Method

This page describes the calculation method. The method is described in detail in the guidelines document .

Currently TUCAVOC can only be applied to online GC measurements, but in the future it is planned to extend it to other techniques.

If you want to use TUCAVOC for other techniques, please contact us.

Calculation of VOC amount fraction

Default method based on calibration

This method compares the peak area obtained during the calibration of the instrument/GC-FID - using reference gas mixtures of known amount fractions - to the sample (measurement) area to retrieve the correct amount fraction.

This is based on the assumption that the area in the chromatograms is linearly dependent on the amount fraction of the substance in the sample.

The calculation is based on the guidelines document:

Equation (1)

\[\chi _{\mathrm{sample}}=\frac{A_{\mathrm{sample}}-A_{\mathrm{blank}}}{V_{\mathrm{sample}}}*f_{\mathrm{calib}}\]

• \(\chi _{\mathrm{sample}}\): Amount fraction of a substance in a sample

• \(A_{\mathrm{sample}}\): Peak area of sample measurement

• \(A_{\mathrm{blank}}\): Possible blank area value determined in zero gas measurements

• \(V_{\mathrm{sample}}\): Volume of measured samples

• \(f_{\mathrm{calib}}\): Calibration Factor

With the calibration factor being

Equation (2)

\[f_{\mathrm{calib}}=\frac{V_{\mathrm{calib}}*\chi _{\mathrm{calib}}}{A_{\mathrm{calib}}-A_{\mathrm{blank}}}\]

• \(f_{\mathrm{calib}}\): Calibration Factor

• \(V_{\mathrm{calib}}\): Volume of calibration gas samples

• \(\chi _{\mathrm{calib}}\): Certified amount fraction of calibration gas

• \(A_{\mathrm{calib}}\): Peak area of calibration gas measurement

• \(A_{\mathrm{blank}}\): Possible blank area value determined in zero gas measurements

Method based on the effective carbon number (for GC-FID)

The effective carbon number concept (ECN) (Sternberg et al., 1962, Dietz et al., 1967) states that the response (peak area) of the FID is proportional to the number of molecules times the effective number of carbon atoms per analyte molecule. This holds for single hydrogen-carbon bonds. If other bonds in a specific molecule occurs, the response of the respective carbon atom is adjusted to yield an effective carbon number.

Equation (4)

\[\chi _{\mathrm{sample}}=\frac{A_{\mathrm{sample}}-A_{\mathrm{blank}}}{V_{\mathrm{sample}}*C_{\mathrm{num}}*y*\overline{C}_{\mathrm{resp}}}\]

• \(\chi _{\mathrm{sample}}\): Amount fraction of a substance in a sample

• \(A_{\mathrm{sample}}\): Peak area of sample measurement

• \(A_{\mathrm{blank}}\): Possible blank area value determined in zero gas measurements

• \(V_{\mathrm{sample}}\): Volume of measured samples

• \(C_{\mathrm{num}}\): Carbon number

• \(y\): ECN contribution

• \(\overline{C}_{\mathrm{resp}}\): Mean carbon response factor

The C-response factor \(C_{\mathrm{resp}}\) is derived for each substance from the measurement of the certified standard reference gas mixture. Using the ECN-concept, reliable calibration factors can also be estimated for substances not present in the calibration gas mixture. In this case, the amount fraction is calculated via the mean carbon-response factor \(\overline{C}_{\mathrm{resp}}\) , which is determined from selected substances in the standard gas measurements averaging the \(\overline{C}_{\mathrm{resp}}\) for those substances.

Equation (3)

\[C_{\mathrm{resp}}=\frac{A_{\mathrm{calib}}-A_{\mathrm{blank}}}{C_{\mathrm{num}}*y*V_{\mathrm{calib}}*\chi _{\mathrm{calib}}}=\frac{1}{C_{\mathrm{num}}*y*f_{\mathrm{calib}}}\]

• \(C_{\mathrm{resp}}\): Carbon Response Factor (CRF)

• \(A_{\mathrm{calib}}\): Peak area of calibration gas measurement

• \(A_{\mathrm{blank}}\): Possible blank area value determined in zero gas measurements

• \(C_{\mathrm{num}}\): Carbon number

• \(y\): ECN contribution

• \(V_{\mathrm{calib}}\): Volume of calibration gas samples

• \(\chi _{\mathrm{calib}}\): Certified amount fraction of calibration gas

• \(f_{\mathrm{calib}}\): Calibration Factor

Uncertainties

This section describes the sources of uncertainty considered by TUCAVOC to calculate the overall uncertainty of the measurements. The main uncertainties taken into account are associated with the reproducibility of the measurement, calibration procedure, sampling method and analytical system used.

Combined Standard Uncertainty of the measurement

The combination of all the standard uncertainties associated with the input quantities in the measurement model (VIM (BIPM)). Also called overall uncertainty.

The combined uncertainty, or overall uncertainty, is calculated using the law of propagation of the uncertainties (considering that the standard uncertainties are not correlated) according to the Guide to the Expression of Uncertainty in Measurement .

Formula:

\[u\left(\chi _{\mathrm{sample}}\right)^{2} = u\left(\chi _{\mathrm{precision}}\right)^{2}+u\left(\chi _{\mathrm{calibration}}\right)^{2}+u\left(\chi _{\mathrm{instrument}}\right)^{2}+u\left(\chi _{\mathrm{sampling}}\right)^{2}\]

• \(u\left(\chi _{\mathrm{precision}}\right)\) : Uncertainty of the measurement method associated to the reproducibility

• \(u\left(\chi _{\mathrm{calibration}}\right)\) : Uncertainty of the calibration RGM

• \(u\left(\chi _{\mathrm{instrument}}\right)\) : Uncertainty of the analytical system

• \(u\left(\chi _{\mathrm{sampling}}\right)\) : Uncertainty of the sampling system

The combined uncertainty, or overall uncertainty is calculated using the law of propagation of the uncertainties (considering that the standard uncertainties are not correlated) according to the Guide to the Expression of Uncertainty in Measurement .

Uncertainty linked to the reproducibility of the measurement method (Precision)

The precision is a measure for the closeness of the agreement between measured values obtained by replicate measurements on the same or similar objects under specified conditions (VIM (BIPM)). This is expressed as standard uncertainty reflecting the variability of the measurement system due to random errors.

Formula:

\[u\left(\chi _{\mathrm{precision}}\right)^{2} = (\chi _{\mathrm{sample}} * \sigma^{\mathrm{rel}}_{\mathrm{series}})^2+\left(\frac{\mathrm{LOD}}{3}\right)^{2}\]

• \(\chi _{\mathrm{sample}}\) : Amount fraction of a substance in a sample

• \(\sigma^{\mathrm{rel}}_{\mathrm{series}}\) : relative standard deviation of calibrations

• \(\mathrm{LOD}\) : Detection Limit

Uncertainty of the Calibration

Standard uncertainty due to the calibration. Behaviour not defined for calculation using the FID formula.

Formula:

\[u\left(\chi _{\mathrm{calibration}}\right)^{2} = \left(\frac{\left(A_{\mathrm{sample}}-A_{\mathrm{blank}}\right)*V_{\mathrm{calib}}}{V_{\mathrm{sample}}*\left(A_{\mathrm{calib}}-A_{\mathrm{blank}}\right)}*u_{\mathrm{calib}}\right)^{2}=\left(\frac{\chi _{\mathrm{sample}}}{\chi _{\mathrm{calib}}}*u_{\mathrm{calib}}\right)^{2}\]

• \(A_{\mathrm{sample}}\) : Peak area of sample measurement

• \(A_{\mathrm{calib}}\) : Peak area of calibration gas measurement

• \(A_{\mathrm{blank}}\) : Possible blank area value determined in zero gas measurements

• \(V_{\mathrm{calib}}\) : Volume of calibration gas samples

• \(V_{\mathrm{sample}}\) : Volume of measured samples

• \(u_{\mathrm{calib}}\) : Certified uncertainty of the RGM amount fraction

• \(\chi _{\mathrm{sample}}\) : Amount fraction of a substance in a sample

• \(\chi _{\mathrm{calib}}\) : Certified amount fraction of calibration gas

Uncertainty of the Instrument

The overall uncertainty of the instrument is the result of combining the standard uncertainties of the peak integration, sample volume, further instrumental problems (e.g. sampling line artefacts) and the uncertainty due to the lack of linearity.

Formula:

\[u\left(\chi _{\mathrm{instrument}}\right)^{2} = u\left(\chi _{\mathrm{peak\ integration}}\right)^{2}+u\left(\chi _{\mathrm{volume}}\right)^{2}+u\left(\chi _{\mathrm{further\ instrumental\ problems}}\right)^{2}+u\left(\chi _{\mathrm{linearity}}\right)^{2}\]

• \(u\left(\chi _{\mathrm{peak\ integration}}\right)\) : Uncertainty of the Peak Integration

• \(u\left(\chi _{\mathrm{volume}}\right)\) : Uncertainty of the Volume

• \(u\left(\chi _{\mathrm{further\ instrumental\ problems}}\right)\) : Uncertainty of the Further Instrumental Problems

• \(u\left(\chi _{\mathrm{linearity}}\right)\) : Uncertainty of the Linearity

Uncertainty of the Peak Integration

The standard uncertainty due to peak integration.

Formula:

\[u\left(\chi _{\mathrm{peak\ integration}}\right)^{2} = \left(\frac{f_{\mathrm{calib}}}{V_{\mathrm{sample}}}*\frac{u\left(A_{\mathrm{int,}sample}\right)}{A_{\mathrm{sample}}}\right)^{2}+\left(\frac{A_{\mathrm{sample}}*V_{\mathrm{calib}}*\chi _{\mathrm{calib}}}{V_{\mathrm{sample}}*A_{\mathrm{calib}}^{2}}*\frac{u\left(A_{\mathrm{int,}calib}\right)}{A_{\mathrm{calib}}}\right)^{2}\]

• \(f_{\mathrm{calib}}\) : Calibration Factor

• \(V_{\mathrm{sample}}\) : Volume of measured samples

• \(\frac{u\left(A_{\mathrm{int,}sample}\right)}{A_{\mathrm{sample}}}\) : Uncertainty from peak integration in the measurement

• \(A_{\mathrm{sample}}\) : Peak area of sample measurement

• \(V_{\mathrm{calib}}\) : Volume of calibration gas samples

• \(\chi _{\mathrm{calib}}\) : Certified amount fraction of calibration gas

• \(A_{\mathrm{calib}}\) : Peak area of calibration gas measurement

• \(\frac{u\left(A_{\mathrm{int,}calib}\right)}{A_{\mathrm{calib}}}\) : Uncertainty from peak integration in the calibration

Uncertainty of the Volume

The standard uncertainty due to the difference between sampling and calibration volumes.

Formula:

\[u\left(\chi _{\mathrm{volume}}\right)^{2} = \left(\frac{\chi _{\mathrm{sample}}}{V_{\mathrm{sample}}}*u\left(V_{\mathrm{sample}}\right)\right)^{2}+\left(\frac{\chi _{\mathrm{sample}}}{V_{\mathrm{calib}}}*u\left(V_{\mathrm{calib}}\right)\right)^{2}\]

• \(\chi _{\mathrm{sample}}\) : Amount fraction of a substance in a sample

• \(u\left(V_{\mathrm{sample}}\right)\) : Uncertainty of the measured sample volume

• \(u\left(V_{\mathrm{calib}}\right)\) : Uncertainty of the calibration volume

• \(V_{\mathrm{sample}}\) : Volume of measured samples

• \(V_{\mathrm{calib}}\) : Volume of calibration gas samples

Uncertainty of the Further Instrumental Problems

Standard uncertainty due to specific instrumental problems.

Formula:

\[u\left(\chi _{\mathrm{further\ instrumental\ problems}}\right)^{2} = \left(\chi _{\mathrm{sample}}*u_{\mathrm{instrument}}\right)^{2}\]

• \(\chi _{\mathrm{sample}}\) : Amount fraction of a substance in a sample

• \(u_{\mathrm{instrument}}\) : Systematic Instrument Error

The standard uncertainty due to specific instrumental problems (e.g. sampling line artefacts, carry over, changes of split flow rates) has to be evaluated for each site specifically. This uncertainty can be derived from tests, audits or intercomparison results.

Uncertainty of the Linearity

Standard uncertainty due to lack of linearity of the measurement system.

Formula:

\[u\left(\chi _{\mathrm{linearity}}\right)^{2} = u_{\mathrm{linearity}}^{2}\]

• \(u_{\mathrm{linearity}}\) : Uncertainty from non-linearity

Uncertainty of the sampling method

The standard uncertainty due to application of off-line sampling techniques depends on the technique used. Contributions to the uncertainty common to all off-line techniques (cleaning of the samplers, storage, adsorption effects, etc.) should be evaluated case-by-case and per individual component. If not available in literature, a proper validation of the sorbent tubes is recommended prior to their use in the field to establish the efficiency of adsorption/desorption and the safe sampling volume at different composition levels and atmospheric conditions.

Formula:

\[u\left(\chi _{\mathrm{sampling}}\right)^{2} = u_{\mathrm{sampling}}^{2}\]

• \(u_{\mathrm{sampling}}\) : Uncertainty from sampling volume accuracy

Uncertainty of the Blank

The uncertainty due to the deviation of blank samples from the mean blank values.

Formula:

\[u\left(\chi _{\mathrm{blank}}\right)^{2} = \sigma _{\mathrm{blank}}^{2}\]

• \(\sigma _{\mathrm{blank}}\) : standard deviation of the amount fraction of a serie of blank runs

Expanded Uncertainty

The combined uncertainty is the product of the combined standard uncertainty of the measurement by a number greater than 1 (the coverage factor k).

Formula:

\[U\chi _{\mathrm{sample}} = 2*u\left(\chi _{\mathrm{sample}}\right)\]

• \(u\left(\chi _{\mathrm{sample}}\right)\) : Combined Standard Uncertainty

Finally, the overall uncertainty (or the combined standard uncertainty) is multiplied by a coverage factor \(k=2\) to provide the expanded uncertainty.

Calibration Values

To calculate the calibration value of each measurements TUCAVOC uses an interpolation method that helps estimating better the real reference value at the time of the measurements. TUCAVOC assumes linear deviation with time. The uncertainties of the calibration are also obtained based on interpolation between the neighboring calibration series.

On the following plot you can see how the calibration value (in orange) changes between calibration runs over time. The area around the orange line shows the standard deviation of the calibration value

Blank Correction

Incorporate blank measurements in the measurement sequence is highly recommended to correct by substances under study that might appear due to artefacts [Guidelines] .

The blank correction will correct the area measured by substracting from it the area of the blank, as indicated in equations (1) (2) (3) (4) .

As the blank measured value can vary over time, TUCAVOC interpolates between the measurements to approximate the real blank value.

When using the widget, you can select if the blank areas are present in the data, or you can select if you want to specify a blank value to the substances.

When specifying the blank amount fraction, TUCAVOC will use equations (5) and (6) to calculate the blank area.

Flagging

Flagging in TUCAVOC.

TUCAVOC add a flag value for each measurement of each substance.

enum tucavoc.flags.Flags(value)

Flags supported by TUCAVOC.

They are based on https://projects.nilu.no/ccc/flags/flags.html .

Member Type:

int

Valid values are as follows:

VALID = <Flags.VALID: 0>

Valid measurement

BELOW_DETECTION_LIMIT = <Flags.BELOW_DETECTION_LIMIT: 147>

Below theoretical detection limit or formal Q/A limit, but a value has been measured and reported and is considered valid

UNSPECIFIED_LOCAL_CONTAMINATION = <Flags.UNSPECIFIED_LOCAL_CONTAMINATION: 559>

Unspecified contamination or local influence, but considered valid

MISSING_MEASUREMENT_UNSPECIFED_REASON = <Flags.MISSING_MEASUREMENT_UNSPECIFED_REASON: 999>

Missing measurement, unspecified reason

tucavoc.flags.set_flags(df: DataFrame, df_substances: DataFrame)

Set automatic flags to the dataframe.

This will add a sub column to all the substances based on automatic recognition of the data.

• Flags.VALID by default for any measurement

• Flags.MISSING_MEASUREMENT_UNSPECIFED_REASON if

  the amount fraction value is nan. This is the case when the base value was nan.

• Flags.BELOW_DETECTION_LIMIT if conc is

  below the detection_limit or is smaller than u_precision / 3

tucavoc.flags.set_group_flags(df: DataFrame, df_substances: DataFrame, group_dict: dict[str, list[str]])

Set flags for the groups.

Similar to set_flags() but adapted for groups.

• Flags.VALID by default for any measurement

• Flags.MISSING_MEASUREMENT_UNSPECIFED_REASON if

  the amount fraction value is nan. This is the case when the base value was nan.