The survey was carried out in the summer (23 July–3 August) and Autumn (23 October–6 November) of 2020 and a total of 60 stations were investigated ( Figure 1 ). Water samples were collected from two to three water layers with a 4 L×6 SBE 55 eco multi-channel water sample collector. Vertical distributions of temperature and salinity were simultaneously obtained with a RBRmaestro multi-parameter logger (RBR, Ottawa, Canada). On board, DO, N₂O, and pH samples were instantly transferred from the water sample collector into 100 mL brown glass bottles, 60 mL brown glass bottles, and 250 mL polypropylene bottles, respectively. We followed the Winkler method to transfer, store, and analyze the DO samples (Grasshoff et al., 2009); pH samples were measured on board using the Mettler Toledo Seven Compact series pH meter (S210-K) (Mettler Toledo Technologies, Zurich, Switzerland) equipped with an Expert Pro pH probe (Mettler Toledo Technologies, Zurich, Switzerland).

N₂O samples were collected by the following procedure. A silicone sampling tube was inserted into the bottom of the glass bottle (60 ml, CSN, Shanghai City, China) and filled with seawater (avoiding air bubbles). When the sample was full and overflowed at least twice the volume of the glass bottle, the silicone sampling tube was slowly withdrawn and the convex surface was maintained while saturated mercury chloride solution (0.2 ml) was added. Each bottle was covered with a butyl rubber stopper and sealed with a polyethylene cap. After collection, samples were transferred and stored in the dark under refrigeration at 4°C. Dissolved N₂O concentrations in seawater samples were determined by static headspace-gas chromatography, with HP-Plot/column (J&WGC column, Agilent Technologies, USA) with an electron capture detector. We used standard gases of N₂O (291, 617, and 4980 ppb) to calibrate the ECD.

The apparent oxygen utilization (AOU) is calculated as the difference between the equilibrium concentrations of dissolved oxygen ([O₂]_eq) at in-situ water temperature and salinity and the observed oxygen concentration. [O₂]_eq was estimated based on the equation of Weiss (1970). Excess N₂O (ΔN₂O) is the difference between the observed N₂O concentration (([N₂O]_obs)) and the equilibrated N₂O concentration ([N₂O]_eq) at the in-situ temperature and salinity. The [N₂O]_eq was calculated using the equation of Weiss and Price (1980).

The sample collection and determination of DIN ( NH 4   + , NO 2   ‐ , and NO 3   ‐ ) were conducted according to the following steps. Water samples (200 mL) were filtered with a GF/F filter membrane (25 mm diameter, 0.7 μm pore size, Whatman, UK) at low pressure (<0.05 MPa). The filtrate was frozen until it was transported to the laboratory and analyzed. The concentration of DIN was measured with an AA3 Auto-Analyzer (SEAL Analytical, Norderstedt, Germany) according to the classical colorimetric methods. NH 4   + was measured by the indophenol blue method. NO 3   ‐ and NO 2   ‐ were measured by the copper-cadmium column reduction method and α-Naphthylamine method, respectively (Ehrhardt and Kremling, 2007).

The N₂O saturation (R, %) and sea-air emission flux (F, μmol m^-2 d^-1) were estimated as follows:

where the [ N 2 O ] obs and [ N 2 O ] eq refer to the observed dissolved N₂O concentration in the surface layer and equilibrated N₂O concentration corresponding to the temperature and salinity at the site (Weiss and Price, 1980). K (cm h^-1) is the gas transport velocity, calculated from the wind speed (U₁₀) and the Schmidt number (Sc). There are different equations for calculating K (Liss and Merlivat, 1986; Nightingale et al., 2000; Ho et al., 2006; Wanninkhof, 2014). Recently, the equations of K by Nightingale et al. (2000) and Wanninkhof (2014) were widely used in the shelf seas, such as the BS, the East China Sea, and the Yellow Sea (Chen et al., 2021; Gu et al., 2021). In order to compare the N₂O fluxes between BHB and other shelf seas, the above two equations of K were supplied in our study. The formulas are as follows:

where U₁₀ (m s⁻¹) is the average of wind speeds measured at a height of 10 m above the sea surface with a shipboard automatic weather station for each cruise.

We used an aggregated boosted tree (ABT) to analyze and estimate the relative influence of the environmental variables of the water column on the N₂O concentrations based on the “gbmplus” package in R (De’ath, 2001; Elith et al., 2008). Multiple linear regression (MLR) models with forward selection were applied to analyze the relative quantitative effect of the environmental parameters on the N₂O concentration, according to the regression coefficients of the MLR equation (Duan et al., 2012). Generalized additive models (GAM) were used to analyze the correlation between N₂O response and the top three most dominant environmental variables ( NH 4   + , DO, and temperature). The fitting of GAM models was performed by the ‘mgcv’ package in R to individually fit the responses of NH 4   + , DO, and temperature to N₂O concentrations. Moreover, the relationships between the AOU and NO 3   ‐ versus ΔN₂O were investigated with simple unary linear regression analysis. Both the multiple and unary linear regression were performed using SPSS software (version 23.0).

Temperature and salinity in seawater showed spatial-temporal variation ( Figure 2 ). The average temperature of seawater in summer (25.4 ± 2.7 °C) from all the water layers was observed to be higher than in autumn (15.8 ± 1.0 °C). In summer, the temperature in the three layers exhibited a declining gradient from the coastal to the offshore area, especially in the bottom layer. The temperature distribution patterns of the three layers in autumn were completely different from that in summer, with low temperatures in the coastal area and high temperatures in the center of BHB. The average temperature in summer was approximately 10°C higher than in autumn. Compared to temperature, the variation of salinity in BHB was relatively small and mainly occurred in the estuary as controlled by diluted water input from rivers. Evident gradients of salinity occurred in the estuary of the Hai River and the Yellow River, which deliver the largest freshwater input into BHB. In addition, the ranges of the depth for each layer (surface layer, middle layer and bottom layer) were set by averagely dividing the depth of water column into three parts. The temperature and salinity show relatively small vertical gradients and exhibit similarities between the surface, middle, and bottom layers.

The average NH 4   + concentrations were higher in summer (2.6 ± 1.6 μmol L^-1) than in autumn (1.7 ± 2.1 μmol L^-1) ( Figure 3 ). The hotspots of NH 4   + mainly occurred in the Hai River estuary, the coast of Caibeidian and Huanghua, and central BHB. The DO temporal distribution showed the mean DO concentrations in autumn was higher than in summer. Low DO concentrations were mainly observed in the Hai River estuary areas ( Figure 3 ).

Average N₂O concentrations were found to be higher in summer (32.3 ± 6.5 nmol L^-1) than in autumn (23.2 ± 4.6 nmol L^-1) and the N₂O distribution patterns of the two seasons were also distinct ( Figure 4 ). In summer, the three layers exhibited a similar distribution pattern of N₂O concentration, with average concentrations of 32.6 ± 6.4, 32.9 ± 6.6, and 32.4 ± 7.7 nmol L^-1 in the surface, middle, and bottom layers, respectively. N₂O hotspots occurred in the estuaries of the Yellow River and the Hai River, and the coastal waters adjacent to the Caofeidian and Huanghua. Other areas had relatively low concentrations and the lowest concentrations occurred at the northern mouth of BHB because of the inflow of water with low N₂O concentration from the central basin of the BS. In autumn, N₂O distributions were still similar in the three layers, with average concentrations of 23.6 ± 8.1, 23.1 ± 3.1, and 22.7 ± 4.4 nmol L^-1 in the surface, middle, and bottom layers, respectively. Unlike summer, besides the Hai River estuary and coastal waters adjacent to the Caofeidian, high N₂O concentrations were found at the center of BHB.

A section in BHB was chosen to study the seasonal and spatial variations in the vertical distributions of N₂O as well as temperature, salinity, DO, and NH 4   + ( Figures 5 , S1 ). The transect spans the entire BHB from the Hai River estuary to the Yellow River estuary ( Figure 5 ). The temperature decreased from the Hai River estuary (summer: 27.1 ± 1.2 °C; autumn: 16.0 ± 0.4 °C) to the Yellow River estuary (summer: 24.2 ± 0.6 °C; autumn: 15.3 ± 0.02 °C), while salinity decreased from the Hai River estuary (28.5 ± 3.1 pus) and the Yellow River estuary (29.7 ± 0.2 pus) to the offshore sea (31.4 ± 0.8 pus) in the two seasons. Low DO concentrations were found in the Hai River estuary with the lowest DO concentrations observed in the bottom layer. Elevated NH 4   + concentrations occurred in the Hai River estuary with higher concentration observed in autumn than in summer. In addition, the vertical profiles of N₂O in BHB exhibited a higher variation in summer than in autumn. In summer, the highest N₂O concentrations occurred at the bottom of the Yellow River and the Hai River estuary, whereas low N₂O concentrations were found far from the estuaries. In autumn, except for a N₂O hotspot in the surface water of Hai River estuary, the transect showed relatively uniform vertical distribution, likely due to strong vertical mixing generated by high wind speeds (up to 10.4 m s^-1) and shallow water depths.

In general, N₂O saturations in the surface layer were found to be higher in summer than in autumn, with a mean value of 495.1 ± 101.0% and 249.8 ± 80.4% in summer and autumn, respectively ( Table 1 ; Figure S2 ). Figure 6 and Table 1 show the N₂O emissions from the two seasons. We found that fluxes estimated by the equations of Nightingale were on average 93.9% of fluxes estimated by Wanninkhof. Figure 6 shows that all fluxes of N₂O were observed to be positive for the two seasons in BHB, with average fluxes in summer (32.0 ± 8.3 μmol m^-2 d^-1) higher than in autumn (19.1 ± 11.5 μmol m^-2 d^-1).

Variations of N₂O concentrations in different seasons were evident and average N₂O concentrations were observed to be higher in summer than in autumn, which was similar to results reported in the central BS, the East China Sea, and the Yellow Sea (Chen et al., 2021; Gu et al., 2021). As the main substrate of nitrification in N₂O production (Katipoglu-Yazan et al., 2012), average concentrations of NH 4   + were higher in summer than in autumn, which is beneficial for the promotion of N₂O. Moreover, owing to the development of the monsoon in July and August, rainfall and heat become abundant in summer. On one hand, high temperature in summer supports high N₂O production; on the other hand, due to high precipitation and riverine runoff, the diluted water with high N₂O concentrations, e.g., the Yellow River (Ma et al., 2016), elevates N₂O input from rivers in summer. However, since the nutrients and organic matter in the water column and sediment are largely consumed in summer at high temperatures, the activities of microbes decline in autumn (Liu et al., 2016), which limits in situ production of N₂O from nitrification and denitrification in the water and sediment in autumn.

The horizontal distribution of N₂O was not uniform. N₂O hotspots mainly occurred in the estuarine and coastal areas due to riverine and coastal discharge, mixing of water masses, and in situ N₂O production, which is discussed in the following section of “main sources of N₂O”. Wind and shallow depths in BHB led to well vertical mixing in summer and autumn, with a similar spatial distribution of N₂O concentrations found in the three water layers ( Figure 4 ).

The dominant environmental factors that influence N₂O concentrations in the water column of BHB were NH 4   + , DO, and temperature base on ABT analysis over different seasons and regions in BHB. According to the multiple linear regression, N₂O was also mainly controlled by the three factors and the relationship can be described as: [N₂O] =1.5 × [ NH 4   + ]-1.4 × [DO] + 0.4 × Temperature +26.4 (P< 0.0001, R² = 0.74).

The ABT analysis shows that the influence of NH 4   + on the N₂O concentrations surpassed other factors ( Figure 9 ). NH 4   + concentration, a good indicator of pollution, was positively related to N₂O concentrations. This is reasonable because the high NH 4   + -N level may increase N₂O accumulation via nitrification, which also had been demonstrated in high population density areas (Xia et al., 2013; Hu et al., 2016). According to the results of the non-linear GAM, N₂O concentrations increased with increasing NH 4   + concentration, and rates of NH 4   + /N₂O were higher when NH 4   + exceeded approximately 8 μmol L^-1. In addition, the stations with high NH 4   + (> 8 μmol L^-1) are generally in the estuaries in summer. Therefore, in addition to in-situ production, riverine N₂O input could also contribute to the positive relationship between NH 4   + and N₂O. Based on the ABT model, DO was the second most important controlling factor, and N₂O concentrations increased with decreasing DO. The temperature was the third important factor and had a dual effect on the N₂O concentrations. With higher temperatures, the N₂O solubility decreases, whereas the microbial activity of nitrification and denitrification are promoted, increasing N₂O production (Bo et al., 2018). Figure 8 points out that the N₂O concentrations in BHB were positively related to temperature, indicating the promotion of microbial activity exceeded the influence of lower solubility of the gas in the water column.

All N₂O air-sea fluxes were positive in the two seasons and the average fluxes in both seasons indicated that the BHB region was an evident source of N₂O to the atmosphere. High spatiotemporal variability of N₂O emission fluxes was observed in BHB. N₂O fluxes were calculated based on ΔN₂O and the gas transport velocity which is positively related with the wind speed in the surface layer. The mean wind speeds in summer (3.8 ± 1.4 m s^-1) were a bit lower than in autumn (4.7 ± 2.7 m s^-1); however, the fluxes still reached their peak in the summer. Therefore, the wind speed was not the major factor driving the higher N₂O flux in summer. In summer, N₂O concentration was higher, while the lower [N₂O]_eq also occurred due to the higher surface temperature and consequently lower N₂O solubility. Thus, the combination of the two factors above leads to higher ΔN₂O in summer, which is the main reason for seasonal variation of N₂O flux in BHB. Previous researches have shown a relatively higher flux in summer compared to autumn in Jiaodong Bay, the central BS and East China Sea (Zhang et al., 2006; Chen et al., 2021; Gu et al., 2021), which is consistent with our results.

High fluxes were observed in the estuaries, along the coast, and in central BHB, which coincided with the N₂O hotspots in BHB. Because the emissions have been estimated from the average wind speed for each cruise, wind speeds cannot account for intra-season spatial variability. In summer, surface temperatures were relatively similar in terms of spatial distribution, and thus N₂O concentration dominated the pattern of N₂O flux distribution. In autumn, because of the high temperatures and N₂O concentrations in central BHB, the flux of N₂O was relatively high.

Based on the N₂O fluxes of summer and autumn, the annual mean N₂O flux was 25.5 ± 11.8 μmol m^-2 d^-1. The total area of BHB is 1.6 × 10⁴ km², which is about 0.0044% of the total global ocean area, and the corresponding area-integrated flux was 1.5 × 10⁸ mol yr^-1 (6.5 Gg yr^-1), accounting for about 0.15% of the world marine N₂O emission (4.2 × 10³ Gg yr⁻¹) (Yang et al., 2020). Results are comparable to the N₂O fluxes observed in the bays with high human pollution ( Table 2 ), e.g., Tokyo Bay and Jiaozhou Bay (Hashimoto et al., 1999; Zhang et al., 2006), but they are higher than those reported for open oceans (Han and Zhang, 2015; Ma et al., 2020; Heo et al., 2021), an unpolluted bay (Prydz Bay, Antarctica) (Zhan et al., 2015) and two continental shelf seas (the BS and the Yellow Sea) (Gu et al., 2021). Although we reported relatively high annual fluxes in BHB based on summer and autumn data, the fluxes could be overestimated due to relatively higher fluxes in summer compared to other seasons (Chen et al., 2021; Gu et al., 2021). Therefore, more studies covering all four seasons are needed to improve the flux estimates.