National nitrogen budget for Germany

Emissions of reactive nitrogen (Nr) give rise to a wide range of environmental problems. Nitrogen budgets for various systems and on different scales are an established tool to quantify the sources and fate of Nr. The national nitrogen budget (NNB) for Germany calculates the nitrogen flows for eight pools: Atmosphere, Energy and Fuels, Material and Products in Industry, Humans and Settlements, Agriculture, Forest and Semi-natural Vegetation, Waste, and Hydrosphere, as well as for the transboundary N-flows. In Germany, in total 6,275 kt Nr a−1 has been introduced into the nitrogen cycle annually (mean 2010 to 2014), of which 43% stem from ammonia synthesis. Domestic extraction and import of nitrogenous fossil fuels (lignite, coal, crude oil) releases another 2,335 kt Nr a−1. Import of food, feed and materials contributes 745 kt Nr a−1, while biological N fixation converts 308 kt Nr a−1 into organically bound nitrogen. In terms of Nr sinks, the combustion and denoxing of fuels and the refining of crude oil converts 2,594 kt Nr a−1 to N2. In waters, soils, and wastewater treatment plants, denitrification leads to the release of 1,107 kt Nr a−1 as N2. Via the atmosphere and hydrosphere, Germany exports 755 kt Nr a−1 to neighbouring countries and into coastal waters. On balance, Germany releases 1,627 kt Nr a−1 annually to the environment. However, the NNB as a whole and the individual pool balances involve substantial uncertainties, which have to be considered when interpreting the results.


Introduction
Since the development of the Haber-Bosch process for large-scale ammonia synthesis a century ago, humans have intervened in the nitrogen cycle more than in any other geochemical cycle (Galloway et al 2008). The total world ammonia production reached around 150 Mt N in 2019 (USGS 2020), by far the largest part of which is used as N fertilizer in agriculture (estimated 79% in 2013/14, calculated after Heffer and Prud'homme (2016). The planetary boundary for industrial and intentional biological fixation of nitrogen were quantified by Steffen et al (2015) to 63 Mt N per year, which is exceeded by a factor of more than two. The excessive release into the environment of reactive nitrogen (N r ; defined as all N forms other than N 2 ) causes numerous problems, including the loss of aquatic and terrestrial biodiversity, the formation of greenhouse gases, air pollution, and increased nitrate levels in groundwater and marine ecosystems. A nitrogen budget (NB) quantifies the N r emission from the various sources, the circulation of N r compounds through the biosphere and technosphere, and the final sinks of N r , termed the eco-systemic nitrogen cascade by Galloway et al (2003). The NB has been introduced as an efficient instrument for determining the N r flows, which helps to raise awareness of their potential impacts. Furthermore, the NB provides policymakers with information for identifying intervention points and developing efficient emission reduction measures (UNECE 2013).
Several studies on NBs have been published across a range of scales, various system boundaries of N flows, and different regional entities. On the global scale, Smil (1999) estimated nitrogen flows in crop production, while Fowler et al (2013) described the processing and fluxes of N r in terrestrial and marine systems and the atmosphere. Quite a number of studies focus on agriculture and the food sector, e.g. Pierer et al (2015) assessed the consumer-related N flows with food and material use in Austria, and Lassaletta et al (2014) balanced the socalled hydrologic agro-food system in Spain. Agricultural nitrogen emissions to the atmosphere and the hydrosphere were calculated for Canada by Janzen et al (2003) and for New Zealand by Parfitt et al (2008). Olsthoorn and Fong (1998) focused on nitrogen losses from anthropogenic N inputs in the Netherlands. Based on these data, Kroeze et al (2003) illustrated the uncertainties and knowledge gaps in the fate of nitrogen in natural and terrestrial systems. The studies by Domene and Ayres (2001) and Saikku et al (2007) give examples of national nitrogen flow analysis in the industry and energy sector.
A national nitrogen budget (NNB) covers the relevant N inflows and outflows for all economic sectors within a nation. The US NNB is based on a total nitrogen turnover of 34,900 kt N in 2002 (Doering III et al 2011). Houlton et al (2013) interpreted the turnover of 37,000 kt N in 2002 as the total N fixation and assessed the intentional N fixation as five times higher than the unintentional N fixation for the US in 2007. Three NNBs have been calculated for China (Cui et al 2013, Gu et al 2013, Luo et al 2018, varying in the number of subsystems and N flows considered. Gu et al (2013) calculate 22,500 kt N a −1 as N accumulation in soil, biomass, products and inland water, while 2010Cui et al (2013 reports 31,000 kt N accumulation for the same year, and Luo et al (2018) quantify the N loss and accumulation only in the food sector to 47,200 t N a −1 in 2014. A nitrogen flow analysis for Switzerland concluded that an N r emission reduction by more than 70% is required to meet the national environmental targets Heldstab et al (2014). Projecting the temporal trend of the N budget surplus 1990 to 2012 for the United Kingdom, Worrall et al (2016) predict that the UK will become a net sink of total N in 2031. While all studies mentioned above rely mostly on statistical databases, the European Union nitrogen budget (Leip et al 2011) was almost completely model-based and illustrated the wide range of N r emissions within the EU with high spatial resolution.
The above listed NNB applications differ considerably in the number of subsystems and N flows, the methodology to determine them, and the consideration of stock changes. The results are therefore only comparable with each other to a very limited extent. To overcome this problem, an international agreement under the revised 1999 'Gothenburg Protocol to the Convention on Long-Range Transboundary Air Pollution' (CLTRAP) established a NNB reporting scheme. With the 'Guidance document on national nitrogen budgets' (UNECE 2013) the Expert Panel on Nitrogen Budgets (EPNB) of the Task Force on Reactive Nitrogen (TFRN) presented guidelines on NNB calculation, mainly addressed to the bodies of the 'Cooperative Programme for Monitoring and Evaluation of the Long-range Transmission of Air Pollutants in Europe' (EMEP). To the best of our knowledge, a NNB based on the NNB Guidance Document has not yet been carried out. We calculated the NNB for Germany adopting the UNECE (2013) methodology and focused on two questions: (i) What are the sources, quantities and species of N r emissions in Germany and what are the final N r sinks?(ii) What is the uncertainty of the NNB?Are the N inflows and outflows for Germany in balance, or are there significant gaps in the sources, fate and/or sinks of N r ?

Material and methods
We applied the NNB scheme of the 'Guidance document on national nitrogen budgets' (UNECE 2013) and calculated the N r flows between eight pools for Germany: Atmosphere, Energy and Fuels, Material and Products in Industry, Humans and Settlements, Agriculture, Forest and Semi-natural Vegetation, Waste, and Hydrosphere. Additionally, the transboundary nitrogen flows with the Rest of the World are assessed. With the exception of Atmosphere, pools are subdivided into two to four sub-pools, based on the sector structuring used for the national greenhouse gas emissions inventory (IPCC 2006, EEA andEMEP 2013). In total, we determined N inflow and outflow for 20 sub-pools (table 1). For each of the eight major pools, the EPNB has developed an annex, which explains the methodology for the computation of the relevant pool's N flows (to date six annexes are available online).
The N flow calculation is based on different types of data. For the majority of pools, the N inflow and outflow involve nitrogen that is bound in biogenic or technical materials. These N flows are mainly calculated from the transported material flow multiplied by its mean nitrogen content, using data taken from official statistics and data bases. The emission of greenhouse gases (N 2 O, NO x ) and ammonia is taken directly from the National Inventory Reports. The German Ministry of Agriculture reports the agricultural NB in tonnes N per year (BMEL 2020). Atmospheric transport models are applied to assess the atmospheric N deposition (model LOTOS-EUROS, Schaap et al 2018) and the import and export of NH y and NO x (model MSC-W, Norwegian Meteorological Institute 2017). The N flows in the Hydrosphere pool are assessed using the MoRE model (Fuchs et al 2017). The statistics and data bases used, approaches to calculate the individual N flows, and results are explained in detail in the Supplement. The criterion for NNB inclusion was an N flow 1 kt N per year. For reasons of clarity, in the following all figures are rounded to full digits, outflows are indicated by a minus sign.

National nitrogen flow analysis
In total, we quantified some 150 individual nitrogen flows for Germany. Figure 1 shows the (partly aggregated) annual N flows for the eight pools (mean 2010-2014). Summarizing the flows and allocating emissions from aggregated anthropogenic sources to air and surface waters (table 2), the values show that agriculture accounts for two-thirds of all reactive nitrogen released in Germany, it remains by far the most important source of N r emissions into the air and into surface waters. Furthermore, it shows that two thirds of the overall anthropogenic nitrogen emissions are released to air and one third to the surface waters.
The annual N turnover for the eight NNB pools totals 22,760 kt N a −1 (here N denotes N r and N 2 ). Ammonia synthesis, import and domestic extraction of fuels, import and export of chemical products, food and feed are the largest N r flows in Germany's NNB. With regard to the primary sources and final sinks of N r in Germany, two main domains can be distinguished (table 2). Energy production, domestic extraction and import of fossil fuels as well as the formation of thermal NO x in combination release −2,527 kt N a −1 . This corresponds very closely to the N amount of 2,594 kt N a −1 , which is converted into N 2 by fuel combustion, flue gas denoxing and crude oil refining. Thus, power generation (including traffic) is obviously a sector with a large N turnover. Due to our assumptions this is largely closed, however it contributes to a relevant extent to the overall NO x emissions (table 3).
The second domain includes all other N conversions. The most important input is the ammonia synthesis of 2,695 kt N a −1 , of which 1,664 kt N a −1 is used as nitrogen fertilizer. There are net imports of 745 kt N a −1 as constituents of food, feed, and chemicals and manufactured non-food products. With 308 kt N a −1 , biological N fixation plays only a minor role in Germany, and the major part of this is by legume cropping. This gives a total of 3,748 kt N a −1 for which the final sinks are only partially known. The denitrification in soils, groundwater, surface water and wastewater treatment plant is estimated at −1,107 kt N a −1 . With the transport of N r species via the atmosphere und in rivers, a net total of −744 kt N a −1 leaves Germany. The disposal of wastes and an increase in timber storage is calculated to lead to only a very small N stock change in the German NNB. Thus, there is a gap of 1,804 kt N a −1 between the N r quantities in the primary sources and final sinks, which corresponds to ∼29% of the N r sources. Theoretically, the sums of the N inflows and outflows should be nearly equal. However, table 4 demonstrates that this is not the case for several pools, nor for the overall German NNB. A surplus of 2,126 kt N a −1 , corresponding to ∼9% of the total N inflow, indicates the magnitude of the uncertainties in the NNB  calculation. In the following section, we explain in more detail the most important N flows and the possible reasons for the differences between inflow and outflow in the individual pools.   between total atmospheric N r inflow and outflow (tables 5, S2-S10). Since no stock change occurs in the atmosphere, the difference might be due to disparate assumptions when modelling atmospheric NO x and NH y flow with the LOTOS-EUROS model on the one hand and the EMEP model on the other. Excluding N 2 O, which is not deposited and for which none of the models include imports or exports, the difference between total inflow and total outflow is reduced to 126 kt N a −1 , or some 10% of the total atmospheric N r turnover. N 2 O can be taken up by soils, but the uptake rate is assumed to be marginal compared to the emission (Syakila et al 2010). According to our mass balance approach, about 60% of the national NH 3 emissions and 45% of the national NO x emissions are redeposited in Germany. Overall, Germany is a net exporter of air pollutants, mainly due to its high spatial density of emissions (especially in the north-west and south-east region due to livestock farming). A large proportion of the emissions are transported in the atmosphere over long distances and carried beyond national borders.

Energy and fuels
The NB for the Energy and Fuels pool is based on the Energy Balance for Germany (AGEB 2017; tables S3-2) which is structured primarily to register the conversion and use of energy. The material flow data of the Energy Balance for Germany include double counting and uncertainties for various positions, as is pointed out in the comments (AGEB 2017). Double counts in the statistics cannot be corrected by an external user and as a consequence these effects carry over to the N flow calculation. With a difference of 30 kt N a −1 , the budget seems quite well balanced (tables 6, S3-S8). However, this is primarily due to the fact that we calculate two key N outflows as differences: (i) The N inflow with the combustion of fossil fuels (lignite, coal, mineral-oil products), wood for power and heat generation (Energy Conversion sub-pool) and the NH 3 -consumption for flue gas denoxing, which totals 1,606 kt N a −1 (tables S3-S6). Of this, 188 kt N a −1 is converted to non-thermal NO x . For the remaining 1,418 kt N a −1 , we assume that the combustion residues (ashes, filter dust, wastewater, etc.) are nitrogen-free and this share of N r in fuels is completely converted to N 2 . (ii) A statistical difference of 818 kt N a −1 occurs between the 932 kt N a −1 in crude oil refined for domestic consumption and the 144 kt N a −1 in the resulting mineral-oil products (tables S3-3). We assume that this N loss in refining of crude oil can also be regarded as an N r -neutral process, because the oil is hydrotreated for removal of mainly sulfur, in which case probably most of the N flows out as NH 3 in the sour gas and is subsequently oxidized to N 2 in a Claus process burner. However, German petroleum companies are not able to provide any evidence for this assumption.
Overall, the calculation of the N r turnover with combustion and crude oil refining depends to a large extent on the assumptions about the nitrogen contents of the fuels. For coal and mineral oil, this depends strongly on the origins (deposits) of the fuels; the data on this vary widely.

Materials and products in industry
Materials and Products in Industry is by far the largest pool for N r turnover due to the large amount of nitrogen used in chemical processes (tables 7, S4-S9). For the Food and Feed Processing sub-pool, the N inflows and outflows are nearly balanced (tables S4-S10). Obviously, the statistics on food and feed production and consumption quantities and the data on N content in products correspond quite well. For the manufacturing industry and the associated Nitrogen Chemistry sub-pool, the German Production Survey (Statistisches Bundesamt 2020) provides data on production, import and export of commodities. The survey distinguishes between 'initial products' and 'products intended for sale'. However, an evaluation of the German Production Survey raises problems. It is not possible to rule out double counting in the statistics; all products that are not 'intended for sale' are initial products for further processing, but they may re-occur in a number of subsequent production steps. Also, items which are 'intended for sale' may nevertheless be used as initial products in another production process. Finally, for various types of goods, the data on production quantities are not published for data protection reasons. Despite these problems, inflow and outflow to the Nitrogen Chemistry sub-pool is calculated based on the German Production Survey. For this, the individual items are grouped in accordance with the Eurostat classification of commodities (at the 4-figure code level) to 28 classes of chemicals containing nitrogen (tables S4-S7). For each group, average N content is calculated from the chemical structure of a typical compound or is estimated according to the UNECE (2013), Annex 6. Key process in the nitrogen chemistry is ammonia synthesis with 2,695 kt N a −1 . Together with 2,262 kt N a −1 in imported chemical products (plus 32 kt N a −1 in mineral-oil products for processing in chemical industry), the inflow in the Nitrogen Chemistry subpool totals 4,989 kt N a −1 . Given the known outflows of −1,664 kt N a −1 with mineral N fertilizer, −1,797 kt N a −1 in chemical products and −217 kt N a −1 in N emissions and waste, we define the remaining 1,311 kt N a −1 as inflow in the Other Producing Industry sub-pool as precursors and chemicals for the production of consumer goods. Production, import and export of commodities for use by consumers in the Other Producing Industry subpool is also derived from the German Production Survey (AGEB 2017). Note that the groups of manufactured commodities contain very heterogeneous materials (in terms of N contents; tables S4-S8). Furthermore, quantities of consumer goods may be expressed in various units, e.g. numbers of items, square meters, or cubic meters. These reasons may in part explain the discrepancy of 1,520 kt N a −1 between the calculated inflow and outflow in this sub-pool.

Humans and settlements
The calculation of N flows to Humans and Settlement pool links data from several sets of statistics and from other pools (tables 8, S5-2). The inflow of 668 kt N a −1 in food and pet feed consumption (including uptake and kitchen wastes) and of 166 kt N a −1 in consumption of commodities stems from the Materials and Products in Industry pool. Outflow of -590 kt N a −1 only takes place in form of solid waste and wastewater, and nitrate leaching. The difference of 395 kt N a −1 represents some 40% of the total N inflow, which is more than twice the inflow of 166 kt N a −1 with consumer goods (tables S5-S3). Since no other N outflow comes into question for consumer goods apart from solid waste, these two quantities ought to be nearly equal. An increase in N stock in the Humans and Settlements pool is not plausible on this scale. Obviously, the uncertainties in calculating the N flow with nitrogenous products for sale to end consumers in the Materials and Products in Industry pool carry over to the Humans and Settlements pool. Furthermore, the N inflow with wastewater from households and runoff from sealed areas are only rough estimates. Finally, the N outflow of only −46 kt N a −1 in solid waste derived from waste generation statistics (section 3.2.7.) is somewhat lower than the N inflow of 166 kt N a −1 with consumption of commodities included in the consumer goods.

Agriculture
The Agriculture pool forms the second largest pool of N r turnover in Germany. The calculation of NBs for German agriculture is well-established (Bach et al 2011, Häußermann et al 2019, 2020 and state-of-the-art data is annually published by the German Federal Ministry of Agriculture (BMEL 2020). The BMEL budget scheme is more differentiated than the OECD/EUROSTAT approach, furthermore the BMEL surplus figures are the reference values for the German nitrate report to the EU Commission, for the calculation of the nitrate river load within the Water Framework Directive reporting, and for the implementation of the Integrated National Nitrogen Target for Germany (Geupel et al 2021). Inflow of 1,619 kt N a −1 with mineral N fertilizer and 1,102 kt N a −1 with feed from industry production together account for 82% of the total N input (tables 9, S6-S5). The withdrawal of −1,548 kt N a −1 in marketed plant and livestock products represents the utilized part of the N outflow, while a substantial share of −659 kt N a −1 gets lost to the atmosphere as gaseous N r species. Denitrification in the root zone of crops and grasses may vary widely from nearly zero up to a complete nitrate degradation. As an average denitrification rate, Well et al (2016) estimated 14 kg N ha −1 a −1 , corresponding to a denitrification rate of −234 kt N a −1 . Only one soil survey for the agricultural land in Germany has been carried out just once do date (Jacobs et al 2018). Thus, data on soil N stock changes are currently unavailable. According to a modelling approach based on long-term soil monitoring sites (Jacobs et al 2018), German cropland mineral soils probably show a moderate loss rate in soil organic substance over the past 20 years, and thus a slight decrease in soil N stock. In peat soils used for cropping in Germany, a preliminary estimate suggests that soil N stock depletion could be in the order of −500 kt N a −1 (Jacobs et al 2018). However, due to the large uncertainty, this value is not taken into consideration for the Agriculture N fluxes. We calculate the agricultural N budget under the premises that (i) there are no further N outflows from the Agriculture pool than marketed products, gaseous N emissions (including N 2 ) and transport by water, and (ii) the soil N stock remains unchanged. Given this, the difference of 879 kt N a −1 between total inflow and subtotal of 'known' (directly calculated) outflows is interpreted as the N r emissions into the hydrosphere from agricultural land (tables S6-S6). The emissions cover the nitrate leaching from the soil root zone (as system boundary of the Agriculture pool) towards groundwater, as well as the N discharge into surface waters via run- Nitrate leaching (below the root zone) −757 Total outflow −3,320 Net inflow 0 b a Seed and planting material, manure import, biogas co-substrates, compost, sludge, meat-and-bone-meal b Budget is based on the premise that the total outflow equals to the total inflow off, erosion and tile drainage. From the Hydrosphere pool −122 kt N a −1 is modelled as N in lateral discharge into surface waters from agricultural land. Subtracting this N amount from the difference of 879 kt N a −1 leaves as residual a N outflow of −757 kt N a −1 for nitrate leaching towards groundwater as the second pathway from agricultural land into the hydrosphere.

Agriculture forests and semi-natural vegetation
The Forest and Semi-natural Vegetation budget shows the largest relative inflow-outflow discrepancy, with a difference of 458 kt N a −1 , corresponding to 77% of the N inflow (tables 10, S7-7, S7-8). Currently, major processes such as biological N fixation, denitrification, and nitrate leaching cannot be quantified with the accuracy needed to close the NB for this pool. Only rough estimates are available for average biological N fixation . An average annual loss in forest soil N stock (0-60 cm depth) of 26.5 kg N ha −1 a −1 was measured between the two monitoring periods, which results in a decrease in forest soil N in Germany of −293 kt N a −1 (tables S7-5). Related to the total N stock of~6, 000 kg N ha −1 in forest soil humus (0-60 cm) the decrease is equivalent to a loss of around −7.5% over a period of~17 years (estimate based on numbers from Fleck et al 2019). With respect to the NB, a soil N decrease represents a mobilization of N r , and therefore an N inflow within the budget. Even if the soil stock decrease is not taken into account, a rather large difference of 165 kt N a −1 remains in the budget of the Forest and Semi-natural Vegetation pool.

Waste
The Waste pool is characterized by a high degree of data uncertainty, despite its overall rather small share of the NB. For solid waste, the German statistics on waste generation (Statistisches Bundesamt 2016) deviates considerably from the waste balance statistics (Statistisches Bundesamt 2020) which records the disposal and recycling of wastes. The waste generation statistics list 15 classes of waste materials (potentially) containing nitrogen to which we assigned N contents according of UNECE (2013), accounting for a total N inflow of 249 kt N a −1 (tables 11, S8-2). However, the flow of primary solid waste materials through the various sorting and treatment stages, the recycling of materials, and the quantities of final disposal and incineration cannot be traced transparently on the basis of the waste balance statistics. Furthermore, double counting occurs at all stages to an unknown extent. Assessed by the waste balance statistics (tables S8-3), the outflow with material recycling and landfill deposition of solid wastes from households and industry totals −349 kt N a −1 , while the solid waste incineration additionally converts −182 kt N a −1 in organic substances to N 2 (sludge not included). Thus, between the calculated inflow and outflow for the Solid Waste sub-pool there is a substantial gap of −282 kt N a −1 , which is more than the total inflow according to the waste generation statistics (tables S8-9). The difference illustrates the discrepancies in the two underlying statistics. Nitrogen inflow in the wastewater system was calculated as part of the MoRE model (Fuchs et al 2017) resulting in 514 kt N a −1 (tables S8-5). The calculation is based on data on wastewater discharge from households, industry and sealed areas and their mean N contents. The outflow with treated wastewater discharge is calculated to −144 kt N a −1 , and the denitrification in wastewater plants to −211 kt N a −1 . For the Wastewater sub-pool, the difference between inflow and outflow amounts only to 37 kt N a −1 (tables S8-10). Since the Wastewater sub-pool does not contain any N stocks, the difference is due to the uncertainties in the calculation.

Hydrosphere
The nutrient flow in the hydrosphere on the national level is calculated regularly in the context of the EU Water Framework Directive implementation, in recent years using the MoRE model (Fuchs et al 2017). Assessed from the NBs for the Agriculture, Humans and Settlement and Forest and Semi-natural Vegetation pools, the leaching of 857 kt NO 3 -N a -1 below the root zone forms the major N inflow to the Hydrosphere pool (tables 12, S9-2). MoRE estimates the denitrification (termed as N-retention by the MoRE model) along the water flow from the root zone through the vadose zone and the groundwater and finally into the river system up to the mouth of the North Sea and Baltic Sea to −648 by kt N a −1 . Deducting this estimata from the leached 857 kt N a −1 nitrate (below the root zone), −209 kt N a −1 (24%) effectively reaches the surface water system. This approach results in an almost balanced NB for the Hydrosphere pool (tables S9-7). It should be noted, however, that this approach is only valid under the assumption that there is no change in the N stock in the aquifers, i.e. that the groundwater nitrate concentration in Germany shows no change over time.

Transboundary nitrogen flows
Summed up over all pools, the German import-export budget is balanced (tables 13, S10-1; excluding the N r import in fuels which is mainly converted to N 2 by fuel combustion). However, this result is due to two opposing factors. With the atmospheric transport of gaseous N species and the N river transport, −744 kt N a −1 of reactive nitrogen leaves the German territory into the biosphere of neighboring countries and the seas. On the other hand, there are budget-closing net imports of 745 kt N a −1 by food and feed products and for material for the chemical industry (fuels not included).

Discussion
We applied the UNECE (2013) NNB calculation scheme to quantify the N inflows and outflows and the N budget on the national level and for eight pools in Germany. Anthropogenic activities introduce a total of 6,275 kt N a −1 reactive N corresponding to annually 76 kg N per capita in Germany. As with all NNBs, ammonia synthesis is the largest N r source, followed by the release of N r from the organic N compounds in fuels. With the decision of the German government to phase out power generation from coal and lignite by 2038, the dimension of this N r source will decline significantly in the next two decades. Due to the small proportion of legume cropping, biological N fixation is currently only of minor importance in German agriculture. The N r net import consists mainly of nitrogen chemistry products, followed by food and feed. For manufactured goods, the N r import-export budget is nearly balanced, but must be interpreted with caution in view of the uncertainties in the statistics. Considering the output side, from the total 4,471 kt N a −1 quantified final N r sinks, some ∼82% is converted back to molecular nitrogen by combustion and denoxing, refining of crude oil, and denitrification in soils, waters and wastewater treatment plant. Only 18% remains in the form of reactive N species, of which the largest proportion leaves Germany via the atmosphere and as river load. Only a very small amount remains in Germany with an increased disposal of waste and timber stock. However, there is a considerable difference of ∼29% of the inflow between the N r sources and the known or estimated sinks. With the current state of knowledge, we cannot judge to what extent this difference of 1,804 kt N a −1 is due to an overestimation of N r releases from individual sources or to an underassessment of the N r fluxes on the side of sinks. In the case of under-reporting of sinks, the question is whether these N r quantities are also entirely converted to N 2 by combustion or denitrification, or whether there are additional releases of N r that have not yet been recorded in the specific emission reports.
The NBB provides quantitative information on N r emissions and N r sinks. However, this does not yet evaluate the environmental impacts of N r emissions and does not indicate the extent to which they must be reduced. For this, the NNB for Germany is linked to the 'Integrated National Nitrogen Target' implemented by the German Federal Environment Agency (Geupel et al 2021). The target value is based on six environmental impact indicators: nitrogen sensitive vegetation, terrestrial ecosystems, surface water quality, groundwater quality, climate change and human health. To protect these environmental goods the national N target quantifies the maximum amount of total acceptable N r losses in Germany to nearly 1,000 kt N a −1 . Compared to the estimated 1,574 kt N r a −1 losses into susceptible environmental sectors in 2015, the N r losses in Germany have to be reduced by approximately one third.
A basic finding of our study is the rather large inflow-outflow differences discovered both for the NNB Germany amounting to 9% of the total inflow, as well as for the individual pools. Similar to results for other countries, the NNBs are not closed. Rather, we find even larger ranges of NNB imbalances in several cases. Positive differences, with the sum of inflows greater than the sum of outflows, are given by Houlton et al (2013) for the US with a surplus of 12% to 25%, for Austria 27% (Pierer et al 2015), for the Netherlands 8% (Olsthoorn and Fong 1998) and for China 28% (Gu et al 2013). In contrast, a compilation of NNBs for six European countries by Leip et al (2011) indicates larger outflows than inflows for all cases, ranging from −8% for Germany and the UK up to −25% for the Netherlands. However, one has to note that the values by Leip et al (2011) are based on a different methodological approach than that used by the other studies. The compilation of Leip et al (2011) further illustrates the large variability of results for identical sectors between the different approaches. For example, the authors report a balance surplus of 2,534 kt N a −1 for the agricultural sector in France, but only 62 kt N a −1 for the German agriculture, which is close to the assumption of a balanced Agriculture pool in our study. Obviously, the NNB calculation methods are handled very differently, which leads to considerable biases in the results.
To build an NNB is a challenging task. Several elements of the nitrogen budget are only quantifiable with some uncertainty, and the magnitude of this uncertainty is often not quantified as stated by Leip et al (2011). Consistent with this, only a few studies quantify the uncertainties of their NNB. Doering III et al (2011) estimated the uncertainties of +/−50% for emission and deposition and terms that derived by differences and Worrall et al (2016) assumed a percentage error of +/−80% of the median for data sources without providing an explicit uncertainty estimate. A spatialized European wide estimate of the N surplus by four models indicated an uncertainty close to 50% for individual countries (de Vries et al 2011). We estimate uncertainty ranges according to the EEA and EMEP (2013) scheme (ref. Supplement) for the individual N flows of our NNB. However, similar to Doering III et al (2011) andWorrall et al (2016), these are more or less speculative and should be interpreted with reservation.
Imbalances in the NNB and the different pools of the N budgets are caused mainly by three components, namely the uncertainties in our knowledge of the rates of biological nitrogen fixation, the conversion of N r to N 2 by denitrification and combustion, and the changes over time in N r stocks in all NNB pools. The information on these three components is insufficient and often contradictory. Some authors attribute the differences in their NNB mainly to the uncertainties in the calculation of the output and then explain a budget surplus with denitrification losses and an accumulation in the N stocks. For example, Janzen et al (2003) estimated that the 200 kt N a −1 surplus in their budget for Canada is stored in the agricultural soils. To balance the NNB for the Spanish agricultural and food system, Lassaletta et al (2014) ascribe 50% of the total inflow of 1,810 kt N a −1 to the potential retention within the hydrosystem, while 35% leave the county by products and N r emissions, and 15% is input-output difference. However, they do not discuss whether associated N transformation processes (denitrification and others) within the hydrosystem could realistically cause an N loss rate of this magnitude. Olsthoorn and Fong (1998) attributed 12% of the Dutch NNB inflow to an N loss via soils, which covers nitrate leaching and denitrification, or to changes in the soil's N stock. The comparison of four NNBs for China illustrates the wide range of the differences between inflow and outflow estimate and their interpretation even for a single country. The NNB by Luo et al (2018) specifies 70.1 Mt N a −1 inflow but only 3.1 Mt N a −1 outflow for China in 2014 and explains the difference as the result of denitrification and accumulation in various N stocks. Ti et al (2012) took the difference of 30.1 Mt N a −1 between total N input and the accounted outputs in 2007, which corresponds to 58% of the input, and assigned them to denitrification and N storage changes without further distinction. In contrast, the study of Cui et al (2013) suggests that only around 20% of the annual N r production was denitrified, while a total of 49% (31 Mt N a −1 ) was stored in soil, biomass, products and inland water in 2010. For the same year, Gu et al (2013) estimated the total N accumulation to 22.5 Mt N a −1 in China, most of it in overfertilized cropland.
The studies cited rarely address the question of whether the N accumulations in the stocks of soils, forest, groundwater, landfill and/or human settlement (calculated as a difference term) are in realistic ranges. For the German NNB an increase in N stocks plays only a minor role, if any. There are no significant increases or decreases of stocks in the pools Agriculture (except soils), Energy and Fuels or Material and Products in Industry, as all related statistics indicate. For the Forest pool in Germany, a decrease of the N stock in forest soils was observed at a mean rate of −293 kt N a −1 , corresponding to −7.5% loss of the N in soil humus, which is attributed to climate change by Fleck et al (2019). The increase in the timber stock of 17 kt N a −1 in no way compensates for this N loss in soil. A decrease of the soil N stock can also be assumed for mineral soils and especially for peat soils used as arable land in Germany, although the magnitude cannot be quantified precisely.
In terms of industrial products in China, Gu et al (2013) assumed that 25% of these products tend to accumulate in human settlements due to their long service lives. This estimate could have some justification on a global scale for emerging economies, where urban areas are growing rapidly and construction activities (residential buildings, industrial plants and infrastructure) as well as the furnishing of households with durable consumer goods are considerably expanding. For Germany, however, there is no evidence that N is accumulated on a large scale in the long term with the use of materials containing nitrogen in the construction sector or the household consumption of consumer goods.
The largest uncertainty in N stock changes concerns the root zone-unsaturated zone-groundwater system as the main domain of nitrate turnover: neither the total amount of nitrate in these compartments in Germany is known, nor can its change due to seepage water exchange and/or denitrification be estimated plausibly. According to the four-yearly Member State Reports on the implementation of the EU Nitrate Directive since 2012, the nitrate concentration is nearly constant over time at the 697 groundwater monitoring sites in Germany (BMUB and BMEL 2020). As an approximation, we assume for our NNB that the difference of 648 kt N a −1 between the nitrate leaching from soil root zone (857 kt N a −1 ) and the nitrate load into the surface waters from groundwater effluents (209 kt N a −1 ) is entirely denitrified and thus contributes substantially to neutralizing the N r emissions. However, the denitrification capacity of aquifers mainly depends on iron disulfide and organic carbon which, being finite resources, are susceptible to depletion (Knoll et al 2020). This will generally result in future risk of increasing nitrate concentrations in the groundwater and subsequent higher loads to surface water via the groundwater pathway. The status of denitrification capacity in aquifers and the consequences of its possible decline have been studied in Germany for some time (Wilde et al 2017) and are the subject of intense debate.
The Waste pool is the only sector of Germany's NNB for which a negative inflow-outflow difference in our estimate. The uncertainty is mainly attributed to the Solid Waste sub-pool due to the shortcomings and contradictory data in the two underlying statistics on waste generation and waste balance. The Federal Statistical Office has no sound information about the composition and the further treatment of the solid waste materials. The outputs from waste are classified as 'waste for recycling' and 'waste for disposal' by the plant operators without further verification. It is not possible to determine valid quantities for the individual types of waste or to quote their material recycling. Furthermore, the assumptions about the N contents of the types of waste are speculative and the N fluxes in waste treatment as well as the N accumulation by waste landfilling are therefore generally subject to large uncertainties, as also illustrated by the discrepancy for consumer products. According to the statistics, 166 kt N a −1 enters households in non-food consumer goods, but the waste statistics calculates only an outflow of −46 kt N a −1 with solid waste. Since there are no appreciable increases in stocks of commodities in the private households and no other outflow for consumer goods apart from waste is known, these two figures do not match in any way. For future calculation of N flows for the solid waste sector, the material flows must be broken down further to separate various material groups whose generation and final sinks are traced clearly by the statistics. Further gaps in the information relate to appropriate mean N contents that can be allocated to these material groups. A similar discrepancy was also found by Pierer et al (2015) for Austria. The mismatch between inflow of non-food industrial products and outflow of waste material there amounts to 83% of inflow. The authors assume streams of material waste, which are not accounted for by the statistical survey.
The divergent approaches and the partly contradictory results of the above-mentioned studies underline the urgency to standardize NNB calculations. With the development of the guideline EEA and EMEP (2013) such a standardized methodology is actually available. However, to the best of our knowledge, no NNB in accordance with the methodology of the EEA and EMEP (2013) has yet been established, except our study presented here. While we could make use of many of the equations and the wealth of underlying detail material provided, there were several instances that requires work-arounds because the NNB guidance still shows considerable room for further improvements. Specifically, we had to (i) adjust for some heterogeneous calculation schemes offering different levels of detail, (ii) add the N contents of material flows when unavailable, or use specific German data when the default value seemed implausible. Furthermore, (iii) the flow description and coding had to be adjusted occasionally as being incoherent between pools, and (iv) sink terms and stock changes had to be added into the concept in order to cover situations when flow balances did not match for a specific pool or the total NNB.

Conclusions
Our work provides a comprehensive reactive nitrogen data set for Germany. It summarizes the latest knowledge of emissions, production, flows and sinks of reactive nitrogen. It is the most complete dataset of reactive nitrogen data in Germany and therefore is a valuable database for policymaking and scientific activities. However, the quantification of the flows and the closure of the NNB for Germany, i.e. balancing the inflows and outflows, like the other cited NNBs, is characterized by a high degree of uncertainty. Especially the closure of the national budget or the budgets of the individual pools is not possible due to uncertainties in quantification of the numerous N fluxes, the sources of N r emissions and their final sinks, and the changes in N stocks. In particular, further studies are needed on the magnitude of denitrification in soils and waters, which is the most important conversion process of N r to N 2 in the biosphere. The possible accumulation of N in stocks (soil, water, products) is, in our opinion, overestimated in some studies and should be critically reviewed. Additionally, major deficits in the statistical recording of material flows can also be observed with regard to the German NNB, especially in production statistics and waste statistics. Without improvements in the statistical database, N flows in the Material and Products in Industry pool and the Waste pool cannot be captured reliably.
In terms of the EEA and EMEP (2013) initiative, it should be noted that the EEA and EMEP (2013) guidance on NNB calculation needs to be further harmonized and elaborated to facilitate future international comparability.