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Notes 1307 Limnol. Oceanogr., 37(6), 1992, 1 307-1312 0 1992, by the American Society of Limnology and Oceanography, Inc. Oxygen solubility in seawater: Better fitting equations Abstract-We examined uncertainties associ- where Co* is the solubility of O2 per mass ated with the routine computation of 0, solu- or per volume of seawater at the tempera- bility (C,,*) at 1 atm total pressure in pure water ture of equilibrium (the subscript o denotes and seawater in equilibrium with air as a function of temperature and salinity. We propose for- 0,; the asterisk signifies equilibrium with mulae expressing C,* (at STP, real gas) in cm3 an atmosphere of standard composition sat- dm-3 and pmol kg-’ in the range (tF L t z 40°C; urated with water vapor at a total pressure, 0 2 S 1 42%~) based on a fit to precise data including that of the water vapor, of 1 atm), selected from the literature. S is salinity in per mil, and A and B are constant coefficients. Clever (1982) re- viewed the Setschenow relation. Because Precise and accurate values of oxygen sol- seawater is a complex multicomponent so- ubility in seawater are important for esti- lution, disagreement exists on an expression mating oxygen utilization, oxygen-nutrient for, and thermodynamic basis of, an em- equivalent relations, air-sea gas exchange, pirical formula for routine computation of etc. Green ( 196 5 and references therein) re- Co* which fits the experimental data pre- ported measurements of O2 solubility in cisely and accurately while covering the seawater. However, Carpenter (1966) and thermohaline range of the world ocean (Bat- Murray and Riley (1969) obtained more tino et al. 1983). This disagreement com- precise results, and Benson and Krause plicates the use and interpretation of Co* (1984) published yet more precise O2 sol- data. ubility data. For limnological work, Mor- We examined uncertainties associated timer (198 1) proposed using the results of with Co* computations in seawater as func- Benson and Krause (1980), and Miller0 tions of temperature and salinity and eval- (1986) recommended those of Benson and uated several formulae for its routine esti- Krause (1984) for oceanographic work. More mation. Our main concern is that the recently, Sherwood et al. (199 1) have ex- formulae that have been proposed for rou- amined O2 solubility in hypersaline solu- tine computation of C,* in seawater do not tions of NaCl and other salts. behave well at the extremes of the experi- In the past, 0, solubility was difficult to mental data, especially at low temperatures. use for several purposes because it was tab- Although no precise 0, solubility data in ulated for integral values of temperature and seawater are available below -0.5OC, work- salinity (or chlorinity). More recently, sev- ers use empirical formulae to extrapolate to eral empirical formulae have been proposed lower temperatures (Weiss 1970; Chen for expressing the dependence of the loga- 198 1). These formulae do not fit the data rithm of O2 solubility on temperature and well at temperatures below - 1°C and at high salinity (Gilbert et al. 1968; Weiss 1970). salinity. Based on the experimental values The effect of salinity on the logarithm of O2 of Carpenter (1966) Murray and Riley solubility is often expressed with the em- (1969), and Benson and Krause (1984), we pirical Setschenow relation at constant tem- propose a high-precision formula for esti- perature, mating Co* (at STP, real gas) by the method Inc,* = A + SS, (1) of least-squares; it covers oceanic ranges of temperature and salinity. This new fit is well behaved in the temperature and salinity ranges of the data and it does not appear to Acknowledgments deviate significantly at the extremes of tem- We are grateful to R. Battino, F. Millero, and an perature and salinity of the measurements. anonymous reviewer for their comments. Research supported by NSF OCE 88-17359 and We provide formulae and solubility coeffi- NOAA NA16RC0443-0 1. cients for estimating Co* in seawater as a 1308 Notes function of temperature and salinity in cm3 For routine computations of Co* from Eq. dm-3 and pmol kg-l. 4, they fitted values in several units (at STP, Weiss (1970) proposed a least-squares re- ideal gas) in the range (0 1 t 2 40°C; 0 2 gression (LSR) fit for computing O2 solu- s 2 40%0): bility (at STP, real gas) in seawater in the range (- 1 2 t 1 40°C; 0 L S 2 407~) with Inc,* = A, + A,T-’ + A2T-2 the experimental data of Carpenter (1966) in the range (0.5 L t 2 36°C; 5.2 L Cl L + A3T-3 + A4T-4A4 207~) and Murray and Riley (1969) in the + S(B, + BIT-’ range (0.7 L t 2 35°C; 0 L S 1 407~): + B2T -2 + B3T-3). (5) Inc,* = A, + AIT-’ + A,10 + A,T + S(B, + BIT + B,T2) Given the high precision of the current (2) O2 solubility data, it is not clear from Eq. where T is temperature in Kelvin and Ai 2, 3, and 5 that all provide the same values and Bi are constants. Equation 2 is based over oceanic ranges of T and S. The uncer- on the Van’t Hoff and the Setschenow re- tainty arises because certain formulae are lations for, respectively, T and S effects. more robust (statistical sensitivity to the ex- Weiss indicated a root-mean-square (rms) perimental data). The behavior of the gas deviation of kO.016 cm3 dm-3 from the solubility formulae at high and low T and combined data of Carpenter and Murray S is of importance. It is critical that a gas and Riley. Similarly, Chen (198 1) examined solubility equation behaves well at the ex- the same data, proposing LSR fits for Co* tremes of the experimental values. The Co* in the range (0 1 t L 35.5”C; 0 L S 1 407~) data of Carpenter, Murray and Riley, and with an rms deviation of kO.0 15 cm3 dm-3. Benson and Krause do not cover the whole range of temperature of the world ocean and Inc,* = A, + A,T-l + A,10 + A,T extrapolation is required. + S(B, + BIT-‘) + CoS2. (3) We compared the Co* values derived from the formulae of Weiss (Eq. 2), Chen (Eq. 3) Benson and Krause (1984) made mea- and Benson and Krause (Eq. 5) in the range surements of the Henry’s coefficient for O2 (-2 1 t 1 40°C; 0 1 S L 42%). We con- in seawater (K,) in the range (0.2 L t 1 sidered temperatures greater than or equal 45°C; 0 L S L 50?&), and proposed an LSR to the freezing point (tF) from Fofonoff and fit with an rms deviation from the mea- Millard ( 1983). Using the formulae and co- surements of +0.08%. They expressed Co* efficients of Weiss (1970) and Chen (198 l), (at STP, real gas) in mol kg- 1 as a function we converted their Co* values from cm3 of K, at unit standard atmospheric concen- dm-3 to pmol kg- 1 at a molar volume of tration per unit mass of seawater: O2 of 22,39 1.6 cm3 mol- 1 and the equation of state of seawater of Miller0 and Poisson Co* = 0.20946F(l - P-)(1 - B,) (198 1). The difference between the molar *u-o&.x ’ volume of O2 (at STP) as an ideal gas and (4) as a real gas is -0.1%. Thus, all Co* values (at STP, real gas) were expressed in units where P,, is the equilibrium water vapor independent of pressure and temperature. pressure in air (Green and Car&t 1967) F A computer program was written to fit the and M, are a salinity factor and the gram Co* values from Eq. 4 by singular value de- molecular mass of water, respectively (Mil- composition in the least-squares sense. Our lero 1982), B, is the second virial coefficient objective was to examine the relative pre- for O2 (Benson and Krause 1980) and the cision of the fit of these solubility equations constant 0.20946 is the mole fraction of O2 over the oceanic range of T and S when Eq. in dry air (Glueckauf 195 1). 2, 3, and 5 were used to fit values from Eq. For Eq. 4, Benson and Krause (1984) in- 4. We also examined the relative precision dicated an uncertainty of +O. 1% or better. of these equations to estimate the data of -. _--. - --...-.-. Notes 1309 1.2. , . , . , . , . , . (01 Carpenter (1966) (01 Carpenter (1966) (4 Murray and Riley (1969) (3 Murray and Riley (1969) * 0 40 Lnpero2&re (OF) Fig. 1. Difference between the C,* values from Weiss Fig. 2. As Fig. 1, but for the results of Chen (198 1). (1970, curves), Carpenter (1966, o), and Murray and Riley (1969, V), relative to the results of Benson and Krause (1984). (3.01 pmol kg-l), and &0.3% (kO.85 pmol kg-l). In all cases, the discrepancy between Co* values derived from these fits was sig- Carpenter (1966) and Murray and Riley nificant at low T and high S. (1969). In each case, we used from 2 to 10 For low-precision estimates of Co*, de- Tterms to fit the constant coefficients of Eq. viations of I 1% are probably unimportant. 1. Because of its empirical nature, we also However, differences in C,,* at low T and examined addition of S terms to the Set- high S are important in high-precision mea- schenow relation. After adding a Tor S term, surements for the following reasons. First, we analyzed the goodness-of-fit and behav- in recent years analytical precision in dis- ior of the fit at the extremes of the Co* data. solved oxygen measurements in seawater at Because of the behavior of the equation sea and in the laboratory have been im- of state of seawater, chemical concentration proved to +O. 1% or better (Culberson et al. units on a per-mass basis should be com- 199 1). High precision and accuracy in mea- pared separately from those on a per-vol- surements of dissolved 0, and C,* are im- ume basis. Other than for the seawater den- portant in the detection of ocean climatic sity effect, systematic deviations in one set changes where relatively small variations of dissolved O2 concentration units apply might be significant. Second, water masses in others. Figure 1 shows the relative per- responsible for the thermohaline character- cent deviation between the Co* values from istics of the deep ocean have T and S ranges Eq. 4 and those of Weiss (Eq. 2) in the range where the greatest discrepancies occur be- (tF 2 t 2 40°C; 0 2 S L 4Oo/oo). max-The tween the Co* values from Eq. 2, 3, and 5. imum and minimum relative deviations be- In pure water, Eq. 1 reduces to a form tween their Co* values were +0.7% (2.60 dependent on T, allowing the examination pmol kg-r) and -0.2% (0.51 pmol kg-‘), of solubility equations without considera- respectively, with an rms deviation of tion of S effects. Because we use the same + 0.3% (* 1.O1 pmol kg-l). Similarly, Fig. C,,* values (Eq. 4), LSR method, and the 2 shows the relative deviations between the same equation of state for seawater, any dif- Co* values from Eq. 4 and those of Chen ferences between Eq. 2,3, and 5 reflect their (Eq. 3) in the range (tF L t 1: 40°C; 0 or S relative precision and accuracy, assuming 2 ~O?&J).In this case, the minimum, max- that the data of Benson and Krause (1984) imum, and rms deviations in the range (0 from Eq. 4 are the most precise and accu- L t L 35.5”C; 0 2 S L 4O?b) were, respec- rate. In pure water and in the range (tF L t tively, -0.2% (0.40 pmol kg-l), + 0.9% 1 4O”C), Eq. 2 and 3 attained an rms de- 1310 Notes viation from Eq. 4 of & 1.2 l%, +O. 16%, well within the experimental uncertainty of &0.02%, and +O.O 1% after addition of, re- Co* measurements in the past, it became spectively, two, three, four, and five Tterms. evident from our analysis that a S2 term is Additional T terms did not significantly significant for the dependence of Inc,* on change the ,rms deviation of the Weiss ex- salinity. This finding is consistent with pre- tended equation. When Eq. 5 was used, four vious results (Carpenter 1966; Chen 198 1; T terms were required to obtain an rms de- Sherwood et al. 199 1). Values of Co* in cm3 viation of + 0.0 1%. For seawater, terms must dm-3 and pmol kg- 1 can be obtained with be added to Eq. 1 for the salinity effect on Eq. 8 and the solubility coefficients in Table Inc,*. For this case, we used the original 1. The fit to Eq. 4 with Eq. 8 has rms de- form of the Weiss (Eq. 2) and Chen (Eq. 3) viations of +4 x 10-4cm3 dm-3 and + 1O-3 equations as well as extended forms, Eq. 6 pmol kg-l (Fig. 3) in the range (tF 1 t 2 and 7, respectively: 40°C; 0 L S 1 42?&). Because of the agreement in the Co* data Inc,* = A, + A,T-l + A&T + A,T of Carpenter and Murray and Riley (Weiss + A,T2 + A,T3 1970), we examined the precision of Eq. 8 + S(& + B,T + B2T2), (6) to estimate their measurements. Chlorinity (Cl, Ym) values were converted to salinity and with the expression S = 1.80655 x Cl from Inc,* = A, + A,T-1 + A,lnT Wooster et al. (1969). From this analysis, + A,T + A,T2 + A,T3 solubility coefficients for computing C,* in +S(B, + B,T-’ + B2T-2) cm3 dm-3 and pmol kg-l can be obtained from Table 1 and Eq. 8. The fit to the results + c,s2. (7) of Carpenter and Murray and Riley has rms The extended or the original equations of deviations from their combined data of Weiss and Chen gave greater rms deviations 50.015 cm3 dm-3 and +0.67 pmol kg-l. when fitting values from Eq. 4 over the oce- The rms deviations of the fit from Carpen- anic thermohaline range than using Eq. 5. ter’s data are kO.013 cm3 dm-3 and +0.58 This is because a T series of the form T-” pmol kg- l, while for Murray and Riley the fits the Inc,* values from Eq. 4 better than rms deviations are +O.O 18 cm3 dme3 and the Van’t Hoff relation that Weiss or Chen +0.78 pmol kg- l. The rms deviations be- used for the same number of coefficients. tween the data of Carpenter and Murray and We examined several formulae to build a Riley from those of Benson and Krause are high-precision LSR fit for Co* based on Eq. 20.019 cm3 dm-3 and kO.82 pmol kg-l. 4. From our analysis, Eq. 8 proved to be We compared our fits to the data of Car- the best expression for estimating Co* in the penter, Murray and Riley, and Benson and range (tF 1 t L 40°C; 0 L S 1 427~): Krause. When comparing the results of sev- eral workers, it is important to weight the Inc,* = A, + A,T, + A2TS2+ A3TS2 precision of their data. When we assigned + A, TS3+ A,TS4 + A, TS5 weights to the solubility data equal to their + S(B, + B, T, + B2TS2+ B3TS3) respective rms deviations from the experi- + c(ys2 mental data, the resulting fit is significantly (8) influenced by those fitted C,* values with where T, is a newly defined, scaled temper- better precision. Although the rms of the fit ature: T, = ln[(298.15 - t)(273.15 + t)-‘1. to the data of Benson and Krause is con- This temperature (T,) transformation sig- siderably better, it is not clear that there are nificantly improves the rms deviation of the significant differences in accuracy between fit, particularly at high and low T and S. A the Co* data of Carpenter, Murray and Riley, logarithmic transformation of the depen- and Benson and Krause. For this reason, we dent or independent variables or both is assigned equal weights to their solubility common in LSR of curvilinear relations. values to combine their fitted data. From Though the Setschenow relation in its lin- this analysis, Co* values in cm3 dm-3 and ear form has been shown to hold reasonably pmol kg-l can be obtained from the solu- Notes Nz 6- x _ h ‘T 4- 2 a 5 2- _ = 4 o- 'B B -2 - -4 - Fig. 3. Residual difference (pm01 kg- ‘) between the C,* (at STP, real gas) values from Eq. 4 of Benson and Krause (1984) and their fit with Eq. 5 and our fit with Eq. 8 using coefficients in Table 1 in the range (tF I t 2 40°C; 0 2 S 2 40%~).Solid lines represent the re- sidual of our fit in the same range oft and S. bility coefficients in Table 1 and Eq. 8. The rms deviations of the fits from the com- bined measurements of Carpenter and Mur- ray and Riley are +0.016 cm3 dme3 and kO.72 pmol kg- l. Similarly, the rms devi- ations of these fits from the results of Ben- son and Krause are kO.005 cm3 dme3 and kO.23 pmol kg-‘. We examined several empirical formulae for estimating O2 solubility at 1 atm total pressure in pure water and seawater in equi- librium with air as a function of tempera- ture and salinity. From our analysis of the data of Carpenter (1966) Murray and Riley (1969), and Benson and Krause (1984) we propose a new fit (Eq. 8) and solubility co- efficients (Table 1) for the routine compu- tation of 0, (at STP, real gas) solubility in seawater (tF 2 t L 40°C; 0 L S 2 42o/oo). This new fit estimates the Co* data with relatively high precision in the ranges of T and S of the experimental values and seems to extrapolate more reliably beyond these ranges than do previous formulae. Clearly, extrapolation beyond the range of the ex- perimental data should be viewed with cau- tion. When relatively high precision of Co* is not required, it probably makes no dif- ference which O2 solubility formula (Weiss 1970; Chen 198 1; Benson and Krause 1984; this work) is used because the Co* values 1312 Notes estimated from these formulae agree to FOFONOFF, N. P., AND R. C. MILLARD, JR. 1983. Al- within an rms deviation of +0.3% (+ 1.Ol gorithms for computation of fundamental prop- erties of seawater. UNESCO Tech. Pap. Mar. Sci. pmol kg-l). The deviations in Co* at low T 44. and high S, between these formulae, are of GILBERT, W., W. PAWLEY, AND K. PARK. 1968. Car- importance in the context of the current an- penter’s oxygen solubility tables and monograph alytical precision of dissolved O2 measure- for seawater as a function of temperature and sa- linity. Oregon State Univ. Coll. Oceanogr. Ref. ments and the need to extrapolate to the 68-3. thermohaline range of the world ocean. For GLUECKAUF, E. 195 1. The composition of atmo- routine computation of Co* in seawater, we spheric air, p. 3-10. In Compendium of meteorol- recommend using Eq. 8 and the solubility ogy. Am. Meteorol. Sot. coefficients in Table 1 derived from the more GREEN,E. J. 1965. A redetermination ofthe solubility of oxygen in seawater and some thermodynamic precise data of Benson and Krause ( 1984) implications of the solubility relations. Ph.D. the- Herncin E. Garcfa sis, Mass. Inst. Technol. 137 p. -, AND D. E. CARRITLT. 1967. New tables for Louis I. Gordon oxygen saturation of seawater. J. Mar. Res. 25: 140-147. College of Oceanography MILLERO, F. J. 1982. The thermodynamics of sea- Oregon State University water. Part 1. The PVT properties. Ocean Sci. Eng. Corvallis 9733 l-5503 7: 403-460. 1986. Solubility of oxygen in seawater. References UNESCO Tech. Pap. Mar. Sci. 50. -, ANDA. POISSON.1981. The international one- BAITINO, R., T. R. RETTICH,AND T. TOMINAGA. 1983. atmosphere equation of state of seawater. Deep- The solubility of oxygen and ozone in liquids. J. Sea Res. 28: 625-629. Phys. Chem. Ref. Data 12: 163-178. MORTIMER, C. H. 198 1. The oxygen content of air B. BENSON, B., AND D. KRAUSE, JR. 1980. The con- saturated fresh waters over the ranges of temper- centration and isotopic fractionation of gases dis- ature and atmospheric pressure of limnological in- solved in freshwater in equilibrium with the at- terest. Mitt. Int. Ver. Theor. Angew. Limnol. 22, mosphere: 1. Oxygen. Limnol. Oceanogr. 25: 662- p. l-23. 671. MURRAY, C. N., ANDJ. P. RILEY. 1969. The solubility -, AND -. 1984. The concentration and of gasesin distilled water and seawater. 2. Oxygen. isotopic fractionation of oxygen dissolved in fresh- Deep-Sea Res. 16: 3 1l-320. water and seawater in equilibrium with the at- SHERWOOD, J. E., F. STAGNITTI, M. J. KOKKINN, AND mosphere. Limnol. Oceanogr. 29: 620-632. W. D. WI-S. 199 1. Dissolved oxygen con- J. CARPENTER, H. 1966. New measurements of ox- centrations in hypersaline waters. Limnol. Ocean- ygen solubility in pure and natural water. Limnol. ogr. 36: 235-250. Oceanogr. 11: 264-277. WEISS,R. F. 1970. The solubility of nitrogen, oxygen CHEN, C.-T. A. 198 1. Oxygen solubilities up to 200 and argon in water and seawater. Deep-Sea Res. kPa, p. 4 l-43. In Oxygen and ozone. IUPAC Sol- 17: 721-735. ubility Data Ser. V. 7. Pergamon. W. WOOSTER, S., A. J. LEE, AND G. DIETFUCH. 1969. CLEVER, H. L. 1982. The Sechenov salt effect param- Redefinition of salinity. Deep-Sea Res. 16: 321- eter, p. xxix-xlv. In Nitrogen and air. IUPAC Sol- 322. ubility Data Ser. V. 10. Pergamon. CULBERSON, C. H., G. KNAPP, M. C. STAL~UP, R. T. WILLIAMS, AND F. ZEMLYAK. 199 1. A compari- son of methods for the determination of dissolved Submitted: 23 October 1991 oxygen in seawater. Woods Hole Oceanogr. Inst. Accepted: 2.5 February 1992 WHPO 91-2. 77 p. Revised: 17 March 1992

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