Review of the manuscript “Estimating scalar turbulent fluxes with slow-response sensors in the stable atmospheric boundary layer” by M. Allouche et al.

General comments

This manuscript aims to evaluate the performance of different scalar flux quantification methods that can be applied to measurements at one height, especially when only slow-response sensors are available that do not suffice for direct eddy covariance (EC); these methods are disjunct eddy covariance (DEC), relaxed eddy covariance (REA) and the mixing length model of A22. They are tested for two real-world data sets of high-frequency turbulence measurements that are artificially deteriorated or filtered. The paper is generally well written and clearly structured, but I have one main concern, which is that the authors do not apply the DEC and REA method as is it usually applied in other studies, thereby potentially giving the false impression that these methods create a systematic bias in flux estimates. This should not be the case if everything is done properly. Normally, only the random uncertainty or the scatter should increase. At least from this manuscript, I cannot rule that the authors have a fundamental misconception about the DEC method. It still requires a fast sampling, even if a slow-response sensor is applied, and the sampled air can then be analysed for a while before the next fast (instantaneous) grab sample is taken. Hence there is no low-pass filtering involved. Only the number of samples per averaging period is decreased, which usually leads to a larger random error but no systematic error (Karl et al. 2002, Rinne et al. 2001, 2008). Similarly, it should be clear to any micrometeorological practitioner that the REA method requires fast switching valves that can change the air flow in less than 0.1 s. However, the authors apply filtering time scales of several seconds. This is not how REA is done in reality. Because of this shortcoming, I can only recommend a major revision of this manuscript.

Specific comments

L4: The abstract is rather short, I would welcome one or two more sencentes describing the two field experiments.

L8-9: I am not sure what you try to say with this sentence, be more specific. Under which circumstances?

L120-125: Any references for the DEC method?

L167: What sonic anemometer model was used?

L187-193: I am not sure about the purpose of this paragraph here. I is not really suited as an overarching introduction to section 4, but rather belongs to only to section 4.1, since it does not mention DEC, which is treated in section 4.2 and 4.3

L205-210: Based on this text passage I have the impression the authors have a misconception about the DEC method, since normally only grab samples are analyses but now low-pass filtering is applied.

L239: As the authors rightfully state, REA with fast-switching valves will lead to a good agreement with EC, and that is the only way REA should be applied in the first place. The authors should make sure to avoid the impression that this strong bias shown in Fig. 2 is the result of the REA method itself, while it is actually an effect of the strong (artificial) low-pass filtering.

Figure 2: The results for DEC are confusing since such a systematic bias is not to be expected based on the literature on DEC. If DEC is applied properly, only the time interval between grab samples should be altered, and any low-pass filtering should be avoided. The REA results are also misleading, since they imply that slow-switching valves are used or some other form of low-pass filtering is applied. This is not how REA is or should be done in practice.

Karl TG, Spirig C, Rinne J, et al (2002) Virtual disjunct eddy covariance measurements of organic compound fluxes from a subalpine forest using proton transfer reaction mass spectrometry. Atmos Chem Phys 2:279–291. https://doi.org/10.5194/acp-2-279-2002

Rinne HJI, Guenther AB, Warneke C, Gouw JA De (2001) Disjunct eddy covariance technique for trace gas flux measurements. Geophys Res Lett 28:3139–3142

Rinne J, Douffet T, Prigent Y, Durand P (2008) Field comparison of disjunct and conventional eddy covariance techniques for trace gas flux measurements. Environ Pollut 152:630–635

The objective of this study is to assess and compare the performance of relaxed eddy accumulation (REA), disjunct eddy-covariance (DEC), and a mixing length parameterization labelled A22 in comparison to the eddy covariance (EC) technique using high-frequency measurements collected at two sites. The high-frequency measurements of scalars were filtered to supply scalar quantities that were then used with high-frequency wind speed measurements to compute the REA and DEC fluxes. I concur with Referee 1 that by low-pass filtering the scalar signal, the authors unrealistically deteriorated it for input into both the REA and DEC flux calculation. Fast valve switching is done in REA, and fast (instantaneous) sampling is done in DEC, in order to avoid apparent biases as are depicted in Figure 2. As such, I recommend that the authors undertake a major revision of the work in this manuscript.