N₂O fluxes from the sea surface to the atmosphere were calculated to be the difference between measured N₂O (C _mea) concentration and computed N₂O equilibrium concentration with the equation as below:

where F suggests the flux of N₂O (μmol/m²/d); and C _eq denotes the air-equilibrated seawater N₂O concentration, which can be computed for in situ temperatures and salinities based on solubility data (Weiss and Price, 1980). N₂O in the atmosphere had not been observed by the surveys. In this study, global mean atmospheric N₂O mixing ratios of 330 ppb in 2017 and 331 ppb in 2018 from NOAA/ESRL (http://www.esrl.noaa.gov/gmd) were employed in the calculations. k (cm/h) suggests the gas transfer velocity, often indicated by the function of wind speed and Schmidt number (Sc). Sc is the Schmidt number of N₂O that can be computed according to the equation from Wanninkhof (2014). For shallow and tidal estuaries, turbulence arising from the friction between bottom flow and side topography also contributes to water turbulence (Raymond and Cole, 2001; Gwenaël Zappa et al., 2003; Abril et al., 2004). The model developed by Raymond and Cole, 2001 was selected in this study due to its median value and because it has been widely used in other researches (Li et al., 2021). In this study, the gas transfer velocity was computed using monthly average wind speeds (10-m height, Table 1 ) obtained from the Xiamen airport (14 km from the estuary) documented by Weather Underground (https://www.wunderground.com).

The budget of N₂O at the estuary involves import and export mechanisms that include riverine inputs, groundwater inputs, in situ production and consumption, water-air exchange and export to the bay. To look at the N₂O budget and distinguish unidentified N₂O sources or sinks in the estuary, we used the modeling framework of Eyre et al. (2016) and Chen et al. (2022), the input of N₂O should be equal to the output of N₂O in the estuary, and it could be assessed with the equation as below:

where X is the unidentified N₂O source or sink in the estuary, S is the sediment-water N₂O effluxes, W is the water column of N₂O production or consumption, R is the river input, G is the groundwater input, B is the loss of N₂O because of transport to the bay, E refers to the loss of N₂O caused by sea-to-air emissions, and the ± sign indicates the gain or loss of N₂O of the estuary (+ means gain/production, - means loss/consumption). Incubation for water column (W) and sediments (S) are not carried out in this study, which needed to better interpret the mechanisms of production of N₂O in the Jiulong River Estuary with further work.

Tests for the normality and homogeneity of the data were carried out with the Shapiro–Wilk test and Levene’s test. As the data failed to satisfy the assumptions of normality and homogeneity, we used the nonparametric Wilcoxon test to compare the average values between surface and bottom waters with paired samples, and Kruskal-Wallis test for seasonal and longitudinal differences with independent samples. Before the principal component analysis (PCA) calculation, a correlation matrix presenting the correlations was performed with the Spearman coefficient analysis with the same variables. All statistical tests and PCA steps were performed with SPSS (Statistics 23, IBM).

During the sampling period, water discharge was highest in August and lowest in December, a certain degree of interannual and seasonal variability was revealed compared to the long-term (1961– 2006) pattern of seasonal variation (Huang, 2008) ( Figure 2 ). Table 1 and Figure S1 show the principal physicochemical properties of surface water from the Jiulong River Estuary in the 6 survey cruises. The lowest water temperature was 16.3°C in December, and the highest reached 31.9°C in September ( Figure S1A ). An obvious salinity gradient was seen across the estuary ( Figure S1B ), and a dramatic fall of salinity could be seen upstream. For middle reaches, the lowest salinity range (0–9.5) was in August and September (flood period), when the survey was after heavy rain and the river had the largest discharge of all the surveys, the salinity range increased to 9.5–22.5 in May (dry season), low discharge and large tidal amplitude (5.8 m) during the sampling day.

Saturation of dissolved oxygen (DO) augmented progressively along with the salinity gradient except in August ( Figure S1D ) and varied from being mildly undersaturated to slightly supersaturated (43–119%). In the lower reaches, mixing with seawater, which was rich in oxygen, also exerted great effects on the verified growing DO content, and no noticeable discrepancy was revealed between surveys (p>0.05, Kruskal-Wallis test). Generally, nutrients levels decreased from upper reaches to lower reaches in the estuary. The upper reaches were characterized by high nutrient levels ( Figure S1D–F ), which was the outcome of riverine input. In the lower reaches, the lowest level of nutrients occurred subject to relatively less eutrophic coastal seawater. Nitrate presented high concentrations (mean: 87 μmol/L) and seemed dominant, standing for ~ 65% of the total DIN (mean: 134 μmol/L); in contrast, nitrite concentrations reached as ~ 8% (mean: 11 μmol/L). Notably, a storm-caused flood took place prior to the August survey, during which the runoff was 2 times that of July. The fresh water from upstream areas seemed to significantly affect the nutrients in the estuary, presenting different patterns compared to other surveys.

N₂O concentrations in water surface and bottom along the Jiulong River Estuary are plotted against longitude (a) and salinity (b) in Figure 3 and displayed significant spatial and temporal variability, between 11 and 185 nmol/L, corresponding to the saturation within 113–2926%. Therefore, the Jiulong River Estuary was a net source of atmospheric N₂O. Generally, N₂O exhibited a high level in the upper reaches, but decreased in lower reaches in overall seasons. During the surveys in August and September (flood period), the maximum values were located in the middle reaches ( Figure 3A ), which might result from the discharge from South Creek ( Figure 1 , it was hard to reach because of the shallow water depth). During flood period, floodwater carrying N₂O from the upstream areas of South Creek could be another contributor to the Jiulong River Estuary N₂O budget.

We also tested the differences of N₂O concentrations in different conditions of discharge and tidal amplitude. If the discharge was<200 m³/s, the sampling campaign conditions were considered representative of the dry season (November-2017, December-2017 and May-2018), and if the discharge was >200 m³/s, the sampling campaigns were considered representative of the flood period (September-2017, July-2018 and August-2018). If the tidal amplitude< 5 m, the campaigns were considered during neap tide, if the tidal amplitude was >5 m, the campaigns were considered during spring tide. The differences for N₂O concentrations were not significant between dry and flood conditions, as well as between neap and spring tides (p > 0.05, Kruskal-Wallis Test).

Table 2 presents a comparison of N₂O, temperature, salinity, DO, DIN, and turbidity between the surface and bottom waters in 3 cruises in 2018. The mean turbidity value of the bottom water seemed higher than the values of surface water. However, the differences in all these parameters between the surface and bottom waters were not significant (p>0.05, Wilcoxon Test).

Figure S2 and Table S1 show the seasonal variation in N₂O concentration using the Kruskal-Wallis Test, which reached the maximum generally in September and the minimum in July, the differences among these 2 campaigns were significant. For longitudinal differences, significant differences of N₂O values among surveys could be found in the upper and middle reaches, however, in lower reaches, variation of N₂O concentrations showed not pronounced.

Results of the principal component analysis (PCA) are shown in Figure 4 . Factors 1 and 2 together explain for about 73% of the data variance. Factor 1 is dominated by DIN ( NO 3 − , NH 4 + , and NO 2 − ) and N₂O in one hand and by salinity and DO on the other hand. Factor 2 shows the influence of wind and temperature, as well as the tides and discharge. The PCA and correlation matrix ( Table 3 ) consistently reveal that the controlling processes over N₂O concentrations. N₂O were shown to be strongly positively correlated with DIN ( NO 3 − , NH 4 + , and NO 2 − ) and strongly inversely correlated with salinity and DO.

The measured N₂O concentrations in the groundwater showed high spatial variability, ranging from 6 to 301 nmol/L with an average of 133 ± 99 nmol/L along the north bank and from 4 to 5380 nmol/L with an average of 1233 ± 2054 nmol/L along the south bank. Generally, N₂O concentration of the groundwater exceeded that of the estuary, demonstrating groundwater was possibly one N₂O source to the Jiulong River Estuary.

The monthly average wind speeds, ranging from 3.9 to 6.5 m/s ( Table 1 ), were used to calculate N₂O flux. In agreement with N₂O concentrations, the sea-to-air N₂O fluxes exhibited great spatial variability in the Jiulong River Estuary. The maximum N₂O flux as 1731 μmol/m²/d was observed in the low salinity region, while the N₂O flux decreased to 80 μmol/m²/d toward the mouth of the estuary ( Figures 3E, F ; Table S1 ). The average N₂O flux across the whole estuary was estimated to be 597 ± 490 μmol/m²/d. Previous investigations in 2009 (Zhan et al., 2011) found N₂O fluxes from 3 to 94 μmol/m²/d, and then increased to 0.5-168 μmol/m²/d in 2013-2014 (Chen J. et al., 2015). In this study, it has increased to 80-1741 μmol/m²/d, indicating an increasing trend in the N₂O emissions of the Jiulong River Estuary during the last 10 years. To test the differences in the upper reaches between N₂O values sampled in 2009 (Zhan et al., 2011) with N₂O values in our study, a comparison was made using Kruskal-Wallis Test, N₂O values in this study were much higher ( Figure S3 ) than that sampled in 2009 (Zhan et al., 2011).

Factors contributing to the variations of N₂O in an estuarine system include its production primarily via nitrification/denitrification that is related to the substrate level (DIN: NO 2 − , NH 4 + , and NO 3 − ). Ambient environmental conditions such as DO level, salinity conditions including estuarine mixing, river discharge as well as N₂O emission also play a role. The mixing diagram reflects the nonconservative behavior of NH 4 + and NO 3 − in August and September (flood period), with the system acting as an NH 4 + sink and NO 3 − source ( Figure 5 ). In view of this, the removal of NH 4 + and addition of N₂O in the middle reaches ( Figure 3 ) of the Jiulong River Estuary should partly be a result of nitrification, which is consistent with a previous report that suggested N₂O accumulation primarily came from nitrification instead of denitrification in the Jiulong River Estuary (Wu et al., 2013; Chen N. et al., 2015). Moreover, the significance of nitrification to estuary seems noticeable: a distinct positive correlation between NH 4 + and N₂O concentrations supports N₂O production through nitrification to some extent (de Wilde and de Bie, 2000).

N₂O distribution of the Jiulong River Estuary also came under the influence of other environmental factors. Specifically, N₂O concentrations were correlated with DO and turbidity ( Table S2 ). The relationships between N₂O and DO show negative correlations in overall seasons, i.e., high N₂O concentrations and low DO concentrations. Such a pattern resembles those found in other estuaries by previous studies (de Wilde and de Bie, 2000; Brase et al., 2017). Low dissolved O₂ (suboxic conditions) makes for nitrification and then N₂O production (Codispoti, 2010; Kim et al., 2013), which can also be observed from our sediment incubation experiment. High N₂O is usually observed near the maximum turbidity district (Barnes and Owens, 1998; Abril et al., 2000; Gonçalves et al., 2010), which exists year round in the Jiulong River Estuary (Chen et al., 2018). Lots of nitrifiers adhere to particles (Stehr et al., 1995), and a great many surveys concerning estuaries show that particle accumulation helps enhance nitrifying population growth as well as nitrifying action (Abril et al., 2000; de Wilde and de Bie, 2000). N₂O concentration was shown to be strongly related to salinity ( Table 3 ), N₂O rapidly dropped with increasing salinity ( Figure 3B ). Nevertheless, in the middle reaches, the lowest N₂O value ( Figure 3A ) was found in July (spring tide, Table 1 ), the higher tidal amplitude means more seawater intrusion to the estuary, indicating that low N₂O seawater was diluting the high N₂O estuarine water, thus the estuarine mixing process is another dominant process in the Jiulong River Estuary. The N₂O concentration in the upper/middle reaches showed a certain degree of variation ( Figure S2 ); however, we found no significant differences between dry and flood conditions, or among tidal amplitudes. Specific factors that control dynamic spatial pattern of N₂O should be addressed in August (flood period), the lowest N₂O value was found in the upper reaches ( Figure 3A ), when the survey was after a rain storm and the river had the highest discharge of all the surveys, significantly higher water discharge ( Table 1 ) may substantially dilute both the N₂O and its substrate such as DIN ( Figure 3 ).

All these results suggest that the N₂O distribution in the Jiulong River Estuary was subject to many factors, impact of such factors seems additive rather than exclusive. Specific factors that control dynamic spatial pattern of N₂O should be confirmed by follow-up research which takes into account more details existing in the estuary.

The Jiulong River Estuary was divided into 3 zones, namely, the upper, middle and lower reaches. The average N₂O sea-to-air fluxes (μmol/m²/d) were 1111, 617 and 147, and the water areas (km²) were 14.3, 79.1 and 46.6 in the upper, middle and lower reaches, respectively. The daily N₂O emissions of the Jiulong River Estuary (E) were estimated to be 71,542 mol/d.

Using the N₂O concentrations of the freshwater endmembers (average: 118 nmol/L, S<1) multiplied by the annual average daily water discharge (0.405×10⁸ m³/d) to assess the riverine N₂O fluxes (R) to the estuary yields a N₂O flux of 4785 mol/d, which is equal to 1.7×10⁶ mol/yr in terms of annual input.

Groundwater could be another source of N₂O in the Jiulong River Estuary. Based on average N₂O concentrations (725 nmol/L) and daily groundwater discharge of 0.17×10⁸ m³/d (Guo et al., 2011), N₂O input from the groundwater to the estuary (G) is estimated as 12,331 mol/d, which accounts for 28% of N₂O emissions from the sediment.

N₂O loss due to export to the bay could be another sink (B), and N₂O surface water concentrations observed at estuary mouth (S>28) were used to calculate the N₂O transport to the bay, and were multiplied by the annual average water discharge (0.405×10⁸ m³/d), giving a flux of 593 mol/d, indicating a minor sink of N₂O in the estuary.

Incubations for water column and sediments are not carried out in this study. No clear consumption or production during incubation was found from the Brisbane River Estuary, Australia (Sturm et al., 2016). Nevertheless, the water column plays a major part in N₂O production in other estuarine studies (Law et al., 1992; Barnes and Owens, 1998; de Wilde and de Bie, 2000), indicating variability among estuaries. According to other research, sediment-water N₂O fluxes ranged between -5 and 600 μmol/m²/d, showing high spatiotemporal variability with fluxes (Barnes and Owens, 1998; Laursen and Seitzinger, 2002; Zhang et al., 2010; Allen et al., 2011).

The N₂O budget (equation 2) demonstrates the Jiulong River Estuary indistinct N₂O sources (X) of around 55,019 mol/d, there are some possible unidentified inputs, including sediment efflux, tributaries and sewage inputs are potential sources of N₂O. Conceptual model for sources and sinks of N₂O in the Jiulong River Estuary could be seen in Figure 6 . Intensity of denitrification can be regulated through the presence of nitrate and nitrite (Dong et al., 2004). Hence, in the presence of sufficient nitrate, sedimentary denitrification site is ideal, and N₂O may well derive from denitrification in sediment from the Jiulong River Estuary. In the middle reaches, South Creek joins the Jiulong River Estuary and the N₂O concentrations are elevated between the 117.85 and 117.9°E (south creek) during the flood seasons, we conclude that the south creek join the estuary and provide fresh water with high concentration of N₂O to the waterbody in the estuary. Sewage investigations are not covered in this survey; although wastewater is partially treated, the nutrients released into the estuary continually increase (Chen et al., 2014), which in turn plays a major role as a N₂O source in the estuary.

The plot concerning N₂O vs. salinity ( Figure 3B ) is characterized by concave curves, and the concave profile indicates that N₂O in the estuary decreased faster compared with that of the conservative mixing with N₂O-poor seawater. N₂O consumption has traditionally been considered active only in anoxic environments (Codispoti and Christensen, 1985). Recently, some studies have found that N₂O reduction may occur in oxygenated waters (Raes et al., 2016; Rees et al., 2021; Sun et al., 2017; Sun et al., 2021; Tang et al., 2022; Wyman et al., 2013). According to incubations experiment for water column, N₂O had not been obviously produced or consumed (section 4.2). Therefore, N₂O reductions are primarily caused by gas emissions into the to the atmosphere. N₂O saturation of surface water varied between 113% and 2926% in the 6 surveys of the research ( Table 4 ), showing N₂O concentrations in the Jiulong River Estuary were at a higher level with respect to the atmospheric N₂O concentrations throughout the year. Hence, the Jiulong River Estuary represents one net source of N₂O discharged into the atmospheric environment. The average N₂O flux of the Jiulong River Estuary was estimated to be 597 μmol/m²/d ( Table 4 ). This flux is comparable to the flux in the Colne Estuary (Dong et al., 2004) and far higher compared with that in estuaries such as the Scheldt, Humber, Indian and Pearl Estuaries (de Wilde and de Bie, 2000; Lin et al., 2016; Rao and Sarma, 2016), indicating that saturations and emissions of N₂O in the Jiulong River Estuary rank top in the world ( Figure 7 ). In accordance with the coverage in the Jiulong River Estuary (see section 4.2), the annual N₂O emissions were estimated to be 0.26× 10⁸ mol/yr (equal to 1.1 Gg N/yr), which accounted for approximately 3.3% of the riverine DIN (34.3 Gg N/yr) load to the estuary (Yan et al., 2012), which was one order of magnitude higher than the 0.3% from DIN input employed in global scale models for estuaries (Seitzinger and Kroeze, 1998), indicating very high yields of N₂O of the Jiulong River Estuary compared to global estuaries. Areal nutrient flux yield rates of the Jiulong River were much higher than those in major world rivers, and although the water discharge in the Jiulong River merely reaches 1.1% of that in the Changjiang River and 2.5% of that in the Pearl River, the areal DIN yield rates from the Jiulong River watershed are 4.1 and 2.4 times those from the Yangtze River and Pearl River watersheds, separately (Yan et al., 2012). Many studies have shown that DIN has a significant relationship with N₂O, with increased N₂O emissions due to the increased DIN inputs (Borges et al., 2018; Wells et al., 2018; Reading et al., 2020), Zhang et al. (2010) made a plot of estuarine N₂O versus DIN on a global scale, and by compiling N₂O data from 50 estuaries (Reading et al., 2020), they both found N₂O saturation showed a positive relationship with DIN on a global scale, and our data nicely match the correlation they show. Thus, the higher N₂O saturation could be attributed to greater DIN loadings as well as greater yields of N₂O rates of the Jiulong River Estuary.

We made a comparison for the trend of nutrient loads and N₂O saturations in the past 10 years ( Table 4 ). Previous investigations in 2009 found N₂O saturations around 280% (Zhan et al., 2011); since then, the saturations of N₂O has been increasing, and the mean N₂O saturations has increased by 2 folds of magnitude during the last 10 years ( Table 4 ). In addition, riverine N₂O flux to the Jiulong River Estuary increased more than 15-fold during the 1985–2012 period (Chen N. et al., 2015). This is in contrast to some European estuaries, such as the Elbe and Schelde Estuaries (de Wilde and de Bie, 2000; Brase et al., 2017), where reduced N₂O concentrations were observed during the last 20 years, following a significant decrease in DIN loads and an improvement in environmental conditions. However, the DIN in the Jiulong River Estuary presented an increasing trend, reached a maximum in 2011 and then decreased ( Table 4 ), which conformed to the historical nutrient fluxes of the Jiulong River Estuary (Wu et al., 2017). Based on the correlation of DIN and N₂O mentioned above, N₂O saturation should have declined after 2011; instead, it is remarkable that N₂O saturation continued to increase. One possible reason for the contrast phenomenon between the correlations and our finding is probably the increased oxygen concentration (Cai et al., 2016; Wu et al., 2017) in the Jiulong River Estuary during the past decade. In line with high nutrient loads and low oxygen saturation in the Elbe estuary in the 1980s (Hanke and Knauth,1990), it is concluded that denitrification was the dominant contributor to N₂O production at that time (Brase et al., 2017). N₂O can be reduced to N₂ under anoxic conditions via denitrification (Upstill-Goddard et al., 2017), whereas, the yields of N₂O from microbial processes are enhanced under suboxic conditions (Zhang et al., 2010; Brase et al., 2017). With the improved environmental conditions in the Jiulong River Estuary especially with increased oxygen concentrations, the importance of denitrification appears to have ceased in the contemporary estuary, and our data also support that obvious nitrate addition in the middle reach points toward nitrification playing an important role in N₂O production in the contemporary estuary. It remains unclear why N₂O saturation continued to increase to such a high level, while it seems plausible that intense nitrification/denitrification and high yields of N₂O in the sediment, may still play an important role in overall N₂O production in the Jiulong River Estuary.