General Comments

I want to commend the authors on an innovative study aiming to enhance the utilization of data from urban atmospheric tall towers for greenhouse gas measurements. The study's objective to enable viewing the underlying surface through two lenses - atmospheric concentration "stocks" and eddy covariance fluxes "flows" - is compelling and well-articulated. The manuscript demonstrates considerable technical prowess in various analytical methodologies, from robust statistics and time-frequency decomposition to footprint analysis.

However, the presentation of the findings can be improved. The manuscript currently appears fragmented and would benefit from a more focused and cohesive narrative. The use of intricate wavelet methodologies for flux calculations, while not standard but used in a growing number of studies, occasionally overlooks certain conventional assumptions and necessary considerations. Here are my detailed comments and suggestions to improve the manuscript.

Scientific Significance: Good

The manuscript represents a significant contribution to scientific progress within the scope of Atmospheric Measurement Techniques, presenting new concepts and methodologies for urban atmospheric measurements. However, it could benefit from a more integrated approach to link the different analytical tools employed.

Scientific Quality: Fair

The scientific approaches and applied methods are mostly valid. However, the manuscript sometimes fails to fully address the complexities introduced by non-stationary conditions and surface heterogeneity, which is imperative for credible flux measurements in the urban context. More thorough discussion and contextualization of these issues within the underlying conservation equation framework would strengthen the manuscript.

Presentation Quality: Good

The scientific results and conclusions are generally presented clearly, but the manuscript's length and the complexity of the methodologies discussed can make it challenging to read. A more concise and focused presentation would enhance the overall readability and impact.

Major Comments

1. Focus and Completeness

The manuscript's focus is not always clear. It oscillates between making slow eddy covariance (EC) urban measurements interoperable, deriving surface fluxes from urban towers, and describing boundary layer dynamics. Each of these topics is valuable, but the manuscript would benefit from a clear, central theme.

Recommendation: Separate the components on interoperability of slow and fast eddy covariance turbulence measurements including measurement height, transfer function, traditional quality flagging and wind directional interpretations into a standalone manuscript. These components are robust and well-substantiated. The more complex discussions on relating tower top turbulence measurements to surface emissions and removals including storage flux, and the intricate wavelet and footprint analyses, could then be expanded and focused in a subsequent manuscript.

2. Scientific Foundation for Improving Data Utilization with Wavelets

The claim that wavelet-based EC does not require stationarity (lines 20, 90, 230, 378, 608, 640, 645) needs further substantiation. The primary reason for requiring stationarity in EC is the simplification of the conservation equation. Wavelet transformation alone does not remove the requirement for stationarity/homogeneity without additional considerations. For example, Cliff et al. (2023) provide additional reasoning and pointers for future research.

Recommendation: Provide a thorough discussion on why stationarity is needed in EC methodologies and how wavelets may be able to relax some of these requirements. Include an uncertainty budget to account for potential compensatory fluxes across different conservation equation terms or move these discussions to a separate publication.

3. Considerations for Expressing Surface Flux

Stationarity is essential in EC methodologies to simplify the conservation equation, which involves at least seven terms (storage, and advective and turbulent transport in three dimensions). These terms can only be simplified to a vertical turbulent flux point measurement and a storage column measurement under conditions of stationarity and homogeneity, allowing the other terms to vanish.

Virtual transformations of a single term, such as wavelet decomposition of the vertical turbulent flux, do not inherently create stationary and homogeneous conditions across all conservation equation terms. For example, the manuscript attributes storage dilution/enrichment partly to boundary layer dynamics (e.g., line 561). Without also including vertical advection that would compensate said phenomena, this leads to a flawed interpretation of storage flux and the combination of turbulent and storage flux as surface emissions/removals, as these phenomena are artifacts of boundary layer dynamics.

Recommendation: Explicitly derive and discuss the relationship between surface flux and the conservation equation terms, showing how relaxing stationarity and homogeneity may be warranted. Alternatively, include an uncertainty budget that accounts for compensatory fluxes across conservation equation terms, or move these discussions to a separate publication.

4. Source Areas for Turbulent and Storage Flux Measurements

Storage flux measurements and their footprints differ substantially from those of turbulent flux measurements. Combining these measurements without spatial rectification can violate the assumptions of stationarity and homogeneity, skewing and scattering the results.

Recommendation: Address how the footprints of storage and turbulent fluxes have been assessed and combined, considering their different measurement heights and magnitudes. Discuss potential methods for spatial rectification to reconcile these differences or move these discussions to a separate publication.

Specific Comments

• Sect. 3.2: How can we reconcile the conundrum of resolving surface heterogeneity (footprint, Wavelet) while holding on to conventional mass conservation simplifications (e.g., only two instead of seven terms in Eq. (1); traditional stationarity and turbulence development tests for remaining terms)?
• Sect. 3.2.1: How have footprints been assessed and combined for storage flux and turbulent flux per Eq. (1), considering their different measurement heights and corresponding differences in extent and flux magnitudes?
• Lines 20, 90, 378, 608, 640: Clarify statements regarding the requirement of stationarity for standard EC and wavelet-based EC.
• Line 170: Confirm whether mass-based mixing ratios (kg kg^-1 dry air; e.g., Foken, 2017) or more conventional mole-based dry mole fractions (mol mol^-1 dry air; e.g., LI-COR Inc., 2019) were used in calculations.
• Line 185: The statement “For the scope and goals of this work, vertical and horizontal advection were considered negligible, assuming dynamic horizontal homogeneity of the surface” and Eq. (1) portraying the surface flux as the sum of the turbulent vertical flux measured at a single point on the tower top, and the storage flux measured at three heights in the air column below, is violated for measurements from three different heights over a heterogeneous surface and for changes in wind direction and wind speed. The authors appear to claim a method to process EC data through Wavelets, postulating a condition referred to as “dynamic homogeneity” to satisfy the conservation equation from EC point and storage profile measurements alone. Please explain. If true, wavelet-based EC would solve systematic biases like energy imbalance for all surface types and complexities. However, the manuscript lacks detail on orthogonal stationary wavelet scales, the definition of “dynamic homogeneity,” and their justification for assuming vanishing 3D advective and turbulent fluxes required by simplifying the conservation equation to two terms. To avoid appearing as a "magic trick," the authors should explicitly derive, document, and discuss the relationship between Wavelets and conservation, showing how relaxing stationarity may be warranted, and include an uncertainty budget also considering compensatory fluxes across conservation equation terms. Alternatively, move these explorations to a subsequent, separate publication, touching on some considerations in the discussion section of the present manuscript, or establish explicit proof for the claimed relationships and vanishing terms in the conservation equation.
• Line 201: Wilczak et al. (2001) are typically cited for their planar fit rotation, but the authors mention double rotation here. Please clarify.
• Line 230: The statement “Standard eddy covariance (EC) cannot be used for non-stationary events but wavelet decomposed series are stationary in each scale eliminating the need to flag out these data” needs clarification. “Virtual” transformations do not create stationary homogeneous conditions for all conservation equation terms, necessary for individual terms as well as cross-term compensatory fluxes to cancel out. Section 4.1.2 attributes storage dilution/enrichment to boundary layer dynamics (i.e., boundary layer growth/shrinking), which would be compensated in the conservation equation when including vertical advection. Without including vertical advection, relating storage flux and consequently the combination of turbulent and storage flux to surface emissions/removals is flawed, as this phenomenon is an artifact of boundary layer dynamics. Can the authors show that Wavelet transformation incorporates non-zero 3D advection and turbulent transport terms, or otherwise substantiate this claim?
• Line 289: Kljun (2015) is a simple parameterization of a backward Lagrangian stochastic particle dispersion model (LPDM-B), rather than LPDM-B itself. Suggest adding: “we used a [simple parameterization of] a backward...”
• Lines 318, 352: Mention H2O which is not shown in the manuscript. Please check.
• Line 345: The statement “largest occurrence of stable conditions during the summer” is counterintuitive as convection is expected during this time of year. Please check.
• Line 368: The statement “We note that strong winds in neutral conditions and especially medium winds in stable conditions would be favorable to horizontal advection” needs explanation. Advection is a zero-sum game unless there is 3D scalar or flux divergence from surface heterogeneity, and then a whole host of additional consideration applies (see above).
• Line 378: Revise: “The stationarity test is required for standard EC but not for wavelets, thus the use of the latter increases the data amount by 34% if only high-quality observations are used and 55% if medium-quality data is included (Figure 8). This savings happens more often during the day due to a higher coincidence of both flags during night.” Explain why ITC flagging is important if we have a full storage profile below EC turbulence measurement height.
• Line 434: CO fluxes are presented while high sensor noise is discussed in the transfer function section. Explain the credibility of these CO fluxes and substantiate with an uncertainty estimate.
• Sections 4.1.2 and 4.2 discuss storage and vertical advection, and the plausibility of the resulting fluxes: The manuscript explains negative storage flux as partly due to an expanding mixed layer. This artifact results when compensatory fluxes are not accounted for. Atmospheric dilution from vertical advection is not a surface emission/removal but is interpreted as such without considering all conservation equation terms. If appropriately accounted for, vertical advection and atmospheric dilution from ABL growth cancel each other out. Partitioning resulting CO2 fluxes, as proposed, would not be meaningful when confounding surface activity with ABL dynamics. How can this be rectified? Considering conservation equation terms in concert allows accounting for net vertical advection (after discounting compensatory fluxes). To work towards a solution, consult Finnigan et al. (2003), Finnigan (2004), and Finnigan (2008) for flux measurements over complex terrain and mass conservation. Metzger (2018), Xu et al. (2018), and Xu et al. (2020) reconcile these with two-term EC measurements in spatial heterogeneity, improving resilience to advection, including low-frequency fluxes, and accounting for compensatory fluxes by combining Wavelet EC with an explicit "virtual control volume" approach and spatial attribution.
• Line 601: Given boundary layer dynamics in storage flux and surface heterogeneity, caution against referring to the sum of storage flux and turbulent flux as “surface flux.” Suggest referring to it as “combined flux,” also in Eq. (1), lines 649, 661, and throughout the manuscript.
• Sect. 4.3, lines 646, 669: These are great examples of focusing on what the manuscript does well. Consider pruning everything else to a separate follow-on manuscript.
• Line 640 following: Suggest revising the paragraph based on considerations of Wavelets, conservation equation, and ABL dynamics.

Resources and Next Steps

I recommend the authors consult the following resources for additional guidance on flux measurements and mass conservation in complex conditions (such as the urban emission/removal landscape):

• Finnigan et al. (2003, 2008), Finnigan (2004);
• Metzger (2018);
• Xu et al. (2018, 2020).

These references provide extensive insights into the challenges and methodologies relevant to the authors' work and can help in refining the manuscript's scientific foundation and practical applications.

In conclusion, I believe the manuscript has substantial potential and can make a significant contribution to the field. Focusing on the core components, addressing the outlined challenges, and separating the more complex discussions into a follow-up manuscript will enhance its clarity, impact, and scientific rigor.

References

Cliff, S. J., Drysdale, W., Lee, J. D., Helfter, C., Nemitz, E., Metzger, S., and Barlow, J. F.: Pandemic restrictions in 2020 highlight the significance of non-road NOx sources in central London, Atmos. Chem. Phys., 23, 2315-2330, 10.5194/acp-23-2315-2023, 2023.

Finnigan, J. J., Clement, R., Malhi, Y., Leuning, R., and Cleugh, H. A.: A re-evaluation of long-term flux measurement techniques. Part 1: Averaging and coordinate rotation, Boundary Layer Meteorol., 107, 1-48, doi:10.1023/A:1021554900225, 2003.

Finnigan, J. J.: A re-evaluation of long-term flux measurement techniques. Part 2: Coordinate systems, Boundary Layer Meteorol., 113, 1-41, doi:10.1023/B:BOUN.0000037348.64252.45, 2004.

Finnigan, J.: An introduction to flux measurements in difficult conditions, Ecological Applications, 18, 1340-1350, doi:10.1890/07-2105.1, 2008.

Foken, T.: Micrometeorology, 2, Springer, Berlin, Heidelberg, 362 pp.2017.

LI-COR Inc.: LI-7200RS CO₂/H₂O gas analyzer instruction manual, LI-COR Inc., Lincoln, Nebraska, USA, 226, 2019.

Metzger, S.: Surface-atmosphere exchange in a box: Making the control volume a suitable representation for in-situ observations, Agric. For. Meteorol., 255, 68-80, doi:10.1016/j.agrformet.2017.08.037, 2018.

Xu, K., Metzger, S., and Desai, A. R.: Surface-atmosphere exchange in a box: Space-time resolved storage and net vertical fluxes from tower-based eddy covariance, Agric. For. Meteorol., 255, 81-91, doi:10.1016/j.agrformet.2017.10.011, 2018.

Xu, K., Sühring, M., Metzger, S., Durden, D., and Desai, A. R.: Can data mining help eddy covariance see the landscape? A large-eddy simulation study, Boundary Layer Meteorol., 176, 85–103, doi:10.1007/s10546-020-00513-0, 2020.

This is a well-written and interesting article comparing surface fluxes observed using relatively slow response instruments with traditional eddy-covariance techniques. In my opinion, the core innovation of this work is to advance capability of surface flux measurements using slow-response sensors. This has significant potential to increase utility of existing atmospheric tower observation platforms and expand the suite of gas fluxes we currently measure.

Significance: Good

Scientific Quality: Good. Technical expertise is evident, approaches and techniques are appropriate and well-justified, and descriptions are generally of high quality. However, I feel the results and discussion could be streamlined (see next comment) for greater impact and readability.

Presentation: Fair. The manuscript is well-written, however, I suggest a greater narrative focus on the core novelty (i.e. development and evaluation of slow-response flux measurements) to improve overall clarity and readability. I suggest certain pieces (for example Section 3.2.1, 3.4-3.5, and 4.2) could be shortened or moved to the appendices.  

Specific Comments:

Line 95: Wavelet analysis. This technique may be less familiar to some readers. I suggest more explicit explanation of advantages and challenges of this approach is needed.

Lines 340 & 445: How do source area uncertainties impact results and interpretation? Uncertainties in the source area model, and also arising from differences between turbulent and scalar (storage tower profile) measurements.

Lines 570: What about entrainment during mixed layer growth? This isn’t mentioned explicitly in the text

This study (amt-2024-71) investigates the suitability of slow response gas analyzers used in atmospheric concentration measurements at high elevation for turbulent flux measurements. I believe in general the study fits the quality scale and the scope of the journal. My assessment of its main features (significance, quality and presentation) is followed by further comments on technical aspects, structure and minor issues, which are presented in the order of importance.

Significance: Good

The study presents an innovative concept to enhance the existing flux measurement network with the addition of relatively cheap equipment to the atmospheric stations. It significantly improves the understanding of the slow response gas analyzers’ performance for turbulent flux estimations. Even though the study is limited to urban environment, their meticulous technical analysis sets a good example to encourage other researchers to adopt their approach at other sites.   

Scientific Quality: Good

The analysis conducted to assess the performance of slow-response analyzer is well executed and described, indicating technical excellence. Specific comments regarding the spectral correction and other details are presented below.

Presentation: Fair

The manuscript is orderly written, the results are sound and presented with easy-to-follow visuals. However, the detailed description of technical analysis and the sink/source processes of three gases resulted in a lengthy manuscript, shifting the focus. Specific comments to improve the flow is detailed below.

Comments on technical aspects

Spectral correction

• The spectra go through a noise-removal procedure prior to fitting Eq. 12 when Fratini et al. (2012) or Ibrom et al. (2007) is chosen in EddyPro. Which range was used for noise removal fitting? I am afraid the same default range was used for all gases, i.e. 1Hz onwards. See Aslan et al. (2021) for a detailed description of the procedure and its consequences. Since the spectral correction is of great importance for this study, this should be clarified and if possible, power spectra of all scalars and temperature should be shown. This would be beneficial to understand the effect of noise, hence the reason behind the unexpected deviations in TF in Figure 3, which I presume represents noise removed spectra. The small peak around 4s for CO2 and CH4 from CRDS seems interesting. In the end the response time can be calculated using CO2 for the other gases measured in the same instrument and setup as practiced in the paper already. However, the very high normalization factor (Fn) for CO2 from CRDS is concerning. Thus, I am not sure if it is doing more good than harm using CO2 based response time for other gases. Please clarify.

• P11L272: I think you used only Equation 8, 10 and 12. The other equations are just used in the arguments. Please adjust the sentence to prevent confusion.
• Also in Equation 12, the normalization is done with variance (σ²_s), not standard deviation (σ_s). I think the calculation is done accurately, so this is just a typo. Please correct.
• P27L545: Larger than expected attenuation might be related to erroneous noise removal, which removes part of the signal and attenuates the data (again see Aslan et al. 2021). This should be fine-tuned as explained above.
• Last but not least, repeating the same value for 30 times would create sharp corners in time series, which FFT decomposition struggles with. This is especially important for power spectra. It might create additional noise contamination as well as systematic problems in frequency and amplitude of sine&cosine waves. This shouldn’t be necessarily addressed here, but possible shortcomings should be highlighted to guide future research and remind researchers to be aware.

Storage and advection

• The vertical advection can be calculated by changing the coordinate rotation method. Here, 2D coordinate rotation was applied, setting the mean vertical wind velocity to zero. If you prefer planar fit method, which is the default method in ICOS protocol (see Sabbatini et al. 2018), then vertical advection at least can be calculated (since you have the profile setup to calculate the concentration difference between the level of instrument and the air column below). In some cases (see Mammarella et al 2007), including vertical advection was sufficient to reach a closed mass balance (i.e. fluxes are independent of turbulence). It is not a must, but I believe it is worth checking. At least this should be mentioned in Section 4.1.2.
• Profile sampling indicates a 10 min interval for each level, resulting in only one value for each level within 30 min. This would create big uncertainty for interpolation. The time-lag is set for ca. 60 seconds (from 100m distance). I think it is safe to alternate the levels every 5 minutes, which would improve the storage estimation. Maybe this should be mentioned in the discussion (Section 4.1.2) as a possible shortcoming.

Comments on Structure/Flow

Introduction is written in a great detail, which is a good work. However, this made it rather long and hard to read. I believe the fluxes shown here are not the main story, but the technical aspect is, i.e. applicability of slow-response analyzers for flux calculation. So, this is not a sole case study where the fluxes from an urban area are measured. Thus, the redundant information is shifting the focus. Accordingly, I recommend the following adjustments to improve flow.

• The paragraph starting at P2L57 should be reworded with better conjunctions to streamline the 3 differences between atmospheric and ecosystem stations highlighted.
• In the following paragraph starting at P3L64, where the constraints of slow vs fast are described, the description should be very brief and maybe the whole content should be moved to “Material and methods” section. Here this section might start with a sub-section titled as “Requirements and constraints of slow and fast response analyzers”. This would provide more room for better description. Alternatively, the material can be dissolved in the discussion.
• The paragraphs describing the sink and source dynamics of CO (P4L114) and CH4 (P4L123) should be removed. The importance of monitoring such gases can be described very shortly by the end of the paragraph starting at P4L111.

Minor comments

• P5L135: …supplemented with a “fast-response” sonic anemometer… The paper simply recommends complementing the existing slow-response gas analyzer with a fast-response sonic anemometer. So, this should be clear to prevent confusion. It should be also mentioned in Section 4.3 as well. 
• Section 2.2.2 Wasn’t there any filtering due to possible tower disturbance on flow?
• Figure 4. H2O is not shown.
• Figure 5. The caption indicates “average”, whereas text indicates median in P14L327. Please clarify.
• P15L339 – 340: Are those percentages based on 90% or 80% footprint area? Please clarify both in the text and in the caption of Figure 6.
• Probably a single roughness parameter was used for the footprint calculations. Forest dominates the southern part, while cropland dominates northern within 80% of the footprint area. I think this is a big uncertainty especially for Kjlun et al. (2015) model as it is very sensitive to roughness parameters. Either in methodology or in results this should be mentioned. That said, there is no need to update the analysis since this is not affecting any important outcome of the paper.
• P18L396: Note that CH4 never reaches a plateau in ogive for any stability condition.
• P18L397: The atypical shape of CO cannot be attributed to noise as noise does not covariate with other signals. Please adjust.
• Figure 11. Does the shaded area refer to standard deviation?
• P20L429: No information was shown regarding evapotranspiration.
• Figure 18. I don’t understand why the area of interest is a sink of carbon in early morning. Is there any explanation for that? I think the storage fluxes are overestimated.
• P28L572: … indicate horizontal advection →→→ … indicate advection

References

Mammarella, I., Kolari, P., Rinne, J., Keronen, P., Pumpanen, J. and Vesala, T., 2007. Determining the contribution of vertical advection to the net ecosystem exchange at Hyytiälä forest, Finland. Tellus B: Chemical and Physical Meteorology, 59(5), pp.900-909.