A nitrate budget of the Bohai Sea based on an isotope mass balance model

. The Bohai Sea (BHS) is a semi–closed marginal sea impacted by one of the most populated areas of China. The supply of nutrients, markedly that of reactive nitrogen, via fluvial and atmospheric transport has strongly increased in parallel with the growing population. Therefore, it is crucial to quantify the reactive nitrogen input to the BHS and understand the 15 processes and determine the quantities of nitrogen eliminated in and exported from the BHS. The nitrogen budget and in particular the internal sources and sinks of nitrate were constrained by using a mass-based and dual stable-isotope approach based on δ 15 N and δ 18 O of nitrate. Samples of water, suspended matter and sediments were taken in the BHS in spring (March and April) and summer (July and August) 2018. The Yellow River (YR) was sampled in May, July to November and Daliao River, Hai River, Luan River and Xiaoqing River were sampled in November of 2018. In addition to nutrient, particulate 20 organic carbon and nitrogen concentrations, the dual isotopes of nitrate (δ 15 N and δ 18 O), δ 15 N of suspended matters and sediments were determined. Based on the available mass fluxes and isotope data an updated nitrogen budget is proposed. Compared to previous estimates, it is more complete and includes the impact of interior cycling (nitrification) on the nitrate pool. The main nitrate sources are rivers contributing 19.2–25.6 % and the combined terrestrial runoff (including submarine fresh groundwater discharge of nitrate) accounting for 27.8–37.1 % of the nitrate input to the BHS while atmospheric input 25 contributes 6.9–22.2 % to total nitrate. An unusually active interior nitrogen cycling contributes 40.7–65.3 % to total nitrate via nitrification. Nitrogen is mainly trapped in the BHS and mainly removed by sedimentation (70.4–77.8 %) and only very little is exported to the Yellow Sea (YS) (only 1.8–2.4 %). At present denitrification is active in the sediments and removes 20.4–27.2 % of nitrate from the pool. However, a further eutrophication of the BHS could induce water column hypoxia and denitrification, as is increasingly observed in other marginal seas and seasonally off river mouths.

For this study, we analyzed water, suspended matter and sediments in the Bohai Sea sampled during the spring and summer seasons for nutrient concentrations, carbon and nitrogen contents, dual isotopes ( 15 N and  18 O) of nitrate and  15 N of particulate nitrogen. The aim of the study is to characterize and quantify Nr sources and sinks, in particular those from internal cycling processes that have not been included in previous budgets (Zhang et al., 2004;Liu et al., 2003;Liu et al., 2009;Liu et 75 al., 2011) to track the fate of Nr in the present Bohai Sea. The observation data presented here are the basis for a combined mass and isotope balance model, results of which will be a basis for future studies on the rising impact of fast-growing megacities in the BHS catchment and their possible impact on the adjacent YS.

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Research cruises were carried out by R/V Dongfanghong 2 in spring and summer 2018 with 24 sampling sites in April and 25 sites in August, respectively (Fig. 1). Water samples were taken from several depths by 12 L Niskin bottles attached to a CTD rosette (911plus, Seabird, USA). The water samples were filtered using nucleopore polycarbonate filters (0.4 μm) with plastic Nalgene filtration units. The filtered water was collected in Falcon PE tubes (45 mL), frozen immediately (-20 ℃) and kept frozen until analyses in the home laboratory in Germany. Between 1 to 8 L of water were filtered through pre-weighted 85 GF/F filters (0.7 μm, Φ = 47 mm, Sigma Aldrich) which had been pre-combusted at 450 ℃ for 4 h. The filters were subsequently dried on board under 45 ℃ for 24 h. Surface sediments were taken with a box corer and surface samples were transferred into plastic bags with a metal spoon, frozen at -20 ℃ and were kept frozen until later analysis in the home lab.
YR water samples were taken from the Kaiyuan floating bridge in Lijin, located 44 km upstream of the river mouth.
Samples were taken in the middle of the river course with a plastic reversing water sampler at 1 m under the surface. The water

Measurements of nutrients and nitrate isotopes
100 Nutrient concentrations were measured with an AutoAnalyzer 3 system (Seal Analytics) using standard colorimetric methods (Grasshoff et al., 2009). The relative error of duplicate sample measurements was below 1.5 % for NOx and phosphate concentrations, below 0.3 % for ammonium. The detection limit was < 0.05 µmol kg −1 for NOx, > 0.1 µmol kg −1 for PO 4 3− , and >0.013 μmol L -1 for ammonium.

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× 1000 ‰,) were determined with the denitrifier method (Sigman et al., 2001;Casciotti et al., 2002). Only the samples with nitrate concentrations > 1.7 μmol kg -1 were analyzed and δ 15 N and δ 18 O were analyzed in one sample run. Water samples were injected into a suspension of the denitrifier Pseudomonas aureofaciens with injection volumes adjusted to yield 10 nmol N2O.
The N2O gas was purged by helium into a GasBench 2 (Thermo Finnigan) for purification. Afterwards the N2O gas was analyzed by a Delta V Advantage and a Delta V Plus mass spectrometer. Samples were measured in duplicate and the two 110 international standards IAEA-N3 (δ 15 N-NO3 -= +4.7 ‰, δ 18 O-NO3 -= +25.6 ‰) and USGS-34 (δ 15 N-NO3 -= -1.8 ‰, δ 18 O-NO3 -= -27.9 ‰) and an internal potassium nitrate standard were measured in each batch. The data were corrected by applying a bracketing correction  and the standard deviations of the international and in-house standards was found to be ≤ 0.2 ‰ for δ 15 N and ≤ 0.5 ‰ for δ 18 O. The standard deviations of duplicate samples were in the same range. Nitrite affects the results and was removed following the protocol of Granger and Sigman (2009)

Measurements of suspended matters and sediments
The tared GF/F filters were weighed to calculate the amount of suspended particulate matter (SPM) per liter of water.
Total carbon and nitrogen concentrations in SPM and sediment samples were measured by a Euro EA 3000 (Euro Vector SPA) Elemental Analyzer, and SPM samples with high carbon and nitrogen contents and sediments were acidified to measure organic 120 carbon content. The precision of total and organic carbon determination is 0.05 %, that of nitrogen is 0.005 %, and the standard deviations are less than 0.08 for total and organic carbon and 0.02 for nitrogen. Nitrogen isotope ratios were determined with a FlashEA 1112 coupled to a MAT 252 (Thermo Fisher Scientific) isotope ratio mass spectrometer. The precision of nitrogen isotope analyses is better than 0.2 ‰, and the standard deviation less than 0.03.

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The dissolved oxygen (DO) samples were collected, fixed, and titrated on board following the Winkler procedure at an uncertainty level of < 0.5 %. A small quantity of NaN3 was added during subsample fixation to remove possible interferences from nitrite (Wong, 2012). The DO saturation (DO %) was calculated from field-measured DO concentration divided by the DO concentration at equilibrium with the atmosphere which was calculated from temperature, salinity and local air pressure, as per the Benson and Krause Jr (1984) equation.

Hydrodynamic model of nutrient export from BHS to the Yellow Sea
The regional three-dimensional hydrodynamic Hamburg Shelf Ocean Model, HAMSOM (Backhaus, 1985), was applied in the East China Seas (23°-45° N, 117°-131° E) to calculate the water and nutrient transport through the Bohai Strait for the year 2018. The HAMSOM model has been applied to investigate the Bohai Sea physical circulation for several decades now and has been extensively validated in the Bohai Sea (Jia and Chen, 2021;Hainbucher et al., 2004;Huang et al., 1999). The spatial resolution of the model is 2' (approx. 3.7 km) with 20 layers in vertical direction, while the calculation time step is 3 minutes. The upper 50 m of the HAMSOM model are resolved by layers of 5 m thickness. The topography data (resolution of 2') were obtained from marine navigation charts. The meteorological forcing was derived from an hourly ERA5 dataset with a spatial resolution of 0.25° (CCCS, 2017). The open boundary SSH and the boundary T and S data and for the initial T and S fields were extracted from the daily Mercator-Ocean dataset (1/12 degrees) (Lellouche et al., 2019). 13 partial tides derived 140 from the TPXO8-atlas v1 were superimposed to the SSH along the open boundary (Egbert and Erofeeva, 2002). The observed monthly river discharge were available for the two largest rivers, i.e., Changjiang andYR (China Water Resources Bulletin, 2015-2018), while the inputs for the remaining rivers were derived from the Watergap dataset (0.5°, monthly climatology) (Müller Schmied et al., 2014). The spin-up period of this model is 1 year.
Four sites on a north-south section through the Bohai Strait, i.e., B33, B34, B35, and B36, have been selected to represent 145 the open boundary of the BHS (Fig. 1). The simulated SSH and current velocities (west-east-component) were extracted along this section. In addition, nutrient concentrations were interpolated from the observed data at the four sites to the grid of the hydrodynamic model along the Bohai Strait section. Since the observational data just include spring and summer values, the mean value of nitrate in spring and summer had to be extrapolated to an entire year.

Hydrological properties
Averages of salinity and temperature in spring were 32.3 ± 0.5 (n = 72) and 4.7 ± 0.8 °C (n = 72), respectively, and the water column was vertically mixed ( Fig. 2 and Fig. 3). The YR discharged relatively warm water and the lowest salinity was observed in the southeast of YR estuary (site B68, T > 6 ℃, S < 31). Thus, the Yellow River Diluted Water (YRDW) is here 155 defined as the water off the YR estuary with salinities lower than 31. In summer, averages of salinity and temperature were 31.6 ± 0.8 (n = 88) and 22.4 ± 4.2 °C (n = 88), respectively, and the surface layer was stratified. The YRDW extended to an even larger area than in spring caused by high river discharge. The YRDW turned northeast towards LiaoDong Bay into the central BHS in the surface layer (T > 27 ℃, S < 31).
The water column oxygen concentrations (see Supplement 1) in the study area in spring and summer were 10.27-11.47 160 mg L and 3.84-8.86 mg L -1 , respectively, and thus much higher than the threshold for water column denitrification (0.15 mg L -1 ). The detailed results of DO and other parameters are shown in Supplement 2. 165 Figure 3. Temperature (℃) and salinity (psu) of section 2 of spring (a and c) and summer (b and d).

Suspended particulate matter
In spring suspended particulate matter (SPM) concentrations were mostly vertically homogenous along both transects with high values (>15 mg L -1 ) close to the YR mouth (see Supplement 3). Corg % and N % are anti-correlated with SPM concentrations and high values occurred in the central BHS and north of Shandong Peninsula. In summer SPM concentrations 210 were significantly higher than in spring and maxima occurred in deep water off the YR (> 30 mg L -1 ) and in the west part of the BHS. Corg % and N % maxima occur in surface waters in the eastern Laizhou Bay and the central BHS.
The lowest values were observed in the southern Bohai Strait and northeast of YR estuary. The other samples varied in a narrow range of 3.9-4.7 ‰ (n = 11). In summer, the average of δ 15 N was 5.7 ± 0.8 ‰ (n = 34) and ranged from 3.9 ‰ to 215 7.2 ‰. Systematic variation of δ 15 N of SPM was barely discernable and only exhibited a weak decline from the YR mouth into the northeastern BHS (section 1) and into the Bohai Strait (section 2) (see Supplement 3), thus tracking the salinity dilution gradient in the surface layer.

The discharge of the Yellow River
The water discharge of the year 2018 determined at the Lijin hydrography station was 333.8×10 9 m 3 which was by 14 % 220 higher than the multi-year average of 292.8×10 9 m 3 (1952-2015) (MWR, 2019). The monthly mean discharge was 27.80 ± 20.21×10 9 m 3 per month (n = 12), which was higher than the multi-year average value by 14-51 %, indicating that in YR basin 2018 was a flood year. The water discharge maximum was from July to October (

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Based on current velocities and nutrient concentrations along the section crossing the Bohai Strait, the annual water and nitrate export from BHS to the YS in the year 2018 was calculated to 1.26×10 -3 Sv (1 Sv=10 6 m 3 s -1 ) and 0.9×10 9 mol year -1 , respectively. In this study, the exported nitrate are assumed with the average isotopes values of the BHS (δ 15 N = 8.9 ‰ and Making use of the three-dimensional model (HAMSOM) results, it is also possible to determine a spatial distribution of 240 the annual nutrient flux through the Bohai Strait section (Fig. 9). Positive values represent a nutrient flux out of the Bohai Sea, while negative ones indicate a flux into the Bohai Sea. The strongest nutrient export occurs at the southern part of the Bohai Strait, while the major import takes place in the upper 15 m in the northern Bohai Strait (Fig. 9).

The hydrographic and nutrients characteristics in spring and summer
The sampling in early spring occurred during a season of low biological activity so that nutrients behaved almost conservatively. YR discharged 333.8 × 10 9 m 3 water and 8.0 × 10 9 mol nitrate to the Bohai Sea in 2018, accounting for 85 % 250 and 84 % of water and nitrate discharge of all large rivers in the Bohai Sea, respectively. As is indicated by the negative correlations of NO 3 − (r = -0.78, p < 0.01), and NH 4 + (r = -0.79, p < 0.01) with salinity, the YR is one of the major sources of these nutrients in the BHS, whereas PO 4 3− is contributed by the inflow of saline waters from the YS as indicated by the positive correlation with salinity (r = 0.43, p < 0.01). Concentrations of nitrate were relatively high in the southern Bohai Strait but low in its northern part, suggesting that in spring nitrate-rich water flows out of Bohai Strait along the northern shore of Shandong Peninsula in the LCC, while nitrate-depleted water flows in from the northern YS via the northern strait.
In summer, the water is stratified with the thermocline at about 8 m water depth and coinciding with halo-and nutriclines.
Nutrients are depleted to trace amounts above the thermocline. In contrast to the other nutrients, phosphate concentrations did not increase with depth in the southwestern part of BHS (i.e. Bohai Bay and Laizhou Bay). Similar to the spring situation, salinity was weakly positively correlated with PO 4 3− (r = 0.29, p < 0.05) and NO 2 − (r = 0.32, p < 0.05), whereas it was negatively correlated with NO 3 − (r = -0.69, p < 0.01) and NH 4 + (r = -0.37, p < 0.01), respectively. The average N/P ratio in BHS in spring and summer was 28.2 ± 38.2 and 86.9 ± 126.3, respectively, implying that productivity in BHS was phosphorus limited. Thus, diazotrophic N2 fixation is excluded as a significant input of Nr because of high N:P ratios.

The main sources and sinks of nitrate in the BHS
Most of the external and internal sources of nitrate to the BHS are characterized by distinct dual isotope values. These 265 fingerprints combined with mass flux estimates are in the following used to constrain the mass and isotope budget of nitrate in the BHS. Specifically, the role of internal cycling processes can thus be quantified, which were lacking in previous budgets.
In the following, each of the sources and sinks is described, along with isotope composition or isotope fractionation associated with cycling processes.

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The main input from this source of BHS Nr is from the YR and we calculated a nitrate input of YR of 7.95 × 10 9 mol year -1 , based on the annual average discharge (MWR, 2019) and the load-weighted nitrate concentration during our sampling period during the year 2018. The water discharge of the other 7 important rivers (Hai River, Shuangtaizi River, Daliao River, Luan River, Xiaoqing River, Daling River and Xiaoling River) sums up to 59.86 × 10 8 m 3 year -1 (MWR, 2019; Ma et al., 2004;Yu et al., 2018;Zhang et al., 2004). Nitrate fluxes of these rivers were calculated based on water discharge and our nitrate 275 measurements in YR, Hai River, Daliao River, Luan River and Xiaoqing River. Owing to a lack of data on nitrate concentrations of Shuangtaizi River, Daling River and Xiaoling River and considering that these rivers drain basins adjacent to Daliao River, we assume that nitrate concentration of these rivers were same as those of the Daliao River. The total riverine input of nitrate summed up to 9.49 × 10 9 mol.
The mass-weighted average annual values for δ 15 N and δ 18 O of nitrate in these rivers were 10.0 ‰ and 1.3 ‰, respectively, 280 taken here to represent the river nitrate isotopic composition discharged into BHS.

Submarine groundwater input
The DIN supplied to BHS by submarine groundwater discharge (SGD) flux has been estimated to be 2-10 times the YR discharge (Luo and Jiao, 2016;Peterson et al., 2008;Wang et al., 2015). These fluxes of SGD are a mixture of submarine fresh groundwater discharge (SFGD) and recirculated saline groundwater discharge (RSGD) (Liu et al., 2011;Peterson et al., 2008; 285 Liu et al., 2017a), but only the freshwater component is relevant as a source for the budget.
The latest estimates of SGD for the BHS are 10.0 × 10 9 m 3 year -1 (Liu et al., 2017a) and 19.1 × 10 9 m 3 year -1 (Wang et al., 2015), respectively. The nitrate concentration of SFGD is not documented, but the nitrate concentration of groundwater in YR Delta was 304.2 ± 254.2 μmol L -1 (Liu et al., 2011). For reducing the error of these indirectly measured data, we decided to use the value of 4.25 × 10 9 mol year -1 for the nitrate flux of SFGD, which is the averaged products of SFGD water fluxes and 290 nitrate concentrations shown above. This value is only approximately 10 % of previous estimates of the input nitrate for SGD into BHS (Liu et al., 2011) due to the exclusion of RSGD.
Because of pollution and denitrification processes in soils, aquifers and groundwater Chen et al., 2007;Soares, 2000), the value of δ 15 N and δ 18 O of nitrate in SFGD is more enriched than those of river runoff and this is illustrated by the observed δ 15 N value of 20.2 ± 9.0 ‰ ( n = 19) of on-land groundwater near the YR delta (Chen et al., 2007). As there

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are as yet no reported δ 15 N values of SFGD and RSGD inputs, we decided to take this value as the signal of nitrate δ 15 N imported by SFGD into the BHS. There are no data available for δ 18 O of nitrate of SFGD, and we will discuss possible constraints in the box model discussion (Sect. 4.3.2).

Atmospheric deposition
Combined atmospheric input by wet and dry deposition ranged from 3.14 × 10 9 mol year -1 to 3.42 × 10 9 mol yr -1 (Zhang 300 et al., 2004;Liu et al., 2003) . We adopted the annual mass of NOx deposition for China of 6.2 Tg year -1 (Zhao et al., 2017) and related this value to the area of the BHS, which results in an annual deposition of 3.6 × 10 9 mol year -1 . Owing to a lack of directly measured data for atmospheric NOx the BHS, we adopt 3.42 ± 2.29 × 10 9 mol year -1 (Zhang et al., 2004)  The ammonium deposited from the atmosphere is assimilated by phytoplankton and is subsequently entrained into the N cycle via remineralization and nitrification or is nitrified directly in the water. Thus, the nitrified atmospheric ammonium is included here as a source bearing on  15 N of nitrate in the seawater. The ammonium deposition in BHS was 6.15 × 10 9 mol year -1 , which is more than the nitrate deposition of 3.42 × 10 9 mol year -1 (Zhang et al., 2004).

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The atmospheric ammonium has low δ 15 N values of -6.53 to -1.2 ‰ (Zhang et al., 2008;Chang et al., 2019). Given that the δ 15 N value of ammonium of the North China Plain is -1.2 ‰ ± 4.5 ‰ (Zhang et al., 2007), and that there is no obvious accumulation of ammonium in the surface layer in the observations, we assume that this isotope value is identical to the δ 15 N value of nitrified atmospheric ammonium.

Nitrate diffusing from water to sediment
A latest number of benthic reactive nitrogen loss including denitrification and annamox for the BHS and northern YS is 330 3.5 × 10 9 t N year -1 . Combining the area of the BHS and assuming that 82 % benthic nitrogen loss was by denitrification, the denitrification flux calculates to 10.1 × 10 9 mol year -1 . Globally, the sediment denitrification rate varies in the range of approximately 0.5 to 2 mmol m -2 d -1 (Devol, 2015), which is equivalent to 14.1 ×10 9 mol year -1 to 28.2 ×10 9 mol year -1 in the BHS. We assume that diffusion is not accompanied by isotope fractionation (Devol, 2015), so that δ 15 N and δ 18 O of nitrate diffusing into the sediment are the same as the nitrate pool in BHS (8.9 ‰ and 10.4 ‰, respectively).

Sedimentation
The mass flux of Nr sedimentation is unknown. In terms of the effects of Nr sedimentation on nitrate dual isotopes, phytoplankton organisms that assimilate nitrate from the dissolved phase are the main source of sinking particles, so that the N and O will be removed from the nitrate pool following the assimilation fractionation factor. Sinking particles in the BHS have a δ 15 N of 5.2 ‰ (δ 15 Nsink) corresponding to the average values of spring and summer, which integrates multiple processes such as photosynthesis of phytoplankton, heterotrophic synthesis of bacteria, and heterotrophic degradation (remineralization).

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There is no observed data of δ 18 O of nitrate removed from the pool during assimilation (δ 18 Osink), but this value can be estimate by the assimilation fractionation factor ( 18 ε). The per mil fractionation factors  of N ( 15 ε) and O ( 18 ε) in nitrate during assimilation are generally assumed to be around 5 ‰, so that 15 ε : 18 ε = 1 : 1. Here we adopt the average of 15 ε and 18 ε as 5 ‰

The nitrate budget in the BHS
A box model of the nitrate budgets for the Bohai following the LOICZ approach (Zhang et al., 2004) balanced sources and sinks of nitrate in BHS and was updated by several other nitrate budgets for the BHS during last two decades (Zhang et al., 2004;Liu et al., 2003;Liu et al., 2011;Liu et al., 2009). All were, in general, not completely constrained because of a lack of data on some important source or loss terms. We here associate the nitrate isotope compositions of pools, sources, and sinks of nitrogen with a box model of the BHS nitrate in order to improve the understanding of nitrate cycling in the BHS. Finally, based on the combined mass and isotope box model informed by new data on the isotopic composition of nitrate, surface sediment, and suspended particulate nitrogen in the water column discussed above, we propose an updated N-budget that is internally consistent. where the terms m with different subscripts refer to the corresponding nitrogen mass fluxes, m atm refers to atmospherically deposited nitrate, m r refers to river nitrate, m N refers to nitrified ammonium deposited from the atmosphere, m SFGD refers to nitrate in submarine fresh groundwater discharge, m ntr refers to nitrification in the water column. In terms of sinks, m net refers to the mass fluxes associated with net export of nitrate from BHS to the YS, refers to nitrate sedimenting from seawater as particulate N, and m denitr refers to denitrification in the sediment. The unit of the mass fluxes is 10 9 mol. The "δ 15 N" refers to the δ 15 N value of the N mass flux which with the same subscripts. As mentioned previously, the mass fluxes for m N , m ntr , m sink and δ N ntr 15 are unknown and need to be constrained. Ammonium diffusing out of the sediment will either be mixed into the euphotic layer and subsequently assimilated by the phytoplankton, or nitrified in the water column. The accumulating of ammonium beneath the thermocline was a significant process in summer, as shown by the high nitrite and ammonium concentrations beneath the thermocline. The ratio of these two branching processes is not known in the BHS. If all of the ammonium from sediment is nitrified, the produced nitrate will have 400 a δ 15 N of 3.4 ‰ (see above). If the ammonium is only partially nitrified (especially in summer beneath the thermocline), the produced nitrate will have a δ 15 N of 1.4 ‰ at a fractionation factor of nitrification of 2 ‰ (Sigman and Fripiat, 2019). Thus, the δ 15 N value of the nitrate produced by nitrification (δ 15 Nntr) of ammonium from sediment is in the range of 1.4 ‰ to 3.4 ‰.
According to Eq. (1), (2) and (3) As the only constraint, δ 18 OSFGD is expected to be higher than the value of nitrate imported from the rivers (δ 18 Or = 1.3 ‰) due to the fractionation associated with denitrification in the anaerobic aquifers (see Sect. 4.2.2). The results can be summed up in three different cases: (1) When setting the value of δ 15 Nntr to 3.4 ‰, we obtain estimates for m N that range from 0.00 to 4.83 × 10 9 mol yr -1 , for 420 m ntr in the range of 15.08 to 32.27 × 10 9 mol year -1 and m sink in the range of 26.08-38.45 × 10 9 mol year -1 . The corresponding values of δ 18 OSFGD range from 1.3-15.9 ‰, and the upper range of δ 18 OSFGD yields m N = 0.0 due to the assumption that any mass flux must be equal or greater than 0.
(2) When we choose a δ 15 Nntr value of 3.2 -2.4 ‰, respectively, to explore effects of the methodological error of δ 15 N for our isotope method (0.2 ‰, see Sect. 2.2), again under the premise that the mass fluxes are positive numbers, results in m N , 425 m ntr and m sink estimates in a narrower range than when δ 15 Nntr is 3.4 ‰; these results are not shown.
Thus, reasonable solutions only are reached when δ 15 Nntr is between 3.4 ‰ and 2.4 ‰. The results of the budget are shown in Fig. 10 and Table 1, respectively.  Kang et al. (1994); Wu (1991) The mass flux of nitrate (m N ) originating from nitrification of atmospheric ammonium ranges from 0.00 to 4.83 × 10 9 mol year -1 and accounts for up to 79 % of the total ammonium deposition (6.15 × 10 9 mol year -1 ; Zhang et al. (2004)). This in turn implies that most of the atmospherically deposited ammonium is directly assimilated rather than nitrified to nitrate. This agrees with phytoplankton preference to assimilate ammonium rather than nitrate (Glibert et al., 2016). The bulk of internal sources of nitrate originates from nitrification in the water column (from water column ammonification and ammonium diffusing from 440 sediment). This single source (m ntr ) accounts for 40.7-65.3 % of the total sources of nitrate in BHS and appears to be much more important than in other coastal environments. For example, between 15-27 % of productivity was supported by nitrified ammonium in the seawater in Monterey Bay (Wankel et al., 2007). Likewise, nitrification supplied 34 % of the surface nitrate in eastern Hainan Island, which like Monterey Bay is also an upwelling area (Chen et al., 2020). This indicates that nitrate regeneration by nitrification may play a more important role in shallow and land-input dominated marginal seas than in 445 upwelling dominated marine settings.

Assessment of model uncertainties
The River input of nitrate is 9.49 × 10 9 mol in the year 2018 as suggested above. Considering that the river fluxes are variable 455 annually, we also adopt the multi-year average value  water discharge of YR of 292.8 km 3 instead of 333.8 km 3 in 2018 (MWR, 2019). Hence the annual nitrate discharge is 8.52 × 10 9 mol and is 10 % less than our preferred estimate; the resulting relative deviations are shown in Table 2 We consider the mass flux of atmospheric deposition of nitrate to be reliable, because differences in estimates from previous studies are quite small. According to these previous estimates (Zhao et al., 2017;Liu et al., 2003), we adopt the minimum and maximum in mass flux of 3.14 × 10 9 mol to 3.65 × 10 9 mol for uncertainty estimates.

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The flux of SFGD into the BHS varies in the range of 2.68 × 10 9 mol to 5.82 × 10 9 mol, which is mainly due to the different SFGD water fluxes assumed in our budget. Only if m SFGD is assumed to be > 2.90 × 10 9 mol the results match our assumption. When m SFGD = 5.82 × 10 9 mol, the relative deviations are large ( Table 2), implying that our budget is very sensitive to m SFGD .
The flux of denitrification in the BHS has a confidence interval of 15 % , resulting in the m dentr to 475 range from 8.57 × 10 9 mol to 11.60 × 10 9 mol. The results of tests with these two fluxes are shown in Table 2.
Overall, these tests indicate that and δ O SFGD 18 vary by ±50 % and are particularly sensitive to uncertainties of the assumed endmembers, whereas the relative deviations of m ntr , m sink normally vary in the range of ±20 %. Uncertainties will be significantly reduced if any of these terms can be constrained by further empirical studies.

Biogeochemical implications of the box model
In other coastal eutrophic regions, such as the North Sea, a high δ 15 N of river nitrate is reflected in a halo of high δ 15 N in surface sediments in offshore areas . In the Bohai Sea, such an isotopic halo of river-borne eutrophication is not observed despite similar water exchange rates of 1-2 years Serna et al., 2010) and similarly isotopically 485 enriched river inputs. We speculate that the lack of a fingerprint of river nitrate in the δ 15 N of sediments of BHS may be masked by active nitrification and atmospheric deposition that rapidly eradicate and homogenise spatial gradients.
Despite the uncertainties that are related to the box model approach, combining mass and isotope budgets of nitrate sources and sinks is clearly superior to solely nitrate mass balance considerations, especially when it comes to segregating the anthropogenic nitrate and the recycled nitrate inputs. It is of note that the BHS does not appear to pass on significant amounts 490 of nitrate to the adjacent northern YS, so that the effects of excessive loading of this shallow mixing zone between land and ocean with anthropogenic nitrogen are yet mitigated by internal cycling processes.

Conclusions
Rivers contributed 19.2-25.6 % and the combined terrestrial runoff (including submarine discharge of nitrate with fresh groundwater) account for 27.8-37.1 % of the total nitrate input to the BHS. Atmospheric input contributes 6.9-22.2 % of 495 nitrate to the BHS. Nitrification contributes 40.7-65.3 % of the total nitrate, indicating an unusually active interior nitrogen cycling of in the BHS. Nitrate was mainly trapped in the BHS and only very little was exported to the YS (only 1.8-2.4 %).
Furthermore, nitrate was rather assimilated than exported to the YS along the main transport pathway Lubei Coastal Current, effectively retaining Nr in BHS. Sedimentation trapped 70.4-77.8 % of nitrate inputs, whereas denitrification was only active in the sediments that removed 20.4-27.2 % of nitrate from the pool. Seasonal biogeochemical variations were observed in the 500 BHS in that dissolved inorganic nitrogen increased during summer under the thermocline, implying significant biological regeneration. If the interior cycling increases, for instance fueled by increased terrestrial and atmospheric Nr inputs, respiration coupled to organic matter and N recycling will increase and water-column hypoxia could consequently spread in the future and compromise ecosystems in the BHS. Whether this will invigorate water-column denitrification to balance the additional inputs is an open question, as is the capacity of BHS as a nitrate buffer between the growing source of Nr on land and the open 505 ocean.