Forest-atmosphere exchange of reactive nitrogen in a low polluted area – temporal dynamics and annual budgets

Accurate modeling of nitrogen deposition is essential for identifying exceedances of critical loads and designing effective mitigation strategies. However, there are still uncertainties in modern deposition routines due to a limited availability of long-term flux measurements of reactive nitrogen compounds for model development and validation. In this study, we investigate the performance of dry deposition inferential models with regard to annual budgets and the exchange patterns of total reactive nitrogen (ΣNr) at a low-polluted mixed forest located in the Bavarian Forest National Park (NPBW), Germany. Flux 5 measurements of ΣNr were carried out with a Total Reactive Atmospheric Nitrogen Converter (TRANC) coupled to a chemiluminescence dectector (CLD) for 2.5 years. Average ΣNr concentration was approximately 5.2 ppb. Denuder measurements with DELTA samplers and chemiluminescence measurements of nitrogen oxides (NOx) have shown that NOx has the highest contribution to ΣNr (∼ 52%), followed by ammonia (NH3) (∼ 22%), ammonium (NH4 ) (∼ 14%), nitrate NO3 (∼ 7%), and nitric acid (HNO3) (∼ 6%). We observed mostly deposition fluxes at the measurement site with median fluxes ranging from 10 -15 ng N m−2s−1 to -5 ng N m−2s−1 (negative fluxes indicate deposition). In general, highest deposition was recorded from May to September. ΣNr deposition was enhanced by higher temperatures, lower relative humidity, high ΣNr concentration, and dry leaf surfaces. Our results suggest that dry conditions seem to favour nitrogen dry deposition at natural ecosystems. For determining annual dry deposition budgets we used the bidirectional inferential scheme DEPAC (DEPosition of Acidifying Compounds) with locally measured input parameters, called DEPAC-1D, as gap-filling strategy for TRANC measurements. 15 In a second approach, the mean-diurnal-variation method (MDV) was applied to gaps of up to five days whereas DEPAC-1D was used for remaining gaps. We compared them to results from the chemical transport model LOTOS-EUROS (LOng Term Ozone Simulation – EURopean Operational Smog) v2.0 and from the canopy budget technique conducted at the measurement site. After 2.5 years, dry deposition based on TRANC measurements resulted in (11.1± 3.4) kg N ha−1 with DEPAC-1D as gap-filling method and (10.9±3.8) kg N ha−1 with MDV and DEPAC-1D as gap-filling methods. Both values are close to dry 20 deposition by DEPAC-1D (13.6 kg N ha−1) considering the uncertainties of measured fluxes and possible uncertainty sources of DEPAC-1D. The difference of DEPAC-1D to TRANC can be related to parameterizations of reactive gases or the missing exchange path with soil. 16.8 kg N ha−1 deposition were calculated by LOTOS-EUROS for considering land-use class weighting. We further showed that predicted NH3 concentrations, an input parameter of LOTOS-EUROS, were the main reason for the discrepancy in dry deposition budgets between the different methods. On average, annual TRANC dry deposition was 25 1 https://doi.org/10.5194/bg-2020-364 Preprint. Discussion started: 14 October 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
Reactive nitrogen (N r ) compounds are essential nutrients for plants. However, an intensive supply of nitrogen by fertilisation or atmospheric deposition is harmful for natural ecosystems and leads to a loss of biodiversity through soil acidification and eutrophication and may also threaten human health (Krupa, 2003;Galloway et al., 2003;Erisman et al., 2013). Atmospheric nitrogen load increased significantly during the last century due to intensive crop production and livestock farming (Sutton 35 et al., 2011;Flechard et al., 2011Flechard et al., , 2013Sutton et al., 2013) (mainly through ammonia) and fossil fuel combustion by traffic and industry (mainly through nitrogen dioxide and nitrogen oxide). The additional amount of N r enhances biosphere-atmosphere exchange of N r (Flechard et al., 2011), affects plant health  and influences the carbon sequestration of ecosystems such as forests (Magnani et al., 2007;Högberg, 2007;Sutton et al., 2008;Flechard et al., 2020), although the impact of increasing nitrogen deposition on forests carbon sequestration is still under investigation. 40 For estimating the biosphere-atmosphere exchange of N r compounds such as nitrogen monoxide (NO), nitrogen dioxide (NO 2 ), ammonia (NH 3 ), nitrous acid (HONO), nitric acid (HNO 3 ) and particulate ammonium nitrate (NH 4 NO 3 ), the eddycovariance (EC) approach has proven its applicability on various ecosystems. The sum of these compounds is called total reactive nitrogen (ΣN r ) throughout this manuscript. For evaluating fluxes of NO and NO 2 the EC technique has been tested in earlier studies (Delany et al., 1986;Eugster and Hesterberg, 1996;Civerolo and Dickerson, 1998;Li et al., 1997;Rummel et al., corresponded to the average of measurements from 20 m and 40 m. Since profile measurements of temperature and relative humidity started in April 2016, measurements by the NPBW were used until end of March 2016. Pressure and global radiation were provided by the NPBW. Indicators of stability and turbulence such as Obukhov-Length L and u * were taken from momentum flux measurements of the sonic anemometer. All micrometeorological and turbulent flux data were aggregated half-hourly. For determining compensation points and additional deposition corrections, SO 2 and NH 3 concentrations collected by DELTA samplers were used. Passive sampler measurements were used to replace missing or low-quality NH 3 measurements in DELTA 265 time series, and gaps in the SO 2 data were filled by the long-term average. Leaf area index (LAI) was modeled as described by van Zanten et al. (2010). For modeling R a the solar zenith angle, which is calculated by using celestial-mechanic equations, the roughness length z 0 and displacement height d are needed. By using the same height as proposed by LOTOS-EUROS for z 0 (2.0 m), fluxes were slightly underestimated. However, influence on the dry deposition budget was negligible. Thus, we set z 0 to 2.0 m and d to 12.933 m for coniferous forest and to 11.60 m for deciduous forest. Shifting z 0 or d by ±50% caused 270 a change of +5.0%/-3.2% and +5.6%/-9.1%, respectively, in the dry deposition after 2.5 years. An incorrect assessment of the LAI by ±50% has significant influence on the dry deposition. It leads to a change of +18.9%/-27.7%. The calculation of the dry deposition was done for NH 3 , NO, NO 2 , and HNO 3 with the mentioned parameters on half-hourly basis. Fluxes of DEPAC-1D were weighted after the actual land-use classes (81.1% coniferous forest and 18.9% deciduous forest). The LAI, which is based on the LOTOS-EUROS land-use weighting, ranges between 1.9 and 2.8 while considering only deciduous and 275 coniferous forest land-use classes in the flux footprint. The LAI based on the actual land-use weighting ranges between 4.1 and 4.8. Including grassland in the determination of LAI is less useful since characteristics, for example an increase in LAI from the beginning of year, is not representative for the vegetation within the flux footprint. Thus, modeled nitrogen budgets of LOTOS-EUROS should be seen as lower and upper estimates.
After post-processing of TRANC data, we applied two gap-filling strategies. In the first one, DEPAC-1D was used for 280 replacing all missing values in flux data. The second one used MDV for filling gaps up to five days and DEPAC-1D for longer gaps. For comparing the methods with each other we developed a validation strategy: After filling the gaps in the TRANC time series with DEPAC-1D, we used LOTOS-EUROS with the corrected weighting of land-use classes for closing remaining gaps in DEPAC-1D results as well as in TRANC data ensuring a comparison for every time step. Gaps in DEPAC-1D are mostly related to power outages causing gaps micrometeorological data. Since DEPAC-1D did not include deposition of particles 285 and the actual land-use class in the grid cell did not agree with the land-use class used in LOTOS-EUROS, recalculations of LOTOS-EUROS with a corrected land-use class and/or without considering particulate deposition were performed. Averaged flux time series of LOTOS-EUROS, DEPAC-1D, and TRANC were compared to look for seasonal deviations throughout the observation period. Finally, the annual dry deposition sums of LOTOS-EUROS, DEPAC-1D, TRANC, and CBT were evaluated.   ΣN r concentrations exhibit highest values during winter months. For example, values were higher than 20 ppb during January 2017 and February 2018. NO x shows a relatively high concentration level during winter, too. During spring and summer NO x values are mostly lower than 5 ppb and hence, their contribution to ΣN r decreases. However, ΣN r values remain around 5 ppb and reach values up to 10 ppb, which is related to higher NH 3 concentrations during these periods. ΣN r concentration is 5.2 ppb on average, NH 3 is approximately 1.8 ppb, and NO x is 2.5 ppb on average. Values are in agreement with concentrations 300 reported by Beudert and Breit (2010). The elevated NO x concentration level also affects its contribution to ΣN r measured by the TRANC. Figure B1 shows the contribution of N r species, which are converted inside the TRANC, to ΣN r as pie charts.
Contributions from NO 3 , NH 3 , NH 4 , and HNO 3 are determined from monthly DELTA measurements. NO x concentrations are averaged to the exposition periods of the DELTA samplers. The ΣN r concentration measurements are dominated by NO x . On average, NO x contributes with 51.6% to ΣN r . At lowest and highest ΣN r concentrations, its influence on ΣN r differs only 305 slightly. NH 3 exhibits a contribution of 21.6% on average, which is lower than the sum of HNO 3 , NH 4 , and NO 3 (∼ 26.8%).
Compared to NO x , NH 3 varies significantly from lowest to highest ΣN r concentrations. At the lowest average ΣN r concentration, the contribution of NH 3 is significantly high whereas the contribution of NH 3 gets negligible compared to the contribution of particulate and acidic N r compounds (∼ 35.5%) at the highest average ΣN r concentration.  . Time series of measured high-quality (flags "0" and "1") ΣNr fluxes depicted as box plots on monthly basis (box frame = 25% to 75% interquartile ranges (IQR), bold line = median, whisker = 1.5· IQR) in ng N m −2 s −1 . Colors indicate different years. The displayed range was restricted from -100 to 50 ng N m −2 s −1 .
Almost all ΣN r flux medians are between -15 and -5 ng N m −2 s −1 indicating that mainly deposition of ΣN r occurred at our measurement site. Quality assured half-hourly fluxes showed 85% deposition and 15% emission fluxes. On half-hourly basis, fluxes are in the range from -409 to 216 ng N m −2 s −1 . The mean flux error of non-gapfilled, half-hourly fluxes is 5.7 ng N 315 m −2 s −1 after Finkelstein and Sims (2001). The flux detection limit is calculated by multiplying 1.96 with the flux error (95% confidence limit) (see Langford et al., 2015). The latter is 11.3 ng N m −2 s −1 . Both values refer to the entire measurement campaign. Similar values were found by Zöll et al. (2019).
In general, median deposition is almost on the same level for the entire campaign with slight seasonal differences. For instance, median deposition is slightly higher during spring and summer than during winter for 2016. However, median de-320 position during winter 2017 is similar to median deposition in summer 2017. Median deposition was significantly stronger from June 2016 till September 2016 than for the same period in 2017. IQR and whisker cover a wider range, too. The pattern month with sporadic emission events. Such phenomenons were not observed in the years before. In the following month, the deposition is slightly higher from March to April 2017 than for the same period in 2018. Fig. 3 shows averaged daily cycles for every month. In general, the ΣN r daily cycle exhibits low deposition or neutral exchange during nighttime/evening and increasing deposition during daytime. Deposition rates are similar during the night for the entire campaign except for February 2018. Maximum 330 deposition is reached between 9:00 and 15:00 CET. Deposition is enhanced from May until September showing fluxes between -40 and -20 ng N m −2 s −1 . During autumn (October-November) and winter (December-February), the daily cycle weakens with almost neutral or slightly negative fluxes, mostly lower than -10 ng N m −2 s −1 . The daily cycles of the respective same months are mainly similar. However, during certain months, which differ in their micrometeorology and/or in the composition of ΣN r , differences can be significant. For example, the daily cycle of March and April 2017 is clearly different to daily cycle of  parameters such as temperature (Wolff et al., 2010), humidity (Wyers and Erisman, 1998;Milford et al., 2001), concentrations (Brümmer et al., 2013;Zöll et al., 2016), and dry/wet leaf surfaces (Wyers and Erisman, 1998;Wentworth et al., 2016) were reported to control the deposition of N r compounds. Therefore, we investigate the dependency of ΣN r fluxes on temperature, humidity, dry/wet leaf surface, and ΣN r concentration. We separate half-hourly fluxes into classes of low and high temperature, humidity, and concentration. The threshold values, which are calculated from May to September, based on the median of the 350 mentioned parameters. Leaf wetness value is calculated after the scheme described in Sec. 2.2 for same time period. No significant influence of the different installation height on leaf surface wetness was found. For separating dry and wet leaf surfaces, the scheme proposed in Sec. 2.2 is applied. The shaded area represents the standard error of the mean.
In general, higher temperatures, less humidity, higher concentrations, and dry leaf surfaces favour deposition of ΣN r . Temperature seem to affect ΣN r fluxes from 6:00 to 18:00 CET stronger leading to differences of more than -10 ng N m −2 s −1 , for instance around 9:00 and 15:00 CET. During dawn/nighttime fluxes show no significant temperature dependence. Con-355 centration has the strongest impact on the deposition. The effect is increased from 6:00 to 15:00 CET exhibiting a difference -5.5 ng N m −2 s −1 on average, but also nighttime deposition fluxes are enhanced at higher concentrations. The impact of less humidity and dry leaves is slightly lower than concentration and temperature, but they affect nighttime deposition stronger than temperature. Finally, it should be mentioned that the shapes of the daily cycles for each parameter shown in Fig. 4 are similar for both threshold values and differ only in amplitude. It indicates that other drivers may influence the pattern of ΣN r fluxes 360 stronger than the shown parameters here.

Cumulative N exchange and method comparison
For determining the ΣN r dry deposition, gaps were filled in flux time series with DEPAC-1D and MDV (see Sec. 2.4.3). Fluxes estimated through the EC technique covered 47.8% of the measurement period after quality filtering. The low amount of valid flux measurements was expected, for example, related to insufficient turbulence during nighttime, performance issues of the 365 instruments, etc. Applying MDV allows to increase the coverage to 65.0%. With DEPAC-1D alone nearly all gaps were closed.
Remaining gaps in DEPAC-1D were about 4% due to power failures and were filled with LOTOS-EUROS results. Afterwards, 14 https://doi.org/10.5194/bg-2020-364 Preprint. Discussion started: 14 October 2020 c Author(s) 2020. CC BY 4.0 License. fluxes were added up to get a cumulative sum. In the following, the results of the method comparison described in Sec. 2.4 are presented. Figure 5 shows the cumulative ΣN r dry deposition of the different methods for the duration of the campaign. The ΣN r dry deposition values estimated by each method for 2.5 years are listed in Table 1. CBT upper estimate -22.6 6.44 6.98 9.14 Overall, DEPAC-1D and and LOTOS-EUROS seem to overestimate ΣN r dry deposition compared to our measurements, in particular LOTOS-EUROS with the corrected land use. The dry deposited ΣN r modeled by DEPAC-1D consists of 76% NH 3 , 13% HNO 3 , 11% NO 2 , and less than 1% NO. It shows that modeled deposition of DEPAC-1D is mostly driven by NH 3 .
HNO 3 and NH 3 deposition velocities are nearly equal (1.81 cms −1 and 1.86 cms −1 ). Also, emission phases are modeled for NH 3 due to the low compensation point indicated by the negative whisker of the box plot ( Fig.C1.). However, their influence 375 on total deposition is negligible since only short emission phases of NH 3 were modeled. Deposition velocity for NO 2 and NO are relatively low. 0.08 cms −1 is determined for NO 2 and 0.0 cms −1 for NO.
ΣN r exchange of DEPAC-1D is rather neutral during the entire winter, and thus the difference to measured deposition is close to zero. During summer a systematic overestimation of DEPAC-1D to measured fluxes is observed. Modeled deposition by LOTOS-EUROS is slightly lower than DEPAC-1D during summer and consequentially closer to measured fluxes. How-380 ever, during autumn and spring predicted deposition by LOTOS-EUROS is significantly higher than deposition determined by DEPAC-1D and TRANC. The agreement of the measured, non gap-filled ΣN r fluxes (results not shown) with LOTOS-EUROS for the same half-hours without particulate input is conspicuous after 2.5 years. TRANC measurements show a cumulative, non gap-filled dry deposition of 4.7 kg N ha −1 , LOTOS-EUROS exhibits 4.5 kg N ha −1 . This agreement has to be regarded with caution since the TRANC also converts particulate ΣN r compounds and the land-use class weighting of LOTOS-EUROS 385 is not valid for the measurement site. Correcting the land-use class based on actual vegetation of the flux footprint, exhibit a significant overestimation of the dry deposition. We determined 8.2 kg N ha −1 with LOTOS-EUROS for measured, non gapfilled half-hours including particulate deposition and the actual land-use class weighting, and 16.8 kg N ha −1 is calculated for the entire measurement campaign. The applied gap-filling strategies result in similar dry deposition after 2.5 years ( Table 1).
The difference between both curves is enhanced from July 2017 to mid February 2018. Due to the strong deposition occurring 390 in late February 2018, the difference between the curves is significantly reduced. Obviously, DEPAC-1D could not model the deposition event accurately.
Since all cumulative curves exhibit generally the same shape, we conclude that the variability in fluxes is reproduced by DEPAC-1D and LOTOS-EUROS well, although the amplitude and duration of certain deposition events is different. This observation is valid for the strong deposition event in late February 2018 observed by the TRANC, but it is treated differently 395 by DEPAC-1D and LOTOS-EUROS. As stated before, it is not accurately modeled by DEPAC-1D and also not by LOTOS-EUROS without considering particle deposition. Including particle deposition in LOTOS-EUROS leads to better agreement with TRANC measurements for a few weeks. It seems that the deposition during late February 2018 is most likely driven by particulate N r compounds. Such compounds are not implemented in DEPAC-1D. After the deposition event, measured ΣN r exchange is almost neutral whereas modeled deposition of LOTOS-EUROS increases resulting in significant disagreement in 400 ΣN r deposition. However, the emission event, which is calculated from TRANC measurements for December 2017, is not captured by LOTOS-EUROS and DEPAC-1D.
In the following, a comparison of the ΣN r dry deposition separated by method and measurement years is given in Fig. 6.  et al., 2001). Air temperature controls the influence of the emission potential, the apoplastic concentration ratio, at surfaces on the NH 3 compensation point (Sutton et al., 1994;Nemitz et al., 2000). Relative humidity is used as approximation for the canopy humidity and controls the cuticular deposition (Sutton et al., 1994). NH 3 concentration is proportional to the NH 3 flux (van Zanten et al., 2010), global radiation enhances the opening width of the stomata (Wesely, 1989), and friction velocity is a 435 measure of the turbulence and has an influence on the aerodynamic and quasi-laminar resistance (Webb, 1970;Paulson, 1970;Garland, 1977;Hummelshøj, 1995, 1997). NH 3 was chosen since it is the most abundant compound in modeled ΣN r (see Fig. E1), and resistance models are most developed for NH 3 . Fig. 7 illustrates the results of the sensitivity study. Overall, the agreement of measured and modeled input data is excellent for temperature and global radiation. Values of r 2 are 0.78 for global radiation and 0.97 for temperature. A slight difference is visible for relative humidity in the first half of 2016 440 with r 2 being 0.67. In case of relative humidity, using locally measured values leads to a reduction in deposition by 6%. The deposition increases by approximately 6% if measured temperature values are used. The impact on deposition using measured global radiation is negligible. u * of LOTOS-EUROS is systemically higher, and the seasonal pattern is different to values determined from the sonic anemometer. Thus, r 2 is only 0.43 but using measured values for u * leads only to 10% less deposition.
The difference between measured and modeled NH 3 is most pronounced. Modeled concentrations are approximately 2 to 3 445 times larger in spring and autumn. Furthermore, the seasonal pattern of the measured NH 3 disagrees with the modeled values.
Using measured NH 3 concentration reduces the deposition by approximately 42% compared to the modeled deposition. Consequentially, NH 3 concentration is most responsible for the discrepancy of modeled and measured ΣN r fluxes. The generally high NH 3 concentration also influences its contribution to ΣN r concentration modeled by LOTOS-EUROS. Figure E1 shows the contribution of the N r species to modeled ΣN r as pie charts. LOTOS-EUROS states out NH 3 as the main contributor. NO x , 450 which is identified as main contributor to ΣN r from measurements, takes only 22.2% of the modeled ΣN r . At highest ΣN r concentration, NH 3 corresponds to almost half of the ΣN r . Particulate and acidic N r compounds have a higher contribution than NO x on average (∼ 41.7%). Their contribution is also higher than values extracted from DELTA measurements, but decreases  The snow layer acts as an insulator for the soil, prevents soil from frost penetration effectively, and thus protects plants and 490 microorganisms (Bleak, 1970;Vogt et al., 1983;Moore, 1983;Inouye, 2000). Thus, processes, which lead a decomposition of leaves, needles or lichens by microorganisms, can happen under the snow layers with substantial losses, especially for lichens (Taylor and Jones, 1990). The authors further discovered an increase in nitrogen concentration in the investigated samples.
Since we observed a slower varying air temperature with temperatures below zero for 2 to 3 days followed short periods of less than one day with temperatures close to zero degrees and even higher, the accumulation of nitrogen under the snow layer and 495 a immediate release due to freeze-thaw cycles probably happened. The determined order of magnitude by Hansen et al. (2015) is comparable to our flux measurements.
Since we also measured other N r compounds such as HNO 3 and NO 2 , which exhibit mostly deposition (Horii et al., 2004(Horii et al., , 2006, deposition fluxes predominated at our measurement site compared to Hansen et al. (2015). NO is mainly observed as emission from soil if it is produced through (de)nitrification processes (Butterbach-Bahl et al., 1997;Rosenkranz et al., 2006).

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The contribution of NO to ΣN r is probably negligible because NO is rapidly converted to NO 2 in the presence of O 3 within the forest canopy, especially close to the ground (Rummel et al., 2002;Geddes and Murphy, 2014). Therefore, a comparison with chamber measurements, which could had been conducted at the ground for measuring N r compounds was considered as less useful due to the large footprint of the flux measurements, fast conversion processes within the forest canopy, and uptake possibilities like leaf surfaces for N r compounds (e.g., Wyers and Erisman, 1998;Rummel et al., 2002;Sparks et al., 2001;505 Geddes and Murphy, 2014; Min et al., 2014).
The findings of DELTA measurements revealed that NO x , in particular NO 2 , is the most abundant compound in ΣN r followed by NH 3 . Both gases account for 73.2% of ΣN r . The values of NO x and NH 3 differ significantly from values proposed by Zöll et al. (2019), in particular NO x . This is related to the different periods, which were considered for averaging. Zöll et al.
(2019) reported values for summertime. In this study, values are influenced by seasonal impacts. It has to be considered that 510 the contribution of NH 3 differs with increasing ΣN r concentration whereas the contribution NO x remain almost similar. At the highest average ΣN r concentration, we determined a substantial contribution of particulate and acidic N r species, which is higher than the influence of NH 3 on ΣN r at that concentration level. Findings of Tang et al. (2020) had shown that HNO 3 concentrations measured by DELTA system using carbonate coated denuders may be significantly overestimated (45% on average) since HONO sticks also at those prepared surfaces. Thus, the HNO 3 contributions should be seen as an upper estimate.

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Consequentially, other compounds such as NO 2 and HNO 3 are also important for the interpretation of the ΣN r flux pattern.
NO 2 deposition and emission fluxes, which depend on the concentration level, were observed during the day by Horii et al.
(2004) above a mixed forest, and mostly deposition of NO 2 during the night. NO 2 exhibits also a bidirectional exchange pattern in natural ecosystems (Horii et al., 2004;Geddes and Murphy, 2014;Min et al., 2014). The diurnal cycle of NO is reversed to NO 2 during the day and is almost neutral with a tendency of slight emission during the night (Horii et al., 2004;Geddes 520 and Murphy, 2014). It has to be taken into account that NO 2 is removed from the atmosphere by the reaction with O 3 . During the day and night NO 3 reacts with NO 2 to N 2 O 5 . The latter can react with H 2 O to HNO 3 . HNO 3 is an effective removal for NO 2 and has a significant impact on the measured deposition flux (Munger et al., 1996). However, Min et al. (2014) (2004). They measured only deposition fluxes for NO y . Fluxes were mostly below -40 ng N m −2 s −1 , but could achieve up to -80 ng N m −2 s −1 . HNO 3 fluxes were almost as high as the NO y fluxes. Munger et al. (1996) did also NO y flux measurements above the same forest some years earlier and took measurements at less polluted spruce forest. At the latter location, only slight deposition of NO y occurred. At the former location, results are similar to Horii et al. (2006). It shows that HNO 3 seems to 530 have a significant influence on the deposition of ΣN r even at sites exhibiting a low concentration level of ΣN r compounds like NO 2 .
The observed daily cycle, which exhibits low negative or neutral fluxes during the night, increasing deposition in the morning, and decreasing deposition in the evening, is in agreement with other studies dealing with ΣN r compounds above different forest ecosystems. For example, Wyers and Erisman (1998)  ) and total nitrate NO − 3 fluxes, the aqueous phase of NH 4 NO 3 , above a spruce forest during the day. Apparently, fluxes measured at our location have high NO x , or, more precisely, a high NO 2 fraction, a generally low NH 3 fraction, which is higher for low ΣN r fluxes, and considerable fraction of particulate and acidic N r species, especially for 540 high ΣN r fluxes. In principle, the order of magnitude of the ΣN r flux is similar to values reported in the above-mentioned publications. Even if other NO y compounds are not the main flux contributors, they change the composition of the ΣN r flux. NO y compounds have an influence on the NO-NO 2 -O 3 cycle and on the reaction pathways of NH 3 and HNO 3 . These are not limited to gas phase reactions (Meixner, 1994), but also gas-particle interactions (Wolff et al., 2010) can occur. Thus, individual measurement devices are needed to measure single N r species for a precise quantification of the ΣN r flux. Implementing such 545 a setup will be challenging due to high technical requirements of the instruments in case of technical complexity, dimensions, and power consumption. Running such a setup for at least a year should also be considered for a representative data set.

Influence of micrometeorology on deposition and emission
Overall, the shape and maximum deposition of the daily cycles shown in Fig. 3 is mostly driven by global radiation, which acts as primary driver for the ΣN r exchange, recently verified by an artificial neural network approach conducted by Zöll . The authors identified ΣN r concentration as secondary driver for ΣN r deposition. The influence of concentration on ΣN r fluxes and its compounds had been reported in several studies (e.g., Brümmer et al., 2013;Zöll et al., 2016). Also, micrometeorological parameters such as relative humidity and temperature favor the exchange of ΣN r compounds (Wyers and Erisman, 1998;Milford et al., 2001;Wolff et al., 2010;Wentworth et al., 2016). Global radiation was not identified as primary controlling factor for NH 3 by Milford et al. (2001). They found that NH 3 exchange was mostly driven by canopy  Therefore, an in-depth investigation of relative humidity, temperature, leaf surface wetness, and concentration was conducted. The analysis of Fig.4 has shown that dry conditions, induced by higher temperatures and low relative humidity, favour  Horii et al. (2006) for NO y , Horii et al. (2004) for NO x , and by Zöll et al. (2016) for NH 3 . The 575 effect of temperature on the ΣN r fluxes is most pronounced during daytime. Higher temperatures increase the opening size of the stomata leading to increased photosynthetic activity. Wolff et al. (2010) observed higher deposition for total ammonium and total nitrate under dry conditions, which correspond to temperatures higher than 15 • C and relative humidity below 70%.
During foggy or rainy conditions, deposition was close to neutral or even emission occurred. Their ranges and corresponding limits for temperature and humidity are comparable to the values examined at our site. However, Wyers and Erisman (1998) 580 reveal that NH 3 deposition is maximized if canopy exhibits a high canopy water storage level (> 2 mm). They found that leaf surfaces could act as a sink and as a source of NH 3 . An elevated relative humidity level increase the thickness of the water layer covering the leaf surface, and thus wet leaves act as an effective removal of atmospheric NH 3 until a certain equilibrium in concentration is reached. Thus, we examined the influence of precipitation on measured fluxes. A separation of fluxes into different precipitation classes is shown in Fig. F1. In general, median deposition gets lower with increasing precipitation, and 585 emission fluxes can be found in classes with significant rainfall (>0.5 mm h −1 ). Strongest dry deposition occurs mainly during dry conditions, which is in contrast to the observations of Wyers and Erisman (1998). It has to be considered that the catchment, in which the flux tower is located, has a size of approximately 0.69 km 2 (Beudert and Breit, 2010) and is larger than the catchment of Wyers and Erisman (1998). Also, the surrounding forested area is much larger and the entire area is mountainous.
The forest stand is relatively young since it is recovering from a bark beetle outbreak in the 1990s and 2000s (Beudert and 590 24 https://doi.org/10.5194/bg-2020-364 Preprint. Discussion started: 14 October 2020 c Author(s) 2020. CC BY 4.0 License. Breit, 2014). Wyers and Erisman (1998) determined an average NH 3 concentration of 5.2 µgm −3 and median concentration of 3.5 µgm −3 . Their values are at least two times higher than measured NH 3 concentrations at our site. Presumably, if NH 3 concentrations are low, ΣN r dry deposition seems to be favored by dry conditions. Also, Wolff et al. (2010) measured low NH 3 concentrations at their forest site. Figure F1 also demonstrates that concentrations of ΣN r are elevated if leave surfaces are dry.
It shows that wet deposition is important for the uptake of ΣN r compounds at our measurement site. As mentioned in Sec. 2.1, 595 we measured substantial rainfall during 2.5 years at our measurement site. Due to the remoteness of the measurement site, air mass transport starting at potential nitrogen emission sources has to overcome long distances before reaching the site. Thus, a significant amount of ΣN r is probably deposited outside the footprint of the flux tower during rainy periods.

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The different gap-filling approaches led to almost the same deposition after 2.5 years. The advantage of inferential modeling is that long gaps in flux time series can be filled. This is not possible with MDV or other recently published gap-filling methods (e.g., Falge et al., 2001;Reichstein et al., 2005;Moffat et al., 2007;Wutzler et al., 2018;Foltýnová et al., 2020;Kim et al., 2020) because the latter are optimized for inert gases. Statistical methods like MDV assume a periodic variability of fluxes.
This assumption is mostly valid for inert gases, which have a distinctive daily cycle. Reactive gases mostly do not exhibit a 605 predictable flux variability. Their flux variability depends on micrometeorological conditions and their chemical and physical properties sometimes leading to instationarities in the data time series. Therefore, the application of statistical methods is rather questionable. However, also DEPAC-1D has some issues, which are not solved or implemented yet. For example, particle deposition is not considered, the implementation of N r species like HNO 3 is relatively straightforward compared to NH 3 , an exchange path with soil is not implemented yet, and the cuticular compensation point of NH 3 is underestimated under 610 high concentrations and temperatures . DEPAC-1D fluxes during winter were close to neutral whereas TRANC measurements show slight deposition and even emission under special circumstances. Further comparison to flux measurements at different sites can help to solve these issues. Gap-filling techniques based on artificial neural networks may be a further valuable option -if available. Uncertainties of the ΣN r fluxes were estimated with the method by Finkelstein and Sims (2001). The uncertainties of gap-filled fluxes through MDV were calculated by the error of the average. Gap-filled fluxes 615 through DEPAC-1D were not assigned with an uncertainty by the model. As an approximation, we assigned DEPAC-1D fluxes with a relative error of 20%. This relative error is a guess based on uncertainties in the implementation of DEPAC-1D and of the input data. In the following, possible uncertainties sources are mentioned. Considering the input data needed for site based modeling, uncertainties in concentration of N r compounds and turbulence measurements seem to have the largest impact on the modeled fluxes. Besides some power outages of a few days, instruments for recording meteorological data were operating 620 continuously. The agreement with modeled data from the ECMWF for the investigated grid cell was excellent (Fig. 7). Thus, uncertainties in meteorological data have a negligible impact on the modeled fluxes. Due to the low time resolution of DELTA and passive samplers, short-term variability is missing in NH 3 and HNO 3 concentration time series, especially for HNO 3 . NH 3 measurements were conducted by the NH 3 QCL, which allows to measure NH 3 with a high time resolution. The low deposition fluxes modeled by DEPAC-1D during winter are caused by measurement outages of QCL, which led to a missing 625 variability in concentrations of NH 3 . Thus, missing values had to be replaced by monthly averages measured by passive and DELTA samplers. Lower temperatures, which are (at mid-latitude sites) directly related to high stomatal resistances, also lead to low deposition values during winter. Since NH 3 concentration level is generally low during winter and assigned with a low variability as found by measurements, this procedure is reasonable for a limited time period. Differences in half-hourly fluxes during these times are difficult to interpret due to the low time resolution of the input data. No fast recording of HNO 3 630 was available at the measurement site. Since HNO 3 has also a significant contribution to the ΣN r flux, using fast-response measurements of HNO 3 (Farmer et al., 2006;Farmer and Cohen, 2008) in DEPAC-1D or other site-based inferential deposition models would be a much needed approach for further campaigns. At the moment, the implementation of HNO 3 in DEPAC is relatively simple (see Sec. 4.3.2). At agricultural sites, such an instrumentation for HNO 3 is not needed since exchange processes of ΣN r are most likely driven by a high NH 3 background concentration.

635
Uncertainties also arise from the measurement setup: Insufficient pump performance, issues in temperature stability of the TRANC and CLD, sensitivity loss of the CLD, and problems in the O 2 and CO supply. Therefore, regular maintenance and continuous observation of instrument performance parameters such as TRANC temperature and flow rate were done. With manual screening of measured half-hours and the recording of these parameters, compromised half-hours could be effectively excluded from analysis. Since certain sonic anemometers give an incorrect sonic temperature signal, which can be biased or 640 exhibit a non-linear relationship (Aubinet et al., 2012), sonic temperature was adjusted with the averaged temperature determined from measurements at 20 m and 40 m. Incorrect high-frequency temperature measurements affect the high-frequency damping, and therefore the determination of damping factors for ΣN r . Periods of insufficient turbulence were ruled out with a threshold for u * lower than 0.1 ms −1 (for details see Zöll et al., 2019, Sec. 2.4) and with the criteria of Mauder and Foken (2006). A basic assumption for the eddy covariance method is that the terrain needs to be flat, and the canopy height and 645 density should be uniform (Burba, 2013). These site criteria are not perfectly fulfilled at our measurement site. The site is located in a low mountain range and tree density is rather sparse south of the flux tower. Such diverse terrain characteristics could lead to unwanted turbulent fluctuations (non-stationarity of time series), which introduce noise in flux cross-covariance function. Consequentially, time lag estimation is compromised, and in particular fluxes close to the detection limit may not be determined correctly. However, situations of insufficient turbulence are mostly likely identified by the applied quality selection 650 criteria.
Adding the random flux errors determined with Finkelstein and Sims (2001) to the assumed relative errors that correspond to 20% of DEPAC-1D fluxes results in approximately ±3.4 kg N ha −1 for TRANC+DEPAC-1D and ±3.8 kg N ha −1 if MDV is used before applying DEPAC-1D. An uncertainty of ±2.6 kg N ha −1 is determined for DEPAC-1D. The dry deposition budget errors of the different approaches are similar. It shows that the discrepancy to DEPAC-1D lies in the upper range of 655 the estimated flux uncertainties. Yearly uncertainties of ΣN r fluxes were between ±1.0 kg N ha −1 a −1 and ±1.3 kg N ha −1 a −1 for 2016 and between ±1.2 kg N ha −1 a −1 and ±1.7 kg N ha −1 a −1 for 2017 resulting in an agreement with annual dry The influence of emissions caused by management processes at adjacent sites on measured ΣN r fluxes could not be verified.
The largest amount of N r released from those processes into the atmosphere will be deposited close to their sources. A small amount will be transported up to distances of 100 km (Asman et al., 1998;Ferm, 1998;Loubet et al., 2009). The released NH 3 going into long-range transport is highly variable (Loubet et al., 2009), and the distance depends on several parameter like atmospheric stability, atmospheric chemistry, topology, etc. In case of stable stratification, inversion layers often occurring in mountain ranges can prohibit air mass exchange. Probably, the measurement site is mostly outside the transport range. Thus, nitrogen enriched air-masses are deposited before reaching the height of the flux tower. A reduction in grid cell size could lead to a more precise localisation of potential nitrogen emission sources. Since all exchange processes contribute to single concentration within a grid cell, an improvement in horizontal resolution will lead to a refinement in predicted concentrations.
The aerodynamical reference height, which is used by LOTOS-EUROS for flux calculation, is also lower than the measure-735 ment height of the flux tower. Thus, slight differences in micrometeorological data can be expected, for example the difference in relative humidity in the first half of 2016. Differences for that time period are related to the usage of meteorological data provided by the NPBW, with their instrumentation being installed at the 50 m platform. The deviations in u * are most likely related to the complex terrain within the foot print of the flux tower. The surface roughness length and the tree composition is not uniform for the entire footprint. It is not possible to model such a diverse canopy structure within 7×7 km 2 grid cell 740 accurately. As stated earlier, the weighting of the land-use classes within the grid cell was not representative for the foot print.
The class "semi-natural grassland" has the highest contribution. However, Norway spruce and European Beech were found to be the most dominated tree type within the flux foot print. This issue could be partly solved by increasing the spatial resolution. The reduction in grid cell size could affect the fractions of N r compounds to modeled ΣN r concentrations (Fig. E1). The influence of NH 3 on ΣN r could change, and thus the predicted ΣN r dry deposition can be lowered since reduction in NH 3 has 745 the strongest influence on the deposition (Fig. 7).
As stated in Sec. 2.4.3, an incorrect setting of the LAI and z 0 can have a significant influence on ΣN r deposition. The results of our sensitivity analysis for LAI and z 0 are comparable to values presented recently by van der Graaf et al. (2020), who used satellite-derived LAI and z 0 data from Moderate Resolution Imaging Spectroradiometer (MODIS) to calculate ΣN r deposition with LOTOS-EUROS for a grid cell size of 7×7 km 2 . Overall, they observed changes in ΣN r dry deposition of 750 up to 30%. However, there is almost no change in ΣN r dry deposition and in NH 3 concentration observable for the Bavarian Forest measurement site if LAI and z 0 from MODIS are used. However, the attempts of van der Graaf et al. (2020) and Ge et al. (2020) did not provide a solution for the general overestimation of NH 3 deposition above southern Germany. It seems that the larger scale and temporal discrepancies in input NH 3 concentrations in LOTOS-EUROS are mainly responsible for the disagreement to flux measurements, and overestimation is only partly related to other issues, for example, the grid cell size of 755 7×7 km 2 .
Finally, two special ΣN r exchange events need to be discussed, the ΣN r emission fluxes in December 2017 and the deposition fluxes in February 2018. The emission phase in December 2017 may be related to the decomposition of fallen leaves (Hansen et al., 2015). Since the compensation point of the soil is set to zero for all land-use classes, the decomposition of fallen leaves is not considered in the models, and thus emissions from the soil could not be modeled. The deposition event in February 760 29 https://doi.org/10.5194/bg-2020-364 Preprint. Discussion started: 14 October 2020 c Author(s) 2020. CC BY 4.0 License. 2018 seen by the TRANC seems to be driven by particulate N r . Comparing the different runs of LOTOS-EUROS shows that the contribution of particulate deposition to total deposition is much larger than gaseous deposition during that time. However, the amount of deposited ΣN r of this event is underestimated by DEPAC-1D and LOTOS-EUROS. A second deposition event, which occurred directly after the mentioned one, was predicted by the models, but not confirmed by the measured fluxes.

Conclusions
Our study is the first one presenting 2.5 years flux measurements of ΣN r measured with a custom-built converter (TRANC) coupled to fast-response CLD above a protected mixed forest. We investigated temporal dynamics of ΣN r exchange, discussed 780 conditions favouring natural exchange characteristics of ΣN r under low atmospheric concentrations, and compare annual budgets of flux measurements to an in-situ deposition model, DEPAC-1D, and a long-range chemical transport model, LOTOS-

EUROS.
Measured concentrations of ΣN r were 5.2 ppb on average. Reactive compounds such as NH 3 and NO 2 had a concentration level of 1.8 ppb and 2.5 ppb, respectively. The latter exhibits highest concentrations during winter, the former during spring.

785
Elevated concentration level is possibly related to anthropogenic emission during those periods. DELTA measurements showed that NH 3 and NO 2 are the main contributors to ΣN r . On average, these gases contribute with 73.2% to ΣN r . These reactive gases are most responsible for observed exchange pattern of ΣN r at the measurement site. However, also particulate and acidic N r compounds are important for the dynamics of ΣN r exchange, especially at high ΣN r concentrations. We observed mostly deposition during 2.5 years of flux measurements. Median deposition ranges from -15 to -5 ng N m −2 s −1 . Highest 790 deposition was observed during mid spring and summer, lowest deposition occurred during late autumn and winter. From May to September deposition was favored under high ambient concentration (> 4.7 ppb), low humidity level (< 77 %), and high temperatures (> 14.3 • C). Additionally, dry leaf surfaces seem to enhance deposition. We conclude that dry conditions seem to favour ΣN r dry deposition at natural ecosystems supposedly related to a low contribution of NH 3 to the ΣN r fluxes. We found that concentrations of ΣN r were elevated in presence of dry leaf surfaces. Thus, wet deposition seems to be important for ΣN r 795 deposition at our measurement site during rainy periods. After 2.5 years, nitrogen dry deposition of TRANC measurements resulted in (11.1 ± 3.4) kg N ha −1 with DEPAC-1D as gap-filling method, and (10.9 ± 3.8) kg N ha −1 was determined with MDV and DEPAC-1D as gap-filling methods. Both values are rather close to modeled fluxes of DEPAC-1D (13.6 kg N ha −1 ) considering the uncertainties of measured fluxes and possible uncertainty sources of DEPAC-1D. Difference of DEPAC-1D to TRANC could be related to the parameterizations of reactive gases or the missing exchange path with soil. Further comparisons 800 of in-situ models to flux measurements are needed to address these issues. Both gap-filling approaches result in similar nitrogen dry deposition values. The advantage of DEPAC-1D is based on the gap-filling of long time series of missing data. However, there are still issues in the bidirectional resistance model DEPAC, which need to be solved. Up to now, there is no further option in replacing long-term gaps because most gap-filling methods are designed for inert gases. Gap-filling methods, which based on artificial neural networks, could also be useful for reactive gases.

805
LOTOS-EUROS exhibited the highest discrepancy to flux measurements, in particular for the actual land use of the grid cell (16.8 kg N ha −1 ). We showed that modeled NH 3 concentrations used as input parameter by LOTOS-EUROS were significantly higher than measured concentrations, and they disagreed in their seasonal pattern. Thus, modeled NH 3 concentrations were the main reason for the discrepancy in annual budgets. Also, the vegetation of the grid cell does not correspond to the vegetation of the flux footprint. Increasing the horizontal resolution could be a solution to that issue. Supposedly, a large-scale issue is 810 related to the overestimation of NH 3 concentration by LOTOS-EUROS.
Averaged annual ΣN r dry deposition was 4.5 kg N ha −1 a −1 for both gap-filling approaches applied to TRANC measurements, DEPAC-1D showed 5.3 kg N ha −1 a −1 , and LOTOS-EUROS modeled 5.2 kg N ha −1 a −1 to 6.9 kg N ha −1 a −1 depending on the weighting of land-use classes. The application of CBT resulted in 7.5 kg N ha −1 a −1 as upper estimate and 4.6 kg N ha −1 a −1 as lower estimate. Dry deposition estimated by TRANC, DEPAC-1D, and LOTOS-EUROS is within the 815 frame of minimum and maximum deposition estimated by CBT. The difference of flux measurements to CBT could be induced by the discrepancy in tree age of the selected trees for CBT compared to the forest stand within the footprint, and leaf area surfaces may also be different.
For a further improvement of deposition models and the investigation exchange characteristics of ΣN r , long-term flux measurements are needed for different ecosystems differing in their nitrogen stress. However, installing a setup presented in this 820 study at several locations is quite challenging due to power consumption, costs of the instruments, and their high technical requirements. A continuous monitoring of N r species by low-cost samplers complemented by high-frequency measurements of ΣN r and selected compounds like NH 3 for a limited time, for example during fertilization periods, can result in a better understanding of exchange processes and thus in a improvement of deposition models (Schrader et al., 2018). Recently, Schrader et al. (2020) showed that stomatal conductances, essential for controlling the NH 3 exchange between vegetation and atmo-825 sphere, can be determined from CO 2 flux measurements. Using CO 2 -derived stomatal conductances will lead to a significant improvement of biosphere-atmosphere exchange models making them sensitive to climate change effects.