Nitrous oxide (N 2 O) and methane (CH 4 ) in rivers and estuaries of northwestern Borneo

. Nitrous oxide (N 2 O) and methane (CH 4 ) are atmospheric trace gases which play important roles in the climate and atmospheric chemistry of the Earth. However, little is known about their emissions from rivers and estuaries, which seem to contribute signiﬁcantly to the atmospheric budget of both gases. To this end concentrations of N 2 O and CH 4 were measured in the Rajang, Maludam, Sebuyau and Simunjan rivers draining peatland in northwestern (NW) Borneo during two campaigns in March and September 2017. The Rajang River was additionally sampled in August 2016 and the Samunsam and Sematan rivers were additionally sampled in March 2017. The Maludam, Sebuyau, and Simunjan rivers are typical “blackwater” rivers with very low pH (3.7–7.8), very high dissolved organic carbon (DOC) concentrations (235–4387 mmol L − 1 ) and very low O 2 concentrations (31–246 µmol L

Abstract. Nitrous oxide (N 2 O) and methane (CH 4 ) are atmospheric trace gases which play important roles in the climate and atmospheric chemistry of the Earth. However, little is known about their emissions from rivers and estuaries, which seem to contribute significantly to the atmospheric budget of both gases. To this end concentrations of N 2 O and CH 4 were measured in the Rajang, Maludam, Sebuyau and Simunjan rivers draining peatland in northwestern (NW) Borneo during two campaigns in March and September 2017. The Rajang River was additionally sampled in August 2016 and the Samunsam and Sematan rivers were additionally sampled in March 2017. The Maludam, Sebuyau, and Simunjan rivers are typical "blackwater" rivers with very low pH (3.7-7.8), very high dissolved organic carbon (DOC) concentrations (235-4387 mmol L −1 ) and very low O 2 concentrations (31-246 µmol L −1 ; i.e. 13 %-116 % O 2 saturation). The spatial and temporal variability of N 2 O and CH 4 concentrations (saturations) in the six rivers or estuaries was large and ranged from 2.0 nmol L −1 (28 %) to 41.4 nmol L −1 (570 %) and from 2.5 nmol L −1 (106 %) to 1372 nmol L −1 (57 459 %), respectively. We found no overall trends of N 2 O with O 2 or NO − 3 , NO − 2 or NH + 4 , and there were no trends of CH 4 with O 2 or dissolved nutrients or DOC. N 2 O concentrations showed a positive linear correlation with rainfall. We conclude, therefore, that rainfall is the main factor determining the riverine N 2 O concentrations since N 2 O production or consumption in the blackwater rivers themselves seems to be low because of the low pH. CH 4 concentrations were highest at salinity = 0 and most probably result from methanogenesis as part of the decomposition of organic matter under anoxic conditions. CH 4 in the concentrations in the blackwater rivers showed an inverse relationship with rainfall. We suggest that CH 4 oxidation in combination with an enhanced river flow after the rainfall events might be responsible for the decrease in the CH 4 concentrations. The rivers and estuaries studied here were an overall net source of N 2 O and CH 4 to the atmosphere. The total annual N 2 O and CH 4 emissions were 1.09 Gg N 2 O yr −1 (0.7 Gg N yr −1 ) and 23.8 Gg CH 4 yr −1 , respectively. This represents about 0.3 %-0.7 % of the global annual riverine and estuarine N 2 O emissions and about 0.1 %-1 % of the global riverine and estuarine CH 4 emissions. Therefore, we conclude that rivers and estuaries in NW Borneo -despite the fact their water area covers only 0.05 % of the global river/estuarine areacontribute significantly to global riverine and estuarine emissions of N 2 O and CH 4 . to 3.3 Tg N 2 O yr −1 and from 0.09 to 5.7 Tg N 2 O yr −1 , respectively (see overview in Maavara et al., 2019). Thus, the combined riverine and estuarine emissions may contribute up to 32 % of the global natural and anthropogenic emissions of N 2 O (28.1 Tg N 2 O yr −1 ; IPCC, 2013). CH 4 emission estimates for rivers and estuaries are in the range of 1.5-26.8 Tg CH 4 yr −1 (Bastviken et al., 2011;Stanley et al., 2016) and 0.8-6.6 Tg CH 4 yr −1 (see overview in Borges and Abril, 2011), respectively. The combined emissions from rivers and estuaries can contribute up to 6 % of the global natural and anthropogenic atmospheric emissions of CH 4 (556 Tg CH 4 yr −1 ; IPCC, 2013). As indicated by the wide range of the estimates cited above, the emission estimates of both gases are associated with a high degree of uncertainty, which is mainly caused by an inadequate coverage of the temporal and spatial distributions of N 2 O and CH 4 in rivers and estuaries and the inherent errors of the model approaches to estimate their exchange across the water-atmosphere interface (see, e.g., Alin et al., 2011;Borges and Abril, 2011).
N 2 O is produced by microbial processes such as nitrification (i.e. oxidation of ammonia, NH 3 , to nitrite, NO − 2 ) in estuarine waters (see, e.g., Barnes and Upstill-Goddard, 2011) and heterotrophic denitrification (i.e. reduction of nitrate, NO − 3 , to dinitrogen, N 2 ) in river sediments (Beaulieu et al., 2011). The yields of N 2 O from these processes are enhanced under low-oxygen (i.e. suboxic) conditions (see, e.g., Brase et al., 2017;Zhang et al., 2010), whereas N 2 O can be reduced to N 2 under anoxic conditions via sedimentary denitrification in rivers (see, e.g., Upstill-Goddard et al., 2017). Apart from ambient oxygen (O 2 ) concentrations, riverine and estuarine N 2 O production is also dependent on the concentrations of dissolved inorganic nitrogen (DIN; = NH + 4 + NO 2− + NO − 3 ) and organic carbon (Quick et al., 2019). There seems to be a general trend towards high estuarine/riverine N 2 O concentrations when DIN concentrations are high as well (Barnes and Upstill-Goddard, 2011;Quick et al., 2019;Zhang et al., 2010). However, this trend masks the fact that in many cases the spatial and temporal variability of riverine and estuarine N 2 O is often not related to DIN (see, e.g., Borges et al., 2015;Brase et al., 2017;Müller et al., 2016a;Quick et al., 2019). CH 4 is produced during microbial respiration of organic matter by anaerobic methanogenesis in riverine and estuarine sediments (see, e.g., Borges and Abril, 2011;Romeijn et al., 2019;Stanley et al., 2016). A significant fraction of the CH 4 produced in sediments can be oxidized to carbon dioxide (CO 2 ) via anaerobic CH 4 oxidation in sulfate-reducing zones of estuarine sediments (see, e.g., Maltby et al., 2018) and aerobic CH 4 oxidation in riverine sediments (see, e.g., Shelley et al., 2017). When released to the overlying riverine or estuarine water, CH 4 can be oxidized by aerobic CH 4 oxidation before reaching the atmosphere (see, e.g., Borges and Abril, 2011;Sawakuchi et al., 2016;Steinle et al., 2017).
In general, the temporal and spatial distributions of N 2 O and CH 4 in rivers and estuaries are driven by the complex interplay of microbial production and consumption pathways (see above) as well as physical processes such as input via shallow groundwater, river discharge, tidal pumping, release to the atmosphere and export to coastal waters (Barnes and Upstill-Goddard, 2011;Borges and Abril, 2011;Quick et al., 2019;Stanley et al., 2016).
Peatlands, which are found in the tropics and at high latitudes, constitute one of the largest reservoirs of organicbound carbon worldwide (Minasny et al., 2019;Treat et al., 2019;Yu et al., 2010). Rivers and streams draining peatlands have exceptionally high concentrations of dissolved organic carbon (DOC) and low pH and, thus, belong to the "blackwater" river type, which is also found in southeast (SE) Asia (see, e.g., Alkhatib et al., 2007;Martin et al., 2018;Moore et al., 2011).
Despite the fact that a number of studies about N 2 O and CH 4 emissions from peatlands in SE Asia have been published (see, e.g., Couwenberg et al., 2010;Hatano et al., 2016;, only a few studies about their emissions from peatland-draining rivers in SE Asia have been published so far Mü et al., 2016a). Therefore, our knowledge about the biogeochemistry and emissions of N 2 O and CH 4 from peatlanddraining rivers is still rudimentary at best.
Here we present measurements of dissolved N 2 O and CH 4 in six rivers and estuaries in northwestern (NW) Borneo during August 2016, March 2017 and September 2017. The objectives of our study were (i) to measure the distributions of dissolved N 2 O and CH 4 , (ii) to identify the major factors influencing their distributions, and (iii) to estimate the N 2 O and CH 4 emissions to the atmosphere.

Study site description
Discrete samples of surface water were taken at several stations along the salinity gradients of the Rajang, Maludam, Sebuyau and Simunjan rivers in NW Borneo during two campaigns in March and September 2017 ( Fig. 1, Table 1). The Rajang River was additionally sampled in August 2016, and the Samunsam and Sematan rivers were additionally sampled in March 2017. The environmental settings of the river basins are summarized in Table 2. Based on the areas affected by oil palm plantations and logging in combination with our own observations during several sampling campaigns, we classified the Rajang and Simunjan River basins as "disturbed" and the Maludam, Sebuyau, Sematan and Samunsam River basins as "undisturbed" (Table 2).

Measurements of N 2 O and CH 4
Water was collected from 1 m depth by using a Niskin sampler. Subsamples for N 2 O and CH 4 were taken as duplicates or triplicates in 20 or 37 mL glass vials. The vials were  Table 1. Overview of sampling and sampled ranges of salinity, pH as well as O 2 concentration and saturation (in percent, given in parentheses) and concentrations of dissolved inorganic nitrogen (DIN = NO − 3 + NO − 2 + NH + 4 ), silicate (SiO 2 ) and dissolved organic carbon (DOC). All concentrations are given in µmol L −1 . NA stands for not available and "Stat." stands for sampling station. DOC data were taken from Martin et al. (2018). first rinsed with sample water, then filled to the maximum (without air bubbles), and finally sealed on the spot using a crimper. The samples were kept on ice for a maximum of 3 h. When returned to the field station, 50 µL of saturated aqueous mercuric chloride (HgCl 2 ) solution was immediately added to stop any biological activity, and samples were stored at tron capture detector (ECD; for N 2 O) and a flame ionization detector (FID; for CH 4 ) as described in Bastian (2017) and Kallert (2017). Calibration of the ECD and FID was performed with standard gas mixtures of 348.4-1476.1 ppb N 2 O and 1806.10-3003.79 ppb CH 4 in synthetic air which have been calibrated against NOAA-certified primary gas standards in the laboratory of the Max Planck Institute for Biogeochemistry in Jena, Germany.

River
Dissolved N 2 O/CH 4 concentrations (C obs in nmol L −1 ) were calculated with where x is the dry mole fraction of N 2 O or CH 4 in the headspace of the sample, P is the ambient pressure (set to 1013.25 hPa), and V hs and V wp are the volumes of the headspace and the water phase, respectively. R stands for the gas constant (8.31451 m 3 Pa K −1 mol −1 ), T is the temperature during equilibration, and β is the solubility of N 2 O or CH 4 (Weiss and Price, 1980;Wiesenburg and Guinasso Jr., 1979). The estimated mean relative errors of the measurements were ±9 % and ±13 % for N 2 O and CH 4 , respectively. These comparably high relative errors most probably resulted from the long storage time (6-7 months after sampling) for some of the samples. The higher mean measurement error of the CH 4 samples (compared to the N 2 O measurements) was attributed to the fact that CH 4 samples are more sensitive to storage time than N 2 O samples .

Ancillary measurements
Water temperature, dissolved oxygen and salinity were recorded with an Aquaread ® 2000. Nutrient measurements are described in detail in Sia et al. (2019). In short, all samples were collected within the upper 1 m (surface) using pre-washed bottles via a pole sampler to reduce contamination from the surface of the boat and engine coolant waters (Zhang et al., 2015). Samples were filtered through a 0.4 µm pore-size polycarbonate membrane filter (Whatman) into pre-rinsed bottles, conserved with concentrated HgCl 2 solution and kept in a cool, dark room. Nutrients were determined utilizing a Skalar SANplus auto analyser with an analytical precision < 5 %. pH was measured using a YSI Aquaread ® multiple-parameter probe (AP-2000). The measurements of DOC are described in detail in Martin et al. (2018). The performance of the DOC measurements was monitored by using deep-sea water samples with a certified DOC concentration of 42-45 µmol L −1 provided by the Hansell Laboratory, University of Miami. Our analyses consistently yielded slightly higher concentration for the reference water, with a long-term mean (±1 SD) of 47±2.0 µmol L −1 (n = 51). The DOC data are available from the Supplement in Martin et al. (2018).

Computations of saturations and flux densities
The saturations (Sat, %) for N 2 O, CH 4 and O 2 were calculated as where C eq is the equilibrium concentration of N 2 O/CH 4 /O 2 calculated according to Weiss and Price (1980), Wiesenburg and Guinasso Jr. (1979), or Weiss (1970) k w is the gas transfer velocity and Sc is the Schmidt number, which was calculated with the equations for the kinematic viscosity of water (Siedler and Peters, 1986) and the diffusion of N 2 O or CH 4 in water (Jähne et al., 1987;Rhee et al., 2009). k 600 was determined in a study for the Lupar and Saribas rivers which are located in close vicinity to the Maludam River (Müller et al., 2016a, b). Both rivers have similar environmental and morphological settings in comparison to the rivers studied here. Therefore, we assume that the k 600 values measured by Müller et al. (2016a) are representative of the rivers in NW Borneo studied here. Mean k 600 ranges from 13.2 ± 11 to 23.9 ± 14.8 cm h −1 . On the basis of the data in Müller et al. (2016a), we computed a mean k 600 of 19.2 cm h −1 (5.33 × 10 −5 m s −1 ), which we used to estimate the flux densities of N 2 O and CH 4 . This k 600 is in good agreement with the mean k 600 for rivers < 100 m wide (22.4±14.3 cm h −1 ) and estuaries/rivers > 100 m wide (10.3 ± 7.7 cm h −1 ) listed in Alin et al. (2011), which range from 6.0 to 35.3 and 4.8 to 30.6 cm h −1 , respectively. k w in rivers depends on the turbulence at the river is wateratmosphere interface, which in turn is mainly affected by water current velocity, water depth and riverbed roughness and to a lesser extent by the wind speed (Alin et al., 2011;Borges and Abril, 2011). Since the k 600 reported by Müller et al. (2016a) was determined only during the wet season (March 2014), our mean k 600 is biased because it does not account for a lower k 600 , which is to be expected during the dry season (resulting from a lower water current velocity; Alin et al., 2011). This results in an overestimation of the flux densities.

Rainfall data
In order to account for the regional variability of the rainfall in NW Borneo, we used rainfall data with a 3 h resolution recorded at the weather stations in Kuching, Bandar Sri Aman and Sibu (all in NW Borneo). The rainfall data were provided by World Weather Online (Dubai, UAE, and Manchester, UK) and are available via https://www. worldweatheronline.com/ (last access: 4 November 2019). Representative weather stations were chosen for each river basin studied here and allocated as follows. The rainfall data for the Simunjan, Sematan and Samunsam River basins are represented by the data from Kuching; the Maludam-Sebuyau and the Rajang River basins are represented by the data from the Bandar Sri Aman and Sibu weather stations, respectively. We also included the N 2 O and CH 4 concentration data from two measurement campaigns to the Lupar and Saribas rivers in June 2013 and March 2014 (Müller et al., 2016a). The Lupar and Saribas data were associated with the rainfall data from the weather station in Bandar Sri Aman. Accumulated rainfall amount was computed by summing up the 3 h rainfall data for the periods of 1-4 weeks prior to the sampling dates.

Nitrous oxide
The measured ranges of N 2 O concentrations and saturations are listed in Table 3 (Müller et al., 2016a). In contrast with our study, no N 2 O undersaturations have been observed by Müller et al. (2016a). Our results are at the lower end of N 2 O concentrations reported from rivers around the globe, which can range from extreme undersaturation (down to about 3 %, i.e. almost devoid of N 2 O) as measured in a tropical river in Africa (Borges et al., 2015) to extreme supersaturation (of up to 12 500 %) as measured in an agriculture-dominated river in Europe .
Maximum N 2 O saturations measured in March 2017 were in the range of 106 % to 142 % for the rivers classified as undisturbed (Maludam, Sebuyau, Sematan and Samunsam), whereas the maximum saturation for the rivers classified as disturbed (Rajang and Simunjan) was in the range of 329 % to 570 % (Tables 2 and 3) indicating higher emissions from the disturbed rivers. The maximum N 2 O saturations in September 2017 ranged from 329 % to 390 %, and no differences were observed between undisturbed and disturbed rivers (Table 3).
We found no overall trends of N 2 O with O 2 or NO − 3 , NO − 2 , NH + 4 and DIN. Therefore, it is difficult to decipher the major consumption or production processes of N 2 O or to locate the influence of (local) anthropogenic input of nitrogen compounds on riverine N 2 O cycling. This is in line with results from studies of other tropical rivers (Borges et al., 2015;Müller et al., 2016a). There are, however, occasional observations of N 2 O correlations with O 2 or nutrients in tropical rivers which were attributed to river types such as swamp and savannah rivers (Upstill-Goddard et al., 2017). Figure 3 shows the N 2 O concentrations along the pH gradients. Obviously there are no trends except for an enhancement of the N 2 O concentrations in September 2017. N 2 O production via nitrification depends on the prevailing pH because nitrifiers prefer to take up ammonia (NH 3 ). The concentration of dissolved NH 3 drops significantly at pH < 8-9 (Bange, 2008) because of its easy protonation to ammonium (NH + 4 ). A low pH of about 5-6 can reduce nitrification (NH + 4 oxidation) significantly as was recently shown for the Tay Ninh River in Vietnam (Le et al., 2019). Moreover, the optimum for a net N 2 O production by nitrification, nitrifier denitrification and denitrification lies between a pH of 7 and 7.5 (Blum et al., 2018). Therefore, a net N 2 O production may be low in the blackwater rivers studied here because of their low pH (see Table 1). The observed N 2 O supersaturations, therefore, might have been mainly the result of external inputs of N 2 Oenriched waters or groundwater. The observed N 2 O undersaturations were most probably resulting from heterotrophic denitrification which could have taken place either in organic matter-enriched anoxic river sediments or in anoxic environments of the surrounding soils. However, the main factor for riverine N 2 O under-or supersaturation might be rainfall because rainfall events determine the height of the water table in the surrounding soils, which, in turn, determines the  amount of suboxic-anoxic conditions favourable for N 2 O production or consumption (Jauhiainen et al., 2016). See also discussion in Sect. 4.3.

Methane
The measured ranges of CH 4 concentrations and saturations are listed in Table 3, and the distributions of CH 4 satura-tions along the salinity gradients are shown in Fig. 4. CH 4 concentrations (saturations) were highly variable and ranged from 2.5 nmol L −1 (106 %) in the Simunjan River (at salinity = 0 in September 2017) to 1372 nmol L −1 (57 459 %) in the Simunjan River (at salinity = 0 in March 2017).
(Please note that we also measured a CH 4 concentration of 14 999 nmol L −1 (624 070 %) at one station in the Simunjan River at salinity = 0 in March 2017, which, however, was not included in Fig. 4 and which was excluded in the emission estimates for statistical reasons.) CH 4 saturations in the Rajang, Maludam, Sebuyau and Simunjan rivers were higher in March 2017 compared to September 2017. Maximum CH 4 concentrations were measured at salinity = 0, and there was a general decrease in CH 4 concentrations with increasing salinity. Exceptions from this trend occurred at individual stations in the Maludam, Sebuyau and Samunsam rivers which point to local sources of CH 4 (Fig. 3). The range of CH 4 concentrations (saturations) from our study is larger compared to the concentration range measured in the Lupar and Saribas rivers (3.7-113.9 nmol L −1 ; 168 %-5058 %) (Müller et al., 2016a). Borges et al. (2015) reported a maximum CH 4 concentration (saturation) of 62 966 nmol L −1 (approx. 954 000 %) in their study of tropical rivers in Africa, which is much higher than the maximum concentration measured in our study. We found no differences in the CH 4 saturations between the rivers classified as undisturbed and those classified as disturbed in both March and September 2017. We found no overall trends of CH 4 with O 2 or dissolved nutrients or DOC along the salinity gradients. There are, however, occasional observations in tropical rivers of CH 4 relationships with O 2 , which were attributed to different river types such as swamp and savannah rivers (Upstill-Goddard et al., 2017). High CH 4 concentrations, which were often asso-ciated with high DOC and low O 2 concentrations at salinity = 0 and pH < 7 (see Fig. 3b), might have been produced by methanogenesis in anoxic riverine sediments rich in organic material or in anoxic parts of the surrounding soils drained by the rivers. The decrease in CH 4 with increasing salinity can be attributed to the gas exchange across the river water-atmosphere interface in combination with CH 4 oxidation (Borges and Abril, 2011;Sawakuchi et al., 2016).

N 2 O/CH 4 concentrations and rainfall
Mean N 2 O concentrations showed linear correlations with accumulated rainfall during different periods from 1-4 weeks before the dates of sampling (Fig. 5, Table 6). Enhanced N 2 O emissions from (peat) soils are usually associated with rainfall when the water table approaches the soil surface (Couwenberg et al., 2010;Jauhiainen et al., 2016). A high water table, in turn, allows decomposition of previously deposited fresh organic material (Jauhiainen et al., 2016) and, thus, will result in favourable conditions for microbial N 2 O production mainly via denitrification in a suboxic-anoxic soil environment (Espenberg et al., 2018;Pihlatie et al., 2004). N 2 O production via nitrification may be less important at a high water table (Pihlatie et al., 2004;Regina et al., 1996). Therefore, the positive linear relationship of the riverine N 2 O concentrations with rainfall might result from enhanced N 2 O production in the adjacent soils drained by the rivers. A decreasing trend of N 2 O concentrations, which would be expected to be caused by enhanced river discharge after the rain events -which in turn can lead to dilution of the concentrations and enhanced fluxes across the riveratmosphere interface (Alin et al., 2011) -is obviously outcompeted by an enhanced input of N 2 O.
In contrast with N 2 O, the response of riverine or estuarine CH 4 concentrations to increasing rainfall does not result in increasing CH 4 concentrations (Fig. 5). When considering the periods of 1 or 1.5 weeks of accumulated rainfall there seems to be a pronounced decrease in CH 4 concentrations with increasing rainfall (Fig. 5c and Table 6). This trend is no longer significant when considering the periods of 2-4 weeks of accumulated rainfall (Table 6). A closer inspection of the data reveals that the response to increasing rainfall seems to be different for individual rivers or estuaries. There is a clear negative relationship with rainfall for the Maludam, Sebuyau and Simunjan rivers, whereas no obvious trends were observed for the other rivers ( Fig. 5c and d). Under the assumption that rainfall is a predictor for river discharge/high water we can argue that our results are in agreement with the often observed inverse relationship between CH 4 concentrations and river discharge (Anthony et al., 2012;Bouillon et al., 2014;Dinsmore et al., 2013;Hope et al., 2001). This re-lationship can be explained by an interplay of various processes such as (i) a decrease in CH 4 concentrations caused by a higher water flow (i.e. dilution under the assumption that the net CH 4 production does not change significantly), (ii) higher flux across the river-atmosphere interface during periods of higher discharge (caused by an enlarged river surface area and/or a more turbulent water flow) (Alin et al., 2011) and (iii) the enhancement of CH 4 oxidation during high waters: Sawakuchi et al. (2016) showed that CH 4 oxidation in blackwater rivers of the Amazon Basin was maximal during the high-water season.

Emission estimates
The N 2 O flux densities from the six rivers studied here are comparable to the N 2 O flux densities from other aqueous and soil systems reported from Borneo and other sites in SE Asia; see Table 4. The corresponding CH 4 flux densities are higher than the CH 4 flux densities reported for the Lupar and Saribas rivers but much lower than the flux densities from drainage canals in Central Kalimantan and Sumatra   (Table 4). Our CH 4 flux densities are, however, comparable to recently published CH 4 eddy covariance measurements (Tang et al., 2018) in the Maludam National Park, which is drained by the Maludam River, and measurements of the CH 4 release from peat soils when the water table is high and CH 4 from rice paddies (Couwenberg et al., 2010); see Table 4. The mean annual N 2 O and CH 4 emissions for the individual rivers were calculated by multiplying the mean flux density, F , for each river (Table 4) with the river surface area given in Table 2. The results are listed in Table 5. The resulting total annual N 2 O emissions for the rivers in NW Borneo -including the emissions from the Lupar and Saribas rivers (Müller et al., 2016a) -are 1.09 Gg N 2 O yr −1 (0.7 Gg N yr −1 ). This represents about 0.3-0.7 % of the global annual riverine and estuarine N 2 O emissions of 166-322 Gg N 2 O (106-205 Gg N yr −1 ) recently estimated by Maavara et al. (2019). The total annual CH 4 emissions from rivers in NW Borneo are 23.8 Gg CH 4 yr −1 . This represents about 0.1 %-1 % of the global riverine and estuarine CH 4 emissions of 2300-33 400 Gg CH 4 yr −1 (the emission range is based on the minimum and maximum estimates given in Bange et al., 1994;Bastviken et al., 2011;Borges and Abril, 2011;and Stanley et al., 2016). However, we caution that our estimates are associated with a high degree of uncertainty because (i) our data are biased by the fact that for some rivers it was not possible to cover the entire salinity gradient, (ii) seasonal and interannual variabilities of the N 2 O and CH 4 concentrations are not adequately represented in our data set, (iii) the windspeed-driven gas exchange in estuaries is not adequately represented, and (iv) the mean k 600 used here is most probably too high (see Sect. 3.3), resulting in an overestimation of the emissions. correlation with rainfall. We conclude, therefore, that rainfall, which determines the N 2 O production or consumption in the surrounding soils, is the main factor determining the riverine N 2 O concentrations. N 2 O production in the blackwater rivers themselves seems to be low because of the low pH. CH 4 concentrations were highest at salinity = 0 and most probably result from methanogenesis as part of the decomposition of organic matter under anoxic conditions. CH 4 concentrations in the blackwater rivers showed an inverse relationship with rainfall. We suggest that enhanced CH 4 oxidation in combination with a higher flux across the river-atmosphere interface during  periods of higher river flow (after rainfall events) is responsible for the reduction in the CH 4 concentrations along the salinity gradient. The rivers and estuaries studied here were an overall net source of N 2 O and CH 4 to the atmosphere. The total annual N 2 O and CH 4 emissions were 1.09 Gg N 2 O yr −1 (0.7 Gg N yr −1 ) and 23.8 Gg CH 4 yr −1 , respectively. This represents about 0.3 %-0.7 % of the global annual riverine and estuarine N 2 O emissions and about 0.1 %-1 % of the global riverine and estuarine CH 4 emissions. Rivers and estuaries in NW Borneo contribute only 0.05 % (= 7.9 × 10 2 km 2 including the surface areas of the Lupar and Saribas rivers; Müller et al., 2016a) to the global water surface area of rivers and estuaries (= 1.7 × 10 6 km 2 ; Maavara et al., 2019). Therefore we conclude that rivers and estuaries in NW Borneo contribute significantly to the global riverine and estuarine emissions of both N 2 O and CH 4 . The environment of Borneo (and SE Asia) is affected by rapid changes due to (i) anthropogenic activities such as conversion of peatland into oil palm plantations (see, e.g., Austin et al., 2018;McAlpine et al., 2018;Schoneveld et al., 2019) and (ii) climatic changes (see, e.g., Sa'adi et al., 2017a, b;Tang, 2019) which, in turn, could significantly affect N 2 O and CH 4 emissions from soils (see, e.g., Jauhiainen et al., 2016;Oktarita et al., 2017). But little is known about how these changes will affect N 2 O and CH 4 emissions from aqueous systems such as rivers and estuaries in the future. The obvious relationship of N 2 O and CH 4 concentrations and rainfall could be used to predict future concentrations and its associated emissions to the atmosphere. However, the trends of rainfall and river discharge in Borneo show a high local variability and no general common trend (Sa'adi et al., 2017a;Tang, 2019). Therefore, predictions of future trends of N 2 O and CH 4 emissions will be associated with a high degree of uncertainty. In order to improve our knowledge of predicted future changes in N 2 O and CH 4 riverine or estuarine emissions, we suggest establishing regular measurements in the rivers and along the salinity gradients. This will help decipher the temporal and spatial variability of N 2 O and CH 4 emissions from tropical rivers and estuaries. Moreover, studies of the relevant production or consumption pathways (and their main driving factors) for both gases are required. A suitable framework for this could be the recently published concept of the global N 2 O Ocean Observation Network (N2O-ON) (Bange et al., 2019). Author contributions. MM, CHS, AM and HWB designed the study. CHS performed the sample preparation during the campaigns. DB and JK performed the N 2 O/CH 4 measurements with support from AK. HWB prepared the paper with contributions from all co-authors.

Summary and conclusions
Competing interests. The authors declare that they have no conflict of interest.
Special issue statement. This article is part of the special issue "Biogeochemical processes in highly dynamic peat-draining rivers and estuaries in Borneo". It is not associated with a conference.
tions to the Maludam, Sebuyau and Simunjan rivers. Faddrine Yang, Gonzalo Carrasco, Florina Richard and Fakharuddin Muhamad assisted greatly during fieldwork and with logistics. We thank Edwin Sia and Faddrine Holt for the fantastic support of the N 2 O/CH 4 sampling during the fieldwork campaigns. We acknowledge the help of Lasse Sieberth with the N 2 O/CH 4 measurements. We thank two anonymous reviewers for their comments, which helped to improve the paper significantly.
The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.
Review statement. This paper was edited by Palanisamy Shanmugam and reviewed by two anonymous referees.