The WPL (Webb,
Pearman, and Leuning) correction is fully accepted to
correct trace gas fluxes like CO

The WPL (Webb,
Pearman, and Leuning)
correction (Webb et al., 1980) has been fully accepted in
the international scientific community for many years. After initial
discussions on the derivation of the correction up to the beginning of the
2000s, no further discussions took place after the clarification by Leuning (2007, 2004). The correction is used in the textbook literature
(Aubinet et al., 2012) and integrated in a similar form in all
software packages for the calculation of eddy-covariance measurements and
must be applied predominantly for open-path devices when the input variables
are not measured as mixing ratios. The correction is necessary because
fluctuations in temperature and humidity cause fluctuations in trace gas
concentrations and can simulate a flux, for instance of CO

The size of the WPL correction on the CO

In a recently published article on CO

Such low fluxes occur, for example, over burned areas
(Oliveira et al., 2021) or over sandy deserts
(Su et al., 2013). This paper uses an example from
the Arctic (Jentzsch et al., 2021) to show that the WPL
correction may well lead to misjudgements of water vapour and carbon dioxide
measurements with an open-path gas analyser. The conditions under which the
WPL correction has a considerable influence on the CO

The WPL correction is relevant for the measurement of the partial density,
e.g. of CO

Most quantities in Eq. (1) are temperature dependent. It is obvious to
investigate whether there is a temperature dependence of the WPL correction.
The relevant temperature-dependent quantities of the second term of Eq. (1) are

The measurements shown are from the Bayelva site located at

Figure 1 shows a measurement example for short-term CO

Comparison of WPL-corrected and uncorrected CO

WPL correction (in

In Fig. 2, both terms were explicitly calculated with the measured data and not by EddyPro with identical results. It is shown that temperature fluctuations have a much stronger influence on the size of the WPL correction.

In the case of a CO

The influence of the WPL correction on the latent heat flux is not shown. It is known to be relatively small, and in the present case for the period from 08:00 to 11:00 CET it was about 3 %; at all other times it was 1 %–2 %. This is below the typical flux measurement error (Foken et al., 2012) for most of the fluxes of about 10 %.

Comparison of WPL-corrected and uncorrected CO

A variable CO

Table 1 shows the WPL correction as a function
of the size of the sensible and latent heat flux for standard atmospheric conditions (1013 hPa, 15

For small CO

Small errors could have a large impact on cumulative fluxes, especially if the errors have a bias. Therefore, the interpretation of such fluxes has to be done very carefully. However, in the case of a carbon uptake and positive sensible heat fluxes, these fluxes would be reduced and, as the above example has shown, emissions with negative sensible heat fluxes would also be reduced. This could compensate for the errors, but this would have to be shown in each individual case.

Furthermore, small CO

Since the specificity of possible errors in WPL correction is not taken into
account by usual error analyses of eddy-covariance data
(e.g. Mauder et al., 2013), measurement data with very
large WPL corrections should be marked. A possible parameter could be the
ratio of WPL correction and corrected CO

Quality flags of the WPL correction according to Eq. (4) for the example given in Fig. 1.

Due to the significant problems with the additive WPL correction, other
possible influencing factors, such as spectral cross-sensitivities between
CO

According to the original work on the WPL correction (Webb
et al., 1980), it should be noted that in some conditions the correction is
expected to be on the same order of magnitude as the flux. This fact has
only been given the necessary attention in a few works on the error analysis
of CO

We strongly suggest that the WPL correction should be subjected to a special quality analysis. For this purpose, the quality flag of the correction expressed in Eq. (4) or/and Eq. (6) could, for example, be explicitly output for all eddy-covariance software packages. At least for small fluxes it would have to be included in the quality considerations.

We propose that special events in time series of trace gas fluxes should only be interpreted if the WPL quality flag is below a maximum limit values and can be clearly qualitatively and quantitatively assigned to physical processes. Otherwise, these data should be identified with a MAD analysis and interpolated if necessary.

We suggest that respiration data for the derivation of the gap-filling
algorithm (Lloyd and Taylor, 1994) should be obtained at times when
the sensible heat flux is near 0 W m

If CO

In addition to the WPL correction, we recommend that all corrections used in the eddy-covariance method, which are made by adding correction terms to the measured flux, should be critically reviewed. This applies, for example, to the Burba correction for open-path gas analysers and the various corrections for closed-path devices. It may also be necessary to investigate whether errors in the application of the WPL correction and the above-mentioned corrections lead to a bias in accumulated fluxes for which appropriate simulations will probably have to be performed.

These remarks suggest that a discussion on alternative measurement
methods and minor imperfections in field calibrations should be continued.
This includes the direct measurement of the mixing ratio (Kowalski
and Serrano-Ortiz, 2007) as realized in closed-path instruments when
complete isothermal condition is guaranteed in the measurement volume. This also means that density-averaged measurement of CO

The eddy flux data are openly available under CC-BY-4.0
in the FLUXNET database (

The supplement related to this article is available online at:

KJ made first investigations of the WPL term under Arctic conditions guided by JB. These first analyses were extended by TF to the present paper. After the discussion of the results, KJ, JB, and TF completed the paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This publication was funded by the German Research Foundation (DFG) and the University of Bayreuth under the open-access publishing funding programme.

This open-access publication was funded by the University of Bayreuth.

This paper was edited by Christian Brümmer and reviewed by George Burba and one anonymous referee.