Edinburgh Research Explorer Measurement and modelling of the dynamics of NH3 surface-atmosphere exchange over the Amazonian rainforest

. Local and regional modelling of NH 3 surface exchange is required to quantify nitrogen deposition to, and emissions from, the biosphere. However, measurements and model parameterisations for many remote ecosystems—such as tropical rainforest—remain sparse. Using one month of hourly measurements of NH 3 ﬂuxes and meteorological parameters over a remote Amazon rainforest site (Amazon Tall Tower Observatory, ATTO), six model parameterisations based on a bi-directional, single-layer, canopy compensation point resistance model were developed to simulate observations of NH 3 surface exchange. 5 Canopy resistance was linked to either relative humidity at the canopy level ( RH z 0 0 ), vapour pressure deﬁcit, or a parameter value based on leaf wetness measurements. The ratio of apoplastic NH +4 to H + concentration, Γ s , during this campaign was inferred to be 38.5 ± 15.8. The parameterisation that reproduced the observed net exchange of NH 3 most accurately was the model that used a cuticular resistance ( R w ) parameterisation based on leaf wetness measurements and a value of Γ s = 50 (Pearson correlation r = 0.71). Conversely, the model that performed the worst at replicating measured NH 3 ﬂuxes used an 10 R w value modelled using RH z 0 0 and the inferred value of Γ s = 38.5 ( r = 0.45). The results indicate that a single layer, canopy compensation point model is appropriate for simulating NH 3 ﬂuxes from tropical rainforest during the Amazonian dry season, and conﬁrmed that a direct measurement of (a non-binary) leaf wetness parameter improves the ability to estimate R w . Current inferential methods for determining Γ s were noted as having difﬁculties in the humid conditions present at a rainforest site. precipitation ( ≥ 0.1 mm rainfall per hour), the leaf is considered fully wet and the raw signal from the sensor is at a maximum value. During prolonged dry periods the leaf is considered to be dry, and the lowest recorded conductivity of the sensor pair during these periods is designated as a “zero signal”. The net signal from each sensor pair is determined by subtracting the corresponding zero signal from the raw signal for each period of data considered. The cumulative time period of precipitation is then determined from rainfall measurements. For 220 this study, precipitation occurred during 15% of the total campaign time. Consequently, the signal percentile for each sensor that represents periods of precipitation was 85% in this study. Finally, the zero corrected net signals are divided by the value of signal percentile to give a leaf wetness parameter (LWP) whose values range from 0 (dry) to 1 (wet).


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The global cycling of nitrogen is of critical importance to Earth's biogeochemistry. One of the major contributors to the global atmospheric reactive nitrogen (N r ) budget is ammonia (NH 3 ), which is primarily generated from anthropogenic sources (Galloway et al., 2003). The emission of NH 3 , and the subsequent deposition of NH 3 or other forms of reactive nitrogen, have impacts on terrestrial and marine ecosystems (Erisman et al., 2013). In particular, forests can be impacted through changes to N input in several ways. Fowler et al. (2013) detail how increased deposition of N can lead to increased vegetation growth rates in 20 forests, leading to potentially greater carbon sequestration rates. This potential positive impact, however, is offset by the effect Increasingly complex models include further pathways of exchange (Kruit et al., 2010), with the most important for the current study being the canopy compensation point model, initially proposed by Sutton et al. (1995), which incorporates two parallel pathways of exchange at the canopy level ( Figure 1). In the first pathway, a stomatal compensation point (χ s ) is introduced, which represents the concentration of NH 3 in the leaf stomata in (temperature dependent) equilibrium with the NH + 4 and pH of the apoplastic fluid. This stomatal compensation point controls the exchange of NH 3 to and from the canopy 60 to the leaf stomata, together with the associated stomatal resistance (R s ). In the parallel pathway, a unidirectional deposition flux is modelled from canopy to the leaf cuticle, with a separate cuticular resistance (R w ) controlling deposition. In a modified version of this model (the cuticular capacitance model), the leaf cuticle is considered to be both a sink and source for NH 3 (Sutton et al., 1998). Here, the ability of water films on the leaf cuticle surface to act as a storage of previously deposited NH 3 is introduced as an analogue of an electrical capacitor, with emission fluxes of NH 3 from the cuticle possible with the evaporation of "charged" water films. Further models include ones which simulate the potential for soil and leaf litter below canopy to act as emission sources of NH 3 (Nemitz et al., 2000;Sutton et al., 2009). Using this existing model framework of NH 3 surface Figure 1. Schematic of the canopy compensation point model of Sutton et al. (1995). Ft, Fs, and Fw, are, respectively, the total, stomatal, and cuticular fluxes of NH3; Ra, R b , Rw, and Rs, are, respectively, the aerodynamic, quasi-laminar boundary layer, cuticular and stomatal resistances; and χa, χc, and χs are, respectively, the atmospheric concentration of NH3, the canopy compensation point, and the stomatal compensation point.
exchange, in combination with new NH 3 flux and meteorological data measured at a remote, tropical rainforest site, this study aims to present a series of local model formulations forχ s and R w which accurately simulate the bi-directional fluxes of NH 3 observed by Ramsay et al. (2020), with focus on the most suitable control metric for R w . Statistical comparison between models 70 diffuses through the laminar air flow onto the sorption solution coating the walls of the WRD, and the solution is subsequently transported to the detector box at ground level for analysis.
The detector box contains a flow injection analysis unit (FIA) based on a selective ion membrane to analyse the concentration of NH 3 within the WRD samples. WRD samples are fed to the FIA unit, where NaOH (0.1 M) is first added to the sample to form gaseous NH 3 . The gaseous NH 3 then passes through a semi-permeable polytetrafluoroethylene (PTFE) membrane 110 to enter a counterflow of DDI water to re-form NH + 4 . The temperature-corrected conductivity of NH + 4 is then measured in the conductivity cell of the FIA unit, from which the atmospheric concentration of NH 3 at the height from which the sample was drawn can be determined. Through a valve control system within the detector box, the WRD sample from each height is analysed for NH 3 by FIA once per hour, resulting in an hourly-resolved concentration gradient of NH 3 . The FIA unit is calibrated autonomously using three liquid NH + 4 solutions (0, 50, and 500 ppb NH + 4 concentration), with the first calibration 115 conducted 24 h after the GRAEGOR begins measurements, and every 72 h afterwards. Fresh standards were prepared prior to each calibration. A total of 10 autonomous calibrations were conducted during this campaign.

Meteorology
Wind speed (u), wind direction (wd), friction velocity (u * ) and sensible heat flux were measured via eddy covariance by a Gill Windmaster mounted at 46 m on the 80 m walk-up tower. Relative humidity and air temperature were measured at 22 m, 120 36 m and 55 m using a series of Campbell HygroVUE™5 Temperature and Relatively Humidity Sensors. Net radiation and photosynthetically active radiation were measured at 75 m by, respectively, a net radiometer (Kipp and Zonnen NR-LITE2) and a quantum sensor (Kipp and Zonnen PAR LITE). Hourly rainfall was measured using a HS Hyquist TB4-L.

Modified Aerodynamic Gradient Method
In the constant flux layer over homogeneous surfaces, the flux of a chemical tracer χ can be determined using the aerodynamic 125 method (AGM) if the vertical concentration gradient of χ and its diffusion coefficient are known (Foken, 2008). A modified form of the AGM, based on the vertical concentration difference (∆ c ) between measurements of NH 3 at 42 m and 60 m, a series of stability parameters determined from meteorological measurements, and u * as measured at 46 m by eddy-covariance (Flechard, 1998), was used to determine the flux of NH 3 as: where κ = 0.41 is the von Kármán constant and d is the zero-plane displacement height, determined as 0.9h c = 33.4 m. The integrated form of the heat stability correction term, Ψ H , is included to account for deviations from the log-linear wind profile, while the term (z-d)/L is a dimensionless measure of atmospheric stability, where L is the Obukhov length.
The aerodynamic gradient method strictly holds for measurements made within the inertial sublayer. Corrections must be applied to fluxes calculated using the AGM if measurements are made close to the canopy, within the roughness sublayer, as 135 was the case in this study. Fluxes were corrected using a correction factor, γ F , whose magnitude was determined from the stability conditions present at the time of measurement (Chor et al., 2017). The validity of this correction was confirmed via the flux measurements of HNO 3 and HCl by Ramsay et al. (2020).

Canopy Resistance Method
The basic resistance model that describes deposition to a non-perfectly absorbing surface approximates the ability of the surface 140 to regulate NH 3 deposition through a canopy resistance, R c , which can be calculated from the difference between (a) the total resistance towards deposition (i.e., the inverse of the deposition velocity (V d ) of NH 3 at a reference height) and (b) the sum of the atmospheric aerodynamic resistance, R a , and the quasi-laminar boundary layer resistance, R b , Fowler and Unsworth (1979); Wesely et al. (1985): 145 R a and R b can be determined from Eq. (3) and (4), respectively (Garland, 1977): where B is the sublayer Stanton number (Foken, 2008). However, this canopy resistance approach can only successfully 150 be applied if there is no bi-directional exchange. Since both emission and deposition of NH 3 was observed in this study, a bi-directional exchange model was required to simulate surface atmosphere exchange of NH 3 . The simplest bi-directional exchange model for NH 3 is the static canopy compensation point (SCCP) model ( Figure 1) in which the exchange between the canopy and the atmosphere is controlled by a conceptual canopy compensation point (χ c ).
In this SCCP model, the total surface-atmosphere exchange of NH 3 (F t ) is the sum of two constituent fluxes, the unidirec-155 tional deposition of NH 3 to the cuticle surface (F w ), and a bidirectional flux of NH 3 through the leaf stomata (F s ) (Sutton et al., 1995): where For the stomatal exchange flux, the difference between the notional mean concentration at canopy height, the canopy compensation point concentration (χ c ), and the stomatal compensation point concentration (χ s ) provides the numerator on the right-hand-side term in Eq. (7). When χ s exceeds χ c , emission occurs. χ s is proportional to the ratio of dissolved NH + 4 to 165 H + in the leaf apoplast, which represents a dimensionless emission potential (Γ), via a temperature function that describes the combined Henry solubility and dissociation equilibrium (Nemitz et al., 2004): Here T is the temperature of the canopy in K.
The stomatal resistance, R s , is primarily dependent on global radiation (S t ), with additional potential influences from factors 170 such as temperature, vapour pressure deficit, and leaf and root water potentials. Here the generalised function for bulk stomatal resistance as per (Wesely, 1989) with the parameters recommended for tropical vegetation is used to calculate the stomatal resistance for NH 3 (R s (NH 3 )): where R i represents the minimum bulk resistance stomatal resistance for water vapour (for deciduous forest during summer:

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R i = 70 s m −1 ); S t is the global radiation in W m −2 ; and T z 0 is the temperature in • C at the mean canopy height.
This parallel cuticular pathway in the SCCP model treats the flux to the leaf cuticle (F w ) to be unidirectional to a perfectly absorbing sink, given by the ratio of the canopy compensation point (χ c ) and the cuticular resistance (R w ). R w has been described successfully by a number of empirically derived parameterisations in various studies as outlined by Massad et al. (2010), with most using either relative humidity or water vapour pressure deficit as proxies for the ability of NH 3 to absorb to 180 the leaf surface. The term R w is discussed further in Section 3.4.
The canopy compensation point (χ c ) is the conceptual mean concentration of NH 3 inside the canopy, at which the stomatal, cuticular and above-canopy fluxes balance each other. It is therefore dependent upon the ambient concentration of NH 3 (χ a ) and various physical and chemical parameters, both on the surface of the leaf and the surrounding atmosphere, as described by the resistances (stomatal, cuticular, aerodynamic and quasi-laminar boundary layer) and the stomatal compensation point 185 previously described. In this study, χ c was calculated as: Prompted by the observation of morning emissions of NH 3 which could not be explained by stomatal exchange alone, this model was further extended by Sutton et al. (1998) to account for bi-directional exchange with leaf surfaces, by allowing NH 3 to be absorbed and desorbed to/from leaf water layers. The extended model calculated the NH 3 holding capacity by estimating 190 the leaf water amount in relation to RH, which was implemented into the resistance framework by analogy to an electric capacitor, the charge of which depended dynamically on previously deposited NH 3 and tended to be released as dew dried out in the morning. Similarly, Nemitz et al. (2001) extended the model by a second model layer to describe additional exchange with the ground level or soil.

Determination of concentrations and meteorological parameters at the aerodynamic mean canopy height
The aerodynamic resistance R a and the quasi-laminar boundary layer R b can be used to determine the temperature and NH 3 concentration at the aerodynamic mean canopy height, z 0 , if their respective values at a reference height are known : 200 The relative humidity at z 0 can be determined if the saturation pressure at z 0 (ε sat (z 0 )) and the water vapour pressure at z 0 (ε (z 0 )) are known: From measurements of T z 0 and RH z 0 , the vapour pressure deficit (VPD) in kPa was determined.

Leaf Wetness Measurements
Leaf surface wetness was measured using a sensor array as described in Sun et al. (2016), which was based on the design by Burkhardt and Eiden (1994). Six sensors arranged in pairs of two, each consisting of gold-plated electrodes arranged as a clip, were each attached to a leaf situated 27 m above ground level and within the canopy surrounding the 80 m walk-up tower. Each clip provided a measurement in mV that was related to the electrical conductivity between the two electrodes. Data 210 were recorded using a Raspberry Pi Model 2 B (Raspberry Pi Foundation, Cambridge) at a temporal resolution of one minute.
The sensor array was checked daily to ensure good contact between the clips and the leaf. Leaf wetness was measured from 6 October to 5 November 2017. Unlike conventional (binary) wetness grid sensors, this approach provides some gradation between fully dry and fully wet canopies.
Raw values from each sensor pair were converted to a leaf wetness parameter value, ranging from 0 to 1, according to the 215 methodology outlined by Klemm et al. (2002). During periods of significant precipitation (≥0.1 mm rainfall per hour), the leaf is considered fully wet and the raw signal from the sensor is at a maximum value. During prolonged dry periods the leaf is considered to be dry, and the lowest recorded conductivity of the sensor pair during these periods is designated as a "zero signal". The net signal from each sensor pair is determined by subtracting the corresponding zero signal from the raw signal for each period of data considered. The cumulative time period of precipitation is then determined from rainfall measurements. For 220 this study, precipitation occurred during 15% of the total campaign time. Consequently, the signal percentile for each sensor that represents periods of precipitation was 85% in this study. Finally, the zero corrected net signals are divided by the value of signal percentile to give a leaf wetness parameter (LWP) whose values range from 0 (dry) to 1 (wet).
3.1 Temperature, relative humidity, VPD and LWP at canopy

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The time series of calculations of T z 0 , RH z 0 and V P D z 0 , together with measurements of the leaf wetness parameter, are shown in Figure 2. The measurements can broadly be split into four distinct periods of warmer, drier conditions and cooler, wetter conditions. Period One, from 6 to 18 October, is typified by an average leaf wetness at the canopy of 0.7, with an average RH of 82%, suggesting the prevalence of humid, wet conditions. Period Two extends from 19 to 25 October, where leaf wetness at the canopy decreases, while VPD increases, which is paired with a drop in average RH. Conditions resume the same pattern as 230 Period One during Period Three, which lasts between 26 October and 1 November, but gives way to drier, warmer conditions (Period Four) from 2 November until the end of the campaign. A distinct lag exists between the relative humidity at the canopy level and the leaf wetness measurements, particularly during the drier conditions from 19 to 25 October. RH minima, which occur on average between 11:00 and 13:00, are not reflected in leaf wetness measurements until several hours later. Minima leaf wetness measurements during this period are recorded between 13:00 and 16:00.  Relative humidity appears to be a somewhat stronger driver of NH 3 surface exchange behaviour (R 2 = 0.08; p = 3.98 × 10 −4 ) than temperature. The slope and density contours suggest that emissions are more likely as relative humidity decreases. The strongest predictor of the three meteorological parameters investigated is the leaf wetness parameter (R 2 = 0.19; p = 2.72 × 10 −5 ). Emissions predominately occur during periods when leaf wetness parameter values fall below 0.5, with deposition occurring predominately during periods when the leaf surface is wet (>0.6) or completely saturated (1).

Determination of stomatal compensation points and emission potentials
One of the elements of modelling of NH 3 flux through the static canopy compensation point model is the stomatal flux (F s ), which, from Eq. (7), depends on the canopy concentration of NH 3 (χ c ) and the stomatal compensation point (χ s ). The value of χ s is determined by the leaf surface temperature (in this study, taken as T z 0 ) and the apoplastic ratio (Γ s ). If Γ s is known, which varies with vegetation type (Hoffmann et al., 1992;Mattsson et al., 2009), environmental stressors such as drought 255 (Sharp and Davies, 2009) and nitrogen nutrition (Massad et al., 2008), then χ s and subsequently F s can be modelled. The fact that emissions at this site regularly occurred during midday (when T z 0 is at its maximum) and were related to drier, warmer conditions ( Figure 4) is consistent with the emission flux originating from the stomata.
Γ s can be inferred from measurements during conditions where the NH 3 surface exchange is judged to be dominated by stomatal exchange, with a negligible contribution from desorption of NH 3 from the leaf surface.

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Under conditions where R w is very large compared with R s , the ambient NH 3 concentration (χ a ) at which a zero net flux occurs (i.e., when the difference between χ c and χ s is 0) is implicitly equal to χ c and χ s . Therefore, if NH 3 surface exchange is driven by stomatal exchange, χ s may be determined from the values of χ a at which the flux changes from deposition to emission, or vice versa (Nemitz et al., 2004). Figure 5 presents the ambient NH 3 concentrations measured during the campaign at which such flux sign changes occurs as a function of T z 0 , for conditions under which R w is expected to be fairly large (RH 265 < 60%). Eq. (8) can therefore be rearranged to give an expression for Γ s that is dependent upon T z 0 and χ s , where χ s can be substituted with a value of χ a at which a sign change in the flux of NH 3 occurs: Using the values of χ a measured in this campaign that are inferred to be equal to χs, the apoplastic ratio applicable to the period of measurement was determined as 38.5 ± 15.8. Also shown in Figure 5 is the temperature response curve of χ s consistent 270 with this value of Γ. Consequently, modelled values of χ s based on a value of Γ s = 38.5 were determined for the campaign period, and subsequently used to determine values of χ c and total modelled flux. As this value resulted in an under-prediction of the peak emissions, an alternative, enhanced value of Γ s = 50 was also explored to develop further parameterisations for comparison. Furthermore, with this approach, all emissions from the leaf surface are implicitly considered to originate from leaf stomata, rather than cuticular desorption or other potential sources of NH 3 emissions, such as soil or leaf litter.

Determination of Rw parameterisations based on three alternative proxies for leaf water volume
Considering the observed drivers for NH 3 surface exchange discussed in Section 3.2, three different parameterisations for the cuticular resistance R w were developed for this study, based upon three alternative proxies of the NH 3 holding capacity of the leaf water layers: RH z 0 , V P D z 0 , and leaf wetness. Subsequently, each parameterisation of R w was used to develop three distinct values for F w , the unidirectional flux component of the cuticular-resistance-based single-layer model, each describing 280 the surface atmosphere exchange of NH 3 at the ATTO site.
The first parameterisation was based on measurements of RH z 0 using the following equation (Sutton et al., 1993): Here, α determines the minimum cuticular resistance (which is α = 1 s m −1 ), while β 1 is a constant scaling coefficient controlling the increase of R w with decreasing relative humidity. The coefficients α and β 1 were fitted by least-squares optimisation 285 between total modelled and observed values of NH 3 flux taken during the campaign to arrive at values of α = 2 s m −1 and β 1 = 9, which were used for modelling R w based on RH z 0 for the entirety of the campaign. The second parameterisation was based on measurements of the vapour pressure deficit, using a formulation for R w based upon that employed by Flechard et al. (1999):

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As with the parameterisation of R w in Eq. (15), the coefficient α is the minimum value for R w at zero VPD, set at 2 s m −1 .
β 2 and γ 1 are constant scaling coefficients which, respectively, control the scaling of the exponential term and the scaling of the vapour pressure deficit response. Through least-squares optimisation, a value of 5 was chosen for β 2 and 1.7 for γ 1 , for the determination of R w based on Eq. (16) for the entirety of the campaign.
Finally, a novel parameterisation for R w based upon measurements of leaf wetness was developed for this campaign based 295 on least-squares optimisation: As with the parameterisations of R w described in Eq. (15) and (16), α is the minimum value of R w at maximum leaf wetness, set at 2 s m −1 , β 3 is a scaling coefficient, similar to that of the parameterisation in Eq. (16), set at a value of 5, and γ 2 is a scaling coefficient controlling the increase in R w with the decrease in leaf wetness, set in this study to 4.8. With this parameterisation, 300 R w approaches αfor a fully wet canopy and is capped at R w = 605 s m −1 for a fully dry canopy.

Temporal dynamics
The observed bidirectional surface exchange of NH 3 from a remote tropical rainforest site was modelled using a series of canopy compensation point, cuticular resistance based models using a variety of different R w parameterisations and apoplastic 330 ratios.
As highlighted in the Introduction, measurements of NH 3 surface exchange over natural ecosystems such as forests remain sparse. This is particularly true for measurements over remote environments such as tropical vegetation. To our knowledge, there have not been any direct flux measurements over tropical vegetation to date; although Trebs et al. (2004) and Adon et al. (2010; derived fluxes from concentration measurements. Exchange of NH 3 has been measured previously at temperate 335 forest sites and reported to be bi-directional: for example, Langford and Fehsenfeld (1992)  When using models to determine the drivers of surface exchange above forest sites, these studies often stress the importance of 340 cuticular desorption as a further process that dominated in the morning when emission could not have originated from stomatal compensation points. Indeed, in the case of Neirynck and Ceulemans (2008), the static canopy compensation point model (SCCP) was unable to simulate their observed emissions.
At ATTO, there is no indication that the single layer SCCP model was unable to reproduce the temporal dynamics of the measured NH 3 surface exchange. Indeed, an exploratory application of the dynamic CCP model did not result in an 345 improvement in model performance and therefore the modelling work here focused on the static model as a simpler approach able to reproduce the measurements. The absence of morning desorption peaks at the ATTO forest is likely due to the small night-time adsorption of NH 3 into leaf water layers associated with the low night-time NH 3 concentrations at this site. Dry deposition of aerosol ammonium nitrate (NH 4 NO 3 ) is another source of volatile NH + 4 on leaf surfaces, and concentrations of this compound are again typically very small in Amazonia (Wu et al., 2019). In addition, given the high RH, the water layers 350 may not dry out as rapidly and completely as at other sites. The measured median NH 3 atmospheric concentration at the canopy height during the measurement period was 0.23 µeq m −3 , with an estimated annual total reactive N dry deposition input of 1.74 kg N ha −1 yr −1 (Ramsay et al., 2020). This is far lower than reported by Neirynck and Ceulemans (2008) and by Wyers and Erisman (1998), both of whose sites were subject to high levels of agricultural pollution. As noted by Massad et al. (2010) and Zhang et al. (2010), higher atmospheric inputs of N to forest systems lead to an increase in the stomatal emission potential.

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Conversely, with lower atmospheric NH 3 concentrations, the potential for forests to act as a source of NH 3 is increased, as the likelihood of the canopy compensation point exceeding the ambient concentration increases. The low N status of the tropical vegetation may also favour transfer of N absorbed to the cuticle into the leaf, e.g., via liquid films that extend from the cuticle into the stomata (Burkhardt et al., 2012).
In general, the fluxes measured at ATTO could also be reproduced without including a further soil layer, potentially with 360 one exception (see below). Such a layer is needed where night-time emissions are observed that are clearly not under stomatal control (Nemitz et al., 2000;Hansen et al., 2017).
The consistently warmer noon-time conditions at the leaf canopy during measurements at the ATTO site would also favour stomatal exchange. An increase in leaf temperature leads to greater gas exchange through increased stomatal openings Urban et al. (2017), while alterations to the Henry and dissociation equilibria would lead to a change in the stomatal compensation 365 point favouring increased stomatal emissions. Similarly, the unstable conditions at noon above the canopy over tropical rainforest leads to reductions in R a , which would increase any emissions occurring at the time that were driven by stomatal exchange (Flechard et al., 2015). In the study of forest NH 3 emissions that is most similar in ambient NH 3 concentrations, canopy compensation points and apoplast ratios to this study, Hansen et al. (2017) comes to a similar conclusion on the observed daytime emissions from a remote, temperate forest in Indiana, USA.

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Despite the low N inputs and apoplastic NH + 4 /H + ratio, significant emission periods were observed above the ATTO site. One driver is clearly the high daytime leaf temperature. Nevertheless, over infinitely large areas and in the absence of other sources and sinks, the concentration in the air should adjust to the emission potential of the terrestrial landscape and, once this equilibrium is established, fluxes should go to zero. This argument has been used to assume that oceanic NH 3 emissions should be small. The observed flux dynamics of emission and deposition above the Amazon rainforest therefore suggest that 375 such steady state equilibrium is not reached. The average flux amounted to a small deposition of ¬2.8 ng m −2 s −1 suggesting that, on average, the site receives more N as NH 3 than it loses. Possible sources include small-scale farming and biomass burning.

Apoplast Ratio
The apoplastic ratio of NH + 4 /H + (Γ s ) inferred from the measurements in this study was 38.5 ± 15.8; the models investigated The disparity in the emission potentials between other forest sites and the tropical rainforest site at ATTO is again linked to nitrogen input. With larger N inputs where nitrogen is deposited in excess, the stomatal concentration is increased (Schjoerring et al., 1998). Consequently, at polluted areas such as the forest sites studied by Neirynck and Ceulemans (2008), apoplastic 390 ratios are increased, while at sites with lower N input, such as semi-natural vegetation with low ambient NH 3 concentrations (Hanstein et al., 1999), values of Γ s can be as low as 5-10. The species of vegetation is also critical  with plants which are reliant on mixed nitrogen sources (ammonium, nitrate, and organic N) and which are more reliant on root rather than shoot assimilation of nitrogen, exhibiting lower apoplast ratios than nitrate reliant, shoot assimilating species (Hoffmann et al., 1992). While the N source has not been established for the tree species constituting the canopy layer at the 395 ATTO site, a nitrogen-poor soil substrate would potentially impact on overall apoplastic ratio through diminished intracellular NH + 4 concentrations. Considering this possibility, the value of 38.5 which was inferred from measurements lies comfortably in the range of Γ s values exhibited by semi-natural vegetation with low N inputs, and in the lower range of overall forest values quoted by Massad et al. (2010).

Model Performance with respect to R w parameterisation 400
An assessment of the performance of the individual parameterisations against calculated NH 3 fluxes is included in Figure   6, which displays the results of simple linear regression models for the simulated values of each NH 3 flux model against observed NH 3 fluxes. With regards to the Pearson correlation coefficient (r), the rank of models from most strongly correlated with observed NH 3 fluxes to least correlated is model b, model a, model f, model e, model d, model c. The R w parameterisation was a stronger determinant of model-measurement correlation than the choice of Γ. Correlation with measurements is highest 405 for the models using an R w based upon LWP, followed by those which use VPD and finally RH. Within each grouping, models statistical metrics visualised in Figure 7 are summarised in Table 2 Therefore, from these values and the ability of the parameterisations to reproduce the measured average fluxes (Table 1) it can be concluded that parameterisation b, in which the value R w is parametrised using leaf wetness parameter values and where the apoplastic ratio is set to 50, is the best performing model in simulating NH 3 surface-atmosphere exchange at the ATTO site,  empirical, it is not surprising that it appears to reflect the actual leaf water amount more closely than the proxies via VPD and RH. All three parameters should be closely linked. Even after optimisation of the models, however, extensive differences in model output remain, principally between leaf wetness parameter and RH. Figure 8 presents a scatter plot of leaf wetness measurements against RH normalised to the canopy height. The relationship between them is best described through a power 425 equation, which suggests that leaf wetness decreases more sharply than RH across the campaign. Indeed, Figure 2 shows a distinct lag between observed RH (as well as VPD) and the leaf wetness parameter. While RH minima are detected between 11:00 and 13:00, and ranges in a fairly narrow band between 100% and 80%, leaf wetness reaches minima between 13:00 to 16:00, and can decrease significantly, particularly during Period Two of the campaign. Overall, the results indicate that there is significant value for interpreting field measurements in making direct measurements of leaf wetness using leaf wetness clip 430 sensors of the type used here. However, such a parameter is not typically available in chemistry transport models, in which case the results here would favour VPD-based parameterisations over RH based parameterisations.

Model Performance with respect to the choice of stomatal emission potential
As is visually apparent in Figure 7, the influence of the apoplastic ratio is relatively minimal for reproducing flux variability in comparison to the effect of R w parameterisation over the Γ s range explored (38.5 to 50). However, the choice of Γ does affect 435 the model's ability to reproduce the overall magnitude of the fluxes during daytime ( Table 2).
Models that used the Γ s value of 50 (b, d and f) simulated values better in agreement with observations in comparison to their paired R w models (respectively, a, c, and e) which used the value of 38.5. In particular, the use of 38.5 as a value led to models underestimating the scale of the emissions.
The discrepancy highlights a potential problem with using the method of inferring Γ s as outlined in Section 3.3 in tropical 440 conditions. As outlined by Nemitz et al. (2004), the validity of equating χ a to χ c only holds for dry conditions (e.g. RH < 50%), when R w can reliably be expected to be large. At higher humidity values, leaf cuticles may start to become a small sink and χ c becomes an underestimate of χ s . At the ATTO site, where median humidity at the canopy level throughout the campaign was 87%, with only a few occurrences during the drier Periods Two and Four where it fell below 60%, this approach of inferring Γ s from NH 3 measurements was likely affected. However, the impact does not appear to have completely invalidated the use 445 of the method, as the somewhat larger value of 50 that resulted in models with best agreement still lies within one standard deviation of the inferred Γ s value. However, while suitable for this campaign in modelling NH 3 surface exchange, the need for an accurate determination of apoplastic ratio for tropical rainforest remains an important concern, particularly for larger scale surface exchange models.

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Modelled values diverge significantly from observations at several points during the campaign. In particular, on 30 October every model predicts an earlier, less sustained emission in comparison to the observation, while on 2 November, no model predicts any emission, contrary to observations, which suggest a strong emission of NH 3 from 13:00 to 15:00. With regards to the divergence in models from the observations on 2 November, the possibility of other sources of NH 3 emission could be considered that would not be accounted for using the single layer model. For example, from the evening of 31 October to the 455 early morning of 2 November, heavy periods of precipitation were recorded, coupled with increased deposition fluxes of NH 3 on 1 November. Increased wet deposition of N through NH + 4 in rainwater and washed from the canopy (Nemitz et al., 2000) to the forest floor or the higher soil moisture itself could have led to an increase in soil or leaf litter microbial activity below canopy. Subsequent drying of the soil and leaf litter throughout 2 November might have led to an evaporation of NH 3 from the litter or soil layer from the forest floor (Hansen et al., 2017), leading to observed emissions of NH 3 in the afternoon. This 460 potential scenario would not be modelled with the single layer canopy resistance model, and consequently models would not capture this source of emission.
Average modelled values for daytime tended to agree better with their corresponding period of observations than night-time values. Overall, the six models tended to overestimate nocturnal NH 3 deposition, particularly during Period Two and Four when all six models overestimated the average deposition by more than 25% from the corresponding average observations. Of 465 course, the flux measurement itself is not without error, especially during the calmer and more stable night-time conditions.
Observations of the bi-directional surface-atmosphere exchange of NH 3 at a tropical rainforest site have been successfully replicated using a static single-layer resistance model. Application of a capacitance model that additionally incorporates the process of cuticular desorption did not lead to improved model results, suggesting that the emission periods were under stomatal 470 control. This is in contrast with past studies above temperate forests in areas with high ambient NH 3 concentrations where clear desorption events were observed following sunrise. Models that used a single layer canopy resistance approach, where the cuticular resistance was governed either by RH, VPD or a measurement of leaf wetness, were able to replicate the pattern of observed NH 3 deposition with frequent periods of afternoon emissions. Of all the models used, the most successful was a cuticular resistance modelling approach based on using leaf wetness measurements, and where modelled χ c was governed by 475 an apoplast Γ = NH + 4 /H + ratio of 50, somewhat larger than the mean inferred from the measurements. The periods when the most frequent emissions of NH 3 occurred, and which were most successfully modelled by cuticular resistance models, are typified by conditions that diverge from the overall expected climate, i.e., above-average temperatures, and below average relative humidity. This campaign took place in the dry season, and so comparison with the surface exchange of NH 3 during the wet season would be a necessary first step in determining if stomatal exchange is the principal driver of NH 3 480 surface exchange throughout the year. Long-term observations would also be required to determine whether the temperature increases, drought conditions and elevated ambient NH 3 concentrations that are anticipated from climate change and human development over this region have any impact on NH 3 surface exchange; and whether prolonged reactive nitrogen input from biomass burning activities raise compensation points.
One outcome of this study has been to establish the suitability of leaf wetness measurements, converted to a suitable pa-485 rameter, as a factor for modelling cuticular resistance in NH 3 surface exchange modelling. Leaf wetness measurements, albeit from wetness grid sensors, have been used previously in NH 3 modelling, but these were first converted to an associated value of RH before being used in RH-based R w parameterisations. Using leaf contact sensors, this study demonstrates that leaf wetness can be used directly, with a R w parameterisation that here proved to be the most sensitive and accurate in simulating cuticular NH 3 exchange. However, VPD may be the parameter of choice for chemistry transport models because it is more 490 readily simulated.
A Γ value of 50 led to the best modelling of χ c values, and hence to the best fit with observed values. While within one standard deviation from the initially inferred value of 38.5, this did highlight that the method used to infer apoplastic ratio perhaps suffered under the high humidity conditions present at the rainforest site. An accurate determination of emission potential for this region is required for global scale modelling, necessitating accurate measurements of apoplast ratio. Future studies of 495 NH 3 surface exchange above rainforest should therefore seek to incorporate accurate determinations of leaf apoplastic ratio as a necessary part of their methodology.
Some periods of divergence between the models and observed values highlight that other sources of NH 3 surface exchange (such as soil or leaf litter exchange) should be incorporated into future investigation, while also emphasising the difficulty in measuring and modelling NH 3 surface exchange in remote, challenging conditions. A complete understanding of NH 3