Measurements were conducted on an 80 m walk-up tower located at the Amazon Tall Tower Observatory site (2∘ 08.637′ S, 58∘ 59.992′ W). The Amazon Tall Tower Observatory (ATTO) site lies on a level plateau 120 m above sea level and is situated within a region of dense, undisturbed terra firme rainforest, with a mean canopy height of 37.5 m . The nearest large urban centre, Manaus, Brazil, is located 150 km to the south-west. A full description of the ATTO site, its permanent instrumentation, and the floristic composition of the surrounding rainforest is given in .

The rainforest extends homogenously for many hundreds of kilometres to the north and east but gives way to shrub forest (campina) 5.5 km to the south, where the plateau descends to meet the Uatumã River. The flux fetch requirement for these gradient measurements with a geometric mean height of 50.2 m as determined from the approximation given by is 5.2 km. Therefore, NH3 fluxes can be considered representative of a homogeneous rainforest. During convective daytime conditions, the flux footprint is much shorter, typically < 2 km.

Measurements were made between 6 October and 5 November 2017, during the region's dry season. Lasting typically from August to November, the dry season is characterised by warmer, drier conditions in comparison to the wet season, which lasts from February to May. Air masses that arrive at the site during the dry season typically travel over some urban and agricultural areas located to the south and south-east of the site, which can give rise to periods of elevated black carbon (BC) and carbon monoxide (CO) concentrations .

In the constant flux layer over homogeneous surfaces, the flux of a chemical tracer χ can be determined using the aerodynamic method (AGM) if the vertical concentration gradient of χ and its diffusion coefficient are known . A modified form of the AGM – based on the vertical concentration difference (Δc) between measurements of NH3 at 42 and 60 m, a series of stability parameters determined from meteorological measurements, and u* as measured at 46 m by eddy covariance – was used to determine the flux of NH3 as 1Fx=-u*κΔcln⁡z2-dz1-d-ΨHz2-dL+ΨHz1-dL, where κ=0.41 is the von Kármán constant and d is the zero-plane displacement height, determined as 0.9 hc=33.4 m. The integrated form of the heat stability correction term, ΨH, 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 was the case in this study. Fluxes were corrected using a correction factor, γF, whose magnitude was determined from the stability conditions present at the time of measurement . The validity of this correction was confirmed via the flux measurements of HNO3 and HCl by .

The aerodynamic resistance Ra and the quasi-laminar boundary layer Rb can be used to determine the temperature and NH3 concentration at the aerodynamic mean canopy height, z0′, if their respective values at a reference height are known : 2Tz0′=T(z-d)HρcpRa(z-d)+Rb,3χz0′=χ(z-d)+FχRa(z-d)+Rb.

The relative humidity at z0′ can be determined if the saturation pressure at z0′ (εsat(Tz0′)) and the water vapour pressure at z0′ (εz0′) are known. εz0′ can be calculated as 4εz0′=ε(z-d)+FH2ORa(z-d)+Rb, where FH2O is the measured water vapour flux, as taken at the 80 m tower. RHz0′ is then calculated as 5RHz0′=εz0′εsatTz0′×100.

From measurements of Tz0′ and RHz0′, the vapour pressure deficit (VPD) in kilopascals (kPa) was determined.

The basic resistance model that describes deposition to a non-perfectly absorbing surface approximates the ability of the surface to regulate NH3 deposition through a canopy resistance, Rc, which can be calculated from the difference between (a) the total resistance towards deposition (i.e. the inverse of the deposition velocity (Vd) of NH3 at a reference height) and (b) the sum of the atmospheric aerodynamic resistance, Ra, and the quasi-laminar boundary layer resistance, Rb : 6Rc=1Vd(z-d)-Ra(z-d)-Rb. Ra and Rb can be determined from Eqs. () and (), respectively : 7Ra(z-d)=u(z-d)u*2-ΨH(ζ)-ΨM(ζ)κu*, 8Rb=Bu*-1, where B is the sublayer Stanton number . However, this canopy resistance approach as outlined in Eq. () can only successfully be applied if there is no bidirectional exchange. Since both emission and deposition of NH3 were observed in this study, a bidirectional exchange model was required to simulate surface atmosphere exchange of NH3. The simplest bidirectional exchange model for NH3 is the static canopy compensation point (SCCP) model (Fig. 1) in which the exchange between the canopy and the atmosphere is controlled by a conceptual canopy compensation point (χc).

In this SCCP model, the total surface–atmosphere exchange of NH3 (Ft) is the sum of two constituent fluxes, the unidirectional deposition of NH3 to the cuticle surface (Fw), and a bidirectional flux of NH3 through the leaf stomata (Fs) : 9Ft=Fw+Fs, where 10Fw=-χcRw and 11Fs=χs-χcRs.

For the stomatal exchange flux, the difference between the notional mean concentration at canopy height (the canopy compensation point concentration (χc)) and the stomatal compensation point concentration (χs) provides the numerator on the right-hand-side term in Eq. (). When χs exceeds χc, an emission occurs. χs is proportional to the ratio of dissolved NH4+ to H+ in the leaf apoplast (the apoplastic ratio), which represents a dimensionless emission potential (Γ), via a temperature function that describes the combined Henry solubility and dissociation equilibrium : 12χs=161500Texp⁡-10380TΓs.

Here, T is the temperature of the canopy in kelvin (K).

The stomatal resistance, Rs, is primarily dependent on global radiation (St), with additional potential influences from factors such as temperature, vapour pressure deficit, and leaf and root water potentials. Here the generalised function for bulk stomatal resistance as per with the parameters recommended for tropical vegetation is used to calculate the stomatal resistance for NH3 (RsNH3): 13RsNH3=Ri1+200St+0.1-12400Tz0′400-Tz0′-1, where Ri represents the minimum bulk resistance stomatal resistance for water vapour (for deciduous forest during summer: Ri=70 sm-1), St is the global radiation in watts per square metre (Wm-2), and Tz0′ is the temperature in degrees Celsius (∘C) at the mean canopy height.

The appropriateness of this parameterisation and the choice of parameter Ri was evaluated against the water vapour fluxes that were measured during fairly dry conditions when stomatal evapotranspiration is expected to be the dominant source.

The bulk stomatal resistance (Rsb) for water exchange can be calculated from the measured water vapour flux (FH2O) as 14Rsb=εsatTz0′-εz0′FH2O.

To avoid periods during which sources other than evapotranspiration contribute to the water flux, we applied a stringent filter criterion to exclude periods during or within 2 h of rainfall or with RH > 80 %. This left fifty-five 30 min values for the assessment. Measurement-derived values of Rsb for H2O were converted to the equivalent resistance for NH3, accounting for the differences of the molecular diffusivities of the two gases (e.g. ), and the comparison was carried out on their reciprocal values (stomatal conductances, Gs and Gsb), because it is the uncertainty in the stomatal conductances that propagates directly into the predicted flux. A linear regression analysis revealed a very high R2 value of 0.97 and a slope of 0.95 (using an intercept of 0), suggesting that the modelled resistances were slightly larger but well within the range of the measurement uncertainty of Rsb. Therefore, the parameterisation based on is appropriate for this site.

This parallel cuticular pathway in the SCCP model treats the flux to the leaf cuticle (Fw) to be unidirectional to a perfectly absorbing sink, given by the ratio of the canopy compensation point (χc) and the cuticular resistance (Rw). Rw has been described successfully by a number of empirically derived parameterisations in various studies as outlined by , with most using either relative humidity or water vapour pressure deficit as proxies for the ability of NH3 to absorb to the leaf surface. The term Rw is discussed further in Sect. .

The canopy compensation point (χc) is the conceptual mean concentration of NH3 inside the canopy, at which the stomatal, cuticular, and above-canopy fluxes balance each other. It is therefore dependent upon the ambient concentration of NH3 (χa) 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 previously described. In this study, χc was calculated as 15χc=χs×Rw×Ra+Rb+χa×Rw×RsRw×Rs+Ra+Rb×Rw+Ra+Rb×Rs.

Prompted by the observation of morning emissions of NH3 which could not be explained by stomatal exchange alone, this model was further extended by to account for bidirectional exchange with leaf surfaces, by allowing NH3 to be absorbed and desorbed to/from leaf water layers. The extended model calculated the NH3 holding capacity by estimating the leaf water amount in relation to RH. The ammonia holding capacity was implemented into the resistance framework by considering it analogous to an electric capacitor. The charge of this “capacitor” depended dynamically on previously deposited NH3 and tended to be released as dew dried out in the morning. Similarly, extended the model by a second model layer to describe additional exchange with the ground level or soil.

Leaf surface wetness was measured using a sensor array as described in , which was based on the design by . 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 millivolts (mV) that was related to the electrical conductivity between the two electrodes. Data were recorded using a Raspberry Pi 2 Model B (Raspberry Pi Foundation, Cambridge) at a temporal resolution of 1 min. 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 methodology outlined by . 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 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).

The time series of calculations of Tz0′, RHz0′, and VPDz0′, together with measurements of the leaf wetness parameter and measured and modelled fluxes of NH3 (see Sect.  below), are shown in Fig. . 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 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 (all times presented in this work are given as local time: Amazon time, UTC-4), 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.

Figure  shows the time series of the measured fluxes together with model results (see below). Both (positive) emission and (negative) deposition fluxes were recorded during the campaign, ranging from +9.5 to - 30.2 ngm-2s-1. Figure  presents calculated NH3 fluxes as scatter plots for the duration of the campaign against paired canopy values of temperature and relative humidity as well as the leaf wetness parameter. Shaded contour areas – from green to red for low to high density of measurements – are added to the scatter plots to highlight temperature, relative humidity, and leaf wetness conditions where measurements of NH3 fluxes were particularly concentrated. A statistical summary of linear regression models for calculated NH3 flux and the respective parameter plotted is given for each subplot in Fig. .

While emission and deposition occur across the full range of temperatures recorded during the campaign, a weak correlation (R2=0.02; p=0.02) in the linear regression model of NH3 flux against temperature suggests that emissions were more likely to be observed during warmer conditions. Relative humidity appears to be a somewhat stronger driver of NH3 surface exchange behaviour (R2=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 (R2=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 (Fig. 2).

One of the elements of modelling of NH3 flux through the static canopy compensation point model is the stomatal flux (Fs), which, from Eq. (), depends on the canopy concentration of NH3 (χc) and the stomatal compensation point (χs). The value of χs is determined by the leaf surface temperature (in this study, taken as Tz0′) and the apoplastic ratio (Γs). If Γs is known, which varies with vegetation type , environmental stressors such as drought , and nitrogen nutrition , then χs and subsequently Fs can be modelled. The fact that emissions at this site regularly occurred during midday (when Tz0′ is at its maximum) and were related to drier, warmer conditions (Fig. ) is consistent with the emission flux originating from the stomata.

Γs can be inferred from measurements during conditions where the NH3 surface exchange is judged to be dominated by stomatal exchange, with a negligible contribution from desorption of NH3 from the leaf surface.

Under conditions where Rw is very large compared with Rs, the ambient NH3 concentration (χa) at which a zero net flux occurs (i.e. when the difference between χc and χs is 0) is implicitly equal to χc and χs. Therefore, if NH3 surface exchange is driven by stomatal exchange, χs may be determined from the values of χa at which the flux changes from deposition to emission, or vice versa . Figure  presents the ambient NH3 concentrations measured during the campaign at which such flux sign changes occur as a function of Tz0′ for conditions under which Rw is expected to be fairly large (RH < 60 %).

Equation () can therefore be rearranged to give an expression for Γs that is dependent upon Tz0′ and χs, where χs can be substituted with a value of χa at which a sign change in the flux of NH3 occurs: 16Γs=1161500Tz0′+273exp⁡-10380Tz0′+2731χs. Using the values of χa 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 Fig.  is the temperature response curve of χs consistent with this value of Γ. Consequently, modelled values of χs based on a value of Γs=38.5 were determined for the campaign period and subsequently used to determine values of χc and total modelled flux. As this value resulted in an under-prediction of the peak emissions, an alternative enhanced value of Γs=50 was also explored to develop further parameterisations for comparison. By using an enhanced value for Γs, all emissions from the leaf surface are implicitly considered to originate from leaf stomata rather than cuticular desorption or other potential sources of NH3 emissions, such as soil or leaf litter.

Considering the observed drivers for NH3 surface exchange discussed in Sect. , three different parameterisations for the cuticular resistance Rw were developed for this study, based upon three alternative proxies of the NH3 holding capacity of the leaf water layers: RHz0′, VPDz0′, and leaf wetness. Subsequently, each parameterisation of Rw was used to develop three distinct values for Fw, the unidirectional flux component of the cuticular-resistance-based single-layer model, each describing the surface atmosphere exchange of NH3 at the ATTO site.

The first parameterisation was based on measurements of RHz0′ using the following equation : 17Rw=α+exp⁡100-RHβ1.

Here, α determines the minimum cuticular resistance (which is α=1 sm-1), while β1 is a constant scaling coefficient controlling the increase of Rw with decreasing relative humidity. The coefficients α and β1 were fitted by least-squares optimisation between total modelled and observed values of NH3 flux taken during the campaign to arrive at values of α=2 sm-1 and β1=9, which were used for modelling Rw based on RHz0′ for the entirety of the campaign. The second parameterisation was based on measurements of the vapour pressure deficit, using a formulation for Rw based upon that employed by : 18Rw=α+β2exp⁡γ1(VPD).

As with the parameterisation of Rw in Eq. (), the coefficient α is the minimum value for Rw at zero VPD, set at 2 sm-1. β2 and γ1 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 β2 and 1.7 for γ1 for the determination of Rw based on Eq. () for the entirety of the campaign.

Finally, a novel parameterisation for Rw based upon measurements of leaf wetness was developed for this campaign based on least-squares optimisation: 19Rw=α+β3exp⁡γ2(1-LWP)-1.

As with the parameterisations of Rw described in Eqs. () and (), α is the minimum value of Rw at maximum leaf wetness, set at 2 sm-1; β3 is a scaling coefficient, similar to that of the parameterisation in Eq. (), set at a value of 5; and γ2 is a scaling coefficient controlling the increase in Rw with the decrease in leaf wetness, set in this study to 4.8. With this parameterisation, Rw approaches α for a fully wet canopy and is capped at Rw=605 sm-1 for a fully dry canopy.

Six discrete model runs of NH3 surface exchange were investigated, via Eqs. (), (), and (), using the two values of the apoplastic ratio (Γs=38.5 and Γs=50) combined with one of the three parameterisations for Rw (relative humidity, RH; vapour pressure deficit, VPD; and leaf wetness parameter, LWP) described above. These models are a.

Rw= LWP, Γs=38.5,

Table  presents a summary of the model results, with average mean modelled fluxes for the overall campaign, together with day- (06:00–17:00) and night-time (18:00–05:00) average mean values for the four separate periods of the campaign discussed in Sect. . Also presented are average mean values for calculated fluxes based on NH3 measurements during the campaign and the percentage of modelled values which agree in flux direction with observed values. Modelled mean values highlighted in bold signify where the model value deviates by more than 25 % from the corresponding observed mean. The models which differ least and most from the observed values are models b and c, respectively. Models which use the calculated apoplastic ratio of 38.5 differ more from the observed values than those which use an apoplastic ratio of 50 (near 1 standard deviation from calculated). Modelled daytime values tend to differ less from their corresponding observed value in comparison to night-time values. Modelled values during Period One have the least divergence from the observed overall (day and night), while the greatest divergence in modelled values occurs during Period Four, particularly at night. For model b, 91 % of values agree with the observed direction of fluxes, and it is the best performing model using this parameter. Conversely, model c values agree with only 83 % of the observed direction of fluxes.

Figure  shows the full time series of modelled NH3 fluxes from models b, d, and f alongside the measured flux. In general, periods of emission and deposition are modelled well by all three models, with two exceptions: the emission period from 12:00 to 16:00 on 30 October, where modelled fluxes suggest an earlier emission from 11:00 which lasts for fewer hours; and from 13:00 to 15:00 on 2 November, where no model predicts an emission, in contrast to the measurements. The magnitude of modelled fluxes generally agrees well with the observed flux, although model d, which uses an Rw parameterisation based on RH, tends to estimate smaller emissions in comparison to model f (Rw= VPD). Model b (Rw= LWP) comes closest to replicating the magnitudes of the measured emissions, although as with the other two models it underestimates the magnitude of the measured deposition.

The errors in the observed fluxes of NH3 during this campaign are presented in . Using a Gaussian error propagation approach, a median percentage error of 33 % was calculated for the observed NH3 fluxes.

The error in the simulated fluxes can also be determined using an error propagation method. Equation () highlights that the total simulated flux (Ft) is the sum of the cuticular flux (Fw) and the stomatal flux (Fs). The total uncertainty in Ft, σFt, can therefore be determined by 20σFt=σFw2+σFs2, where σFw and σFs are the associated errors in, respectively, Fw and Fs. In turn, σFw and σFs can be calculated using a Gaussian error propagation based on Eqs. () and () respectively, which rely on the errors in Ra, Rb, Rs, and Rw measurements.

While the error in Fs will remain the same for all simulated values of Ft, the error in Fw will vary on the choice of Rw parameterisation. Thus, the error in Rw is the primary variable which governs the differences in the error in Ft between the simulated values.

Using this framework, the error values were calculated for each Rw and Γs parameterisation for the simulated total flux. In the overall calculated total flux in Table , the associated error, in ngm-2s-1, is also shown.

The observed bidirectional surface exchange of NH3 from a remote tropical rainforest site was modelled using a series of canopy compensation point, cuticular-resistance-based models using a variety of different Rw parameterisations and apoplastic ratios.

As highlighted in the Introduction, measurements of NH3 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 and inferred fluxes from single point concentration measurements. Exchange of NH3 has been measured previously at temperate forest sites and reported to be bidirectional: for example, noted daytime emission from a remote forest near Boulder, Colorado; observed bidirectional NH3 exchange (with median diel emissions recorded between 12:00 and 16:00) over a Scots pine (Pinus sylvestris) forest in Flanders, Belgium; and noted daytime emissions from a Douglas fir (Pseudotsuga menziesii) forest at Speuld in the Netherlands. When using models to determine the drivers of surface exchange above forest sites, these studies often stress the importance of 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 , 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 NH3 surface exchange. Indeed, an exploratory application of the dynamic CCP model did not result in an 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 NH3 into leaf water layers associated with the low night-time NH3 concentrations at this site. Dry deposition of aerosol ammonium nitrate (NH4NO3) is another source of volatile NH4+ on leaf surfaces, and concentrations of this compound are again typically very small in Amazonia . In addition, given the high RH, the water layers may not dry out as rapidly and completely as at other sites. The measured median NH3 atmospheric concentration at the canopy height during the measurement period was 0.23 µeqm-3, with an estimated annual total reactive N dry deposition input of 1.74 kg N ha-1yr-1 . This is far lower than reported by and by , both of whose sites were subject to high levels of agricultural pollution. As noted by and , higher atmospheric inputs of N to forest systems lead to an increase in the stomatal emission potential. Conversely, with lower atmospheric NH3 concentrations, the potential for forests to act as a source of NH3 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 .

In general, the fluxes measured at ATTO could also be reproduced without including a further soil layer, potentially with one exception (see below). Such a layer is needed where night-time emissions are observed that are clearly not under stomatal control .

The consistently warmer noon-time conditions at the leaf canopy during measurements at the ATTO site would also favour stomatal-exchange-driven emissions of NH3. An increase in leaf temperature, with VPD controlled for, has been shown to lead to greater gas exchange through increased stomatal openings , while alterations to the Henry and dissociation equilibria would lead to a change in the stomatal compensation point favouring increased stomatal emissions. Similarly, the unstable conditions at noon above the canopy over tropical rainforest lead to reductions in Ra, which would increase any emissions occurring at the time that were driven by stomatal exchange . In the study of forest NH3 emissions that is most similar in ambient NH3 concentrations, canopy compensation points, and apoplast ratios to this study, come to a similar conclusion on the observed daytime emissions from a remote, temperate forest in Indiana, USA.

Despite the low N inputs and apoplastic NH4+ / H+ ratio, significant emission periods were observed above the ATTO site. One driver is clearly the high daytime leaf temperature. The average flux amounted to a small deposition of - 2.8 ngm-2s-1 suggesting that, on average, the site receives more N as NH3 than it loses. Possible sources include small-scale farming and biomass burning.

The apoplastic ratio of NH4+ / H+ (Γs) inferred from the measurements in this study was 38.5 ± 15.8; the models investigated used either a value of 38.5 or 50 (close to 1 standard deviation from inferred value). Both values are significantly lower than the majority of Γs values obtained for other forest sites. give a value of Γs=400 for green temperate forest canopies, which is also used by . review a range of Γs values derived from measurements of NH3 surface exchange over forest, which range from Γs = 27 (as measured directly through bioassay for unfertilised Spruce forest) to Γ=5604 as determined by for a highly polluted P. menziesii forest. The study by used a value of 3300 in spring and 1375 in summer for a P. sylvestris forest.

The disparity in the emission potentials (the apoplastic ratios) 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 . Consequently, at polluted areas such as the forest sites studied by , apoplastic ratios are increased, while at sites with lower N input, such as semi-natural vegetation with low ambient NH3 concentrations, values of Γs can be as low as 5–10 . The species of vegetation is also critical . 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, exhibit lower apoplast ratios than nitrate-reliant, shoot-assimilating species . The value of 38.5 which was inferred from measurements lies in the range of Γs values exhibited by semi-natural vegetation with low N inputs and in the lower range of overall forest values quoted by .

An assessment of the performance of the individual parameterisations against calculated NH3 fluxes is included in Fig. , which displays the results of simple linear regression models for the simulated values of each NH3 flux model against observed NH3 fluxes. With regards to the Pearson correlation coefficient (r), the rank of models from most strongly correlated with observed NH3 fluxes to least correlated is model b, model a, model f, model e, model d, and model c (model descriptions are found in Table ). The Rw parameterisation was a stronger determinant of model–measurement correlation than the choice of Γ. Correlation with measurements is highest for the models using an Rw based upon LWP, followed by those which use VPD and finally RH. Within each grouping, models using Γ=50 provide simulated values that have a better correlated fit with observed values than Γ=38.5. Overall model performance is in many ways more sensitive to Rw than Γ as is apparent from the Taylor diagram (Fig. ), which summarises in one diagram the three complementary model–measurement performance statistics of the (i) correlation coefficient (r), (ii) centred root mean squared error (RMSE), and (iii) within-model and within-measurement standard deviations (SD) . The statistical metrics visualised in Fig.  are summarised in Table .

The standard deviation in the observed flux dataset is 3.65 ngm-2s-1. The model that comes closest to replicating this same variability is model b (2.65 ngm-2s-1), with model e (2.24 ngm-2s-1) replicating observed values least well, although the overall range between model standard deviation is broadly similar. It should be borne in mind, however, that the standard deviation of the measured flux includes measurement uncertainty in addition to real variability, as do the modelled values, which are based on measured parameters. With regards to r, model b simulated values produce the highest correlation with the observed values at r=0.71, in comparison to model c, which performs the worst at r=0.45. Finally, the model with the lowest root mean square error from the observed is model b at 2.79 ngm-2s-1, with the highest error found in model c, at 3.31 ngm-2s-1. Therefore, from the ability of the parameterisations to reproduce the measured average fluxes as presented in Figs. , , and (Table ), it can be concluded that parameterisation b, in which the value Rw is parameterised using leaf wetness parameter values and where the apoplastic ratio is set to 50, is the best performing model in simulating NH3 surface–atmosphere exchange at the ATTO site, while model c is the worst performing.

Although the leaf wetness parameter measured with the leaf clip sensors is somewhat 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 the models using leaf wetness parameter and RH as model inputs. Figure  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 equation, which suggests that leaf wetness decreases more sharply than RH across the campaign. Indeed, Fig.  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 and 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 sensors of the type used here. Although leaf wetness or surface wetness measurements are not typically available for use in chemistry transport models, canopy wetness is often simulated by land surface models and within chemical transport models . Simulated surface wetness data, as a leaf wetness parameter, could therefore be used to model NH3 fluxes using the LWP-dependent Rw parameter as described here. Alternatively, VPD-based parameterisations, over RH-based parameterisations, could be employed instead.

As is visually apparent in Fig. , the influence of the apoplastic ratio is relatively minimal for reproducing flux variability in comparison to the effect of Rw parameterisation over the Γs range explored (38.5 to 50). However, the choice of Γ does affect the model's ability to reproduce the overall magnitude of the fluxes during daytime (Table ).

Models that used the Γs value of 50 (the upper bound to the inferred values of 38.5 for Γs) (b, d, and f) simulated values better in agreement with observations in comparison to their paired Rw 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 Γs as outlined in Sect.  in tropical conditions. As outlined by , the validity of equating χa to χc only holds for dry conditions (e.g. RH < 50 %), when Rw can reliably be expected to be large. At higher humidity values, leaf cuticles may start to become a small sink, and χc becomes an underestimate of χs. At the ATTO site, where median humidity at the canopy level throughout the campaign was 87 %, with only a few occurrences during the drier Period Two and Period Four where it fell below 60 %, this approach of inferring Γs from NH3 measurements was likely affected. However, the impact does not appear to have completely invalidated the use of the method, as the somewhat larger value of 50 that resulted in models with best agreement still lies within 1 standard deviation of the inferred Γs value. An accurate determination of apoplastic ratio for tropical rainforest, derived from leaf assays, would improve the accuracy of the model and therefore remains an important area for future investigation. However, its variability across the large plant species diversity would likely provide a challenge in deriving a bottom-up mean value that governs the net exchange.

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 NH3 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 NH3 emission that would not be accounted for using the single-layer model could be considered. For example, from the evening of 31 October to the early morning of 2 November, heavy precipitation periods were recorded, coupled with increased deposition fluxes of NH3 on 1 November. Increased wet deposition of N through NH4+ in rainwater and washed from the canopy 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 NH3 from the litter or soil layer from the forest floor , leading to observed emissions of NH3 in the afternoon. This potential scenario would not be modelled with the single-layer canopy resistance model.

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 NH3 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 course, the flux measurement itself is not without error, especially during the calmer and more stable night-time conditions.