Forest–atmosphere exchange of reactive nitrogen in a remote region – Part II: Modeling annual budgets

. To monitor the effect of current nitrogen emissions and mitigation strategies, total (wet + dry) atmospheric nitrogen deposition to forests is commonly estimated using chemical transport models or canopy budget models in combination with throughfall measurements. Since ﬂux measurements of reactive nitrogen (N r ) compounds are scarce, dry deposition process descriptions as well as the calculated ﬂux estimates and annual budgets are subject to considerable uncertainties. In this study, we compared four different approaches to quantify annual dry deposition budgets of total reactive nitrogen ( (cid:54) N r ) at a mixed forest site situated in the Bavarian Forest National Park, Germany. Dry deposition budgets were quantiﬁed based on (I) 2.5 years of eddy covariance ﬂux measurements with the Total Reactive Atmospheric Nitrogen Converter (TRANC); (II) an in situ application of the bidirectional

Abstract. To monitor the effect of current nitrogen emissions and mitigation strategies, total (wet + dry) atmospheric nitrogen deposition to forests is commonly estimated using chemical transport models or canopy budget models in combination with throughfall measurements. Since flux measurements of reactive nitrogen (N r ) compounds are scarce, dry deposition process descriptions as well as the calculated flux estimates and annual budgets are subject to considerable uncertainties. In this study, we compared four different approaches to quantify annual dry deposition budgets of total reactive nitrogen ( N r ) at a mixed forest site situated in the Bavarian Forest National Park, Germany. Dry deposition budgets were quantified based on (I) 2.5 years of eddy covariance flux measurements with the Total Reactive Atmospheric Nitrogen Converter (TRANC); (II) an in situ application of the bidirectional inferential flux model DEPAC (Deposition of Acidifying Compounds), here called DEPAC-1D; (III) a simulation with the chemical transport model LOTOS-EUROS (Long-Term Ozone Simulation -European Operational Smog) v2.0, using DEPAC as dry deposition module; and (IV) a canopy budget technique (CBT).
Averaged annual N r dry deposition estimates determined from TRANC measurements were 4.7 ± 0.2 and 4.3 ± 0.4 kg N ha −1 a −1 , depending on the gap-filling approach. DEPAC-1D-modeled dry deposition, using concentrations and meteorological drivers measured at the site, was 5.8 ± 0.1 kg N ha −1 a −1 . In comparison to TRANC fluxes, DEPAC-1D estimates were systematically higher during summer and in close agreement in winter. Modeled N r deposition velocities (v d ) of DEPAC-1D were found to increase with lower temperatures and higher relative humidity and in the presence of wet leaf surfaces, particularly from May to September. This observation was contrary to TRANC-observed fluxes. LOTOS-EUROS-modeled annual dry deposition was 6.5 ± 0.3 kg N ha −1 a −1 for the sitespecific weighting of land-use classes within the site's grid cell. LOTOS-EUROS showed substantial discrepancies to measured N r deposition during spring and autumn, which was related to an overestimation of ammonia (NH 3 ) concentrations by a factor of 2 to 3 compared to measured values as a consequence of a mismatch between gridded input NH 3 emissions and the site's actual (rather low) pollution climate. According to LOTOS-EUROS predictions, ammonia contributed most to modeled input N r concentrations, whereas measurements showed NO x as the prevailing compound in N r concentrations. Annual deposition estimates from measurements and modeling were in the range of minimum and maximum estimates determined from CBT being at 3.8 ± 0.5 and 6.7 ± 0.3 kg N ha −1 a −1 , respectively. By adding locally measured wet-only deposition, we estimated an annual total nitrogen deposition input between 11.5 and

Introduction
In the last century, global nitrogen emissions have increased significantly due to anthropogenic activities . Reactive nitrogen compounds, such as ammonia (NH 3 ) and nitrogen oxides (NO x ), contribute most to the emissions. Ammonia emissions originate mostly from animal husbandry and fertilizer application , whereas NO x emissions are mainly related to combustion processes in, e.g., transport and industry (Erisman et al., , 2013. Although fertilizer use and the internal combustion engine are vital for the world's food security and the economy, the release of these compounds into the atmosphere has a wide range of negative effects (Krupa, 2003;Galloway et al., 2003;Erisman et al., 2013). Deposition of reactive nitrogen into ecosystems has been identified as a reduction factor for biodiversity (Bobbink et al., 1998;Krupa, 2003;Galloway et al., 2003;Sutton et al., 2011). In particular, ecosystems with nutrient-poor soils are highly sensitive to additional nitrogen inputs, resulting in a change in plant species (Damgaard et al., 2011;Paulissen et al., 2016) and species composition in forests (Dirnböck et al., 2014(Dirnböck et al., , 2018Roth et al., 2022). Critical loads are used to show at which level long-term nitrogen deposition may lead to adverse impacts (Hettelingh et al., 1995). Investigations by Hettelingh et al. (2013) have shown that half of the European ecosystems receive nitrogen above the critical level. In Germany, the fraction of ecosystems with a critical load exceedance is estimated to be about 70 % .
Quantitative estimation of the total nitrogen deposition is needed to assess exceedances of critical loads and to develop successful mitigation strategies. Although wet deposition is relatively straightforward to measure, the accurate quantification of dry N deposition remains a challenge. Recent progress in fast and robust measurement techniques allows for the investigation of the temporal dynamics in concentrations and dry deposition fluxes (using the eddy covariance (EC) approach) for total reactive nitrogen ( N r ) Ammann et al., 2012;Brümmer et al., 2013Brümmer et al., , 2022aZöll et al., 2019;Ammann et al., 2019;Wintjen et al., 2020Wintjen et al., , 2022 and its individual compounds, e.g., for NH 3 (Whitehead et al., 2008;Ferrara et al., 2012Ferrara et al., , 2021Zöll et al., 2016;Moravek et al., 2020). For N r , the Total Reactive Atmospheric Nitrogen Converter (TRANC)  coupled to a chemiluminescence detector (CLD) has shown its suitability for flux measurements in various field applications (see references for N r above). Despite the recent progress, the number and temporal coverage of available datasets remains small. As these in situ measurements are only valid for the ecosystem where the specific observations took place, a large-scale assessment based on observations alone is not feasible without a dense observation network.
Chemical transport models (CTMs) are used to assess nitrogen deposition over large regions. For Germany, the CTM LOTOS-EUROS (Wichink Kruit et al., 2012;Manders et al., 2017;van der Graaf et al., 2020) is applied for the mapping of nitrogen deposition fluxes across the country. LOTOS-EUROS predicts the dry deposition of various N r compounds -namely, nitrogen dioxide (NO 2 ), nitric oxide (NO), nitric acid (HNO 3 ), ammonia (NH 3 ), particulate ammonium (NH + 4 ), and nitrate (NO − 3 ) -in each grid cell by utilizing meteorological data from the European Centre for Medium Range Weather Forecasts (ECMWF), modeled concentrations of the mentioned compounds based on their emission sources and chemical processing, and information about the land-use distribution within each grid cell. The deposition module DEPAC (Deposition of Acidifying Compounds) is applied for calculating the dry deposition velocities of those compounds . DEPAC is a dry deposition inferential scheme featuring bidirectional NH 3 exchange (van Zanten et al., 2010;Wichink Kruit et al., 2012), which is also implemented in the Operational Priority Substance (OPS) model (van Jaarsveld, 2004;Sauter et al., 2020). DE-PAC can be used as a stand-alone model for estimating the dry deposition of N r compounds. For site-based modeling with DEPAC, decoupled from a CTM and henceforth called DEPAC-1D, only measurements of common micrometeorological variables and concentrations of the individual N r compounds are needed. In the past, deposition estimates have often been obtained through such an inferential modeling approach (Flechard et al., 2011(Flechard et al., , 2020Li et al., 2016;Schwede et al., 2011).
To evaluate modeled annual total dry deposition and seasonal patterns in modeled fluxes and deposition velocities, a careful comparative analysis to flux measurements may provide feedback on the representativeness of the input data and the bidirectional parameterizations . Wintjen et al. (2022) presented and analyzed novel flux measurements of N r and several subcomponents, focusing on temporal dynamics above a remote, mixed forest site spanning a 2.5-year period. This dataset provides a unique opportunity for the evaluation of different approaches to quantify dry deposition fluxes. Such comparisons with novel measurement techniques are sparse and only available from a few field campaigns Brümmer et al., 2013Brümmer et al., , 2022aZöll et al., 2019). Since the adoption of the Geneva Convention on Long-Range Transboundary Air Pollution (CLRTAP) in 1979, throughfall measurements have been carried out at many sites of the International Co-operative Programmes on Assessment and Monitoring of Air Pollution Effects on Forests (ICP Forests, http://www.icp-forests.net, last access: 14 March 2022) and forested catchments (ICP Integrated Monitoring, http://www. syke.fi/nature/icpim, last access: 14 March 2022) according to standardized protocols. Using the so-called canopy budget technique (CBT), throughfall measurements also allow one to give an estimate of the annual nitrogen dry deposition (Draaijers and Erisman, 1995;de Vries et al., 2003).
In this study, we provide a comparison of four independent methods for estimating nitrogen dry deposition for a remote mixed forest site in the Bavarian Forest National Park. The comparison is made for a 2.5 year period for which novel flux measurements were available (see companion paper Wintjen et al., 2022). The aim of this measurement campaign, covering the timeframe January 2016-June 2018, was to quantify background concentrations and deposition levels as well as their temporal dynamics to further improve the modeling of nitrogen deposition, which may be used for further defining environmental protection guidelines. Therefore, in this paper, we (1) present modeled concentrations, deposition velocities, and fluxes of N r and compare them to measurements of the same compounds, (2) discuss the influence of micrometeorological parameters on modeled deposition velocities and the impact of measured and modeled input parameters on modeled fluxes, (3) compare annual N r budgets of LOTOS-EUROS with DEPAC-1D, flux measurements, and nitrogen deposition estimates based on CBT and review them in the context of critical loads, and (4) finally discuss uncertainties affecting modeled dry deposition estimates.

Dataset description
For the comparison to modeled N r deposition fluxes, TRANC EC flux measurements, described in detail in Wintjen et al. (2022), were used. These flux measurements were available at a half-hourly resolution, were carried out 30 m above the forest floor, and had a data coverage of 41.0 %, considering the entire campaign period. Data gaps were related to violations of the EC theory and performance issues of the instruments.
For the application of DEPAC-1D, time series of micrometeorological parameters (i.e., temperature, atmospheric pressure, relative humidity, global radiation, Obukhov length (L), friction velocity (u * )) and air pollutant concentrations (NO, NO 2 , HNO 3 , NH 3 , pNO − 3 , pNH + 4 , and sulfur dioxide (SO 2 )) are required for flux calculations. NH 3 concentrations obtained from quantum cascade laser measurements taken at 30 m above ground, NO 2 and NO obtained from chemiluminescence measurements taken at 50 m above ground, and micrometeorological parameters were aggregated at a halfhourly resolution, whereas the remaining N r species and an additional NH 3 determination were obtained on a monthly basis from DELTA (DEnuder for Long-Term Atmospheric sampling, e.g., Sutton et al., 2001;Tang et al., 2009) and passive-sampler (NH 3 only) measurements of the IVL type (Ferm, 1991). DELTA measurements were made at 30 m and passive-sampler measurements at 10, 20, 30, 40, and 50 m above ground. Temperature and relative humidity were collected in a profile at 10, 20, 40, and 50 m above ground. Pressure and global radiation measurements were taken at 50 m. Indicators of stability and turbulence, such as L and u * , were obtained from momentum flux measurements of the sonic anemometer.
Gaps in DEPAC-1D were related to gaps in micrometeorological input data and issues in the measurements of N r compounds. Respective half-hourly values in the flux time series of each gas (approx. 3.4 % for NH 3, HNO 3, pNH + 4 , and pNO − 3 and 9.3 % for NO and NO 2 ) were filled with results from LOTOS-EUROS. A detailed description of the site and the instrumentation is given in Wintjen et al. (2022). For LOTOS-EUROS flux modeling, modeled input data of the European Centre for Medium-Range Weather Forecasts (ECMWF) and the national emission inventory of Germany (Schneider et al., 2016) were used to predict deposition fluxes for NO, NO 2 , HNO 3 , NH 3 , pNO − 3 , and pNH + 4 . LOTOS-EUROS fluxes were resampled to half-hourly timestamps from the original hourly resolution, and missing fluxes were linearly interpolated. For the canopy budget technique, throughfall measurements under spruce and beech trees in close proximity to the station  and bulk deposition measurements at an open site (Wintjen et al., 2022) were taken at weekly intervals and were used for the determination of total nitrogen dry deposition on an annual basis (Sect. 2.3). An overview of all the methods is given in Table 1.
To compare dry deposition estimates from modeling to TRANC measurements, we filled gaps in the TRANC flux data with results from DEPAC-1D and, henceforth, called this dataset TRANC(DEPAC-1D). In a second approach, we applied the mean diurnal variation (MDV) method (Falge et al., 2001) to short-term gaps, analogous to Wintjen et al. (2022), and replaced remaining gaps with results from DEPAC-1D. This approach was called TRANC(MDV + DEPAC-1D). Both approaches, DEPAC-1D alone and the combination of DEPAC-1D and MDV, were able to fill all gaps in the TRANC flux time series. Uncertainties of the gap-filled fluxes determined by MDV were calculated as the standard error of the mean. Cumulative uncertainties of TRANC fluxes were solely based on the uncertainty of the gap filling and were calculated according to Eq. (3) of Wintjen et al. (2022). The error calculation scheme proposed by Brümmer et al. (2022a, Eq. 1) was applied to fluxes filled with DEPAC-1D. Flux uncertainty of those halfhourly values was given as whereX represents the median of the ratio of the uncertainty of the measured fluxes (F unc,meas ) to their corresponding flux values (F meas ). The uncertainty of the measured fluxes was estimated after Finkelstein and Sims (2001). Systematic uncertainties were not accounted for in the error calculation. A discussion on systematic uncertainties is given in Wintjen et al. (2022). In surface-atmosphere flux exchange models, fluxes are calculated by using resistance schemes. In the case of gases exhibiting bidirectional exchange behavior, the flux F is defined as follows: The flux is a product of the deposition velocity (v d ) with the concentration difference between the atmospheric concentration, χ a , and the compensation point, χ tot , of the trace gas. In DEPAC, a compensation point is only implemented for NH 3 . Both the dry deposition or exchange velocity and the atmospheric concentration are height dependent and are given for an aerodynamic reference height (z − d), where z is the geometric height and d the zero-plane displacement height. The following convention is used for the fluxes: nega-tive values represent deposition, and positive values represent emission. Following the conductivity-resistance analogy, v d is the inverse of the sum of the aerodynamic resistance (R a ), the quasi-laminar layer resistance (R b ), and the canopy resistance (R c ).
DEPAC (van Zanten, et al., 2010) can be used to calculate the dry deposition of reactive nitrogen gases. R a and R b are required by DEPAC as input variables. Hence, the module is oriented toward determining R c for NO, NO 2 , HNO 3 , and NH 3 . R c is treated differently for each N r compound but basically as the sum of parallel resistances, which model the exchange behavior of the atmosphere and vegetation: The stomatal resistance (R stom ) is calculated following Emberson et al. (2000a, b). In this scheme, stomatal conduc-tance is determined by vegetation type, dependent on maximum conductance lowered by factors controlling stomatal opening -i.e., light intensity, ambient temperature, vapor pressure deficit, and soil water content -using well-known Jarvis functions (Jarvis, 1976). For NH 3 , a stomatal compensation point (χ stom ) is calculated following Wichink . The cuticular resistance (R w ) is described by Sutton and Fowler (1993) for NH 3 , and the corresponding cuticular compensation point is based on the works of Wichink . For NO and NO 2 , R w is set considerably high to 10 000 and 2000 s m −1 , respectively, allowing hardly any deposition on external surfaces. The in-canopy resistance (R inc ) is given by van Pul and Jacobs (1994), and the soil resistance (R soil ) is described following Erisman et al. (1994). In the current version of DE-PAC, the soil compensation point is set to zero for all surface types. In the case of HNO 3 , a fast uptake to any surface is assumed through a low, constant R c of 10 s m −1 . The total compensation point (χ tot ) is determined as written in van Zanten et al. (2010).

Modeling of N r deposition (LOTOS-EUROS)
LOTOS-EUROS (Manders et al., 2017) simulations were performed for the entire measurement period. For this purpose, a large-scale simulation was set up for Europe, in which a second domain covering northwestern Europe at 7 × 7 km 2 was nested. The simulations were forced with weather data from the ECMWF and the CORINE-2012 landuse classification. For the European background simulation, the CAMS-REG European emission inventory (Kuenen et al., 2021) was used. For the inner domain, the emission data for Germany were replaced by the national emission inventory. For Germany, the gridded emissions were obtained from the GRETA system (GRETA -Gridding Emission Tool for ArcGIS v1.1; Schneider et al., 2016). On an hourly basis, the land-use-specific total dry deposition was calculated in LOTOS-EUROS by applying DEPAC for NH 3 , NO, NO 2 , and HNO 3 . Dry deposition of pNO − 3 and pNH + 4 was calculated according to Zhang et al. (2001) (see Manders-Groot et al., 2016, Sect. 5.2). In the model, the dry deposition velocity and flux are calculated for the mid-layer height of the first model layer, which has a depth of ca. 20 m. By assuming a constant flux and using the stability parameters, the concentrations can be estimated for the canopy top and the typical observation height (2.5 m above roughness length (z 0 )) in air quality networks. The Corine Land Cover 2012 classification of the grid cell, in which the measurement site was located, was divided into 46.0 % seminatural vegetation, 37.2 % coniferous forest, 15.9 % deciduous forest, 0.7 % water bodies, and 0.2 % grassland. However, the actual structure of the forest stand showed 81.1 % coniferous forest and 18.9 % deciduous forest within the footprint of the flux measurements during the measurement campaign. Due to differences in the distribution of vegetation types in the footprint, results from LOTOS-EUROS were calculated with the site-specific weighting of land-use classes of the flux tower's footprint. The low contribution of coniferous forest and deciduous forest within the grid cell may be related to the evaluation of older aerial photographs showing larger areas of deadwood. Finally, the dry deposition of N r was calculated as the sum of the individual N r fluxes. A detailed documentation of LOTOS-EUROS is given in Manders-Groot et al. (2016) and Manders et al. (2017).

Site-based modeling of N r deposition (DEPAC-1D)
DEPAC-1D is a stand-alone version of LOTOS-EUROS's dry deposition module DEPAC, using a FORTRAN90 wrapper program to accept arbitrary input datasets. DEPAC-1D used micrometeorological variables and parameters measured at the site to estimate R c and the compensation point of NH 3 . The atmospheric resistances -R a and R b -and the fluxes of NH 3 , NO, NO 2 , HNO 3 , pNO − 3 , and pNH + 4 were calculated outside DEPAC following Garland (1977) and Hummelshøj (1995, 1997), with stability corrections after Webb (1970) and Paulson (1970). The deposition of particles was calculated following Zhang et al. (2001) (see also Manders-Groot et al., 2016, Sect. 5.2) and was therewith equal to LOTOS-EUROS. For the fine fraction of pNO − 3 and pNH + 4 , a mass median diameter of 0.7 µm was used. For the coarse fraction of pNO − 3 , 8 µm was taken (Manders-Groot et al., 2016, Sect. 5.2). Note that particle deposition is, strictly speaking, not part of the DEPAC module and was modeled with a separate program, implementing the particle deposition scheme used within LOTOS-EUROS.
Half-hourly gaps in the NH 3 QCL concentration time series were filled with their monthly integrated concentration value obtained from DELTA samplers. If these measurements were not available, missing values were replaced by monthly integrated results from passive-sampler measurements of NH 3 . During winter, the uncertainty introduced by this gap-filling approach seems to be low, as suggested by Schrader et al. (2018). We did not superimpose gap-filled concentration values with a diurnal pattern or use monthly averages of half-hours to fill gaps in the concentration time P. Wintjen et al.: Forest-atmosphere exchange of reactive nitrogen in a remote region series, since abrupt changes in the NH 3 concentration pattern -i.e., periods of low autocorrelation -could not be reproduced by a synthetic diurnal cycle or by monthly averages of half-hourly values. Fluxes of HNO 3 , pNO − 3 , and pNH + 4 were based solely on monthly DELTA measurements. Gaps in the time series of these compounds and SO 2 were replaced by monthly averages from adjacent years. NO and NO 2 fluxes were based on half-hourly concentration measurements. The difference in measuring height was considered in the calculation of R a . SO 2 and NH 3 concentrations from gap-filled DELTA time series were used to determine compensation points and additional deposition corrections.
Since measurements of temperature and relative humidity data were not available at the measurement height of the EC system, we took the average of measurements from 20 and 40 m height above ground. These profile measurements started in April 2016 (Wintjen et al., 2022); thus, measurements at 50 m were used until end of March 2016. For modeling R a , the solar zenith angle (which is calculated by using celestial mechanic equations), z 0 , and d are needed. We set z 0 to 2.0 m and d to 12.933 m for the coniferous forest and to 11.60 m for the deciduous forest, corresponding to LOTOS-EUROS defaults for these land-use classes. Leaf area index (LAI) was modeled as described by van Zanten et al. (2010). The LAI determined from the site-specific landuse class weighting ranged between 4.1 and 4.8 due to leaf growth and shedding.
The calculation of the dry deposition was made with the mentioned input data on a half-hourly basis for NH 3 , NO, NO 2 , HNO 3 , pNO − 3 , and pNH + 4 . Results from DEPAC-1D were weighted with the site-specific land-use distribution within the flux measurement's footprint (81.1 % coniferous forest and 18.9 % deciduous forest).

Measuring nitrogen outflow from the canopy using the canopy budget technique (CBT)
The canopy budget technique (CBT) is the most common method for estimating total (wet + dry) atmospheric deposition of dissolved inorganic nitrogen (DIN t ) based on wet inorganic nitrogen fluxes of NO − 3 and NH + 4 ions estimated from open-site precipitation (bulk deposition) and throughfall of NO − 3 and NH + 4 ions measurements (see Staelens et al., 2008, Table 1). DIN t was estimated on a monthly basis after the CBT approach of Draaijers andErisman (1995) andde Vries et al. (2003). The results from the two methods differed only marginally and were therefore averaged. The biological conversion of deposited inorganic nitrogen into dissolved organic nitrogen (DON) in the phyllosphere (bacteria, yeasts, and fungi) or the dry deposition of atmospheric DON onto the canopy or the exudation of DON from plant tissues is not addressed in CBT. Here, it was estimated by the difference of DON fluxes between throughfall and bulk deposition and is henceforth called DON. Adding DON to throughfall DIN or to DIN t reveals a frame of lower and upper es-timates of total (wet + dry) nitrogen deposition (N t ) and, by subtracting DIN deposition at an open land site from these N t , of lower and upper estimates of dry deposition (Beudert and Breit, 2014).

Comparison of modeled and measured concentrations
3.1.1 High resolution concentration measurements of NH 3 , NO x , and N r Figure 1 shows the comparison of measured half-hourly NH 3 , NO x , and N r concentrations (see Wintjen et al., 2022) to their modeled concentrations of LOTOS-EUROS, represented as monthly box-whisker plots. From highresolution concentration measurements, we found average concentrations and standard deviations of 1.0 ± 0.6, 1.4 ± 1.2, and 3.1 ± 1.7 µg N m −3 for NH 3 , NO x , and N r for the entire campaign, respectively. Corresponding averages of LOTOS-EUROS of NH 3 and N r were higher by 0.8 and 1.9 µg N m −3 , whereas NO x was slightly underestimated. Substantial mismatches in standard deviations of NH 3 and N r indicate that the variability in concentrations of NH 3 and N r was overestimated by LOTOS-EUROS. In the case of NH 3 , the largest discrepancies were observed for spring and partially for autumn. NO x concentrations were systematically underestimated by LOTOS-EUROS in summer. During winter, the difference between measured and modeled NO x concentrations was lower than during the summertime. Except for the summer, modeled half-hourly concentrations of N r were 2 to 3 times higher than the measured values. The slight seasonal differences in measured N r concentrations could not be reproduced by LOTOS-EUROS. The largest discrepancy during spring clearly correlates with the modeled NH 3 concentrations.

Passive samplers and DELTA measurements
The large modeled NH 3 concentrations by LOTOS-EUROS could also not be verified by the observed levels of the passive samplers and the DELTA system. Figure S1 shows a comparison of the applied NH 3 measurement techniques with NH 3 concentrations predicted by LOTOS-EUROS. Figures and Tables denoted with an S can be found in the Supplement. A two-to threefold overestimation of NH 3 concentrations by LOTOS-EUROS is visible. In addition, the modeled seasonal pattern was also not in agreement with the results from wet chemical samplers.
A comparison of the individual N r compounds measured by DELTA to those measured by LOTOS-EUROS is displayed in Fig. 2. Considering the entire campaign, we measured average concentrations of 0.55, 0.17, 0.42, and 0.19 µg, N m −3 for NH 3 , HNO 3 , pNH + 4 , and pNO − 3 , respec- tively. For the same exposure periods, the concentration averages of LOTOS-EUROS for NH 3 , HNO 3 , pNH + 4 , and pNO − 3 were 1.8, 0.1, 1.2, and 0.8 µg N m −3 , respectively. Differences considering the entire campaign duration are shown in Fig. S2. Like NH 3 , particulate nitrogen compound concentrations were also higher in the LOTOS-EUROS simulations. Predicted seasonality for pNH + 4 and pNO − 3 could only partially be verified by DELTA measurements. For HNO 3 , concentrations were in close agreement. In total, N r values of DELTA and TRANC showed a reasonable agreement, and N r concentrations showed only small seasonal differences, whereas LOTOS-EUROS overestimated N r of the TRANC by ca. 2 µg N m −3 (Fig. S2).
According to Wintjen et al. (2022), NO x was the predominant compound in the N r concentrations. For the entire campaign, NO x contributed 51.4 % and NH 3 20.0 % to measured N r , whereas LOTOS-EUROS predicted NH 3 as the most important compound (∼ 35.7 %) contributing to N r , followed by pNH + 4 (∼ 24.3 %), NO x (∼ 22.8 %), pNO − 3 (∼ 15.2 %), and HNO 3 (∼ 1.9 %), as shown by Fig. S3. Furthermore, LOTOS-EUROS showed deviations from measurements in seasonal contributions. During winter, the contribution of NH 3 to N r was surprisingly high (28.6 %) compared to the observations (4.9 %). HNO 3 contributions were comparable and on a low level between LOTOS-EUROS and DELTA. On average, particle contribution was higher in the model. Contributions of pNO − 3 and pNH + 4 were highest during spring, according to measurements, but lowest in LOTOS-EUROS in that season. Apart from springtime, seasonal contributions of pNO − 3 and pNH + 4 were higher by 6.6 %-14.4 % in LOTOS-EUROS.

Comparison of modeled and measured deposition velocities
3.2.1 Comparison of modeled and measured deposition velocities for each N r compound NH 3 deposition velocities of LOTOS-EUROS and DEPAC-1D exhibited similar values in winter, but disagreements were found in summer and autumn. In summer, DEPAC-1D determined systematically larger median deposition velocities, whereas LOTOS-EUROS predicted a large variability in NH 3 deposition velocities during autumn, which was not supported by DEPAC-1D. For NO 2 , deposition velocities of LOTOS-EUROS and DEPAC-1D agreed well in their temporal pattern and the median deposition velocities, but the variability in DEPAC-1D deposition velocities was slightly higher during summer. In both model applications, NO deposition velocities were practically zero (medians always <0.06 cm s −1 ). For pNH + 4 , deposition velocities of DEPAC-1D and LOTOS-EUROS agreed well, with median deposi- tion velocities close to zero, but a large disagreement was found during winter. Deposition velocities of pNO − 3 were close to zero during the entire campaign in DEPAC-1D, but LOTOS-EUROS showed a large scattering of v d in the winter months. For HNO 3 , a discrepancy in v d was also found during winter, and, similar to NH 3 , deposition velocities of DEPAC-1D were generally larger from May to September. The comparison of the deposition velocities for each N r compound modeled by DEPAC-1D and LOTOS-EUROS is shown in Fig. S4.

Comparison of modeled and measured N r deposition velocities
A comparison of the modeled and measured v d for the N r flux is provided in Fig. 3. The modeled total nitrogen dry deposition velocities were obtained by dividing the modeled dry deposition flux for all compounds by the modeled total nitrogen concentrations in ambient air. When subtracting the median v d of TRANC from LOTOS-EUROS results, differences typically ranged between −0.3 and 1.0 cm s −1 . Particularly during the summer months, an overestimation of v d by DEPAC-1D was observed with respect to TRANC measurements. During those months, the median v d of DEPAC-1D was ca. 2 to 3 times higher than their measured entities. LOTOS-EUROS v d of the N r flux were generally lower than DEPAC-1D but still larger than those found in the measurements within that period. During the winter months, DEPAC-1D N r showed the lowest median values and variability, whereas deposition velocities of TRANC and LOTOS-EUROS were comparable, caused by the influence of pNO − 3 and pNH + 4 on LOTOS-EUROS v d predictions. Modeled and measured medians v d and their lower and upper quartiles are given in Table S1.
Inspection of the diurnal cycles of N r deposition velocities for May to September in the year 2017 (Fig. S7) shows that both the DEPAC-1D and measured data exhibit a clear diurnal pattern, with the lowest deposition during the night and the highest values around noon. However, in those periods where the measured data are close to zero during the night, the modeled fluxes show considerable nighttime exchange, with deposition velocities between 0.5 and 1 cm s −1 .
To further examine the reasons behind these discrepancies, we show the diurnal cycles of v d after classifying the N r deposition velocities for half-hours without precipitation during May-September into two groups, being below or above the median temperature (T air = 14.6 • C), relative humidity (RH = 74.0 %), and total N r concentration (c( N r ) = 2.7 µg N m −3 ). Leaf surface wetness was measured at the site by means of sensors attached to a spruce and a beech tree. In order to classify the sensor as dry or wet, the half-hourly leaf wetness value was compared to a threshold value based on the calculation scheme given by Wintjen et al. (2022).
The diurnal cycles illustrate the same diurnal biases as discussed above. Figure 4 shows that DEPAC-1D results indicate that lower temperatures, higher relative humidity, and wet leaf surfaces enhance the N r dry deposition velocity. This behavior was expected based on the models' parameterizations, but it is contradictory to the TRANC measurements. In particular, the differences for the relative humidity regimes are remarkable. Smaller differences are observed for the dependency on temperature and the N r concentration, although both have a stronger influence in the model than on their measured counterpart.
In the case of LOTOS-EUROS, separating diurnal cycles of v d led to similar observations being made for DEPAC-1D regarding relative humidity and leaf surfaces. In addition, lower temperatures and concentration tend to increase v d , which contradicts the results of DEPAC-1D. Generally, values of v d are closer to TRANC deposition velocities, but the diurnal pattern differs from those of TRANC and DEPAC-1D, showing maxima in the morning (∼ 06:00 LT) and evening (∼ 18:00 LT) and low values around noon, except in the case of high relative humidity and wet leaf surfaces. The statements made for v d can be transferred to the flux predictions. Differences to the observations made for v d (Fig. S4) are related to the concentration input data. For example, due to overestimations of modeled NH 3 concentrations in spring and autumn, differences in the fluxes were higher during the same time. Modeled NO 2 and HNO 3 concentrations of LOTOS-EUROS were lower than their measured values, resulting in flux underestimations by LOTOS-EUROS for NO 2 and HNO 3 during summer. High modeled input concentrations of particulate nitrogen led to substantial deposition fluxes in the LOTOS-EUROS simulations. Following the model predictions, NH 3 fluxes had the largest contribution to the modeled N r flux, with an average flux of −12.5 and −13.0 ng N m −2 s −1 in the DEPAC-1D and LOTOS-EUROS applications, respectively, considering the entire campaign. Averaged fluxes of NO 2 and HNO 3 showed -although on a low level in absolute terms -higher deposition fluxes for DEPAC-1D, namely 2.0 and 1.3 ng N m −2 s −1 , respectively, compared to 1.2 and 0.3 ng N m −2 s −1 in the case of LOTOS-EUROS. Substantial flux differences were found for particulate nitrogen. DEPAC-1D averaged fluxes were close to zero (0.9 and 0.1 ng N m −2 s −1 for pNH + 4 and pNO − 3 , respectively), whereas LOTOS-EUROS showed substantially higher aerosol deposition, with averaged fluxes of 3.7 and 2.2 ng N m −2 s −1 for pNH + 4 and pNO − 3 , respectively. The comparison of fluxes for each N r compound of LOTOS-EUROS and DEPAC-1D is shown in Fig. S5.
Apart from concentrations being responsible for the differences in modeled flux estimates, other parameters may have also contributed to the deviations. To further investigate the impacts of the input data used in the LOTOS-EUROS simulations, we made a comparison of the measured and modeled input parameters used for the dry deposition modeling of NH 3 in LOTOS-EUROS (Fig. S6). The agreement of temperature and global radiation in terms of their coefficient of determination R 2 was good. We found differences of approximately 1.5 • C and −6.1 W m −2 of modeled to measured values on average. High R 2 values were determined for the entire campaign duration using half-hourly values -namely, 0.97 for temperature and 0.78 for global radiation. A slight difference was found for relative humidity during the first half of 2016. However, modeled values were higher by only 2.4 % on average, and the R 2 was still 0.67. In the case of u * , we found a systematic difference, and the seasonal pattern did not agree well, resulting in a lower R 2 of 0.43 compared to the other micrometeorological parameters. In particular, from November 2017 to February 2018, the difference . Averaged diurnal cycles of N r v d for low and high temperature, relative humidity, and concentration during the timeframe May-September. The top row refers to TRANC measurements (a-d), the middle row refers to DEPAC-1D modeling (e-h), and the bottom row refers to LOTOS-EUROS simulations (i-l). Data were stratified after their median was calculated for the entire period. Dry and wet leaf surfaces (d, h, l) were identified following the calculation scheme of Wintjen et al. (2022). Shaded areas represent the standard error of the mean. between modeled and measured u * values was considerably large.
The largest discrepancy was found for NH 3 concentrations, as illustrated in detail by Figs. 2 and S1. All of the investigated input parameters play an important role in the modeling of NH 3 exchange. In order to determine the impact of these parameters on modeled NH 3 fluxes, we calculated NH 3 fluxes for the land-use class spruce forest with DEPAC-1D by replacing a specific input parameter with its measured entity, while all other input data were from LOTOS-EUROS. Figure 5 illustrates the results of this comparison. Since modeled and measured values of global radiation agreed well, deposition of NH 3 was only marginally reduced if measured values were used. Using measured values of temperature as input parameters led to an increase (by 0.82 kg N ha −1 ) in modeled NH 3 deposition, whereas measured relative humidity led to a decrease (by 0.80 kg N ha −1 ) in modeled NH 3 deposition. We found significant differences in u * , but considering measured values in the flux calculation leads only to a reduction of 1.3 kg N ha −1 . As expected from the analysis of Fig. S6, the NH 3 concentration had the largest impact on deposition. Using measured NH 3 concentrations reduced the deposition substantially, by 5.3 kg N ha −1 , compared to using modeled concentrations. All reported differences refer to the entire campaign duration.

Comparison of modeled and measured N r deposition fluxes
The comparison of modeled N r fluxes with TRANC fluxes is presented in Fig. 6. Only periods during which high quality flux measurements were available were considered for the analysis. Models were basically able to capture the seasonal pattern of the N r fluxes well but generally overestimated the measured flux amplitude. The N r exchange of DEPAC-1D is near zero during the entire winter, and thus, the difference compared to measured deposition was nearly zero. During summer, a systematic overestimation of DEPAC-1D compared to measured fluxes was observed. Modeled deposition of LOTOS-EUROS was slightly lower than DEPAC-1D during summer and was consequentially closer to measured fluxes. However, during autumn and spring, the predicted deposition of LOTOS-EUROS was significantly higher than the deposition determined by DEPAC-1D and TRANC measurements due to the overestimated input NH 3 concentrations. Deposition was considerably high in LOTOS-EUROS during winter, whereas the median N r deposition of DEPAC-1D and TRANC was close to zero. Note that, during February 2018, high aerosol concentrations were both modeled and observed. The TRANC flux data also show the impact of the aerosol deposition, though to a larger extend than LOTOS- Figure 5. Comparison of NH 3 fluxes calculated with DEPAC-1D for the land-use class spruce forest based on measured (black) and modeled input data (red). The comparison was made for temperature, relative humidity, global radiation, friction velocity, and NH 3 concentrations.
In the first row, NH 3 fluxes are shown as cumulative sums in kg N ha −1 . In the second row, scatter plots of NH 3 fluxes in ng N m −2 s −1 are given. Linear regressions are shown as black, solid lines; black, dashed lines represent 1 : 1 lines.
EUROS. Median fluxes for each season and the entire campaign are given in Table S2. Figure S8 shows exemplary monthly diurnal cycles of N r based on TRANC, DEPAC-1D, and LOTOS-EUROS. As previously written, during winter, LOTOS-EUROS overestimated deposition, whereas measurements showed nearzero exchange, with occasional emission phases. From May to September and October, DEPAC-1D exhibited a clear diurnal pattern, with the lowest deposition during the night and the highest values around noon, which was in line with results from TRANC measurements. However, fluxes were systematically overestimated, as indicated by Figs. 6 and S8, during those months. During the same period, N r deposition of LOTOS-EUROS was lower but still higher than TRANC fluxes, except in September. During that month, LOTOS-EUROS was similar to DEPAC-1D. Generally, the diurnal deposition pattern of LOTOS-EUROS was considerably dampened, thereby not agreeing well with DEPAC-1D and TRANC.

Cumulative N exchange and method comparison
To derive annual deposition numbers, the gap-filling procedures were applied to the time series of TRANC and DEPAC-1D (see Sect. 2.1). Figure 7 shows the cumulative N r dry deposition of each method from January 2016 to the end of June 2018. The contributions of the individual components to the dry N r deposition of DEPAC-1D were 67.9 % NH 3 , 15.3 % HNO 3 , 10.4 % NO 2 , 5.2 % NH + 4 , 1.0 % NO − 3 , and 0.1 % NO, showing that modeled deposition was clearly driven by NH 3 . Since emission processes could only be treated for NH 3 , the observed emission of N r -for example, in December 2017 (Wintjen et al., 2022) -could not be sufficiently modeled. Due to issues in the parameterization of stability in LOTOS-EUROS (see Sect. 4.2.2), particle deposition was enhanced in the LOTOS-EUROS results compared to those of DEPAC-1D (Fig. 7). The deposition of gases only was higher in DEPAC-1D compared to LOTOS-EUROS due to the higher deposition velocities for NH 3 , NO 2 , and HNO 3 during summer (Sect. 3.2.1). We used a combination of MDV and DEPAC-1D for gap filling measured TRANC fluxes called TRANC(MDV + DEPAC-1D). Comparing these with LOTOS-EUROS and DEPAC-1D, we found differences in total dry deposition estimates of 5.4 and 2.8 kg N ha −1 after 2.5 years, respectively.
Since all cumulative curves generally exhibit 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 are different. Furthermore, both gap-filling strategies resulted in similar deposition estimates, showing that the application of MDV as a gap-filling tool is reasonable. Uncertainties related to the gap-filled TRANC time series through MDV and DEPAC-1D (Eq. 1) were negligible. In Fig. 8, a comparison of the N r dry deposition separated by methods and measurement years is shown. Corresponding values of the dry deposition estimates are given in Table 2.
In 2016, annual TRANC deposition was higher than in 2017. Using only DEPAC-1D as a gap-filling technique resulted in slightly higher dry deposition estimates. In 2018, the difference to TRANC estimates until June was caused by the deposition fluxes in February 2018, which had an influence on the MDV method, leading to significantly larger gap-filled fluxes. Hence, the DEPAC-1D estimate was lowest among all the methods for the first half of 2018. In 2016 and  2017, deposition estimates of DEPAC-1D were nearly identical due to similarities in micrometeorological and concentration input values. As expected from Fig. 7, annual LOTOS-EUROS estimates were highest in comparison to DEPAC-1D and TRANC. All deposition estimates were within the range of long-term lower and upper estimates of the CBT approach, as estimated from 2010 to 2018, with TRANC measurements being close to the lower average and LOTOS-EUROS predictions being close to the higher average.
Averaging of the annual sums of each method for 2016 and 2017 resulted in a TRANC dry deposition of 4.3 ± 0.4 and 4.7 ± 0.2 kg N ha −1 a −1 , depending on the gap-filling approach. DEPAC-1D showed 5.8 ± 0.1 kg N ha −1 a −1 , and LOTOS-EUROS predicted 6.5 ± 0.3 kg N ha −1 a −1 . We determined 6.7 ± 0.3 kg N ha −1 a −1 with CBT as the averaged upper estimate and 3.8 ± 0.5 kg N ha −1 a −1 as the averaged lower estimate.

Comparison of concentrations, fluxes, and annual budgets
Differences in the concentration contribution of N r species to N r According to the LOTOS-EUROS simulations, NH 3 had a predominant role in the N r concentration pattern. This result was in contrast to concentration measurements of individual N r species at the site highlighting NO x as the prevailing compound in the concentration pattern of N r (Wintjen et al., 2022). The predominant role of NH 3 in the modeled concentrations is caused by the emission inventory used in this study. The emission inventory spatially allocates NH 3 manure-derived emissions through a procedure in which the animal numbers per region and the agricultural land within a region are the two proxies used. Emissions from fertilizer application are allocated solely on land use. Hence, within a region, all agricultural land is assumed to emit the same amount of NH 3 , although the intensity of the agricultural practice and the distribution of housing may vary substantially within such a region. Only south of the site, agricultural lands are located within a 7 × 7 km 2 model resolution representing the site. This means that, in the grid cell of the model in which the station is located, there is an emission source that contributes an increased NH 3 concentration, even when the wind directions do not transport air from this agricultural region towards the station.
In LOTOS-EUROS, particulate nitrogen also demonstrated a significant contribution to modeled N r , which could not be confirmed by measurements. However, the comparison of particulate nitrogen concentrations is difficult because of the aerosol cut-off size in DELTA measurements being at 4.5 µm (Tang et al., 2015). Aerosols available in fine mode, like ammonium sulfate ((NH 4 ) 2 SO 4 ) and ammonium nitrate (NH 4 NO 3 ), are associated with an aerodynamic diameter of less than 2.5 µm (Kundu et al., 2010;Putaud et al., 2010;Schwarz et al., 2016) and could be sufficiently sampled. Concentrations of coarse-mode aerosols with larger diameters than the cut-off size were partly underestimated. However, concentrations of sodium, magnesium, and calcium ions were negligible at the site (Wintjen et al., 2022), indicating that coarse-mode nitrate aerosols had no significant contribution to the N r concentration. In addition, carbonate-coated denuders used for collecting HNO 3 overestimate concentrations by approximately 45 %, since nitrous acid also sticks to those prepared surfaces (Tang et al., 2021). Thus, disagreements could be related to the emission inventories of PM 2.5 and PM 10 , the chemical process modeling, or the DELTA measurements. NO x concentrations agreed in their seasonal dynamics; thus, processes responsible for modeling the temporal dynamics of NO x emissions are implemented reasonably in LOTOS-EUROS. However, the systematic underestimation of NO x concentration by LOTOS-EUROS shows that NO x P. Wintjen et al.: Forest-atmosphere exchange of reactive nitrogen in a remote region sources within this grid cell, most likely emissions from road transport and private households due to the absence of large industrial areas or power plants in the surroundings of the station, are presumably not tracked sufficiently by the emission inventory.
Generally, the low measured concentrations of N r compounds show that the site was mostly outside the transport range of nitrogen-enriched air masses. Improvements in the close-range transport in LOTOS-EUROS with regard to the atmospheric lifetime of N r species or in the definition of atmospheric layers are likely needed. A reduction in grid cell size could lead to a more accurate localization of potential nitrogen emission sources and a better description of closerange transport and dilution effects. The impact of an increase in model resolution is elaborated on in Sect. 4.2.2.

Differences in measured and modeled N r fluxes
Overall, measured and modeled N r deposition were comparable in terms of order of magnitude and partly agreed in temporal dynamics but still exhibited disagreements in flux amplitude, which were related to differences in concentration, micrometeorology, and the integration of exchange pathways in DEPAC. Currently, a compensation point is only implemented for NH 3 , and thus, only deposition fluxes could be modeled for other compounds. Since the total compensation point of NH 3 was negligible in DEPAC, emission fluxes of NH 3 observed for a deciduous forest by Hansen et al. (2015), probably due to a decay of fallen leaves (Hansen et al., 2013), could not be reproduced. The soil compensation point, which is integrated in the calculation of the NH 3 compensation point but is currently set to zero, may reduce the observed differences to TRANC fluxes. The observed temporal pattern in v d of NO 2 is related to the stomatal uptake, which is close to zero in winter and is highest in summer. The slight difference in the deposition velocities of NO 2 were caused by higher measured concentrations of NO x (see Fig. S2). In addition, no compensation point is implemented for NO 2 , and deposition on leaves is hardly allowed. Both assumptions are in disagreement with findings by Horii et al. (2004), who identified non-stomatal deposition as being the strongest contributor to the flux, and by Thoene et al. (1996), who proposed the existence of a compensation point for NO 2 . However, nitrogen concentrations in leaf samples taken from surroundings of the site showed no unusually high enrichment of nitrogen in leaves and needles (Beudert and Breit, 2014). Thus, neglecting the emission pathway of oxidized nitrogen compounds like NO 2 seems reasonable for the measurement site.
To reduce the difference between measured and modeled fluxes, considering nitrogen emissions from soil may lead to a closer agreement with flux measurements. As written above, soil compensation point has no influence on the deposition of N r species in DEPAC yet, and soil resistance implementation is kept simple: a constant value is assumed, de-pending on the soil wetness (dry, wet, or frozen). Improvements in the description of the exchange with the soil surface may allow one to describe the observed TRANC emission fluxes in December 2017, as reported by Wintjen et al. (2022). Changes made to the soil exchange path may lower the flux contribution of NH 3 , as outlined before, but may also increase the contribution of NO, since the latter is generally observed as an emission from soil if it is produced through (de)nitrification processes (Butterbach-Bahl et al., 1997;Rosenkranz et al., 2006). At the reference height, the contribution of NO may still be low due to fast conversion processes to NO 2 in the presence of ozone (O 3 ) within the forest canopy, especially close to the ground (Rummel et al., 2002;Geddes and Murphy, 2014). Increased NO 2 concentrations within the forest canopy may alter concentrations of various N r species, e.g., resulting in the formation of HNO 3 , which may contribute substantially to the deposition flux (Munger et al., 1996;Horii et al., 2006). Consequently, a soil compensation point may be also relevant for the exchange of other N r species next to NH 3 .
The observed large deposition fluxes in February 2018 were reproduced in the model simulations, although the modeled flux amplitude was smaller. During that time, modeled concentrations and fluxes of particulate N r were the largest contributor to total N r , leading to the assumption of particle-driven N r deposition. DELTA measurements suggested that particulate NH + 4 was most likely responsible for the measured N r deposition (Wintjen et al., 2022, Fig. 10). Modeled and measured NH + 4 concentrations differed by only 0.75 µg N m −3 , whereas a significant disagreement was found between NH 3 measurements and LOTOS-EUROS (approx. 2.7 µg N m −3 ). According to DELTA measurements, the NH 3 concentration was approximately 0.17 µg N m −3 . The averaged SO 2 concentrations obtained from LOTOS-EUROS and DELTA were comparable during the exposure period of the samplers (1.5 and 2.0 µg m −3 , respectively). According to the LOTOS-EUROS simulations, an excess of pNH + 4 over pNO − 3 was modeled, suggesting that particle deposition was most likely caused by pNH + 4 , which is in agreement with DELTA measurements. In conclusion, the high deposition fluxes seem to be driven by particulate NH + 4 compounds, ammonium sulfate, and ammonium nitrate. During February 2018, DELTA measurements revealed a slightly lower concentration of the SO 2− 4 than the NO − 3 aerosol -1.28 and 1.63 µg m −3 , respectively -suggesting that NH 4 NO 3 was most responsible for the observed N r deposition fluxes. Still, the dominant aerosol is not fully known due to missing high-resolution measurements of nitrogen aerosols. Apart from February 2018, winter fluxes of LOTOS-EUROS were large compared to DEPAC-1D, although the same size-resolved model for determining aerosol deposition velocities was used. By comparing dry deposition of DEPAC-1D and LOTOS-EUROS caused by gases + particles and gases only (Fig. 7), a substantial disagreement in aerosol deposition was found. The large par-ticulate nitrogen fluxes of LOTOS-EUROS are caused by uncertainties in the stability parameterization (Sect. 4.2.2). Issues in the description of turbulence-controlled deposition also had an effect on HNO 3 , since its R c is set to a relatively low constant value. Thus, LOTOS-EUROS deposition fluxes of HNO 3 were substantially higher in winter than deposition fluxes of DEPAC-1D. During summer, differences in the deposition velocities were related to higher measured concentrations of HNO 3 (see Fig. S2).

Analysis of N r deposition estimates
The N r dry deposition estimates of TRANC, DEPAC-1D, and LOTOS-EUROS were in the same range after 2.5 years, but differences in seasonal flux patterns were found. In addition, both gap-filling methods applied to flux measurements led to similar dry deposition estimates, indicating that the MDV approach is suitable for gap-filling of short-term gaps in TRANC flux time series. During summer, we found differences in the gap-filled fluxes due to systematic overestimation of DEPAC-1D, which was related to the different response of DEPAC-1D to micrometeorological conditions compared to TRANC (Fig. 4). It should be kept in mind that monthly integrated pNO − 3 , pNH + 4 , and HNO 3 concentration estimates may not be able to fully capture local events. Moreover, the aerosol cut-off size of DELTA was probably lower than that of the TRANC measurements, as supposed by Wintjen et al. (2022). Saylor et al. (2019) also noted that the v d of particles for forests are highly uncertain. Thus, differences in the measurements and predictions of LOTOS-EUROS in particle deposition could be expected. Besides missing emission fluxes in DEPAC-1D, the agreement of the dry deposition estimates was reasonable, indicating that an inferential model like DEPAC-1D can be a valuable alternative to purely statistical gap-filling tools at sites or seasons with predominant N deposition.
Annual dry deposition estimates from TRANC, LOTOS-EUROS, and DEPAC-1D were found to be within the range of the lower and upper estimates of the CBT approach. Adding the wet-only deposition results reported in Wintjen et al. (2022) to the determined dry depositions, we calculated annual total depositions ranging between 11.5 and 14.8 kg N ha −1 a −1 , as noted in Table 3 for each year.
Comparing the results obtained from the measurement site to results obtained for other forest ecosystems using a similar validation procedure is rather difficult due to the large temporal and spatial variability in N r compounds contributing to N r . Additionally, micrometeorological measurements, as carried out in this study, require substantial effort in the maintenance and processing of the acquired data. Thus, most currently available EC measurements are limited to time periods covering a few weeks or months and are only available for certain locations.
Recently, Ahrends et al. (2020) compared deposition estimates of a CBT approach, an inferential method, and LOTOS-EUROS for several forest ecosystems. However, their CBT was based on the variant suggested by Ulrich (1994), which is different to the version used in this study, and their inferential method (IFM) was only applied to NO 2 and NH 3 due to the limited availability of ambient concentration measurements for other N r compounds. In addition, deposition velocities for NO 2 and NH 3 were calculated based on literature research for different forest types and were accompanied by various correction factors. They reported similar annual dry deposition estimates for CBT and IFM, which were found to be 12.6 and 12.9 kg N ha −1 a −1 , respectively. Minimum dry deposition was 3.8 kg N ha −1 a −1 for CBT and 1.0 kg N ha −1 a −1 for IFM. The lowest average dry deposition was 9.3 kg N ha −1 a −1 , given by LOTOS-EUROS, but its minimum dry deposition was highest (approx. 6.3 kg N ha −1 a −1 ). Since we measured N deposition in a low-polluted environment, the agreement to the minimum dry deposition estimates of Ahrends et al. (2020) seems reasonable.
In the consideration of critical loads, total nitrogen deposition is within the proposed limits. Critical loads ranging from 10 to 15 kg N ha −1 a −1 and 10 to 20 kg N ha −1 a −1 were defined by Bobbink and Hettelingh (2011) for Picea abies and Fagus sylvatica, respectively. Since Picea abies was the prevailing tree species in the flux footprint (approx. 80 %), the critical load of the investigated forest ecosystem is probably closer to the limits of Picea abies. The state of tree physiological parameters suggested that the critical load concept, which indicated that the exposure of the forest to N deposition is still below critical limits, is a valuable tool to evaluate the functionality of an ecosystem. Long-term observations of nitrogen input to this ecosystem showed nitrogen concentrations in trees and water reservoirs, but ecosystem functionality was not impaired. According to leaf examinations done by Beudert and Breit (2014) at the site, balanced ratios of nitrogen to other nutrient concentrations in tree foliage were found, and usual tree growths were reported. Jung et al. (2021) found low nitrate concentrations in soil water, aquifers, and streams at the site, showing an intact nitrogen retention and storage system. Moreover, green algae coatings on spruce needles, usually indicating higher NH x dry deposition (Grandin, 2011), were not found at the site.

Influence of micrometeorological parameters
In both DEPAC-1D and LOTOS-EUROS, wet leaf surfaces and high relative humidity were identified as conditions enhancing N r deposition from May to September. In the case of temperature, dry leaf surfaces, and low relative humidity, diurnal cycles of v d showed a different behavior: for DEPAC-1D, lower temperatures were found to increase v d , whereas the opposite observation was made for LOTOS-EUROS, and their shapes were different. These disagreements were prob- ably related to the stomatal uptake of NH 3 prevailing in the N r deposition flux of LOTOS-EUROS. Only for wet leaf surfaces and high relative humidity, which generally play an important role in the deposition of NH 3 (Wentworth et al., 2016), were diurnal shapes of DEPAC-1D and LOTOS-EUROS similar, suggesting that the cuticular deposition of NH 3 seemed to be most responsible for the modeled N r dry deposition at the measurement site. Similar observations were made by Wyers and Erisman (1998), who identified the cuticular pathway as a larger sink for NH 3 than the stomatal pathway.
However, the results from TRANC measurements highlighted higher temperatures, lower relative humidity, and dry leaf surfaces as important factors enhancing N r deposition, and diurnal cycles of the TRANC were different in shape from those of LOTOS-EUROS. The differences in night-time deposition are probably related to low aerodynamic resistances in the model applications indicating high u * values, which could not be verified by EC measurements. However, measuring night-time exchange with the EC method and micrometeorological methods in general is challenging. Common detection algorithms for a u * threshold (Reichstein et al., 2005;Barr et al., 2013) are not applicable to N r species yet, since they are optimized for CO 2 . The contradiction in wet and dry conditions lead to the assumption that the current implementation of the NH 3 exchange pathways in DEPAC was not fully suited for predicting NH 3 deposition correctly and needs further investigation. It should be kept in mind that we measured N r exchange at a low-polluted, mixed forest site. Sites with different micrometeorology, vegetation, and pollution climate may exhibit other parameters -like surface wetness, canopy temperature, and ambient concentrationthat are responsible for the N r exchange, as found by Milford et al. (2001). Further comparisons to flux measurements of N r and NH 3 are needed to investigate the role of stomatal and cuticular deposition.

Influence of soil resistance and soil compensation point
In DEPAC, soil resistance is set to a constant value, depending on soil status: frozen (R soil = 1000 s m −1 ), dry (R soil = 100 s m −1 ), or wet (R soil = 10 s m −1 ). In addition, the in-canopy resistance (as part of the effective soil resistance) is dependent on the inverse of u * , surface area index (LAI + area index of stems and branches, van Zanten et al., 2010), and may lower the exchange with the soil. A soil compensation point is currently set to zero for NH 3 and is not implemented for other N r species, since an appropriate parameterization or value is not known, so far as is argued by van Zanten et al. (2010). Consequently, deposition through the soil pathway is close to zero for most half-hourly records according to the current parameterization. Including a soil compensation point in DEPAC and improvements in the soil resistance parameterization may lead to a better agreement with flux measurements. However, modifications related to soil exchange are probably challenging, since they may affect the contribution of various N r species to the N r flux; additionally, a parameterization of soil resistance, e.g., depending on soil moisture and temperature, is probably required instead of assuming a constant value.
At the site, no measurements of soil conductance, soil moisture, and soil temperature were made. Thus, we cannot evaluate the representativeness of the current soil parameterization. Moreover, those measurements would have been challenging at the site due to the large spatial variability in the wide flux footprint area. For further measurement campaigns of a similar nature, measurements of soil-specific parameters are highly recommended.

Cuticular compensation point of NH 3
Schrader et al. (2016) discovered problems in the calculation of the cuticular NH 3 compensation point under high ambient NH 3 concentrations and high temperatures -for instance, during summer. The current implementation of Wichink  in DEPAC likely underestimates the cuticular compensation point at high temperatures. This issue is not solved yet and could not be verified for our measurement site due to generally low NH 3 concentrations and, to some extent, the implementation of monthly averaged NH 3 concentrations instead of half-hourly values in the concentration time series of NH 3 . Moreover, the cuticular emission potential was estimated from monthly averaged concentrations in LOTOS-EUROS and DEPAC-1D instead of from instanta-neous values, as in the original parameterization of Wichink , which likely somewhat alleviates the issue discussed in Schrader et al. (2016). Thus, this issue could not be the main reason for the difference to flux measurements at our site.

Influence of emission fluxes on N r
With the TRANC system, the contribution of N r emission fluxes above the limit of detection was estimated to be 16 % (Wintjen et al., 2022). Unfortunately, robust QCL-based NH 3 flux measurements using the EC method were not possible at the measurement site (Wintjen et al., 2022). Thus, the contribution of individual N r species -at least the NH 3 and, hence, the reduced N contribution -to the measured N r flux is not known. However, the presence of emission fluxes shows that the implementation of a compensation point for soil and/or mechanisms describing emissions of oxidized N r species like NO 2 and HNO 3 should be considered. As described above, fully integrating the soil compensation point in the exchange of NH 3 may explain emissions fluxes of N r . For HNO 3, emission fluxes were reported in recent publications (Tarnay et al., 2002;Farmer andCohen, 2006, 2008). The latter conducted flux measurements of HNO 3 above a pine forest and found a significant contribution by emission fluxes during summer. Those emissions could also be induced by the evaporation of NH 4 NO 3 from leaf surfaces, occurring at higher temperatures (Wyers and Duyzer, 1997;Van Oss et al., 1998), or by particles deposited or formed on leaf surfaces, as discussed by Nemitz et al. (2004). Emission fluxes of NO and NO 2 were reported in several publications -e.g., Farmer and Cohen (2006), Horii et al. (2004), and Min et al. (2014) -leading to the assumption of the existence of a compensation point (Thoene et al., 1996), whereas other authors still critically discuss such a compensation point for NO and NO 2 (Chaparro-Suarez et al., 2011;Breuninger, et al., 2013;Delaria, et al., 2018Delaria, et al., , 2020. Since no significant N concentrations in leaves were found at the site (Beudert and Breit, 2014), the integration of a compensation point for NO 2 is probably less useful for the measurement site. Still, further flux comparisons of oxidized nitrogen compounds to their modeled entities are needed -this would possibly lead to improvements in the representation and accurate apportionment of exchange pathways in (bi)directional resistance models.

Leaf area index and displacement height
Besides the current implementation of the exchange pathways in DEPAC, deposition estimates would be more accurate if concentration measurements at a higher time resolutions and measurements of the LAI were to be available. We did not take measurements of the LAI or other vegetation properties at the measurement site. Still, the interpretation of differences to flux measurements would be challenging, since the vegetation inside the flux footprint was not uniform. Inside the footprint, we identified dead wood in a southern direction and a mix of rather young and matured trees in an easterly direction. Differences in tree age were related to a dieback by bark beetle in the mid-1990s and 2000s (Beudert and Breit, 2014), from which the forest stand is still recovering. Shifting z 0 or d by ± 50 % caused a change of +5.0 % to −3.2 % and +5.6 % to −9.1 %, respectively, in the nitrogen dry deposition after 2.5 years. An incorrect assessment of the modeled LAI by ± 50 % had a significant influence on the dry deposition. It led to a change of +18.9 % to −27.2 %. It shows that, in further field applications of DEPAC-1D measurements, the LAI should be considered, but an incorrect assessment of the LAI alone would not explain the overestimation of DEPAC-1D to TRANC measurements.

Using long-term concentration averages
The main uncertainty of DEPAC-1D fluxes was most likely the usage of monthly integrated DELTA concentrations for the N r compounds. Thus, the large variability in the time series of these compounds -happening on timescales of a few seconds -was not accounted for in deposition modeling. Even with high-resolution measurements of the QCL, the short-term variability in NH 3 concentrations was not detectable (Wintjen et al., 2022). As stated in Sect. 2.2.3, we did not superimpose monthly concentration values with synthetic diurnal patterns. Concentrations of N r compounds are highly variable during the day and depend on various parameters, such as turbulence, temperature, relative humidity, precipitation, and emission sources. Thus, it is not possible to capture the short-term variability of N r species, which is induced by those parameters, with long-term averages. We found that the NH 3 concentration was generally low during winter and demonstrated a low variability, as found by the measurements. During those times, using monthly integrated averages is reasonable (Schrader et al., 2018). However, we probably overestimated modeled fluxes due to the use of monthly averaged concentrations. In order to get at least an impression of which N r compounds' fluxes may be biased by this approach, we compared monthly averaged fluxes of LOTOS-EUROS (A1) with fluxes calculated by multiplying monthly averaged v d with their monthly concentration averages (A2) and subsequently corrected them by applying Eqs. (9) and pounds was relatively high compared to measurements during that time, R a and R b were probably low or even close to zero. R a and R b depend on various parameters like u * , the integrated stability corrections functions after Webb (1970) and Paulson (1970), surface roughness, and leaf area index. L determines the integrated stability functions and depends on wind speed close to the surface, cloud cover, and solar zenith angle (Manders-Groot et al., 2016). Snow cover is not considered in the parameterization of L yet. Including snow cover in the parameterization affects the albedo of the surface and thus the prevailing stratification of the boundary layer, which probably leads to more occurrences of stable stratification. An implementation of snow cover in the parameterization of L may reduce the deviations of simulated vs. measured stability and u * .
An incorrect setting of the LAI and z 0 can have a significant influence on modeled N r deposition, as shown in Sect. 4.2.1. The relative changes in modeled N r deposition caused by LAI and z 0 were comparable to values recently presented by van der Graaf et al. (2020), who used satellitederived LAI and z 0 data from the Moderate Resolution Imaging Spectroradiometer (MODIS) to calculate N r deposition with LOTOS-EUROS for a grid cell size of 7 × 7 km 2 . Overall, they observed changes in N r dry deposition ranging from −20 % to +30 %. However, if LAI and z 0 from MODIS were used, there was almost no change observable in N r dry deposition and in NH 3 concentration for the Bavarian Forest measurement site. The attempts of van der Graaf et al. (2020) and Ge et al. (2020) did not provide a solution for the general overestimation of the NH 3 deposition above southern Germany. We assume that the spatially and temporally imprecise allocation of emission data is most responsible for the disagreement to flux measurements. Further investigations on these issues are needed.

Conclusions
The annual total reactive nitrogen ( N r ) dry deposition estimates of all methods were in the same range, considering uncertainties of measured fluxes and model applications. Annual estimates from the Total Reactive Atmospheric Nitrogen Converter (TRANC) were lower than the results from an in situ inferential modeling approach using the bidirectional flux model DEPAC (Deposition of Acidifying Compounds) (here called DEPAC-1D) and the chemical transport model LOTOS-EUROS (Long-Term Ozone Simulation -European Operational Smog) v2.0. Annual dry deposition estimates of TRANC, DEPAC-1D, and LOTOS-EUROS were within the minimum and maximum dry deposition estimates of the canopy budget technique (CBT), showing ecological and micrometeorological measurements that provide reasonable estimates. According to the critical load concept, annual nitrogen deposition was below critical values. Findings were supported by local vegetation samplings showing no indica-tions of nitrogen exceedances, leading to the conclusion that the critical load concept is a useful tool to describe the health status of an ecosystem.
Differences between DEPAC-1D and TRANC measurements could be related to uncertainties in parameterizing the exchange pathways of reactive gases, the usage of lowresolution input data, or the missing exchange pathway with soil. Modeled N r deposition velocities of DEPAC-1D were enhanced with regard to wet conditions, which was in contrast to TRANC measurements, leading to systematically larger deposition fluxes. To a smaller extent, the same observation was made for LOTOS-EUROS; additionally, deposition velocities of DEPAC-1D and LOTOS-EUROS did not agree well in their diurnal pattern. Thus, a further investigation of stomatal vs. non-stomatal deposition pathways needs to be conducted, as these are likely the main factors for discrepancies in modeled vs. measured results. Besides possible uncertainty sources in DEPAC-1D, measured dry deposition estimates using DEPAC-1D for gap-filling were similar, showing that DEPAC-1D (and by extension, inferential modeling in general) is a valuable gap-filling tool at sites with prevailing N deposition. The difference to dry deposition estimates of LOTOS-EUROS was mainly related to an overestimation of NH 3 concentrations by a factor of 2 to 3 compared to measured concentrations. Consequently, NH 3 contributed most to the N r concentration pattern in LOTOS-EUROS, whereas NO x was identified as a predominant compound by measurements. The imprecise allocation of emission data may be responsible for the discrepancies to measured NH 3 concentrations, since the general overestimation of NH 3 concentrations by LOTOS-EUROS has still not been solved by the attempts of model developers (van der Graaf et al., 2020;Ge et al., 2020).
Further comparisons of flux measurements and model applications are needed to investigate the exchange characteristics of N r and its individual compounds simultaneously and at different ecosystems, if possible. Measuring several N r compounds and N r at a high time resolution is probably not affordable due to operating and maintenance costs, high technical requirements, and time-consuming processing of the acquired data. A solution could be continuous monitoring of N r compounds by low-cost samplers complemented by high-frequency measurements of N r and selected compounds like NH 3 for a limited time, which will result in a better understanding of exchange processes and, thus, an improvement of deposition models (see Schrader et al., 2020).
Code and data availability. All data are available upon request from the first author of this study (pascal.wintjen@thuenen.de). Concentration, flux, and micrometeorological data from measurements and ecological information about the site are included in the following repository: https://zenodo.org/record/5841074 (Brümmer et al., 2022b). Also, Python 3.7 code for flux data analysis can be requested from the first author.