Towards a coupled paradigm of NH3‐CO2 biosphere–atmosphere exchange modelling

Stomatal conductance, one of the major plant physiological controls within NH3 biosphere–atmosphere exchange models, is commonly estimated from semi‐empirical multiplicative schemes or simple light‐ and temperature‐response functions. However, due to their inherent parameterization on meteorological proxy variables, instead of a direct measure of stomatal opening, they are unfit for the use in climate change scenarios and of limited value for interpreting field‐scale measurements. Alternatives based on H2O flux measurements suffer from uncertainties in the partitioning of evapotranspiration at humid sites, as well as a potential decoupling of transpiration from stomatal opening in the presence of hygroscopic particles on leaf surfaces. We argue that these problems may be avoided by directly deriving stomatal conductance from CO2 fluxes instead. We reanalysed a data set of NH3 flux measurements based on CO2‐derived stomatal conductance, confirming the hypothesis that the increasing relevance of stomatal exchange with the onset of vegetation activity caused a rapid decrease of observed NH3 deposition velocities. Finally, we argue that developing more mechanistic representations of NH3 biosphere–atmosphere exchange can be of great benefit in many applications. These range from model‐based flux partitioning, over deposition monitoring using low‐cost samplers and inferential modelling, to a direct response of NH3 exchange to climate change.

based on H 2 O flux measurements suffer from uncertainties in the partitioning of evapotranspiration at humid sites, as well as a potential decoupling of transpiration from stomatal opening in the presence of hygroscopic particles on leaf surfaces. We argue that these problems may be avoided by directly deriving stomatal conductance from CO 2 fluxes instead. We reanalysed a data set of NH 3 flux measurements based on CO 2 -derived stomatal conductance, confirming the hypothesis that the increasing relevance of stomatal exchange with the onset of vegetation activity caused a rapid decrease of observed NH 3 deposition velocities. Finally, we argue that developing more mechanistic representations of NH 3 biosphere-atmosphere exchange can be of great benefit in many applications. These range from model-based flux partitioning, over deposition monitoring using low-cost samplers and inferential modelling, to a direct response of NH 3 exchange to climate change.

K E Y W O R D S
ammonia, Ball-Woodrow-Berry, CO 2 , modelling, nutrients/nitrogen, stomata is that NH 3 can easily be absorbed and desorbed, and the exchange is highly variable in space and time. There have been considerable efforts to improve the parameterization of the bidirectional NH 3 exchange estimates in recent years (Massad, Nemitz, & Sutton, 2010;Personne et al., 2009;Wichink Kruit et al., 2010;Zhang, Wright, & Asman, 2010, and others); however, major uncertainties still prevail.
For instance, Schrader et al. (2016), among others, have recently highlighted uncertainties with the treatment of the non-stomatal pathway that can generally be attributed to (a) computational effort associated with a more realistic treatment of bidirectionality in the fluxes (e.g. Flechard, Fowler, Sutton, & Cape, 1999;Sutton, Burkhardt, Guerin, Nemitz, & Fowler, 1998) and (b) a lack of available measurement data across a wide range of ecosystems and pollution levels that are necessary for calibration and validation of new schemes (Flechard et al., 2013). Additionally, Flechard et al. (2013) note a lack of coupling of the exchange processes of different chemical compounds in current models. This include not only the often-neglected gas-particle interconversion within and above the canopy, or the still rather unrefined treatment of NH 3 -SO 2 codeposition parameterizations based on relatively few observations (Nemitz, Milford, & Sutton, 2001;Wichink Kruit et al., 2017), but also within the representation of stomatal exchange. Most chemistry transport models (CTMs) nowadays employ multiplicative Jarvis (1976)-type functions or other (semi-)empirical approaches for modelling stomatal conductance (e.g. Simpson et al., 2012;Van Zanten, Sauter, Wichink Kruit, Van Jaarsveld, & Van Pul, 2010)-one of the most important plant physiological controls of NH 3 exchange. However, these models might be unfit for tasks that require direct site-specific measurements of the stomatal conductance instead of parameterizations based on proxy variables. Many measurement sites that are used for measuring and modelling NH 3 exchange are readily equipped with instrumentation that may be used to directly infer stomatal conductance from existing observations. We suggest leveraging these observations to avoid uncertainty associated with empirical approaches that were only built to be, on average, representative for a large number of potentially different sites within one land-use class.
One commonly used approach is to model the stomatal conductance based on measured fluxes of H 2 O (e.g. Shuttleworth, 2012).
However, these often suffer from an inherent uncertainty in the partitioning of transpiration and evaporation, especially at humid sites, where the latter is expected to be significant. Tower-based measurements of H 2 O can generally only be representative for an ecosystem-integrated flux of evapotranspiration. Even if it can be partitioned successfully, recent research hints at a potential decoupling of transpiration fluxes and stomatal opening in the presence of hygroscopic particles on leaves (Grantz, Zinsmeister, & Burkhardt, 2018). Similar problems arise from directly inferring stomatal conductance of NH 3 from dry periods (e.g. Nemitz, Sutton, Wyers, & Jongejan, 2004), assuming that deposition to non-stomatal surfaces is negligible below a certain relative humidity threshold. While this assumption may be valid to a certain degree given our current understanding of NH 3 exchange processes, measuring NH 3 exchange in itself is still highly uncertain and few studies span a long enough time to gather sufficient high-quality data during dry periods for a valid fit. Finally, purely empirical stomatal conductance parameterizations currently cannot account for stomatal responses to rising CO 2 concentrations (Ainsworth & Rogers, 2007), making them unfit for global change scenario modelling.
With this study, we aim to make a case for the use of a CO 2 exchange-based treatment of the stomatal pathway within the context of NH 3 dry deposition inferential modelling. Through the stomata, CO 2 and NH 3 share a common major exchange pathway, and the underlying physiological mechanisms of CO 2 biosphere-atmosphere exchange are generally well understood. Since the emergence of continent-wide research infrastructures for monitoring CO 2 exchange, such as ICOS or NEON, and even global networks like FLUXNET, CO 2 exchange measurements have become widely available, with the eddy covariance method as the de facto standard measurement technique.
The limited NH 3 exchange studies are often carried out at existing flux towers within one of those networks, and it is only natural to want to use as much additional available information as possible to improve our estimates of reactive nitrogen deposition. Further to pure modelling studies, information gained about stomatal behaviour may help interpret direct NH 3 flux measurements, as recently demonstrated by Hansen et al. (2017) and in the article at hand. But not only experimental studies at individual sites with standard half-hourly concentration measurements may benefit-it may also pave the road towards a valid low-cost model-based NH 3 deposition monitoring network.
Such a network could equip existing flux towers with inexpensive slow-response sensors, derive site-specific parameterizations for the non-stomatal pathway as well as corrections for the lowered temporal resolution (Schrader, Schaap, Zöll, Kranenburg, & Brümmer, 2018) and use stomatal conductance estimates directly inferred from available CO 2 flux measurements. Finally, new knowledge gained from these applications can be useful to evaluate the potential benefits of coupling CO 2 and NH 3 exchange within large-scale CTMs.
In the following, we will briefly outline the fundamental assumptions and equations behind modern bidirectional NH 3 exchange models. We propose coupling such models to a well-established function that relates CO 2 fluxes to stomatal conductances, and discuss in detail the potential benefits of doing so. One example is given in a case study on how we used CO 2 -derived stomatal conductance to support the interpretation of an NH 3 flux measurement data set. The results are used to confirm a hypothesized ecosystem response that could not be explained with empirical models alone in an earlier analysis. In the end, we discuss options for how to incorporate existing information about CO 2 exchange in modelling and data analysis workflows, as well as future perspectives for the development of more mechanistic NH 3 exchange models.

| Basic concepts
Biosphere-atmosphere exchange of NH 3 is commonly modelled using an inferential resistance analogy, that is, the total NH 3 flux density at a given time, F t (µg m −2 s −1 ), is estimated from a measured or modelled ambient concentration at a certain reference height, χ a (µg/m 3 ), minus the canopy compensation point, χ c (µg/m 3 ), divided by the sum of the aerodynamic and quasi-laminar boundary layer resistances, R a (s/m) and R b (s/m) respectively (Equation 1). By convention, a negative flux is directed to the surface and a positive flux is directed to the atmosphere. χ c can be interpreted as the equilibrium air NH 3 concentration at the mean notional height of trace gas exchange and is calculated as: for a simple single-layer model with parallel stomatal and non-stomatal pathways for surface exchange of NH 3 (Figure 1a; Nemitz et al., 2001). R s (s/m) and R w (s/m) are the stomatal and non-stomatal resistance respectively. The parameterization of R s is discussed in detail in the rest of this manuscript; R w is most commonly modelled using humidity response functions (Sutton & Fowler, 1993), often with additional terms used to describe the effects of other atmospheric constituents on deposition (Massad, Nemitz, et al., 2010;Nemitz et al., 2001;Wichink Kruit et al., 2017). The stomatal pathway is nowadays usually modelled under consideration of a non-zero, near-surface air NH 3 concentration in equilibrium with NH 3 in the apoplastic fluid, called the stomatal compensation point, χ s (μg/m 3 ), which allows for the representation of bidirectional fluxes (i.e. both deposition and emission) within the model. It can be parameterized based on tabulated values for different ecosystems, direct or indirect estimates of deposition history to the site or more mechanistic plant physiological approaches that directly relate the compensation point to the C-and N-metabolisms at the leaf level (Massad, Nemitz, et al., 2010;Massad, Tuzet, Loubet, Perrier, & Cellier, 2010). Note that some researchers apply a similar concept to the non-stomatal pathway, with a non-stomatal compensation point, χ w (μg/m 3 ), representing an air NH 3 concentration in equilibrium with NH 3 solved in water films or otherwise adsorbed to surfaces (Flechard et al., 2013;Van Zanten et al., 2010;Wichink Kruit et al., 2010). Even so, to date, many CTMs still employ a deposition-only paradigm for non-stomatal exchange, which is in contrast with observations of emission fluxes that are likely due to NH 3 release from non-stomatal surfaces (Wentworth et al., 2016). However, they are much more straightforward to be parameterized from micrometeorological measurements. In general, all models using the resistance analogy consider the surface component as a static component where memory effects are not taken into account. Prior deposition of NH 3 and/or other components affects, for example, the acidity of water layers, the aerosol composition and the χ w and χ s concentrations.
For convenience, the model may be simplified to a strictly serial structure ( Figure 1b However, note that R * f can be negative in the case of emission fluxes, even though that is generally an ill-defined concept in a resistance modelling framework. R f is equal to the sum of R s and R w ; the derivation of expressions for χ f and R * f is straightforward and documented, for example, in Van Zanten et al. (2010). We here calculate χ f as and R * f as The reciprocal of any resistance is called the corresponding conductance, that is, Both are used throughout this text, since conductances are the more commonly used quantity in some disciplines which we borrow concepts from. They have the additional advantage of being directly (instead of inversely) proportional to the flux, as well as directly relatable to deposition velocities. Note that the units used in this context are sometimes inconsistent across communities: while micrometeorologists usually express conductances as length per time unit, plant physiologists tend to work with moles per area per second. We here follow the former convention unless specified otherwise. (1) (

| Stomatal controls and NH 3 -CO 2 coupling
The stomatal resistance to NH 3 exchange, or its inverse, the stomatal conductance G s (m/s), can be modelled using a number of different approaches: Most commonly, CTMs employ a multiplicative Jarvis (1976)-type scheme, such as the one of Emberson, Ashmore, Cambridge, Simpson, and Tuovinen (2000), which estimates the stomatal conductance as the product of a baseline resistance (or conductance) and a number of stress functions based on environmental factors (Flechard et al., 2013). Other authors use relatively simple light-and/or temperature-response functions in the absence of more detailed measurements, such as the one of Wesely (1989).
However, these models are usually not suitable to directly incorporate measurable effects of rising greenhouse gas concentrations and the physiological effects that are associated with them (Ainsworth & Rogers, 2007;Leakey et al., 2009). They also often rely on certain land-use-specific effective parameters to be used over a wide array of ecosystems that can be aggregated into one class, but do not incorporate site-specific effects other than meteorological conditions.
Finally, these models are usually used with ambient measurements of relative humidity, temperature and other environmental factors as input data, even though the actual flux-controlling conditions near the surface may very well be significantly different. While this weakness is not inherently built into the models' structure and they can theoretically be used with surface values of the respective variables instead, this may lead to bias when they were originally parameterized on ambient measurements. However, whether or not modelling these processes with surface variables is possible and meaningful strongly depends on an individual models' configuration, spatial resolution and degree of simplification of related processes.
One approach to avoid these issues and to incorporate as much information about a specific ecosystem into their models as possible is to rely on using measured H 2 O flux-based estimates of stomatal conductance (Shuttleworth, 2012). These, in turn, suffer from a number of uncertainties due to the non-trivial partitioning of measured evapotranspiration (ET) into evaporation (E) from wet surfaces and transpiration (T) through the stomata, which can be especially problematic at very humid sites where ground-based fluxes and loss of water from leaf surfaces are a significant part of ET. Additional bias may be introduced from 'wick-effects' due to hygroscopic particles lining the walls of the stomatal cavity, called 'hydraulic activation of stomata' in the recent literature (Burkhardt, 2010;Burkhardt, Basi, Pariyar, & Hunsche, 2012), which can lead to a decoupling of T and G s (Grantz et al., 2018).
We argue that these issues may largely be avoided by basing Additionally, CO 2 flux-based estimates of G s may be used as an interpretation tool for measured fluxes of gaseous compounds that are exchanged via the stomata, such as NH 3 or NO 2 .
We propose to use the well-known Ball-Woodrow-Berry model (Ball, Woodrow, & Berry, 1987) to derive G s from measured or modelled fluxes of CO 2 . It can be written as: where m (-) is the slope and b (mol m −2 s −1 ) is the offset (minimum stomatal conductance) of the Ball-Woodrow-Berry function. For C 3 plants, m and b are commonly assumed to be around 9 and 0.01 mol m −2 s −1 respectively (Collatz, Ball, Grivet, & Berry, 1991;Sellers et al., 1996).
Naturally these parameters are also subject to uncertainty, but we assume that the benefit of directly relating G s to photosynthetic activity instead of similarly uncertain parameterizations based on proxy variables outweighs this fact. h s is the leaf surface relative humidity (expressed as a fraction of 1) and C s (ppm) is the leaf surface concentration of CO 2 . The latter can be obtained through simple resistance modelling-based extrapolation from measured or modelled concentrations and fluxes at the reference height to the notional height of trace gas exchange. A n is net CO 2 uptake (µmol m −2 s −1 ). Lowercase g s in Equation (5) indicates that values obtained through this method are representative for leaf-level fluxes; bulk canopy G s can be obtained from an upscaling via measurements or modelled estimates of the leaf area index, as outlined in detail, for example, by Sellers, Berry, Collatz, Field, and Hall (1992) and Anderson, Norman, Meyers, and Diak (2000). To use it in an NH 3 inferential modelling context, the resulting bulk canopy G s needs to be scaled by the ratio of NH 3 to H 2 O molecular diffusivities.

| Site description and measurement setup
Fast-response measurements of CO 2 and NH 3 were carried out at a temperate ombrotrophic bog in North-western Germany the reader is referred to Hurkuck, Brümmer, and Kutsch (2016) and Zöll et al. (2016).   Wesely, 1989; E00: Emberson et al., 2000) and from eddy covariance fluxes of CO 2 using the Ball-Woodrow-Berry model (B87: Ball et al., 1987) Sellers et al. (1992). CO 2 net ecosystem exchange (NEE) was partitioned into gross primary productivity (GPP) and ecosystem respiration (R eco ) following Reichstein et al. (2005), as described in Hurkuck et al. (2016), and the resulting GPP was used as bulk canopy A n in the canopy-scale Ball-Woodrow-Berry model. G s obtained via this procedure was used to model fluxes of NH 3 using the parameterization of a two-layer canopy compensation point model after Massad, Nemitz, et al. (2010). Note that for semi-natural peatland sites like the 'Bourtanger Moor', the model is essentially reduced to a one-layer model by setting the ground layer resistance to infinity, due to the difficult partitioning of ground layer and other non-stomatal fluxes in unmanaged ecosystems. The minimum resistance and temperature response used in the non-stomatal resistance parameterization were recently reported to be likely too high for some sites . Thus, we derived site-specific values for these two parameters by assuming that foliar resistances derived from night-time flux measurements of NH 3 were representative for the non-stomatal resistance, R w , that is, assuming perfect stomatal closure at night.

| Reanalysis of observed NH
We then globally minimized the sum of squared residuals between measured and modelled non-stomatal conductance using a Python 3.7 implementation of the differential evolution method (scipy.opti-

| Results and discussion
Daily averages of stomatal conductance of NH 3 derived from CO 2 flux measurements were relatively constant until the last week of March 2014, after which they exhibited a strong and seemingly linear increase up to more than twice their initial magnitude, whereas a selection of empirical models (Emberson et al., 2000;Wesely, 1989) show an initial increase at the beginning of the measurement campaign (mid-February) and remain on a relatively low level below 0.1 cm/s with an only slightly positive trend (Figure 2c). At first glance, CO 2 -derived stomatal conductance does not appear to be correlated with the strong decrease in observed deposition velocity (Figure 2c), while empirically modelled stomatal conductance seems to be anti-correlated to a certain degree. That said, it is unlikely that the decrease in deposition velocities can be attributed to the stomatal pathway in a mono-causal manner. In fact, this decrease is also observed in night-time data, where stomatal fluxes are assumed to play a negligible role, and both observed night-time foliar conductance (as a proxy for the non-stomatal conductance) and site-calibrated modelled non-stomatal conductance decrease at the same time. This is further reflected in an increasing contribution of CO 2 -derived stomatal conductance to daytime foliar conductance from a minimum of around 20% up to more than 80%, which is apparently anti-correlated with observed deposition velocities (Figure 2d). Note that it follows from the governing equations of the resistance framework used in this study that this relation (G s G −1 f ) is approximately equal to the ratio of stomatal to total exchange flux when the compensation point is considerably smaller than the ambient NH 3 concentration.  (Hurkuck et al., 2014). Since the stomatal compensation point is expected to be dependent on historical N-inputs, it can reasonably be assumed to be significant at this site. To put it into context, the parameterization of Massad, Nemitz, et al. (2010) predicts a stomatal emission potential of 635 for this site, which is well above the average (mean 502, median 190) for short semi-natural and forest ecosystems found in an extensive literature review by the same authors. An increase in the contribution of the stomatal conductance to the foliar conductance directly leads to an increase in the contribution of the stomatal compensation point to the foliar compensation point (Figure 4a).

F I G U R E 3
Linear regression of observed daily mean daytime NH 3 dry deposition velocities against daytime ratio of CO 2 fluxderived stomatal conductance to total modelled foliar conductance. One outlier (v d > 1.5 cm/s on 25 February 2014) was removed from the regression data set. The shaded area envelopes a 95% confidence interval of the regression based on 10,000 bootstrap samples Assuming that the non-stomatal compensation point is zero, which is commonly done in modelling NH 3 exchange, this also directly leads to a reduced NH 3 concentration gradient and therefore a reduced deposition velocity. We thus conclude that the hypothesis of Zöll et al. (2016) regarding a reduction of the deposition velocity at least partially due to the onset of vegetation activity is justified and likely plays a significant role in the observed flux patterns, based on our reanalysis using CO 2 -derived stomatal conductance.
Theoretically, the relationship explaining this phenomenon is linear when non-stomatal fluxes are modelled unidirectionally: If the stomatal compensation point is twice the air NH 3 concentration, a 50% contribution of the stomatal conductance to the foliar conductance means zero gradient and therefore zero flux. This is irrespective of the magnitude of the aerodynamic and boundary layer conductance. However, note that taking these into account the relationship of an effective foliar resistance to the actual foliar resistance becomes non-linear between the extreme cases of zero compensation point or compensation point equal to the ambient concentration at the reference height (Figure 4b).
The main uncertainties in this approach can be attributed to three sources, apart from noise or systematic errors that affect all measurements: (a) Potential bias in the CO 2 flux partitioning algorithm.
The magnitude of GPP and thus of G s is naturally directly affected by this. Recent evidence suggests that both of the most commonly applied methods-the night-time method of Reichstein et al. (2005) and To our knowledge, no systematic effort at quantifying uncertainties in state-of-the-art NH 3 biosphere-atmosphere exchange models has been published in the recent literature.

| CON CLUS I ON S AND FUTURE PER S PEC TIVE S
We successfully demonstrated that a model-driven approach for flux data analysis using CO 2 flux-derived stomatal conductance can help reveal otherwise hidden processes. Simple regression-and  observation-based approaches only indirectly allowed the conclusions here drawn from a leaf-level analysis of drivers for the biosphere-atmosphere exchange of NH 3 at the 'Bourtanger Moor' field site . Yet, this case study is merely one example of how CO 2 flux data-based estimates of stomatal conductance can be used to improve our understanding of NH 3 biosphere-atmosphere exchange.
There is great potential in improving the predictive power of inferential models, both on the field-scale, as well as in spatially explicit modelling studies, and global change projections, by linking NH 3 and CO 2 models at this shared pathway using well-known and easy-toimplement modelling tools. Potential applications include, but are certainly not limited to: • Using CO 2 -derived stomatal conductances in a model-driven flux data analysis workflow to interpret direct flux measurements of NH 3 (as demonstrated in the case study).
• Coupling an NH 3 inferential and a photosynthesis model and using measured CO 2 data to validate the latter. This has recently been demonstrated in an NH 3 flux-partitioning study with the SURFATM-NH 3 model (Personne et al., 2009) by Hansen et al. (2017. • Improving the predictive capabilities for global change projections from large-scale CTMs by joining CO 2 , NH 3 and potentially other compounds' exchange submodules, for example, following the example of Anav, Menut, Khvorostyanov, and Viovy (2012) for O 3 , as recognized by Flechard et al. (2013).
• Retrofitting existing flux tower networks such as ICOS with lowcost, low-labour NH 3 measurements (e.g. with passive samplers).
Models for the non-stomatal pathway may be calibrated on shortterm measurements of night-time NH 3 fluxes acquired with a roving system, and using correction factors accounting for the lowered temporal resolution compared to fast-response analysers (Schrader et al., 2018). The stomatal pathway can be modelled by validating (or calibrating) a coupled photosynthesis-stomatal conductance model (e.g. Collatz et al., 1991) on the existing CO 2 measurements, giving a continuous data set of stomatal conductance independent of data gaps in the CO 2 eddy covariance setups.
To achieve optimal suitability for local air quality and global change studies alike, future research should strive towards a more mechanistic representation of all biosphere-atmosphere exchange pathways. This is not limited to physiological controls, but also potential chemical interactions (e.g. Flechard et al., 1999). Long-term simultaneous micrometeorological measurements of both greenhouse gas and reactive nitrogen exchange across a wide range of ecosystems are desperately needed to further develop valid frameworks for modelling interrelations between them, and to accurately identify areas where action is necessary to mitigate negative effects of excess nitrogen deposition.