The Tamsui River is located in northern Taiwan (Figure 1) and has a total length of 159 km. The catchment area of the Tamsui River is 2,726 km², and it covers the whole metropolitan area of Taipei, the capital city of Taiwan. The drainage basin includes several regions along the main tributaries where large amounts of nutrients, resulting from industrial and agricultural activities, enter the river (Wen et al., 2008). The Tamsui River delivers materials, including suspended particles, nutrients, organic matter, and pollutants, from land into its estuary and adjacent marine areas. There were 7.13 million people living in the catchment, and approximately 60% of the population utilized the sanitary sewers in 2019 (Tseng et al., 2021). The largest wastewater treatment plant (WWTP) in Taiwan is located near the Tamsui River estuary (Figure 1), and its ocean outfall pipe extends from the shore and enters the ocean. The outlet of the ocean outfall pipe of the WWTP was located near sampling station 11 (Figure 1) and its diffuser tubes are 3 km from shore at water depths between 30 m and 40 m.

The regional climate is subtropical, with temperatures varying between 10 and 35 °C and annual precipitation ranging between 1500 and 2500 mm (Wen et al., 2008). The dry season ranges from November to April, and the wet season ranges from May to October. According to the historical data from the Tamsui weather station (Figure 1) over the past 25 years (1995-2020), the average rainfall is 776 ± 269 mm during the dry season, while it is 1322 ± 440 mm during the wet season (Central Weather Bureau: https://www.cwb.gov.tw/eng/).

Seasonal samples were taken in the Tamsui River estuary adjacent sea area (Figure 1) during four cruises onboard R/V Ocean Researcher 2 and R/V New Ocean Researcher 2: OR2-2390 (November 2019), NOR2-0004 (May 2020), NOR2-0009 (August 2020), and NOR2-0027 (January 2021). Discrete water samples were taken at various depths at 16 sampling stations in autumn (November 2019) and 20 sampling stations in spring (May 2020) and summer (August 2020). Due to the adverse weather conditions in winter (January 2021), discrete water samples were taken at various depths at 6 sampling stations, and surface water samples were taken at 10 sampling stations. The vertical profiles of seawater temperature and salinity were measured with a conductivity–temperature–depth instrument (CTD; SBE 9/11, Seabird Scientific, USA). Seawater samples from various depths were collected using a carousel water sampler (SBE32, Seabird Scientific, USA) that was fitted with 20 L Teflon-coated Go-Flo bottles (General Oceanic, USA) mounted on a CTD assembly.

Water samples for nutrient analysis were placed in 100 mL polypropylene bottles and immediately frozen with liquid nitrogen. The methods employed for nitrate (NO₃-) and phosphate PO₄³⁻ analysis are described in detail elsewhere (Gong et al., 1996; Gong et al., 2000), and the precision was ±0.3 and ±0.01 μmol L^-1, respectively. Dissolved oxygen (DO) was measured by spectrophotometry (Pai et al., 1993) with a precision of approximately ± 0.32% at the 190 μmol L^-1 level. Water samples for chlorophyll a (Chl a) analysis were immediately filtered through GF/F filter paper (Whatman, 47 mm) and stored at -20°C. A Turner Designs model 10-AU-005 fluorometer (Turner Inc., USA) was utilized to measure the Chl a concentration following extraction by 90% acetone (Strickland and Parsons, 1972; Gong et al., 1993; Gong et al., 1995).

Water samples for CH₄ concentration were collected in 120 mL dark borosilicate serum bottles. The bottles were rinsed three times with the sampled water. After a 2-fold bottle volume was allowed to overflow the bottle, 0.2 mL saturated HgCl₂ was added. It was then sealed with a butyl stopper and crimped with an aluminum cap. The samples were stored in a dark box and kept at 4°C. All the water samples were transferred to a laboratory and analyzed within three months of collection. Measurements were made with the headspace technique (Weiss, 1981) and a gas chromatograph (GC; Agilent 7890) with a flame ionization detector (FID). The GC-FID had a 1.8 m long stainless steel column with a diameter of 3.2 mm, which was filled with a 60/80 mesh molecular sieve 5A. The FID was calibrated with pure N₂ (Yeong Her, Taiwan) and three commercial gas mixtures with CH₄ mixing ratios of 1.16 ppmv (MESA Specialty Gas, USA), 3.02 ppmv (Yeong Her, Taiwan) and 9.60 ppmv (Yeong Her, Taiwan).

The saturation (R, %) and sea-to-air flux (F, μmol·m⁻²·d⁻¹) of CH₄ were calculated using the following formulas:

C_obs represents the observed concentration of gas dissolved in water, and C_eq is the expected equilibrium water concentration. The expected equilibrium water concentration was calculated using the solubility equation of (Wiesenburg and Norman, 1979), together with the in situ temperature, salinity and molar fraction of CH₄ in the air. The atmospheric CH₄ concentrations were taken from the NOAA/ESRL in situ program (http://www.esrl.noaa.gov/gmd). The monthly average atmospheric CH₄ concentrations at Mauna Loa (Hawaii, United States station) in November, 2019, May 2020, August 2020 and December 2020 were 1900, 1901, 1878 and 1912 ppb, respectively. (The data for Jan. 2021 have not yet come out; therefore, December 2020 monthly average atmospheric CH₄ concentrations were used).

Fluxes (μmol·m⁻²·d⁻¹) of CH₄ across the air-water interface were determined by C_obs−C_eq and the gas exchange coefficient k. The value of k is a specific function of the properties of the gas, the temperature (°C) and turbulence and is frequently parameterized as a function of the wind speed. In this study, wind speed at a height of approximately 15 m above the sea surface from a meteorological platform (121.3758°E 25.1817°N; Figure 1) was used. Daily wind speed data were provided by the Harbor and Marine Technology Center (https://www.ihmt.gov.tw/). We calculated k by using the equation established by Wanninkhof (2014). A positive flux indicates gas transfer from the water to the atmosphere.

In autumn, the seawater temperature and salinity ranged from 18.9 to 24.0°C and 33.45 to 34.30 (Table 1), respectively. The seawater temperature gradually decreased with depth (Figure 2A), and the lowest salinity values were observed near shore (Figure 2B). The P O 4 3 − and N O 3 − concentrations ranged from 0.26 to 0.78 μM and 2.9 to 9.4 μM (Table 1), respectively. The nutrient concentrations increased with depth and from offshore to inshore (Figures 2C, D). Chl a concentrations ranged between 0.15 and 1.50 mg m^-3 (Table 1) and gradient descent from the surface water (Figure 2E). DO concentrations ranged between 186.7 and 228.9 μM (Table 1) and had the same pattern as the Chl a distributions (Figure 2F). CH₄ concentrations ranged from 1.4 to 78.0 nM (Table 1), and high CH₄ concentrations were observed near station 11, where the outlet of the ocean outfall pipe which discharged the WWTP effluents was located (Figure 2G). The average surface seawater CH₄ concentration was 13.7 ± 18.7 nM. Long-term wind speed data from the meteorological platform were used, and the average wind speed in November between 2005 and 2019 was 7.9 ± 0.8 m/s. The sea-to-air CH₄ flux was 46.3 ± 75.4 μmol m^-2 d^-1 (Table 2).

In winter, only surface water was taken between stations 5 and 9 so there was no cross-sectional figure due to the adverse weather conditions caused by the prevailing northeast monsoon. According to the data from 10 sampling stations, the seawater temperature and salinity ranged from 18.4 to 19.4°C and 33.06 to 34.35 (Table 1), respectively. Although nutrient concentrations were comparably high, with P O 4 3 − and N O 3 − concentrations ranging from 0.44 to 0.85 μM and 6.0 to 8.5 μM, the Chl a concentrations were low, ranging between 0 and 0.30 mg m^-3 (Table 1). DO concentrations were comparably high and ranged between 227.7 and 252.4 μM (Table 1), which might be caused by low temperature and high wind ventilation. Wind speed data between 2005 and 2019 from the meteorological platform were used, and the average wind speed in January was 8.0 ± 0.8 m/s. CH₄ concentrations ranged from 5.4 to 69.6 nM, and the average surface CH₄ concentration was 27.0 ± 21.4 nM. With a comparably high wind speed, the sea-to-air CH₄ flux was as high as 90.4 ± 79.3 μmol m^-2 d^-1 (Table 2).

In spring, the seawater temperature and salinity ranged from 26.0 to 27.2°C and 31.68 to 34.46 (Table 1), respectively. The seawater temperature was homogeneous throughout the water column (Figure 2H). The P O 4 3 − and N O 3 − concentrations ranged from 0.12 to 0.87 μM and 0 to 3.7 μM (Table 1), respectively. Low salinity and high nutrient concentrations were observed in the surface water and near the shore (Figures 2I–K) due to heavy precipitation on the sampling date. Chl a concentrations ranged between 0 and 0.77 mg m^-3 (Table 1) and had higher concentrations nearshore (Figure 2L). DO concentrations ranged between 193.1 and 216.0 μM (Table 1) and had a similar pattern as the Chl a distributions (Figure 2M). CH₄ concentrations ranged from 4.3 to 77.4 nM (Table 1), and high CH₄ concentrations were observed near the shore (Figure 2N). The average surface seawater CH₄ concentration was comparably high at 29.3 ± 19.8 nM. The average wind speed in May 2005 and 2019 from the meteorological platform was 5.0 ± 0.6 m/s. The sea-to-air CH₄ flux was 47.2 ± 34.3 μmol m^-2 d^-1 (Table 2).

In summer, the seawater temperature and salinity ranged from 27.0 to 30.8°C and 33.62 to 34.20 (Table 1), respectively. The seawater temperature gradually decreased with depth (Figure 2O), and low salinity values were observed near shore (Figure 2P). The P O 3 − and N O 3 − concentrations ranged from 0.09 to 0.49 μM and 0 to 4.7 μM (Table 1), respectively. Chl a and DO concentrations ranged from 0.15 to 1.60 mg m^-3 and 185.0 to 209.4 μM (Table 1), respectively. High nutrient and Chl a concentrations appeared nearshore (Figures 2Q-S) with low salinity (Figure 2P), which indicated freshwater input from the shore. CH₄ concentrations ranged from 5.0 to 58.5 nM (Table 1), and high CH₄ concentrations were observed near the outlet of the ocean outfall pipe (Figure 2U). The average surface seawater CH₄ concentration was 21.8 ± 13.9 nM. The average wind speed in August between 2005 and 2019 from the meteorological platform was 5.0 ± 0.7 m/s. The sea-to-air CH₄ flux was 37.0 ± 26.2 μmol m^-2 d^-1 (Table 2).

Wastewater is a major anthropogenic source of CH₄ and one of the fastest growing sources of CH₄ emissions (Kirschke et al., 2013). According to the IPCC (2013), the wastewater CH₄ emissions from 2000 to 2009 represented 22.7% of all anthropogenic CH₄ emissions. Du et al. (2018) reported that CH₄ emissions from wastewater in China increased from 1349.01 Gg in 2000 to 3430.03 Gg in 2014, and the highest proportion of emissions was from WWTPs. Cotovicz et al. (2016) found that high CH₄ concentrations could be sustained by allochthonous sources, such as sewage networks and polluted rivers, especially under high accumulated precipitation conditions. Yu et al. (2017) also pointed out that high CH₄ concentrations are frequently found in the water of urban drainage systems, composed of sewer systems, and WWTPs. According to Figure 2, CH₄ concentrations were high from the bottom to the surface water near station 11, where the outlet of the ocean outfall pipe of the WWTP was located. In addition, most of the water samples near the ocean outfall pipe of the WWTP did not follow the Redfield ratio (Figure 3) and were high in surface CH₄ concentrations (Figure 4). Moreover, the highest CH₄ concentrations in the water column were found near the ocean outfall pipe of the WWTP (Figures 2G, N, U). The inputs from WWTP effluents contributed to the increase in the CH₄ concentrations in the study area. The average seasonal surface CH₄ concentrations were 13.7 ± 18.7, 29.3 ± 19.8, 21.8 ± 13.9 and 27.0 ± 21.4 nM in autumn, spring, summer and winter, respectively. If water samples near the ocean outfall pipe of the WWTP were excluded, the average seasonal surface CH₄ concentrations then became 9.6 ± 8.9, 21.5 ± 13.2, 18.0 ± 8.2 and 15.4 ± 9.1 nM in autumn, spring, summer and winter, respectively. This finding shows that approximately 17-43% of the surface CH₄ concentrations in the study area were influenced by the WWTP effluents. The average annual sea-to-air CH₄ flux was 56.5 ± 22.3 μmol m^-2 d^-1 and reached 35.2 ± 8.4 μmol m^-2 d^-1 when excluding the water samples near the ocean outfall pipe of the WWTP. This result indicated that WWTP effluents influenced approximately one-third of the CH₄ emissions in the study area.

In addition to the inputs from WWTP effluents, freshwater also contributed to the CH₄ concentrations in the Tamsui River estuary adjacent marine area. The Tamsui River is a small mountain river with an average flow rate of approximately 210 m³/s. Although the Tamsui River transferred a comparably small amount of water mass to its adjacent marine areas, it brought high concentrations of CH₄ and nutrients. Figure 2 shows high concentrations of CH₄ and nutrients with slightly low salinity nearshore. Dissolved inorganic nitrogen (DIN) concentrations represented the nitrogen level in the water and were well correlated with CH₄ concentrations (Figure 5A). CH₄ and P O 4 3 − concentrations also showed a positive correlation (Figure 5B). According to Nijman et al. (2021), nutrients increased methane-oxidizing bacterial (MOB) abundance and methane oxidation potential, while warming only increased MOB abundance without altering methane oxidation potential. Thus, the differences of seawater temperature might result in different linear regressions between wet and dry seasons (Figures 5A, B).

Seasonal variations of CH₄ concentration in the Tamsui River ranged between 362 and 2961nM (unpublished data). Rivers brought high concentrations of CH₄ and organic matter to coastal water (Chen et al., 2008; Zhang et al., 2008; Tseng et al., 2017; Sun et al., 2018). Coastal sediment which is rich in organic matter has been proposed to be the origin of CH₄ (Borges and Abril, 2011; Tseng et al., 2017). In addition, high CH₄ concentrations are frequently attributed to sedimentary methanogenesis in coastal environments (Bange, 2006; Zhou et al., 2009), especially in shallower waters. Borges et al. (2018) also found a seasonal peak of CH₄ in the nearshore and shallow seep areas in the Belgian coastal zone during summer, which was related to sediment organic matter content. Figure 6 shows that CH₄ concentrations in the bottom water gradually decreased with the bottom depth. This result might be related to low abundance of methanotrophs in shallow coastal zones so more CH₄ seeps escaping from the sediment and higher CH₄ concentrations in the bottom water (Broman et al., 2020). According to our results, the CH₄ concentration in the bottom water did not influenced by the sediment input when the depth deeper than 90m. This might be due to CH₄ oxidized in the sediment before it released to the bottom water. According to the Sewerage Systems Office of the Public Works Department of the Taipei City Government, the ocean outfall pipe of a WWTP extends from shore, and its diffuser tubes are at water depths between 30 m and 40 m. Samples in the bottom water near the diffuser tubes were high in CH₄ concentrations (Figure 6).

Except for four individual observations in autumn, the surface water was supersaturated in CH₄ with respect to the atmosphere at most stations in the Tamsui River estuary adjacent marine area during the four cruises, which indicated that the study area was a net source of atmospheric CH₄. The average surface seawater CH₄ concentration varied between 13.7 and 29.3 nM (Table 2). The average surface seawater CH₄ concentrations were higher in spring, summer and winter (29.3, 21.8 and 27.0 nM) and lower in autumn (13.7 nM). In spring and summer (wet seasons), river discharge was more due to high precipitation and brought high concentrations of nutrients and CH₄ from land to sea. In addition, relatively strong vertical mixing and disturbances might bring high CH₄ concentrations from the bottom to the surface water in winter.

Figure 7 shows the average 15-year (2005-2019) monthly wind speed from the meteorological platform. In autumn, low river discharge and the wind speed was just picking up after October so the vertical mixing was relatively weak comparing with that in winter, which resulted in the lowest average surface seawater CH₄ concentrations. The wind speeds were higher in autumn and winter than in spring and summer (Table 2). The sea-to-air CH₄ flux variability was within the range of -3.0–308.9 μmol m^-2 d^-1. The average sea-to-air CH₄ flux was the highest in winter (90.4 μmol m^-2 d^-1), followed by spring and autumn (47.2 and 46.3 μmol m^-2 d^-1) and was lowest in summer (37.0 μmol m^-2 d^-1).

When compared globally, the Scheldt estuary in the North Sea has the highest surface CH₄ concentrations in its adjacent marine area, followed by the Tamsui River, Changjiang, and Pearl River (Table 3). In regard to the sea-to-air CH₄ fluxes, the adjacent marine areas of Scheldt and Tamsui River are the highest. Extremely high CH₄ was observed near the Scheldt estuary adjacent marine area due to gassy sediments (Borges et al., 2016), and its emission may be increased when the ocean warms (Borges et al., 2018). Furthermore, inputs from WWTP effluents increased CH₄ concentrations in the Tamsui River estuary adjacent marine area, and this situation may be worsened when the population grows.