Inland Waters Increasingly Produce and Emit Nitrous Oxide

Nitrous oxide (N2O) is a long-lived greenhouse gas and currently contributes ∼10% to global greenhouse warming. Studies have suggested that inland waters are a large and growing global N2O source, but whether, how, where, when, and why inland-water N2O emissions changed in the Anthropocene remains unclear. Here, we quantify global N2O formation, transport, and emission along the aquatic continuum and their changes using a spatially explicit, mechanistic, coupled biogeochemistry–hydrology model. The global inland-water N2O emission increased from 0.4 to 1.3 Tg N yr–1 during 1900–2010 due to (1) growing N2O inputs mainly from groundwater and (2) increased inland-water N2O production, largely in reservoirs. Inland waters currently contribute 7 (5–10)% to global total N2O emissions. The highest inland-water N2O emissions are typically in and downstream of reservoirs and areas with high population density and intensive agricultural activities in eastern and southern Asia, southeastern North America, and Europe. The expected continuing excessive use of nutrients, dam construction, and development of suboxic conditions in aging reservoirs imply persisting high inland-water N2O emissions.


Contents:
Supporting Texts: Text S1.Summary of observational ratios of N2O production to groundwater denitrification Text S2.Method of statistical comparison of observation and simulation: Root Mean Squared Error Text S3.Method of sensitivity analysis Text S4.Summary of sensitivity analysis results Text S5.Uncertainty and limitations Supporting Figures: Figure S1.Global average N2O atmospheric concentration during 1750-2020.Figure S2.N (of different forms) and N2O inputs to global inland waters from different sources.Figure S3.Global reservoir volume, population, wastewater N discharge to surface water, gross production value of agriculture, manure production and fertilizer use. Figure S4.IMAGE-DGNM scheme of water and nutrient flows in the soil-hydrosphere system.Figure S5.Range of observation-based ratios of N2O production to groundwater denitrification.Supporting Tables: Table S1.Methodology of inland-water N2O dynamics in IMAGE-DGNM Table S2.Parameters used to simulate inland-water N2O dynamics in IMAGE-DGNM.Table S3.Summary of observation data from databases and literature used for comparison with model outputs of TN and DO concentrations, N2O concentration and emission, and water discharge per variable per site per river basin in global inland waters for the period since the 1920s.Table S4.Comparison with reported estimates of global N2O emissions from inland waters.Table S5.Contribution of inland waters to global N2O emissions in the 1980s, 1990s, 2000s and 2010s

References
Text S1.Summary of observational ratios of N2O production to groundwater denitrification: range from literature and value used in the model.
Among the total number of 278 of the reported data, the median value of the ratios of N2O production to groundwater denitrification is 0.010, the average value is 0.041, the lower quartile is 0.002, the upper quartile is 0.041, and outliers account for 14% of all data (Figure S5).The mean value of the data within the range from the lower to upper quartiles is 0.014, which is close to the median of 0.010.Taking ±1 standard deviation as the uncertainty range of data within the lower and upper quartiles, the uncertainty of the ratios of N2O production to groundwater denitrification is ±0.011 (±76%).
Therefore, in this study, a constant fraction (  2  =1%, median of the 278 reported observationbased values) of shallow groundwater denitrification is calculated as the N2O produced in shallow groundwater, which is transported to surface waters (Figure S4).

Text S2. Method of statistical comparison of observation and simulation: Root Mean Squared Error
DISC-simulated and observed yearly averages are compared for each variable of water discharge and concentrations of TN, N2O and DO, for each monitoring site in inland waters using data from published databases and literature (Figure S7 and Table S3), for years since the 1920s with at least 4 measurement months (for representativity concerns).At each monitoring site, we assess the discrepancies between simulated and measured results for each variable by calculating the Root Mean Squared Error (RMSE) (Chai and Draxler, 2014) using the equation below: where Obsi and Simi are the observed and simulated yearly average values of the variable, respectively,  ̅̅̅̅̅ is the mean of the observations, and n is the number of observations.RMSE values smaller than 50% are considered acceptable (Beusen et al., 2015).RMSE results for validation are summarized in Figure S8.

Text S3. Method of sensitivity analysis
Since our model is based on mass conservation, the modelled global N (including N2O) fluxes are internally consistent, and temporal changes are the combined result of the changes in hydrology, climate, and N inputs from the land.Therefore, in addition to extensive validation (Figures S6-S9 and Table S3), we perform an analysis of the sensitivity of modelled fluxes to the variation of model input parameters (Figure S10 and Texts S3-S4).
In this study, we use a one-factor method to quantify the sensitivity of model output results to varying input parameter values with a relatively limited number of runs.According to the results shown in the Main text and Supporting Information, the large increase in the global inland-water N2O emissions for the period 1900-2010 is due to increased N2O inputs (mainly from groundwater) and increased inland-water N2O production (mainly via nitrification in the water column and denitrification in sediment) (Figures 2-3).N2O inputs are mainly from groundwater and minorly from atmospheric deposition (Figure 2), while inland-water N2O production is closely related to the reactive N availability in waterbodies and N2O production rates via nitrification and denitrification (Figures 2 and S12).Temperature and discharge are also important environmental factors for N2Orelated transformation and transport processes in inland waters (Figure 1 and Table S1).Therefore, we identify N2O input from groundwater, N2O input from atmospheric deposition, N2O inlandwater production rate via nitrification, N2O inland-water production rate via denitrification, TN delivery in inland waters, discharge and temperature as the most important model input parameters (Xi) to the simulated global inland-water N2O emissions and export (Y).We perform model runs for sensitivity to the variations in these input parameters (Xi), and examine the results of multi-year averages over the period 1995-2000 for the following output parameters (Y): yearly total N2O emissions from inland waters, N2O emission from low-order streams, N2O emission from high-order rivers, N2O emission from lakes, N2O emission from reservoirs, and river dissolved N2O export to oceans (see Figure S10 below).
In each run, the values of one of the selected model parameters (Xi, except for temperature) are multiplied with a factor of 0.95 or 1.05 (i.e., ±5% variation, Xim and Xip, respectively), while the values of other model parameters maintain original default values; for the run of model sensitivity to temperature, an addition of -1℃ or 1℃ is applied to the default temperature (Xim and Xip, respectively), while the values of other model parameters maintain original default values.With the runs for each input parameter performed (with outputs of Yio, Yim and Yip matching inputs of the default Xio, and changed Xim and Xip, respectively), the linear regression can be used for evaluating the contribution of the variation in input parameter Xi to the variation in output parameter Y if the coefficient of determination (R 2 ) is close to 1, i.e., when there is no variation in Y that is not explained with the linear regression model.The output parameter Y corresponding to the variation in input parameter Xi can be expressed using a linear regression approach below: where βi is the slope of parameter Xi and e is the intercept of the approximation of Y.The relative variation in Y corresponding to the relative variation in Xi by an increase of 5%, i.e., Cxi, can be thus expressed as follows: where Cxi is independent of units and scale of parameters, a positive Cxi value indicates that an increased Xi leads to an increased output Y, and a negative Cxi indicates a decreased output Y with an increased Xi.

Text S4. Summary of sensitivity analysis results
Sensitivity analysis which was earlier conducted for IMAGE-DGNM and the DISC-NITROGEN module revealed the importance of model parameters and input data on the inland-water N cycle (Beusen et al., 2015;Beusen et al., 2016;Vilmin et al., 2020).For example, inputs of multiple N forms and sources influence river N retention and export (Beusen et al., 2016;Vilmin et al., 2020), runoff influences river N delivery, retention and export (Beusen et al., 2015), optimal temperatures for nitrification and denitrification in river basins influence the inland-water transformation of multiple N forms (Vilmin et al., 2020).
In this study, we further analysed the sensitivity of simulated freshwater N2O emissions (including those from different waterbodies of low-order streams, high-order rivers, lakes and reservoirs) and river export of dissolved N2O to the variations in N2O input from groundwater, N2O input from atmospheric deposition, N2O inland-water production rate via nitrification, N2O inlandwater production rate via denitrification, TN delivery in inland waters, discharge and temperature (Text S3).The results show that the global total inland-water N2O emissions are sensitive to N2O input from groundwater, total reactive N delivery in global inland waters and N2O inland-water production rate via nitrification, and will increase by 2.1-2.6% as one of these parameters increases by 5% (Figure S10).Total inland-water N2O emissions are less sensitive to discharge (-1.3%),N2O inland-water production rate via denitrification (+0.6%), and input from atmospheric deposition (-0.2%).N2O emission from low-order streams is mainly sensitive to N2O input from groundwater, and will increase by 4.4% with a 5% increase in N2O input from groundwater.N2O emissions from high-order rivers, lakes and reservoirs will increase by 1.0-1.2%with a 5% increase in N2O input from groundwater, but will increase by 2.4-3.3% with a 5% increase in N2O inland-water production rate via nitrification and by 2.8-3.8% with a 5% increase in the total reactive N delivery.A 5% increase in N2O inland-water production rate via denitrification will increase the N2O emissions from the four individual waterbodies by 0.4-0.9%.This indicates that N2O emissions from high-order rivers, lakes and reservoirs are mainly sensitive to the total reactive N delivery in global inland waters and N2O inland-water production rate via nitrification, which are both closely related to the inland-water N2O production.The dissolved N2O export also increases (by 3.0, 2.1, 0.7%, and 0.6%, respectively) as the total reactive N delivery, N2O inland-water production rate via nitrification, N2O inland-water production rate via denitrification, or N2O input from groundwater increase by 5%.A 5% increase in water discharge will reduce N2O emissions from four waterbodies individually and collectively by 1.2-1.3%but will increase river export of dissolved N2O by 3.3%.An increase in temperature will slightly increase N2O emissions from four waterbodies individually and collectively (+0.2-1.4%),but slightly reduce river export of dissolved N2O in turn (-1.5%).

Text S5. Uncertainty and limitations
The discrepancy between simulations and observations can be partly attributed to their different time scales.Though we have used the yearly means of observational data with at least 4 measurement months within the year to reduce relevant influences, available observational data may not be representative due to incomplete temporal coverage or inhomogeneous distribution within each year.Our simulated results are on an annual basis, which may not appropriately capture the pattern of short-term (i.e., daily, monthly or seasonal) observations while some available measurements were only conducted in one or several months (with inhomogeneous distribution within the year) instead of the whole year.Moreover, freshwaters are heavily under-sampled and the lack of representativeness of the few N2O measurements available before the year 2010 may also contribute to the minor mismatch.
Another reason may be the issue of spatial scales.The spatial input data IMAGE-DGNM can be uncertain due to the coarse resolution, which may have significant influences on the description of N cycling in low-order streams with extremely spatially variable topography (Vilmin et al., 2020) or in draining areas across boundaries of grid cells (Beusen et al., 2015), while the available site-level observations may not represent the average condition of the entire coarse 0.5°×0.5°grid.Moreover, IMAGE-DGNM estimates that low-order streams account for 61-66% of the total inland-water area during 1900-2010, which is lower than the 69% estimated using data from HydroSHEDS (Lehner et al., 2008) by Raymond et al. (2013) and the even higher value by Allen and Pavelsky (2018).This may thus lead to the underestimation of the contribution of low-order streams.
Except for the N, N2O oxygen, and hydrological flows in global inland waters validated for the period since the 1920s, sensitivity results show that global inland-water N2O emissions are sensitive to groundwater N2O input (Figure S10).N2O was reported to be supersaturated in groundwater compared to the atmosphere, and production (as an intermediate product during the denitrification process of the stepwise reduction of NO3 -to N2) or accumulation of N2O in groundwater, especially under agricultural land cover, was widely reported (Lemon and Lemon, 1981;Bowden and Bormann, 1986;Spalding and Parrott, 1994;Weller et al., 1994;Groffman et al., 1998;Groffman et al., 2000;Well et al., 2005a;Deurer et al., 2008;von der Heide et al., 2008;Jahangir et al., 2012;Jurado et al., 2017).The large uncertainties of the measured ratio of N2O:denitrification may be subject to vertical and lateral diffusive or convective transport of N2O in groundwater; i.e., the site where groundwater N2O is sampled may not necessarily be where N2O is produced.Besides, N2O can be produced by nitrification, nitrifier denitrification or denitrification and leached from the unsaturated zone (Spalding and Parrott, 1994;Muhlherr and Hiscock, 1998;Well et al., 2001;DeSimone et al., 2010).Furthermore, N2O in groundwater (from denitrification) depends on the infiltration of NO3 -and electron-contributors into the saturated zone in the historical year and denitrification progress during the groundwater transport (Böhlke, 2002;Van Drecht et al., 2003;Keuskamp et al., 2012), which depend on the travel times that are highly variable because groundwater flow to surface water is generally a mixture of water with highly varying travel times.Depending on the local environmental and biogeochemical conditions, denitrification progress can control both the production and consumption of N2O in groundwater (Bouwman et al., 2013a).Consequently, N2O production via groundwater denitrification may have a nonlinear relationship with these various controlling factors (Keuskamp et al., 2012).
Though with uncertainties above, our estimate of 0.5 Tg N yr -1 of N2O inputs from groundwater for the mid-1980s is comparable to 0.4-1.0Tg N yr -1 based on observations in aquifers for the same period by Ronen et al. (1988).Moreover, our estimate of N2O inputs from groundwater to low-order streams of 0.41 Tg N yr -1 for the year 2000 is similar to 0.39 Tg N yr -1 for the 2000s estimated by Yao et al. (2020).Our estimates of freshwater N2O concentrations and emissions for the period since the 1970s also agree with observations and some observation-based studies, respectively (Sections 3.2,3.3,3.5,and 3.6 in Main text).The differences between our estimates and some recent studies can be explained by the differences in estimates of N inputs and inland-water process flows, representations of reservoir and groundwater contributions, and considerations of temporal changes and spatial heterogeneity.
Overall, the agreement between our simulations and existing observations and estimates gives confidence to the methodologically consistent, process-based approach of IMAGE-DGNM to obtain historical N and N2O conditions.Furthermore, as the N2O fluxes in global inland waters simulated by IMAGE-DGNM account for spatial and temporal heterogeneities in N loading and transfers in river networks as well as the hydrological conditions and climate changes that control N transport, transformations and exchange at interfaces, this integrated approach can further be used to identify the controlling factors of N2O emissions from inland waters regionally and globally over time as next steps, and has the potential to predict future changes in freshwater N2O emissions under various scenarios.The statistics of RMSE per variable for all stations worldwide are shown in its boxplot, with the median marked with dark blue color and RMSE=200% marked with light blue color.Information on the observational data used is in Table S3.S3.The distribution of sites for observations is in Figure S7.

Descriptions and equations NIT (nitrification in the column)
Nitrification in the water column, i.e., oxidation of NH4 + to NOx -, depends on ambient temperature, oxic condition (oxygen concentration), and the amount of reaction substrate NH4 + .

Temperature dependency:
The inland-water temperature (T, in ℃) with a 0.5×0.5°resolution for each year during 1900-2010 is from the global mass-balanced hydrology model PCR-GLOBWB (Van Beek et al., 2011;Sutanudjaja et al., 2018), which simulates hydrological metrics with 5-arcmin resolution.Temperature-dependency for nitrification in the water column is represented according to Billen et al. (1994) and Garnier et al. (2007), using the theoretical function of the process' optimal temperature (Topt,NIT) and standard deviation (σNIT) as well as the local ambient water temperature for that time: Oxic-condition-dependency (limiting factor by ambient oxygen concentrations): The oxic and anoxic conditions are represented using the theoretical half-saturation oxygen concentration (Helder and de Vries, 1983;Cox, 2003) and the local ambient oxygen concentration simulated by the mass-balanced process-based model: Limiting factor for oxic conditions for nitrification:

Nitrification:
As was described in Vilmin et al. (2020), in IMAGE-DGNM, the equation of massbalanced nitrification using the reaction stoichiometry of NOx -and O2 and taking into account temperature dependency, oxic-condition-dependency and theoretical maximum nitrification rate (knit, from Thomann and Mueller (1987); (Cox, 2003)) is represented as: As the reaction substrate, NH4 + and O2 can limit the nitrification process by both their absolute amounts and their ratio relative to the reaction stoichiometry.

Production of N2O during nitrification:
While the above function in IMAGE-DGNM assumes that all nitrification in the water column transforms NH4 + to NOx -, this study focuses on N2O fate by simulating both the oxidation of NH4 + to N2O and the oxidation of NH4 + to NOx -, which depend on the above environmental conditions for nitrification and additional conditions for N2O production.Based on Garnier et al. (2007), IMAGE-DGNM assumes a constant fraction (  2 _ =1%) of NH4 + converted to N2O during the nitrification process.NOx -production via nitrification in IMAGE-DGNM is represented as: N2O production via nitrification in IMAGE-DGNM is represented as:

DENIT
(denitrification in the column) Denitrification in the water column, i.e., reduction of NOx -to N2O and N2, and reduction of N2O to N2, depends on ambient temperature, anoxic condition (oxygen concentration), availability of detrital organic matter, and concentrations of substrates (NOx -or N2O).

Temperature dependency:
Temperature-dependency for denitrification in the water column is represented according to Billen et al. (1994) and Garnier et al. (2000), using the theoretical function of the process' optimal temperature (Topt,DENIT) and standard deviation (σDENIT) as well as local water temperature for that time: Anoxia-dependency (limiting factor by ambient oxygen concentrations): The oxic and anoxic conditions are represented using the theoretical half-saturation oxygen concentration (Garnier et al., 2007) and the local ambient oxygen concentration simulated by the mass-balanced process-based model: Limiting factor for anoxic conditions for denitrification:

Organic matter availability:
Only detrital (i.e., dead) organic matter can be utilized to provide energy for the denitrification process.The detrital organic matter in carbon is converted from detrital organic nitrogen (ONDET) using the ratio of C:N = 106:16 according to Billen et al. (1994) and Garnier et al. (2000), as can be found in the full model description of the mass-balanced process-based IMAGE-DGNM model (Vilmin et al., 2020).

Denitrification:
As was described in Vilmin et al. (2020), in IMAGE-DGNM, the equation of massbalanced denitrification using the reaction stoichiometry of organic matter and NOx - and taking into account temperature dependency, anoxia-dependency and theoretical maximum denitrification rate (kDENIT, from Garnier et al. (2000)) is represented as: As reaction substrates, detrital organic matter and NOx -can limit denitrification by both their absolute amounts and their ratio relative to the reaction stoichiometry.

Incomplete denitrification (producing N2O) vs. complete denitrification (producing N2):
While the above function in IMAGE-DGNM assumes that all denitrification in the water column is complete, this study focuses on N2O fate by simulating both the incomplete denitrification (transforming NOx -to N2O) and complete denitrification (transforming NOx -and N2O to N2), which depend on the above environmental conditions for denitrification and additional conditions for N2O production.
Based on Billen et al. (2020) and Beaulieu et al. (2011), IMAGE-DGNM assumes that a constant fraction (  2 _ =1%) of NO3 -used as electron acceptor for organic matter mineralization is converted to N2O during the denitrification.Besides, according to Baulch et al. (2011), when the ambient temperature is not lower than the temperature threshold Tlim,N2O reduc, N2O production via incomplete denitrification can occur; when the ambient temperature is lower than Tlim,N2O reduc, N2O produced via denitrification cannot be preserved and will be fully denitrified, i.e., only complete denitrification occurs.In addition, according to Baulch et al. (2011), if NOx - concentration is lower than the threshold KNO3,N2O reduc, consumption of inland-water N2O via complete denitrification will also occur, i.e., using N2O as the electron acceptor for organic matter mineralization and transforming N2O to N2. • N2O to N2, i.e., N2O consumption: N2O reduction limiting factor for NOx -concentration using the threshold KNO3,N2O reduc (Baulch et al., 2011):

N2O production via incomplete denitrification
Nitrifier denitrification (NIT_DENIT) in IMAGE-DGNM depends on the environmental conditions for nitrification, the amount of nitrification substrate NH4 + , as well as the theoretical half-saturation oxygen concentration, the theoretical halfsaturation NOx -concentration, the threshold of maximum oxygen concentration for nitrifier denitrification and the concentrations of reaction substrates oxygen and NOx -.
Limiting factor for oxygen conditions using the theoretical half-saturation oxygen concentration and the threshold of maximum oxygen concentration for nitrifier denitrification: Limiting factor for NOx -concentrations using the theoretical half-saturation NOx - concentration for nitrifier denitrification:

N2O production via nitrifier denitrification:
While the above function in IMAGE-DGNM assumes that all nitrifier denitrification in the water column is complete, this study focuses on N2O fate by simulating both the incomplete (transforming NOx -to N2O) and complete nitrifier denitrification (transforming NOx -to N2), which depend on the above environmental conditions for nitrifier denitrification and additional conditions for N2O production.Based on Garnier et al. (2007), we assume a constant fraction (  2 __ =1%) of NH4 + converted to N2O during the nitrifier denitrification processes NIT_DENIT when the oxygen concentration is lower than the threshold SO2,NIT_DENIT (Garnier et al., 2007).Nitrification in sediments, i.e., NH4 + uptake from the water column due to nitrification in the benthic layer, depends on the depth of the uncompacted sediment layer (Zf, in m), total bed area (A, in m 2 ), temperature, oxic condition (oxygen concentration), and the concentration of reaction substrate NH4 + , according to Billen et al. (2015).

Temperature dependency:
Temperature-dependency for nitrification in sediments is represented according to Billen et al. (2015), using the theoretical function of the process' optimal temperature (Topt,BNIT) and standard deviation (σBNIT) as well as the local temperature for that time:

𝜎 𝐵𝑁𝐼𝑇 2
As was described in Vilmin et al. (2020), in IMAGE-DGNM, the equation of massbalanced nitrification in sediments using the reaction stoichiometry of NOx -and oxygen and taking into account temperature dependency, oxic-condition-dependency, the depth of the uncompacted sediment layer (Zf), and total bed area (A) is represented as: As reaction substrates, NH4 + and O2 can limit the benthic nitrification process by both their absolute amounts and their ratio relative to the reaction stoichiometry.  2 , is calculated using temperature according to APHA (1992).

Production of N2O during nitrification in sediments:
While the above function in IMAGE-DGNM assumes that all nitrification in sediments transforms NH4 + to NOx -, this study focuses on N2O fate by simulating both the oxidation of NH4 + to N2O and the oxidation of NH4 + to NOx -, which depend on the above environmental conditions for benthic nitrification and additional conditions for N2O production.Based on Garnier et al. (2007), IMAGE-DGNM assumes a constant fraction (  2 _ =1%) of NH4 + converted to N2O during the nitrification process.NOx -production via nitrification in sediments in IMAGE-DGNM is represented as: matter, and concentrations of substrate NOx -.

Temperature dependency:
Temperature-dependency for denitrification in the water column is represented according to Billen et al. (2015), using the theoretical function of the process' optimal temperature (Topt,DENIT) and standard deviation (σDENIT) as well as the local ambient water temperature for that time: Organic matter availability: Only detrital (i.e., dead) organic matter in sediments can be utilized to provide energy for the benthic denitrification process.The detrital organic matter in carbon is converted from detrital organic nitrogen (ONDET,b) using the ratio of C:N = 106:16 according to Billen et al. (2015), as can be found in the full model description of the mass-balanced process-based IMAGE-DGNM model (Vilmin et al., 2020).According to Billen et al. (2015), the integrated carbon oxidant demand of organic matter degradation (Coxd, in equ.m -2 •h -1 ) for benthic denitrification depends on amounts of benthic organic matter (ONDET,b) and sediments (TBS), maximum compaction rate (Cmax) and maximum mineralization rate (kBMIN).Coxd (Billen et al., 2015) is thus represented as: Anoxia-dependency (limiting factor by oxygen concentrations): The oxic and anoxic conditions are represented according to Billen et al. (2015) using the relative ratio of the local oxygen and NOx -concentrations: Limiting factor for anoxic conditions for benthic denitrification:

Denitrification in sediments:
As was described in Vilmin et al. (2020), in IMAGE-DGNM, the equation of massbalanced denitrification in sediments using the reaction stoichiometry of benthic organic matter and NOx -and taking into account temperature dependency, anoxiadependency, depth of the uncompacted sediment layer (Zf), and theoretical maximum denitrification rate (kBDENIT, from Billen et al. (2015)) is represented as: As the reaction substrates, benthic detrital organic matter and NOx -can limit the benthic denitrification process by both their absolute amounts and their ratio relative to the reaction stoichiometry.

Incomplete denitrification (producing N2O) vs. complete denitrification (producing N2):
While the above function in IMAGE-DGNM assumes that all sedimentary denitrification is complete, this study focuses on N2O fate by simulating both the incomplete (transforming NOx -to N2O) and complete denitrification in sediments (transforming NOx to N2), which depend on the above environmental conditions for benthic denitrification and additional conditions for N2O production.Based on Billen et al. (2020) and Beaulieu et al. (2011), IMAGE-DGNM assumes that a constant fraction (   2 _ =1%) of NO3 -used as electron acceptor for benthic organic matter mineralization is converted to N2O during denitrification in sediments.
N2O production via incomplete sedimentary denitrification in IMAGE-DGNM is represented as: N2 production via complete sedimentary denitrification in IMAGE-DGNM is represented as:

EXCHN2O
(inland-water N2O exchange with the atmosphere) N2O exchange at the water-atmosphere interface can be positive if N2O is emitted from the water to the atmosphere, or negative if N2O from the atmosphere is taken up by inland waters.According to Alin et al. (2011), N2O exchange at the wateratmosphere interface depends on the temperature-dependent N2O saturation concentration (  2 , (), in mol•m -3 ), gas transfer velocity (ka, in m•h -1 ), waterbody volume (V, in m 3 ) and local inland-water N2O concentration., (2) constant wind speed of 10 km•h -1 for rivers with width ≥ 100 m: k600 = 0.2421, and (3) method and maximum for lakes and reservoirs from Raymond et al. (2013).

Gas transfer velocity ka
The temperature-dependent Sc(T) for N2O is represented according to Wanninkhof (1992)  The N2O saturation concentration    , () for each location and time point is represented using temperature and the mole fraction of atmospheric N2O in dry air (pN2O, data in Figure S1) according to Weiss and Price (1980):   2  =   • (  2 , −   2  ) •  Note: Process rates are expressed in mol•h −1 .For species i, the amount of i is expressed as Xi (e.g., ONpp) in mol, Ci is the concentration of i in the water column in mol•m −3 .The units, values, and sources of the mentioned parameters are in Table S2.For the equations, stoichiometry, parameters, units and descriptions of other N processes in IMAGE-DGNM, see the full model description in Vilmin et al. (2020).

Cmax
Maximal compaction rate h -1 0.0005 (Billen et al., 2015) Topt,BNIT Optimal temperature for benthic nitrification ℃ 20 (Billen et al., 2015) σBNIT Standard deviation of temperature-dependency function for benthic nitrification ℃ 17 (Billen et al., 2015) Note: * assuming 40, 40 and 20% of highly biodegradable, moderately biodegradable and refractory organic matter, respectively.For descriptions of other N processes in IMAGE-DGNM, see the full model description in Vilmin et al. (2020).Sturm et al., 2014;Borges et al., 2015;Chen et al., 2015a;Chen et al., 2015b;Zhu et al., 2015;Mach et al., 2016;Schade et al., 2016;Soued et al., 2016;Wang et al., 2016;Audet et al., 2017;Hama-Aziz et al., 2017;He et al., 2017;Upstill-Goddard et al., 2017;Wang et al., 2017a;Wang et al., 2017b;Davis and David, 2018;Yan et al., 2018;Borges et al., 2019;Smith and Böhlke, 2019;Xiao et al., 2019a;Xiao et al., 2019b;Yang et al., 2019;Zhou et al., 2019;Kortelainen et al., 2020;Wang et al., 2020;Zhao and Zhang, 2021;Barthel et al., 2022;Wang et Figure S6.Validation of long-term temporal patterns of water discharge, TN and DO for different up-, mid-and downstream sites covering different waterbodies in Mississippi since the 1930s.Figure S7.Validation: Distribution of sites of observational data from datasets and literature for validation of water discharge, TN, N2O and DO in global inland waters since the 1920s.Figure S8.Validation: RMSE of simulations and observations for water discharge, TN, N2O and DO at monitoring sites in global inland waters for long time series since the 1920s.Figure S9.Validation: Comparison of simulated and observed N2O concentrations and emissions per site per year in global inland waters since the 1970s.Figure S10.Sensitivity results for variations in model parameters.Figure S11.Spatial distributions of N2O inputs to global inland waters in 1900 and 2010 simulated by IMAGE-DGNM. Figure S12.Spatial distributions of N2O production and multiple-form N loads in global inland waters in 1900 and 2010 simulated by IMAGE-DGNM. Figure S13.Temporal changes in spatial distributions of the global freshwater N2O emissions during 1900-2010.

FigureFigure S2 .
Figure S2.N (of different forms) and N2O inputs to global inland waters from different sources.

Figure S3 .
Figure S3.Global reservoir volume, population, gross production value of agriculture and wastewater N discharge to surface water during 1900-2010.

Figure
Figure S4.IMAGE-DGNM scheme of water and nutrient flows in the soil-hydrosphere system.

Figure S5 .
Figure S5.Range of observation-based ratios of N2O production to groundwater denitrification

Figure S6 .Figure S6 .
Figure S6.Validation of long-term temporal patterns of water discharge, TN concentrations, and DO concentrations for different up-, mid-and downstream stations (covering different waterbodies) within the Mississippi River Basin since the 1930s.

Figure S8 .
Figure S8.Validation: RMSE of simulations and observations for water discharge, TN, N2O and DO at monitoring sites in global inland waters for long time series since the 1920s.

Figure S8 .
Figure S8.Root Mean Squared Error (RMSE) of the simulated and observed long time series of annual average concentrations of N2O, TN, DO, and water discharge at monitoring sites in global inland waters for long time series since the 1920s: (a) TN, (b) N2O, (c) DO, and (d) water discharge.The statistics of RMSE per variable for all stations worldwide are shown in its boxplot, with the median marked with dark blue color and RMSE=200% marked with light blue color.Information on the observational data used is in TableS3.

Figure S9 .
Figure S9.Validation: Comparison of simulated and observed N2O concentrations per site per year in global inland waters since the 1970s.

Figure S10 .
Figure S10.Sensitivity results for variations in model parameters, expressed as Cxi (for Cxi see Text S3)

Figure S11 .Figure S12 .Figure S13 .
Figure S11.Spatial distributions of N2O inputs to the global river network in 1900 and 2010 simulated by IMAGE-DGNM

Table S3 . Summary of observation data from databases and literature used for comparison with model outputs of TN and DO concentrations, N2O concentration and emission, and water discharge per variable per site per river basin in global inland waters for the period since the 1920s, covering
different waterbodies, up-, mid-and downstream sites and river basins in different climate zones.The spatial distribution of all observational sites used for validation is in FigureS7.Validation results are in FiguresS8-S9.