Preparation of gravimetric standards for measurements of atmospheric oxygen and reevaluation of atmospheric oxygen concentration



[1] Fourteen standard mixtures composed of ambient levels of CO2, Ar, O2, and N2 have been prepared in 10-L high-pressure aluminum cylinders by a gravimetric technique for atmospheric O2 measurements. A highly precise balance with a precision of 2.5 mg is used to determine the masses of individual components in the cylinders. To balance the buoyant forces on both sides of the balance beam during weighing the gravimetric standard cylinder, a same sized cylinder is placed on a pan on the opposite side of the beam. In addition, the cylinders of the gravimetric standards and a tare cylinder are alternately weighed to compensate for the drift of the zero-point of the balance. To determine the mole fractions accurately, the mass of each component is corrected for the buoyancy changes caused by the expansion of the cylinder, and the molecular masses of the source O2 and N2 gases are corrected for their isotopic compositions. The differences in the O2 mole fractions of the 14 gravimetric standards range about 100 ppm (μmol mol−1). The gravimetric mole fractions are compared with the analyzed values of CO2, Ar, O2 + Ar, and (O2 + Ar)/N2. The reproducibility of the gravimetric technique is determined from the standard deviations of the differences between the gravimetric and analyzed values, and is quantified as 15.5 per meg for the O2/N2 ratio and 2.9 ppm for the O2 mole fraction. The gravimetric scale is applied to the measurements from air samples collected at Hateruma Island, Japan. The average Ar mole fraction for the air samples collected from June 2003 through June 2004 is 9333 ± 2 ppm. On the basis of this Ar mole fraction, the annual average mole fractions of O2 and N2 in 2000 are evaluated to be 209392 ± 3 ppm and 780876 ± 2 ppm, respectively.

1. Introduction

[2] There has been an increasing interest in the measurements of atmospheric O2 concentration variations because they give us important additional information about the global carbon cycle. For example, secular changes in the atmospheric O2 content can be used to constrain the global net carbon fluxes from the terrestrial biosphere and the oceans [Keeling and Shertz, 1992; Keeling et al., 1996; Bender et al., 1996; Langenfelds et al., 1999; Battle et al., 2000; Ishidoya et al., 2003; Tohjima et al., 2003]. This approach exploits the fact that the terrestrial CO2 uptake releases O2 to the atmosphere while the oceanic CO2 uptake does not. Therefore, the difference between the observed atmospheric O2 loss rate and the O2 consumption rate estimated from fossil fuel burning gives terrestrial carbon uptake.

[3] Several techniques for detecting the variations in the O2 concentration of the background air have been developed, including an interferometric technique [Keeling, 1988], a mass spectrometric technique [Bender et al., 1994], a paramagnetic technique [Manning et al., 1999], a fuel-cell technique [Stephens et al., 2001], a vacuum-ultraviolet absorption technique [Stephens et al., 2003], and a gas chromatographic technique [Tohjima, 2000]. Since the instruments used in all these techniques cannot give absolute values, stable reference gases are required for calibration.

[4] Changes in the atmospheric O2 concentration are usually reported as relative deviations of O2/N2 ratio from an arbitrary reference gas according to

equation image

where subscripts “sam” and “ref” refer to the sample and reference gases, respectively. Keeling and Shertz [1992] denote δ(O2/N2) multiplied by 106 as “per meg” units, and 4.8 per meg is equivalent to 1 μmol mol−1 (hereinafter abbreviated as “ppm”) of O2 in dry air. The δ-notation defined by equation (1) is similar to the δ-notation used to express stable isotope ratios, such as the carbon isotope ratio (13C/12C).

[5] There are accepted primary standard materials for the stable isotope ratios, such as Pee Dee Belemnite (PDB) for carbon. However, primary standard materials that can provide a stable O2/N2 ratio have not been found. In addition, there is no reference gas in which O2 concentration or O2/N2 ratio has been related to the absolute values in ppm. Each laboratory, therefore, uses its own ambient air or synthesized air compressed into high-pressure cylinders as reference gases, and arbitrarily determines the zero point of its own scale. Although these reference gases have functioned relatively well in determining the atmospheric O2 variations, such practices result in divergence of the absolute values among laboratories with different O2 scales. Such divergence can, of course, be minimized by inter-laboratory comparison of the scales.

[6] The most serious drawback in using such reference gases is that there is no way to check the drift of the O2/N2 ratios of the reference gases over time. Each laboratory has been monitoring the relative changes in the O2/N2 ratios of the reference gases it uses and has determined a O2/N2 scale based on the reference gases that have shown no systematic trends relative to each other [e.g., Keeling et al., 1998; Bender et al., 1996]. However, even if there is no systematic trend, we cannot exclude the possibility that the O2/N2 ratios of the reference gases change in the same direction at the same rate.

[7] The lack of relationship between the δ(O2/N2) and the absolute O2 mole fraction or the absolute O2/N2 mole ratio can also cause another problem. In order to determine atmospheric O2 change in a distant future, the reference scales based on arbitrary air in cylinders need to be kept for a similar period. Even now, for example, the figure of 0.20946 ± 0.00006 is often cited from Machta and Hughes [1970] for the atmospheric O2 concentration. But the uncertainty is considerably larger than the current analytical precision. Moreover, the present O2 concentration might be significantly lower than the above figure because of the O2 consumption by fossil fuel burning during the last thirty years. Therefore, it is important to relate the relative O2/N2 scale to the absolute value, or to re-evaluate the absolute value of the atmospheric O2 mole fraction.

[8] To solve these problems, methods for determining the absolute standardization are required. Recent systematic measurements of the atmospheric O2/N2 ratio have revealed that the annual average loss rate has ranged from 10 to 20 per meg yr−1 [Keeling et al., 1996; Bender et al., 1996; Battel et al., 2000; Tohjima et al., 2003]. The uncertainty of 1 per meg yr−1 corresponds to an uncertainty of 0.4 PgC yr−1 in a carbon budget calculation. If we succeed in making an absolute O2/N2 scale with the accuracy of 10 per meg, we can evaluate the stability of the reference scale with an uncertainty of ±1 per meg yr−1 by repeatedly preparing the absolute scale over a 10-year period.

[9] One of the reliable procedures for making highly accurate standard gases is the gravimetric method, in which the mass of each gas component in a cylinder is determined accurately by an analytical balance. A mass mixing ratio can then be converted to a mole fraction. At the present time, the gravimetric method can provide us with very reliable standard scales for such gases as CO2 [Tanaka et al., 1983], CH4 [Matsueda et al., 2004], and CO [Novelli et al., 1991]. There have been few attempts to prepare gravimetric reference gases with a sufficient level of accuracy for atmospheric O2 measurements. Keeling et al. [1998] prepared a gravimetric standard mixture of N2, O2, Ar, and CO2 in a small high-pressure cylinder to calibrate the span sensitivity of the interferometric O2 analyzer. The precision of their gravimetric mixture was about 5 ppm with respect to the O2 mole fraction (R. Keeling, personal communication, 2004).

[10] In this study, we discuss preparation of a N2, O2, Ar, and CO2 mixture by the gravimetric method and evaluate the reproducibility of the gravimetric mixture. Section 2 describes the procedure for preparing the gravimetric mixture. Section 3 describes the various methods for measuring CO2, Ar, and O2(+Ar) concentrations and (O2 + Ar)/N2 ratios of the gravimetric mixture. Section 4 presents an estimate of the reproducibility of the gravimetric mixture and a relationship between the gravimetric and the δ(O2/N2) scales at the National Institute for Environmental Studies (NIES). Section 5 presents reevaluation of the atmospheric O2 concentration of air samples collected at Hateruma Island using the newly derived gravimetric scale.

2. Preparation of Gravimetric Standards

[11] The earth's atmosphere consists of N2, O2 and Ar, and other minor constituents such as CO2 and CH4. Table 1 lists the atmospheric constituents and their globally averaged mole fractions around 1968 (1965–1972), as well as the annually averaged values at Hateruma Island (latitude 24°03′N, longitude 123°49′E) for 2000. (A description of the determination of N2, O2 and Ar mole fractions for Hateruma will be described in section 5.) Although there are a number of trace gases that are not listed in Table 1, the total mole fraction of any individual trace gas does not exceed 0.1 ppm except in highly polluted air. It is not practical to prepare a standard mixture of gases with known amounts of minor constituents that have mole fractions in dry-air less than several ppm. Mixtures of O2 and N2 could be used as standard gases for the measurements of O2/N2 ratio or O2 mole fraction. However, the GC/TCD method, which we employ in this study, requires the inclusion of atmospheric level of Ar in a standard gas because the (O2 + Ar)/N2 ratio is actually measured.

Table 1. Atmospheric Composition in the Tropospherea
SpeciesAverage Concentration Around 1968Annual Average at Hateruma in 2000
N2780840b780876 ± 2j
O2209460 ± 60c209392 ± 3j
Ar9340 ± 10d9333.2 ± 2j

[12] Consequently, gravimetric mixtures of pure N2, O2, Ar, and CO2 gases with the atmospheric levels of mole fractions were prepared in this study. A target mole fraction of about 390 ppm for CO2 was set to be slightly higher than the atmospheric value to compensate for the summed mole fraction effect of other minor constituents such as Ne, He, CH4 listed in Table 1. With a final pressure of about 10 MPa in a 10-L cylinder, masses of the individual components were determined to be about 880 g for N2, 270 g for O2, 15 g for Ar, and 0.7 g for CO2.

2.1. Preparation Procedure

[13] First we prepared a CO2-Ar mixture in which the Ar:CO2 mole ratio was set equal to the ratio of the target mole fractions of Ar (9340 ppm) and CO2 (390 ppm) in a 10-L aluminum cylinder by gravimetric method. The CO2-Ar mixture, O2, and N2 gases were then used as source gases for the gravimetric standard mixtures. Using the CO2-Ar mixture can improve the accuracy in the determination of the CO2 mole fraction because a two-step dilution procedure prevents loss of accuracy in mass measurements of a relatively low-level constituent. Furthermore, the precisely determined Ar:CO2 mole ratio can be used to crosscheck the Ar analyses of the standard gases, as described in section 4. In this study, we have prepared fourteen gravimetric standard mixtures.

[14] The procedure for preparing standard mixtures that is fundamentally the same as that used for preparing CO2-Ar mixtures is as follows. A 10-L aluminum cylinder, after being evacuated to less than 0.1 Pa, is put into a balance room for at least half a day before weighing to allow equilibration of the cylinder temperature with the room temperature. The cylinder mass is determined by a precise balance (Shimadzu, Kyoto, Japan) with a nominal precision of 1 mg. After determining the mass, the evacuated cylinder is set on a platform balance (Sartorius, Goettingen, Germany, model IS 34 EDE-P) with a capacity of 34 kg and a nominal precision of 0.1 g; it is connected to a gas manifold with stainless steel tube (O. D. 1/8 inch). The CO2-Ar mixture is then transferred into the cylinder until the cylinder mass reaches the target mass, which gives the target concentration when the final pressure reaches about 10 MPa. Disconnected from the gas manifold, the cylinder is again weighed by the balance. The amount of gas filled into the cylinder is calculated from the difference in the mass between before and after the filling process. Following the same procedure as above, the cylinder is set on the platform balance and is filled with O2 gas, and then the O2 mass is determined by the balance. Finally, the filling and weighing procedure is repeated for the N2 gas.

[15] The weighing procedure by the precise balance is as follows. In weighing the cylinders for the gravimetric standard mixture, another 10-L aluminum cylinder is placed on the pan on the opposite side of the beam to equalize the volume and mass on both pans. Because changes in the ambient temperature, pressure and humidity can cause changes in the buoyant forces on the volumes, equalizing the volumes on the two pans can reduce changes in the difference between the buoyant forces on the both sides of the beam. However, the zero-point of the balance can still show a gradual drift. Thus, in order to compensate for this drift, we take another 10-L aluminum cylinder as a tare cylinder, and determine the mass of the standard cylinder as the difference relative to the tare cylinder. The masses of the gravimetric standard cylinder and tare cylinder are alternately determined in a sequence TCTCTCT, where ‘T’ and ‘C’ denote the tare cylinder and the gravimetric standard cylinder, respectively. Loading and unloading of the cylinders are automated. Three differences in the mass between the standard cylinder and the average of the bracketing tare cylinders are computed for the above sequence. We use the average of the triplicate measurements as the mass of the cylinder.

2.2. Estimations of Precision in Determining the Mass of Cylinder

[16] Using the sets of triplicate measurements of the cylinder mass, we estimate the precision of individual determination of the mass in the sequence of TCT by the precise balance. The standard deviation of a hypothetical parent distribution of replicate measurements is computed as a distribution of scaled residuals defined according to

equation image

where wi represents the individual values of the triplicate weighing and equation image represents the average. Figure 1 shows a cumulative probability plot of the scaled residuals obtained for the 14 standard cylinders (14 × 4 = 56 sets of the triplicate weighing) in this study. The scaled residuals are nearly normally distributed and the standard deviations (1σ) is 2.5 mg. Accordingly, the standard error for the individual mass based on the triplicate measurements is expected to be 1.4 mg.

Figure 1.

Normal probability plots of the scaled residuals for cylinder masses determined by the precise balance. The straight line represents a least-square fit of normal probability distribution to the residuals.

2.3. Calculation of Gravimetric Mole Fractions

[17] In the following sections, we examine several effects on the determination of the mole number in a gravimetric standard mixture. Taking into account these effects, we calculate the mole fractions in the gravimetric standards (Table 2).

Table 2. List of Gravimetric Standardsa
CylinderPreparation DateGravimetric AbundanceMeasured Value
CO2ArO2N2CO2Arδ{(O2 + Ar)/N2bδ(O2 + Ar)b
  • a

    Values for CO2, Ar, O2, and N2 are given in μmol mol−1 (ppm), and for δ{(O2 + Ar)/N2} and δ(O2 + Ar) in per meg.

  • b

    Uncertainties represent standard deviations (±1σ).

CPB172792002.2.16389.559329.6209335780945389.619331.0−427.6 ± 2.9−125.8 ± 1.5
CPB268552002.2.17390.129343.5209403780864390.129344.864.1 ± 3.3258.1 ± 6.1
CPB268562002.2.18390.839360.3209421780828390.919362.8289.7 ± 3.1433.1 ± 4.0
CPB184772002.5.27390.239346.0209365780899389.979340.4−198.9 ± 1.357.2 ± 3.6
CPB189842002.5.27389.799335.6209409780866389.279323.4−47.6 ± 2.8168.4 ± 11.2
CPB30212002.5.28390.259346.4209353780911390.119344.3−248.6 ± 3.010.8 ± 3.5
CPB30982002.5.29390.509352.4209356780901390.769358.6−132.8 ± 3.7103.8 ± 7.4
CPB167772002.5.29390.099342.7209391780877390.039341.2−58.2 ± 3.0159.6 ± 8.1
CPB280832002.8.20390.339348.5209415780846390.399350.5164.8 ± 0.9337.4 ± 5.0
CPB281482002.8.25390.489352.0209377780880390.119343.7−67.2 ± 3.4156.0 ± 6.6
CPB268492002.9.3389.809335.8209356780918389.919338.2−282.0 ± 3.9−16.1 ± 4.3
CPB172802003.1.18389.429326.7209315780969389.249321.6−597.5 ± 3.5−257.8 ± 6.6
CPB280842003.1.25390.149343.8209341780925390.159343.6−337.6 ± 2.9−57.9 ± 9.2
CPB280852003.1.26388.519304.8209421780885388.499303.8−92.8 ± 4.3133.3 ± 10.4

2.3.1. Effect of Impurities in the Source Gases

[18] We used highly-purified CO2, Ar, O2, and N2 gases (G1-grade, Japan Fine Products Corp., Kawasaki, Japan) as source gases for the standard mixture. The lower limits of purity and the upper limits of major impurities in the source gases, guaranteed by the manufacturer, are listed in Table 3. The manufacturer uses carefully prepared calibration gases for the impurity measurements, and estimates that the accuracy is less than half of the limits listed in Table 3. From these limits, we find that the absolute values of the impurity effect do not exceed 0.5 ppm. Each gravimetric mole fraction listed in Table 2 is not corrected for the impurity effect, which is included in the uncertainties, as discussed in section 2.4.

Table 3. Impurities in the Source Gases
Source GasDegree of Purity, %Impurity, ppm

2.3.2. Effect of Isotopic Composition in the Source Gases to the Molecular Masses

[19] The standard atomic masses of N and O (see Table 4) have large uncertainties, because they reflect the variability in the individual isotopic abundance of natural terrestrial matters. These uncertainties result in uncertainties of 11 ppm for N2 and 4 ppm for O2 of the gravimetric standards. To reduce the uncertainties of the atomic masses for the source O2 and N2 gases, the isotopic compositions (14N and 15N, and 16O, 17O and 18O) need to be determined precisely.

Table 4. List of Atomic Masses of Oxygen and Nitrogen for Some Sources
SourcesAtomic MassaIsotope Ratiob
  • a

    The numbers in the parenthesis are uncertainties on the last digits.

  • b

    δ17O and δ18O are given with respect to V-SMOW, and δ15N is given with respect to atmospheric N2.

  • c

    From Coplen [2001].

  • d

    The atomic mass and the uncertainty are calculated from the absolute isotope ratios and the uncertainties from Li et al. [1988] for 17O/16O and Baertschi [1976] for 18O/16O.

  • e

    The atomic masses are calculated from the isotope ratios relative to V-SMOW.

  • f

    From Johnston and Thiemens [1997].

  • g

    From Kroopnick and Craig [1972].

  • h

    Yoshida and Toyoda (personal communication, 2003).

  • i

    The atomic mass and the uncertainty are calculated from the absolute 15N/14N ratio from Junk and Svec [1958].

  • j

    The atomic mass is calculated from the isotope ratio relative to atmospheric N2.

Standard atomic mass15.9994(3)c 
VSMOW15.999304(6)dδ17O = 0‰, δ18O = 0‰
Atmospheric O215.999403(6)eδ17O = 12.2‰f, δ18O = 23.5‰g
Source O2 (this study)15.999481(8)eδ17O = 23.5‰h, δ18O = 42.0‰h
Standard atomic mass14.0067(2)c 
Atmospheric N214.006726(4)iδ15N = 0‰
N2 (this study)14.006677(4)jδ15N = −13.6‰h

[20] The isotope ratios 15N/14N, 18O/16O and 17O/16O for the source O2 and N2 gases were measured and the results are listed in Table 4 (Yoshida and Toyoda, personal communications, 2003). The isotope ratios are expressed in the δ-notation with units of per mil (‰) defined by δ = (Rsa/Rstd − 1) × 1000, where Rsa and Rstd are the isotope ratios of a sample and standard, respectively. The standards are atmospheric air for nitrogen and the Vienna Standard Mean Ocean Water (V-SMOW) for oxygen. The source O2 gas is enriched in 17O and 18O in comparison with the atmospheric O2 and the source N2 gas is depleted in 15N in comparison with the atmospheric N2. Taking account of the isotope compositions for the atmospheric nitrogen and V-SMOW [Rosman and Taylor, 1998, and references therein], we calculate the molecular masses of the source O2 and N2 gases (see Table 4). The difference in the molecular mass between the atmospheric N2 and the source N2, and between the atmospheric O2 and the source O2 corresponds to a difference in the mole fractions of 1.4 ppm for both N2 and O2 and 8.4 per meg for the O2/N2 ratio. The mole fractions shown in Table 2 are based on the corrected molecular masses.

[21] As for CO2 and Ar, we used the molecular masses and uncertainties shown in the Table of Standard Atmoic Weights 1997 [Vocke, 1999]. These uncertainties in the molecular masses do not significantly affect the gravimetric calculations.

2.3.3. Buoyancy Effect Caused by the Expansion of Cylinder

[22] The volume of the 10-L aluminum cylinder increases almost linearly with internal pressure. An average increase in the cylinder volume against the pressure of 10 MPa, evaluated from changes in the water level of water tank in which cylinders are sunk, is about 22 ± 4 cm3, which corresponds to an increase in buoyancy of about 26 ± 5 mg. Since the molecular masses of CO2, Ar, O2 and N2 gases are different, the ratios of the buoyancy-to-mass increase for the individual gas filling procedures are different. Therefore, the buoyancy effect results in errors in the gravimetrically determined mole fractions. In our study, the buoyancy effects are 0.01 mg for CO2, 0.2 mg for Ar, 5.5 mg for O2, and 20.3 mg for N2, which cause changes in the gravimetric mole fraction by about +0.5 ppm for O2 and about −0.5 ppm for N2. The mole fractions shown in Table 2 are corrected for the buoyancy effects.

2.4. Estimates of Uncertainties in Gravimetric Values

[23] There are uncertainties associated with the measurements of mass, of purity and molecular mass of source gases, and of buoyancy change caused by the expansion of cylinder. In addition, there are uncertainties in the weights used in the precise balance; the uncertainties associated with weights ≥100 g are ±1.5 ppm (±0.15 mg for the 100 g weight) and are better than ±0.1 mg for weights ≤50 g. These uncertainties propagate into the uncertainties in the determination of mole fractions and ratios for the gravimetric standards. However, since the analytical calculation of the propagated errors is complicated and difficult, we compute these uncertainties by the Monte Carlo method. The method allows individual uncertainties in the mass measurement, purity, molecular mass, for example, to be simulated by random sampling from a normal distribution, and the individual gravimetric mole fractions are then calculated. Such simulations are repeated more than ten thousand times. The uncertainties in the mole fractions and mole ratios are estimated as the standard deviations.

[24] Table 5 summarizes the sources of errors and estimates of the uncertainties in the mole fractions and ratios for the gravimetric standards. The definitions of δ(O2 + Ar) and δ{(O2 + Ar)/N2} are given in section 3.2. The overall uncertainties are 1.6 ppm for the O2 mole fraction and 9.2 per meg for the O2/N2 ratio. The largest source of error is the uncertainty associated with the mass determination by the balance.

Table 5. Estimates of Accuracy of Gravimetric Mixture
Sources of ErrorΔCO2ΔArΔO2ΔN2Δδ(O2/N2)Δδ(O2 + Ar)Δδ{(O2 + Ar)/N2}
ppmper meg
  • a

    To calculate the root mean square, larger absolute value is used for the uncertainty caused by gas impurity.

Precision of balance±0.05±1.1±1.5±1.3±8.8±6.3±8.1
Impurity - lower limita−0.02−0.01−0.10−0.39−0.55−0.50−0.57
Impurity - upper limita+0.08+0.01+0.08+0.05+0.88+0.42+0.91
Molecular mass±0.01±0.23±0.1±0.2±0.57±1.1±1.3
Buoyancy effect±0.00±0.00±0.08±0.08±0.50±0.36±0.46
Ar/CO2 ratio±0.02±0.02±0±0±0±0.09±0.09
Root Mean Square±0.10±1.2±1.6±1.5±9.2±6.7±8.6

3. Analytical Methods

3.1. CO2 Measurements

[25] The CO2 concentrations in the gravimetric standards have been measured by a nondispersive infrared (NDIR) analyzer (Shimadzu, Kyoto, Japan, model URA-207) with an analytical precision of about 0.01 ppm. The CO2 mole fractions are determined against the NIES CO2 standard scale, which is calibrated relative to a set of 8 primary standard gases. These primary standard gases are gravimetric mixtures of pure CO2 and purified air, prepared by Nippon Sanso Corp. in 1995 using a method consistent with the procedure developed by Tanaka et al. [1983]. The absolute accuracy of the gravimetric standard for CO2 is estimated to be better than 0.3 ppm [Tanaka et al., 1983]. Previous results from repeated interlaboratory comparisons of CO2 in dry air from high-pressure cylinders show that the NIES scale agrees with the NOAA scale to within 0.12 ppm in a range 340 to 370 ppm.

3.2. O2/N2 Measurements by Gas Chromatography

[26] Details of the O2/N2 measurement by a GC/TCD method have been described elsewhere [Tohjima, 2000]. Here, we give only a brief description of the GC/TCD method. The O2 and N2 of an aliquot air sample (2 cm3) are separated by a column filled with molecular sieve 5A with H2 carrier gas and detected by TCD (thermal conductivity detector). To achieve high-precision measurements, the pressures at the GC column head and at the outlet of the TCD are actively stabilized. In addition, the precision is improved statistically by repeating the alternate analyses of sample and reference gas. Because the separated O2 includes Ar, the ratio of the (O2 + Ar) peak area to the N2 peak area is measured. Following the definition of δ(O2/N2) expressed by equation (1), we define δ{(O2 + Ar)/N2} according to

equation image

where k represents the TCD sensitivity ratio of Ar relative to O2. We evaluated k to be 1.13 by comparing gravimetric mixtures of O2 + N2 and Ar + O2 + N2. This value of k is negligibly different from k = 1.10 derived by Tohjima [2000]. In the atmosphere, changes in the δ{(O2 + Ar)/N2} are caused substantially by changes in the O2/N2 ratio. This is because the atmospheric Ar/N2 variations [Battle et al., 2003; Keeling et al., 2004] result in only a few per meg change in the δ{(O2 + Ar)/N2}. Therefore, for the air samples we can easily convert δ{(O2 + Ar)/N2} to δ(O2/N2) with the introduction of only a small error:

equation image

We also define δ(O2 + Ar) as

equation image

The δ(O2 + Ar) values multiplied by 106 are also reported in per meg units.

[27] The standard deviations of the δ{(O2 + Ar)/N2} and δ(O2 + Ar) values based on the alternate analyses of the reference and sample gases are about 18 per meg and 50 per meg, respectively. To determine the δ{(O2 + Ar)/N2} values for the gravimetric standards, we usually repeat the alternate analyses more than 50 times. Thus the expected standard errors for the individual measurements of the gravimetric standards are less than 3 per meg for the δ{(O2 + Ar)/N2} values and about 7 per meg for the δ(O2 + Ar) values.

[28] The δ{(O2 + Ar)/N2} and δ(O2 + Ar) values are reported with respect to the NIES original scales, which are based on more than 10 high-pressure cylinders. The δ{(O2 + Ar)/N2} zero point does not correspond to the δ(O2 + Ar) zero point because the individual scales are based on different cylinders.

3.3. Ar Measurements

[29] A tight mole ratio between Ar and CO2 in the gravimetric standard is expected because Ar and CO2 gases are derived from the same gravimetric CO2-Ar mixture. Therefore, we can obtain Ar mole fraction from the product of the analyzed CO2 mole fraction and the Ar:CO2 mole ratio (23.950 ± 0.001) of the CO2-Ar mixture.

[30] In addition, the Ar mole fractions in the standard gases have been measured by a gas chromatographic method similar to that used in the O2/N2 measurements [Tohjima, 2000], except for the separation column and the operational temperatures. The separation of Ar is achieved by a series of three columns packed with 60/80 mesh molecular sieve 5A (1/8 inch OD × 3 m), 30/80 mesh palladium metal catalyst (1/8 inch OD × 1 m), and 60/80 mesh Porapak Q (1/8 inch OD × 2 m). The temperatures of oven and TCD are kept at 100°C and 150°C, respectively. Under these conditions, the palladium catalyst in the hydrogen carrier gas converts the O2 of an aliquot air sample completely to H2O, of which elusion is delayed by the Porapak Q column.

[31] The measurement interval of an aliquot air sample is 5 minutes. The alternate analyses of sample and reference gases are repeated to improve the precision statistically. We calculate the mole fractions of the sample gases by comparing the peak area of a sample with the average peak area of two bracketing reference gases; we have assumed linear response of Ar peak area. The standard deviation (1σ) of the replicate cycles of reference and sample analyses is about 1.5 ppm. Since we usually repeat the alternate analyses more than 50 times for the gravimetric standards, the expected standard error for the individual measurements is less than 0.3 ppm. Purified air from a high-pressure aluminum 48-L cylinder, CQB-15649, is used as a temporal reference gas. As described below, the Ar mole fraction of CQB-15649 (9354 ppm) is calibrated against the gravimetric standards.

4. Evaluation of the Gravimetric Standards

[32] The analyzed CO2 and Ar mole fractions, and the δ{(O2 + Ar)/N2} and δ(O2 + Ar) values for the 14 gravimetric standards are listed in Table 2. We repeated measurements of Ar, δ{(O2 + Ar)/N2} and δ(O2 + Ar) several times after the preparation of the gravimetric standards and did not find any significant trends in those values during the few years of this study.

4.1. Comparison Between Gravimetric and Analyzed Values

[33] Figure 2a shows a plot of gravimetric mole fractions versus the analyzed mole fractions for CO2. The average and standard deviation (±1σ) of the differences between the gravimetric and analyzed CO2 mole fraction (gravimetric − NDIR) are 0.07 ± 0.21 ppm. The two standards, CPB-18984 and CPB-28148, indicated by arrows in Figure 2a have the largest and the second largest deviations of 0.52 and 0.37 ppm, respectively. Without these two standards, the average and the standard deviation of the differences are reduced to 0.01 ± 0.14 ppm.

Figure 2.

Scatterplots of (a) gravimetric CO2 mole fractions versus CO2 mole fractions by NDIR and (b) gravimetric Ar mole fractions versus Ar mole fraction by GC/TCD for the 14 gravimetric standards. The Ar mole fractions calculated from the products of NDIR-CO2 multiplied by the gravimetric Ar/CO2 mole ratio are also plotted against analyzed Ar as solid circles. The arrows indicate two cylinders, (left) CPB-18984 and (right) CPB-28148, of which gravimetric mole fractions of CO2 and Ar are significantly higher than the analyzed values. A line through the origin with 1:1 slope is shown in each figure.

[34] A plot of gravimetric Ar mole fractions against the gas chromatographic Ar mole fractions shows a similar distribution to the plot of CO2 (open circles in Figure 2b). The standard deviations (±1σ) of the differences between the gravimetric and gas chromatographic Ar mole fractions are 4.7 ppm for all the data, and 3.3 ppm for the data that exclude values from CPB-18984 and CPB-28148 indicated by the arrows in Figure 2b. On the other hand, a plot of Ar mole fractions based on the CO2 analysis against the gas chromatographic values shows a good linear relationship (solid circles in Figure 2b), with a standard deviation of 0.6 ppm for the differences between them. The small standard deviation means that the Ar:CO2 mole ratio in the gravimetric standards are conserved through the whole gas handling processes. Therefore, fractionation of CO2 and Ar during the gas transfer process or contamination of CO2 and Ar are considered to be negligible.

[35] The Ar mole fraction of the working reference gas used in this study (CQB-15649) is determined against these gravimetric standards, except for the two cylinders, CPB-18984 and CPB-28148, of which gravimetric CO2 mole fractions are found to be significantly higher than the analyzed values. The average of the Ar mixing ratios of CQB-15649 based on the twelve gravimetric standards is 9354.0 ± 2.1 ppm (uncertainty represents 95% confidence interval).

[36] The absolute (O2 + kAr)/N2 ratios calculated from the gravimetric mole fractions are plotted against the measured δ{(O2 + Ar)/N2} values in Figure 3a as open circles. The absolute (O2 + kAr)/N2 ratio can be easily converted to δ{(O2 + Ar)/N2} in accordance with equation (3) if a reference is determined. The right axis of Figure 3a indicates the scale for the corresponding gravimetric δ{(O2 + Ar)/N2} value with respect to a hypothetical reference with 9340 ppm of Ar, 20.9375% of O2 and 78.0895% of N2. Similarly, the absolute O2 + kAr values are plotted against the measured δ(O2 + Ar) values as open circles in Figure 3b, where the right axis indicates the scale for the gravimetric δ(O2 + Ar) values with respect to the same hypothetical reference. The standard deviations ( ±1σ) of the differences between the gravimetric and the analyzed values are 31 per meg for δ{(O2 + Ar)/N2} and 25 per meg for δ(O2 + Ar).

Figure 3.

Scatterplots of (a) gravimetric (O2 + kAr)/N2 versus δ{(O2 + Ar)/N2} and (b) gravimetric O2 + kAr versus δ(O2 + Ar) for the 14 gravimetric standards. The right axes represent corresponding δ{(O2 + Ar)/N2} and δ(O2 + Ar) with respect to a hypothetical reference air. Open circles represent (O2 + kAr)/N2 and O2 + kAr values based on the gravimetric mole fractions, and solid circles represent those based on the gravimetric O2 and N2 mole fractions and analyzed Ar mole fraction. The straight lines represent the least squares fits to the corrected data indicated by the solid symbols.

[37] Because the analytical uncertainties for CO2, Ar, δ{(O2 + Ar)/N2} and δ(O2 + Ar) are sufficiently small, the observed standard deviations of the differences between the gravimetric values and the analyzed values represent the level of reproducibility of the gravimetric standards. The observed standard deviations are about 4 times as large as the estimated uncertainties (Table 5) except for CO2. This suggests that there are additional sources of error in the determination of cylinder mass. Most plausible source of error may be the actual change in the mass of the cylinder caused by adsorption/desorption of water vapor and adhesion/removal of dust particles on the outer surface of the cylinder.

4.2. Estimates of the Reproducibility for the O2/N2 Ratio and O2 Mole Fraction

[38] The error in the gravimetric Ar mole fraction contributes substantially to the error in the gravimetric (O2 + kAr)/N2 and O2 + kAr values. To remove the contribution of Ar error from the gravimetric (O2 + kAr)/N2, and O2 + kAr, we substitute the gravimetric Ar mole fractions with the analyzed values and recalculate the gravimetric (O2 + kAr)/N2 and O2 + kAr values. The corrected (O2 + kAr)/N2 and O2 + kAr values are also plotted against the analyzed values in Figures 3a and 3b, respectively, as solid circles. The standard deviations of the differences between the corrected gravimetric values and the analyzed values are reduced to 14.8 per meg for δ{(O2 + Ar)/N2} and 13.1 per meg for δ(O2 + Ar). From the relationship between δ(O2/N2) and δ{(O2 + Ar)/N2} expressed in equation (4), we estimate the standard deviation of the O2/N2 ratio for the gravimetric standards to be 15.5 per meg (=14.8 × 1.050). Similarly, the standard deviation of the O2 mole fraction for the gravimetric standards is estimated to be 2.9 ppm (=13.1 × 1.050 × 0.2095). These standard deviations indicate the degree of reproducibility of the gravimetric standards. The estimated standard deviations of the O2/N2 ratio and the O2 mole fraction for the gravimetric standards are about 1.7 times larger than the estimated uncertainties (Table 5). The relatively large errors with respect to the estimated uncertainties suggest that there are additional sources of errors.

4.3. Relationship Between the NIES Scale and Gravimetric Scale

[39] Using the analyzed δ{(O2 + Ar)/N2} value and the absolute (O2 + kAr)/N2 ratio corrected for the Ar mole fraction with respect to each gravimetric standard, we calculate the (O2 + kAr)/N2 ratio for the zero point of the NIES δ{(O2 + Ar)/N2} scale. The average (O2 + kAr)/N2 ratio for δ{(O2 + Ar)/N2} = 0 is 0.2816768 ± 0.0000024. Similarly, the average O2 + kAr for the zero point of the NIES δ(O2 + Ar) scale is 0.2199074 ± 0.0000016. Here the uncertainties represent 95% confidence intervals, with k = 1.13. Based on the atmospheric Ar and N2 mole fractions evaluated in section 5 (see Table 1), we estimate that δ(O2/N2) = 0 in the NIES scale corresponds to the O2/N2 mole ratio of 0.2681708 ± 0.0000036.

[40] In Figures 3a and 3b, we depict least squares fit to the individual data sets. The zero points of (O2 + kAr)/N2 and O2 + kAr on the NIES scales, evaluated from these best fit lines, are 0.2816759 and 0.2199078, respectively. These values are almost identical to the above averages. The inverse slopes of the best fit lines (analyzed/gravimetric) are 1.02 ± 0.02 (per meg/per meg) for (O2 + kAr)/N2 and 1.01 ± 0.02 (per meg/per meg) for O2 + kAr, suggesting that the response of our GC/TCD system is almost linear within the uncertainty.

4.4. Change in the O2/N2 Ratio of Air Derived From High-Pressure Cylinder Caused by Fractionation

[41] The O2/N2 ratio of gases from the high-pressure cylinders may be different from the gravimetric O2/N2 ratio, because there are several potential fractionation mechanisms, including the diffusive fractionation and the Knudsen diffusion. Recently, Keeling et al. [2004] suggested that the O2/N2 ratio of a gas from a cylinder could be fractionated by several per meg due to thermal diffusion near the cylinder outlet, where a temperature gradient can be produced by adiabatic expansion. Such fractionation can result in errors in determining absolute mole fractions of the atmospheric O2, and can cause a gradual change in the gas composition in the cylinders as the gas is released.

[42] To evaluate the actual degree of fractionation, we measured the O2/N2 ratio of air from a 10-L aluminum cylinder at certain intervals while the air was continuously released into the room at a rate of 8 cm3 min−1, corresponding to a usual flow rate for O2/N2 measurements. If the O2/N2 ratio of the air from the cylinder were to be fractionated, a gradual change in the O2/N2 ratio of the remaining air in the cylinder would be observed. For example, if a cylinder were to be half emptied, a 10 per meg enrichment in the released air would reduce the O2/N2 ratio of the remaining air in the cylinder by about 7 per meg, and by about 23 per meg after a 90% release. Figure 4 shows deviations in the δ{(O2 + Ar)/N2} from the initial ratio plotted against the fraction of air released. A linear regression fit to the data is 0.0 ± 2.0 per meg. This result indicates that the fractionation in the O2/N2 ratio of the gas released from the cylinder is insignificant, with negligible impact on the gravimetric ratio.

Figure 4.

Deviations of δ{(O2 + Ar)/N2}, relative to its initial value, of the air derived from a 10-L aluminum cylinder plotted against the fractional gas release. Initial pressure of the air in the cylinder was about 8 MPa. The straight line represents a least squares fit to the data.

5. Reevaluation of the Atmospheric Composition

5.1. Atmospheric O2 at Hateruma Island in 2000

[43] We have been collecting air samples at Hateruma Island for O2/N2 measurements since July 1997 [Tohjima et al., 2003]. The air samples are drawn from the top of a tower (47 m above sea level) by a diaphragm pump, passed through a cold trap (−40°C), and then introduced into Pyrex glass flasks. The sampling frequency was once per month until December 1999, but has been increased to once every 4 days since then by introducing an automatic sampling system. Figure 5 shows the δ{(O2 + Ar)/N2} and δ(O2 + Ar) variations at Hateruma in 2000, together with smoothed curve fits to the data. The smoothed curve fits are obtained by fitting the data to a function composed of a linear polynomial and sum of four-harmonics of the annual cycle, along with a digital filtering technique [Thoning et al., 1989] with a cutoff frequency of 4.6 cycles yr−1 (corresponding to an 80-day period).

Figure 5.

Observed variations in (a) δ{(O2 + Ar)/N2 and (b) δ(O2 + Ar) for the air samples in glass flasks collected at Hateruma Island. The solid lines are the smooth curve fits to the data.

[44] Based on the relationship between the gravimetric scale and the NIES scale, we have estimated the atmospheric O2 mole fractions at Hateruma Island for the year 2000. From the smoothed curve fits, the annual averages of the δ{(O2 + Ar)/N2} and δ(O2 + Ar) are −73 per meg and 143 per meg on the NIES scale, respectively. These annual averages correspond to the absolute (O2 + kAr)/N2 and O2 + kAr values of 0.2816563 and 0.2199388, respectively.

[45] The O2 mole fraction can be easily calculated from the O2 + kAr value and the Ar mole fraction. The sum of the N2, O2, and Ar mole fractions for Hateruma in 2000, evaluated from the mole fractions of the rest of the atmospheric constituents (Table 1), is 0.9996014, with an uncertainty of less than 0.1 ppm. Although the O2 mole fraction can be calculated from the (O2 + kAr)/N2 and Ar mole fraction, the presently known Ar mole fraction of 9340 ppm has a large uncertainty of 10 ppm and thus limits the accuracy of the calculated O2 mole fractions.

[46] In order to determine the atmospheric Ar mole fraction more accurately, we have collected air samples into two 3-L glass flasks at Hateruma every month since June 2003 (Figure 6). The Ar mole fractions have been measured by the gas chromatographic method described in section 3.3. The observed Ar shows very little variability, and the average mole fraction for the 1-year period from June 2003 to June 2004 is 9333.2 ± 0.3 ppm (±1σ). Because of the geological time scale of the degassing of 40Ar (a decay product of 40K) from the earth's crust and its subsequent accumulation in the atmosphere, the atmospheric Ar abundance is considered to be constant in this study. The rate of degassing of Ar from the oceans due to possible solubility decrease caused by the global warming is estimated to be negligible for the study period [Keeling et al., 2004]. Therefore, we conclude that the atmospheric Ar mole fraction is 9333.2 ± 2.1 ppm (Table 1). Here the uncertainty is evaluated from the uncertainty associated with the Ar standard scale determined in this study.

Figure 6.

Observed Ar mole fractions for the air samples in 3L glass flasks collected at Hateruma Island during the period from June 2003 to June 2004.

[47] Using the above Ar mole fraction, we calculate the O2 mole fraction at Hateruma in 2000 to be 209392.2 ± 2.7 ppm for (O2 + kAr)/N2 and 209392.3 ± 2.9 ppm for O2 + kAr. The uncertainties are estimated from the uncertainties in the NIES scales of δ{(O2 + Ar)/N2} and of δ(O2 + Ar) and the Ar mole fraction. These O2 mole fractions agree very well. In addition, the N2 mole fractions at Hateruma in 2000 are calculated to be 780876.1 ± 1.5 ppm for (O2 + kAr)/N2 and 780876.0 ± 1.7 ppm for O2 + kAr. The uncertainties in the N2 mole fractions are smaller than those in the O2 mole fractions because the O2 + Ar mole fraction is determined more accurately than the Ar mole fraction in the GC/TCD measurements, and the calculation of the N2 mole fraction is not affected by the uncertainty in the Ar mole fraction. We conclude that the averages of the above two values for O2 and N2 represent the atmospheric mole fractions at Hateruma in 2000 (Table 1).

5.2. Comparison With Previous Data

[48] The figure of 209460 ± 60 ppm is often cited from Machta and Hughes [1970] for the atmospheric O2 mole fraction. It is about 70 ppm higher than the O2 mole fraction at Hateruma in 2000 determined in this study. To validate the change in the O2 mole fraction over about 30 years, we reconstruct the O2 mole fraction in 1968 from the available data.

[49] The longest record of the atmospheric O2/N2 is from the analyses of archived air samples collected at Cape Grim; the results show that the loss rate was 16.7 ± 0.5 per meg yr−1 over a 19-year period (1978–1997) [Langenfelds et al., 1999]. The average rate of decrease in the O2/N2 ratio at Hateruma during 1997–2000 was 18.0 ± 0.4 per meg yr−1. Therefore we estimate that the decrease in the O2/N2 ratio for the 22-year period (1978–2000) was 371 ± 11 per meg, which is equivalent to 1.38 ± 0.04 × 1016 mol O2. During the 10-year period from 1968 to 1978, combustion of fossil fuel consumed 5.26 × 1015 mol of O2, which is calculated from the fossil CO2 emissions [Marland et al., 2003] and the O2:C combustion ratios of different fuel types [Keeling, 1988]. Atmospheric O2 change also depends on terrestrial O2 fluxes, because the terrestrial carbon uptake releases O2 with a O2:C exchange ratio of about −1.1 [Severinghaus, 1995]. We use the terrestrial CO2 uptake for the 10-year period of 0.5 ± 1 GtC yr−1 from the results of terrestrial carbon cycle models [McGuire et al., 2001]. We therefore estimate the O2 decrease during the 32-year period (1968–2000) to be 1.86 ± 0.12 × 1016 mol.

[50] The net terrestrial CO2 uptakes have been estimated by three atmospheric inversions to be 0.4 ± 0.2 GtC yr−1 for the 1980s and 1.0 ± 0.5 GtC yr−1 for the 1990s. Here, the uncertainties represent the range of estimates from the three inversions. Again we adopt the terrestrial CO2 uptake of 0.5 ± 1 GtC yr−1 for the 12-year period from 1968 to 1980. By taking into account the O2 consumption of 2.03 × 1016 mol by the fossil fuel combustion during the 32-year period (1968–2000), we obtain an atmospheric O2 decrease for the 32-year period of 1.85 ± 0.17 × 1016 mol.

[51] There is good agreement between the estimated O2 decrease based on the atmospheric O2/N2 observations and that derived from the atmospheric inversions. The O2 decrease of 1.86 ± 0.17 × 1016 mol corresponds to a decrease in the atmospheric O2 mole fraction of 93 ± 8 ppm, where we take the atmospheric CO2 increase of 46.4 ppm observed at Mauna Loa [Keeling and Whorf, 2004]. Accordingly, we conclude that the most probable mole fraction of atmospheric O2 in 1968 was 209485 ± 8 ppm. Although our 1968 estimate falls with the value of 209460 ± 60 ppm obtained by Machta and Hughes [1970], their estimate is about 25 ppm lower and falls outside of our uncertainty rage.

6. Conclusion

[52] We have developed a gravimetric technique to prepare a set of standard mixtures, composed of ambient levels of CO2, Ar, O2, and N2, for atmospheric O2 measurements. To determine the mole fractions at an accuracy of ppm level, masses of gases determined by a precise balance must be corrected for buoyancy changes caused by expansion of the cylinder due to inner pressure increase. In addition, molecular masses of the O2 and N2 source gases must be corrected for their isotopic compositions. Estimates of the uncertainties in the O2/N2 ratio and the O2 mole fraction for the gravimetric standard mixture are 9.2 per meg and 1.6 ppm, respectively, and the largest source of error is uncertainty associated with the mass measurement by the precise balance.

[53] We have prepared fourteen gravimetric standards and analyzed them. The reproducibility of the gravimetric technique evaluated from the standard deviations of the differences between the gravimetric and the analyzed compositions are 15.5 per meg for the O2/N2 ratio and 2.9 ppm for the O2 mole fraction. The variability in the prepared gravimetric standards is larger than the expected uncertainty, suggesting that there is another source of error. A change in the cylinder mass caused by, for example, adsorption/desorption of water vapor is the most plausible source of the error. It may be possible to improve the reproducibility by controlling more precisely the temperature and humidity, and removing dust particles in the laboratory.

[54] Based on the gravimetric scale and the atmospheric Ar mole fraction (9333.2 ± 2 ppm), we have evaluated the annual averages of the atmospheric O2 and N2 mole fractions at Hateruma Island for 2000 to be 209392 ± 3 ppm and 780876 ± 2 ppm, respectively. The atmospheric O2 mole fraction estimated for 1968 from the observed atmospheric O2/N2 changes, statistics of the fossil fuel consumption, and the terrestrial biosphere models, agrees with the O2 mole fraction obtained by Machta and Hughes [1970] and falls within their range of uncertainty.


[55] We wish to thank Naohiro Yoshida and Sakae Toyoda, Tokyo Institute of Technology, for the isotopic measurements of O2 and N2 gases. Kaz Higuchi, Meteorological Service of Canada, helped to improve the manuscript with critical comments and suggestions.