- Email: [email protected]
Density of standard seawater solutions at atmospheric pressure
Deep-Sea Research, Vol. 27A, pp. 1013 to 1028 © Pergamon Press Ltd 1980. Printed in Great Britain
01984)149/80/1201-1013 $02.00/0
Density of standard seawater solutions at atmospheric pressure A. POISSON*, C. BRUNET* and J. C. BRUN-COTTAN* (Received 1 February 1980; in revised form 12 May 1980; accepted 15 June 1980)
Abstract--The density of standard seawater P75 (S = 35%0) has been measured from 0 to 30°C with a suspension balance. This batch of standard seawater has been used together with a distilled water to calibrate a vibrating densimeter with which the density of diluted and concentrated standard seawater solutions has been determined at atmospheric pressure. The measurements have been carried out from 0 to 42%0 salinity and 0 to 30°C. Equations for density of standard seawater (S = 35%0) vs the temperature and for density of standard seawater solutions vs the temperature and salinity have been fitted. The smoothed densities are compared with previous works.
INTRODUCTION
As EARLY as the beginning of the century, oceanographers were able to determine density accurately from a chlorinity titration by using the Hydrographical Tables of KNUDSEN (1901). The increase in accuracy and precision of some techniques in later years, in particular the determination of the salinity from electrical conductance, together with the measurement of density at atmospheric pressure with modern densimeters (magnetic float densimeter, MILLERO, 1967 ; vibrating densimeter, PICKER, TREMBLAYand JOLICOEUR, 1974) has made it possible to check the data of Knudsen and to obtain more reliable sets of data on larger ranges of temperature and salinity. The slight variations in ionic ratios that exist in the world ocean imply variations of density--specific to the chemical species--which are significant relative to the accuracy of modern apparatus; the density-salinity-temperature relationships determined from direct measurements on samples from all the world ocean (THOMPSON and WIRTH, 1931 ; COX, MCCARTNEY and CULLEN, 1970; KREMLING, 1972) have therefore a standard deviation which will never be smaller than a few ppm. Recently MILLERO carried out measurements on artificial seawater (MILLERO and LEPPLE, 1973) and on standard seawater solutions (MILLERO, GONZALESand WARD, 1976a). The relationship between density and salinity is unique then, and the standard deviation of the densitysalinity-temperature relationships becomes very small because it arises only from experimental error. It is then necessary to check the agreement between the density determined from the artificial relationships and the density of natural seawater of different oceans and seas. Recent works seem to show that this agreement is excellent in the Mediterranean Sea (MILLERO, MEANS and MILLER, 1978a) and in the Baltic Sea when seawaters are compared at the same total dissolved solid concentration (MILLERO and KREMLING, 1976), but corrections are often needed, specially for deep waters (MILLERO, GONZALEZ, BREWER and B~L~SnAW, 1976b; MILLERO, FORSnT, MEANS, GIESKES and * Laboratoire de physique et chimie marines, Universit6Pierre et Marie Curie, tour 24, 4, place Jussieu, 75230, Paris Cedex 05, France. 1013
1014
A. Poisso~, C. BRUNET and J. C. BRUN-COTTAN
KENYON, 1978b). Some measurements carried out in our laboratory (PoISSON, BRUNETand MENACHE, 1979) disagree at high temperatures with the relationship of MILLERO et al. (1976a), and we have, according to the recommendation of the Joint Panel on Oceanographic Tables and Standards (UNESCO, 1979) carried out a second set of measurements of the density of standard seawater at a salinity of 350/00. We present the results in this paper together with the polynomials that we have fitted.
D E N S I T Y OF S T A N D A R D SEAWATER (S = 35% 0) AS A F U N C T I O N OF T E M P E R A T U R E
The standardization of the vibrating densimeter we have used to measure the density of seawater solutions at different temperatures and salinities requires two reference fluids of known density. We have chosen to use standard seawater and distilled water for the standardization. The density of the distilled water was measured at the "Bureau International des Poids et Mesures" (S6vres) relatively to the S.M.O.W. (Standard Mean Ocean Water); the density of standard seawater was measured at different temperatures relative to the distilled water by means of a suspension balance. Apparatus and methods The apparatus and methods used are similar to those described in detail elsewhere (PoISSON and CrtANU, 1976). The sinker used is made of P y r e x ; i t s volume is about 63 cm 3 and its weight is about 72 g; the nickel-chromium suspension thread has a diameter of 35 ttm. The balance is a Mettler balance M 5 G D (20 g maxi + 2 x 10-6 g). The temperature is maintained constant in the measurement cell by using a thermostat and a special stirrer. The temperature is measured with a platinum resistance thermometer of 25 (2 (Rosemount, type E 109-25) and a thermometric bridge (A.S.L., type H7) with an accuracy of + 2 x 10-a°C. As the volume of the cell is approximately 500 cm 3, we need two ampoules of standard seawater for each measurement. Before they are opened, the ampoules are set at a temperature slightly higher than the one of measurement, so as to avoid degassing in the cell and to prevent microbubbles from sticking on the sinker. Standard seawater is introduced fairly slowly into the cell, limiting as much as possible its contact with air. Seawater is stirred intermittently until the temperature remains constant. Salinity of seawater, measured immediately after determining the apparent weight of the sinker with a Guildline Autosal salinometer, is the same as at the beginning. Moreover, the pH variation during the measurement is less than a few hundredths of a pH unit. The evaporation and the exchange of CO2 between seawater and air are negligible, and the variation of corresponding density remains smaller than 1 x 10 -6 g cm -3. The absolute density (Pt) of seawater at temperature t is, M - msw p,
-
-
-
v,
(i)
where M is the mass of the sinker in vacuum and msw its apparent weight in seawater; Vt is the volume of the sinker at temperature t; M was determined by using a Mettler balance B5 (200 g maxi __+1 x 10 -4 g); the air buoyancy correction is calculated from the pressure, measured with a mercury barometer, the temperature and the relative humidity of air, measured with a psychrometer.
Density of standard seawater solutions at atmospheric pressure
1015
The volume Vs of the sinker was measured at different temperatures (Table 1) by using distilled water with an absolute density, at 22°C and at atmospheric pressure, as measured at the "Bureau International des Poids et Mesures", smaller than that of S.M.O.W. by 7 x 10 -6 g c m - 3 . The absolute density PmPM of the distilled water was therefore chosen as equal to that of S.M.O.W. (equation 5) minus 7 x 10-6 g c m - 3 for all the temperatures. Vt was calculated with Vt
-
M-m
w
- -
(2)
RB1PM where mw is the apparent weight of the sinker in the distilled water from B.I.P.M. The determined values of V~have been fitted in a linear relationship Vt = Vo+yt
(3)
where Vo is the volume of the sinker at 0°C, y is the coefficient of expansion of the sinker, equal to 6.1892)< 10 -4 cm -3 °C -1. The standard deviation is equal to 1.4× 10 -4 cm 3, equivalent to 2.8 × 10 -6 g cm -3 of the density of pure water. Table 1.
Volume (cm3) of the sinker measured at different temperatures and calculated with equation (3)
t (°C) 30.040 29.091 25.410 24.834 20.348 20.325 5.104 5.094 1.071
Measured v o l u m e (cm3) 63.4567 63.4556 63.4538 63.4533 63.4506 63.4505 63.4410 63.4411 63.4385
Calculated volume (cm3)
Volume difference (10-4 cm3)
63.4565 63.4559 63.4537 63.4533 63.4505 63.4505 63.4411 63.4411 63.4386
-2 +3 - 1 0 - 1 0 +1 0 +1
Experimental results
The absolute densities of standard seawater P75 (CI = 19.374%o) determined at different temperatures are given in Table 2. The results are presented as differences between the absolute density p of seawater and that of pure water Po at the same temperature. Differences in the density of pure waters arising from isotopic composition (MENACHEand GmARD, 1972) are thus eliminated; moreover the differences of absolute densities p - P o are measured with the same value as the differences of relative densities d - d o of seawater, whatever the temperature and salinity. The maximum difference between p - Po and d - do is 1 x 10 . 6 for 0°C ~< t ~< 30°C and 0%o ~< S ~< 40%0. The results have been fitted to the form of a polynomial 1 0 a ( p - p o ) = 28.255-0.11813t + 1.937 x 10-3t 2 - 1.399 x 10-5t 3
(4)
the standard deviation of which is 2.9 x 10-6 g c m - 3 ; Po, absolute density of S.M.O.W., is calculated from the relationship 103po = 999.842594+6.793952 x 1 0 - 2 t - 9 . 0 9 5 2 9 0 x 1 0 - a t 2 + 1.001685 x 10-4t 3 - 1.120083 x 10-6t4+6.536332 x 10-9t 5. (5)
1016
A. POISSON, C. BRUNET and J. C. BRUN-COTTAN
Table 2. Differences between absolute density of standard seawater P75 and absolute density of S.M.O.W. measured at different temperatures and calculated with equation (4) P-Po
P-Po
t (°C)
measured (10 - 3 g c m -3)
Pmeas- P¢~c ( 1 0 - 6 g c m -3)
t (°C)
measured (10 -3 g c m -3)
Pmeas-- Pealc ( 1 0 - 6 g c m -3)
30.067 30.006 25.577 25.435 25.423 25.368 24.239 20.932 20.759 20.725
26.075 26.079 26.262 26.268 26.274 26.279 26.330 26.504 26.511 26.511
- 1 -3 +5 +5 0 --3 0 -- 1 + 1 +3
19.717 19.697 15.681 10.478 10.412 7.100 5.220 5.215 2.340 1.163
26.576 26.576 26.828 27.217 27.217 27.505 27.688 27.690 27.987 28.124
- 4 -3 -3 - 3 +2 +4 + 1 0 +2 -4
based on the table given by Bic,6 (1967), the use of which has recently been suggested by the International Union of Pure and Applied Chemistry (1974). The absolute density of seawater (S = 35%0) can be obtained by adding relationships 4 and 5. To calculate the relative density we divided p thus obtained by the value of the maximum density of S.M.O.W. used by KELL (1975), Pmax = 0.999975 g cm -3.
Comparison with previous work We have calculated for a seawater of salinity 35%0 the difference between the density of KNUDSEN (1901) and the corresponding density of pure water given in the table by TmESEN (1900) that Knudsen had taken as a reference, for temperatures ranging from 0 to 30°C. The difference for a seawater of salinity S and temperature t is (Hydrographical Tables, 1901) 103(d-do) = (a0 +0.1324){1 - A +B(ao-0.1324)}
(6)
where a o = - 0.069 + 1.4708 C1 - 1.570 × 10- 3 C12 + 3.98 × 10- 5 C13 A = t(4.7867-0.098185t +0.0010843t 2) × 10 -3
B = t(18.030-O.8164t+O.O1667t 2) x
10 - 6 .
The salinity S is deduced from the chlorinity C1 by S = 0.030+ 1.8050 C1. The values obtained at different temperatures for a seawater of salinity 35%0 are compared to the values calculated with equation (4) on Fig. 1. We have also calculated the differences between density do of pure water given in the table of TILTONand TAYLOR(1937) and density d obtained by using the polynomial of Cox et al. (1970): d = 1 + 8.00969062 x 10- 5 + 5.88194023 × 10- 5t + 7.97018644 × 10-aS -8.11465413 x 1 0 - 6 t 2 - 3 . 2 5 3 1 0 4 4 1 x 1 0 - 6 S . t + 1.31710842 x 1 0 - 7 S 2 + 4.76600414 x 10 - st3 + 3.89187483 x 10 - aS. t 2 + 2.87971530 x 10 - 9S2. t -6.11831499 × 10-11S 3. (7) The standard deviation of the polynomial is 11 x 1 0 - 6 g c m - 3 . The values obtained for S = 35%0 at different temperatures are compared with those calculated using polynomial 4
Density of standard seawater solutions at atmospheric pressure
,2-
[P-P.]o.~-[p-~ot..rs
o Po, . . . .
C.q')-
(10./* g.c m.3~
• Poi . . . .
{eq 4) - M i i l e r o
10-
POISSON - KNUDSEN
/
/
_~
'
~
Poi . . . . . . . . . . .
-----
P o i sso n
{eq 4 ) - M i l l e r o
....
Poisson
(eq 9 ) - M i l l e r o
7"o--..
"~,.
1017
d
measured
o
o
POISSON - COX -15
Fig. l. Comparisonofp -Po ( 10-6 g cm-3) calculated by equation (4) or (9) with d - d o or P - P o calculated by equations fitted by others, and comparison of our and Millero's experimentaldata with equation (4). on Fig. 1. MILLERO e t al. (1976a) presented their data under the form of differences of absolute densities, so we have calculated p - P0 directly from the polynomial he proposed : (8)
P - Po = A S + B S 3/2 + C S 2
where S is the salinity obtained by diluting or evaporating standard seawater. A = 8.25938 × 1 0 - 4 - 4 . 4 4 9 1 x 1 0 - 6 t + 1.0485 × 10-7t 2 - 1.2580 x 10-9t3 +3.315 x 10-12t4 B = -6.33777 × 1 0 - 6 + 2.8442 × 10-Tt - 1.6871 x 10-8t2 + 2.83265 x 10-~°t3 C = 5.4706 x 10 -7 - 1.9798 x 1 0 - s t + 1.6641 x 10-9t 2 - 3.1204 × 10-~1t3. The standard deviation is 3 . 3 x 1 0 -6 g cm -3. The deviations between Millero's measurements and the above polynomial (8) being at 35%0 higher than the standard deviation, we have also put his experimental data on Fig. 1. Whereas the differences between polynomial (4) and (8) are always negative, Millero's experimental data are, except at 0°C, in agreement with equation (4) (mean deviation = 0.4 x 10 -6 g cm-3). This is not the case at low and high temperatures for his polynomial (equation 8) reduced at 35%0. As the experimental data are relatively few--measurements were carried out at only nine temperatures--the shape and the degree of the polynomial chosen to fit the data can have an important influence. To check the influence of this on the work we have calculated the coefficients of a quadratic polynomial from the same data as in Table 2. 103(p-p0) = 28.262-0.1219t+2.473 x 1 0 - 3 t 2 - 4 . 0 3 2
x
10-st3+4.159
×
10-7t 4. (9)
The values calculated from polynomial (9) have been compared with those calculated from Millero's equation (equation 8); the deviations are collected on Fig. 1 (dotted curve); it is evident that the degree of the polynomial has an important influence at the lowest and the highest temperatures and especially at 0°C, which is below our lower temperature of measurement. Nevertheless, the standard deviation of polynomials (4) and (9) are very close (2.9 and 2.3 x 1 0 - 6 g cm -3) and we shall use polynomial (4) for
1018
A. POISSON,C. BRUNETand J. C. BRUN-COTTAN
calculations and comparisons in the next paragraphs, because its curve has the advantage of being less bent than that of the quadratic equation.
DENSITY
OF
FUNCTION
STANDARD OF
SEAWATER
TEMPERATURE
SOLUTIONS AND
AS A
SALINITY
As we now have two liquids whose absolute densities are known as a function of temperature we can standardize the densimeter and measure the density of standard seawater solutions at different temperatures and salinities.
Apparatus and method The principle of the high precision digital readout flow densimeter we have used is explained in detail elsewhere (PICKER et al., 1974). It has been standardized at each temperature for each set of measurements by using distilled water provided by the B.I.P.M. and standard seawater P75. The absolute density of distilled water is determined with equation (5) (S.M.O.W.) and that of standard seawater with equation (4). The seawater solutions with a salinity smaller than 3500 are directly prepared from batch P75 and a distilled water prepared in our laboratory. Each sample is prepared in a 100 cm 3 screwtopped flask so that the quantity of dilute seawater should always be close to 60 cm 3. This made it possible to prepare a set of dilution (from 35 to 5%0) from the same ampoule of standard seawater. The salinities of the samples are determined from the ratio of the weight of standard seawater and the final weight of solution. The flasks are weighed by using a Mettler balance B5 (200 g m a x + 1 x 10 - 4 g). The distilled water and the seawater ampoules are placed in the balance room at least one day before the dilutions--carried out in a humid box--and the weighings. All the density measurements were within 4 h of the preparation of the solution. For each temperature, two sets of dilutions were prepared and the density of each sample was determined twice. There were no corrections for evaporation and air buoyancy in the calculation of salinity from weights of standard seawater and distilled water. The shift of the densimeter was controlled by making a measurement of the density of the laboratory distilled water every two samples. The densimeter constant was determined every day and densities were calculated using the mean constant for each temperature. By using the equation of S.M.O.W. for the calculations we internally correct the effect of dilution with a distilled water whose isotopic composition differs from that of S.M.O.W. (or seawater). Solutions of seawater with a salinity higher than 35%0 were prepared by diluting from standard seawater of batches P75 and P82, previously concentrated to a salinity close to 42%0. Evaporation was at 30°C using a rotating evaporator. At the beginning, pressure was slowly reduced inside the evaporator for degassing without boiling. Pressure was then set at about 10 mmHg and the rotation of the flask was set at its minimum speed. Under these conditions approximately 40 g of water are evaporated from the 250 of seawater in an hour; when the salinity is around 42%0, atmospheric pressure is slowly re-established in the evaporator, temperature is set at 25°C, and seawater is saturated by circulating air in the evaporator. Saturation was checked by oxygen titration according to Winckler's method. Salinity of the concentrated seawater was calculated from the ratio of the initial and the final weights of standard seawater and solution. Solutions of salinity 40, 38, and 35°o were then prepared by diluting the 42°o salinity seawater. The salinity of the solutions was
1019
Density of standard seawater solutions at atmospheric pressure
deduced from that of the 42%o salinity seawater and the ratio of weights of the concentrated seawater and of the diluted solution. Experimental results The Table
densities 3. D u r i n g
causing
Table 3.
of diluted
solutions
the concentration
of standard process
a slight shift of the CO2/carbonate
seawater
dissolved
(S < 35°0o) a r e p r e s e n t e d
gases escaped,
equilibrium,
which
particularly
is c l e a r l y s h o w n
in
CO2, by the
Differences of absolute density of diluted standard seawater solutions with that of pure water at the same temperature, measured and calculated with equation (10) at different temperatures and salinities P-Po
t (°C)
S (%)
29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009
35.000 35.000 29.981 29.981 24.968 24.968 20.017 20.017 14.998 14.998 10.069 10.069 5.021 35.000 35.000 29.983 29.983 24.955 24.955 20.018 20.018 14.989 14.989 10.028 10.028 35.000 35.000 29.969 29.969 24.964 24.964 20.007 20.007 15.011 15.011 10.045 10.045 5.012 5.012 35.000 35.000 29.996 29.996
P-Po
measured Pmeas- Pete ( l O - 3 g c m -3) ( l O - 6 g c m -3) 26.080 26.081 22.318 22.321 18.583 18.579 14.888 14.885 11.157 11.153 7.494 7.488 3.742 26.084 26.079 22.323 22.317 18.564 18.566 14.884 14.887 11.154 11.146 7.468 7.460 26.295 26.292 22.490 22.496 18.731 18.730 15.003 15.007 11.256 11.255 7.537 7.537 3.766 3.766 26.293 26.293 22.513 22.509
+ 1 0 +3 0 -7 - 3 - 2 + 1 -4 0 - 2 +4 0 - 3 +2 0 +4 +3 + 1 +3 0 -8 0 -6 +2 -2 + 1 +7 + 1 -2 -1 +2 -2 +4 +5 +4 +4 +4 +4 0 0 +4 +8
t (°C)
S (%o)
15.035 15.034 15.035 15.034 15.035 15.034 15.035 15.034 15.035 15.306 15.307 15.306 15.307 15.306 15.307 15.306 15.307 15.306 15.307 15.306 15.307 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.186 10.186 10.186 10.186 10.186 10.186 10.186 10.186
24.957 20.021 20.021 15.014 15.014 10.234 10.234 5.028 5.028 35.000 35.000 24.921 24.921 20.031 20.031 14.981 14.981 9.999 9.999 5.006 5.006 35.000 35.000 29.986 29.986 24.975 24.975 20.019 20.019 14.995 14.995 10.040 10.040 5.050 5.050 35.000 35.000 29.993 29.993 20.019 20.019 14.983 14.983
measured Pmeas- Pcalc (lO-3g cm-3) (lO-6gc m-3) 19.151 15.347 15.344 11.523 11.526 7.864 7.868 3.877 3.872 26.850 26.853 19.105 19.105 15.354 15.361 11.488 11.488 7.675 7.679 3.853 3.854 27.235 27.237 23.325 23.328 19.424 19.426 15.571 15.571 11.673 11.675 7.822 7.825 3.949 3.951 27.237 27.240 23.332 23.332 15.574 15.576 11.664 11.665
-9 +8 + 11 -3 -6 - 2 - 6 - 5 0 + 1 - 3 -4 -4 - 2 -9 - 1 -2 + i - 3 - 1 - 2 +3 + 1 +2 - 2 +1 - 1 + 1 + 1 -2 -4 +4 + 1 - 2 -4 +1 -2 0 0 -2 -4 -2 -3
1020
A. PolSSON, C. BRUNET and J. C. BRUN-COTTAN
Table 3-continued
t (°C)
S (%0)
25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.034 15.035 15.034 15.035
24.953 24.953 20.004 20.004 14.995 14.995 10.042 10.042 5.016 5.016 35.000 35.000 29.973 29.973 24.961 24.961 20.017 20.017 14.995 14.995 10.058 10.058 5.008 5.008 35.000 35.000 29.973 29.973 24.965 24.965 20.004 20.004 15.561 15.561 10.048 10.048 5.031 5.031 35.000 35.000 29.964 29.964 24.979 24.979 20.018 14.979 14.979 10.034 10.034 5.029 5.029 35.000 35.000 29.971 29.971
P--Po measured Pmeas- Pcalc (10-3 g cm -3 ) (10-6 g cm -3) 18.729 18.728 15.005 15.001 11.245 11.247 7.540 7.538 3.775 3.771 26.554 26.554 22.722 22.723 18.919 18.919 15.166 15.167 11.363 11.366 7.629 7.630 3.810 3.812 26.558 26.554 22.725 22.724 18.921 18.924 15.152 15.156 11.787 11.795 7.616 7.622 3.827 3.830 26.868 26.868 22.985 22.988 19.163 19.159 15.356 11.491 11.492 7.707 7.705 3.876 3.877 26.873 26.867 23.000 22.993
-8 -7 -2 +2 +3 + t - 2 0 - 2 +2 + 1 + 1 +4 +3 -2 - 2 +1 0 +2 - 1 +2 + 1 -2 -4 - 3 + 1 + 1 +2 - 1 -4 +5 + 1 +6 -2 +7 + 1 -2 -5 +1 + 1 +6 +3 -4 0 -3 +2 + 1 + 1 +3 -3 -4 -4 +2 -4 +3
t (°C)
S (%)
10.186 10.186 10.186 10.186 5.035 5.054 5.035 5.054 5.035 5.054 5.054 5.035 5.054 5.054 5.035 5.054 5.055 5.055 5.055 5.055 5.055 5.055 5.055 5.055 5.055 5.055 0.271 0.272 0.271 0.271 0.272 0.271 0.272 0.271 0.272 0.271 0.272 0.271 0.272 0.271 0.272 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271
10.022 10.022 5.023 5.023 35.000 35.000 29.904 29.904 24.863 24.863 20.002 14.548 14.548 10.020 5.051 5.051 35.000 35.000 20.013 20.013 14.994 14.994 10.047 10.047 5.040 5.040 35.000 35.000 35.000 29.991 29.991 24.967 24.967 20.011 20.011 14.976 14.976 10.041 10.041 5.006 5.006 35.000 35.000 29.981 29.981 29.981 24.968 24.968 19.994 19.994 14.999 10.032 10.032 5.019 5.019
P--Po measured Pmeas- Pcalc (10-3 g c m - 3) (10-6 g cm -~ ) 7.805 7.811 3.919 3.923 27.708 27.700 23.666 23.664 19.685 19.681 15.832 11.526 11.524 7.949 4.014 4.024 27.703 27.704 15.842 15.847 11.885 11.885 7.974 7.976 4.017 4.017 28.222 28.221 28.224 24.188 24.187 20.141 20.147 16.150 16.147 12.108 12.104 8.129 8.137 4.068 4.067 28.224 28.226 24.181 24.181 24.179 20.150 20.142 16.137 16.136 12.124 8.133 8.123 4.082 4.083
+7 +1 +7 +3 0 +6 +3 +4 - 5 -2 +5 +5 +6 +6 +8 - 2 +3 +2 +3 - 2 - 3 - 3 +2 0 - 4 - 4 + 1 +2 - 1 - 1 0 0 - 6 +4 +7 -4 0 +4 -4 + 1 +2 - 1 -3 -2 -2 0 - 8 0 +3 +4 - 1 -7 +3 -3 -4
Density of standard seawater solutions at atmospheric pressure
1021
increase of 0.5 pH unit during concentration. Although the concentrated seawater is reequilibrated with air, the new equilibrium differs from that of standard seawater in the ampoules, which is the chlorinity standard and which in the near future will be made an electrical conductivity standard and may even become a density standard (MILLERO, CHETIRKIN and CULKIN, 1977 ; POISSON, DAUPHINEE, Ross and CULKIN, 1978). Moreover, it is the seawater we used directly to standardize the densimeter and therefore our measurements are relative to it. We have fitted all the experimental data (S > 35%0) from concentrated seawater to a temperature-salinity cubic equation. For a given temperature the density at S -- 35%0 calculated with the equation is slightly lower (10 x 10 -6 g cm -3 for t = 30°C and 8 x 10 -6 g cm -3 for t = 0°C) than that obtained with relationship (4). The salinity (S measured) previously determined by the ratio of weights--42% o salinity concentrated seawater/solution--has been corrected for each temperature by S* Scorrected ~ Smeasured " ~ ,
where S* is the salinity corresponding to the density of equation (4) (S = 35.000%0) calculated from the above-mentioned temperature-salinity cubic equation. The surface representing this equation is then moved so as to pass through the curve representing equation (4). The experimental points thus readjusted are listed in Table 4. All the data of Tables 3 and 4 have been fitted in a polynomial of the form 103(p - P0) = where
S{~h(t) + (S- 35)g(t, S)}
(10)
h(t) is polynomial (4) and
g(t, S) = - 0 . 3 1 0 7 × 1 0 - 3 + 0 . 2 1 2 0 × 1 0 - 4 S + 0 . 1 4 2 7 x 10-4t - 0 . 5 4 2 3 × 1 0 - 6 S 2 - 0 . 1 9 5 3 × 1 0 - 6 S t - 0 . 3 6 1 3 x 10-6t2 +0.524 × 10-aS a + 0 . 3 1 0 × 10-8S2t+0.130 x 10-9St2+0.50× 10-st 3. Table 4.
Differences of absolute density of concentrated standard seawater solutions with that of pure water at the same temperature, measured and calculated with equation (10) at different temperatures and salinities P-Po
t (°C)
S (%0)
29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 25.059 25.059 25.059
34.841 34.841 38.029 38.029 40.236 40.236 41.576 41.576 34.707 34.707 38.098 38.098 39.723 39.723 41.981 41.981 35.196 35.196 37.760
measured
P-Po
Praeas- Pc~c
(10- 3 g cm -3) (10-6 g cm -3) 25.962 25.954 28.348 28.352 30.021 30.017 31.022 31.017 25.864 25.858 28.406 28.404 29.627 29.623 31.328 31.326 26.438 26.438 28.381
- 5 +3 +4 0 -9 -5 + 1 +6 -7 - 1 -3 - 1 - 1 +3 +1 +3 + 1 + 1 -2
t (°C)
S (%0)
15.185 15.185 15.143 15.143 15.143 15.143 15.143 15.034 15.034 15.034 15.034 15.034 15.034 15.034 15.034 10.042 10.042 10.042 10.042
39.855 42.076 35.011 35.011 37.581 39.943 43.076 35.133 35.133 37.950 37.950 40.146 40.146 41.848 41.848 34.648 34.648 37.948 37.948
measured
Pmeas- Pcalc
(10-a g cm -3) (10-6 g cm - a ) 30.607 32.322 26.872 26.871 28.853 30.675 33.105 26.975 26.972 29.150 29.148 30.843 30.844 32.158 32.159 26.976 26.977 29.547 29.561
0 +3 -2 - 1 0 +3 - 1 -3 0 -4 -2 + 1 0 +3 +2 - 1 -2 +7 -7
1022
A. POISSON, C. BRUNET and J. C. BRuN-COTTAN
Table 4~continued P-Po t (°C) 25.059 25.059 25.059 25.059 25.059 25.054 25.054 25.054 25.054 25.054 25.054 25.054 25.054 25.054 24.910 24.910 24.910 24.910 24.910 24.905 24.905 24.905 24.905 24.905 24.889 24.889 24.889 20.076 20.076 20.076 20.076 20.076 20.076 20.076 20.076 20.065 20.065 20.065 20.065 20.065 20.065 20.065 20.065 20.065 20.065 20.060 20.060 20.060 20.060 20.060 20.060 20.060 20.060 15.185 15.185 15.185
S (°0) 37.760 39.723 39.723 41.852 41.852 34.680 34.680 34.680 37.931 37.931 37.931 39.798 39.798 39.798 34.925 34.925 36.986 37.882 39.166 35.001 35.001 37.465 40.093 42.028 34.171 34.171 39.675 34.987 34.987 37.970 37.970 40.143 40.143 41.797 41.797 34.749 34.749 37.981 40.096 41.944 34.718 34.718 38.009 36.543 42.584 34.704 34.704 37.867 37.867 40.154 40.154 41.959 41.959 34.747 34.747 37.950
P-Po
measured Pmeas- Pc~ac ( l O - 3 g c m -3) ( l O - 6 g c m -3) 28.380 29.865 29.864 31.485 31.484 26.049 26.052 26.046 28.513 28.509 28.508 29.927 29.920 29.920 26.242 26.243 27.797 28.484 29.451 26.296 26.298 28.165 30.156 31.626 25.669 25.671 29.843 26.542 26.543 28.817 28.818 30.479 30.478 31.745 31.746 26.362 26.359 28.825 30.447 31.859 26.335 26.341 28.845 27.729 32.350 26.327 26.324 28.742 28.743 30.487 30.487 31.869 31.872 26.667 26.662 29.136
- 1 + 1 +2 -2 - 1 0 - 3 + 3 -5 - 1 0 -4 +3 +4 0 - 1 + 3 - 5 + 1 + 3 + 1 - 2 - 1 - 1 +3 + 1 -4 - 1 - 2 + 1 0 0 + 1 +2 + 1 - 1 + 2 +2 - 3 + 1 + 2 -4 + 3 0 + 1 - 1 +2 - 2 - 3 +2 +2 + 3 0 -4 + 1 -2
t (°C) 10.042 10.042 10.042 10.042 10.042 10.042 10.018 10.018 10.018 10.018 10.018 10.018 10.018 10.018 5.001 5.001 5.001 5.001 5.001 5.001 5.001 5.001 5.001 4.998 4.998 4.998 4.998 4.998 4.998 4.998 4.998 1.783 1.783 1.783 1.783 1.780 1.780 1.780 1.780 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.029 0,029 0.029 0.029 0.029 0.029 0.029 0.029
S (%o) 37.948 40.203 40.203 40.203 41.861 41.861 34.866 37.992 37.992 34.864 39.917 39.917 41.779 41.779 37.986 37.986 37.986 39.927 39.927 39.927 42.082 42.082 42.082 36.589 36.589 37.901 37.901 39.694 39.694 41.579 41.579 34.795 37.771 40.021 41.848 34.807 37.783 40.034 41.862 34.760 34.760 38.226 38.226 39.877 39.877 41.673 41.673 35.098 35.098 37.841 37.841 39.714 39.714 41.790 41.790
measured Pmeas- Pcal¢ ( l O - 3 g c m -3) ( l O - 6 g c m -3) 29.555 31.321 31.323 31.322 32.621 32.617 27.149 29.589 29.595 27.148 31.098 31.102 32.554 32.556 30.078 30.084 30.082 31.622 31.625 31.623 33.337 33.337 33.340 28.972 28.974 30.012 30.016 31.440 31.441 32.937 32.936 27.890 30.275 32.076 33.546 27.896 30.288 32.090 33.555 28.058 28.056 30.855 30.856 32.190 32.188 33.638 33.642 28.331 28.326 30.544 30.544 32.059 32.059 33.734 33.736
- 1 - 2 -4 -3 - 2 + 2 - 2 +2 -4 - 3 0 -4 +3 + 1 +3 - 3 - 1 + 1 - 2 0 - 1 - 1 - 4 0 -2 + 1 -3 -2 - 3 0 + 1 -4 - 2 +3 +2 0 - 5 0 +4 - 1 + 1 +1 0 - I + 1 + 3 - 1 - 1 +4 0 0 - 2 -2 + 1 - 1
Density o f standard seawater solutions at atmospheric pressure
1023
The standard deviation between the values calculated with this polynomial (10) and the measured values is 3.2x 10-6g crn -a. The form of the polynomial has been chosen because it corresponds exactly to the measurement procedures we used. The surface representing this polynomial passes through the curve p = Po for S = 0 and p = equation (4) for S = 35O/0o.
Comparison with previous work We have compared our results (equation 10) with those of KNUDSEN(1901) (equation 6), Cox et al. (1970) (equation 7) and MILLEROet al. (1976a) (equation 8). The contours of differences in the density obtained from our results and the data of others are presented in Fig. 2. The samples used by the different authors had different origins: KNUDSEN (1901) used pycnometers to determine the density of surface water samples from the North, Baltic, and Mediterranean seas and the North Atlantic at zero and 24.6°C, and their thermal expansibility between 0 and 30°C. The chlorinity of the samples ranged from 2.5 to 22.5°o, i.e., salinity from 4.5 to 40.60/00. Cox et al. (1970) used a suspension balance to determine the density of samples collected between 0 and 200 m in the Atlantic, the Pacific, and the Mediterranean, Baltic and Red seas. MILLEROet al. (1976a) carried out their measurements on diluted and evaporated standard seawater solutions. Agreement with Millero's results (Fig. 2) is the best (standard deviation of 3.7x 10-6g cm-3), but at very low and high temperatures and high salinities, the disagreement is higher than combined experimental error. As the samples used by Cox and KNUDSENwere natural seawater, the disagreement with our results is more important. Our results differ from Cox's by about 70 ppm at 10%o whatever the temperature, whereas they differ about 50 ppm from Knudsen's result at 5%0 whatever the temperature. For the two sets of data, the agreement is best around 35%0, which is certainly because most of the samples with a salinity close to 35%0 came from the North Atlantic, as did the standard seawater used by Millero and in this work. E X P A N S I B I L I T Y OF S T A N D A R D SEAWATER S O L U T I O N S
The expansibility ct = - 1/p(Sp/t~t) of standard seawater solutions can be determined by differentiating equations (10) and (5) with respect to temperature, =
(P-Po)+pol
\(~P°~t + ~(P~t -- Po))_"
(11)
Some values of a thus determined (Table 5) are compared with values obtained previously by other workers in Fig. 3. To do this we have calculated the derivative of the equations proposed by KNUDSEN(1901), COX et al. (1970) and MILLEROet al. (1976a). The comparisons have been carried out only for the temperature and salinity areas reported in the three papers. The best agreement is between 5 and 20°C. At low and mainly at high temperatures, deviations are more important for Cox's results. This may be because the polynomial fitted for each set of measurements has been fitted for the entire temperature and salinity range studied by the author, but in extreme temperature and salinity ranges, the number of data points is sometimes small. There may be an end effect for the polynomials that leads to an excess of the curvature of the surface representing the polynomials at temperature and salinity extremes. The agreement with Millero's results is
1024
A. PoISSON, C. BRUNET and J. C. BRUN-COTTAN
(P - Po)ours-- (d - do)Kaudma
~Xours - - ~Knudsen
a0
T(°CI
T(*C)
~
'
~
~
,o
20
Fig. 2a.
30
S (~0)
,o
Fig. 3a.
(d - do)cox
30
20
~
~o--J
//° (/9 -- P0)ours --
'
~ours
S
--
~Cox
[Xo)
Fig. 2b.
Fig. 3b.
(,O -- PO)ours -- (P --/90)Millero
~ . . . . -- ~Millero
.
.
.
.
o o
T (°
(
T(°C) -i
io
io
_lJ .3 / ~o
S (~o0)
Fig. 2c.
Fig. 3c.
Fig. 2. (Left) Contour diagrams of the differences of density ( 1 0 - 6 g c m -3) calculated by equation (10) and those of KNUDSEN (a), Cox et al. (b) and MILLERO et al. (C).
Fig. 3. (Right) Contour diagrams of the differences of expansibility (10- 6 ° C - t ) calculated by equation (11) and those calculated from the equations of KNUDSEN (a), Cox et al. (b) and MILLERO et al. (C).
,o
1025
Density of standard seawater solutions at atmospheric pressure
Table 5. Expansibility (× 10 -6 *C -1) of standard seawater solutions at atmospheric pressure for different temperatures and salinities calculated with equation (11 ) Temperature Salinity (%o) 0 5 10 15 20 25 30 35 40
-
0°C
5°C
10°C
15°C
20°C
25°C
30°C
68.0 48.9 30.8 13.5 3.0 18.9 34.2 48.8 62.8
16.0 31.7 46.5 60.7 74.4 87.6 100.4 112.7 124.5
88.1 100.8 112.8 124.4 135.5 146.4 156.9 167.2 177.0
150.9 161.1 170.8 180.0 189.0 197.8 206.3 214.7 222.7
206.7 214.8 222.5 229.8 236.9 243.9 250.7 257.3 263.8
257.0 263.5 269.6 275.4 280.9 286.4 291.7 296.8 301.8
303.1 308.5 313.3 317.9 322.2 326.3 330.4 334.2 337.9
within _ 1 × 10-60C - 1 except at very low temperatures and very high salinities, but the values are out of the oceanic range. The agreement of our results with those of K n u d s e n - which is also about + 1 x 10-6°C -1 except at extreme temperatures--confirms what Millero wrote, i.e., the expansibilities of Knudsen are reliable at + 1 x 10-60C - 1 in all the oceanic range. CONCLUSION
All the densities measured with the vibrating densimeter are relative to the density values attributed to standard seawater (S = 3%o) used for its calibration. To compare better the consistency between the set of measurements that we carried out with the vibrating densimeter and the set of measurements by MILLERO et al. (1976a), we have normalized both sets of data at S = 35%o. To carry out this normalization, we corrected the densities we obtained by attributing the density given by Millero's equation (equation 8) to the standard seawater (S = 35%0) used for its calibration. The differences between the corrected values and those calculated with Millero's equation are represented in Fig. 4a. The standard deviation between the two sets of data is only 2.0 x 10 - 6 g cm -a here; we have also calculated expansibilities with our polynomial normalized at S = 3500 and compared them with those obtained by Millero (Fig. 4b). The standard deviation is only 0.5 × 10-o°C -1. Although the form of Millero's equation is different from that of our equation (10), it is clear that the differences between the two sets of data that we pointed out previously are due to differences between the two sets of data at S = 35O/o0. We have seen (Fig. 1) that Millero's experimental data for S = 35%0 are quite consistent with ours but the values calculated at S = 35°0 for his polynomial (equation 8) are shifted. By normalizing the two sets of data at S = 35%o, we eliminate the shift, and the agreement becomes excellent. Besides, the degree of the polynomial chosen for S = 3500 (cubic, equation 4, or quadratic, equation 9) has an importance that is not negligible--as we have seen before--especially on our set of data with measurements carried out at 1, 2, 5, 7, and 10°C, which is the region of the curve where the curvature is greater. This is clearly shown in Table 6 where we have calculated expansibilities at different temperatures with the cubic and quadratic equations. End effects are evident. If we use only measurements at 1, 5, and 10°C to calculate the equations (4) and (9), the effects become very small.
~°I ~-_----- 5 ~ ~ ~ " T(°C) -2 -3
20
-~
0~ 0
+1
\
J
0"f -2 f
0
0
10
30
20
Fig. 4a. 30 •
~
j l
j
S(%o)
~o \ -0.5 \
J
T(°C) 20
y 10 f
f E
O
0 -'-"
~
f
/
/,
-0.5
0
/
20 30 S(~o) Fig. 4b. Fig. 4. Comparison of our data with those of Millero normalized at 35°/oo;(a) contour diagram of the differences of density (10-6 g cm-a); (b) contour diagram of the differences of expansibility (10-6 oC-1). 0
10
-1
4o
1027
Density of standard seawater solutions at atmospheric pressure
Table 6. Comparisonof the expansibilities (10-6 oC-1) calculatedfrom the derivatives of the equations (4) and (9) Temperature (°C)
al~. 4) (10 -6 °C -1)
~(eq. 9)
~t(¢q. 4) - - ~t(eq, 9)
(10 -6 ° C - t )
(10 -6 °C-I)
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 27.5 30
52.5 83.7 112.9 140.4 166.5 191.1 214.5 236.8 258.0 278.1 297.2 315.2 332.1
48.8 82.1 112.7 141.0 167.2 191.6 214.7 236.5 257.3 277.4 296.8 315.7 334.2
+ 3.7 + 1.6 +0.2 - 0.6 -0.7 -0.5 -0.2 +0.3 + 0.7 +0.7 + 0.4 -0.5 - 1.9
All the data presented in this paper together with those published by MILLEROet al. (1976a) will be used to define a new equation of state of seawater at atmospheric pressure (MILLERO and POISSON, in preparation). To do this it will be necessary, as we have just seen, to normalize the two sets of data for S = 35%o. The use of vibrating densimeters aboard research vessels will probably become general soon, because they make measurements very easy. Therefore it is important to propose a way of calibrating the instruments. The easiest procedure is obviously to use pure water--whose absolute density is that of S.M.O.W.--and standard seawater at S = 35%o--whose absolute density, relative to that of S.M.O.W. is given as a function of temperature with an equation similar to equation (4) or (9). All the results thus obtained will be immediately comparable. The use of standard seawater as a density standard is suggested because it is easy to use and its density is reproducible from one batch to another (MILLERO et al., 1977; PoISSON et al., 1978) to + 2 × 10 - 6 g cm -3, which is the maximum accuracy obtainable by the vibrating densimeter. It is of course the seawater contained in the ampoule that constitutes the density standard and that must be used directly to calibrate the densimeter without exposure to air. Finally, the density calculated by using equation (10) or equation of state at atmospheric pressure of MILLEROet al. (in preparation) will have to be compared to the density of in-situ natural seawaters. The investigations up to n o w (MILLERO and KREMLING, 1976 ; MILLERO et al., 1976b; MILLEROet al., 1978a; MILLEROet al., 1978b) were carried out on samples brought to the laboratory to measure their salinity and their density. However, the rapid shift of the CO2/carbonate system alters the conductivity and density. For valid comparisons, conductivity and density must be determined immediately after the samples are collected. The results of a recent study of surface waters of the Indian Ocean, the Red Sea, and the eastern Mediterranean (PoIsSON et al., in preparation) tend to show that the differences between the density of natural seawater and that of standard seawater solution having the same conductivity salinity are greater in some places than those given in the studies discussed above. What is interesting is that such comparisons could be made directly on board ship relative to the standard seawater used to establish the equation of state at atmospheric pressure. Acknowledgement--This study was supported by the C.N.R.S., Contract A.T.P. "Chimie marine 76" No. 1661.
1028
A. POISSON, C. BRUNET and J. C. BRuN-COTTAN
REFERENCES BIGG P. H. (1967) Density of water in S.I. units over the range 0-40°C. British Journal of Applied Physics. 18, 521-537. Cox R. A., M. J. McCARTNEY and F. CULKrS (1970) The specific gravity/salinity/temperature relationship in natural seawater. Deep-Sea Research, 17, 679-689. KELL G. S. (1975) Density, thermal expansibility and compressibility of liquid water from 0 to 100°C: corrections and tables for atmospheric pressure and saturation reviewed and expressed on 1968 temperature scale. Journal of Chemical Engineering Data, 20, 97-105. KNUDSEN M. (1901) Hydrographical tables. GEC-Gad, Copenhagen, 63 p. KREML~G K. (1972) Comparison of specific gravity in natural seawater from hydrographical tables and measurements by a new density instrument. Deep-Sea Research, 19, 377-383. MENACHE M. and G. GIRARD (1972) Concerning the different tables of the thermal expansion of water between 0 and 40°C. Internal Report jointly published by Institut Oc6anographique, Paris and Bureau International des Poids et Mesures, S6vres. MILLERO F. J . (1967) High precision magnetic float densimeter. Review of Scientific Instruments, 38, 1441 1444. MILLERO F. J. and K. KREMLING (1976) The densities of Baltic seawaters. Deep-Sea Research, 23, 1129-1138. MILLERO F. J. and F. K. LEPPLE (1973) The density and expansibility of artificial seawater solutions from 0 to 40°C and 0 to 21%o chlorinity. Marine Chemistry, 1, 89-104. MILLERO F. J., A. GONZALEZand G. K. WARD (1976a) The density of seawater solutions at one atmosphere as a function of temperature and salinity. Journal of Marine Research, 34, 61-93. MILLERO F. J., A. GONZALEZ,P. BREWERand A. BRADSHAW(1976b) The density of North Atlantic and North Pacific deep waters. Earth and Planetary Science Letters, 32, 468-472. MILLERO F. J., P. CHETIRKIN and F. CULKIN (1977) The relative conductivity and density of standard seawaters. Deep-Sea Research, 24, 315-321. MILLERO F. J., D. MEANSand C. MILLER (1978a) The densities of Mediterranean seawaters. Deep-Sea Research, 25, 563-569. MILLERO F. J., D. FORSHT, D. MEANS, J. GIESKESand K. E. KENYON (1978b) The density of North Pacific Ocean waters. Journal of Geophysical Research, 83, 2359-2364. PICKER P., E. TREMBLAYand C. JOLICOEUR (1974) A high-precision digital readout flow densimeter for liquids. Journal of Solution Chemistry, 3, 377-384. POISSON A. and J. CIJANU (1976) Partial molal volumes of some major ions in seawater. Limnology and Oceanography, 21, 853-861. POISSONA., C. BRUNETand M. MENACHE(1979) Equation d'etat des solutions d'eau de met Normale ~. la pression atmosph6rique. Ocbanis, 5, 651-660. POISSONA., T. DAUPHINEE,C. K. Ross and F. CULKIN (1978) The reliability of standard seawater as an electrical conductivity standard. Oceanologica Acta, 1,425-433. THIESEN M. (1900) Untersuchungen fiber die thermische Ausdehnung yon festen und tropfbar fliissigen K6rpern. Wissenschaftliche Abhandlungen tier Physikalischtechnischen Reichsanstalt, 3, 1-70. THOMPSON T. G. and H. E. WmT8 (1931) The specific gravity of seawater at zero degree in relation to chlorinity. Journal du Conseil, Conseilpermanent Internationalpour l'Exploration de la Mer, 6, 232-240. TILTON L. W. and J. K. TAYLOR (1937) Accurate representation of the refractivity and density of distilled water as a function of temperature. Journal of Research of the National Bureau of Standards, 18, 205-214. UNESCO (1979) Ninth report of the Joint Panel on Oceanographic Tables and Standards. 31 pp, UNESCO Technical Papers in Marine Science No. 30, Paris.
01984)149/80/1201-1013 $02.00/0
Density of standard seawater solutions at atmospheric pressure A. POISSON*, C. BRUNET* and J. C. BRUN-COTTAN* (Received 1 February 1980; in revised form 12 May 1980; accepted 15 June 1980)
Abstract--The density of standard seawater P75 (S = 35%0) has been measured from 0 to 30°C with a suspension balance. This batch of standard seawater has been used together with a distilled water to calibrate a vibrating densimeter with which the density of diluted and concentrated standard seawater solutions has been determined at atmospheric pressure. The measurements have been carried out from 0 to 42%0 salinity and 0 to 30°C. Equations for density of standard seawater (S = 35%0) vs the temperature and for density of standard seawater solutions vs the temperature and salinity have been fitted. The smoothed densities are compared with previous works.
INTRODUCTION
As EARLY as the beginning of the century, oceanographers were able to determine density accurately from a chlorinity titration by using the Hydrographical Tables of KNUDSEN (1901). The increase in accuracy and precision of some techniques in later years, in particular the determination of the salinity from electrical conductance, together with the measurement of density at atmospheric pressure with modern densimeters (magnetic float densimeter, MILLERO, 1967 ; vibrating densimeter, PICKER, TREMBLAYand JOLICOEUR, 1974) has made it possible to check the data of Knudsen and to obtain more reliable sets of data on larger ranges of temperature and salinity. The slight variations in ionic ratios that exist in the world ocean imply variations of density--specific to the chemical species--which are significant relative to the accuracy of modern apparatus; the density-salinity-temperature relationships determined from direct measurements on samples from all the world ocean (THOMPSON and WIRTH, 1931 ; COX, MCCARTNEY and CULLEN, 1970; KREMLING, 1972) have therefore a standard deviation which will never be smaller than a few ppm. Recently MILLERO carried out measurements on artificial seawater (MILLERO and LEPPLE, 1973) and on standard seawater solutions (MILLERO, GONZALESand WARD, 1976a). The relationship between density and salinity is unique then, and the standard deviation of the densitysalinity-temperature relationships becomes very small because it arises only from experimental error. It is then necessary to check the agreement between the density determined from the artificial relationships and the density of natural seawater of different oceans and seas. Recent works seem to show that this agreement is excellent in the Mediterranean Sea (MILLERO, MEANS and MILLER, 1978a) and in the Baltic Sea when seawaters are compared at the same total dissolved solid concentration (MILLERO and KREMLING, 1976), but corrections are often needed, specially for deep waters (MILLERO, GONZALEZ, BREWER and B~L~SnAW, 1976b; MILLERO, FORSnT, MEANS, GIESKES and * Laboratoire de physique et chimie marines, Universit6Pierre et Marie Curie, tour 24, 4, place Jussieu, 75230, Paris Cedex 05, France. 1013
1014
A. Poisso~, C. BRUNET and J. C. BRUN-COTTAN
KENYON, 1978b). Some measurements carried out in our laboratory (PoISSON, BRUNETand MENACHE, 1979) disagree at high temperatures with the relationship of MILLERO et al. (1976a), and we have, according to the recommendation of the Joint Panel on Oceanographic Tables and Standards (UNESCO, 1979) carried out a second set of measurements of the density of standard seawater at a salinity of 350/00. We present the results in this paper together with the polynomials that we have fitted.
D E N S I T Y OF S T A N D A R D SEAWATER (S = 35% 0) AS A F U N C T I O N OF T E M P E R A T U R E
The standardization of the vibrating densimeter we have used to measure the density of seawater solutions at different temperatures and salinities requires two reference fluids of known density. We have chosen to use standard seawater and distilled water for the standardization. The density of the distilled water was measured at the "Bureau International des Poids et Mesures" (S6vres) relatively to the S.M.O.W. (Standard Mean Ocean Water); the density of standard seawater was measured at different temperatures relative to the distilled water by means of a suspension balance. Apparatus and methods The apparatus and methods used are similar to those described in detail elsewhere (PoISSON and CrtANU, 1976). The sinker used is made of P y r e x ; i t s volume is about 63 cm 3 and its weight is about 72 g; the nickel-chromium suspension thread has a diameter of 35 ttm. The balance is a Mettler balance M 5 G D (20 g maxi + 2 x 10-6 g). The temperature is maintained constant in the measurement cell by using a thermostat and a special stirrer. The temperature is measured with a platinum resistance thermometer of 25 (2 (Rosemount, type E 109-25) and a thermometric bridge (A.S.L., type H7) with an accuracy of + 2 x 10-a°C. As the volume of the cell is approximately 500 cm 3, we need two ampoules of standard seawater for each measurement. Before they are opened, the ampoules are set at a temperature slightly higher than the one of measurement, so as to avoid degassing in the cell and to prevent microbubbles from sticking on the sinker. Standard seawater is introduced fairly slowly into the cell, limiting as much as possible its contact with air. Seawater is stirred intermittently until the temperature remains constant. Salinity of seawater, measured immediately after determining the apparent weight of the sinker with a Guildline Autosal salinometer, is the same as at the beginning. Moreover, the pH variation during the measurement is less than a few hundredths of a pH unit. The evaporation and the exchange of CO2 between seawater and air are negligible, and the variation of corresponding density remains smaller than 1 x 10 -6 g cm -3. The absolute density (Pt) of seawater at temperature t is, M - msw p,
-
-
-
v,
(i)
where M is the mass of the sinker in vacuum and msw its apparent weight in seawater; Vt is the volume of the sinker at temperature t; M was determined by using a Mettler balance B5 (200 g maxi __+1 x 10 -4 g); the air buoyancy correction is calculated from the pressure, measured with a mercury barometer, the temperature and the relative humidity of air, measured with a psychrometer.
Density of standard seawater solutions at atmospheric pressure
1015
The volume Vs of the sinker was measured at different temperatures (Table 1) by using distilled water with an absolute density, at 22°C and at atmospheric pressure, as measured at the "Bureau International des Poids et Mesures", smaller than that of S.M.O.W. by 7 x 10 -6 g c m - 3 . The absolute density PmPM of the distilled water was therefore chosen as equal to that of S.M.O.W. (equation 5) minus 7 x 10-6 g c m - 3 for all the temperatures. Vt was calculated with Vt
-
M-m
w
- -
(2)
RB1PM where mw is the apparent weight of the sinker in the distilled water from B.I.P.M. The determined values of V~have been fitted in a linear relationship Vt = Vo+yt
(3)
where Vo is the volume of the sinker at 0°C, y is the coefficient of expansion of the sinker, equal to 6.1892)< 10 -4 cm -3 °C -1. The standard deviation is equal to 1.4× 10 -4 cm 3, equivalent to 2.8 × 10 -6 g cm -3 of the density of pure water. Table 1.
Volume (cm3) of the sinker measured at different temperatures and calculated with equation (3)
t (°C) 30.040 29.091 25.410 24.834 20.348 20.325 5.104 5.094 1.071
Measured v o l u m e (cm3) 63.4567 63.4556 63.4538 63.4533 63.4506 63.4505 63.4410 63.4411 63.4385
Calculated volume (cm3)
Volume difference (10-4 cm3)
63.4565 63.4559 63.4537 63.4533 63.4505 63.4505 63.4411 63.4411 63.4386
-2 +3 - 1 0 - 1 0 +1 0 +1
Experimental results
The absolute densities of standard seawater P75 (CI = 19.374%o) determined at different temperatures are given in Table 2. The results are presented as differences between the absolute density p of seawater and that of pure water Po at the same temperature. Differences in the density of pure waters arising from isotopic composition (MENACHEand GmARD, 1972) are thus eliminated; moreover the differences of absolute densities p - P o are measured with the same value as the differences of relative densities d - d o of seawater, whatever the temperature and salinity. The maximum difference between p - Po and d - do is 1 x 10 . 6 for 0°C ~< t ~< 30°C and 0%o ~< S ~< 40%0. The results have been fitted to the form of a polynomial 1 0 a ( p - p o ) = 28.255-0.11813t + 1.937 x 10-3t 2 - 1.399 x 10-5t 3
(4)
the standard deviation of which is 2.9 x 10-6 g c m - 3 ; Po, absolute density of S.M.O.W., is calculated from the relationship 103po = 999.842594+6.793952 x 1 0 - 2 t - 9 . 0 9 5 2 9 0 x 1 0 - a t 2 + 1.001685 x 10-4t 3 - 1.120083 x 10-6t4+6.536332 x 10-9t 5. (5)
1016
A. POISSON, C. BRUNET and J. C. BRUN-COTTAN
Table 2. Differences between absolute density of standard seawater P75 and absolute density of S.M.O.W. measured at different temperatures and calculated with equation (4) P-Po
P-Po
t (°C)
measured (10 - 3 g c m -3)
Pmeas- P¢~c ( 1 0 - 6 g c m -3)
t (°C)
measured (10 -3 g c m -3)
Pmeas-- Pealc ( 1 0 - 6 g c m -3)
30.067 30.006 25.577 25.435 25.423 25.368 24.239 20.932 20.759 20.725
26.075 26.079 26.262 26.268 26.274 26.279 26.330 26.504 26.511 26.511
- 1 -3 +5 +5 0 --3 0 -- 1 + 1 +3
19.717 19.697 15.681 10.478 10.412 7.100 5.220 5.215 2.340 1.163
26.576 26.576 26.828 27.217 27.217 27.505 27.688 27.690 27.987 28.124
- 4 -3 -3 - 3 +2 +4 + 1 0 +2 -4
based on the table given by Bic,6 (1967), the use of which has recently been suggested by the International Union of Pure and Applied Chemistry (1974). The absolute density of seawater (S = 35%0) can be obtained by adding relationships 4 and 5. To calculate the relative density we divided p thus obtained by the value of the maximum density of S.M.O.W. used by KELL (1975), Pmax = 0.999975 g cm -3.
Comparison with previous work We have calculated for a seawater of salinity 35%0 the difference between the density of KNUDSEN (1901) and the corresponding density of pure water given in the table by TmESEN (1900) that Knudsen had taken as a reference, for temperatures ranging from 0 to 30°C. The difference for a seawater of salinity S and temperature t is (Hydrographical Tables, 1901) 103(d-do) = (a0 +0.1324){1 - A +B(ao-0.1324)}
(6)
where a o = - 0.069 + 1.4708 C1 - 1.570 × 10- 3 C12 + 3.98 × 10- 5 C13 A = t(4.7867-0.098185t +0.0010843t 2) × 10 -3
B = t(18.030-O.8164t+O.O1667t 2) x
10 - 6 .
The salinity S is deduced from the chlorinity C1 by S = 0.030+ 1.8050 C1. The values obtained at different temperatures for a seawater of salinity 35%0 are compared to the values calculated with equation (4) on Fig. 1. We have also calculated the differences between density do of pure water given in the table of TILTONand TAYLOR(1937) and density d obtained by using the polynomial of Cox et al. (1970): d = 1 + 8.00969062 x 10- 5 + 5.88194023 × 10- 5t + 7.97018644 × 10-aS -8.11465413 x 1 0 - 6 t 2 - 3 . 2 5 3 1 0 4 4 1 x 1 0 - 6 S . t + 1.31710842 x 1 0 - 7 S 2 + 4.76600414 x 10 - st3 + 3.89187483 x 10 - aS. t 2 + 2.87971530 x 10 - 9S2. t -6.11831499 × 10-11S 3. (7) The standard deviation of the polynomial is 11 x 1 0 - 6 g c m - 3 . The values obtained for S = 35%0 at different temperatures are compared with those calculated using polynomial 4
Density of standard seawater solutions at atmospheric pressure
,2-
[P-P.]o.~-[p-~ot..rs
o Po, . . . .
C.q')-
(10./* g.c m.3~
• Poi . . . .
{eq 4) - M i i l e r o
10-
POISSON - KNUDSEN
/
/
_~
'
~
Poi . . . . . . . . . . .
-----
P o i sso n
{eq 4 ) - M i l l e r o
....
Poisson
(eq 9 ) - M i l l e r o
7"o--..
"~,.
1017
d
measured
o
o
POISSON - COX -15
Fig. l. Comparisonofp -Po ( 10-6 g cm-3) calculated by equation (4) or (9) with d - d o or P - P o calculated by equations fitted by others, and comparison of our and Millero's experimentaldata with equation (4). on Fig. 1. MILLERO e t al. (1976a) presented their data under the form of differences of absolute densities, so we have calculated p - P0 directly from the polynomial he proposed : (8)
P - Po = A S + B S 3/2 + C S 2
where S is the salinity obtained by diluting or evaporating standard seawater. A = 8.25938 × 1 0 - 4 - 4 . 4 4 9 1 x 1 0 - 6 t + 1.0485 × 10-7t 2 - 1.2580 x 10-9t3 +3.315 x 10-12t4 B = -6.33777 × 1 0 - 6 + 2.8442 × 10-Tt - 1.6871 x 10-8t2 + 2.83265 x 10-~°t3 C = 5.4706 x 10 -7 - 1.9798 x 1 0 - s t + 1.6641 x 10-9t 2 - 3.1204 × 10-~1t3. The standard deviation is 3 . 3 x 1 0 -6 g cm -3. The deviations between Millero's measurements and the above polynomial (8) being at 35%0 higher than the standard deviation, we have also put his experimental data on Fig. 1. Whereas the differences between polynomial (4) and (8) are always negative, Millero's experimental data are, except at 0°C, in agreement with equation (4) (mean deviation = 0.4 x 10 -6 g cm-3). This is not the case at low and high temperatures for his polynomial (equation 8) reduced at 35%0. As the experimental data are relatively few--measurements were carried out at only nine temperatures--the shape and the degree of the polynomial chosen to fit the data can have an important influence. To check the influence of this on the work we have calculated the coefficients of a quadratic polynomial from the same data as in Table 2. 103(p-p0) = 28.262-0.1219t+2.473 x 1 0 - 3 t 2 - 4 . 0 3 2
x
10-st3+4.159
×
10-7t 4. (9)
The values calculated from polynomial (9) have been compared with those calculated from Millero's equation (equation 8); the deviations are collected on Fig. 1 (dotted curve); it is evident that the degree of the polynomial has an important influence at the lowest and the highest temperatures and especially at 0°C, which is below our lower temperature of measurement. Nevertheless, the standard deviation of polynomials (4) and (9) are very close (2.9 and 2.3 x 1 0 - 6 g cm -3) and we shall use polynomial (4) for
1018
A. POISSON,C. BRUNETand J. C. BRUN-COTTAN
calculations and comparisons in the next paragraphs, because its curve has the advantage of being less bent than that of the quadratic equation.
DENSITY
OF
FUNCTION
STANDARD OF
SEAWATER
TEMPERATURE
SOLUTIONS AND
AS A
SALINITY
As we now have two liquids whose absolute densities are known as a function of temperature we can standardize the densimeter and measure the density of standard seawater solutions at different temperatures and salinities.
Apparatus and method The principle of the high precision digital readout flow densimeter we have used is explained in detail elsewhere (PICKER et al., 1974). It has been standardized at each temperature for each set of measurements by using distilled water provided by the B.I.P.M. and standard seawater P75. The absolute density of distilled water is determined with equation (5) (S.M.O.W.) and that of standard seawater with equation (4). The seawater solutions with a salinity smaller than 3500 are directly prepared from batch P75 and a distilled water prepared in our laboratory. Each sample is prepared in a 100 cm 3 screwtopped flask so that the quantity of dilute seawater should always be close to 60 cm 3. This made it possible to prepare a set of dilution (from 35 to 5%0) from the same ampoule of standard seawater. The salinities of the samples are determined from the ratio of the weight of standard seawater and the final weight of solution. The flasks are weighed by using a Mettler balance B5 (200 g m a x + 1 x 10 - 4 g). The distilled water and the seawater ampoules are placed in the balance room at least one day before the dilutions--carried out in a humid box--and the weighings. All the density measurements were within 4 h of the preparation of the solution. For each temperature, two sets of dilutions were prepared and the density of each sample was determined twice. There were no corrections for evaporation and air buoyancy in the calculation of salinity from weights of standard seawater and distilled water. The shift of the densimeter was controlled by making a measurement of the density of the laboratory distilled water every two samples. The densimeter constant was determined every day and densities were calculated using the mean constant for each temperature. By using the equation of S.M.O.W. for the calculations we internally correct the effect of dilution with a distilled water whose isotopic composition differs from that of S.M.O.W. (or seawater). Solutions of seawater with a salinity higher than 35%0 were prepared by diluting from standard seawater of batches P75 and P82, previously concentrated to a salinity close to 42%0. Evaporation was at 30°C using a rotating evaporator. At the beginning, pressure was slowly reduced inside the evaporator for degassing without boiling. Pressure was then set at about 10 mmHg and the rotation of the flask was set at its minimum speed. Under these conditions approximately 40 g of water are evaporated from the 250 of seawater in an hour; when the salinity is around 42%0, atmospheric pressure is slowly re-established in the evaporator, temperature is set at 25°C, and seawater is saturated by circulating air in the evaporator. Saturation was checked by oxygen titration according to Winckler's method. Salinity of the concentrated seawater was calculated from the ratio of the initial and the final weights of standard seawater and solution. Solutions of salinity 40, 38, and 35°o were then prepared by diluting the 42°o salinity seawater. The salinity of the solutions was
1019
Density of standard seawater solutions at atmospheric pressure
deduced from that of the 42%o salinity seawater and the ratio of weights of the concentrated seawater and of the diluted solution. Experimental results The Table
densities 3. D u r i n g
causing
Table 3.
of diluted
solutions
the concentration
of standard process
a slight shift of the CO2/carbonate
seawater
dissolved
(S < 35°0o) a r e p r e s e n t e d
gases escaped,
equilibrium,
which
particularly
is c l e a r l y s h o w n
in
CO2, by the
Differences of absolute density of diluted standard seawater solutions with that of pure water at the same temperature, measured and calculated with equation (10) at different temperatures and salinities P-Po
t (°C)
S (%)
29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 29.903 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009
35.000 35.000 29.981 29.981 24.968 24.968 20.017 20.017 14.998 14.998 10.069 10.069 5.021 35.000 35.000 29.983 29.983 24.955 24.955 20.018 20.018 14.989 14.989 10.028 10.028 35.000 35.000 29.969 29.969 24.964 24.964 20.007 20.007 15.011 15.011 10.045 10.045 5.012 5.012 35.000 35.000 29.996 29.996
P-Po
measured Pmeas- Pete ( l O - 3 g c m -3) ( l O - 6 g c m -3) 26.080 26.081 22.318 22.321 18.583 18.579 14.888 14.885 11.157 11.153 7.494 7.488 3.742 26.084 26.079 22.323 22.317 18.564 18.566 14.884 14.887 11.154 11.146 7.468 7.460 26.295 26.292 22.490 22.496 18.731 18.730 15.003 15.007 11.256 11.255 7.537 7.537 3.766 3.766 26.293 26.293 22.513 22.509
+ 1 0 +3 0 -7 - 3 - 2 + 1 -4 0 - 2 +4 0 - 3 +2 0 +4 +3 + 1 +3 0 -8 0 -6 +2 -2 + 1 +7 + 1 -2 -1 +2 -2 +4 +5 +4 +4 +4 +4 0 0 +4 +8
t (°C)
S (%o)
15.035 15.034 15.035 15.034 15.035 15.034 15.035 15.034 15.035 15.306 15.307 15.306 15.307 15.306 15.307 15.306 15.307 15.306 15.307 15.306 15.307 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.189 10.186 10.186 10.186 10.186 10.186 10.186 10.186 10.186
24.957 20.021 20.021 15.014 15.014 10.234 10.234 5.028 5.028 35.000 35.000 24.921 24.921 20.031 20.031 14.981 14.981 9.999 9.999 5.006 5.006 35.000 35.000 29.986 29.986 24.975 24.975 20.019 20.019 14.995 14.995 10.040 10.040 5.050 5.050 35.000 35.000 29.993 29.993 20.019 20.019 14.983 14.983
measured Pmeas- Pcalc (lO-3g cm-3) (lO-6gc m-3) 19.151 15.347 15.344 11.523 11.526 7.864 7.868 3.877 3.872 26.850 26.853 19.105 19.105 15.354 15.361 11.488 11.488 7.675 7.679 3.853 3.854 27.235 27.237 23.325 23.328 19.424 19.426 15.571 15.571 11.673 11.675 7.822 7.825 3.949 3.951 27.237 27.240 23.332 23.332 15.574 15.576 11.664 11.665
-9 +8 + 11 -3 -6 - 2 - 6 - 5 0 + 1 - 3 -4 -4 - 2 -9 - 1 -2 + i - 3 - 1 - 2 +3 + 1 +2 - 2 +1 - 1 + 1 + 1 -2 -4 +4 + 1 - 2 -4 +1 -2 0 0 -2 -4 -2 -3
1020
A. PolSSON, C. BRUNET and J. C. BRUN-COTTAN
Table 3-continued
t (°C)
S (%0)
25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 25.009 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 20.002 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.035 15.034 15.035 15.034 15.035
24.953 24.953 20.004 20.004 14.995 14.995 10.042 10.042 5.016 5.016 35.000 35.000 29.973 29.973 24.961 24.961 20.017 20.017 14.995 14.995 10.058 10.058 5.008 5.008 35.000 35.000 29.973 29.973 24.965 24.965 20.004 20.004 15.561 15.561 10.048 10.048 5.031 5.031 35.000 35.000 29.964 29.964 24.979 24.979 20.018 14.979 14.979 10.034 10.034 5.029 5.029 35.000 35.000 29.971 29.971
P--Po measured Pmeas- Pcalc (10-3 g cm -3 ) (10-6 g cm -3) 18.729 18.728 15.005 15.001 11.245 11.247 7.540 7.538 3.775 3.771 26.554 26.554 22.722 22.723 18.919 18.919 15.166 15.167 11.363 11.366 7.629 7.630 3.810 3.812 26.558 26.554 22.725 22.724 18.921 18.924 15.152 15.156 11.787 11.795 7.616 7.622 3.827 3.830 26.868 26.868 22.985 22.988 19.163 19.159 15.356 11.491 11.492 7.707 7.705 3.876 3.877 26.873 26.867 23.000 22.993
-8 -7 -2 +2 +3 + t - 2 0 - 2 +2 + 1 + 1 +4 +3 -2 - 2 +1 0 +2 - 1 +2 + 1 -2 -4 - 3 + 1 + 1 +2 - 1 -4 +5 + 1 +6 -2 +7 + 1 -2 -5 +1 + 1 +6 +3 -4 0 -3 +2 + 1 + 1 +3 -3 -4 -4 +2 -4 +3
t (°C)
S (%)
10.186 10.186 10.186 10.186 5.035 5.054 5.035 5.054 5.035 5.054 5.054 5.035 5.054 5.054 5.035 5.054 5.055 5.055 5.055 5.055 5.055 5.055 5.055 5.055 5.055 5.055 0.271 0.272 0.271 0.271 0.272 0.271 0.272 0.271 0.272 0.271 0.272 0.271 0.272 0.271 0.272 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271 0.271
10.022 10.022 5.023 5.023 35.000 35.000 29.904 29.904 24.863 24.863 20.002 14.548 14.548 10.020 5.051 5.051 35.000 35.000 20.013 20.013 14.994 14.994 10.047 10.047 5.040 5.040 35.000 35.000 35.000 29.991 29.991 24.967 24.967 20.011 20.011 14.976 14.976 10.041 10.041 5.006 5.006 35.000 35.000 29.981 29.981 29.981 24.968 24.968 19.994 19.994 14.999 10.032 10.032 5.019 5.019
P--Po measured Pmeas- Pcalc (10-3 g c m - 3) (10-6 g cm -~ ) 7.805 7.811 3.919 3.923 27.708 27.700 23.666 23.664 19.685 19.681 15.832 11.526 11.524 7.949 4.014 4.024 27.703 27.704 15.842 15.847 11.885 11.885 7.974 7.976 4.017 4.017 28.222 28.221 28.224 24.188 24.187 20.141 20.147 16.150 16.147 12.108 12.104 8.129 8.137 4.068 4.067 28.224 28.226 24.181 24.181 24.179 20.150 20.142 16.137 16.136 12.124 8.133 8.123 4.082 4.083
+7 +1 +7 +3 0 +6 +3 +4 - 5 -2 +5 +5 +6 +6 +8 - 2 +3 +2 +3 - 2 - 3 - 3 +2 0 - 4 - 4 + 1 +2 - 1 - 1 0 0 - 6 +4 +7 -4 0 +4 -4 + 1 +2 - 1 -3 -2 -2 0 - 8 0 +3 +4 - 1 -7 +3 -3 -4
Density of standard seawater solutions at atmospheric pressure
1021
increase of 0.5 pH unit during concentration. Although the concentrated seawater is reequilibrated with air, the new equilibrium differs from that of standard seawater in the ampoules, which is the chlorinity standard and which in the near future will be made an electrical conductivity standard and may even become a density standard (MILLERO, CHETIRKIN and CULKIN, 1977 ; POISSON, DAUPHINEE, Ross and CULKIN, 1978). Moreover, it is the seawater we used directly to standardize the densimeter and therefore our measurements are relative to it. We have fitted all the experimental data (S > 35%0) from concentrated seawater to a temperature-salinity cubic equation. For a given temperature the density at S -- 35%0 calculated with the equation is slightly lower (10 x 10 -6 g cm -3 for t = 30°C and 8 x 10 -6 g cm -3 for t = 0°C) than that obtained with relationship (4). The salinity (S measured) previously determined by the ratio of weights--42% o salinity concentrated seawater/solution--has been corrected for each temperature by S* Scorrected ~ Smeasured " ~ ,
where S* is the salinity corresponding to the density of equation (4) (S = 35.000%0) calculated from the above-mentioned temperature-salinity cubic equation. The surface representing this equation is then moved so as to pass through the curve representing equation (4). The experimental points thus readjusted are listed in Table 4. All the data of Tables 3 and 4 have been fitted in a polynomial of the form 103(p - P0) = where
S{~h(t) + (S- 35)g(t, S)}
(10)
h(t) is polynomial (4) and
g(t, S) = - 0 . 3 1 0 7 × 1 0 - 3 + 0 . 2 1 2 0 × 1 0 - 4 S + 0 . 1 4 2 7 x 10-4t - 0 . 5 4 2 3 × 1 0 - 6 S 2 - 0 . 1 9 5 3 × 1 0 - 6 S t - 0 . 3 6 1 3 x 10-6t2 +0.524 × 10-aS a + 0 . 3 1 0 × 10-8S2t+0.130 x 10-9St2+0.50× 10-st 3. Table 4.
Differences of absolute density of concentrated standard seawater solutions with that of pure water at the same temperature, measured and calculated with equation (10) at different temperatures and salinities P-Po
t (°C)
S (%0)
29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 29.997 25.059 25.059 25.059
34.841 34.841 38.029 38.029 40.236 40.236 41.576 41.576 34.707 34.707 38.098 38.098 39.723 39.723 41.981 41.981 35.196 35.196 37.760
measured
P-Po
Praeas- Pc~c
(10- 3 g cm -3) (10-6 g cm -3) 25.962 25.954 28.348 28.352 30.021 30.017 31.022 31.017 25.864 25.858 28.406 28.404 29.627 29.623 31.328 31.326 26.438 26.438 28.381
- 5 +3 +4 0 -9 -5 + 1 +6 -7 - 1 -3 - 1 - 1 +3 +1 +3 + 1 + 1 -2
t (°C)
S (%0)
15.185 15.185 15.143 15.143 15.143 15.143 15.143 15.034 15.034 15.034 15.034 15.034 15.034 15.034 15.034 10.042 10.042 10.042 10.042
39.855 42.076 35.011 35.011 37.581 39.943 43.076 35.133 35.133 37.950 37.950 40.146 40.146 41.848 41.848 34.648 34.648 37.948 37.948
measured
Pmeas- Pcalc
(10-a g cm -3) (10-6 g cm - a ) 30.607 32.322 26.872 26.871 28.853 30.675 33.105 26.975 26.972 29.150 29.148 30.843 30.844 32.158 32.159 26.976 26.977 29.547 29.561
0 +3 -2 - 1 0 +3 - 1 -3 0 -4 -2 + 1 0 +3 +2 - 1 -2 +7 -7
1022
A. POISSON, C. BRUNET and J. C. BRuN-COTTAN
Table 4~continued P-Po t (°C) 25.059 25.059 25.059 25.059 25.059 25.054 25.054 25.054 25.054 25.054 25.054 25.054 25.054 25.054 24.910 24.910 24.910 24.910 24.910 24.905 24.905 24.905 24.905 24.905 24.889 24.889 24.889 20.076 20.076 20.076 20.076 20.076 20.076 20.076 20.076 20.065 20.065 20.065 20.065 20.065 20.065 20.065 20.065 20.065 20.065 20.060 20.060 20.060 20.060 20.060 20.060 20.060 20.060 15.185 15.185 15.185
S (°0) 37.760 39.723 39.723 41.852 41.852 34.680 34.680 34.680 37.931 37.931 37.931 39.798 39.798 39.798 34.925 34.925 36.986 37.882 39.166 35.001 35.001 37.465 40.093 42.028 34.171 34.171 39.675 34.987 34.987 37.970 37.970 40.143 40.143 41.797 41.797 34.749 34.749 37.981 40.096 41.944 34.718 34.718 38.009 36.543 42.584 34.704 34.704 37.867 37.867 40.154 40.154 41.959 41.959 34.747 34.747 37.950
P-Po
measured Pmeas- Pc~ac ( l O - 3 g c m -3) ( l O - 6 g c m -3) 28.380 29.865 29.864 31.485 31.484 26.049 26.052 26.046 28.513 28.509 28.508 29.927 29.920 29.920 26.242 26.243 27.797 28.484 29.451 26.296 26.298 28.165 30.156 31.626 25.669 25.671 29.843 26.542 26.543 28.817 28.818 30.479 30.478 31.745 31.746 26.362 26.359 28.825 30.447 31.859 26.335 26.341 28.845 27.729 32.350 26.327 26.324 28.742 28.743 30.487 30.487 31.869 31.872 26.667 26.662 29.136
- 1 + 1 +2 -2 - 1 0 - 3 + 3 -5 - 1 0 -4 +3 +4 0 - 1 + 3 - 5 + 1 + 3 + 1 - 2 - 1 - 1 +3 + 1 -4 - 1 - 2 + 1 0 0 + 1 +2 + 1 - 1 + 2 +2 - 3 + 1 + 2 -4 + 3 0 + 1 - 1 +2 - 2 - 3 +2 +2 + 3 0 -4 + 1 -2
t (°C) 10.042 10.042 10.042 10.042 10.042 10.042 10.018 10.018 10.018 10.018 10.018 10.018 10.018 10.018 5.001 5.001 5.001 5.001 5.001 5.001 5.001 5.001 5.001 4.998 4.998 4.998 4.998 4.998 4.998 4.998 4.998 1.783 1.783 1.783 1.783 1.780 1.780 1.780 1.780 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.029 0,029 0.029 0.029 0.029 0.029 0.029 0.029
S (%o) 37.948 40.203 40.203 40.203 41.861 41.861 34.866 37.992 37.992 34.864 39.917 39.917 41.779 41.779 37.986 37.986 37.986 39.927 39.927 39.927 42.082 42.082 42.082 36.589 36.589 37.901 37.901 39.694 39.694 41.579 41.579 34.795 37.771 40.021 41.848 34.807 37.783 40.034 41.862 34.760 34.760 38.226 38.226 39.877 39.877 41.673 41.673 35.098 35.098 37.841 37.841 39.714 39.714 41.790 41.790
measured Pmeas- Pcal¢ ( l O - 3 g c m -3) ( l O - 6 g c m -3) 29.555 31.321 31.323 31.322 32.621 32.617 27.149 29.589 29.595 27.148 31.098 31.102 32.554 32.556 30.078 30.084 30.082 31.622 31.625 31.623 33.337 33.337 33.340 28.972 28.974 30.012 30.016 31.440 31.441 32.937 32.936 27.890 30.275 32.076 33.546 27.896 30.288 32.090 33.555 28.058 28.056 30.855 30.856 32.190 32.188 33.638 33.642 28.331 28.326 30.544 30.544 32.059 32.059 33.734 33.736
- 1 - 2 -4 -3 - 2 + 2 - 2 +2 -4 - 3 0 -4 +3 + 1 +3 - 3 - 1 + 1 - 2 0 - 1 - 1 - 4 0 -2 + 1 -3 -2 - 3 0 + 1 -4 - 2 +3 +2 0 - 5 0 +4 - 1 + 1 +1 0 - I + 1 + 3 - 1 - 1 +4 0 0 - 2 -2 + 1 - 1
Density o f standard seawater solutions at atmospheric pressure
1023
The standard deviation between the values calculated with this polynomial (10) and the measured values is 3.2x 10-6g crn -a. The form of the polynomial has been chosen because it corresponds exactly to the measurement procedures we used. The surface representing this polynomial passes through the curve p = Po for S = 0 and p = equation (4) for S = 35O/0o.
Comparison with previous work We have compared our results (equation 10) with those of KNUDSEN(1901) (equation 6), Cox et al. (1970) (equation 7) and MILLEROet al. (1976a) (equation 8). The contours of differences in the density obtained from our results and the data of others are presented in Fig. 2. The samples used by the different authors had different origins: KNUDSEN (1901) used pycnometers to determine the density of surface water samples from the North, Baltic, and Mediterranean seas and the North Atlantic at zero and 24.6°C, and their thermal expansibility between 0 and 30°C. The chlorinity of the samples ranged from 2.5 to 22.5°o, i.e., salinity from 4.5 to 40.60/00. Cox et al. (1970) used a suspension balance to determine the density of samples collected between 0 and 200 m in the Atlantic, the Pacific, and the Mediterranean, Baltic and Red seas. MILLEROet al. (1976a) carried out their measurements on diluted and evaporated standard seawater solutions. Agreement with Millero's results (Fig. 2) is the best (standard deviation of 3.7x 10-6g cm-3), but at very low and high temperatures and high salinities, the disagreement is higher than combined experimental error. As the samples used by Cox and KNUDSENwere natural seawater, the disagreement with our results is more important. Our results differ from Cox's by about 70 ppm at 10%o whatever the temperature, whereas they differ about 50 ppm from Knudsen's result at 5%0 whatever the temperature. For the two sets of data, the agreement is best around 35%0, which is certainly because most of the samples with a salinity close to 35%0 came from the North Atlantic, as did the standard seawater used by Millero and in this work. E X P A N S I B I L I T Y OF S T A N D A R D SEAWATER S O L U T I O N S
The expansibility ct = - 1/p(Sp/t~t) of standard seawater solutions can be determined by differentiating equations (10) and (5) with respect to temperature, =
(P-Po)+pol
\(~P°~t + ~(P~t -- Po))_"
(11)
Some values of a thus determined (Table 5) are compared with values obtained previously by other workers in Fig. 3. To do this we have calculated the derivative of the equations proposed by KNUDSEN(1901), COX et al. (1970) and MILLEROet al. (1976a). The comparisons have been carried out only for the temperature and salinity areas reported in the three papers. The best agreement is between 5 and 20°C. At low and mainly at high temperatures, deviations are more important for Cox's results. This may be because the polynomial fitted for each set of measurements has been fitted for the entire temperature and salinity range studied by the author, but in extreme temperature and salinity ranges, the number of data points is sometimes small. There may be an end effect for the polynomials that leads to an excess of the curvature of the surface representing the polynomials at temperature and salinity extremes. The agreement with Millero's results is
1024
A. PoISSON, C. BRUNET and J. C. BRUN-COTTAN
(P - Po)ours-- (d - do)Kaudma
~Xours - - ~Knudsen
a0
T(°CI
T(*C)
~
'
~
~
,o
20
Fig. 2a.
30
S (~0)
,o
Fig. 3a.
(d - do)cox
30
20
~
~o--J
//° (/9 -- P0)ours --
'
~ours
S
--
~Cox
[Xo)
Fig. 2b.
Fig. 3b.
(,O -- PO)ours -- (P --/90)Millero
~ . . . . -- ~Millero
.
.
.
.
o o
T (°
(
T(°C) -i
io
io
_lJ .3 / ~o
S (~o0)
Fig. 2c.
Fig. 3c.
Fig. 2. (Left) Contour diagrams of the differences of density ( 1 0 - 6 g c m -3) calculated by equation (10) and those of KNUDSEN (a), Cox et al. (b) and MILLERO et al. (C).
Fig. 3. (Right) Contour diagrams of the differences of expansibility (10- 6 ° C - t ) calculated by equation (11) and those calculated from the equations of KNUDSEN (a), Cox et al. (b) and MILLERO et al. (C).
,o
1025
Density of standard seawater solutions at atmospheric pressure
Table 5. Expansibility (× 10 -6 *C -1) of standard seawater solutions at atmospheric pressure for different temperatures and salinities calculated with equation (11 ) Temperature Salinity (%o) 0 5 10 15 20 25 30 35 40
-
0°C
5°C
10°C
15°C
20°C
25°C
30°C
68.0 48.9 30.8 13.5 3.0 18.9 34.2 48.8 62.8
16.0 31.7 46.5 60.7 74.4 87.6 100.4 112.7 124.5
88.1 100.8 112.8 124.4 135.5 146.4 156.9 167.2 177.0
150.9 161.1 170.8 180.0 189.0 197.8 206.3 214.7 222.7
206.7 214.8 222.5 229.8 236.9 243.9 250.7 257.3 263.8
257.0 263.5 269.6 275.4 280.9 286.4 291.7 296.8 301.8
303.1 308.5 313.3 317.9 322.2 326.3 330.4 334.2 337.9
within _ 1 × 10-60C - 1 except at very low temperatures and very high salinities, but the values are out of the oceanic range. The agreement of our results with those of K n u d s e n - which is also about + 1 x 10-6°C -1 except at extreme temperatures--confirms what Millero wrote, i.e., the expansibilities of Knudsen are reliable at + 1 x 10-60C - 1 in all the oceanic range. CONCLUSION
All the densities measured with the vibrating densimeter are relative to the density values attributed to standard seawater (S = 3%o) used for its calibration. To compare better the consistency between the set of measurements that we carried out with the vibrating densimeter and the set of measurements by MILLERO et al. (1976a), we have normalized both sets of data at S = 35%o. To carry out this normalization, we corrected the densities we obtained by attributing the density given by Millero's equation (equation 8) to the standard seawater (S = 35%0) used for its calibration. The differences between the corrected values and those calculated with Millero's equation are represented in Fig. 4a. The standard deviation between the two sets of data is only 2.0 x 10 - 6 g cm -a here; we have also calculated expansibilities with our polynomial normalized at S = 3500 and compared them with those obtained by Millero (Fig. 4b). The standard deviation is only 0.5 × 10-o°C -1. Although the form of Millero's equation is different from that of our equation (10), it is clear that the differences between the two sets of data that we pointed out previously are due to differences between the two sets of data at S = 35O/o0. We have seen (Fig. 1) that Millero's experimental data for S = 35%0 are quite consistent with ours but the values calculated at S = 35°0 for his polynomial (equation 8) are shifted. By normalizing the two sets of data at S = 35%o, we eliminate the shift, and the agreement becomes excellent. Besides, the degree of the polynomial chosen for S = 3500 (cubic, equation 4, or quadratic, equation 9) has an importance that is not negligible--as we have seen before--especially on our set of data with measurements carried out at 1, 2, 5, 7, and 10°C, which is the region of the curve where the curvature is greater. This is clearly shown in Table 6 where we have calculated expansibilities at different temperatures with the cubic and quadratic equations. End effects are evident. If we use only measurements at 1, 5, and 10°C to calculate the equations (4) and (9), the effects become very small.
~°I ~-_----- 5 ~ ~ ~ " T(°C) -2 -3
20
-~
0~ 0
+1
\
J
0"f -2 f
0
0
10
30
20
Fig. 4a. 30 •
~
j l
j
S(%o)
~o \ -0.5 \
J
T(°C) 20
y 10 f
f E
O
0 -'-"
~
f
/
/,
-0.5
0
/
20 30 S(~o) Fig. 4b. Fig. 4. Comparison of our data with those of Millero normalized at 35°/oo;(a) contour diagram of the differences of density (10-6 g cm-a); (b) contour diagram of the differences of expansibility (10-6 oC-1). 0
10
-1
4o
1027
Density of standard seawater solutions at atmospheric pressure
Table 6. Comparisonof the expansibilities (10-6 oC-1) calculatedfrom the derivatives of the equations (4) and (9) Temperature (°C)
al~. 4) (10 -6 °C -1)
~(eq. 9)
~t(¢q. 4) - - ~t(eq, 9)
(10 -6 ° C - t )
(10 -6 °C-I)
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 27.5 30
52.5 83.7 112.9 140.4 166.5 191.1 214.5 236.8 258.0 278.1 297.2 315.2 332.1
48.8 82.1 112.7 141.0 167.2 191.6 214.7 236.5 257.3 277.4 296.8 315.7 334.2
+ 3.7 + 1.6 +0.2 - 0.6 -0.7 -0.5 -0.2 +0.3 + 0.7 +0.7 + 0.4 -0.5 - 1.9
All the data presented in this paper together with those published by MILLEROet al. (1976a) will be used to define a new equation of state of seawater at atmospheric pressure (MILLERO and POISSON, in preparation). To do this it will be necessary, as we have just seen, to normalize the two sets of data for S = 35%o. The use of vibrating densimeters aboard research vessels will probably become general soon, because they make measurements very easy. Therefore it is important to propose a way of calibrating the instruments. The easiest procedure is obviously to use pure water--whose absolute density is that of S.M.O.W.--and standard seawater at S = 35%o--whose absolute density, relative to that of S.M.O.W. is given as a function of temperature with an equation similar to equation (4) or (9). All the results thus obtained will be immediately comparable. The use of standard seawater as a density standard is suggested because it is easy to use and its density is reproducible from one batch to another (MILLERO et al., 1977; PoISSON et al., 1978) to + 2 × 10 - 6 g cm -3, which is the maximum accuracy obtainable by the vibrating densimeter. It is of course the seawater contained in the ampoule that constitutes the density standard and that must be used directly to calibrate the densimeter without exposure to air. Finally, the density calculated by using equation (10) or equation of state at atmospheric pressure of MILLEROet al. (in preparation) will have to be compared to the density of in-situ natural seawaters. The investigations up to n o w (MILLERO and KREMLING, 1976 ; MILLERO et al., 1976b; MILLEROet al., 1978a; MILLEROet al., 1978b) were carried out on samples brought to the laboratory to measure their salinity and their density. However, the rapid shift of the CO2/carbonate system alters the conductivity and density. For valid comparisons, conductivity and density must be determined immediately after the samples are collected. The results of a recent study of surface waters of the Indian Ocean, the Red Sea, and the eastern Mediterranean (PoIsSON et al., in preparation) tend to show that the differences between the density of natural seawater and that of standard seawater solution having the same conductivity salinity are greater in some places than those given in the studies discussed above. What is interesting is that such comparisons could be made directly on board ship relative to the standard seawater used to establish the equation of state at atmospheric pressure. Acknowledgement--This study was supported by the C.N.R.S., Contract A.T.P. "Chimie marine 76" No. 1661.
1028
A. POISSON, C. BRUNET and J. C. BRuN-COTTAN
REFERENCES BIGG P. H. (1967) Density of water in S.I. units over the range 0-40°C. British Journal of Applied Physics. 18, 521-537. Cox R. A., M. J. McCARTNEY and F. CULKrS (1970) The specific gravity/salinity/temperature relationship in natural seawater. Deep-Sea Research, 17, 679-689. KELL G. S. (1975) Density, thermal expansibility and compressibility of liquid water from 0 to 100°C: corrections and tables for atmospheric pressure and saturation reviewed and expressed on 1968 temperature scale. Journal of Chemical Engineering Data, 20, 97-105. KNUDSEN M. (1901) Hydrographical tables. GEC-Gad, Copenhagen, 63 p. KREML~G K. (1972) Comparison of specific gravity in natural seawater from hydrographical tables and measurements by a new density instrument. Deep-Sea Research, 19, 377-383. MENACHE M. and G. GIRARD (1972) Concerning the different tables of the thermal expansion of water between 0 and 40°C. Internal Report jointly published by Institut Oc6anographique, Paris and Bureau International des Poids et Mesures, S6vres. MILLERO F. J . (1967) High precision magnetic float densimeter. Review of Scientific Instruments, 38, 1441 1444. MILLERO F. J. and K. KREMLING (1976) The densities of Baltic seawaters. Deep-Sea Research, 23, 1129-1138. MILLERO F. J. and F. K. LEPPLE (1973) The density and expansibility of artificial seawater solutions from 0 to 40°C and 0 to 21%o chlorinity. Marine Chemistry, 1, 89-104. MILLERO F. J., A. GONZALEZand G. K. WARD (1976a) The density of seawater solutions at one atmosphere as a function of temperature and salinity. Journal of Marine Research, 34, 61-93. MILLERO F. J., A. GONZALEZ,P. BREWERand A. BRADSHAW(1976b) The density of North Atlantic and North Pacific deep waters. Earth and Planetary Science Letters, 32, 468-472. MILLERO F. J., P. CHETIRKIN and F. CULKIN (1977) The relative conductivity and density of standard seawaters. Deep-Sea Research, 24, 315-321. MILLERO F. J., D. MEANSand C. MILLER (1978a) The densities of Mediterranean seawaters. Deep-Sea Research, 25, 563-569. MILLERO F. J., D. FORSHT, D. MEANS, J. GIESKESand K. E. KENYON (1978b) The density of North Pacific Ocean waters. Journal of Geophysical Research, 83, 2359-2364. PICKER P., E. TREMBLAYand C. JOLICOEUR (1974) A high-precision digital readout flow densimeter for liquids. Journal of Solution Chemistry, 3, 377-384. POISSON A. and J. CIJANU (1976) Partial molal volumes of some major ions in seawater. Limnology and Oceanography, 21, 853-861. POISSONA., C. BRUNETand M. MENACHE(1979) Equation d'etat des solutions d'eau de met Normale ~. la pression atmosph6rique. Ocbanis, 5, 651-660. POISSONA., T. DAUPHINEE,C. K. Ross and F. CULKIN (1978) The reliability of standard seawater as an electrical conductivity standard. Oceanologica Acta, 1,425-433. THIESEN M. (1900) Untersuchungen fiber die thermische Ausdehnung yon festen und tropfbar fliissigen K6rpern. Wissenschaftliche Abhandlungen tier Physikalischtechnischen Reichsanstalt, 3, 1-70. THOMPSON T. G. and H. E. WmT8 (1931) The specific gravity of seawater at zero degree in relation to chlorinity. Journal du Conseil, Conseilpermanent Internationalpour l'Exploration de la Mer, 6, 232-240. TILTON L. W. and J. K. TAYLOR (1937) Accurate representation of the refractivity and density of distilled water as a function of temperature. Journal of Research of the National Bureau of Standards, 18, 205-214. UNESCO (1979) Ninth report of the Joint Panel on Oceanographic Tables and Standards. 31 pp, UNESCO Technical Papers in Marine Science No. 30, Paris.