Sometimes uncertainties are not reported with the concentration measurements, usually when the data were submitted before the reporting of uncertainties became mandatory. In such cases, the uncertainties are estimated using fixed and relative standard deviations derived from the uncertainties that have been reported to the ICES data base (extraction date: 1 February 2021).
Suppose \(c\) is a concentration reported with missing uncertainty. Then the uncertainty \(u\) is estimated from:
\[u^2 = s^2 + v^2 c^2\]
where:
The reporting of uncertainties has been mandatory since the 2010 monitoring year. For earlier years, alternative quality assurance information is available which allows estimates of missing uncertainties to be inflated if there is evidence of poor analytical quality. Specifically, the relative error is multiplied by an ‘inflation factor’ \(f\) giving uncertainty estimates of the form:
\[u^2 = s^2 + f^2 v^2 c^2\]
The inflation factors are based on QUASIMEME Z-scores supplied to ICES on CD by analytical laboratories and Certified Reference Material (CRM) concentrations held in the ICES database. The CRM concentrations (for the relevant compartment, contaminant and year) are converted to Z-scores
\[Z_i = \frac {M_i-A_i} {0.125A_i}\]
where \(M_i\) are the measured concentrations and \(A_i\) are the certified reference values. These are then combined with the QUASIMEME Z-scores (for the compartment, contaminant and year) to give
\[f^2 = \frac {1} {n} \sum_i Z_i^2\]
where \(n\) is the total number of Z-scores. In practice, Z-scores that are large (possibly due to unit misreporting) can unduly influence the inflation factors, so are truncated at 3, leading to a maximum inflation factor of 3. The inflation factors are also truncated below at 1, since this corresponds to good analytical performance. If there is no quality assurance information (for the compartment, contaminant and year) the inflation factors are set to 3.
The inflation factors are only used for biota and sediment. They are set to 1 for water as QUASIMEME information was not collected for water measurements.
1 The detection limits reported to the ICES data base are sometimes unreliable. Basing \(s\) on one third of the detection limit (when reported) can therefore sometimes yield implausible uncertainties. To provide some robustness a more complicated procedure has evolved which involves the fixed standard deviation estimated from the uncertainties in the ICES data base, the detection limit, the quantification limit, the quality flag, and the measured concentration: