Taylor Maavara
email: tmaavara@lbl.gov

Ronny Lauerwald

G Goulven

Zahra Laruelle

Nicholas Akbarzadeh

Philippe Bouskill

Pierre Van Cappellen

Régnier

Goulven G Laruelle

Zahra Akbarzadeh

Nicholas J Bouskill

Philippe Van Cappellen

Pierre Regnier

Nitrous oxide emissions from inland waters: Are

come

Introduction

Nitrous oxide (N 2 O) is an ozone-depleting greenhouse gas (GHG), considered to be the third most important GHG contributing to radiative forcing and global climate change [START_REF] Ravishankara | Nitrous oxide (N2O): the dominant ozonedepleting substance emitted in the 21st century[END_REF][START_REF] Syakila | The global nitrous oxide budget revisited[END_REF][START_REF] Neubauer | Moving beyond global warming potentials to quantify the climatic role of ecosystems[END_REF]. Most N 2 O is produced by microbial processes such as nitrification and denitrification in terrestrial and aquatic systems, including rivers, estuaries, coastal seas and the open ocean [START_REF] Freing | Global oceanic production of nitrous oxide[END_REF]. The production of N 2 O shows large spatial and temporal variability and emission estimates for aquatic systems are uncertain. In particular, emissions from rivers, estuaries and continental shelves have been the subject of debate for many years [START_REF] De Klein | N2O emissions from managed soils, and CO2 emissions from lime and urea application. IPCC Guidelines for National Greenhouse Gas Inventories[END_REF]Seitzinger & Kroeze, 1998). The 5th IPCC Assessment Report [START_REF] Ciais | Carbon and Other Biogeochemical Cycles[END_REF] proposed that, together, rivers, estuaries and coastal zones emit 0.6 Tg N (N 2 O) yr -1 (based on IPCC's 2006 guidelines, [START_REF] Kroeze | Future trends in emissions of N2O from rivers and estuaries[END_REF][START_REF] Syakila | The global nitrous oxide budget revisited[END_REF]. This corresponds to about 3% of all N 2 O emissions and about one third of IPCC's previous estimate of 1.7 Tg N yr -1 in the 4 th Assessment Report for the same systems. Several studies have highlighted that emissions from rivers might be underestimated [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF] or significantly overestimated [START_REF] Hu | Modeling nitrous oxide emission from rivers: a global assessment[END_REF][START_REF] Macdonald | Contribution of the cotton irrigation network to farm nitrous oxide emissions[END_REF] in the IPCC assessments (Table 1). A recent review of estuarine emissions [START_REF] Murray | Nitrous oxide fluxes in estuarine environments: response to global change[END_REF] also suggested that these aquatic systems could emit about 3 times more N 2 O (0.31 Tg N yr -1 ) than the latest IPCC estimate. Recently, [START_REF] Deemer | Greenhouse gas emissions from reservoir water surfaces: a new global synthesis[END_REF] provided the first global estimate of N 2 O evasion from dam reservoirs at 0.03 Tg N yr -1 .

Global N 2 O flux estimations from open inland waters (rivers, reservoirs and estuaries) have followed two distinct approaches. The first approach involves upscaling direct N 2 O flux measurements from aquatic systems, by multiplying local fluxes by the estimated global areal extents of water bodies. This methodology has been followed by [START_REF] Deemer | Greenhouse gas emissions from reservoir water surfaces: a new global synthesis[END_REF] for reservoirs and by [START_REF] Bange | Nitrous oxide and methane in European coastal waters[END_REF], [START_REF] Law | Nitrous oxide: estuarine sources and atmospheric flux[END_REF], [START_REF] Robinson | Hypernutrified estuaries as sources of N 2 O emission to the atmosphere: the estuary of the River Colne, Essex, UK[END_REF], de Wilde and de [START_REF] De Wilde | Nitrous oxide in the Schelde estuary: production by nitrification and emission to the atmosphere[END_REF], and [START_REF] Murray | Nitrous oxide fluxes in estuarine environments: response to global change[END_REF] for estuaries. To our knowledge, this approach has never been applied to estimate river N 2 O emissions globally. The most recent global N 2 O budgets rely on 58 local measurements in reservoirs [START_REF] Deemer | Greenhouse gas emissions from reservoir water surfaces: a new global synthesis[END_REF] and 74 local measurements in estuarine environments [START_REF] Murray | Nitrous oxide fluxes in estuarine environments: response to global change[END_REF] including open waters, mangroves, intertidal sediments, salt marshes and seagrasses. According to [START_REF] Murray | Nitrous oxide fluxes in estuarine environments: response to global change[END_REF], about 75% of the estuarine N 2 O evasion originates from open water bodies, i.e. the portion of estuaries flooded throughout the entire tidal cycle. In addition to the uncertainties associated with using a limited pool of data to generate global estimates, uncertainties arise from the highly skewed spatial distributions of the local datasets, which are focused in industrialized countries, and from the uncertainties associated with the estimated areal extents of different types of water bodies [START_REF] Dürr | Worldwide typology of nearshore coastal systems: defining the estuarine filter of river inputs to the oceans[END_REF][START_REF] Laruelle | Global multi-scale segmentation of continental and coastal waters from the watersheds to the continental margins[END_REF][START_REF] Lehner | High-resolution mapping of the world's reservoirs and dams for sustainable river-flow management[END_REF].

The second approach for estimating large-scale N 2 O emissions relies on semi-empirical models, in which N 2 O emission rates are calculated as the product of an emission factor (EF) and estimates of N loading to water bodies. However, both N load estimates and EFs are subject to large uncertainties. In particular, EFs (generally defined as the fraction of N load to the water body that is emitted as N 2 O-N) vary by more than one order of magnitude, with reported values ranging from 0.17 to 5.6% [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF][START_REF] Hu | Modeling nitrous oxide emission from rivers: a global assessment[END_REF]Seitzinger & Kroeze, 1998). Several studies argue that the current default IPCC EF used to estimate worldwide emissions (0.25%) may be either overestimated [START_REF] Clough | Nitrous oxide dynamics in a braided river system, New Zealand[END_REF][START_REF] Clough | Diurnal fluctuations of dissolved nitrous oxide (N2O) concentrations and estimates of N2O emissions from a spring-fed river: implications for IPCC methodology[END_REF][START_REF] Kroeze | Future trends in emissions of N2O from rivers and estuaries[END_REF] or underestimated [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF][START_REF] Yu | Nitrous oxide emissions in the Shanghai river network: implications for the effects of urban sewage and IPCC methodology[END_REF]. Much of the disagreement arises from local values differing substantially from IPCC's default EF values, due to factors such as intense urbanization (where there may be disproportionately high emissions, e.g. [START_REF] Yu | Nitrous oxide emissions in the Shanghai river network: implications for the effects of urban sewage and IPCC methodology[END_REF] or diurnal variability (where instream concentrations decrease at night, indicating that the majority of studies that sample during the day may overestimate emissions e.g. [START_REF] Clough | Diurnal fluctuations of dissolved nitrous oxide (N2O) concentrations and estimates of N2O emissions from a spring-fed river: implications for IPCC methodology[END_REF]. [START_REF] Kroeze | Future trends in emissions of N2O from rivers and estuaries[END_REF] further discuss the uncertainty associated with whether the EF is taken with regard to total N (TN) or dissolved inorganic N (DIN) loads to the water body (Table 1), as TN includes refractory N species while DIN excludes other bioavailable species. Inconsistencies in assumptions and methodologies such as these confound our ability to make direct comparisons between literature estimations.

Model-derived estimates of global N 2 O evasion require inclusion of natural as well as anthropogenic N loadings, of which the anthropogenic loadings are dominant in most river systems [START_REF] Seitzinger | Global distribution of N2O emissions from aquatic systems: natural emissions and anthropogenic effects[END_REF]. For rivers, loadings have been constrained using the IPCC methodology [START_REF] Mosier | Closing the global N2O budget: nitrous oxide emissions through the agricultural nitrogen cycle[END_REF], which assumes that the only TN sources are from global synthetic fertilizer use and N excreted by livestock, with 30% lost to leaching and surface runoff. The Global Nutrients in Watersheds (NEWS) model [START_REF] Dumont | Global distribution and sources of dissolved inorganic nitrogen export to the coastal zone: Results from a spatially explicit, global model[END_REF][START_REF] Mayorga | Global Nutrient Export from WaterSheds 2 (NEWS 2): Model development and implementation[END_REF] computes DIN and TN loadings according to empirical relationships between loading and an array of controlling factors including biophysical watershed characteristics, population density, socioeconomics, land cover and land use, and climatic conditions. Discrepancies in N 2 O evasion between studies can partly be explained by different N load estimates (Table 1). For estuaries, only the NEWS model approach has been used, with the inputs derived from the NEWS loads delivered to coastal zones [START_REF] Seitzinger | Sources and delivery of carbon, nitrogen, and phosphorus to the coastal zone: An overview of Global Nutrient Export from Watersheds (NEWS) models and their application[END_REF]Seitzinger & Kroeze, 1998).

All model studies scale the global N 2 O emissions to the N loads, either considering only DIN [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF][START_REF] Hu | Modeling nitrous oxide emission from rivers: a global assessment[END_REF]Seitzinger & Kroeze, 1998), or including dissolved inorganic, organic and particulate N forms (DIN + DON + PN = TN) together [START_REF] Mosier | Closing the global N2O budget: nitrous oxide emissions through the agricultural nitrogen cycle[END_REF][START_REF] Syakila | The global nitrous oxide budget revisited[END_REF]. This upscaling can either be done directly by applying an EF to the N load following the IPCC methodology of [START_REF] Mosier | Closing the global N2O budget: nitrous oxide emissions through the agricultural nitrogen cycle[END_REF], or via an intermediate step (Seitzinger & Kroeze, 1998) where N loads are first used to constrain global denitrification and nitrification rates and, next, N 2 O emissions are assumed to be fixed fractions of these N transformation pathways. Nevertheless, the second approach is somewhat equivalent to the first because all studies have so far assumed that the N lost via denitrification and the N oxidized via nitrification are themselves fixed fractions of TN or DIN loadings [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF]Seitzinger & Kroeze, 1998).

By far, most of the differences in model-derived estimates result from the choice of prescribed fractions of N loads which are lost in the form of N 2 O, either via the direct approach or via the intermediate step of estimated denitrification-nitrification rates. With the notable exception of the recent study by [START_REF] Hu | Modeling nitrous oxide emission from rivers: a global assessment[END_REF], all studies have applied EFs and fractions determined from a very limited number of observations, and their values have thus been subject to intense debate in past decades. Interestingly, the proposed EF of [START_REF] Hu | Modeling nitrous oxide emission from rivers: a global assessment[END_REF], based on a meta-analysis of 169 N 2 O flux observations covering a wide range of rivers, is significantly lower (0.17%) than previously applied values. Similarly, the fraction of N that is oxidized via nitrification has been traditionally scaled to denitrification rates, but the scaling factor has varied between 1 and 2 among various studies [START_REF] Kroeze | New estimates of global emissions of N2O from rivers and estuaries[END_REF]Seitzinger & Kroeze, 1998;[START_REF] Seitzinger | Global distribution of N2O emissions from aquatic systems: natural emissions and anthropogenic effects[END_REF].

All models applied thus far have relied on simple semi-empirical approaches. As pointed out by [START_REF] Ivens | Modeling global N 2 O emissions from aquatic systems[END_REF], alternative approaches that better account for spatial variability and model uncertainties should be developed. More specifically, developing a global-scale mechanistic model that represents both N cycling and transport rates in a spatially-and dynamically-explicit way remains a critical priority. Such a mechanistic model should include representations of nitrification, denitrification and N assimilation rates, as well as N 2 O inputs from land and N 2 O production and transport along the river system [START_REF] Ivens | Modeling global N 2 O emissions from aquatic systems[END_REF]. This objective is particularly timely because [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF] have recently reported denitrification N 2 O yields (percentage of denitrified N released as N 2 O) for a number of streams and rivers (n=72) that can be used to parameterize a mechanistic modeling approach.

In a first step in this direction, we have developed the first integrated model of global N 2 O emissions along the entire land-ocean aquatic continuum (LOAC). We focus our study on open waters, including rivers, dammed reservoirs, and estuaries. This analysis does not include lakes or wetlands including freshwater wetlands, seagrasses, salt marshes, intertidal sediments, mangroves, or coastal aquaculture ponds. We calculate DIN, DON, and PN yields in watersheds worldwide, and track the changes to these species' loads as they are delivered to rivers, reservoirs, and estuaries. We quantify cascading TN losses via burial and denitrification, and additions via N fixation. In each water body, we quantify the N 2 O emissions associated with in-stream, in-estuarine or in-reservoir denitrification and nitrification. We contextualize the results of our model by performing a scenario-based uncertainty analysis, which relies on the range of emissions factors reported in the existing literature. We further compare to existing global estimates for both anthropogenic and natural N 2 O emissions. Through our explicit quantification of the interacting changes of N loads along the LOAC and of the load-specific N 2 O production mechanisms, our study represents the most comprehensive estimate of LOAC N 2 O emissions to date.

Materials and Methods Overview

A mechanistic mass balance model was developed to represent generalized stream, reservoir, and estuarine N fluxes and transformations (Figure 1). The model development followed an approach similar to that used for phosphorus (P) [START_REF] Maavara | Global phosphorus retention by river damming[END_REF], organic carbon (OC) [START_REF] Maavara | Global perturbation of organic carbon cycling by river damming[END_REF] and N (Akbarzadeh et al., in review) cycling in dam reservoirs. River, reservoir, and estuary kinetic parameters associated with physical and biogeochemical processes were implemented using probability density functions (PDFs) that account for the global distributions of the corresponding parameter values (Table S1). The fluxes in the model represent lumped sediment-water column rates and were resolved at the annual timescale. Water residence time controls the magnitude of the in-system transformation and elimination fluxes through an inverse relationship with nutrient effluxes from the water body. The N 2 O model was coupled to OC and P models of [START_REF] Maavara | Global phosphorus retention by river damming[END_REF][START_REF] Maavara | Global perturbation of organic carbon cycling by river damming[END_REF] in order to represent P-and OC-dependencies into processes such a primary productivity and N fixation.

A Monte Carlo analysis of the model was performed, in which parameters were randomly selected from the pre-assigned PDFs. After 6000 iterations, a database of hypothetical worldwide N dynamics, including N 2 O production and emissions, was generated for inland open waters. Each of the 6000 Monte Carlo realizations combined a unique set of parameter values obtained stochastically from the PDFs to quantify rates and fluxes for all N cycling processes. Next, global relationships relating N processes and N 2 O emissions to water residence time and TN loads were extracted from the Monte Carlo output. These relationships were then applied to N loads delivered to all river, reservoir and estuarine systems along a spatially routed network representing the global LOAC. We predicted N loads following the methods used in the NEWS model and described in [START_REF] Mayorga | Global Nutrient Export from WaterSheds 2 (NEWS 2): Model development and implementation[END_REF]. Rather than applying an average EF to all water bodies, the use of water residence time as independent variable explicitly adjusts for the extent of N 2 O production and emission that is kinetically possible within the timeframe available in a given water body. In the following sections we describe the modeling steps and parameter constraints in detail.

Emission factors: terminology

Emission factors (EFs) have variable definitions throughout the literature. In this study, we utilize a variety of these literature definitions in addition to our own to develop a suite of scenarios based on a variety of assumptions related to N 2 O emissions. Henceforth, the following EF definitions apply:

(1) [START_REF] Seitzinger | Nitrogen biogeochemistry in an unpolluted estuary: the importance of benthic denitrification[END_REF] (3)

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This article is protected by copyright. All rights reserved. is the annual riverine load of total N delivered to the water body. In the literature, has typically been used as the conventional definition.

Mechanistic modeling approach

The N pools in the model were nitrate (NO 3 -) and ammonium (NH 4 + ), dissolved organic N (DON) and particulate organic N (PON) pools, and the key transformation and transport fluxes associated with these species (Figure 1). Specifically, we took into account the influxes and effluxes of NH 4 + , NO 3 -, DON and PON to and from water bodies, primary productivity, PON solubilization and burial, mineralization of DON, nitrification, denitrification, plus N 2 O production and consumption via the latter two processes, and N 2 O exchanges with the atmosphere. Each model realization was solved using the Runge-Kutta 4 integration method, with a 0.01-year time step and, in the case of reservoirs, run for the number of years since dam closure, or for at least 100 years in the case of rivers and estuaries, hence ensuring steady state conditions were reached under the majority of parameter combinations in the Monte Carlo simulations. We constrained one PDF for rivers, reservoirs, and estuaries as a compiled dataset. In this section, we will focus on describing the model parameters specifically associated with N 2 O production and emissions. A full description of the parameterization of the physical and other biogeochemical processes included in the model can be found in Section S1.

Two approaches were used to bracket our estimates of N 2 O emissions from inland waters. For both model structures, N 2 O production in mol N yr -1 was obtained from:

(7)

In the first, more simple, approach (referred to as Default Scenario 1, or DS1), N 2 O emissions were calculated by multiplying average and values of 0.9%, proposed by [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF], by model-calculated nitrification and denitrification fluxes (see section S1), assuming all was emitted to the atmosphere. A Monte Carlo simulation was performed, generating 6000 hypothetical "observations" from which globally applicable relationships were extracted that relate denitrification, nitrification, and N 2 O emissions to water residence times and TN loads ( , mol yr -1 ). Nitrification in rivers, reservoirs and estuaries was fitted to the following equation:

R 2 = 0.16 (8)
where is the fixation flux in mol yr -1 , calculated using Equations S6 and S7. Denitrification was similarly fitted to: R 2 = 0.29 (9) and were multiplied by for each river, reservoir and estuary worldwide, where we assumed that and = .

In the second scenario (Default Scenario 2, or DS2), we explicitly included N 2 O as a pool in the model (Figure 1), with Equation 7representing the input to the N 2 O pool. To account for consumption of N 2 O produced via denitrification in water bodies with long residence times ( , we computed the inverse of Equation 9and multiplied it by an average value of of 0.9% (Figure S6). The resulting emission factor associated with denitrification was therefore:

(10) With this approach, net N 2 O production accounted for the interplay between increasing denitrification rates and decreasing when increases.

For nitrification, was assumed equal to 0.9% with no further scaling because there is no N 2 O consumption step associated with nitrification. We then calculated the emissions, N 2 O em , assuming that only the fraction of N 2 O that is super-saturated with respect to the equilibrium atmospheric N 2 O concentration ([N 2 O] sat ) was emitted. In other words:

[N 2 O] sat = K H pN 2 O atm (11)
and

N 2 O em = ([N 2 O] aq -[N 2 O] sat ) Q (12)
where [N 2 O] aq is the concentration of N 2 O in the water body calculated by the model, and pN 2 O atm is the average atmospheric partial pressure of N 2 O, equal to 315 ppb in year 2000 (EPA 2016), and K H is the temperature dependent Henry's Law coefficient, equal to 2.4 x 10 -4 mol m -3 Pa -1 at 298.15 K, and temperature corrected to model-predicted temperatures (see Section S1) using the Van't Hoff equation. The gradient between actual and equilibrium concentration is multiplied by the amount of water passing through that system per year Q [km 3 yr -1 ]. Using this emission estimate, it was possible to back-calculate , , and for comparison with literature values. Equations 11 and 12 assume that, on a yearly time scale, aqueous N 2 O reaches equilibrium with the atmosphere. (Note: for shorter times scales, more sophisticated kinetics-based approaches may be more appropriate, e.g. [START_REF] Lauerwald | ORCHILEAK (revision 3875): a new model branch to simulate carbon transfers along the terrestrial-aquatic continuum of the Amazon basin[END_REF].

A second Monte Carlo simulation was run for DS2, and from the output we fitted a single equation for the total N 2 O emissions in rivers, reservoirs and estuaries:

(13) where a = 0.002277 and b = 1.63 (R 2 = 0.11, Figure S1a). Though the literature is divided on whether emissions should be normalized to the TN or DIN load, we chose to normalize our estimates of N 2 O emissions and denitrification to TN because this yielded better fits of the entire set of equations to the Monte Carlo data than using DIN. The fraction of the total N 2 O produced in the water body originating from denitrification was fitted to a Gaussian function:

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This article is protected by copyright. All rights reserved. ( 14)

where c = 0.7789, d = -1.366, and e = 2.751 (R 2 = 0.66, Figure S1b). Equation 13was multiplied by Equation 14to obtain the N 2 O evasion from denitrification. Evasion from nitrification was then calculated as the difference between total evasion and that associated with denitrification.

Application to global river network

To calculate the cascading loads of TN delivered to each water body along the riverreservoir-estuary continuum, we spatially routed reservoirs from the Global Reservoirs and Dams (GRanD) database [START_REF] Lehner | High-resolution mapping of the world's reservoirs and dams for sustainable river-flow management[END_REF], with river networks from Hydrosheds 15s [START_REF] Lehner | New global hydrography derived from spaceborne elevation data[END_REF] and Hydro1K (USGS, 2000) at higher latitudes, which was in turn connected to estuaries as represented in the "Worldwide Typology of Nearshore Coastal Systems" of [START_REF] Dürr | Worldwide typology of nearshore coastal systems: defining the estuarine filter of river inputs to the oceans[END_REF]. A detailed description of the process used to develop this global water body network is given in the Section S2 and Figure S2.

To calculate biogeochemical transformation rates and emission fluxes for river reaches, reservoirs and estuaries in a consistent way, the water residence times for each of these water bodies was required. For rivers, the average travel distance (Length, km) along an undammed reach discharging into a reservoir or estuary was estimated using the empirical equation of Rosso et al. (1991): (15) where is the undammed catchment area upstream of the kth dam or estuary in km 2 . The undammed upstream is defined for each dam and estuary as the total tributary area from which water flows in without passing another dam. The total upstream areas of all the dams and estuaries were spatially delineated based on the Hydrosheds15s [START_REF] Lehner | New global hydrography derived from spaceborne elevation data[END_REF] and Hydro1k (USGS, 2000) data sets. They were calculated by subtracting the upstream areas of other dams were overlays occurred. For each dam, the contributing area was derived from the Hydrosheds15s and/or Hydro1k routing schemes. In river catchments with multiple dams, the travel distance of water flowing out of a given dam to the next downstream dam or estuary was calculated as the shortest distance between the dams, or between the dam and the receiving estuary. This distance was multiplied by a sinuosity index of 2.26 (Shen et al., 2017) to estimate the actual travel distance. Next, the water residence time along the given river segment was estimated by dividing the travel distance by an average flowing velocity of 0.6 m s -1 for tributaries and 0.8 m s -1 for the river mainstem [START_REF] Schulze | Simulating river flow velocity on global scale[END_REF].

For reservoirs, the residence time was calculated using the representative storage capacity (volume) divided by the annual discharge reported in GRanD [START_REF] Lehner | High-resolution mapping of the world's reservoirs and dams for sustainable river-flow management[END_REF]. Only dams constructed during or before year 2000 were included. For estuaries, water residence times were derived from the nearshore coastal systems database compiled by [START_REF] Dürr | Worldwide typology of nearshore coastal systems: defining the estuarine filter of river inputs to the oceans[END_REF], which includes estuarine residence times from the literature for 130 systems that account for 20% of the world's TN loads from rivers. Following [START_REF] Mckee | Transport and transformation of dissolved and particulate materials on continental margins influenced by major rivers: benthic boundary layer and seabed processes[END_REF] it was assumed that most of the biogeochemical processing of material exported by the largest rivers of the world takes place in external river plumes located beyond the boundaries of estuarine systems. The estuarine residence time of such large rivers (e.g. Amazon, Ganges, Zaire…) was thus assumed to be negligible [START_REF] Dürr | Worldwide typology of nearshore coastal systems: defining the estuarine filter of river inputs to the oceans[END_REF][START_REF] Laruelle | Global multi-scale segmentation of continental and coastal waters from the watersheds to the continental margins[END_REF]. The remaining estuarine systems with no estimate were assigned type-specific median residence times for four different geomorphological classes of estuaries [START_REF] Laruelle | Global multi-scale segmentation of continental and coastal waters from the watersheds to the continental margins[END_REF]. These median residence times were derived from the compiled database and were equal to 0.08, 0.27, 0.78 and 10.2 years for deltas, tidally-dominated estuaries, lagoons and fjords, respectively. The calculation of N 2 O emissions from a given water body required computation of TN in , which accounted for terrestrial inputs and N fixation delivered to the water body, minus the upstream losses by burial and denitrification. Because N fixation (Fix) depends on the relative availability of P (Equations S6-S7), the computation of N 2 O fluxes required the full coupling of the N and P cycles along the river-reservoir-estuary continuum.

Similar to the procedure in [START_REF] Maavara | Global perturbation of organic carbon cycling by river damming[END_REF], we obtained the average terrestrial DIN, DON, PN, DIP, DOP and PP yields (Y in mol km -2 yr -1 ) from the undammed catchment area upstream of each dam and estuary from NEWS [START_REF] Mayorga | Global Nutrient Export from WaterSheds 2 (NEWS 2): Model development and implementation[END_REF]. However, instead of using the average yield per STN-30p basin as in NEWS, we refined the approach to account for the spatial variability in terrestrial N and P sources within each watershed. Based on the input data used in NEWS [START_REF] Bouwman | Human alteration of the global nitrogen and phosphorus soil balances for the period 1970-2050[END_REF][START_REF] Van Drecht | Global nitrogen and phosphate in urban wastewater for the period 1970 to 2050[END_REF], we reproduced the spatially explicit representation of N and P sources at a 0.5-degree resolution. Nutrient loads to the undammed upstream catchment area of a given reservoir or estuary, (mol yr -1 ), were then calculated as:

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This article is protected by copyright. All rights reserved.

(16)

where is the yield for that watershed area (mol km -2 yr -1 ) and is the undammed catchment area lying directly upstream of the dam (see section S2).

N inputs along the aquatic continuum via N fixation were calculated using Equations S6 and S7. Losses via denitrification were computed with Equation 9, while burial in reservoirs was calculated using the following equation fitted to the results of the Monte Carlo simulations: R 2 = 0.50 (17

)
The global equation derived in [START_REF] Maavara | Global phosphorus retention by river damming[END_REF] was used to estimate the corresponding burial fluxes of TP. Reduction of the N load by denitrification and addition via N fixation were calculated for mainstem river reaches transporting N downstream from a dam, yielding an "effective" load to the next downstream reservoir or receiving estuary. N burial in river systems, which primarily takes place in adjacent floodplains, occurs via a different mechanism than reservoirs and we therefore did not generate river residence time-dependent retention equations or attempted to estimate this process [START_REF] Aufdenkampe | Riverine coupling of biogeochemical cycles between land, oceans, and atmosphere[END_REF].

The net nutrient loads delivered to a given dam or estuary can be summarized as:

(18

)
where is the flux into the reservoir or estuary k, is the sum of all effective fluxes discharging from dams upstream of reservoir or estuary k (if any), and is the flux from the undammed catchment area, with denitrification and N fixation accounted for. N 2 O emissions from undammed river reaches and mainstems downstream of dams were summed to yield the total river emissions reported in Table 2.

To analyze the global spatial patterns in N 2 O emissions, we mapped the combined emissions from rivers, reservoirs and estuaries obtained for DS1 and DS2 at 0.5° resolution. In addition, we plotted the N inputs to the river network and the related N 2 O emission factors (EF(d)) at the same resolution. A complete description of the method used to perform these calculations can be found in Section S3.

Scenario-based uncertainty analysis

In addition to the N 2 O emission estimates made in DS1 and DS2, we predicted N 2 O emissions according to three supplementary scenarios (UQ1-3, Table 2), which helped to contextualize the existing, often contradictory, observations in the literature. UQ1-3 incorporate various EFs and assumptions reported in the literature and, hence, provide insights into the uncertainty associated with the predicted N 2 O emissions.

In UQ1 and UQ2, we followed the same assumptions as DS1, but set at 3% and 0.3%, respectively, based on [START_REF] Seitzinger | Global distribution of nitrous oxide production and N inputs in freshwater and coastal marine ecosystems[END_REF]. In these scenarios the transformation of N 2 O to N 2 was not explicitly computed; instead the EFs were assumed to represent net production, that is, all N 2 O produced in the water body was assumed to be emitted to the atmosphere. In UQ3, the emission was calculated as in DS2: consumption of N 2 O via denitrification was accounted for (Equation 10) and only supersaturated N 2 O was emitted to the atmosphere. Rather than fixing = 0.9% to scale Equation 10, UQ3 randomly generated values from a Burr distribution fitted to the [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF] data which range from 0.04 to 5.63%. values were generated from the same Burr distribution, but independently of The Monte Carlo analysis was repeated for UQ3, generating an additional set of 6000 hypothetical observations from which relationships relating N 2 O emissions to water residence times and TN loads were extracted. Upscaling was performed using the same method as in DS2, whereby fitting of the results of the Monte Carlo analysis to Equations 13 and 14 yielded a = 0.002204, b = 1.955, c = 0.6801, d = -1.131, and e = 2.945 (R 2 = 0.04 and 0.57).

Results

Nitrogen input to rivers

According to our re-distributed estimates of allochthonous N inputs to the global river network (after [START_REF] Mayorga | Global Nutrient Export from WaterSheds 2 (NEWS 2): Model development and implementation[END_REF][START_REF] Van Drecht | Global nitrogen and phosphate in urban wastewater for the period 1970 to 2050[END_REF], Bouwman et al., 2009), the total loading amounts to 13.2 Tmol yr -1 (184.3 Tg N yr -1 ), of which 4.39 Tmol yr -1 (61.4 Tg N yr -1 ) are delivered as DIN, 0.85 Tmol yr -1 (11.9 Tg N yr -1 ) as DON, and the remaining 2.19 Tmol yr -1 (30.7 Tg N yr -1 ) as PN. Note that only 16.5% of the TN input (2.18 Tmol yr -1 ) is supplied from catchment areas that are intercepted by at least one dam. The global spatial pattern of allochthonous N inputs to rivers (Figure 2) is characterized by high yields across Europe, the eastern half of North America and Southern and Eastern Asia, in particular for DIN as the dominant fraction of TN. Low yields are observed for dryer regions of North Africa, Central Asia, and the Western half of North America.

Nitrification and denitrification fluxes

Worldwide, nitrification fluxes exceed denitrification fluxes in inland waters on average by 5-20%, depending on the system. Global nitrification fluxes in rivers, reservoirs, and estuaries are 0.20 Tmol yr -1 (2.8 Tg N yr -1 ), 0.30 Tmol yr -1 (4.3 Tg N yr -1 ), and 0.69 Tmol yr -1 (9.6 Tg N yr -1 ), respectively. In comparison, denitrification fluxes are 0.19, 0.26 and 0.55 Tmol yr -1 (2.6, 3.7, and 7.7 Tg N yr -1 ) for rivers, reservoirs and estuaries, respectively. Upon averaging each water body or stream segment arithmetically, 0.24% of is nitrified in rivers, 27% in reservoirs, 22% in estuaries, and 0.22% of is denitrified in rivers, 22% in reservoirs, and 17% in estuaries. On a per-watershed basis, the Amazon, Ganges, Nile, St. Lawrence, and Mississippi River basins account for 18% and 17% of all the denitrification and nitrification in inland waters worldwide, respectively (Figure S3 and S4), with the Amazon accounting for a third of both values. In what follows, we briefly compare our results with global denitrification fluxes published in the literature. A similar comparison is not possible for nitrification, as there are no previous global scale nitrification flux estimates for inland waters.

Our low denitrification estimate in river systems can partly be explained by the exclusion of denitrification occurring in groundwater and riparian zones [START_REF] Laursen | Measurement of denitrification in rivers: an integrated, whole reach approach[END_REF][START_REF] Marzadri | Role of surface and subsurface processes in scaling N2O emissions along riverine networks[END_REF][START_REF] Saunders | Nitrogen retention in wetlands, lakes and rivers[END_REF] in our modeling approach. Our results predict that the maximum proportion of TN delivered to river reaches that is lost via denitrification is 18%. In existing studies, watershed-scale denitrification losses have been suggested to be as high as 65% using empirical relationships from regional datasets [START_REF] Mccrackin | Factors influencing export of dissolved inorganic nitrogen by major rivers: A new, seasonal, spatially explicit, global model[END_REF][START_REF] Seitzinger | Nitrogen retention in rivers: model development and application to watersheds in the northeastern[END_REF]. However, these studies include the effects of reservoirs in basinwide budgets, which increases the contribution of denitrification substantially. Indeed, when we account for riverine plus reservoir denitrification, up to 57% of the TN load to river basins is removed via denitrification (with a few exceptions in watersheds with extremely high N fixation), which is in good agreement with the 65% loss cited above. Overall, our results highlight that for most river networks worldwide, N loss via denitrification along undammed river stretches rarely exceeds a few percent, due to their short residence times (median =1.2 days and mean = 4 days; Figure 5).

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Denitrification rates reported for individual reservoirs vary from 0.01 to 108 g N m -2 yr -1 [START_REF] David | Denitrification and the nitrogen budget of a reservoir in an agricultural landscape[END_REF][START_REF] Grantz | Partitioning whole-lake denitrification using in situ dinitrogen gas accumulation and intact sediment core experiments[END_REF][START_REF] Han | Nitrogen dynamics at the sedimentwater interface in a tropical reservoir[END_REF][START_REF] Koszelnik | The significance of denitrification in relation to external loading and nitrogen retention in a mountain reservoir[END_REF]. Local studies have shown that denitrification usually accounts for between 4% and 58% of the elimination of supplied to reservoirs [START_REF] David | Denitrification and the nitrogen budget of a reservoir in an agricultural landscape[END_REF][START_REF] Garnier | Biogeochemical mass-balances (C, N, P, Si) in three large reservoirs of the Seine Basin (France)[END_REF][START_REF] Koszelnik | The significance of denitrification in relation to external loading and nitrogen retention in a mountain reservoir[END_REF][START_REF] Kunz | Sediment accumulation and carbon, nitrogen, and phosphorus deposition in the large tropical reservoir Lake Kariba (Zambia/Zimbabwe)[END_REF]. Globally, only [START_REF] Seitzinger | Denitrification across landscapes and waterscapes: A synthesis[END_REF] differentiated between N removal mechanisms in reservoirs, and proposed that denitrification originating from land-derived N in lakes and reservoirs falls in between 19 to 43 Tg N yr -1 , an order of magnitude larger than our estimates.

Published estimates of the denitrification efficiency (in % N loss) in estuaries vary between 10 and 75% of TN in [START_REF] Akbarzadeh | Enhancement of coupled nitrification-denitrification by benthic photosynthesis in shallow estuarine sediments[END_REF][START_REF] Eyre | Denitrification, N-fixation and nitrogen and phosphorus fluxes in different benthic habitats and their contribution to the nitrogen and phosphorus budgets of a shallow oligotrophic sub-tropical coastal system (southern Moreton Bay, Australia)[END_REF][START_REF] Eyre | The contribution of denitrification and burial to the nitrogen budgets of three geomorphically distinct Australian estuaries: Importance of seagrass habitats[END_REF][START_REF] Nixon | The fate of nitrogen and phosphorus at the land-sea margin of the North Atlantic Ocean[END_REF][START_REF] Seitzinger | Nitrogen biogeochemistry in an unpolluted estuary: the importance of benthic denitrification[END_REF][START_REF] Smyth | Assessing nitrogen dynamics throughout the estuarine landscape[END_REF]. However, most systems displaying very high denitrification efficiencies are tropical shallow oligotrophic systems with extensive sea grass coverage (Smyth et al., 2012;[START_REF] Eyre | The contribution of denitrification and burial to the nitrogen budgets of three geomorphically distinct Australian estuaries: Importance of seagrass habitats[END_REF], which are not representative of the global coastline [START_REF] Dürr | Worldwide typology of nearshore coastal systems: defining the estuarine filter of river inputs to the oceans[END_REF]. The bulk of the remaining estimates falls in the 10-50% range, which is consistent with our results where estuarine systems characterized by short residence times of several days like small deltas only denitrify a few percent of TN in , while systems such as fjords with residence times of several years denitrify up to 38% of TN in . Our results are also in line with the study of [START_REF] Volta | Linking biogeochemistry to hydrogeometrical variability in tidal estuaries: a generic modeling approach[END_REF] who used a generic, physically based estuarine modeling approach spanning a wide range of estuarine geometries; these authors report mean N losses via denitrification in the range 15-25%.

Global N 2 O emissions from inland waters

Our results indicate that the IPCC EF(d) values for rivers and estuaries of 0.25% for denitrification only and 0.75% for denitrification plus nitrification [START_REF] Mosier | Closing the global N2O budget: nitrous oxide emissions through the agricultural nitrogen cycle[END_REF], or 0.25% for both processes [START_REF] Ciais | Carbon and Other Biogeochemical Cycles[END_REF], are likely over-estimated. The arithmetically averaged catchment-scale EF(d) values for denitrification plus nitrification are 0.003% for upland tributaries, 0.007-0.008% for river mainstems, 0.17-0.44% for reservoirs and 0.11-0.37% for estuaries, with all values comprised between 0 and 1.2% (note: the ranges given are for scenarios DS1 and DS2). When calculated by dividing the global N 2 O emission fluxes by the global TN in fluxes, the EF(d) values are 0.025-0.027% for rivers, 0.07-0.12% for reservoirs and 0.062-0.16% for estuaries (Table 1). The two sets of EF(d) differ because the latter values depend on the TN in fluxes delivered to the water bodies, in addition to the intrinsic N 2 O production dynamics of the different types of water bodies. The higher EF(d) values for reservoirs and estuaries compared to those for rivers dominate the global spatial patterns in simulated EF(d) values (Figure 3). High EF(d) values prevail along the coasts and across North America, Europe, Southern and Eastern Asia, southeast Africa, and eastern Australia, where dams are numerous.

We predict worldwide N 2 O emissions of 10.6-19.8 Gmol N yr -1 (148-277 Gg N yr -1 ) for inland waters, 3.03-5.11 Gmol yr -1 (42.4-71.5 Gg N yr -1 ) for reservoirs, 4.29-11.12 Gmol yr -1 (60.0-156 Gg N yr -1 ) for estuaries, and 3. 26-3.53 Gmol yr -1 (45.6-49.4 Gg N yr -1 ) for rivers. Generally, spatial patterns in N 2 O emission are linked to those of N inputs into river systems (Figure 2), which explains the high emission rates over the populated areas of North America, Europe, Southeast Asia, and throughout the tropics (Figure 4 and Figure S5). The global scale spatial patterns of N 2 O emissions are also clearly influenced by the distribution of dams and estuaries. However, other factors can also play a role: Arctic rivers such as the Mackenzie and Yenisei Rivers have basins with small TN yields compared to agricultural watersheds (70 th and 33 rd percentiles of average yields for all watersheds), but due to the large residence times, they rank in the top 20 watersheds for emissions.

Discussion

Anthropogenic N 2 O emissions

Our estimated inland water N 2 O emissions represent 0.8-1.5% of the 1.28 x 10 3 Gmol yr -1 of N 2 O-N (17.9 x 10 3 Gg N yr -1 ) emitted worldwide [START_REF] Ciais | Carbon and Other Biogeochemical Cycles[END_REF]. Furthermore, our revised NEWS estimates predict that 1.14 x 10 3 Gmol yr -1 (15.9 Tg N yr -1 ) of the total dissolved N (TDN) load to watersheds is anthropogenic in origin, which corresponds to 52% of the TDN load. (Note: we cannot estimate the proportion of the PN load that is anthropogenic in origin using the NEWS model approach, because enhanced erosion of PN from anthropogenic drivers such as deforestation are not accounted for). We can therefore estimate that 2.6 -9.9 Gmol yr -1 additional N 2 O-N is evaded from rivers and estuaries due to enhanced anthropogenic loading to watersheds (this range assumes that either all or none of the 14.3 Tg N yr -1 PN load is anthropogenic in origin), which is at least fivefold lower than [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF] who estimate that 49 Gmol yr -1 (0.68 Tg N yr -1 ) of anthropogenic N inputs to river systems are converted to N 2 O.

We consider all emissions from reservoirs to be anthropogenic. Reservoirs also alter the riverine fluxes of TN through enhanced denitrification, burial, and fixation, affecting the N 2 O emission fluxes downstream of dams. Taking into account the effects of dams, we estimate that the total human-driven increase in N 2 O emissions from inland waters, relative to preindustrial conditions, falls in the range 5.6-14.5 Gmol N yr -1 , or 1.1-3.0% of the 493 Gmol yr - 1 (6.9 Tg N yr -1 ) anthropogenic N 2 O emitted worldwide from all sources combined [START_REF] Ciais | Carbon and Other Biogeochemical Cycles[END_REF]. This flux represents between 23.4 and 60.7 Tg CO 2 -equiv. yr -1 . The upper bound of our range is larger than the national emissions from any country in Europe. The fact that these are sustained emissions has been shown to be especially problematic from a global warming potential point of view. [START_REF] Neubauer | Moving beyond global warming potentials to quantify the climatic role of ecosystems[END_REF] quantify the global warming potential of sustained emissions, and compared them with pulse fluxes (which is traditionally how global warming potential has been measured). Their results show that even after 500 years, ecosystems must sequester 181 kg of CO 2 to offset 1 kg of N 2 O emissions, compared with 132 kg as predicted using the traditional global warming potentials metric.

System-specific emissions efficiencies and mechanisms

By comparing the results of DS1 and DS2, we can evaluate the effect of explicitly accounting for consumption of N 2 O during the last step of denitrification in each water body type (rivers, reservoirs and estuaries). The EF(a) values in [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF] are field measurements and thus may already have been affected to some degree by N 2 O consumption. A comparison of the results of DS1 and DS2 therefore provides some measure of the uncertainty associated with using the [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF] data to parameterize N 2 O emissions in the model calculations. Essentially, in DS1 we assume that the field-based EF values account for both N 2 O production and consumption during denitrification, while in DS2 they do not include the reduction of N 2 O to N 2 . Despite the relatively wide ranges predicted in both default scenarios, the relative trends in predicted emissions are quite similar. The estimates for both DS1 and DS2 indicate that estuaries emit more N 2 O worldwide than reservoirs or river systems, accounting for 41-56% of the total emissions fluxes along the LOAC. This reflects their much larger global areal extent (and correspondingly, their volume and residence times) of 1067 x 10 3 km 2 , compared with the smaller 45 x 10 3 km 2 surface area of reservoirs and 662 x 10 3 km 2 of rivers (Table 1).

Per unit area, N 2 O emissions from estuaries and rivers are significantly lower than for reservoirs: average surface-area-normalized emission rates are 4.0-10.4 x 10 -3 mol N m -2 yr -1 for estuaries, 4.9-5.3 x 10 -3 mol N m -2 yr -1 for rivers, and 67.3-114 x 10 -3 mol N m -2 yr -1 for reservoirs. The differences in areal emissions largely reflect the residence time distributions of the water bodies (Figure 5). The median residence time for reservoirs is close to 10 months, corresponding to an EF(d) of 0.3% in DS1 and 0.2% in DS2. Estuaries, by comparison, have a median residence time of about 3 months, which corresponds to an average EF(d) of 0.1% in both scenarios (Figure 5). Water bodies with residence time below 2-3 days, which account for 70% of river systems in our analysis, produce negligible N 2 O in both scenarios.

River systems exhibit the lowest emissions of the three systems, directly as a result of their much lower water residence times. When consumption of N 2 O via denitrification is explicitly accounted for in DS2, a larger proportion of N 2 O emissions originates from denitrification in rivers than in reservoirs and estuaries. At residence times below 6 months, N 2 O produced via denitrification exceeds N 2 O produced via nitrification (Figure 5). In rivers, 46% of the global N 2 O emissions originate from nitrification and 54% from denitrification (Table 2). In DS2, the average EF(a) denit for rivers is 1.2%, compared with the EF(a) nitrif of 0.76%. By comparison, in the same scenario at least 59% of emissions in both reservoirs and estuaries are from nitrification. Hence, in DS2 the N 2 O emission flux by denitrification for all rivers worldwide (1.76 Gmol yr -1 ) exceeds those for reservoirs (1.24 Gmol yr -1 ) and estuaries (1.31 Gmol yr -1 ).

The larger role of denitrification as the source of N 2 O in river systems is not seen for DS1, where consumption is assumed to have already been accounted for in the EF(a) values reported by [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF]. EF(a) nitrif and EF(a) denit are both fixed at 0.9% in this scenario, so any differences between emission pathways are due entirely to the relative magnitudes of the denitrification and nitrification fluxes. Nitrification accounts for a slight majority (52%) of riverine N 2 O emissions because of the larger nitrification fluxes predicted at residence times above ~5-6 months (Figure S6). At residence times below 5-6 months, the magnitudes of nitrification and denitrification fluxes are roughly equal (Figure S6), which is why in rivers, which have low residence times, both N 2 O production pathways contribute about the same to the global riverine emissions, compared to rivers and estuaries, where nitrification is the dominant pathway (Table 2). A discussion of the mechanisms driving spatially explicit N 2 O emissions, and worldwide hotspots, can be found in Section S4.

Evaluating literature observations

In this section, we first compare our model results with published global-scale N 2 O emission estimates for reservoirs and estuaries obtained by scaling up local measurements. We then move on to rivers where previous estimates have all relied on semi-empirical modeling approaches. Additional discussion related to uncertainties in existing literature and fieldbased studies needed to improve global estimates can be found in Section S5.

Reservoirs and estuaries

Using a bottom-up approach (n = 58), [START_REF] Deemer | Greenhouse gas emissions from reservoir water surfaces: a new global synthesis[END_REF] obtained a global N 2 O emission flux from reservoirs of 2.14 Gmol yr -1 (30 Gg N yr -1 ). Despite the entirely different approach, this estimate agrees well with our prediction of 3.03 -5.11 Gmol yr -1 . Estimates of N 2 O emissions from estuaries vary greatly from 7 to 407 Gmol yr -1 (100 to 5700 Gg N yr -1 , Table 1). It is worth noting that all estimates higher than 43 Gmol N yr -1 (600 Gg N yr -1 ) were calculated by applying the average emission of a very small number of estuaries (between 1 and 12) to all estuaries worldwide, possibly implying that the estuaries studied may have disproportionately large emissions relative to the global average. Only the most recent bottom-up estuarine emissions estimate of [START_REF] Murray | Nitrous oxide fluxes in estuarine environments: response to global change[END_REF] and the older estimate of [START_REF] Robinson | Hypernutrified estuaries as sources of N 2 O emission to the atmosphere: the estuary of the River Colne, Essex, UK[END_REF] overlap with our range of values (Table 1). In contrast, calculations relying on semi-empirical modeling approaches predict emissions on the order of 7 Gmol N yr -1 (100 Gg N yr -1 ) that agree with our range of 4.29-11.1 Gmol N yr -1 (60.0156 Gg N yr -1 ) [START_REF] Kroeze | Future trends in emissions of N2O from rivers and estuaries[END_REF][START_REF] Kroeze | New estimates of global emissions of N2O from rivers and estuaries[END_REF][START_REF] Seitzinger | Global distribution of nitrous oxide production and N inputs in freshwater and coastal marine ecosystems[END_REF][START_REF] Seitzinger | Global distribution of N2O emissions from aquatic systems: natural emissions and anthropogenic effects[END_REF].

Rivers

Published estimates of riverine N 2 O emissions show the greatest variability of all the water body types considered (Table 1), with the highest values two orders of magnitude larger than the lowest ones (32.2 -2100 Gg N yr -1 ). All existing river emission estimates rely on semi-empirical modeling approaches, and thus the differences are entirely dependent on the predicted loads to rivers, the EF values used and, perhaps most importantly, the assumptions made. For all estimates except one, one of the following sets of assumptions applies:

(1) EF(d) = 3% or 0.3%; all of the N load to the river system is nitrified once and half the N load is denitrified once, i.e. EF(a) nitrif = 2 EF(a) denit = EF(d) (as in [START_REF] Kroeze | New estimates of global emissions of N2O from rivers and estuaries[END_REF]Seitzinger & Kroeze, 1998;[START_REF] Seitzinger | Global distribution of N2O emissions from aquatic systems: natural emissions and anthropogenic effects[END_REF]; ( 2) EF(a) denit = 0.25% and EF(a) nitrif = 0.50%, with EF(a) denit + EF(a) nitrif = 0.75% = EF(d) (as in [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF][START_REF] Mosier | Closing the global N2O budget: nitrous oxide emissions through the agricultural nitrogen cycle[END_REF], or (ii) EF(d) = EF(a) denit = EF(a) nitrif = 0.25% (as in [START_REF] Ciais | Carbon and Other Biogeochemical Cycles[END_REF][START_REF] De Klein | N2O emissions from managed soils, and CO2 emissions from lime and urea application. IPCC Guidelines for National Greenhouse Gas Inventories[END_REF][START_REF] Kroeze | Future trends in emissions of N2O from rivers and estuaries[END_REF]. These values also constitute the IPCC guidelines.

Both of these sets of assumptions, however, fail to consider the kinetic limitations imposed by the short water residence times characteristic of most rivers. In our model scenarios, we apply the same EF(a) values as in the above assumptions but introduce a water residence time dependence on EF(d). The corresponding river N 2 O emissions fall between 1.18 and 11.8 Gmol N yr -1 (16.5-165 Gg N yr -1 ) (Table 2). These values imply that rivers likely emit significantly less N 2 O than proposed in the majority of previous studies, largely because of the limited amount of time available for nitrification and denitrification to occur in most undammed river reaches.

Seitzinger and Kroeze (1998) predict that 75.1 Gmol N yr -1 of N 2 O are emitted from rivers, based on a global DIN load to rivers of 3.0 Tmol yr -1 , assuming that TN:DIN = 2:1 and that watersheds yielding more than 10 kg N ha -1 yr -1 have an EF(d) of 3% while the remainder have an EF(d) of 0.3%. In comparison, scenarios UQ1 and UQ2, which bracket the EF(d) range of 3-0.3%, yield riverine emissions of 1.18 -11.8 Gmol yr -1 , with a TN load of 7.42 Tmol yr -1 (104 Tg N yr -1 ). Thus, even with a load to rivers that is less than half that in UQ1 and UQ2, Seitzinger and Kroeze's riverine N 2 O emissions far exceed our estimates. We suggest that the assumed denitrification efficiency in [START_REF] Seitzinger | Global distribution of nitrous oxide production and N inputs in freshwater and coastal marine ecosystems[END_REF], namely that half the N load to rivers is denitrified, is a severe over-estimation and not attainable for the short residence times in these systems. According to our results, on average only 0.22% of TN in is denitrified in undammed river segments while, globally, denitrification in rivers eliminates 1.4% of the total TN in load to watersheds. The large discrepancy is in part explained by the implicit inclusion of higher residence time water bodies such as reservoirs in the older estimates. However, even when we include reservoirs in our calculations only 19% of the global TN loads to river networks is denitrified. [START_REF] Beaulieu | Nitrous oxide emission from denitrification in stream and river networks[END_REF] To our knowledge, the only study that explicitly departs from either of the two sets of assumptions listed above is that of [START_REF] Hu | Modeling nitrous oxide emission from rivers: a global assessment[END_REF], who included 6200 watersheds in their analysis. Our predicted riverine emissions in DS1 and DS2 of 3.26 -3.53 Gmol yr -1 (45.6-49.4 Gg N yr -1 ), align well with Hu et al.'s prediction of 0.89-4.78 Gmol yr -1 (12.4-66.9 Gg N yr -1 ) N

Outlook

Our calculated global N 2 O emissions from rivers, reservoirs and estuaries fall in the range 10.6-19.8 Gmol N yr -1 (148-277 Gg N yr -1 ), more than half, and up to an order of magnitude, lower than most studies based on IPCC's guidelines. Despite the much reduced N 2 O flux estimates, we find that anthropogenic perturbations to river systems have doubled to quadrupled N 2 O emissions from inland waters. We suggest that the IPCC emissions factors of 0.25% and 0.75% are too high to be applied across all rivers, estuaries and reservoirs. Instead, we estimate the following ranges of emissions factors: 0.004-0.005% for rivers, 0.17-0.44% for reservoirs, and 0.11-0.37% for estuaries. These values, obtained by arithmetically averaging all individual emission factors for a given water body type, directly reflect the water residence time distributions of rivers, reservoirs and estuaries. The majority of emissions in estuaries and reservoirs originate from nitrification, while denitrification tends to dominate in rivers because of the shorter residence times. We find that reservoirs are the most efficient N 2 O emitters on a per-area basis, with average areal emissions rates an order of magnitude larger than for rivers and estuaries. We therefore expect worldwide N 2 O emissions from inland waters to rise substantially in the coming decades as a result of the ongoing global boom in dam construction [START_REF] Zarfl | A global boom in hydropower dam construction[END_REF], which will nearly double the number of large hydroelectric dams on Earth. A systematic analysis of predicted changes to water residence times caused by these new dams needs to be conducted to aid in forecasting changes in worldwide N 2 O emissions. et al., 2012), reservoirs [START_REF] Lehner | High-resolution mapping of the world's reservoirs and dams for sustainable river-flow management[END_REF] and estuaries [START_REF] Dürr | Worldwide typology of nearshore coastal systems: defining the estuarine filter of river inputs to the oceans[END_REF]. [START_REF] Dürr | Worldwide typology of nearshore coastal systems: defining the estuarine filter of river inputs to the oceans[END_REF] and [START_REF] Woodwell | Carbon in estuaries[END_REF].

Study

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Figure captions

Accepted Article

This article is protected by copyright. All rights reserved.

  flux of N 2 O emitted across the water-air interface relative to the nitrification or denitrification flux, is the annual denitrification flux, is the annual nitrification flux, is the annual production of N 2 O in the water body via nitrification or denitrification, is the annual production of N 2 O via denitrification minus the N 2 O subsequently transformed to N 2 , and

  assume that all N 2 O produced in rivers is emitted, i.e. EF(a) = EF(b) = EF(c) = EF(d) = 0.9%. In DS1 we assume EF(a) = EF(b) = EF(c) = 0.9% but calculate residence time dependent EF(d) values, which yields a mean EF(d) value of 0.004% and a river N 2 O emission flux of 3.53 Gmol N yr -1 , much smaller than Beaulieu's 48.6 Gmol N yr -1 estimate.

Figure 1 :

 1 Figure 1: Mechanistic box model used to represent reservoir, river, and estuarine nitrogen dynamics. Note that N 2 concentrations and evasion are shown for completeness, but not explicitly represented in the model.

Figure 2 :

 2 Figure 2: Mobilization of DIN, DON and PN to the river network as prescribed by Global-NEWS, after Van Drecht et al. (2009) and Bouwman et al. (2009), re-distributed at 0.5degree resolution.

Table 2 :

 2 Summary of scenarios used to estimate N 2 O emissions, and predicted emissions for rivers, reservoirs and estuaries. D = N 2 O emissions flux associated with denitrification; N = N 2 O emissions flux associated with nitrification; U = N 2 O emissions associated with flux leaving upstream dams; T = total N 2 O emissions flux. Units are 10

Figure 3 :

 3 Figure3: EF(d) values per 0.5-degree grid cell for rivers, reservoirs, and estuaries worldwide, shown for both default scenarios. The EF(d) of rivers is given per 0.5° cell and refers to the residence time within the part of the river network contained in each cell. A river basin consisting of multiple 0.5° cells will have an EF(d) that is a weighted average of all grid cell values contained in the basin.

Figure 4 :

 4 Figure 4: Total N 2 O emissions (in 10 6 mol N yr -1 ) from rivers, reservoirs and estuaries combined, for major watersheds worldwide in year 2000, for (a) Default scenario 1, and (b) Default scenario 2. Pie charts show the 10 watersheds with the greatest emissions globally, with the size of the chart representing its relative emission flux compared with the other nine watersheds shown (total magnitude of flux shown in brackets after watershed name). The pie charts show the proportion of emissions from denitrification or nitrification in reservoirs, estuaries or rivers.

Figure 5 :

 5 Figure 5: Left axis: N 2 O emissions flux, normalized by TN inflow flux to water body, as a function of water residence time. Shaded green curves represent DS1 results where TN influx included riverine and fixation sources, and shaded yellow curves represent DS2 results, where TN influx includes only riverine sources (as per Equations 12, 13 and 14). In both cases, solid curves shows total emissions and dashed curves show the proportion of emissions from denitrification. Box plot (right axis): Distribution of water residence times based on water body type. Solid lines inside boxes are the median, box edges are 1 st and 3 rd quartiles, whiskers are standard deviations. For clarity, outliers are not shown.

  2 O emissions. While our calculations were performed at a higher spatial resolution than Hu et al.'s, the general global spatial trends are comparable. In both studies, the largest hotspot for riverine N 2 O emissions is Southeast Asia. Furthermore,[START_REF] Hu | Modeling nitrous oxide emission from rivers: a global assessment[END_REF] predict that 86% of the riverine N 2 O outgassing takes place in equatorial and subtropical regions, which is exactly the proportion of global riverine N 2 O emissions between 40°N and 40°S according to our simulations. Other regions characterized by high emission rates include western Europe, the Amazonian basin, central Africa and eastern North America. Hu et al. also suggest that commonly used EF estimates are generally too high. They further estimate that EFs relative to DIN loads are somewhere in the range 0.08-0.31%, based on a statistical analysis in which 82 regression models were tested against a dataset of 169 measured riverine N 2 O emissions. Thus, despite using two entirely independent approaches, both our work and that of Hu et al. support the conclusion that previous EFs are overestimated.

Table 1 :

 1 Literature survey of all published global estimates for N 2 O emissions for rivers, reservoirs and estuaries. The table provides the source of the N loads used for the calculations, its value (and under which form, i.

e. Total N -TN, Total Dissolved N -TDN, or Dissolved Inorganic N -DIN), the N 2 O emission factor, the global N 2 O emissions and an estimate of the corresponding emission rate per surface area. The latter are calculated using published estimates of the surface areas of rivers (Downing

  Based on four studies with 0.3% and 3% (N 2 O : N 2 ) for DIN load of <10 and >10 kg N ha -1 yr -1 , respectively b Based on six studies made in Europe and North America c Based on two studies in England and New Zealand for relatively short river systems d IPCC default EF5-r (0.25%) was used for low case and 2.5% was assumed as the high case based on Seitzinger & Kroeze (1998) e Based on observations conducted for 72 headwater streams in North America with 0.25% observed for denitrification and 0.5% assumed for nitrification f Based on meta-analysis of global data with 169 observations covering a wide range of rivers g Based on mean flux density from 58 measurements, multiplied by reservoir surface area (GranD, Lehner et al., 2011) h IPCC default EF5-r (0.25%) was used for low case and 2.5% was assumed as the high case based on Seitzinger & Kroeze (1998)

	THIS STUDY							derived from	61 TN	Scenario	42.4 -71.5	0.94 -1.6
								NEWS	dependent
	Estuaries (1067 10	3 km	2 )
	Law et al. (1992)						bottom-up (n=5)	NA	NA	220	0.20
	Bange et al. (1996)					bottom-up (n=12)	NA	NA	3700 -5700	3.47 -5.34
	Robinson et al. (1998)		bottom-up (n=4)	NA	NA	130 -450	0.12 -0.42
	Seitzinger and Kroeze		NEWS model	20.8 DIN	1	220 [70 -690]	0.21 [0.06 -0.65]
	(1998)
	De Wilde and De Bie			bottom-up (n=1)	NA	NA	1500	1.41
	(2000)
	Kroeze et al. (2005)				NEWS model	25 DIN	1	250	0.24
	Kroeze et al. (2010) h			NEWS Model	44 TN 30 TDN	0.25 or 2.5	100 -600	0.09 -0.56
	Murray et al. (2015)	i			bottom-up (n=56)	NA	NA	310 [150 -910]	0.29 [0.14 -0.85]
	THIS STUDY							derived from	97.5 TN	Scenario	60.0 -155.4	0.06 -0.15
								NEWS	dependent
	Notes:
								N loads	N load value	Emission factor	Global N 2 O emission N 2 O emission rate
								(10 3 Gg N yr	-1 )	(%)	(Gg N yr -1 )	(g N m	-2 yr -1 )
	Rivers (662 10	3 km	2 )
	Seitzinger & Kroeze				NEWS model	41.6 DIN	2.5	1050 [190 -1870]	1.59 [0.29 -2.82]
	(1998) and Seitzinger et
	al. (2000) a
	Kroeze et al. (2005) a			NEWS model	50.3 DIN	2.5	1256	1.90
	Mosier et al. (1998) b			IPCC	93 TN	0.75	700	1.06
	De Klein et al. (2006) c		IPCC	93 TN	0.25	350	0.53
	Kroeze et al. (2010) d			NEWS model	88 TN 60 TDN	0.25 or 2.5	300 -2100	0.45 -3.17
	Beaulieu et al. (2011) e		IPCC	90 TN	0.75	680	1.03
	Hu et al. (2016) f						NEWS	18.8 DIN	0.17 [0.08-0.31] 32.2 [12.4 -66.9]	0.05 [0.02 -0.10]
	THIS STUDY							derived from	184.3 TN	Scenario	45.6 -49.4	0.07
								NEWS	dependent
	Reservoirs (45 10 3 km	2 )
	Deemer et al. (2016)	g		bottom-up (n=58)	NA	NA	30 [20 -70]	0.67 [0.44 -1.56]

a i Based on mean flux density from 56 measurements, multiplied by estuarine and tidal surface areas (average of

Acknowledgments

This research received funding from the European Union's Horizon 2020 research and innovation programs under the Marie Sklodowska-Curie grant agreement no. 643052 (C-CASCADES project) and under a grant agreement no. 776810 (VERIFY project). TM was funded by a Natural Sciences and Engineering Research Council of Canada (NSERC) postdoctoral fellowship (no. PDF-516575-2018), RL received funding from the European Union's Horizon 2020 research and innovation program under grant agreement no. 703813 for the Marie Sklodowska-Curie European Individual Fellowship 'C-Leak', and GL was supported by Labex L-IPSL, which is funded by ANR (grant #ANR-10-LABX-0018). TM and NJB are supported as part of the Watershed Function Scientific Focus Area funded by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research under Award Number DE-AC02-05CH11231.