Fiber-Optic Distributed Temperature Sensing to quantify turbulence over space and time: A feasibility study

Vis, Gijsbert A.; Hartogensis, Oscar K.; ten Veldhuis, Marie-Claire; van de Wiel, Bas J. H.; Coenders-Gerrits, Miriam

doi:10.5194/egusphere-2025-6125

Preprints

https://doi.org/10.5194/egusphere-2025-6125

Preprints

08 Jan 2026

| 08 Jan 2026

Fiber-Optic Distributed Temperature Sensing to quantify turbulence over space and time: A feasibility study

Gijsbert A. Vis, Oscar K. Hartogensis, Marie-Claire ten Veldhuis, Bas J. H. van de Wiel, and Miriam Coenders-Gerrits

Abstract. Turbulence is essential for land atmosphere interactions; however, it is difficult to quantify due to its statistical and three dimensional nature. Typically, turbulence is determined using time series data to obtain turbulent data over a length scale (through Taylor's hypothesis). Ideally, turbulence is measured directly over multiple spatial dimensions as well as time, at high frequency. Currently turbulence measurements are limited to either time series (e.g., sonic anemometers) or integrated spatial measurements (e.g., scintillometers). However, direct spatiotemporal measurements of turbulence are lacking. In this study we aim to quantify turbulence over both time and space using fiber-optic distributed temperature sensing (DTS) using the structure parameter of temperature C_T². We conducted an experiment in the northeast of Spain in July 2021, where we measured temperature over a 70 m horizontal extent at a height of 2 m using a thin 0.5 mm fiber optic cable. The DTS experiment had a response time of 1.3 s and a response length of 0.35 m. We determined C_T² both spatially and temporally, through its definition as well as through the temperature turbulent spectrum, resulting in 4 results for C_T² from the DTS for each 30 minutes. Several (spectral) correction steps were applied to compensate for limited response rates, spatial averaging and noise. The C_T² values were compared with reference values from a sonic anemometer and a pair of scintillometers. For wind regimes with crosswind lower than 1.9 ms^-1 and mean absolute wind speed higher than 1.5 ms^-1, a correlation of R between 0.86 and 0.92 was found. The spectral DTS underestimates by a factor 3-4 in comparison to the sonic and by a factor 6 for the scintillometer. Similar results are found for the definition method and include a persistent offset of 0.04 for C_T². Hence, DTS correlates well with conventional reference instruments within the current limitations of DTS and it provides a direct and independent spatial measurement of turbulence. This opens the door to the use of DTS as a relative and spatial turbulence instrument to be used alongside an absolute reference instrument. The used setup and methodology can be scaled up to enable direct spatial measurements of turbulence at the km scale while keeping a spatial resolution in the order of meters.

Received: 08 Dec 2025 – Discussion started: 08 Jan 2026

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Gijsbert A. Vis, Oscar K. Hartogensis, Marie-Claire ten Veldhuis, Bas J. H. van de Wiel, and Miriam Coenders-Gerrits

Status: final response (author comments only)

RC1: 'Comment on egusphere-2025-6125', Anonymous Referee #1, 28 Jan 2026

This manuscript evaluates DTS derived temperature structure functions relative to baseline observations from sonic anemometers and a scintillometer. The authors present four ways of calculating the structure function which are equivalent when the assumption of ergodicity is valid and for the inertial scales: one spatially-explicit, one temporal using ergodicity, and two using spectra along space and time dimensions. The methods are evaluated over a flat experimental site using a harp of DTS observations along a 70 m transect. The authors find that the DTS-derived structure functions are biased relative to the baselines, but evaluates well enough to be used as a sensor for small-scale turbulence. The methods are robust and well-presented and I am happy to see someone attempting to get relevant turbulent quantities out of DTS data. The approach is interesting!
However, it is not well justified why we care to investigate such small-scale turbulence using a device like DTS, and thus it is not clear that deriving the temperature structure function is a useful step. One of the major benefits of DTS is that we are not limited by temporal sparsity (e.g., LIDARs) or spatial sparsity (e.g. point observations) all at a relatively high spatiotemporal resolution. Thus, we do not need to invoke Taylor’s Hypothesis. Structure functions, and similar statistics, are what I will refer to as a “uni-scale” approaches: they collapse higher-dimensional and multi-scale information. Uni-scale approaches aggregate over scales and ignore the simultaneous information in space and time. This collapsing of dimensions is an unfortunate necessity when we have sparse observations but not for the highly multi-scale information from DTS.
This is not to say that deriving the structure function is not without value, but in my humble opinion we should not seek to cram DTS observations into the uni-scale approach necessary for traditional statistics and theory and instead embrace the multi-scale nature of the data we get from DTS. The authors thus need to address two issues. (1) What is the value and meaning of a baseline that is only valid when classical assumptions are met? (2) What is the value and meaning of uni-scale methodologies for high-dimensional data?
Choice of baseline:
The citation the authors use of Cheng et al., 2017 explicitly uses DTS to question the validity of Taylor’s hypothesis in the inertial subrange and thus undermines the choice of baseline. At larger spatiotemporal scales the data (e.g., Figure 3) clearly show that Taylor’s hypothesis would not be valid for the entire period, even if it is valid for the sub-period. Thus, what is the value of the baseline evaluations that invoke Taylor’s hypothesis? I encourage the authors to consider the possible drawbacks from invoking a questionably valid hypothesis as the baseline.
The authors need to better motivate what additional value the evaluation of the structure function offers over the existing evaluations they mention. Most of the issues in the error of the structure function seem to be regarding the smallest resolvable scales and under-sampling, all of which were already known. What makes the structure function evaluation distinct and necessary?
Imposing uni-scale assumptions:

I question the value of deriving a measure of small-scale turbulence in a spatially-explicit fashion that is only valid in the limit of existing theory. We, as a field, like to focus strongly on representing the smallest scale turbulent fluctuations because that is where our assumptions are most valid. I argue that the novel value of DTS is that it gives us information that are missed by traditional observational platforms, explicitly at the scales excluded in Figure 9, without the need to invoke questionable assumptions. The major, open questions in turbulence are related to multi-scale interactions (Jimenez 2018, Stiperski et al., 2025), in particular at larger scales at which similarity theory is less valid. These scales are uniquely observable with DTS.
I suggest the authors examine approaches like from Zeeman 2021 in which a method that is not uni-scale is presented. The results from that study also place a limit on the smaller scale eddies that are resolvable but then push into the rich information contained in DTS that is missing in something like a sonic anemometer.
The existing DTS studies largely evaluate DTS observations at a point or over very short spatial distances. This is an fantastically interesting gap in the literature that could be filled by considering larger separation distances! If Taylor’s hypothesis is not valid at certain wind speeds and you have a definition of turbulence intensity that does not need to invoke it and you have continuously varying separation distances, you can explore something that could not be measured before!
In essence, I challenge the authors to transform their paper from a simple methodological evaluation that invokes questionable assumptions to one that challenges the limitations of traditional approaches. The disagreement between the structure function from the traditional observation platforms are potentially the most interesting aspects of this study and one which could help transform the use of DTS.
Technical Issues:
Section 5.4: I think every point mentioned has already been discussed in other manuscripts and thus does not bear repeating here. I know it is frustrating that we all seem to rediscover that same issues with each DTS experiment.
References
Stiperski, I. et al. Open questions in atmospheric turbulence: A synthesis from the centenary workshop “100 years of turbulence: Innsbruck 1922 -2022”. Journal of the European Meteorological Society 3, 100022 (2025).
Jiménez, J. Coherent structures in wall-bounded turbulence. Journal of Fluid Mechanics 842, P1 (2018).
Zeeman, M. Use of thermal signal for the investigation of near-surface turbulence. Atmospheric Measurement Techniques 14, 7475–7493 (2021).

Citation: https://doi.org/10.5194/egusphere-2025-6125-RC1
RC2:
'review', Anonymous Referee #2, 13 Feb 2026
Review of ” Fiber-Optic Distributed Temperature Sensing to quantify turbulence over space and time: A feasibility study”
Manuscript ID: egusphere-2025-6125
GENERAL COMMENTS
The authors evaluate the feasibility of the distributed temperature sensing (DTS) technique for doing spatiotemporal observations of turbulent flows in the atmospheric boundary layer. They cross compare temperature structure parameter (CT2) values derived from the DTS measurements against values derived from sonic anemometer and scintillometer data.
Instrument cross‑comparison studies are essential for establishing confidence in measurements; however, the novelty of such studies diminishes once they have been repeated several times. DTS observations have been compared against sonic anemometers already in several published articles and hence in my view such comparisons do not warrant a publication. However, turbulence statistics calculated from DTS data over space have not been compared with reference instruments before and the comparison against scintillometer is the main novelty of this study.
The manuscript lacks clarity in places and reasoning is partly difficult to follow. In my view major revisions are needed before accepting this manuscript for publication. Please see more details below.
SPECIFIC COMMENTS
MAJOR COMMENTS
Like stated above, the main novelty of this manuscript is in the comparison between DTS spatial statistics and scintillometer results. Hence, I argue the emphasis should be put on that comparison instead of comparing DTS temporal data (time series in a fixed location) against sonic anemometer data. Currently, scintillometer results appear only in one figure and the text revolves around the DTS vs sonic anemometer comparison. The focus should be put on spatial statistics and comparison against scintillometer.

Second-order structure function (SOSF; numerator in Eq. (1)) and power spectrum contain the same information about the flow, but expressed in different domains (structure function: spatial or temporal domain; power spectrum: wavenumber or frequency domain). Hence, I argue that the CT2 values obtained from Eq. (1) or Eq. (2) in the manuscript should be equivalent with each other. If they are not, then this first and foremost tells something about the algorithms you use in the CT2 calculation, and it is not necessarily linked to instrument performance. This should be acknowledged throughout the text. In addition, I suggest you add some figures showing the SOSF since they are underlying the “definition method”.

SOSFs are also contaminated by noise, but this is not taken into account in your “definition method”. I argue that you should first estimate the noise variance e.g. by estimating to which value SOSF approaches when the separation distance r (or time separation Dt) approaches zero and subtract the obtained value from Eq. (1) before estimating CT2. This should be done separately for each 30-min period you analyse. To be exact, SOSF at r=0 gives you the noise variance multiplied by 2, this is straightforward to show for uncorrelated white noise. Hence, consider the noise also in the case of “definition method”. This likely explains why e.g. in Fig. 10 CT2 values derived using Eq. (1) are never close to zero.

It is unclear why power spectra calculated over time and space are treated differently in this manuscript and the treatment of the spatial spectra should be rectified in the manuscript. For temporal spectra, noise floor is first subtracted from the temporal spectra and then the high frequency attenuation is accounted for with a transfer function before estimating CT2 from the inertial subrange. To me this approach makes sense, since you are trying to recover the unattenuated, noise-free inertial subrange from the observations and the noise sits on top of an attenuated signal. However, the treatment of spatial spectra follows a different approach which is difficult to understand, and I argue to be false. The authors low-pass filter the spatial spectra and argue that this filtering recovers the inertial subrange. Why would you apply an additional filter to a signal that is already attenuated and contaminated by noise? I argue you should follow similar approach as is done for temporal spectra, i.e. first remove the noise floor and then try to recover the inertial subrange with the inverse of the low-pass filter and not apply an additional filter to the spectra. If this suggested procedure does not recover reasonable inertial subrange in the spatial spectra, then there might be artefacts in DTS spatial measurements or peculiarities in the flow which are worth discussing. One should also note that there are studies that argue that the eddy advection velocity depends on scale (Higgins et al., 2012; Cheng et al., 2017; Hilland and Christen, 2024) which suggests that the conversion from frequencies to wavenumbers is not linear. This means that power spectra calculated over time from sonic anemometer data is not a perfect point of reference for power spectra calculated over space when standard Taylor’s hypothesis is used to convert frequencies to wavenumbers.

Somewhere in the text you need to describe the noise level of your DTS measurements and compare it to the actual temperature variance, i.e. you should report signal-to-noise ratios. You could estimate the noise from the SOSF (see comment 3 above) and the actual temperature variance from the sonic anemometer data. This is crucial for assessing how much your observations are affected by noise.

MINOR COMMENTS
L13 Please specify in the text what is meant with crosswind
L15 Underestimates what, please specify in the text
L16 At this point the reader does not know what “definition method”, please adjust the text
L16 Please add unit for 0.04. This offset is likely due to the fact that you do not consider the noise in the definition method, see major comment 3 above.
L23 “convective turbulence” are you claiming that turbulence produced by shear is not transporting heat, e.g. in a weakly unstable situation? Please adjust
L25 “However, this is currently not technically feasible.” DTS has been used for atmospheric flows already from 2012 onwards (Thomas et al., 2012), please adjust the text.
L79-80 If it does not appear later, please add typical Bowen ratio or evaporative fraction + midday sensible heat flux during the campaign. This helps in evaluating the magnitude of typical heat fluxes and corresponding T fluctuations. Also, you need to describe what were the typical turbulence intensity levels (sigma_u/U) during your campaign, since you rely on Taylor’s hypothesis in several locations and the hypothesis is not valid in highly turbulent conditions.
Fig. 3 caption: Add information on how far the DTS locations shown in subplot d were from the anemometer. Fig. 3d looks like that DTS and anemometer were not sampling the same eddies. Compare e.g. with Fig. 8 in Peltola et al. (2021), there you can see clear correspondence between DTS and sonic anemometer since they were colocated. If you plot the time series like this, the reader is expecting to see similarities between the time series.
Fig. 4 I argue that this figure is not needed, consider removing it
Fig. 7 Consider adding the individual ensemble members also in this figure, similarly as in Fig. 6. It is a nice way of illustrating the variability between locations/time steps. Dotted black line in the figure is the inverse of Hx given in the text, please correct. Hx given in the text should increase with k, black dotted line decreases.
L217 usually H is used for transfer functions, this is inverse of transfer function. For clarity I suggest adjusting
L231-232 Why not to remove the data from the pole locations? And then replace with e.g. linear interpolation
L236-237 I argue that this is false. Noise is an additive component in the measurements that is on top of the attenuated signal and hence noise should not be attenuated as is proposed here. I argue that you should see similar flattening in the spatial spectra as you see in the temporal spectra. Please adjust the text. This relates to the major comment 4. Only if the DTS instrument spatially smooths the primary observations after the measurement (e.g. running mean over space) you should see attenuation of noise.
L253-254 This relies fully on Taylor's hypothesis and further assumes that the same advection velocity applies at all scales. There are studies that argue that the advection velocity is scale dependent (Higgins et al., 2012; Cheng et al., 2017; Hilland and Christen, 2024). This should be considered throughout the manuscript. We do not have a solid understanding on how to accurately link spatial and temporal scales in the flow. Taylor’s hypothesis provides a handy tool for this, but its limitations should be acknowledged.
Fig. 9 Good illustration, however relies fully on Taylor's hypothesis. Eq. (4) describes how fPA is calculated and based on that, fPA does not depend on U. Please clarify why the blue dotted line is slanted in this figure. "Scales too large to capture" is misleading. I argue that fluctuations at these scales are captured with your DTS setup, since you had 70 m long measurement section. 70 m is ten times 7 m and hence you can observe ten of this scale of eddies with your setup at the same time. However, these scales likely start to be outside the inertial subrange since they are clearly larger than z. Please adjust the text so that it is clear that fluctuations at these scales are captured with your DTS, but they start to fall outside inertial subrange and hence not usable for estimating CT2.
Fig. 10 Explicitly mention that the sonic curves are the same in both subplots and derived over time domain, otherwise confusing (you cannot estimate spectra over wavenumber from sonic data). Please add scintillometer results into Fig. 10b or clearly describe in the text why this is not possible.
L277 Please remind the reader that the time scales related to the length scales r= 2m and r=5m are estimated with the Taylor's hypothesis separately for each 30-min period. Otherwise this is very difficult to understand. “TimeDef and SpaceDef results” TimeDef is in Fig. 10a and SpaceDef in Fig. 10b, right? Please adjust the text, now it reads like these both are in Fig. 10a
L278 “TimeSpec and SpaceSpec results” Similar comment as for TimeDef and SpaceDef, please see the previous comment. Please fix
Fig. 11 I suggest adding a comparison between sonic and scintillometer for giving a point of reference. Such comparison is given in the Appendix, but I suggest moving it here.
L292 Why wind speed would limit the applicability of SpaceDef or SpaceSpec? Please adjust the text
L301-302 You have estimated the fiber time response and you account for this in your calculation procedure. Please clarify.
L320-321 CT2 should be constant with f in the inertial subrange. Please correct the text
L328-330 I do not understand this sentence, please adjust
L333 what overestimation? It has not been mentioned before. Please adjust the text
L333-335 I disagree with this sentence. Based on your results, the CT2 values estimated from DTS with your algorithms were clearly underestimates when compared to the CT2 values derived from sonic anemometer data. You should discuss why this is the case
L341-343 I think this minimum CT2 value is because you did not consider the noise in Eq. (1), see major comment 3 above. Hence 0.04 is not the lower limit of detection for this DTS configuration, but rather lower limit for this DTS configuration + calculation algorithms. Please adjust the text
L369-370 I would argue that it is not difficult to resolve the spectra on the time scale of 2 minutes if you calculate it over time. It is difficult only over space due to your finite cable length. Please adjust the text
L373-374 Unclear, please clarify
L379-383 Unclear, please modify
L384-389 I suggest removing this part since here you discuss results that are not shown in this manuscript
L399-400 Such solid copper blocks have been built already, see Thomas et al. (2022).
L421 I suggest replacing “turbulence intensity” with “structure parameter”
L423-425 or measuring with the current instrumentation higher above the surface where the eddies are larger, consider mentioning

TECHNICAL CORRECTIONS
L129 & L131 I think you are referring to a wrong figure here, please correct
L210 Consider replacing “correct” with “account” or similar
L212 remove “corrected”
L222 replace “and over” with “to over”
L238 replace “frequencies” with “wavenumbers”
L295 replace “SpecDef” with “SpaceDef”

REFERENCES
Cheng, Y., Sayde, C., Li, Q., Basara, J., Selker, J., Tanner, E., Gentine, P., 2017. Failure of Taylor’s hypothesis in the atmospheric surface layer and its correction for eddy-covariance measurements. Geophysical Research Letters. https://doi.org/10.1002/2017GL073499
Higgins, C.W., Froidevaux, M., Simeonov, V., Vercauteren, N., Barry, C., Parlange, M.B., 2012. The Effect of Scale on the Applicability of Taylor’s Frozen Turbulence Hypothesis in the Atmospheric Boundary Layer. Boundary-Layer Meteorology 143, 379–391. https://doi.org/10.1007/s10546-012-9701-1
Hilland, R., Christen, A., 2024. A Systematic Investigation of the Applicability of Taylor’s Hypothesis in an Idealized Surface Layer. Boundary-Layer Meteorology 190, 22. https://doi.org/10.1007/s10546-024-00861-1
Peltola, O., Lapo, K., Martinkauppi, I., O’Connor, E., Thomas, C.K., Vesala, T., 2021. Suitability of fibre-optic distributed temperature sensing for revealing mixing processes and higher-order moments at the forest–air interface. Atmos. Meas. Tech. 14, 2409–2427. https://doi.org/10.5194/amt-14-2409-2021
Thomas, C.K., Huss, J.-M., Abdoli, M., Huttarsch, T., Schneider, J., 2022. Solid-Phase Reference Baths for Fiber-Optic Distributed Sensing. Sensors 22, 4244. https://doi.org/10.3390/s22114244
Thomas, C.K., Kennedy, A.M., Selker, J.S., Moretti, A., Schroth, M.H., Smoot, A.R., Tufillaro, N.B., Zeeman, M.J., 2012. High-Resolution Fibre-Optic Temperature Sensing: A New Tool to Study the Two-Dimensional Structure of Atmospheric Surface-Layer Flow. Boundary-Layer Meteorology. https://doi.org/10.1007/s10546-011-9672-7
Citation: https://doi.org/10.5194/egusphere-2025-6125-RC2

Gijsbert A. Vis, Oscar K. Hartogensis, Marie-Claire ten Veldhuis, Bas J. H. van de Wiel, and Miriam Coenders-Gerrits

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Short summary

Heat exchange between land and air mainly happens through turbulence. Usually turbulence is measured at one location over time, but it also happens over space. In this study, we use fiber optic cables (DTS) that can measure temperature to capture turbulence over time, as well as directly over space. If compared with conventional instruments, we found a good correlation but also an underestimation. We recommend using DTS alongside with conventional instruments so they can complement each other.


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