The TEOS-10 Solution Absolute Salinity of seawater is essentially based on adding up the mass of solute in a seawater sample: 1SAsoln=∑i=1NcMici, where ci is the molar concentration of component i in seawaterkg-1, Mi is the molar mass of the component, and Nc is the number of species of component in seawater. However, it is impractical to carry out a full chemical analysis for the seawater to get the SAsoln 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: 2ρ=fTEOS-10(SA,t,p), where fTEOS-10 is a specified function. Therefore, SA is also called a Density Salinity.

Unfortunately, although for many purposes we can treat SA and SAsoln interchangeably, at highest precisions SA≠SAsoln 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 of dissolved material in a sample of arbitrary salinity with the RC. This estimate is based on the widely used Practical Salinity SP (UNESCO, 1981): 3SR=uPS⋅SP,2<SP<42. In Eq. (), the factor uPS between the Reference Salinity of Standard Seawater and the Practical Salinity is (35.16504/35) gkg-1 and is not equal to 1 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 regarded 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: 4SA=SR+δSA. At present there are three methods for determining the Absolute Salinity Anomaly δSA. First, it can be obtained by comparisons with direct density measurements performed in the laboratory (Millero et al., 2008; Wright et al., 2011). According to the density difference ρ=ρlab-ρ(SR,25∘C,0dbar) and the haline contraction coefficient, which is 0.7519 for SSW, δSA is determined by 5∂ρ∂SAt=25∘C,p=0dbar≈0.7519kgm-3(gkg-1)-1. 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 whether chemical measurements of the most variable seawater constituents in the open ocean (carbonate system and macro-nutrients) are also available (Pawlowicz et al., 2011; IOC et al., 2010). 6δSAdens/mgkg-1=55.6×Δ[NTA]+4.7×Δ[NDIC]+38.9×NO3-+50.7×Si(OH)4 The units of each component on the right are all millimole per kilogram, Δ[NTA]=TA-2.3×SP/35 is the standardized change in Total Alkalinity (TA), and Δ[NDIC]=DIC-2.08×SP/35 is the standardized change in total Dissolved Inorganic Carbon (DIC). Note that the coefficients of this model are calculated using a numerical model for chemical interactions (Pawlowicz, 2008, 2010; Pawlowicz et al., 2011), which performed well against lab studies and were shown to have reasonable accuracy for seawater samples by Wooseley et al. (2014). An important aspect of this modeling is that, in order to maintain a charge balance in the dissolved constituents, it was assumed that calcium concentrations also changed according to 7Δ[NTA]=2ΔNCa2+-ΔNO3-, in which ΔNCa2+=Ca2+-10656.6⋅SP/35/(µmolkg-1) and Ca2+ and SP are the measured value of Ca2+ and Practical Salinity of seawater, respectively. Calcium was chosen to balance charge since it is (a) not usually measured but (b) it is known to vary in its relative composition by a few percent in the open ocean. However, the accuracy of this relationship is not known.

Third, Absolute Salinity Anomaly δSA can be found from a global δSA climatology created by McDougall et al. (2012). Due to the lack of seawater component data, McDougall et al. (2012) carried out regression calculation on the Practical Salinity, density, and silicate concentration data of 811 seawater samples worldwide and found that δSA can be directly related to Si(OH)4: 8δSA/(gkg-1)=SA-SR/gkg-1=98.24Si(OH)4/molkg-1, although for further work the numerical coefficient was tuned for specific ocean basins. Taking the effects of evaporation and rainfall on ocean salinity into consideration, Eq. () can be simplified as 9δSA=RδSR(except the Baltic Sea), in which Rδ=δSAatlas/SRatlas; both the SRatlas and δSAatlas are from the Gouretski and Koltermann (2004) hydrographic atlas. 10SA=uPSSP1+Rδ=35.16504/(gkg-1)35SP1+Rδ Equation () is adopted in the official Gibbs SeaWater Oceanographic Toolbox (available from http://www.teos-10.org, last access: 8 June 2021, McDougall and Barker, 2011) to calculate that δSA with uncertainty in the ocean is less than 0.0047 gkg-1. For the semi-enclosed Baltic Sea, Feistel et al. (2010a) have fitted an empirical formula for calculating δSA, which is mainly due to rivers bringing material of anomalous composition into the Baltic Sea, and this formula has also been incorporated into the Gibbs SeaWater (GSW for short) algorithm library.

In the work described here we compare the latter two methods.

The near-synchronous oceanographic and ocean chemical data used here are from 1480 stations covering Chinese offshore waters that were set up for the Marine Integrated Investigation and Evaluation Project of the China Sea conducted by the State Oceanic Administration of China (Xiong, 2012; Ji, 2016), as shown in Fig. 1. At these sites, surface, 10 m, 30 m and bottom values for nutrients, as well as TA and pH, are available for the four seasons of spring (April–June), summer (July–September), autumn (October–December), and winter (January–March) of 2006 to 2007. Since in situ observation of DIC is missing in this project, it is derived from pH and TA data using the CO2SYS software released by the Department of Ecology of Washington State, USA, based on the carbonate equilibrium (Lewis and Wallace, 1998).

The first step in determining Absolute Salinity 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<SP<42, values for samples in the mouth of the Yangtze River, Qiantang River, and Pearl River (labeled in Fig. 1) whose SP values less than 2 are recalculated with a modified form of the Hill et al. (1986) formula based on the in situ conductivity, temperature, and pressure. Then Eq. () is used to get SR.

Based on our observations (Fig. 1), the Reference Salinity SR of Chinese offshore seawater diluted by low-salinity river runoff ranges from 0.01 to 34.66 gkg-1. The extreme minimum SR of 0.01 gkg-1 appears in the south branch of Yangtze River in the summer of 2006, and the maximum of 34.66 gkg-1 appears in the path of the Kuroshio Current (Fig. 2). Low salinities are also seen in the Pearl River estuary and to a lesser degree in shallow areas of the southern Yellow Sea, as well as near a few other river mouths.

Using Eq. (), the estimated δSA of Chinese offshore waters ranges from -0.05 to 0.28 gkg-1 (Fig. 3). The largest Absolute Salinity Anomalies are 1 order higher than those of the open ocean. As much as 90 % of the calculated δSA arises from the Δ[NTA] term in Eq. (), so that areas with high δSA also have high Δ[NTA] (Fig. 4). The largest δSA values appear in the Yangtze River estuary, Hangzhou Bay, Laizhou Bay, Bohai Bay, North Jiangsu Shoal, and the 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 the same water composition as the Yangtze River estuary. Thus, in this paper, the waters in the Yangtze River estuary and Hangzhou Bay are analyzed as a single water mass. The δSA values in the above coastal regions, which are often in excess of 0.05 gkg-1, are given in Table 1.

The maximum δSA of 0.28 gkg-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 sea, the silicate concentration exceeds 100 µmolkg-1, Δ[NTA] is larger than 1 mmolkg-1, and the δSA is greater than 0.1 gkg-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 gkg-1 isocline varies with seasons and depths and reaches a maximum in summer but with little variation in other seasons. In this region, 54 % and 26 % of negative δSA appear in spring and winter, respectively, which also mainly arises from Δ[NTA].

In the northern North Jiangsu Shoal, the maximum δSA of 0.23 gkg-1 appears in the bottom layer in winter. Centered at 33.4∘ N and 121∘ E, many points have a δSA greater than 0.05 gkg-1 all year round, which gradually decreases from the coast to the offshore. The δSA of the bottom layer is higher than that of the surface layer in a dry season (spring and winter) but smaller in a flood (summer and autumn) season, in which more terrestrial input is brought by Huai River system.

The largest δSA of 0.20 gkg-1 in the Bohai Sea appears at the bottom of Laizhou Bay in winter, and seasonal characteristics are basically the same as the North Jiangsu Shoal, although in summer more terrestrial material is input by the Yellow River. As the Bohai Sea is 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 gkg-1 and the δSA difference between the bottom and the surface within the same season is not as significant as its seasonal variation in the area.

A δSA of greater than 0.05 gkg-1 also occurs at the mouth of the Pearl River and Min River in summer, but values are less than 0.02 gkg-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 0.005 gkg-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 Eq. (), which is meant for seawater of relatively high salinity, to estimate the Absolute Salinity Anomaly near river mouths where the salinity is far smaller, a more complex calculation of the δSA, based on a full chemical analysis of river water composition, was plotted for some of these rivers (the Yangtze, the Pearl and Min rivers) in Pawlowicz (2015). The values calculated in that work are consistent with those found here (Table 2).

Although the Absolute Salinity Anomalies within rivers are always non-zero, the Absolute Salinity Anomaly is significantly non-zero 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 the Absolute Salinities Anomalies in each can be parameterized separately.

China offshore seawater is a mixture of the Kuroshio water originating from the North Equatorial Current and the runoff into the sea. The Absolute Salinity Anomaly in Pacific surface waters in any case is generally small; it is the deeper waters that have (relatively) large Absolute 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 Feistel et al. (2010b), these four water masses are regarded as the mixture of Standard Seawater that has standard-ocean salinity, with the local coastal water which contains unknown amounts of unknown solute. The related regression lines of the four water masses between Absolute Salinity Anomaly and the Reference Salinity can be computed from the samples with salinity SR>2 gkg-1, in which the seawater endpoints are chosen to be SSW with a δSA of zero, as shown in Eq. () and Fig. 5. SA-SR=412236150107/mgkg-1⋅1-SRSSO,11Laizhou Bay and Bohai BayNorth Jiangsu ShoalYangtze River estuary and Hangzhou BayPearl River estuary

The linear correlation between Absolute Salinity Anomaly and SR in the Pearl River estuary is the strongest among the four regions, which shows that the mixture between the coastal seawater and that of the open ocean is relatively conservative. There are many measurements over all salinities for the Yangtze River water. The strong scatter visible in Fig. 5 at low salinities is likely due to the rich (and highly variable) nutrient loading brought by Yangtze River draining from land.

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 gkg-1. The fitted curves are somewhat steeper. Note that Pawlowicz (2015) also finds that Absolute Salinity Anomalies in the Yellow River of about 0.2 gkg-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 heavily influenced by many high values when salinities are between 20 and 25 gkg-1 and lies somewhat above a smaller number of values spread over lower salinities.

It can be seen from Fig. 5 that the relative composition anomalies decrease from north to south. The exchange of coastal waters with the open-ocean waters increases gradually from the northernmost (and somewhat enclosed) Bohai Sea estuary to the southernmost Pearl River area, which is open to the South China Sea.

In Eq. (), the coefficients are determined by fitting to the results of more complete calculations that assume changes to Ca2+ to maintain a charge balance according to Eq. (). We cannot directly check the accuracy of this assumption. However, Ca2+ was directly measured from samples in 13 cruises from April 2011 to February 2012 (Qi, 2013). Although these measurements do not occur at the same time as our larger dataset, we can group these measurements in the same regions (labeled in Fig. 1) in which we find large Absolute Salinity Anomalies. Then, we find that the ΔN[Ca2+], ΔNO3-, and Δ[NTA] (first column) values from our dataset (Table 3) are approximately consistent with Eq. ().

The other nutrient of phosphate is not considered in the calculation, for its concentrations range from 0 to 0.01 mmolkg-1 in the existing observation, which is much smaller than those items in Eq. () above, and its effect is negligible. In this case, ΔNO3- is mostly negligible and ΔN[Ca2+] is about 43%∼58% of Δ[NTA], in the Bohai Sear, southern Yellow Sea, East China Sea, and the Yangtze River.

The importation of Ca2+ and the carbon system suggest that the major source of Absolute Salinity Anomalies in shelf areas is the high CaCO3 content of rivers. This is consistent with Absolute 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 Huai rivers. The importation fluxes of Ca2+ into the sea from the Yellow River and the Yangtze River are 3.6×1010 and 6.5×1011 molyr-1, respectively, in 2011 (Qi, 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 CaCO3 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 southern Yellow Sea near China has always been high; even when strong biological activity in spring reduces the surface Δ[NTA], the sediment of particulate inorganic carbon will resuspend and maintain the high level of dissolved CaCO3 of seawater through the solid–liquid balance (Hong, 2012; Zhang et al., 1995).

Using the GSW function library and the corresponding climatological silicate and Practical Salinity data, the calculated δSA of China offshore waters ranges from 0 to 0.002 gkg-1. This is 2 orders of magnitude less than the values calculated in Sect. 3.2. The spatial distribution characteristics are also significantly different. These differences mainly come from the following aspects:

Instead of silicate, CaCO3 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 gkg-1.