The determination of salinity by means of electrical
conductivity relies on stable salt proportions in the North Atlantic Ocean,
because standard seawater, which is required for salinometer calibration, is
produced from water of the North Atlantic. To verify the long-term stability
of the standard seawater composition, it was proposed to perform
measurements of the standard seawater density. Since the density is
sensitive to all salt components, a density measurement can detect any
change in the composition. A conversion of the density values to salinity
can be performed by means of a density–salinity relation. To use such a
relation with a target uncertainty in salinity comparable to that in
salinity obtained from conductivity measurements, a density measurement with
an uncertainty of 2 g m
For almost 40 years, the salinity “Salinity” refers strictly to
practical salinity unless there is an exact specification. Standard seawater
recognized by the International Association for the Physical Sciences of the
Oceans (IAPSO) prepared from seawater of the North Atlantic Ocean.
Recently, the long-term comparability of salinity measurement results was discussed, with two main deficiencies being elaborated (Pawlowicz et al., 2016): a lack of traceability to a long-term stable and ubiquitous reference like the International System of Units (SI) and chemical composition variabilities in standard seawater. These variabilities are likely to increase in the coming decades, due especially to the absorption of carbon dioxide into the ocean resulting from accumulation in the atmosphere (Millero, 2007). Both of these deficiencies entail a risk of inconsistent long-term salinity values. To remedy the deficiencies, Seitz et al. (2011) proposed to perform routine measurements of the standard seawater density. In practice, this would be achieved by determining the salinity of a standard seawater batch not only by conductivity measurement, but also by density measurement; the conversion to salinity is carried out in this second approach by means of a density–salinity relation. Since the salinity obtained from density is sensitive to all components of the standard seawater, a change in its composition would lead to an inconsistency of the “density salinity” and the “KCl salinity”.
To obtain a reliable statement about the consistency of the density salinity
and the KCl salinity, they have to be compared against the background of
their uncertainties. The reproducibility of the KCl salinity is 0.0004
(Bacon et al., 2007). However, this reproducibility is only valid for the
time of preparation (Seitz et al., 2010), as, during storage, glass
container material dissolves in the seawater, which is mainly silicate (e.g.
Poisson et al., 1978; Higgs and Ridout, 2011; Uchida et al., 2011). The uncertainty
in the “conductivity salinity” obtained by means of a salinometer is at
least 0.0022 (Le Menn, 2011), and requires freshly prepared standard
seawater for calibration. The corresponding values in terms of density are
0.3 g m
In this article, a new density–salinity relation is presented, whereby the
salinity can be determined by means of density measurement with an accuracy
of up to 0.003 for salinities up to 35, temperatures between 5
and 35
The new density–salinity relation may be used to reliably verify the stable composition of standard seawater by means of routine density measurements. On the one hand, the determination of salinity by means of conductivity is retroactively ensured in case of consistency; on the other hand, in case of inconsistency, a need for action is demonstrated.
Determining salinity by means of conductivity measurement is supported by
the relations of PSS-78. To develop the density–salinity relation in such a
way that it is consistent with PSS-78, the density measurements have to be
obtained from seawater whose salinity determination is consistent with the
salinity determination of the seawater used to develop PSS-78. In addition
to the consistency of salinity determination, the accuracy of the density
measurement is decisive. The more accurate the density measurement is, the
more accurately the salinity can be determined (by means of the
density–salinity relation). To achieve an accuracy in the density salinity
that is equal to that in the conductivity salinity, a density uncertainty of
2 g m
In this section, the preparation of the seawater measured and the determination of its salinity are described. The consistency of the salinities determined in the present, which were used to develop the density–salinity relation, with the salinities determined in 1978, which were used to develop PSS-78, is discussed. The substitution method and the apparatus used for the density measurement are briefly outlined, as they have already been described in detail by Schmidt et al. The uncertainty in density is discussed with regard to the uncertainty in salinity obtained from a density measurement and the subsequent calculation by means of the density–salinity relation.
In a substitution method, a sample (seawater) with an unknown density and a
similar, well-known reference (water) are measured (ideally, at the same
time) using the same measurement device (densimeter). Deviations in the
measurement results caused, for example, by a drift or a temperature
deviation can be corrected, as they cause similar effects on seawater and on
water. As a result, the measured densities of seawater and water have similar
deviations from their true value. The difference equation for calculation of
the corrected density from the measurements obtained from seawater and water
is
The water reference density was calculated using the equation of state
developed by Wagner and Pruß (2002). A description of the calculation is
given in Appendix A. The reference density uncertainty is 1 g m
The water used as the reference liquid in the substitution measurements was
prepared using tap water from Braunschweig, Germany. It was purified using a
reverse osmosis module, an ion exchanger, and a 0.2
All seawater samples were obtained from Ocean Scientific International Ltd. (OSIL), Havant, UK, which also determined the salinity values. Samples with salinities of 10, 30, and 35 were taken from batches 10L13, 30L15, and P153.
Additionally, diluted seawater with salinities of 5, 15, 20, and 25 was studied. These seawater batches were prepared using the same procedure as that used for the standard batches with salinities 10 and 30: First, a large amount of natural seawater (as used for the preparation of standard seawater) was diluted with water until its salinity was approximately equal to the target salinity. The raw salinity was determined using a modified 8400B Autosal salinometer (Bacon et al., 2007). Then, for calibration, a set of five samples per salinity was obtained by means of weight dilution of standard seawater (from batch P154 with a salinity of 34.9962). The balance used had a readability of 0.1 mg and was calibrated using weight standards traceable to the National Physical Laboratory, Teddington, UK (B. Childs, personal communication, 2017). The salinity was again determined by the Autosal salinometer, on the one hand, and by means of the weights of the standard seawater and the water used for dilution on the other hand. The deviations found between the salinometer salinities and the weight-calculated salinities were used as calibration offsets for the raw salinities of the diluted seawater.
The salinity homogeneity and calibration measurements yielded the values and
corresponding standard deviations given in Table 1. The uncertainty in the
salinity of standard seawater was adopted from Bacon et al. (2007). The
uncertainty in the salinity of diluted seawater includes the standard
deviations of homogeneity and calibration measurements, as well as the
uncertainty in the salinity of standard seawater. The systematic uncertainty
contributions of weighing and refilling are negligible compared to the
standard deviations. The uncertainty in the salinity of dilute samples is
0.0006, which corresponds to a density uncertainty of 0.5 g m
Summary of the batches of the standard seawater samples.
Vibrating-tube densimeters (VTDs) were used for density measurements performed using the substitution method. The core of such a densimeter is a U-shaped tube that is fixed in place on both ends. This tube is filled with the liquid to be measured and then forced to oscillate; the resulting oscillation period is a measure of the liquid density. Since the vibrating tube can be easily accessed from the outside, liquids can be filled in and changed quickly. This feature, together with short-term stability, is necessary for the application of the substitution method. Since the seawater sample and water reference cannot be measured simultaneously, stability is important for the duration of the alternating measurements. Under these conditions, the drift of the densimeter can be quantified using the deviations from the reference density (of water) to correct the sample density (of seawater).
Set-up used to measure the seawater density
The set-up used for the density measurements at atmospheric pressure is outlined in Fig. 1a. It comprises a fully automated filling system, a VTD, and a peristaltic pump. The filling system was created specifically for small filling volumes to allow more repetitions in the substitution measurements from a limited sample amount. To this end, a sequence of humid air bubbles is used to rinse the previous liquid out of the measuring cell. The bubbles of humid air are inserted into the sample filling tubes using the V2 and V3 valves in addition to the V1 valve to switch between the seawater sample and the water reference. The VTD used for the measurements is a DMA 5000M (Anton Paar GmbH, Graz, Austria). The peristaltic pump used to move the liquids is installed behind the VTD to avoid any interaction of the peristaltic tube material with the seawater or the water before the measurement.
The set-up used for density measurements at high pressures is illustrated in Fig. 1b. It uses an equal filling system to fill the water and seawater like the set-up used for atmospheric pressure. In addition to the filling system, the VTD, and the peristaltic pump, a pressurization part is installed between the VTD and the peristaltic pump. In this part, wherein the pressure is generated and measured, is a syringe pump filled with oil to prevent corrosion of the pressure sensors. The oil transmits the pressure generated in the syringe pump directly to the water without using a pressure transmitter. A long tube is installed between both parts (VTD and pressurization part) to avoid diffusion of oil into the measurement cell of the VTD. Two pressure sensors (P1 up to 14 MPa and P2 up to 70 MPa) are used to increase the accuracy of the pressure measurement. The offsets of these sensors at atmospheric pressure are corrected by the values gained with the atmospheric pressure manometer before each measurement. The VTD used for the measurements at high pressures is a DMA HP (Anton Paar GmbH, Graz, Austria). Details that have been given by Schmidt et al. (2016) are complemented by the Supplement to this article.
The substitution measurements at atmospheric pressure were performed at a constant temperature. The water and seawater were filled and measured in alternation. The water densities measured were thus compared with the reference density; the deviations found were used to correct the seawater measurements.
The procedure for high pressures is similar to that used for atmospheric pressure; however, the liquid is not replaced during a high-pressure run at a constant temperature. Instead, the liquid is replaced after decreasing the pressure back to atmospheric conditions.
The seawater density was measured in the temperature range of 5 to 35
Since the salinity uncertainty, which is 0.5 g m
To determine salinity by means of conductivity, the PSS-78 relations were
developed based on five data sets All publications cited here were
also reprinted together (JPOTS, 1981b).
Both the salinities of the samples used to develop the conductivity–salinity relation PSS-78 and the salinities of the samples used to develop the density–salinity relation were thus determined by weighing measurements. If a relation between density and conductivity is set using both relations, then both (relation) uncertainties have to be taken into account. It should be noted that the density–conductivity relation is only valid if standard seawater is consistent in its composition. Conversely, this relation can therefore be used to check the standard seawater composition.
The uncertainty in a salinity determined by means of conductivity measurement
that is supported by PSS-78 is (in a best-case scenario) 0.0022 using a
laboratory salinometer and 0.0034 using a conductivity–temperature–depth
device (Le Menn, 2011). These uncertainties are 2 and 3 g m
Since the aim of developing the density–salinity relation was to determine
the salinity by measuring density with higher accuracy than by measuring
conductivity, a
Standard seawater is prepared using natural seawater taken from the North Atlantic Ocean. To adjust the required salinity, the natural seawater is diluted with water prepared using groundwater taken from the British mainland; since the groundwater is isotopically depleted, the isotopic water composition of the natural seawater changes during dilution. After preparation, the seawater is poured into borosilicate glass vessels for delivery; these vessels are not completely inert against seawater. Since the seawater was stored in these vessels until the density measurements were made, glass material was dissolved into the seawater, changing the chemical composition by mainly increasing the dissolved silicate.
For the substitution measurements, the seawater was taken directly from
these vessels and pumped into the substitution densimeter, where the
temperature is altered; since the seawater was air-saturated at
20
In this section, corrections for these density effects to the following
uniform conditions are presented: the hydrogen–deuterium (H–D) and
oxygen-16, 17, and 18 (
Water shows a variation in its isotopic composition. The natural variation
comprises the H–D relation and the
Isotopic abundances of water and seawater (NSW – natural, DSW – diluted).
The D and
The density difference due to the isotopic abundance change during
preparation,
Density difference
The seawater used for the measurements was stored in 230 mL borosilicate glass vessels (Bacon et al., 2007) from the time of preparation at OSIL to the time of measurement. During this time, glass material that dissolved into the seawater has significantly altered the chemical composition, and thus the density.
Uchida et al. (2011) analysed the silicate increase in standard seawater
delivered by OSIL that was stored in the vessels mentioned above. The
silicate increase is related to the dissolution of silica from the glass
vessel material. Uchida et al. measured the silicate molality of samples from
batches P144 to P152 depending on their storage time. These data were used to
estimate the initial silicate molality of the standard seawater used for the
density measurements
The silicate concentrations of some DSW samples from the batches with
salinities of 5, 10, 15, 20, 25, and 30 were measured shortly after all
density measurements had been performed. The silicate concentration was
measured at the Alfred-Wegener-Institut, Helmholtz-Zentrum für Polar- und
Meeresforschung in Bremerhaven, Germany, using an Evolution III flow-through
spectrophotometer (Alliance Instruments GmbH, Salzburg, Austria) according to
Grasshoff et al. (1999). The device was calibrated before, between, and after
the DSW sample measurements by measuring Merck Millipore Certipur silicon
standard solutions (Merck KGaA, Darmstadt, Germany), which had a salinity of
36 and reference concentrations of around 7 and 50
The silicate concentration values of the DSW samples were converted to the molality values that are given in Table 3, including the corresponding storage time. The silicate molality of the seawater that had salinities of 10, 30, and 35 is higher than that of the other batches, as it was stored longer in the vessels (see Table 1 for details).
Dissolved silicate molality of some DSW samples.
The reproducibility of a silicate concentration measurement that uses the standards and method described above is usually within 3 % (K.-U. Ludwichowski, personal communication, 2015). Since the dissolution of the vessel material partly depends on the individual vessel, the difference in the silicate molalities of two measurements (e.g. for salinity 10) may be higher.
According to Grasshoff et al. (1999), the accuracy of the measured silicate concentrations also depends on the difference in salinity between the Certipur standard solutions and the DSW samples. Grasshoff et al. (1999) recommend to correct this effect by applying a constant, device-dependent correction factor derived from calibration measurements. The resulting correction increases linearly based on the salinity difference between the sample (higher salinity) and the standard (lower salinity). For measurements of samples with a salinity of greater than 30, the correction is smaller than 3 %. Assuming a correction due to the salinity effect of 3 % at a salinity difference of 6 and a linear increase thereof, the correction increases to 10 % at a salinity of 15 and to 16 % at a salinity of 5. We considered this by including the effect in the uncertainty and estimated the uncertainty in silicate molalities to be dominated by the batch homogeneity for salinities above 20; for salinities lower than 20 we estimated the uncertainty to be dominated by the correction due to the salinity. Values of the estimated uncertainty in silicate molality are given in Table 3.
Since the density measurements obtained from seawater samples were performed before the silicate molality measurements, the storage time and the silicate molality were different at that time.
Uchida et al. (2011) estimated the relation between the silicate molality
The borosilicate vessels used to store the seawater samples are assumed to
consist of
The increase in seawater density due to the dissolution of glass material
during storage,
Some values of the density correction that were applied to the measured
seawater densities are shown in Fig. 3. The corrections are about
1 to 3 g m
Seawater density increase
Usually, seawater samples used in highly accurate density measurements in laboratories are air-saturated, as any degassing procedure may change the salt composition. For water, the effect of air solubility on density has been measured directly, e.g. by Bignell (1983), by comparing the densities of saturated and desaturated water.
For our density measurements, the seawater samples were taken directly from
the vessels delivered by OSIL as shown in Fig. 1a. The vessels were stored
in our laboratory at a temperature of approximately 20
The density correction is estimated taking into account the fact that the
amount of air molecules remains constant while the liquid temperature
changes from 20
Carbon dioxide exists in three different significant forms in seawater, i.e.
as free aqueous molecule, CO DIC was
calculated using the CO The density change was
calculated using
The complex calculation showed that the different gas solubilities in water
and seawater are negligible in terms of density, as the deviation between the
calculated density change of seawater and that of water (of Harvey et
al., 2005) is around 0.1 g m
At measurement temperatures higher than 20
Density correction due to air saturation correction based on 100 %
saturation at 20
Based on a measured substitution density,
In this section, the development of the density–salinity relation is
described. Although this relation should be used to determine the salinity
by means of density, it was set up as a density function of salinity,
temperature, and (absolute) pressure, i.e.
The density of air-saturated seawater is modelled based on degassed water,
whose density is given by
If the salt is added at the atmospheric pressure
The solubility of gases in liquids is described well at infinite dilution and
low pressure by means of Henry's law, according to which the number of
absorbed gas molecules is proportional to the gas pressure above the liquid.
However, since there is no reservoir for additional gas at high pressure,
only the air absorption at the gas pressure
The solubility of air in seawater depends on salinity (Hamme and Emmerson,
2004; Garcia and Gordon, 1992). The comparison of the N
The values of the seawater density for atmospheric pressure,
The values of the relative density of air-saturated seawater
The values of the relative density of degassed seawater,
The linear fit coefficients
Values of the coefficients
The residuals of the fit using the coefficients given in Table 4 are
illustrated in Fig. 5, where they are compared with the density–salinity
relation uncertainty,
If the density of air-saturated seawater is calculated using the
density–salinity relation, the (fitted) relative seawater density plus the
(artificially inserted) density change due to absorbed air is used, i.e.
Since the density–salinity relation may be used for calculations in a wider
region, e.g. salinities up to 40 and temperatures from 0 to
40
Residuals
Uncertainty in the density–salinity relation at
101 325 Pa.
To calculate salinity using relative density and temperature values by means
of the density–salinity relation, the uncertainty in salinity was also
determined in the measurement and extrapolation region. The salinity
uncertainty was calculated by multiplying the density uncertainty by the
partial derivative of salinity by density, i.e.
Since the mathematical formulation of the density-salinity relation is
empirical and does not contain any theoretical boundary conditions for
infinite dilution, as for example implemented in TEOS-10, the question
arises whether the relation correctly predicts the density for very low
salinities. Additionally, no uncertainty verification in the extrapolation
region is possible using the fitting data set. Therefore, additional
substitution density measurements were conducted: The density of diluted
standard seawater with salinity 2 was measured at some temperatures and the
density of some samples of the seawater used for determination of the
density–salinity relation was measured at 1
Deviation of measured from predicted seawater densities
The values of the seawater density for high pressures,
The values of the relative density of air-saturated seawater,
The values of the density change due to dissolved salt,
The resulting values of the density difference
The linear fit coefficients
Values of the coefficients
Residuals
The data set for fitting
Uncertainty in the density–salinity relation at high
pressures. Uncertainty in the relative density of air-saturated seawater,
As pointed out above, the mathematical formulation of the density–salinity relation is empirical and does not contain any theoretical boundary conditions for infinite dilution. This is also an issue for the density at high pressures, as here the measurement uncertainty in density is higher, thereby causing more variability in the shape of the relation for very low salinities. Therefore, additional measurements were conducted on diluted standard seawater with salinity 2 for some temperatures. The samples used were obtained from the same seawater as described above in Sect. 4.2; the corrections were similar. The density deviations of the corrected values from predicted values of the density–salinity relation are shown in Fig. 10. The deviations are well within the uncertainty in the relation. No inconsistencies are caused by the non-compliance with theoretical boundary conditions for very low salinities and high pressures.
The present reference equation of state for thermodynamic properties of
seawater is the Thermodynamic Equation of Seawater (TEOS-10) adopted by the
Intergovernmental Oceanographic Commission (IOC et al., 2010). TEOS-10
describes the properties of degassed seawater in wide ranges of salinity,
temperature, and pressure relative to degassed water with the VSMOW isotopic
composition. Relative density values calculated using TEOS-10 with salinities
from 0 to 40 and temperatures from 0 to 40
Deviation of measured from predicted seawater densities
For atmospheric pressure, the density deviation of TEOS-10 from the
density–salinity relation is shown in Fig. 11a. TEOS-10 density values are
always higher than those of the density–salinity relation. The increase in
the deviation with salinity is approximately linear. At salinities higher
than 25, the deviation exceeds the estimated uncertainty of 8 g m
Density deviation of TEOS-10 from the density–salinity
relation (i.e. TEOS-10 minus DSR) for degassed seawater at selected
temperatures and atmospheric pressure.
To leave the linear increase in the deviation with salinity seen in Fig. 11a
out of consideration, a reduced form is shown in Fig. 11b. Here,
To find possible causes of the unexpectedly high density deviation, the
density data on which TEOS-10 is based were examined, where the uncertainty
in salinity was considered negligible. In the
Deviation of densities obtained from standard seawater using a
magnetic float densimeter by Millero et al.
Millero et al. (1976) measured the density of diluted and standard seawater of batch P63 using a magnetic float densimeter. The comparison between the normalized densities measured by Millero et al. and TEOS-10 shown in Fig. 12a suggests that TEOS-10 is well fitted to these densities. Furthermore, for salinities less than 30 (compared to for salinities greater than or equal to 30), the deviation is strongly scattered and the salinity value of each deviation value is different. This may be explained by the fact that not all density measurements were carried out in a closed measuring vessel (JPOTS, 1981c, p. 35), thereby avoiding evaporation, which would increase the salinity and density during a measurement. To exclude the impact of the data normalization, a comparison of the original densities of Millero et al. (1976) and the density–salinity relation is shown in Fig. 12b, where the measurements that were carried out in a closed measuring vessel are separated from those that were putatively carried out in an open measuring vessel. The deviations of the closed-vessel measurements (for salinity 30 and 35) are the smallest and scatter the least, whereas the deviations of the open-vessel measurements (for all other salinities) scatter highly. If it is assumed that evaporation occurred during the open-vessel measurements, then the measured densities can be systematically too high (or the assigned salinities too small), which would cause the open-vessel deviations to be too high. Furthermore, a linear fit curve that was developed using the closed-vessel deviations is shown, as it is possible that there is a systematic deviation increasing linearly with salinity besides the evaporation. The smallest open-vessel deviations, which are most likely not significantly affected by evaporation, correlate conspicuously with this fit curve, thereby supporting the possibility of systematic deviation. The open-vessel densities for salinity 40, which are visible as the highest deviations in Fig. 12b, were corrected (using the closed-vessel densities) when the density data of Millero et al. and Poisson et al. were normalized (JPOTS, 1981c, pp. 35 and 58), which is why there are no significant deviations for salinity 40 in Fig. 12a. It should be noted that for calculation of the density deviations given in Fig. 12a and b, the temperatures at which Millero et al. made their measurements were converted from the International Practical Temperature Scale 1968 to the International Temperature Scale 1990 (CCT, 1997). To identify plausible causes of the systematic deviation, we thoroughly examined the magnetic flotation method used by Millero et al. for possible issues.
Magnetic float densimeters have the advantage over hydrostatic weighing densimeters that no mechanical coupling by means of a suspension is needed to determine the buoyancy force acting on a float (or sinker). Instead, this is achieved with a magnetic coupling by placing a magnet into a float. The float is brought to mechanical equilibrium, i.e. floats in the liquid, by means of a current-carrying coil; here, the current is a measure of the force, and thus of the liquid density. However, for density measurement the characterization of the magnetic coupling is necessary in addition to the determination of the float volume, as in the case of a hydrostatic weighing densimeter.
The densimeter used by Millero et al. for measuring the seawater density
consisted of a hollow float in the measuring liquid of a vessel that had a
volume of 250 mL, with the coil mounted underneath. The float was made of
Pyrex, contained a permanent magnet that was a stirring bar and was
therefore probably made of Alnico, and had a volume of 32 cm
Bignell (2006) discussed various methods for determining the buoyancy force
in magnetic float densimeters. For the design of the magnetic coupling
system, the magnetic force exerted on a permanent magnet by a
current-carrying, circular coil (without a metal core) was given by
Bignell pointed out that the force on the magnet is also dependent on the
magnetic field, even for magnetically hard materials. The magnetic force is
therefore not linearly (as in Eq. 15) but quadratically dependent on the
equilibrium current, i.e.
Millero et al. used a cylindrical (instead of a circular) coil and
summarized the magnetic force as
Since seawater and water have different magnetic properties, it is possible
that the calibration factor
Since the volume of the float was also determined by means of the calibration
measurement using water, it is possible that this resulted in a significant
deviation in the relative seawater density. We therefore carried out a
further representative calculation using the values (i–iv). Using this
calculation, a density deviation of only 3 g m
We performed a final calculation to estimate how significant the precise height positioning of the permanent magnet is, i.e. the distance from the coil. Two reasons for a change of the distance are conceivable. On the one hand, the position of the magnet (inside the float) or of the coil can change in the time between the calibration measurement obtained from water and the measurement obtained from seawater; the permanent magnet was fixed in the hollow float using wax (Millero, 1967). Density deviations that result from such position changes are minimized if, after each measurement obtained from seawater, a measurement obtained from water had also been carried out (a quasi-substitution measurement). On the other hand, the “lift-off” process, wherein the equilibrium current is determined by sight, is not the same for seawater and water in terms of speed (among other factors). Density deviations that result from such dissimilarities are minimized, if, in additional to the “lift-off” current, the “drop-down” current had been determined in the opposite manner and both currents had been averaged for seawater and water, respectively. Or, if in the measurement obtained from seawater, the float was weighted with the aim to yield the same current as in the calibration measurement using water.
For the calculation, it was assumed that the height dependence of the
magnetic force given by
The high sensitivity of the measurement density to the magnet height position
is one reason why magnetic flotation densimeters that were developed later
and that share a similar principle, e.g. that of Bignell (1982), use position
sensing systems with accuracies that are at least in the micrometre range to
keep the height,
TEOS-10 may be used to calculate densities for pressures up to 100 MPa. In
the
An overview of the density deviation of TEOS-10 from the density–salinity
relation in the entire salinity–temperature region for atmospheric pressure
is given in Fig. 13a. The increase in the deviation with salinity seen in
Fig. 11a for 5, 20, and 35
Density deviation of TEOS-10 from the density–salinity
relation (i.e. TEOS-10 minus DSR) for degassed seawater
Chen and Millero measured the seawater density using a densimeter that is
similar to that for atmospheric pressure used by Millero et al. (1976), which
is why similar systematic deviations are likely. Both the thermal expansion
data of Bradshaw and Schleicher and the speed-of-sound data of Del Grosso can
only be compared with the density–salinity relation if the absolute seawater
and water density are included in the calculation. The uncertainty in the
water density calculated using IAPWS-95 is 10 g m
A density–salinity relation for IAPSO standard seawater was developed by
means of highly accurate density measurements performed using a recently
developed substitution method. This relation makes it possible to
consistently determine (practical) salinity by means of density measurement
at a level of accuracy that is comparable to that achieved by means of a
conductivity measurement supported by PSS-78 and related application
routines. The relation has been developed as a function of salinity, i.e.
Density corrections for standard seawater were developed. Because the
chemical composition was changed by interactions with borosilicate glass
material of the storage vessel, and because the seawater samples used in the
measurements were stored for different periods, the measured densities were
corrected to a uniform (i.e. the original) chemical composition. These
corrections are up to 3 g m
The density–salinity relation was compared with the reference equation of
state for seawater TEOS-10. For atmospheric pressure, density deviations of
up to 15 g m
Seawater is changed during storage. Mainly silicon dioxide dissolves from borosilicate glass material and forms silicic acid, but over the long term, the solubility of other glass components is also important. This affects the density of stored seawater. If standard seawater is to be used as a density reference material, the solubility of all glass components must be quantified so that the change in the chemical composition and in density can be calculated. This also includes the dependence of this solution on temperature during storage; storage at low temperatures may minimize this interaction. For long-term storage, container materials that have a greater chemical resistance should be investigated.
Knowledge of the isotopic composition is essential for measurements obtained from seawater samples that are artificially diluted with water from different locations, as the local isotopic water composition varies significantly. For natural seawater, this may be important in marginal seas.
The data situation of recent highly accurate density measurements of standard seawater is poor, which is why further measurements should be carried out using state-of-the-art methods. The data of the density–salinity relation obtained in the present study should be used as a correction to TEOS-10.
Salinity is usually measured by means of a salinometer measuring conductivity and by being calibrated by standard seawater, which is of natural origin. A long-term change in the salt proportions in seawater cannot be detected in this way, as it will be overwritten by the (re-)calibrations with standard seawater.
The density is sensitive to all components, including dissolved salts and gases (and even isotopes), and can be determined without natural reference materials. If the salt composition of standard seawater is changing in the long term, the density–salinity relation provides a metrological basis for detecting this change.
As possible changes in the seawater density are expected to be of the order
of measurement uncertainty or even smaller, a periodic assessment should be
carried out over several
decades. Since the introduction of the salinity determination using standard
seawater, 40 years have passed without this. We propose a density measurement
of any freshly prepared standard seawater batch. A well-known example of such
a long-term assessment is the Keeling curve of the CO
The complete data used to develop and validate the density–salinity relation are provided in the Supplement.
The calculation of the reference densities
The correction for air saturation was taken from Harvey et al. (2005) and is
(valid for 0 to 50
We assumed the corrections for isotopic composition and air saturation are
dependent on temperature and pressure and applied corrections in the
following manner:
The density–salinity relation is an empirical thermophysical equation of state, the formulation of which is determined by the underlying measurement values and their associated uncertainties, which were determined in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM) adopted by the Joint Committee for Guides in Metrology (JCGM) in 2008 (JCGM GUM, 2008).
To calculate the uncertainty in predicted results of the density–salinity
relation, the Monte Carlo method (MCM) as described in Supplement 2 to the
GUM (JCGM GUM S2, 2011) was applied. In the MCM,
Since the applicability of MCM described in the GUM S2 is by definition limited to measurement models that usually involve the use of physical laws, the uncertainty in a predicted value determined in this way may not be consistent. For this reason, the consistency of the predicted uncertainties has to be evaluated.
A common approach to evaluate the consistency of a fit equation is to
compare the values of the fit residual
Next, every calculated residual uncertainty at a probability of 95.45 % was
compared to the corresponding residual to evaluate the uncertainty, which is
associated with the predicted value. In the case of the density–salinity
relation consistency verification, 95.45 % of the residuals had to be
smaller than their associated uncertainties; thus,
The authors declare that they have no conflict of interest.
This work was funded by the European Metrology Research Programme, EMRP Project ENV05. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.
The authors greatly value the silicate concentration measurements obtained from seawater performed by Kai-Uwe Ludwichowski at the Alfred-Wegener-Institut, Helmholtz-Zentrum für Polar- und Meeresforschung (AWI), and would like to thank Gereon Budéus (AWI) for valuable discussions on oceanographic matters.
This article contributes to the tasks of the Joint SCOR/IAPWS/IAPSO Committee on the Properties of Seawater (JCS).Edited by: Mario Hoppema Reviewed by: two anonymous referees