Estimating the Absolute Salinity of China Sea Using Nutrients and Inorganic Carbon Data

In June 2009, the Intergovernmental Oceanographic Commission of UNESCO released the international thermodynamic equation of seawater – 2010 (TEOS-10 for short) to define, describe and calculate the 10 thermodynamic properties of seawater. Compared to the Equation of State-1980 (EOS-80 for short), the most obvious change with TEOS-10 is the use of Absolute Salinity as salinity argument, replacing the Practical Salinity used in the oceanographic community for 30 years. Due to the lack of observational data, the applicability of the potentially increased accuracy in Absolute Salinity algorithms for coastal and semi-enclosed seas is not very clear to date. Here, we discuss the magnitude, distribution characteristics and formation mechanism of Absolute Salinity and Salinity Anomaly 15 in Chinese shelf waters, based on the Marine Integrated Investigation and Evaluation Project of China Offshore and other relevant data. The Absolute Salinity SA ranges from 0.1 to 34.66 g·kg. Instead of silicate, CaCO3 originating from terrestrial input and re-dissolution of shelf sediment is most likely the main composition anomaly relative to SSW and the primary contributor to the Absolute Salinity Anomaly δSA. Finally, relevant suggestions are proposed for the accurate measurement and expression of Absolute Salinity of the China offshore. 20

constituents whereas Practical Salinity depends only on their conductivity. Since the relative amounts of different 25 constituents change from place to place and from time to time, accounting for the biases that are introduced by these changes may be important. However, appropriate methods for frequent and regular measurements of the dissolved content directly in ocean studies are still a topic of research.
At present, the TEOS-10 Absolute Salinity of a seawater sample is obtained by adding Absolute Salinity Anomaly δSA to Reference Salinity SR, in which SR is the mass fraction of dissolved material in a stoichiometric composition model 30 (the Reference Composition or RC) of seawater, defined by Millero (2008), for which the reference material known as IAPSO Standard Sea Water (SSW for short), is a good approximation, of the same conductivity as that of the sample. Although there have only been very few direct measurements of conductivity and density in such areas (Millero 1984, Feistel et al., 2010a, Pawlowicz (2015) used chemical composition/conductivity/density modelling and climatological 40 data to estimate the Absolute Salinity Anomaly near many rivers around the world, finding values of up to one order of magnitude higher than those extrapolated from the open ocean.
The coastal areas of China comprise one of the widest shallow seas in the world, with a large north-south span, numerous estuaries and bays, and a large amount of fresh water input from rivers. The relative composition of this coastal seawater may not only differ from that of the open ocean but also vary from place to place. However, the 45 influence of relative composition variation on the Absolute Salinity in this area has never been systematically studied, although salinity measurement has played an important role in Chinese national ocean survey projects since 1957 (CSTPRC,1964) and for metrological purposes a Chinese primary seawater standard has been developed (Li et al., 2016). Moreover, in any efforts to detect salinity variations associated with climate change variability in Bohai and northern Yellow Sea (Wu et al., 2004a;Wu et al., 2004b;Xu, 2007;Lv, 2008;Song, 2009) , Practical Salinity S P is still 50 used as the simplicity of Absolute Salinity and its change caused by the relative composition variation is ignored. That will raise obvious problems in the correct presentation of time series and/or transects that begin near the coast and end well offshore . Therefore, in this paper we first clarify the definition, status and application of TEOS-10 Absolute Salinity. Second, based on the measured data and related research results, we estimate the magnitude, temporal and spatial distribution 55 characteristics and formation mechanisms giving rise to Salinity Anomalies in Chinese coastal seawaters. Finally, based on the above results, we put forward relevant suggestions and future research directions for the accurate measurement and expression of absolute salinity of Chinese offshore seawaters.

2
Methods and data

Calculation of Absolute Salinity 60
The TEOS-10 Solution Absolute Salinity of seawater is essentially based on adding up the mass of solute in a sea water sample, Where, c i is the molar concentration of component i in seawater per kilogram, M i is the molar mass of the component, and N c is the number of species of component in seawater. However, it is impractical to carry out a full chemical 65 analysis for the seawater to get the soln regularly. The primary and most demanding purpose of oceanographic salinity measurements is the calculation of seawater density to estimate significant ocean currents driven by sometimes tiny horizontal pressure gradients. In TEOS-10, Absolute Salinity is instead defined so that the density of seawater can be accurately calculated by the following equation.
where f_ TEOS-10 is a specified function. Therefore, SA is also called a density salinity. Unfortunately, although for many purposes we can treat A and soln interchangeably, at highest precisions A ≠ A soln due to small changes in the relative composition of sea salt. In order to get SA at this highest precision, Millero (2008) first defines a stoichiometric composition model (the Reference Composition or RC), based on a reference material (IAPSO Standard Seawater), and specifies an algorithm to determine a consistent estimate of the mass fraction 75 of dissolved material in a sample of arbitrary salinity with the RC. This estimate is based on the widely-used Practical Salinity S P (UNESCO, 1981): In Eq. (3), the factor PS between the reference salinity of standard seawater and the practical salinity is (35.16504/35) g· kg -1 , and is not equal to one mainly because an evaporative technique used by Sørensen in 1900(Forch et al., 1902 led to the loss of some volatile components of dissolved material.
General seawater can be considered as the mixture of standard seawater concentrated/diluted with pure water and a small amount of other components. The calculation formula of Absolute Salinity from Reference Salinity requires the addition of a correction, the Absolute Salinity Anomaly δSA: At present there are three methods for determining Absolute Salinity Anomaly δSA. First, to obtain it by comparisons with direct density measurements performed in the laboratory (Millero et al., 2008;Wright et al., 2011). According to the density difference = − ( R , 25℃, 0 dbar) and the haline contraction coefficient which is 0.7519 for SSW, δSA is determined by This procedure is useful for laboratory studies or in situations where ocean water can be obtained from sampling bottles retrieved from certain depths for subsequent laboratory measurements of density.
Second, it can be estimated using a correlation equation, if chemical measurements of the most variable seawater constituents in the open ocean (carbonate system and macro-nutrients) are also available , IOC et al., 2010 (Pawlowicz,2008, Pawlowicz et al., 2010, which performed well against lab 100 studies, and were shown to have reasonable accuracy for seawater samples by Ryan (2014). An important aspect of this modelling is that, in order to maintain a charge balance in the dissolved constituents, it was assumed that calcium concentrations also changed according to: Calcium was chosen to balance charge since it is a) not usually measured, but b) it is known to vary in its relative 105 composition by a few percent in the open ocean. However, the accuracy of this relationship is not known. (1 + ) (10) 115 Eq.(10) is adopted in the official GSW software toolbox (available from www.teos-10.org) to calculate δSA with uncertainty in the ocean is less than 0.0047g· kg -1 . For the semi-enclosed Baltic sea, Feistel (2011) has fitted an empirical formula for calculating δSA which is mainly due to rivers bringing material of anomalous composition into the Baltic, and this formula has also been incorporated into GSW algorithm library.
In the work described here we compare the latter two methods.

Observation data
The near-synchronous oceanographic and ocean chemical data used here are from 1,480 stations covering Chinese offshore waters that were set up for the Marine Integrated Investigation and Evaluation Project of China offshore Since in-situ observation of DIC is missing in this project, it is derived from pH and TA data using CO2SYS software released by the department of ecology of Washington State based on the carbonate equilibrium (Lewis, et al. 1998).

Reference Salinity SR of the China offshore seawater
The first step in determining salinity anomalies is to estimate the Reference Salinity based on the Practical Salinity.
Because the standard PSS-78 algorithm for Practical Salinity is only valid in the range 2 < S P < 42, values for samples in the mouth of Yangtze River, Qiantang River and Pearl River (labelled in Fig.1) whose S P less than 2 are recalculated 135 with a modified form of the Hill et al. (1986) formula based on the in-situ conductivity, temperature and pressure. Then Based on our observations (Fig. 1), the Reference Salinity S R of Chinese offshore seawater diluted by low salinity river runoff ranges from 0.01 to 34.66 g· kg -1 . The extreme minimum S R of 0.01 appears in the south branch of Yangtze River in the summer of 2006 and the maximum of 34.66 appears in the path of the Kuroshio current (Fig. 2). Low 140 salinities are also seen in the Pearl River estuary and to a lesser degree in shallow areas of the South Yellow Sea, as well as near a few other river mouths.

Absolute salinity Anomaly δSA of Chinese offshore waters
Using Eq. (6), the estimated δS A of Chinese offshore waters ranges from 0 to 0.30 g· kg -1 (Fig. 3). The largest Salinity 145 Anomalies are one order higher than those of the open ocean. As much as 90% of the calculated δS A arises from Δ[NTA] term in Eq. (6), so that areas with high δS A also have high Δ[NTA] (Fig. 4). The largest δS A values appear in Yangtze River estuary, Hangzhou Bay, Laizhou Bay, Bohai Bay, North Jiangsu Shoals and Pearl River estuary.
Hangzhou Bay, which is adjacent to the Yangtze River estuary, has continuously transported water from the Yangtze River estuary due to its current and tidal characteristics (Yuan, 2009) and has almost same water composition with 150 Yangtze River estuary. Thus, in this paper, the waters in Yangtze River estuary and Hangzhou Bay are analyzed as a single water mass. The δS A in the above coastal regions, which are often in excess of 0.05 g· kg -1 , are given in Table 1.  The maximum δSA of 0.30 g· kg -1 appears at the sea surface of the Yangtze River Estuary and in Hangzhou Bay in summer. As China's largest runoff into the sea, the Yangtze River is rich in nutrients from land. At its entrance to the 160 sea, the silicate concentration exceeds 100 umol· kg -1 , Δ[NTA] is larger than 1 mmol· kg -1 and the δSA is greater than 0.1 g· kg -1 all year round, but these nutrient concentrations decrease rapidly away from the entrance. Δ[NTA] is the primary contributor to δSA. The surface coverage of the 0.05 g· kg -1 isocline varies with seasons and depths, reaches to the maximum in summer but with little variation in other seasons.
In the northern North Jiangsu Shoal, the maximum δSA of 0.23 g· kg -1 appears on the bottom layer in winter. Centered at 165 33.4°N and 121°E, many points have δS A greater than 0.05 g· kg -1 all the year round and gradually decreases from the coast to the offshore. The δSA of the bottom layer is higher than that of the surface layer in dry season (spring and winter), while smaller in flood (summer and autumn) season in which more terrestrial input is brought by Huaihe River system.
The largest δSA of 0.20 g· kg -1 in the Bohai Sea appears on the bottom of the Laizhou Bay in winter and seasonal 170 characteristics are basically the same as the North Jiangsu Shoal although in summer more terrestrial materials are input by the Yellow River. As a semi-enclosed shallow sea with lower exchange with the open ocean, the δSA in the whole Bohai Sea is always larger than 0.02 g· kg -1 and the δSA difference between of the bottom and that of the surface within the same season is not as significant as its seasonal variation in the area.
A δSA of greater than 0.05g· kg -1 also occurs at the mouth of the Pearl River and Minjiang River in summer, but values 175 are less than 0.02g· kg -1 in other seasons. However, these values are seen within the estuary with very little presence on the shelf. In the remaining areas, the magnitude of δSA is below 0.005g· kg -1 , which is about the same as the magnitude of the statistical uncertainty of the Absolute Salinity Anomaly in the open ocean, and so is essentially zero.
Although we have used eqn. (6), which is meant for seawater of relatively high salinity, to estimate the Salinity Anomaly near river mouths where the salinity is far smaller, a more complex calculation of the Salinity Anomaly, based 180 on a full chemical analysis of river water composition, was plotted for some of these rivers (the Yangtze, the Pearl and Minjiang Rivers) in Pawlowicz (2015). The values calculated in that work are consistent with those found here (Table   2). Table 2. δSA in some rivers as estimated in this paper, compared with values estimated using a more complete theory in Pawlowicz (2015). Units are mg· kg -1 . 185

Parameterisation of the Absolute Salinity of the China offshore waters
Although Salinity Anomalies within rivers are always non-zero, the Salinity Anomaly is significantly nonzero in only four areas along the Chinese coast and river mouths (hatched areas in Fig.3). They are occupied by different coastal water masses (Xiong, 2012) and Salinities Anomalies in each can be parameterized separately. The seawater of China offshore is a mixture of the Kuroshio water originating from the North Equatorial Current and 190 the runoff into the sea. The Salinity Anomaly in Pacific surface waters in any case is generally small; it is the deeper waters that have (relatively) large Salinity Anomalies arising from remineralization in the subsurface branch of the ocean's overturning circulation. In this paper, we ignore the relative composition difference between the Kuroshio and SSW for now. Following The linear correlation between Absolute Salinity Anomaly and S R in the Pearl River Estuary is the strongest among the four regions, which shows that the mixture between the coastal seawater and that of open ocean is relatively conservative. There are many measurements over all salinities for the Yangtze River water. The strong scatter visible in The regressions for the two northernmost areas are less precise, as the oceanographic sampling pattern does not enter into the rivers and measured salinities are larger than 25 g· kg −1 . The fitted curves are somewhat steeper. Note that Pawlowicz (2015) also finds that Salinity Anomalies in the Yellow River of about 0.2 g· kg −1 are also higher than in the other rivers (Table 2), although not as high as our fits in Fig. 5 suggest. The fit for the North Jiangsu Shoal region is 210 heavily influences by many high values when salinities are between 20 and 25 g· kg −1 , and lies somewhat above a smaller number of values spread over lower salinities.
It can be seen from

Relative composition anomaly of China offshore seawater
In Eq. (6), the coefficients are determined by fitting to the results of a more complete calculations that assume changes to Ca 2+ to maintain a charge balance according to Eq. (7). We cannot directly check the accuracy of this assumption.
However, Ca 2+ was directly measured from samples in 13 cruises from April 2011 to February 2012 (Qi Di, 2013).
Although these measurements do not occur at the same time as our larger dataset, we can group these measurements in 220 the same regions (labelled in Fig.1 (Table 3) , are approximately consistent with Eq. (7). The importation of Ca 2+ and the carbon system suggests that the major source of Salinity Anomalies in shelf areas is the high CaCO 3 content of rivers. This is consistent with Salinity Anomalies in the Baltic Sea, which were found to be mostly related to the calcium carbonate input from rivers (Feistel et al., 2010a). These rivers would be the Yangtze, Yellow River, and Huaihe Rivers. The importation fluxes of Ca 2+ into the sea of Yellow River and Yangtze River are 235 3.6×10 10 and 6.5×10 11 mol· yr -1 respectively in 2011 (Qi Di, 2013). In addition, there may be re-dissolution of sediments in the Yellow River Estuary and North Jiangsu Shoal. Due to the accumulation of materials entering the sea from the old Yellow River and the ancient Yangtze River, the CaCO 3 concentration of surface sediments on the seafloor of the North Jiangsu Shoal ranges from 2.8% to 10.5% (Qin, et al, 1989;Yang and Youn, 2007). The ΔNDIC of the south Yellow Sea near China has always been high, even when strong biological activity in spring reduces the surface 240 Δ[NTA], the sediment of PIC will resuspend and maintain the high dissolved CaCO 3 of seawater through the solidliquid balance (Hong, 2012;Zhang, et al, 1995).

Contrast to the δSA calculated by GSW
Using the GSW function library and the corresponding climatological silicate and practical salinity data, the calculated δSA of China offshore ranges from 0 to 0.002 g· kg -1 . This is two orders of magnitude less than values calculated in 245 Section 3.2. The spatial distribution characteristics are also significantly different. These differences mainly come from the following aspects: (1) Instead of silicate, CaCO 3 is most likely the main relative composition anomaly of China offshore seawater and the primary contributor to the δSA where it is greater than 0.05 g· kg -1 .
(2) High silicate concentrations (up to 100μmol·kg -1 ) do appear in Chinese coastal seawaters from the effects of river 250 (Fig 6), but these do not appear in the global silicate climatology used for the GSW calculations. However, even if they did, in these places NTA is even larger, so that the effects of this coastal silicate on the Salinity Anomaly is small. In the remaining areas, the silicate concentration is less than 20μmol· kg -1 , as shown in Fig.6. At 95 % degree of confidence, the difference between the observation and the GSW climatological dataset is [5.46, 6.21] μmol· kg -1 which does not change much with the seasons. It can be indicated the GSW climatological dataset basically reflects the 255 distribution characteristics of silicate in these areas.

Conclusion and analysis
The proposal and implementation of the concept of SA in TEOS-10 is meant to accurately quantify the total mass of 260 inorganic substance dissolved in sea water, to ensure that the density and related quantities are accurately represented by the Gibbs function for seawater and correct errors caused by the measuring the properties of seawater such as chloride and conductivity to get the salinity. In this paper, based on observations and calculations, the magnitude, distribution characteristics of Absolute Salinity in China offshore are described: 1) The Absolute Salinity SA ranges from 0.1 to 34.66 g· kg -1 , in which S R ranges from 0.01 to 34.66 g· kg -1 and the 265 Absolute Salinity Anomaly δSA ranges from 0 to 0.30g· kg -1 , this is an order of magnitude larger than the largest values in the open ocean. 2) The largest δSA are located in four distinct regions: the Yangtze River mouth/Hangzhou Bay, North Jiangsu Shoal, Bohai Sea, and the Pearl River mouth, all of which are areas where the Δ[NTA] is high; 3) Instead of silicate, CaCO 3 is most likely the main composition anomaly relative to SSW and the primary contributor 270 to the δSA in the above four areas; 4) Under the combined effects of different water system dynamics, terrestrial input, marine biological activities, and redissolution of marine sediments, the δSA in China offshore seasonal variations are obvious, and the maximum can be as high as 0.05g· kg -1 ; the difference between the surface layer and the bottom layer is also up to 0.1g· kg -1 ; With the observations available, this paper only lists the magnitude and distribution characteristics of δSA in China 275 offshore from 2006 to 2007, although it is likely that similar features will occur in other years. At present, we have collated the long-term series of seawater composition data to continue the study on δSA changes and get an empirical formula to calculate it.
The current researches are only based on the existing seawater composition data, and the exact influence of other changes to composition is still not very clear. To verify these findings, a complete chemical analysis and/or direct 280 measurements of seawater density would be useful in the estuaries of the Yangtze River, Qiantang River, Pearl River, Minjiang River, and the semi-enclosed Bohai Sea.