Retention of deposited ammonium and nitrate and its impact on the global forest carbon sink

The impacts of enhanced nitrogen (N) deposition on the global forest carbon (C) sink and other ecosystem services may depend on whether N is deposited in reduced (mainly as ammonium) or oxidized forms (mainly as nitrate) and the subsequent fate of each. However, the fates of the two key reactive N forms and their contributions to forest C sinks are unclear. Here, we analyze results from 13 ecosystem-scale paired 15N-labelling experiments in temperate, subtropical, and tropical forests. Results show that total ecosystem N retention is similar for ammonium and nitrate, but plants take up more labelled nitrate (201525\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${20}_{15}^{25}$$\end{document}%) (meanminimummaximum\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{\rm{mean}}}}}}}_{{{{{{\rm{minimum}}}}}}}^{{{{{{\rm{maximum}}}}}}}$$\end{document}) than ammonium (12816\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${12}_{8}^{16}$$\end{document}%) while soils retain more ammonium (574965\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${57}_{49}^{65}$$\end{document}%) than nitrate (463259\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${46}_{32}^{59}$$\end{document}%). We estimate that the N deposition-induced C sink in forests in the 2010s is 0.720.490.96\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${0.72}_{0.49}^{0.96}$$\end{document} Pg C yr−1, higher than previous estimates because of a larger role for oxidized N and greater rates of global N deposition. A study using paired 15N tracers shows atmospheric N deposited in oxidized form is more likely retained by trees, while the reduced form is retained in soil. The authors argue that this is a greater contribution of deposited N to the global forest C sink than previously reported.

H uman activities have greatly accelerated reactive N emissions to the atmosphere and have increased rates of N deposition globally [1][2][3] . Depositional fluxes of the two dominant forms of deposited N (NH x and NO y ) are unevenly distributed in space and changing over time 4,5 . Increased N deposition enhances ecosystem carbon (C) sinks 6,7 , decreases biodiversity 8 , and increases N leaching losses, leading to downstream eutrophication and acidification 9 . Critically, the impacts of N deposition depends on the fate of N inputs to ecosystems, i.e., its retention in biomass and soil organic matter pools versus its losses via leaching and denitrification. The fates of deposited N are expected to differ depending on whether it is in reduced (mainly as ammonium) or oxidized (mainly as nitrate) form. Trees, especially conifers, have often been shown to take up more ammonium than nitrate [10][11][12] , probably because the energetic cost is higher for nitrate assimilation 11,13 and ammonium is more abundant in forest soil 14 .
However, field-scale 15 N-tracer experiments are needed to unambiguously quantify and understand how deposited ammonium and nitrate are retained in plant and soil pools. Because of few ecosystem-scale 15 N-labelling experiments in forests 15 , the differential fates of deposited ammonium and nitrate in forests from the tropics to high-latitude are currently unknown and thus the latitudinal pattern of retention of ammonium and nitrate and its consequences for forest C sinks remain uncertain. Given the large spatial variation (Fig. 1a) in reduced and oxidized N deposition across forest biomes [16][17][18] , elucidating the fates of ammonium and nitrate is essential for reliably scaling up the contribution of N deposition to the global C sink.
In this study, we analyze results from ecosystem-scale paired 15 N-tracer (separate additions of 15 N-labelled ammonium vs nitrate as 15 NH 4 + and 15 NO 3 − , respectively) experiments at 13 forests across tropical, subtropical, warm temperate, and cool temperate climate regions to investigate the fate of atmospheric N deposited in ammonium and nitrate form into the forests. We found a similar total N retention fraction for the two forms, but different allocation to plant and soil pools. Nitrogen retention in plants and soils across sites is predicted by a combination of climate, plant, and soil variables. Using a stoichiometric upscaling approach 19 , we estimate a greater N deposition-induced C sink in forests than previous estimates and with greater C gain per unit N deposited in oxidized than in reduced forms.
The greater recovery of 15 NO 3 − than 15 NH 4 + in plants suggests that deposited nitrate is taken up by plants proportionally more than ammonium. This is not intuitive since plants are viewed to favour ammonium 12,22 because it is generally more abundant in forest soil (Supplementary Table 2) and because both uptake (against a steep electrochemical gradient) and assimilation of nitrate (reduction to NH 4 + ) are energetically more expensive than that of ammonium 11,13 unless nitrate is reduced in leaves under light-saturated conditions 23 . Less plant uptake of deposited ammonium in our experiment could be attributed to preferential assimilation and retention of ammonium by microbes and abiotic mechanisms such as soil adsorption 20,24 , which results in ammonium being retained on soil particles. In contrast, nitrate is mobile in soil solution and hence it moves more easily than ammonium to the root surface by diffusion and mass flow 14,25 . This makes nitrate more readily available for plant uptake and could be the main reason for the greater uptake of deposited nitrate by plants in our experiments. While the added 15 NO 3 − was less diluted in the soil than 15 NH 4 + , due to the nitrate pool being smaller than the ammonium pool in 11 out of 13 sites (Supplementary Table 2), differences across the study sites in the background soil ammonium to nitrate ratio were unrelated to plant biomass 15 N recovery ratio for 15 NO 3 − and 15 NH 4 + ( Supplementary Fig. 4). This indicates that the consistently higher uptake of deposited nitrate than ammonium by plants across a range of soil ammonium to nitrate conditions was not caused by the greater dilution of exogenous 15 NH 4 + by soil endogenous ammonium.
Variation of N retention across sites. Our 15 N recovery data show that the partitioning to different ecosystem compartments and the total ecosystem retention of deposited ammonium and nitrate both vary across forests (Fig. 1b, Supplementary Fig. 3). In general, plants retained similar amounts of N in either form in both temperate and tropical forests. However, the two N forms experienced different biome-specific fates in soils ( Supplementary  Fig. 5). The soil organic layer retained significantly more ammonium and nitrate in temperate forests while the mineral soil retained more ammonium and nitrate in tropical forests. The higher N retention in organic soil in temperate forests is likely due to the lower precipitation and thicker organic soil layer in temperate regions than in the tropics 26,27 that provide longer contact time for new N input to be immobilized in the soil organic layer. In tropical forests where the organic layer is usually poorly developed, new N input is likely transported to the mineral soil. In addition, a greater anion adsorption capacity of highly weathered tropical mineral soils could increase retention of the highly leachable nitrate in tropical mineral soil 28 . Ecosystem retention (soil plus plant) was also greater in temperate forests than in tropical forests for nitrate (t-test, p < 0.05) (Supplementary Fig. 5), possibly because the higher N availability and precipitation in tropical forests led to higher leaching losses of deposited nitrate. These insights from our paired 15 N-tracer results suggest that varied assimilation and retention efficiency of inorganic N inputs among forest biomes are mainly due to differences in climate, N status, and soil attributes.
We explored the relationship between 15 N recovery dynamics and sets of factors that potentially predict the capacity of forest ecosystems to retain N (Supplementary Table 4, see Method). We assessed N status from the C/N ratio of the mineral soil and hypothesized that N-limited ecosystems with higher C/N ratios would retain more deposited N than N-rich sites with low C/N ratios 9 . In support of this hypothesis, the fraction of 15 NH 4 + and 15 NO 3 − lost was negatively correlated with the soil C/N ratio (R 2 = 0.43, p < 0.05 for 15 NH 4 + and R 2 = 0.32, p < 0.05 for 15 NO 3 − ) (Fig. 2a). For 15 NO 3 − , the fraction of 15 N lost was also positively correlated with N deposition (Supplementary Fig. 6a). The fraction of 15 N retained in the organic soil layer was positively correlated with its mass (R 2 = 0.73, p < 0.001 for 15 NH 4 + and R 2 = 0.51, p < 0.01 for 15 NO 3 − ) (Fig. 2b), suggesting that plant-derived soil organic matter strongly controls N retention 29,30 . For 15 NH 4 + , retention in organic soil was also negatively correlated with mean annual temperature (MAT) ( Supplementary Fig. 6b) and the ratio of 15 N recovery in plants to that in plants plus mineral soil was negatively correlated with net primary production (NPP) (R 2 = 0.64, p < 0.01 for 15 NH 4 + and R 2 = 0.63, p < 0.01 for 15 NO 3 − ) (Fig. 2c). This negative correlation between NPP and 15 N recovery in plants relative to the total recovery in plant and mineral soil implies that plant growth (and NPP) in N-rich productive ecosystems including most tropical forests is less dependent on external N from deposition than in N-limited temperate and boreal forests 31,32 . With NPP primarily controlled by climate 33 , the correlation could be an indirect climatic control, but MAT or MAP did not appear as important predictors of plant-and mineral soil-related N retention (Supplementary Table 4). In addition, the fraction of 15 N retained in plants that was allocated to woody biomass varied from 20 to 60% and increased with woody biomass (R 2 = 0.86, p < 0.001 for 15 NH 4 + and R 2 = 0.87, p < 0.001 for 15 NO 3 − ) (Fig. 2d).
Global deposition and retention pattern of deposited NH x and NO y in forest ecosystems. Despite extensive monitoring and modelling efforts to assess global patterns of N deposition, attempts to separate N deposition rates and its forms for the world's forests have been limited. To quantify global inorganic N deposition to forests and its speciation between reduced and oxidized forms, we used results from four different models (Supplementary Table 5). Total inorganic N deposition on Earth's 42 million km 2 of forest 34 in 2000 to 2010 averaged 24.9 Tg N yr −1 , of which 13.8 Tg N yr −1 was NH x and 11.2 Tg N yr −1 was NO y (Supplementary Table 6). N deposition was higher in tropical (13.1 Tg N yr −1 ) than temperate (8.1 Tg N yr −1 ) and boreal forests (3.7 Tg N yr −1 ) (Supplementary Table 6), although high N deposition occurs in many temperate forests in Asia and central Europe (Fig. 1a). High N deposition was associated with a greater NH x contribution (Fig. 1a). We used relationships linking plants and soils and the variables described above (NPP, woody biomass, organic layer mass, and soil C/N ratio) to extrapolate the retention of deposited N in global forests (Fig. 2). We then created global maps for the fractions of deposited NH x and NO y retained in plants and soil or lost from the ecosystem (Fig. 3, see Methods). We used average values for modelled N deposition (Fig. 1a) and the extrapolated N retention fraction in plant and soil pools (Fig. 2) for both NH x and NO y to estimate that 2:0 2:7 1:3 Tg N yr −1 and 2:9 3:7 2:0 Tg N yr −1 of deposited NH x and NO y , respectively, were retained in plant biomass (Supplementary Table 6). In woody biomass, 0:7 1:0 0:5 Tg N yr −1 of deposited NH x and 1:0 1:2 0:7 Tg N yr −1 of deposited NO y was retained. Retention in soil organic layer was 2:8 3:6 2:3 Tg N yr −1 for NH x and 2:4 3:1 1:8 Tg N yr −1 for NO y whereas retention in mineral soil was 4:6 6:0 3:3 Tg N yr −1 for NH x and 3:2 4:3 2:4 Tg N yr −1 for NO y (Supplementary Table 6). The resulting spatial pattern of N retention indicates that N-limited forests in higher latitudes retain deposited N mostly in the vegetation and the organic soil, whereas in N-rich forests in lower latitudes the mineral soil is the dominant sink for deposited N (Fig. 3, Supplementary Fig. 7). The spatial analysis of N allocation clearly indicates that a similar fraction of deposited NH x is allocated to plants across biomes, while the retention fraction of deposited NO y in plants is larger in boreal forests than in temperate and tropical forests (Fig. 3). Biome-scale total retention per unit area of NH x and NO y is lower in tropical than in temperate and boreal forests (Fig. 3, Supplementary Table 6). Lower ecosystem N retention in tropical forests is likely due to higher gaseous losses and more leaching of deposited N (ref. 35 ).
Global carbon sink in forests from deposited NH x and NO y . Finally, we used our 15 N-tracer-derived global maps of N retention in woody biomass and soils (Fig. 3, Supplementary Fig. 7) to estimate the C sink (annual net C gain) of global forests due to N deposition via the stoichiometric scaling method (see the Method). We estimated the total C sink due to N deposition in global forests at 0:72 0:96 0:49 Pg C yr −1 (Fig. 4, Supplementary Table 7), which is 1.5-4 times the estimates from previous studies for forest ecosystems 19,[36][37][38][39][40][41] and larger than most estimates for all terrestrial ecosystems (Supplementary Table 9). This larger estimate is partly because of the updated (and higher) N deposition values (23-27 vs 5-21 Tg N yr −1 ) and partly because of greater C gain per unit N deposited obtained in this study (29 38 20 kg C kg −1 N) than in the previous studies (Supplementary Table 9). Only the studies by Nadelhoffer et al. 19 and Thomas et al. 40 reported a higher C gain per unit N deposited, although their estimates of global N deposition (and the corresponding C sink) were low. Note that estimates by other approaches such as model analysis 39 account for the C sink over multi-decadal timescales. Our estimate based on retention of deposited N over 1 year reflects short-term (annual to decadal) effects of N deposition on C uptakes as the loss of previously deposited and retained N from the system could not be measured with the labelling technique. Our estimate indicates a likely ceiling for the N deposition contribution to the annual global terrestrial C sink over the last decade (≈3.4 Pg C yr −1 ) 42 of 21 28 14 % if past N deposition has had no effect on the C sink over time.
The global distribution of N-induced forest C sinks largely follows N deposition patterns, showing strong sinks in eastern North America, central Europe, South and East Asia, and parts of central Africa (Supplementary Fig. 9a). At biome scales, the largest N-induced C sink per unit area occurs in temperate forests (Supplementary Table 7). Although less NO y than NH x is deposited in global forests, it makes larger contributions to N-induced forest   C sink estimates at both the biome scale and the global scale because of higher C gain per unit N deposited for NO y (35 46 23 kg C kg −1 N) than for NH x (24 33 17 kg C kg −1 N) (Supplementary Table 7). This emphasizes the need to account separately for differential fates of reduced and oxidized N in deposition so that the contribution of deposited N to forest C sink and its implication for land C balance can be fully assessed.
Our global estimates have several limitations. First, the few paired 15 N-labelling experiments are unevenly distributed. The absence of sites in African and South American forests reduces confidence in those regions' estimates. Our study sites were also located in regions with moderate and high ambient N deposition. Second, the 15 N-labelling at most of our study sites was undertaken during the growing season when plants are likely to be highly active. The upscaling method assumes that deposited N across the year is retained with the same efficiency, which likely overestimates plant N uptake and consequently the C sink. Third, the estimated C sink is based on the first-year fate of deposited N. Over a longer timescale, N loss or distribution and the turnover of C and N in plant tissues and soil organic matter may modify the effect of deposited N on C sink. Thus, our estimate likely provides an upper limit to the global forest C sink induced by N deposition.
In summary, by quantifying the differential fates of 15 NH 4 + and 15 NO 3 − tracers, we showed that N from deposited NO y is preferentially assimilated by plants, while N from deposited NH x is preferentially retained in soil. Deposited NO y is more effective than NH x at increasing C sinks in forest biomass due to its higher uptake by trees. We estimated the maximum potential contribution of deposited N to forest C sinks at 0:72 0:96 0:49 Pg C yr −1 . Our a b c d e f findings imply future changes in the ratio of NH x and NO y inputs due to land use, technology, and policy changes will alter the retention pattern of deposited N and its potential contribution to C sinks in forest ecosystems.

Methods
Study sites. The paired 15 N-tracer experiments were conducted in 13 forest sites, of which nine were in China, two in Europe and two in the USA. These sites vary in mean annual precipitation (MAP) from 700 to 2500 mm, in mean annual temperature (MAT) from 3 to > 20°C, and in soil types (Fig. 1 Sampling. Major ecosystem compartments including trees, understory vegetation, fine roots, and organic and mineral soil layers were sampled before and~1 year after the 15 N-labelling in each plot. Understory plants and tree compartments including mature leaves, twigs, branches, and stem woods were collected. Organic and mineral soil layers were sampled separately. For mineral soil, sampling depth varied among sites depending on the local soil conditions; 0-40 cm at all Chinese sites except at the Changbai forest (0-15 cm) and Tieshanping (0-30 cm), 0-65 cm at Wülfersreuth, 0-100 cm at Solling, and 0-20 cm at the two Harvard Forest sites.
Chemical analysis. At each site, analyses for 15 N were conducted using isotoperatio mass spectrometry on the two sets of plant and soil samples taken before and 1 year after the 15 N-labelling. The preparation of plant and organic layer samples consisted of oven-drying at 50-70°C, while soil samples were mostly air-dried, but sometimes oven-dried at temperatures varying between 40-70°C and then sieved (< 2 mm), varying with the site considered. The 15 N content of all samples at all sites were analyzed using elemental analyser-isotope ratio mass spectrometry while using slightly different systems. Details on the variation in temperatures used in the preparation of the plant, organic layer, and soil samples and in measuring systems used are given in the supplementary material and related data source references.
Where N added is the mass of 15 N we experimentally added (kg N ha −1 ); N pool-before and N pool-after are the N pool (kg N ha −1 ) in each ecosystem compartment before and 1 year after 15 N labelling, respectively; % 15 N atom-before and % 15 N atom-after are 15 N abundance (%) before and after 15 N labelling, respectively; 15 N lost is the mass of the 15 N experimentally added that is lost from the ecosystem.
From Eq. (1), we can derive Eq. (2) to calculate the mass of 15 N recovered ( 15 N rec ) at ecosystem level as: Assuming that N pool did not change significantly over the study period, we can get Eq. (3) to calculate the 15 N rec as per cent of the added 15 N as follows: We used equation (3) to calculate the 15 N-tracer recovery as we also did not account for net N increment in both plant and soil compartments change in N pool over the relatively short experimental period (about 1 year). Such a small net change in N pool is difficult to detect using the traditional inventory method, which requires repeated measurement on N pool during a longer time (usually every 5 years), especially for soil N pool due to its large background N pool and spatial heterogeneity.
Upscaling of 15 N recovery to global forest N retention. We established conceptual pathways of 15 N retention and partitioning after the 15 N-labelling (Supplementary Fig. 1) and assumed that the unrecovered 15 Fig. 4 Estimates of C sink in global forests due to atmospheric N deposition. In the current study, the C sink estimated due to N deposition (24.9 Tg N yr −1 ) on lands with > 10% forest cover assumes that 80% of atmospheric N retained in the soil is immobilized in the soil organic matter (see Method). The contribution of NH x and NO y deposition to the total N-induced C sink in the global forests is shown in Supplementary denitrification. To predict global N retention from results of 15 N recoveries in our paired 15 N-labelling experiments, we considered nine potential predictors from factors that influence ecosystem N retention as suggested in the literature 9,15,20,30,45 including variables that define climate (MAT, MAP), ecosystem N status or soil fertility (soil C/N ratio, soil clay content, leaf C/N ratio, N deposition), N pool (soil organic mass, wood biomass), and annual net primary production (NPP). Then, we fitted all possible regressions of 15 N retention in plant and soil pools and the 15 N loss fraction with the set of predictor variables across the 13 sites (Supplementary Table 4) using the glmulti package in R. Then, the best regression model was selected based on the minimum corrected Akaike information criterion 46 , constrained by the cutoff of variance inflation factor (VIF) > 3 to avoid multicollinearity among predictors. Global maps of partitioning of deposited NH x and NO y (Fig. 1a) to plants, woody biomass and soil as well as loss patterns (Fig. 3, Supplementary Fig. 7) were derived based on the best regression models summarized in Supplementary Table 4, using globally gridded products of the corresponding predictors. In addition, the key variables with significant and the highest explanations for predicting variations in 15  Litter mass and C/N ratios of wood, organic, and mineral soil layers were obtained from GOLUM-CNP v1.0. Soil clay content data was also obtained from BNU.
Global N deposition map. The global map of average NH x and NO y deposition to forests between the years 2000 and 2010 was created using forest-specific values of NH x and NO y inputs obtained from four different models (Supplementary  Table 5). This map of global N deposition was combined with a global forest cover map with a spatial resolution of 1 km that is derived from a consensus land-cover product 34 . Here, a forest cover fraction > 20% in a 1-km pixel was defined as forest.
Based on this, we estimated the total global forest area to be ≈42 million km 2 .
Calculation of N-induced C sink. The N-induced C sink was estimated via the stoichiometric upscaling method 19 , i.e., by multiplying the N retention in woody tissues of stems, branches, and coarse roots and in the soil with the C/N ratios in these compartments. The C sink due to NH x and or NO y deposition was calculated separately using Eq. (4) as follows: where N dep is NH x or NO y deposition (kg N ha −1 yr −1 ); 15 N R org , 15 N R min and 15 N R wood indicate the fraction of deposited NH x or NO y allocated to organic layer, mineral soil, and woody biomass, respectively; and C Norg , C Nmin , and C Nwood indicate C/N ratios in the soil organic layer, soil mineral layer and woody plant biomass, respectively. f is the fraction we applied to account for flexible C/N in response to elevated N deposition. At elevated N deposition, wood C/N ratio may decrease, and N accumulates without stimulating additional ecosystem C storage. To account for this scenario, we adopted a flexible stoichiometry 51 , in which the effects of N deposition on wood C/N ratios are accounted for by multiplying the C/N ratios of wood with a fraction f (from 1 to 0) depending on plant growth response to different rates of N deposition level (kg N ha −1 yr −1 ). Results of growth responses to experimental N addition and field N gradient studies show plant growth increased with increasing N deposition, flattening near 15-30 kg N ha −1 yr −1 and a reversal toward no enhanced growth response at about 100 kg N ha −1 yr −1 (ref. 36,52 ). Therefore, for N deposition < 15 kg N ha −1 yr −1 , we assumed that N deposition has no effect on C/N ratios of wood (f = 1). Then, we assumed that f decreases to 0.5 when N deposition reaches 30 kg N ha −1 yr −1 and assumed that f decreases to 0 when N deposition reached 100 kg N ha −1 yr −1 (i.e., N deposition will not increase tree growth anymore, and no new C is gained due to N deposition).
In the soil, deposited N can be retained through assimilation into microbial biomass, immobilization in soil organic matter (SOM), and abiotic immobilization in the soil. It is the fraction of soil retained N that are immobilized in the persistent pool of SOM (as organic N) that can contribute to long-term C sinks in the soil. We assume the fraction to be ≈ 80% based on results from previous 15 N-tracer studies [53][54][55][56] .
We used four sets of global N deposition (Supplementary Table 5), six different wood C/N values (Supplementary Table 8), and three different soil C/N values that varied with plant functional type 50 in our stochastic calculations of the N-induced C sink.
Analysis of uncertainties in global N retention and associated C sink. To estimate uncertainty of the global N retention map, we considered the uncertainty of regression coefficients and the input data for upscaling in Supplementary Fig. 8 for each grid. We randomly sampled 10 out of the 13 sites to do the regression and then upscaled with one randomly selected input dataset for 1000 times using Monte Carlo methods to generate 1000 sets of global maps for retention or loss of deposited NH x and NO y (Fig. 3). The standard deviations of these 1000 sets of global maps are defined as the uncertainty of retention maps shown in Supplementary Fig. 8. For the uncertainties of the N-induced C sink, we considered the uncertainty of global retention maps (1000 sets), the uncertainty of global N deposition (four global N deposition maps; Supplementary Table 5), and the uncertainty of wood C/N ratios (six sets; Supplementary Table 8). Thus, we derived 24000 maps of N-induced C sink (4 global N deposition maps × 1000 sets of retention maps × 6 wood C/N ratios × 1 soil organic C/N ratio) for both deposited NH x and NO y . The total uncertainty of the N-induced C sink is defined by 95% confidence intervals.
Reporting summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.