Uncertainty and bias of surface ozone measurements at selected Global Atmosphere Watch sites

Authors


Abstract

[1] The Global Atmosphere Watch (GAW) program currently coordinates 22 ground-based atmospheric background monitoring stations of global scope. The GAW World Calibration Centre for Surface Ozone, Carbon Monoxide and Methane (WCC-EMPA) is responsible for tracing surface ozone measurements at these stations to the designated reference within the GAW program, the Standard Reference Photometer SRP 2 maintained at the National Institute of Standards and Technology (NIST). The recommended method for surface ozone measurements is based on UV absorption at 254 nm (Hg line). Repeated and regular intercomparisons of station instruments are necessary to achieve and maintain high and known data quality. In this paper, the traceability chain is explained, and standard uncertainties for each element are evaluated. Data of 26 intercomparisons performed at 14 stations between 1996 and 2002 are analyzed. On 23 occasions, the instruments passed the audit with “good” agreement, in one case with “sufficient” agreement. On 2 occasions, both first audits at the site, the audited instrument did not comply with the minimal data quality requirements. The best instruments in use exhibit a median absolute bias of approximately 0.32 ppbv and a standard uncertainty of approximately 0.8 ppbv (0–100 ppbv). The quantitative improvement of data quality as a result of repeated audits can be demonstrated with several stations.

1. Introduction

[2] Tropospheric (surface) ozone is a greenhouse gas and today one of the strong contributors to radiative forcing, i.e., to warming of the Earth [Houghton et al., 2001]. It is also a reactive gas that is potentially harmful for vegetation, animals, and human beings. Although the uncertainties attributed to the earlier measurements are difficult to assess, it is evident that the concentrations of tropospheric ozone over Europe have increased substantially since the late 19th century [Marenco et al., 1994; Staehelin et al., 1994; Volz and Kley, 1988].

[3] Global Atmosphere Watch (GAW) is a program coordinated by the World Meteorological Organization (WMO) with the objective of providing data on the chemical composition and related physical characteristics of the atmosphere and their trends, required to further the understanding of the behavior of the atmosphere and its interactions with the oceans and the biosphere. The data collected at the GAW monitoring stations must be of high and known quality to be useful in the assessment of the relationship between the changing atmospheric composition and changes of global and regional climate; the long-range atmospheric transport and deposition of potentially harmful substances over terrestrial, fresh-water and marine ecosystems; and the natural or perturbated cycling of chemical elements in the global atmosphere/ocean/biosphere system. Currently, 22 ground-based stations with global scope (“global stations”) and some 300 stations with more regional scope (“regional stations”) participate in the program. Data obtained since about 1975 at a number of these stations reveal important regional differences with respect to temporal and spatial trends [Oltmans et al., 1998].

[4] The traceability of measurements in a monitoring network to a common point of reference is strictly required to produce data sets that can be evaluated in terms of spatial and temporal trends. Proper evaluation of spatial distribution requires the data to be unbiased while the number of data points necessary to identify a trend is in part controlled by the uncertainty of the individual data points. A review of the more recent literature on ozone trends [Harris et al., 1997; Low et al., 1991; Marenco et al., 1994; Oltmans and Komhyr, 1986; Oltmans et al., 1998; Pavelin et al., 1999; Staehelin et al., 1994, 1998; Zanis et al., 1999] reveals that the uncertainty of the data used has received relatively little attention up to now. For ozone measurements, GAW has adopted the Standard Reference Photometer 2 (SRP 2), manufactured and maintained by the U.S. National Institute of Standards and Technology (NIST), as the common point of reference. Several nominally identical SRPs have been built and distributed to various institutions [Paur et al., 1998] (available on the Web at http://patapsco.nist.gov/ts_sbir/standref.pdf). SRPs 15 and, more recently, 23 have been acquired by the GAW World Calibration Centre for Surface Ozone, Carbon Monoxide and Methane (WCC-EMPA) located at the Swiss Federal Laboratories for Materials Testing and Research (EMPA). The main task of the WCC with respect to surface ozone is to ensure that the measurements performed at all global stations are fully traceable to SRP 2 and within the margins of uncertainty defined in Table 1.

Table 1. Data Quality Objectives (DQOs) for Surface Ozone Measurements
Organization/ProgramRange, ppbvDQOaCommentMaximum Allowed Standard Difference From SRP, ΔOA,SRPReference
  • a

    The DQO defines the maximum value of the expanded uncertainty of a measured value that is deemed acceptable (normal distribution and coverage factor k = 2 assumed). Here, it is further assumed that all concentrations refer to the same value for the ozone absorption cross-section.

  • b

    The terms “precision” and “accuracy” should only be used in a qualitative sense [ISO, 1995].

GAW≤202 ppbvSum of “precision” and “accuracy”b1 ppbvWMO [1995]
GAW>2010%Sum of “precision” and “accuracy”b5%WMO [1995]
WCC-EMPA≤20(2.1 ppbv + 3%)Sufficient agreement(1.05 ppbv + 1.5%)Hofer et al. [2000]
WCC-EMPA>20(1.3 ppbv + 7%)Sufficient agreement(0.65 ppbv + 3.5%)Hofer et al. [2000]
WCC-EMPA≤20(1.8 ppbv + 2%)Good agreement(0.9 ppbv + 1%)Hofer et al. [2000]
WCC-EMPA>20(1.4 ppbv + 4%)Good agreement(0.7 ppbv + 2%)Hofer et al. [2000]
NIST≤1002 ppbvAt T = 273.15 K and P = 101.3 kPa1 ppbvPaur et al. [1998]
NIST>100–10002%At T = 273.15 K and P = 101.3 kPa1%Paur et al. [1998]

[5] The objectives of this paper are (1) to document the traceability chain for surface ozone measurements performed within the GAW, (2) to calculate the uncertainty of surface ozone measurements, (3) to assess the conformity of surface ozone measurements performed at selected global stations with defined data quality objectives (DQOs, Table 1), and (4) to demonstrate the benefits for data quality of repeated audits.

2. Methodology

2.1. Traceability Chain for Surface Ozone Measurements Within GAW

[6] Assessments of surface ozone measurements involve the evaluation of measurements by the respective ozone analyzer (OA) of given ozone concentrations. Such measurements require an intercomparison of the OA with a standard instrument. Shipment of monitoring instruments to and from a central calibration laboratory is impractical because it introduces the possibility of changes or even damage to the analyzer and unduly interrupts the monitoring effort. Hence a traveling (or transfer) standard (TS) with an internal ozone generator is used for intercomparison of the OA on-site (Figure 1). The TS is compared against SRP 15 immediately before and after each intercomparison. These three intercomparisons define the scope of a so-called “performance audit.” SRP 15, in turn, is periodically compared to SRP 2 and our back-up instrument SRP 23. The OAs operated at the various sites are thus linked to SRP 2 through a series of intercomparisons.

Figure 1.

Traceability chain for surface ozone measurements within the Global Atmosphere Watch network, indicating (a) the various steps involved and the scope of a performance audit at the station and (b) the uncertainties in the various measurements/intercomparisons. SRP: standard reference photometer, TS: transfer standard, OA: ozone analyzer.

2.2. Bias of the Ozone Analyzer

[7] A suitable mathematical model for the traceability chain consists of a series of linear regressions:

equation image

where aOA and bOA are the coefficients of the linear regression of the intercomparison data, and the symbols in brackets represent the readings of the instrument,

equation image

where equation imageTS and equation imageTS are the coefficients of the linear regression of the combined data set of the intercomparisons before and after the audit.

[8] The coefficients equation imageTS and equation imageTS will normally be very close to zero and one, respectively, because the TS is calibrated against SRP 15 before each audit and exhibits only a small drift. Equation (3) states the requirement that all SRPs must give equal readings that correspond to our best estimate of the ozone concentration, C, within uncertainty limits.

equation image

The bias of an OA with respect to the SRP at the time of the intercomparison can thus be compensated by correcting the readings of the OA,

equation image

where C is the ozone concentration on the SRP scale. Regular intercomparisons ensure that potential instrument drifts can be detected and taken into account in the final data treatment.

2.3. Uncertainty of the Ozone Analyzer

[9] The uncertainty of ambient ozone measurements made with the OA is obtained by combining the uncertainties of all elements in the traceability chain. It is worth pointing out that the uncertainty of a measurement should be understood as the uncertainty about the correctness of the stated result after appropriate corrections of all known or suspected components of error have been applied [International Organization for Standardization (ISO), 1995]. It is obvious that the compensation of these systematic effects is imperfect and the uncompensated bias contributes to the uncertainty of the measurement. The uncertainty of a measured quantity can be evaluated either by the statistical analysis of a series of observations (type A) or by other means (type B) [ISO, 1995]. Type B evaluation of uncertainty typically requires professional judgment and/or a priori assumptions on the distribution of values, or obtaining standard uncertainties in any manner from standard certificates or reference books. Both types of evaluation are based on probability distributions and the derived uncertainties are quantified by variances s2 or standard deviations s. The combined standard uncertainty, u, is the estimated standard deviation of a measurement result that has been obtained from the values of a number of other input quantities. The combined standard uncertainty is equal to the positive square root of the combined variance of all variance and covariance components. The combined uncertainty of ozone measurements by the OA is obtained by applying the general Gaussian law of error propagation to equation (4),

equation image

[10] The covariance terms, cov(i, j), describe the interdependence of the regression slope and intercept, respectively. They are always negative and may be ignored if overestimating the combined uncertainty is considered acceptable. Equation (5) then reduces to the first sum and yields explicitly, after simple algebraic transformations

equation image

[11] Thus the squared standard uncertainty of compensated readings of an ozone analyzer may be expressed as the sum of an instrument-specific uncertainty, uOA, as well as contributions due to the regression analyses involved. To correctly estimate the standard uncertainties of these regression parameters, the individual uncertainties of the OA, the TS and the SRP must be considered in the regression analyses. In the following, the uncertainties of the SRP and the TS are evaluated and assessment criteria for the TS are developed. Further, uncertainty components of a range of widely used OAs are given and OA-TS intercomparisons conducted at global GAW stations are discussed. Finally, equation (6) is written in a way that can be directly applied for the assessment of individual instruments (compare section 3.4). A worked example detailing all steps involved in the evaluation of audit results is given in the supporting material.

[12] In this paper, whenever expanded uncertainties U are reported, they were calculated by multiplying the combined standard uncertainties with a coverage factor k = 2 (equation (7)). In the case of normally distributed values and for combined standard uncertainties that are obtained solely by type A evaluation with sufficient degrees of freedom, these expanded uncertainties cover approximately 95% confidence intervals.

equation image

2.4. Model of the Measurement Process

[13] Within the GAW surface ozone monitoring network, the recommended measurement method is based on the absorption of ultraviolet light at 254 nm (Hg line) by ozone molecules [World Meteorological Organization (WMO), 2002], and all instruments in the traceability chain described above exploit this physical principle. The mathematical model relating the observed transmittance τ = l/l0 to the ozone density ρO3 (molecule cm−3) in the cell is known as the Lambert-Beer law,

equation image

where I and I0 are the intensities of light transmitted to a suitable detector through a cell of length L in the presence and absence of ozone, respectively, and σ = 1.147E-17 cm2 molecule−1 [DeMore et al., 1994] is the absorption cross-section at 254 nm. The molar absorption coefficient at standard temperature (T0 = 273.15 K) is defined as

equation image

where k is the Boltzmann constant. For convenience, ρO3 of ambient air is usually expressed as a mixing ratio C with units of ppbv (parts-per-billion by volume). Using the ideal gas law, ρO3 = pO3/kT, and dividing the ozone partial pressure pO3 by the total pressure P in the cell, we obtain

equation image

[14] The relative standard uncertainty of ozone measurements based on equation (10) can be estimated by applying the law of error propagation, allowing for a contribution ε due to imperfect realization of the measurement principle. Thus, assuming that correlations between input quantities are negligible,

equation image

[15] Equation (11) states that the squared relative uncertainty in the concentration C is essentially the sum of the squared relative uncertainties of the right-hand-side terms of equation (10). As stated above, all instruments within the GAW surface ozone network are based on Lambert-Beer's law and use the same value for the molecular absorption coefficient of ozone. It therefore makes sense to treat the molecular absorption coefficient as a “defined” value (with zero uncertainty) and to refer all measurements to this value of the molecular absorption coefficient. Equation (11) then simplifies to equation (12).

equation image

[16] For the limiting case of zero ozone concentration (τ = 1), the standard uncertainty uC under repeatability conditions is proportional to uτ (equation (13)).

equation image

[17] In the concentration range relevant for ambient air monitoring, the transmittance τ remains close to unity and equation (12) can be approximated as follows:

equation image

2.5. Other Sources of Uncertainty

[18] It is important to realize that our analysis covers the uncertainty of surface ozone measurements under the assumption of negligible ozone loss in the sampling and transfer lines. Within GAW, this assumption is verified during the so-called “system audit” of a station. In general, ozone loss in the sampling and transfer lines can be avoided or at least reduced by proper design (to minimize the residence time) and choice of materials, as well as regular maintenance of the air intake system. Experience from the Swiss National Air Pollution Network (NABEL) shows that losses of less than 0.3% can be achieved [Nationales Beobachtungsnetz für Luftfremdstoffe (NABEL), 2000] while a European assessment of NO, NO2 and SO2 found losses of 5% for NO2 and up to 27% for SO2 [Payrissat et al., 1997]. It is important to realize that the reasons for loss in the sampling system vary for different compounds and the values given here may not be directly applicable to ozone.

3. Results and Discussion

3.1. Uncertainty of the Standard Reference Photometer (SRP)

[19] Table 2 gives values for the components in equation (11) as derived from Paur et al. [1998] as well as the contribution of these components to the combined standard uncertainty (repeatability) of the SRP. It is apparent that, at low concentrations, the combined uncertainty of the SRP is dominated by the uncertainty in the transmission measurement (equation (13)). At higher concentrations, the uncertainty of the molecular absorption coefficient dominates by far (not shown).

Table 2. Nominal Parameter Values and Their Estimated Standard Uncertainties for the NIST SRP Realization of Equation (10)
ParameterValueUncertainty StatementaDistribution AssumedCalculation PerformedStandard Uncertainty uContribution to uSRPb
  • a

    Reference, Paur et al. [1998].

  • b

    uSRP is the combined standard uncertainty of the SRP at τ = 0.9995.

  • c

    Representative values.

  • d

    Optical path length of SRP.

  • e

    Corresponding to about 10 ppbv ozone.

  • f

    This work (see text).

α, cm−1 atm−1308.321%Rectangularequation image1.78 cm−1 atm−10.057 ppbv
P, atm1.000cinaccuracy 0.05% full scale, repeatability 0.01% full scaleRectangularequation image0.00031 atm0.0030 ppbv
T, K298.15cinaccuracy 0.2% of reading (in °C) ±0.1°C, repeatability 0.05 KRectangularequation image0.082 K0.0027 ppbv
L, cm179c,d0.05 cm per cellRectangularequation image0.041 cm0.0023 ppbv
τ, -0.9995eExpanded uncertainty 0.000017 (k = 2)Normal0.000017/2 –0.0000085 0.000018f0.168 ppbv 0.350 ppbvf

[20] The SRP reports with each reading a standard deviation derived from n (typically 10–20) successive transmittance measurements. Under conditions of zero ozone (“zero air”), the calculated combined standard uncertainty is independent of the uncertainty in the values of P, T and L (equation (13)) and the values themselves can be assumed to remain constant during the short period of time necessary to obtain an SRP reading (repeatability conditions). Therefore the standard deviation reported by the SRP is an indirect measure of the uncertainty in the transmission measurement, uτ. These standard deviations are likely to be χ2-distributed (with a heavier tail toward larger values in comparison to the normal distribution), and the mean is an efficient estimator for the expected value. Figure 2 shows the distribution of the standard deviation reported by a number of SRPs under zero-air conditions. The mean standard deviation, equivalent to the combined standard uncertainty of the SRP at zero ozone was computed as uSRP(C = 0) = 0.35 ± 0.13 ppbv (μ ± σ, N = 432). Using equation (13), the value for the standard uncertainty of the transmission measurement computed from these data is uτ = 0.000018 ± 0.000006 (μ ± σ) which is about a factor of 2 larger than the value reported by Paur et al. [1998] (uτ = 0.0000085, compare Table 2).

Figure 2.

Box plot with marginal histogram of standard deviations of SRP readings under zero-air conditions. The boxes are limited by the first and third quartile with the median in between. The whiskers represent the largest and smallest observed data points that are within 1.5 box lengths from the end of the box. Extreme values are indicated by open circles. The data were collected with SRPs 0, 2, 14, 15, 17, 18, and 23 between 1994 and 2001. The mean standard deviation was 0.35 ppbv, and the median was 0.33 ppbv (N = 432). The widths of the boxes are proportional to the square-root of the individual number of data points used, which is given in parentheses.

[21] For practical purposes, the uncertainty in the transmittance measurement is assumed to be independent of the ozone concentration and the contributions of the uncertainties in L, P, and T to the combined standard uncertainty of the SRP can be lumped into one term. With the values reported by Paur et al. [1998] and the value for uτ derived above, and neglecting ε for the moment, equation (14) can be parameterized to give the combined standard uncertainty of the SRP,

equation image

[22] In Figure 3, the calculated combined standard and expanded uncertainty are compared with the standard deviations reported by a number of SRPs over the course of several years. At higher concentrations, the reported standard deviations tend to be smaller than the calculated combined standard uncertainty. This is expected because the uncertainties in L, P and T, which are not related to repeatability, are not reflected in the standard deviations reported by the SRP.

Figure 3.

Standard deviations reported by SRPs 0, 2, 14, 15, 17, 18, and 23 between 1994 and 2002 (circles) and calculated combined uncertainty of the SRP according to equation (15) (solid line, lower: k = 1, upper: k = 2; see text for discussion).

[23] Equation (15) states the combined standard uncertainty of a single SRP as a function of concentration and must also encompass differences between SRPs that are due to imperfect realization of equation (8). Systematic or random differences between SRPs (but not systematic errors of the SRP as such) can be evaluated with SRP-SRP intercomparisons. Two SRPs independently measuring a given ozone concentration produced by one and the same ozone source are expected to produce, on average, readings that are equal within the root-sum-of-squares of the standard uncertainties of the individual instrument in 67% of all cases (1σ). According to equation (15), the (standard) difference between two SRPs measuring zero-air should not exceed ΔSRP,SRP = equation image × 0.35 ppbv = 0.49 ppbv (1 σ). Figure 4 shows box plots based on data of all SRP-SRP intercomparisons available to us to date. It is apparent that the observed differences between any two SRPs under zero-air conditions are within the stated limit.

Figure 4.

Box plots of SRP-SRP intercomparisons displaying the difference (in ppbv) between guest and host instrument under zero-air conditions. In all cases, the ozone source of the designated host instrument (right number) served also the guest instrument (left number). The allowed standard difference between two un-correlated SRPs is also shown (dotted line). The widths of the boxes are proportional to the square-root of the individual number of data points used, which is given in parentheses.

[24] Two SRPs must also agree to within the limits of uncertainty over the relevant concentration range. Figure 5 shows intercept versus slope of linear regression analyses of SRP-SRP intercomparisons over the range 0–250 ppbv. For these analyses, uncertainties (taken to be the standard deviation for each data point as reported by the SRP) for both SRPs were considered [Press et al., 1995]. The rhomboids displayed in Figure 5 enclose the range of slope-intercept combinations for which the standard difference between two SRPs (in the range 0–250 ppbv ozone) is less than the combined standard uncertainty of two uncorrelated SRPs (i.e., equation imageuSRP(C); compare equation (15)). Of 19 intercomparisons evaluated for this range and displayed in Figure 5, only 7 (37%) are covered by the rhomboid. With a coverage factor of k = 2, this number becomes 14 (74%), which is still well below the expected 95%. It is apparent that the range of slopes is less well captured than the range of intercepts. Notably, the values obtained for the intercomparisons between SRP 15 and SRPs 2, 14, and 23 are clustered, indicating a time-invariant, systematic difference between them. For example, SRP 15 that served as the common point of reference in these intercomparisons has been reading consistently lower than SRP 2 by about 0.17% over the course of several years. Experiments in our laboratory involving SRP 15 and SRP 23 have indicated that part of the observed difference may be attributed to slightly different realization of the various instruments. It is conceivable, although unfortunate, that such differences might lead to small systematic differences between the SRPs. Nevertheless, none of the SRPs can be considered more “correct” than any other; it is only by designation that SRP 2 is the world reference within the GAW program. A statement of the combined uncertainty of the SRP must therefore cover the (systematic or random) difference between them for the majority of intercomparisons. It thus appears that equation (15) with ε = 0 slightly underestimates the combined standard uncertainty of a single SRP at higher ozone levels. To better capture the observed differences, ε2 in equation (14) was (arbitrarily) set so that

equation image
Figure 5.

Plot of intercept versus slope for SRP-SRP intercomparisons conducted between 1993 and 2002 and evaluated from 0 to 250 ppbv. SRP 15 was host in all cases except in the intercomparison with SRP 2, where it was still considered to be the “independent” instrument for the regression analyses. Standard deviations in the readings of both SRPs were considered. Error bars are estimated standard errors of the regression parameters. The rhomboids displayed cover the range of slope-intercept combinations for which the difference of any two SRPs is smaller than the combined uncertainty of two uncorrelated instruments according to equation (15) (dashed line) and equation (16) (solid line) for a coverage factor of k = 1 (67%, inner rhomboid) and k = 2 (95%, outer rhomboid).

[25] The rhomboid calculated for equation (16) and a coverage factor of k = 2 covers 18 of the 19 cases (≈95%). In conclusion, equation (16) appears to adequately describe the standard uncertainty of the SRP.

3.2. Uncertainty of the Transfer Standard (TS)

[26] The transfer standard used by WCC-EMPA is a TEI49C-PS primary standard photometric analyzer with built-in ozone source (Thermo Environmental Instruments, Franklin, Massachusetts). In contrast to the SRP, the TS can be calibrated and the readings produced depend upon the chosen values of the adjustable parameters “background correction” (intercept) and “span coefficient” (slope). The instrument operates according to the same principle as the SRP and, in principle, equation (12) could be used to assess its combined standard uncertainty. The specifications of this instrument (Table 3) do not permit such an evaluation because the standard uncertainties for the individual parameters are not available. Instead, manufacturer specifications given in Table 3 were compared to experimentally derived quantities obtained with the TS under repeatability conditions. In addition, the month-to-month uncertainty (drift) was evaluated on the basis of TS-SRP intercomparisons.

Table 3. Specifications of the TEI 49C Primary Standard
Uncertainty StatementaInterpretationDistribution Assumed
Photometer
Zero noise 0.5 ppb RMSuzero = 0.5 ppbvNormal (k = 2)
Precision 1 ppbbuspan = equation image ppbvNormal (k = 2)
Linearity ±1% full-scaleulinearity = equation image with Cmax = 200 ppbvcRectangular
 
Ozonator
Stability ±4 ppb or ±1% of reading, whichever is greaterNot usedn/a

[27] Figure 6 shows box plots of the uncertainty contributions relevant under repeatability conditions. The uncertainty of the transmission measurement is characterized by the distribution of the standard deviations of the TS, i.e., by short-term variations of the instrument. No dependence of the standard deviations on ozone concentration was evident in the data, therefore the zero and span readings (obtained from 10–20 thirty-second values) were pooled, giving a mean of unoise = 0.21 ± 0.09 ppbv (μ ± σ, N = 807). The uncertainty associated to linearity of the instrument, ulinearity = 0.21 ppbv (N = 807), was calculated as the standard deviation of the TS-SRP regression residuals, noting that no dependence of the residuals on ozone concentration was evident in the data. The combination of these uncertainty components yields a combined uncertainty (repeatability) of

equation image
Figure 6.

Box plots of the components contributing to the combined uncertainty of the transfer standard (TS) under repeatability conditions. The data were collected during intercomparisons of the TS with SRP 15 between 1996 and 2002 and were evaluated from 0 to 200 ppbv. The widths of the boxes are proportional to the square-root of the number of available data points, which is given in parentheses.

[28] The uncertainty obtained with the values given in Table 3 is considerably larger (1.26 ppbv). Note, however, that the TS is operated in a much narrower temperature and pressure range than allowed by the manufacturer. In the absence of other information, one has to assume that the uncertainty calculated from manufacturer specifications covers systematic effects due to imperfect calibration (bias) that are not included in equation (17).

[29] The TS is intercompared with the SRP before and after the OA-TS intercomparison at the station (compare Figure 1). Figure 7 shows the differences in intercept and slope, respectively, of regression lines obtained before and after the audit for 23 audits conducted between 1996 and 2002. The changes observed characterize the long-term uncertainty (month-to-month drift) of the TS, notably under often harsh conditions during transport. These uncertainties were estimated as the standard deviation of the differences in intercept and slope, uTS,drift.zero = 0.30 ppbv (N = 23) and uTS,drift.span = 0.0034 (N = 23), respectively. On the 95% confidence level, this translates into a maximum acceptable drift of the TS during a particular audit of ΔZEROTS = 0.61 ppbv and ΔSPANTS = 0.67%. To the extent that the observed drift is a good estimator of the average drift, the combined standard uncertainty of the TS due to drift is conservatively estimated by

equation image

The combined standard uncertainty of the TS considering both repeatability and drift is given by the combination of equations (17) and (18)

equation image

In a conservative assessment of the uncertainty of the audited ozone analyzer, equation (19) should be used to reflect the uncertainty of the TS.

Figure 7.

Plot of the differences in intercept versus the difference in slope for TS-SRP intercomparisons evaluated from 0 to 200 ppbv before and after station audits. Data points near the origin (0, 0) indicate that similar regression lines were obtained before and after the audit. SRP 15 was host in all cases and was considered to be the “independent” instrument for the regression analyses. Standard deviations in the readings of both instruments were considered. Error bars (1 σ) were calculated from estimated standard deviations of the regression parameters. The standard deviation of the differences in intercept was 0.30 ppbv, and the standard deviation of the differences in slope was 0.0034 (N = 23). The ellipse indicates the maximum acceptable drift criterion on the 95% confidence level (k = 2).

3.3. Assessment of the Transfer Standard (TS)

[30] The TS-SRP 15 intercomparison conducted prior to every audit of an ozone analyzer (OA) can be evaluated with a linear regression analysis, considering the uncertainties in the readings of both instruments, to obtain the parameters of equation (2) [Press et al., 1995]. The relevant weights for the SRP data are given by equation (16) and the empirical standard deviations obtained at each ozone level for the TS, respectively. The instrument must be re-calibrated by WCC-EMPA before use as TS if the following conditions are true:

equation image
equation image

where image and image are the estimated standard uncertainties of the intercept and slope, respectively. On the basis of 38 TS-SRP intercomparisons, image = 0.18 ± 0.02 ppbv (μ ± σ, N = 38), and image = 0.0011 ± 0.0002 (μ ± σ, N = 38). Equations (20a) and (20b) translate into a maximum acceptable zero-offset of 0.36 ppbv and a maximum acceptable span-offset of 0.21%. These conditions correspond to deviations of the regression line from the ideal 1:1 line that are significant on the 95% confidence level. The maximum difference allowed between TS and SRP in the intercomparison after an audit is given by the combination of equations (16) and (19) and applying a coverage factor of k = 2,

equation image

If the difference between TS and SRP after the audit exceeds these limits, the reason should be evaluated and the audit considered unsuccessful.

3.4. Bias of the Ozone Analyzer (OA)

[31] A bias of the OA at the time of the audit can be evaluated by regression analysis of the data obtained during the OA-TS intercomparison. Long-term drift of the OA cannot be assessed during a single intercomparison. The relevant weights for the regression analysis are the empirical standard deviations of the OA and uTS as given by equation (19) for the TS. The bias of the OA (with respect to the SRP) is statistically significant on the 95% confidence level if the following limits are exceeded:

equation image
equation image

[32] The bias of the OA with respect to the SRP thus obtained should be compensated using equation (4). As stated earlier, it is not recommended to include a known bias in the uncertainty statement and to report uncompensated results [ISO, 1995]. Because of possible instrument drift, however, the bias may not necessarily be time-invariant and compensated results will have to be considered provisional until confirmed by subsequent audits.

[33] The maximum allowed bias of the OA is given by the data quality objectives shown in Table 1. The audit only tests compliance of the OA at the time of the intercomparison as drift cannot be properly assessed. Table S3 of the supporting material lists the summary statistics of OA-TS intercomparisons conducted during field audits during 1996–2002. Figure 8 displays the slopes and intercepts obtained. In those cases where multiple instruments were operated at a particular site, only the data for the main OA were used. The rhomboids shown are for “sufficient” and “good” agreement, respectively, according to WCC-EMPA recommendations (Table 1) [Hofer et al., 2000]. Of the 26 intercomparisons performed on the primary station OAs, 17 (65%) are covered by the standard uncertainty rhomboid and 23 (88%) by the expanded uncertainty rhomboid calculated for “good” agreement, while for “sufficient” agreement, the corresponding numbers were 20 (77%) and 24 (89%). In two cases, the instrument did not meet either quality criterion.

Figure 8.

Slope/intercept combinations obtained for intercomparisons of ozone analyzers (OA) and WCC-EMPA transfer standard (TS) evaluated between 0 and 100 ppbv ozone (open squares: 5 < C < 100 ppbv). Error bars are estimated standard deviations of the regression parameters. For stations operating multiple instruments, only the main instrument was considered. The rhomboids displayed cover the maximum bias for which the OA meets the assessment criteria given in Table 1 for “sufficient” agreement (dashed line) and “good” agreement (solid line) for a coverage factor of k = 1 (67%, inner rhomboid) and k = 2 (95%, outer rhomboid).

[34] The improvements in reducing bias as a result of repeated audits at a station are further demonstrated by Figure 9. The metric used here is the mean absolute bias of the OA with respect to the TS, calculated as the standardized area between the regression line of the OA-TS intercomparison and the ideal 1:1 line. In many cases where two or more audits can be compared, an improvement in the mean bias was found for the second or third such audit.

Figure 9.

Mean absolute bias of OA, calculated as the absolute area between regression line and the ideal 1:1 line divided by the maximum concentration in the range considered (0–100 ppbv, except for the asterisk: 5 < C < 100 ppbv) for 26 OA-TS intercomparisons conducted between 1996 and 2002. Empty squares indicate that only a single audit of a particular station was performed up to 2002. The lines connect data that were obtained at a particular station during consecutive audits.

3.5. Uncertainty of the Ozone Analyzer (OA)

[35] Table S1 in the supporting material gives the specifications and calculated uncertainty components for some ozone analyzers that are used at global GAW stations. Similar to the TS, the total combined uncertainty of the OA may be expressed as the sum of a repeatability and a drift component,

equation image

[36] An estimate for the combined uncertainty of the OA under repeatability conditions is obtained by conservative combination of the pooled components zero, and span (labeled “noise”), and linearity.

equation image

[37] Figure S1 in the supporting material shows box plots of the empirical standard deviations of ozone readings obtained during audits at the sites. In general, the values found were not significantly dependent on concentration (not shown). Therefore unoise was calculated as the mean of the standard deviations of OA readings and ulinearity was calculated as the standard deviation of the regression residuals from OA-TS intercomparisons. Table 4 lists empirical values for the individual uncertainty components and states the average uncertainty of the various instrument types under repeatability conditions. For a particular instrument, the same approach applies but the actual numbers may be different. It is apparent from both Figure S1 and Table 4 that some instrument types were more stable than others. Table S2 in the supporting material gives more details on the variability among the individual instruments. The manufacturers' specifications were never exceeded.

Table 4. Combined Standard Uncertainty of Some Ozone Analyzers in Use at Global GAW Stations
Instrumentunoise, ppbvulinearity, ppbvuOA,repeatability, ppbvuOA,drift, ppbv CalculatedauOA, ppbv Calculatedb
EmpiricalCalculateda
  • a

    Using “precision” and “linearity” as specified in Table S1.

  • b

    Using the empirical uncertainty for the repeatability and the calculated uncertainty for the drift component. The main instrument was considered for stations that operate multiple instruments. The number of data points is given in parentheses.

API 400A0.21 ± 0.05 (21)0.14 (21)0.250.64equation imageequation image
Dasibi 10080.25 ± 0.12 (21)0.17 (21)0.300.76equation imageequation image
ML 88101.04 ± 0.61 (84)1.03 (84)1.462.08equation imageequation image
TEI 490.38 ± 0.22 (238)0.23 (238)0.441.15equation imageequation image
TEI 49C0.22 ± 0.10 (175)0.20 (175)0.300.76equation imageequation image

[38] The combined uncertainty due to instrument drift can be defined as

equation image

where uOA,drift.zero refers to the uncertainty due to the zero-drift and uOA,drift.span refers to the uncertainty due to the span-drift of the OA. In the absence of empirical data, manufacturer specifications usually define maximum (“worst case”) values for these parameters.

[39] Table 4 also gives the combined uncertainty obtained by combining the uncertainty components of empirical repeatability with the calculated drift according to equation (25).

[40] Equation (6) describes the combined uncertainty of the OA remaining after compensation of systematic effects (bias). For a well-calibrated TS, this equation can be simplified by considering equation imageTS ≈ 1 and equation imageTS ≈ 0 ppbv. The uncertainty in these parameters for the audits discussed here was equation image = 0.0010 ± 0.0000 (μ ± σ, N = 23) and equation image = 0.14 ± 0.02 ppbv (μ ± σ, N = 23). Considering equations (23) and (25), the uncertainty of ozone measurements obtained with the OA during normal operation (i.e., when the OA is used to measure ambient ozone concentrations) can then be expressed as

equation image

[41] If the parameters uOA,drift.zero and uOA,drift.span that describe instrument drift are not known for a particular instrument from experience, manufacturers' specifications may have to be used. On the basis of these specifications and the results of the individual OA-TS intercomparisons, the uncertainties shown in Figure 10 were calculated. It is apparent that the Monitor Labs instruments exhibited significantly larger standard uncertainties. The smallest uncertainties were obtained for the TEI49C instruments. Figure S2 in the supporting material demonstrates that the instrument drift that was derived from manufacturers' specifications can represent a substantial contribution to the standard uncertainty (as much as 50%) calculated here, however, the overall picture remains unchanged.

Figure 10.

Lower (for C = 0 ppbv) and upper (for C = 100 ppbv) limits of the combined standard uncertainty of surface ozone measurements at selected GAW stations. Multiple lines indicate results of consecutive audits. The values were estimated using equation (26) and reflect the standard uncertainty (k = 1) of the readings that cannot be compensated, using manufacturer specification for instrument drift. Data for MAC and NYA (top bar) are both for ML8810 instruments, and the data for NYA (lower bar) are for the API400A instrument.

4. Summary and Conclusions

[42] The performance of ozone analyzers (OA) at GAW sites can be characterized by stating a bias with respect to the Standard Reference Photometer 2 (SRP 2) and a measurement uncertainty. The bias of the OA is estimated by intercomparison with the transfer standard (TS) of the GAW World Calibration Centre (WCC) at EMPA that is itself frequently calibrated against SRP 15 to eliminate any bias. Regular intercomparison between SRP 15 and SRP 2 provides the link between the OA and the designated world reference (SRP 2). The model for this traceability chain is a series of linear regressions for which uncertainties both in the dependent and the independent variable are taken into account. As all SRPs are considered equivalent, the slight, time-invariant, difference between SRPs observed in the past is incorporated in the uncertainty of the SRP (equation (16)). The uncertainty of the TS is composed of a repeatability and a drift component. For the evaluation of TS-SRP intercomparisons, the uncertainty of the TS may be expressed by the empirical standard deviations. For the evaluation of OA-TS intercomparisons, the uncertainty of the TS includes both the repeatability and the drift component (equation (19)). The uncertainty of the OA is itself composed of a repeatability and a drift component. For the analysis of OA-TS intercomparisons, the uncertainty of the OA may be expressed by the empirical standard deviations. The bias of the OA with respect to the SRP (equation (4)) can and, according to ISO [1995], should be compensated before data submission. The uncertainty that is attached to corrected data and that cannot be compensated is due to the inherent uncertainty of the OA as well as the added uncertainty due to the use of a TS and may be estimated using equation (25). The supporting material contains a step-by-step example illustrating the necessary calculations.

[43] Intercomparisons of OA and TS at a number of GAW sites have been performed about every two years since 1996. Apart from improvements in good measurement practice, data availability and awareness of data quality issues, the quantitative benefit of repeated audits has been demonstrated as generally decreasing bias with time (Figure 9). The associated standard uncertainty of appropriately compensated OA readings is, however, mostly a function of instrument type (Figure 10).

[44] GAW observations are used to assess the spatial and temporal surface ozone variability. Our results indicate that the mean absolute bias of ozone analyzers currently in use at global GAW stations can be reduced to the level of the standard uncertainty of these instruments. Both the remaining bias as well as the standard measurement uncertainty of a well-maintained instrument are smaller than the typical (natural) variations in the ambient ozone concentration at “background” monitoring sites and therefore do not control the variance of (e.g., monthly) means calculated from the data. In other words, the number of data points used to identify a statistically significant trend is not controlled by the standard measurement uncertainties as calculated here. However, a change in the bias with time that goes unnoticed and hence cannot be compensated, may mask a real trend or, alternatively, may suggest a trend that is not there. Regular intercomparisons are therefore needed to ensure that instruments remain in calibration, i.e., produce readings that are unbiased or whose bias is known and can be compensated.

[OA]

readings obtained from an ozone analyzer.

[TS]

readings obtained from the transfer standard.

[SRP 15]

readings obtained from SRP 15.

aOA

intercept from linear regression of ([OA], [TS]) data pairs.

bOA

slope from linear regression of ([OA], [TS]) data pairs.

equation imageTS

intercept from linear regression of pooled ([TS], [SRP#15]) data pairs obtained before and after an audit.

equation imageTS

slope from linear regression of pooled ([TS], [SRP#15]) data pairs obtained before and after an audit.

C

unbiased ozone concentration (usually given in ppbv).

ux

standard uncertainty of x.

Ux

expanded uncertainty of x (using a coverage factor k = 2).

τ

transmittance at 254 nm (Hg line), equal to l/l0.

P

total pressure in absorption cell.

T

absolute temperature of gas in absorption cell.

α

molar extinction coefficient of ozone at standard temperature and pressure.

ΔZEROTS

maximum acceptable zero drift of the TS during an audit, ppbv.

ΔSPANTS

maximum acceptable span drift of the TS during an audit, ppbv.

ε

uncertainty due to imperfect realization of the measuring principle.

Acknowledgments

[45] This work was partially funded by MeteoSwiss. We would like to thank Erwin Hack for helpful discussions and Volker A. Mohnen, Christoph Hüglin, Samuel Müller and two anonymous referees for carefully reviewing the manuscript and for their thoughtful comments.

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