moor (BM) in Germany, as well as three grassland sites, Oensingen (OE) in Switzerland, and Solleveld (SV) and Veenkampen (VK), in the Netherlands. At AM, OE, SV, and VK, the aerodynamic gradient method was used and at BM the eddy covariance method was used. For detailed site and measurement setup descriptions, the reader is referred to Flechard et al. (1999) for AM, Zöll et al. (2016) and Hurkuck et al. (2014) for BM, and Spirig et al. (2010) for OE. SV and VK datasets are unpublished as of now. SV is best characterized as a semi-natural grassland and is located in the dune area west of The Hague, NL. NH3 concentration profiles were measured using a Gradient Ammonia High Accuracy Monitor (GRAHAM; Wichink Kruit et al., 2007) system with inlets at 0.8, 1.7, and 3.6 m above ground. VK is an experimental grassland site used by Wageningen UR for meteorological measurements, where NH3 was sampled at 0.8 and 2.45 m above ground using differential optical absorption spectroscopy (DOAS; Volten et al., 2012). A brief overview of measurement conditions at the five sites is given in Table 1. LAI and canopy height hc (m) measurements were available for AM and OE, and the default values proposed in Table 6 of Massad et al. (2010) were used at the other sites. Emission events at OE not suitable for this study were filtered out by removing 9 days of measurements after a fertilization event, based on the e-folding time of 2.88 days used for fertilizer emission potentials in Massad et al. (2010), which translates into a 95 % “extinction time” of 8.63 days for the management influence. For VK, no management logs for the measurement site or the surrounding fields were available and only two strong emission periods were removed manually after visual inspection of the dataset.

The Wichink Kruit et al. (2010) parameterization was developed for frameworks within which the use of dynamic cuticular capacitance models in conjunction with leaf surface chemistry modules may not be practical (e.g., to limit computation time of large scale CTMs). While it is capable of modeling saturation effects with an ambient ammonia concentration-dependent non-stomatal compensation point, it only relies on χa at the current calculation step. A compromise between the truly dynamic models of Sutton et al. (1998) and Flechard et al. (1999) and the steady-state simplification of Wichink Kruit et al. (2010) would respect the site's history of reactive nitrogen inputs without falling back to a numerically dynamic model and, consequently, the same difficulties that limit the application of existing dynamic approaches in large-scale models, i.e., it would need to use a proxy for previous nitrogen deposition without relying on the model's flux predictions at an earlier calculation time. Here we additionally investigate the feasibility of a Γw parameterization based on backward-looking moving averages of air ammonia concentrations as a proxy for prior NH3 inputs into the system, which might saturate leaf water layers and enhance the compensation points. If such a relationship exists, it can provide an easy-to-use metric that can be calculated from readily available observations without the need for spinning up and iteratively solving a model for Ft estimates, while still allowing the use of a more mechanistic bidirectional approach to non-stomatal exchange. Γw values are derived as done by Wichink Kruit et al. (2010), i.e., Rw is parameterized for clean air according to Eq. (6), χw is calculated as χw=χa{z-d}+Ft⋅Ra{z-d}+Rb+Rw,WK, and finally, Γw is calculated by rearranging Eq. (7) to Γw=T+273.152.75×1015⋅e1.04×104T+273.15⋅χw. The relationship was investigated for moving-windows of different lengths (1, 3, 7, and 14 days) under exclusion of periods with substantial rainfall (> 5 mm day-1).

The MNS model tends to underestimate nighttime Ft at all five sites, whereas the WK model overestimates Ft for BM, OE, and SV, underestimates it for VK, and only very slightly underestimates it for AM (Fig. 3). Note that total cumulative Ft in Fig. 3 is by no means representative for an estimate for total NH3 input during these times, but based on non-gap filled nighttime fluxes only. Additionally, a mismatch between modeled and measured flux densities early in the time series propagates through the whole time series of cumulative fluxes. For example, at BM the MNS model performs very well after a mismatch during the first week, whereas the WK model fits the observations closely until mid-March 2014. Similarly, the strong deposition event early in the VK time series is not reproduced by either of the models. Comparing differences in modeled and measured nighttime Rw (Fig. 4, upper row) supports these observations: while using the MNS model leads to an overestimation of the majority of observed Rw at all sites, as hypothesized, the picture is not as clear for WK. Here, the majority of modeled Rw values lie below the observations for BM, OE, SV, and VK; however, for AM and VK both frequent over- and underestimations of Rw canceled each other out, thereby leading to fairly reasonable predicted net fluxes at these two sites. The inverse of these resistances, the non-stomatal conductance Gw=Rw-1, may be a better predictor for the resulting fluxes, as very high resistances have a negligible effect on fluxes. Differences between modeled and measured Gw are shown in the lower row of Fig. 4 and generally lead to similar conclusions (note that here underestimations of Gw directly lead to underestimations of Ft), but emphasize the relatively good predictive capabilities of MNS at BM and WK at VK during most times, which may not immediately be obvious from looking at cumulative fluxes (Fig. 3).

We attribute the mismatch of the MNS model results and measurements to the relatively high baseline minimum allowed Rw and the strong response of the temperature correction function (Fig. 5, left panel). Note that AR at all sites is lower than 1, ranging from 0.1 at BM to 0.7 at AM, which results in minimum Rw of 315 and 45 s m-1 before LAI and T correction, respectively. For example, at OE with an AR of 0.4 and an average LAI of approximately 2 m2 m-2, even under conditions highly favoring deposition towards the external leaf surface in the MNS model (RH = 100 %, T=0 ∘C), deposition velocity is restricted to an upper bound of 1.8 cm s-1, although observations regularly exceeded this threshold. In their comprehensive literature review, Massad et al. (2010) themselves report Rw,min between 1 and 30 s m-1 for grassland and between 0.5 and 24 s m-1 for semi-natural ecosystems. In contrast, in their parameterization of Rw the actual deposition velocity can never approach the theoretical limit allowed by turbulence (Eq. 11), although this case was regularly observed in the field. This is of course true for all unidirectional Rw parameterizations of the commonly used Rw=Rw,min⋅ea⋅(100-RH) form; however, in the WK model a small minimum Rw of 2 s m-1 allows vd{z-d} to approach vd,max{z-d} closely. Regarding the temperature correction, the parameter β=0.15 ∘C-1 translates into an increase of Rw by a factor of 4.5 with a T increase of 10 K. Equation (7), however, only predicts an increase of the compensation point χw by a factor of approximately 2.8 to 4.1 for a T increase of 10 K, depending on the starting temperature, which translates into a significantly smaller factor for Rw,eff. considering the influence of other variables in Eqs. (9) and/or (10). Note, the relatively good agreement with measured fluxes at BM, despite the very low AR.

Reasons for strikingly diverse performance of the WK model are not straightforward, but may be explained based on the combined effect of T and χa on the Γw parameterization, as depicted in Fig. 2. For example, at BM the model performs relatively well until mid-March 2014 (Fig. 3), when measured fluxes decrease, whereas modeled fluxes remain at a similar level and later even increase. This observation corresponds to an increase in both T and χa at the site (cf. Zöll et al., 2016), leading to a decrease in effective Rw and therefore an increase in modeled Ft. In fact, with all sites pooled into one combined dataset, two interesting characteristics of the parameterization emerge from a plot of differences in modeled and measured Rw against χa (Fig. 5, right panel): (i) The underestimation of Rw does indeed increase with rising temperatures and χa, as hypothesized. (ii) There is an additional tendency to actually overestimate Rw when temperatures are relatively low, which strongly responds to increasing χa and may be an indication of a too high modeled Γw under these conditions. These two contrasting effects may explain the good agreement of net modeled and measured cumulative fluxes e.g., at AM, where concentrations were relatively low during most times and both low and high temperatures without extremes were measured.

Estimated non-stomatal emission potentials Γw appear to have a strong dependency on backward-looking moving averages of measured air ammonia concentrations χa,MA (µg m-3) (Fig. 6). While this may indicate some potential as an easy-to-use and readily available proxy for prior NH3 inputs without the need for more complex and/or computationally intensive mechanistic models, estimated Γw values are extremely noisy and span multiple orders of magnitude in the < 5 µg m-3 range. An increase in the moving-window length from 1 day (Fig. 6a) to 14 days (Fig. 6d) does not lead to a substantial decrease in the magnitude of the noise. There is a very clear linear relationship when log-transforming both Γw and χa,MA (R2=0.62 for the 1 day moving average case; not shown); however, the strong variability of the data, especially in the low-concentration region, leads to a best fit that predicts large Γw even at concentrations as low as 1 µg m-3 (Γw≈380), which eventually ends in unreasonably high emission fluxes. Without further noise reduction, this approach appears unfeasible as an alternative to more sophisticated dynamic models (e.g., Flechard et al., 1999) or those featuring additional dependencies such as the one of Wichink Kruit et al. (2010). Making the moving-window width dependent on time since the last substantial precipitation event might help reduce this noise and lead to a more realistic representation, but in turn complicates the implementation and increases the degrees of freedom in this approach, thereby reducing its advantage over mechanistically more accurate models.

Since we hypothesized the reasons for the mismatch between MNS-modeled Rw and measured Rw,obs. to be based on two easily accessible parameters with relatively obvious effects on modeled resistances (Rw,min and the temperature response parameter β in Eq. 5), we additionally investigated the effects of adjusting them towards smaller values. Figure 7 shows the effects of simply halving both Rw,min and β on predicted nighttime fluxes. Doing so decreases the mismatch between modeled and measured fluxes in most cases, even though there still remains significant scatter. However, in one case (BM) predicted fluxes actually turn out to fit the measurements worse than with the original parameters, and in another case (VK) this only leads to a marginal improvement. This exercise highlights the potential for a significant overall improvement in NH3 flux predictions by optimizing these two parameters based on independent data from all four ecosystem types (grassland, arable, forest, and semi-natural ecosystems) used in the MNS parameterization.

Parts of both models used in this study were developed using an estimate of surface temperatures, either by extrapolating T from the reference height z-d to the notional height of trace gas exchange z0′ using sensible heat flux H (W m-2) measurements, or by estimating T{z0′} from outgoing long wave radiation measurements and the Stefan–Boltzmann law. Additionally, the temperature response function of Flechard et al. (2010), which is used within the MNS model, was fitted using surface level values of relative humidity RH{z0′}, which were derived using measured latent heat fluxes LE (cf. Nemitz et al., 2009). Since H and LE measurements were not available at all sites and introduce an additional source of uncertainty, especially during moderately stable nighttime conditions, and the WK model is routinely being used with air temperatures within the DEPAC3.11 code, here we used both T and RH at the reference height as input data. Figure 8 (upper row) illustrates the effects of using T and RH at different conceptual model heights for AM. While there are of course numerical differences, they do not lead to significant differences in the main findings of this study. Generally, the WK model appears to be less sensitive to these choices than the MNS model.

For both SV and VK, no measurements of [HNO3] and [HCl] were available. We estimated AR for the MNS model based on the observations of Fowler et al. (2009), which show that across NitroEurope sites [SO2] makes up around 40 % of the sum [SO2] + [HNO3] + [HCl] to be approximately 3.5 times the ratio of [SO2] / [NH3]. From the definitions AR = (2[SO2] + [HCl] + [HNO3]) / [NH3] and SN = [SO2] / [NH3], a lower bound of AR ≥ 2 ⋅ SN is obvious. Using a symmetrical range around our initial estimate of AR≈3.5⋅SN, we set an additional upper bound of AR≤5⋅SN and tested the effects of using these values on Rw differences for both affected sites (Fig. 8, lower row). Again, there are apparent numerical differences, but they do not affect the main observations made here (i.e., they neither change the sign of the differences in modeled and measured Rw, nor do they change the general magnitude of the differences, for example from a strong overestimation to an insignificant one).

Nighttime Rw,obs. are affected by (i) the uncertainty in the flux measurements, which can be high due to insufficient turbulent mixing, and (ii) uncertainty in modeled Ra{z-d} and Rb, which results from increasingly high stability corrections (ΨMz-dL and ΨHz-dL) under increasing atmospheric stability, possible inaccuracy of estimated z0 and d, and possible inadequacy of the Rb model for some surfaces. We therefore emphasize that the results of this study are to be interpreted qualitatively and can only reveal overall tendencies in the models' accuracy, not provide a precise quantification of the mismatch between models and measurements. Propagation of these uncertainties through the analysis resulted in some negative values of Rw,obs.. There are generally two possible reasons for negative canopy resistance values to occur: (i) emission (i.e., positive fluxes), or (ii) “overfast” deposition (vd{z-d}>vd,max{z-d}) that is not compatible with the resistance modeling framework used here. As a rule, we set an upper tolerance threshold for vd{z-d} of 1.5⋅vd,max{z-d}, considered to be within the limits of nighttime flux measurement uncertainty and representing perfect sink behavior, and consequently set Rw,obs. to zero in these cases. Measurements where vd{z-d}>1.5⋅vd,max{z-d} were discarded and assumed to be either resulting from incompatibility with the atmospheric resistance (Ra{z-d}, Rb) model or from measurement error. During emission events, Rw,obs. was set to infinity. Ranges from 2 to 16 % invalid values, 63 to 93 % deposition and 4 to 29 % emission were observed across the five sites during near-neutral nighttime conditions. The latter especially highlights the importance of further research towards a truly bidirectional paradigm for non-stomatal exchange (i.e., cuticular desorption, ground-based emissions, or emission fluxes from other environmental surfaces).

An additional investigation of daytime non-stomatal exchange would be beneficial in terms of a significant reduction of uncertainty in the observations and in order to cover a much wider range of temperatures and humidity regimes. However, comparisons based on daytime flux estimates were not made in this study so as not to introduce an additional source of bias via the stomatal pathway. Both Massad et al. (2010) and Wichink Kruit et al. (2010) also presented parameterizations for the stomatal emission potential, Γs (–). However, for MNS information about annual total (dry and wet) N input into the system is necessary. While this issue can be overcome by iteratively solving a model with more reactive nitrogen species so that N input is both a parameter and a result of the simulation, here we used a model that only predicts NH3 dry deposition, which we do not consider to be sufficient information to estimate total N input to our sites. At sites where total N input is known (e.g., BM, from Hurkuck et al. (2014), or from CTM results for other sites), the MNS and WK parameterizations both predict very different Γs estimates. The reasons for this mismatch have, to our knowledge, not been investigated to date. We therefore decided not to model the stomatal pathway explicitly and rely on nighttime fluxes only.

Explicitly modeling the stomatal pathway with physiologically accurate stomatal conductance models may have the additional benefit of being able to assess bias in the estimation of non-stomatal resistances introduced by nighttime stomatal opening, naturally resulting in a lower contribution of the non-stomatal pathway to the total observed flux. However, note that a distinction between physiological accuracy and the purpose for which the derived resistances are used has to be made. While nighttime stomatal opening is a well-known phenomenon (e.g., Caird et al., 2007), it is rarely respected in modeling studies (e.g., Fisher et al., 2007). A physiologically accurate Rw parameterization used in conjunction with a stomatal model that does not account for nighttime stomatal opening would result in biased fluxes. Here we derived Rw under the assumption that stomata are closed at night to ensure comparability with Rw values predicted by the WK and MNS parameterization, respectively, and compatibility with most operational biosphere–atmosphere exchange schemes, but we acknowledge that the physiological meaning may be confounded by stomatal flux contributions at night.

Another source of uncertainty lies in the fact that Rw models are often developed as “cuticular resistance” models with only leaf surface exchange in mind. However, in the one-layer resistance framework used here it is not possible to clearly differentiate between deposition towards or emission from wet leaf surfaces, leaf litter, the soil, stems and branches, and any other environmental surfaces. In fact, the MNS model was originally developed on the basis of the two-layer model of Nemitz et al. (2001), but outside of management events, the ground layer resistance was set to infinity in order to transform the model structure to that of a one-layer model (Massad et al., 2010). While it is indeed conceptually unsatisfactory to ignore the source/sink strength of the ground-layer, an unambiguous identification of multiple non-stomatal pathways' flux contributions by simply inverting the model and inferring resistances from meteorological measurements is not possible, unless there is a signal that can confidently be attributed to originate, for example, from the ground layer (after fertilizer application for instance). Therefore, due to these methodological limitations, both the parameterizations and the measurements of Rw discussed in this paper may very well integrate exchange fluxes with not only wet leaves, but also the soil, stems and branches, or other surfaces, for example.