The density of seawater as a function of salinity ( 5 to 70 g kg − 1 ) and temperature ( 273 . 15 to 363 . 15 K )

Abstract. New seawater density measurements were made as a function of temperature T=(273.15 to 363.15) K and salinity (5 to 70 g kg−1). The measurements (N=230) from T=273.15 to 313.15 K and Practical Salinity (S) from 0 to 40 were found to be in good agreement (σ=0.0036 kg m−3) with the equation of state of seawater (Millero and Poisson, 1981) made on samples with a known chlorinity (Cl). These results indicate that the Practical Salinities (S) are in agreement to within ±0.003 kg m−3 with the values calculated from the Chlorinity, SCl=1.80655 Cl. The measurements from 298.15 to 363.15 were used to extend the equation of state to high temperatures and salinities. All the densities were made relative to pure water (ρ−ρ0 where ρ0 is the density for pure water) were fitted to equations of the form (ρ−ρ0)/(kg m−3)=A SA+B SA1.5+C SA2 where A, B, and C are functions of temperature and SA (g kg−1) is the absolute salinity, SA=(35.16504/35) S g kg−1. The fitted results from SA=0 to 50 g kg−1 and T=273.15 to 313.15 K (N=242) gave standard errors of 0.0037 kg m−3. The fitted results from 298.15 to 363.15 K (N=280) gave standard errors of 0.0063 kg m−3 and all the results (N=522) from 273.15 to 363.15 K gave standard errors of 0.0063 kg m−3. The earlier density measurements (Millero et al., 1976b; Poisson et al.,1980) used to determine the equation of state of seawater (Millero and Poisson, 1981) were combined to derive equations that are valid from 273.15 to 313.15 K and 273.15 to 363.15 K. The standard errors of these fits are respectively, 0.0038 kg m−3 (N=713) and 0.0063 kg m−3 (N=962). These new measurements expand the equation of state of seawater to a wider range of temperature (273.15 to 363.15) K and absolute salinity (0 to 70 kg m−3.


Introduction
The original one atmosphere density measurements used to determine the equation of state of seawater (Millero and Poisson, 1981) were made on seawater of a known Chlorinity (Cl).The salinities of these samples were determined using the relationship S Cl = 1.80655Cl (1) This relationship may or may not be valid at the present time (Millero et al., 1976a).For example, the differences in the Practical Salinity (S) and Chlorinity salinity (S Cl ) calculated from Eq. (1) may vary by as much as 0.0055 (Fig. 1).This difference is equivalent to an error in density of ±0.0041 kg m −3 .
The present one atmosphere equation of state for seawater is limited to Practical Salinities from 0 to 40 and temperatures from 273.15 to 313.15 K.The equation was derived from the measurements of Millero et al. (1976b) and Poisson et al. (1980).A summary of these measurements are given in Table 1.The equation of state derived from the studies of Millero et al. (1976b) and Poisson et al. (1980) had a 1σ =0.0035 kg m −3 similar to the individual studies.Poisson and Gadhoumi (1993) have extended the range to higher Practical Salinities (S=50) from 288.15 to 303.15 K.They give equations that represent this data with standard errors close to those of the equation of state (Millero and Poisson, 1981).Measurements to a higher temperature are not available at the present time.As the physical chemical properties  Millero et al. (1976b) 122 0.0035 kg m −3 273.15 to 313.15 K 1 to 40 Poisson et al. (1980) 344 0.0035 kg m −3 273.45 to 303.15 K 5 to 41 Poisson and Gadhoumi (1993)  of seawater are known to higher temperatures (Millero and Pierrot, 2005;Feistel, 2008), there is a need for density measurements at higher temperatures and salinities.In this paper, measurements of the density of seawater on the Practical Salinity Scale (S) have been made from 273.15 to 315.15 K and are compared to those calculated from the equation of state (Millero and Poisson, 1981).New measurements of the density of seawater to 363.15 K as a function of absolute salinity, S A from 0 to 70 g kg −1 are also reported.This study is part of a work to extend the equation of state of seawater over a wider range of temperature and salinity (Feistel, 2008).The results will be useful in examining the use of ionic interaction models (Pierrot and Millero, 2000) to estimate the density over a wide range of temperature and ionic strength and in the future to examine the PVT properties of hydrothermal waters.

Experimental methods
The seawaters used in this study were Standard Seawater (S=35.00)and surface Gulf Stream seawater (S=36.10).Both waters have low nutrient concentrations and had densities that agreed at similar salinities to ±0.003 kg m −3 .Solutions at low salinities were obtained by adding ion exchange water by weight and the high salinities by slowly evaporating the samples.No visible precipitation appeared during the sample preparation.The Practical Salinities were measured with an Autosal salinometer calibrated with Standard Seawater.The precision of the Practical Salinity is 0.0005 on a given sample.The absolute salinities of the evaporated samples were back calculated from the weight of the added water needed to dilute it to a salinity range that can be measured by conductivity and density at 298.15 K.The salinities of the evaporated samples are estimated to be accurate to ±0.003 g kg −1 .
The densities were measured on a Paar 500 vibrating tube densimeter at a fixed temperature (±0.003K) determined with a Platinum thermometer in the instrument.The densimeter is calibrated with deionized water (Millipore Su-perQ) and dry air.The measurements made at high temperatures were made on degassed samples heated to 363.15 K to avoid bubble formation in the instrument.The measurements were then made from 263.15 to 298.15 K. Densities made on Standard Seawater were repeatable to 1σ =0.003 kg m −3 from 273.15 to 323.15 K and agree with values calculated from the equation of state (Millero and Poisson, 1981) to ±0.0035 kg m −3 from 293.15 to 313.15 K.The measurements at temperature above 323.15K have an estimated uncertainty of ±0.006 kg m −3 based on repeat measurements of the same sample.All of the measurements were made relative to the density of water which is based on the equations of Kell (1975) adjusted to the 1990 temperature scale (Spieweck and Bettin, 1992).These are the densities that are embedded in the densimeter.The values of the relative densities (ρ−ρ 0 ) are not affected by densities used in the calibration of the system.The measured water values from 273.15 to 363.15 K agreed to the calculated values to ±0.002 kg m −3 .Since the density of water (ρ 0 ) in the original equation of state of seawater is based on the less reliable water equations of Bigg (1967) and the values used in the instrument, all of our measurements are reported and compared to the equation of state of seawater (Millero and Poisson, 1981) in terms of the differences in the density of seawater and water (ρ−ρ 0 ) kg m −3 .
A number of density measurements on deep waters in the Atlantic (Millero et al., 1976a;1978), Indian (Poisson et al., 1981;Millero et al., 2008a), and Pacific oceans (Millero et al., 1978;2009) and the Red (Poisson et al., 1981) and Baltic Seas (Millero and Kremling, 1976) are higher than the values determined from the equation of state (Millero and Poisson, 1981).This is attributed to the added salts to seawater from the dissolution of SiO 2 (s) and CaCO 3 (s) and the addition of CO 2 and nutrients from the mineralization of organic matter (Brewer and Bradshaw, 1975;Millero, 2000).Since the conductivity salinity does not respond to all the components in seawater, it is useful to examine the physical properties in terms of the absolute salinity (Millero et al., 2008b;Feistel, 2008).The absolute salinity (g kg −1 ) is defined (Millero et al., 2008b) by where the Reference Salinity (S R ) is related to the Practical Salinity (S) by and S is the increase due to added salts (Brewer and Bradshaw, 1975;Millero, 2000;Millero et al., 2008b).The values of S can be estimated by determining the added Si, Ca, NO 3 , PO 4 and TCO 2 to seawater (Millero et al., 2008a;2009).It can also be estimated (Millero et al., 2009) from the differences between the measured densities and the values determined from the equations of state using the approximate equation where ρ=ρ (measured)ρ (calculated from the equation of state) at 25 • C. For seawater with no added salts the values of S A are equal to the Reference Salinity S R and can be estimated from the Practical Salinity using Eq. ( 3).

Results and discussion
The densities made in this study are given in the Appendix Tables A1 and B1 Fig. 2. The differences in the measured (N=230) densities (ρ−ρ 0 , kg m −3 ) with those calculated from the equation of state (Millero and Poisson, 1981) as a function of temperature and salinity (σ =0.0036 kg m −3 ).
to the values calculated from the equation of state (Millero and Poisson, 1981) as a function of temperature and salinity in Fig. 2. The standard error between the measured and calculated values was 0.0036 kg m −3 .This is similar to the errors in the repeat density measurements (±0.003 kg m −3 ) on the same sample and indicates that the salinities calculated by conductivity (S) and Chlorinity (S Cl ) are in agreement to ±0.004 g kg −1 .It should be pointed out that our measurements made at salinities above 40 are higher by as much as 0.064 kg m −3 with the measurements of Poisson and Gadhoumi (1993) at 288.15, 298.15 and 303.15 K.The internal consistency of the measurements was examined by fitting the relative densities to an equation of the form The variable A, B and C are functions of temperature (T /K) The parameters needed to fit the seawater measurements (N=242) from 273.15 to 313.15 K and S A from 5 to 50 (g kg −1 ) are tabulated in Table 2 along with the standard error of the fit (σ =0.0037 kg m −3 ).This standard error of the 273.15 to 313.15 K fit is similar (Fig. 2) to the differences between our measurements and those calculated from the equation of state of seawater (Millero and Poisson, 1981).The parameters needed to fit the seawater measurements (N=280) from 298.15 to 363.15 K are also tabulated in Table 2 along with the standard error of the fit (σ =0.0063 kg m −3 ).All of the measurements from 273.15 to 363.15 K (N=522) have also been fitted to Eq. ( 5).The parameters for the fits are given in Table 2 along with the standard error of the fit (σ =0.0063 kg m −3 ).The differences between the measured and calculated densities from these fits are shown in Fig. 3.Most of the differences are within 2σ , where σ is the standard error of the fit.The errors appear to be larger at high temperatures, apparently due to difficulties in removing air from the samples.These measurements extend the equation of state to seawater as a function the absolute salinity S A g kg −1 over a wide range of temperature and salinity.
The measurements made in this study from 273.15 to 315.15 K and 273.15 to 363.15 K have been fitted to Eq. ( 5) of Poisson et al. (1980).Millero et al. (1976b), and this study as a function of temperature and salinity (σ =0.0037 kg m −3 ).
with all of the measurements used to determine the International Equation of state of seawater (Millero et al., 1976b;Poisson et al., 1980).The results of these fits (N=713 from 273.15 to 313.15 K and N=962 from 273.15 to 363.15 K) are tabulated in Table 3 along with the standard errors, respectively σ =0.0036 kg m −3 and σ =0.0063 kg m −3 .The differences between the measured and calculated densities from 273.15 to 313.15 K and 273.15 to 363.15 K) are shown respectively, in Figs. 4 and 5.As with our other fits, most of the differences are within 2σ .
It should be pointed out that the earlier measurements (Millero et al., 1976b;Poisson et al., 1980) made on the 1968 temperature scale were converted to the 1990 temperature scale (Preston-Thomas, 1990).Changes in the temperature scale do not significantly affect the values of (ρ−ρ 0 ) which do not vary much with temperature.The results of this study can be used to determine the properties of seawater and most estuarine waters over a wide range of Absolute Salinity and temperature.These results will also be useful in extending the ionic interaction model for seawater (Pierrot and Millero, 2000) to 363.15 K. Future work on the density of seawater above 373.15K at applied pressure are needed to extend the temperature range to the levels available for the thermochemical properties of seawater (Millero and Pierrot, 2005;Feistel, 2008).as a function of temperature and salinity (σ =0.0062 kg m −3 ).The closed circles are from 273.15 to 313.15 K (Poisson et al., 1980;Millero et al., 1976b) and the open circles from this study are from 298.15 to 363.15 K.
Table 3.The coefficients for the densities measured in this study and literature data (Millero et al., 1976b;Poisson et al., 1980)

Figure 1 Fig. 1 .
Figure 1Fig.1.The differences between the Practical Salinity (S P SS ) and the value calculated from the Chlorinity (S Cl =1.80655 Cl) for the last series of Standard Seawater where Chlorinity was measured (P91 to P113).The dotted lines are 2σ .

T
Figure 2

Figure 5 Fig. 5 .
Figure 5Fig.5.The deviations between the measured (N =962) and calculated values from 273.15 to 363.15 K and S A from 0 to 70 g kg −1 as a function of temperature and salinity (σ =0.0062 kg m −3 ).The closed circles are from 273.15 to 313.15 K(Poisson et al., 1980;Millero et al., 1976b) and the open circles from this study are from 298.15 to 363.15 K.

Table 1 .
Summary of the 1 atm density measurements made on seawater.

Table 2 .
The coefficients for the densities measured in this study fitted to Eq. (2).