General comments

The authors present how to identify and study intrinsic non-stationarities of turbulent fluxes. As the authors note, this topic has not received as much attention in the literature as the identification of nonstationarities in the non-turbulent flows or external drivers. In particular, the identification of averaging timescales for which intrinsic nonstationarities make the estimation of turbulent fluxes erroneous is an interesting contribution. I can recommend publishing the article after minor revisions. Generally, I think the authors can spend more time on physical interpretations (indicated below in the specific comments).  

Specific comments

One major concern about the analysis: Lines 62-75: As far as I can tell, the definition of the segments of length “s” implies that not the same data is used for calculating F(s) for each “s” as “N” is not a multiple for all “s”. How does this affect the results, in particular, for larger s (for instance,  s> N/2)?     

Another concern is that, although being a reasonable approximation to the observations, the simple OU process could be fit better through some extensions (as mentioned in lines 144-145). Why are they not tested in this study? At the very least the physical reasons for the difference between the observations and the OU should be discussed? These physical insights should inform the extensions the OU requires in order to fit the data better. 

Lines below indicate where paper coudl benefit from clarifications, further explanations, or physical interpreations 

Line 7: “... we find that the average time should be...” - Do you mean the average time for eddy covariance measurements?

Lines 11-18: The first paragraph and the first two lines of the second paragraph are not related to the rest of the paper. The paper deals with quantifying the intrinsic non-stationarity of carbon fluxes. Such quantification is not related to climate change nor does a better understanding of it allow for reductions in anthropogenic greenhouse gas emissions. In particular, lines 17-18 are unclear how a better understanding of the CO2 transport is helpful in reducing the CO2 reductions. I guess the authors refer to air quality and not reduction in CO2 emissions.  

Lines 93-94: “The time series seriously contaminated by high-frequency white noise are also removed?” Why? How does white noise affect the analysis?

Line 103: Why do you choose these Reynolds averaging timescales? In particular, 6 seconds is not a standard value to decompose the turbulent fluxes from the mean flow. 

Line 110: “The crossover scale in the case with 6 seconds is smaller than that in cases with 900 and 300 seconds.” - what does this tell us? What is the physical interpretation?

Lines 114-115: “Results indicate that the IN is a small-scale phenomenon which is intimately related to the inertial sub-range turbulence” - Isn’t that expected? 

Lines133-134: “..., although the fluctuation exponent of data seems to be greater at large scales and less at small scales, compared to the OU process.” What does this tell us? What are the physical reasons for that behaviour?

Technical corrections:

Line 4: “widespread” sounds as if a spatial analysis has been done which is not the case. I suggest using “common”. 

Correct the citation style. At most places the references should be (Author, year), e.g. line 15 

Lines 63: “m is a positive integer” - I guess 2<= m <= N? This goes back to general comment about the accuracy of estimating F(s) as s gets large

Line 84: “The data were…” suggestion: “Carbon dioxide turbulent fluxes were …”

Lines 91-93: Hard to understand the 2 sentence: “The quality control methods, proposed by Vickers and Mahrt and including spikes…” Do you mean: “The quality control methods proposed by Vickers and Mahrt (1997) are applied to remove problematic data with spikes, dropouts, ...”?

Figure 3: coordinate the colors between the different subplots such that 6 sec, 300 sec, or 900 sec have the same color in each subplots 

Line 115: “The choice of very small Reynolds …” - word missing (averaging timescales?)

GENERAL COMMENT

The manuscript analyses the issue of the intrinsic non-stationarity in observed data, due to turbulence randomness. The importance of accounting for it when using the eddy-covariance method to evaluate the CO₂ vertical transport is discussed. Data measured in an urban context, in the city of Beijing, are considered.

The rationale and goals of the work are clear, the text and discussion are well presented and streamlined. However, in general the discussion remains mostly on a technical level and not much interpretation of the physical processes related to the intrinsic non-stationarity is offered.  Also, while data collected in an urban boundary layer are used, specific considerations of the effect of the urban complexity are missing in the analysis. This could be possibly done by proposing the analysis also for data collected in a homogeneous site, when available: the authors might consider performing this additional work.

There are some choices in the approach that would need more justification or support. Some additional deepening not only on the methodology, but also on the results achieved, would increase the scientific impact of this contribution. In my opinion there is room for improvement and the manuscript can be considered for publication after revision. Specific comments are following, indicating as Lxxx-xxx the lines to refer to in the manuscript.

SPECIFIC COMMENTS AND REMARKS

L11-16:  the first part of the introduction is rather general and goes far beyond the specific topic and purpose of the work presented: a more focused introduction would be worth, with more specific references to the related literature.

L58-60: the improvement achieved using the DFA method and the reasons to choose it should be better introduced and explained, citing the original publication is not enough.

L72: is there any specific reason why n=1 was chosen for this study?

L84-90: besides the description of the instrumentation, given that the data cover a period of just one month in Summer time, some details on the typical meteorological conditions of the area and on how the urban geometries may interfere with and affect the incoming flow would be worth. Also, being Summer time, one can expect that the main pollutant emissions are due to traffic and possible industries: some information on this could be added.

L91-96: since the work of Vickers and Mahrt (1997) is used not only for their quality-control method, but also later on as a reference for discussing the results and the approaches to diagnose the non-stationarity, a brief summary of the their method and paper content would be worth.

L103-104: the averaging time for this type of analysis is generally chosen as 900, 300 and 60 seconds: the use of a 6-s averaging should be explained and supported; why didn't the authors consider a 60-s-order average? The transition from 900-300 s time averaging to 6 s is rather sharp, and it is not surprising that the fluctuation functions differ. It would be interesting to consider an intermediate averaging time.

L118: an introductory sentence explaining why the OU model is used here would be worth.

L130-131: why now a 5-minutes Reynolds average time is used?

L160-165: it is not fully clear to me how the RN-method of Vickers and Mahrt is applied, how the 'proportion of diagnosed stationarity' is computed: since this is an important part, what has been done should be better detailed and clarified.

L179-180: could the authors comment on how much the value of the crossover scale, here found as 27 seconds, can be related to the specific case considered in the study and what could be expected in different conditions? Beside recalling the results, some more discussion on how they contribute to the research field and on what is novel should be included.

TECHNICAL  REMARKS

Figure 3a: comparing the curves in a single plot is hard, I suggest to include a graph for each curve so that the differences are more visible.

Figure captions: maybe better 'dashed line' than 'broken line'?

References: the way the references are cited in the manuscript should be in brackets when simply listed and not explicitly recalled in the sentence.