Alvin Bradshaw

A new high pressure equation of state for seawater

A new high pressure equation of state for water and seawater has been derived from the experimental results of Millero and coworkers in Miami and Bradshaw and Schleicher in Woods Hole. The form of the equation of state is a second degree secant bulk modulus K = Pv0(v0−vp=K0+AP+BP2 K = Kw0+aS+bS32 A = Aw+cS+dS32 B = Bw+eS where ν0 and νP are the specific volume at 0 and P applied pressure and S is the salinity (ℵ). The coefficients KWO, AW, and BW for the pure water part of the equation are polynomial functions of temperature. The standard error of the pure water equation of state is 4.3 × 10−6 cm3 g−1 in νWP. The temperature dependent parameters a, b, c, d, and e have been determined from the high pressure measurements on seawater. The overall standard error of the seawater equation of state is 9.0 × 10−6 cm3 g−1 in νP. Over the oceanic ranges of temperature, pressure, and salinity the standard error is 5.0 × 10−6 cm3 g−1 in νP. This new high pressure equation of state has recently (1979) been recommended by the UNESCO Joint Panel on Oceanographic Tables and Standards for use by the oceanographic community.

Measurements of total carbon dioxide and alkalinity by potentiometric titration in the GEOSECS program

Abstract Approximately 6000 determinations of the alkalinity and total carbon dioxide content of seawater have now been made in the Atlantic, Pacific and Indian Oceans as part of the GEOSECS program by a computer-controlled potentiometric titration technique. The equations used to locate the equivalence points of the carbonic acid system on this titration curve were developed in 1971 but have not previously been published. These functions may be represented by: F 1 = ( V 2 − V ) V 0 N [ H + ] / K 1 C + ( V 0 + V ) V 0 ( [ H + ] + [ H S O 4 − ] + [ H F ] − [ B ( O H ) 4 − ] ) × ( 1 + [ H + ] / K 1 C ) F 2 = ( V 0 + V ) V 0 ( [ H + ] + [ H S O 4 − ] + [ H F ] − [ H C O 3 − ] ) Upon inspection, these functions are analogous to the modified Gran functions of Hansson and Jagner [25] with the omission of the contributions of [OH − ] and [CO 3 2− ], and with the contribution of B(OH) 4 − being assessed at a chlorinity of 19‰ for all samples. Reprocessing the original titration e.m.f.-volume data with appropriate corrections and modified Gran functions reveals an error of about +12 μmol/kg in the GEOSECS total carbon dioxide data. In addition, the protonation of dissolved phosphate species during the titration results in a contribution to measured total carbon dioxide equal to the total phosphate concentration. Differences in the application of the GEOSECS functions between the Atlantic and the Pacific-Indian Oceans expeditions are also to be found so that the error deriving from this source for the Atlantic expedition was only +5 μmol/kg. The application of the correct functions increases precision enabling smaller differences, such as those attributable to fossil fuel carbon dioxide, potentially to be observed, and increases accuracy so that the error in titrator total carbon dioxide previously diagnosed by Takahashi [14] can be logically accounted for.

Measurements of Total Carbon Dioxide and Alkalinity in the North Atlantic Ocean in 1981

The ocean uptake of fossil fuel CO, has long been recognized as the principal modulator of the rising atmospheric CO, level. If we are to observe and understand this effect, then an essential step is the accurate measurement of the CO, properties of the ocean. Historically, this has been quite difficult to achieve. Although measurements of some kind date back to the late 19th century, complete, documented, and verifiable measurements are scarce indeed. This chapter describes and documents the series of total CO, and alkalinity measurements of seawater made on the North Atlantic Ocean during the Transient Tracers in the Ocean (TTO) expedition in 1981, and presents briefly the signals these data reveal.

The carbonate system in the Black Sea

We have measured both alkalinity and total carbon dioxide on a selected set of Black Sea samples from cruise 134 of R.V. Knorr, using gas extraction/coulometry techniques, and improved titration procedures that permit more accurate data than those obtained in earlier expeditions. Earlier results had shown an apparent excess in alkalinity, by a factor of 1.6, from the stoichiometric ratio predicted from the sequential oxidation of Redfield ratio organic matter by the species O2, NO3− and SO42−. Thus both the nature of the organic substrate and our fundamental knowledge of reaction stoichiometry in anoxic systems were called into question. We show that the total CO2 balance is consistent, within narrower limits than found earlier, with oxidation of organic matter by sulfate: 2CH2O+SO42− → 2HCO3−+H2S and consistent with work on sediment interstitial waters in anoxic conditions (Berneret al., 1970, Limnology and Oceanography, 15. 544–549: Ben Yaakov, 1973, Limnology and Oceanography, 18, 86–94). The total CO2 results are lower by 300μmol kg−1 in surface waters, and 50μmol kg−1 in deep waters, than data reported from the 1969 Atlantis II expedition. While changes in Black Sea hydrography have been documented, these CO2 system changes are far too large to be accounted for by these processes and are more likely the result of improved technique, rather than geochemical evolution.

The effect of pressure on the electrical conductance of sea water

Abstract The percentage increase in the electrical conductance of sea water with pressure has been measured at 0°, 5°, 10°, 15°, 20° and 25°C for salinities of 31, 35 and 39% over a pressure range of 0–10,338 decibars above atmospheric pressure. The accuracy of the results is estimated to be equivalent to better than ±0·01% salinity. An interpolation formula which fits the observed values to within an error equivalent to ±0·005% salinity is given. A table of values for the percentage increase in electrical conductance has been computed from this formula at 1000 decibar intervals of pressure from 0–10,000 decibars above atmospheric pressure.

The density of North Atlantic and North Pacific deep waters

Abstract The densities of seventeen samples of seawater from GEOSECS stations 27 (North Atlantic) and 217 (North Pacific) have been measured with a vibrating flow densimeter at 25°C. The densities of the deep samples were found to be 5 ± 1.5and16 ± 3.6ppm greater, for the North Atlantic and North Pacific, respectively, than predicted by the equation of state of Millero, Gonzalez and Ward (1976) derived for seawaters of constant relative composition. The results are in good agreement with the density anomalies predicted by Brewer and Bradshaw (1975) on the basis of the observed increase of dissolved silica, alkalinity and total carbon dioxide in oceanic deep waters. The application of these corrections results in an agreement with the Millero, Gonzalez and Ward (1976) equation of state to ±4 ppm.

Direct measurement of thermal expansion of sea water under pressure

Abstract The thermal expansion of sea water under pressure has been measured over a temperature range of − 2°C to 30°C at 2°C intervals for salinities of 30·50%, 35·00%, and 39·50%. The pressure range was 8–1001 bars (absolute). A direct measurement technique was used in which the change of volume of a water sample in a dilatometer was measured with the sample held under constant pressure and subjected to a temperature change. Temperature derivatives of specific volume were derived; it is estimated that they are accurate to better than 3 × 10−6 (cm3/g°C). An interpolation formula which fits these values to 1 × 10−6 (cm3/g°C) is given. In the temperature and pressure region of oceanographic interest the present results for the temperature derivative of specific volume show very good agreement both with the currently accepted values (Ekman and Knudsen) and with those based on sound velocity measurements (Crease). They do not, however, compare as favorably at low temperatures with the values computed either from the equation of state of Wilson and Bradley or from Eckarts representation of Ekman and Knudsens experimental data.

Compressibility of distilled water and seawater

Abstract The compressions of distilled water and of seawater of approximately 31, 35, and 39% salinity were measured at 10°C for pressures up to 1000 bars. The data were summarized by a ‘best’ least-square fit polynomial in pressure and salinity. The summary formula was combined with Brydens ( Deep-Sea Research , 20 , 401–408, 1973) similar type fit to our earlier thermal expansion data ( Bradshaw and Schleicher , Deep-Sea Research , 17 , 691–706, 1970) and Fofonoff and Brydens ( Journal of Marine Research , in press) recent empirical formula for sigma-0 of seawater to give an expression for the specific volume of seawater as a function of temperature, pressure and salinity in the salinity range 31 to 39%. At 35% specific volumes from this expression in the oceanographic range of temperature and pressure agree within 15 × 10 −6 cm 3 g −1 with those computed using sound velocities ( Wang and Millero , Journal of Geophysical and Research , 78 , 7122–7128, 1973). Our mean compressibilities for distilled water at 10°C also agree with those from sound velocities (to within 0·05%) but disagree with those of Kell and Whalley ( Philosophical Transactions of the Royal Society of London , A, 258 , 565–614, 1965) by about 0·3%.

Accuracy of temperature measurements with the VACM

Abstract : The report describes temperature measurement techniques with the Vector Averaging Current Meter (VACM) designed at WHOI and manufactured at AMF. Included are descriptions of circuitry, calibration techniques and calibration results. Precision calibrations of VACM thermistors began in 1971 at WHOI. Of the thermistors in our pool, 70 have had at least 3 calibrations over a period no shorter than 2 years. Of these 70 thermistors the results described show that 51 are stable.

Calculation of the potential temperature of seawater from the effect of pressure on entropy

Abstract A method of calculating the potential temperature using the pressure integral of the temperature derivative of specific volume is described. The estimation of the uncertainty due to errors in the thermal expansion and specific heat data is straightforward. A comparison is made with values found by Bryden (Deep-Sea Research, 20, 401–408, 1973) from integration of the adiabatic gradient, the same expressions for the temperature derivative and the specific heat being used in both cases. The results agree within the fitting error in Brydens polynomial for potential temperature at 35% salinity by Brydens estimate of the uncertainty in his values is too large. From this analysis, the uncertainty in values of potential temperature in the oceanographic range is estimated to be less than 12 m°C.