Global methane and nitrous oxide emissions from non-marine waters

Non-marine waters (i.e., rivers, reservoirs, lakes, ponds, streams and estuaries) are globally signicant emitters of methane (CH 4 ) and nitrous oxide (N 2 O) to the atmosphere, while global estimates of these emissions have been hampered due to the lack of a worldwide comprehensive database with the collection of complete CH 4 and N 2 O ux components. Here we synthesize 2997 in-situ ux or concentration measurements of CH 4 and N 2 O from 277 peer-reviewed publications to examine the role of non-marine waters in shaping climate change. Here we estimate that inland waters including rivers, reservoirs, lakes and streams together release 94.49 Tg CH 4 yr − 1 (ebullition plus diffusion) and 1.52 Tg N 2 O yr − 1 (diffusion) to the atmosphere, yielding an overall CO 2 -equivalent emission total of 3.05 Pg CO 2 yr − 1 , representing roughly 59% of CO 2 emissions (5.13 Pg CO 2 yr − 1 ) from these four aquatic ecosystems, with lakes acting as the largest emitter for both trace gases. Ebullition is noticed as a dominant ux component, contributing up to 62–84% of total CH 4 uxes across all inland waters. Chamber-derived CH 4 ux rates are signicantly greater than those determined by diffusion model-based methods for commonly capturing of both diffusive and ebullitive uxes. The synthesis of global N 2 O measurements projected that rivers exhibit the highest indirect N 2 O emission factor (EF 5 , 0.028%), while streams have the lowest EF 5 value (0.015%). Our study reveals a major oversight in regional and global CH 4 budgets from inland waters, caused by neglect of the dominant role of ebullition pathways in those emissions. The indirect EF 5 values established in this study generally suggest an order of magnitude downward revision is required in current IPCC default EF 5 values for inland waters and estuaries. Our ndings further indicate that a comprehensive understanding of the magnitude and patterns of CH 4 and N 2 O emissions from non-marine waters is essential in dening the way that these natural ecosystems shape our climate.


Introduction
Non-marine waters (rivers, reservoirs, lakes, ponds, streams and estuaries) constitute important regional and global carbon (C) and nitrogen (N) cycles 1,2 . Large and increasing agricultural organic C and N loading into non-marine waters makes these aquatic systems active and critical in global methane (CH 4 ) and nitrous oxide (N 2 O) budgets. However, estimates of the global exchange of CH 4 and N 2 O between non-marine waters and the atmosphere remain poorly constrained, primarily due to a lack of data and limited geographic distribution of measurements, especially those rarely characterized by distinguishing different ux components and measurement methods 3,4 . Therefore, there is substantial uncertainty in our current understanding of global uvial CH 4 uxes to the atmosphere, and extremely poor accounting for the ebullitive component of CH 4 emissions 4 . Particularly, the patterns and controls of N 2 O emissions from non-marine waters remain to be explored, such as the magnitudes and indirect N 2 O emission factors (EF 5 ) involved in these aquatic systems. A robust estimate of N 2 O emissions from non-marine waters caused by various N loading sources can help in upcoming research work to re ne the regional and global terrestrial greenhouse gas inventories with reduced uncertainties 5,6 .
Multiple approaches have been used to determine CH 4 uxes 7,8 , mainly chamber-based or diffusion model-based methods. Chamber-based methods can generally capture both ebullitive and diffusive ux components of CH 4 , relative to the model-associated methods with only diffusive uxes determined based on surface water dissolved CH 4 concentrations in equilibrium with the atmosphere 4 . Ebullition constitutes an important pathway for CH 4 release from aquatic ecosystems, yet it has long been di cult to quantify due to limited measurements and spatiotemporal heterogeneity, which ultimately hampers accurate estimates of the global CH 4 budget 9 . Thus, the contribution of ebullition from different inland waters to total global freshwater CH 4 emissions remains to be resolved.
Recently, two approaches (top-down vs. bottom-up) have been used to estimate global CH 4 and N 2 O emissions from individual aquatic ecosystems (e.g., rivers, streams or reservoirs), basically showing high spatio-temporal heterogeneity [10][11][12][13] . In general, bottom-up estimates are higher than results obtained from top-down inversion methods. Using a process-based modeling approach, Hu et al. 5  ebullition) and ux-derived methods (chamber-based vs. diffusion model-based). Particularly, except natural wetlands are the largest source of CH 4 to the atmosphere, inland waters, such as lakes, rivers and reservoirs also contribute substantially to the global emission total of CH 4 , yet not included in most global greenhouse gas (GHG) inventories due to lack of robust estimates with su cient simultaneous ux measurement data by collecting complete CH 4 ux components 9,12 . Besides, some small water bodies (i.e., streams or ponds) have been also identi ed as strong sources of CH 4 and N 2 O to the atmosphere, depending on data-derived approaches and the ways to estimate 10,14 . There is thus a need for a comprehensive understanding of the rates and drivers of CH 4 and N 2 O uxes across non-marine waters.
In this study, we established a worldwide dataset by compiling 2997 direct measurements of CH 4 and N 2 O uxes or concentrations from six non-marine aquatic ecosystems (rivers, reservoirs, lakes, ponds, streams and estuaries) based on 277 peer-reviewed publications ( Supplementary Fig. S1). We divided available CH 4 uxes into diffusive and ebullitive components based on simultaneous ux measurement data and distinguished CH 4 and N 2 O ux rates using different ux-derived methods across aquatic ecosystems. Collectively, our ambition was to draw attention to the role of non-marine waters in shaping climate change, particularly by assessing the relative contribution of the diffusive and ebullitive emission pathways to global total freshwater CH 4 emissions, relating CH 4 1a). With the exception of estuaries, ebullitive and diffusive CH 4 uxes varied but showed no signi cant differences among inland waters (Fig. 1a), with the highest ux rates observed through ebullition from reservoirs (4.83 ± 1.20 mg m − 2 h − 1 ) and through diffusion from streams (1.36 ± 0.36 mg m − 2 h − 1 ). The CH 4 uxes released through ebullition were consistently higher than those through diffusion (Fig. 1a). The largest ebullitive CH 4 uxes from reservoirs can be attributed to the degassing that will occur when water is routed through the dam 3,15,16 . Diffusive N 2 O uxes varied from − 0.08 to 1.15 mg m − 2 h − 1 across six non-marine waters. Streams had the highest rate of diffusive N 2 O uxes (0.14 ± 0.02 mg m − 2 h − 1 ), followed by rivers (0.12 ± 0.02 mg m − 2 h − 1 ) and reservoirs (0.05 ± 0.01 mg m − 2 h − 1 ) (Fig. 1b). The uxes of CH 4 from rivers showed a signi cant seasonal variation, with the highest rates observed in summer and lowest rates occurring in autumn and winter ( Supplementary Fig. S2a). However, there was no such signi cant seasonal variation for CH 4  reservoirs (0.41 ± 0.08 mg m − 2 h − 1 ), respectively (Fig. 3a). Generally, CH 4 uxes measured by chamberbased methods were consistently greater than those obtained from the use of model-based methods, and signi cantly different results were observed in rivers, reservoirs, lakes and ponds (Fig. 3a). Chamberbased methods can capture both diffusive and ebullitive ux components, while model-based methods can only obtain diffusive uxes that were determined by the water-air gas exchange model 4 , suggesting that ebullitive uxes from waters may have been overlooked when using the model-based methods 4,8 . Unlike CH 4 , there were no consistent differences in N 2 O uxes between the use of chamber-based and model-based methods. Similarly, the highest mean N 2 O uxes derived from chamber-based and modelbased methods were also observed in rivers (0.13 ± 0.03 mg m − 2 h − 1 ) and streams (0.14 ± 0.02 mg m − 2 h − 1 ), respectively, while the lowest mean N 2 O uxes by the two methods occurred in ponds (Fig. 3b). For chamber-based methods, uncertainties mainly come from the changes in natural turbulence at the waterair interface when deploying oating chambers 18 . However, the uncertainties for using model-based methods are associated with how the wind or water turbulence ow affects gas exchange across the water-air interface 1 . Compared with other aquatic ecosystems, the lower wind and wave conditions in the rivers and streams that were included in our database led to lower uncertainties and higher rates of gas uxes from these water bodies 19 .
Ebullitive and diffusive CH 4 uxes Ebullition and diffusion are two major pathways of CH 4 release from water bodies 7,10,14 . Here we quanti ed the ebullitive and diffusive CH 4 uxes by grouping data from studies that simultaneously Our results con rmed the ndings in some shallow lakes and ponds with a substantial contribution of ebullition to total CH 4 uxes, potentially accounting for 50-90% of the ux from these water bodies 10,14 , while a range of 10-80% was reported on the contribution of ebullition to total CH 4 uxes from streams and rivers 2,21 . The highest mean ebullitive CH 4 uxes were captured in reservoirs (4.83 ± 1.20 mg m − 2 h − Based on simultaneous ux measurement data, we calculated the CO 2 -equivalent uxes of CH 4 and N 2 O that re ect the emission intensity of a given terrestrial ecosystem, independent of the extent of surface area it may cover (Fig. 4b). We found that CH 4 uxes dominated the ux composition (78%) of CH 4 (Fig. 1) 33 .
We simulated indirect emission factors (EF 5r /EF 5e ) of N 2 O for rivers, reservoirs (including lakes and ponds), streams and estuaries (Fig. 2), with a range of 0.002-5.60% across all water bodies. Consistently, N 2 O and NO 3 − concentrations exhibited strong linear positive correlations with relatively narrow uncertainty ranges in all water bodies, indicating that NO 3 − is a primary driver of aquatic N 2 O production.
Of which, rivers (0.028%) showed to have the highest EF 5r value, as compared to streams (0.015%) with the lowest EF 5r value. As shown in Fig. 2, the EF 5 values estimated using the concentration method differed among aquatic ecosystems, which were generally an order in magnitude lower than the IPCC default value of 0.26% (ref. 34 ). These results suggest that a downward revision of IPCC default value is required in the future to more accurately estimate indirect N 2 O emissions from aquatic ecosystems as previously stressed 6,35,36 .

Drivers of CH 4 and N 2 O emissions from non-marine waters
We found that CH 4  To predict CH 4 and N 2 O uxes from non-marine waters, linear stepwise regression models with the personality of Ordinary Least Squares (OSL) were used to t CH 4 and N 2 O uxes by environmental parameters. We found that DO showed as a dominant factor among all variables to in uence CH 4 release from individual freshwaters, such as in reservoirs, lakes and ponds (Table S3). However, when pooling data from all inland waters, dissolved oxygen (DO) together with temperature poorly accounted for the variance in CH 4 uxes (

Methods
Data acquisition. We launched a detailed review of the literature published in peer-reviewed journals through the year 1978-2020 (cut-off date on October 20, 2020). We extracted original experimental data from publications on aquatic CH 4 and N 2 O uxes as well as related parameters from six non-marine waters including rivers, reservoirs, lakes, ponds streams and estuaries. A combination of search terms ["CH 4 " OR "methane" AND "N 2 O" OR "nitrous oxide" AND " ux" OR "emission" OR "release" OR "evasion" AND "river" OR "reservoir" OR "lake" OR "pond" OR "stream" OR "estuary"]. All selected data were extracted from the Web of Science and Google Scholar, and also the publication sources by gathering and reevaluating the older literature cited in the earlier reviews. The experimental locations were mostly clustered in Asia, Europe, and North America, with only several studies scattered in South and Northern Hemispheres with high latitudes (Supplementary Fig. S1). Overall, we established a solid dataset consisting of 2997 in-situ ux or concentration measurements of CH 4 Fig. S1).
We only included in-situ measurements of CH 4 and N 2 O uxes or concentrations from non-marine waters. With the focus on natural aquatic systems, the gas ux data from arti cial constructed ponds used for sewage treatment or agricultural aquaculture ponds were excluded from our dataset due to intensive human impacts. We only incorporated studies in which aquatic systems were clearly de ned. For studies in which the type of riverine systems was not clearly de ned, we grouped them into rivers or streams according to the speci c Strahler stream order 44 . We ensured that the data on gas uxes and geographical information were reported or can be made available from authors. In case of absence of data on climate (e.g., temperature, precipitation) information, we obtained relevant data from the World Meteorological Organization (http://www.worldweather.cn/zh/home.html). When the same site was reported in multiple studies, we used the study that included the largest number of sampling dates, either across seasons or years. If the data were collected across multiple years, we calculated the average uxes or concentrations over the whole measurement period. Generally, diffusive and ebullitive CH 4 uxes spanned over four orders of magnitude, ranging from 0.00 to 56.00 mg m -2 h -1 and 0.00 to 60.42 mg m -2 h -1 in inland waters, and varied from -0. 15 Table S5).
Upscaling and uncertainties. We used a bottom-up approach to upscale CH 4 and N 2 O emissions from non-marine waters by multiplying averaged emission rates by the estimated global areal extents of water bodies 12,18 . In terms of CH 4 emissions, only studies with simultaneous measurement data for both diffusive and ebullitive uxes were included in our estimates to reduce bias. For N 2 O emissions, considering the ebullition was not the representative pathway of N 2 O release from water bodies, we chose to only estimate diffusive N 2 O emissions from non-marine waters, nally leading to exclusion of several sporadic ebullitive N 2 O uxes from our dataset. Moreover, in order to reduce uncertainties, we only estimated diffusive CH 4 emissions from estuaries due to insu cient data on ebullitive CH 4 uxes. To generate annual mean gas uxes, we assumed the average seasonal uxes were representative of the entire year in tropical and frigid regions. In other regions with typical seasonal differences, the seasonal ux data (collected in summer or winter) were recti ed by the annual mean temperature using a temperature-dependent empirical model reviewed by Yan et al. 45 . However, we did not extrapolate CH 4 and N 2 O emissions from ponds in this study due to large uncertainties in current available areal extents determination. All the data on global surface areas of aquatic ecosystems were cited from recently published literature with solid updated estimates 18,46,47 .
Compared to previous global estimates based on limited and localized CH 4 and N 2 O ux rates, we have dedicated to exploring the fractions of global total freshwater CH 4 emissions resulting from two different emission pathways (diffusion and ebullition) by incorporating simultaneous ux measurement data. Meanwhile, we provided a full understanding of the magnitude and drivers of diffusive N 2 O emissions from diverse non-marine waters, relative to previously mostly limited in a single aquatic system 5,18 . However, uncertainties remained existed for our estimates. First, while a wide range in diffusive uxes has been reported for estuarine open waters, measurements of ebullition remain notably scare, especially for the simultaneous measurement data with diffusion (Supplementary Table S4). Second, except in tropical and frigid regions, ux data showed considerable variations with seasons, with general higher ux rates occurring in summer than in other seasons, although we have attempted to account for this in our analysis by rectifying the ux data using an earlier established temperature-dependent empirical model 45 . Third, we did not estimate the indirect EF 5 of N 2 O based on the IPCC methodology to create a comparison in this study due to lack of detailed information on N inputs in most studies. Thus, given that future changes in climate and anthropogenic N loading are expected to increase N 2 O emissions from nonmarine waters, more extensive direct measurements of N 2 O uxes coupled with aquatic N loading rates are highly needed to make the IPCC methodology applicable to bridge the gap between global bottom-up and top-down inventories.
Calculation of indirect N 2 O emission factors (EF 5 ). Indirect N 2 O emission factors for riverine systems (EF 5r ) and estuaries (EF 5e ) were estimated in this study to create a comparison with the recently updated IPCC default value of 0.26% (ref. 34 ). The indirect EF 5 of N 2 O represents N 2 O emissions from a given water body to the atmosphere as a fraction of N loading into the system 6 . IPCC de ned the indirect EF 5 of N 2 O as a ratio of N 2 O-N emitted from leached N and N in runoff divided by the fraction of all N added to, or mineralized within managed soils that is lost through leaching and runoff 48 . Due to incomplete acquisition of the speci c information (e.g., data on N leaching and runoff) required to determine the indirect EF 5  Declarations Figure 1 Comparisons of diffusive and ebullitive CH4 uxes (a) and N2O uxes (b) among aquatic ecosystems.
Estuaries are absent from Fig. 1a due to limited observations available to reduce uncertainties. The number of observations (n) for each water body is shown next to the x-axis. The empty squares, lines within each box, lower and upper edges, bars and grey circles represent the means, median values, 25th and 75th, 10th and 90th percentiles and outliers of data, respectively. Different uppercase and lowercase letters indicate signi cant differences in diffusive CH4 and N2O uxes and ebullitive CH4 uxes, respectively. Asterisks in Fig. 1a indicate statistical differences in CH4 uxes between through diffusion and ebullition pathways (*p < 0.05; **p < 0.01; ***p < 0.001).

Figure 2
Linear simulated indirect emission factors of N2O (EF5r/EF5e) based on the concentration method (N2O-N/NO3--N mass ratio) for speci c aquatic ecosystems. The black dashed line represents the IPCC (2019) default emission factor for riverine systems and estuaries. The indirect EF5r/EF5e of N2O for rivers, reservoirs (including lakes and ponds), streams and estuaries derived from this study are 0.028%, 0.019%, 0.015% and 0.026%, respectively, which are generally one order magnitude lower than the IPCC default value of 0.26%.

Figure 3
Comparisons of CH4 (a) and N2O uxes (b) between chamber-based and diffusion model-based methods across aquatic ecosystems. Asterisks indicate statistical differences in gas uxes between two measuring methods (*p < 0.05; **p < 0.01; ***p < 0.001). The number of observations (n) for each water body is shown next to the x-axis. The empty squares, lines within each box, lower and upper edges, bars and grey circles represent the means, median values, 25th and 75th, 10th and 90th percentiles and outliers of data, respectively.

Figure 4
Relative contributions of diffusive and ebullitive CH4 uxes (a) and CO2-equivalent uxes of CH4 and N2O (b) based on simultaneous ux measurement data across various aquatic ecosystems. Estuaries are excluded from Fig. 4a due to insu cient observations available to reduce uncertainties. Bars represent the mean ± SE. The number of observations (n) for each water body is shown next to the x-axis. The CO2equivalent uxes of CH4 and N2O are calculated using IPCC conversion factors (mass basis) of 28 and 265 over the time horizon of 100 years, respectively.

Figure 5
Global budgets of CH4 and N2O emissions from four major inland waters. The colored arrows represent estimated CH4 and N2O emissions (Tg CH4/N2O yr−1) from speci c freshwater systems, where orange and green parts of the arrows indicate diffusive and ebullitive CH4 emissions, respectively; blue arrows indicate diffusive N2O emissions; The source strength of CH4 and N2O is depicted here by the width of arrows in different inland waters.

Supplementary Files
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