Water was collected from 1 m depth by using a Niskin sampler. Subsamples for N2O and CH4 were taken as duplicates or triplicates in 20 or 37 mL glass vials. The vials were 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 (HgCl2) solution was immediately added to stop any biological activity, and samples were stored at 4 ∘C until shipment. The samples were shipped to GEOMAR Helmholtz Centre for Ocean Research Kiel, Germany, for further analysis within a few weeks after sampling. For the determination of the N2O and CH4 concentrations, we applied the static-headspace equilibration method followed by gas chromatographic separation and detection with an electron capture detector (ECD; for N2O) and a flame ionization detector (FID; for CH4) 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 N2O and 1806.10–3003.79 ppb CH4 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.

Dissolved N2O/CH4 concentrations (Cobs in nmol L-1) were calculated with 1Cobs=x′PVhs/(RTVwp)+x′βP, where x′ is the dry mole fraction of N2O or CH4 in the headspace of the sample, P is the ambient pressure (set to 1013.25 hPa), and Vhs and Vwp are the volumes of the headspace and the water phase, respectively. R stands for the gas constant (8.31451 m3 Pa K-1 mol-1), T is the temperature during equilibration, and β is the solubility of N2O or CH4 (Weiss and Price, 1980; Wiesenburg and Guinasso Jr., 1979). The estimated mean relative errors of the measurements were ±9 % and ±13 % for N2O and CH4, 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 CH4 samples (compared to the N2O measurements) was attributed to the fact that CH4 samples are more sensitive to storage time than N2O samples (Wilson et al., 2018).

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 HgCl2 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).

The saturations (Sat, %) for N2O, CH4 and O2 were calculated as 2Sat=100∘Cobs/Ceq, where Ceq is the equilibrium concentration of N2O/CH4/O2 calculated according to Weiss and Price (1980), Wiesenburg and Guinasso Jr. (1979), or Weiss (1970), respectively, with the in situ temperature and salinity as well as the mean dry mole fractions of N2O/CH4 at the time of the sampling. Mean monthly N2O/CH4 dry mole fractions of 329/1841×10-9 (ppb), 331/1880 and 330/1852 ppb for August 2016, March 2017 and September 2017, respectively, were measured at the atmospheric monitoring station Bukit Kototabang, located on the west coast of Sumatra (Indonesia). This station is operated by the NOAA/ESRL Global Monitoring Division program and data are available from http://www.esrl.noaa.gov/gmd (last access: 4 November 2019). A saturation <100 % indicates a concentration lower than the theoretical equilibrium concentration (i.e. undersaturation), and a saturation >100 % indicates supersaturation.

Flux densities (F, nmol m-2 s-1) were calculated as 3F=kw(Cobs-Ceq),4kw=k600(Sc/600)-0.5. kw 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 N2O or CH4 in water (Jähne et al., 1987; Rhee et al., 2009). k600 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 k600 values measured by Müller et al. (2016a) are representative of the rivers in NW Borneo studied here. Mean k600 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 k600 of 19.2 cm h-1 (5.33×10-5 m s-1), which we used to estimate the flux densities of N2O and CH4. This k600 is in good agreement with the mean k600 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. kw in rivers depends on the turbulence at the river is water–atmosphere 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 k600 reported by Müller et al. (2016a) was determined only during the wet season (March 2014), our mean k600 is biased because it does not account for a lower k600, 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.

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 N2O and CH4 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.

The measured ranges of N2O concentrations and saturations are listed in Table 3 and the distributions of N2O saturations along the salinity gradients are shown in Fig. 2. N2O concentrations (saturations) were highly variable and ranged from 2.0 nmol L-1 (28 %) in the Rajang River (at salinity = 0 in August 2016) to 41.4 nmol L-1 (570 %) in the Simunjan River (at salinity = 0 in March 2017). N2O concentrations in the Rajang, Maludam and Sebuyau rivers were generally higher in September compared to March 2017 (Fig. 2a–c). A decreasing linear trend of the N2O saturations with salinity was only observed for the Rajang River in March 2017 (Fig. 2a) indicating a conservative mixing and no N2O sources or sinks along the salinity gradient. Our results are in general agreement with the N2O measurements in the Lupar and Saribas rivers (which are located in close vicinity of the Maludam River) in June 2013 and March 2014: Müller et al. (2016a) measured N2O concentrations (saturations) from 6.6 to 117 nmol L-1 (102 % to 1679 %) in the Lupar and Saribas rivers. Salinity and N2O concentrations in the Lupar and Saribas rivers were negatively correlated in June 2013 but were not correlated in March 2014 (Müller et al., 2016a). In contrast with our study, no N2O undersaturations have been observed by Müller et al. (2016a). Our results are at the lower end of N2O concentrations reported from rivers around the globe, which can range from extreme undersaturation (down to about 3 %, i.e. almost devoid of N2O) 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 (Borges et al., 2018).

Maximum N2O 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 N2O 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 N2O with O2 or NO3-, NO2-, NH4+ and DIN. Therefore, it is difficult to decipher the major consumption or production processes of N2O or to locate the influence of (local) anthropogenic input of nitrogen compounds on riverine N2O 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 N2O correlations with O2 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 N2O concentrations along the pH gradients. Obviously there are no trends except for an enhancement of the N2O concentrations in September 2017. N2O production via nitrification depends on the prevailing pH because nitrifiers prefer to take up ammonia (NH3). The concentration of dissolved NH3 drops significantly at pH < 8–9 (Bange, 2008) because of its easy protonation to ammonium (NH4+). A low pH of about 5–6 can reduce nitrification (NH4+ oxidation) significantly as was recently shown for the Tay Ninh River in Vietnam (Le et al., 2019). Moreover, the optimum for a net N2O production by nitrification, nitrifier denitrification and denitrification lies between a pH of 7 and 7.5 (Blum et al., 2018). Therefore, a net N2O production may be low in the blackwater rivers studied here because of their low pH (see Table 1). The observed N2O supersaturations, therefore, might have been mainly the result of external inputs of N2O-enriched waters or groundwater. The observed N2O 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 N2O 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 N2O production or consumption (Jauhiainen et al., 2016). See also discussion in Sect. 4.3.

The measured ranges of CH4 concentrations and saturations are listed in Table 3, and the distributions of CH4 saturations along the salinity gradients are shown in Fig. 4. CH4 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 CH4 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.) CH4 saturations in the Rajang, Maludam, Sebuyau and Simunjan rivers were higher in March 2017 compared to September 2017. Maximum CH4 concentrations were measured at salinity = 0, and there was a general decrease in CH4 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 CH4 (Fig. 3). The range of CH4 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 CH4 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 CH4 saturations between the rivers classified as undisturbed and those classified as disturbed in both March and September 2017.

We found no overall trends of CH4 with O2 or dissolved nutrients or DOC along the salinity gradients. There are, however, occasional observations in tropical rivers of CH4 relationships with O2, which were attributed to different river types such as swamp and savannah rivers (Upstill-Goddard et al., 2017). High CH4 concentrations, which were often associated with high DOC and low O2 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 CH4 with increasing salinity can be attributed to the gas exchange across the river water–atmosphere interface in combination with CH4 oxidation (Borges and Abril, 2011; Sawakuchi et al., 2016).

Mean N2O concentrations showed linear correlations with accumulated rainfall during different periods from 1–4 weeks before the dates of sampling (Fig. 5, Table 6). Enhanced N2O 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 N2O production mainly via denitrification in a suboxic–anoxic soil environment (Espenberg et al., 2018; Pihlatie et al., 2004). N2O 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 N2O concentrations with rainfall might result from enhanced N2O production in the adjacent soils drained by the rivers. A decreasing trend of N2O 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 river–atmosphere interface (Alin et al., 2011) – is obviously outcompeted by an enhanced input of N2O.

In contrast with N2O, the response of riverine or estuarine CH4 concentrations to increasing rainfall does not result in increasing CH4 concentrations (Fig. 5). When considering the periods of 1 or 1.5 weeks of accumulated rainfall there seems to be a pronounced decrease in CH4 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 CH4 concentrations and river discharge (Anthony et al., 2012; Bouillon et al., 2014; Dinsmore et al., 2013; Hope et al., 2001). This relationship can be explained by an interplay of various processes such as (i) a decrease in CH4 concentrations caused by a higher water flow (i.e. dilution under the assumption that the net CH4 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 CH4 oxidation during high waters: Sawakuchi et al. (2016) showed that CH4 oxidation in blackwater rivers of the Amazon Basin was maximal during the high-water season.

The N2O flux densities from the six rivers studied here are comparable to the N2O flux densities from other aqueous and soil systems reported from Borneo and other sites in SE Asia; see Table 4. The corresponding CH4 flux densities are higher than the CH4 flux densities reported for the Lupar and Saribas rivers but much lower than the flux densities from drainage canals in Central Kalimantan and Sumatra (Jauhiainen and Silvennoinen, 2012) (Table 4). Our CH4 flux densities are, however, comparable to recently published CH4 eddy covariance measurements (Tang et al., 2018) in the Maludam National Park, which is drained by the Maludam River, and measurements of the CH4 release from peat soils when the water table is high and CH4 from rice paddies (Couwenberg et al., 2010); see Table 4. The mean annual N2O and CH4 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 N2O emissions for the rivers in NW Borneo – including the emissions from the Lupar and Saribas rivers (Müller et al., 2016a) – are 1.09 Gg N2O yr-1 (0.7 Gg N yr-1). This represents about 0.3–0.7 % of the global annual riverine and estuarine N2O emissions of 166–322 Gg N2O (106–205 Gg N yr-1) recently estimated by Maavara et al. (2019). The total annual CH4 emissions from rivers in NW Borneo are 23.8 Gg CH4 yr-1. This represents about 0.1 %–1 % of the global riverine and estuarine CH4 emissions of 2300–33 400 Gg CH4 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 N2O and CH4 concentrations are not adequately represented in our data set, (iii) the wind-speed-driven gas exchange in estuaries is not adequately represented, and (iv) the mean k600 used here is most probably too high (see Sect. 3.3), resulting in an overestimation of the emissions.