Thank you for your assessment and thorough review of the preprint. The review comments were detailed and with clear suggestions for improvement.

For discussion of the comments and preprint, my responses follow a similar outline as RC1 in subsequent messages.

General Comments

The author presents a measurement technique which combines a thermal imaging instrument and distributed temperature sensing system in order to monitor spatial and temporal fluctuations of the temperature. Those measurements are supplemented by point observations of the temporal wind fluctuations, which are used in order to provide a more thorough insight of the local ambient conditions. The article is in general well written and the measuring techniques and the data analysis are presented in detail.

However, I think that the results presented in the submitted manuscript are lacking an assessment of how accurate and precise the estimation of the measured temperature fluctuations are. This is discussed briefly in the text and a qualitive comparison could be performed visually from the results in Figure 3. However, it will contribute to the assessment of the measuring capability of this setup if a direct comparison with the reference sensors is performed.

Response: Assessments of measuring capabilities were the subject of earlier studies and I chose not the repeat those here to avoid redundancy. As the reviewer points out, the reader may be inclined to use Figure 3 for a qualitative comparison of temperature observations, but the presented detail is not well-suited for a performance assessment. I agree that the addition of a comparison between the temperature methods would be helpful. I further suggest to add text to the interpretation of the Alan variance results (Figure A7), which had not been included in previous studies and reveals insights for possible improvement of the calibration of DTS data.

Moreover, I think that it is not explained clearly the reason for selecting the specific shape and size for the experimental setup. This information is going to be useful for understanding and interpreting the results of this study.  

Response: Thank you for the suggestion. In a nutshell, the design was intended to support studies on coherent temperature structures, advection processes and conditional sampling methodology. Both as empirical research and in combination with fluid dynamics models. Placement of the wind sensors at the corners and at the center was used for the determination of a representative wind vector at the walls of the box. It was thought that placing tripods at the center of a wall would result in more uncertainty. The dimensions and shape were primarily limited by the maximum range of the DTS instrument, which can support up to 1.8 km of optical fibre per channel. The DTS profile height was extended to reach sufficiently above the sonic anemometers at 3 m. In an initial design, the guyed mast would be taller and placed in the center. A compromise had to be made during deployment and the mast was moved to a corner. This also had obvious implications for the field of view of the TIR system.

The setup was not a stand-alone experiment. Other experiments were conceptualized to use the setup, as part of cooperative research during the experimental campaign (ScaleX; https://scalex.imk-ifu.kit.edu/; line 70-76). To name a few:

• Adjacent to the setup, a transect of cable temperature observed horizontal and vertical gradients over a distance across the shallow valley, and during a different period in parallel to a transect of sonic anemometers (Mauder and Zeeman 2018);
• The combined DTS setup was included in an area of TIR mapping by UAV (Brenner et al. 2018) with the intend to evaluate an approach similar to the aquatic study mentioned in the specifc comments below (by Dzara et al);
• The setup was located inside a larger valley area observed by a network of multi-Doppler lidar, SODAR/RASS and meteorological stations (Zeeman, Emeis, Obleitner and colleagues);
• Adjacent to the setup, a team observed advection of trace gasses and energy in a similarly oriented 20x20m area (Peng Zhao and colleagues);
• Adjacent to the setup, trace gas and water vapour fluxes were observed by a network of automated chamber systems (e.g., Zhao et al 2018);
• Adjacent to the setup, a team investigated patterns in air pressure perturbations (Manuel Mohr and colleagues)

Specific Comments

Line 1. Organized motions of what? Please specify.

Response: Thank you for the comment. I suggest the following change for clarity.

‘Organised motions of air in the roughness sub-layer of the atmosphere …’.

Line 6. What is meant with the term “Variance Events”?

Response: Thank you for pointing out the use of jargon. The term 'variance event' is used to distinguish signal in the time series without (obvious) periodic pattern, but with significant or characteristic excursions from a mean or trend. I suggest to rephrase ‘variance events’ to help the readerto: ‘Events in the temperature signal...’

Line 9. I suggest replacing the “with the naked eye” with visually.

Response: Thanks for the comment, I agree.

Line 13 – 14. The author states that “the available methods to determine energy and scalar fluxes from terrestrial land surface are relatively imprecise due to a multiscale of irregularities in the land surface and the turbulent transport mechanisms”. I think that this is statement is not very clear. This imprecision originates from limitations in the precision of the measuring methodologies or does the imprecision refer to the need for spatially distributed measurements?

Response: The line refers to limitations in the measuring methodologies, which happen to relate to spatiotemporal irregularities in surface-atmosphere interactions.

The methods are precise, just not applicable everywhere and all the time. As a consequence, there is a pattern, perhaps bias, as to where and when energy and scalar fluxes are observed today using micrometeorological techniques. In general, complex terrain is avoided, and periods with stable atmospheric conditions (e.g., night) or hydrometeorological events (e.g., rain, fog) are excluded. This introduces a systematic uncertainty.

Many researchers have asked the question: ‘what [are we] missing outside the applicable range of the methodology and assumptions?’ (line 19). Spatial distributed measurements may not be the final answer, but I think they could be helpful for the assessment of processes and for the development of empirical methods.

Line 24. An abbreviation should be added after the “roughness sublayer”. Later in the document (line 26) is referred to as RSL.

Response: I agree, thank you for noting the omission.

Line 45. What it is meant by the following statement: “the quantification of Tb outside a controlled laboratory environment is a challenge, in and of itself”?

Response: There are many possible sources of interference in thermal imaging, which in a controlled laboratory environment can be observed and corrected for. In field studies this is much more difficult.

Line 57. I recommend that this statement about the goal of this study is also mentioned in the abstract. It will give a clearer idea to a reader about the objective of this study.

Response: Thank you for the comment. I agree.

Lines 58-61.  I think that references to previous studies that have used the DTS and TIR measuring techniques should be mentioned. An example is:

Dzara, J. R., Neilson, B. T., & Null, S. E. (2019). Quantifying thermal refugia connectivity by combining  temperature modeling, distributed temperature  sensing, and thermal infrared imaging. Hydrol. Earth Syst. Sci., 23(7), 2965–2982. https://doi.org/10.5194/hess-23-2965-2019

Please note that I am not neither the author or any of the co-authors of the aforementioned study.

Response: Thank you, I was not yet aware of this study. It appears that the the authors applied the techniques in an aquatic environment. Please note that in their study TIR was used to generate thermal maps (one per season), which were subsequently compared to statistics of the DTS time series. In contrast, this preprint presents an approach where DTS and TIR are both used to produce high-resolution spatial time series. 

Lines 65: What does ICOS stand for?

Response: Thanks for noting the omission, the definition is indeed missing. The acronym should be added to the text:

‘The study was conducted at the DE-Fen station, Fendt--Peissenberg, Germany, which is a TERerstrial ENvironment Observatories (TERENO) and Integrated Carbon Observation System (ICOS) core site …’

Lines 68 – 69: In these lines the author gives details about elements of the landscape surrounding the experimental area. It is not clear how this information is relevant to the study. I suggest that the author explain briefly the impact of the landscape to the experiment presented in the manuscript or remove that part.

Response: I fully agree with the reviewer’s suggestion to remove this part.

Line 70: What are the ScaleX campaigns?

Response: I agree that this concept is not properly introduced and suggest the following.

‘During intensive field campaigns at DE-Fen, additional experiments were conducted for the investigation of scale interactions between the atmospheric boundary layer and the surface, as well as validation of measurement techniques (ScaleX; …).

Line 74: Why is the period between 18 – 22 Jul 2016 considered as a reference period? 

Response: This is indeed not a necessary qualification. I suggest to remove ‘reference’.

Line 75: What was the purpose of the UAV use? And how could they have an impact on this study?

Response: UAVs were used for mapping surface brightness temperature at a larger spatial scale and for in situ measurement of wind field and air quality properties. Those studies were also part of ScaleX and referenced in the paragraph text. In some instances, horizontal transects were flown above and upwind of the setup. Particularly the heavy airborne platforms, e.g., carrying a gas analyzer, generated a downwash jet that could be sensed at some distance. Also, some UAV operations required teams of people moving in and out of the field, e.g., for hourly off-site charging of batteries. The flight tracks were recorded in detail, the movement of people and vehicles not.

Line 78: What does EC stand for?

Response: The definition used in the preprint is ‘Ultrasonic anemometer (EC)’ (line 77). EC refers to the Eddy Covariance technique in which these instruments are used. No changes are made to the text.

Line 78: I think that it would be very helpful for a reader if the author specify that is the figure 1c and table 1.

Response: I fully agree. The references should be updated as suggested.

Line: 82: What was the reasoning for the number of sonic anemometers used, the selection of the locations of the tripods and the heights of the sonic anemometers?

Response: The number of sonic anemometers was limited by available hardware at the time. Ideally, only 3-axis sonic anemometers would be used. A compromise had to be made for the number of 3-axis sonic anemometers deployed here and elsewhere during the campaign. The height of the 3-axis type instruments on the tripods was chosen to be similar to the ICOS station and other studies using the Eddy Covariance technique on permanent grassland (including DE-Fen; see also the study by Mauder and Zeeman cited on line 80). There are sensitivity limitations for working with current model ultrasonic anemometers close to the surface. A level of 2-axis sonic anemometers closer to the ground (0.25 m) was planned but the appropriate mounting hardware could not be arranged in time for deployment.

Also, from the Figures 1 and 2 it is visible that the sonic anemometers were located between the supporting poles of the DTS mast. Could there be any interference to the sonic anemometers measurements acquired during the period selected in this study from wakes generated from the supporting poles?

Response: Small-scale interference in the wake is possible. The distance from the DTS masts to the EC profiles (on tripods) was 3 m. DTS masts had a diameter of 0.1 m. Increasing the distance would have required for the suspension cable to be mounted higher and with larger tension force to keep the steel cable straight. This could not (safely) be realized during the deployment.

Line 97: Where was the TIR system pointed to?

Response: The TIR system was pointed to the ground at a slanted angle to include as much surface within the DTS box as well as static objects for georeferencing. The guyed lattice mast was planned to be taller, but had to be kept below 10 m for safety of nearby glider planes. This limited our options for the camera viewpoint during the deployment.

Line 101: What is meant that the location was determined in post-processing?

Response: Thank you for the comment. This means that it required a georeferencing step as described in the text below the line and Appendix A. I suggest to change the text to make this clear.

‘Each EC, DTS and TIR record was stored with an accurate time stamp and locations were georeferenced in post-processing. The calibration and georeference details are provided in Appendix A.’

Line 116. The air temperature (Ta) is mentioned here, but it is only discussed how it is measured in Appendix A3.3. I would suggest a brief statement about those measurements also in section 2.4.

Response: I agree. This is an issue and I agree with the suggested solution.

‘Reference air temperature measurements were made using resistance temperature devices in fan-aspirated enclosures (Table 1; Appendix A)’

Additionally, regarding Figure 3. What is the sampling frequency of the time series presented in Figure 3? 

Response: Those are 1 min averages in all panels. I suggest to change the caption accordingly to better inform the reader.

How is the Tc estimated at the presented heights? Is it the average over all the four sides of the box?

Response: Yes, it is the average over all Tc profiles.

Which sonic anemometer’s data is being used in the Figure 3 c?

Response: Only the 3-axis sonic anemometer models provide a measurement for Tv, hence these are data for 3.0, 6.0 and 9.0 m height.

Line 127. The author states that “some turbulence statistics were rarely acceptable … “

What is it meant by the words “some” and “acceptable”?

Response: For the application of the eddy covariance technique, it is currently recommended to perform a number of (self-)validation tests, e.g., based on stability, stationarity and friction velocity. The test results can be simplified as a quality classification for the averaging period. During the nights it was rare to find the quality of averaging period results classified as ‘acceptable’.

I suggest to rephrase this to ‘eddy-covariance flux computations rarely produced acceptable results…’

Line 129-130. It is not clear how what are the assessment criteria used here to assess the quality of the flux computations.

Response: The assessment criteria may be the same, the computation to derive a stability classification is different.

Line 132. How were the temperature gradients calculated?

Response: Thank for noting the omission. This is indeed not mentioned clearly. I suggest to add the definition for temperature gradient to Appendix B.

Line 136. Figures 3a-c allow a visual comparison of the time series. However, there is a lack of a statistical comparison of the different methods (e.g. correlation, mean absolute error). I suggest that the author elaborate more on this part.   

Response: I agree. Please see the response to the General Comments.

Line 140. In Figures 4b-c time series of the normalized by the Obukhov length scale height and the friction velocity are presented. Measurements from which sonic anemometer were used for those calculations. Which criterion has by used to assess the atmospheric stability is stable or unstable?

Response: Only the 3-axis sonics can be used for the computation. I suggest to make this clear in the text of the method section.

Line 145. Is it the air temperature or the cable temperature presented in Figure 6?

Response: These panels are derived from cable temperature. I think this is made sufficiently clear from the caption and legend.

Line 189. The DTS measurement set-up has a rectangular shape. What is meant here the mean wind was mostly aligned to the set-up?

Response: Thanks for the comment. I now recognize the wording can lead to confusion for the reader and this aspect should be rephrased. What was meant is that for a period of time the mean wind was either perpendicular or parallel to the walls of the box.

Line 191: How does the animations reveal scale interactions? And why they are note easily identified in the statistical analysis?

Response: Thanks for the comments. Scale interactions are revealed in statistical analysis, as the results show. Nevertheless, it can be helpful and educational to review those results visually.

Line 196: I do not understand what is meant with this statement. Can the author elaborate explain this a bit more?

Response: Thanks for pointing this out.

The surface was not homogenous in terms of TIR signature. Some signal in the TIR image time series were revealed when and where the background (the surface) and foreground (air that had interacted with the surface upstream) show a different heat signature. Therefore, motion was revealed from hot air advecting away from relatively hot areas in the plant canopy, against a background of cooler surfaces. I agree with the suggestion to rephrase line 196.

Line 213. Why is there a sudden jump in the TKE in Figure 11 between 00:00 and 12:00 in 21 jul 2016?

Response: The jump is correlated to the passing of a short storm with brief precipitation (See panels Figure 3f and Figure 4a, and the text at line 120).

Line 228. The author gives a very thorough list of the limitations of the current measurement technique. It would be very constructive if the author could provide a short recommendation regarding in which applications this setup should or shouldn’t be used.

Response: Thank you for the comment. A short recommendation shall be added here (see the response to the General Comments).

Line 235. Can the author elaborate more on why three-dimensional sonic anemometers at lower heights would be advantageous in this study?

Response: Thanks for the comment. It would have been helpful to show TKE, w’ and stability information, as derived from 3-axis sonic anemometers, at a lower level.

Line 249. How is this precision calculated?

Response: This conclusion refers to results discusses in line 241 and shown in Appendix A). As suggested in the general comments section above, more detail on the performance would benefit the presentation.

Line 250. What is the reference scale for the recommendation for the size spatial domain and what is meant with the “2.5 dimensional or better”?

Response: A setup with a combination of 2-dimensional planes as cross-sections provides more than 2-dimensional information, but less than a 3-dimensional grid. Hence the array is referred to as 2.5-dimensional space. A fully 3-dimensional setup would, for example, resolve locations in a regular grid similar to many fluid dynamics models. In principle such a 3-dimensional setup could be achieved in the field, with some effort, using DTS.

Line 260. Does “turbulence” refer here to wind speed or temperature?

Response: Both.

Line 261. Both here and in the abstract, it is mentioned the development of physics-aware machine learning techniques. The current topic is not discussed in the introduction, so it is difficult to understand what a physics-aware machine learning technique is, assess how this study contributes to their development and understand their potential value. I think that it would increase the comprehension of the manuscript if the author could briefly explain this.

Response: I agree, a brief explanation will be helpful. Please note that the subject is discussed in the results section (lines 244-247).

Line 271. How accurate was the time keeping?

Response: The hardware clock data sheet specifies a 2 ppm accuracy. There was no measurable drift on any of the systems.

Line 285. How did the author recognize the period with winds from the north?

Response: Both the sonic anemometer (EC) network and the wind observations from the DE-Fen station indicated wind direction. The north wind sector is frequently observed in summer due to the proximity of the Alps to the south. The situation is maintained for several half-hour periods during the day. Assumed was, that wind from this sector would have limited wake effects on any of the sonic anemometers by mast structures or topography.

Lines 369 – 380. Why is this paragraph in the appendix? Isn’t this part of the results?

Response: Thanks for pointing this out. Yes, I agree that this paragraph should be in the results section.

What is the physical meaning of the grouping of the clusters presented in Figure A7? 

Response: The original study on the TED method discusses the extraction of key variance features from idealized data for each cluster (e.g., a sine wave, or more a ramp shape). As far as I can tell, it did not suggest the same clusters for the application on real-world data, just use of the same number of clusters. This is a shortcoming of a non-supervised machine learning methods. Some outcomes are not easily translatable or transferable. In this preprint we do see that TED clusters can be shown to appear with different spatiotemporal patterns (Figure 8), which I thinks highlights further promise. In order to explore the physical meaning would require the development of an appraoch to reliably aggregate (and/or normalize) data corresponding to each cluster.

Also, what is the impact of variations of atmospheric stability in the results presented in Figure A7?  

Response: This is a good question. The preprint does not specifically explore possible correlations between the spatiotemporal patterns in stability (Figure 4) and patterns in TED classes (Figure 8 and Figure A7). 

Table 2. What is the reason for mentioning the different ways of parameterizing the atmospheric stability? How is this used in this study?

Response: The different parameterizations of atmospheric stability are used as background information for the reader. I am not sure at this point if or how any of the parameterizations can help improve the classification of turbulence events. Personally, I found the differences between a lower (1.0 m) and higher (3.0 m) location in the gradient intriguing and indicative, without exploring possible explanations.

Figure 1. Units are missing from the x and y axis in all three plots, as well as from the color plot in figure 1a.

Response: Thanks for the comment. I suggest to add text to the caption of Figure 1 to indicate the use of UTM coordinates on both axes and add a unit to the color scale.

Figure 4. Over what time scales the friction velocity has been calculated?

Response: Over a 10 s time scale. This information should be added to the caption.

Figures 3,4 5. I suggest changing the color scale in Figure 3a-c, Figure 4a, Figure 5 a-b, the colors are going to be very difficult distinguished from color blind people.  

Response: Thank you for the suggestion. The colors were picked using recommendations for color blindness safe color scales (see, e.g., Colorbrewer by Cynthia Brewer). An online Daltonism simulator reveals a diverging gradient with distinguishable colors between blue/purple and yellow. I suggest to leave this aspect of the figures unchanged.

Technical Corrections

Line 150: “or were more” should be changed to “or more were”

Response: Thank you for noting this, I agree with the suggested correction.

Line 177: The acronym TED is explained only in line 370. That explanation should be moved here.

Response: Thanks, I agree that the description for TED should be moved from the appendix to the methods.

Line 179: change “though-out” with “through-out”

Response: Thank you for noting this, I agree with the suggestion.

Line 201: I suggest change the “it is assumable” with “it is assumed”

Response: Thank you for noting this, I agree with the suggestion.

Line 242: “eight” -> “eighth”

Response: I agree this should be corrected.

Line 244: “nine” -> “ninth”

Response: I agree this should be corrected.

Line 332: “data are” -> “data is”

Response: Thanks for the suggestion.

Line 425: There is one extra dot before “1”

Response: This should be corrected. Thanks for the comment!

Line 467: “ 17, 0”-> “17: 1-17 180060”

Response: This should be corrected as suggested. Thanks for the comment!

Lines 503, 516, 521,  Please check that all the details in the references Petrides 2011  Sayde 2015, Selker 2006 are written correctly.

Response: Thanks for the comment! I’ve made note to check the conventions for the names of Dutch authors as well as the page number formats in those references.

Response: Thank you for your efforts reviewing the manuscript and for providing helpful comments for discussion. A first response to the comments can be found below.

The manuscript presents a novel approach to combine distributed temperature sensing and thermal imaging instruments to study near-surface turbulence. The new technique enables detailed spatio-temporal analysis of both scale and shape of temperature structures and opens new opportunities to advance micrometeorological research. The manuscript is well written and provides a detailed overview of various aspects related to the application of the new technique. In my opinion, it might make the manuscript more accessible if the data science techniques would be briefly explained in the main text (and not only in the appendix).

Response: I fully agree with the reviewer that a restructuring of the text regarding the data sciences techniques would be helpful to the reader.

It would be also helpful to explain the meaning of variance events since they are at the centre of a part of the analysis. What is their physical meaning?

Response: It is valid to ask what the physical meaning of a variance event is; if there is momentum involved, what processes drive the observed patterns. In this manuscript, a variance event is a significant deviation from a temperature background signal (and noise floor) of less than a few minutes. Their physical meaning can often be explained from context, but not always. For instance, temperature ramp series during unstable conditions have been reported and interpreted from experimental data and fluid dynamics model simulations, often linked to a rolling mode of coherent propagation near the surface. However, single events during unstable conditions can be more elusive in nature. Events coinciding with substantial local destruction of stable stratification may be driven by a non-local process, e.g., waves generated remotely. I refer to AC2 (https://doi.org/10.5194/amt-2020-500-AC2) for an overview of the multi-scale observations that were operated to provide such additional context. Explaining the physical meaning of the events and their impact would be more meaningful when those observations are included in analysis, i.e., following up on this study.

I would also find it helpful if the potential of this technique for long-term monitoring would be discussed. It appears if the instrumentation was only deployed during an intensive measurement campaign. How realistic is it to deploy these instruments year-round?

Response: I agree with the reviewer that a discussion on long-term monitoring would be helpful, but it would be somewhat speculative as it was not the aim of this experiment.

Long term monitoring would be possible. I think this primarily depends on the stability of the support structure used to suspend the fibre-optic cable. In addition, it would be important to prevent accidental damage by animals, particularly wildlife. Precautions can be as simple as increasing the visibility of the set-up during the night with a floodlight and marking the area with bright warning tape. Fibre-optic cable can deteriorate under mechanical stress, but I have not seen evidence thereof based on the used set-up. However, optical cable can be repaired in the field in case of damage or, if the budget allows, can be replaced. A suitable reel of fibre-optic cable cost approximately 500 USD/EUR in 2014. The instruments, particularly the TIR and DTS models used in this study, are designed for long-term (industrial) operation.

Please see below some comments:

Line 17: Please clarify “about additional details contained in such data”. What were the specific research questions that were addressed in these studies? It would also be informative to further elaborate to which research questions the presented new measurement techniques could contribute.

Response: Thank you for the comment. I agree with the reviewer that the formulation is vague.

There is a tangential connection between this manuscript and the cited studies. These studies aim at separating or computing component scalar fluxes, and hinge on (cross-)correlation structure between scalars. Conditional sampling approaches for heat fluxes (e.g., Klosterhafen et al. and the works cited therein) rely on separating ‘high’ and ‘low’ frequency variance signal at the height of typical eddy covariance observation, assuming that the isolated scalar signal (water vapour, carbon dioxide, temperature) observed at some distance away from the surface are a result of coherent exchange, which in turn is driven by coherent shapes and scales that preserve the signature of processes at the surface. Here, an approach is presented to observe the spatio-temporal evolution of such coherent structures (temperature). An outlook could be to use that detailed information to improve said alternatives to the eddy covariance technique. That outlook is expressed later in the text, specifically Line 257: ‘The ability to trace coherent motion in space and time may proof useful for the development of conditional sampling methods that complement the eddy-covariance technique.’

I think it might go beyond the scope of the manuscript to review the various approaches that are in development to quantify vertical scalar fluxes or derivative variables, in much more detail than the first two paragraphs (Line 17 to 34). My suggestion is to replace ‘about additional details contained in such data’ (Line 17) with ‘about additional details contained within the scalar (co-)variance data also used by the eddy covariance technique’.

Line 128: Which criteria were applied to determine if eddy covariance flux computations were “acceptable”?

Response: Thank you for the comment. I agree that this needs to be clarified. The eddy covariance computations followed a (self-)validation procedure, e.g., based on tests for stability and stationarity. The tests results are simplified in a classification: Acceptable, Ambiguous or Incorrect. The quality classification is shown in the top three bars of Figure panel 4f. In the text, ‘acceptable’ indicated that data classified as Incorrect were excluded from the presentation, such as Figure panel 4e. Please note that all computed eddy covariance flux data, correct and incorrect, are included in the support material data sets and the quality classifications are additional variables.

Following up on RC1, I suggest to rephrase the sentence to ‘eddy-covariance flux computations rarely produced acceptable (classified as Acceptable or Ambiguous) results…’

Line 156: Please elaborate how these findings “suggest an interaction between scales”.

Response: I agree with the reviewer that this could be elaborated. The simultaneous occurrence of multiple scales at the same place (height) and time suggests interaction, perhaps cascading energy from one scale to another.