Introduction

One of the primary responsibilities of the CCL is to disseminate the WMO scales consistently over time and with small enough uncertainty to prevent significant biases from developing between various monitoring sites and programs. Scale transfer uncertainty relates solely to how well an individual tertiary standard measurement and its subsequent value assignment is related to the defined scale. It is the relevant measure of uncertainty to use when propagating uncertainties of standards to atmospheric measurements and comparing to other measurements traceable to the same scale. It is generally not the same as the SI traceable uncertainty, which is relevant when comparing measurements traceable to different scales. One exception to this is carbon monoxide (CO) where due to the complexity of maintaining the CO scale at the CCL, there is no distinction between the SI and scale transfer uncertainties.

Historically, the CCL provided rough guidance on its ability to disseminate the scales (via calibrated whole air standards). This was done as a general analytical reproducibility term based on the results from many cylinders over long time periods rather than as values specific to any individual cylinder. This type of guidance was important for the community when trying to put general limits on the ability to distinguish small spatial gradients in the atmosphere. Going forward, the CCL will now provide scale transfer uncertainty calculated for each individual tertiary standard measurement episode.

The calculated uncertainty of an individual episode is, in general, higher than the blanket estimates. However, the magnitude of the change is unlikely to influence interpretation of atmospheric data in most cases. The advantage of the new procedure is that it gives a more representative uncertainty estimate for individual measurement episodes and responds to changes in analytical performance over time.

Calibration episode uncertainty

We define the uncertainty of a calibration episode relative to the scale (u_episode) as the combined standard uncertainty of three terms

The first component (u_meas), referred to as "measurement uncertainty", is calculated using the short-term analytical repeatability observed within the measurement episode and the uncertainty of the calibration curve used to convert instrument response to mole fraction. The calibration curve uncertainty is taken as the predictive interval of the ODR fit and incorporates the uncertainty, relative to the scale, of the value assignment of higher level standards (typically secondary standards) along with the analytical performance during the calibration episode. Measurement uncertainty responds to analytical performance over short time scales (days to weeks) and to longer term issues related to the ability to consistently value assign the higher level standards. We store measurement uncertainty with the calibration results in the database and it serves as a useful diagnostic of analytical performance.

Long term reproducibility (u_{reproducibility}) is a familiar term for CCL users. This term was historically used as general guidance on the ability to propagate the scale over time. The CCL defines reproducibility by accessing the long term consistency of repeated measurements of suites of quality control cylinders. The values are constant across longer time periods (multiple years) and across instruments using similar analytical techniques. Reproducibility values are stored in a lookup table and are paired with measurement results when extracting results from the database.

Type B uncertainty terms (u_typeB) are not related to quantities measured during calibration episodes. Instead, they include uncertainties arising from other sources, such as known bias corrections. These are infrequently used for tank calibrations. Type B terms are stored in the same lookup table as the reproducibility values and are combined with measurement results on extraction from the database.

Certificates issued by the CCL

Certificates issued by the CCL conform to relevant ISO guidelines. For a given trace gas, the assigned value and expanded total uncertainty, including traceability to the SI, are reported. In addition, the CCL reports scale transfer uncertainty separately. This is the expected uncertainty of the calibration results relative to the defined scale.

Values reported on certificates are derived as the weighted average from multiple calibration episodes (typically 3), with weights based on the calibration episode uncertainties. Values reported on certificates are limited to the date range of the calibration request. For example, an initial order for a tertiary standard will result in a certificate based on a weighted mean of the initial calibration episodes. When that cylinder is returned for re-calibration, any additional certificate issued by the CCL would only include the measurement episodes corresponding to the re-calibration request.

Full calibration histories on website

To meet the needs of the atmospheric monitoring community, the CCL provides on its website further information beyond what is included on the certificates. On the website, the CCL reports all measurement results for a given filling of a cylinder. This would include initial calibrations and all re-calibrations requested by the user. We report each calibration episode mean along with the scale transfer uncertainty of the episode. Additional information including the standard deviation of the mean, the measurement uncertainty term, and reproducibility (combined with any additional TypeB terms and listed as TypeB), are available by downloading the associated json file. This information is provided to allow users to assess stability over time and value assign standards using protocols implemented within their own programs. Note, in cases where measurement uncertainty is not calculated (typically the older calibration systems) we use the standard deviation of the episode mean as a measure of the analytical repeatability and combine that with the other terms to calculate the episode uncertainty.

Drift assessment

As a convenience for the community, the CCL also provides an assessment of the stability of standards if they have been re-calibrated. The CCL provides access to the output of a data analysis software package (caldrift.py) developed by GML which the CCL and GML more broadly use to value assign standards. This code uses the full calibration history of a standard, with the associated scale transfer uncertainties of each episode, to assess the cylinder for stability and assign either a constant or a time dependent value to standard. Drift determination is made by comparing to a two-tailed t-distribution for the degrees of freedom at the 95% confidence interval. Value assignments are represented as a 2nd order polynomial. The code outputs include:

• Tzero - Time zero is the weighted mean date of the calibrations.
  
• Coef0 (unc_co) - coefficient 0 of a 2nd order polynomial fit (and uncertainty of the coefficient).
  
• Coef1 (unc_c1) - coefficient 1 of a 2nd order polynomial fit (and uncertainty of the coefficient). Equals 0 for stable cylinders.
  
• Coef2 (unc_c2) - coefficient 2 of a 2nd order polynomial fit (and uncertainty of the coefficient). Equals 0 for stable or linearly drifting cylinders.
  
• sd_resid - standard deviation of the residuals to the fit.

The weighted mean output of this software package is used by the CCL to value assign cylinders for the issuance of certificates for calibration requests. Output from this software package on the website to assess the stability of standards is informational with the hope that it helps users quantify potential drift. However, users are encouraged to also do their own assessments. Indications of non-linear drift should be evaluated carefully since the simple polynomial model displayed may not represent actual tank drift well.

The value and scale transfer uncertainty of the standard on date D_a (as a decimal year) are:

References

• JCGM 100:2008 Evaluation of Measurement Data - Guide to the Expression of Uncertainty in Measurement (ISO GUM 1995 with minor corrections), Joint Committee for Guides in Metrology (2008); https://doi.org/10.59161/JCGM100-2008E.

Additional details on the scale transfer uncertainty are documented here: scale_transfer_unc_details.pdf.